cooperative cellular wireless networks

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Cooperative Cellular Wireless Networks

A self-contained guide to the state-of-the-art in cooperative communications and net-working techniques for next-generation cellular wireless systems, this comprehensivebook provides a succinct understanding of the theory, fundamentals, and techniquesinvolved in achieving efficient cooperative wireless communications in cellular wirelessnetworks.

It consolidates the essential information, addressing both theoretical and practicalaspects of cooperative communications and networking in the context of cellular design.This one-stop resource covers the basics of cooperative communications techniquesfor cellular systems, advanced transceiver design, relay-based cellular networks, andgame-theoretic and micro-economic models for protocol design in cooperative cellularwireless networks. Details of ongoing standardization activities are also included.

With contributions from experts in the field divided into five distinct sections, this easy-to-follow book delivers the background needed to develop and implement cooperativemechanisms for cellular wireless networks.

Ekram Hossain is a Professor in the Department of Electrical and Computer Engineeringat the University of Manitoba, Canada, where his current research interests lie in thedesign, analysis, and optimization of wireless/mobile communications networks. Heserves as an Editor for IEEE Transactions on Mobile Computing, IEEE CommunicationsSurveys & Tutorials, and IEEE Wireless Communications, and is an Area Editor for IEEETransactions on Wireless Communications.

Dong In Kim is a Professor and SKKU Fellow in the School of Information and Com-munication Engineering at Sungkyunkwan University (SKKU), Korea, and Director ofthe Cooperative Wireless Communications Research Center. He is currently an Editorfor IEEE Transactions on Communications, an Area Editor for IEEE Transactions onWireless Communications and co-Editor-in-Chief for Journal of Communications andNetworks.

Vijay K. Bhargava is a Professor in the Department of Electrical and Computer Engi-neering at the University of British Columbia, Canada. He has served on the Boardof Governors of the IEEE Information Theory Society and the IEEE CommunicationsSociety and was President of the IEEE Information Theory Society. He is now thePresident-Elect of the IEEE Communications Society and will serve as its Presidentduring 2012 and 2013.

“Edited by three of the most prominent experts in the field of cooperative communi-cations, this is the defining book on this topic. It is a must have for any practicingresearcher/engineer in this field.”

Vahid Tarokh, Harvard University

“Cooperative communications has been one of the most active areas of research in thecommunications field over the past decade. This research effort has now produced asignificant body of work in the area, and this book is a valuable resource for students orpractitioners wanting to enter the field, or simply to understand the scope and implicationsof the research.”

H. Vincent Poor, Princeton University

Cooperative Cellular WirelessNetworks

Edited by

EKRAM HOSSAINUniversity of Manitoba, Canada

DONG IN KIMSungkyunkwan University, Korea

V IJAY K. BHARGAVAUniversity of British Columbia, Canada

CAMBRIDGE UNIVERSITY PRESS

Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore,Sao Paulo, Delhi, Tokyo, Mexico City

Cambridge University PressThe Edinburgh Building, Cambridge CB2 8RU, UK

Published in the United States of America by Cambridge University Press, New York

www.cambridge.orgInformation on this title: www.cambridge.org/9780521767125

C© Cambridge University Press 2011

This publication is in copyright. Subject to statutory exceptionand to the provisions of relevant collective licensing agreements,no reproduction of any part may take place without the writtenpermission of Cambridge University Press.

First published 2011

Printed in the United Kingdom at the University Press, Cambridge

A catalogue record for this publication is available from the British Library

Library of Congress Cataloguing in Publication dataCooperative cellular wireless networks / edited by Ekram Hossain, Dong In Kim, Vijay K. Bhargava.

p. cm.Includes index.ISBN 978-0-521-76712-5 (hardback)1. Wireless communication systems. 2. Cell phone systems. I. Hossain, Ekram, 1971–II. Kim, Tong-in, 1958– III. Bhargava, Vijay K., 1948– IV. Title.TK5103.2.C6625 2011621.384 – dc22 2010048066

ISBN 978-0-521-76712-5 Hardback

Cambridge University Press has no responsibility for the persistence oraccuracy of URLs for external or third-party internet websites referred toin this publication, and does not guarantee that any content on suchwebsites is, or will remain, accurate or appropriate.

For our families

Contents

List of contributors page xviPreface xx

Part I Introduction 1

1 Network architectures and research issues in cooperative cellular

wireless networks 3Aria Nosratinia and Ahmadreza Hedayat

1.1 Introduction 31.2 Base station cooperation 4

1.2.1 Downlink cooperation 41.2.2 Uplink cooperation 6

1.3 Dedicated wireless relays 71.3.1 IEEE 802.16j 71.3.2 High-spectral-efficiency relay channels 8

1.4 Mobile relays 101.5 Conclusion 11

2 Cooperative communications in OFDM and MIMO cellular relay

networks: issues and approaches 13Mohammad Moghaddari and Ekram Hossain

2.1 Introduction 132.2 Cooperative relay networks 15

2.2.1 Cooperative communication 152.2.2 Relay channel 162.2.3 Overview of relay protocols 172.2.4 Strategies of relay-assisted transmission 18

2.3 General system model of cellular relay networks 192.4 General system model for virtual antenna arrays (VAAs) 202.5 RRA in OFDMA-based relay systems: general form 212.6 Dynamic RA RRA in OFDMA relay networks 23

2.6.1 Centralized RA RRA schemes in single-cell OFDMA relaynetworks 24

viii Contents

2.6.2 Centralized RA RRA schemes in multicell OFDMA relaynetworks 26

2.6.3 Distributed RA RRA schemes in OFDMA relay networks 272.6.4 RA RRA schemes with fairness in OFDMA relay networks 28

2.7 Dynamic centralized margin adaptive RRA schemes in OFDMArelay networks 30

2.8 MIMO communications systems 312.8.1 RRA in MIMO relay networks 312.8.2 Optimal design and power allocation in single-user

single-relay systems 322.8.3 Optimal design and power allocation in single-relay

multiuser systems 352.9 RRA in MIMO multihop networks 362.10 Conclusion 38

Part II Cooperative base station techniques 45

3 Cooperative base station techniques for cellular wireless networks 47Wibowo Hardjawana, Branka Vucetic, and Yonghui Li

3.1 Introduction 473.1.1 Related work 473.1.2 Description of the proposed scheme 483.1.3 Notation 49

3.2 System model 493.2.1 Transmitter structure 493.2.2 THP precoding structure 51

3.3 Cooperative BS transmission optimization 533.3.1 Iterative weight optimization (first step) 553.3.2 Power allocation (second step) 57

3.4 Modification of the design of R 583.5 Geometric mean decomposition 593.6 Adaptive precoding order (APO) 603.7 The complexity comparison of the proposed and other known

schemes 613.8 Numerical results and discussions 63

3.8.1 Convergence study 643.8.2 Performance of the individual links 653.8.3 Overall system performance 66

3.9 Conclusion 70Appendix 72

4 Turbo base stations 77Emre Aktas, Defne Aktas, Stephen Hanly, and Jamie Evans

4.1 Introduction 77

Contents ix

4.2 Review of message passing and belief propagation 814.2.1 Factor graph review 824.2.2 Factor graph examples 85

4.3 Distributed decoding in the uplink: one-dimensional cellular model 884.3.1 Hidden Markov model and the factor graph 894.3.2 Gaussian symbols 91

4.4 Distributed decoding in the uplink: two-dimensional cellulararray model 964.4.1 The rectangular model 964.4.2 Earlier methods not based on graphs 984.4.3 State-based graph approach 984.4.4 Decomposed graph approach 1024.4.5 Convergence issues: a Gaussian modeling approach 1024.4.6 Numerical results 1074.4.7 Ad-hoc methods utilizing turbo principle 1094.4.8 Hexagonal model 110

4.5 Distributed transmission in the downlink 1104.5.1 Main results for the downlink of a single-cell network 1104.5.2 Main results for downlink of a multicellular network 1144.5.3 BS cooperation schemes with message passing 115

4.6 Current trends and practical considerations 122

5 Antenna architectures for network MIMO 128Li-Chun Wang and Chu-Jung Yeh

5.1 Introduction 1285.2 System model 1305.3 Network MIMO 132

5.3.1 ZF network MIMO transmission 1335.3.2 ZF-DPC network MIMO transmission 133

5.4 Effects of intergroup interference 1345.4.1 SINR analysis 1345.4.2 Example of IGI: network MIMO with omni-directional

cell planning 1345.4.3 Unbalanced signal quality caused by IGI 135

5.5 Frequency-partition-based three-cell network MIMO 1365.5.1 Fractional frequency reuse (FFR) 1365.5.2 FFR-based network MIMO with regular frequency partition 1385.5.3 FFR-based network MIMO with rearranged frequency

partition 1405.5.4 Effect of frequency planning among coordinated cells 1425.5.5 Effect of cell planning with different sectorization 143

5.6 Simulation setup numerical results 1455.7 Conclusion 147

x Contents

Part III Relay-based cooperative cellular wireless networks 151

6 Distributed space-time block codes 153Matthew C. Valenti and Daryl Reynolds

6.1 Introduction 1536.2 System model 1556.3 Space-time block codes (STBCs) 1576.4 DF distributed STBC 162

6.4.1 Performance analysis 1626.4.2 Numerical results 165

6.5 AF distributed STBC 1686.5.1 Performance analysis 1696.5.2 Practical distributed STBC for AF systems 170

6.6 The synchronization problem 1706.6.1 Delay diversity 1716.6.2 Delay-tolerant space-time codes 1716.6.3 Space-time spreading (STS) 172

6.7 Conclusion 173

7 Collaborative relaying in downlink cellular systems 176Chandrasekharan Raman, Gerard J. Foschini, Reinaldo A. Valenzuela,

Roy D. Yates, and Narayan B. Mandayam

7.1 Introduction 1767.1.1 Research challenges 1767.1.2 Related work 1787.1.3 Overview of contribution 179

7.2 System model 1807.3 Collaborative relaying in cellular networks 1847.4 CPA with peak power transmissions (P-CPA) 186

7.4.1 Principle of operation 1867.4.2 User discarding methodology 1887.4.3 Network operation and simulation aspects 1907.4.4 Simulation results 190

7.5 Power-control-based collaborative relaying (PC-CPA) 1927.5.1 Principle of operation 1927.5.2 Optimization framework 1947.5.3 User discarding methodology 1977.5.4 Network operation and simulation aspects 1987.5.5 Simulation results 199

7.6 Orthogonal relaying 1997.6.1 Network operation and simulation aspects 2007.6.2 User discarding method 2017.6.3 Simulation results 202

7.7 Conclusion 202

Contents xi

8 Radio resource optimization in cooperative cellular wireless networks 205Shankhanaad Mallick, Praveen Kaligineedi, Mohammad M. Rashid,

and Vijay K. Bhargava

8.1 Introduction 2058.2 Networks with single source–destination pair 206

8.2.1 Three-node relay network 2078.2.2 Dual-hop relay networks 213

8.3 Multiuser cooperation 2208.3.1 System model 2218.3.2 Centralized power allocation 2228.3.3 Distributed power allocation 223

8.4 Relay selection 2288.5 Conclusion 230

9 Adaptive resource allocation in cooperative cellular networks 233Wei Yu, Taesoo Kwon, and Changyong Shin

9.1 Introduction 2339.2 System model 235

9.2.1 Orthogonal frequency-division multiplexing (OFDM) 2359.2.2 Adaptive power, spectrum, and rate allocation 2379.2.3 Cooperative networks 237

9.3 Network optimization 2389.3.1 Single-user water-filling 2389.3.2 Network utility maximization 2409.3.3 Proportional fairness 2419.3.4 Rate region maximization 242

9.4 Network with base station cooperation 2449.4.1 Problem formulation 2449.4.2 Joint scheduling and power allocation 2459.4.3 Performance evaluation 248

9.5 Cooperative relay network 2509.5.1 Problem formulation 2519.5.2 Joint routing and power allocation 2549.5.3 Performance evaluation 254

9.6 Conclusion 256

10 Cross-layer scheduling design for cooperative wireless two-way

relay networks 259Derrick Wing Kwan Ng and Robert Schober

10.1 Introduction 25910.2 Cross-layer scheduling design – some basic concepts 263

10.2.1 Utility function-based cross-layer optimization 26410.2.2 Quality-of-service (QoS) measure 26610.2.3 Multiuser diversity gain 266

xii Contents

10.3 Network model for relay-assisted OFDMA system 27010.3.1 System model 27010.3.2 Channel model 27110.3.3 Channel state information (CSI) 273

10.4 Cross-layer design for two-way relay-assisted OFDMA systems 27410.4.1 Instantaneous channel capacity and system goodput 27410.4.2 Cross-layer design problem 275

10.5 Cross-layer optimization solution 27610.5.1 Transformation of the optimization problem 27610.5.2 Dual problem formulation 27910.5.3 Distributed solution – subproblem for each relay station 27910.5.4 Solution of the master problem at the BS 280

10.6 Asymptotic performance analysis and computational complexityreduction scheme 28110.6.1 Asymptotic analysis of system goodput 28110.6.2 Scheme for reducing computational burden at each relay 283

10.7 Results and discussions 28310.7.1 Convergence of the distributed resource allocation algorithm 28410.7.2 Average system goodput vs. transmit power and user

mobility 28410.7.3 Asymptotic system goodput performance of PF scheduling 289

10.8 Conclusion 290Appendix 292

11 Green communications in cellular networks with fixed relay nodes 300Peter Rost and Gerhard Fettweis

11.1 Introduction 30011.1.1 Two motivating examples 30011.1.2 Scope and key problems 30211.1.3 Outline and contributions 303

11.2 System model 30311.2.1 Propagation scenarios 30311.2.2 Air interface and scheduling 305

11.3 System and protocol design 30611.3.1 Non-relaying protocols 30711.3.2 Relay-only protocol 30711.3.3 An integrated approach 30811.3.4 Simplifications 309

11.4 Numerical analysis 30911.4.1 Simulation methodology 30911.4.2 Throughput performance in the wide-area scenario 31011.4.3 Throughput performance in the Manhattan-area scenario 31211.4.4 Femto-cells vs. relaying 31311.4.5 Computation-transmission-power tradeoff 315

Contents xiii

11.4.6 Reduced backhaul requirements 31611.4.7 Cost–benefit tradeoff 317

11.5 Conclusion 320

12 Network coding in relay-based networks 324Hong Xu and Baochun Li

12.1 Introduction 32412.2 Network coded cooperation 326

12.2.1 Simple network coded cooperation 32712.2.2 Joint network and channel coding/decoding 331

12.3 Physical-layer network coding 33412.4 Scheduling and resource allocation: cross-layer issues 33712.5 Conclusion 341

Part IV Game theoretic models for cooperative cellular wirelessnetworks 345

13 Coalitional games for cooperative cellular wireless networks 347Walid Saad, Zhu Han, and Are Hjørungnes

13.1 Introduction 34713.2 A brief introduction to coalitional game theory 34813.3 A coalition formation game model for distributed cooperation 350

13.3.1 Motivation and basic problem 35113.3.2 Distributed virtual MIMO coalition formation game 355

13.4 Coalitional graph game among relay stations 36813.4.1 Motivation and basic problem 36813.4.2 A network formation game among relay stations 369

13.5 Conclusion 378

14 Modeling malicious behavior in cooperative cellular wireless

networks 382Ninoslav Marina, Walid Saad, Zhu Han, and Are Hjørungnes

14.1 Introduction 38214.2 Cooperating jammers 384

14.2.1 System model 38514.2.2 The game 38614.2.3 Simulation results 393

14.3 Cooperating relays 39814.3.1 System model 39914.3.2 Secrecy capacity 40014.3.3 Simulation results 404

14.4 Eavesdroppers cooperative model 407

xiv Contents

14.4.1 Coalition formation games for distributed eavesdropperscooperation 411

14.4.2 Simulation results 41614.4.3 Conclusion 418

Part V Standardization activities 423

15 Cooperative communications in 3GPP LTE-Advanced standard 425Hichan Moon, Bruno Clerckx, and Farooq Khan

15.1 Introduction 42515.2 LTE and LTE-Advanced 426

15.2.1 Carrier aggregation 42815.2.2 Latency improvements 42915.2.3 DL multiantenna transmission 43015.2.4 UL multiantenna transmission 431

15.3 Cooperative multipoint transmission 43115.3.1 Interference mitigation techniques in previous releases of LTE 43215.3.2 Overview of CoMP techniques 43315.3.3 Release 10 of LTE-Advanced 450

15.4 Wireless relay 45115.4.1 Key technologies 45215.4.2 Standard trends on Release 10 and future works 454

15.5 Heterogeneous network 45415.5.1 Key technologies 45415.5.2 Standard trends on Release 10 and future work 457

15.6 Conclusion 457

16 Partial information relaying and relaying in 3GPP LTE 462Dong In Kim, Wan Choi, Hanbyul Seo, and Byoung-Hoon Kim

16.1 Introduction 46216.2 Partial information relaying with multiple antennas 463

16.2.1 Per-antenna superposition coding (PASC) 46516.2.2 Multilayer superposition coding (MLSC) 46616.2.3 Rate matching for superposition coding 46816.2.4 Overall rate capacity 46916.2.5 Features of partial information relaying 470

16.3 Analysis of PASC with zero-forcing decorrelation 47016.4 Multinode partial information relaying 474

16.4.1 Two-stage superposition coding 47516.4.2 Successive decoding in cooperating phase 47716.4.3 Relay selection for maximum capacity 477

16.5 Concluding remarks on partial information relaying 47916.6 Relaying in 3GPP LTE-Advanced 480

Contents xv

16.6.1 Functionality of RNs 48116.6.2 Separation of the backhaul and access links 488

17 Coordinated multipoint transmission in LTE-Advanced 495Sung-Rae Cho, Wan Choi, Young-Jo Ko, and Jae-Young Ahn

17.1 Introduction 49517.2 CoMP architecture 496

17.2.1 Joint processing and transmission (JPT) 49717.2.2 Coordinated scheduling and beamforming (CS/CB) 49717.2.3 Cell clustering 49717.2.4 Inter-eNodeB and intra-eNodeB coordination 499

17.3 CoMP design parameters 49917.3.1 Reference signal (RS) 49917.3.2 Precoding 50117.3.3 Feedback 502

17.4 CoMP performance evaluation methodologies 50417.4.1 Link level simulation 50417.4.2 System level simulation 506

17.5 Conclusion 509

Index 514

Contributors

Jae-Young Ahn

Electronic Telecommunication and Research Institute (ETRI), Korea

Defne Aktas

Bilkent University, Turkey

Emre Aktas

Hacettepe University, Turkey

Vijay K. Bhargava

The University of British Columbia, Canada

Sung-Rae Cho

Korea Advanced Institute of Science and Technology (KAIST), Korea

Wan Choi

Korea Advanced Institute of Science and Technology (KAIST), Korea

Bruno Clerckx

Samsung Electronics, Korea

Jamie Evans

University of Melbourne, Australia

Gerhard Fettweis

Technische Universitat Dresden, Germany

Gerard J. Foschini

Bell Laboratories, USA

Zhu Han

University of Houston, USA

List of contributors xvii

Stephen Hanly

National University of Singapore, Singapore

Wibowo Hardjawana

University of Sydney, Australia

Ahmadreza Hedayat

CISCO Systems, USA

Are Hjørungnes

UNIK – University of Oslo, Norway

Ekram Hossain

University of Manitoba, Canada

Praveen Kaligineedi


Farooq Khan


Byoung-Hoon Kim

LG Electronics, Inc., Korea

Dong In Kim

Sungkyunkwan University (SKKU), Korea

Young-Jo Ko

Electronic Telecommunication and Research Institute (ETRI), Korea

Taesoo Kwon


Baochun Li

University of Toronto, Canada

Yonghui Li


Shankhanaad Mallick


Narayan B. Mandayam

Rutgers University, USA

xviii List of contributors

Ninoslav Marina

Princeton University, USA

Mohammad Moghaddari

University of Manitoba, Canada

Hichan Moon


Derrick Wing Kwan Ng


Aria Nosratinia

University of Texas at Dallas, USA

Chandrasekharan Raman


Mohammad M. Rashid


Daryl Reynolds

West Virginia University, USA

Walid Saad

UNIK – University of Oslo, Norway

Robert Schober


Hanbyul Seo

LG Electronics, Inc., Korea

Changyong Shin


Matthew C. Valenti

West Virginia University, USA

Reinaldo A. Valenzuela

Bell Laboratories, USA

Peter Rost

NEC Euro Labs, Germany

List of contributors xix

Branka Vucetic


Li-Chun Wang

National Chiao Tung University, Taiwan

Hong Xu


Roy D. Yates


Chu-Jung Yeh

National Chiao Tung University, Taiwan

Wei Yu


Preface

Cooperative communications and networking represent a new paradigm whichuses both transmission and distributed processing to significantly increase thecapacity in wireless communication networks. Current wireless networks facechallenges in fulfilling users’ ever-increasing expectations and needs. This ismainly due to the following reasons: lack of available radio spectrum, the unreli-able wireless radio link, and the limited battery capacity of wireless devices. Theevolving cooperative wireless networking paradigm can tackle these challenges.The basic idea of cooperative wireless networking is that wireless devices worktogether to achieve their individual goals or one common goal following a commonstrategy. Wireless devices share their resources (i.e., radio link, antenna, etc.)during cooperation using short-range communications. The advantages of coop-eration are as follows: first, the communications capability, reliability, coverage,and quality-of-service (QoS) of wireless devices can be enhanced by cooperation;second, the cost of information exchange (i.e., transmission power, transmissiontime, spectrum, etc.) can be reduced. Cooperative communication and network-ing will be a key component in next generation wireless networks. In this bookwe particularly focus on cooperative transmission techniques in cellular wirelessnetworks.

Although cellular wireless systems are regarded as a highly successful tech-nology, their potential in throughput and network coverage has not been fullyrealized. Cooperative communication is a key technique to harness the potentialthroughput and coverage gains in these networks. Cooperation is possible amongmobile stations (MSs) inside a cell as well as among base stations (BSs). In addi-tion, specialized relay stations (RSs) can be installed in the network to facilitatecooperative communications. In addition to improving throughput and cover-age, cooperative communication can improve the energy saving performance atthe mobile devices, increase reliability in transmission, and decrease the overallinterference in the network. However, successful deployment and operation ofa cooperative cellular wireless network hinges on the development of advancedradio transmission and resource management techniques and optimization ofthese techniques considering the different network parameters. This has spurreda vibrant flurry of research on different aspects of cooperative communicationduring the last few years.

Preface xxi

With BS cooperation, neighboring cells can exchange information aiming atmitigating intercell interference by coordinating the multicell transmission to amobile or reception from a mobile. In a relay-based cooperative cellular wirelessnetwork, an MS may communicate with a BS via potential relays, and similarly,a BS can send data to distant nodes through relays. The potential relays couldbe either preinstalled fixed RSs or relay-capable MSs. The RSs are much cheaperthan conventional BSs because they have far fewer functionalities compared toBSs. If the relay is positioned suitably, it is possible to increase the data rate(especially at the cell boundaries) and the reliability of the system. Similar tomultiantenna transceivers, relays provide diversity by creating multiple replicasof the signal of interest. By properly coordinating different spatially distributednodes in the system, a virtual antenna array can be synthesized that emulatesthe operation of a multiantenna transceiver. With cooperation at all layers ofthe protocol stack, the network can achieve higher throughput, higher systemreliability, higher energy efficiency, a lower bit-error rate, and a smaller packetloss rate. For cooperation at physical, medium access control (MAC), network,and application layers, various cooperative signaling methods are being widelyexplored and many new mechanisms are under development with respect tomedium access, routing, location management, scheduling, energy management,etc.

This book provides a comprehensive treatment of the state-of-the-art of coop-erative communications and networking techniques for cellular systems (e.g.,Beyond 3G, Long-Term evolution systems). It consists of chapters covering dif-ferent aspects of cooperative cellular wireless network design which include thefollowing: architectures and protocols for cooperative cellular wireless networks;cooperative BS techniques (e.g., cooperative beamforming technique); radioresource management protocol design and network planning for relay-based coop-erative cellular wireless systems (e.g., relaying strategies and protocols, resourceallocation, energy management, network coding, and cross-layer issues); and thelatest IEEE standardization activities pertaining to cooperative cellular wirelesssystems. The chapters are written by the distinguished researchers in these areas.This book is targeted at graduate students, or researchers working in the areaof cellular wireless networks. It can also be used for self-study to become famil-iar with the state-of-the-art in cooperative communications for cellular wirelesssystems.

This book contains 17 chapters which have been organized into five parts. Abrief account of each chapter in each of these parts is given next.

Part I: Introduction

In Chapter 1, Nosratinia and Hedayat outline the trends in research into coop-erative cellular wireless networks, as well as some of the outstanding prob-lems in this area. In particular, the issues related to BS cooperation (for both

xxii Preface

downlink and uplink transmission) and cooperation through dedicated wirelessrelays (fixed and mobile) are discussed from the physical layer perspective.

In Chapter 2, Moghaddari and Hossain focus on the resource allocation prob-lem for cooperative communications in relay-based orthogonal frequency-divisionmultiple access (OFDMA) and multiple-input multiple-output (MIMO) wirelessnetworks. Starting with the basics of cooperative relay networks and strategiesfor relay-assisted transmission, a survey on the different approaches for radioresource allocation in OFDMA relay networks is provided. To this end, researchissues on resource allocation in multihop MIMO relay networks and some relatedwork in the literature are discussed.

Part II: Cooperative base station techniques

In Chapter 3, Hardjawana, Vucetic, and Li focus on BS cooperation for inter-ference cancelation where each BS transmitter uses the transmitted signal infor-mation from other BS and channel state information to precode its own signal.A spectrally efficient cooperative downlink transmission scheme is designed byemploying precoding and beamforming. The proposed scheme achieves fairnessamong different users in terms of symbol error rate.

In Chapter 4, Aktas et al. focus on an approach for implementing BS cooper-ation in a distributed manner via message passing in network MIMO systems.This approach is based on a graphical model (in particular, a factor graph) ofthe network MIMO communication processes. Both uplink and downlink trans-missions are considered. As an example, a graph-based approach for distributedbeamforming and power allocation is discussed.

In Chapter 5, Wang and Yeh discuss the antenna architectures for the net-work MIMO schemes based on BS cooperation in a multicellular system. Onefundamental question when applying the network MIMO technique in such ahigh interference environment is: how many BSs should cooperate together toprovide satisfactory signal-to-interference-plus-noise ratio (SINR) performance?Considering the interferences from the other cooperating groups, it is foundthat on top of the tri-sector directional antenna and fractional frequency reuse(FFR), the network MIMO based on the three-cell coordination strategy canoutperform seven-cell-based network MIMO with omni-directional antenna. Theauthors also consider the effect of different cell sectorizations by using 120 and60 beamwidths directional antennas.

Part III: Relay-based cooperative cellular wireless networks

In Chapter 6, Valenti and Reynolds focus on space-time block coding (STBC)strategies in a cooperative system to forward signals efficiently from mul-tiple relays to the destination by exploiting the spatial diversity presentin a multirelay network. Both decode-and-forward distributed STBC and

Preface xxiii

amplify-and-forward distributed STBC are considered for a two-phase trans-mission protocol in a network with one source node, one destination node, and aset of relay nodes. The end-to-end outage probability, coding gain, and achiev-able diversity as well as the optimal ratio of the power used in the two phasesof transmission are analyzed for different space-time codes. Unlike conventionalspace-time codes, the distributed space-time codes have to deal with the syn-chronization problem at the destination receiver. Delay diversity, delay-tolerantdistributed space-time codes, and space-time spreading are some effective meth-ods of dealing with this problem.

In Chapter 7, Raman et al. present a simulation study of the downlink of acellular system with relays in order to evaluate peak and average power sav-ings for a given target common rate requirement for users. In particular, threeschemes, namely, the collaborative power addition (CPA) scheme, the powercontrol-based collaborative power addition (PC-CPA) scheme, and an orthogo-nal relaying scheme are simulated. In the CPA scheme, when a relay receives thecomplete message, it collaborates with the BS to transmit the complete messageto the user using its peak power. In the PC-CPA scheme, power control is per-formed jointly at the BS and RS. In the orthogonal relaying scheme, the BSs andthe RSs transmit in orthogonal time slots. The peak power savings (at the BSs)are rate gains (for the users) and are observed to be better with the PC-CPAscheme.

In Chapter 8, Mallick et al. study the radio resource (i.e., bandwidth,transmit power) allocation problem in relay-based cooperative cellular wirelessnetworks. For the different relaying schemes (i.e., amplify-and-forward, decode-and-forward) in single- and multiuser network scenarios, different optimizationmodels for resource allocation and their solution approaches are described. Also,the problem of relay selection for individual communication between source anddestination nodes is discussed. The problem of joint optimization of resourceallocation and relay selection is an open research issue.

In Chapter 9, Yu, Kwon, and Shin study the resource (i.e., power, spectrum,and rate) allocation problem for OFDMA-based cooperative cellular wirelessnetworks. Two types of cooperative networks are considered: the multicell net-work with BS cooperation where multiple BS cooperatively allocate power to thedifferent frequency subchannels, and networks with RSs. With a view to max-imizing the sum of utilities of multiple uses in a multicell network, a networkutility maximization (NUM) framework is used to solve the scheduling, and thepower, frequency, and rate allocation problem. A key observation here is that,with OFDMA, the network utility maximization problem often decomposes intoa tone-by-tone optimization problem, which is easier to solve.

In Chapter 10, Ng and Schober focus on the problem of cross-layer schedulingdesign for two-way half-duplex amplify-and-forward relay-assisted OFDMA cel-lular networks. Such a scheduling scheme has to satisfy the different data rateand outage probability requirements of different users. Starting with the basicsof cross-layer scheduling design and the related implementation challenges, the

xxiv Preface

problem considered is formulated as a mixed combinatorial and non-convex opti-mization problem. In the problem formulation, the objective is to obtain theoptimal power, rate, and subcarrier allocation policies while taking the imper-fect channel state information (CSI) as well as heterogeneous QoS requirementsof the users into account. The problem is then solved by dual decomposition.Also, a distributed iterative algorithm is designed to reduce the computationalload at the relays.

In Chapter 11, Rost and Fettweis focus on the system-wide energy consump-tion in cooperative cellular networks. Two deployment scenarios are considered,namely, a macrocellular deployment and a microcellular deployment, both ofwhich use OFDMA air interface for uplink/dowlink transmission in time-divisionduplex (TDD) mode. The system performance is simulated considering multi-cell MIMO transmission only (nonrelaying protocol), a relay only protocol, andan integrated approach (which supports both multicell MIMO and relaying).The achievable throughput performance, the energy saving potentials, and thedeployment costs are compared. In addition, performance comparison is carriedout between femto-cells and relaying.

In Chapter 12, Xu and Li study the potential application of network codingand the related issues in relay-based networks. Also, the idea of physical-layernetwork coding is discussed; this has the potential to improve the throughputperformance of relay-based networks significantly. One key observation is that,since network coding is mostly applied at the lower layers of the protocol stack,the scheduling and resource allocation at the upper layers have to be coding-aware. Such a cross-layer approach for network coded cooperation may reap thebenefits of network coding, however, at the expense of increased complexity.

Part IV: Game theoretic models for cooperative cellularwireless networks

In Chapter 13, Saad, Han, and Hjørungnes explore the application of coalitionalgame theory to model the various aspects of cooperative behavior in cellularwireless networks. For example, cooperation among the BSs can be modeled bya class of coalitional games, known as coalition formation games, and thereby,algorithms can be derived which help in analyzing the groups of cooperatingBSs that will emerge in a given network scenario. As another example, networkformation games, a class of coalitional graph games, can be used to model theinteractions among RSs. The key message is that coalitional game theory pro-vides a rich framework to design efficient, fair, and robust models for resourceallocation and sharing in cooperative cellular wireless networks.

In Chapter 14, Marina et al. use game theory to analyze the secrecy capacityin cooperative networks in the presence of malicious users (e.g., eavesdroppers).The secrecy capacity refers to the maximum reliable data rate at which a per-fectly secret communication is possible between a sender and a receiver. Three

Preface xxv

different communications scenarios are considered. In the first scenario, severalfriendly jammers help the source in transmitting data to a destination by jam-ming the eavesdropper. The interaction between the source and the friendlyjammers is analyzed using a Stockholder type of game. In the second scenario,several relay nodes help the source by relaying the transmitted data in the pres-ence of a malicious node, and this cooperation improves the secrecy capacity.In this cooperative system, the number and locations of the relay nodes deter-mine the secrecy region, i.e., the geometric area in which the secrecy capacityis positive. In the last scenario, the eavesdroppers cooperate to improve theirreception performance. A coalitional game-based model is proposed for formingcooperative groups among the eavesdroppers. This modeling will be useful todevelop defense mechanisms against the eavesdroppers’ cooperation.

Part V: Standardization activities

In Chapter 15, Moon, Clerckx, and Khan discuss the standard trends on coopera-tive communications in the Third Generation Partnership Project (3GPP) Long-Term Evolution Advanced (LTE-Advanced) system. In particular, an overview ofthe key technical features of LTE-Advanced Release 10 including carrier aggre-gation, cooperative multipoint transmission/reception (CoMP), extended multi-antenna systems, and wireless relays is provided. Carrier aggregation provideswider transmission bandwidth and makes full use of the existing fractional spec-trum bands. The other techniques provide higher cell spectrum efficiency, bettercoverage, and lower handover interruption time. CoMP transmission refers to anew class of intercell interference mitigation technique, which is also called mul-ticell MIMO, collaborative MIMO (Co-MIMO), or network MIMO. The basicidea is to extend the conventional single-cell-to-multiple-user transmission to amultiple-cell-to-multiple-user transmission through BS cooperation.

In Chapter 16, Kim et al. develop methods for partial information relayingin multiantenna decode-and-forward relay networks. These methods use a two-phase transmission strategy and exploit the asymmetric link conditions in cellularnetworks, where the source–relay link and the relay–destination link are rela-tively better than the source–destination link. With multiple antennas availableat source, relay, and destination, multiple parallel data streams are transmittedwhich consist of basic data streams and superposition coded (SC) data streams.The relay forwards only the SC streams (i.e., partial information in the secondhop). Two methods, namely, per-antenna superposition coding (PASC) and mul-tilayer superposition coding (MLSC), are proposed for power allocation amongbasic and superposed layers, and across the spatial layers. It is observed thatpartial information relaying results in significant capacity gain over full infor-mation relaying. To this end, the authors summarize the issues, discussions, andcurrent conclusions on relaying in the LTE-Advanced standard.

xxvi Preface

In Chapter 17, Cho et al. discuss the proposals and current conclusions on theCoMP technique in the 3GPP LTE-Advanced standard. Many companies andresearch groups are confident that CoMP systems are feasible in real systems andhave put forth effort to find and evaluate what type of cooperation scheme shouldbe standardized. The authors outline the issues discussed in the LTE-Advancedstudy group, for downlink CoMP, and present related simulation methodologies.

Part I

Introduction

1 Network architectures and researchissues in cooperative cellularwireless networks

Aria Nosratinia and Ahmadreza Hedayat

1.1 Introduction

The systematic study of relaying and cooperation in the context of digital com-munication goes back to the work of Van der Meulen [1] and Cover and ElGamal [2]. The basic relay channel of [1, 2] consists of a source, a destination,and a relay node. The system models in [1, 2] are either discrete memorylesschannels (DMC), or continuous-valued channels which are characterized by con-stant (nonrandom) links and additive white Gaussian noise.

The study of cooperative wireless communication is a more recent activitythat started in the late 1990s, and since then has seen explosive growth in manydirections. Our focus is specifically on aspects of cooperative communicationrelated to cellular radio. Aside from the fading model, the defining aspects of acellular system are base stations that are connected to an infrastructure knownas the backhaul, which has a much higher capacity and better reliability thanthe wireless links. The endpoints of the system are mobiles that operate subjectto energy constraints (battery) as well as constraints driven by the physical sizeof the device that lead to bounds on computational complexity and the numberof antennas, among other considerations. There are multiple mobiles in each cellas well as frequency reuse, leading to intracell interference and intercell interfer-ence, respectively. The exponential path-loss laws lead to significant variationsin signal power at various points in the cell. In this chapter we are concernedwith cooperative radio communication that specifically engages one or more ofthese defining aspects.

Within the context of cellular radio, cooperative communication may be usedto enhance capacity, improve reliability, or increase coverage. It may be used inthe uplink or the downlink. In the communication between a base station and amobile, the cooperating entity may be another base station, another mobile, ora dedicated (often stationary) wireless relay node. The cooperating entity mayhave various amounts of information about the source data and channel stateinformation. Cooperation may happen in the physical layer, data link layer, net-work layer, transport layer, or even higher layers. The large number of different

Cooperative Cellular Wireless Networks, eds. Ekram Hossain, Dong In Kim, and Vijay K.Bhargava. Published by Cambridge University Press. C© Cambridge University Press, 2011.

4 Network architectures and research issues

ways that cooperation may be exploited to improve the quality of service in cel-lular radio has given rise to much research and a rich and expanding literature.There are many questions that remain unanswered, among them the relationbetween the various forms of cooperation and their relative merits are in generalnot fully known. In this chapter, we aim to catalog some of the directions ofresearch in this area, and outline some of the open questions.

1.2 Base station cooperation

Base station cooperation can take multiple forms. The simplest form of basestation cooperation, especially with multiantenna base stations, involves theexchange of information among neighboring cells regarding their cell-edge nodesand remote-cell aware processing at each of the base stations. Then, each ofthe base stations can put a null on the channel gain vector of the nodes thatgenerate and/or are harmed by the most cochannel interference. This and othersimple scenarios like it are in the realm of interference management, and arepossible without fully coordinated action from base stations. Specifically, thisform of action does not require the base stations to know the traffic for otherbase stations (therefore the issue of a wideband backbone and its delay does notcome into play), nor is it required to know the codebooks used by the other basestation, and nor does it require the base stations to be synchronized.

1.2.1 Downlink cooperation

For downlink base station cooperation, base stations can generate a virtual multi-antenna array with zero-forcing beamforming. There are a variety of ways toexploit this general idea. Somekh et al. [3] used the circular Wyner cellularmodel [4] to find expressions for downlink (and uplink) capacities with basestation cooperation, which is also sometimes called multicell processing. In [5]the same model and a zero-forcing beamforming approach were used for datatransmission in multiple cells. In particular, the approach is to transmit to thebest user in each cell, and the high-load asymptotics are derived in an informationtheoretic approach. Mundarath et al. [6] considered the scheduling aspects ofdistributed downlink zero-forcing beamformers under finite loads.

Such downlink strategies require certain assumptions about sharing of infor-mation among cells. To begin with, the data must be shared among the basestations. Secondly, the base station transmitters must be synchronized. Finally,the channel state information of the users must be shared among the base sta-tions, and must be kept up-to-date, so that beamforming vectors can be reliablydetermined.

The nascent area of distributed beamforming has seen much activity; we brieflymention a representative sample of the results.

1.2 Base station cooperation 5

The effect of channel state statistics on distributed beamforming was inves-tigated in [7]. Ng et al. [8] developed a distributed method of beamformingby message passing between adjacent base stations instead of sharing the databetween many base stations.

Mudumbai et al. [9] investigated the feasibility of distributed beamformingfrom the viewpoint of local oscillator phase errors, showing encouraging results.However, the results were tempered by the fact that in this study it was assumedthat the frequency of the oscillators is stable. Brown and Poor [10] proposed amethod of carrier synchronization for distributed beamforming.

Other works in this area include [11–18]. A tutorial on the challenges andprogress in distributed beamforming is given in [19].

There is a key difficulty that limits the usefulness of conventional beamformingtechniques in the distributed scenario: because the antennas are not colocated,the difference of propagation delay from different antennas to a node will becomea relevant parameter. For beamforming to a single node (single-beam solution)any difference in delays can be absorbed into the beamforming coefficients. Mul-tiple beams may also be generated in the same manner, but only as long as thetarget nodes are close to each other, i.e., the delay vectors for various nodes mustbe approximately similar. If the target nodes are far from each other and thetransmit antennas are also far from each other, then the conventional methodsof beamforming may not work.

The degradation of distributed beamforming systems due to the distributionof the antennas and the target nodes is a subject that, to our knowledge, has notbeen systematically investigated. Also, the design of new optimization techniquesto develop beamforming vectors in the presence of different delays remains anopen problem.

To study this issue further, it is useful to separate the two difficulties raised bythis delay variance. The first one is the induced change in phase, which can beaddressed via, e.g., systems of equations that impose the constraints at variousnodes. The second, more challenging, problem is due to the variance in the timeof arrival of the leading edge of each symbol at various nodes. Assuming thatthe arrival of symbols from the distributed antennas is calibrated to be cotimedat node A, the leading edge of the symbols may not arrive cotimed at node B.

To our knowledge, no comprehensive method is known to address this problem.Intuitively, if the symbol duration is much larger than the differences in time ofarrival, then there is a chance that if the phases can be appropriately adjusted,the overall effect can be brought under control. This also suggests the use ofsystems with longer symbol duration, e.g., OFDM. It would be interesting toinvestigate whether variations of techniques used in OFDM, such as cyclic prefix,can be used to “collect” the various components of the distributed beamformingthat may be out of phase and out of time.

Aside from the above-mentioned fundamental issue, there are also practicalissues that require careful consideration and design. In particular, distributedbeamforming requires delicate accounting for various types of delay, not just


in the channel but also within the base station and signal delivery path. Anyunaccounted for delay, or delay variation anywhere within the transmit or receivepath, would cause transmitted signals to arrive at the mobile station unaligned,causing loss in beamforming gain. These are requirements that often do notappear in theoretical studies, but in fact play an important role in any practicalimplementation.

To summarize, base station cooperation offers the opportunity for improventin two opposing directions: incorporating more theoretical results and addressingpractical issues. Among various aspects that call for further investigation, onemay name:

possibilities with multiantenna mobiles, among them the extension of resultsfrom multiple-input multiple output (MIMO) broadcast channels to the dis-tributed MIMO case;

the effect of partial channel state information or partially outdated channelstate information;

quantized channel-state feedback for distributed beamforming has beenaddressed in [16], but there is room for much more work in this area;

the effect of uneven channel state information across a set of heterogeneousmobiles;

investigation of limits on the backbone, e.g., limits on sharing of traffic data.

1.2.2 Uplink cooperation

The problem of uplink cooperation is rather different from its downlink counter-part. In the uplink cooperation scenario, a mobile might be in a situation whereno single base station can decode its data alone. However, the signals receivedat two or more base stations may be sufficient to decode the mobile data.

The collection of information at various base stations and their combinationpresent new issues. In particular, since each of the base stations cannot decodethe received signal alone, these signals must be sampled and exchanged amongbase stations, which requires significantly larger bandwidth than the data do.Thus, considering the effect of base station cooperation on the backhaul capacitybecomes an important issue. The capacity of the uplink linear cellular networkswith base station cooperation via finite capacity links was broached in [20], andbounds on the rate of the system under the Wyner model were obtained froman information theoretic viewpoint. This work generated broad insights into thegeneral capabilities of uplink base station cooperation, but the specifics of codingand signal design for such systems remain open problems.

Thankfully, the uplink does not suffer in quite the same way from the timingproblem that plagues the downlink distributed beamforming (see Section 1.2.1).The varying propagation times from the mobiles to base stations can be com-pensated in the algorithm that combines the data from multiple base stations,since the signal of each of the mobiles can be extracted separately. However, the

1.3 Dedicated wireless relays 7

problem will remain if we wish to listen to mobile A while simultaneously nullingthe interference from mobile B, and these two mobiles have significantly differentdelay vectors to the set of base stations participating in multicell processing.

The scope for future work in the area of uplink multicell processing is in twodirections: incorporation of communication theoretic results into uplink cooper-ation and addressing issues related to practical limitations. The potential areasof work include:

practical implications of the restrictions on the backhaul capacity and delay; iterative methods based on belief propagation; compute-and-forward (hashing) methods to reduce the cooperation band-

width requirement between the base stations; analysis of nonideal conditions, including uncertainties in channel state infor-

mation; the effect of nonideal synchronization and sampling; investigating possibilities presented by multiantenna mobiles.

1.3 Dedicated wireless relays

Traditional cellular networks provide fixed throughput for all subscribers wherea basic voice service can be supported. Unlike such networks, broadband wirelesscellular networks promise a high data rate throughout the coverage area. Whilesuch promise is feasible for the inner coverage area, at the cell-edge data ratesare limited for various reasons. Decreasing the cell-size is one way to satisfy therequired data rate; however, it is a costly solution because it requires the instal-lation of additional base stations. In contrast, deploying relay stations provides acost-effective solution. Compared with a full-scale base station, a dedicated relaycan save on equipment costs, backhaul link, and deployment.

A relay station assists the main base station to improve its coverage or through-put. A relay station can be used to extend the coverage area of a base station,or to provide coverage in so-called holes.1 In addition, thanks to the advancesin antenna array techniques, relays can also be used to improve throughput andcapacity.

Due to above facts, the IEEE 802.16 Working Group has developed the IEEE802.16j standard with techniques that are compatible with the WiMAX standard.

1.3.1 IEEE 802.16j

The IEEE 802.16j standard was created to be backward compatible with the802.16e standard known as WiMAX. Various modes of operation of 802.16j fitwithin the WiMAX OFDMA frame. In all the various modes of 802.16j, the base

1 For example, in tunnels or in certain areas inside a building.


station allocates part of its uplink and downlinks subframes for communicatingwith the relay station(s). It is envisioned that legacy mobile nodes are able tointegrate seamlessly into 802.16j, therefore the mobiles are oblivious to the relays,i.e., they cannot distinguish between the relay and base station.

Two of the modes of operation considered in the IEEE 802.16j standard aretransparent and nontransparent modes. The usage of these modes depends onwhether it is intended to increase throughput for cell-edge mobile stations, or toextend coverage to the mobile stations unreachable by base station. The transpar-ent mode allows for one-time relaying while the nontransparent mode allows formultiple-time relaying. The transparent mode can be used, e.g., for in-buildingcoverage, while the nontransparent mode can be used to access remote areaswhich might possibly require multiple relaying. There are also differences withinthe downlink and uplink frames of these two modes. In transparent mode onlythe traffic portion is exchanged between relay and mobile stations, while in non-transparent mode in addition to the traffic portion other signals such as syn-chronization, downlink and uplink maps, and ranging need to be exchanged aswell.

Both the transparent and nontransparent modes are multihop modes, i.e., therelay intervenes between the source and destination, and the data portions ofsource–relay and relay–destination communications are performed separately intime. Another mode of operation in the IEEE 802.16j standard is cooperativerelaying, where the base station and relay transmit the same signal, or two copiesof the same signal, to the mobile simultaneously. As long as the timing differencebetween the signal of the base and relay stations as seen by mobile stations iswithin the acceptable range, the mobile station sees the combined signals as asignal with high diversity.

Operational cooperative relaying has multiple requirements. First, traffic dataneed to be exchanged between the relay and base stations. Second, the deploy-ment of the relays needs to be such that the time difference seen by the mobilestation does not cause OFDMA intersymbol interference. With these practicalrequirements fulfilled, research efforts have been focused on the various MIMOtechniques that can be used to achieve cooperation between base and relay sta-tions. The IEEE 802.16j standard says very little about the techniques for imple-menting cooperative relaying, therefore there is significant room for innovationby the wireless industry within the context of the standard.

It must be noted that other broadband wireless standards, such as Long-TermEvolution (LTE) and LTE-Advanced, consider the use of relay stations. Fordetails, the readers are referred to Chapters 15 and 16 of this book.

1.3.2 High-spectral-efficiency relay channels

One of the main drawbacks of relaying is that in effect it requires duplicatetransmissions (e.g., base station to relay and relay to mobile), unlike standardsingle-hop transmission. For instance, in both transparent and nontransparent

1.3 Dedicated wireless relays 9

modes of the IEEE 802.16j there are multiple zones of uplink and downlinksubframes that are assigned for the exchange of traffic between base stationand relay stations. The loss of time and/or bandwidth is more pronounced formultihop relaying.

However, the advantages of relaying often more than offset the loss of band-width. The obvious advantages are the reduction of path loss and shadowing, aswell as providing path diversity, but the advantages of relaying go beyond theobvious. For example, both the base station and the relay are stationary (non-moving) and the base station is often elevated, so it is possible to estimate thechannel gains between the base station and the relay with a very high degree ofaccuracy and stability, far beyond what is possible with mobiles. In addition, itis possible to use antenna arrays in both the base station and the relay, whichcombined with the accurate channel state information leads to a higher spectralefficiency as well as more efficient frequency reuse.

More specifically, the base station can employ space-division multiple access(SDMA) techniques to transmit traffic to several relay stations using the samebandwidth. For efficient implementation of SDMA, the channel state informa-tion of each relay must be known by the base station with high precision. Infact, the more precise the channel state information, the larger the number ofrelay stations that can be served within the same bandwidth. Thanks to thefixed location of relay and base stations, it is possible to obtain a high-qualitychannel state information of each relay station. Likewise, it is possible to use asimilar technique in the uplink to increase uplink spectral efficiency. For instance,collaborative spatial multiplexing, which is also introduced in the IEEE 802.16eand other wireless broadband standards, allows multiple relay stations to trans-mit uplink traffic utilizing the same burst location, i.e., the same bandwidth. Ifrelay stations are equipped with antenna arrays, other MIMO techniques suchas spatial multiplexing can also be used to further enhance spectral efficiency ofdownlink and uplink.

Improving spectral efficiency of relay channels can further increase the utiliza-tion of relays in broadband cellular networks, and therefore is one of the impor-tant research topics in this area. For instance, the design of adaptive MIMOprecoding techniques that can provide robustness as well as higher throughputcan facilitate cellular relays. This could lead to precoding weights that adapt tospatial multiplexing, beamforming, or nulling.

The various costs related to the backhaul channel constitute a big portion ofthe cost of cellular network deployment, operation, and maintenance. Increasedutilization of wireless resources will result in shrinking cell sizes and an increase inthe number of base stations, therefore it is expected that backhaul link expenseswill be in future broadband networks, generating interest in backhaul links thatare cheaper than laying cable or dedicated microwave links. It has been notedthat one can use the same family of broadband wireless technologies that areservicing end-users to connect to some base stations. The similarity of operationand use of wireless backhaul links and relaying technologies suggests a potential


unification of these two applications. Thus, spectrally efficient relay channelscould eventually also pave the way to less-expensive and easily deployable back-haul links, and might even lead to unified technologies or standards for both.

1.4 Mobile relays

In the previous two sections, we considered the outlook for base station cooper-ation and dedicated relays. It has been noted that there is nothing in principlethat precludes the possibility of mobile relays, although technologically theirimplementation is much more difficult. In this section, we give a brief overviewof mobile relays. We begin by considering the distinguishing characteristics ofmobile relaying.

One of the fundamental differences between mobile and fixed relays is thelimitations on power/energy in the mobile nodes. Fixed relays can be connectedto the power grid, while the mobiles are dependent on resident energy storage,which with the present-day technologies is a severe limiting factor. This situationseems a fairly stable one, since neither energy storage devices with orders-of-magnitude higher energy densities, nor an efficient means of tetherless deliveryof energy to mobiles, is visible on the technological horizon.

Another distinguishing factor of most mobile nodes, compared to fixed relays,is one of size. Mobile nodes are no more than several centimeters in each dimen-sion, and this puts fundamental restrictions on the number of antennas that canbe deployed on a mobile. Polarization diversity antennas offer some improvement,but a fixed relay has much more flexibility in the number of antennas.

An aspect of mobile relaying, which is not unrelated to size and energy, iscomputational complexity. However, unlike size, this is less of a fundamental lim-itation. In the past, advances in computational power, measured in MIPS/mm3,have been much more rapid than, e.g., advances in battery technology measuredin terms of energy density (joules/mm3). Thus it is not unreasonable to assumethat near-future technologies in mobiles will become ever more computationallycomplex, while the power available to them will grow at a much slower pace.

Due to limited resources, any mobile relay must balance the needs of the nodeitself with relaying for other nodes. This includes not only power and computa-tion, but also the total spectral efficiency available to a node. The fundamen-tal tradeoff between a node’s own communications and relayed bandwidth wasaddressed in [21], which showed that the competition between its own bandwidthand the relayed bandwidth does not constitute a zero-sum game. However, therewill still be questions of the motivation of a relay node to use local resources forother nodes. The specific aspects of network-wide management of resources, andthe development of network control algorithms that guide the action of mobilerelay nodes that also have individual incoming/outgoing traffic, have attractedsome attention but a complete understanding of these algorithms has still notbeen achieved. Some interesting advances have been made using game theory andpricing analysis. However, a good part of the work in this area is not relevant

1.5 Conclusion 11

to the design of cooperative cellular networks, because the nodes in a cellularnetwork are not autonomous agents and most decisions are, in fact, made in acentralized manner. Resource allocation and network control for mobile coopera-tive nodes (including aspects such as local rate splitting) are interesting problemsthat, under the practical conditions that are of interest to the designers of cellularsystems, remain for the most part unsolved.

1.5 Conclusion

Cooperative communication is one of the promising wireless technologies thathas been reintroduced in the last decade, and it has promising applications inthe context of cellular networks. This chapter has presented a brief overview ofsome of the aspects of research in cooperative cellular networks. To summarize,several important directions of future work seem to beckon wireless researchers.One direction points to the more sophisticated algorithms and harnessing the fullpower of the coding and signaling methods that are emerging from informationtheory. Another direction is to refine the models in order to get a more realisticgrip on the practical aspects of operation in a cellular network. Finally, mostsystematic study and analysis of cooperation has concentrated on the physicallayer. However, cooperative action at other layers of the communication hierarchyis also possible, but has not been studied quite as much, and this may present ahost of opportunities to future wireless engineers.

References

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[2] T. Cover and A. El Gamal, “Capacity theorems for the relay channel,” IEEETrans. Inform. Theory, 25, 1979, 572–584.

[3] O. Somekh, B. Zaidel, and S. Shamai, “Sum rate characterization of jointmultiple cell-site processing,” IEEE Trans. Inform. Theory, 53, 2007, 4473–4497.

[4] A. Wyner, “Shannon-theoretic approach to a Gaussian cellular multiple-access channel,” IEEE Trans. Inform. Theory, 40, 1994, 1713–1727.

[5] O. Somekh, O. Simeone, Y. Bar-Ness, A. M. Haimovich, and S. Shamai,“Cooperative multicell zero-forcing beamforming in cellular downlink chan-nels,” IEEE Trans. Inform. Theory, 55, 2009, 3206–3219.

[6] J. Mundarath, P. Ramanathan, and B. Van Veen, “A distributed downlinkscheduling method for multi-user communication with zero-forcing beam-forming,” IEEE Trans. Wireless Commun., 7, 2008, 4508–4521.

[7] V. H. Nassab, S. Shahbazpanahi, A. Grami, and Z.-Q. Luo, “Distributedbeamforming for relay networks based on second-order statistics of the chan-nel state information,” IEEE Trans. Signal Processing, 56, 2008, 4306–4316.


[8] B. L. Ng, J. Evans, S. Hanly, and D. Aktas, “Distributed downlink beam-forming with cooperative base stations,” IEEE Trans. Inform. Theory, 54,2008, 5491–5499.

[9] R. Mudumbai, G. Barriac, and U. Madhow, “On the feasibility of distributedbeamforming in wireless networks,” IEEE Trans. Wireless Commun., 6,2007, 1754–1763.

[10] D. Brown and H. Poor, “Time-slotted round-trip carrier synchronization fordistributed beamforming,” IEEE Trans. Signal Processing, 56, 2008, 5630–5643.

[11] H. Ochiai, P. Mitran, H. Poor, and V. Tarokh, “Collaborative beamform-ing for distributed wireless ad hoc sensor networks,” IEEE Trans. SignalProcessing, 53, 2005, 4110–4124.

[12] V. H. Nassab, S. Shahbazpanahi, and A. Grami, “Optimal distributed beam-forming for two-way relay networks,” IEEE Trans. Signal Processing, 58,2010, 1238–1250.

[13] H. Chen, A. B. Gershman, and S. Shahbazpanahi, “Filter-and-forward dis-tributed beamforming in relay networks with frequency selective fading,”IEEE Trans. Signal Processing, 58, 2010, 1251–1262.

[14] K. Zarifi, A. Ghrayeb, and S. Affes, “Distributed beamforming for wirelesssensor networks with improved graph connectivity and energy efficiency,”IEEE Trans. Signal Processing, 58, 2010, 1904–1921.

[15] Z. Ding, W. H. Chin, and K. Leung, “Distributed beamforming and powerallocation for cooperative networks,” IEEE Trans. Wireless Commun., 7,2008, 1817–1822.

[16] E. Koyuncu, Y. Jing, and H. Jafarkhani, “Distributed beamforming in wire-less relay networks with quantized feedback,” IEEE J. Select. Areas Com-mun., 26, 2008, 1429–1439.

[17] M. Ahmed and S. Vorobyov, “Collaborative beamforming for wireless sensornetworks with Gaussian distributed sensor nodes,” IEEE Trans. WirelessCommun., 8, 2009, 638–643.

[18] E. Zacarias, S. Werner, and R. Wichman, “Distributed Jacobi eigen-beamforming for closed-loop MIMO systems,” IEEE Commun. Lett., 10,2006, 825–827.

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2 Cooperative communications inOFDM and MIMO cellular relaynetworks: issues and approaches

Mohammad Moghaddari and Ekram Hossain

2.1 Introduction

The continually increasing number of users and the rise of resource-demandingservices require a higher link data rate than the one that can be achieved incurrent wireless networks [1]. Wireless cellular networks, in particular, have tobe designed and deployed with unavoidable constraints on the limited radioresources such as bandwidth and transmit power [2]. As the number of newusers increases, finding a solution to meet the rising demand for high data rateservices with the available resources has became a challenging research problem.The primary objective of such research is to find solutions that can improve thecapacity and utilization of the radio resources available to the service providers[3]. While in traditional infrastructure networks the upper limit of the source–destination (S–D) link’s data capacity is determined by the Shannon capacity [4],advances in radio transceiver techniques such as multiple-input multiple-output(MIMO) architectures and cooperative or relay-assisted communications haveled an enhancement in the capacity of contemporary systems.

In the MIMO technique the diversity relies on uncorrelated channels, andis achieved by employing multiple antennas at the receiver side, the transmit-ter side, or both, and by sufficiently separating the multiple antennas (of samepolarization) [5]. The MIMO technique can be used to increase the robustnessof a link as well as the link’s throughput. Unfortunately, the implementationof multiple antennas in most modern mobile devices may be challenging due totheir small sizes [3].

Cooperative diversity or relay-assisted communication has been proposed asan alternative solution where several distributed terminals cooperate to trans-mit/receive their intended signals. In this scheme, the source wishes to transmita message to the destination, but obstacles degrade the S–D link quality. Themessage is also received by the relay terminals, which can retransmit it to adesired destination, if needed. The destination may combine the transmissionsreceived by the source and relays in order to decode the message.


14 Cooperative communications in OFDM and MIMO cellular relay networks

The limited power and bandwidth resources of the cellular networks and themultipath fading nature of the wireless channels have also made the idea ofcooperation particularly attractive for wireless cellular networks [6]. Moreover,the desired ubiquitous coverage demands that the service reaches the users inthe most unfavorable channel conditions (e.g., cell-edge users) by efficient distri-bution of the high data rate (capacity) across the network [7, 8]. In conventionalcellular architectures (without relay assistance) increasing capacity along withcoverage extension dictates dense deployment of base stations (BSs) which turnsout to be a cost-wise inefficient solution for service providers [9]. A relay station(RS), which has less cost and functionality than the BS, is able to extend thehigh data rate coverage to remote areas in the cell under power and spectralconstraints [10–13].

By allowing different nodes to cooperate and relay each other’s messages tothe destination, cooperative communication also improves the transmission qual-ity [14]. This architecture exhibits some properties of MIMO systems; in fact avirtual antenna array is formed by distributed wireless nodes each with oneantenna. Since channel impairments are assumed to be statistically indepen-dent, in contrast to conventional MIMO systems, the relay-assisted transmissionis able to combat these impairments caused by shadowing and path loss in S–Dand relay–destination (R–D) links. To this end, an innovative system has beenproposed in which the communication between transmitter and receiver is donein multiple hops through a group of relay stations. This cooperative MIMOrelaying scheme creates a virtual antenna array (VAA) [15] by using the anten-nas of a group of RSs. These RSs transmit the signal received from the BS(or previous hops) cooperatively on different channels to the receiving terminal(downlink case) or the signal that the transmitting terminal wants to send to theBS (uplink case). This system can be modeled as a MIMO system although thereal receiver (downlink) or transmitter (uplink) only has one antenna. Since therelaying mobile stations (MSs) introduce additional noise and there is a doubleRayleigh channel effect, the scheme is expected to perform below the correspond-ing MIMO diversity gain when used for spatial multiplexing.

The combination of relaying and orthogonal frequency-division multiple access(OFDMA) techniques also has the potential to provide high data rate to user ter-minals everywhere, anytime [7, 8, 16]. Interest in orthogonal frequency-divisionmultiplexing (OFDM) is therefore growing steadily, as it appears to be a promis-ing air-interface for the next generation of wireless systems due, primarily, to itsinherent resistance to frequency-selective multipath fading and the flexibility itoffers in radio resource allocations. Likewise, the use of multiple antennas at bothends of a wireless link has been shown to offer significant improvements in thequality of communication in terms of both higher data rates and better reliabil-ity at no additional cost of spectrum or power [17]. These essential properties ofOFDMA and MIMO, along with the effectiveness of cooperative relaying in com-bating large-scale fading and enhancing system capacity immediately motivatethe integration of these technologies into one network architecture.

2.2 Cooperative relay networks 15

Figure 2.1. Example of a traditional infrastructure network.

However, adequate and practical radio resource allocation (RRA) strategieshave to be developed to exploit the potential gain in capacity and coverageimprovement in the integration of relaying, OFDMA, and MIMO techniques[18]. This chapter surveys algorithms proposed in the literature to adaptivelyallocate the available resources in a relay-enhanced OFDMA-based and MIMOwireless networks. We also briefly review resource management approaches indistributed-MIMO multihop systems.

2.2 Cooperative relay networks

Wireless networks can be classified into two major categories: traditional infras-tructure networks and multihop networks. In traditional networks the communi-cation is performed directly between the BS and the MS and vice versa, so, thereis only one hop. Though obstacles may degrade the line-of-sight (LoS) S–D linkquality in this scheme, the source makes no use of the cooperation potential ofother terminals in the network to compensate for the impairments (Figure 2.1).

2.2.1 Cooperative communication

The method of relaying, which was introduced by Van der Meulen in 1971 [19],was studied from an information theoretical point of view by Cover and El


S

R

D

Figure 2.2. The relay channel, source (S), relay (R), and destination (D).

Gamal in [20]. In these contributions, a source MS communicates with a tar-get MS directly and via a relaying MS. In [20], the capacity of such a relayingconfiguration was shown to exceed the capacity of a simple direct link. In laterstudies, a very simple but effective user cooperation protocol was suggested toboost the uplink capacity and lower the uplink outage probability for a givenrate [21]. The designed protocol stipulates an MS to broadcast its data frameto the BS and to a spatially adjacent MS, which then retransmits the frame tothe BS. Such a protocol certainly yields a higher degree of diversity because thechannels from both MSs to the BS can be considered uncorrelated. Coopera-tive communication was introduced in [10] using the scenario depicted in Figure2.2 but with the relay terminal being another source. Both sources (associatedpartners) are also responsible for transmitting the information of their partners.It was assumed that the sources are working in full-duplex mode, so that bothsources are transmitting to the destination and receiving a noisy version of thepartner’s transmission. Results in terms of ergodic achievable rate regions andoutage probability of the cooperative and noncooperative transmission show thebenefits of this scheme.

2.2.2 Relay channel

The relay channel was introduced in [19]. It assumes that there is a source thatwants to transmit information to a single destination. However, there is a relayterminal that is able to help the destination (relay-assisted transmission). Basedon the previously received symbols, it can transmit an additional message to thedestination if needed. Figure 2.2 illustrates the channel model. When the channelto relay terminal is in a better condition than the LoS channel, this scheme is ableto improve the S–D transmission. In general, it is assumed that the relay worksin full-duplex mode, i.e., receiving and transmitting simultaneously. The duplexcommunication problem can be solved by assuming that the frequency bandsfor the main link (S–D) and the relaying links (R–D) differ. Since full duplexterminals are currently unrealistic in practical systems, relays are forced to workin half-duplex mode. However, the half-duplex constraint impacts negatively onthe theoretical spectral efficiency provided by an ideal full-duplex assisting relay.Multiplexing gains are not possible in half-duplex relaying, although significantadditive capacity gains are still possible [15, 22].

2.2 Cooperative relay networks 17

S

R

D S

R

D S

R

D

Protocol I Protocol II Protocol III

Figure 2.3. Half-duplex relay protocols. Solid lines correspond to the transmissionduring the relay-receive phase and dashed lines to the transmission during therelay-transmit phase.

2.2.3 Overview of relay protocols

In the half-duplex mode there is an orthogonal duplexing (in time or frequency)between the phase that the relay is receiving (relay-receive phase) and the one itis transmitting in (relay-transmit phase). This phase separation allows the defi-nition of several half-duplex relay protocols with various degrees of broadcastingand receiving collision in each relay-receive and relay-transmit phase among thethree terminals (source, destination, and relay). The number of options leads tothe four protocol definitions presented in Figure 2.3, (called protocols I, II, andIII) and in Figure 2.4 (called forwarding) [23, 24].

In protocol I, the source communicates with the relay and destination duringthe relay-receive phase (solid lines in Figure 2.3). Then, in the relay-transmitphase, the relay terminal communicates with the destination (dashed line inFigure 2.3).

On the other hand, in protocol II, during the relay-receive phase the sourceonly transmits to the relay (solid line in Figure 2.3). It is assumed that thedestination is not able to receive the message from the source in that phase. Inthe relay-transmit phase, the source and relay transmit simultaneously to thedestination (dashed lines in Figure 2.3). Hence in the relay-transmit phase thechannel becomes a multiple access channel.

Protocol III can be seen as a combination of protocols I and II. The sourcetransmits to the relay and the destination (solid lines in Figure 2.3) in the relay-receive phase. Then, in the relay-transmit phase, the source and the relay transmitto the destination (dashed lines in Figure 2.3). Notice that the relay is transmit-ting during the second phase, so that it cannot be aware of the signal transmittedby the source in the second phase. This protocol can achieve a better spectralefficiency than the previous ones. For example, this protocol was considered forobtaining the achievable rates of the relay channel in [22].

The traditional forwarding protocol consists of a transmission from the sourceto the relay during the relay-receive phase and a transmission from the relayto the destination in the relay-transmit phase, as in Figure 2.4. It should be


S

R

D

Figure 2.4. Half-duplex forwarding protocol.

emphasized that the half-duplex relay protocols defined in Figure 2.3 make gooduse of the S–D link in contrast to the forwarding protocol. Likewise, if that linkpresents very bad quality compared with the S–R and R–D links, the performanceobtained by protocols I, II, and III converges to the forwarding one.

2.2.4 Strategies of relay-assisted transmission

The paradigm of the conventional S–D communication is now changed to S–R–D,and the role played by the relay can be selected from different modes of operationinfluencing the total achievable rate of the system. Additionally, when there isa half-duplex relay, the resources allocated for each phase of the relay-assistedtransmission also have an important impact on the achievable rate. Therefore,the strategies of relay-assisted transmission have to consider the decoding modeat the relay and the resource allocation. Basically, the three decoding modesanalyzed in the literature are: amplify-and-forward (AF), decode-and-forward(DF), and compress-and-forward (CF).

Amplify-and-forward (AF)This is the simplest strategy that can be used at the relay. The relay amplifies thereceived signal from the source and transmits it to the destination without doingany decoding. For this reason, it is also called nonregenerative relaying. Themain drawback of this strategy is that the relay terminal amplifies the receivednoise at the same time. Applying this strategy to cooperative communicationleads to a better bit error rate (BER) than direct transmission [1]. The outageprobability of the cooperative communication was derived in [1], demonstratingthat a diversity order of 2 is obtained for two cooperative users. When the relayis equipped with multiple antennas and there is channel state information (CSI)available for the S–R/R–D links, the AF strategy can attain significant gainsover the direct transmission by means of optimum linear filtering of the data tobe forwarded [25].

Decode-and-forward (DF)In this strategy the complexity at the receiver increases in comparison to thatin the AF strategy. Now the relay terminal has to estimate the message received

2.3 General system model of cellular relay networks 19

from the source, therefore the total performance depends on the success of thismessage decoding. Depending on the type of symbols retransmitted, the strategyat the relay is repetition coding (RC) or unconstrained coding (UC). In RC,the relay retransmits the same symbols previously estimated, while in UC thesymbols transmitted are not the same as the received ones, but are related tothe same information sent by the source (source and relay are using differentcodebooks). Hence, this protocol is also called regenerative relaying: the termsare used interchangeably in this chapter.

Compress-and-forward (CF)In this strategy, the relay does not decode the data but uses Wyner–Ziv lossysource coding [26] on the estimated symbols of the received signal. Then, thecompressed signal is transmitted to the destination by the relay. This strategywas suggested in [20]. Depending on the channel gains of the different links,the CF strategy can be superior to the DF strategy. However, it adds morecomplexity to the system.

2.3 General system model of cellular relay networks

A partial network in a multicellular relay network is shown in Figure 2.5, which isthe general topology for reviewed algorithms and strategies in this chapter. It isassumed that the BS could continuously measure the quality of link, e.g., signal-to-interference-plus-noise ratio (SINR) per subcarrier when OFDM is applied.Furthermore, for slowly varying channels, BSs and RSs can be assumed to haveaccurate estimates of the channel states. Despite being a common assumption inliterature, this may not always be the case, especially for relay station to sub-scriber station (RS–SS) links. RRA based on partial CSI has been addressed in anumber of references such as [27]. The BSs can optimize the resource allocationor they can involve a central network controller as shown in Figure 2.5.

Consider a two-hop multiuser OFDM system with one BS at the center ofeach cell, K users, and N subcarriers, where each transceiver has only a singleantenna. The RSs are assumed to be fixed and evenly distributed on a circlewith a radius equal to one half of the cell radius in order to eliminate the effectof RS placements. The RS forwards the received signal to the BS (uplink) orSS (downlink) by employing either the amplify-and-forward (AF) or the decode-and-forward (DF) strategy on the same subcarrier. We consider a two-time-slottransmission pattern which is half-duplex in the sense that transmission andreception at any station do not occur simultaneously in the same frequencyband. In the first time slot, the BS (SS) transmits while the RS and the SS (BS)receive. In the second time slot, only the RS transmits to the SS (BS). Whenthe regenerated message is encoded to provide additional error protection for theoriginal message, this is referred to as coded cooperation [2].


SSSS

SS

SS

SSSS

SS

Subscriber station

S

BS

BS

BS Networkcontroller

Relay station

Back-bone link

RS

RS

RS

RS

RS

RS

RS

SS

SS

Figure 2.5. A partial network in a multicellular relay network.

2.4 General system model for virtual antenna arrays (VAAs)

The underlying principle for cellular deployment of VAAs is depicted in Figure2.6. A BS array, consisting of several antenna elements, transmits a space-timeencoded data stream to the associated mobile terminals which can form sev-eral independent VAA groups. Each mobile station within a group receives theentire data stream, extracts its own information, and concurrently relays furtherinformation to the other mobile terminals. It then receives more of its own infor-mation from the surrounding mobile terminals and, finally, processes the entiredata stream. The wired links within a traditional receiving antenna array arethus replaced by wireless links. The same principle is applicable to the uplink[15].

In this situation, the VAA accomplishes a special type of network which bridgescellular and ad-hoc concepts to establish a heterogeneous network with increasedcapacity. It calls for intelligent synchronization, relaying, and data schedulingalgorithms, the exact realization of which depends on the access scheme, thechoice of main link technology, the choice of relaying technology, the technolog-ical limits, the number of antennas within a given geographical area, and otherfactors, e.g., the ability of the cellular system to synchronize users, etc. [15].

The deployment of VAAs creates various challenges which need to be ad-dressed, for instance, how to enable the terminals to transmit and receive simul-taneously and thus to operate in full-duplex mode. Of greater importance is theactual relaying process. Like in satellite transponders, the signal can be retrans-mitted using a transparent or regenerative relay. A transparent relay is generally

2.5 RRA in OFDMA-based relay systems 21

MS

MS

MSMS

MS

MS

MS

MS

MS

MS

VAA cell

VAA

BS

VAA

VAA

Figure 2.6. VAAs in cellular deployment.

easier to deploy since only a frequency translation is required. However, additionsto the current standards are required. For a simple adaptation of VAA to cur-rent standards, regenerative relays should be deployed. This generally requiresmore computational power, but has been shown to increase the capacity of thenetwork [28].

A generic realization of VAAs, which is henceforth referred to as distributed-MIMO multihop relaying network was introduced in [29]. An example realizationis depicted in Figure 2.7. Here, a source MS communicates with a target MS viaa number of relaying MSs. Spatially adjacent relaying MSs form a VAA; eachMS receives data from the previous VAA and relays data to the next VAA untilthe target MS is reached. Note that each of the terminals involved may havemore than one antenna element. Furthermore, an arbitrary number of MSs ofthe same VAA may cooperate with each other. The suggested topology, depictedin Figure 2.7, encompasses a variety of communications scenarios.

For instance, a cellular system operating on the downlink is obtained by replac-ing the source MS by the BS antenna array which communicates directly withthe VAA containing the target MS. It may also represent a system where a BSarray communicates with a VAA formed somewhere in the cell, which in turnrelays the data to another VAA containing the target MS. This allows the cov-erage area of the BS to be extended. But as mentioned before, RRA algorithmsshould be designed to exploit the potential gains in all aforementioned wirelessrelay networks, by adaptively distributing scarce communication resources toeither maximize or minimize some network performance metrics. We review theRRA algorithms proposed in the literature for relay-enhanced OFDMA-basedand MIMO wireless networks as well as distributed-MIMO multihop systems.

2.5 RRA in OFDMA-based relay systems: general form

In relay-enhanced OFDMA-based wireless networks, a typical resource allocationproblem statement might be as follows [30]:


1st hop 2nd hop Lth hop

S D

Figure 2.7. Distributed-MIMO multistage communications system.

How many information bits, how much transmit power (for SSs, RSs, or BSs), whichand how many subcarriers (subcarrier assignment and allocation, respectively) shouldbe assigned to SSs to either maximize or minimize a desired performance metric, e.g.,system throughput (capacity) or total transmit power in the network, respectively?

Assume Ku = 1, 2, ...,K and Nu = 1, 2, ..., N are the sets of users and sub-carriers respectively. The data rate of the kth user Rk is given by [30]

Rk =B

N

N∑n=1

ck,n log2(1 + γk,n ), (2.1)

where B is the total bandwidth of the system and ck,n is the subcarrier assign-ment index indicating whether the kth user occupies the nth subcarrier. ck,n = 1only if subcarrier n is allocated to user k; otherwise it is zero. The bandwidthof each subchannel is B/N = 1/T where T is the OFDM symbol duration. γk,n

is the signal-to-noise ratio (SNR) of the nth subcarrier for the kth user and isgiven by [30]

γk,n = pk,nHk,n =pk,nh2

k,n

N0B/N, (2.2)

where pk,n is the power allocated for user k in subchannel n, and hk,n and Hk,n

denote the channel gain and channel-to-noise ratio for user k in subchannel n,respectively.

From (2.1), the total data rate RT of a zero margin system is given by

RT =B

N

K∑k=1

N∑n=1

ck,n log2(1 + γk,n ). (2.3)

Knowing the modulation scheme, γk,n , the effective SNR, is adjusted accordinglyto meet the BER requirements.

The general form of the subcarrier and power allocation problem is [30]:

maxck , n ,pk , n

RT =B

N

K∑k=1

N∑n=1

ck,n log2(1 + γk,n ) (2.4)

2.6 Dynamic RA RRA in OFDMA relay networks 23

or

minck , n ,pk , n

PT =B

N

K∑k=1

N∑n=1

ck,npk,n , (2.5)

subject to:

C1: ck,n ∈ 0, 1, ∀k, n,

C2:K∑

k=1ck,n = 1, ∀n,

C3: pk,n ≥ 0, ∀k, n,

C4:K∑

k=1

N∑n=1

ck,npk,n ≤ Ptotal ,

C5: user rate requirement.

(2.6)

The problem can be formulated with two possible objectives followed by var-ious constraints (C1–C5). The first two constraints are on subcarrier allocationto ensure that each subchannel is assigned to only one user. C4 is only effec-tive in problems where there is a power constraint Ptotal on the total transmitpower of the system PT (e.g., rate adaptive algorithms). C5 determines the fixedor variable rate requirements of the users. In each class, the problem is formu-lated accordingly and the optimal solution is derived using different optimizationtechniques. Due to the high computational complexity of the optimal solutions,they may not be practical in real-time applications. As a result, suboptimal algo-rithms have been developed which differ mostly in the approach they choose tosplit the procedure into several (preferably independent) steps to make the prob-lem tractable and, in their simplifying assumptions to reduce the complexity ofthe allocation process. The performance of each algorithm greatly depends onthe formulation of the problem and the validity of these simplifying assumptions.

Two major classes of dynamic resource allocation schemes have been reportedin literature [30]: margin adaptive (MA) schemes [31–33], and rate adaptive (RA)schemes [34–36]. The optimization problem in MA allocation schemes is formu-lated with the objective of minimizing the total transmit power while providingeach user with its required QoS in terms of data rate and BER. The objectiveof the RA scheme is to maximize the total data rate of the system with the con-straint on the total transmit power. Both classes are overviewed and discussedin the following sections.

2.6 Dynamic RA RRA in OFDMA relay networks

Different scenarios of centralized or distributed algorithms, along with single-celland multicell network topologies have been considered in the literature for theRA RRA problem.


2.6.1 Centralized RA RRA schemes in single-cell OFDMA relay networks

A downlink single-cell network with a single fixed RS was considered in [37],while such a network with multiple fixed RSs was studied in [38]. In both [37]and [38], time-division-based half-duplex transmission and adaptive modulationand coding (AMC) were assumed. In [37] two algorithms (fixed time-divisionand adaptive time-division) were proposed to improve the cell throughput andcoverage while minimizing complexity and overhead requirements. However, theobjective function in [38] was the total average throughput of both the directand relayed links presented as a function of SNRs and some indicator (optimiza-tion) variables, with constraints as in [37]. In both the proposed algorithms, theBS transmission frame is followed by the transmission of an RS frame. The firstalgorithm performs subcarrier allocation with a predetermined equal power allo-cation (the same level for both BS and RS). The second algorithm achieves anoptimal joint power and subcarrier allocation. Simulation results showed that asthe number of RSs increases, the sum rate increases, while the joint allocationalgorithm continues to outperform the fixed power allocation algorithm.

In [39], the authors used the concept of utility functions to formulate theproblem of RA in multiuser OFDM systems. Utility maps the network resourcesa user utilizes into a real number and is a function of the user’s data rate. Theutility-based dynamic resource allocation problem is formulated as:

maxck , n ,pk , n

K∑k=1

Uk (Rk ), (2.7)

subject to:

C1: Si ∩ Sj = ∅, ∀i, j ∈ Ku, i = j,

C2: ∪k Sk ⊆ 1, 2, ..., N,C3: pk,n ≥ 0, ∀k, n,

C4:K∑

k=1

N∑n=1

ck,npk,n ≤ Ptotal , (2.8)

where Uk (Rk ) is the utility function for the kth user. Rk is defined as in (2.1), Sk

is the set of subcarriers assigned to user k for which ck,n = 1. In [39] the extremecase of an infinite number of orthogonal subcarriers each with an infinitesimalbandwidth was investigated by introducing two theorems: theorem I gave theoptimal subcarrier allocation assuming a fixed power allocation on all the sub-carriers and theorem II gave the optimal power allocation given a fixed subcarrierallocation. Combining the results of the two theorems, the optimal frequency setand the power allocation for the extreme case were obtained. It is obvious from(2.7) and (2.8) that fairness among users was not considered.

For RA schemes for OFDMA without relaying, it has been shown in literature,e.g., [40], that optimization can be achieved when a subcarrier is assigned toonly one user who has the best channel gain for that subcarrier, and also that


equal power allocation among subcarriers has almost the same performance aswaterfilling transmit power adaptation but with less complexity. In [34], theauthors imposed proportional rate constraints in the OFDMA relaying networkto ensure that each user could achieve the required data rate. However, all thetransmitters, including the BS and RSs, are limited to one fixed transmittingpower, which is not flexible and this is not practical in a relaying network.

To tackle the mixed integer and continuous variable optimization problem in(2.7)–(2.8) with Uk (Rk ) = Rk , the authors of [41] proposed a greedy subcarrierand power coallocation algorithm based on a new theorem. The theorem statesthat in general situations, i.e., when all link gains between RSs and SSs aredifferent from each other, for each SS and subcarrier allocated, there is only oneRS among all RSs that has pk,n = 0. In other words, for each symbol transmittedfrom the BS to the SS, only one RS needs to relay this symbol, given the powerconstraint on each RS. This also suggests that using subcarrier allocation withoutconsidering power allocation may not work well because many subcarriers at eachRS may not have been allocated power even though they have been chosen [41].

The centralized subcarrier and power allocation algorithm which maximizessystem capacity with a constraint on the overall transmission power when thereis an LoS between the BS and the SS was studied in [42]. Hence, the aggregatesystem throughput was defined as

RT =∑i∈D

Ri +K∑

k=1

Rk , (2.9)

where D represents the set of direct links. Similar to the approach taken in[34], the problem was broken down into two steps. In the first step, a heuristicalgorithm was proposed to assign the subcarriers to each link based on the chan-nel condition. In the second step, an iterative power allocation algorithm wasproposed to balance the two-hop links for maximizing the end-to-end capacityof two-hop SSs. In the proposed algorithm, firstly, the subcarriers are allocatedto the links with the best channel gain as an initialization. The overall capac-ity of each transmission slot is maximized in this step. In the next step, thesubcarriers are reallocated to improve the system capacity by iteration. In otherwords, the basic idea is to take out the worst subcarrier allocated to the first-hop(second-hop) link of the richest (poorest) RS and to reassign it to the first-hop(second-hop) link of the poorest (richest) RS. Two cases are compared and theone that can achieve more gain is exploited. The subcarrier reassigning procedureis repeated until no improvement can be achieved [42].

Another interesting technique to deal with the mixed integer optimizationproblem in (2.7)–(2.8) was proposed in [18]: an OFDMA relay network withmultiple sources, multiple relays, and a single destination was investigated andresource allocation was considered with fairness (load balancing) constraints onrelay nodes. The authors’ approach was to transform the integer optimizationproblem into a linear distribution problem in a directed graph to allow the use of


BS

S2S2 S1S1

Inner (single-hop) regionRelay (multihop) region

Figure 2.8. Network layout and spatial reuse pattern.

the linear optimal distribution algorithms available in the literature. The requiredinformation is collected at the central unit for allocation decisions (Figure 2.5).It was assumed that the subcarriers allocated in the first hop (S–R) are the sameas those in the second hop (R–D). This reduction in available frequency diversitygain results in a potential system performance loss.

To address this issue, the concept of subcarrier pairing was employed in [43]to attain extra gain in the average system rate. It was shown that a higherperformance in terms of mutual information can be achieved if the subchannelsof both links, S–R and R–D, are paired according to the actual magnitude ofthe link gains, i.e., a strong first hop subchannel is coupled with a strong secondhop subchannel and not with a weak one.

2.6.2 Centralized RA RRA schemes in multicell OFDMA relay networks

A centralized downlink OFDMA scenario in a multicellular network enhancedwith six fixed relays per cell was considered in [44] and [45]. The proposed schemeallows efficient use of subcarriers via opportunistic spatial reuse within the samecell, as shown in Figure 2.8 (i.e., a set of subcarriers used in a BS–RS link (S1)can be reused after 180-degree angular spacing in a RS–SS link), even when nodirectional antennas are employed. These are probably among the first papers toconsider such spatial reuse in a multicell environment, although, with a greatlysimplified model. Fading was not considered except for independent log-normalshadowing on links, which means that subcarriers are similar on any particularlink. Consequently, the problem was formulated as the minimum number of sub-carriers required to satisfy a SS’s QoS. This was used in the transmit schemeselection algorithm (TSSA) that switches among single-hop, multihop, and mul-tihop with spatial reuse [7].


In the TSSA, the only scheme allowed in the interior hexagon is the single hopdirectly from the BS, whereas outside this region (relay region), the TSSA canchoose the multihop with spatial reuse scheme or the multihop scheme, whichrequires fewer subcarriers to satisfy the QoS requirements. With this strategy,an integer programming optimization problem is formulated to maximize thenumber of SSs with satisfied QoS requirements. It was observed that a signif-icant increase in the number of supported SSs is achieved when applying theTSSA compared with the case where the transmission scheme is restricted inthe cell region to a particular scheme, regardless of the channel conditions. Thissuboptimal scheme potentially reduces the performance gains.

By considering latency, overhead and system, and computational complexity,it may be seen that centralized RRA schemes are not the best option for futurewireless networks. This has led to the importance of distributed schemes beingrecognized. However, there has not been much progress on this front.

2.6.3 Distributed RA RRA schemes in OFDMA relay networks

A semi-distributed downlink OFDMA scheme in the form of two algorithmsof separate and sequential allocation (SSA) and separate and reuse allocation(SRA), in a single cell enhanced by M half-duplex fixed relays was considered in[46]. The scheme divides the SSs into disjoint sets located in the neighborhoodsof the BS and RSs, an approach that is common in the literature. The SSsattached to the BS and relays are referred to as the BS–SS and RS–SS clusters,respectively. The BS allocates some resources to the BS–SS cluster directly and tothe RS–SS clusters through the RS. Implicitly, it is assumed that all routes havebeen established prior to resource allocation, regardless of the channel conditions,and that the same subcarrier is used on the two hops, BS–RS and RS–SS.

The starting point of both the two-step SSA and the SRA algorithm allocationschemes is basically the same. In the first step, each RS, along with its SS cluster,is treated as a large SS with a required minimum rate equal to the sum ofall the minimum required rates of the SSs in its cluster. The BS allocates theresources among its own SSs and these virtual large SSs. In the second step, theRS allocates resources to the SSs in its cluster based on one of two allocationschemes:

Resources assigned to that BS-RS link in the first step are allocated amongthe connected SSs (SSA).

The RS reallocates all the N subcarriers to its connected SSs regardless ofthe BS assignments (SRA).

Simulation results for a single cell with one relay showed that the semi-distributed scheme, SSA in particular, has a comparable capacity and outageprobability performance to the centralized scheme [7]. The SSA algorithm showedsignificant performance stability over the SRA. Since both RS and BS may


assign the same subcarriers to their respective SSs in the SRA algorithm, intra-cell interference may occur, which results in a considerable increase in outageprobability.

In general, the proposed semi-distributed schemes reduce the amount of over-head required to feedback the CSI and minimum rates to the BS. However, in thecase of SRA, there is no need to communicate such information to the BS. Theseschemes fail to exploit the interference avoidance and traffic diversity gains. Inaddition, there is an inherent loss in performance due to the decoupling of routingand scheduling processes.

2.6.4 RA RRA schemes with fairness in OFDMA relay networks

Looking back at utility-function-based optimizations, such as in [39], one way toaccomplish both efficiency and fairness is to use utility functions that are bothincreasing and marginally decreasing. As a result, the slope of the utility curvedecreases with an increase in the data rate. Choosing a marginally decreasingutility function also guarantees its strict concavity which ensures global opti-mality as well as the uniqueness of the optimal solution. A logarithmic utilityfunction U(R) = ln(R) is both increasing and marginally decreasing. Therefore,a resource allocation policy using a logarithmic utility function is said to be pro-portionally fair. Different types of utility functions were proposed in [36], [47],and [48], depending on the type of application. A utility function that ensuresboth efficiency and fairness is better obtained through subjective survey than byapplying theory.

For the general resource allocation problem formulated in (2.4)–(2.6), the opti-mization with variable rate constraints is given in (2.10)–(2.11), in which theobjective is to maximize the total rate within the total power constraint ofthe system while maintaining rate proportionality among the users indicatedin C5:

maxck , n ,pk , n

RT =B

N

K∑k=1

N∑n=1

ck,n log2

(1 +

pk,nh2k,n

N0BN

), (2.10)

subject to:

C1: ck,n ∈ 0, 1, ∀k, n,

C2:K∑

k=1

ck,n = 1, ∀n,

C3: pk,n ≥ 0, ∀k, n,

C4:K∑

k=1

N∑n=1


C5: R1 : R2 : . . . : RK = α1 : α2 : . . . : αK . (2.11)


Here α1 , α2 , . . . , αK is a set of predetermined proportional constraints inwhich αk is a positive real number with αmin = 1 for the user with the lowestrequired proportional rate. When all αk terms are equal, the objective functionin (2.10) is similar to the objective function of the max–min problem introducedin [49].

The authors of [49] studied the max–min problem, where by maximizing theworst user’s capacity, it was ensured that all users achieve the same data rate.It was reported that in a single-user waterfilling solution the total data rate of azero margin system is close to capacity, even with flat transmit power spectraldensity (PSD), as long as the energy is poured only into subchannels with goodchannel gains. Hence, in a system with N subchannels, a flat transmit powerover all the subcarriers would always give close to optimum performance.

Though acceptable fairness amongst users is achieved in [49] by allocatingpower uniformly across all subcarriers, the frequency selective nature of a user’schannel is not fully exploited. To improve its performance, Shen et al. [34] addeda second adaptive power allocation step to further enforce the rate proportion-ality among the users. The two-step approach adopted in [34] is as follows: inthe first step, the modified version of the algorithm outlined in [49] is employedfor subcarrier allocation to achieve coarse proportional fairness. Hence, insteadof giving priority to the user with the lowest achieved data rate Rk , prior-ity is given to the user with the lowest achieved proportional data rate, i.e.,Rk/αk . In this step, the achieved rate is calculated assuming equal power onall the subcarriers. After subcarrier allocation is carried out, the problem issimplified into maximization over continuous variables of power. In the secondstep, the power is reallocated among the users and then among the subcarriersthrough the use of waterfilling to enforce the rate proportionality among theusers.

Another suboptimal algorithm to solve RA RRA was formulated in [50] as abinary integer programming problem to maximize the Nash product of all usersin the form

∏Kk=1(Rk −Rreq

k ) and, at the same time, satisfy users’ minimumrate requirements. It was demonstrated in [51] that the solution achieves a Nashbargaining solution (NBS) fairness, which is a generalization of the well-knownproportional fairness.

The algorithm can be divided into two steps. In the first step, a subcarrieris randomly selected and then allocated to the user whose required minimumrate is not satisfied and whose achievable rate on this subcarrier is the largest,either by direct or by relayed transmission. The process loops until all usersachieve their required rates. In the second step, the NBS algorithm assignsthe remaining subcarriers to users in such a way that the Nash product foreach assignment is maximized. While this scheme is fair in the sense that theuser’s rate is determined only by its own channel condition, and not by othercompeting users’ conditions, it was also shown that the algorithm provides agood tradeoff between the overall system performance and the fairness amongusers.


2.7 Dynamic centralized margin adaptive RRA schemes inOFDMA relay networks

In deriving this group of algorithms, a given set of user data rates is assumedwith a fixed QoS requirement. The optimization problem can then be formulatedas [30]:

minck , n ,pk , n

PT =K∑

k=1

N∑n=1

ck,npk,n , (2.12)

subject to:

C1: ck,n ∈ 0, 1, ∀k, n,

C2:K∑

k=1

ck,n = 1, ∀n,

C3: pk,n ≥ 0, ∀k, n,

C4:K∑

k=1

N∑n=1


C5: Rk ≥ Rk,min , k = 1, 2, . . . ,K (2.13)

with the rate requirements indicated in C5.This problem was first addressed in [52], where the focus was only on sub-

carrier allocation, and further in [32], where adaptive power allocation was alsoconsidered. With the help of constraint relaxation and to make the problemtractable, the authors of [31] introduced a new parameter to the cost function,taking values within the interval [0,1], which can be interpreted as the sharingfactor for each subcarrier; the same technique was also used in [3] and [53] tosimplify the optimization problem. With the help of the new parameter, it wasshown that the optimization problem can be reformulated as a convex mini-mization problem over a convex set [30]. Using the standard optimization tech-niques, the Lagrangian of the new problem is obtained along with the necessaryconditions under which not only the minimum total transmit power occurs butalso the data rate constraint of each user is satisfied. Lagrange multipliers whichsatisfy the individual data rate constraints can be found using an iterativesearch algorithm. Each subcarrier is then assigned to only the user that has thelargest sharing factor on that subcarrier, using the set obtained in the previousstep.

However, the iterative computation and search for this algorithm make it pro-hibitively expensive and highly complex. One solution to simplify the algorithmis to assume that the channel is flat for a certain number of subcarriers, as in[54].

Adaptive resource allocation methods have been shown to offer higher userdata rates due to the additional degree of freedom provided by multichannelsystems [30]. One way to create multiple channels in a frequency domain is to

2.8 MIMO communications systems 31

use multiple carrier frequencies with the methods and algorithms discussed inthis chapter. The other way is with multiple transmit and receive antennas inthe spatial domain. The latter is also referred to as MIMO.

2.8 MIMO communications systems

MIMO systems have been shown to hold the promise of providing capacity anddata rates far exceeding those offered by conventional single-input single-output(SISO) communications systems, and hence are being widely studied for use inwireless systems. MIMO channels have a number of advantages over traditionalSISO channels such as beamforming (or array) gain, diversity gain, and multi-plexing gain. The beamforming and diversity gains are not exclusive for MIMOchannels and also exist in single-input multiple-output (SIMO) and multiple-input single-output (MISO) channels. The multiplexing gain, however, is a uniquecharacteristic of MIMO channels. Some gains can be simultaneously achieved,while others compete and establish a tradeoff. An excellent overview of the gainsof MIMO channels is avaiable in [55]. In a nutshell, the use of multiple dimen-sions at both ends of a communication link offers significant improvements interms of spectral efficiency and link reliability.

2.8.1 RRA in MIMO relay networks

The main challenge in point-to-multipoint fixed relaying is to provide a high-capacity link between the BS and the RS, while at the same time providing mul-tiple data links to multiple users [56]. A natural solution to this problem is toexploit the advantages of MIMO systems. A wireless MIMO relay can be regener-ative or nonregenerative. It was suggested in [57] that a nonregenerative MIMOrelay has the following potential advantages over a regenerative MIMO relay.First, a nonregenerative relay can relay signals faster than a regenerative relayif separate frequency channels are used for the relay’s input and output. Second,deployment of a nonregenerative relay can have little effect on the operations atthe source and the destination as there is no handshaking requirement for eachpacket going through the nonregenerative relay using two frequency channels.Third, a nonregenerative relay contains virtually no information for decodingthe source and hence exposes no security information even if it is stolen by anenemy.

There has been much research into nonregenerative MIMO relay systems [56–61]. The focus in the literature has been on the optimal design and power allo-cation of these systems. In the context of MIMO relays, the power allocationproblem is to determine the source covariance matrix and the relay matrix thatmaximize the system performance. Here we present a review of work on two maincategories of MIMO-enhanced relaying systems, single-user single-relay MIMO


Source1

2

M N

2

1Relay

Encode (Decode/encode

DestinationQ F

HSR HRd

Figure 2.9. DF MIMO relaying system.

and multiuser single-relay MIMO systems as well as distributed-MIMO multihopsystems.

2.8.2 Optimal design and power allocation in single-user single-relay systems

For a single-user two-hop MIMO relay system, an optimal structure of the relaymatrix that maximizes the S–D mutual information was presented in [57] and[58], and an optimal structure for both the source precoder matrix and the relaymatrix was established in [59]. Optimal designs of beamforming and forwardingmatrices for both the DF and the AF relaying protocols are presented in thefollowing subsections.

DF relay systemWe first consider a single-user DF MIMO downlink relay system as illustratedin Figure 2.9, where s ∈ C

M×1 denotes the signal transmitted from the sourceequipped with M antennas, Q ∈ C

M×M the source precoder (beamforming)matrix, and HSR ∈ C

M×M the S–R channel matrix. Then the signal receivedat the relay, yR , is given by yR = HSRQs + nR , where nR is the zero-meanGaussian noise at the relay. The achievable rate at the first hop (S–R) can berepresented as [62]

R1(Q) = 12 log det

(σ2

RIM + HSRQE[ssH ]QH HHSR

)(2.14)

= 12 log det

(σ2

RIM + HSRQQH HHSR

), (2.15)

where E[ssH ] = IM , and E[nRnHR ] = σ2

RIM . The 12 represents the rate loss due

to transmission in two hops. In the second phase, the relay decodes data (withthe assumption of no outage) and forwards them to the destination using theforwarding matrix F. The received signal at the destination is given by yD =HRDFs + nD . The achievable rate at the second hop (R–D) can be representedas

R2(F) = 12 log det

(σ2

D IN + HRDFFH HHRD

). (2.16)

Finally, the achievable rate of the relay system is bounded by the minimum ofR1 and R2 , i.e., R(Q,F) =min(R1(Q), R2(F)). Similarly to Section 2.6, the RAoptimization problem can be formulated as

maxQ ,F

R(Q,F), (2.17)


subject to:

C1: tr(QQH ) ≤ PS ,

C2: tr(FFH ) ≤ PR, (2.18)

where PS and PR are the total power constraints at the source and relay, respec-tively and tr(·) represents the trace of the matrix. From (2.15) and (2.17), wenote that the optimization problem can be divided into two MIMO channel ratemaximization problems as:

maxQ

R1(Q) maxF

R2(F)

subject to:

tr(QQH ) ≤ PS tr(FFH ) ≤ PR. (2.19)

It is well known that the optimal solution of (2.19) is singular value decomposi-tion (SVD) with waterfilling power allocation.

AF relay systemConsider the single-user AF MIMO downlink relay system as illustrated in Figure2.10. The achievable rate at the first hop (S–R) can be obtained as [62]

R1(Q) = 12 log det

(σ2

RIM + HSRQQH HHSR

). (2.20)

In the second phase, the relay simply amplifies its received data and forwardsthe data to the destination using the forwarding matrix F. The received signalat the destination is given by

yD = HRDFyR + nD (2.21)

= HRDF(HSRQs + nR ) + nD (2.22)

= HRDFHSRQs + HRDFnR + nD . (2.23)

From (2.23), it is obvious that relay amplifies not only data vector s, but thenoise of the first hop nR . Though amplifying the noise causes rate loss in theAF relay protocol, the implementation is easy and delay is much smaller than inDF.

The achievable rate of the second phase can be derived as

R2(Q,F)=12 log det

(I+HRDFHSRQQH HH

SRFH HHRD (I+HRDFFH HH

RD )−1).

(2.24)As with DF, the achievable rate of the relay system is bounded by the minimum

of R1 and R2 , i.e., R(Q,F) =min(R1(Q), R2(Q,F)). Hence, the RA optimization


Source

Channel state information

1

2

M N

2

1Relay

EncodeDestination

Q F

HSRHSR

Figure 2.10. AF MIMO relaying system.

problem can be formulated as

maxQ ,F

R(Q,F),

subject to:

C1: tr(QQH ) ≤ PS ,

C2: tr(F(HSRQQH HH

SR + σ2RI)FH

)≤ PR. (2.25)

This is more complex than the problem for the DF case and cannot be dividedinto individual optimization problems. To tackle (2.25), the authors in [57–59]proposed different approaches though with the same basic idea.

In [57] it was proved that for a relay system without a direct S–D link theoptimal relay matrix is given by

F = V2ΛF UH1 , (2.26)

where ΛF is a diagonal matrix, and H1HH1 = U1Σ1UH

1 and HH2 H2 = V2Σ2VH

2are the eigenvalue decomposition (EVD) of channel matrices H1 = HSR andH2 = HRD . Hence, F can be considered as a matched filter along the singularvectors of the channel matrices. When the weighting matrix F obeys a set ofcanonical coordinates given by (2.26), the MIMO relay channel is decomposedinto several parallel SISO channels. If we substitute (2.26) into (2.23) with Q =IM , the signal received at the destination is

yD = Λ2ΛF Λ1 s + Λ2ΛF nR + nD , (2.27)

where we used the SVD of H1 = U1Λ1VH1 and H2 = U2Λ2VH

2 . Also, yD =UH

2 yD , s = UH1 s, nD = UH

2 nD , nR = UH1 nR .

Since the MIMO channel is decomposed into (orthogonal) parallel SISO sub-channels, the problem now is how to allocate the total power to those sub-channels. The optimization objective is now concave and since the constraint isconvex, the problem is easily transformed into a standard convex optimizationproblem.


2.8.3 Optimal design and power allocation in single-relay multiuser systems

A generalized convex optimization problem was introduced in [63] as

minQ≥0

J = − log | I + HQHH |, (2.28)

subject to: tr(BiQBHi ) ≤ Pi, ∀i ∈ 1, . . . , m, (2.29)

where H and Bi are complex matrices, Q is a complex positive semidefinitematrix, and Pi are positive numbers. If m = 1, the solution to the above problemcan be found by a well-known waterfilling algorithm. It can be proved that thesolution of (2.28)–(2.29) is given by

Q = W−H V(I− Σ−2)+VH W−1 , (2.30)

where W =(∑m

i=1 µiBHi Bi

) 12

(assumed to be nonsingular), V and Σ are deter-

mined by the SVD HW−H = UΣVH , (.)+ replaces all negative diagonal ele-ments by zeros and leaves all nonnegative diagonal elements unchanged, andµ = (µ1 , . . . , µm ) is the solution to the following dual problem:

minµ≥0

− log | I + HQHH | +m∑

i=1

µi(tr(BiQBHi )− Pi), (2.31)

subject to: Q = W−H V(I− Σ−2)+VH W−1 . (2.32)

A multiuser MIMO relay downlink/uplink system was treated in [63], whererate adaptive and margin adaptive algorithms were presented to maximize thesystem throughput (i.e., sum rate) under a power constraint, and to minimize thesystem power consumption under individual user rate constraints, respectively.Similarly, the problem of maximizing the sum rate for all users under a powerconstraint for the downlink case was considered in [56] where each user has asingle antenna.

In [56] and [63], the authors showed that with the use of zero-forcing dirtypaper coding (ZFDPC) [64] the multiuser interference could be eliminated ina consecutive way, so the problem could eventually be reformulated as (2.28)–(2.29) and solved using (2.30). In other words, with dirty paper coding and QRdecomposition, the interference from the first stream to the second stream canbe virtually eliminated, and so forth. In this way, the source covariance matrixis matched to the right singular vectors of the S–R channel matrix [63], theoptimality of which for a single-user relay system was shown in [59]. Also, therelay matrix is matched to the left singular vectors of the S–R channel matrix.


2.9 RRA in MIMO multihop networks

In this section we review the resource allocation strategies in a wireless multi-hop network, where a source communicates with the destination via a number ofrelays. In order to avoid interference between the relaying hops, orthogonal accessschemes such as frequency-division multiple access (FDMA) or time-divisionmultiple access (TDMA) are usually used. However, it can be shown that bothaccess schemes achieve the same capacities [15].

At each relaying node the DF relaying protocol is applied, whereby the dataare first detected and decoded completely, then reencoded and transmitted to thenext relaying nodes [65]. The end-to-end connection is therefore accomplishedthrough a number of topologically imposed VAAs.

In [66], a suboptimal bandwidth and power allocation algorithm was proposedto maximize the ergodic end-to-end link capacity for FDMA-based multihop net-works. However, its allocated bandwidth was assumed to be consecutive, whichmakes it impractical in an OFDMA-based system. In each hop, the capacitycan be considered as parallel narrowband subchannels. So the capacity of the ithhop is

Ci = αiBEγi

[log2

(1 +

βiP

αiσ2RB

γi

)], i = 1, . . . , L, (2.33)

where L is the number of hops (Figure 2.7), αi and βi are the ith hop bandwidthand power fractions, respectively, and P is the source transmit power. Also sincethe statistics of channel gain do not depend on the frequency, we use γi to denotethe channel gain of the ith hop. The capacity of the end-to-end link is dictatedby the smallest Ci and the goal is to find the fractional bandwidth and powerallocations for given γi for all i, such as to maximize the minimum capacity.In other words, an optimal resource allocation strategy should assign fractionalpower and bandwidth to each hop in such a way that the end-to-end capacity ismaximized:

C = maxαi ,βi

minC1 , . . . , CL,

subject to:L∑

i=1

αi = 1,

L∑i=1

βi = 1. (2.34)

The strategy was shown to be of low complexity and to achieve near-maximumend-to-end ergodic capacity [66].

Similar resource allocation strategies were introduced in [28] to maximize theend-to-end data throughput over ergodic fading channels under the assumption offixed total transmit power. For the same power constraint, an allocation strategyfor minimizing the error rate was given in [67], where a power allocation solutionto reduce pair-wise error probability (PEP) for a two-hop wireless network withan AF relaying protocol was introduced. It was shown that the optimal powerallocation assigns half the total power to the source and the other half is shared

2.9 RRA in MIMO multihop networks 37

between the relays. However, as the majority of today’s wireless communicationshappen over slow-fading channels, i.e., nonergodic in the capacity sense, the con-sideration of the end-to-end outage probability is of greater practical relevance.Outage probability can be expressed as the probability that the channel cannotsupport an error-free transmission at a specific data rate. In addition, approachesfor minimizing the transmit power are desired.

The task of minimizing the total power while meeting a given end-to-endoutage probability constraint was analyzed in [68] and [69]. In [68], the authorsintroduced an efficient near-optimal power allocation strategy for symmetric dis-tributed MIMO networks by solving a high-order equation in one variable. Forthe case of a large number of relaying nodes per VAA, a closed-form solutionwas proposed by approximating the high-order equation to a quadratic equation.Based on these results an efficient closed-form solution for an arbitrary numberof nodes per VAA was presented in [69].

According to the capacity of a MIMO channel determined in [4], the capacityof a MISO system is given by

Ck,j = αkB log2

(1 +

1αiσ2

RB

tk∑i=1

Pk,i

dεk,i,j

| hk,i,j |2)

(2.35)

where Pk,i is the transmission power of the ith node at the kth hop. The channelfrom the tk transmit nodes to the jth receive node at the kth hop is expressed ashk,j and its elements hk,i,j obey the same uncorrelated Rayleigh fading statistics.It is assumed that the relaying nodes belonging to the same VAA are spatiallysufficiently close to justify a common path-loss between the two VAAs; thispath-loss is given by dε

k,i,j , where dεk is the distance between two nodes and ε

is the path-loss exponent, which is within the range of 2–5 for most wirelesschannels.

The outage probability Pout,k ,j can be expressed as Pout,k ,j = PrR > Ck,j. Ifall of the receiving nodes of a hop cannot decode the message, the correspondinghop is in outage. Consequently, the end-to-end connection is in outage if any hopis broken, and the end-to-end outage probability corresponds to [70]

Pe2e = 1−L∏

k=1

rk∏j=1

(1− Pout,k ,j ), (2.36)

where rk is the number of successful receivers at the kth hop. Therefore, theoptimization task could be defined as

min Ptotal =L∑

k=1

Pk (1− Pout,k ,j ),

subject to: Pe2e ≤ e,

L∑k=1

αk = 1. (2.37)


The assumption that should be noted and modified here is that the number ofnodes at each VAA is considered constant and equal to tk .

Optimally assigning resources in terms of fractional time and transmissionpower to the hops on the basis of network geometry, i.e., the number of nodesper VAA and the distances of the hops was considered in [70] and [71]. A powerallocation problem and a joint power and time allocation (JPTA) problem wereformulated. As shown in [70], the optimization problems are convex and cantherefore be solved by common optimization tools. All of the resource alloca-tion schemes require the solution of the optimization task at a central positionand the distribution of the time fractions and power allocations to the differ-ent nodes. However, if the geometry changes, i.e., the number of nodes perVAA or the hop distance changes, the resource allocation solution has to beadapted.

2.10 Conclusion

In this chapter, we have first presented a brief overview of relaying and itsbasic protocols, and introduced the concept of VAA as the main idea behindthe MIMO multihop systems. This has been followed by a survey of algorithmsin the literature which adaptively allocate the available resources in a single-user/multiuser relay-enhanced OFDMA-based, MIMO, and distributed MIMOwireless networks. Different classes of algorithms consider different objectivesand attempt to obtain a solution that is close to optimum but at the sametime simple enough to be implemented. Numerous publications have highlightedthe need for efficient resource management in such networks. Although RRA inOFDMA-based relay networks has begun to attract attention, only a few papershave investigated OFDMA-based relay networks in multicellular environments.Some of the proposed algorithms are designed to reduce the required signal-ing overhead compared with the optimal solution, when the optimal solutioninvolves prohibitive complexity. There are ongoing research efforts towards find-ing more efficient centralized RRA algorithms, since most of those proposed inthe literature are overly complex. Furthermore, significant savings in overheadand system complexity can be obtained through distributed resource allocationschemes. Therefore, research into distributed RRA algorithms in OFDMA-basedrelay networks has begun to attract attention.

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Part II

Cooperative base stationtechniques

3 Cooperative base stationtechniques for cellularwireless networks

Wibowo Hardjawana, Branka Vucetic, and Yonghui Li

3.1 Introduction

The spectral efficiency of existing cellular networks [1] is limited by interference.In cellular mobile networks, the dominant interference comes from adjacent cells[2]. This is especially true when the users are located near the cell edges wherethe interference from the adjacent cells is very strong. By getting the adjacentbase stations (BS) to cooperate, spatial antenna diversity in each BS can beutilized to cancel the interference. To obtain BS cooperation, multiple BSs shareinformation about the transmitted messages to their respective users and wirelesschannels via a backbone network. Each BS can transmit either a single symbolstream or multiple symbol streams to its respective mobile station (MS). Indi-vidual BSs and MSs are equipped with multiple transmit and receive antennas,respectively. Each BS transmitter uses the transmitted signal information fromother BSs and wireless channel conditions to precode its own signal. The pre-coded signal for each BS is broadcast through all BS transmit antennas in thesame frequency band and time slots. The precoding operation and transmit–receive antenna coefficients are chosen in such a way as to minimize the inter-ference coming from other BS transmissions. The calculated receive antennacoefficients are then sent from the transmitter to the receiver through a wirelesschannel prior to the data transmission. In this chapter, we consider the use of acooperative BS system to eliminate the interference in cellular networks. We willfirst start by reviewing related work in the literature, and follow this by present-ing first a system model, and then a cooperative BS system design and its advan-tages over other existing schemes. Lastly, numerical results and conclusions arepresented.

3.1.1 Related work

Most of the published papers in this area consider only a downlink multiusermultiple-input single-output (MISO) broadcast channel. A variety of methods tosuppress interference from other users have been developed. In [3], a method to


48 Cooperative base station techniques for cellular wireless networks

maximize individual signal-to-interference-plus-noise ratios (SINRs) by jointlyadjusting the transmit weights and transmission powers was developed. A dif-ferent approach was proposed in [4] where a combination of a zero-forcing (ZF)method, which determines transmit weights by forcing part of the interferenceto zero, and dirty paper coding (DPC) [5] was used to suppress interference fromother users. A more practical approach than the one in [4] was considered in [6] byreplacing DPC with Tomlinson–Harashima precoding (THP) [7, 8]. These algo-rithms, however, only consider single receive antenna scenarios, which are notdirectly applicable to multiple-input multiple-output (MIMO) systems. Theseworks on downlink multiuser MISO systems have been extended to incorporatemultiple receive antennas. In [9], the authors showed how a ZF method canbe used to exploit the availability of multiple receive antennas. Here transmit–receive antenna weights are first jointly optimized by a ZF diagonalization tech-nique and then a waterfilling power allocation method is applied to allocatepower to each user. The scheme in [9] was further improved by using an itera-tive method in [10]. Nonlinear methods, utilizing a combination of a ZF methodwith DPC and a combination of a ZF method with THP [7, 8] for a multiuserMIMO system were considered in [11, 12], respectively. The authors use the ZFmethod to eliminate part of the interlink interference. DPC or THP is then usedto cancel the remaining interference. These schemes, however, are not practicalfor cooperative MIMO systems, since their symbol error rate (SER) performancevaries from user to user. In particular, this SER variation is not desirable sincethe MIMO systems can be deployed by different operators and they expect thesystems to have a similar performance.

3.1.2 Description of the proposed scheme

In this chapter, we propose a cooperative transmission scheme employing precod-ing and beamforming for the downlink of a MIMO system. In this algorithm, theTHP cancels part of the interference while the transmit–receive antenna weightscancel the remaining interference. A novel iterative method based on [13] isused to generate the transmit–receive antenna weights. The receive and trans-mit weights are optimized iteratively until the SINR for each user converges toa fixed value. In addition to the iterative joint transmit–receive antenna weightsoptimization and THP above, we also employ SINR equalization, and an adap-tive precoding ordering (APO) in the algorithm. The SINR equalization process[3] is used to allocate power to users in such a way that all users have the sameSINRs. This ensures SER fairness among all users. We consider two types ofpower constraints. The first one is a total BS power constraint, where the totalpower for all BSs is constrained to a particular value. The second one is a perBS power constraint where the power for each BS is constrained to a particularvalue. We derive expressions for optimum power allocation under these two powerconstraints. The APO is then used to improve the performance of MIMO sys-tems further by maximizing the minimum SINR for each user [14]. The proposedmethod offers a significant improvement over a nonlinear cooperative precoding

3.2 System model 49

algorithm presented in [9–12]. The improvements are a significant enhancementof the SER performance and a significant computational complexity reduction.These features allow the proposed algorithm to be applied to a wider range ofscenarios than the schemes in [9–12], while providing a capacity-approachingperformance in cellular mobile systems.

3.1.3 Notation

The notation used in this chapter is as follows. We use boldface lower caseletters to denote vectors and boldface upper case letters to denote matrices. Thesuperscripts .H , .T , I and Diag() denote the conjugate transpose, transpose, anidentity matrix, and a diagonal matrix, respectively. Ca×b indicates a complexmatrix with a rows and b columns. x , ‖ · ‖ and | · | are the greatest integersmaller than x, the Euclidean distance, and the absolute value, respectively.LoT(A) is defined as the operation to extract the lower triangular componentsof A and to set the other components to zero. UpT(A) is defined as the operationto extract the upper triangular components of A and to set the other componentsto zero. DiT(A) is defined as the operation to extract the diagonal componentsof A and to set the other components to zero. Lastly, we define 1 as a columnvector with all entries equal to 1.

3.2 System model

In this chapter, we consider a multiuser MIMO system, where K BSs transmitto K MSs. Each BS and MS is equipped with NBSk

and NM Skantennas, for

k = 1, ...,K, respectively. All BSs cooperate with each other to transmit S sym-bol streams to their respective MSs via NBS =

∑k=Kk=1 NBSk

antennas. Each ofthese transmissions is defined as a link. In a practical cellular wireless network,if frequency-division multiple access (FDMA) or orthogonal frequency-divisionmultiple access (OFDMA) is used, a frequency or time slot can only be allocatedto one user at a given time instant. Therefore, only one user can be served by aBS at any one time or frequency slot. Thus, to simplify the analysis, we considera scenario where each BS transmits at a given time slot to a single mobile sta-tion. In a practical system, the proposed scheme enables a BS to communicatewith multiple MSs through FDMA and time-division multiple access (TDMA).The proposed method aims to enable K such base stations deployed by dif-ferent network operators in the same location to communicate simultaneouslywith K respective mobile stations, using the same frequency band at a giventime slot.

3.2.1 Transmitter structure

The proposed transmitter structure with joint precoding and beamforming isshown in Figure 3.1.


BS 1

MS 1

MS 2

K non cooperative MSs

Cooperative transmitter for K BSs

APO THP precoding

(a) (b)

THP decodingPower

allocation Transmit–receive antenna weights optimization

modM' (•)

modM' (•)

modM' (•)

P

1

1

1

NBS1

NBS2

NBSK

T

d1

v1H1

H2

HK

R1

R2

RK

u1

u2

MS KuKˆ

ˆ

ˆ

n1

n2

nK

y1

y2

NR

NR

NR

y11

1

1

v2

vK

d2

dK

– +

+

+

+

–

–

+

+

x1

x2

xKuK

u2

u1

BS 2

Mperm

MTHP

BS K

y2

yK

Figure 3.1. (a) Nonlinear cooperative precoding transmitter structure;(b) receiver structure (adapted from [27] c© 2009 IEEE).

Let xk = [x1,k · · ·xs,k · · ·xS,k ]T represent the modulated signal vector, con-sisting of K M -ary quadrature amplitude modulation (M-QAM) modulatedsymbols, where xs,k is the sth modulated symbol stream from BS k intendedfor MS k. Thus, we have a multistream transmission where S symbol streamsare transmitted from BS k to MS k simultaneously. The constellation points forM -QAM are drawn from the signal set A = ±1± j, ...±

√M ± j

√M. The

modulated symbols for K MSs can then be written as x = [xT1 · · ·xT

k · · ·xTK ]T .

The transmitted symbols for each user are first permuted by a block diagonalpermutation matrix Mperm = [m1 ...mK ], where mi = [0...1S (i−1)+i ...1iS ...0]T ,i = 1, ...,K, is a KS × 1 vector with its elements S(i− 1) + i to iS set to 1and its other elements set to 0. The permutation operation is done by chang-ing the location of mi in Mperm . By doing this, we have K! possible Mperm .The operation of selecting Mperm is referred to as the APO. The APO adap-tively selects the precoding order of x that maximizes the minimum SINR ofK users. It selects a suitable permutation matrix Mperm to permute x. Letu = Mpermx = [uT

1 · · ·uTj · · ·uT

K ]T be the permutated transmitted symbol vec-tor, where uj = [u1,j · · ·us,j · · ·uS,K ]T . Thus, after the APO, xk for MS k ispermuted into uj , which will be transmitted in link j. We will explain the APOin more detail later in Section 3.6.

Let us first assume that we do not use the THP scheme at the BS transmitter.Thus, we omit THP precoding and decoding in Figure 3.1. The SINR equaliza-tion module then allocates powers to each symbol in u in such a way that thereceived SINRs for all KS symbols are equal. This is done by multiplying u withthe matrix P = Diag(P1 , ...,PK ), Pj = Diag(√p1,j , ...,

√pS,j ) where ps,j is the

downlink power allocated to the sth symbol in link j, denoted by us,j . The signalfor K links is then given as Pu.

3.2 System model 51

The interference in each link needs to be suppressed by multiplying the signalfrom each link by the transmit antenna weights of all BSs, T ∈ CN B S ×K S , andby the receive antenna weights matrix at the receiver of link j, Rj ∈ CNM S j

×S .The transmitted signal is thus given as xT = TPu.

The receiver for each link is shown in Figure 3.1(b). Note that there is nocooperation among the receivers. Let yj ∈ CNM S j represent the received signalmatrix for link j. The received signal matrix for K links, denoted by y, y =[yT

1 ...yTK ]T , can be written as

y = HTPu + N, (3.1)

where H = [H1 ...Hj ...HK ]T in which Hj ∈ CNM S j×N B S is the channel matrix for

link j. N = [nT1 , ...,nT

K ]T and T = [T1 , ...,TK ]. nj ∈ CNM S j×1 is the noise vector

for link j. The transmit weight for link j is defined as Tj = [t1,j ...tS,j ] ∈ CN B S ×S ,where ts,j is the transmit weight vector for the sth symbol transmitted in link j.After multiplying y by the receive weights matrix R, the received signal vectorbecomes

y = RHTPu + RN, (3.2)

where R = Diag(RH1 , ...,RH

K ) is a block diagonal matrix with RH1 , ...,RH

K as itsblock diagonal components. Rj is the receive signal matrix for link j and isdefined as Rj = [r1,j ...rS,j ], where ri,j is the receive weight vector for streami in link j. The signal received at MSs is defined as y = [y

1...y

j...y

K]T ,y

j=

[y1,j

, ..., yS,j

]T , where ys,j

is the received signal at the input of the THP decoderfor sth symbol transmitted in link j. The received signal y, can be further writtenas

y = RHTPu + RN = (D + F + B)Pu + RN, (3.3)

where D = DiT(RHT), B = UpT(RHT), and F = LoT(RHT); DPu is a vec-tor of scaled replicas of the transmitted symbols for K links.

We define interlink interference as the interference between symbol streams indifferent links and interstream interference as the interference between symbolstreams in the same link. FP is defined as the front-channel interference matrix,since the rows j = 1, ...,KS of FP represent the interlink interference caused bylinks 1, ..., j − 1 and interstream interference caused by symbol streams 1, ..., s−1 transmitted in link j to symbol stream s in link j. Similarly, BP is defined asthe rear-channel interference matrix, since the rows j = 1, ...,KS of BP representthe interlink interference caused by rear links j + 1, ...,K and the interstreaminterference caused by symbols s + 1, ..., S in link j to symbol stream s in link j.

3.2.2 THP precoding structure

To further improve system performance, we presubtract some of the interferenceprior to transmission instead of using the transmit–receive weights for symbol


stream s in link j to cancel front-channel and rear-channel interference. Becauseof this, the transmit–receive weight matrix needs to suppress less interference.We will use the THP scheme proposed in [7, 8] and choose to presubtract thefront-channel interference FP. Thus, prior to the power allocation module, THPprecodes u into v = [v1 · · ·vj · · ·vK ]T ∈ CK S , where vj = [v1,j · · · vS,j ]T . Thefront-channel interference is then subtracted from u as in [15],

v = u + d︸︷︷︸v

− (DP)−1FP︸︷︷︸MT H P

v, (3.4)

where (DP)−1 is used to normalize the front-channel interference with respectto u, d = [d1,1 , ..., dS,K ]T , ds,j = 2

√M∆, and ∆ is a complex number whose

real and imaginary parts are suitable integers selected to ensure the real andimaginary parts of vs,j are constrained into (

√M,√

M ]. Here, the integers for∆ can be found by an exhaustive search across all integers [15]. d is an offsetto ensure the energy of v lies between (−

√M,√

M ], since the value of v afterpresubtraction of the front-channel interference can be very large and exceed(√

M,√

M ].Note that if ds,j is selected as above, adding ds,j to us,j is equivalent to per-

forming a modulo operation on ds,j+us,j [1, 12, 15]:

us,j = mod√M (vs,j ) = mod√M (ds,j + us,j ), (3.5)

s = 1, ..., S,j = 1, ...,K, where the modulo operation is defined as [6]

mod√M (us,j ) = us,j −√

M

⌊(us,j +

√M

2

)/√

M

⌋(3.6)

for s = 1, ..., S and j = 1, ...,K. In addition, if we apply (3.6) to (3.4), the oper-ation in (3.6) actually maps v into the interval of (−

√M,√

M ] [15]. Thus, byusing the modulo operations, we implicitly find d that forces the THP precodedsymbols v to lie within this interval. In addition as mentioned in [15], the varianceof v is E[v2

s,j ] = 2M/3 and it is distributed uniformly in (−√

M,√

M ]. Note thatE[x2

s,j ] is 2(M − 1)/3. Thus, there is a power enhancement of M/(M − 1) dueto THP. This enhancement needs to be taken into consideration when design-ing the transmit–receive weights and power allocation. In general, the transmitsymbol energy is normalized, i.e., E[v2

s,j ] = 1. To ensure this, we scale down theds,j and xs,j by 3/2M . This is discussed in detail in [15]. By taking this intoconsideration, the operation of the THP precoder in (3.4) can be rewritten as

[v]j =

⎧⎪⎪⎨⎪⎪⎩√

3(2M − 1)

[u]j , j = 1,

modM ′(√

32M

[u]j − aj ), j = 2, ..,KS,

(3.7)

where aj =∑j−1

l=1 [MT H P ]j,l [v]j and M ′ =√

3/2M√

M . [MT H P ]j,l denotes the(j, l)t component of MT H P and [a]l is the lth component of vector a. Note thatthe first line of (3.7) comes from the fact that, when precoding [v]1 , there is no

3.3 Cooperative BS transmission optimization 53

front-channel interference to be canceled. Thus, we can simply set [v]1 as thenormalized u1,1 .

Since now we are using the THP scheme, we are transmitting THP precodedsymbol streams v instead of u. After THP precoding, the received signal y in(3.3) can be rewritten by replacing u by v. By using (3.4) and (3.3), the receivedsignal now becomes

y = (D + F)Pv + BPv + RN = DPv + BPv + RN. (3.8)

The estimates of the transmitted symbols for link j, denoted by uj =[u1,j ...uS,j ]T , can be recovered from y

j, by applying an element-wise modulo

operator in (3.6) to each ys,j

, as

us,j =

y

s,j, s = 1, j = 1,

modM ′(ys,j

) , otherwise,(3.9)

where us,j is the estimate of us,j . Here, the effect of offset vector d on thedesired transmitted signal is removed at the MS receiver by applying the modulooperation in (3.6) to each y

s,jin (3.8). This is shown in (3.5) and in Figure

3.1(b). In the proposed scheme, THP cancels the interference caused by thefront-channel, while the interference caused by the rear-channel is eliminated bythe transmit–receive antenna weight optimization process. Note that no modulooperation is performed on the first stream to be transmitted in link 1. Thus,MSs need to know which one of them will be scheduled in the first link. Thisinformation can be appended in the signal preamble of wireless systems suchas cellular networks, WiMax or WLANs. However, if high modulation rates areused, (e.g., M = 16, 64), the power enhancement of THP is negligible. The THPperformance loss is given as M/(M − 1) [15] and decreases as the modulationrate increases. Thus the THP performance loss for M = 16 and M = 64 is 0.28and 0.07 dB, respectively. Thus, if a higher modulation rate is used, we couldapply the modulo operation to the first stream of the first link in (3.7) and(3.9).

3.3 Cooperative BS transmission optimization

In this section, we propose a joint iterative transmit–receive antenna weightoptimization and power allocation method based on ZF to cancel the rear-channelinterference, while maximizing the SINR for each link and maintaining the sameSER for all links. The transmitted signal estimate of stream s in link j at each


receiver, ys,j

, can be obtained from (3.8) and expressed as

ys,j

=√

ps,jrHs,jHjts,j vs,j +

S∑l=1

K∑i=j+1

√pl,irH

s,jHjtl,ivl,i

+S∑

l=s+1

√pl,jrH

s,jHjtl,j vl,j + rHs,jnj . (3.10)

By using the fact that the effect of vector d on the received signal is completelyremoved by the THP decoder modulo operator, the SINR for the sth transmittedsymbol in link j, can be written as

SINRs,j =ps,jrH

s,jHjts,j (Hjts,j )H rs,j

rHs,jRs,jrs,j

, (3.11)

where

Rs,j =S∑

l=1

K∑i=j+1

pl,iHjtl,i(Hjtl,i)H +S∑

l=s+1

pl,jHjtl,j (Hj tl,j )H + σ2I (3.12)

is the interference in link j. Maximizing the minimum SINR for each link, whilemaintaining its equality for all links, can be formulated as follows:

maxR ,T ,P

min1≤i≤K,1≤s≤S

SINRs,i

subject to: (1) TH T = I, (2) rHs,jrs,j = 1, (3) 1T p = Pmax

(4) rHs,jHjts,i = 0, (5) rH

s,jHjts ′,j = 0 (3.13)

for j = 1, ...,K, i = j + 1, ...,K, s = 1, ..., S, s′ = s + 1, ..., S, where Pmax and p =[p1,1 , ..., pS,K ]T = P21 are the power constraint at the cooperative transmitterand the set of powers assigned to each link, respectively. Here the objectiveof (3.13) is to maximize the minimum SINR for each link. The first, second,and third constraints in (3.13) are to ensure that the transmit–receive weightvectors are unitary vectors and the sum of the power allocated to each linkdoes not exceed the maximum power available at the transmitter (total BSspower constraint). These constraints bound the possible solution for R, T, andP and ensure the convergence of (3.13) to a solution. Finally, the fourth and fifthconstraints are the ZF constraints which ensure the interlink interference fromlinks j + 1, ...,K to link j and the interstream interference from symbol streams + 1, ..., S in link j are fully canceled. Here, to maximize the minimum SINR in(3.13), we reduce the SINR of the best symbol streams until the SINRs of all linksare equal. Thus, the optimal solution is reached when all symbol streams attainthe same SINR [3]. This optimization problem, however, is difficult to solve asit is not jointly convex in variables R,T, and p. To solve (3.13), we propose asuboptimal solution that splits the problem into a two-step optimization. Thefirst step is to solve R and T iteratively, when p is fixed. Hence in this step wesimply ignore the equalization of SINRs among all links. The second step is to


R(i)

T(i) R(i), T(i) p,R(i),T(i)SINR

equalization

Feedbackmatrix

MTHP = (DP)–1FP

f1(R(i–1)) gj(T(i))R(0)

Figure 3.2. Iterative weight optimization, SINR equalization, and feedbackmatrix process (adapted from [26] c© 2009 IEEE).

solve p in a way that equalizes SINRs for all links under fixed R and T. Once R,T, and p are obtained, MT H P = DP−1FP is computed. The process is describedin Figure 3.2, where i, f1(·) and gs,j (·) are the iteration number, a function togenerate transmit antenna weights for K links, and a function to generate thereceive antenna weights vector for symbol stream s in link j, respectively.

3.3.1 Iterative weight optimization (first step)

In the first step, we assume an equal power allocation for each link by settingP = I. Then (3.13) can be simplified as

maxR ,T

SINRs,i ,

subject to: (1) TH T = I, (2) rHs,jrs,j = 1,

(3) rHs,jHjts,i = 0, (4) rH

s,jHjts ′,j = 0 (3.14)

for j = 1, ...,K, i = j + 1, ...,K, s = 1, ..., S, s′ = s + 1, ..., S. To solve (3.14), wepropose to alternately optimize R and T until they converge, under the ZFconstraints in (3.14). We first assign the initial value of the receive antennaweights for K links. The initial receive weights of K links are given as r(0)

s,j =vsvd(Hj ) , j = 1, ...,K, s = 1, ..., S, where vsvd(·) is the singular value decompo-sition operation (SVD) [16], to select the S left singular vectors of Hj , corre-sponding to the Sth largest singular value. We then transform the system into

a downlink multi-link MISO system by fixing R = Diag(R(0)1

H, ...,R(0)

K

H). Then

(3.3) can be written as

y = RHTv + RN = HeTv + N. (3.15)

Here, we know from (3.8) that the interference from the front-channel does notexist at the receiver. The remaining interference at symbol stream s in link j

that needs to be canceled is the rear-channel interference, coming from linksj + 1, ...,K to links j = 1, ...,K and stream s + 1, ..., S in link j, respectively. Ateach iteration, we apply a QR decomposition [16] to HH

e to find T that forces


this interference to zero:

T = f1(R) , f1(R) = [Q|QR(HHe )]. (3.16)

We choose the unitary matrix Q obtained from the QR decomposition of HHe

in (3.16) as T. We need to compute R that gives a maximum SINRs,j for eachlink for the derived T. This can be calculated as

rs,j = gs,j (T), (3.17)

where j = 1, ...,K. gs,j (T) is a function that generates the receive weight vectorrj for the derived T such that the gain SINRs,j for each link is maximized. Wenow describe how gs,j (T) operates. By using (3.11), the SINR maximization forthe sth symbol in link j can be written as

maxrs , j

ps,jrHs,j hs,j hH

s,jrs,j

rHs,jRs,jrs,j

, (3.18)

where hs,j = Hjts,j and Rs,j is the interference in link j as given in (3.12). Toobtain rs,j that maximizes SINR in (3.18) we use the spectral/eigenvalue decom-position [16]. Thus the functions to generate r1,1 , ..., rS,K , gs=1,...,S,j=1,...,K (T)can now be written as

gs,j (T) = vEV D (ps,jR−1s,j hs,j hH

s,j ) , s = 1, ..., S, j = 1, ...,K, (3.19)

where vEV D (·) is the spectral/eigenvalue decomposition operation [16] to selectthe left singular vector of ps,jR

−1s,j hs,j hH

s,j , corresponding to the largest singularvalue. We can obtain a simpler expression for rs,j that gives the same maximumSINR, as in (3.18), by using the following fact:

maxrs , j

rHs,j hs,j hH

s,jrs,j

rHs,jRs,jrs,j

= maxrs , j

rHs,j hs,j

rHs,jRs,jrs,j

. (3.20)

Here we state that the optimum SINRs,j obtained by using the term on the lefthand side of (3.20) is equal to the optimum SINRj obtained by using the termon the right hand side of (3.20). The proof of SINR equivalence is shown in theAppendix. By solving the term on the right hand side of (3.20), the normalizedreceive antenna weight vector for stream s in link j can be obtained as [17]

rs,j = gs,j (T) =R−1s,jHjts,j

‖Rs,jHjts,j‖. (3.21)

It is straightforward to show that the SINRs,j generated by using the receiveantenna weight vector from (3.21) yields the optimum SINRj given in (3.20).We can conclude from this fact and (3.20) that the normalization process of thereceive weight vector in (3.21) will not affect the SINR. Note that this receiverdesign is also known in the literature as the minimum variance distortionlessresponse (MVDR) design [18]. The iterative calculations of R and T continue


by fixing one and optimizing the other one, until they converge to a fixed solu-tion. The proof of convergence of the proposed iterative method is shown in theAppendix.

3.3.2 Power allocation (second step)

In the second step, we use the R and T obtained in the first step to find p. Byusing the fact that at the optimal solution all links will attain equal SINR, (3.11)can be written as

S∑s ′=1

K∑i=j+1

|rs ′,jHjts ′,i |2ps ′,i +S∑

s ′=s+1

|rs ′,jHjts ′,j |2ps ′,j + σ2 =ps,j |rs,jHjts,j |2

SINR

(3.22)for s = 1, ..., S, j = 1, ...,K. Equation (3.22) can be represented in a matrix for-mat as

A−1Bp + σA−11 =p

SINR, (3.23)

where A = DiT(M), B = UpT(M), and M is a KS by KS matrix with entries|rs,jHjts ′,j ′ |2 , s = s′ = 1, ..., S, j = j′ = 1, ...,K in row S(j − 1) + s and columnS(j′ − 1) + s′. By multiplying both sides of (3.23) with 1T , we obtain [3]

1Pmax

(1T A−1Bp + σ1T A−11) =1

SINR. (3.24)

By defining the extended power vector pe = [pT 1]T , we can then combine (3.23)and (3.24) to obtain [3][

A−1B σA−111T A−1B/Pmax σ1T A−11/Pmax

]pe =

pe

SINR. (3.25)

Hence the optimum p can be obtained by selecting the pe that correspondsto the maximum eigenvalue of Ψ. This is the only possible solution of (3.25)satisfying ps,j ≥ 0 for j = 1, ...,K and SINR ≥ 0. The proof is described in detailin Theorems 1 and 2 of [19]. The above SINR equalization process can be furthersimplified. By using the proof of SINR convergence in the Appendix, we canassume that after i iterations, we are very close to the local optima (i.e., therear-channel interference is zero, UpT(M) = 0). The solution for (3.25) can begiven as

ps,j =Pmax∑S

s ′=1∑K

i=1|rs,jHjts,j |2|rs ′,iHits ′,i |2

, s = 1, ..., S, j = 1, ...,K. (3.26)

Even though the power constraint used above allocates the power to each linkin an optimal manner, it is not very practical. This power constraint does nottake into account the power constraint for each BS in a real system. A morepractical power allocation that takes into account the power constraint for eachBS can also be derived. We refer to this power constraint as the per BS power


constraint. We denote the maximum power available at each BS j as Pmax,j

and the modified transmit weights ti,s,j ∈ CNB S ×1 as the entries of ti,s,j used asantenna weights by BS i. A power allocation formulation that takes into accountthe power constraint for each BS can be derived as

maxp

σ2SINR,

subject to: (1) σ2SINR ≤ pj |rs,jHjts,j |2 ,

(2)S∑

s ′=1

K∑i=1

‖tj,s ′,i‖2ps ′,i ≤ Pmax,j (3.27)

for j = 1, ...,K, s = 1, ..., S. After some manipulations, the solution for (3.27) canbe given as

|rs,jHjts,j |2ps,j = minj=1,...,K,s=1,...,S

Pmax,j∑Ss ′=1

∑Ki=1

|tj,s ′,i |2|rs ′,iHits ′,i |2

(3.28)

for j = 1, ...,K, s = 1, ..., S.

3.4 Modification of the design of R

In this section, we modify the receive antenna weight calculations in (3.21) tospeed up the convergence to the local maxima and improve the SINR during theiteration process. We define r(i)

s,j and t(i)s,j as the receive and transmit antenna

weights found in step 1 in Section 3.3.1 at the ith iteration, for link j. Theentries of the rear-channel interference matrix BP at the ith step of the iterativeprocess, ε

(i)l,k can be written as follows:

ε(i)l,k =

√ps ′,j ′(HH

j r(i)s,j )

H t(i)s ′,j ′ , (3.29)

where l = jS + s− S, k = j ′S + s′ − S. The interlink and interstream compo-nents of the rear-channel interference in stream s in link j correspond to row l

and column k of BP when s′ = 1, ..., S, j′ = j + 1, ...,K and when s = s + 1, ..., S,respectively.

Similarly, the diagonal entries of matrix D at the ith step of the iterative pro-cess, denoted by β

(i)l=jS+s−S , represent the signal gain for stream s in link j. This

can be written as β(i)l=jS+s−S = (HH

j r(i)s,j )

H t(i)s,j , s = 1, ..., S, j = 1, ...,K at the ith

iteration. In the Appendix, we show the proof of transmit–receive weight opti-mality. There we prove that

∏l β

(i)l ≤ det(R∗HT∗), where β

(i)l = (HH

j r(i)s,j )

H t(i)s,j

and (R)∗ and (T)∗ are the optimal transmit–receive antenna weight vectors forK links satisfying the proof of convergence in the Appendix.

From the proof of convergence and transmit–receive weight optimality in theappendix, we know that at the local maximum: (1)

∏l β

(i)l achieves the maximum

value equal to det(R∗HT∗); (2) the front-channel interference BP converges to

3.5 Geometric mean decomposition 59

0 since (3.16) forces R∗HT∗ to have a lower triangular structure. Hence, wecould simply maximize β

(i)l to achieve the local maxima. By using the Matrix

Inversion Lemma [20], (3.12), and (3.21) in β(i)l , we can rewrite β

(i)l=jS+s−S for

stream s in link j as

cβ(i)l=jS+s−S = (Hj t

(i)s,j )

H (σ−1I− (Z−1 + σI)−1)Hjt(i)s,j , (3.30)

where

Z =S∑

s ′=1

K∑a=j+1

Hjt(i)s ′,a(Hjt

(i)s ′,a)H +

S∑s ′=s+1

Hjt(i)s ′,j (Hjt

(i)s ′,j )

H (3.31)

and c is a scaling/normalization factor given by c = ‖Rs,jHjts,j‖. It is obviousthat (Hjt

(i)s,j )

H (Z−1 + σI)−1Hjt(i)s,j in (3.30) reduces the value of β

(i)l . There-

fore, if we omit this term in calculating the receive antenna weights, we canreach the maximum β

(i)l faster. Thus, we can simply ignore this term to speed

up the convergence of the iterative process. Therefore by omitting the term(Hj t

(i)s,j )

H (Z−1 + σI)−1Hjt(i)s,j , we have

β(i)l=jS+s−S ∼ (Hjt

(i)s,j )

H (σ−1I)t(i)s,j = σ−1(r(i)

s,j )H Hjt

(i)s,j . (3.32)

The maximum β(i)l can be obtained by aligning r(i)

s,j in the direction of Hjt(i)s,j .

The total power of the receive weight vector, r(i)s,j is normalized to 1 to ensure it

satisfies the second constraint in (3.13),

r(i)s,j =

Hjt(i)s,j

‖Hj t(i)s,j‖

. (3.33)

We refer to this receiver structure as a matched filter (MF) design.

3.5 Geometric mean decomposition

In [22, 23], geometric mean decomposition (GMD) has been shown to give thebest BER performance for multistream transmission while at the same timemaintaining an equal SINR across S symbols within each link and the lowertriangular structure required by THP [12]. We want to further maximize thechannel gain for each stream in each link j by modifying the found iterativetransmit and receive weights using GMD. We first define a new effective channelmatrix for each link j Hj as

Hj = HjTj , (3.34)

where Tj is the transmit weight matrix for link j previously defined in Section3.2.1. The GMD is used to decompose Hj into a lower triangular matrix withan equal diagonal component. The process is as follows. We first decompose Hj


Algorithm 3.1. Cooperative transmission algorithm

1 Initialize receive weights and set Maxiteration2 For i=2 to Mit

3 Find transmit weights using (3.16)4 Find receive weights using (3.21) or (3.33)5 end

6 Use GMD to modify transmit–receive weights (3.37) and (3.38)7 Equalize SINR for all links using (3.28) or (3.26) or (3.25)8 THP precoding operation using (3.7)

by using the SVD [24] as follows:

HjTj = [US U0 ](

DS 00 D0

)[VS V0 ]T , (3.35)

where US and VS consist of the first S left and right singular vectors of HjTj

and DS is a diagonal matrix with entries that are the first S nonnegative squareroots of the eigenvalues of HjHH

j . The GMD takes US , VS , and DS as inputsand produces Uj , VS , and DS . The GMD transforms DS into a lower triangularmatrix with equal diagonal entries, DS , by rotating US and VS . This is givenas

Hj Tj = UjDS VHS . (3.36)

The goal of our transmit–receive design is to create a lower triangular structurewithin each link. Thus, by using (3.36), the new transmit–receive weights denotedby Tj and Rj can be written as

Tj = Tj VS , j = 1, ...,K (3.37)

and

Rj = Uj , j = 1, ...,K. (3.38)

The cooperative transmission algorithm is shown in Algorithm 3.1, where i rep-resents the iteration number and Mit is the maximum number of iterations.

3.6 Adaptive precoding order (APO)

In the algorithm in Table 3.1, we fix the order of uj , resulting in a fixed permu-tation matrix Mperm . The performance of the system, however, differs when adifferent Mperm is used. In addition, the performance of the system also dependson the weakest link. In this section we propose an APO scheme. APO arrangesthe order of links, x, by selecting on Mperm that maximizes the minimum SINR

3.7 Complexity comparison of the proposed and other known schemes 61

for each link. We formulate the optimization process to find a permutation matrixMperm ∈Mperm that gives the maximum SINR as

Mperm = argM p e r mmax min(SINR1(Mperm ), ..., SINRK (Mperm )), (3.39)

where SINRj (Mperm ) is the SINR of link j, given that the permutation matrixMperm is used. Note that here, due to the use of GMD, the SINRs for eachstream in link j are equal. To find the Mperm without searching K! possibleorderings, we use the idea of the myopic optimization method proposed in [14],which has been proven to be optimal. Using this idea we now only need to search∑K−1

i=0,i =1 K − i possible orderings.

3.7 The complexity comparison of the proposedand other known schemes

In this section, we discuss the advantages of the proposed scheme over otherexisting schemes. We first compare the proposed method with the scheme in [9]and the iterative scheme in [10] that work by finding transmit–receive weightsthat diagonalize the receive signal matrix of K users without the receiver noisein (3.3). To have a fair comparison with the proposed method, we replace thewaterfilling power allocation in [9] with (3.26) and (3.28), which equalize theSINR for all links under total BS and per BS power constraints, respectively. Thisis required as the waterfilling power allocation used in [9] tends to assign morepower to stronger links and less power to weaker links. Hence, the performanceof a weaker link will decrease the overall SINR.

The main differences between the methods in [9, 10] and the proposed methodare (1) [9, 10] suppress both the front-channel and rear-channel interferenceusing transmit–receive weights, while the proposed method suppresses the rear-channel and front-channel interference using THP and iterative transmit–receiveweights, respectively. (2) Unlike [9, 10], the proposed scheme does not calcu-late null spaces. To compute these null spaces, the iterative scheme in [10] andthe noniterative scheme in [9] perform K SVD operations per iteration and K

SVD operations, respectively. (3) Within a single iteration, a QR decomposi-tion [16] and K matched filter (MF) receiver calculations are required to find alltransmit–receive antenna weights, while in [10] K SVD operations per iterationare required to find the transmit–receive weights of all links. Note that [9] requiresK SVD operations to find the transmit–receive weights of all links. The com-plexity order requirements in terms of the number of floating point operations(flops), for the proposed method and the methods in [9, 10] are listed in Table3.1, where Mit and Mit,P an denote the total number of iterations for the pro-posed method and the scheme in [10], respectively. Hence for K = 3, NM S = 2,and NBS = 2, the number of flops for the proposed method is approximately93% less than the number of flops for [9] per iteration.

Tab

le3.

1.C

ompu

tation

alco

mpl

exity

oflin

ear

and

nonl

inea

rpr

ecod

ing

algo

rith

ms

(in

flops

)

Sche

mes

Com

puta

tion

alco

mpl

exity

orde

r(i

nflo

ps)

Pro

pose

dal

gori

thm

O(K

3S

MitN

2 BS)

Pan

etal

.[1

0]O

(Mit

,PanK

(4K

SN

2 BS

+8(

KS

)2N

2 BS

+9N

3 BS))

Spen

cer

etal

.[9

]O

(K(4

KS

N2 B

S+

8(K

S)2

N2 B

S+

9N3 B

S))

Liu

and

Wit

old

[12]O

(0.5

K2(4

KN

MSN

2 BS

+8K

N2 M

SN

2 BS

+9K

N3 B

S+

KN

MSN

2 BS(K−

1)+

KN

2 MS

+K

NM

SN

BS))

Fosc

hini

etal

.[1

1]O

(0.5

K2(4

KN

MSN

2 BS

+8K

N2 M

SN

2 BS

+9K

N3 B

S+

KN

MSN

2 BS(K−

1)))

3.8 Numerical results and discussions 63

The second comparison is done using the nonlinear precoding methods in[11, 12]. Again to have a fair comparison with the proposed method, after thealgorithm in [11, 12], we apply (3.25) to equalize the SINR, instead of usingthe original power allocation. Unlike [11, 12], we do not require the constraintof (K − 1)NM S < KNBS because we do not create null spaces. Thus, there isno relationship between the required number of transmit antennas and receiveantennas. This is a definite advantage, since to support say five users withNM S = 4 receiving one stream each, the proposed method only needs five trans-mit antennas while [9] needs 12 transmit antennas.

Another important difference is in the ZF condition definition. In our schemewhen S = 1 for example we have rH

1,jHjt1,i = 0 , j = 1, ...,K, i = j + 1, ...,K,while [11, 12] have Hjt1,i = 0 , j = 1, ...,K, i = j + 1, ...,K for the ZF condition.By using the ZF condition in our scheme, the proposed algorithm allows someinterlink interference to be transmitted (e.g., Hjt1,i = 0), and cancels the inter-ference by steering Hjt1,i to be perpendicular with the receive antenna weightsvector r1,j . Hence the receive and the transmit antenna weights jointly cancelthe interference. The ZF constraint in [11, 12], on the other hand, does not allowany interlink interference to be transmitted. Here, the receive antenna weightsare not used at all to cancel the interference. The computational complexityrequired for the methods in [11, 12] is shown in Table 3.1. The complexity of themethods in [11, 12] for a system with K = 3, NM S = 2, S = 1 and NBS = 2, isapproximately 47 628 and 47 844 flops, respectively.

3.8 Numerical results and discussions

For convenience, in our simulations, we will use the notation (NBS ,NM S , S,K)in all figures to denote a system with NBS transmit antennas per BS, NM S

receive antennas per MS, S data streams transmitted in each link, and K BSs.Monte Carlo simulations have been carried out to assess the performance of theproposed method. We investigate its performance and compare it with [9, 11, 12]and with an interference-free performance.

An interference-free performance is defined as the performance of any ran-dom single link i assuming there is no interference from other links at all. Inthis case, the received signal of the cooperative transmission system is given asyi = rH

i (Hitixi + ni), where ri and ti are the left and right eigenvectors asso-ciated with the maximum eigenvalue of HiHH

i . To generate an interference-freeperformance for multistream transmission with S symbols transmitted in eachlink, we use the left and right eigenvectors associated with the S largest eigen-values of HiHH

i found by using the SVD. We then maximize the minimum SINRof S symbols by applying the power allocation method given in [25].

The comparison of the schemes is performed at SER = 10−4 . We use a fixedpermutation matrix that orders MSs 1, ...,K as links K, ..., 1, when we are notusing APO, for all the simulation results except when stated otherwise. Perfect


channel state information (CSI) is assumed to be available at both ends. Rectan-gular 64-QAM (M = 64) modulation is used for all transmissions. The wirelesschannel model we used is a Rayleigh fading channel. This channel model is com-monly used for cellular networks or WLANs, since in most cases there is no line-of-sight path between the transmitter and receiver in these networks. In order tosimulate the wireless channel, we set each entry of the Hj channel matrix as anindependent and identically distributed (i.i.d.) complex Gaussian variable witha zero mean and unit variance. In all simulations, we fix the signal-to-noise ratioof each THP precoded symbol to be SNR = E[vH

s,j vs,j ]/2σ2 , where E[vHs,j vs,j ]

is normalized to 1, Pmax = K and Pmax,i=1,...,K = Pmax/K . In all simulationfigures, the proposed method refers to the algorithm with THP, joint iterativetransmit-receive weight optimization, SINR equalization (SINRE) under a totalBS power constraint unless stated otherwise and APO.

3.8.1 Convergence study

Figure 3.3 shows the convergence characteristics of the proposed method with atotal BS power constraint for (2, 2, 1, 3) and (1, 2, 1, 4) systems. Note that hereit does not matter whether total power or per BS constraints are used. Thisis because, as shown in Figure 3.2, the SINR equalization is not an iterativeprocess. We plot the number of iterations versus the average error and scaledoutput SINR (after SINR equalization), while fixing the SNR at 21 dB. Theaverage error is defined as the average of the maximum entries of the front-channel interference BP, ε(i) = maxj,l |ε(i)

j,l | defined previously in (3.29) over allchannel realizations. The output SINRs for (1, 2, 1, 4) and (2, 2, 1, 3) systems arescaled up by 4 dB and 0 dB to fit in one figure. The scaling does not matter heresince we only want to observe the convergence rate. The figure also shows theconvergence characteristics when the MF receiver design, represented by (3.33),and the MVDR receiver design, represented by (3.21) are used.

An interesting observation is that during the first few iterations the MVDRdesign outperforms the MF design. This improvement is due to the smaller errorsobtained using MVDR and is not due to a higher signal gain β

(i)j . During the

first few iterations, the second term of (3.30) for the MF receiver design is largerthan for the MVDR receiver design, thus leading to a higher average error forthe MF receiver. This happens because MF ignores the interference when calcu-lating the receive antenna weights. However, its average error decreases rapidly.The average error for the (1,2,1,4) and (2,2,1,3) systems, denoted by (1,2,1,4)-MF and (2,2,1,3)-MF in Figure 3.3, approaches the average error of the MVDRmethod. The SINR using the MF method from that point onwards is alwaysgreater than the SINR using the MVDR method. This is shown in the analysisin Section 3.4. This analysis is consistent with the results shown in Figure 3.3.MF converges much faster to the optimal SINR solution than MVDR. This isshown in Figure 3.3 and agrees with the proof of convergence in the Appendix.MF’s SINR reaches a plateau after eight iterations, since it almost converges


Figure 3.3. SINR and average error convergence comparison for proposed scheme(adapted from [26] c© 2009 IEEE).

to the optimal solution while MVDR’s SINR is still rising. A similar conclusionis found for all other configurations. Not much performance improvement canbe obtained by increasing the number of iterations further. In all simulations forSER comparison, we set the maximum iteration number for the proposed schemeto ten.

3.8.2 Performance of the individual links

Figure 3.4 shows the SER of the worst user and the best user versus the SNR ina (2, 2, 1, 3) system. Note that it does not matter whether total power or per BSconstraints are used to compare the performance of the individual links. This isbecause, as shown in Section 3.2.2, the SINR for all links is the same under bothconstraints. As shown in Figure 3.4, when the proposed method does not performSINRE and APO (denoted by w/o in the figures), MS 3 has the best performancewhile MS 1 has the worst performance. The SER performance difference betweenlinks 1 and 3 exceeds 3 dB. When SINRE is used, the SER difference betweenlinks disappears. This is shown in Figure 3.4. Here, the performance of link 1 isimproved at the expense of links 2 and 3. This results in a similar SER acrossall links. An interesting point here is that APO tends to equalize the perfor-mance of K users even without the use of SINRE. This is shown in Figure 3.4.Hence, it seems sufficient to use APO without SINR equalization to maximize the


Figure 3.4. SER performance comparison of individual links for the (2, 2, 1, 3)system when SINRE is not used and when SINRE and APO are used (adaptedfrom [26] c© 2009 IEEE).

minimum SINR in the system. The performance of APO without SINRE, how-ever, is still worse than when the proposed method does not perform APO. This isdenoted as “Proposed w/o APO” in Figure 3.4. This suggests that SINR equal-ization plays a more important role than APO in performance improvement.In other words, using a good power allocation scheme might be more benefi-cial than searching for the best order of the users to achieve a higher diversitygain.

3.8.3 Overall system performance

We first show the overall SER of the proposed scheme and compare it withother available methods [9–12]. Overall SER is defined as the average SER ofK links. The overall SER performances for a (2, 2, 1, 3) system for both theproposed method with or without APO and for [9–12] are shown in Figure 3.5.The proposed method without APO outperforms the methods in [11, 12] and[9] by 5 dB and 3 dB, respectively, and is only 1 dB away from an interference-free performance when SER = 10−4 . The large improvement in performance inthe proposed scheme with respect to [11, 12] comes from an increase in thedegree of freedom and the iteration process used in determining the transmit–receive antenna weights. In addition, the proposed method without APO is ableto achieve much better performance with much less complexity (we only use


Figure 3.5. Average SER performance comparison for (2, 2, 1, 3) system usingvarious non-linear precoding algorithms (adapted from [26] c© 2009 IEEE).

ten iterations). The computational complexity of the proposed method for a(2, 2, 1, 3) system is on average about 75% less than the complexity of methodsin [10–12]. In essence, the proposed method fully utilizes THP, transmit antennas,and receive antennas in a more optimal way with much less complexity to createnoninterfering spatial channels. Figure 3.5 also shows the performance of theproposed method with APO. APO moves the SER performance of the proposedmethod to within 0.25 dB of an interference-free transmission when SER = 10−4 .Thus, APO gives about 1 dB gain over the proposed method without APO. Thisgain, however, comes at the cost of complexity since now the proposed methodneeds to do a search over

∑K−1l=0,l =1 K − l possible user orderings. As a result,

the complexity of the proposed method is∑K−1

i=0,i =1 K − i times more than theproposed method without APO. This is shown in the last column of Table 3.1.

The performance of the iterative scheme in [10] depends on the number ofiterations. To show that the proposed method performs better than the schemein [10], we set the iteration number for the scheme in [10] to five, giving acomputational complexity of around 74 520 flops for a (2, 2, 1, 3) system. Thecomputational complexity of the proposed method using ten iterations is 4860flops. The performance of [10] is shown in Figure 3.5. Here, we can see clearly that[10] is worse than the proposed method with or without APO. It is not possibleto get much improvement in performance in [10] by raising the SNR above 21 dB.We refer to this SNR value, above which there is no further SER decrease, as thesaturation point. Here, we must stress that the performance of [10] can be furtherimproved by increasing the number of iterations. This is shown in Figure 3.5


Figure 3.6. Average SER performance comparison for a (2, 2, 2, 3) system usingvarious nonlinear precoding algorithms.

when we increase the number of iterations to 11. However, the performance ofthe scheme in [10] is worse than the performance of the proposed method and thescheme in [10] is much more complex than the proposed method. Lastly, we alsoplot the performance of the proposed method under a per BS power constraint.There is only a 1 dB performance degradation by switching from total BS to perBS power constraints. The performance of the proposed method under a per BSpower constraint is much better than the performance of other schemes underboth total BS and per BS power constraints.

In Figure 3.6, we illustrate how the proposed method performs under a differ-ent configuration. We show the performance when the number of users, K, thenumber of transmit antennas per BS, NBS , the number of streams per user,S, and the number of receive antennas per MS, NM S , are three, two, two,and two, respectively. Here, the total number of transmit antennas KNBS isequal to the number of MSs. Even when the proposed method does not per-form APO, it still significantly outperforms the one in [10, 11]. This improve-ment is even greater than that shown in Figure 3.6 (>4 dB). Interestingly, theperformance in [12] is exactly the same as the performance of the proposedmethod. Note that here, the complexity of the proposed scheme is 80% lessthan that in [12], making the proposed method most practical for implemen-tation. We also plot the performance of the proposed method under per BSpower constraints for a (2, 2, 2, 3) system. Its performance is still better than the


12 14 16 18 20 22 24 26 28 300

5

10

15

20

25

30

35

40

SNR

bps/

Hz Proposed (total power constraint)

Scheme [10] 11 iterations (total BS constraint)

Proposed (per BS constraint)

Scheme [10] 11 iterations (per BS constraint)

Interference free

Figure 3.7. Capacity performance comparison for a (2, 2, 1, 3) system usingvarious nonlinear precoding algorithms.

performance of the other schemes under both the total BS and per BS powerconstraints.

As the system has an error performance close to an interference-free system,its capacity should approach the capacity of individual interference-free links. Intypical cellular networks, only one user signal can be transmitted in a frequencyband at a given time slot. The proposed method enables K base stations in thesame location to simultaneously transmit to K users using the same frequencyband and time slots. By using the proposed method, instead of transmittingto one user at a time with a power of 1, we can simultaneously transmit toK users with a power of K with the performance of each user approachingan interference-free performance. For example, the capacity of cellular mobilenetworks for a (2, 2, 1, 3) system can be increased by up to K times, as shownin Figure 3.7, by using BS cooperation. Note that the capacity of the proposedmethod is higher than the capacity of its best competitor [10].

An interesting point here is that the capacity of a (2, 2, 2, 3) system using themethod in [12] is the same as the capacity of the proposed method. Note thatthese two significantly outperform any other methods. This is shown in Figure3.8. In a (2, 2, 2, 3) system, we have six cooperative transmit antennas at BSstransmitting to users each with two receive antennas. The maximum possiblenumber of independent transmissions for each user is two. Thus, if the numberof streams is two, we fully use the transmission space and it is not possible to usethis transmission space for other users without violating the ZF constraint. On


12 14 16 18 20 22 24 26 28 3010

15

20

25

30

35

40

45

50

55

60

SNR

bps/

Hz

Proposed (total power constraint)

Scheme [10] (11 iterations) (per BS constraint)


Scheme [10] (11 iterations) (per BS constraint)

Scheme [11] (total power constraint)

Scheme [11] (per BS constraint)



Interference free

Figure 3.8. Capacity performance comparison for a (2, 2, 2, 3) system usingvarious nonlinear precoding algorithms.

the other hand, for a (3, 3, 2, 3) system, we have three receive antennas for eachlink and only use two out of three possible transmission spaces for each user. Itis possible to use the remaining available transmission space without violatingthe ZF constraint. In our proposed method, we allow the transmission space foreach user to overlap. Our proposed scheme will outperform that in [12] in thistype of configuration. This is shown in Figure 3.9 where the capacity of the pro-posed scheme is 20% more than the capacity of its nearest competitor, i.e., thatin [12].

3.9 Conclusion

In this chapter, we have proposed a method to design a spectrally efficient coop-erative downlink transmission scheme by employing precoding and beamform-ing. THP and iterative transmit–receive weight optimization have been usedto cancel multiuser interference. A new method to generate transmit–receiveantenna weights has been proposed. SINRE and APO have been used to achieveSER fairness among different users and further improve the system perfor-mance, respectively. The error performance for two sets of system parameters(NBS ,NM S , S,K) has been shown. For a (2, 2, 1, 3) cooperative system, the pro-posed method outperforms existing schemes by at least 3 dB and is only 0.25 dBaway from an interference-free performance when SER = 10−4 . For a (3, 3, 2, 3)system, the proposed method has a 20% higher spectral efficiency than existing

3.9 Conclusion 71

12 14 16 18 20 22 24 26 28 3010

20

30

40

50

60

70

80

SNR

bps/

Hz

Proposed (total power constraint)




Interference free

Figure 3.9. Capacity performance comparison for a (3,3,2,3) system using variousnonlinear precoding algorithms.

schemes. In addition, the proposed method eliminates the dependency betweenthe numbers of transmit and receive antennas. The complexities of the proposedmethod have been shown to be on average 75% less than the complexities of theschemes in [9–12] with the same configurations. Thus, we can conclude that ourproposed scheme has the best capacity, the lowest SER, and the lowest compu-tational complexity compared to those in [9–12] in most cases. These featuresmake the proposed method suitable for practical implementation.

Appendix

Proof of SINR equivalence

We first calculate SINRs,j using the term on the left hand side of (3.20). Wefirst need to prove that R

−1s,j hs,j hH

s,j only has one eigenvalue. Let us assume

that hHs,j = 0. We denote R

−1s,j hs,j by a and hH

s,j by b, where a = [a1 ...aNM S]T ∈

CNM S ×1 and b = [b1 ...bNM S] ∈ C1×NM S . We then express R

−1s,j hs,j hH

j as

R−1s,j hs,j hH

s,j = ab = [b1a...bNM Sa]. (3.40)

Here, R−1j hs,j hH

s,j is a matrix that has NM S columns and rows. We can see that

the vectors represented by each column of matrix R−1j hs,j hH

s,j can be rewrittenusing vector a as a basis. This indicates that the rank of this matrix is 1 and asa consequence, there is only one eigenvalue.

The receive weight vector computation in (3.19) can be written asR−1s,j hs,j hH

s,jrs,j = λs,jrs,j , where λs,j is the eigenvalue for stream s in link j.By multiplying both sides of this equation by hH

s,j , we have

(hHs,jR

−1s,j hs,j − λs,j )hH

s,jrs,j = 0. (3.41)

The eigenvalue of hHs,jR

−1s,j hs,j is the same as the eigenvalue of R

−1s,j hs,j hH

s,j .

As a consequence, hHs,jR

−1s,j hs,j only has one eigenvalue. This eigenvalue is the

solution for the term on the left hand side of (3.20). Thus, the SINRs,j for itis given as SINRs,j = λs,j = hH

s,jR−1s,j hs,j . We now find the SINRs,j by solving

the term on the right hand side of (3.20). The optimum receive weights vectoris given by [17] as rs,j = R

−1s,j hs,j /c where c = hH

s,jR−1s,j hs,j . By inserting this

receive weights vector into (3.11) and replacing its numerator with rHs,jRs,jrs,j ,

we obtain SINRs,j = hHs,jR

−1s,j hs,j .

Proof of convergence

In order to calculate SINRs,j in (3.11), we need to know the receive weight vectorfor stream s in link j, rs,j and all transmit weight vectors t1,1 ,...,tS,K , obtained

Appendix 73

by using (3.17) and (3.16), respectively. We write SINRs,j as SINRs,j (rs,j ,T)since it is a function of rs,j and T. Since in the proposed scheme, we optimizeone variable at a time, while fixing the other one, we have

SINRs,j (gs,j (T),T) = maxa∈A 1

SINRs,j (a,T), gs,j (T) ∈ A1 , (3.42)

where T is fixed while the best rs,j = gs,j (T) in the set A1 is searched and

SINRs,j (rs,j , f1(R)) = maxa∈A 2

SINRs,j (rs,j , a), f1(R) ∈ A2 , (3.43)

where rs,j is fixed while the transmit weight vectors for K links, T = f1(R),in the solution set A2 are searched. To describe the proposed alternating opti-mization process, we denote the number of iterations by i, the receive weightvector by r(i)

s,j and transmit weight vectors by T(i) . First, r(0)s,j , j = 1, ...,K,

are arbitrarily chosen as initial vectors. T(1) is then calculated by using thefunction in (3.16), f1(R0). For i ≥ 1, we then have, r(i)

s,j = gs,j (T(i)) , s =

1, ..., S, j = 1, ...,K, where T(i) = [t(i)1,1 ...t

(i)S,K ], and T(i) = f1(R(i−1)), where

R(i) = Diag(rH1,1

(i), ..., rH

S,K(i)). Here, r(i)

s,j and T(i) are generated in the order

r(0)s=1,...,S,j=1,...,K , T(1) , r(1)

s=1,...,S,j=1,...,K , T(2) and so on. From (3.42) and (3.43),and by using the fact that SINRs,j (rs,j ,T) is nondecreasing and bounded fromabove by constraints in (3.14), we can write

SINRj (r(i)j ,T(i)) ≥ SINRj (r

(i)j ,T(i−1))

≥ SINRj (r(i−1)j ,T(i−1)). (3.44)

The terms on the right hand side of (3.44) come from the fact that since we areperforming an alternate optimization of the transmit–receive weights by using(3.42) and (3.43), the SINR obtained at iteration i− 1 could only be eitherequal or less than the SINR obtained at iteration i. This shows that as thenumber of iterations increases, the SINRs,j (r

(i)s,j ,T

(i)) will converge to a localmaximum and simultaneously satisfy (3.17) and (3.16). The former will alsocause the remaining interference to converge to 0 as the number of iterations goesto ∞.

Proof of transmit–receive weight optimality

We know from the proof of convergence in this Appendix that we can writethe optimal solution as det(R∗HT∗) = det(Z) =

∏l |zl,l |, where Z and zi,i with

i = S(j − 1) + s, are a lower triangular matrix and the entry of the diagonal ofZ, respectively. Thus the channel gain for stream s in link j corresponds to theith diagonal entry of Z. R∗ and T∗ indicate the optimal transmit–receive weightvectors for K links. We also need (3.16) to be satisfied for the optimal solutionfor each stream s in link j, where (HH

j r∗s,j )H t∗s,l = 0, s = 1, ..., S, l = j + 1, ...,K,


and (HHj r∗s,j )

H t∗s ′,j = 0, s′ = s + 1, ..., S. The vector created by multiplying thechannel matrix by the receive antenna weight vector is perpendicular to thetransmit weight vector for links j + 1, ...,K and stream s + 1, ..., S in link j. Asa result, there is no interference at all at link j. This is so since the transmis-sion spaces of link j + 1, ...,K and stream s + 1, ..., S in link j do not overlapwith the transmission space of stream s in link j. The interference from link1, ..., j − 1 and stream 1, ..., s− 1 in link j to stream s in link j is canceled byTHP. However, prior to finding the optimal solution, the receiver design from(3.17) destroys the orthogonality created by QR decomposition in (3.16). As aresult at the ith iteration, for link j, we have (HH

j r(i)j )H t(i)

l = 0, l = j + 1, ...,K

and (HHj r(i)

s,j )H t(i)

s ′,j = 0, s′ = s + 1, ..., S. This means the transmission space forstream s in link j intersects with the transmission spaces of link j + 1, ...,K

and stream s + 1, ..., S in link j prior to convergence. In other words, the vectorgenerated by HH

j r(i)s,j also has components in other directions. This reduces the

optimal signal gain for stream s in link j, zi,i where i = S(j − 1) + s. Thus, wecan then conclude that

∏j |β

(i)s,j | ≤

∏j |zj,j |.

References

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[2] R. Morrow, Wireless Network Coexistence. The McGraw-Hill CompaniesInc., 2004.

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[4] G. Caire and S. Shamai, “On the achievable throughput of a multiantennaGaussian broadcast channel,” IEEE Transactions on Information Theory,49, 2003, 1691–1706.

[5] M. Costa, “Writing on dirty paper,” IEEE Transactions of InformationTheory, 29, 1983, 439–441.

[6] C. Windpassinger, R. F. H. Fischer, T. Vencel, and J. B. Huber, “Precod-ing in multiantenna and multiuser communications,” IEEE Transactions onWireless Communications, 3, 2004, 1305–1316.

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4 Turbo base stations

Emre Aktas, Defne Aktas, Stephen Hanly, and Jamie Evans

4.1 Introduction

Cellular communication systems provide wireless coverage to mobile users acrosspotentially large geographical areas, where base stations (BSs) provide serviceto users as interfaces to the public telephone network. Cellular communicationis based on the principle of dividing a large geographical area into cells whichare serviced by separate BSs. Rather than covering a large area by using asingle, high-powered BS, cellular systems employ many lower-powered BSs eachof which covers a small area. This allows for the reuse of the frequency bands incells which are not too close to each other, increasing mobile user capacity witha limited spectrum allocation.

Traditional narrowband cellular systems require the cochannel interferencelevel to be low. Careful design of frequency reuse among cells is then crucial tomaintain cochannel interference at the required low level. The price of low inter-ference, however, is a low frequency reuse factor: only a small portion of the sys-tem frequency band can be used in each cell. More recent wideband approachesallow full frequency reuse in each cell, but the cost of that is increased intercellinterference. In both approaches, the capacity of a cell in a cellular network,with six surrounding cells, is much less than that of a single cell operating in anintercell interference-free environment. In this chapter, we survey an approachthat allows the cell with neighbors to achieve essentially the same capacity asthe interference-free cell.

In a conventional cellular system, each mobile user is serviced by a singleBS, except for the soft-handoff case – a temporary mode of operation where themobile is moving between cells and is serviced by two base stations. A contrastingidea is to require each mobile station to be serviced by all BSs that are withinits reception range. In this approach all the BSs in the cellular network arecomponents of a single transceiver with distributed antennas, an approach knownas “network multiple-input multiple-output (MIMO).”



Network MIMO requires cooperation between BSs. On the uplink, the BSsmust cooperate to jointly decode the users, whilst on the downlink, the BSsmust cooperate to jointly broadcast signals to all the users in the network. Thisapproach may appear unrealistically complex, but information-theoretic studieshave highlighted the potentially huge capacity gains from such an approach [23,49, 59]. In a nutshell, these works (and others) have shown that such cooperationeffectively eliminates intercell interference. In other words, the per-cell capacityof a network of interfering cells is roughly the same as a non-interfering systemwhere the cells are isolated and do not interfere at all (in fact, there is a diversityadvantage for the interfering system, which means its capacity is higher than thecapacity of the isolated cell model). In the network of interfering cells there isno wasted interference: all received signals contain useful information. Crucially,to obtain this advantage, it is necessary for there to be intercell interference:it was shown in [23, 59] that full frequency reuse in each cell is required inorder to achieve the full information-theoretic capacity. This is in contrast tothe conventional cellular model with single cell processing which usually requiresfractional frequency reuse.

The question then arises: how can such cooperation be realized in practice?It is natural to conceive first a centralized system in which a central processoris connected to all the base stations, so that the network is operated as a singlecell MIMO system, but with distributed antennas. Such an architecture is, how-ever, expensive to build, has a single point of failure, and does not satisfactorilyaddress issues of complexity and delay. A more feasible and desirable solution isto distribute the processing among the base stations. In this chapter we presentdistributed BS cooperation methods for joint reception and transmission, whichallow the desired network MIMO behavior to emerge in a distributed manner.

For distributed processing, communication among the BSs is mandatory. Thedesired properties of a feasible distributed method are: (1) communication shouldonly be required between neighboring BSs, as opposed to message passing amongall BSs, and (2) the processing per BS and message passing delay should remainconstant with increasing network size. In this chapter, we survey an approach toBS cooperation (and provide new results for this approach) based on a graphicalmodel of the network-MIMO communication processes. In essence, we show thatboth uplink and downlink modes of communication reduce to belief propagationon graphs derived from the way BSs are interconnected in the backhaul, andfrom the signal propagation between BSs and mobiles, and vice versa, across theair interface.

To give a simple picture of what we mean by message passing between BSs,consider a cellular network where the BSs and the cells are placed on a line.In this model, every cell has two neighboring cells. Although this simple modelis far from being realistic, it provides a framework where the main concepts ofdistributed processing with message passing can be developed and explained,and it can then be generalized to less restrictive models. The one-dimensionalcellular array is illustrated in Figure 4.1.

4.1 Introduction 79

MS 1

BS 1

x1

y1

MS 2

BS 2

x2

y2

MS 3

BS 3

x3

y3

MS n

BS n

xn

yn

Figure 4.1. Linear cellular array. The cells are positioned on a line. Each cell hasone active mobile station (MS). Dashed lines show boundaries between cells. Atcell i, xi and yi represent the transmitted symbol and the received signal.

Let xi denote the data symbol transmitted by mobile station (MS) i and yi

denote the channel output observed at BS i. In the linear cellular array model,the relationship between the transmitted symbols and the received signals is

yi = hi(−1)xi−1 + hi(0)xi + hi(1)xi+1 + zi, (4.1)

where hi(j) is the channel coefficient from MS i + j to BS i, and zi is the additiveGaussian noise with variance σ2 . We assume that the channel coefficients hi(j)and the noise variance are known at BS i. For convenience, for the cells at theedges of the network, add dummy symbols x0 and xn+1, and set the correspond-ing hi(j)s to zero. The signal model for the one-dimensional cellular array modelis depicted in Figure 4.2.

∑ ∑ ∑ ∑

xi−1

yi−1

zi−1

xi

yi

zi

xi+1

yi+1

zi+1

xi+2

yi+2

zi+2

hi−

1(0

)

hi(

0)

hi+

1(0

)

hi+

2(0

)

h i(−1

)

h i+1(−1

)

h i+2(−1

)hi−1 (1)

hi (1)

hi+1 (1)

Figure 4.2. Linear cellular array signal model. The symbol transmitted in onecell is received at that cell, and also in the two neighboring cells (one neighboringcell if it is one of the two edge cells).

In the traditional single-cell processing (SCP) approach, BS i tries to detectsymbol xi based on yi alone. Using a frequency-reuse factor of 1/2 avoids theintercell interference, but this halves the capacity of the system. With full fre-quency reuse, MS i receives interference from MSs i− 1 and i + 1, as is clear in(4.1). One could treat this interference as Gaussian noise, and use a mis-matcheddecoder to decode the desired signal, but information theory tells us that inter-cell interference can be completely eliminated via multicell processing (MCP)[23, 49, 59].


MCP requires cooperation between the BSs, but how much cooperation isrequired in the simple model we are considering here? At first sight, it mightseem sufficient for BS i to use (yi−1 , yi , yi+1) in the detection of symbol xi ,as these are the only outputs to which xi actively contributes. This is not thecase, but it is certainly true that BS i can do a much better job of detecting xi

in this scenario. The BS’s task is first to compute the conditional distributionp(xi |yi−1 , yi , yi+1) and then to pick the maximum a posteriori estimate for xi .One approach to realize this detection strategy would be for each BS to pass theobserved channel output to its immediate neighbors: thus, BS i sends yi to BSsi− 1 and i + 1 respectively. This strategy involves one single message passingbetween adjacent BSs.

Considering this further, however, we see that intercell interference has notbeen eliminated after a single message passing step. For example, yi−1 receivesa contribution from data symbol xi−2 and the uncertainty in xi−2 must beaccounted for in the above probabilistic model. Again, it could be treated asGaussian noise, or it could be modeled more accurately than that, depending onwhat is measured or known by the BSs, and what information is passed fromone to the other. For example, BS i may know the constellations from whichthe interfering symbols xi−2 and xi+2 have been chosen. The BS may also havephase information (the coherent case) or the phase may be unknown (incoher-ent). The exact model used by BS i depends on which particular assumptionsbest describe the real-world scenario, but in all these possible models, intercellinterference remains after one message passing step in the effect of the unknownsymbols xi−2 and xi+2, which cannot be reliably detected.

The above interference model may remind the reader of standard intersymbolinterference (ISI) channels that arise in frequency-selective digital communica-tion scenarios. Such models are linear, and if we assume in addition that the apriori distributions on the input symbols are Gaussian, then the optimal equal-izer is to apply the matched filter (in this case, the linear minimum mean squarederror (LMMSE) filter) to the observed symbols y1 , y2 , ..., yn . This makes it clearthat it is not optimal for BS i to have access only to (yi−1 , yi , yi+1): to be opti-mal, BS i requires all the channel outputs y1 , y2 , ..., yn , as well as all the channelgains, and information about the a priori distributions on the symbols. Withthat information, it can apply the optimal filter, and obtain an optimal estimateof xi . In other words, there is a system-wide coupling of the interference betweencells. This approach might be called centralized MCP .

The problem with centralized MCP is that it requires a huge amount of mes-sage passing. All BSs require global channel knowledge in order to each applythe globally optimal filter. Note, however, that distributed methods can be usedin ISI equalization. In the Gaussian case, the LMMSE estimates can be obtainedby the recursive Kalman smoother . In the case of discrete input constellations,the maximum a posteriori (MAP) detector can be obtained by the forward–backward or BCJR algorithm [8] . Such methods are special cases of Bayesianestimation for graphical models. This suggests the idea of representing the

4.2 Review of message passing and belief propagation 81

cellular network by a graphical model, and obtaining distributed versions ofMCP that do not require each BS to obtain the complete global channel stateinformation (CSI). Further, these methods will allow us to investigate how wellperformance improves with the number of message passing steps. For example,in some scenarios, we will see that a single message passing step is sufficient toget most of the gains of MCP, whereas in other scenarios, many more messagepassing steps are required.

The challenge in the area of turbo BSs is to distribute the computations ofthe conditional distributions of the xis, so that they can be obtained by messagepassing between neighboring BSs only. We do this for the uplink in Sections 4.3,and 4.4. In Section 4.5, we apply similar ideas to the downlink broadcast channelproblem in which the BSs are sending data symbols to the MSs. To initiate thisstudy, our first step will be to review message passing and belief propagationmethods in a more generic framework, and then to apply the results from thistheory to the cellular models of interest in this chapter.

4.2 Review of message passing and belief propagation

The distributed algorithms presented in this chapter are built on the key conceptsof factor graphs and the sum-product algorithm. We begin with a brief reviewof these concepts.

The use of iterative, or turbo, receiver methods defined on graphs has becomean important focus of research in communications since the success of turbo codesand the rediscovery of low-density parity-check codes. Both the turbo decoder[38] and the low-density parity-check code decoder [20] are instances of beliefpropagation on associated graphs.

A factor graph is a graphical representation on which message passing algo-rithms are defined. There are at least two other popular graphical representationsemployed in the communications literature. Firstly, there are graphs on whichcodes are defined. These graphs represent sets of constraints which describe acode and include Tanner graphs [51], Tanner–Wiberg–Loeliger (TWL) graphs[58], and Forney graphs [17]. These graphs also provide iterative decoding of theassociated codes via message passing algorithms. Secondly, there are probabilis-tic structure graphs including Markov random fields [29] and Bayesian networks[44]. These graphs represent statistical dependencies among a set of randomvariables. Markov random fields are based on local Markov properties, whereasBayesian networks are based on causal relationships among the variables andfactoring the joint distribution into conditional and marginal probability distri-bution functions. The message passing algorithms defined on these structuresprovide methods of probabilistic inference: compute, estimate, and make deci-sions based on conditional probabilities given an observed subset of randomvariables.


Factor graphs are not specifically based on describing code constraints or prob-abilistic structures. They indicate how a joint function of many variables factorsinto a product of functions of smaller sets of variables. They can be used, how-ever, for describing codes and decoding codes, and in describing probabilisticmodels and statistical inference. In fact, factor graphs are more general thanTanner, TWL, and Forney graphs for describing codes [34], and they are moregeneral than Markov random fields and Bayesian networks in terms of expressingfactorization of a global distribution [19].

4.2.1 Factor graph review

In this subsection, we provide just enough review for the uninitiated reader to beable to grasp the BS cooperation material presented in this chapter. For furtherinformation, the reader may refer to [30] and the excellent tutorials [32, 33]. Thereader experienced in factor graphs may skip this section.

Let g(x1 , x2 , . . . , xn ) be a function of variables x1 , . . . , xn , where for each i, xi

takes on values in a set Ai .

Definition of marginal function and summary notationWe are interested in a numerically efficient computation of the marginal function

gi(xi) =∑∼xi

g(x1 , x2 , . . . , xn ) (4.2)

for some i. The right hand side of (4.2) denotes the summation for xi of functiong as defined in [30]: for each a ∈ Ai the value of gi(a) is obtained by summing thevalue of g(x1 , x2 , . . . , xn ) over all (x1 , . . . , xn ) ∈ A1 × · · · ×An such that xi = a.For example, for n = 3, the summation for x2 of g is

g2(x2) =∑∼x2

g(x1 , x2 , x3) =∑

x1 ∈A 1

∑x3 ∈A 3

g(x1 , x2 , x3).

Relationship to the APPFor probabilistic models, the computation of the marginal in (4.2) is related tothe computation of the a posteriori probability (APP), a quantity of particularinterest to us in this chapter. Let (x1 , . . . , xn ) denote the realization of somerandom variables in a probabilistic model, let (y1 , . . . , ym ) denote some observedvariables in the model, and let p(x1 , . . . , xn , y1 , . . . , ym ) denote the joint distri-bution. Taking a given (y1 , . . . , ym ) as fixed, (i.e., observed) define the globalfunction g:

g(x1 , . . . , xn ) = p(x1 , . . . , xn , y1 , . . . , ym ). (4.3)

Typically, g is factorized into two as

g(x1 , . . . , xn ) = p(y1 , . . . , ym |x1 , . . . , xn )p(x1 , . . . , xn ),


where the first term is the likelihood function and the second term is the apriori distribution of (x1 , . . . , xn ). Depending on the probabilistic model, thesetwo factors themselves are further factorized. The APP of xi for any desiredi ∈ 1, . . . , n is proportional to the marginal of g for xi :

p(xi |y1 , . . . , ym ) ∝ gi(xi), (4.4)

where gi(xi) is the marginal of the joint distribution in (4.3), and the notation“∝” means “proportional to”, i.e., the right hand side of “∝” is scaled by aconstant to obtain the left side. If the left hand side is a probability function,this scaling constant can be found using the fact that this function adds up tounity over all possible values of its argument.

Definition of factor graphSuppose that g(x1 , . . . , xn ) is in the form of a product of local functions fj :

g(x1 , . . . , xn ) =J∏

j=1

fj (Xj ), (4.5)

where Xj is a subset of x1 , . . . , xn, and the function fj (Xj ) has the elementsof Xj as arguments.

A factor graph represents the factorization of g(x1 , . . . , xn ) as in (4.5). Thecorresponding factor graph has two types of nodes: variable nodes and factornodes. For each variable xi there is a variable node shown by a circled xi , andfor each local function fj there is a factor node shown by a solid square in thegraph. Thus there are n variable nodes and J factor nodes in the graph. Thereis an undirected edge connecting variable node xi to factor node fj if and only ifxi is an argument of fj . Thus connections are only between variable and factornodes; two factor nodes are never connected, and two variable nodes are neverconnected. We define the neighbors of a variable node to be those factor nodesto which it is directly connected in the graph. We correspondingly define theneighbors of a factor node to be those variable nodes in the graph to which it isdirectly connected.

Definition of sum–product algorithmThe goal of the sum–product algorithm is to obtain the marginal function in(4.2) for some i ∈ 1, . . . , n. This is done in a numerically efficient manner,based on the factorization in (4.5) using the distributive law to simplify thesummation. The algorithm is defined in terms of messages between connectedfactor and variable nodes. A message from node a to node b is computed basedon previously received messages at node a from all its neighbors except for nodeb. A message from variable node xi to factor node fj is a function with argumentxi that can take on values in Ai . A message from factor node fj to variable nodexi is also a function of xi . After the messages from all nodes propagate throughthe factor graph in a sequential manner, at termination, the incoming messages


at desired variable nodes are combined in order to obtain the associated marginalfunction. The rules for message updates are given below.

Message from variable node x to factor node f :

µx−f (x) =∏

h∈n(x)\f µh−x(x). (4.6)

Message from factor node f to variable node x:

µf−x(x) =∑∼x

⎛⎝f(n(f))∏

y∈n(f )\xµy−f (y)

⎞⎠ , (4.7)

wheren(x) : set of all factor node neighbors of variable node x in the

factor graph,n(x)\f : set of all neighbors of x except for f ,

n(f) : set of all variable node neighbors of factor node f in thefactor graph.

We make the following observations on the messages in the sum–product algo-rithm. The computations done by variable nodes in (4.6) are a simple multiplica-tion of incoming messages, whereas the computations done by the factor nodesin (4.7) are more complex. A variable node of degree 2 (i.e., a node with twoneighbors) simply replicates the message received on one edge onto the otheredge. A factor node of degree 1 simply outputs the function of the variable thatit is connected to as the message.

The computation typically starts at the leaf nodes of the factor graph. Eachleaf variable node sends a trivial identity function. If the leaf node is a factornode, it sends a description of f . If the computation is started from nonleaf nodes,it is assumed that it has received trivial identity messages during initiation. Eachnode remains idle until it receives all required messages based on which it cancompute outgoing messages.

To terminate the computations, the messages are combined at the desiredvariable nodes. The rule for combining messages at a variable node is to take theproduct of all incoming messages:

µx(x) =∏

h∈n(x)

µh−x(x). (4.8)

Equivalently, µx(x) can be computed as the product of the two messages thatwere passed in opposite directions over any single edge incident on x:

µx(x) = µf−x(x)µx−f (x) for any f ∈ n(x). (4.9)

If the factor graph is a tree, then µx(x) will be the marginal function g(x)defined in (4.2). If the factor graph has loops, then the message passings can berepeated, and at termination µx(x) will be an approximation of the marginal


function g(x). In many cases, scaled versions of the messages are computed,which results in a µx(x) scaled by a constant. Thus the final µx(x) is obtainedafter a proper normalization.

Definition of [P ] notationIf P is a Boolean proposition involving some set of variables, then [P ] is the0, 1-valued truth function

[P ] =

1, if P is true,

0, if P is false.(4.10)

4.2.2 Factor graph examples

Example 1 Hidden Markov modelConsider a probabilistic model where we have the states vector s =(s1 , s2 , . . . , sn ) and output variables vector u = (u1 , u2 , . . . , un ). The statess1 , . . . , sn form a Markov chain, and the transition from si−1 to si producesan output variable ui .

The local function Ti computes the conditional probability of transitioningfrom si−1 to si , and the output ui :

Ti(si−1 , ui , si) = p(si |si−1)p(ui |si, si−1) for i = 1, . . . , n. (4.11)

In several examples, ui is a function of only si , so in those examples,

Ti(si−1 , ui , si) = p(si |si−1)[ui = d(si)],

where d is the function that determines ui .Corresponding to each output variable ui is the “noisy” observation yi , where

the relationship between the output variable and its observation is characterizedby the conditional distribution p(yi |ui). The global function of (s, u) is

g(s, u) = p(y|s, u)p(s, u)

=

(n∏

i=1

p(yi |ui)

)(n∏

i=1

Ti(si−1 , ui , si)

). (4.12)

Note that y is fixed for any realization of observation, so we consider g(s, u) tobe a function of (s, u) only, and regard y as a vector of parameters.

The factor graph corresponding to the factorization in (4.12) is given inFigure 4.3 for n = 3. The dummy nodes added in this graph do not alter thefunction g nor the resulting algorithm, but they allow a convenient descriptionof the algorithm. For T1 , the state transition from s0 to s1 is independent of s0 .

During initialization, each pendant factor node sends the messages, which aretheir function descriptions to their corresponding variable nodes. Then, since thecorresponding variable nodes are all of order 2, they replicate the messages at theother edge. Afterwards, forward (si−1 to si for i = 1, . . . , n) and backward (si to


s1

u1

s2

u2

s3

u3

s0

T1 T2 T3

f(y1|u1) f(y2|u2) f(y3|u3)

α(s0) α(s1) α(s2)α(s1) α(s2) α(s3)

β(s1) β(s2) β(s3)β(s1) β(s2)

γ(u1) γ(u2) γ(u3)

f(s0) = 1 f(s3) = 1

Figure 4.3. Factor graph for hidden Markov model for n = 3. Dummy nodesf(s0), s0 , and f(s3) are added to handle the initialization of the algorithm atthe edges of the Markov chain. Since the variable nodes in this graph have degree2, they simply replicate the message received on one edge on the other edge.

si−1 for i = n, . . . , i + 1) message passing occurs along the chain. The resultingalgorithm is known as the forward–backward or BCJR algorithm [8]. In theliterature, the message µui−Ti

(ui) is denoted by γ(ui), the message µTi−si(si) is

denoted by α(si), and the message µTi−si−1 (si−1) is denoted by β(si−1). Usingthat notation, at initialization, we have

γ(ui) = p(yi |ui) = f(yi |ui) for i = 1, . . . , n,

α(s0) = 1,

β(sn ) = 1.

Then the forward recursion is computed as the message from Ti to si , using(4.7):

α(si) =∑∼si

Ti(si−1 , ui , si)α(si−1)γ(ui) for i = 1, . . . , n (4.13)

and the backward recursion is computed as the message from Ti to si−1

β(si−1) =∑∼si−1

Ti(si−1 , ui , si)β(si)γ(ui) for i = n, . . . , 2. (4.14)

This is the general form of the forward–backward algorithm. For differentspecific cases, the local functions are different but the general structure of thealgorithm is the same, outlined by the forward and backward recursions in (4.13)and (4.14).

After the forward and backward recursions are complete, at termination, foreach state variable node si , the incoming messages are combined as

µsi(si) = α(si)β(si) for i = 1, . . . , n. (4.15)

Since the factor graph is a tree, µsi(si) is, in fact, the true marginal gi(si)

and a scaled version of the APP p(si |y). This model is directly applicable tothe uplink of the simple one-dimensional cellular network that we examine inSection 4.3. It is the simplest model of turbo BS cooperation that we encounterin this chapter.


x1 x2 x3 x4 x5

p(x1) p(x2) p(x3) p(x4) p(x5)

p(y1|·) p(y2|·) p(y3|·) p(y4|·)

µx1−y1(x1) µy1−x1(x1)

Figure 4.4. Factor graph for the interference channel model for n = 5, m =4, ny1 = x1 , x2, ny2 = x1 , x3, ny3 = x2 , x3 , x4 , x5, and ny4 = x3 , x4 , x5.The notation p(yi |·) refers to the conditional distribution of yi given the neighborvariable nodes: p(yi |·) = p(yi |nyi

). In the following sections, the prior distributionfactor nodes, p(xi), will not be shown in the graphs.

Example 2 Interference channelConsider a channel with n input variables x = x1 , . . . , xn and m output vari-ables y = y1 , . . . , ym. Each output variable is a noisy observation of a linearcombination of the elements in a subset of the inputs, indexed by ni ⊂ 1, . . . , n,

yi =∑j∈ni

hi,j xj + zi, (4.16)

where hi,j is the complex channel coefficient of input xj at the channel outputyi , and zi is the additive white circularly symmetric complex Gaussian noise.Suppose that the channel coefficients and the variance of zi (σ2) are known. Letnyi

denote the set of the input variables indexed by ni : xj : j ∈ ni. Then thedistribution of yi conditioned on nyi

is

p(yi |nyi) =

1πσ2 exp

⎧⎨⎩− 1σ2

∣∣∣∣∣∣yi −∑j∈ni

hi,j xj

∣∣∣∣∣∣2⎫⎬⎭ . (4.17)

Suppose that the inputs are independent, then the joint distribution ofx1 , . . . , xn is

g(x1 , . . . , xn ) = p(x1 , . . . , xn , y1 , . . . , ym )

=m∏

i=1

p(yi |nyi)

n∏j=1

p(xj ). (4.18)

We can use the (loopy) factor graph corresponding to the factorization in (4.18)and the sum–product algorithm on that graph to compute (an approximationof) the APP p(xi |y1 , . . . , ym ) ∝ gi(xi). The factor graph corresponding to (4.18)is given in Figure 4.4.

There are two types of messages in Figure 4.4: x-to-y messages, and y-to-xmessages. Let nxj

denote the set of yi nodes such that yi is a neighboring factornode of the variable node xj in the graph. If yi ∈ nxj

, the message from variable


node xj to factor node yi is, from (4.6),

µxj −yi(xj ) = p(xj )

∏yk ∈nx j

\yi µyk −xj

(xj ). (4.19)

If xj ∈ nyi, the message from factor node yi to variable node xj is, from (4.7),

µyi−xj(xj ) =

∑∼xj

⎛⎝f(yi |nyi)

∏xl ∈ny i

\xj µxl−yi

(xl)

⎞⎠ . (4.20)

During initialization, the pendant factor nodes p(xj ) send their description tovariable nodes xj . In addition, the factor nodes p(yj |·) send trivial messages totheir neighboring variable nodes: µyi−xj

(xj ) = 1 for i = 1, . . . ,m, and xj ∈ nyi.

Afterwards, we have an iterative algorithm, where at each iteration we compute

(1) x-to-y messages for each j ∈ 1, . . . , n and yi ∈ nxjin (4.19);

(2) y-to-x messages for each i ∈ 1, . . . ,m and xj ∈ nyiin (4.20).

Notice that the graph in Figure 4.4 is loopy, and this means that the algorithmwill not terminate in a finite number of steps, nor will it be guaranteed to find thecorrect marginalizations. If the algorithm does converge, however, then it can beterminated after a sufficiently large number of steps, and then an approximationto the marginal distribution on the variable nodes can be obtained as follows.The messages at variable node xj for j ∈ 1, . . . , n are combined as

µxj(xj ) = p(xj )

∏yk ∈nx j

µyk −xj(xj ). (4.21)

Models that lead to factor graphs with loops like this simple interference chan-nel example will arise when we turn our attention to two-dimensional cellularnetwork models in Section 4.4. First, however, we will look at one-dimensionalcellular networks where the corresponding factor graphs are loop-free.

4.3 Distributed decoding in the uplink: one-dimensionalcellular model

Consider again the cellular network where the BSs and the cells are placed on aline, as depicted in Figure 4.1. In this model, every cell has two neighboring cells.Although this simple model is far from being realistic, it provides a framework inwhich the main concepts of distributed processing with message passing can bedeveloped and explained, and it can then be generalized to less restrictive models.

Let xi denote the symbol transmitted by MS i and yi denote the channeloutput observed at BS i, as depicted in Figure 4.2. In the linear cellular arraymodel, the relationship between the transmitted symbols and the received signalsis described by (4.1). As discussed in Section 4.1, the goal is to obtain optimaldetection of any particular xi given all observations y1 , . . . , yn , in a distributed

4.3 Distributed decoding in the uplink: one-dimensional cellular model 89

manner with cooperating BSs, as an alternative to the traditional approach ofSCP. In SCP, BS i has access to the channel output yi only. In contrast, we areinterested here in distributed, message-passing algorithms to accomplish MCP,based on probabilistic graphical models.

4.3.1 Hidden Markov model and the factor graph

The linear cellular array model is highly reminiscent of a standard linear ISImodel in digital communications, and hence we expect to be able to applythe BCJR algorithm [8]. In [8], a state-based hidden Markov model is used,as described in Example 1 in Section 4.2.2. In a state-based model, several inputvariables are combined to form a state such that each channel output is only afunction of that state, and the state sequence forms a Markov chain.

The key idea in [21] is to treat the one-dimensional cellular model as anISI channel. In fact, this idea goes back to [59]. The state for cell i is si =(xi−1 , xi , xi+1) and we assume the symbols from different mobiles are indepen-dent, taking values in some finite alphabet (which can be different for the differentusers). Thus, there are several possible values for the state si , so we will write(xi−1(si), xi(si), xi+1(si)) for the values of the data symbols corresponding to aparticular state value si . It is clear that the state sequence is a Markov chain,with the following transition probabilities:

p(s1) = p(x0(s1))p(x1(s1))p(x2(s1)),

p(si+1 |si) = [xi(si) = xi(si+1)][xi+1(si) = xi+1(si+1)]p(xi+2(si+1)),

where the [P ] notation was defined in (4.10). Note that [xi(si) =xi(si+1)][xi+1(si) = xi+1(si+1)] indicates whether state si+1 conforms with statesi , i.e., whether a transition from si to si+1 is possible.

Note that each cell has one channel output, yi , which is dependent only on thestate si , as in the hidden Markov model of Section 4.2.2. To complete the matchwith the model in that section, we define the output variable corresponding tothe transition from si−1 to si to be ui , where

ui = d(si) := hi(−1)xi−1(si) + hi(0)xi(si) + hi(+1)xi+1(si),

and we note that the conditional distribution of the observation, yi , given ui ,is f(yi |ui) = N(yi ;σ2 , ui), where N(x;σ2 ,M) denotes the Gaussian distributionwith mean M and variance σ2 . The corresponding factor graph is shown inFigure 4.5, where the function node Ti computes the function:

Ti(si−1 , ui , si) = p(si |si−1)[ui = d(si)]. (4.22)

It follows that the forward–backward algorithm can be applied to obtain the APPp(si |y1 , . . . , yn ), which can be further marginalized to obtain p(xi |y1 , . . . , yn ), theAPP of the mobile data symbols.

The implementation of the forward–backward recursions is distributed amongthe BSs, where BS i performs the computations done by node Ti in the algorithm.


s1

u1

s2

u2

s3

u3

sn

un

s0

T1 T2 T3 Tn

f(y1|u1) f(y2|u2) f(y3|u3) f(yn|un)

f(s0) f(sn)

Figure 4.5. Factor graph for the hidden Markov model for the linear cellulararray. Dashed lines show boundaries between cells. The computations of thenodes within a cell are done by the BS of that cell. Any message passing througha cell boundary corresponds to actual message passing between correspondingBSs.

For example, upon receiving the message α(si−1) from cell i− 1, BS i computesα(si) and forwards it to cell i + 1. Thus, α messages ripple across the BSs fromleft to right, and β messages ripple in the reverse direction. After the forwardand backward recursion is complete, the APP p(si |y1 , . . . , yn ) is obtained as ascaled version of (4.15). In this formulation, the middle BS is the first to be ableto decode its mobile.

This serial formulation of the forward–backward algorithm is the natural oneto use in solving an ISI equalization problem. It is not natural, however, incellular radio networks to designate a leftmost or rightmost BS. In fact, wecannot do that at all for an infinite linear array model. Fortunately, the sum–product algorithm has flexibility in terms of node activation schedules [30]. Initialconditions can be arbitrary, and each node can operate in parallel. This allowsall BSs to immediately begin computing their messages starting with the a prioridistributions on the input symbols. At each iteration, a BS passes an α messageto the right, and a β message to the left. In a finite linear array, this parallelversion of the forward–backward algorithm converges to the same solution asobtained from the serial implementation, but an important point is that it canbe terminated early giving a suboptimal estimate of the mobile’s data symbolat an earlier time. In the infinite linear array, the algorithm must be terminatedat some point in time. This approach allows an investigation of estimation errorversus delay, as can be found in [39].

The actual values that the variables can take have not been specified. In thissection, we have in mind that each xi takes a value from a discrete constella-tion, and, as such, the BSs are engaged in the demodulation of the users’ datasymbols. If the symbol xi is replaced by the transmitted codeword of mobile i

and yi is replaced by the channel outputs corresponding to a codeword, i.e., ifwe include the time dimension, then we can use the described method for decod-ing as opposed to the detection of individual symbols, as considered in [21].In the present section, the forward–backward algorithm is accomplishing joint


multiuser detection (MUD) of the users’ data symbols, prior to single-user decod-ing. After the detection of the symbols, each BS can decode its own user usinga single-user decoder.

Note that the complexity of MUD is typically exponential in the number ofusers [54], but it is known that in some special cases the complexity can bemuch reduced [47, 52], for example when the signature sequences have constantcross-correlation [48]. In the present section, we have a distributed MUD that islinear in the number of users, and this is due to the highly localized interferencemodel: the cross-correlations of most signature sequences are zero. Indeed, theBCJR algorithm implements the optimal MAP detection of the users’ symbols,and this is known to have a complexity that is linear in time [8], i.e., in thenumber of symbols.

To approach Shannon capacity at high SNR, it is required to send many bitsper symbol, which requires a large alphabet size (large signal constellations),and the BCJR algorithm is exponential in the alphabet size. So even if thecomplexity is linear in the number of users, the overall complexity can be veryhigh. This observation also applies to the decoding of codewords in the modelconsidered in [21]. A standard approach to limit the complexity of MUD is torestrict attention to suboptimal linear techniques, which we consider further inSection 4.3.2. Unfortunately, this does not avoid the complexity of the overalldecoding problem, but at least one can then focus attention on well-establishedtechniques for decoding single-user codes.

4.3.2 Gaussian symbols

A standard approach in MUD is first to estimate the individual symbols fromdifferent users using linear MUD techniques. Once the BS has estimated symbolxi from mobile i it then passes this soft estimate to a single-user decoder formobile i. The decoder waits until it receives the estimates of all symbols in thecodeword, and then it attempts to decode the codeword. This approach limitsthe complexity of the MUD component of the receiver.

It is well known that optimal MUD is in fact linear if the underlying sym-bols being estimated are jointly Gaussian. In this section, we assume that theinput symbols are drawn from joint Gaussian distributions (independent acrossmobiles) and then we apply the corresponding optimal linear filters, and thetask of the present section is to show how these filters can be implemented viamessage passing between the BSs in the cellular network. Another motivationfor this section is that the developed methods will prove useful in designing iter-ative message-passing algorithms to accomplish beamforming on the downlinkof a cellular system, as we will see in Section 4.5.

When the input symbols are modeled as Gaussian random variables, we canstill employ factor graph methods. The global function is now a continuous func-tion and the marginalization is done by integrating (as opposed to summing)with respect to unwanted variables. Since the messages are now continuous


functions, each message in general corresponds to a continuum of values. How-ever, if the message functions can be parameterized, they can be represented bya finite number of parameter values. For example, if a message function is theprobability density function of a Gaussian vector, then it is characterized by amean vector and covariance matrix pair, which is the case for the Gaussian inputmodel.

We will now describe the Kalman-smoothing-based distributed algorithm in[39] for the linear cellular array. The model is the same as in (4.1) except thatnow the xis are independent zero-mean Gaussian distributed with variance p.We are going to use matrix-vector notation, so define the state for cell i to bethe column vector si = [xi−1 , xi , xi+1]T . The states again form a Markov chain,but we now express the transition from state si to si+1 as

si+1 = Af si + bf xi+2 ,

where

Af =

⎡⎣0 1 00 0 10 0 0

⎤⎦ , bf =

⎡⎣001

⎤⎦ .

Then the state transition is characterized by the conditional distribution

f(si+1 |si) = N(si+1; pbf bf T,Af si), (4.23)

where we use the notation

N(s;M,m) ∝ exp−1

2(s−m)T M−1(s−m)

to denote a Gaussian distribution, scaled by an arbitrary constant that is not afunction of the argument of the function. Here, s is the argument of the functionand M and m are parameters.

Define the column vector

hi =[hi(−1) hi(0) hi(1)

]T,

then the observation in cell i can be expressed in vector form as

yi = hTi si + zi.

The factorization of the joint distribution again has the form in (4.12). Thecorresponding factor graph is shown in Figure 4.6.

Since the sis and yis are jointly Gaussian, all of the messages turn out to beGaussian distributions. Thus the actual messages will be the mean vector andcovariance matrix pairs.

Before deriving the messages, let us present some useful results for the Gaus-sian distribution. Remember that in our notation the distribution is scaled by


s1 s2 s3 s4

f(s1) f(s2|s1) f(s3|s2) f(s4|s3)

f(y1|s1) f(y2|s2) f(y3|s3) f(y4|s4)

p1|1 (s1) p2|2 (s2) p3|3 (s3)p1|0(s1) p2|1(s2) p3|2(s3) p4|3(s4)

Figure 4.6. Factor graph for a hidden Markov model for n = 4 used for the linearcellular array with Gaussian inputs. Dashed lines show boundaries between cells.The computations of the nodes within a cell are done by the base station of thatcell. Any message passing through a cell boundary corresponds to an actualmessage passing between corresponding base stations.

an arbitrary constant.

N(s;M,m) = N(m;M, s), (4.24)

N(As + b;M,m) = N(s;A−1MA−1T,A−1(m− s)), (4.25)

N(s;M1 ,m1)N(s;M2 ,m2) = N(s;M3 ,m3),

where

M3 = (M−11 + M−1

2 )−1 , m3 = M3(M−11 m1 + M−1

2 m2); (4.26)

N(s;M1 ,m1)N(s;M2 ,m2)−1 = N(s;M4 ,m4),

where

M4 = (M−11 −M−1

2 )−1 , m4 = M4(M−11 m1 −M−1

2 m2); (4.27)∫N(s;M1 ,m1)N(As;M2 , t) ds = N(t;AM1AT + M2 ,Am1). (4.28)

We know that the messages are going to be Gaussian. Denote them by

pi|i−1(si) = N(si ;Mi|i−1 , si|i−1), (4.29)

pi|i(si) = N(si ;Mi|i , si|i). (4.30)

From the observation node, we have the message

f(yi |si) = N(yi ;σ2 ,hTi si).

From (4.6), the message from variable node si to factor node f(si+1 |si) is

pi|i(si) = pi|i−1(si)f(yi |si)

∝ exp−1

2

[(si − si|i−1)T M−1

i|i−1(si − si|i−1)]

exp−1

2

[1σ2 (yi − hT

i si)2]

∝ exp−1

2

[(si − si|i)T M−1

i|i (si − si|i)]

,


where

Mi|i =(M−1

i|i−1 +1σ2 hihT

i

)−1

, (4.31)

si|i = Mi|i

(M−1

i|i−1 si|i−1 +1σ2 hiyi

). (4.32)

Thus the pair (4.31)–(4.32) is the message from si to f(si+1 |si). This pair ofequations is another form of the more familiar Kalman filter correction update[27]:

Mi|i =(I−KihT

i

)Mi|i−1 , (4.33)

si|i = si|i−1 + Ki

(yi − hT

i si|i−1), (4.34)

where

Ki =Mi|i−1hi

σ2 + hTi Mi|i−1hi

.

The equivalence of (4.31)–(4.32) and (4.33)–(4.34) can be shown using inver-sion of matrix sum identities.

Next, let us obtain the message function pi|i−1(si) using (4.7):

pi|i−1(si) =∫

f(si |si−1)pi−1|i−1(si−1) dsi−1 . (4.35)

Note that the summation in (4.7) becomes integration in (4.35) since we aredealing with continuous variables. From (4.23) and (4.30):

pi|i−1(si) =∫

N(si ; pbf bf T,Af si−1)N(si−1 ,Mi−1|i−1 , si−1|i−1) dsi−1

∝ N(si ; pbf bf T+ Af Mi−1|i−1Af T

,Af si−1|i−1), (4.36)

where (4.36) is due to (4.24) and (4.28). As a result, the message functionpi|i−1(si) is represented by the mean-covariance pair:

si|i−1 = Af si−1|i−1 , (4.37)

Mi|i−1 = pbf bf T+ Af Mi−1|i−1Af T

. (4.38)

Equations (4.37)–(4.38) are Kalman filter prediction updates [27].Note that the message pi|i(si) is the posterior distribution of si giveny1 , . . . , yi, and pi|i−1(si) = f(si |y1 , . . . , yi−1). We desire the posterior distri-bution of si given all observations: f(si |y1 , . . . , yn ). For that purpose, form agraph similar to Figure 4.6 but in the backward direction: states are orderedfrom sN to s1 and connected by the transition nodes f(si−1 |si), where [39]

f(si−1 |si) = N(si−1 ; pbbbbT,Absi),

Ab =

⎡⎣0 0 01 0 00 1 0

⎤⎦ , bb =

⎡⎣100

⎤⎦ .


For the backward graph, denote the message from factor node f(si |si+1) tovariable node si by

pi|i+1(si) = N(si ;Mi|i+1 , si|i+1),

which will be the posterior distribution of si given yi + 1, . . . , yn. Combinationof the backward message pi|i+1(si) with the forward message pi|i(si) to obtainf(si |y1 , . . . , yn ) can be done as follows:

f(si |y1 , . . . , yn ) ∝ f(si , y1 , . . . , yn )

= f(y1 , . . . , yi |si , yi+1 , . . . , yn )f(si , yi+1 , . . . , yn )

∝ f(y1 , . . . , yi |si)f(si |yi+1 , . . . , yn ) (4.39)

∝ f(si |y1 , . . . , yi)f(si |yi+1 , . . . , yn )f(si)−1

= pi|i(si)pi|i+1(si)f(si)−1

= N(si ;Mi|i , si|i)N(si ;Mi|i+1 , si|i+1)N(si ; pI,0)−1 (4.40)

= N(si ;M3 ,m3)N(si ; pI,0)−1 (4.41)

= N(si ;Mi , si). (4.42)

Equation (4.39) is due to the fact that given si , y1 , . . . , yi and yi+1 , . . . , ynbecome independent. In (4.40) the fact that the prior distribution of si is zero-mean Gaussian with covariance pI is used. Equation (4.41) is from (4.26), where

M3 = (M−1i|i + M−1

i|i+1)−1 , (4.43)

m3 = M3(M−1i|i si|i + M−1

i|i+1 si|i+1). (4.44)

Equation (4.42) is from (4.27), where

Mi = (M−13 − p−1I)−1 , (4.45)

si = Mi(M−13 m3). (4.46)

Combining (4.43)–(4.46), we obtain the result

Mi =(M−1

i|i + M−1i|i+1 −

1pI)−1

,

si = Mi(M−1i|i si|i + M−1

i|i+1 si|i+1).

For the one-dimensional cellular network we have seen how message passingalgorithms can be applied on the uplink to detect discrete data symbols and esti-mate Gaussian data symbols. The one-dimensional nature of these models leadsto underlying factor graphs without loops and thus to guaranteed convergenceof the sumproduct algorithm on these factor graphs. In the sequel, we will seethat the situation is quite different when we move to two-dimensional cellularnetworks.


BS11 BS12 BS13 BS14

BS21 BS22 BS23 BS24

BS31 BS32 BS33 BS34

BS41 BS42 BS43 BS44

MS11 MS12 MS13 MS14

MS21 MS22 MS23 MS24

MS31 MS32 MS33 MS34

MS41 MS42 MS43 MS44

Figure 4.7. Rectangular cellular array model. The cells are positioned on a rect-angular grid. Each cell has one active MS. The signal transmitted in one cellis received at that cell, and also four neighboring cells (except for edge cells).Dashed lines show boundaries between cells.

4.4 Distributed decoding in the uplink: two-dimensionalcellular array model

4.4.1 The rectangular model

A model that is more general than the linear array model is the model where BSsare positioned on a two-dimensional grid. For example, consider the rectangularmodel where the BSs are on a rectangular grid. Again, assume flat fading andorthogonal multiple access channels within a cell. The received signal at the BSof any cell, in any channel, is the superposition of the signal from its own MS,and the signals of the four adjacent cell cochannel users. The positioning of theBSs and MSs is shown in Figure 4.7.

For cell (i, j) in the rectangular grid, let xi,j denote the symbol transmittedby the MS, yi,j the signal received at the BS, hi,j (xm,n ) the channel from mobile(m,n) to BS (i, j), and zi,j additive Gaussian noise. The relationship betweenthe observations yi,j and the transmitted symbols xi,j is expressed as

yi,j =∑

xm , n ∈ny i , j

hi,j (xm,n )xm,n + zi,j , (4.47)

4.4 Distributed decoding in the uplink: two-dimensional model 97

APP

BCJRcolumns

BCJRrows

y

APP

Figure 4.8. Iterative implementation of BCJR algorithm along the columns androws of the rectangular array ( c© 2008 IEEE).

where

nyi , j= xi,j , xi−1,j , xi+1,j , xi,j−1 , xi,j+1 (4.48)

is the set of transmitted symbols that can be heard at BS (i, j). For the cells atthe edges of the rectangular network, dummy symbols x0,j , xn+1,j , xi,0 , xi,n+1

are added and the corresponding hi,j (xm,n ) are set to zero.The goal is again to obtain the global APP p(xi,j |y), where y =

y1,1 , . . . , y1,n , . . . , yn,1 , . . . , yn,n is the set of all observations. It is still pos-sible to obtain exact inference by forming a Markov chain via clustering (e.g.,states obtained by clustering along the rows of the two-dimensional array) andthen apply the BCJR algorithm, but the complexity grows exponentially withn (the number of columns or rows in the rectangular array) and is intractableas the network size grows. It is possible that the inherent complexity is onlypolynomial in the network size (we have not investigated this issue) but in anycase, we are looking for distributed approaches using message passing betweenneighboring base stations.

Encouraged by the elegance of the implementation of the BCJR algorithmfor the one-dimensional array, one can be tempted to use this approach alongthe columns and rows of a rectangular array in an iterative manner. The APPoutputs of the BCJR along one direction will be used as a priori probabilitiesfor the BCJR along the other direction. Thus the global decoder is built as aniterative decoder where the two modules of the iterative decoder are the BCJRin each direction (Figure 4.8 from [5]).

The details of this approach, and a discussion of its implementation are in [4].The idea of running BCJR along the rows and columns of a rectangular cellulararray was also proposed for two-dimensional ISI channels by Marrow and Wolfin [35].

Although applying the BCJR algorithm along the rows and columns of therectangular array seems to work [5, 35], we see that it does not directly exploit thetwo-dimensional structure of the problem but instead imposes a one-dimensionalstructure on parts of it. As this is an ad-hoc iterative method, it will result inonly an approximation to the desired APPs. However, if we are looking for anapproximation of the APP, there is no need to impose the use of the BCJRalgorithm which gives the optimum result only if the problem is one-dimensional.


Thus we can accept an approximate APP and form loopy graphs that reflect thetrue two-dimensional nature of the problem.

4.4.2 Earlier methods not based on graphs

Research has considered distributed global demodulation in two-dimensional cel-lular channels [53, 57]. In [53], the authors considered BSs computing soft esti-mates of the symbols, and then sharing and combining them to obtain a finalsoft estimate. This strategy was compared with BSs sharing channel outputs andperforming maximum-ratio combining of the channel outputs. In [57], a reducedcomplexity maximum-likelihood (ML) decoder was developed, which was moti-vated as an extension of the Viterbi algorithm which exploits the limited inter-ference structure. Although the general large two-dimensional cellular structurewas not treated, it seems that the algorithm, if applied to that structure, wouldresult in increasing complexity per symbol with growing network size.

Alternatively, graph-based iterative message passing methods for distributeddetection for two-dimensional cellular networks were proposed in [3–5, 50].

4.4.3 State-based graph approach

One way to model the two-dimensional case is to adapt the state-based graphicalidea from the one-dimensional case. Remember that in a state-based graph, eachchannel output depends only on one state variable, and everything else in thesystem is modeled by the transitions among the states. For the one-dimensionalcase, the states form a Markov chain, but in the two-dimensional case they donot.

For cell (i, j), define the state to be

si,j = nyi , j, (4.49)

where nyi , jis the set of symbols defined in (4.48), upon which yi,j depends, as

in

yi,j = mi,j (si,j ) + zi,j ,

where the conditional mean mi,j (si,j ) is a deterministic function of si,j ,

mi,j (si,j ) =∑

xm , n ∈ny i , j

hi,j (xm,n )xm,n . (4.50)

It can be observed that the states form a Markov random field, a fact that wewill exploit in (4.51).

As in the one-dimensional model, the variables in the sum–product algorithmare not the channel input symbols xi,j , but the states si,j . The goal of BS (i, j)is to obtain the APP p(si,j |y), from the marginalization of which it can obtainthe APP p(xi,j |y). Let s = si,j denote the set of all states. The global function


s22 s23 s24

s32 s33 s34

s42 s43 s44

p(s22|s12, s21)

p(y22|·)

p(s23|s13, s22)

p(y23|·)

p(s24|s14, s23)

p(y24|·)

p(s32|s22, s31)

p(y32|·)

p(s33|s23, s32)

p(y33|·)

p(s34|s24, s33)

p(y34|·)

p(s42|s32, s41)

p(y42|·)

p(s43|s33, s42)

p(y43|·)

p(s44|s34, s43)

p(y44|·)

Figure 4.9. Factor graph for the state-based probabilistic model for the rectangu-lar cellular array. Dashed lines show boundaries between cells. The computationsof the nodes within a cell are done by the BS of that cell. Any message passingthrough a cell boundary corresponds to actual message passing between corre-sponding BSs.

to be marginalized to compute the p(si,j |y) ∝ gi(si) is

g(s) = p(y, s)

=n∏

i=1

n∏j=1

p(yi,j |si,j )p(si,j |si−1,j , si,j−1), (4.51)

where s0,j and si,0 are dummy states: p(s1,j |s0,j , s1,j−1) = p(s1,j |s1,j−1) andp(si,1 |si−1,1 , si,0) = p(si,1 |si−1,1).

The factor graph for the factorization in (4.51) is depicted in Figure 4.9. Notethat this is a loopy graph and hence the sum–product algorithm is not guaranteedto give the exact APP. Nevertheless, we now describe the algorithm which willbe observed to provide good performance in practical settings. Uniform priordistributions p(xi,j ) are assumed on the input symbol constellations. Define the


set of states

pi,j = p1i,j , p

2i,j,

where

p1i,j = si−1,j ,

p2i,j = si,j−1 .

The system is modeled by transitions from pi,j to si,j . Note that not everytransition pi,j → si,j is possible. Similarly to the one-dimensional case, we saythat si,j is conformable with pi,j if there is transition from pi,j to si,j , i.e.,p(si,j |pi,j ) > 0 for some prior distribution on the xi,j s. The set of all configura-tions of pi,j that are conformable with si,j will be denoted by pi,j : si,j , and theset of all configurations of si,j that are conformable with pi,j will be denoted bysi,j : pi,j .

The message computations described next for cell (i, j) can be implementedat BS (i, j), simultaneously in parallel by all BSs. The message from p(yi,j |·) tosi,j is

µyi , j −si , j(si,j ) = p(yi,j |si,j )

= CN(yi,j ;m(si,j ), σ2),

where CN(y;m,σ2) is the distribution function of the complex Gaussian withmean m and variance σ2 . This message is computed only once given an observa-tion yi,j at BS (i, j).

Next, for convenience, define the following factor nodes corresponding to theconditional distribution functions in the factorization in (4.51):

c1i,j : factor node p(si,j+1 |si−1,j+1 , si,j );

c2i,j : factor node p(si+1,j |si,j , si+1,j−1);

di,j : factor node p(si,j |si−1,j , si,j−1).The messages between nodes si,j and di,j are internal calculations in BS (i, j).

The message from factor node di,j to variable node si,j , from (4.7), is

µdi , j −si , j(si,j ) =

∑∼si , j

p(si,j |si−1,j , si,j−1)2∏

k=1

µpki , j −di , j

(pki,j )

=∑pi , j

p(si,j |pi,j )2∏

k=1

µpki , j −di , j

(pki,j )

∝∑

pi , j :si , j

2∏k=1

µpki , j −di , j

(pki,j ) (4.52)


∑

p1i , j :si , j

p2i , j :si , j

2∏k=1

µpki , j −di , j

(pki,j ) (4.53)

=2∏

k=1

µpki , j −di , j

(ski,j ), (4.54)

where (4.52) is because p(si,j |pi,j ) is a constant if pi,j is conformable with si,j ,as prior distribution of xi,j s is uniform, and in (4.54)

µpki , j −di , j

(ski,j ) =

∑pk

i , j :si , j

µpki , j −di , j

(pki,j )

can be considered as a preprocessed message from pki,j to di,j . Note that (4.52)

and (4.53) are not, in general, equal because in (4.52) the summation is over p1i,j

and p2i,j , which conform with each other as well as with si,j , whereas in (4.53)

we also include p1i,j and p2

i,j , which do not conform with each other. Specifically,xi−1,j−1s in p1

i,j and p2i,j should be the same for the summation in (4.52), but

they may be different in (4.53). The additional terms in (4.53) lead to the sim-plification in (4.54), which results in a considerable saving in complexity. Themessage from variable node si,j to factor node di,j , from (4.6), is

µsi , j −di , j(si,j ) = µyi , j −si , j

2∏k=1

µcki , j −si , j

(si,j ). (4.55)

The message from variable node si,j to factor node cki,j for k = 1, 2 is

µsi , j −cmi , j

(si,j ) = µdi , j −si , jµyi , j −si , j

µcli , j −si , j

(si,j ), (4.56)

where l = 1, 2\k. The message in (4.56) is an actual message from BS (i, j) tothe corresponding BS. Finally, we need the message from di,j to pk

i,j for k = 1, 2,which also should be implemented as an actual message from BS (i, j) to adjacentcells. Using (4.7),

µdi , j −pki , j

(pki,j ) =

∑∼pk

i , j

p(si,j |pki,j , s

li,j )µsi , j −di , j

(si,j )µpli , j −di , j

(pli,j )

=∑si , j

µsi , j −di , j(si,j )

∑pl

i , j

p(si,j |pki,j , p

li,j )µpl

i , j −di , j(pl

i,j ) (4.57)

∝∑

si , j :pki , j

µsi , j −di , j(si,j )

∑pl

i , j :si , j

pli , j :pk

i , j

µpli , j −di , j

(pli,j ) (4.58)

α∑

si , j :pki , j

µsi , j −di , j(si,j )µpl

i , j −di , j(si,j ), (4.59)

where l = 1, 2\k, (4.58) is due to the fact that p(si,j |pki,j , p

li,j ) is a constant

for all si,j : pki,j and pl

i,j : si,j . The approximation in (4.59) is similar to (4.53)


in that we have extra terms in the summation with nonconforming pki,j and pl

i,j .Combining everything, the approximation (due to loops) of the marginal functiongi(si) is, from (4.8),

µsi(si) = µyi , j −si , j

(si,j )µdi , j −si , j(si,j )µc1

i , j −si , j(si,j )µc2

i , j −si , j(si,j ). (4.60)

For some related work on state-based method for rectangular grids the readeris referred to [50].

4.4.4 Decomposed graph approach

As an alternative to the state-based graph approach, let us remember the signalmodel in (4.47). It is seen that this model is the same as (4.16) in Example 2 ofSection 4.2.2. Therefore, for each observation yi,j , the conditional distributiongiven the contributing symbols has the same form as (4.17). As the input symbolsare independent, the joint distribution of all symbols and observations has thesame form as (4.18). Thus, a factor graph, in the form of Figure 4.4 can beobtained for the purpose of obtaining APPs of the symbols. For the rectangulararray model, corresponding to cell (i, j), there will be variable node xi,j andfactor node yi,j in this graph, and each factor node yi,j will be connected to thevariable nodes in the neighborhood: nyi , j

defined as in (4.48). Such a graph forthe rectangular model in Figure 4.7 is depicted in Figure 4.10.

Having the factor graph in Figure 4.10, we can perform message passing asdescribed in Example 2 in Section 4.2.2 in order to obtain estimates of thetransmitted symbols (the graph clearly has loops). Equations (4.19) and (4.20)are the x-to-y and y-to-x messages, respectively, except that now we have twoindices for each variable, denoting the two-dimensional location of the cell. Anytime a message is passed along an edge that crosses a dashed line in Figure 4.10,an actual message passing among corresponding BS is required. At termination,the posterior probability of the transmitted symbol xi,j at cell (i, j) is computedby combining all incoming messages, using (4.21).

In addition to its conceptual simplicity, the decomposed graph approach hasthe advantage that it does not require the regular positioning of the cells. Themethod can be applied to any irregular network shape, where each cell has anarbitrary number of neighbors in arbitrary directions.

4.4.5 Convergence issues: a Gaussian modeling approach

Unlike in the one-dimensional cellular models, where the graphs are trees, wecannot provide definitive convergence results for our two-dimensional cellularmodels, in general. It is well known that the sum–product algorithm is not guar-anteed to converge when there are loops in the graph. This is the Achilles’ heelof our approach to BS cooperation, and it is an area that requires much furtherstudy. However, some insights into the convergence properties can be obtainedfrom the Gaussian model, which we consider next.


x1,1 x1,2 x1,3 x1,4

x2,1 x2,2 x2,3 x2,4

x3,1 x3,2 x3,3 x3,4

x4,1 x4,2 x4,3 x4,4

p(y1,1|·) p(y1,2|·) p(y1,3|·) p(y1,4|·)

p(y2,1|·) p(y2,2|·) p(y2,3|·) p(y2,4|·)

p(y3,1|·) p(y3,2|·) p(y3,3|·) p(y3,4|·)

p(y4,1|·) p(y4,2|·) p(y4,3|·) p(y4,4|·)

Figure 4.10. Factor graph for the decomposed probabilistic model for the rect-angular cellular array model. Dashed lines show boundaries between cells. Thecomputations of the nodes within a cell are done by the BS of that cell. Anymessage passing through a cell boundary corresponds to actual message passingbetween corresponding base stations.

In Example 2 in Section 4.2.2, modeling the source symbols xj as circularlysymmetric complex Gaussian in (4.16) also leads to a tractable solution. In thatcase, all yis and xj s are jointly Gaussian, and also every local function in thefactorization in (4.18) is a Gaussian distribution. As a result, the messages onthe graph in Figure 4.10 will also be Gaussian.

Let the pair (µxj −yi, σxj −yi

) denote the mean-variance pair of the messagefrom xj to yi , and (µyi−xj

, σyi−xj) denote the mean-variance pair of the message

from yi to xj . Note that they are both means and variances of the variable xj .Using the properties of complex Gaussian distributions, the mean and varianceof the message from yi to xj can be shown to be

µyi−xj=

yi −∑

xl ∈ny i\xj

hi(xl)µxl−yi

hi(xj ), (4.61)

σyi−xj=

σ2 +∑

xl ∈ny i\xj |hi(xl)|2σxl−yi

|hi(xj )|2. (4.62)


The mean and variance of the message from xj to yi can be shown to be

µxj −yi=

µπxj

σπxj

+∑

k∈nx j\i

µyk −xj

σyk −xj

1σxj

+∑

k∈nx j\i

1σyk −xj

, (4.63)

σxj −yi=

⎛⎝ 1σπ

xj

+∑

k∈nx j\i

1σyk −xj

⎞⎠−1

, (4.64)

where (µπxj

, σπxj

) denotes the prior mean and variance of the symbol xj . At ter-mination, estimates of the mean and variance of the posterior distribution are

µxj=

µπxj

σπxj

+∑

i

µyi−xj

σyi−xj

1σxj

+∑

i

1σyi−xj

, (4.65)

σxj=

(1

σxj

+∑

i

1σyi−xj

)−1

. (4.66)

The goal here is to analyze how the means and variances evolve, as the y-to-xmessage updates in (4.61)–(4.62) and x-to-y message updates in (4.63)–(4.64)are computed iteratively.

Next, we provide results from [40] which say that the convergence of the vari-ances is always guaranteed, whereas the convergence of the means is closelyrelated to the spectral radius of an iteration matrix Ω. First, consider the con-vergence of the variances. Equations (4.62) and (4.64) show that the evolutionof the variances is independent of the means or the observations themselves.

To simplify notation define:

σi,j = σyi−xj.

Let the graph be for a system with n input variables x1 , . . . , xn and also n

output variables y1 , . . . , yn. For iteration t define the vector of variances ofmessages from y to x nodes

v(t) =[σ1,1 . . . σ1,n σ2,1 . . . σ2,n . . . σn,1 . . . σn,n

]T.

The following result is proven in [40], and is described in detail (but withoutproof) in [41]. This result, and the next one, make the simplifying assumptionthat the variances of all the observation variables (the yis) are unity.

Theorem 4.1 The sequence of vectors v(t) always converges to a unique fixedpoint for any v(0), i.e.,

limt→∞

v(t) = v∗.


Moreover, the sequence is monotonically decreasing under the initializationσ

(0)xj −yi

= 1.

Next, consider the convergence of the means in the updates in (4.61) and (4.63)assuming that the variance messages are fixed to the converged values:

v(t) = v∗.

Define

µi,j = µyi−xj(4.67)

and for iteration t

m(t) =[µ1,1 . . . µ1,n . . . µn,1 . . . µn,n

]Tthe channel matrix

H = diagh1,1 , . . . , h1,n , . . . , hn,1 . . . , hn,n,

where hi,j is the channel coefficient from source xj to observation yi . Let Ω be

Ω = H−1(Σx − I)H(I +D(Σf V∗−1Σf )−V∗−1)−1(Σf − I)V∗−1 , (4.68)

where

Σx = diag1n×n , . . . ,1n×n,V∗ = diagv∗,

Σf =

⎡⎢⎣In In . . . In

......

...In In . . . In .

⎤⎥⎦ ,

1n×n is an n× n block of ones, In is the n× n identity matrix, and D(·) is theoperator defined as D(A) = diagA11 , A22 , . . . , Ann for a n× n matrix A.

The following theorem provides a necessary and sufficient condition for theconvergence of the means. It was proven in [40] where it was shown to followfrom Theorem 5.3 in [7].

Theorem 4.2 The sequence of vectors m(t) converges to the fixed point

m∗ = (I + Ω)−1H−1y

for any m(0) if and only if the spectral radius ρ(Ω) < 1.

This theorem confirms that in some scenarios, where the spectral radius con-dition is not met, the sum–product algorithm will not converge. When the condi-tion is violated it is necessary to switch to another form of preprocessing, perhapsat a lower data rate using SCP – or one can declare an outage. Note that the


same issue arises for power control algorithms, where instability can also occurif the system loading is too high. Preliminary investigation of practical methodsto deal with this issue have been examined in [40], but much further work, bothpractical and theoretical, is required to characterize properly the conditions ofconvergence in more general settings, and to determine what to do about lack ofconvergence when it arises.

We have undertaken extensive numerical experiments using different channelparameter values. For a deterministic channel model, where the channel coeffi-cient for a mobile user is 1 to its own BS and α (cross-coupling factor) to anadjacent cell’s BS (symmetric deterministic channel model), we have observedthe following for the case of Gaussian symbols: at realistic SNRs less than 30 dB,and cross-coupling factors less than 1/2 (the typical cross-coupling between twoadjacent cells is quite low, usually less than 1/2), we have never observed lack ofconvergence of the sum–product algorithm. However, convergence is not guaran-teed at higher levels of the cross-coupling factor, when the SNR is high. Similarconvergence problems were also observed for the discrete symbol model, whenthe deterministic channel described above was utilized.

On the other hand, the convergence problems are greatly mitigated when wereplace the deterministic channel gains with independent, Rayleigh fading gainswith the same means as above. Thus, even if the network is symmetric withrespect to average gains, convergence problems almost completely disappear ifthe instantaneous gains are random (e.g., Rayleigh distributed).

From our numerical experiments, we found that when the sum–product algo-rithm failed to converge, it was typically due to a symmetric network realizationof channel coefficients. However, symmetry can be perturbed by noise. If theSNR is sufficiently low, the realizations of noise amplitudes are large enough toperturb the symmetry of the network. On the other hand, when the channel coef-ficients are modeled as independent random variables (e.g., complex Gaussian),the system lacks symmetry with high probability. In other words, the probabilityof a realization of h that is symmetric enough to cause failure of convergence isextremely small.

In a practical system, the channels of different mobile users are indeed inde-pendent, due to the fact that they are located in different cells. The simulationsin Figures 4.11–4.13 are for such a scenario: in each simulation realization, inde-pendent samples of channel coefficients hi,j (m,n) are generated. In those figures,no error floors are observed, even for very low uncoded bit error rates. There maystill be an error floor, but it is too low to be detected. Note that if there were aset of channel realizations that always cause convergence failure, irrespective ofSNR, then the probability of such a set must be very small, as it would providean error floor at this probability. We emphasize that here convergence means theconvergence to the true posterior probabilities of the symbols, not to the truevalues of the symbols. The true APP can still result in an incorrect estimate ofthe symbol, however if the true APP can be attained, the lowest possible errorrate is obtained.


0 4 8 12 16 20 24 2810

−5

10−4

10−3

10−2

10−1

100

α=0.5, SNR = 7 dB

α=0.5, SNR = 11 dB

α=1, SNR = 5 dB

Number of serial real number passings

Pb

SP: state−basedSP: decomposedInd. optimumSU lower bound

Figure 4.11. Probability of error of the algorithms and the single-user lowerbound as a function of the number of serial real number transmissions betweenBSs for node (2, 2) of a 4× 4 network ( c© 2008 IEEE).

In the next section, we present some numerical results that indicate the relativeperformance of the different schemes we have proposed so far.

4.4.6 Numerical results

We now present some numerical results [5] comparing the aforementionedapproaches for rectangular cellular arrays given in Figures 4.11, 4.12, and 4.13.In these simulations, a fading channel model is considered where each hi,j (m,n)is complex Gaussian distributed with zero mean and variance 1 if (m,n) = (0, 0)and variance α2 otherwise. Thus α2 represents the average power of the intercellinterference (ICI) from each neighbor. The additive noise zi,j is complex Gaus-sian with zero mean and variance σ2 . The signal to noise ratio (SNR) is definedas 1/σ2 . The transmitted symbols are binary and from the set −1, 1. For com-parison, the performance of individually optimum multiuser detection and thesingle-user lower bound is also given. The single-user lower bound is the perfor-mance of a system with a single user (with no interference) and multiple receivingbase stations. Each message passing requires an amount of serial real numbertransmissions among base stations, and in Figure 4.11 the performance is shownas a function of those transmissions. Figure 4.11 illustrates that performancevery close to the interference-free case can be achieved after 3–4 message passingsteps, with the decomposed model outperforming the clustered approach.

In Figure 4.12, the performance of the optimum receiver for a base station thatcannot communicate with other base stations is also shown. For the cooperative


3−5 0 5 10 15 20

10−4

10−3

10−2

10−1

100

α=0

α =0.25

α=0.25

α =0.5

α=0.5

α =1

α=1

SNR (dB)

Pb

Single−cell processingBCJRBP−clusteredBP−decomposedInd. optimumSU lower bound

Figure 4.12. Probability of error of the algorithms and the single-user lowerbound as a function of the SNR for cell (2, 2) of a 4× 4 network ( c© 2008 IEEE).

−5 0 5 1010

−4

10−3

10−2

10−1

100

α = 0.5

SNR (dB)

Pb

Pb

0 4 8 12 16 20 24 2810

−4

10−3

10−2

10−1

100

Number of serial real number passings

α =0.5, SNR = 9 dB

BCJRSP: state−basedSP: decomposedSU lower bound

SP: state−basedSP: decomposedSU lower bound

Figure 4.13. Probability of error of the algorithms and the single-user lowerbound as a function of the SNR and as a function of number of real numbertransmissions in series for cell (10, 10) of a 20× 20 network ( c© 2008 IEEE).

cases, the values plotted are the error probabilities after enough iterations haveoccurred to satisfy the convergence criterion. As the ICI power increases, itis observed that the distributed decoding algorithms not only can handle theICI, but they can also exploit the extra energy and diversity provided by it.


The error rate performance of the sum–product algorithms on the clustered anddecomposed graphs is very close to the single-user lower bound at low errorprobabilities. Thus, we observe a very large gain is possible from local messagepassing to reduce the ICI. The BCJR algorithm, implemented iteratively onthe columns and rows of the rectangular array, does not perform as well as thesum–product algorithms; a 0.5 dB gap is observed.

In Figure 4.13 performance is shown for a larger network. We observe thatthe performance on this 20× 20 network is essentially the same as in the smallernetwork of size 4× 4. The observation that the speed of convergence remainsroughly the same is explained by the fact the ICI is a local effect even thoughthe overall network size is growing.

Simplification of messages sent by factor nodesIn the decomposed graph approach, there are two types of computations: com-putation of variable-to-factor node messages in (4.19), and the computation offactor-to-variable node messages in (4.20). Upon examining these two typesof messages, one sees that the main cause of computation complexity of thisapproach is the computation of the latter: factor-to-variable node messages.

In [9], a simplification of the messages sent by the factor nodes was proposed.The key idea here is to recognize that the message µyi−xj

(xj ) is the individuallyoptimal soft MUD of xj given the observation yi and the prior distributions ofnyi\xj. If this is computationally unacceptable, suboptimal MUD methods

can be substituted for this purpose. An arbitrary choice of MUD may, however,not be suitable. The MUD should be able to incorporate the prior distributionsof nyi

\xj to produce a posterior distribution of xj . If the MUD uses priordistributions of all nyi

, then the prior information xj should be canceled in themessage to xj . This is because the information received from a node is not fedback to that node in factor graph methods. In [9], an iterative groupwise MUDwas considered.

4.4.7 Ad-hoc methods utilizing turbo principle

One approach to BS cooperation is to have the BSs share their soft (or hard)bit estimates and reconstruct the interference components at the output. Aftersubtracting the interference components from the observation, the BSs repeatthe decoding. This approach was suggested in [37] for a two-cell model. In thismodel, the received signal at a BS comprises a desired signal component andan interference component from other-cell mobiles. For a convolutionally codedsystem, the BSs perform single-user decoding, ignoring the interference compo-nent completely. Then the soft bit estimates are shared between the BSs, whichuse this information to reconstruct and subtract the interference componentsfrom their received signals. Repeating this procedure, an iterative “turbo” BS


cooperation method is obtained. The performance of this method was investi-gated for various quantization strategies and constellation sizes in [37]. Note,however, that this iterative approach is ad hoc, and is not based on graph algo-rithms. The turbo principle and sharing soft information with the adjacent BSswas also considered in [28]. Again, coding is included in the interference recon-struction and cancellation in [28]. The turbo principle is utilized for a generalcellular network. The BS cooperation methods in [28, 37] are not explicitly basedon algorithms on graphs. They are ad-hoc implementations of the turbo principleamong BSs which exchange soft decisions in order to improve their decisions.

4.4.8 Hexagonal model

All of the methods described for the rectangular cellular array model can beextended to the more realistic hexagonal array model. The positioning of thecells is shown in Figure 4.14: for example, the decomposed factor graph for thismodel is as in Figure 4.15.

4.5 Distributed transmission in the downlink

So far our focus has been on BS cooperation for the uplink of a wireless com-munication network. In this section, we will shift our attention to the downlinkof a wireless network. The scenario where a BS simultaneously transmits inde-pendent information to multiple uncoordinated users over the wireless channelcan be classified as a broadcast channel (BC) . We will first summarize the maininformation-theoretic results for a MIMO (vector) BC and present some practicaltransmission techniques proposed in the literature. Since wireless communicationnetworks for commercial applications are multicellular, we will then briefly dis-cuss the impact of ICI and some possible solutions. Finally, we will present turboBS cooperation in the downlink as a practical approach for providing high spec-tral efficiency in the presence of ICI.

4.5.1 Main results for the downlink of a single-cell network

Consider the downlink of a single-cell MIMO network where a BS with n antennasis transmitting information to m users each with a single antenna. Assuming thechannel is flat fading with no mobility, the vector of received signals at the usersis modeled as

y = Hx + z, (4.69)

where y =[y1 y2 · · · ym

]Tdenotes the vector of received signals at the

users, x =[x1 x2 · · · xn

]Tdenotes the transmitted signal vector, and H

is the m× n channel matrix with the (i, j) entry representing the channel gain

4.5 Distributed transmission in the downlink 111

BS11 BS12 BS13

BS21 BS22 BS23 BS24

BS31 BS32 BS33 BS34 BS35

BS41 BS42 BS43 BS44

BS51 BS52 BS53

MS11S11 MS12 MS13

MS21 MS22 MS23 MS24

MS31 MS32 MS33 MS34 MS35

MS41 MS42 MS43 MS44

MS51 MS52 MS53

Figure 4.14. Hexagonal cellular array model. The cells are positioned on a hexag-onal grid. Each cell has one active MS. The signal transmitted in one cell isreceived at that cell, and also six neighboring cells (except for edge cells). Dashedlines show boundaries between cells.

from the jth antenna of the BS to the ith user. Let hi denote the 1× n channelvector for user i. Then the (i, j) entry of H can be written hi(j). The elementsof the noise vector, z, are assumed to be independent zero-mean Gaussian dis-tributed random variables. Unless stated otherwise, we assume that both thebase stations and the users have perfect CSI.

This system model is classified as a BC in network information theory [14].Even though the capacity region of a general BC is still an open problem, for thespecial case of a degraded BC superposition coding [10] is shown to achieve thecapacity region. However, when the transmitter has more than one antenna, i.e.,n > 1, the system can in general no longer be modeled as a degraded BC. Rather,the capacity region of this vector Gaussian BC is shown to be equal to the dirtypaper coding (DPC) [12] rate region [56]. DPC is a nonlinear coding techniquebased on the observation that if the Gaussian interference is known noncausallyat the transmitter but not the receiver, under a transmit power constraint, theeffect of the interference can be precanceled. In the case of a vector Gaussian BC


x11 x12 x13

x21 x22 x23 x24

x31 x32 x33 x34 x35

x41 x42 x43 x44

x51 x52 x53

p(y1,1|·) p(y1,2|·) p(y1,3|·)

p(y2,1|·) p(y2,2|·) p(y2,3|·) p(y2,4|·)

p(y3,1|·) p(y3,2|·) p(y3,3|·) p(y3,4|·) p(y3,5|·)

p(y4,1|·) p(y4,2|·) p(y4,3|·) p(y4,4|·)

p(y5,1|·) p(y5,2|·) p(y5,3|·)

Figure 4.15. Factor graph for the decomposed probabilistic model for the hexag-onal cellular array model. Dashed lines show boundaries between cells. The com-putations of the nodes within a cell are done by the BS of that cell. Any messagepassing through a cell boundary corresponds to actual message passing betweencorresponding BSs.

under perfect CSI the BS can precalculate noncausally the interference createdby one user to the other. In this case for an arbitrary ordering of the users, usingthe DPC technique it is possible to encode the information of a user such thatit is not affected by the interference caused by previously encoded users.

The capacity region of a vector Gaussian BC described in (4.69) under transmitcovariance constraint Q = E[xxH ] S for positive semidefinite S (where A Bimplies that B−A is a positive semidefinite matrix) is given as [56]

C = qhull

⋃π∈Π

R(π,S, σ2 ,H)

, (4.70)

where qhull denotes the convex closure of the sets, π is an arbitrary permutationof user indices, Π corresponds to the set of all possible user permutations, σ2


denotes the variance of the elements of the noise vector z, and

R(π,S, σ2 ,H) =

(R1 , . . . , Rm )

∣∣∣∣∣Ri = log

(hi(∑i

l=1 Bπ (l))hHi + σ2

hi(∑i−1

l=1 Bπ (l))hHi + σ2

)

for some B1 , . . . ,Bm such that Bi 0 ∀i and S m∑

i=1

Bi

,

(4.71)

where hi is the 1× n channel vector for user i and π(l) denotes the index of theuser encoded in the lth position.

Correspondingly, the sum capacity of the vector Gaussian BC under totaltransmit power constraint P is computed as

Csum = maxQ :Q0,tr(Q)≤P

log(|σ2Im + HQHH |), (4.72)

where Im denotes an identity matrix of size m, | · | denotes a matrix determi-nant and tr(·) denotes the trace operator. In [24] it was shown that CSI at thetransmitter is essential in achieving the capacity gains of a vector Gaussian BCand at high SNR, with perfect CSI at the BS, the sum capacity scales linearlywith n provided that m > n.

The capacity achieving transmission strategy is a combination of nonlinearDPC and linear precoding (beamforming). The difficulties in implementing apractical DPC encoder have led to most attention being focused on suboptimallinear precoding schemes. In linear precoding the user data symbols are mappedto the transmitted signal vector via

x = Td, (4.73)

where d is the m× 1 vector of data symbols with dj , the data symbol intendedfor user j, taken from a finite constellation with E[|dj |2 ] = 1 and where the ithcolumn of the n×m beamforming matrix, ti , is the beamforming vector foruser i. It should be noted that the power allocated to the ith user is given byPi = tH

i ti .One approach for dealing with multiuser interference is to use zero-forcing

(ZF) beamforming, where T satisfies HT = D with D being a diagonal matrix.One solution is

T = HH (HHH )−1D, (4.74)

where D is determined according to the power constraint. The drawback ofZF beamforming is that transmit power might not be used as efficiently whenattempting to cancel multiuser interference completely.

An alternative linear precoding scheme is regularized channel inversion (RCI)where the beamforming matrix is of the form

T = HH (HHH + βI)−1D, (4.75)


where D is determined according to the power constraint and β is a regularizationparameter. For small β the RCI beamformer approaches the ZF beamformerwhile for large β the RCI beamformer tends towards the maximal ratio combiningbeamformer, the beamformer that maximizes the received signal strength whileignoring the resultant interference.

The power allocation to users is done based on an optimization criterion undera power constraint. Optimization problems considered in the literature typicallyinclude maximization of the sum rate under a total power constraint and min-imization of the total transmit power under individual minimum rate require-ments for each user. However, a total transmit power constraint might result inan unbalanced power output over the transmit antennas, which is undesirable inpractical systems since each antenna is limited by the linear region of the poweramplifiers in its own RF chain. Power allocation based on more practical perantenna power constraints has been considered [60].

Optimization problems involving RCI and related beamformers are challengingsince the beamformer vectors of the users are coupled. An alternative design cri-terion is to maximize the signal-to-leakage-and-noise ratio (SLNR), where leak-age refers to the interference caused by the user considered to other users [46].Leakage-based precoding is attractive since the optimization problem becomesdecoupled.

There are several works proposing practical nonlinear precoding techniquesbased on the DPC idea [16, 25, 31]. These works mainly use vector quantizationor trellis/lattice precoding approaches to achieve a performance close to DPC.

4.5.2 Main results for downlink of a multicellular network

In a multicellular network where several BSs simultaneously serve the users intheir respective cells, cochannel interference is the major performance limitingfactor. This is especially true for users near cell boundaries. This communicationscenario is referred to as the interference channel [2]. The capacity region of ageneral interference channel is still an open problem. There are some results forthe extreme cases of strong interference [13] and weak interference [6]. There arealso several inner and outer bounds, the best-known inner bound for discretememoryless interference channels being the Han–Kobayashi bound [22].

As discussed in Section 4.1, the traditional method for mitigating cochannelinterference in multicellular networks has been to use frequency planning suchthat neighboring cells use different frequency bands for transmission. If a suffi-ciently low frequency-reuse factor is used, one can ignore the effect of cochannelinterference and the communication scenario is reduced to a number of inde-pendent single-cell downlink problems. However, as the data rate requirementsfor next generation wireless networks increase, it has become evident that newparadigms to mitigate cochannel interference are required.

In order to increase the spectral efficiency of the system a frequency-reusefactor of 1 can be used, i.e., the whole frequency band is utilized simultaneously


in every cell. However, this results in a reduction in the achievable data rates dueto interference, especially for users near cell edges. At this point BS cooperationin the downlink is an attractive solution which actually takes advantage of theinterference to increase the spectral efficiency of the system.

Assuming that the BSs are connected to each other with high capacity linksover the backhaul, the cooperative system can be viewed as a virtual MIMO BCwith macrodiversity, i.e., transmit antennas are distributed geographically. Inthat case the problem is reduced to downlink transmission in a single-cell networkas discussed in Section 4.5.1, the only difference being that the transmissionschemes have to be implemented in a distributed manner.

Several works have considered simple and suboptimal linear precoding schemesfor the cooperative downlink. In [18], performance gains of cooperative zero-forcing beamforming were analyzed. In [26] several linear precoding techniquesfor downlink BS cooperation were compared in terms of sum rate per cell in theasymptotic regime. Most of the literature on downlink BS cooperation assumesthat the backhaul is very high capacity. In [36], however, a finite capacity back-haul was considered and the performances of several transmission schemes involv-ing DPC compared. Another assumption made in most of the literature is thatthe BSs can perfectly synchronize their transmissions. In practice, network-widesynchronization is very difficult to achieve. In [62] it was demonstrated that eventhough BSs can perform timing advancement perfectly such that the transmis-sions from different BSs arrive at the user at the same time, the interferenceis inevitably asynchronous. This asynchronicity causes significant performancedegradation for linear precoding techniques. The techniques considered are thenmodified to better handle asynchronous interference.

4.5.3 BS cooperation schemes with message passing

As we have highlighted previously, cooperative schemes that can be implementedin a distributed manner offer several advantages over schemes requiring a centralprocessing unit. Firstly, distributed schemes are more robust since they do nothave a central processing unit as a single point of failure. Secondly, they are morescalable since schemes requiring a central processing unit require new BSs to beconnected to the central processing unit as the network expands. Therefore itis of great interest to develop cooperative transmission and resource allocationschemes that only require local information exchange between BSs.

In this section, we discuss several iterative BS cooperation algorithms thatrequire information exchange between BSs. We first focus on distributed beam-forming and power allocation schemes in the literature. We then present a graph-based approach that requires only local information exchange between BSs.

Distributed beamforming and power allocation schemesIn [15] an iterative algorithm for computing the optimal beamforming vectorsand power allocation was presented for a cooperative multicellular system. The


algorithm iteratively finds the solution of the following optimization problem:

minimizeb∑

j=1

αj tr(THj Tj ), (4.76)

subject to: Γi ≥ γj , i = 1, 2, . . . , m, (4.77)

where Tj is the n×mj beamforming matrix used at the BS in the jth cell withmj users, b is the number of BSs (cells) in the network each with n transmitantennas, αj is the weighting factor of the transmit power of the jth BS, γj

denotes the target SINR constraint for user i, and Γi is the SINR of user i

expressed as

Γi =|hi,j (i)tH

j (i),i |2m∑

k=1k =i

|hi,j (k)tHj (k),k |2 + σ2

. (4.78)

In (4.78) hi,j denotes the 1× n channel vector between user i and BS j, j(i)denotes the index of the cell at which user i is located, tH

j (i),i is the beamformingvector used for user i by the BS in its cell, and σ2 is the variance of the Gaussiannoise at the user i.

Note that in this scheme BSs do not jointly transmit data to all the users inthe network, rather each BS transmits data to the users in its cell. However, thebeamforming vectors used by BSs are jointly chosen to achieve the target SINRsof the users, taking the ICI into account while minimizing the weighted transmitpower. The iterative algorithm utilizes uplink–downlink duality by solving theLagrangian dual of the optimization problem.

Alternatively, in [11] an iterative joint transmission and power allocationscheme was proposed. In the joint transmission scheme considered, a multicellprecoding approach is employed where the data of each user are available atall BSs and all BSs simultaneously serve each user using a beamforming vector.In this case the transmitted signal vector at BS j is expressed as xj = Tjd,where d is the data vector of all the users in the network and the ith column ofbeamforming matrix Tj is the beamforming vector used by BS j for user i.

The optimization problem of maximizing the sum rate of the users underindividual transmit power constraints at each BS is difficult to implement ina distributed manner and requires channel knowledge to be shared by all BSs.As a result, the authors proposed a heuristic beamforming and power allocationscheme that is fully distributed and requires only statistical channel knowledge.The scheme utilizes the leakage-based beamforming approach described in Sec-tion 4.5.1 to simplify the optimization of the beamforming vectors. Furthermore,the beamforming vectors were selected to maximize the average SLNR averagedover channel realizations. The power allocation proposed is also heuristic, allo-cating more of the transmit power to the user with the best channel gain.


In [61], an iterative beamforming scheme for multicellular networks is pro-posed. The system model assumed is similar to the one in [15], where BSs donot employ multicell precoding, each BS serves a single user in its cell using abeamforming vector and the beamforming vectors are chosen such that observedICI is taken into account. The proposed scheme can be implemented in a dis-tributed manner as it only requires local channel knowledge. The idea is to selectthe beamforming vector for each BS as a linear combination of the zero-forcingbeamformer and maximum ratio combining beamformer (which maximizes thereceived signal power ignoring the interference generated at other users). Thecombining weights are iteratively updated based on feedback from the users,until a Pareto optimum point is reached.

Cooperative beamforming based on factor graphsWe now present a cooperative downlink beamforming approach that can beimplemented in a truly distributed manner based on message passing on graphs.We will first demonstrate how the downlink beamforming problem can be for-mulated as a virtual LMMSE estimation problem [42]. Once this is done we willbe able to make use of the message passing algorithms developed for the uplinkin the earlier parts of this chapter.

We focus on a cooperative downlink beamforming scenario where a cellularnetwork with n cells employs an orthogonal multiple access scheme within eachcell so that users do not experience intracell interference. However, since a fre-quency reuse factor of 1 is used, users will experience interference from neigh-boring cells. For simplicity, it is assumed that each BS and user has only oneantenna. The vector of received signals at the users is as given in (4.69) wherethe data vector of the users is mapped to the transmitted signal vector usingjoint linear precoding as in (4.73).

We wish to implement regularized channel inversion beamforming as discussedin Section 4.5.1. Define

T = HH (HHH + βI)−1 , (4.79)

where β is a regularization parameter [45], and the beamforming matrix is writtenas

T = TD. (4.80)

The diagonal matrix D denotes the power allocation matrix whose diagonalscorrespond to power allocated to the corresponding user under a given power(total or per BS) constraint.

The key observation is that defining d = Dd, the transmitted signal x = Tdcan be seen as the LMMSE estimate of some vector u under the signal model

d = Hu + w, (4.81)

where u and w are n× 1 vectors of i.i.d. random variables with zero mean andvariance 1 and β, respectively. Note that u and w have no physical relationship


with the original beamforming problem and also that the problem in (4.81) isquite different to the uplink–downlink duality concept used to simplify the down-link problem [55]. With the observation that the downlink beamforming problemcan be seen as a virtual LMMSE estimation problem, one can employ distributedLMMSE estimation techniques such as the distributed Kalman smoothing algo-rithm described in Section 4.3.2 for one-dimensional cellular networks and tech-niques based on the sum–product algorithms for two-dimensional cellular net-works presented in Section 4.4.5.

We first consider the one-dimensional linear cellular array depicted in Fig-ure 4.1 which models the communication scenario with BSs placed evenly onthe side of a highway or subway tunnel or access points along a corridor. Thechannel matrix entries hi,j are of the form

hi,j =

hi(k), j = i + k,

0, |i− j| > 1,(4.82)

where i, j ∈ 1, 2, . . . , n and k ∈ −1, 0,+1. One can take advantage of thelocal connectivity of the network to implement a distributed beamforming algo-rithm. Assuming that appropriate power allocation is already performed, thedata symbol vector d is treated as the observation vector from which the trans-mitted signal vector x is obtained as the LMMSE estimate of u.

Due to the Markov structure of the problem, one can apply the message passingalgorithm described in Section 4.3.2 for the uplink problem with Gaussian inputsymbols. Defining the state vector for cell i as si =

[ui−1 ui ui+1

]T, the state-

space model is

si+1 = Af si + bf ui+2 , (4.83)

si−1 = Absi + bbui−2 , (4.84)

di = hisi + wi, (4.85)

where Af , Ab , bf , and bb are defined in Section 4.3.2, hi =[hi(−1) hi(0) hi(1)

]with u0 = un+1 = h1(−1) = hn (+1) = 0. Running

a forward and backward Kalman estimator based on this state-space modeland combining the two estimates, we obtain a forward–backward beamformingalgorithm for the cooperative downlink.

Assuming the virtual data vector u is Gaussian distributed (an assumptionwe are free to make since u does not have a physical meaning), the LMMSEestimate is u = E[u|d], i.e., the conditional mean vector of the jointly Gaussianconditional density f(u|d). As a result, BS i can find the signal that it shouldtransmit by computing the mean of the marginal distribution, f(ui |d), using thesum–product algorithm described in Section 4.3.2 running on the factor graphdepicted in Figure 4.6. The steps of the algorithm are summarized below [43].


Combine the estimates: Having computed both sfi|i and sb

i−1|i , they are com-bined using

si = Mi

((Mf

i|i)−1 sf

i|i + (Mbi−1|i)

−1 sbi−1|i

), (4.99)

Mi =((Mf

i|i)−1 + (Mb

i−1|i)−1 − Ii

)−1, (4.100)

where Ii = I3 for n = 2, . . . , n− 1 and I1 and In are defined in (4.88). Thetransmitted signal from the ith BS, xi , is set to be the middle element of thevector si .

It should be pointed out that the algorithm described above has a fully dis-tributed nature requiring only local information exchange between the BSs. Priorto running the algorithm, however, the power allocation to users is assumed tohave been done (D is known), and this might well require network-wide know-ledge of quantities such as the channel gains. Fortunately, since the channel gainstypically change much more slowly than the data symbols, global sharing of thenetwork knowledge might still be feasible at this slower time scale.

Another point we would like to emphasize is that, as stated in Section 4.3.2,since the factor graph depicted in Figure 4.1 is free of loops, the message passingalgorithm described above is guaranteed to converge to the optimal solution.

It should further be noted that the delay experienced by the BSs at the edgesof the cellular array grows linearly with the size of the array. In fact, the pre-coding delay experienced by BSs is location-dependent with the minimum delayexperienced by the BS in the middle of the array. In [43] a suboptimal limitedextent distributed beamforming algorithm was proposed based on the observa-tion that due to the local connectivity structure of the channel, the informationsent by BS i is expected to be less important for BS j if |i− j| is sufficiently large.Therefore, one can achieve a fixed delay, if the extent of the information exchangebetween BSs is limited. In the proposed limited extent beamforming algorithm,each BS starts by computing a ‘self-estimate’ based on di using (4.86) and (4.87).Then this information is shared with both neighbors and received estimates arecorrected using forward and backward correction equations (4.93)–(4.98). Afterτ phases of information exchange between the BSs, forward, backward and self-estimates are combined and the middle element of the state vector si is then anapproximation to xi . With this algorithm, the precoding delay experienced byall BSs is τ . Numerical results in [43] demonstrate the clear tradeoff between theperformance and the precoding delay.

Finally, we will discuss the extension of the proposed distributed beamformingalgorithm to two-dimensional networks. As an example, we will consider a hexag-onal network with n = 7 cells, a special case of the hexagonal network depicted inFigure 4.14. As in the one-dimensional linear array case, the downlink beamform-ing problem can be posed as the virtual LMMSE problem of estimating a virtualdata vector u from the observation vector d. Assuming the virtual data vectoris Gaussian distributed, the LMMSE estimate corresponds to the mean vector


of the MAP estimate, i.e., u maximizing the conditional distribution f(u|d). Asa result, one can use the sum–product algorithm on the factor graph in Fig-ure 4.15. For the downlink, the same factor graph, in which variable nodes nowrepresent ui and the factor nodes represent the local function fdi

= f(di |u). Inaddition, assume that for each variable node there is a pendant factor node thatis connected only to that variable node, fui

= p(ui) = N(ui ;σfu i−ui

, µfu i−ui

),denoting the prior distribution of the virtual data symbols.

Since all the distributions are Gaussian, the messages passed between vari-able and factor nodes are actually the mean vector and covariance matrix of theunderlying distribution. Assuming a flooding schedule [30] where at each iter-ation the messages on the graph are updated simultaneously, the sum–productupdate equations for kth iteration are summarized as follows [43]:

µ(k)fd i−uj

=

di −∑

ul ∈nfd i\uj

hi,l µ(k−1)uk −fd i

hi,j, (4.101)

σ(k)fd i−uj

=

β +∑

ul ∈nfd i\uj

(hi,l)2σ(k−1)fd i−uj

(hi,j )2 , (4.102)

µ(k)uj −fd i

= σ(k)uj −fd i

⎛⎝ ∑f∈nu j

\fd i

µ(k)f−uj

σ(k)f−uj

⎞⎠ , (4.103)

σ(k)uj −fd i

=

⎛⎝ ∑f∈nu j

\fd i

1

σ(k)f−uj

⎞⎠−1

(4.104)

with initialization as

µ(0)uj −fd i

= 0, σ(0)uj −fd i

= 1 (4.105)

for all i, j for which uj is connected to fdi, nk denoting the set of nodes connected

to node k on the factor graph and hi,j denoting the channel gain between thejth BS and the user in cell i. After the termination conditions are met at stepm, the transmitted signal from BS j is obtained as

x(m )j = σ

(m )uj −fd

⎛⎝ ∑f∈nu j

µ(m )f−uj

σ(m )f−uj

⎞⎠ (4.106)

with

σ(m )uj −fd

=

⎛⎝ ∑f∈nu j

1

σ(m )f−uj

⎞⎠−1

. (4.107)


Since the factor graph in Figure 4.15 contains loops, the convergence of thesum–product algorithm is not guaranteed. However, since the underlying distri-butions are all Gaussian, following the discussion in Section 4.4.5 it can be shownthat the variance updates always converge [40, 41]. The necessary and sufficientcondition for the convergence of the mean updates is that the spectral radius ofthe iteration matrix in (4.68) is strictly less than 1. As observed for the uplinkproblem, the convergence conditions are violated when the SNR is high and theinterference created by the channel is strong. In [40], two approaches to improvethe convergence of the algorithm for the downlink were proposed. In the firstapproach, a tunable parameter ε is introduced that multiplies the regularizationparameter β. The value of ε is chosen so that the sum–product algorithm con-verges or converges at the desired rate. The disadvantage of this approach is thatthe sum–product algorithm no longer computes the desired LMMSE estimatesresulting in some loss in performance. In the second approach, a switched beamsystem is used where a cell is divided into angular sectors and each sector iscovered by a narrow beam generated by a directional antenna. Comparing thesignal strength from all sectors, the BS selects the best beam to transmit datato a user. In this way interference is reduced, and the loops in the factor graphcan be reduced or eliminated.

4.6 Current trends and practical considerations

Much work has demonstrated the huge performance gains that are possible whenBSs cooperate to receive signals from mobile users on the uplink, and to senddata to mobile users on the downlink. In this chapter we have examined methodsfor implementing BS cooperation in a distributed manner via message passing.These message passing techniques require communication between neighboringBSs only and have processing and communication requirements that remain con-stant with increasing network size. They are, in some sense, the natural algo-rithms to use in large cellular networks.

However, in terms of both theoretical analysis and practical implementation ofthese turbo-style approaches, we have only scratched the surface. We list belowsome exciting areas where much work is still to be done.

(1) Convergence issues. Many questions are still unanswered regarding the con-vergence of the sum–product algorithm on graphs with loops, as mentioned inSection 4.4.5. A more thorough treatment of convergence is required in orderto understand the limitations of the distributed BS processing techniquespresented in the chapter and to find methods to improve the convergenceproperties.

(2) Limited backhaul traffic. Backhaul traffic is the traffic between BSs requiredto implement cooperative schemes. For a practical system, the backhaul traf-fic is not unlimited. Given a certain limit on the backhaul traffic, can we still

References 123

get the performance gains we see in this chapter? How should the messagepassing techniques be modified to reduce the backhaul traffic load?

(3) Synchronization. Perfect synchronization of BSs in the downlink has beenassumed in this chapter. We have also assumed it for the uplink, althoughthe assumption may be less critical there. What is the impact of synchroniza-tion errors on the performance? It may be possible that a synchronizationimperfection that is tolerable in conventional single-cell processing may havemore degrading effects in the case of BS cooperation.

(4) Imperfect channel information. We have assumed that perfect CSI is availableat the BS transceiver. What will be the impact of imperfections in channelestimates on the attainable gains due to base station cooperation? What willbe the impact on the convergence of the proposed methods?

(5) Coded systems. We have not considered error control coding in this chapter.In practice, common decoders are often based on graphical methods and itwould be possible to combine the factor graphs we use for joint detectionof mobile users and the graphs which model the code constraints, to formone large graphical model on which message passing algorithms could beapplied. What will happen to the convergence properties of the sum–productalgorithm on this space-time factor graph? What are the other issues toconsider for distributed decoding in a cellular system?

(6) Distributed resource allocation. If we are allocating channels to mobile usersin order to maximize the throughput, how can this be done in a BS-cooperating network in a distributed manner?

Some excellent work has already begun to answer some of these questions:channel estimation and coding [63], limited backhaul traffic and coding [28, 37],and resource allocation [1]. However, many questions remain unanswered andnumerous challenges must be overcome if we are to realize the full potential ofturbo-based methods for BS cooperation.

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5 Antenna architectures fornetwork MIMO

Li-Chun Wang and Chu-Jung Yeh

5.1 Introduction

In conventional cellular systems, cochannel interference is a serious issue thatdegrades system performance. The spectral efficiency of cellular networks is fun-damentally limited by the interference between cells and users sharing the samechannel for both downlink and uplink. Generally, there are two kinds of co-channel interference: intracell interference and intercell interference.

The intracell interference can be resolved by allocating orthogonal frequencyresources. To mitigate intercell interference, there are several general approachessuch as frequency reuse, cell sectoring, and spread spectrum transmission. Themost commonly used technique is to avoid using the same set of frequencies inneighboring cells. This approach leads to the decrease of the number of availablechannels within each cell.

Universal frequency reuse, i.e., reuse factor of 1, is preferred for future broad-band wireless communications systems, such as the Third Generation Partner-ship Project (3GPP) long-term evolution (LTE) and worldwide interoperabilityfor microwave access (WiMAX). In the orthogonal frequency-division multipleaccess (OFDMA) systems, which do not have processing gain as the code-divisionmultiple access (CDMA) system, how to achieve the goal of both universal fre-quency reuse and reducing intercell interference is a key challenge.

The concept of fractional frequency reuse (FFR) has been suggested to improvespectrum efficiency by applying reuse partition techniques, in which the innerregion of the cell is assigned the whole frequency spectrum and the outer regionis only assigned a small fraction of the frequency spectrum [1]. The capacityand outage rate of an FFR-based OFDMA cellular system with proportional fairscheduling was studied in [2]. To analyze the joint effect of the FFR factor, the cellinner region, and the bandwidth assignment on cell throughput, an optimizationproblem was formulated in [3]. The resource allocation problem in an FFR-basedmulticell OFDMA system was translated to a graph coloring problem in [4]. In[5] FFR was applied to a tri-sector cellular OFDMA system. It was shown thatthe intercell interference is reduced and cell throughput was improved by the


5.1 Introduction 129

proposed subcarrier scheduling according to location or signal-to-interference-plus-noise ratio (SINR) of users. Under a similar FFR-based tri-sector cellularOFDMA system, an interference mitigation scheme using combining partial reuseand soft handover was proposed in [6].

The network multiple-input multiple-output (MIMO) technique has becomea hot topic which aims to mitigate the intercell interference by coordinatingthe multicell transmission for downlink or reception for uplink among a fewgeographically separated antennas (base stations, BSs). To effectively reduce theintercell interference, the network MIMO requires a reliable and high-speed back-haul connection between BSs to pass the channel state information (CSI) andmobile messages between those cooperating cells. With full BS cooperation, thedownlink transmission can be modelled as a multiuser MIMO broadcast system[7–9]. The interstream interference-free transmission of a MIMO broadcast sys-tem is now translated to intercell interference cancelation in a multicell networkMIMO system. For downlink transmission in a cellular network, the concept ofcoprocessing at the transmitting end was proposed in [10]. In [11] a distributednetwork beamforming in a cellular system was proposed and its performancewas analyzed based on Wyner’s circular array model [12]. Coordinated strate-gies with grouped interior and edge users based on Wyner’s circular array modelwere studied in [13]. Downlink network MIMO transmission with multiple trans-mit and receive antennas under a general channel model was analyzed in [14–17].In [18] downlink network MIMO coordination was compared with a denser BSdeployment. For uplink network MIMO, coordinated BSs perform the recep-tion of user signals within their coverage area and suppress interference betweenusers by means of coherent linear (received) beamforming across BSs. The spec-tral efficiency gain with different numbers of neighboring rings with which a BSis coordinated was investigated in [19]. In [20], the data rates of users assignedto each coordinated cluster were further chosen to be proportionally fair.

A fundamental question for network MIMO is: how many cells should be coor-dinated to provide adequate SINR performance. Most of the studies on networkMIMO assumed a global coordination which can eliminate the intercell interfer-ence completely. However, it is impractical to have cooperation (or coordination)among too many cells. The huge computational complexity and synchronizationneeded with a large number of cells are quite challenging. In practice, only alimited number of BSs can coordinate and jointly process the received or trans-mit signals. For uplink network MIMO, an isolation-based user grouping algo-rithm to optimize the capacity under a strongly constrained backhaul betweenseven coordinated sites was proposed in [21]. An uplink BS coordination with adynamic BS clustering approach was investigated in [22]. This approach leadsto significant sum rate gain compared with the static BS clustering schemesproposed in [19, 20]. For the downlink network MIMO, the isolation-based usergrouping algorithm used in [21] was modified to the downlink scenario for capac-ity improvement under a limited backhaul [23]. In [24], downlink coordinationwith limited distributed antenna arrays was compared with centralized antenna

130 Antenna architectures for network MIMO

arrays. Under a fixed number of antennas per cell, the impact of different num-bers of sectoring per cell was evaluated in [25]. Also the impact of the numberof coordinated cells was investigated.

The objective of this chapter is to discuss a FFR-based network MIMO inter-ference cancelation scheme for a downlink multicell system. Although both FFRand inter-BS coordination are being considered as possible intercell interferencecancelation techniques in both WiMAX and LTE, combining network MIMOwith FFR to mitigate the intercell interference is still an interesting problem.Due to the geographical distribution of cells and mobiles, the potential advan-tages of network MIMO can be further explored by utilizing different frequencypartition and cell sectorization instead of complex joint multicell transmissiontechniques. In addition, a group of coordinated cells still cause interference inthe neighboring coordinated groups. This intergroup interference (IGI) should betaken into account for network MIMO under arbitrary coordinated sizes. In thischapter, we will also explore the potential gain of network MIMO by using a nearminimum number of coordinated cells, i.e., only three cells. In a cellular systemwith an omni-directional antenna, the received signal quality is severely affectedby IGI under three- and seven-cell coordinated network MIMO. However, theproposed FFR-based three-cell network MIMO architecture can approach thetraditional seven-cell network MIMO with omni-directional antenna.

The rest of this chapter is organized as follows. In Section 5.2 we define thesystem model. In Section 5.3, we briefly review the concept of network MIMO.In Section 5.4 we examine the IGI issue for network MIMO systems. In Sec-tion 5.5, we present the proposed three-cell network MIMO architecture withFFR. In Section 5.6, we show numerical results and give concluding remarks inSection 5.7.

5.2 System model

We consider a cellular system with Ncell = 19 cells, where the center cell has two-tier neighboring cells, as shown in Figure 5.1. For simplicity, we assume that eachBS of a cell has a single transmit antenna and each mobile user has a single receiveantenna. For a cellular system with three-sectored cells, the number of transmitantennas per sector is also 1. The sectors are created using directional antennaat the BS. The antenna gain pattern used for each BS sector is specified as

A(θ)dB = −min

[12(

θ

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, Am

], (5.1)

where A(θ)dB is the antenna gain measured in decibels in the direction θ andθ ∈ [−180, 180] is the direction of the mobile user with respect to the broadsidedirection of the considered BS. The 3 dB beamwidth θ3dB is the angle at whichthe antenna gain is 3 dB lower than the peak (the broadside direction). Theparameter Am = 20 dB is the maximum attenuation for the sidelobe.

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The general transmission model for mobile user k served by BS j is

yk = hk,jxj +∑

i =j, i∈Ihk,ixi + nk , (5.2)

where hk,j is the channel response between mobile k and BS j, xj is the trans-mitted signal from BS j, nk is the additive noise at the kth mobile, and I is theinterference set for mobile k. The detailed channel response is

hk,j = αk,j

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(dk,j

dref

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, (5.3)

where αk,j is the fast (Rayleigh) fading between BS j and mobile k, βk,j is thelog-normal shadowing from BS j to mobile k, A(θk,j ) is the antenna gain formobile k with respect to BS j, dk,j is the distance between BS j and mobilek, dref is a reference distance, and µ is the path-loss coefficient. The value ofA(θk,j ) is a function of θk,j based on (5.1) for the sectorized cell and A(θk,j ) = 1for an omni-directional transmission cell. Note that the reference distance dref

is the distance between the cell center and the cell vertex.The received SNR of mobile k from BS j is

SNRk,j = |αk,j |2 βk,j A(θk,j )(

dk,j

dref

)−µ

Γ, (5.4)

where the reference SNR Γ represents the interference-free SNR defined as theSNR measured at the cell boundary (i.e., at the reference distance dref ) for onlyconsidering path-loss and ignoring shadowing and fast fading. The parameter Γcaptures the effect of various channel and antenna parameters including transmitpower, cable loss, transmit and receive antenna heights, thermal noise power, andother link budget parameters. Noise power is normalized to unity. The reference


SNR Γ = 18 dB for a BS-to-BS distance RB2B = 2 km macrocellular system with30 watts transmit power in 1 MHz bandwidth [26]. In this case, the referencedistance dref

∼= 1.1547 km. For mobile k served by BS j, the corresponding SINRof mobile k can be expressed as

γk,j =SNRk,j

1 +∑

i =j, i∈I SNRk,i(5.5)

and the corresponding Shannon capacity is given by log2(1 + γk,j ) bps/Hz.

5.3 Network MIMO

Network coordination is a means to eliminate the intercell interference andimprove spectral efficiency in a downlink multicell system [14, 15]. With a high-speed backhaul, the BSs can be connected and synchronized. Assume that allBSs can cooperate and report CSI at each BS via the central coordinator. Withfull BS cooperation, the downlink transmission can be modeled as a multiuserMIMO broadcast system. Consider a network MIMO system with M coordi-nated BSs (each site with a single transmit antenna), each of which transmits adata stream to its own target mobile station. The received signal is given by

Y = Hx + n, (5.6)

where H = [hk,j ]M×M denotes the channel matrix with element hk,j beingthe channel response between mobile k and BS j as defined in (5.3), and ndenotes the noise vector. The transmitted signals vector is denoted by x =Ws = [w1 . . .wM ][s1 . . . sM ]T , where sk is the kth mobile user’s data symbol,wk = [w1,k . . . wM,k ] is the corresponding precoding weight column vector, and(·)T is the transpose operation. For a network MIMO system, the antenna out-put of the jth transmission site is a linear combination of M data symbols, i.e.,xj =

∑Mk=1 wj,k sk . The received signal of mobile k can be written as

yk = sk ||hkwk ||+M∑

i=1, i =k

si ||hkwi ||+ nk , (5.7)

where hk = [hk,1 . . . hk,M ] is the channel vector of the kth user.Let pk = E[|sk |2 ] denote the average power of symbol sk . According to the

network MIMO principle, the following constraint should be satisfied: E[|xj |2 ] ≤PBS for each BS j = 1, . . . ,M .⎡⎢⎣ |w1,1 |2 · · · |w1,M |2

.... . .

...|wM,1 |2 · · · |wM,M |2

⎤⎥⎦⎡⎢⎣ p1

...pM

⎤⎥⎦ ≤ PBS1M , (5.8)

where PBS is the maximum transmit power at each BS and IM is an M × 1vector will all one elements.

5.3 Network MIMO 133

It is well known that dirty paper coding (DPC) can achieve the capacity of amultiuser MIMO broadcast system. Due to the high complexity of DPC, somesuboptimal but practical schemes were proposed. In this chapter, we considertwo suboptimal network MIMO schemes, including zero-forcing (ZF) and zero-forcing dirty paper coding (ZF-DPC).

5.3.1 ZF network MIMO transmission

The goal of ZF transmission is to invert the channel to obtain HW = I. Thisfunction can be achieved by using the pseudo-inverse of the channel matrix asthe weight matrix W. The received signal vector is hence given by

Y = Hx + n = HWs + n = s + n. (5.9)

For the network MIMO system with per-base power constraint (5.8), the objec-tive is to maximize the minimum rate among the coordinated cells subject tothe power constraint. The corresponding solution is the maximum equal rateassignment [15]

pk =PBS

maxj [WW∗](j,j )=

PBS

maxj

∑k |wj,k |2

, for all k. (5.10)

Therefore, the corresponding mobile’s rate is given by log2(1 + pk/σ2) bps/Hzamong all coordinated cells, where σ2 represents the noise power. Note thatthere is an excessive transmission power penalty for ZF transmission due to therequired interference cancelation power for constructing weight matrix W.

5.3.2 ZF-DPC network MIMO transmission

ZF-DPC transmission constructs the linear weight matrix W = Q∗ through theQR decomposition of the channel matrix H = LQ, where L is a lower triangularmatrix, Q is a unitary matrix with QQ∗ = Q∗Q = IM , and (·)∗ is the conjugatetranspose operation. The received signal is written as

Y = Hx + n = LQQ∗s + n = Ls + n (5.11)

and the corresponding kth mobile’s received signal is yk = Lk,k sk +∑i<k Lk,isi + nk . Note that the weight matrix W = Q∗ ensures that no inter-

ference is from symbols with indices i > k. The remaining interference fromsymbols i < k is taken care of by DPC successive interference cancelation.Based on the result of ZF transmission, if we set pk = p for all k, the per-site power constraint (5.8) becomes E[|xj |2 ] = [WW∗](j,j )p =

∑k |wj,k |2p ≤ PBS

for all transmitted signal xj . Recall that the weight matrix W = Q∗. We have[WW∗](j,j ) = [Q∗Q](j,j ) = [I](j,j ) = 1. Thus, we can set pk = PBS for each coor-dinated BS. Given the received signal in (5.11), mobile k can achieve the ratelog2(1 + |Lk,k |2pk/σ2) bps/Hz.


5.4 Effects of intergroup interference

5.4.1 SINR analysis

When applying network MIMO to group coordinated cells in a multicellularsystem, the effects of IGI need to be taken into account. That is, a group ofcoordinated cells still cause interference in the neighboring coordinated groupsof cells even if the intragroup interference has been canceled via network MIMOtransmission. Consider a cell with a two-tier surrounding cells layout under M -cell network MIMO coordination. There are some interfering neighboring cellswhich belong to its corresponding M -cell network MIMO group Gi for i ∈ IG ,where IG is the index set of the interference group. For a M -cell network MIMOgroup Gi , the transmit antenna output of BS a ∈ Gi is

xGia =

M∑b=1

wGi

a,bsGi

b , (5.12)

where [wGi

a,b ]M×M is the precoding weight designed for M -cell network MIMOgroup Gi and sGi

b is the data symbol of mobile b ∈ Gi . The SINR of mobile k

considered in (5.7) becomes

γIGIk =

pk ||hkwk ||2

1 +∑

i∈IG∑

a∈Gi

∑Mb=1 pGi

b |hGi

k,awGi

a,b |2, (5.13)

where pGi

b is the data symbol power for mobile b ∈ Gi and hGi

k,a is the channelresponse between the considered mobile k and the interfering BS a ∈ Gi . As in(5.5), the noise power has been normalized to unity. The kth mobile’s rate is nowlog2(1 + γIGI

k ) when considering the effect of IGI in a multicellular system. Byapplying the ZF-based network MIMO coordination, the SINR of (5.13) becomes

γIGIk,ZF =

pk

1 +∑

i∈IG∑

a∈Gi

∑Mb=1 pGi |hGi

k,awGi

a,b |2, (5.14)

where pGi

b = pGi for all b can be found via (5.10). For network MIMO withZF-DPC transmission, the corresponding SINR is

γIGIk,ZFDPC =

PBS |Lk,k |2

1 +∑

i∈IG∑

a∈Gi

∑Mb=1 PBS |hGi

k,awGi

a,b |2. (5.15)

5.4.2 Example of IGI: network MIMO with omni-directional cell planning

In this subsection, we show examples of IGI in the network MIMO system.We consider a conventional cellular network with omni-directional cell planning.Figure 5.2 shows IGI for the three-cell and seven-cell network MIMO systems.Take cell 0 as an example, it forms a three-cell network MIMO group G0 withcells 4 and 5. The intragroup interference coming from cells 4 and 5 is can-celed via network MIMO transmission. However, the remaining two-tier cells still

5.4 Effects of intergroup interference 135

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cause interference to cell 0. In this case, IG = G1 , G2 , . . . , G8, where the corre-sponding cells in each group are G1 = 1, 2, 8, G2 = 3, 10, 11, G3 = 12, 13,G4 = 14, G5 = 15, 16, G6 = 6, 17, 18, G7 = 7, and G8 = 9. There arestill four first-tier interfering cells and all the second-tier interfering cells. Notethat all interferers transmit coordinated signaling via M -cell network MIMO.With seven-cell network MIMO, the coordinated partners of cell 0 are cells 1,2, 3, 4, 5, 6. The IGI from the second-tier cells is still unavoidable even if theinterferences from surrounding cells 1, 2, 3, 4, 5, 6 are canceled.

Figure 5.3 shows the effects of IGI for network MIMO with ZF-DPC transmis-sion. We first consider the advantage of using network MIMO. The dotted linerepresents the SINR for cells with omni-directional antenna. The SINR is evalu-ated according to (5.5) with I = 18 neighboring cells. We consider 19-cell, 7-cell,and 3-cell network MIMO without IGI (denoted by solid lines). In this case, thereceived signal quality is averaged over M coordinated cells. Clearly, the receivedsignal quality is largely improved via network MIMO. More importantly, we findthat the SINR performance of seven-cell network MIMO is close to that of 19-cellnetwork MIMO. This result implies that the coordination size M = 7 is suffi-cient when designing network MIMO systems. However, this result is obtainedby ignoring the effects of IGI. The received signal quality will be greatly affectedwhen interference from the other groups is considered. The dashed lines denotethe SINRs for 3-cell and 7-cell network MIMO with IGI as shown in Figure 5.2.The SINR degradation for 7-cell network MIMO is about 14 dB and that for3-cell network MIMO is about 23 dB. The received signal quality for M = 3 isalmost equivalent to the case in which there is no multicell coordination.

5.4.3 Unbalanced signal quality caused by IGI

Based on the observations for the seven-cell network MIMO system, the IGIresults in an unbalanced signal quality when using larger coordination size. That


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Figure 5.3. Effect of IGI for the three-cell and seven-cell network MIMO systems.(CDF: cumulative density function.)

is, the central cells in a coordinated group have better signal quality than the cellsat the edge. Take the seven-cell network MIMO as the example: the IGI of cell0 is from the second-tier interferers as mentioned before. However, for the edgecells 1, 2, 3, 4, 5, 6, each of them has three first-tier IGIs and 15 second-tierIGIs. As a result, in a cooperating group of Mcells, the edge cells suffer moreserious IGI than the central cells. The signal quality among M coordinatedcells is unbalanced in conventional network MIMO coordination. This unfairperformance metric in a group becomes more obvious as coordination size M

increases. To sum up, the IGI causes not only severe performance degradationbut also results in unfairness in multicell network MIMO systems.

Note that three-cell-based network coordination does not suffer from thisunbalanced service since each member of a coordinated group has the samegeographic condition. In other words, each cell can be considered to be an “edgecell” within the three-cell group with the same interference distribution. How-ever, the performance improvement induced by a small group of coordinatingcells is poor. In the following section, we propose novel network MIMO architec-tures to improve the signal quality and simultaneously achieve fairness among agroup.

5.5 Frequency-partition-based three-cell network MIMO

5.5.1 Fractional frequency reuse (FFR)

FFR, also called reuse partition, allows different frequency reuse factors to beapplied over different frequency partitions during the period of transmission.Figure 5.4 shows the considered FFR partition for a tri-sector cellular system.

5.5 Frequency-partition-based three-cell network MIMO 137

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Figure 5.4. Frequency partition and cell planning for proposed three-cell networkMIMO coordination.

The FFR partitions the frequency into inner frequency bands fA and outer fre-quency bands fB , where fB is further partitioned into three subbands fB1 , fB2 ,and fB3 (the gray, slash, and cross-hatched areas, respectively). In general, theinner frequency band fA adopts a reuse factor of 1 and is used by interior cellusers; the outer frequency band fB adopts a reuse factor of 1/3 for each sectorfor cell edge users. By means of the tri-sector FFR, the intracell interference canbe avoided due to four orthogonal subbands, and the intercell interference canbe significantly reduced. For use in a wireless broadband system (like the OFDMsystem), the frequency partitions can be assumed to be such that fB1 , fB2 , andfB3 have the same bandwidth and there are N frequency resource units (RU)in each outer subband, i.e., fBp

= fBp , 1 , . . . , fBp , N for p = 1, 2, 3. Note that

FFR is usually integrated with other functions such as power control or antennatechnologies for adaptive control.

In this chapter, we consider two kinds of frequency planning: regular andrearranged frequency partitions. In regular frequency partition, each cell hasthe same frequency planning in the outer region (e.g., the left hand cellularsystem in Figure 5.4). Similar designs can be found in [5, 6]. In rearrangedfrequency partition, each cell has different frequency planning compared with itssurrounding cells as shown in the right hand cellular system in Figure 5.4. Laterwe will design network MIMO systems based on the two frequency partitions. Weknow intuitively that the rearranged frequency partition will suffer from moresevere cochannel intercell interference than the regular frequency partition. Withthe network MIMO technique, we find that the three-cell network MIMO underthe rearranged frequency partition has the better performance.


5.5.2 FFR-based network MIMO with regular frequency partition

In this section, we consider a novel multicell architecture combining FFR withnetwork MIMO. As mentioned before, the entire frequency band is partitionedinto different zones by FFR frequency planning. Compared with the conventional19-cell layout, the tri-sector cellular system combined with FFR can significantlyreduce the interference sources, while fully utilizing the frequency band in eachcell. As an example, in Figure 5.1 when a mobile user at cell 0 uses an RU fB1 , n

(n = 1, . . . , N) in frequency band fB1 , the interference comes from cells 4, 5, 12,13, 14, 15, and 16 under the assumption of perfect 120 sectoring by directionalantenna. In conventional systems, the mobile receives interference from all theother 18 cells. Here, the question is: how can we further improve the SINR ontop of FFR? The solution proposed in this chapter is to integrate FFR with thenetwork MIMO technique.

From Figure 5.1, we find that among the seven interfering sources, two criticalinterferers are first-tier neighbors (i.e., neighboring cells 4 and 5) and five weakerinterferers (due to larger path-loss) are second-tier neighbors. Therefore, we usethe network MIMO technique to cancel out the two most severe interferences.Instead of a huge number of coordinated cells, we propose a coordination schemewith only three coordinated cells. We define those coordinated cells as a groupshown in Figure 5.4. For arbitrary group Gi , we label the three cells as CellGi

a ,CellGi

b , and CellGic . For the three-cell coordination structure, we can apply net-

work MIMO transmission to each subband fBp , nfor p = 1, 2, 3 and n = 1, . . . , N .

For the example on cell 0, under the assumption of perfect sectoring by direc-tional antenna, the channel matrix of fB1 , n

in the group 0, 4, 5 is

H(fB1 , n) =

⎡⎣ h(0),0 h(0),4 h(0),5

0 h(4),4 00 0 h(5),5

⎤⎦ , (5.16)

where (x) denotes the corresponding served user in cell x. We eliminate the inter-ference caused by h(0),4 and h(0),5 (coming from cells 4 and 5) by network MIMO.As a result, the two most severely interfering sources are canceled through a small(3× 3) matrix computation. Importantly, for system design, this cooperation canbe applied to all cells. For example, at a certain time slot we have many cooperat-ing groups among the 19 cell in the layout: cells 0, 4, 5, 8, 2, 1, 10, 11, 3, and18, 6, 17. Not only is the middle cell (cell 0) coordinated with its neighboringcells, but the cells in the outer layer are also coordinated simultaneously.

Cell regrouping and partner selectionWe now discuss a cell regrouping and partner selection scheme that addresses theservice fairness issue for the regular partition-based network MIMO system. We


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Figure 5.5. Example of cell regrouping and partner selection for cell 0.

consider the service fairness issue in the following. Among an arbitrary groupGi , the cell labeled “CellGi

a ” can be free from intragroup interference withinthe whole subband fB1 = fB1 , 1 , . . . , fB1 , N

under network MIMO. That is, thetwo most severely interfering sources are canceled via network MIMO. However,subbands fB2 and fB3 still suffer interference from seven interferers, i.e., two first-tier cells and five second-tier cells. We therefore define fB1 as the primary bandsof CellGi

a for group Gi . Similarly, we define fB2 and fB3 as the primary bandsof CellGi

b and CellGic , respectively. Therefore, the cell users served by different

subbands from a group will have different signal quality. Note that this servicefairness issue is different from the unbalanced signal quality issue mentioned inSection 5.4.3.

The service fairness issue can be resolved by the proposed regrouping andpartner selection scheme. Assume that cell 0 is grouped with cells 4 and 5 withprimary band fB1 at time slot 1 as shown in Figure 5.5. Cell 0 regroups withcells 1 and 6 at the next time slot, slot 2 by rotating counter-clockwise to reselectcoordinating partner. After this regrouping, the primary band of cell 0 becomesfB2 . Similarly, cell 0 regroups with cells 2 and 3 at time slot 3 by anothercounter-clockwise selection of the coordinated partner and the correspondingprimary band becomes fB3 . In this way, all cells simultaneously “rotate” andregroup with two new neighboring cells at each new time slot, where “rotate”means selecting with the coordinated partner reselection procedure. Take thecells 0, 4, 5 as an example: those cells form a group at time slot 1. At time slot2, cell 0’s regroup set is now 1, 0, 6, cell 4’s regroup set is 3, 12, 4, and cell 5’sregroup set is 5, 14, 15. Similarly, at time slot 3 cell 0’s regroup set becomes2, 3, 0, cell 4’s regroup set is 4, 13, 14, and cell 5’s regroup set is 6, 5, 16.Each cell has the chance to cooperate with its neighboring six cells in order andeach sector has the opportunity to become the primary band under this kind oftime-division multiple access (TDMA) based regrouping and partner selectionscheme.


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1B1B 1B

1B

1B 1B

1B

1B

1B

Three kinds of frequencypartition for cell

2B

3B

1B

3B

1B

2B

1B

2B

3B

Figure 5.6. Interference example for the FFR-based three-cell network MIMOsystems with rearranged frequency partition (consider cell 0).

5.5.3 FFR-based network MIMO with rearranged frequency partition

We now propose another multicell architecture with rearranged frequency par-titions among cells. As shown in Figure 5.4, there are in total three kinds offrequency partitions for cell planning, for example, the different frequency par-titions for cell 0, cell 1, and cell 2. After this rearranged frequency partitionamong a multicell system, a cell coordinates with six neighboring cells to formthree individual network MIMO groups for each subband. Take cell 0 as anexample: it coordinates with cells 1 and 2 for subband fB1 , with cells 3 and 4for subband fB2 , and with cells 5 and 6 for subband fB3 . In other words, weperform three-cell network MIMO transmission in each subband (or frequencypartition).

As the example in Figure 5.6 shows when a mobile user of cell 0 uses an RUfB1 , n

(n = 1, . . . , N) in frequency band fB1 , the interference sources are cells1, 2, 11, 12, 14, 16, and 17 under the assumption of perfect 120 sectoring by adirectional antenna. Similarly we use the network MIMO technique to cancel thetwo severest interferences, i.e., the only two first-tier interferences from cells 1and 2 (the dotted area in Figure 5.6). The channel matrix for the group 0, 1, 2in fB1 , n

is

H(fB1 , n) =

⎡⎣ h(0),0 h(0),1 h(0),2

h(1),0 h(1),1 h(1),2

h(2),0 h(2),1 h(2),2

⎤⎦ . (5.17)

For the user in cell 0, we eliminate the interference caused by h(0),1 and h(0),2

(coming from cells 1 and 2) by network MIMO. As a result, the two severestsources of interference are canceled through a small (3× 3) matrix computation.Ideally, there are only five second-tier interferers for each subband. As with


−30 −20 −10 0 10 20 30 40 500

0.1

0.2

0.3

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0.5

0.6

0.7

0.8

0.9

1

Received SINR (dB)

CD

F

FFR-based 3-cell network MIMO (ZFB)

FFR-based 3-cell network MIMO (ZF–DPC)

Regular frequency partition

Omni-cell with reuse 1

Diamond-shaped (120°) sector FFR

Figure 5.7. The CDFs of received SINR for the omni-directional cellular sys-tems with universal frequency reuse 1, tri-sector FFR cellular systems and theproposed regular partition-based three-cell network MIMO systems (120 cellsectoring).

−30 −20 −10 0 10 20 30 40 500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Received SINR (dB)

CD

F

Rearranged frequency partition

FFR-based 3-cell network MIMO (ZF−DPC)

FFR-based 3-cell networ kMIMO (ZFB)

Omni-cell with reuse 1

Diamond-shaped (120o) sector FFR

Figure 5.8. The CDFs of received SINR for the omni-directional cellular systemswith universal frequency reuse 1, tri-sector FFR cellular systems and the pro-posed rearranged partition-based three-cell network MIMO systems (120 cellsectoring).

the regular partition-based network MIMO systems, this cooperation can alsobe applied to all cells not only to a particular cooperating group. Comparedwith the regular partition-based network MIMO, there is no service fairnessissue for network MIMO systems with a rearranged partition. As a result, weavoid the necessity for cell regrouping which reduces the complexity of systemdesign.


Table 5.1. Spectral efficiency for three-cell network MIMO with regular frequencypartition

Reuse 1 Tri-sector FFR ZFB ZF-DPC

(bps/Hz)/base 2.5437 3.7844 2.4977 4.4275Improvement 48.78% -1.81% 74.06%

5.5.4 Effect of frequency planning among coordinated cells

We next present the received SINR performance for the proposed three-cell coor-dination architectures. The regular and rearranged partition frequency partitionscenarios are shown in Figures 5.7 and 5.8, respectively. The cell planning is120 sectoring. The results for the conventional 19-cell layout with universalfrequency reuse 1 (denoted by the dotted line) and the tri-sector FFR layoutwith directional antenna (denoted by the bold black line) are also presented forcomparison. From Figure 5.7, by comparing the dotted line with the bold linewe see that the gain in interference sources reduction (from 18 reduce to 7) ofthe tri-sector FFR layout is quite significant: about 10 dB improvement at 90thpercentile (i.e., CDF = 0.1) of the received SINR. However, the gain is not soobvious (2 dB improvement) for the rearranged partition-based cellular layout.This is because there are two neighboring interferers for each RU in the rear-ranged partition-based cellular layout. In this case the advantage of using justfrequency partition and directional antenna is limited.

With the three-cell network MIMO techniques, both ZF and ZF-DPC trans-missions, can indeed improve the received SINR, especially for ZF-DPC schemeas shown in Figure 5.8. At the 90th percentile of the received SINR, theimprovement (compared to the tri-sector FFR layout) is about 9 dB for ZF and15 dB for ZF-DPC. Although rearranged frequency partition causes interferencefrom neighboring cells, network MIMO can enhance signal quality effectively byinterferences cancelation. As for cells with regular partition, the gain of execut-ing network MIMO shown in Figure 5.7 is not as significant as that in Figure5.8. The gain of ZF-based network MIMO is actually lower than that of thetri-sector FFR layout using the regular partition-based cellular system. Recallthe TDMA-based regrouping and partner selection scheme for regular partition-based network MIMO. Equivalently, the signal quality of only one third of theresources can be enhanced in each time slot. Additionally, because of the trans-mission power penalty of ZF transmission, the actual data symbol power (5.10)becomes weaker even if there is no first-tier interference (due to coordination).Note that there is no power penalty for ZF-DPC transmission.

From the perspective of capacity improvement, Tables 5.1 and 5.2 show thespectral efficiencies of regular and rearranged partition-based cellular systemsunder 120 cell sectoring, respectively.


Table 5.2. Spectrum efficiency for three-cell network MIMO with rearrangedfrequency partition (120 sectoring)


(bps/Hz)/base 2.5437 3.2890 3.2553 5.7534Improvement – 29.30% 27.97% 126.18%

Figure 5.9. Interference example for FFR-based three-cell network MIMO sys-tems with 60 cell sectoring (consider cell 0).

5.5.5 Effect of cell planning with different sectorization

Cell planning for 60 cell sectorizationTo address the effect of cell planning with different sectorization, we design three-cell network MIMO systems with 60 cell sectoring. Here we consider rearrangedpartition-based frequency planning to avoid the cell regrouping procedure. Fig-ure 5.9 shows an example of the proposed rearranged partition-based 60 sector-ing network MIMO systems. In this design, each cell has three hexagon-shapedsectors with different frequency partitions. Cells with 60 and 120 sectoringare also called clover-leaf-shaped cells and diamond-shaped cells, respectively[27, 28]. Due to the antenna pattern, the clover-leaf-shaped cells can match thesector contour better than cells with diamond-shaped sectors [27]. Additionally,


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0.4

0.5

0.6

0.7

0.8

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1

Received SINR (dB)

CD

F

FFR-based 3-cell network MIMO (ZF–DPC)

Rearranged frequency partition

Omni- cell with reuse 1

Clover-leaf-shaped (60°) sector FFR

FFR-based 3-cell network MIMO (ZFB)

Figure 5.10. The CDFs of received SINR for omni-directional cellular systemswith universal frequency reuse 1, tri-sector FFR cellular systems and the pro-posed rearranged partition-based three-cell network MIMO systems (60 cellsectoring).

cells with 60 sectoring can use spectrum more efficiently [28]. Similarly to 120

sectorized cell planning, each cell forms three individually three-cell networkMIMO coordinations with its six neighboring cells for each frequency partition.The two first-tier interferers (the dotted areas in Figure 5.9) are canceled via net-work MIMO transmissions. The three-cell coordination structure can be imple-mented for all cells, not only for a particular cell.

Note that actual cell sectorization is not perfect when using a directionalantenna pattern (5.1). The other cells also affect the received signal quality ofcell 0. However, the harm caused by sidelobe and backlobe transmissions (thecross-hatched areas in Figures 5.1, 5.6, and 5.9) is not significant compared tothe cell planning with omni-directional transmission. Finally, the features of theproposed FFR-based three-cell network MIMO systems can be summarized as:(i) they use a small coordination size M = 3 to obtain low complexity networkMIMO systems, (ii) they reduce the effect of IGI via the combination of FFR anddirectional antennas, (iii) they avoid the unbalanced signal quality issue causedby a larger coordination size M .

Performance comparison under 60 cell sectorizationNext, we consider the effect of cell planning with different directional anten-nas. Figure 5.10 shows the corresponding received SINR performance using 60

5.6 Simulation setup numerical results 145

Table 5.3. Spectrum efficiency for three-cell network MIMO with a rearrangedfrequency partition (60 sectoring)


(bps/Hz)/base 2.4933 4.0360 2.9478 5.6337Improvement – 61..88% 18.23% 125.96%

sectorized cell planning. We find that the advantage of using pure sectorizationis obvious under 60 cell sectoring. Traditionally, a cell with 60 sectoring hasbetter performance than one with 120 sectoring. The poor signal quality of 120

tri-sector FFR with rearranged partition in Figure 5.8 can be improved using60 cell sectoring (see Figure 5.10). When applying three-cell network MIMO,the SNR performance of 60 sectorized cells is similar to that of 120 sector-ized cells by the ZF-DPC transmission. However, the gain of the ZF scheme isnot very significant at the 90th percentile of the received SINR, and is actuallylower than that obtained by using the tri-sector FFR scheme. In other words,under rearranged partition-based cellular systems, the proposed three-cell net-work MIMO enhances signal quality more efficiently on cell planning with 120

sectoring. Note that the performance of the 19-cell layout with universal fre-quency reuse 1 will be different to that in Figure 5.8 due to the different cellplanning. However, the difference is not very significant. Table 5.3 shows theaverage spectrum efficiency improvements of three-cell network MIMO with arearranged frequency partition under 60 cell sectoring.

5.6 Simulation setup numerical results

We have shown the SINR performance of the proposed FFR-based three-cellnetwork MIMO schemes. In our simulation environment, we consider a multicellsystem with BS-to-BS distance RB2B = 2 km. The interference-free SNR at thecell edge is Γ = 18 dB for 120 sectorized cells. The same values of BS-to-BSdistance and Γ (for same transmission power comparison) are used for clover-leaf-shaped cells. The standard deviation of shadowing is 8 dB, the path-lossexponent µ = 4. Mobile users are uniformly distributed within each sector/cell.The channel response between any user-and-cell pair is represented by (5.3),where the angle-dependent antenna pattern is taken into consideration. In thischapter, we do not consider the effect of the inner cell. In fact, how to design theinner region is an important issue for a FFR multicell broadband system. We donot discuss this issue here and leave it as a future work.


Table 5.4. Spectrum efficiency improvement for network MIMO with FFR anddirectional antenna

Proposed three-cell networkConventional setup MIMO

Three-cell 7-cell network 60 120

network MIMO MIMO sectorization sectorization

(bps/Hz)/base 3.0946 5.1579 5.6337 5.7534Improvement 66.67% 82.05% 85.92%

−20 −10 0 10 20 30 40 500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Received SINR (dB)

CD

F

3-cell omni-coordination(with IGI)

7-cell omni-coordination(with IGI)

Diamond: FFR-based 3-cell network MIMO under 120 −shaped cello

Square: FFR-based 3-cell network MIMO under 60 −shaped cello

Figure 5.11. Performance comparison of proposed three-cell FFR-based networkMIMO with general omni-directional three-cell and seven-cell network MIMOsystems.

Finally, we show the potential gains of combining frequency partition and net-work MIMO in Figure 5.11. Take ZF-DPC as an example. As studied in Section5.4.2, the performance degradation caused by IGI for three-cell and seven-cellnetwork MIMO systems is significant. However, taking advantage of joint fre-quency partition and network MIMO, the proposed FFR-based three-cell net-work MIMO architecture (for both cell sectorizations) can even outperform con-ventional seven-cell network MIMO system using omni-directional cell planning.The improvement is about 2 dB for 60 sectorized cell planning and 3 dB for 120

sectorized cell planning at the 90th percentile of the received SINR. This resultindicates that network MIMO systems with a small number of coordinated cellsare also comparable to network MIMO systems with a large number of coor-dinated cells as long as directional antennas and sector frequency arrangementtechniques can be adopted appropriately. Table 5.4 shows the spectrum efficiency

5.7 Conclusion 147

improvement of the three-cell network MIMO with the proposed frequency rear-ranged method for different sector antennas.

5.7 Conclusion

We have discussed joint FFR and network MIMO architecture for multicellularsystems. Taking advantage of FFR to reduce cochannel interference by partition-ing the frequency band into different zones, we have exploited the performancegain of the coordinated network MIMO techniques. We have provided a three-cellcoordinated scheme for network MIMO based on a sector frequency rearrange-ment method, rather than a huge number of coordinated cells. We have shownthat using a small number of coordinated cells can outperform the seven-cell-based coordination with omni-directional transmission. Future research topicsfor small network MIMO could include the design of the inner region of the FFRsystem and the low-complexity joint multicell transmission techniques. We hopethat this study will focus the attention of future researchers on BS architectureand system deployment for network MIMO systems.

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[11] O. Somekh, O. Simeone, Y. Bar-Ness, and A. M. Haimovich, “Distributedmulti-cell zero-forcing beamforming in cellular downlink channels,” in Proc.of IEEE Global Telecommunications Conference, pp. 1– 6, Nov. 2006. IEEE,2006.

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[14] M. K. Karakayali, G. J. Foschini, R. A. Valenzuela, and R. D. Yates, “On themaximum common rate achievable in a coordinated network,” in Proc. ofIEEE International Conference of Communications, vol. 9, pp. 4333– 4338,June 2006. IEEE, 2006.

[15] M. K. Karakayali, G. J. Foschini, and R. A. Valenzuela, “Network coor-dination for spectrally efficient communications in cellular systems,” IEEETrans. on Wireless Commun., vol. 13, no. 4, pp. 56–61, Aug. 2006.

[16] G. J. Foschini, M. K. Karakayali, and R. A. Valenzuela, “Coordinating mul-tiple antenna cellular networks to achieve enormous spectral efficiency,” IEEProc. Commun., vol. 153, no. 4, pp. 548–555, Aug. 2006.

[17] H. Zhang and H. Dai, “Cochannel interference mitigation and cooperativeprocessing in downlink multicell multiuser MIMO networks,” EURASIPJournal on Wireless Commun. and Networking, pp. 222–235, Feb.2004.

[18] Y. Liang, A. Goldsmith, G. Foschini, R. Valenzuela, and D. Chizhik, “Evo-lution of base stations in cellular networks: Denser depolyment versus coor-dination,” in Proc. of IEEE International Conference on Communications,pp. 4128–4132, Jan. 2008. IEEE, 2008.

[19] S. Venkatesan, “Coordinating base stations for greater uplink spectral effi-ciency in a cellular network,” in Proc. of IEEE International SymposiumPersonal, Indoor and Mobile Radio Communications, Sep. 2007. IEEE,2007.

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Part III

Relay-based cooperativecellular wireless networks

6 Distributed space-time block codes

Matthew C. Valenti and Daryl Reynolds

6.1 Introduction

In this chapter, we consider space-time coding strategies for multiple-relay coop-erative systems that effectively harness available spatial diversity. More specif-ically, the goal is to examine ways to forward signals efficiently from multiplerelays to the destination while addressing the important practical issue of syn-chronization among the relays. We assume a general two-phase transmissionprotocol as illustrated in Figure 6.1. In the first phase of the protocol, the sourcebroadcasts a message which is received by the relays and (possibly) the desti-nation. During the second transmission phase, a subset of the relays, possiblyin conjunction with the source, transmits additional information to the desti-nation. This protocol is useful in practical scenarios where signals received atthe destination due to transmissions directly from the source (Phase 1) will notcarry enough useful information because of noise, fading, and/or interference.

Phase 2Phase 1

Figure 6.1. Illustration of the two-phase transmission protocol using a distributedspace-time code. In the first phase (left) the source transmits to several relays,while in the second phase (right), the relays simultaneously transmit to thedestination.



It is expected that Phase 2 will dramatically increase the reliability of the sys-tem, but if the symbols cannot be decoded correctly after the second phase, theprotocol can restart by returning to Phase 1 or Phase 2.

The primary problem associated with forwarding information from multiplerelays to the destination is determining how the information should be spreadout among the relays over space and time. This is analogous to the classic space-time coding problem in point-to-point multiple-transmit-antenna systems, andso it is often called the distributed space-time coding problem. Similar to thepoint-to-point scenario, performance can vary dramatically based on the codingscheme, so care must be taken to achieve high performance in terms of diversityand coding gain while accounting for the practical limitations of cooperativesystems. In fact, poorly designed distributed space-time coding schemes mayperform worse than point-to-point systems, especially considering that the two-stage protocol consumes additional degrees of freedom (time resources) relativeto direct transmission.

A conservative solution to the distributed space-time coding problem is foreach terminal that participates in the second phase to transmit using orthogo-nal subchannels, which could be implemented using disjoint time slots, differentfrequency subbands, or orthogonal spreading codes (assuming that they can besynchronized). When disjoint time slots are used, this strategy is a distributedform of delay diversity [22]. However, there are two problems associated with thisapproach: (1) it is known that orthogonalizing system resources is suboptimal[18], and (2) enforcing orthogonalization in time, frequency, or code space wouldrequire significant additional signaling overhead, e.g., feedback and/or synchro-nization, and, in many cases, may not even be possible.

A more efficient, albeit more aggressive, approach is for the terminals trans-mitting in the second phase to use a distributed space-time block code1 [10, 15].There are two main varieties of forwarding mechanisms that can be used with dis-tributed space-time coded systems: decode-and-forward (DF) [10] and amplify-and-forward (AF) [8]. In DF protocols, the source’s signal is encoded with a for-ward error correcting code that must be successfully decoded by a relay beforethat relay may participate in the transmission of the distributed space-time code.After decoding, the information is reencoded and remodulated. A linear combi-nation of the remodulated symbols and their conjugates is transmitted by eachparticipating relay. While the DF protocol avoids error propagation or the ampli-fication of noise received over the source–relay channel, its implementation iscomplicated by fact that the set of relays that are able to decode and so partic-ipate in the space-time code in the second phase is random and unknown to thesystem. Therefore, unlike with point-to-point multiple-antenna systems, extra

1 Distributed space-time trellis codes can be used as well, but we focus here on block codesand refer the interested reader to, for example, [13].


care must be taken to ensure that the relays coordinate in the transmission ofthe space-time codeword.

With AF protocols, a fixed number of relays participate in the second phaseby transmitting a linear combination of the time samples of the noisy receivedsignal (not decoded symbols) they receive from the source. Because the numberof relays is fixed, AF does not have to manage which relays transmit which partof the space-time codeword, unlike DF. However, with AF the noise receivedover the source–relay channels is amplified, which has the potential to degradeperformance.

There are a number of challenges associated with practical distributed space-time code implementation, some of which are shared with conventional space-time coding used in point-to-point multiple-antenna systems, but some areunique to the distributed scenario. As with conventional space-time codes, dis-tributed codes typically (but not always) require the destination receiver to haveknowledge of the channels between the relays and the destination. Unlike con-ventional space-time codes, however, distributed space-time codes are subjectto some challenging synchronization issues. Because the transmitters are widelyseparated and have different time references, and due to differences in the propa-gation delay between the relays and the destination, the different signals receivedby the destination will generally be offset in time. Although this problem canperhaps be overcome with appropriate synchronization protocols, it can be han-dled more effectively with delay diversity, delay-tolerant distributed space-timecodes, or space-time spreading.

The remainder of this chapter is as follows. In Section 6.2, we give a sys-tem model that will be used throughout the chapter. In Section 6.3, we reviewconcepts related to fixed space-time block codes (STBCs). In Section 6.4, wedescribe the DF protocol, and in Section 6.5 we describe the AF protocol. Wediscuss synchronization issues in Section 6.6, and conclude in Section 6.7.

6.2 System model

Consider a wireless network consisting of a source node, a destination node, and aset of R relay nodesN = Ni : 1 ≤ i ≤ R. Each node has a half-duplex radio anda single antenna. Messages are transmitted according to a two-phase protocol.During the first phase, a signal of duration T1 symbol periods is broadcast by thesource and received by the relays. During the second phase, a subset of the relayssimultaneously, but perhaps not synchronously, transmits signals of duration T2

symbol periods, and the destination receives a noisy sum of the relay signals.After approximately T = T1 + T2 consecutive symbol periods (depending upontransmission and channel delays), the source moves on to the next message (or aretransmission of a failed message). For ease of exposition, we assume that there


is no direct link between the source and destination, although the protocols andperformance analyses can easily be generalized to allow for such a link.

We adopt a discrete-time model, whereby the signal transmitted by the sourceduring the first phase is represented by the vector s = [s1 , ..., sT1 ]

t . The individualsymbols s, 1 ≤ ≤ T1 are each drawn from a complex constellation X of M

symbols. The signal constellation is normalized so that its average energy is unity,i.e., (1/M)

∑s∈X |s|2 = 1. The normalized signal is amplified and transmitted by

the source with power P1 during the first phase. Let fi represent the complexgain of the channel between the source and node Ni . Then the signal receivedby node Ni during the first phase is

ri = fi

√P1s + vi , (6.1)

where vi = [vi,1 , ..., vi,T1 ]t is a noise vector containing independent circularly

symmetric complex Gaussian random variables with zero mean and unitvariance.

In the second phase, a subset K ⊆ N of the relays simultaneously, but perhapswithout symbol-level synchronization, transmits to the destination. During thisphase, node Ni ∈ K transmits a signal represented by the discrete-time vectorti = [ti,1 , ..., ti,T2 ]

t with power P2 . When the signals are perfectly synchronized,the signal received at the destination is

x =∑

i:Ni ∈Kgi

√P2ti + w, (6.2)

where gi is the complex gain of the channel between node Ni and the desti-nation, and the noise vector w = [w1 , ..., wT2 ]

t contains independent circularly-symmetric complex Gaussian random variables with zero mean and unit vari-ance. When the signals are not synchronized, the model must be generalized toaccount for time offsets.

In general, the powers E[|fi |2 ] and E[|gi |2 ] of the channel gains fi and gi willdepend on the topology of the network and the propagation characteristics of thewireless channel, and will usually be unequal. However, for ease of exposition,we make the simplifying assumption that the fis and gis are independent andidentically distributed (i.i.d.). In particular, each fi and gi is assumed to be acircularly symmetric complex Gaussian with zero mean and unit variance, sothat their envelopes |fi | and |gi | are Rayleigh distributed. The coefficients fi areheld fixed for the transmission of the signal s, and the coefficients gi are heldconstant for the transmission of the ti , i.e., we assume a Rayleigh block fadingmodel.

Just as the channel gains might have unequal powers, the powers P2 trans-mitted by the relays can, in general, be selected such that they are unequal, inwhich case our notation needs to be modified to indicate the different powers.However, in the following discussion we impose the simplifying limitation thatall relays transmit with the same power P2 , which is optimal when the average

6.3 Space-time block codes (STBCs) 157

channel powers are all equal and the transmitters operate without channel stateinformation.

Note that this is a fairly general model which leaves unaddressed several criticaldesign and implementation issues. For example, the composition of the set Kdepends on the protocol being used. In DF protocols, K contain only relays thatsuccessfully decoded the source’s transmission, while in AF protocols, K maycontain any (or all) of the relays. Another key issue is the selection of the signalsti that are to be transmitted by the nodes in K during the second phase of theprotocol. These signals can be jointly coded, but in a distributed way, using aspace-time code, or they can use simpler strategies, e.g., delay diversity or space-time spreading. We will discuss all of these options in this chapter. Finally, theallocation of power between P1 and P2 for the two transmission phases and theallocation of time over the two time phases are protocol-dependent optimizationproblems that must be solved to maximize performance.

6.3 Space-time block codes (STBCs)

As described in the introduction, one of the primary problems associated withforwarding information from relays to a destination in a cooperative wirelessnetwork is how information is transmitted from the relays over time, i.e., thespace-time transmission scheme. One natural strategy is to extend the conceptof STBCs, typically used for point-to-point multiple transmit antenna systems,to relay networks, where they are called distributed space-time block codes. Webegin with a description of conventional STBCs under the quite general lineardispersion paradigm [6].

Suppose for the moment that the first-phase transmission is perfectly receivedby all R relays. Under the linear dispersion paradigm, the ith relay transmits alinear combination of the T1 symbols in s and their complex conjugates,

ti = Ais + Bi s, (6.3)

where s is the column vector containing the complex conjugates of s and the com-plex T2 × T1 matrices Ai and Bi are called dispersion matrices. These matricesdefine the space-time code. Each nonzero matrix Ai or Bi is constrained to beunitary, and since the signal set X is normalized to unit energy, the symbolstransmitted by the relays will also have unit energy.

The family of space-time block codes that can be represented by (6.3) arecalled linear dispersion (LD) codes [6]. This family of codes includes many well-known space-time codes as special cases. For example, one linear dispersion codethat has been proposed for cooperative communications with R = 2 relays is


described by the dispersion matrices [9]

A1 =[

+1 00 +1

], A2 = 02×2 , B1 = 02×2 , B2 =

[0 −1

+1 0

], (6.4)

where 0m×n is an m× n matrix of all-zeros. This code is simply a transpose ofthe well-known Alamouti space-time block code [1].

For many codes of interest, including the one specified by (6.4), either Ai or Bi

is a matrix of zeros for every i. This means that a particular relay will transmita linear combination of the symbols in s or s, but not both. If we define

Ci =

Ai, if Bi = 0,

Bi, if Ai = 0(6.5)

and

s(i) =

s, if Bi = 0,

s, if Ai = 0(6.6)

then we can write (6.3) more compactly as

ti = Cis(i) . (6.7)

Assume that nodes N1 , ..., NR participate in the second-phase transmission withthe same power P2 . The signal received at the destination is

x =√

P2Sh + w, (6.8)

where

S =[

C1s(1) ... CRs(R)]

(6.9)

is the T2 ×R space-time codeword, and

h =[

g1 ... gR

]t(6.10)

is the channel vector. The maximum-likelihood (ML) detector at the destinationestimates the source signal as

s = arg mins∈X T 1

∥∥∥x−√P2Sh∥∥∥ , (6.11)

where ‖ · ‖ indicates the Frobenius norm.


Unless the distributed space-time code, described by the set of all pos-sible codewords S, has some special structure, ML detection will haveexponential complexity in the number of source symbols T1 . Fortunately, severalclasses of codes admit reduced complexity ML decoding, including the well-known orthogonal design family [15], whose orthogonal structure allows decou-pling of the symbols in the codeword, permitting symbol-by-symbol ML detec-tion with linear complexity in T1 . The (Alamouti) code given by (6.4) is oneexample of an orthogonal design. Another orthogonal design which has beenapplied to cooperative diversity with R = 4 relays is described by the dispersionmatrices [9]

A1 =

⎡⎢⎢⎣1 0 00 0 00 0 00 0 0

⎤⎥⎥⎦ , A2 =

⎡⎢⎢⎣0 1 00 0 00 0 00 0 0

⎤⎥⎥⎦ , A3 =

⎡⎢⎢⎣0 0 10 0 00 0 00 0 0

⎤⎥⎥⎦ ,

A4 =

⎡⎢⎢⎣0 0 00 0 10 1 0−1 0 0

⎤⎥⎥⎦ , B1 =

⎡⎢⎢⎣0 0 00 −1 00 0 10 0 0

⎤⎥⎥⎦ , B2 =

⎡⎢⎢⎣0 0 01 0 00 0 00 0 1

⎤⎥⎥⎦ ,

B3 =

⎡⎢⎢⎣0 0 00 0 0−1 0 00 −1 0

⎤⎥⎥⎦ , B4 = 04×3 .

(6.12)

Note that for this code, only B4 is all-zero and thus the model given by (6.5)–(6.10) must be generalized slightly. See [8, 9] for details.

The rate of a STBC is T1/T2 , and a code is said to be full rate if it has arate of unity. While the rate of the code specified by (6.4) is unity, the rate ofthe R = 4 code specified by (6.12) is only 3/4. No full-rate orthogonal STBCexists for R > 2 when complex symbols are used [11], although reduced-rateorthogonal codes can be designed for any number of transmit antennas. Thus,for R > 2, the convenience (linear ML decoding complexity) of using an orthog-onal design comes at the cost of reduced spectral efficiency. An alternative tousing orthogonal designs is to use quasi-orthogonal designs [7], which can achievefull rate with four antennas with higher complexity than orthogonal designs,but much lower than worst-case ML complexity. The additional complexity overorthogonal designs is because quasi-orthogonal codes reduce the ML detectionproblem to the joint detection of pairs of complex symbols, whereas orthogonaldesigns reduce it to the detection of individual complex symbols. The ML detec-tor for a quasi-orthogonal code thus requires that each of the T1/2 pairs of sym-bols be compared against M 2 hypothesis. An example quasi-orthogonal STBC


considered for cooperative-diversity with R = 4 relays is given by [9]

A1 =

⎡⎢⎢⎣1 0 0 00 1 0 00 0 1 00 0 0 1

⎤⎥⎥⎦ , A2 = 04×4 , A3 = 04×4 ,

A4 =

⎡⎢⎢⎣0 0 0 10 0 −1 00 −1 0 01 0 0 0

⎤⎥⎥⎦ , B1 = 04×4 , B2 =

⎡⎢⎢⎣0 −1 0 01 0 0 00 0 0 −10 0 1 0

⎤⎥⎥⎦ ,

B3 =

⎡⎢⎢⎣0 0 −1 00 0 0 −11 0 0 00 1 0 0

⎤⎥⎥⎦ , B4 = 04×4 .

(6.13)

In Figure 6.2, four systems are compared by plotting the bit error rate (BER) ofeach system as a function of the signal-to-noise ratio (SNR). Three values of R areconsidered, R = 1, 2, 4, and all systems transmit with a spectral efficiency of 3(bits per second) per Hertz (bps/Hz). The signals are transmitted over Rayleighfading channels, and the power is split evenly across the R transmit antennas.Since the noise power is unity, the transmitted power is P2 = SNR/R. The R = 1system represents conventional point-to-point communications between a pairof terminals, each with a single antenna and no space-time coding. The R =2 system uses the transposed Alamouti code given by (6.4). Two systems arecompared for use with R = 4 transmitting antennas, the orthogonal code of(6.12) and the quasi-orthogonal code (6.13). The rate of the orthogonal space-time code used with R = 4 antennas is 3/4, while the rates of the other STBCare all unity. In order for the spectral efficiency to be maintained at 3 bps/Hz,gray-labeled 8-PSK modulation is used for the full-rate systems (including thesystem with no space-time coding), while gray-labeled 16-QAM modulation isused for the rate 3/4 system. The worst-performing system is the one that usesjust one transmit antenna (R = 1), while the next worst-performing system isthe one with two transmit antennas (R = 2). The two systems’ four transmitantennas (R = 4) exhibit the best performance.

The most significant feature to notice in Figure 6.2 is the steepness of thecurves. At high SNR, these curves become straight lines, implying that asymptot-ically there is a linear relationship between the logarithm of the error probabilityand the SNR expressed in decibels. The negative slope is called the diversity ofthe system, also known as the diversity order or diversity gain. Inspection ofthe diagram reveals that the diversity of the R = 1 system is equal to 1 (i.e.,the BER drops by an order of magnitude with every decade of SNR), while thediversity of the R = 2 system is equal to 2. Although the SNR is not sufficientlyhigh in the figure to show it, the diversity of both two R = 4 systems is equal to4. A system with R antennas is said to have full diversity if its diversity order is


RR

Figure 6.2. BER performance of four systems: An uncoded system with R = 1transmit antenna, an Alamouti-coded system with R = 2 transmit antennas, anorthogonal STBC with R = 4 transmit antennas, and a quasi-orthogonal STBCwith R = 4 transmit antennas. In each case, the spectral efficiency is 3 bps/Hzand the signals are transmitted over independent Rayleigh fading channels.

R. Thus, all four systems shown in Figure 6.2 exhibit full diversity, as seen bythe fact that their error probabilities decay proportional to 1/SNRR .

The performance of a space-time coded system can be determined by analyzingthe pairwise error probability (PEP) between all pairs of distinct space-timecodewords Sk and S . The PEP can be bounded by, for example, a Chernoffbound. By taking the limit with respect to the SNR, the diversity order is thendetermined. Full diversity is achieved by ensuring that Sk − S is full rank forall k = [15].

Linear dispersion codes need not be orthogonal or quasi-orthogonal. Forinstance, the linear dispersion codes presented in [6] were designed to maximizethe mutual information between the transmitter and receiver under a power con-straint. However, such codes do not lend themselves to the very simple decoderstructures that are possible with orthogonal or quasi-orthogonal codes. Whilea brute-force ML decoder requires comparison against all MT1 hypotheses, thecomplexity can be greatly reduced by using a sphere decoder [2]. Another optionis to use the designs in [17], which permit decoupled symbol-by-symbol decodingand full-rate at the cost of reduced diversity.


6.4 DF distributed STBC

Returning to the two-phase relay network configuration, consider the case thatthe first-phase transmission must take place over a channel that is corruptedby noise and fading. Now, there is no guarantee that any particular node willreceive the transmission correctly. With a DF protocol, the source encodes itstransmissions with a channel code. Each relay attempts to decode using thesignal it receives, and can only participate in the second-phase transmissionif it successfully decodes the message sent by the source. The condition that anode can only transmit in the second phase if it successfully decodes the messagerequires that the code be used not only as an error correcting code, but also as anerror detecting code (i.e., the relay needs to detect the existence of uncorrectableerrors). The set of nodes K that successfully decode the source’s message andmay transmit during the second phase is called the decoding set [10], and thenumber of nodes in the decoding set is K = |K|.

During the second phase, nodes in K transmit using a distributed space-timecode. A major complicating factor is that the size of the decoding set is random,yet the space-time code must be designed with a certain number of transmittingantennas in mind. Because of this, the number of relays that actually transmitshould be limited to the maximum number of antennas supported by the space-time code, which we denote Kmax . It is possible that K < Kmax , which meansthat there are not enough relays participating in the second phase to use theentire space-time code. This implies that the space-time code should be “scalefree”, meaning that it still offers the maximum possible diversity even if someof the transmitting antennas are not used. When K < Kmax , the maximumpossible diversity order is reduced from Kmax to K. It is known that orthogonalspace-time codes have this scale-free property [9].

If relay Ni ∈ K transmits during the second phase, then it does so by transmit-ting a signal vector ti of the form given by (6.3), where s is the signal obtainedby decoding, reencoding, and remodulating, and the Ai and Bi are the disper-sion matrices currently assigned to that relay. Note that since the compositionof the set of transmitting nodes changes after each source transmission, the setof dispersion matrices assigned to a particular relay may also change. The pro-tocol must be careful to make sure that each transmitting relay is allocated adistinct set of dispersion matrices. When either Ai or Bi is all zeros for all i,the received signal at the destination is as given by (6.8), where the columns ofthe space-time codeword S will be the signals transmitted by the relays. WhenK < Kmax , fewer relays transmit than there are columns in S and Kmax −K

columns in S will be all zeros.

6.4.1 Performance analysis

The performance of a DF system depends on the error control code or codesused. If the system uses a capacity-approaching code, such as a turbo code or a

6.4 DF distributed STBC 163

low-density parity-check (LDPC) code, then the codeword error rate over a par-ticular link may be approximated by the information-outage probability of thatlink. The information-outage probability is the probability that the conditionalmutual information between the channel input and output is below some thresh-old. For the first phase, the channel between the source and each relay is anadditive white Gaussian noise (AWGN) channel when it is conditioned on thefading gain fi . The conditional mutual information between the signal transmit-ted by the source and the signal received by the ith relay is given by

I(s, ri |fi) = log2(1 + P1 |fi |2), (6.14)

where P1 |fi |2 is the “instantaneous” SNR of the link between the source and theith relay. Note that (6.14) represents the mutual information when the source–relay channel is used all the time. However, in the DF protocol, the relay source–relay link is only used for T1 out of every T symbol periods. Thus, the mutualinformation needs to be scaled by the ratio T1/T when computing the probabilitythat a relay is in an outage.

The information-outage probability of the link from the source to node Ni is

pi = Pr[T1

TI(s, ri |fi) < r

], (6.15)

where r is the rate of the error control code. Substituting (6.14) into (6.15) gives

pi = Pr[T1

Tlog2(1 + P1 |fi |2) < r

]= Pr

[|fi |2 < Γ1

], (6.16)

where

Γ1 =2rT /T1 − 1

P1. (6.17)

Equation (6.16) is the cumulative distribution function (CDF) of the randomvariable |fi |2 evaluated at Γ1. If we assume that fi is circularly symmetric com-plex Gaussian with zero mean and unit variance, then |fi |2 will be exponentialwith unit mean. By recalling the CDF of an exponential random variable, theinformation-outage probability is

pi = 1− e−Γ1 . (6.18)

Because the fis are i.i.d. and the threshold Γ1 is common to all relays, pi is thesame at all R relays and may be denoted as p.

Let Zi = 0, 1 be an indicator variable that equals unity when the ith relay isin an outage. Zi is a Bernoulli random variable with P [Zi = 1] = p. The numberof relays K = |K| that successfully decode the first-phase transmission is K =∑R

i=1 Zi . Because the channels are independent, so are the Zis, and it followsthat K is a binomial random variable. The probability that the random variable


K is equal to k is given by the probability mass function of K,

pK [k] = Pr[K = k]

=(

R

k

)(1− p)kpR−k . (6.19)

The second-phase transmission may also be characterized in terms of an outageprobability. However, the outage probability at the destination depends on thenumber of nodes K in the decoding set as well as the maximum number of nodesKmax that may transmit during the second phase of the protocol. Define theconditional end-to-end information-outage probability for the second phase ofthe DF protocol as

Pr[Outage|k] = Pr[I(S,x|h) < r

∣∣K = k], (6.20)

where S is the space-time codeword and h is a length min(k,Kmax) vector con-taining the coefficients gi corresponding to those relays that transmit during thesecond phases. Equation (6.20) represents the probability that the destination isin an outage during the second phase given that the decoding set has k relaysin it.

When using a rate T1/T2 orthogonal STBC over a point-to-point link, themutual information is [11]

I(S,x|h) =T1

T2log2

(1 + P2 ||h||2

). (6.21)

This mutual information expression assumes full use of the channel. However, inthe DF protocol, the relay–destination link is only active for T2 out of every T

channel uses, and thus (6.21) must be scaled by T2/T .Substituting the scaled version of (6.21) into (6.20) results in

Pr[Outage|k] = Pr[T1

Tlog2

(1 + P2 ||h||2

)< r∣∣K = k

]= Pr

[||h||2 < Γ2

∣∣K = k], (6.22)

where

Γ2 =2rT /T1 − 1

P2. (6.23)

This is the CDF of ||h||2 evaluated at Γ2. When there are min(k,Kmax) relaystransmitting in the second phase, then ||h||2 is Erlang-m with min(k,Kmax)degrees of freedom. Using the CDF of an Erlang-m distribution, the outageprobability becomes

Pr[Outage|k] = 1−min(k,Km a x )−1∑

n=0

Γn2

n!e−Γ2 . (6.24)


Of course, when k = 0, Pr[Outage|k] = 1 since the system is always in an end-to-end outage when no relays receive the source transmission (recall that we assumeno direct link from source to destination).

From the theorem on total probability, the overall end-to-end outage proba-bility may be found from the conditional outage probabilities as

Pr[Outage] =R∑

k=0

pK [k]Pr[Outage|k]. (6.25)

By substituting (6.19) and (6.24) into (6.25), we get the following expression forend-to-end outage probability

pD = pR +R∑

k=1

(R

k

)(1− p)kpR−k

⎛⎝1−mink,Km a x −1∑

n=0

Γn2

n!e−Γ2

⎞⎠ .

(6.26)

6.4.2 Numerical results

By using (6.26), we can determine the outage probability for a network compris-ing R relays that uses a particular space-time code. Consider two examples, onethat uses the transposed Alamouti code with dispersion matrices given by (6.4),and another that uses the orthogonal STBC with dispersion matrices given by(6.12). Both systems use a rate r = 1/2 error control code. With the Alamouti-coded system, no more than Kmax = 2 relays may transmit during the secondphase, while with the other orthogonal system, no more than Kmax = 4 relaysmay transmit. Let K ′ = min(K,Kmax) be the number of relays that actuallytransmit during the second phase, where K is the number of relays that suc-cessfully decode the source’s transmission. The total transmitted power of allrelays is P = P1 + K ′P2 . As explained later in this section, the powers P1 andP2 are selected to minimize the outage probability subject to the total powerconstraint.

Figure 6.3 shows the information-outage probability as a function of SNR forboth space-time codes and a variable number of relays. Since the noise power isunity, the SNR is equal to the total power P . For the Alamouti-coded system, thenumber of relays is between 2 and 8, while for the other orthogonal system, thenumber of relays is between 4 and 10. For both systems, performance improveswith increasing R. Even though no more than Kmax relays can be used duringthe second transmission phase, it is still advantageous to have more than Kmax

relays present in the network. This is due to the diversity present in the firstphase transmission. Having more than Kmax relays makes it more likely that atleast Kmax relays will be able to decode the source’s transmission, and thus it isvery likely that Kmax relays will transmit the entire space-time codeword duringthe second phase. From the curves, it is seen that the Alamouti code providesa diversity order of Kmax = 2 while the other orthogonal system provides a


Kmax

Kmax

Figure 6.3. Comparison of the information-outage probability of several systems:direct, DF using the Alamouti code and up to Kmax = 2 transmitting relays, DFusing orthogonal STBC and up to Kmax = 4 transmitting relays. For each valueof Kmax , a set of seven curves is shown corresponding to a different number ofrelays R. For the Kmax = 2 system, the total number of relays R is between 2and 8, while for the Kmax = 4 system there were between 4 and 10 relays. Foreach value of Kmax performance improves with increasing R.

diversity order of Kmax = 4. Using additional relays does not improve the overallsystem’s diversity order, but it does provide an additional coding gain.

Also shown in Figure 6.3 is the performance of a direct point-to-point linktransmitting with transmission power P = SNR and using a single antenna ateach end of the communication link. Because this is just a single-input single-output (SISO) system, the diversity order is only equal to 1, and thus asymp-totically the performance of the direct transmission is worse than the consideredDF protocols. However, at very low SNR, the performance of the direct link isactually better than the systems that use a distributed STBC. This is becausethe system using a direct link may concentrate all of its power into the singletransmission rather than diluting the energy across the transmissions of the twohops. Thus, at very low SNR, a direct link might be more effective than usingthe distributed STBC. However, keep in mind that these results assume thatall channels have unity power gain. When relays are placed between the sourceand destination, then it is possible that channels used by the system with the


0 10 20 300

0.1

(a) (b)

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SNR (in dB)

Opt

imal

pow

er r

atio

0 5 10 15 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SNR (in dB)

Opt

imal

pow

er r

atio

Figure 6.4. The optimal power ratio for: (a) the Kmax = 2 system and between2 and 8 relays and (b) the Kmax = 4 system with between 4 and 10 relays. Theoptimal power ratio decreases with increasing R.

distributed STBC (i.e., the gains from source to relays and the gains from relaysto destination) will have a higher gain than the channel used by the system thatuses direct transmission.

Let P1/(K ′P2) be the ratio of the power used during the first phase to thepower used during the second phase. The results shown in Figure 6.3 assume thatthe power is selected to minimize the information-outage probability subject tothe total power constraint P = P1 + K ′P2 . To find the optimal power ratio foreach SNR point, we compute the information-outage probability for all ratiosbetween 10−4 and 1 in increments of 10−4 , and pick the ratio that minimizesthe information-outage probability. The result of this optimization is shown inFigure 6.4. Figure 6.4(a) shows the optimal power ratios for the Kmax = 2 system(Alamouti coded) and Figure 6.4(b) shows the optimal power ratios for theKmax = 4 system. For each system, a family of curves is shown corresponding tothe different values of R considered in Figure 6.3. The power ratio decreases withincreasing R and with increasing SNR. This is because as R grows, the likelihoodthat Kmax relays can decode the source’s signal improves as a function of P1 ,and thus the system can afford to decrease P1 and devote more power to thesecond-phase transmission.


6.5 AF distributed STBC

In contrast to DF protocols, AF protocols do not require that each relay fullydemodulates and decodes the signal it receives from the source. Instead, relayNi obtains the vector ri given in (6.1) by down-converting the received signal tobaseband and passing it through a pair of filters matched to the in-phase andquadrature basis functions. The matched filters are sampled at the symbol rate,resulting in a set of T1 complex samples that are placed into the vector ri . Ratherthan demodulating and decoding ri , the relay transmits a linear combination ofthe samples in ri and its conjugates at power P2 [8].

We can write the normalized signal transmitted by node Ni in vector form as

ti =√

1P1 + 1

(Airi + Bi ri) , (6.27)

where Ai and Bi are the dispersion matrices assigned to node Ni . The twomajor differences between (6.27) and the DF transmitted signal in (6.3) are:(1) in AF, the transmitted signal is a linear combination of the samples in thereceived vector ri (and its conjugates) rather than a linear combination of theremodulated symbols in the vector s (and its conjugates), and (2) because thenoise power is unity, the average received signal power is P1 + 1, and the scaling√

1/(P1 + 1) is required to normalize the signal.For the important special case where either Ai or Bi is zero, we can simplify

the transmitted signal similar to (6.7) as

ti =√

1P1 + 1

Cir(i) , (6.28)

where

r(i) =

r, if Bi = 0,

r, if Ai = 0(6.29)

and Ci is as given by (6.5).Using (6.2) and assuming perfect symbol-level synchronization, the resulting

received signal vector at the destination can be written as

x =R∑

i=1

gi

√P2ti + w. (6.30)

Substituting (6.1) into (6.29) and (6.30) results in

x =R∑

i=1

gifi

√P1P2

P1 + 1Cis(i) +

√P2

P1 + 1

R∑i=1

giCivi + w.︸︷︷︸n

(6.31)

This may be represented compactly as

x =√

P1P2

P1 + 1Sh + n, (6.32)

6.5 AF distributed STBC 169

where the T2 ×R space-time codeword S is as given in (6.9), the channel vectoris

h =

⎡⎢⎢⎢⎣f1g1

f2g2...

fRgR

⎤⎥⎥⎥⎦ , (6.33)

and the complex noise vector n is Gaussian when conditioned on the gi andwill generally be colored because the signal transmitted by the relay will containa linear combination of the elements of the white noise vector vi .

Compared with the DF case (6.8), the AF received signal in (6.32) differs inthree ways: (1) all R relays transmit a signal during the second phase, not justthose that can decode the source’s transmission, (2) the channel vector consistsof the product of the source–relay and relay–destination channel gains insteadof just the relay–destination channel gains, and (3) the additive noise will havea higher power and will generally be colored.

As was the case for DF, the T2 ×R matrix S in (6.32) plays the same role as aspace-time code matrix in a conventional point-to-point multiple-input multiple-output (MIMO) system, except that, in the distributed space-time code scenario,the matrix is generated without access to s. For this reason, we say that S

defines a distributed space-time code operating in AF mode. We can think of has the equivalent channel matrix and n as additive noise, although n is clearlya function of the space-time code. Because of the similarities to conventionalSTBCs, we can analyze the diversity gain and coding gain performance of thisfamily of distributed AF space-time codes using the same technique we use forconventional codes, i.e., bounding the pairwise error probability.

6.5.1 Performance analysis

The achievable diversity of LD codes operating in an AF system can be deter-mined using the same technique that is often used for point-to-point space-timecoded systems, i.e., by bounding the pairwise error probability. The exact resultsare complex and we refer the reader to [8] for details. The main result, however,is that the achievable diversity is

d = R

(1− log log P

P

), (6.34)

which is achieved whenever the Sk − Sl is full rank for all l = k. This resultconverges to R for very large power P , so LD coding operating in AF systemsachieves approximately the same diversity as a point-to-point system with R

antennas.2

2 Note that here we assume that no information is passed directly between the source anddestination. If such a link exists, the diversity result simply increases by 1.


Interestingly, when the number of relays is large and the power is also large,the coding gain for distributed LD codes is the same as for LD codes operating inpoint-to-point systems. On the other hand, when the power P is moderate, thecode matrices should be designed such that the code is “scale-free,” i.e., it shouldperform well when some relays are not working. Mathematically, this requiresthe codeword difference matrices to remain full rank when some columns aredeleted.

6.5.2 Practical distributed STBC for AF systems

Although arbitrary LD codes can achieve almost full diversity with mild con-ditions on the Ai matrices, they are generally difficult to decode because MLdecoding, i.e.,

arg mins

∥∥∥∥∥x−√

P1P2

P1 + 1Sh

∥∥∥∥∥ , (6.35)

has high computational complexity for the general case. This problem can be alle-viated by using extending well-known orthogonal [15] or quasi-orthogonal [7] codedesigns for point-to-point systems to the distributed scenario, as discussed in [9].The results are distributed codes that are fully diverse, allow low-complexitydecoding, and are scale-free, yielding good coding gain for moderate transmitpowers. Because the noise vector n is not generally white, true-ML detectioncannot be achieved through linear processing methods such as the decoupled-decoding approach commonly used for orthogonal codes operating over point-to-point links. However, as reported in [9], the performance when using decoupleddecoding is only slightly inferior to that of using true ML detection (i.e., around0.5 dB).

6.6 The synchronization problem

One of the key challenges when designing high-performance distributed space-time coded systems is symbol-level synchronization among the relay nodes. Inconventional point-to-point space-time coded MIMO systems, colocated anten-nas obviate this issue. In cooperative systems, sometimes described as virtualMIMO, the antennas are separated by wireless links. One approach is simply touse appropriate hardware and higher-layer protocols to ensure that transmissionsfrom every participating relay are synchronized. Unfortunately, this may not bepossible in practice and, in any case, it would require significant signaling over-head that may dramatically increase bandwidth requirements. Other approachesthat effectively circumvent the synchronization problem include delay diversity,delay-tolerant distributed space-time codes, and space-time spreading (STS). Wewill next consider each of these approaches briefly.

6.6 The synchronization problem 171

6.6.1 Delay diversity

It is well known that point-to-point communication over multipath fading chan-nels provides diversity that can be exploited by appropriate receiver design[18]. In cases where intersymbol interference (ISI) is negligible, as is commonin spread-spectrum systems, RAKE reception is sufficient. When ISI cannot beignored, ML sequence detection can be performed using the Viterbi algorithmto extract full diversity in the number of resolvable paths. Mathematically, thisinvolves transforming the frequency selective SISO system into an equivalentflat-fading multiple-input single-output (MISO) system that uses a particularspace-time code induced by the frequency selective channel. Interestingly, thereverse is also possible. That is, we can transform a flat-fading MISO system intoa virtual frequency selective SISO system by using a space-time code describedby the following scheme: in the first time slot, the symbol x[1] is transmittedon antenna 1 and all other antennas are silent. In the second time slot, x[1] istransmitted from antenna 2 and x[2] is transmitted by antenna 1 and all otherantennas remain silent. At time slot m, x[m− l] is transmitted on antenna l + 1for l = 0, 1, . . . , L− 1. This transmission scheme yields a received signal that isidentical to that received in a SISO frequency selective channel with L paths.This special point-to-point space-time coding scheme is called delay diversity[22].

Delay diversity cannot be implemented in cooperative communication systemsin exactly this way without requiring what we are trying to avoid, i.e., syn-chronization to determine which relay transmits which symbol in which order.Fortunately, it is straightforward to implement delay diversity in a distributedmanner. The simplest way to do this is simply for the relays to wait a ran-dom amount of time before they retransmit the symbol or signal they havemost recently received. The destination will receive a signal that is equivalentto that received in a SISO multipath channel, so full diversity will be achievable(with probability 1), assuming ML detection at the destination. Linear detec-tors/equalizers can also be used at the destination, e.g., minimum mean-squarederror (MMSE), or decorrelating equalization, with some diversity loss. Inter-estingly, MMSE detection in conjunction with serial interference cancellation(decision feedback implementation) achieves full diversity [21] with much lowercomplexity than ML detection when the number of relays is large.

6.6.2 Delay-tolerant space-time codes

Another approach to distributed space-time coding without synchronizationinvolves the use of so-called delay-tolerant distributed space-time codes whoseperformance is insensitive to delays among the received signals from each relay.

It is well known that the diversity order of a STBC is equal to the minimumrank of the difference matrix over all pairs of distinct code matrices [15]. A space-time code is said to be τ -delay tolerant if for all distinct code matrices Sk and


S , the difference matrix Sk − S retains full rank even though the columns ofthe code matrices are transmitted or received with arbitrary delays of durationat most τ symbols. Let S be a codeword matrix from a synchronized STBC,as in (6.9), and let ∆S be the code matrix received at the destination due totransmission or propagation delays. Then ∆S can be written as

∆S =

⎡⎣ 0∆1 0∆2 · · · 0∆R

C1s(1) C2s(2) · · · CRs(R)

0τ−∆1 0τ−∆2 · · · 0τ−∆R

⎤⎦ . (6.36)

The collection of all such codewords ∆S constitutes a τ -delay-tolerant space-timecode if for all delay profiles ∆kRk=1 such that ∆k ≤ τ for all k, it achieves thesame diversity as the synchronized code. Work on delay-tolerant codes under thisframework includes [3, 5, 13, 16]. Although delay diversity extracts full diversityin the number of relays, delay-tolerant space-time codes promise better codinggain and, in some circumstances, lower decoding complexity.

6.6.3 Space-time spreading (STS)

Delay diversity is successful in achieving full diversity in part because the distinctdelays for the received signals from each relay provide a unique signature enablingthe receiver to separate each resolvable path before cophasing and combining. Asimilar unique signature can be implemented with coding, i.e., STS.

One of the simplest STS strategies is to assign the source and each relay aunique spreading code, as in code-division multiple access (CDMA) communica-tions. When the relays are not synchronized, the signal received at the destina-tion is similar to that obtained in a conventional (noncooperative) asynchronousCDMA uplink, so that the transmissions from the source and each relay can beseparated using well-known multiuser detection (MUD) signal processing strate-gies, cophased, and recombined to extract full diversity without symbol-levelsynchronization. Note that, although CDMA is a spread-spectrum signaling for-mat, it does not need to operate in a spectrally inefficient mode. In fact, it wasshown in [19] that the information outage probability of an asynchronous coop-erative CDMA uplink under decorrelating MUD is minimized when the systemis slightly overloaded, i.e., when the number of relays is slightly larger than theprocessing gain. This is not surprising because an overloaded CDMA system isoperating at high spectral efficiency.

A more sophisticated STS strategy was designed in [14]: it does not requiresynchronization among the relays, channel estimation, or complex multiuser sig-nal processing at the destination or relays. The necessity for channel informationis obviated by the use of differentially encoded symbols from each source, as in[4], during the first transmission phase. During the second transmission phase,dedicated relays use an STS AF strategy described in [4] that allows low com-plexity decoding and large diversity gain without channel estimation. Becausehigh-complexity MUD strategies are not used here, the residual multiple access

References 173

interference (MAI) and ISI must be mitigated by the use of specially designedspreading codes that provide an “interference-free window” (IFW), where the off-peak aperiodic autocorrelation and crosscorrelation values become zero, resultingin zero MAI and ISI, provided the maximum asynchronous delay is within theIFW [20]. The resulting system extracts full diversity without channel knowledgeor complex MUD at the destination or relays.

6.7 Conclusion

Distributed STBCs are able to effectively exploit the spatial diversity present ina multirelay network. With a distributed space-time code, each relay transmitsa particular column of a space-time codeword. The DF strategy is appropriatewhen there are more relays than there are columns in the space-time codeword,since only a subset of relays may participate in the transmission of the distributedspace-time codeword, namely those that receive the source’s transmission. How-ever, DF protocols require coordination among the relays to ensure that eachrelay transmits a specific column of the space-time codeword. AF protocols arewell suited to the case that the number of relays is equal to the number ofcolumns in the space-time code, since with AF protocols every relay participatesin the transmission of the space-time codeword regardless of the quality of thesource–relay transmission.

In addition to the implementation challenges that are common to conven-tional MIMO systems, the lack of synchronization at the destination receiverimposes additional challenges to systems that use distributed space-time codes.The synchronization problem can be alleviated by using delay diversity, STS, ordelay-tolerant space-time codes.

References

[1] S. M. Alamouti, “A simple transmit diversity technique for wireless commu-nications,” IEEE Journal on Selected Areas in Communications, 16, 1998,1451–1458.

[2] M. O. Damen, A. Chkeif, and J. Belfiore, “Lattice code decoder for space-time codes,” IEEE Communications Letters, 4, 2000, 161–163.

[3] M. O. Damen and A. R. Hammons, “Delay-tolerant distributed TAST codesfor cooperative diversity,” IEEE Transactions on Information Theory, 53,2007, 3755–3773.

[4] M. El-Hajjar, O. Alamri, S. X. Ng, and L. Hanzo, “Turbo detection ofprecoded sphere packing modulation using four transmit antennas for dif-ferential space-time spreading,” IEEE Transactions on Wireless Communi-cations, 7, 2006, 943–952.


[5] A. R. Hammons and M. O. Damen, “On delay-tolerant distributed space-time codes,” in Proc. of IEEE Military Communications Conference(MILCOM), 2007. IEEE, 2007.

[6] B. Hassibi and B. M. Hochwald, “High-rate codes that are linear in spaceand time,” IEEE Transactions on Information Theory, 48, 2002, 1804–1824.

[7] H. Jafarkhani, “A quasi-orthogonal space-time block code,” IEEE Transac-tions on Communications, 49, 2001, 1–4.

[8] Y. Jing and B. Hassibi, “Distributed space-time coding in wireless relaynetworks,” IEEE Transactions on Wireless Communications, 5, 2006, 3524–3536.

[9] Y. Jing and H. Jafarkhani, “Orthogonal and quasi-orthogonal designs inwireless relay networks,” IEEE Transactions on Information Theory, 53,2007, 4106–4118.

[10] J. N. Laneman and G. W. Woernell, “Distributed space-time-coded proto-cols for exploiting cooperative diversity in wireless networks,” IEEE Trans-actions on Information Theory, 49, 2003, 2415–2425.

[11] E. G. Larsson and P. Stoica, Space-time Block Coding for Wireless Commu-nications. Cambridge University Press, 2008.

[12] R. Nabar, H. Bolcskei, and F. Kneubuhler, “Fading relay channels: Perfor-mance limits and space-time signal design,” IEEE Journal on Selected Areasin Communications, 22, 2004, 1099–1109.

[13] Y. Shang and X. G. Xia, “Shift-full-rank matrices and applications in space-time trellis codes for relay networks with asynchronous cooperative diver-sity,” IEEE Transactions on Information Theory, 52, 2006, 3153–3167.

[14] S. Sugiura, S. Chen, and L. Hanzo, “Cooperative differential space-timespreading for the asynchronous relay aided CDMA uplink using interferencerejection spreading code,” IEEE Signal Processing Letters, 17, 2010, 117–120.

[15] V. Tarokh, H. Jafarkhani, and A. Calderbank, “Space-time block codes fromorthogonal designs,” IEEE Transactions on Information Theory, 45, 1999,1456–1467.

[16] M. Torbatian and M. O. Damen, “On the design of delay-tolerant distributedspace-time codes with minimum length,” IEEE Transactions on WirelessCommunications, 8, 2009, 931–939.

[17] D. Torrieri and M. C. Valenti, “Efficiently decoded full-rate space-time blockcodes,” IEEE Transactions on Communications, 58, 2010, 480–488.


[19] K. Vardhe, D. Reynolds, and M. C. Valenti, “The performance of multiusercooperative diversity in an asynchronous CDMA uplink,” IEEE Transac-tions on Wireless Communications, 7, 2008, 1930–1940.

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[22] A. Wittneben, “A new bandwidth efficient transmit antenna modulationdiversity scheme for linear digital modulation,” in Proc. of IEEE Interna-tional Conference on Communications (ICC), 1993. IEEE, 1993.

7 Collaborative relaying in downlinkcellular systems

Chandrasekharan Raman, Gerard J. Foschini, Reinaldo A. Valenzuela,Roy D. Yates, and Narayan B. Mandayam

7.1 Introduction

The deployment of relays in cellular system has been standardized in theWiMAX, IEEE 802.16j [1] standard and is a topic of discussion in the advancedspecifications of Third Generation Partnership Project (3GPP) long-term evolu-tion (LTE) [3]. Although commercial relay deployments in cellular systems arenot prominent at present, future wireless cellular systems will involve operationwith dedicated relays to improve coverage, increase cell-edge throughput, deliverhigh data rates, and assist group mobility. The proposed architecture is suchthat relays would be placed at certain locations (planned or unplanned) in thecell to help in forwarding the message from the base station to the user in thedownlink, and from the user to the base station in the uplink. Relays will be moresophisticated than simple repeaters and could perform some digital base bandprocessing to help the destination terminal get better reception. These relays willrely on air interfaces, and hence avoid the considerable backhaul costs involvingdata aggregation and infrastructure costs associated with backbone connectivity.However, there are a lot of open issues that require research to answer.

7.1.1 Research challenges

Some of the major research issues in relay-based cellular systems are as follows:

(1) Throughput gains due to relay deployments In cellular networks that arecoverage limited, deploying relays can help in multihop transmission andprovide power gains due to a reduction of distance attenuation [4]. Thesepower gains, in turn, translate to throughput improvements for the edgeusers. However, in interference limited settings, as is common in cellular sys-tems, uncoordinated transmission by relays leads to an increase in the overallinterference levels in the cell and could be counter-productive by reducing thesignal-to-interference-plus-noise (SINR) levels of users in the system. Coor-dination of transmissions in the system would require centralized control andincur high costs and overheads, especially in the uplink.



Thus, there is a need for a thorough evaluation of throughput improve-ments in a cellular system. In the cellular systems literature, there havebeen simulation studies to evaluate throughput gains in cellular systems,e.g., [5, 6, 8]. Even though the studies were conducted under different setsof (idealized) assumptions, throughput improvements in interference-limitedcellular systems were shown to be around 30–40% for the edge users. In thischapter, we evaluate the gains due to relay deployment by two different relay-ing strategies and the results indicate that throughput gains are of the sameorder. However, there may exist better practical schemes – which remainopen – or specific scenarios where relays provide larger throughput improve-ments. A simple case where relays provide throughput improvements is thedownlink scenario where the edge user is in a deep canyon and the relayis placed in the line of sight of both the base station and the shadoweduser.

(2) Relay placement The benefits from relay deployment depend on where therelays are placed in the cell. Throughput improvements depend on the trans-mit power, relay antenna pattern, and location of the relays in the system.Placing relays closer to an edge user helps the edge user. However, whenrelay transmissions are uncoordinated, the relays may cause near line-of-sightinterference to an edge user of the neighboring cell. The optimal relay place-ment depends on the transmission and scheduling strategies, transmit powerof the relays, etc. An issue closely related to the relay placement problem isthe choice of height of the deployed relays. In macrocellular environments,propagation characteristics of the base–relay link and the relay–user linkcould be completely different, depending on whether the relays are mountedon tall poles or on roof tops. These factors may very well affect the systemperformance due to relay deployments. There are not many measurement-based models to cover all the scenarios of relay placement; some empiricalmodels were described in [2]. These issues apart, service providers often donot have much choice in placing the relays in a given geographical area.

(3) Lack of good models for relaying in cellular systems Multihopping in wire-less networks has been studied in the context of ad-hoc networks and peer-to-peer networks [7]. The main issue addressed in such networks is the rout-ing problem. Interference constraints are abstracted as combinatorial con-straints and many insightful results and good algorithms have been proposedto improve the throughput of such networks. Cellular networks, however, areunique in that the traffic is one-to-many in the downlink and many-to-onein the uplink. Direct application of the solutions obtained in the contextof ad-hoc networks is not optimal for cellular systems. Hence, performanceevaluation of relays in cellular system requires fresh thought to be given tothe problem.

On the other hand, the information theoretic relay channel [9] has beenan active area of research since the 1980s. However, for some coding strate-gies proposed by Cover and El Gamal in [10] for special cases of the

178 Collaborative relaying in downlink cellular systems

single-relay channel, the capacity of the general relay channel is stillunknown [11]. Though most of the earlier work assumes that the relay cantransmit and listen over the same band, the half-duplex constraint (the relaycannot simultaneously transmit and receive in the same band) is taken intoaccount in later work, for example [12, 13]. Information theoretic studiesreveal that when there are one or two relays, the best strategy is to makeuse of both the source and relay transmissions at the user location, ratherthan multihopping from the source to the destination through the relay(s).The user can make use of signals from both the source and the relay to geta better signal strength and hence a better rate. Multihopping, on the otherhand, ignores the signal from the source, however strong it is.

The information theoretic relaying protocols mentioned above ofteninvolve complicated multiuser coding and decoding techniques, which arefar from practical implementation. There has been some work trying tobridge the gap between the information theoretic and practical multihop-ping schemes, e.g., [14, 15]. Most of the results in these works correspondto the case of a linear network of nodes, where there is a single commod-ity flow of message from the source node to the sink node through a setof relay nodes. Any interference is due only to simultaneous transmissionsfrom different relay nodes. This can be completely eliminated by multiusercoding/decoding techniques. Such an analysis does not carry over directly tothe cellular systems since there are multiple simultaneous flows and multiusertechniques may incur significant overheads.

(4) Fairness Service level agreements between cellular service providers entailcertain fairness requirements. For example, in the cellular system, the edgeusers and the users near the cell require the same level of service. Manyother fairness schemes, including proportional fairness [16] and max–minfairness [17, Chapter 6] have been proposed for cellular systems serving voiceand data. Present-day cellular systems implement schedulers in the MAClayer to provide various degrees of fairness to users. In this work, we assumethat 90% of users are required to be served at a common rate. When relays arepresent in the system, designing distributed scheduling schemes to providefairness is an active area of research.

In this chapter, we evaluate the performance of low-cost half-duplex relays inthe downlink of a cellular system. The deployment scenario we consider is tomount a low-cost (preferably low-powered) device per sector over roof-tops ofbuildings. Such devices can relay the information from the base station to usersin the cell.

7.1.2 Related work

Relay deployment in a cellular system has been proposed to solve the issue of alack of coverage over a large area [1]. The use of relays in cellular systems has also


been proposed to bring capacity improvements [18]. Viswanathan and Mukher-jee [5] studied the performance of a centralized throughput-optimal scheduler ona cellular network with relays. They presented a centralized downlink schedulingscheme that guarantees the stability of user queues for the largest set of arrivalrates into the system. Each user has a queue at the base station and a queue at itsserving relay and the objective of the scheduler is to stabilize both queues whilemaximizing the throughput. The throughput results obtained by simulationsin [5] suggest that simultaneous transmissions (due to multihopping) exploitingspatial reuse could lead to cell-wide throughput gains in a cellular network.

7.1.3 Overview of contribution

In addition to a multihopping model, wherein the message travels to the destina-tion in two hops, in this chapter we evaluate the performance of a collaborativepower addition (CPA) scheme with a single relay available per user. We bring anadditional dimension to the benefits of relays in a cellular system, by quantifyingthe power savings due to the deployment of relays. Peak power savings in cellularnetworks are very important elements of amplifier costs in base stations. Signif-icant peak power savings can reduce the cost of amplifiers and hence the capitalexpenses for deploying cellular networks. Also, average power savings while oper-ating cellular networks can save operational expenses such as electricity bills forthe cellular operators.

In the peak CPA (P-CPA) scheme, we first consider a hypothetical modelwhere 90% of the users are required to be served a file (henceforth, we use theterms message and file interchangeably) of a fixed size before a certain deadline.Depending on the interference seen by each user, the mutual information (MI) orthe instantaneous “rate” of the users varies over time. Users leave the system asthey get the complete file before the deadline. We use an offline computation tofind the 10% of users who are least able to get the whole file before the deadlineand discard them at the beginning. We run the real system without the usersin outage. When relays are present in the system, we evaluate the peak powersavings at the base station to deliver a file of the same size to the same numberof users in the system as when the base stations and relays are transmitting attheir peak power limits. We also find the improvements in common rate for theusers in the presence of the relays when the peak power of the base stations isfixed for both the baseline and the system with relays.

We then consider the power control capability to the base stations and relays.We evaluate the power savings and throughput improvement in the power con-trol CPA scheme (PC-CPA). For a desired common rate requirement for 90% ofusers in the system, we find the common peak power constraint in the baselinecase and in the system with relays to guarantee the common rate. When therelays get the complete message, they collaborate with the base station to trans-mit the message to the users. Each time a relay becomes eligible to transmit,the optimal set of powers are found to satisfy the desired rate requirement. The


set of users that violate the peak power constraint are discarded at the begin-ning. The improvements in common rate are also evaluated through a similarprocedure.

The second relaying scheme we evaluate is simple multihopping, wherein thebase stations and relays transmit in orthogonal time slots. The baseline systemis similar to the baseline in the P-CPA scheme described above. When relaysare present in the system, we simulate a time-slotted system. For a commonrate requirement for 90% of users in the system, the base stations transmit atpeak power in odd time slots. The relays and users are in the receive mode. Inthe even time slots, the base stations are turned off and relays transmit to therespective users. The relays employ power control to target the remainder of theuser population to provide the residual rate to the users. We describe the systemin detail in Section 7.2.

We do not consider multiuser scheduling gains, MIMO gains, or any othercomplex interference mitigation techniques. Thus the gains shown in the net-work arise purely from the power gains at the user location due to the relaytransmissions.

7.2 System model

Our work evaluates the power savings and improvement in common rate amongusers due to relay deployments in a cellular system. However, to model andsimulate all dynamics of a cellular system may be too complicated. In order toovercome such difficulties, we make some reasonable simplifying assumptions andtake an idealized look at the model and operation of a cellular system. In orderto make a fair comparison, the assumptions are kept consistent across systemswith and without relays. We consider a cellular system with idealized hexagonalcells with a base station at the center of each cell. The topology is shown inFigure 7.1. The first two tiers of interferers are considered and the activities ofthe farther tiers of cells are mirrored by the central ring of 19 cells. The site-to-site distance (distance between any two base stations) is taken to be 1 mile. Thecells are divided into 120 degree sectors, with each sector illuminated by a basestation antenna pattern given by

A(θ) = −min

(12(

θ

θ3dB

)2

, Amax

)(7.1)

where A(θ) is the antenna gain in dBi in the direction θ, −180 ≤ θ ≤ 180, min(.)denotes the minimum function, θ3dB = 70 degrees is the 3 dB beamwidth andAmax = 20 dB is the maximum attenuation. The antenna gain pattern is shownin Figure 7.2.

At the receiving terminal (relay or user), the transmitted power undergoesattenuation due to the distance traveled and shadowing effects around the


Figure 7.1. Wrap-around simulation model. The central ring of 19 cells is usedfor the simulation. The surrounding cell activity is mirrored in the center ring.The directions of the arrows represent the directions of the main lobe of thesectorized antenna.

receiver. The propagation attenuation between a transmitting terminal (basestation or relay) and a receiving terminal (relay or user) consists of the path-loss and the shadowing component. At any receiving terminal, the transmittedpower is attenuated in dB as PL(d) = −31.5− 38 log10 d, where d is in meters.The shadowing is modeled as lognormal with mean 0 dB and a standard devia-tion of 8 dB. The shadowing is assumed to be spatially uncorrelated and fixedfor a given set of user locations. The base station and the relay antenna gainsare taken to be 15 dB (at zero degree horizontal angle) and user antenna gainas −1 dB. Other losses account for 10 dB. Together with the above losses, weinclude the antenna pattern loss to calculate the received power. The receivernoise figure is set at 5 dB, and the thermal noise power at each receiving terminal


Figure 7.2. Antenna gain pattern (from [2]) as a function of the horizontal anglein degrees. The mathematical expression for the gain is given in (7.1).

(relay or user) is assumed to be −102 dBm. The effect of multipath small-scalefading is ignored in our simulations.

All users share the same band of frequencies and hence simultaneous trans-missions can interfere with each other. The total interference at each receivingterminal from all transmitters in the system is modeled as Gaussian noise andassumes that other users use Gaussian codebooks. The achievable rate to a useri at time t is calculated as the Shannon rate

Ri(t) = log2(1 + ρi(t)), (7.2)

where ρi(t) denotes the SINR for user i at time t The parameters used in theabove-mentioned simulation set-up are summarized in Table 7.1. We use thissimulation set-up to evaluate all relaying methodologies proposed in this chapter.

We simulate a downlink OFDM-like system wherein users in orthogonal timeor frequency slots do not interfere with each other. However, users in the sameresource unit interfere with the other transmissions in the band. We simulate theworst-case scenario where the system is fully loaded, i.e., users are present in allavailable resource units (or time–frequency slots) in all the sectors. The time–frequency slots are reused in each sector. We assume that the time–frequencyslots are orthogonal, and focus only on a particular time–frequency slot withinwhich we simulate the complete cellular system such that there is one activeuser per sector at a given time. Hence, in a 19-cell network with three sectors


Table 7.1. Simulation parameters

Network topology 19 cells, three sectors per cell with wraparoundSite-to-site distance 1 mileBandwidth 5 MHzPath-loss model COST-231 Hata modelPath-loss exponent α = 3.8Shadowing Lognormal, with zero mean, 8 dB standard deviation

for access and backhaulMultipath fading NoneAntenna pattern Sectorized for base stations;

omnidirectional for relaysAntenna gains 15 dB (for base station and relays);

−1 dB for usersOther losses 10 dBThermal noise power at −102 dBmthe receiverOutage 10% for baseline and relays

per base antenna, at most 57 users are served in a given time–frequency slot. Inour simulations, we use the following heuristic to create a random user popula-tion along with an association rule. Users are placed one-by-one in a uniformlyrandom fashion across the network until all 57 base station sectors are occupied.For each random realization of a user location, the base station sector with thehighest received signal strength is chosen to associate with the user. If the basestation sector is already occupied by another user, the user is not allowed into thesystem and a new user location is generated. Along with a random realization ofa user location, independent lognormal random variables are also instantiated toaccount for the shadow fading gains between each base station and the user inthe baseline system. If relays are present in the system, the fading gains are alsogenerated for base station–relay links and relay–relay links. In this way, randomplacement is carried out until all 57 sectors are occupied by exactly one user persector. Each user is equipped with an omni-directional antenna.

A relay with an omni-directional antenna is placed in the direction of themain lobe of each base station sector antenna as shown in Figure 7.3. The relaysalways associate with the corresponding base station sector. The relay placementis an important parameter to be considered since the power gains and through-put improvements depend on the interference generated by the relays, which inturn depends on the transmit power, geographic location of the relays, and thepropagation environment. In our simulations, we experiment with various relayplacements and the simulation results are presented for the relay locations forwhich the gains are found to be maximum. The relay powers are also varied sothat we get the maximum peak power savings.


Figure 7.3. Position of relay location in a cell. The relays (represented by smallcircles) are placed at half the cell radius in the direction (given by the arrows)of the main lobe of the sector antenna. The base station at the center of the cellis represented by a square.

7.3 Collaborative relaying in cellular networks

In the CPA scheme devised in [19], the relay collaborates with the base stationto help the message reach the destination. In our simulation model, each basestation sector has a single user to be served and a relay that may help the sourceto deliver the message to the user associated with the source. In what follows,we focus our attention on an isolated triplet of base station (source), relay, anduser in a single sector. Gaussian encoding is used across all other sectors, theinterference from other sectors is considered as if it were additive Gaussian noise.Suppose the source wants to transmit one of the M messages to the destination,under a power constraint P . The source transmits a Gaussian codeword of lengthN = (log M)/R, where R is the rate of the code. By Shannon’s channel codingtheorem [20, Chapter 9], if N is large enough, the message can be decodedreliably at the destination provided R < log(1 + ρ), where ρ is the received SINR.In our simulations, we are interested in achievable rates and assume that theinstantaneous mutual information at the receiver is exactly R = log(1 + ρ).

Assume that the source picks a rate R code C1 and sends one of M equallyprobable messages to the destination, using a codeword of length N . Let thereceived SINR ρSR between the source and relay be greater than the receivedSINR ρSD at the destination. Then, there exists some β > 1 such that

log(1 + ρSR ) = β log(1 + ρSD ), (7.3)

i.e., the capacity of the channel from source to relay is β times greater than thatof the channel from source to destination. We can now construct codebook C2derived from C1 by observing only the first N/β symbols of every codeword.The relay can then reliably decode the received message since the rate of C2 is

R′ =log M

N/β < log(1 + ρSD ). (7.4)

7.3 Collaborative relaying in cellular networks 185

Source Relay Destination

Figure 7.4. Collaborative relaying: before the relay decodes the message.

SourceRelay Destination

Figure 7.5. Collaborative relaying: after the relay decodes the message.

In [21, Appendix F], the authors discuss the coding interpretation of a similarcollaborative strategy. They also discuss the connection of such a coding set-ting with coding for an arbitrary varying channel (AVC), which was first dealtwith in [22] and subsequently studied in [23]. We simulate a similar collabora-tive coding strategy wherein before the relay decodes the message as shown inFigure 7.4, the received power at the destination node is only due to the base sta-tion transmission. After it decodes the message, the relay joins the base stationto help the base station in delivering the message to the destination as shown inFigure 7.5. At this point, if we assume that transmit symbol time slots at the relayand base station are synchronized and the code books are shared, the system canbe viewed as a 2× 1 multiple-input single-output (MISO) system without chan-nel information at the transmitter. There is an effective power addition of thebase station and relay transmissions at the destination [24, Chapter 3]. A similarscheme has been proposed in the literature as the dynamic decode-and-forward(DDF) scheme [25].

We simulate this collaborative relaying strategy in two ways:

Base station and relay transmit at their respective peak powers. In this case,the transmit power is fixed and the users get variable rates depending onSINR at the user locations. When a target rate is obtained by a user, theuser leaves the system and the corresponding base station sector is turnedoff, thus reducing the amount of interference in the system. We term this


the peak collaborative power addition (P-CPA) scheme. This is described inSection 7.4.

Base station and relay operate with power control so that the users obtaina target desired rate. In the baseline case, for a given desired rate require-ment r0 bps/Hz, a feasible set of powers are found to better satisfy the raterequirement, allowing certain users to be in outage. When the relays decodethe message in the collaborative scheme, the optimal powers are recalculatedto find another feasible set of powers to satisfy the rate requirement at thesame outage level. This is the PC-CPA scheme. It is described in Section 7.5.

7.4 CPA with peak power transmissions (P-CPA)

7.4.1 Principle of operation

P-CPA baselineIn the baseline of the P-CPA scheme, each base station sector transmits at itspeak power to its own intended user. Since all users share the same band offrequencies, they receive interference from all the base station sectors in thesystem. If at time t, pi(t) is the peak power of the transmitting base stationsector corresponding to the ith user, hij is the channel gain, including path-lossand shadowing, from the jth base to the ith user, and σ2 is the variance of thenoise power at the receiver, the instantaneous received SINR for user i is givenby

ρi(t) =hiipi(t)∑

j =i hij pj (t) + σ2 . (7.5)

Since we assume Gaussian signaling, the mutual information (MI) or the instan-taneous “rate” to each user is

Ri(t) = log2(1 + ρi(t)) bits/symbol. (7.6)

At time t = 0, all base stations simultaneously transmit to their associated user.As time progresses, for any small time interval [t, t + ∆t], user i accumulates MIIi(∆t) = Ri(t)∆t. The MI for user i at time t is given by

Ii(t) =∫ t

0log2(1 + ρi(ξ)) dξ. (7.7)

If user i accumulates MI corresponding to the required amount L of data beforethe deadline T , i.e.,

τi = min0≤t≤T

t : Ii(t) = L, (7.8)

7.4 CPA with peak power transmissions (P-CPA) 187

then the user leaves the system and the associated base station sector is turnedoff at time τi , reducing the overall interference levels in the system. Hence,

pi(t) =

P, t < min(τi, T ),0, t ≥ min(τi, T ),

(7.9)

where P is the peak power of the base station transmission. Note that the ρi(t)of user i and the rate Ri(t) are time-varying quantities. At time t = T , the usersthat remain in the system are those users that did not get the complete file. Itis these remaining users that are in outage.

P-CPA system with relaysThe operation of the P-CPA system with relays is as follows. The requirementis the same as for the baseline case: to deliver a file of size L to as many userswithin the time T . At time t = 0, the base stations transmit at peak power tousers associated with them. The relay node placed in the sector also receives thedata sent to the user by the base station. If the relay receives the complete filebefore the user does, the relay can potentially be useful to the user by helping itreceive the message faster. On the other hand, the relay transmission can createadditional interference for the other users in the system. In our simulations,we follow a myopic1 policy on whether to turn on the relay or not: the relaytransmits at peak power to help its user only if the instantaneous sum-rate ofthe whole system increases by turning the relay on. The sum-rate of the systemis calculated as the sum total of the instantaneous rates of the existing users inthe system and is a natural system-wide metric to use in order to decide whetherthe relays should transmit or not. At every epoch, one relay among the set of allrelays that are eligible to be turned on, receives the message, the myopic sum-rate metric is applied, and those relays that increase the sum-rate are turned onto help the users in the system.

If the relay increases the sum-rate of the system, the relay is turned on andhelps the user with a transmission reinforcing the same message as the basestation using the code described in Section 7.3. If qi(t) is the power transmittedfrom relay i at time t and gij is the channel gain from user i to relay j, theeffective SINR at ith user location when the relay is active is given by

ρrelayi (t) =

hiipi(t) + giiqi(t)∑j =i hij pj (t) + gij qj (t) + σ2 . (7.10)

1 The policy is myopic since, at the time when the relay receives the message, the globaloptimal decision whether the relay should transmit or not is unknown.


The instantaneous rate and the mutual information for user i at time t are givenby

Rrelayi (t) = log2(1 + ρrelay

i (t)), (7.11)

Irelayi (t) =

∫ t

0Rrelay

i (ξ)) dξ. (7.12)

If Hij denotes the channel gain from the jth base station to the ith relay,

Ji(t) =∫ t

0log2

(1 +

Hiipi(ξ)∑j =i Hij pj (ξ) + σ2

)dξ (7.13)

represents the cumulative MI at the relay at time t.Suppose relay i becomes eligible to transmit at time t, i.e., Ji(t) > L, then

denote the sum-rate of the system at time t as a function of qi(t) as

SR(t, qi(t)) =∑

i

log2

(1 +

hiipi(t) + giiqi(t)∑j =i hij pj (t) + gij qj (t) + σ2

). (7.14)

The relay power at time t is given by

qi(t) =

Q, if Ji(t) > L,SR(t,Q) > SR(t, 0) and t < T,

0, otherwise,(7.15)

where Q is the peak power constraint of the relays. Each user sees a time-varyingSINR and the time-varying rate given by Ri(t) = log2(1 + ρrelay

i (t)). As with thebaseline case, for any interval of time [t, t + ∆t], user i accumulates MI amountingto Ii(∆t) = Ri(t)∆t and the MI for user i at time t is

Ii(t) =∫ t

0log2(1 + ρrelay

i (ξ)) dξ. (7.16)

Similarly to the baseline case, if the user accumulates MI amounting to the fullfile size L within the stipulated time T , the user leaves the system and theassociated base station and relay are switched off. Thus the effective interferencein the system is reduced. At time t = T , the users that remain in the system arethose users that did not receive the complete file.

7.4.2 User discarding methodology

The user discarding procedure can be divided in two phases:

(i) A learning phase where we learn the power threshold, which is used as acriterion to determine the users in outage. All the users that are not inoutage require their corresponding base stations to have peak powers lowerthan the power threshold. The network will be operated with peak powersof all base stations capped at the power threshold.

(ii) After the power threshold is found, we assume the availability of a veryfast computing facility and perform an off-line computation to find out the


set of users that are in outage. Such users could be discarded before thestart of the simulations so that the other users benefit from the absence ofinterference from these users. Hence, this takes care of the causality of thediscarding phase from the operation of the real network.

We conduct Monte Carlo simulation runs for the baseline case as well as thecase with relays in this chapter. For each simulation run random instantiationsof 57 user locations (as per Section 7.2) and associated statistically independentshadow fading values are generated. Once the random values are instantiated,they are stored in our simulation software program. The same set of user locationsand shadow fading values serve as inputs to the baseline and the system withrelays.

We now explain the learning phase. Consider that a single instance of thesimulation runs in the baseline case. For the given instantiation, there are 57users, one in each sector. We fix a peak power threshold P for the base stationsand also fix the desired common rate for users as r0 bps/Hz. When the baselinesystem operation is over, the users that are in outage remain in the system at timeT . Let the number of users in outage for the kth instantiation when the powerthreshold is P and desired common rate r0 be Ok (P, r0). For the same powerthreshold P and common rate r0 , we run a large number K of instantiations.We then find the total number of users in outage as

O(P, r0) =K∑

k=1

Ok (P, r0). (7.17)

The percentage of users in outage for the threshold P and desired rate r0 is then

O(P, r0)57K

× 100%. (7.18)

If O(P, r0) > 10%, we increase the power threshold to P ′ > P . On the other hand,if O(P, r0) < 10%, we decrease the power threshold to P ′′ < P . Proceeding in thisfashion, the base station peak power thresholds are adjusted such that exactly90% of the users are guaranteed the desired rate of r0 bps/Hz and the remaining10% of the users are in outage.

We could improve the performance of the system by discarding the users inoutage upfront, since the interference due to the presence of these users will beeliminated at time t = 0. In our simulations, for a large user population over K

instantiations, we identify 10% users in outage2 by first running K instantiationsof the system with all the users present in the system. We store the coordinatesof all the users that were in outage at the end of each of the K instantiations. Wethen eliminate the outage users from the system (by preserving the coordinatesof the user locations of only those users not in outage for all the K instantiations)

2 We remark that the eliminated set of 10% of the users in outage is not claimed to be theoptimum set as would be obtained by evaluating all possible subsets amounting to 10% ofthe users. The latter is computationally prohibitive.


at time t = 0 in the real network simulations. Thus, the existing users in thesystem experience less interference due to the absence of those users in outagewhen the real network is simulated.

7.4.3 Network operation and simulation aspects

Our objective is to obtain power savings and throughput improvement due todeployment of relays in a cellular system. To compare systems with and withoutrelays in the CPA-based relaying scheme, we simplify the operation of a cellulardownlink system such that 90% of the users in the system are guaranteed to bedelivered a file of fixed size L, within a fixed period of time T . The file couldbe different for all users but the file sizes are fixed. Such an operation bringsin the notion of a common rate for the users in the system. In order that thesystem benefits from the users that receive the message within the fixed time T ,the satisfied users leave the system, and thus no longer cause interference to theremaining users. The remaining 10% of the users that are not guaranteed the fileof size L are in outage.

In our simulations, for the sake of simplicity, all base stations are assumedto have the same peak power threshold values. We run K = 200 (amountingto 11 400 user instantiations) different user instantiations in the system. Thecommon rate requirement is set as 1 bps/Hz. We divide the total time T into 1000mini-slots and at the end of each mini-slot, we keep track of the cumulative MIIi(t) of each user i. If at the end of a mini-slot, a particular user’s cumulative MIexceeds the file size L, the base station corresponding to that user is turned off.

We run the baseline for different peak power values of the base station (5 Wto 30 W in increments of 5 W). For each peak power value, the relay powersare varied as a factor of the base station power. Figure 7.6 shows the variationof outage probability for various base station powers and various relay powers.For the case when there are no relays in the system (ratio of relay power to basestation power is zero), increasing the peak powers of the base station decreasesthe outage. The percentage of outage saturates below a certain threshold asthe interference limit sets in. As we increase the relay powers by increasing theratio of relay power to base station power, the outage reduces but quickly satu-rates to a certain threshold outage value, because of the interference limit. FromFigure 7.6 it is clear that the interference limit is quickly reached and this limitsthe performance of a system with relays. This is because there is no interferencemanagement and peak power transmissions from the base stations and relayslead to a highly interference limited scenario.

7.4.4 Simulation results

Power savingsThe peak power required to guarantee the remaining 90% of the users (after the10% of users in outage have been removed) a rate of 1 bps/Hz is 21 W in the


Table 7.2. P-CPA relaying (base station and relays transmit at peak power)

Peak power required to Peak power required to

Savings in dBguarantee 1 bps/Hz guarantee 1 bps/Hz

at 10% outage; at 10% outage;baseline (no relays) with relays

21 W 15 W 1.46

Common rate for 90% users; Common rate for 90% users; Percentage ratebaseline (no relays) with relays increase

1 bps/Hz 1.21 bps/Hz 21 %

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 15

6

7

8

9

10

11

12

13

14

Ratio of relay power to base station power

Out

age

perc

enta

ge a

t 1 b

ps/H

z

Base station power = 15 WBase station power = 20 WBase station power = 25 W

Figure 7.6. Variation of outage with relay powers and base station powers. Aswe increase the base station powers with no relays in the system (ratio = 0), theoutage decreases and saturates at around 5%, due to the inteference limit. Theinterference limit sets in very quickly even for smaller values of relay powers.

baseline case and it requires 15 W for a system with relays. The relays transmit1 W of peak power. Hence the peak power saving at the base station locationsin this case is 1.46 dB as shown in Table 7.2.

Rate gainsIn order to evaluate the throughput improvement, we find how much the commonrate of 90% of users can be improved with the peak power of the base stations


being fixed. For the baseline, we fix the power of the base stations to 21 W,so that 90% of the users are guaranteed to receive 1 bps/Hz (as obtained inthe previous section); 10% of the users in outage are eliminated as explained inSection 7.4.2. For the P-CPA system with relays, the peak power threshold of thebase stations is fixed to 21 W (the same value as in the baseline case). For thesame peak power for the base stations and with relays present in the system, weexpect the common rate to be better than 1 bps/Hz. To find the improvement incommon rate, we fix a desired common rate r′ > 1 bps/Hz and run the sytem withrelays. If this desired common rate is feasible,3 we double the desired commonrate and run the simulations again. Or, if the desired common rate is not feasible,we fix the new desired common rate at half the difference between the highestfeasible common rate and the lowest not feasible common rate and rerun thesimulations. In this manner, we converge to the achievable common rate in thepresence of relays. In our simulations, we find that the common rate can beimproved to 1.21 bps/Hz in the CPA-based relaying scheme. Hence the commonrate improvement is 21%.

7.5 Power-control-based collaborative relaying (PC-CPA)

In Section 7.4.3, we observed that for P-CPA the interference from the otherrelays and base station sectors limited the peak power savings in the systemwith relays. The reason for that is that when the relays transmit to help theusers, they transmit with peak powers and hence increase the interference levelsin the system. If we could find the optimal set of powers to transmit for thebase station and the relays, we could reduce the overall interference levels in thesystem. This may improve the gains in the system.

In the following, we describe a framework for power control in the downlinkof a cellular system with relays. When the relays are not present, downlinkpower control in a cellular system has been well studied and understood [26].When relays are present in the system, power control, if performed jointly atthe base stations and relay locations, can provide power savings and throughputimprovement. We describe the PC-CPA relaying scheme in the following sections.

7.5.1 Principle of operation

PC-CPA baselineFor the PC-CPA baseline, the aim is to deliver a desired common rate for 90%of the user population by employing a simple power control scheme. Each basestation sector powers down its transmitted power within the peak power limita-tions so that 90% of users are guaranteed a desired common rate of r0 bps/Hz.

3 The common rate is feasible if all the users present in the system are able to get the desiredrate.

7.5 Power-control-based collaborative relaying (PC-CPA) 193

Since all users share the same band of frequencies, they observe interference fromall the base station sectors in the system. We use a common subscript for a basestation or a user in a particular sector. If at time t, pi is the power of the trans-mitting base antenna corresponding to the ith user (we drop the argument t),hij is the channel gain, including path-loss and shadowing, from the jth base tothe ith user, and σ2 is the noise power at the receiver, the instantaneous SINRof the ith user in the system is given by

ρi(t) =hiipi∑

j =i hij pj + σ2 . (7.19)

Since the transmission uses Gaussian codebooks, the corresponding instanta-neous rate for the user i is given by

Ri(t) = log2(1 + ρi(t)) bps/Hz. (7.20)

The set of feasible powers such that the users not in outage are guaranteed arate r0 is obtained by solving for the feasibility of instantaneous rates subject topeak power constraints, specified by

log2(1 + ρi(t)) ≥ r0 , (7.21)

i.e., ρi(t) ≥ 2r0 − 1, (7.22)

subject to: pi ≤ pi,max (7.23)

for all users i not in outage. In practice, each base station increases its powerautonomously in small increments, until it hits the peak power limit or untilthe user associated with it attains the desired rate r0 . Users that achieve thepower constraint to go active before attaining the desired rate are discarded. Wesimulate the system without the users in outage such that all users achieve thedesired rate. Since the transmit powers of the base stations are such that allusers attain a common rate, none of the users leave the system.

PC-CPA system with relaysIn the PC-CPA system with relays, 10% of users are discarded in a mannersimilar to that in the baseline system. At time t = 0, the relays do not have thecomplete message required to relay to the user. Hence, the system starts out as itdoes for the baseline case. The base stations increase their powers autonomouslyin small increments targeting the user rates to increase. Users that do not meetthe peak power constraints in (7.23) are eliminated one after the other. Theremaining users attain the desired rate without violating the peak power con-straint at the base stations. While the base station transmissions are targetedto the users, the relay in each sector also listens to the transmission by the basestations. Depending on the channel conditions and coupling of interference fromthe adjacent sectors, the relays receive their message at different points in time.When the relay in the sector decodes the message from the base station, therelay collaboratively helps the base station such that the user gets a rate corre-sponding to the total SINR from the relay and the base station. As described


in Section 7.3, the code books at the base stations and relays are designed suchthat the mutual information at the receiver corresponds to the sum of receivedpowers at the user location [19]. In order to maintain the common desired rate forall users, the relay and base station jointly adjust their powers so that the userreceives the desired rate. This ensures that the base station and relay transmitjust enough power to the user to obtain the desired rate.

Let pi denote the power transmitted by the base station sector i at time t andhij be the channel gain, including path-loss and shadowing, from the jth baseto the ith user. Let qi be the power transmitted from the relay i at time t andgij be the channel gain to the user i from the relay j. Then, when the relay andbase station transmit simultaneously, the effective SINR at the ith user locationwhen the relay is active is given by

ρrelayi (t) =

hiipi + giiqi∑j =i hij pj + gij qj + σ2 . (7.24)

As with the baseline case, the set of feasible powers (for both base station anten-nas and relays) such that the users not in outage are guaranteed a rate r0 isobtained by solving for the feasibility of instantaneous rates subject to peakpower constraints

log2(1 + ρrelayi (t)) ≥ r0 , (7.25)

i.e., ρrelayi (t) ≥ 2r0 − 1, (7.26)

subject to: pi ≤ pi,max (7.27)

and qi ≤ qi,max (7.28)

for all users i not in outage. If we consider the transmit powers of the base stationsand relays to be variables of optimization, we have a total of 2N variables, forN base station sectors in the system. Thus, power control in cellular systems inthe presence of relays gives us an additional N degrees of freedom over whichto optimize. The transmit powers in the system can be optimized to reduce themaximum peak power transmission in the system, to reduce total energy in thesystem, etc. In what follows, we assume that a central controller has knowledge ofall the channel gains between the base stations as well as relays and the users. Weexplain ways to achieve various aforementioned objectives using linear program(LP) formulations.

7.5.2 Optimization framework

Minimizing the total instantaneous transmit powerWe are interested in evaluating the benefits of relays in minimizing the totalinstantaneous sum power in the system while delivering the common rate r0

with 10% of the users being omitted from the system. The practical benefit ofminimizing the total sum of transmit powers in a cellular system is to save the


energy costs in the network. Saving energy costs translates to saving electricitybills at the cell sites for the cellular service provider.

The desired common rate for the users is fixed at r0 bits/symbol. We defineA(t) as the set of all active relays at time t, i.e., the set of relays that haveobtained the message and are ready to help the base station. Ac(t) denotes thecomplementary set of all inactive relays. For simplicity, we drop the argument andwrite pi and qi for the base station powers pi(t) and qi(t) at time t, respectively.

At a given time t, the central controller solves the following optimization prob-lem:

minp1 ,...,pNq1 ,...,qN

∑i

pi + qi, (7.29a)

subject to: log2

(1 +

hiipi + giiqi∑j =i hij pj + gij qj + σ2

)≥ r0 , i = 1, . . . , N, (7.29b)

0 ≤ pi ≤ pi,max , i = 1, . . . , N, (7.29c)

0 ≤ qi ≤ qi,max , i ∈ A(t), (7.29d)

qi = 0, i ∈ Ac(t). (7.29e)

The solution to the optimization problem (7.29), p∗i , q∗i , i = 1, . . . , N defines the

powers pi(t) = p∗i and qi(t) = q∗i that are used at time t. The optimization prob-lem (7.29) is an LP, since we can write the constraint (7.29b) as

12r0 − 1

(hiipi + giiqi)−∑j =i

(hij pj + gij qj ) ≥ σ2 (7.30)

for i = 1, . . . , N . Rewriting (7.29) in vector form, we have

s∗(t) = minp,q

1T (p + q), (7.31a)

subject to: Ap + Bq ≤ −σ21, (7.31b)

0 ≤ p ≤ pmax , (7.31c)

0 ≤ q ≤ qmax , (7.31d)

where

A =

⎛⎜⎜⎜⎝−h11/(2r0 − 1) h12 · · · h1N

h21 −h22/(2r0 − 1) · · · h2N

......

. . ....

hN 1 hN 2 · · · −hN N /(2r0 − 1)

⎞⎟⎟⎟⎠ , (7.32)

B =

⎛⎜⎜⎜⎝−g11/(2r0 − 1) g12 · · · g1N

g21 −g22/(2r0 − 1) · · · g2N

......

. . ....

gN 1 gN 2 · · · −gN N /(2r0 − 1)

⎞⎟⎟⎟⎠ , (7.33)


and

p(t) = [p1(t) . . . pN (t)]T ,

q(t) = [q1(t) . . . qN (t)]T ,

pmax = [p1,max . . . pN ,max ]T , (7.34)

qmax = [q1,max . . . qN ,max ]T ,

with qi,max = 0, i ∈ Ac(t). The solution to the above LP provides the optimalpower values that minimize the instantaneous total power in the system. We takea myopic approach of minimizing the total sum power of the system at time t inorder to reduce the total average power transmission in the system. Each timea relay becomes eligible for transmission, the LP is solved to find the best setof powers by minimizing the instantaneous powers in the system. Note that insome cases, when a relay is eligible to help the base station, turning off the basestation may be the optimal thing to do. This choice comes out as a solution tothe optimization program.

Minimizing the peak transmit powerMinimizing the peak transmit power leads to peak power savings in the sys-tem. A practical benefit of peak power savings is the significant savings in thecost of power amplifiers for the cellular base stations. If by deploying low-powerrelays in the system, we save on the cost of the power amplifiers of the basestations, cellular operators could save on capital expenses. To this end, we solvethe following optimization problem of minimizing the maximum instantaneoustransmit powers at the base stations:

minp1 ,...,pNq1 ,...,qN

maxi

pi , (7.35a)

subject to: log2

(1 +


)≥ r0 , i = 1, . . . , N, (7.35b)

0 ≤ pi ≤ pi,max , i = 1, . . . , N, (7.35c)

0 ≤ qi ≤ qi,max , i ∈ A(t), (7.35d)

qi = 0, i ∈ Ac(t). (7.35e)

Rewriting the above LP in vector form yields,

p∗(t) = minp,q

α, (7.36a)

subject to: Ap + Bq ≤ −σ21, (7.36b)

0 ≤ p ≤ pmax , (7.36c)

0 ≤ q ≤ qmax , (7.36d)

α1 ≥ pmax , (7.36e)

where A and B are given by (7.32) and (7.33), respectively.


Improving the common rateAs a corollary to the above approaches, if we keep the peak power constantacross both the baseline and the system with relays, we can increase the commontargeted rate in the system with relays. The problem of maximizing the commonrate can be posed as an optimization program with the transmit powers of thebase station and relays as the variables. A central controller then solves theoptimization program:

maxp1 ,...,pN

r0 , (7.37a)

subject to: log2

(1 +


)≥ r0 , i = 1, . . . , N, (7.37b)

0 ≤ pi ≤ pi,max , i = 1, . . . , N, (7.37c)

0 ≤ qi ≤ qi,max , i ∈ A(t), (7.37d)

qi = 0, i ∈ Ac(t). (7.37e)

The optimization program can be viewed as a sequence of linear feasibility prob-lems because the constraint set is nonconvex. We solve this program by an iter-ative approach. We start with a low easily achievable target rate r0 so that theconstraint set (7.37b)–(7.37e) is feasible. We increase the target rate in smallincrements until the constraint set becomes infeasible. In each step, we get a setof feasible power assignments. The last set of feasible power assignments is thesolution to the optimization program. The method converges, since the iterationsgenerate a bounded sequence of increasing rates.

7.5.3 User discarding methodology

In our simulations, we eliminate 10% of users (over a large number of user real-izations) in the following way. The procedure is identical for both the baselineand the system with relays. We simply assume the same peak power constraintsfor all base stations across the network. We fix the peak power threshold pmax

for each base station. Consider a single instantiation, where there are 57 users inthe system. We increase the transmit power in all base stations in small incre-mental steps to improve the rate of the users in the system. As we do so, wediscard the user associated with the base station whose power constraint goesactive first. The base station is also turned off. This reduces the interferencecoupled with other users. Within the remaining set of users, we can increasethe transmit powers further. We then discard the next user causing the powerconstraint to become active and continue in this fashion until all remaining usersin the system are guaranteed the desired rate of r0 bps/Hz, without violatingthe peak power constraints. This procedure is repeated for a large number K ofusers instantiations. Let the number of users in outage for the kth instantiationwhen the power threshold is pmax and desired common rate r0 be Ok (pmax , r0).


We then find the total number of outage users for K instantiations when thepeak power threshold is pmax and the desired rate is r0 is calculated as

O(pmax , r0) =K∑

k=1

Ok (pmax , r0). (7.38)

The percentage of users in outage for the threshold pmax and desired rate r0 isthen

O(pmax , r0)57K

× 100 %. (7.39)

If O(pmax , r0) > 10%, we increase the power threshold to p′max > pmax . On theother hand, if O(pmax , r0) < 10%, we decrease the power threshold to p′′max <

pmax . Proceeding in this fashion, the base station peak power threshold pmax isadjusted such that exactly 90% of the users are guaranteed the desired rate ofr0 bps/Hz and the remaining 10% of users are in outage.

The coordinates of the discarded users are stored and the same set of users arediscarded when relays are present in the system too. We remark here that theorder in which the users are discarded results in different power levels from thebase stations, due to variations in the interference coupling among the users.Hence, the order in which the users are dismissed must be chosen carefullydepending on the peak powers limitations at the base stations.


Baseline operationWe operate the baseline system as well as the system with relays such that,over a large number of user loading iterations, 90% of users obtain a commonaverage rate of 1 bps/Hz. We follow the approach described in Section 7.5.3to discard users in the system. For the PC-CPA baseline, we solve a series oflinear feasibility problems to obtain the base station powers that guarantee thedesired common rate. One after another, we discard users that would cause thepeak power constraint to became active. Hence we find the feasible set of powersp1 , . . . , pN for the baseline such that 90% of the users receive exactly 1 bps/Hz.

PC-CPA with relays: average power savingsThe peak power constraint of the base stations is fixed at pmax such that thebaseline can deliver 1 bps/Hz at 10% outage. Since the relays are assumed to beinexpensive, we assume small peak power constraints for the relays. In our work,the peak power of the relays is fixed at 1 W. Let us consider a single instantiationof 57 users in the system. We start off similarly to the baseline system afterdiscarding the same set of users. The base stations target the users to deliverthe common rate of 1 bps/Hz. Only relays that have a better SINR to the basestations than the user are eligible to help the user. The other relays are alwaysinactive. At time t = 0, all relays are inactive. The aim in this experiment is to

7.6 Orthogonal relaying 199

maintain a constant rate of 1 bps/Hz throughout the course of the simulation.When relay i is eligible to transmit at time t, we include relay i in the set ofactive relays A(t) and solve the LP (7.29). We stop when all the eligible relaysare included in the set of active relays. The total power in the system when alleligible relays are active is noted for this instantiation. We repeat this experimentfor all the K instantiations.

PC-CPA with relays: peak power savingsThe peak power constraints of the base stations are fixed at a value smaller thanthe baseline, say p′max . We assume that inexpensive relays are deployed in thesystem. Thus, the peak power constraints of the relays are fixed at 1 W. Sincethe peak power value of the base stations is reduced from the baseline and thecommon rate is fixed at 1 bps/Hz, the outage will be more than 10%. Let usconsider a single instantiation of 57 users in the system. We start similarly tothe baseline after discarding the same set of users. The base stations target theusers to deliver the common rate of 1 bps/Hz. Only relays that have a betterSINR to the base stations than the user are eligible to help the user. The otherrelays are always inactive. At time t = 0, all relays are inactive. Let relay i beeligible to transmit at time t. We include relay i in the set of active relays A(t)and solve the LP (7.35). We stop when all the eligible relays are included in theset of active relays. We repeat this experiment for all the K instantiations andthe outage is calculated. If the outage is less than 10%, the peak power of thebase stations reduces to p′′max < p′max , otherwise the peak power value of the basestations increases to p′′max > p′max and the above procedure is repeated until theoutage is close to 10%.


Power savingsThe average power saving over K = 200 instantiations is 3 dB and the peakpower saving in the downlink when power control is employed is close to 2.6 dB.

Rate gainsWe have observed 34% improvement in the throughput for 90% of users in thesystem, with the baseline system being served at 1 bps/Hz. The results aresummarized in Table 7.3.

7.6 Orthogonal relaying

In Sections 7.4 and 7.5, we saw that in an interference-limited setting, theimprovement in throughput was limited by the interference due to multiple trans-missions in the cell. In some cases the transmissions from the base stations areredundant. For instance, for a user located at the edge of the cell, the received


Table 7.3. PC-CPA-based relaying (base station and relays employ power control)

Peak power required to Peak power required to

Savings in dBguarantee 1 bps/Hz guarantee 1 bps/Hz

at 10% outage; at 10% outage;baseline (no relays) with relays

10 W 5.5 W 2.6

Common rate for 90% users; Common rate for 90% users; Percentage ratebaseline (no relays) with relays increase

1 bps/Hz 1.34 bps/Hz 34%

power from the base station may be weak and the base station’s signal may beof little use. In that case, it might be better to turn the base station off since thismay benefit the system overall in terms of reducing the interference levels. More-over, the practical implementation of such collaborative schemes can be complexwith the state of the art technology. Hence, we investigate how much gain dueto collaborative addition can be obtained if we just use simple multihopping,where the base station transmits to a relay in one slot and then that relay passeson the message to the destination in the next time slot. In this section, we exploitthe half-duplex property of the relays in a downlink cellular system to staggerthe transmissions of the base station and relays over two time slots. A naturalway to operate these relays is for them to receive in one time slot and transmitin another time slot. This gives us a natural orthogonality in the transmissionscheme. Henceforth, we term this scheme orthogonal relaying .


The simulation set-up is the same as that described in Section 7.2. Unlike CPAschemes, where the relay can start transmitting immediately after it decodes themessage, relays can start transmitting only at specific times in the orthogonalrelaying scheme. The system is assumed to be synchronous and time is dividedinto equal slots. The baseline and the system with relays are operated as follows.

BaselineThe baseline system operates similarly to the P-CPA baseline as described inSection 7.4.1. All base stations transmit with peak powers and the users arerequired to receive a fixed sized file with a specified deadline. Satisfied usersleave the system as soon as they receive the file. The associated base stationsector is turned off. The users that do not receive the file are in outage. Thepeak transmit powers of the base stations are fixed such that 10% of the usersover a large population of users are in outage. However, in the orthogonal relayingcase, we do not discard the users in outage and rerun the simulations.

7.6 Orthogonal relaying 201

System with relaysWhen relays are present in the system, time is divided into slots of equal dura-tions, and the duration of a time slot is half of that in the baseline system. Theoperation of the system is periodic with odd and even time slots recurring atregular intervals. The base stations transmit in the odd time slots and the relaystransmit in the even time slots. The peak power of the base stations is fixed asin the baseline and the peak power of the relays is fixed as 1 W.

In the odd time slots, the base stations transmit at peak power. Relays are inreceive mode in this time slot. The users and relays in each sector accumulatemutual information, depending on their channel qualities. If some of the usersreceive the desired rate from the base station transmission itself, those usersare satisfied users and leave the system as soon as they receive the desiredrate. The corresponding base stations and relays are turned off. Let us denotethe 57× 1 vector of rates obtained by users in the odd time slots by ro .

In the even time slots, only those users that have yet to receive the desiredrate of 1 bps/Hz remain in the system. The base stations are turned off inthis time slot. The relays that are required to help the users start transmittingsimultaneously at the beginning of the even time slots. Simple power controlis employed at the relay locations to reduce the interference caused to theother sectors. The power control is performed to achieve the desired residualcommon rate re = 1− ro , where 1 is a 57× 1 vector all 1’s vector (representingthe 1 bps/Hz desired common rate). The users that require the relays totransmit more than their peak power constraint are discarded at the beginningof the even time slots. There may be cases where the user has a better channelto the base station than to the relay. Such users are not given the benefit ofreceiving the complete message from the base station. The base stations areswitched off on the even time slots and are in outage if they do not receivethe message at the end of the even time slots.

7.6.2 User discarding method

BaselineThe users that remain in the system are in outage. However, the users are notdiscarded in the baseline scheme.

System with relaysThe user elimination procedure is the same as that explained in Section 7.5.3.The users that violate the peak power constraint of the relays are discarded atthe beginning of the even time slots. The discarded users do not receive thedesired common rate at the end of odd and even time slots, and hence are saidto be in outage. The system is operated such that there is 10% outage in thesystem over a large number of user instantiations. The peak power threshold ofthe relay nodes is adjusted such that the outage percentage is exactly 10%.


Table 7.4. Summary of gains due to relaying

Baseline System with relays Results

57 sectors 57 sectors Power saving Common rate gain1 user/sector 1 user/sector and (baseline at (baseline at

1 relay/sector 1 bps/Hz) 1 bps/Hz)

Peak power Peak power transmissions1.46 dB (peak)transmissions by by base stations 25%

base stations and relays (CPA)

Base station Base station and 2.6 dB (peak)34%power control relays power control 3 dB (average)

(PC-CPA)

Peak power Relays power control3 dB (average) 35%transmissions by to users

base stations (orthogonal relaying)


The average power saving in the base station locations is 3 dB, since the basestations transmit only for half the time. There is no peak power saving since thebase stations transmit at peak power in the odd time slots. We obtain 35% rategain due to orthogonal relaying when there is 10% outage in the system. It isinteresting to note that simpler relaying methods, such as orthogonal relaying donearly as well as the more complex forms of relaying, such as CPA schemes, inobtaining throughput gains and power savings. This observation is in agreementwith the studies in simple linear settings [19, 27].

7.7 Conclusion

We have presented a simulation study of the downlink of a cellular system withrelays. We evaluated the power saving and common rate increase for users whena common rate of 1 bps/Hz is required by 90% of users in the system. We firstdescribed the CPA scheme of relay collaboration. In the CPA scheme, wheneverthe relay receives the complete message from the base station, it collaborateswith the base station such that the mutual information at the user locationcorresponds to the sum of the received power at the user location, thus boostingthe average rate. We observed that when the system is interference-limited thepeak power savings are hard to come by. Consequently, the PC-CPA schemealong with a framework for power control was proposed. The power controlframework can be posed as a formulation when the objective is to minimizepeak power or to minimize average energy in the system. This formulation canbe used to evaluate the average and peak power savings in the system. The peakpower savings and the rate gains improve when power control is employed. We

References 203

then evaluated a simple multihopping scheme where the base stations and therelays transmit in orthogonal time slots. In the odd time slots, the base stationstransmit at peak power and in the even time slots, the base stations are turnedoff and the relays employ simple power control to deliver the residual rate to theusers. A summary of the results is given in Table 7.4.

References

[1] Harmonized Contribution on 802.16j (Mobile Multihop Relay) Usage Mod-els. http://ieee802.org/16.

[2] Multi-hop relay system evaluation methodology. http://ieee802.org/16.[3] Y. Yang, H. Hu, J. Xu, and G. Mao, “Relay technologies for WiMAX and

LTE-advanced mobile systems,” IEEE Commun. Magazine, 47(10): 100–105, Oct. 2009.

[4] L. Le and E. Hossain, “Multihop cellular networks: Potential gains, researchchallenges, and a resource allocation framework,” IEEE Commun. Maga-zine, 45(9): 66–73, Sep. 2007.

[5] H. Viswanathan and S. Mukherjee, “Performance of cellular networks withrelays and centralized scheduling,” IEEE Trans. Wireless Commun., 4(5):2318–2328, Sep. 2005.

[6] O. Oyman, J. N. Laneman, and S. Sandhu, “Multihop relaying for broad-band wireless mesh networks: From theory to practice,” IEEE Commun.Magazine, 45(11): 116–122, Nov. 2007.

[7] C. E. Perkins, Ad Hoc Networking. Addison-Wesley, 2001.[8] O. Oyman, “Oppurtunistic scheduling and spectrum reuse in relay-based

cellular OFDMA networks,” in Proc. of IEEE Globecom, Washington DC,USA, 2007. IEEE, 2007.

[9] E. C. van der Meulen, Transmission of Information in a T-terminal discretememoryless channel. PhD thesis, University of California, Berkeley, 1968.

[10] T. M. Cover and A. A. El Gamal, “Capacity theorems for the relay channel,”IEEE Trans. Inf. Theory, 25(5): 572–584, Sep. 1979.

[11] G. Kramer, M. Gastpar, and P. Gupta, “Cooperative strategies and capacitytheorems for relay networks,” IEEE Trans. Inf. Theory, 51: 3037–3063, Sep.2005.

[12] M. A. Khojastepour, A. Sabharwal, and B. Aazhang, “On the capacity of‘cheap’ relay networks,” in Proc. of 37th CISS, Baltimore, MD, USA, 2003.The John Hopkins University, 2003.

[13] G. Kramer, “Models and theory for relay channels with receive constraints,”in Proc. of Allerton Conf. on Commun., Control, and Comp., UIUC, IL,USA, 2004. University of Illinois at Urbana-Champaign, 2004.

[14] D. Chen, M. Haenggi, and J. N. Laneman, “Distributed spectrum-efficientrouting algorithms in wireless networks,” IEEE Trans. Wireless Commun.,7(12):5297–5305, Dec. 2008.


[15] M. Sikora, J. N. Laneman, M. Haenggi, Jr., D. J. Costello, and T. E. Fuja,“Bandwidth- and power-efficient routing in linear wireless networks,” IEEETrans. Inf. Theory, 52(6): 2624–2633, June 2006.

[16] P. Bender, P. Black, M. Grob, R. Padovani, N. Sindhushayana, andA. Viterbi. “CDMA/HDR: A bandwidth-efficient high speed wireless dataservice for nomadic users,” IEEE Commun. Magazine, 38(7): 70–77, July2000.

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[27] N. Jacobsen, “Practical cooperative coding for half-duplex relay channels,”in Proc. of CISS 2009, March 2009. The John Hopkins University, 2009.

8 Radio resource optimizationin cooperative cellularwireless networks

Shankhanaad Mallick, Praveen Kaligineedi, Mohammad M. Rashid,and Vijay K. Bhargava

8.1 Introduction

Wireless cellular networks have to be designed and deployed with unavoidableconstraints on the limited radio resources such as bandwidth and transmit power.With the boom in the number of new users and the introduction of new wirelesscellular services that require a large bandwidth or data rate, the demand forthese resources, however, is rising exponentially. Finding a solution to meet thisincreasing demand with the available resources is a challenging research problem.The primary objective of such research is to find solutions that can improve thecapacity and utilization of the radio resources that are available to the serviceproviders. Based on the concept of relay channels, cooperative communication1

has been found to greatly enhance the performance of a resource-constrainedwireless network [2–6]. It can achieve benefits similar to those of the multiple-input multiple-output (MIMO) system without the need for multiple antennasat each node. By allowing users to cooperate and relay each other’s messagesto the destination, cooperative communication also improves the transmissionquality [7]. Because of the limited power and bandwidth resources of the cellularnetworks and the multipath fading nature of the wireless channels, the idea ofcooperation is particularly attractive for wireless cellular networks.

Proposed cooperative schemes or strategies, such as decode-and-forward (DF),amplify-and-forward (AF), and coded cooperation [4, 8–10], usually involve twosteps of operation. In the first step, a user (called the source node), transmitsits message to both the assigned partner (called the relay node) and to thedestination. If the relay node employs a DF scheme, it will first decode andregenerate the message and then transmit it to the destination in the second step.When the regenerated message is encoded to provide additional error protectionto the original message, it is referred to as coded cooperation. If an AF scheme is

1 The term cooperation was introduced in [1] in which the capacity of a three-node relaynetwork was analyzed.


206 Radio resource optimization in cooperative cellular wireless networks

employed, the relay simply amplifies the received message and forwards it to thedestination in the next step. At the destination, the signals from both the sourceand the relay are then combined for detection, using methods such as maximalratio combining (MRC) or by selection combining.

However, the benefits of a relay-based cooperation often depend on the channelquality between the source, relay, and destination involved in the transmission.This is because the transmission quality of a relayed message is limited by thechannel signal-to-noise ratio (SNR). For example, a relay can fail to forwarda message reliably to the destination if the received message from the sourceis already corrupted due to poor channel quality. Therefore, cooperation maynot be always useful. In general, when the complete channel state information(CSI) between the source, relay, and destination is known to the system, relaysshould be selected to forward the source message only if the quality of thechannels between source and relay and relay and destination meet certain crite-ria. Whenever cooperation is beneficial, the next goal is to allocate the limitedresources (e.g., power, bandwidth) appropriately among the source and relay.Therefore, resource allocation among the cooperative nodes can be formulatedas an optimization problem to exploit the maximum possible advantage of coop-eration [11, 12].

The focus of this chapter is to formulate the resource allocation problemsof different cooperative networks and strategies as optimization problems andto discuss their solution approaches. The chapter is organized as follows: Sec-tion 8.2 discusses the resource allocation problem for networks with a singlesource–destination pair. First the optimal power allocation is studied for themost basic three-node topology using different cooperation schemes, and thecapacity or throughput gain is investigated. Then we consider the dual hop relaynetworks which contain multiple relays and study the relevant resource optimiza-tion problems in detail. Section 8.3 deals with the resource allocation problem ofa cellular network with multiple source–destination pairs. Solution approachesusing both centralized and distributed optimization algorithms are studied. Therelay selection strategies for different networks are also discussed briefly in Sec-tion 8.4. Finally, a chapter summary is provided in Section 8.5.

8.2 Networks with single source–destination pair

In this chapter, our strategy is to start with the problem of resource optimizationin a simple cooperative architecture involving a single source–destination pairand then progress towards a more general system architecture. The simplesttopology for a single source–destination is the three-node relay network shownin Figure 8.1. A more generic topology is the dual hop relay network whichconsists of multiple relays.

8.2 Networks with single source–destination pair 207

User 1

User 2

Destination

(S)

(R)

(D)hSD

hSRhRD

Feedback

Feedback

Figure 8.1. A three-node relay network.

8.2.1 Three-node relay network

Consider the three-node relay network shown in Figure 8.1, where we let user1 be the source node (S) that intends to transmit a message to the destination(D) while user 2 serves as the relay node (R).

Cooperation requires two time slots to send a message to destination, D. Inthe first time slot, source S transmits its message XS to both R and D. Thereceived signals at R and D can be expressed as

XR = hSRXS + ZR,

XD1 = hSD XS + ZD1 ,

respectively, where hSR and hSD are the complex channel coefficients for theS–R and S–D links, and ZR and ZD1 denote the independent and identicallydistributed (i.i.d.) circularly symmetric additive white Gaussian noise (AWGN)with zero mean and variance N0 .

In the second time slot, relay R transmits the message (XR ) received in the firstslot after either decoding and reencoding it or simply amplifying it. Depending onthe cooperative scheme (DF or AF), let Y = f(XR ) be the transmitted message2

in the second slot. The received signal in D can be written as

XD2 = hRD Y + ZD2 = hRD f (XR ) + ZD2 ,

where hRD is the channel coefficient between the R–D pair and ZD2 is the zeromean AWGN with variance N0 . In the following analysis, we assume that thesecoefficients are known (i.e., full CSI is available) to S, R, and D and the AWGNnoise has unit variance, i.e., N0 = 1. The transmit powers of S and R are givenby PS and PR .

2 For the AF scheme Y is XR corrupted with AWGN and for the DF scheme Y is simply XR .


Quality of Service (QoS), a measure of performance, reflects the transmissionquality and the service availability of a transmission system. For example, chan-nel capacity, SNR, outage probability or bit error rate (BER) can be one ofthe QoS measures. Our objective is to formulate the optimization problem sothat the QoS performance of the network is optimal subject to some resourceconstraint. In the following we use the total power budget as the constrainedresource of the network and the channel capacity (or, maximum achievable datarate) as the QoS measure. Therefore, the problem is to maximize the channelcapacity given some total power constraint and the solution will provide theoptimal allocation of PS and PR among the cooperative nodes.

The solution for optimal power allocation depends on whether the direct S–Dlink is taken into account. If the messages from both the source and the relayare combined at the destination for detection, this is referred to as the case withdiversity [13]. For the case without diversity, only the message from the relay(i.e., XD2) is considered. In the following we study optimal power allocation forboth the cases.

Case 1 With direct linkFirst, let us formulate the capacity maximization problem taking the direct linkinto account to examine the optimal power allocation for the three-node networkwith DF cooperative strategy. In a two-time-slot operation, the capacity of theS–R link is given as [14]

Chop1 = 12 log2(1 + |hSR |2 PS ). (8.1)

In the second time slot, the destination combines the messages from both theS–D and R–D links using MRC technique, and the capacity is given by

Chop2 = 12 log2(1 + |hRD |2 PR + |hSD |2 PS ). (8.2)

The channel capacity in the DF cooperative scheme is limited by the minimumof the two hops:

CDF, diversity = min

12 log2(1 + |hSR |2 PS ), 1

2 log2(1 + |hRD |2 PR + |hSD |2 PS )

.

(8.3)Therefore the optimization problem becomes a standard max–min problem:

maximizePS ,PR

min

12 log2(1 + |hSR |2 PS ), 1

2 log2(1 + |hSD |2 PS + |hRD |2 PR )

subject to : PS + PR ≤ P0 ,

PS ≥ 0 , PR ≥ 0.(8.4)


If |hRD |2 ≥ |hSD |2 and |hSR |2 > |hSD |2 , the capacity is maximized with equalcapacity for the two hops, i.e.

12 log2(1 + |hSR |2 PS ) = 1

2 log2(1 + |hSD |2 PS + |hRD |2 PR ). (8.5)

Since the objective is to maximize the capacity, the first inequality constraint of(8.4) should be met at equality. Using PS + PR = P0 in (8.5), we get the optimalpower allocation as

PS = P0|hRD |2

|hSR |2 + |hRD |2 − |hSD |2(8.6)

and

PR = P0|hSR |2 − |hSD |2

|hSR |2 + |hRD |2 − |hSD |2. (8.7)

From (8.6) and (8.7), we see that more power is allocated to the source than tothe relay, which is justified since PS contributes both to the direct path and tothe relay path.

However, if |hSD |2 ≥ |hRD |2 we see that the capacity expressions (8.1) and(8.2) are both monotone increasing functions and the optimal power allocationthat maximizes the objective function in (8.4) is PS = P0 and PR = 0. This resultindicates that, if the direct channel has better quality than any of the S–R orR–D links, it is intuitive to allocate all available power to S alone.

Now let us formulate the problem of optimal power allocation for the AFcooperative scheme. In this case, the message forwarded by the relay contains anamplified version of the noise along with the message transmitted originally bythe source. As a result, the SNR at the destination node plays an important rolein the optimal power allocation problem. The channel capacity of the two-hopAF scheme can be expressed as

CAF,diversity = 12 log2(1 + SNRD ), (8.8)

where SNRD is the SNR at destination node given as [15]

SNRD =|hSR |2 PS |hRD |2 PR

1 + |hSR |2 PS + |hRD |2 PR

+ |hSD |2 PS . (8.9)

For AF cooperation, optimizing the channel capacity is equivalent to SNR max-imization. Therefore, the optimal power allocation problem for the AF schemecan be formulated as

maximizePS , PR

|hSR |2 PS |hRD |2 PR

1 + |hSR |2 PS + |hRD |2 PR

+ |hSD |2 PS

subject to : PS + PR ≤ P0 ,

PS ≥ 0, PR ≥ 0. (8.10)


Applying the Lagrange multiplier, the optimal power allocation of (8.10) isobtained as

PS =|hSR |2 |hRD |2 P0 + |hSD |2 |hRD |2 P0 + |hSD |2

A +

√|hSR |2 P0 + 1|hRD |2 P0 + 1

|hSR |2 |hRD |2 A

(8.11)

and

PR =|hSR |2 |hRD |2 P0 − |hSD |2 |hSR |2 P0 − |hSD |2

A +

√|hRD |2 P0 + 1|hSR |2 P0 + 1

|hSR |2 |hRD |2 A

, (8.12)

where A = |hSR |2 |hRD |2 + |hSD |2 |hRD |2 − |hSR |2 |hSD |2 . Optimal power allo-cation holds if and only if A > 0 and |hSR |2 |hRD |2 P0 > |hSD |2 |hSR |2 P0 +|hSD |2 . Otherwise all available power should be allocated to the source alone,which indicates that the S–D link is better than the S–R or R–D link and thatcooperation is not beneficial in such channel conditions. When |hSR |2 ≈ |hRD |2and both are sufficiently larger than |hSD |2 , the ratio of PS and PR can beapproximated as

PS

PR≈ |hSR |2 |hRD |2 P0 + |hSD |2 |hRD |2 P0 + |hSD |2

|hSR |2 |hRD |2 P0 − |hSD |2 |hSR |2 P0 − |hSD |2. (8.13)

Example 1 In this example, we compare the outage probabilities of the AFand DF schemes with equal and optimal power allocation methods, as shown inFigure 8.2. We consider that an outage occurs when the achieved rate is less than1 (C < 1) at the destination. For simplicity, we assume that the relay node islocated in the middle of the source and the destination and the complex channelcoefficients hSR , hSD , and hRD are i.i.d. circularly symmetric Gaussian randomvariables with zero mean and variances, i.e., σ2

SR = 1, σ2RD = 1, σ2

SD = 1/(2α ),where α = 3 is the path loss coefficient.

From Figure 8.2, we can see that optimal power allocation has significant SNRgain over the equal power allocation method. It is interesting to note that theoutage probability of the AF scheme outperforms that of the DF scheme whenthe SNR value is sufficiently high (over 15 dB). This is because the DF schemedoes not provide additional diversity gain. From the results we can concludethat, whenever there is diversity, it is always better to use the AF scheme overthe DF cooperation.


Figure 8.2. Comparison of outage probabilities of AF and DF schemes withdiversity.

Case 2 Without direct linkWithout diversity, the destination node receives only the relayed message fromR. For DF cooperation, the channel capacity can be written as

CDF, without diversity = min

12 log2(1 + |hSR |2 PS ), 1

2 log2(1 + |hRD |2 PR )

.

(8.14)The capacity maximization problem is thus a max–min problem. The maximumcapacity is reached when the capacities of both hops are equal, i.e.,

12 log2(1 + |hSR |2 PS ) = 1

2 log2(1 + |hRD |2 PR ). (8.15)

The optimal power allocation is obtained using PS + PR = P0 in (8.15) as

PS = P0|hRD |2

|hSR |2 + |hRD |2(8.16)

and

PR = P0|hSR |2

|hSR |2 + |hRD |2. (8.17)

This result is also verified directly, by putting |hSD | = 0 in (8.6) and (8.7).


Figure 8.3. Comparison of outage probabilities of AF and DF schemes withoutdiversity.

Similarly for AF cooperation without diversity, the optimal power allocationis obtained by putting |hSD | = 0 in (8.11) and (8.12) as

PS =P0

1 +

√|hSR |2 P0 + 1|hRD |2 P0 + 1

(8.18)

and

PR =P0

1 +

√|hRD |2 P0 + 1|hSR |2 P0 + 1

. (8.19)

Thus the ratio between PS and PR is given by

PS

PR=

√|hRD |2 P0 + 1|hSR |2 P0 + 1

. (8.20)

Example 2 The outage probabilities for AF and DF cooperation without diver-sity are compared in Figure 8.3. For each scheme, we plot the results obtainedfrom equal and optimal power allocation methods.

It is clear that optimal power allocation has approximately 3 dB SNR gainover the equal power allocation method for both the AF and DF schemes. Sincethere is no diversity, the DF scheme performs better than the AF scheme at low


Source (S)

Feedback

Destination (D)

Relay 1 (R1)

Relay N (RN)

Relay 2 (R2)

X1

X0

X2

XN

UN = fN (XN )

U2= f2(X2)

U1= f1(X1)

hs1

hSNhND

h2D

h1D

hs2Z

Figure 8.4. A dual-hop cooperative relay network.

to moderate SNR. However, at a very high SNR (over 30 dB), the performancesof both the schemes are almost identical.

8.2.2 Dual-hop relay networks

Now let us consider a two-stage cooperative network (also known as a parallelrelay network) consisting of N relay nodes, denoted by Rk , k = 1, 2, . . . , N asshown in Figure 8.4. The complex channel coefficients from the source S to relayRk and from Rk to destination D are given by hSk and hkD respectively. Insuch networks, S broadcasts its message in the first time slot and the set ofrelays Rk , k = 1, 2, · · · , N transmits simultaneously in the second slot. Herewe assume all the channels are orthogonal and perfect CSI is available to all thenodes. The transmit powers of S and Rk are denoted by PS and Pk respectively.

In this section, we focus on the power allocation among the relay nodes only.The power allocation among PS and PR can be determined using techniquessimilar to those derived in the previous section. The optimization problem isformulated as a capacity maximization problem but the total power constraint isimposed on the summation of relay powers, i.e.,

∑Nk=1 Pk ≤ PR . In the following,

we analyze the optimal power allocation for both AF and DF cooperation.

Case 1 AF schemeFor the AF scheme, the capacity of the parallel relay channel is given as [16]

CAF = 12 log(1 + SNRD ), (8.21)


where

SNRD = PS

(|hSD |2 +

N∑k=1

|hSk |2 |hkD |2 Pk

|hSk |2 PS + |hkD |2 Pk + 1

). (8.22)

The goal here is to optimize the power allocation among the parallel relay nodesso that the capacity is maximized. Optimizing CAF is equivalent to maximizingthe SNRD . For a constant source power PS , we define

γk =

√|hSk |2 |hkD |2

|hSk |2 PS + 1, (8.23)

so that we can writeN∑

k=1

|hSk |2 |hkD |2 Pk

|hSk |2 PS + |hkD |2 Pk + 1=

N∑k=1

|hSk |2 γ2kPk

|hSk |2 + γ2kPk

(8.24)

and formulate the following optimization problem:

maximizePk

N∑k=1

|hSk |2 γ2kPk

|hSk |2 + γ2kPk

subject to:N∑

k=1

Pk ≤ PR,

Pk ≥ 0. (8.25)

It can be easily shown that the optimization problem is convex since the objectivefunction is now a concave increasing function of Pk and the constraints are lin-ear. The solutions of any convex optimization problem can be easily obtained byavailable convex programming algorithms [17]. Among these algorithms, subgra-dient methods are the simplest and so are widely used. However, interior-pointmethods, bundle methods, and cutting-plane methods are also well known. Thesolution obtained using these algorithms does not provide any insight into theoptimal power allocation among the relays though. Therefore, we solve the opti-mization problem of (8.25) using the Lagrange dual method. The Lagrangian ofthe problem is given by

L(Pk ,λ, η) =N∑

k=1

|hSk |2 γ2kPk

|hSk |2 + γ2kPk

+N∑

k=1

λkPk − η

(N∑

k=1

Pk − PR

), (8.26)

where λ = λk ≥ 0, k = 1, 2, ..., N and η are the Lagrange multipliers correspond-ing to the inequality constraints on the relay power. From the Karush–Kuhn–Tucker (KKT) conditions,

∂L∂Pk

=|hSk |2 γ2

k (|hSk |2 + γ2kPk )− |hSk |2 γ4

kPk

(|hSk |2 + γ2kPk )2

+ λk − η = 0 (8.27)


and

λkPk = 0. (8.28)

By eliminating λk from (8.28), we get(η − |hSk |2 γ2

k (|hSk |2 + γ2kPk )− |hSk |2 γ4

kPk

(|hSk |2 + γ2kPk )2

)Pk = 0. (8.29)

From (8.29) we see that if Pk = 0, then the expression(η − |hSk |2 γ2

k (|hSk |2 + γ2kPk )− |hSk |2 γ4

kPk

(|hSk |2 + γ2kPk )2

)must be equal to zero. After simplification, we get the optimal power allocationamong the relay nodes as

Pk =|hSk |2

γk

[1√

η− 1

γk

]+

, (8.30)

where [.]+ denotes the projection onto the feasible set of nonnegative orthants.Therefore, the optimal power allocation problem results in the following water-filling solution [18]:

Pk =

⎧⎪⎪⎨⎪⎪⎩|hSk |2

γk(

1√

η− 1

γk), if

1√

η>

1γk

0, else.

(8.31)

The Lagrange multiplier, η, is chosen to meet the total power constraint of therelay nodes. Also note that the relay node Rk is allowed to transmit if and onlyif λk > η.

Example 3 The sum capacities (or maximum achievable data rate) of the AFscheme with different numbers of relays are compared in Figures 8.5 and 8.6.For both the figures, we plot the results obtained from equal and optimal powerallocation methods. In Figure 8.5, we assume that all the S–R and R–D channelcoefficients are i.i.d. circularly symmetric Gaussian random variables with zeromean and unit variances. As in the previous examples, the direct S–D channelcoefficient, hSD is assumed to have zero mean and variance σ2

SD = 1/(2α ). InFigure 8.6, we assume that S–R and R–D channel coefficients are non i.i.d.Gaussian random variables.

From Figures 8.5 and 8.6, it is clear that the rates achieved are much higherfor optimal power allocation than for equal power allocation. As we increase thenumber of relays, the sum capacity increases. However, for the cases where somerelay channels are better than others (in Figure 8.6), it is interesting to notethat two relays with optimal power allocation can achieve a better rate thanfour relays with equal power allocation.


1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5

3

Sum

cap

acity

(bp

s/H

z)

Total relay power (watt)

4 relay equal power4 relay optimal power2 relay optimal power2 relay equal power

Figure 8.5. Comparison of sum capacities of the AF scheme with i.i.d. channels.

1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5

3

Sum

cap

acity

(bp

s/H

z)


4 relay equal power4 relay optimal power2 relay optimal power2 relay equal power

Figure 8.6. Comparison of sum capacities of the AF scheme with non i.i.d chan-nels.


Case 2 DF schemeA relay node can execute the DF scheme only if it is able reliably to decode themessage received from the source node. Let us consider a set of relays denoted byNDF , among the N relay nodes, which are able to correctly decode the messagestransmitted by the source. For given NDF , the dual-hop relay network withorthogonal channels is analogous to a multiple antenna system. The capacity ofsuch networks can be written as [19]:

CDF = 12 log(1 + |hSD |2 PS ) +

∑k∈ND F

12 log(1 + |hkD |2 Pk ). (8.32)

For optimal power allocation the DF scheme, the first task is to find the reliablerelay nodes k ∈ NDF . We assume that a relay will be able to execute the DFstrategy if it is able to reliably communicate with the source at a desired rate,rS . Therefore, a relay node k is reliable if the following condition is met:

12 log(1 + |hSk |2 PS ) ≥ rS . (8.33)

Our goal is to find the optimal power allocation that maximizes the capacityof the network. However, the problem of maximizing the capacity under therelay power constraint,

∑Nk=1 Pk ≤ PR has its dual problem with the objective

to communicate with the destination at the desired rate, rS using minimum relaypower, P ∗k . The analogous solutions of the two problems become identical whenP ∗k = PR . We use binary variables xk to indicate the reliable relays and formulatethe following dual problem:

minimizeN∑

k=1

Pk

subject to: 12 log(1 + |hSD |2 PS ) +

N∑k=1

12 log(1 + |hkD |2 Pk )xk ≥ rS ,

12 log(1 + |hSk |2 PS ) > xkrS ,

xk ∈ 0, 1,

Pk ≥ 0. (8.34)

The formulated optimization problem is a mixed integer problem which is gener-ally very difficult to solve. However, for severely restricted transmitter power orlow SNR cases, i.e. Pk |hkD |2 1, the dual problem simplifies to the wideband


DF relay problem [20]:

minimizeN∑

k=1

Pk

subject to: 12 |hSD |2 PS +

N∑k=1

12 |hkD |2 Pkxk ≥ rS ,

12 |hSk |2 PS > xkrS ,

xk ∈ 0, 1,

Pk ≥ 0. (8.35)

The solution of the above optimization problem is to choose a single relay whichhas the best channel gain towards the destination and allocate the total relaypower to it. This is due to the fact that, at low SNR (Pk |hkD |2 1), a water-filling solution finds the relay which has the best channel gain to the destina-tion node. This means that the selective relaying scheme is optimal for the DFstrategy for dual-hop relay networks with multiple relays. Therefore, the opti-mal power allocation among multiple relays becomes a single relay optimizationproblem:

minimize PS + Pk

subject to: 12 |hSD |2 PS + 1

2 |hkD |2 Pkxk ≥ rS ,

12 |hSk |2 PS ≥ xkrS ,

xk ∈ 0, 1,

Pk ≥ 0, PS ≥ 0. (8.36)

As in the three-node case, one can show that cooperation with relay k is bene-ficial if and only if |hSk |2 > |hSD |2 and |hkD |2 > |hSD |2 . Otherwise it is optimalto allocate all the power to the source for direct transmission. The optimal powerallocation is obtained using the first and second constraints of (8.36) with equal-ity:

P ∗S =rS

|hSk |2(8.37)

and

P ∗k =rS − P ∗S |hSD |2

|hkD |2. (8.38)


0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Sum

cap

acity

(bp

s/H

z)


DF optimal power (best relay)DF equal power (2 relay)DF equal power (4 relay)

Figure 8.7. Comparison of sum capacities of DF scheme in the low SNR regime.

The optimal total power is then

P ∗S + P ∗k = rS

[1

|hSk |2+

1|hkD |2

− |hSD |2

|hSk |2 |hkD |2

]. (8.39)

The best relay will be the one among the set of useful relays which minimizesthe total power P ∗S + P ∗k . If the set of useful relays

RU = k ∈ NDF | |hSk |2 > |hSD |2 , |hkD |2 > |hSD |2

is nonempty, then the optimal relay selection criterion is

k∗ = argmink∈RU

[1

|hSk |2+

1|hkD |2

− |hSD |2

|hSk |2 |hkD |2

]. (8.40)

The maximum capacity of the primal problem for the dual-hop DF scheme inthe low-SNR regime can thus be approximated as

CDF ≈ 12 |hSD |2 PS + 1

2 |hk ∗D |2 PR. (8.41)

Example 4 Similarly to the previous example, we compare the sum capacitiesof DF scheme for the dual-hop network with optimal and equal power allocationin Figure 8.7. The results are shown for the cases of severely restricted transmit-ter power or the low-SNR regime. We assume that the different S–R and R–Dchannels have different channel variances.


Relay

User nearBS

User nearcell edge

Base station(BS)

Relay

Figure 8.8. Typical cooperative cellular network with multiple users.

Unlike that for the AF scheme, the sum capacity of the DF scheme does notdepend on the number of relays at low SNR. Since the DF scheme does notprovide additional diversity gain, it is optimal to find the best relay and allocatetotal relay power to it.

8.3 Multiuser cooperation

In the previous section, we analyzed the problem of resource allocation for asingle source–destination pair. Now we examine the resource allocation problemfor multiuser (or multisource) cooperative networks. Consider the case of cellu-lar networks shown in Figure 8.8, where some relays are deployed to assist theusers located at cell edges for both uplink and downlink transmissions. Since thenumber of relays is smaller than the number of users in a practical scenario, eachrelay is assigned to assist more than one user.

To formulate the power allocation problem for multiuser networks we chooseone of two QoS measures, namely the minimum rate of the users (max–minfairness) or the weighted sum rates of the users (weighted-sum fairness). There-fore, the problem is to maximize either the minimum rate of the users or theweighted-sum rates given total relay power as the constraint. In the following,we will see that both the problems are convex and the problem can be solvedusing centralized or distributed algorithms.

8.3 Multiuser cooperation 221

8.3.1 System model

Consider a multiuser network where M source nodes Si, i ∈ 1, 2, ...,M transmitmessages to their corresponding destination nodes Di, i ∈ 1, 2, ...,M. There areN relay nodes Rk , k ∈ 1, 2, ..., N in the network. The set of relays assisting thetransmission of Si is denoted by R(Si). The set of sources using the Rk relay isdenoted by S(Rk ). Thus we can write

S(Rk ) = Si |Rk ∈ R(Si), (8.42)

which means one relay can forward the messages of several users. For this sectionwe consider that no direct link exists between any source–destination (Si–Di)pair. We also assume all the channels are orthogonal and perfect CSI is availableto all the nodes.

In a multiuser cooperative network with the AF scheme, each source Si trans-mits a message to its chosen relays in the set R(Si) in the first time slot, andeach relay amplifies and forwards its received message to Di in the second timeslot. The transmit powers of the source Si and its assisting relays Rk ∈ R(Si)are denoted by PSi

and PSi

Rkrespectively. Consider that in the first time slot,

source Si broadcasts the message Xi with unit energy to the relays Rk ∈ R(Si).The received message at the relay Rk can be written as

XSi

Rk=√

PSihSi

RkXi + ZRk

, Rk ∈ R(Si). (8.43)

In the second time slot, the relay Rk amplifies the received message and relaysit to the destination node Di . The received message at Di is given by [21]

XDi

Rk=

√√√√√ PSi

RkPSi

PSi

∣∣∣hSi

Rk

∣∣∣2 + 1hDi

RkhSi

RkXi + ZDi

, Rk ∈ R(Si), (8.44)

where hSi

Rkand hDi

Rkdenote the complex channel coefficients for the Si–Rk and

Rk–Di links, and ZRkand ZDi

are the zero mean AWGN with unit variance.The modified AWGN at Di is denoted by ZDi

with equivalent variance

1 +

(PSi

Rk

∣∣∣hDi

Rk

∣∣∣2)(PSi

∣∣∣hSi

Rk

∣∣∣2 + 1) .

Assuming that MRC is employed at the destination node Di , the combined SNRat Di can be written similarly, as given by [22]:

SNRDi=

∑Rk ∈R(Si )

∣∣∣hSi

Rk

∣∣∣2 ∣∣∣hDi

Rk

∣∣∣2 PSi

RkPSi∣∣∣hSi

Rk

∣∣∣2 PSi+∣∣∣hDi

Rk

∣∣∣2 PSi

Rk+ 1

. (8.45)


The above expression for SNRDiis similar to that of (8.22) used in the previous

section for the dual-hop relay network with the AF scheme. The rate ri of useri is given by

ri =12

log2(1 + SNRDi) =

12

log2

⎛⎜⎝1 +∑

Rk ∈R(Si )

∣∣∣hSi

Rk

∣∣∣2 ∣∣∣hDi

Rk

∣∣∣2 PSi

RkPSi∣∣∣hSi

Rk


Rk

∣∣∣2 PSi

Rk+ 1

⎞⎟⎠ .

(8.46)Similarly to the single-user case, it can be shown that, for a constant source powerPSi

, the rate expression (8.46) is a concave increasing function with respect toPSi

Rk, Rk ∈ R(Si). Using this fact, the optimal power allocations for both the

max–min fairness and weighted-sum fairness schemes can be calculated as shownin the following subsection.

8.3.2 Centralized power allocation

Max–min fairnessFor the rate expression given in (8.46), the power allocation problem under themax–min rate can be formulated as

maximize minSi

ri

subject to:∑

Si ∈S(Rk )

PSi

Rk≤ Pmax

Rk, k = 1, 2, ..., N,

PSi

Rk≥ 0, (8.47)

where PmaxRk

is the maximum (or total) power of the relay Rk . The first constraintcan also be written equivalently as a constraint on the maximum sum of powerstransmitted by the corresponding assisted source nodes. The set of linear inequal-ity constraints with positive variable in (8.47) is compact and nonempty. Hencethe optimization problem set is always feasible. Moreover, since the objectivefunction is an increasing function of power, the first inequality constraint shouldmeet with equality at the optimal point. The convex optimization problem canbe written in its standard form:

minimize −t

subject to: t− ri ≤ 0 , i = 1, 2, ...,M,

∑Si ∈S(Rk )

PSi

Rk≤ Pmax

Rk, k = 1, 2, ..., N,

PSi

Rk≥ 0, t ≥ 0, (8.48)

where t is a slack variable. The solution of this problem gives the optimal powerallocation among the relays that maximizes the worst-user rate. In the special


case, in which all the users share the same set of relays the rates of all users areequal at the optimal point. This is easily understood from the max–min problemof single-user case where the capacity is maximized with equality at the optimalpoint.

Weighted-sum fairnessThe problem of the max–min rate-based power allocation is that it degradesthe sum capacity (or total network throughput). This is because it tends toimprove the performance of the worst-user rate by allocating more power tothe poor links. The weighted-sum rate maximization can potentially achievecertain fairness for different users by allocating large weights to the users inunfavorable channel conditions while maintaining good network performance.Let wi denote the weight allocated to user i, then the weighted-sum rate powerallocation problem can be formulated as

maximizeM∑

i=1

wiri

subject to:∑

Si ∈S(Rk )

PSi

Rk≤ Pmax

Rk, k = 1, 2, ..., N,

PSi

Rk≥ 0. (8.49)

The solution of this convex optimization problem gives better network through-put, which indicates that the weighted-sum-rate-based power allocation favorsusers with good channel conditions. However, it does not severely penalizeusers with bad channel conditions either. In fact, because the objective func-tion (weighted-sum rate) is concave and increasing with respect to the allocatedpowers, the increment in the function value is higher when the power is low.Therefore to maximize the objective function value, it is obvious to allocatemore power to ‘bad’ users operating at low SNR.

8.3.3 Distributed power allocation

The centralized allocation discussed in the previous subsection may not be verypractical for a number of reasons. Firstly, it requires a large signaling overheadsince the channel gain estimations between various S–R and R–D have to betransmitted to the base station, which allocates power based on these estimates.Moreover, the wireless channels are time varying and frequency selective. There-fore, the channel gain information needs to be constantly updated, which requiresa lot of data to be transmitted to the base station using the control channels.In fact, in mobile communication systems with constant changes in the chan-nels between various devices, such a centralized power allocation scheme couldbecome impractical. Secondly, these schemes are highly complex and would cre-ate a large computational load at the base station. Thus, it is very important


to devise distributed schemes in which each relay calculates its own optimalpower allocation based on the information available from neighboring nodes andhence reduces the overall signaling overhead as well as the large computationalcomplexity in the base station. Several distributed power allocation schemes forcooperative communication systems have been discussed in the literature. Thedistributed power allocation scheme for the multiuser AF relay network wasdeveloped in [21] using the Lagrange dual decomposition method. For the DFscheme, the distributed power allocation problem with partial CSI was addressedin [23] and computationally efficient optimal schemes were proposed. Both relayselection and power allocation for AF wireless networks with reduced complex-ity were investigated in [24]. In the following we discuss the distributed powerallocation strategy for both AF and DF schemes.

Case 1 AF schemeThe centralized optimization problem for power allocation based on weighted-sum rate maximization is given in (8.49). Here we solve the same problem in adistributed manner. The main idea is to separate the original problem in (8.49)into independent subproblems using the Lagrange dual decomposition method.The Lagrangian of problem (8.49) is

L(PSi

Rk,λ) =

M∑i=1

wiri −N∑

k=1

λk

⎛⎝ ∑Si ∈S(Rk )

PSi

Rk− Pmax

Rk

⎞⎠ , (8.50)

where λ = [λ1 , λ2 , ..., λN ] represents the Lagrange multipliers corresponding tothe N constraints of (8.49). Using (8.42) we can write the following:

N∑k=1

λk

∑Si ∈S(Rk )

PSi

Rk=

M∑i=1

∑Rk ∈R(Si )

λkPSi

Rk. (8.51)

The Lagrangian in (8.50) is rewritten using (8.51) as

L(PSi

Rk,λ) =

M∑i=1

⎡⎣wiri −∑

Rk ∈R(Si )

λkPSi

Rk

⎤⎦+N∑

k=1

λkPmaxRk

=M∑i=1

Li(PSi

Rk,λ) +

N∑k=1

λkPmaxRk

, (8.52)

where Li(PSi

Rk,λ) corresponds to the ith value of the Lagrangian. The corre-

sponding Lagrange dual function is given by

g(λ) = maxP

S iR k≥0L(PSi

Rk,λ). (8.53)


This dual function can be obtained by solving M separate subproblems corre-sponding to M different users as

maximize Li(PSi

Rk,λ)

subject to: PSi

Rk≥ 0, Rk ∈ R(Si). (8.54)

Since the original problem given in (8.49) is convex, strong duality holds and wecan get the optimal power allocation by solving the dual problem:

minimize g(λ)

subject to: λk ≥ 0, k = 1, 2, ..., N. (8.55)

Let the solution of the optimization problem in (8.54) be L∗i (λ), which cor-responds to the optimal value of Li(PSi

Rk,λ). Then the dual problem can be

rewritten as

minimizeM∑i=1

L∗i (λ) +N∑

k=1

λkPmaxRk

subject to: λk ≥ 0, k = 1, ..., N. (8.56)

The distributed power allocation algorithm aims to solve (8.54) and (8.56)sequentially.

Let the Lagrange multiplier λk ≥ 0 denote the price per unit power at relayk. Therefore λkPSi

Rkrepresent the total price that user i must pay for using PSi

Rk

power at each relay Rk ∈ R(Si). Thus each user tries to maximize the weightedrate minus the total price it has to pay given the price coefficients at the relays.

Since the dual function g(λ) is differentiable, the problem can be solved itera-tively by the gradient projection method. The receiver of user i finds its optimalpower with given λ from the assisting relays Rk ∈ R(Si) as

PSi

Rk(λ[t + 1]) = arg max

⎧⎨⎩wiri −∑

Rk ∈R(Si )

λk [t]PSi

Rk(λ[t])

⎫⎬⎭ . (8.57)

The receiver of user i then sends this information to all the relays allocated tosource i. Based on PSi

Rkvalues received from destinations, the relays update their

dual variable λk as follows:

λk [t + 1] =

⎡⎣λk [t]− δ

⎛⎝PmaxRk

−∑

Si ∈S(Rk )

PSi

Rk(λ[t])

⎞⎠⎤⎦+

, (8.58)

where t is the iteration index, [.]+ denotes the projection onto the feasible set ofnonnegative orthants, and δ is the step size parameter. Update equation (8.58)can be interpreted as the price (λk ) change by Rk depending on the requestedpower levels from its users. The price increases when the power allocated to therelay exceeds its maximum limit. This price-based distributed algorithm requires


Figure 8.9. Price-based distributed power allocation algorithm.

message passing only between each receiver and its assisting relays. The overallstructure of the distributed power allocation is shown in Figure 8.9.

Example 5 In Figure 8.10, we compare the worst-user rate for both theweighted-sum and max–min fairness algorithms for a network with number ofsource nodes, M = 8 and number of relays, N = 4. The equal power allocationamong the relays is also included for reference. We see that the worst user obtainsthe best rate under the max–min fairness scheme and the worst rate underweighted-sum scheme with equal weight coefficients. However, Figure 8.11 showsthe weighted-sum scheme results in maximum capacity or network throughput.The max–min scheme targets improving the performance of the worst user, whichresults in a significant loss in the sum capacity of the whole network.

Case 2 DF schemeDistributed power allocation strategies for the two-hop DF scheme were inves-tigated in [23]. Here the relay decides its power so that the destination achievesthe target SNR assuming that it is the only relay to the destination. The relay


-

Figure 8.10. Comparison of the worst-user rate for the weighted-sum rate andmax–min rate algorithms.

Figure 8.11. Comparison of the sum capacity for the weighted-sum rate andmax–min rate algorithms.


decides to forward the received message from the source to the destination if itschannel gain hkD satisfies

|hkD |2 > γ, (8.59)

where γ is a given threshold value. The transmit power of the relay is given by

P ∗k =(SNRtarget − Ps |hSk |2)+

|hkD |2. (8.60)

The distributed power allocation algorithm is formulated as follows:

minimize Ps +∑

k∈NR (Ps )

E[Pk ]

subject to: Prob (SNRD ≤ SNRtarget) ≤ ρtarget ,

Ps |hkD |2 ≥ SNRtarget , k ∈ NR, (8.61)

where NR denotes the set of reliable relays which satisfy (8.61). SNRD is theSNR at destination node and ρtarget is the target outage probability.

Note that, even though a relay ultimately determines its own power, it does nottake much of the computational load. This scheme, however, requires knowledgeof all the channels gains at the receiver. Therefore, several suboptimal schemesshould be derived, in which the source can calculate γ and Ps based on thechannel characteristics without requiring feedback from the receivers.

8.4 Relay selection

Until now we have assumed that the relays are assigned a priori to power alloca-tion. The joint relay selection and power allocation problem is a mixed integeroptimization problem and is very difficult to solve. Therefore, in most of theliterature, the problem is divided into two subproblems [25]. The relays are cho-sen assuming fixed powers (e.g., equal power allocation) at the relays. Once therelays are selected, the techniques mentioned in previous sections of this chapterare used to allocate power to the selected relays. In this section, some of therelay selection algorithms are presented.

In spite of assuming fixed power at the relays, relay selection is still an NP-hard problem and the optimum solution can only be achieved through exhaustivesearch [22]. Several greedy algorithms for relay selection for DF systems havebeen proposed in the literature. The general strategy is to select the best relayor a group of relays which satisfies a certain performance improvement overthe direct S–D link [26]. In [27], a relay is selected based on the amount oftime taken to deliver a fixed number of messages. Two optimal algorithms areprovided where in the first one the relays are adaptively selected and in thesecond one the optimal number of relays is predetermined without relying on

8.4 Relay selection 229

the specific network realization. Alternatively, in [24], a relay is selected if itoffers an increase in capacity compared with source destination channel. In [28], adistributed algorithm is presented to select the ‘best’ relay that provides the bestend-to-end path between the source and the destination. Each relay is assigned atimer with initial value inversely proportional to either hk = min(|hSk |2 |, |hkD |2)or hk = 2|hSk |2 |hkD |2/(|hSk |2 + |hkD |2). The relay with the highest value of hk

is considered to be the one with the best end-to-end path between source anddestination. All relays start their timers simultaneously with different initialvalues which depend upon the channel realizations. The relay whose timer expiresfirst (i.e., the one with maximum hk ) starts relaying the message from the sourceas soon as its time expires. All the relays listen to the other relays and, therefore,know whether some other relay has started forwarding the message or not. Whenthey recognize that a particular relay has started transmission, they do notforward the source message to the destination.

Joint relay selection and power allocation algorithms were studied in [29] formultisource AF systems. The following max–min optimization problem formu-lated:

maximize minSi

12

log2

⎛⎜⎝1 +∑Rk

∣∣∣hSi

Rk

∣∣∣2 ∣∣∣hDi

Rk

∣∣∣2 PSi

RkPSi

xSi

Rk∣∣∣hSi

Rk


Rk

∣∣∣2 PSi

RkxSi

Rk+ 1

⎞⎟⎠

subject to:∑Si

P Si

Rk≤ Pmax

Rk,

∑Rk

xSi

Rk= xSi

max,

P Si

Rk≥ 0,

xSi

Rk∈ 0, 1. (8.62)

This is a nonconvex optimization problem and hence a unique analytical solutioncannot be achieved. Therefore, a suboptimal solution was proposed by relaxingthe integrality constraints on xSi

Rkand allowing them to take all values in the

interval [0, 1]. The relaxed optimization problem is convex and can be easilysolved using convex programming techniques. A rounding technique is then usedto obtain a suboptimal solution for the original optimization problem from thesolution of the relaxed optimization problem.

Joint relay selection and resource allocation is still an open research issue.The challenge is to develop low-complexity schemes that treat all users fairlyand that can be implemented feasibly without the requirement of significantadditional system resources.


8.5 Conclusion

We have studied the problem of radio resource allocation in cooperative wire-less networks. Our objective was to show how the usage of the available radioresources in these networks can be maximized by using different optimizationtechniques. In formulating these optimization models, we have taken into con-sideration the architecture and various cooperation schemes deployed in thesenetworks along with the constraints on the available radio resources such asbandwidth and transmit power. In a cooperative network, relay nodes play a vitalrole in achieving the intended benefit of cooperative communication. The perfor-mance of the entire network depends on how these relays are selected for individ-ual communications between source and destination nodes and how resource isallocated on the links between the relays and the communicating nodes. Jointlyoptimizing relay selection and resource allocation is an NP-hard problem and isoften handled as two separate subproblems. Although the bulk of this chapter hasbeen devoted to analyzing different optimization-based approaches for resourceallocation once relays are selected, we have also highlighted the different relayselection methods that are proposed in the literature and several suboptimalmethods to solve these subproblems jointly. Resource optimization in coopera-tive wireless networks remains, however, an open research problem and demandsin-depth future research.

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[1] T. Cover and A. E. Gamal, “Capacity theorems for the relay channels,”IEEE Transactions on Information Theory, vol. 25, no. 5, pp. 572–584, Sep.1979.

[2] A. Sendonaris, E. Erkip, and B. Aazhang, “User cooperation diversity, partI: System description,” IEEE Transactions on Communications, vol. 51, no.11, pp. 1927–1938, Nov. 2003.

[3] A. Sendonaris, E. Erkip, and B. Aazhang, “User cooperation diversity, partII: Implementation aspects and performance analysis,” IEEE Transactionson Communications, vol. 51, no. 11, pp. 1939–1948, Nov. 2003.

[4] A. Nosratinia, T. E. Hunter, and A. Hedayat, “Cooperative communicationin wireless networks,” IEEE Communications Magazine, vol. 42, no. 10, pp.74–80, Oct. 2004.

[5] J. N. Laneman, D. N. C. Tse, and G. W. Wornell, “Cooperative diversity inwireless networks: Efficient protocols and outage behavior,” IEEE Transac-tions on Information Theory, vol. 50, no. 12, pp. 3062–3080, Dec. 2004.

[6] Y. W. Hong, W. J. Huang, F. H. Chiu, and C. C. J. Kuo, “Cooperativecommunications in resource-constrained wireless networks,” IEEE SignalProcessing Magazine, vol. 24, no. 3, pp. 47–57, May 2007.

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[7] Y. Liang and V. V. Veeravalli, “Gaussian orthogonal relay channel: Opti-mal resource allocation and capacity,” IEEE Transactions on InformationTheory, vol. 51, no. 9, pp. 3284–3289, Sep. 2005.

[8] M. Janani, A. Hedayat, T. E. Hunter, and A. Nosratinia, “Coded coop-eration in wireless communications: Space-time transmission and iterativedecoding,” IEEE Transactions on Signal Processing, vol. 52, no. 2, pp. 362–371, Feb. 2004.

[9] T. E. Hunter and A. Nosratinia, “Outage analysis of coded cooperation,”IEEE Transactions on Information Theory, vol. 52, no. 2, pp. 375–391, Feb.2006.

[10] G. Kramer, M. Gastpar, and P. Gupta, “Cooperative strategies and capacitytheorems for relay networks,” IEEE Transactions on Information Theory,vol. 51, no. 9, pp. 3037–3063, Sep. 2005.

[11] A. H. Madsen and J. Zhang, “Capacity bounds and power allocation forwireless relay channels,” IEEE Transactions on Information Theory, vol.51, no. 6, pp. 2020–2040, Jun. 2005.

[12] L. Le and E. Hossain, “Multihop cellular networks: Potential gains, researchchallenges and resource allocation framework,” IEEE Communications Mag-azine, vol. 45, no. 9, pp. 66–73, Sep. 2007.

[13] Q. Zhang, J. Zhang, C. Shao, Y. Wang, P. Zhang, and R. Hu, “Powerallocation for regenerative relay channel with rayleigh fading,” in Proc. ofIEEE Vehicular Technology Conference (VTC), vol. 2, pp. 1167–1171, May2004. IEEE, 2004.

[14] T. Cover and J. Thomas, Elements of Information Theory, Wiley, 1991.[15] J. Zhang, Q. Zhang, C. Shao, Y. Wang, P. Zhang, and Z. Zhang, “Adap-

tive optimal transmit power allocation for two-hop non-regenerative wirelessrelay system,” in Proc. of IEEE Vehicular Technology Conference (VTC),vol. 2, pp. 1213–1217, May 2004. IEEE, 2004.

[16] E. I. Telatar, “Capacity of multi-antenna gaussian channels,” EuropeanTransactions on Telecommunications, vol. 10, no. 6, pp. 585–595, Nov./Dec.1999.

[17] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge UniversityPress, 2004.

[18] I. Maric and R. D. Yates, “Bandwidth and power allocation for cooperativestrategies in gaussian relay networks,” in Proc. of 38th Asilomar Conferenceon Signal, System and Computers, vol. 2, pp. 1907–1911, Nov. 2004. IEEE,2004.

[19] J. N. Laneman and G. W. Wornell, “Distributed space-time-coded protocolsfor exploiting cooperative diversity in wireless networks,” IEEE Transac-tions on Information Theory, vol. 49, no. 10, pp. 2415–2425, Oct. 2003.

[20] I. Maric and R. D. Yates, “Forwarding strategies for Gaussian parallel-relaynetworks,” in Proc. of Conference on Information Sciences and Systems(CISS), vol. 2, pp. 591–596, Mar. 2004. Princeton University, 2004.


[21] K. T. Phan, L. B. Le, S. A. Vorobyov, and T. Le-Ngoc, “Centralized anddistributed power allocation in multi-user wireless relay networks,” in Proc.of IEEE International Conference on Communications (ICC), pp. 1–5, Jun.2009. IEEE, 2009.

[22] Y. Zhao, R. S. Adve, and T. J. Lim, “Improving amplify-and-forward relaynetworks: Optimal power allocation versus selection,” IEEE Transactionson Wireless Communications, vol. 6, no. 8, pp. 3114–3123, Aug. 2007.

[23] M. Chen, S. Serbetli, and A. Yener, “Distributed power allocation strategiesfor parallel relay networks,” IEEE Transactions on Wireless Communica-tions, vol. 7, no. 2, pp. 552–561, Feb. 2008.

[24] J. Cai, X. Shen, J. W. Mark, and A. S. Alfa, “Semi-distributed user relayingalgorithm for amplify-and-forward wireless relay networks,” IEEE Transac-tions on Wireless Communications, vol. 7, no. 4, pp. 1348–1357, Apr. 2008.

[25] Z. Han, T. Himsoon, W. P. Siriwongpairat, and K. J. R. Liu, “Energy-efficient cooperative transmission over multiuser OFDM networks: Whohelps whom and how to cooperate,” in Proc. of IEEE Wireless Commu-nications and Networking Conference (WCNC), vol. 2, pp. 1030–1035, Mar.2005. IEEE, 2005.

[26] A. Nosratinia and T. E. Hunter, “Grouping and partner selection in coop-erative wireless networks,” IEEE Journal on Selected Areas in Communica-tions, vol. 25, no. 2, pp. 369–378, Feb. 2007.

[27] S. Nam, M. Vu, and V. Tarokh, “Relay selection methods for wireless coop-erative communications,” in Proc. of Conference on Information Sciencesand Systems (CISS), pp. 859–864, Mar. 2008. Princeton University, 2008.

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9 Adaptive resource allocation incooperative cellular networks

Wei Yu, Taesoo Kwon, and Changyong Shin

9.1 Introduction

The cellular structure is a central concept in wireless network deployment. Awireless cellular network comprises base stations geographically located at thecentre of each cell serving users within the cell boundary. The assignment of theusers to the base stations depends on the relative channel propagation character-istics. As a mobile device can usually receive signals from multiple base stations,the mobile is typically assigned to the base station with the strongest channelgain. Signals from all other base stations are regarded as intercell interference.However, at the cell edge, it is often the case that the propagation path-lossesfrom two or more base stations are similar. In this case, the signal-to-noise-and-interference ratio (SINR) could be close to 0 dB, even if the mobile is assignedto the strongest base station. To avoid excessive intercell interference in thesecases, traditional cellular networks employ a fixed frequency reuse pattern sothat neighboring base stations do not share the same frequency. In this man-ner, neighboring cells are separated in frequency so that cell-edge users do notinterfere with each other.

The traditional fixed frequency reuse schemes are effective in minimizing inter-cell interference, but are also resource intensive in the sense that each cell requiresa substantial amount of nonoverlapping bandwidth, so that only a fraction of thetotal bandwidth can be made available for each cell. Consequently, the standard-ization processes for future wireless systems have increasingly targeted maximalfrequency reuse, where all cells use the same frequency everywhere. In these sys-tems, it is crucial to manage intercell interference using dynamic power control,frequency allocation, and rate allocation methods.

Wireless channels are fundamentally impaired by fading, propagation loss, andinterference. Intensive research has been focused on the mitigation of short-termfading, where spatial, temporal, and frequency diversity techniques have beendevised to combat the short-term variation of the channel over time. Large-scalefading, propagation loss, and intercell interference, however, call for differentapproaches. As large-scale channel and interference characteristics can often be


234 Adaptive resource allocation in cooperative cellular networks

estimated at the receivers and made available at the transmitter, rather thancombating large-scale fading the right approach is to adapt to it.

To this end, cooperative communication has emerged as a promising futuretechnology for dealing with the large-scale channel impairments. This chapterconsiders two types of cooperative networks that specifically address the issuesof intercell interference and path-loss.

Base station cooperation This type of cooperative network explores the possi-bility of coordinating multiple base stations. In a traditional cellular network,each base station operates independently. In particular, each base stationadapts to the channel propagation condition within each cell without consid-ering the intercell interference it causes the neighboring cells. The intercellinterference is always treated as part of the background noise. A networkwith base station cooperation is a network in which the transmission strate-gies among the multiple base stations are designed jointly. In particular, thebase stations may cooperate in their power, frequency, and rate allocationsin order to jointly mitigate the effect of intercell interference for users at thecell edge. Such a cooperative network can also be thought of as an adaptivefrequency reuse scheme where the frequency usage and transmission powerspectrum are designed specifically according to the mobile locations and usertraffic patterns.

Relay cooperation This type of cooperative network explores the use of relaysto aid the direct communication between the base station and the remote sub-scribers. The path-loss is a fundamental characteristic of the wireless medium.The path-loss exponent, which is determined by the physics of electromagneticwave propagation environment, typically ranges from 2 to 6. Consequently,propagation distance is a crucial factor that affects the capacity of the wire-less channel. The use of cooperative relays in a cellular network can be thoughtof as a method for reducing the propagation distance. Instead of adding morebase stations to the network (which is costly), the idea of a cooperative relaynetwork is to deploy relay stations within each cell so that the mobile usersmay connect to the nearest relay, rather than the base station which may befar away. Relay deployment substantially improves the area-spectral efficiencyof the network.

In both types of cooperative networks, resource allocation is expected to bea crucial issue. In a network with base station cooperation, base stations mustjointly determine their respective power and bandwidth allocation for the pur-pose of minimizing intercell interference. In a cooperative relay network, powerand bandwidth assignments need to be made for each of the base-station-to-relayand relay-to-mobile links. The optimal allocation of these network resources hasa significant impact on the overall network performance.

This chapter provides an optimization framework for power, bandwidth, andrate allocation in cooperative cellular networks. The network is assumed toemploy orthogonal frequency division multiple access (OFDMA) which provides


flexibility in power, subchannel, and rate assignment for each link. This chap-ter covers the theory and practice of cooperative network design, and makesa case that cooperative communication is a key future technology that couldsignificantly improve the overall capacity of wireless networks.

Throughout this chapter, it is assumed that the network employs an initialchannel estimation phase so that the frequency selective channel gain betweenany arbitrary transmitter and receiver pair can be estimated and made knownthroughout the network. The assumption of channel knowledge is necessary inorder to optimize the allocation of power, bandwidth, and rate in the network. Inthis chapter it is further assumed that channel estimation is perfect. In practicalsituations where channel estimation error exists, robust optimization design isneeded. The impact of imperfect channel knowledge on the resource allocationof cooperative cellular networks has been dealt with in [1, 2], but is not directlyaddressed in this chapter.

It should be noted that in this chapter we consider cooperative networks inwhich transmitting nodes cooperate in their transmission strategies only (e.g.,power, bandwidth allocation), but not in actual signals. It is possible to envisiona network-wide cooperative system where all the antennas from all the basestations are pooled together as a single antenna array at the signal level. Such anetwork multiple-input multiple-output (MIMO) system is capable of achievingthe ultimate area-spectral efficiency limit of the network, but is outside of thescope of this chapter.

9.2 System model

In this chapter we consider wireless cellular networks employing an OFDMAscheme, where the total bandwidth is divided into a large number of subchannels,and where arbitrary scheduling, as well as power, frequency, and rate allocation,may be made for any transmitter–receiver pair throughout the network. Theflexibility of the OFDMA system in assigning resources throughout the networkis one of its key advantages, but it also presents a challenge in resource optimiza-tion, as the number of optimization variables is typically quite large in a realisticnetwork. This section presents a system model for the OFDMA network.

9.2.1 Orthogonal frequency-division multiplexing (OFDM)

The OFDM scheme was originally conceived as a way to combat the multipathor frequency-selective nature of the wireless channel. By utilizing an N -pointinverse fast Fourier transform (IFFT) at the transmitter and an N -point fastFourier transform (FFT) at the receiver, the available frequency band is dividedinto N orthogonal subchannels on which independent data transmissions takeplace. The orthogonalization of frequency dimensions relies on the use of a cyclic


11

1

1

1

223

3

33 2 2

2

1 1 24 4

42

1

2

2 2

321 2 2 2 1 1 2 2 4 4

4

2 214

3 3 3 1 4 2 1 1 4

3

Freq

uenc

y

Time

Figure 9.1. In an OFDMA system, the time and frequency dimensions are par-titioned and can be assigned arbitrarily to multiple users in the cell.

prefix, and on the assumption that the channel is stationary within each OFDMsymbol, an assumption which is made throughout this chapter.

The OFDM system can also be thought of as a multiple-access scheme, in whichmultiple users may occupy orthogonal frequency subchannels without interferingwith each other. For example, in a cellular network, different mobile users maycommunicate with the base station on nonoverlapping sets of frequency tones, sothat different users’ signals are separated in frequency. This is known as OFDMA.The idea of OFDMA can also be extended to a cooperative relay network in whichdifferent transmitter–receiver pairs in the network use nonoverlapping sets offrequency tones.

Orthogonalization within each cell is, in general, a good idea, as whenevera receiver is close in range to a nonintended transmitter, orthogonalization isneeded to avoid mutual interference. The use of OFDM enables orthogonaliza-tion in the frequency domain, which along with scheduling (which is essentiallyorthogonalization in the time domain) allows an arbitrary division of orthogonaldimensions among users within each cell. The assignment of dimensions can bevisualized in a time–frequency map as shown in Figure 9.1.

It is implicitly assumed in the preceding discussion that when multipletransmitter–receiver pairs use OFDMA, the FFT at each receiver orthogonal-izes not only the intended transmit signal, but also all the interfering signals.For this to happen, the received OFDM symbols from all transmitters must besymbol synchronized, as otherwise a leakage would occur from one tone to itsneighboring tones [3]. For the downlink cellular setting, symbol synchronizationis automatic. For the uplink, transmit timing offset can be introduced to ensuresynchronization at the receiver. A more challenging case is the relay cooperativenetwork, where it is possible to have one relay communicating with a mobile onone set of frequency tones, while another relay communicates with a differentmobile on adjacent tones. In this case, simultaneous symbol synchronization at


two different receivers becomes difficult. It is possible to use advanced techniques(such as a cyclic suffix in addition to a cyclic prefix [4]) to correct for these effects.For simplicity, in the rest of this chapter it is assumed that leakage of this typeis sufficiently small that its effect can be ignored.

9.2.2 Adaptive power, spectrum, and rate allocation

An OFDM system allows arbitrary assignment of power, modulation format, andrates across the frequency domain for each transmitter–receiver pair. Assuminga fixed type of modulation, e.g., quadrature amplitude modulation (QAM), anda fixed target probability of error, the maximum bit rate in each OFDM tone isa function of the SINR on that tone. The overall achievable rate of the link isthe sum of the bit rates across the tones, which can be expressed as

R =N∑

n=1

log(

1 +SINR(n)

Γ

), (9.1)

where SINR(n) is the ratio of the received signal power to the noise and interfer-ence power at the receiver in tone n, and Γ is the SNR gap, which is a measureof the efficiency of the particular modulation and coding scheme employed. Withstrong coding, Γ can be made to be close to the information-theoretical limit of0 dB. In practical wireless systems, Γ can range from around 6 dB to 12 dB.The exact value of Γ depends on the modulation scheme, coding gain, and theprobability-of-error target.

The use of the SNR gap to relate the SINR with the transmission rate isan approximation which is accurate for moderate and high SNRs. The exactrelation between the SINR and the rate depends on a detailed probability-of-error analysis, and would give rise to complex functional forms. The advantageof using the SNR gap approximation is that the resulting functional relation isamenable to analytic optimization, and it closely resembles the Shannon capacityformula for the additive white Gaussian noise channel.

Note that because of the presence of intercell and intracell interference withinthe network, the SINRs of different links in a cellular network are interdependent.For this reason, the optimization of achievable rates over all users across thenetwork is, in general, a nontrivial problem.

9.2.3 Cooperative networks

In this chapter we consider two types of cooperative cellular networks: networkswhere multiple base stations from different cells may cooperatively set theirpower allocation across the frequency tones; and networks where relay stationsmay be deployed to transmit and receive information from the mobile users.

It is assumed that an OFDMA scheme is used within each cell, and no twolinks within each cell can use the same frequency tone at the same time. This


eliminates intracell interference. Intercell interference is still present especially forcell-edge users. Given a fixed frequency and power allocation for all transmitters,the SINR for each link in every frequency tone can be easily computed as afunction of the transmit powers and the direct and interfering channel path-losses. The network optimization problem is that of coordinating the allocationof frequency tones and time slots to different links within each cell and theallocation of power across time and frequency subject to total and peak powerconstraints, so that an overall network objective function is maximized.

9.3 Network optimization

9.3.1 Single-user water-filling

The OFDM transmit power optimization problem for a single link has a classicsolution known as water-filling. In this section, we briefly review the optimizationprinciple behind water-filling and set the stage for subsequent development formultiuser network optimization. For the single-link problem where the noise andinterference are assumed to be fixed, the optimization of the achievable ratesubject to a total power constraint can be formulated as

maximizeN∑

n=1

log(

1 +|h(n)|2P (n)

Γσ2(n)

)

subject to :N∑

n=1

P (n) ≤ Ptotal ,

0 ≤ P (n) ≤ Pmax, (9.2)

where the optimization is over P (n), the transmit power on the frequency tonen. The channel path-loss |h(n)|2 and the combined noise and interference σ2(n)are assumed to be fixed. The optimization is subject to a total power constraintPtotal and a per-tone maximum power-spectral-density (PSD) constraint Pmax .

The water-filling solution arises from solving the above optimization problemvia its Lagrangian dual. Let λ be the dual variable associated with the totalpower constraint, then the Lagrangian of the above optimization problem is

L(P (n), λ) =N∑

n=1

log(

1 +|h(n)|2P (n)

Γσ2(n)

)− λ

(N∑

n=1

P (n)− Ptotal

). (9.3)

The constrained optimization problem is now reduced to an unconstrained one inwhich λ can be interpreted as the power price. Optimizing the above Lagrangiansubject to peak power constraints by setting its derivative to be zero gives

P (n) =[

1λ− Γσ2(n)|h(n)|2

]Pm a x

0, (9.4)

9.3 Network optimization 239

Figure 9.2. Single-user water-filling solution.

where [·]ba denotes a limiting operation with lower bound a and upper bound b.The optimal λ can then be found based on the total power constraint, eitherby a bisection or by using algorithms based on the sorting of the subchannelsby their effective noises. Equation (9.4) is the celebrated water-filling solutionfor transmit power optimization over a single link. The name water-filling comesfrom the interpretation that the effective noise and interference Γσ2(n)/|h(n)|2can be thought of as the bottom of a bowl, 1/λ can be thought of as the waterlevel, and the power allocation process can be thought of as that of pouring waterinto the bowl. The optimal power is the difference between the water level andthe bottom of the bowl, as illustrated in Figure 9.2.

The fundamental reasons that an (almost) analytic and exact solution existsfor this problem are that the objective function of the optimization problem (9.2)is a concave function of the optimization variables and the constraints are linear.Therefore, convex optimization techniques such as Lagrangian dual optimizationcan be applied.

Modern wireless communication systems often implement adaptive power con-trol and adaptive modulation schemes that emulate the optimal water-fillingsolution. It should be noted that the exact shape of the optimal power allocationis not important. If one approximates the optimal solution by a constant powerallocation where all subchannels that would receive positive power in the optimalsolution receive equal power in this approximate solution, the value of the objec-tive function would be close to the optimum [5, 6]. This is because the water-filling relation, i.e., (9.4), operates on a linear scale on P (n), whilethe rate expression, i.e., (9.2), is a logarithmic function, which is not sensitiveto the exact value of P (n) when it is large. Thus, in the implementation ofwater-filling in practice, while it is important to identify the minimum channel-gain-to-noise ratio beyond which transmission should take place, the exact valueof P (n) is not as important.


In a cellular setting, whenever a particular cell implements power adaptation,it changes its interference pattern on its neighbors. Thus, when every cell imple-ments water-filling at the same time, the entire network effectively reaches asimultaneous water-filling solution, where the optimal power allocation in eachcell is the water-filling solution against the combined noise and interference fromall other cells. Such a simultaneous water-filling solution can typically be reachedvia an iterative water-filling algorithm in a system-level simulation where thewater-filling operation is performed on a per-cell basis iteratively [7]. Mathe-matically, the most general condition for the convergence of such an iterativealgorithm is not yet known, but iterative water-filling has been observed to con-verge in most practical situations.

9.3.2 Network utility maximization

In a network with multiple users, the transmit power, bandwidth, and rateallocation problem becomes considerably more complicated, as the achievablerates of various users become interdependent. There are several consequencesof such interdependency. First, the improvement in the rate of one user gen-erally comes at the expense of other users in the network. For example, in amulticell OFDMA setup, to improve the rate of one user, one has to increaseeither its frequency allocation or its transmit power. The former comes at theexpense of the bandwidth allocation for other users within the cell. The lat-ter comes at the expense of more interference for users in adjacent cells. Inboth cases, there is a tradeoff between the rates of various users. The con-cept of rate region is often used to characterize such a physical-layer tradeoffamong the rates of various users as a function of their power and bandwidthallocations.

Further, in a realistic network with many users running different applica-tions, the same rate improvement often brings a different amount of bene-fit to different users depending on the application layer characteristics. Forexample, a rate improvement could result in higher video quality for one userengaged in a video-on-demand service, or a faster file transfer by a differentuser. The network must decide which of the two alternatives is preferable.Such a choice depends not only on the nature of the application, but alsoon revenue considerations. Therefore, a tradeoff also exists in the applicationlayer.

Network utility maximization (NUM) is an optimization framework that cap-tures both the physical-layer and the application-layer tradeoffs [8]. In this frame-work, each user has an associated utility, which is a function of its (windowed)average rate, denoted as Ui(Ri). The utility is an increasing function and isassumed to be concave; it captures the desirability of having a rate Ri for theuser i. The NUM problem is that of maximizing the sum of the utilities over allusers in the network, subject to the achievability of these rates in the physical


layer, i.e.,

maximizeK∑

i=1

Ui(Ri)

subject to: (R1 , R2 , · · · , RK ) ∈ R, (9.5)

where the constraint is that each instantaneous rate-tuple must be inside R, theachievable rate region at each time instance, which is defined as the convex hullof the union of all achieveable rate-tuples.

It is implicitly assumed in the above problem formulation that the utilityfunctions for different users in the network are independent. This is a realisticassumption for the case where each user runs a separate application. In a special-ized network, such a sensor network, where users collaborate in a specific task,it is conceivable that the utility of the network could depend jointly on all therates, i.e., the objective is to maximize U(R1 , R2 , . . . , RK ). A generalization ofNUM in this setting has been treated in [9].

9.3.3 Proportional fairness

A common choice of the utility function is the logarithm function, i.e., Ui(Ri) =log(Ri). The choice of log-utility leads to a proportional fair rate allocation,which is described in detail below.

The network’s objective is to maximize the sum utility of the average ratesof different users in the network. The averaging is typically done in a windowedfashion, or more commonly, exponentially weighted as

Ri = (1− α)Ri + αRi, (9.6)

where 0 < α < 1 is the forgetting factor. Assuming that αRi is small, the newcontribution of the instantaneous rate Ri to the overall utility can be approxi-mated as

Ui

((1− α)Ri + αRi

)≈ Ui

((1− α)Ri

)+

∂Ui

∂Ri

∣∣∣∣Ri =R i

(αRi). (9.7)

Under this approximation, the maximization of the sum utility, which is equiv-alent to the maximization of the incremental utility, becomes the maximizationof the weighted sum rate, where the weights are determined by the derivativeof the utility function evaluated at the present average rate. When the utilityfunction is the logarithm function, the equivalent maximization problem reducesto

maximizeK∑

i=1

wiRi

subject to: (R1 , R2 , · · · , RK ) ∈ R, (9.8)


where wi = 1/Ri . This is a weighted rate sum maximization problem for theinstantaneous rates with weights equal to the inverse of the average rates. Asthese weights fluctuate, and as the rate region R changes over time (due to, forexample, user mobility and the fading characteristics of the underlying fadingchannel), the above optimization problem needs to be solved repeatedly.

The proportional fair rate allocation was originally devised in the context ofuser scheduling [10]. The above discussion shows that it is also applicable tothe power allocation problem. The use of proportional fairness utility is notthe only way to reduce the network utility maximization to a weighted ratemaximization problem. Alternatively, one may consider a system in which eachuser has an associated input queue, and where weights of the weighted rate summaximization problem are determined as a function of the input queue lengthof each respective user [11, 12]. The important point is that in either approach,the application layer demand for rates (expressed in either the utility function orthe queue length) is decoupled from the physical layer provision of rates. In bothcases, the physical-layer problem is reduced to a weighted rate sum maximizationproblem.

9.3.4 Rate region maximization

The reduction of the network utility maximization problem to a weighted ratesum maximization problem is a crucial step in the development of resource allo-cation algorithms for OFDMA networks. In an OFDMA network, the rate ofeach link is the sum of bit rates across the frequency tones. The reduction ofthe maximization of a nonlinear utility function of link rates to a weighted ratesum maximization essentially linearizes the objective function and decouples theobjective function on a per-tone basis, which simplifies the problem significantly.

The rate region maximization problem also often has constraints that coupleacross the frequency tones. For example, each user may have a power constraintacross the frequency. In addition, there is typically the constraint that no twousers should occupy the same frequency tone within each cell. To solve the rateregion maximization problem efficiently, it is important to decouple these con-straints across the frequency tones as well.

A key technique for achieving decoupling is to utilize the Lagrangian dualitytheory in optimization. For example, consider the case where

Ri =N∑

n=1

log

(1 +

|hii(n)|2Pi(n)Γ(∑

j =i |hji(n)|2Pj (n) + σ2(n))

)(9.9)

subject to a power constraint

N∑n=1

Pi(n) ≤ Pi,total , (9.10)


where Pi(n) denotes the transmit power of user i in tone n, and hij (n) is thecomplex channel gain from the transmitter of user i to the receiver of the user j.The weighted rate sum maximization problem subject to the power constraintcan be solved by dualizing with respect to the power constraint. This results ina dual function g(λi) defined as

g(λi) = maxPi (n)

wiRi − λi

(N∑

n=1

Pi(n)− Pi,total

). (9.11)

The point is that when the objective function is a weighted rate sum and theconstraint is linearized via the use of Lagrangian dual variable λi , the aboveoptimization problem reduces to N per-tone problems:

maxPi (n)

wi log

(1 +

|hii(n)|2Pi(n)Γ(∑

j =i |hji(n)|2Pj (n) + σ2(n))

)− λiPi(n)

. (9.12)

Just as in single-user water-filling, where the solution to a convex optimizationproblem reduces to solving the problem for each λ, then finding the optimal λ,similar algorithms based on λ search can be applied here. The reduction to anN per-tone optimization problem ensures that the computational complexity foreach step of this optimization problem with fixed λi is linear in the number oftones.

The theoretical justification for the above duality approach is convexity. Forconvex optimization problems where the feasible set has a nonempty interior(which is almost always true in engineering applications), the maximum value ofthe original objective is equal to the minimum of the dual optimization problem

minλi≥0

g(λi). (9.13)

The optimum λi can be found using search methods such as the ellipsoidmethod (which is a generalization of bisection search to higher dimensions) orthe subgradient method (see, for example, [13]).

An interesting fact is that this duality technique remains applicable even whenthe functional form of the rate expression is nonconvex as is the case in (9.9),as long as the OFDM system has a large number of dimensions in the frequencydomain, which allows an effective convexification of the achievable rate regionas a function of the power allocation. More rigorously, under general conditions,the duality gap between the original optimization problem and its dual goes tozero as the number of OFDM tones goes to infinity [13, 14]. This fact allows theduality technique to be used in a wide variety of applications.

To summarize, under the NUM framework, the network optimization problemfor an OFDMA network under per-user power constraints reduces to a per-toneweighted sum rate maximization problem with a linear power penalty term.The weights in weighted rate sum maximization are determined by the utilityfunction. The power penalty weighting can be found using a generalization ofbisection.


Figure 9.3. A multicell network in which the base stations cooperate in userscheduling and power allocation across the frequency spectrum.

The rest of this chapter is devoted to two examples of cooperative OFDMAnetworks where the adaptive scheduling, and power, frequency, and rate alloca-tion problem can be solved efficiently using this methodology.

9.4 Network with base station cooperation

9.4.1 Problem formulation

Consider an OFDMA-based cellular network as shown in Figure 9.3 in whichthe base stations cooperate in setting their downlink transmit power, and themobiles likewise jointly set their uplink transmit power in order to avoid excessiveinterference between the neighboring cells. The optimal design of this multicellcooperative network becomes that of designing a joint scheduling and powerallocation scheme that decides in each frequency tone:

Which user should be served in each cell? What are the appropriate uplink and downlink transmit power levels?

Scheduling can be thought of either as the optimal partitioning of the frequencyamong the users within each cell, or as the optimal assignment of users in eachtime slot for each frequency tone. Scheduling and power allocation need to beconsidered jointly in order to reach an optimal solution for the entire network.

Assuming a proportional fairness objective function, the network optimizationproblem for the downlink is a weighted rate sum maximization problem

maxL∑

l=1

K∑k=1

wD,lkRD,lk , (9.14)

9.4 Network with base station cooperation 245

where RD,lk is the instantaneous downlink rate of the kth user in the lth cellin a network consisting of L cells with K users per cell. The weights wD,lk =1/RD,lk are the proportional fairness variables determined by the exponentiallyweighted average rates. Let k = fD (l, n) be the downlink scheduling function,which assigns a user k to the nth frequency tone in the lth base station. Thedownlink rate expression RD,lk is then

RD,lk =∑

n∈Dl k

log

(1 +

PnD,l |hn

llk |2

Γ(σ2 +∑

j = l PnD,j |hn

jlk |2)

), (9.15)

where the summation is over frequency tones assigned to the kth user in thelth cell, i.e., Dlk = n|k = fD (l, n). Here, hn

jlk is the channel transfer functionfrom the jth base station to the kth user in the lth cell and in the nth tone, andPn

D,l is the downlink power allocation for the lth base station in the nth tone.The optimization is over Pn

D,l . The weighted rate maximization problem is to besolved under the per-base-station power constraint for the downlink

N∑n=1

Pl(n) ≤ Pl,total (9.16)

as well as possibly peak power constraints:

0 ≤ PnD,l ≤ Smax

D . (9.17)

In addition, there is the OFDMA constraint that no two users should occupy thesame frequency tone within each cell. Finally, note that a similar optimizationproblem with corresponding rate and power expressions can be written for theuplink.

The joint scheduling and power allocation problem formulated above has beenstudied in several works [15–17], in which key ideas such as iterative optimizationof scheduling and power allocation and numerical methods for power adaptationhave been proposed. The following section outlines the approach based on theseworks and provides a performance projection for networks with base stationpower cooperation.

9.4.2 Joint scheduling and power allocation

The dual decomposition technique outlined in the previous section can be used totackle the joint scheduling and power allocation problem above. The key fact isthat after dualizing with respect to the total power constraint, the optimizationproblem decouples on a tone-by-tone basis:

maximize∑

l

wD,lk log

(1 +

PnD,l |hn

llk |2

Γ(σ2 +∑

j = l PnD,j |hn

jlk |2)

)− λD,lP

nD,l ,

subject to: 0 ≤ PnD,l ≤ Smax

D ∀l, (9.18)


where the optimization is over both the power variables PnD,l as well as the

scheduling function k = fD (l, n) across the L base stations for a fixed tone n.The duality theory for OFDMA networks states that if the above per-tone

optimization problem can be solved exactly for each set of fixed λD,ls, an ellipsoidor subgradient search over λD,l in an outer loop can be carried out to find theoptimal λD,l , which then leads to the global optimum of the overall networkoptimization problem.

The optimization problem (9.18) is a mixed integer programming problem withnonconvex objective function. Finding the global optimum for such an optimiza-tion problem is known to be a difficult task. However, many approximation algo-rithms that can reach at least a local optimum exist. Although strictly speaking,the duality theory for OFDMA networks requires the global optimum solutionof the per-tone optimization problem, the local optimum solution already worksquite well in practice. The rest of this section focuses on solving (9.18) usinglocal optimum approaches.

Observe first that for the downlink, the scheduling step and the power allo-cation step can be carried out separately. This is because the scheduling choiceat one base station does not affect the amount of intercell interference at theneighboring cells. The intercell interference is a function of the power allocationonly. Thus, an iterative algorithm can be devised so that one can find the bestschedule for a fixed power allocation, then find the best power allocation for thefixed schedule [15]. The iteration always increases the objective function mono-tonically, so it is guaranteed to converge to at least a local optimum of the jointscheduling and power allocation problem.

For the downlink, because the intercell interference is independent of thescheduling decisions at each cell, finding the best schedule for a fixed powerallocation is a per-cell optimization problem. In other words, each base stationonly needs to find the user in each tone that maximizes the weighted rate. Thisamounts to a simple search among the K users in each cell.

For a fixed user schedule, the optimal power allocation problem becomes thatof solving (9.18) for the set of scheduled users in each tone. This is a nonconvexproblem with potentially multiple local optima. The first-order condition forthis optimization problem can be found by taking the derivative of the objectivefunction and setting it to be zero:

wD,lk |hnllk |2

PnD,l |hn

llk |2 + Γ(σ2 +∑

j = l PnD,j |hn

jlk |2)=∑j = l

tnD,j l + λD,l , (9.19)

where k = fD (l, n) for l = 1, . . . , L,

tnD,j l = wD,jk ′Γ|hn

ljk ′ |2

PnD,j |hn

jjk ′ |2

((SINRn

D,j )2

1 + SINRnD,j

), (9.20)


Figure 9.4. Water-filling where the water-filling level is modified by the tnD,j l

pricing terms.

and

SINRnD,j =

PnD,j |hn

jjk ′ |2

Γ(σ2 +∑

i =j P nD,i |hn

ijk ′ |2)(9.21)

with k′ = fD (j, n).The first-order condition gives a water-filling like condition if the terms tnD,j l

are considered to be fixed. In this case, (9.19) suggests that the following powerallocation is a local optimum of the per-tone optimization problem:

PnD,l =

[wD,lk∑

j = l tnD,j l + λD,l

−Γ(σ2 +

∑j = l P

nD,j |hn

jlk |2)|hn

llk |2

]S m a xD

0

, (9.22)

where k = fD (l, n). Note that this is similar to the single-user water-filling powerallocation (9.4), except that the power is allocated with respect to the combinednoise and interference, and that the water-filling level λD,l is modified by theadditional tnD,j l terms. This process is called modified water-filling [18] and isillustrated in Figure 9.4.

The tnD,j l term can be interpreted as a summary of the effect of allocatingadditional power at the lth base station on the downlink rate at the neighboringjth cell. A larger value of tnD,j l signals a larger interference effect from the lthcell to the jth cell. The multiuser water-filling condition in (9.22) implies thatwhen interference is present, the water-filling level needs to be modified. Thewater-filling level should decrease if the effect of interference is strong, whichsuggests that the power allocation should be reduced. Note that the water-fillinglevel is also affected by the proportional fairness weights wD,lk . A larger weightsuggests a higher water-filling level.

The terms tnD,j l also have a pricing interpretation [19–22], which comes fromthe fact that tnD,j l is the derivative of the jth base station’s data rate with respectto the lth base station’s power, weighted by the proportional fairness variable.


A higher value of tnD,j l suggests that the lth base station must pay a higher pricefor allocating its power in tone n, which is reflected in the modification of thewater-filling level.

The water-filling condition (9.22) suggests that one way to coordinate multi-ple base stations in a cooperative cellular network is to allow base stations toexchange values of tnD,j l with their neighbors. Note that the value of tnD,j l dependson the ratio of the direct and the interfering channel gains, which can be easilyestimated using pilot signals.

Knowing tnD,j l , each base station may use (9.22) to update its power alloca-tion. This results in an iterative process. When it converges, it reaches a localoptimum of the weighted rate sum maximization problem (9.18). This procedureis known as the modified iterative water-filling algorithm [18]. In practice, it maybe necessary to damp the iteration to ensure convergence [17].

Alternatively, one may resort to a direct numerical optimization of (9.18)[16, 17]. Starting from an initial power allocation, one may compute a gradi-ent or Newton’s increment direction for the optimization objective, then suc-cessively improve the objective function until a local optimum is reached. Thegradient can be computed locally at each base station based on the pricingterms tnD,j l .

To summarize, the coordination of base stations for the downlink can beefficiently implemented using an approach that iterates between coordinatedscheduling and coordinated power allocation. The scheduling step for the down-link can be efficiently implemented on a per-cell basis; the power allocation stepcan be implemented if certain exchange of pricing information is allowed amongthe base stations. This iterative process, together with an outer loop that findsthe optimal power prices λD,l , reaches a local optimum of the weighted rate summaximization problem.

Much of the discussion in this section is also applicable to the uplink, exceptthat optimal scheduling is no longer a per-cell problem. In the uplink, the assign-ment of users in each cell directly affects the interference in neighboring cells,so an optimal uplink scheduler needs to consider the effect of the interference aswell. However, there is evidence suggesting that if one uses identical schedulingfor both the uplink and the downlink, the network often already performs verywell [17]. This can be justified in part by the fact that there is a duality betweenuplink and downlink channels. The capacity regions of the uplink and downlinkchannels are identical under the same power constraint.

9.4.3 Performance evaluation

To illustrate the performance of the proportionally fair joint scheduling andpower allocation method described in Section 9.4.2, we present simulation resultsfor a multicell network with base station cooperation. The simulated networkconsists of 19 cells hexagonally tiled with 40 users per cell, occupying a totalbandwidth of 10 MHz partitioned into 256 subchannels using OFDMA. For


Table 9.1. Uplink (UL) and downlink (DL) sum rates over 19 cells with 40 cell-edge users per cell with proportional fairness joint scheduling and cooperativepower allocation among the base stations [17]

2.8 km 1.4 km

UL DL UL DLBase to base

distance

Fixed power spectrum 125 Mbps 129 Mbps 137 Mbps 142 MbpsAdaptive power spectrum 185 Mbps 181 Mbps 228 Mbps 227 Mbps

Improvement 48% 40% 66% 60%

simplicity, a maximum transmit PSD of −27 dBm/Hz is imposed at both thebase stations and the remote users, but no total power constraint is imposed. Amultipath fading channel model is used with 8 dB of log-normal shadowing. Thechannel path-loss is modeled as a function of distance d as 128.1 + 37.6 log10(d)(in decibels). The background noise level is assumed to be −169 dBm/Hz.

The joint proportionally fair scheduling and adaptive power allocation isexpected to provide the largest improvement in performance for users at thecell edge where intercell interference is dominant. To illustrate the performancegain for cell-edge users, in the simulation users are placed at the cell edge onpurpose. Table 9.1 illustrates a comparison of the achievable sum rates overall users in 19 cells for the adaptive power allocation algorithm vs. the con-stant transmit PSD scheme with proportionally fair scheduling. These resultswere originally reported in [17] and are consistent with other studies in thisarea [16]. It can be seen that depending on the base station to base stationdistance, a sum rate improvement of 40–60% is possible. The improvementis larger when the base stations are closer, because in this case the intercellinterference is also larger. It is worth emphasizing that the sum rate improve-ment reported in Table 9.1 is for cell-edge users. If averaged over all usersuniformly placed over the cell, the sum rate improvement would have beenabout 15–20%.

Figure 9.5 illustrates the convergence behavior of the joint proportional fairscheduling and power allocation algorithm. Each iteration here consists of eitheran adaptive power allocation step or a scheduling step. Up to ten subiterationsare performed within each power allocation step. The sum rates of each of the19 cells are plotted. Note that the proportional fairness weights are also updatedin each iteration. These weights ensure that the rates are allocated to all userswith fairness.

The simulation results clearly illustrate the value of coordinating base stationPSDs in an interference-limited multicell environment. The projected perfor-mance improvement is obtained by allowing base stations to exchange pricinginformation with each other, and by iteratively converging to a joint network-wide optimum.


0 20 40 60 80 100 120 140 1600

5

10

15

20

25

30

35

40

45

Iterations

Dow

nlin

k su

m r

ate

per

cell

(Mbp

s)

Figure 9.5. Convergence of downlink sum rates in each of the 19 cells usingmodified iterative water-filling with proportional fairness joint scheduling andpower allocation.

9.5 Cooperative relay network

Base station cooperation addresses the intercell interference problem for cell-edgeusers in a cellular network, but the cell-edge users’ performances are also funda-mentally affected by path-loss, which is distance-dependent, and shadowing. Aviable approach for dealing with path-loss is to deploy relay stations through-out the cell, so that a mobile user may connect to the base station via a relay,thereby reducing the effective path distance. This section addresses the networkoptimization problem for the cooperative relay network.

The resource allocation problem for the cooperative relay network hasattracted much attention in the wireless cellular communication literature(e.g., [23–26]). There are many different ways in which a relay may help the com-munication between a transmitter and receiver pair (also known as the sourceand the destination in the relay literature). In a decode-and-forward protocol,the relay decodes the message from the source then reencodes and transmits tothe destination. Alternatively, a relay may amplify and forward, or quantize itsobservation and forward it to the destination.

In general, decode-and-forward is a sensible strategy when the relay is locatedcloser to the source than to the destination, while amplify-and-forward andquantize-and-forward are more suitable when the relay is closer to the desti-nation. However, the question of which strategy is the most suitable is a com-plicated one, as it also depends on the power allocation at the source and atthe relay, as well as the end-user’s rate requirement or utility function. An

9.5 Cooperative relay network 251

optimization framework for choosing the best cooperation strategy has beendealt with for a single-relay link in [27], but the general optimization of relaystrategies for a cellular network is likely to be quite hard.

In the chapter we focus instead on a simplified model where only the decode-and-forward protocol is used. This is done for the following reasons. First, theprimary focus of this chapter is the use of relay for enhancing cellular cover-age at the cell edge, in which case a sensible relay location within the cell issomewhere close to the half-way point between the base station and the celledge. In this case, for both uplink and downlink transmissions, the lengths ofboth the source–relay and the relay–destination paths are about the same, mak-ing decode-and-forward a suitable strategy. Second, decode-and-forward offers adigital approach to relaying. It eliminates the noise enhancement problem inher-ent in amplifying, or quantizing the relay observation. Third, in this chapterwe consider the deployment of fixed infrastructure-based relay stations. Theserelay stations typically have the computational resources to perform decodingand reencoding.

Further, as the primary focus here is the use of relays to combat distance-dependent path-loss, in this chapter attention is restricted to a two-hop relaystrategy, where the direct path from the source to the destination is ignored (asit is typically very weak). In the first hop, the source transmits information to therelay. In the second hop, the relay decodes and retransmits the same informationto the destination.

Under these assumptions, the capacity of a single source–relay–destination linkis simply the minimum of the source–relay and the relay–destination link capaci-ties. The characterization of capacity becomes more involved if one considers thepossibility that a single relay deployed in a cellular network may help multiplemobiles at the same time. Further, each mobile has a choice of either connectingto the base station directly, or through relays. The mobile may even choose touse different relays for different frequency tones. These possibilities are coupledwith the allocation of power across the frequency tones.

In the rest of this section we use the network optimization framework intro-duced earlier and provide a solution based on the duality theory to solve thebandwidth, rate, and power allocation problem for OFDMA relay networks. Themethodology used here is the one proposed in [23] and [26].

9.5.1 Problem formulation

Consider a wireless cellular network in which each cell is equipped with M relaystations located somewhere between the base station and the cell edge and atangles 360/M degrees apart from each other. There are K mobiles in each cell.Each mobile may connect either directly to the base station or through one ofthe relays in each frequency tone, (but the mobile may possibly use differentrelays in different tones.) There are a total of M + 1 links emanating from eachmobile. These mobile-originated links, plus the M links connecting the relays


h(3,2)

h(1,1)

h(0,1)h(2,0)

h(0,3)h(0,2)

h(5,0)

h(5,2)

h(4,2)

Figure 9.6. A cooperative relay network in which the mobiles may connectdirectly to the base station or through the relays.

to the base station, give a total of K(M + 1) + M links in the entire cellularnetwork.

Label the base station as node 0, and the mobiles as nodes k = 1, . . . ,K. Labeleach link by a pair of indices as follows: the base-station–relay links are labeled(0,m), with m = 1, . . . ,M ; the mobile–base-station links are labeled (k, 0) andthe mobile–relay links are labelled (k,m) with k = 1, . . . ,K and m = 1, . . . , M .This labeling convention is illustrated in Figure 9.6.

We consider a setup in which each cell employs an OFDMA scheme. Further,it is assumed that in each frequency tone, at most one link may be active atany given time. This assumption allows the intracell interference to be avoidedcompletely, and simplifies the numerical solution considerably. For simplicity, wealso assume that scheduling and power allocation are done on a per-cell basis (i.e.,without base station cooperation). The problem formulation presented here canbe extended to a more general setting where spatial reuse is enabled within eachcell, or where intercell cooperation is enabled across the cells, but the resultingoptimization problem would become considerably more complex.

Consider now the uplink scenario. Define the scheduling function as a mappingfrom the frequency tone to the link index, i.e., fU (n) = (i, j). With the assump-tions stated above, the achievable rate for each link (i, j), denoted rU,(i,j ) , canbe expressed as

rU,(i,j ) =∑

n∈U( i , j )

log

(1 +

PnU,(i,j ) |hn

(i,j ) |2

Γσ2n

), (9.23)

where the summation is over all frequency tones assigned to that link, i.e.,U(i,j ) = n|(i, j) = fU (n), Pn

(i,j ) denotes the transmit power, |hn(i,j ) |2 denotes


the channel gain for the link (i, j) at tone n, and σ2n denotes the combined inter-

cell interference and noise.The achievable rate for each user, denoted Rk , is the sum of achievable rates

of all links emanating from the mobile, i.e.,

RU,k =M∑

j=0

rU,(k,j ) . (9.24)

At each relay, a flow conservation constraint must be satisfied so that all theincoming traffic can be forwarded to the base station. This results in M con-straints as follows:

K∑k=1

rU,(k,m ) ≤ rU,(0,m ) . (9.25)

The above equation is an example of the general flow conservation formulation[23, 26].

It is now straightforward to write down the uplink per-cell optimization prob-lem for the cooperative relay network, which consists of both the allocation ofpower and bandwidth for each link, and the routing of the information withineach cell. Under the network utility maximization framework, the optimizationproblem can be reduced to a weighted rate sum maximization problem acrossthe K users with weights wU,k = 1/RU,k :

maximizeK∑

k=1

wU,k

(M∑

m=0

rU,(k,m )

),

subject to :K∑

k=1

rU,(k,m ) ≤ rU,(0,m ) ∀m = 1, · · · ,M,

N∑n=1

pnU,(0,m ) ≤ Pmax

U,R,m ∀m,

M∑m=0

N∑n=1

pnU,(k,m ) ≤ Pmax

U,M ,k ∀k,

0 ≤ pnU,(k,m ) ≤ Smax

U,(k,m ) ∀k,m, ∀n,

pnU,(k,m )p

nU,(k ′,m ′) = 0, ∀(k,m) = (k′,m′) ∀n, (9.26)

where rU,(k,m ) is as expressed in (9.23), and the optimization is over powerallocations pn

U,(k,m ) , subject to the per-mobile total power constraint PmaxU,M ,k ,

the per-relay total power constraint PmaxU,R,m , as well as the peak PSD constraints

at both the mobiles and the relays SmaxU,(k,m ) . The last constraint ensures that no

two links share the same frequency tone within each cell. Note that the downlinkproblem can be formulated in a similar fashion.


9.5.2 Joint routing and power allocation

The network utility maximization problem for the cooperative relay network isessentially a joint routing and power allocation problem, as each mobile has theoption of either transmitting information bits directly to the base station orrouting through one or more of the relays.

One way to solve this problem is to dualize with respect to the flow conser-vation constraint (9.25) using dual variables µm , so that the objective functionbecomes a new weighted rate sum maximization problem over all link rates(rather than the end-user rates in (9.26)). The new objective function is

K∑k=1

wU,k

(M∑

m=0

rU,(k,m )

)−

M∑m=1

µm

(K∑

k=1

rU,(k,m ) − rU,(0,m )

)

=M∑

m=1

µm rU,(0,m ) +K∑

k=1

M∑m=0

(wU,k − µm )rU,(k,m ) , (9.27)

subject to the peak and total power constraints in (9.26). Let g(µ1 , · · · , µM )denote the maximum value of (9.27) subject to the power constraints for anyfixed set of µm . Because of the zero-duality-gap property of the OFDMA sys-tem, the solution of the original problem then reduces to the maximization ofg(µ1 , · · · , µM ) over all µm .

The dual variables, µm , enter the new objective function as weights to theweighted rate sum maximization problem over the link rates. Roughly speaking,a higher value for µm indicates congestion in the link between the base stationand the mth relay and that more rate should be allocated to that link to releasecongestion. A lower value of µm indicates the opposite.

The weighted link rate sum maximization problem subject to the power con-straints can itself be solved by yet another dual decomposition step with respectto the total power constraints, as treated earlier in this chapter. In this case, theoptimization problem is again decoupled on a tone-by-tone basis. Because of theassumption that only one link may be active in any given time slot and frequencytone, the weighted rate sum maximization then reduces to the selection of thebest link for each frequency tone, which involves a simple search.

Finally, the optimization of g(µ1 , · · · , µM ) over all µm can be handled byeither an outer loop using the ellipsoid or the subgradient method. The searchover the optimal set of µm balances the incoming and outgoing flows at eachrelay.

9.5.3 Performance evaluation

The optimization framework described above can be used to evaluate the effec-tiveness of deploying relay stations in a cellular network. To take into account thecost of relay deployment, the performance of a baseline system with a cell diam-eter of 1.4 km is compared with a relay network in which the cell area is doubled


Table 9.2. The achievable minimum and sum rates for a seven-cell network: thebaseline vs. relay scenarios (RS) with a varying number of relays per cell andrelay locations [26]

Scenario Baseline RS 1 RS 2 RS 3 RS 4

Relays per cell 0 3 4 5 3Relay distance n/a 2

3 r 23 r 2

3 r 13 r

Mobiles per cell 9 18 20 20 18Cell diameter (km) 1.4 1.98 1.98 1.98 1.98Cell area (km2) 1.54 3.08 3.08 3.08 3.08Mininum rate (Mbps) 0.193 0.583 0.972 0.705 0.578Sum rate (Mpbs) 96.4 75.4 80.2 72.7 87.2

(with diameter 1.98 km), but with three, four or five relays deployed within eachcell. The rationale is that if a relay station costs roughly 1

3 – 15 of a base station,

then the deployment cost of both systems would be approximately the same.In both cases, the achievable uplink transmission throughput is computed for aseven-cell system with users uniformly placed within the area. The user densi-ties in both cases are the same. When the relays are deployed, they are locatedbetween 1

3 r and 23 r from the base station, symmetrically in the angular direction.

Again, standard cellular channel models are used with both distance-dependentpath-loss and log-normal shadowing components. The simulation setting is aspresented in [26].

The simulation methodology presented in the previous section is for a weightedrate–sum maximization problem formulation. However, instead of maximizing aproportionally fair utility function, the numerical results in this section pertainto a maximization of the minimum rate over all users in the system (similar to[23]), which requires a slight modification of the optimization problem (9.26).First, the additional constraint that each user must have a rate larger thansome minimal rate Rmin , where Rmin is a constant added. Then, the resultingoptimization problem is solved with successively larger Rmin until the problembecomes infeasible. The largest such Rmin is the maximum minimal rate. Inpractice, the maximum Rmin can be found efficiently using a bisection.

For simplicity, the adaptive scheduling and power and rate allocation here areimplemented on a per-cell basis. For simulation purposes, the network through-put is computed using an iterative approach, in which the intercell interferenceis updated in each iteration, and the cellular network eventually reaches an equi-librium.

Table 9.2 shows the maximum minimal rates for the baseline network withoutrelays and for a number of relay scenarios. These results were first presentedin [26]. The most interesting feature here is that the addition of relays to theinfrastructure improves the minimal rate dramatically; however, it does not make


much difference at all in the sum rate. This illustrates that the benefit of relaysis concentrated on users at the cell-edge. As far as the sum rate is concerned,when the users are uniformly distributed throughout the cell, the sum rate isdominated by the rates of those users closest to the base station, which are nothelped by the relays.

9.6 Conclusion

In this chapter we have presented a network utility maximization framework forcooperative networks employing OFDMA. It has been shown that the objectiveof maximizing the sum of utilities of multiple users in a multicell network canbe efficiently carried out using a number of techniques, including proportionalfairness scheduling, dual optimization, the descent method for local optimiza-tion, and the network flow conservation principle. A central observation hereis that because the OFDM scheme partitions the frequency domain into manyparallel subchannels, the NUM problem often decomposes into a tone-by-toneoptimization problem, which is considerably easier to solve.

In this chapter we have focused on two types of cooperative networks and for-mulated the corresponding joint scheduling, power adaptive and rate allocationproblem in each case. For networks with base station cooperation, it has beenshown that adaptively adjusting power allocation across the base stations hasthe effect of reducing intercell interference, hence improving the throughput ofthe cell-edge users in the network. The cell-edge performance can also be reducedby deploying relays throughout the cells. The relays have the effect of enhancingthe coverage at the cell edge, which improves the minimal service rate withineach cell.

Base station cooperation and relay deployment are technologies with thepotential to significantly enhance the performance of the traditional wireless cel-lular network structure, especially at the cell edge. The benefits brought by thesecooperative techniques are particularly valuable to network service providers,because cell-edge users are the bottleneck in the current generation of wirelessnetworks.

References

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10 Cross-layer scheduling design forcooperative wireless two-wayrelay networks

Derrick Wing Kwan Ng and Robert Schober

10.1 Introduction

Background. The degrees of freedom introduced by multiple antennas at thetransmitters and receivers of wireless communication systems facilitate multi-plexing gains and diversity gains [1, 2]. A wireless point-to-point link with M

transmit and N receive antennas constitutes an M -by-N multiple-input multiple-output (MIMO) communication system. The ergodic capacity of an M -by-NMIMO fading channel increases almost linearly with minM,N provided thatthe fading meets certain mild conditions [2, 3]. Hence, it is not surprising thatMIMO has attracted a lot of research interest since it enables significant perfor-mance and throughput gains without requiring extra transmit power and band-width. However, limitations on the number of antennas that a wireless device isable to support as well as the significant signal processing power and complexityrequired in MIMO tranceivers limit the gains that can be achieved in practice.

To overcome the limitations of traditional MIMO, the concept of cooperativecommunication has been proposed for wireless networks such as fixed infras-tructure cellular networks and wireless ad-hoc networks [4, 5]. The basic idea ofcooperative communication is that the single-antenna terminals of a multiusersystem can share their antennas and create a virtual MIMO communication sys-tem. Thereby, three different types of cooperation may be distinguished, namely,user cooperation, base station (BS) cooperation, and relaying. Theoretically, usercooperation and BS cooperation are able to provide huge performance gains,when compared with noncooperative networks. However, the required informa-tion exchange between users and BSs may make these options less attractivein practice. In contrast, cooperative relaying with dedicated relays requires sig-nificantly less signaling overhead and allows for low-cost implementations whileachieving significant coverage extensions, diversity gains, and throughput gainscompared with noncooperative transmission. Therefore, cooperative relaying hasattracted significant interest from both academia and industry. In theory, relayscan transmit and receive signals at the same time and over the same frequen-cies; this is known as full-duplex relaying. However, building such relays requires


260 Cross-layer scheduling design for cooperative wireless relay networks

Figure 10.1. One-way half-duplex relaying system.

Figure 10.2. Two-way half-duplex relaying system.

precise and expensive components which is undesirable in practice. Alternatively,relays may operate in a one-way half-duplex mode as shown in Figure 10.1, i.e.,relays do not receive and transmit simultaneously at the same time and fre-quency. These relays are also referred to as cheap relays in the literature [6]. Themain disadvantage of one-way half-duplex relaying is a loss in throughput com-pared with full-duplex relaying. Fortunately, this throughput loss can be recov-ered by two-way half-duplex relaying [12–15]. Compared with traditional one-wayhalf-duplex relaying [16–18], two-way half-duplex relaying achieves higher powerand spectral efficiencies, by allowing simultaneous message exchanges between aBS and the users, see Figure 10.2. Both amplify-and-forward (AF) and decode-and-forward (DF) protocols can be used for two-way half-duplex relaying. TheAF protocol may be more appealing in practice because of its simple transceiverdesign.

Cross-layer design. Combining cross-layer design with cooperative relaying hasbecome an active research area [7–11]. Orthogonal frequency division multipleaccess (OFDMA) is a particularly attractive multiple access technique because of


its flexibility in resource allocation and its robustness against multipath fading.Cross-layer design can lead to significant improvements in the overall systemperformance by facilitating the exchange of useful information between differentlayers of the protocol stack. The effect of cross-layer design on quality of service(QoS) provisioning in multiuser systems is an interesting, yet challenging, topic.Intuitively, by allocating resources to users with better channel qualities, thescheduler can maximize the overall system throughput and exploit the so-calledmultiuser diversity (MUD) gain. However, it may degrade other QoS metricssuch as delay and fairness, since users are suspended from transmission whentheir channels are poor.

Next generation wireless communications systems are expected to provideresource-hungry services such as video streaming and real-time video conferenc-ing with certain QoS requirements. The combination of OFDMA/OFDM withtwo-way half-duplex relaying may be instrumental in meeting these requirements,particularly for users at the cell edge. In [32, 33], best-effort resource allocationfor two-way half-duplex relay-assisted OFDMA and OFDM systems for homo-geneous users is studied. In these works, perfect global channel state informa-tion (CSI) of each link is assumed to be available at the BS such that optimalresource allocation can be performed. However, in practice, users are heteroge-neous with different QoS requirements, such as the maximum tolerable outageprobability and minimum required data rate, which best-effort resource alloca-tion cannot guarantee. Besides, perfect CSI at the transmitter (CSIT) cannotbe achieved in practice for the relay-to-user links due to the mobility of theusers. When the CSIT is imperfect, there is a finite probability that the sched-uled data rate exceeds the instantaneous channel capacity despite the use ofstrong forward error correction (FEC) codes, causing the transmitted packet tobe corrupted which is known as channel outage. The conventional performancemeasure, ergodic capacity, fails to account for the penalty of channel outage.Furthermore, the asymmetric nature of fading in the BS-to-relay and relay-to-user links in relay networks has often been overlooked in the system modeling,e.g., [12–18, 32, 33]), which may lead to inaccurate results with regard to the per-formance gain achievable with relays in a practical system. In addition, thoughthe multiuser diversity capacity gain has been known to scale with the numberof users K in the order of O(log log K) [26, 34] in Rayleigh faded single-hop sys-tems with perfect CSIT, it is not clear how the system performance scales withthe number of users and relays in a two-way half-duplex relay-assisted OFDMAsystem with imperfect CSIT and asymmetric fading links. Furthermore, exist-ing works such as [32–36] focus on centralized resource allocation at the BS. Asthe numbers of users, relays, and subcarriers in the system increase, the over-head in collecting CSI for scheduling becomes significant and the computationalcomplexity increases exponentially at the BS which limits the scalability of thesystem in practice.Contributions. Motivated by the aforementioned prior works, we proposeand analyze in this chapter a novel cross-layer scheduling design for two-way


half-duplex relay-assisted OFDMA systems. In particular, we focus on the fol-lowing issues:

We consider cross-layer scheduling for an AF two-way half-duplex relay-assisted OFDMA system when both delay-sensitive users and non-delay-sensitive users are coexisting in the system. The considered problem is for-mulated as a mixed integer and nonconvex optimization problem which takesinto account imperfect CSIT and the heterogeneous data rate requirements ofusers. After a proper transformation of the original nonconvex problem into aconvex one, dual decomposition is used to derive a novel distributed iterativeresource allocation algorithm with closed-form solutions for the power, datarate, and subcarrier allocation. The proposed algorithm’s fast convergenceand robustness to quantization effects in the information exchanged betweenthe BS and the relays in each iteration make it attractive for implementation.

We investigate the asymptotic behavior of the system goodput of proportionalfair (PF) schedulers in a two-way half-duplex relay system with respect to thenumbers of non-delay-sensitive users and relays by using tools from extremevalue theory. Closed-form asymptotic order growth expressions are derivedwhich reveal that an extra gain from a large number of users and relays canbe achieved only under certain conditions. These expressions also allow us toquantify the penalties on the system performance caused by imperfect CSITand a line-of-sight (LoS) path.

We propose an efficient computational burden reduction scheme which isaimed at alleviating the computational load at each relay. The proposedscheme preserves the essential MUD gain for various scheduling policies, suchas maximum system goodput scheduling and PF scheduling. On the otherhand, the computational load can be explicitly controlled by adjusting a corre-sponding threshold. Simulation results demonstrate significant computationalsavings at the cost of a small performance degradation.

Organization. The rest of the chapter is organized as follows. In Section 10.2,we discuss some basic concepts in cross-layer scheduler design. In Section 10.3, weoutline the model for the considered two-way half-duplex relay-assisted OFDMAsystem, and in Section 10.4, we formulate the cross-layer design for this systemas an optimization problem. In Section 10.5, the problem considered is solved bydual decomposition, and in Section 10.6, we analyze the asymptotic order growthof the system goodput for large numbers of users and relays and introduce acomputational burden reduction scheme. Simulation results for the distributedalgorithm are provided in Section 10.7 and some conclusions are drawn in Section10.8.Notation. E[·] and (·)∗ denote statistical expectation and complex conjugation,respectively. A complex Gaussian random variable with mean µ and variance σ2

is denoted by CN(µ, σ2), and ∼ means “distributed as”. 1(·) denotes an indicatorfunction which is 1 when the event is true and 0 otherwise. O(g(x)) denotes anasymptotic upper bound. Specifically, f(x) = O(g(x)) if limx→∞|f(x)/g(x)| ≤W

10.2 Cross-layer scheduling design – some basic concepts 263

Figure 10.3. Traditional OSI reference model [19].

for W ∈ (0,∞). Moreover, Q(c, d) is the first-order Marcum Q-function, I0(·) isthe zeroth order modified Bessel function of the first kind, J0(·) is the zerothorder Bessel function of the first kind. u(·) is the unit step function and (x)+ =max0, x. Finally, all logarithms, unless further specified in the subscript, areassumed to have base e.

10.2 Cross-layer scheduling design – some basic concepts

Traditional communication systems can be viewed as a hierarchy of layers, whichis known as the open system interconnection (OSI) reference model (Figure 10.3).A layer is a collection of conceptually similar system functions which provideservices to other layers. For example, the duty of the physical (PHY) layer isto transmit a bit stream over a given physical channel with a target bit errorrate (BER), while the media access control (MAC) layer is charged with givingmultiple users access to the channel and error checking. The layering conceptemphasizes the isolation of the different layers which means that each layer isoptimized individually without considering the requirements of other layers. Inother words, a layer treats the other layers as black boxes when performing itsown duty. This isolated approach provides a higher flexibility for the deploymentof new protocols and simplifies debugging and standardization compared witha joint optimization of all layers. However, while the rigid separation of lay-ers is well suited for time-invariant wire-line communication channels, it is not


Figure 10.4. Timing diagram for cross-layer scheduling.

compatible with the requirements of next generation wireless communicationssystems.

Current and future wireless communication systems not only have to supportconcurrent transmission of real-time voice and video data, but also non-real-timeservices such as email and web surfing. In practice, these services require differentlevels and different types of QoS. For instance, real-time video conferencing isa delay-sensitive application but it is relatively robust with respect to decodingerrors. On the other hand, email is a delay nonsensitive application but doesnot tolerate even a single bit error. Unfortunately, the PHY layer as it is definedin the OSI model does not guarantee any QoS since it does not receive anyside information regarding QoS requirements from the upper layers. Therefore,cross-layer design/optimization is essential for a better utilization of the limitedsystem resources, while guaranteeing the required QoS for each application atthe same time.

We would like to point out that it is a common misconception that cross-layerdesign is aimed at removing the concept of layering and performing an overalloptimization of the communication system. Instead, the crux of cross-layer designis to enhance the system performance by allowing minimal information exchangebetween the layers.

10.2.1 Utility function-based cross-layer optimization

In each scheduling slot, the scheduler selects the users for the next transmissionframe and determines their power and rate allocation based on the informationavailable at the scheduler such as the CSI of all users and the length of theirqueues (Figure 10.4). Ideally, a cross-layer scheduler should exploit both the


information from the PHY layer and that from the layers above the MAC layer inorder to achieve the best possible performance. In the literature, utility-function-based cross-layer optimization [20, 21] is one of the widely used methods forsolving resource allocation problems. There are two main functionalities of theutility function U(·). First, it captures the essential scheduling criteria by usingthe available cross-layer information building a bridge between different layers.Second, it maps the users’ utilization of the system resources into a level ofsatisfaction providing a tangible performance metric. In the following, we brieflydiscuss two utility functions commonly used for cross-layer scheduling.

Maximum throughput scheduler. In most wireless applications, the aggre-gate data rate of users is the most important figure of merit for evaluation ofthe system performance from the service provider’s point of view. Considering asystem with K users, the corresponding utility function can be expressed as

UThp(R1 , . . . , RK ) =K∑

k=1

Rk = E[

K∑k=1

rk

], (10.1)

where Rk = E [rk ] is the average throughput of user k and rk is the instantaneousthroughput of user k in each time slot. Schedulers designed to maximize the aboveutility function achieve the highest average system capacity and are referred toas maximum throughput schedulers.

Proportional fair (PF) scheduler. Although the maximum throughputscheduler results in the optimal utilization of the system resources, it does nottake into account fairness in the scheduling process. Users with poor channel con-ditions may suffer from starvation since they are rarely selected for transmissionwhich is undesirable from the users’ point of view. Therefore, PF scheduling [1, 2]was proposed to resolve the fairness issue. PF schedulers are popular becausethey allow a balance to be struck between overall system capacity and fairnessamong users, and they have been implemented in third generation (3G) cellularsystems for delay-tolerant applications. The corresponding utility functions aregiven by

UPF,1(R1 , . . . , RK ) ≈K∑

k=1

log2(Rk ) (10.2)

and

UPF,2(R1 , . . . , RK ) ≈ E[

K∑k=1

rk

Rk

]. (10.3)

The utility functions in both (10.2) and (10.3) achieve proportional fairness. Rk

is the approximation of Rk . In order to implement PF schedulers, the system hasto keep track of the value of Rk . For the (n + 1)th scheduling slot, the average


data rate Rk [n + 1] of user k can be updated as follows:

Rk [n + 1] =

⎧⎪⎪⎨⎪⎪⎩(

1− 1tc

)Rk [n] +

1tc

rk [n] , k = k∗,(1− 1

tc

)Rk [n] , k = k∗,

(10.4)

where tc is the time constant for the averaging window and k∗ is the selecteduser at the (n + 1)th time slot.

10.2.2 Quality-of-service (QoS) measure

The increasing demand for high-data-rate wireless service networks imposes greatchallenges on cross-layer optimization since operators are required to satisfy thediverse QoS requirements of heterogeneous user populations. Different QoS mea-sures have to be incorporated in the cross-layer optimization in order to overcomethese challenges. While many different QoS measures have been considered inthe literature, we discuss here only the two most important ones.

Minimum data rate requirement. In practical systems, users are usuallyheterogeneous with different minimum data rate requirements imposed by themaximum delay constraints for the respective applications they are running.One way to handle these requirements, is to incorporate data rate constraintsin the formulation of the cross-layer optimization problem [22]. Intuitively, thescheduler will first try to serve the delay-sensitive users which have nonzero datarate constraints. Once these users are served, the remaining resources will beallocated to the non-delay-sensitive users. However, it is clear that this kind ofresource allocation results in a degradation of the overall system performancesince the scheduler loses degrees of freedom in the user selection.

Frame error rate (FER). Although at the PHY layer the BER is usuallyconsidered as a performance measure, at the MAC layer the FER is more rele-vant. In general, the FER is hard to calculate analytically and typically resultsin complicated expressions which are not useful for cross-layer scheduling design.However, in slow fading channels, if channel capacity achieving codes are usedfor error protection (such as, e.g., turbo codes or low-density parity-check codes(LDPCs)), the outage probability is a good approximation for the FER [23, 24].This connection between the outage probability and FER can be often exploitedto arrive at a simple resource allocation algorithm.

10.2.3 Multiuser diversity gain

In a multiuser wireless communication system, different users experience differentfading conditions. When the number of users in the system is large, there is ahigh probability that at least one user has a very good channel at any time. This


effect is known as multiuser diversity [25]. It can be exploited by schedulinga user for transmission only when his/her channel is in a favorable condition.Therefore, the average system throughput increases with the number of usersif only good users are selected for transmission in each scheduling slot. Thisperformance gain plays an important role in the cross-layer scheduling design. Inthe following, we present a simple example to illustrate the concept of multiuserdiversity in a system with scheduling and resource adaptation.

Example 10.1 We consider a wireless system with five users having infinite back-log in their buffers as illustrated in Figure 10.5. We assume that only one useris scheduled in each scheduling slot and the channel state of each user is eithergood or bad with equal probability. If the channel states of the users are per-fectly known at the transmitter and a capacity achieving code is applied forerror protection, then 6 bps/Hz and 1 bps/Hz can be successfully delivered1 toscheduled users having good and bad channels, respectively. We consider first asimple round-robin (RR) scheduling2 scheme where users take turns to accessthe channel periodically regardless of their actual channel states. Since all usershave the same channel access probability, the average system throughput ofthis scheduling scheme is 6× 1

2 + 1× 12 = 3.5 bps/Hz. On the other hand, by

taking advantage of CSIT, the scheduler can select a user whose channel isin the good state (provided there is such a user) which results in maximumthroughput scheduling. The average system throughput of the latter schedul-ing scheme is 1

25 × 1 + (1− 125 )× 6 = 5.84375 bps/Hz. Maximum throughput

scheduling tries to operate the system at the peak transmission rate based onCSIT knowledge and the resulting performance gain is the multiuser diversitygain.

In the following, we will quantify the multiuser diversity gain for maximumthroughput scheduling for a large number of users based on extreme value theory.

Asymptotic multiuser diversity gain. Extreme value theory is a branchof statistics which deals with the extreme value, such as the maximum or theminimum, of a set of random variables. It has been widely used for analyzingthe asymptotic performance of maximum throughput scheduling [26, 27]. In thefollowing, we introduce a fundamental theorem from extreme value theory.

Theorem 10.1 (Generalized extreme value distribution [28]) Let x1 , x2 , . . . , xZ ,

be a sequence of Z independent and identically distributed (i.i.d.) random

1 Spectral efficiencies of 6 bps/Hz and 1 bps/Hz correspond to 64-ary quadrature amplitudemodulation (64-QAM) and binary phase shift keying (BPSK), respectively.

2 RR is the simplest scheduling technique for scheduling users and is widely used in TDMAsystems such as GSM.


b

feedback

(6 bps/Hz)(1 bps/Hz)

Figure 10.5. An example for cross-layer scheduling with two channel states.

variables and let xmax denote the maximum among the Z random variables,i.e.,

xmax = max(x1 , x2 , . . . , xZ ). (10.5)

If there exist some constants aZ ∈ R, bZ > 0 and some nondegenerate distribu-tion G(x) such that the distribution of aZ (xmax − bZ ) converges to G(x), thenG(x) must be one of the following three standard extreme value distributions:Gumbel distribution, Frechet distribution, and Weibull distribution.

Next, in the following lemma, we introduce a sufficient condition on the dis-tribution of xi such that the limiting maximum distribution is a Gumbel distri-bution with cumulative distribution function (CDF)

G(x) = PrX ≤ x = exp(− exp(−x)), x ∈ R. (10.6)

Lemma 10.1 (Sufficient conditions for converging to Gumbel distribution [28])Let x1 , x2 , . . . , xK be a sequence of K positive i.i.d. random variables withprobability density function (PDF) f(·) and twice differentiable CDF F (·). Letxmax = maxx1 , x2 , . . . , xK denote the maximum among the K random vari-ables. If the reciprocal hazard function g(x) satisfies

limx→∞

g(x) = limx→∞

1− F (x)f(x)

= c, (10.7)


0 10 20 30 40 50 60 70 80 90 1000

1

2

3

4

5

6

Number of users

Ave

rage

sys

tem

thro

ughp

ut (

bps/

Hz)

Simulation at SNR = 10 dBAsymptotic trend at SNR = 10 dBSimulation at SNR = 5 dBAsymptotic trend at SNR = 5 dBSimulation at SNR = 0 dBAsymptotic trend at SNR = 0 dB

Figure 10.6. Average system throughput vs. number of users for a Rayleigh fadingchannel and different received SNRs.

where c is a constant, then xmax − lK converges to a Gumbel distribution wherelK is given by F (lK ) = 1− 1/K. This suggests that xmax grows like lK for K →∞.

Now, let us consider K Rayleigh distributed channel gain coefficients,h1 , h2 , . . . , hK , i.e., |h1 |2 , |h2 |2 , . . . , |hK |2 are exponentially distributed withunit mean. By evaluating the corresponding reciprocal hazard function, it canbe shown that (1− F (x))/f(x) = 1 and lK = log K. Therefore, by selecting themaximum channel gain among K users, the multiuser gain grows in the orderof log K. Figure 10.6 depicts the system goodput as a function of the numberof users K assuming that all users have i.i.d. Rayleigh fading channels. Bothsimulation results and analytical results obtained by exploiting the asymptoticgrowth of the maximum channel gain are shown. If the maximum throughputscheduler is used for scheduling, it can be observed from Figure 10.6 that themultiuser diversity provides a significant throughput gain as the number of usersincreases. However, as the number of users becomes large the growth rate of themultiuser diversity gain decreases since the average system throughput growswith the number of users in the order of log log(K).

Now, that we have established the basic idea behind cross-layer scheduling, wewill focus in the remainder of this chapter on a particular application, namelycross-layer scheduling for a two-way half-duplex AF relay-assisted OFDMA net-work.


1

2

Figure 10.7. Relay-assisted packet transmission system model with K = 9 users,A = 3 sectors, and M = 3 relays.

10.3 Network model for relay-assisted OFDMA system

In this section, we first establish the adopted system and channel models, andsubsequently discuss the CSI model assumed for cross-layer scheduling.

10.3.1 System model

We consider a single-antenna two-way half-duplex relay OFDMA network whichconsists of one BS, M relays, and K mobile users which belong to one of twocategories, namely, delay-sensitive users and non-delay-sensitive users. Withoutloss of generality, we assume that the first K1 users are delay-sensitive usersbelonging to set D = 1, 2, . . . ,K1 and the remaining K −K1 users are non-delay-sensitive users belonging to set N = K1 + 1,K1 + 2, . . . ,K. A single cellwith two ring-shaped boundary regions as shown in Figure 10.7 is studied. Thecell coverage is divided into A equal size sectors and each user is assigned to agroup of GRj > 0 relays such that M =

∑Aj=1 GRj . In this chapter, we focus

on the cross-layer scheduling design for relay-assisted users and we assume thatthe resource allocation for non-relay-assisted users (e.g., users close to the BS) isdone separately.3 In the model considered, there is no direct link between the BSand the users due to path-loss and heavy blockage. We adopt the frame structure

3 We note that a joint resource allocation for relay-assisted and non-relay-assisted users wouldentail a significantly higher computational complexity at the BS than separate resourceallocations.

10.3 Network model for relay-assisted OFDMA system 271

Figure 10.8. Frame structure and CSI correlation model.

of IEEE 802.16m [30] where a superframe is divided into F frames (Figure 10.8).The channel is assumed to be slowly time varying over a superframe but toremain constant within a frame. In each scheduling slot, at the beginning of eachsuperframe, scheduling and resource allocation are performed. In each frame, theinformation exchange between the BS and the users via the relays is accomplishedin two phases. In the first phase, the BS and the users transmit their signalsto the relay stations through a multiple access channel. Then, in the secondphase, the relay stations amplify the previously received signals and forwardthem to the corresponding users.

10.3.2 Channel model

We consider an OFDMA system with nF subcarriers. The channel impulseresponse is assumed to be time-invariant (slow fading) within a frame. In the firstphase of frame t ∈ 1, . . . , F, the received symbol in subcarrier i ∈ 1, . . . , nF at relay m ∈ 1, . . . , M for user k ∈ 1, . . . , K is given by

Y(t,k)Rm ,i =

√P

(t,k)BRm ,i l

(t)BRm

H(t)BRm ,iX

(t,k)i +

√P

(t,k)U Rm ,i l

(t,k)U Rm

H(t,k)U Rm ,iW

(t,k)i +ZRm ,i ,

(10.8)

where P(t,k)BRm ,i and X

(t,k)i are the transmit power and the transmit symbol for the

link between the BS and relay m in subcarrier i in the first phase of transmissionof frame t, respectively. l

(t)BRm

represents the path-loss between the BS and relay

m. Variables P(t,k)U Rm ,i , W

(t,k)i , and l

(t,k)U Rm

are defined in a similar manner as thecorresponding variables for the BS-to-relay links except that the signaling direc-tion is from the users to the relays. ZRm ,i is the additive white Gaussian noise(AWGN) in subcarrier i at relay m, and H

(t)BRm ,i and H

(t,k)U Rm ,i are, respectively

the small-scale fading coefficients between the BS and relay m and between relaym and user k in subcarrier i. In practice, different links in a relay network canexperience asymmetric fading conditions [37]. For instance, a strong LoS propa-gation channel is expected between the BS and the relays, since they are placed


Signals from the BS and users

Broadcasts to the BS and users

f

ttr

Phase 1 Phase 2

Figure 10.9. Subcarrier mapping in a two-way half-duplex relay OFDMA systemfor users 1, 2, and 3.

in relatively high positions in practice and the number of blockages between themis limited. Hence, H

(t)BRm ,i is modeled as Rician fading with Rician factor κ, i.e.,

H(t)BRm ,i ∼ CN(

√κ/(1 + κ), 1/(1 + κ)). On the other hand, we model H

(t,k)U Rm ,i as

Rayleigh-distributed, i.e., H(t,k)U Rm ,i ∼ CN(0, 1), since the users are generally sur-

rounded by a large number of scatterers. In order to optimize the system perfor-mance [33], the signals received at relay m from the BS and user k in subcarrieri are mapped to subcarrier p ∈ 1, . . . , nF in the second transmission phaseas shown in Figure 10.9. Furthermore, the signal in subcarrier p is forwarded

to the destination after being amplified by a gain factor√

G(t,k)Rm ,i,pP

(t,k)Rm ,p , where

P(t,k)Rm ,p is the transmit power of relay m in subcarrier p for user k and the BS, and

G(t,k)Rm ,i,p normalizes the input power of the relay. Since the channel is assumed

to be time-invariant for the two transmission phases, channel reciprocity is pre-served. Therefore, the signal received at user k in subcarrier p from relay m inframe t is given by

Y(t,k)Um ,p =

√G

(t,k)Rm ,i,pP

(t,k)Rm ,p l

(t,k)U Rm

H(t,k)U Rm ,p

×(√

P(t,k)BRm ,i l

(t)BRm

H(t)BRm ,iX

(t,k)i + I

(t,k)m,i + ZRm ,i

)+ Z(k)

p , (10.9)

where I(t,k)m,i =

√P

(t,k)U Rm ,i l

(t,k)U Rm

H(t,k)U Rm ,iW

(t,k)i represents the self-interference of

user k in subcarrier i and Z(k)p is the AWGN at user k in subcarrier p. For

simplicity and without loss of generality, we assume a normalized noise variance

10.3 Network model for relay-assisted OFDMA system 273

of N0 = 1 at all transceivers. By estimating the channel coefficients in each frameand exploiting the channel reciprocity, the self-interference is perfectly knownat user k and can be subtracted from Y

(t,k)Um ,p [12]. Therefore, the received signal

after self-interference cancellation can be written as

Y(t,k)Um ,p =

√G

(t,k)Rm ,i,pP

(t,k)Rm ,p l

(t,k)U Rm

H(t,k)U Rm ,p

×(√

P(t,k)BRm ,i l

(t)BRm

H(t)BRm ,iX

(t,k)i + ZRm ,i

)+ Z(k)

p . (10.10)

Similarly, the received signal at the BS in subcarrier p from user k is given by

Y(t,k)Bm ,p =

√G

(t,k)Rm ,i,pP

(t,k)Rm ,p l

(t)BRm

H(t)BRm ,p

×(√

P(t,k)U Rm ,i l

(t,k)U Rm

H(t,k)U Rm ,iW

(t,k)i + ZRm ,i

)+ Zp, (10.11)

where Zp is the AWGN at the BS in subcarrier p. Following [12], the gain ischosen as

|G(t,k)Rm ,i,p |−1 = 1 + P

(t,k)BRm ,i l

(t)BRm|H (t)

BRm ,i |2 + P(t,k)U Rm ,i l

(t,k)U Rm|H (t,k)

U Rm ,i |2 . (10.12)

10.3.3 Channel state information (CSI)

In the system considered, both the BS and the users exchange information withthe help of relays. As mentioned before, we assume the CSI of all links to be con-stant for the duration of one frame. Thus, the BS, the relays, and all (scheduled)users can accurately estimate the CSI of their links using training symbols ineach frame for relaying and signal detection purposes. For scheduling, we assumethat the relays perfectly know the path-losses of their respective BS-to-relay andrelay-to-user links due to accurate long-term measurements. Furthermore, toperform scheduling for the next superframe, the relays estimate the small-scalefading coefficients of their respective BS-to-relay and relay-to-user links based ontraining symbols sent by the BS and all users at the beginning of the schedulingslot (Figure 10.8). Since we assume that both the BS and the relays are static,the associated channel is time-invariant and is assumed to remain constant forthe duration of the entire superframe. In contrast, due to the mobility of theusers, the CSI of the relay-to-user links changes slowly and the CSIT of theselinks used for scheduling becomes outdated over the duration of a superframe.To capture this effect, we model the CSI of the relay-to-user links using Jake’smodel [38]. For simplicity, we assume that each scheduling slot has the length ofone frame. As illustrated in Figure 10.8, the correlation between the schedulingslot (frame 0) and frame t in subcarrier i of the link between relay m and userk is given by E[H(t,k)

U Rm ,i(H(0,k)U Rm ,i)

∗] = ρ(t× τ) with ρ(τ) = J0(2πfD τ), where τ

and fD are the time duration of one frame and the maximum Doppler frequency,respectively. Therefore, for scheduling purposes, the actual CSI, H

(t,k)U Rm ,i , in frame

t ∈ 1, . . . , F for the link between user k and relay m in subcarrier i can be


expressed as

H(t,k)U Rm ,i =

√1− σ2

e (t)H(t,k)U Rm ,i + ∆H

(t,k)U Rm ,i , (10.13)

where H(t,k)U Rm ,i = H

(0,k)U Rm ,i is the outdated CSI used for scheduling at the beginning

of the superframe. Here, ∆H(t,k)U Rm ,i ∼ CN(0, σ2

e (t)) represents the CSIT error with

variance σ2e (t) = 1− ρ2(t× τ) and E[H(0,k)

U Rm ,i∆H(t,k)U Rm ,i ] = 0.

10.4 Cross-layer design for two-way relay-assisted OFDMA systems

In this section, we introduce the system goodput as a performance measure forcross-layer scheduling and formulate the cross-layer optimization problem.

10.4.1 Instantaneous channel capacity and system goodput

Given perfect CSI at the receiver (CSIR), the downlink (DL) instantaneous chan-nel capacity between the BS and user k in using subcarrier pair (i, p) throughrelay m in frame t is given by the mutual information which can be expressed asC

(t,k)DLm ,i,p ≈ 1

2 log2

(1 + Γ(t,k)

DLm ,i,p

)with equivalent DL SNR

Γ(t,k)DLm ,i,p =

P(t,k)BRm ,i l

(t)BRm|H (t)

BRm ,i |2P(t,k)Rm ,p l

(t,k)U Rm|H (t,k)

U Rm ,p |2

P(t,k)BRm ,i l

(t)BRm|H (t)


(t,k)U Rm|H (t,k)

U Rm ,i |2 + P(t,k)Rm ,p l

(t,k)U Rm|H (t,k)

U Rm ,p |2,

(10.14)

where the approximation and the prelog factor 12 in the channel capacity equa-

tion are due to a high-SNR assumption and the two channel uses necessary fortransmitting one message, respectively. Similarly, the channel capacity for theend-to-end uplink (UL) from user k in using subcarrier pair (i, p) through relaym in frame t is given by C

(t,k)U Lm ,i,p ≈ 1

2 log2(1 + Γ(t,k)ULm ,i,p) with equivalent UL SNR

Γ(t,k)ULm ,i,p =

P(t,k)U Rm ,i l

(t,k)U Rm|H (t,k)

U Rm ,i |2P(t,k)Rm ,p l

(t)BRm|H (t)

BRm ,p |2

P(t,k)BRm ,i l

(t)BRm|H (t)


(t,k)U Rm|H (t,k)

U Rm ,i |2 + P(t,k)Rm ,p l

(t)BRm|H (t)

BRm ,p |2.

(10.15)

Now, we are ready to define the instantaneous goodput (bps/Hz successfullydelivered) of DL and UL transmission for user k who is assigned to relay m as

ρ(k)DLm

=1

FnF

F∑t=1

nF∑i=1

nF∑p=1

s(t,k)m,i,pr

(t,k)DLm , i , p

1(r(t,k)DLm ,i,p ≤ C

(t,k)DLm ,i,p),

(10.16)

ρ(k)U Lm

=1

FnF

F∑t=1

nF∑i=1

nF∑p=1

s(t,k)m,i,pr

(t,k)U Lm ,i,p 1(r(t,k)

U Lm ,i,p ≤ C(t,k)U Lm ,i,p),

10.4 Cross-layer design for two-way relay-assisted OFDMA systems 275

where FnF= F × nF , s

(t,k)m,i,p ∈ 0, 1 is the subcarrier pair allocation indicator,

and r(t,k)DLm , i , p

and r(t,k)U Lm , i , p

are the transmission data rates for DL and UL, respec-tively. The average weighted system goodput, which is defined as the total averagenumber of bps/Hz successfully decoded at the BS and the K users via the M

relays (averaged over multiple scheduling phases), is given by

Ugoodput(P,R,S) = E

[M∑

m=1

∑k∈Um

w(k)(ρ(k)DLm

+ ρ(k)U Lm

)

], (10.17)

where P, R, and S are the power, rate, and subcarrier allocation policies, respec-tively. Um is the set of users associated with relay m and w(k) is a positive con-stant that can be used to enforce certain notions of fairness such as proportionalfairness and max–min fairness [39].

10.4.2 Cross-layer design problem

In practice, a channel outage occurs in slow fading channels whenever the datarate exceeds the channel capacity. Furthermore, users are heterogeneous with dif-ferent data rate requirements. Therefore, a practical scheduler has to be able tofulfill the different data rate requirements of the users as well as their channel out-age probability requirements. This leads to the following optimization problem.

Problem (Cross-layer optimization problem) The optimal power allocation policy, P∗, rateallocation policy, R∗, and subcarrier allocation policy, S∗, are given by

(P∗,R∗,S∗) = arg maxP,R,S

Ugoodput(P,R,S),

subject to: C1: Pr[r

(t,k)DLm ,i,p > C

(t,k)DLm ,i,p |Ξm

]≤ ε, ∀k, t,m, i, p,

C2: Pr[r

(t,k)U Lm ,i,p > C

(t,k)U Lm ,i,p |Ξm

]≤ ε, ∀k, t,m, i, p,

C3:M∑

m=1

(ρ

(k)DLm

+ ρ(k)U Lm

)≥ R(k) , ∀k ∈ D ∩ Um ,

C4:M∑

m=1

∑k∈Um

F∑t=1

nF∑i=1

nF∑p=1

s(t,k)m,i,p(P

(t,k)U Rm ,i + P

(t,k)BRm ,i + P

(t,k)Rm ,p︸︷︷︸

P( t , k )m , i , p

) ≤ PT ,

C5:M∑

m=1

∑k∈Um

nF∑i=1

s(t,k)m,i,p = 1,∀p, t,

C6:M∑

m=1

∑k∈Um

nF∑p=1

s(t,k)m,i,p = 1, ∀i, t,

C7: s(t,k)m,i,p ∈ 0, 1, ∀m, i, p, k, t,

C8: P (t,k)BRm ,i , P

(t,k)U Rm ,i , P

(t,k)Rm ,p ≥ 0, ∀m, i, p, k, t. (10.18)


Here, Ξm = [HBRm, HU Rm

,Lm ] is the CSI matrix, where HU Rm, HBRm

, and Lm

are vectors which contain the estimated CSIT, H(k)U Rm ,j , for all links from relay

m to users k ∈ Um , the actual CSIT, HBRm ,i , for the link between the BS andrelay m, and the path-loss for all links involving relay m, respectively. D ∩ Um isthe intersection of sets Um and D, and P

(t,k)m,i,p = P

(t,k)U Rm ,i + P

(t,k)BRm ,i + P

(t,k)Rm ,p is the

power usage for one subcarrier pair. Furthermore, C1 (C2) represents the out-age probability requirement of the DL (UL) for user k in each frame and limitsthe maximum outage probability to ε. This constraint is used as a measure forthe QoS with respect to the FER which can be well approximated by the channeloutage probability if capacity achieving codes are applied [23, 24]. C3 enforcesthe minimum required data rate for delay-sensitive users which are chosen bythe application layer. C4 is the joint power constraint for the BS, relays, andusers with total maximum power PT . Although the BS, relays, and users havedifferent power supplies in practice, a joint power optimization provides insightinto the power usage of a whole communication link (both UL and DL) ratherthan the per-hop required power. Furthermore, the global CSI of the entire sys-tem is needed in all devices in order to derive the optimal power allocation ifseparate power constraints are used [32], which would limit the system’s scal-ability due to significant signalling overheads. Constraints C5, C6, and C7 areimposed to guarantee that each subcarrier pair is only used by one user in eachframe.

10.5 Cross-layer optimization solution

In this section, the problem considered is solved by dual decomposition and anovel distributed iterative scheduling algorithm is derived to reduce the compu-tational complexity at the BS.

10.5.1 Transformation of the optimization problem

The problem considered is a mixed combinatorial and nonconvex optimizationproblem. The combinatorial nature of the problem is due to the integer constraintfor subcarrier allocation while the nonconvexity is caused by the power allocationvariables in the objective function. In general, a brute force approach is needed toobtain the globally optimal solution. However, such a method does not provideany system design insights and has limited scalability. In order to obtain aninsightful iterative solution, we first assume that the ratio between the DL andUL transmitted power is fixed, i.e.,

P(t,k)BRm ,i = α

(t,k)m,i P

(t,k)(B+U )m ,i , P

(t,k)U Rm ,i = (1− α

(t,k)m,i )P (t,k)

(B+U )m ,i , (10.19)

P(t,k)(B+U )m ,i = P

(t,k)BRm ,i + P

(t,k)U Rm ,i ,

10.5 Cross-layer optimization solution 277

where 0 < α(t,k)m,i < 1 controls the transmit power ratio between UL and DL, and

P(t,k)(B+U )m ,i represents the power consumption on subcarrier i by the BS and user

k. We introduce the following useful lemma.

Lemma 10.2 (High-SNR power consumption) Assuming a high SNR, the opti-mal power allocation for the BS, relay m, and user k in using subcarrier pair(i, p) in frame t is given by

P(t,k)Rm ,p =

P(t,k)m,i,p

2, P

(t,k)(B+U )m ,i =

P(t,k)m,i,p

2,

(10.20)

P(t,k)U Rm ,i =

(1− α(t,k)m,i )P (t,k)

m,i,p

2, P

(t,k)BRm ,i =

α(t,k)m,i P

(t,k)m,i,p

2.

Proof. Please refer to the Appendix at the end of this chapter.

A key step in solving the optimization problem in (10.18) is to incorporatethe outage probability constraints in C1 and C2 into the objective function. Ingeneral, a very tedious expression will be obtained if we try to incorporate theinequality in C1 and C2 into the objective function and it is virtually impossibleto obtain a tractable resource allocation solution. To obtain first-order designinsight and a simple resource allocation algorithm, we restrict the problem suchthat the constraints in C1 and C2 are fulfilled with equality for the optimal solu-tion. Simulations (not shown here) suggest that C1 and C2 are always satisfiedwith equality for the low outage probabilities required in practical applications(e.g., ε ≤ 0.1). We are now ready to introduce the following lemma.

Lemma 10.3 (Equivalent data rate incorporating outage probability) For agiven outage probability ε in C2, the equivalent UL data rate in using subcarrierpair (i, p) is

C2⇒ r(t,k)U Lm ,i,p =

12

log2

(1 + Λ(t,k)

ULm ,i,p

), ∀i, p (10.21)

with equivalent UL receive SNR

Λ(t,k)ULm ,i,p =

P(t,k)m,i,p(1− α

(t,k)m,i )l(t,k)

U RmF−1(t,k)U Rm ,i (ε)l(t)BRm

|H (t)BRm ,p |2

2(α

(t,k)m,i l

(t)BRm|H (t)

BRm ,i |2 + (1− α(t,k)m,i )l(t,k)

U RmF−1(t,k)U Rm ,i (ε) + l

(t)BRm|H (t)

BRm ,p |2) ,

(10.22)

where F−1(t,k)U Rm ,i (ε) is the inverse CDF of a noncentral chi-square random variable

with two degrees of freedom and noncentrality parameter |H(t,k)U Rm ,j |2/σ2

e (t). Here,σ2

e (t) is the estimation error variance defined in (10.13).


On the other hand, for a given outage probability ε in C1, the equivalent DLdata rate in using subcarrier pair (i, p) is

C1⇒ r(t,k)DLm ,i,p = 1

2 log2

(1 + Λ(t,k)

DLm ,i,p

)(10.23)

with equivalent DL receive SNR Λ(t,k)DLm ,i,p at user k given by

Λ(t,k)DLm ,i,p =

⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩

P(t,k)m,i,pα

(t,k)m,i l

(t)BRm|H (t)

BRm ,i |2 l(t,k)U Rm

F−1(t,k)U Rm ,i (ε)

2(α

(t,k)m,i l

(t)BRm|H (t)

BRm ,i |2 + (2− α(t,k)m,i )l(t,k)

U RmF−1(t,k)U Rm ,i (ε)

) , if i = p,

P(t,k)m,i,pα

(t,k)m,i l

(t)BRm|H (t)

BRm ,i |2(F−1(t,k)U Rm ,i,p(ε))

2

2(α

(t,k)m,i l

(t)BRm|H (t)

BRm ,i |2 + (F−1(t,k)U Rm ,i,p(ε))2

) , if i = p,

(10.24)

where F−1(t,k)U Rm ,i,p(ε) is the inverse CDF of a random variable which is the ratio of

two independent nonidentical Rice distributed random variables (10.42).

Proof. Please refer to the appendix.

A new objective function which incorporates the outage of both UL and DLcan be obtained by substituting (10.21) and (10.23) into the original objectivefunction (10.17). The next step in solving the problem is to handle the combi-natorial constraint in C7. We adopt a time-sharing approach4 by relaxing s

(t,k)m,i,p

to be a real value between 0 and 1 instead of a Boolean, i.e., 0 ≤ s(t,k)m,i,p ≤ 1. Fur-

thermore, since the power constraint is instantaneous, average weighted systemgoodput maximization is equal to the instantaneous weighted goodput maxi-mization in each scheduling slot. Thus, the cross-layer scheduling optimizationproblem is transformed into the following convex optimization problem.

Problem (Transformed cross-layer optimization problem)

arg maxP,R,S

M∑m=1

∑k∈Um

F∑t=1

nF∑i=1

nF∑p=1

w(k)s(t,k)m,i,p

2FnF

C(t,k)m,i,p

subject to: C4:M∑

m=1

∑k∈Um

F∑t=1

nF∑i=1

nF∑p=1

P(t,k)(B+U )m ,i + P

(t,k)Rm ,p︸︷︷︸

P( t , k )m , i , p

≤ PT , C3, C5, C6,

C7: 0 ≤ s(t,k)m,i,p ≤ 1, ∀m, i, p, t, k,

C8: P(t,k)BRm ,i , P

(t,k)U Rm ,i , P

(t,k)Rm ,p ≥ 0, ∀m, i, p, t, k, (10.25)

where C(t,k)m,i,p = log2(1 + Λ(t,k)

DLm ,i,p/s(t,k)m,i,p) + log2(1 + Λ(t,k)

ULm ,i,p/s(t,k)m,i,p) is the data

rate incorporating the effects of outage and time sharing. P(t,k)(B+U )m ,i =

s(t,k)m,i,pP

(t,k)(B+U )m ,i , P

(t,k)Rm ,p = s

(t,k)m,i,pP

(t,k)Rm ,p , and P

(t,k)m,i,p = s

(t,k)m,i,pP

(t,k)m,i,p are auxiliary

4 In which the authors showed that this relaxation is asymptotically optimal w.r.t. the numberof subcarriers.

10.5 Cross-layer optimization solution 279

power variables, and P(t,k)m,i,p = P

(t,k)(B+U )m ,i + P

(t,k)Rm ,p is the total power usage of

subcarrier (i, p) in frame t for user k. Since the Hessian matrix of the objectivefunction in (10.25) is negative semidefinite, the problem is jointly concave w.r.t.the optimization variables, and the duality gap is equal to 0 under some mildconditions [40]. Thus, centralized numerical methods such as the interior-pointmethod can be used to solve the above problem. However, for centralized meth-ods, the overhead required for collecting the CSI of all links and the computa-tional complexity at the BS grows exponentially w.r.t. the number of subcarriersand users. Therefore, an optimal distributed iterative solution with reduced sig-naling overhead in the CSI collection and lower computational complexity willbe derived in the next section.

10.5.2 Dual problem formulation

In this subsection, the transformed cross-layer scheduling optimization problem isdecomposed into one master problem (solved at the BS) and several subproblems(solved at each relay) by using dual decomposition. For this purpose, we firstneed the Lagrangian function of the primal problem. Upon rearranging terms,the Lagrangian is given by

L(λ,β, δ,υ,P,R,S) =M∑

m=1

∑k∈Um

F∑t=1

nF∑i=1

nF∑p=1

s(t,k)m,i,p(w

(k) + δk )2FnF

C(t,k)m,i,p −

M∑m=1

∑k∈Um

R(k)δk

+F∑

t=1

nF∑i=1

(β(t)i + υ

(t)i )− λ

M∑m=1

∑k∈Um

F∑t=1

nF∑i=1

nF∑p=1

P(t,k)m,i,p + λPT −

M∑m=1

∑k∈Um

F∑t=1

nF∑i=1

nF∑p=1

(β(t)p + υ

(t)i )s(t,k)

m,i,p , (10.26)

where λ is the Lagrange multiplier corresponding to the joint power constraintand δ is a vector of Lagrange multipliers corresponding to the data rate con-straint with elements δk , k ∈ 1 . . . K, with δk = 0 for non-delay-sensitive users.Furthermore, Lagrange multiplier vectors β and υ are associated with the sub-carrier usage constraints and have elements β

(t)p , p ∈ 1, . . . , nF , and υ

(t)i ,

i ∈ 1, . . . , nF , t ∈ 1, . . . , F, respectively. Thus, the dual problem is

minλ,β,δ,υ≥0

maxP,R,S

L(λ,β, δ,υ,P,R,S). (10.27)

10.5.3 Distributed solution – subproblem for each relay station

By dual decomposition, relay station m can solve the following subproblem with-out any assistance from other relays.

maxP,R,S

Lm (λ,β, δ,υ,P,R,S),


where Lm (λ, β, δ, υ,P,R,S) =

∑k∈Um

F∑t=1

nF∑i=1

nF∑p=1

(s

(t,k)m,i,p(w

(k) + δk )2FnF

C(t,k)m,i,p− λP

(t,k)m,i,p − (β(t)

p + υ(t)i )s(t,k)

m,i,p

).

(10.28)

Using standard optimization techniques and the Karush–Kuhn–Tucker (KKT)condition, the optimal power allocation in high SNR for subcarrier pair (i, p) isgiven by

P∗(t,k)m,i,p = s

(t,k)m,i,pP

∗(t,k)m,i,p = s

(t,k)m,i,p

((w(k) + δk )

λ− 1

2Λ(t,k)ULm ,i,p

− 1

2Λ(t,k)DLm ,i,p

)+

,

(10.29)

where δk is equal to 0 for non-delay-sensitive users, i.e., δk = 0,∀k ∈ N . Powerallocation (10.29) can be interpreted as a multilevel water-filling scheme as thewater levels of different users can be different. Specifically, the water levels ofdelay-sensitive users, i.e., (w(k) + δk/λ), are generally higher than those of non-delay-sensitive users, in order to satisfy constraint C3 in (10.18). To obtain theoptimal subcarrier allocation, we take the derivative of the subproblem withrespect to s

(t,k)m,i,p and substitute the optimal power allocation (10.29) into the

derivative. The resulting subcarrier pair selection determined by relay station m

is given by

s∗(t,k)m,i,p =

⎧⎪⎨⎪⎩1, if C∗(t,k)m,i,p ≥

2(β(t)p + υ

(t)i )

w(k) + δk+

Λ(t,k)ULm ,i,p

1 + Λ(t,k)ULm ,i,p

+Λ(t,k)

DLm ,i,p

1 + Λ(t,k)DLm ,i,p

,

0, otherwise,

(10.30)

where C∗(t,k)m,i,p = C

(t,k)m,i,p |P ( t , k )

m , i , p = P∗( t , k )m , i , p

. The dual variables β(t)p and υ

(t)i can be inter-

preted as the shadow price associated with the usage of subcarrier pair (i, p) inframe t. Dual variable δk forces the scheduler to assign more subcarrier pairs todelay-sensitive users by lowering the price for satisfying the data rate require-ments. The Lagrange multipliers λ, β, δ, and υ are provided by the BS in eachiteration. Finally, by substituting (10.20) and (10.29) into the equivalent packetoutage constraints in (10.21) and (10.23), the optimal rate allocation r

∗(t,k)DLm ,i,p

and r∗(t,k)U Lm ,i,p can be calculated.

10.5.4 Solution of the master problem at the BS

To solve the master problem at the BS, each relay calculates the local resourceusages and passes this information, i.e., r

∗(t,k)DLm ,i,p , r

∗(t,k)U Lm ,i,p , s

∗(t,k)m,i,p , and P

∗(t,k)m,i,p , to

the BS. Since the dual function is differentiable, the gradient method can beused to solve the minimization in (10.27) at the BS. Thus, the solution is given

10.6 Asymptotic performance analysis 281

by

β(t)p (n + 1) =

[β(t)

p (n)− ξ1(n)

(1−

M∑m=1

∑k∈Um

nF∑i=1

s(t,k)m,i,p

)]+

, ∀p, t, (10.31)

υ(t)i (n + 1) =

[υ

(t)i (n)− ξ2(n)

(1−

M∑m=1

∑k∈Um

nF∑p=1

s(t,k)m,i,p

)]+

, ∀i, t, (10.32)

δk (n + 1) =[δk (n)− ξ3(n)

(∆R(k)1

(∆R(k) < 0

))]+,∀k ∈ D ∩ Um ,

(10.33)

λ(n + 1) =

[λ(n)− ξ4(n)

(PT −

M∑m=1

∑k∈Um

F∑t=1

nF∑i=1

nF∑p=1

P(t,k)m,i,p

)]+

, (10.34)

where ∆R(k) is the difference between the scheduled data rate and the targetdata rate for delay-sensitive user k, i.e., ∆R(k) =

∑Mm=1(ρ

(k)DLm

+ ρ(k)U Lm

−R(k)).Index n is the iteration index, ξ1(n), ξ2(n), ξ3(n), and ξ4(n) are positive stepsizes, and convergence to the optimal solution is guaranteed under some mildconditions on the step sizes [41]. The overall algorithm tries to select the bestuser who can maximize the outage incorporated data rate for both DL and ULwhile any selected subcarrier pair is eventually occupied by one user only. Insummary, in each iteration, the BS broadcasts the Lagrange multipliers, whichindicate the price of global resource usage for all relays. Then each relay solvesthe subproblem based on its local CSI and passes the solution back to the BS.Finally, the BS updates the Lagrange multipliers according to (10.31)–(10.34)and broadcasts them to all relays in the next iteration. This process is repeateduntil convergence or the maximum number of iterations are reached.

10.6 Asymptotic performance analysis and computationalcomplexity reduction scheme

In this section, we analyze the asymptotic order growth of the average systemgoodput with respect to the numbers of non-delay-sensitive users KN = K −K1 and relays M . In addition, an efficient computational complexity reductionscheme is proposed for the relays in order to achieve the simplicity required fora practical implementation.

10.6.1 Asymptotic analysis of system goodput

The schedulers sacrifice system performance in order to fulfill the data raterequirements of the delay-sensitive users, since system resources are allocatedto them regardless of their actual channel conditions. In contrast, non-delay-sensitive users allow a more flexible resource allocation which benefits the overall


system performance. Therefore, in this section, we analyze the asymptotic ordergrowth of the average weighted system goodput w.r.t. the numbers of non-delay-sensitive users KN = K −K1 and relays M . In order to obtain a tractable result,we assume that the distances between the BS and each relay are identical andthat relays do not perform subcarrier mapping, and we focus on the study of PFschedulers with long-term fairness consideration. PF scheduling provides a goodcompromise between maximizing system capacity and achieving fairness amongusers and has been implemented in practical systems such as the high-speeddownlink packet access (HSDPA). For long-term fairness, the path-loss of theusers is disregarded by the PF scheduler and the user selection is based only onthe instantaneous i.i.d. small-scale fading channel gain [29]. In other words, thenear–far effect is omitted and each user is served at its own peak channel gain,and therefore each user has the same channel access probability.

The analysis is divided into two cases. In case I a large number of non-delay-sensitive users KN and a growing number of relays M such that their ratiocan be written as limKN ,M→∞KN /M →∞ are considered. In case II a largenumber of relays M and a growing number of non-delay-sensitive users KN withratio limKN ,M→∞M/KN →∞ are studied. The results are summarized in thefollowing theorem.

Theorem 10.2 (Asymptotic system goodput for PF scheduler in high SNR5)

Case I: Ugoodput(P,R,S) = O

(log2

(log M

κ + 1

)). (10.35)

Case II: Ugoodput(P,R,S)

= O(log2

((1− σ2

e (F × τ)) log KN

))for 0 ≤ σ2

e (·) < 1.

(10.36)

Proof. Please refer to the Appendix.

Theorem 10.2 illustrates that the asymptotic growth of the average sys-tem goodput is indeed the asymptotic growth of the cut-set bound of a two-way relay channel [14] in both cases. If KN and M do not satisfy eitherlimKN ,M→∞M/KN →∞ or limKN ,M→∞KN /M →∞, the gain achieved by eitherlarge KN or large M will be quickly saturated due to noise amplification in theAF relays. On the other hand, both Case I and Case II demonstrate the benefitsof using two-way half-duplex relays which are able to recover the spectral effi-ciency loss of 1

2 asymptotically when compared with one-way half-duplex relays.Moreover, the terms κ + 1 and 1− σ2

e (F × τ) act as penalties on the systemperformance introduced by the LoS path and the imperfect CSIT, respectively.Thus, we need an exponentially larger number of non-delay-sensitive users KN

5 For a better illustration of the effect of imperfect CSIT and LoS path on the system perfor-mance, we preserve some terms which do not grow with either KN or M .

10.7 Results and discussions 283

and relays M to compensate the penalties on the system performance causedrespectively by an LoS path and imperfect CSIT.

10.6.2 Scheme for reducing computational burden at each relay

In this section, a novel computational burden reduction scheme is introduced toreduce the computational load of the relays. In general, the distributed resourceallocation and scheduling algorithm alleviates the computational burden at theBS by distributing computation to the relays. However, the relays may not beable to handle the additional computational complexity when the number ofusers is large, since relays have usually limited computational power. Therefore,a computational burden reduction scheme for the relays is needed. Our proposedscheme offers two advantages. First, it preserves the desirable properties of thescheduler under various scheduling policies. In other words, the essential gainachieved by MUD is preserved as will be demonstrated in the simulation section.Second, the total computational load can be conveniently controlled by adjustinga corresponding threshold.

We assume that subcarrier mapping is not performed such that the combi-nation of subcarrier pairs in the view of each relay increases linearly w.r.t. nF

instead of n2F . As can be observed from (10.30), the subcarrier selection crite-

rion at the relays is based on the data rate incorporating outage and the globalresource usage which is reflected in the shadow price, i.e., β

(t)p and υ

(t)i . For a rea-

sonably large number of users K, due to MUD, the probability that a user witha small value of C

∗(t,k)m,i,p is assigned any subcarrier pairs is low. Hence, computing

and allocating any resources to them is wasteful and should be avoided. In theproposed computational burden reduction scheme, the scheduler only considerssubcarrier i of user k for scheduling when the following condition is fulfilled:

l(t,k)U Rm

F−1(t,k)U Rm ,i (ε) ≥

(2

4 Θ th(w k + δ k ) ( 1−ε ) +4

)4nF

PT, (10.37)

where Θth is a threshold. Since only some users are considered for scheduling, thecomputational burden for the calculation of the resource allocation is reduced.Threshold Θth allows us to trade performance for complexity. The larger Θth ,the fewer the subcarriers that are considered, which leads to a lower complexitybut may cause some degradation in performance. For the derivation of (10.37),please refer to the Appendix.

10.7 Results and discussions

In this section, we evaluate the system performance using simulations. A singlecell with two ring-shaped boundary regions is considered. The outer boundaryand the inner boundary have radii of 1 km and 500 m, respectively. The M

relay stations are equally distributed in the area between the inner and the


outer boundaries, which is divided into A sectors of equal sizes. Each user isserved by GRj = M/A, 1 ≤ j ≤ A, relays. In a superframe, there are N = 5frames and each frame has a length of 2 ms. The number of subcarriers is nF =128 with carrier center frequency 2.5 GHz and the 3GPP path-loss model isadopted [42]. α

(t,k)m,i = 2/3 such that the transmit power of the BS is twice that

of the mobile users. The small-scale fading coefficients of the BS-to-relay links aremodeled as i.i.d. Rician random variables with Rician factor κ = 6 dB, while thesmall-scale fading coefficients of the relay-to-user links are i.i.d. Rayleigh randomvariables. The target packet outage probability is set to ε = 0.01 for illustration.The quantizer used to quantize the information exchanged between the relaysand the BS in each iteration of the distributed resource allocation algorithm isdesigned offline using the Lloyd–Max algorithm. We study the performance of themaximum system goodput and PF schedulers. Maximum goodput scheduling canbe obtained by using weights wk = 1, ∀k, while PF scheduling is performed byadapting the weights of each user according to [29]. The average weighted systemgoodput is obtained by counting the number of packets successfully decoded byall users averaged over both the macroscopic and microscopic fading.

10.7.1 Convergence of the distributed resource allocation algorithm

Figures 10.10, 10.11, and 10.12 illustrate the evolution of the Lagrange multi-pliers λ, β

(1)1 , and δ1 for the distributed maximum goodput and PF schedul-

ing algorithms over time for different maximum transmit powers Pt . There areK = 15 users, A = 3 sectors, and M = 3 relays and the packet outage probabilitywas chosen to be ε = 0.01. Each user has mobility 5 km/h and there are threedelay-sensitive users with data rate requirement R(k) = 1 bps/Hz. The resultsare averaged over 1000 independent adaptation processes.

As can be observed from Figures 10.10–10.12, the proposed distributed algo-rithm converges fast and typically achieves 90–95% of the optimal value withinten iterations even if the value of the dual variables which are exchanged betweenthe BS and relays are quantized to 3 bits.

10.7.2 Average system goodput vs. transmit power and user mobility

Figure 10.13 illustrates the average weighted system goodput vs. the transmitpower for M = 3 relays and A = 3 sectors. In the cell, there are K = 15 users withmobilities of 5 km/h. Three users are delay-sensitive with data rate requirementR(k) = 1 bps/Hz, ∀k ∈ D, while the remaining users are non-delay-sensitive. Westudy the performance of maximum system goodput and PF scheduling with theproposed distributed algorithms. For comparison, we also simulate the central-ized schedulers associated with the scheduling algorithms considered. The cen-tralized scheduler is implemented at the BS which is assumed to have the globalCSI of the entire network and resource allocation is performed by using a bruteforce search. It can be observed that the performance of the proposed distributed


PT=38 dBm,

PT=38 dBm,

PT=38 dBm,

PT=35 dBm,

PT=35 dBm,

PT=35 dBm,

PT=35 dBm,

PT=38 dBm,

PT=38 dBm,

PT=35 dBm,

PT=35 dBm,

PT=35 dBm,

Figure 10.10. Dual variable λ vs. the number of iterations with K = 15 users,A = 3 sectors, M = 3 relays, and packet outage probability ε = 0.01. Each userhas mobility 5 km/h and there are three delay-sensitive users with data raterequirement R(k) = 1 bps/Hz.

Figure 10.11. Dual variable β(1)1 vs. the number of iterations with K = 15 users,

A = 3 sectors, M = 3 relays, and packet outage probability ε = 0.01. Each userhas mobility 5 km/h and there are three delay-sensitive users with data raterequirement R(k) = 1 bps/Hz.


Figure 10.12. Dual variable δ1 vs. the number of iterations with K = 15 users,A = 3 sectors, M = 3 relays, and packet outage probability ε = 0.01. Each userhas mobility 5 km/h and there are three delay-sensitive users with data raterequirement R(k) = 1 bps/Hz.

algorithm closely approaches the optimal centralized scheduling algorithm forboth maximum goodput and PF scheduling after only ten iterations, which con-firms the practicality of the distributed algorithm. On the other hand, although abetter performance can be achieved when subcarrier mapping is implemented atthe relays, it provides less than 1 dB gain in terms of system goodput at the costof a higher implementation complexity. Therefore, subcarrier mapping should beavoided if the system is operating in high SNR and the computational complexityis a concern. We also study the impact of the proposed computational burdenreduction scheme and quantization of the information exchanged between theBS and the relays in each iteration of the distributed algorithm on the systemperformance. In particular, three bits are used for quantization and the thresholdΘth , defined in Section 10.6.1, is chosen such that the relays only need to process20% of the CSI coefficients. It can be observed that the quantization and thecomputational burden reduction scheme cause only a small loss in performancewhile significantly reducing the required signaling overhead and computationalcomplexity. It is not surprising that the maximum goodput scheduler has a bet-ter performance than the PF scheduler in terms of the average weighted systemgoodput. Nevertheless, the maximum goodput scheduler results in a extremelyunfair resource allocation, since only users with good channel conditions (userswho are located near the relays) are selected for transmission. In contrast, thePF scheduler maintains fairness among users by sacrificing performance.

Figure 10.13 also shows the performance of a baseline one-way half-duplexrelay [16] in which subcarrier mapping is performed and a brute force approach


(bps

/Hz)

PT

Figure 10.13. Average weighted system goodput vs. the total transmit power fordifferent scheduling algorithms with K = 15 users, A = 3 sectors, M = 3 relays,and packet outage probability ε = 0.01. Each user has a mobility of 5 km/h andthere are three delay-sensitive users with data rate requirement R(k) = 1 bps/Hz.

is used for resource allocation. The proposed scheduler achieves a substantialgain in average weighted system goodput when compared with the baselinescheme, especially in the high transmit power regime. This is because the pro-posed scheduler acquires a better spectral efficiency by utilizing simultaneousmessage exchanges between the BS and users, while the one-way half-duplexrelay uses two phases to transmit only one message.


Figure 10.14. Average weighted system goodput vs. the user mobility. A = 3sectors, M = 3 relays, packet outage probability ε = 0.01, and K = 15 users.There are three delay-sensitive users in the system. Each curve corresponds todifferent transmit power levels and different data rate requirements for the delay-sensitive users.

Figure 10.14 illustrates the average system goodput vs. the user mobilitiesfor K = 15 users where three users are delay-sensitive with different data raterequirements. It can be observed that as the speed of the users increases, thesystem performance decreases since the corresponding CSI at the proposed sched-ulers becomes more outdated, and the schedulers have to be conservative in the


resource allocation in order to satisfy the outage probability requirements ofeach user. In addition, the PF scheduler is more sensitive to the CSIT qualitydegradation due to the mobility of the users when compared with the maximumgoodput scheduler, since the PF scheduler only considers the small-scale fading inthe long run while the maximum goodput scheduler considers both the path-lossand small-scaling fading. It can be observed that the average weighted systemgoodput diminishes as the data rate requirements become more stringent, sincemost of the resources are consumed by the delay-sensitive users regardless of theiractual channel quality. In other words, the degrees of freedom in the resourceallocation decrease when the delay-sensitive users become more resource hun-gry, and hence the performance gain achieved by multiuser diversity diminishes.In contrast, the non-delay-sensitive users cannot be served even if they havevery good channel conditions, because the scheduler needs to fulfill the data raterequirements of the delay-sensitive users.

10.7.3 Asymptotic system goodput performance of PF scheduling

In this section, we focus on the asymptotic performance of PF scheduling withrespect to the numbers of users K and relays M for A = 3 sectors. All usersin the system have a mobility of 5 km/h. There are three delay-sensitive userswith data rate requirement R(k) = 1 bps/Hz, ∀k ∈ D, and KN = K − 3 non-delay-sensitive users. The number of iterations for the distributed scheduler isset to 20 and subcarrier mapping is not performed. Figure 10.15 illustrates theaverage system goodput vs. the number of relays for K = 300 users and differenttransmit powers. As expected, the average system goodput grows with orderO (log2 (log M/(κ + 1))) which matches the predicted asymptotic trend closely.Although the asymptotic expressions in Theorem 10.2 are derived for non-delay-sensitive users, they can be used to approximate the system performance in theconsidered case as well. This is because the performance can again be mainlyattributed to the non-delay-sensitive users since they provide more degrees offreedom for the resource allocation.

Figure 10.16 illustrates the average system goodput as a function of the numberof users K for M = 300 relays for different total transmit powers and each userhas a mobility of 5 km/h. As can be observed, the average system goodputfollows the order growth of O

(log2

((1− σ2

e (F × τ)) log KN

))closely. This result

suggests that in order to fully exploit the MUD gain in the considered system,the number of relay stations should grow faster than the number of users tocompensate for the noise amplification in the AF process at the relay, whichcorresponds to an impractical scenario.

We also study in Figures 10.15 and 10.16 the impact of the proposed compu-tational burden reduction scheme and quantization on the system performance.It can be observed that both techniques do not change the asymptotic trend ofthe system performance which confirms that the proposed computational burden


PT =38 dBm

(bps

/Hz)

PT =35 dBm

PT =32 dBm

PT

PT

PT

PT

PT

PT

M

t

t

t

t

t

t

Figure 10.15. Average weighted system goodput of PF scheduler vs. the numberof relays M with K = 300 users. Tthree users are delay-sensitive with data raterequirements R(k) = 1 bps/Hz, ∀k ∈ D. The cell is divided into A = 3 sectors,each user has mobility of 5 km/h, and the packet outage probability requirementis ε = 0.01.

reduction scheme is able to preserve the essential multiuser diversity gain evenif the scheduler takes into account only 20% of the users for resource allocation.

10.8 Conclusion

We have explored some basic ideas in cross-layer scheduling design and technicalchallenges arising in practical implementations of cross-layer scheduling. In par-ticular, we have studied the cross-layer scheduling design for two-way half-duplexAF relay-assisted OFDMA systems. The problem considered has been formulatedas a mixed combinatorial and nonconvex optimization problem, in which imper-fect CSIT and heterogeneous user QoS requirements have been taken into con-sideration. After a proper transformation, dual decomposition has been used toderive an optimal, iterative, and distributed resource allocation solution, whichrequires only local CSI at each relay. Furthermore, an efficient computationalburden reduction scheme has been proposed, which reduces the computational

10.8 Conclusion 291

PT =38 dBm

PT =35 dBm

PT =32 dBm

PT

PT

PT

PT

PT

PT

Figure 10.16. Average weighted system goodput of PF scheduler vs. the numberof users K with M = 300 relays. There are three delay-sensitive users with datarate requirements R(k) = 1 bps/Hz, ∀k ∈ D. The cell is divided into A = 3 sec-tors, each user has mobility of 5 km/h and packet outage probability requirementε = 0.01.

complexity at the relays significantly, while preserving the essential gain obtainedfrom multiuser diversity. In addition, the asymptotic order growth of the averagesystem goodput in terms of the number of users and relays has been derived toobtain useful system design insights. Our simulation results have demonstratedthe excellent performance of the proposed schedulers which approach the optimalcentralized solution within a small number of iterations.

Appendix

Proof of Lemma 10.2

For convenience of notation, we define |H1 |2 , |H2 |2 , |H3 |2 , and |H4 |2 to representl(t)BRm|H (t)

BRm ,p |2 , l(t)BRm|H (t)

BRm ,i |2 , l(t,k)U Rm|H (t,k)

U Rm ,p |2 , and l(t,k)U Rm|H (t,k)

U Rm ,i |2 , respec-tively. Without loss of generality, we assume that |H1 |2 ≥ |H2 |2 ≥ |H3 |2 ≥ |H4 |2 .Furthermore, for high SNR, log2(1 + Γ(t,k)

DLm ,i,p) and log2(1 + Γ(t,k)ULm ,i,p) can be

approximated as log2(Γ(t,k)DLm ,i,p) and log2(Γ

(t,k)ULm ,i,p), respectively. By applying

(10.20) in (10.14) and (10.15), upon rearranging terms, the channel capacitybecomes

C(t,k)DLm ,i,p + C

(t,k)U Lm ,i,p ≈

12

log2(α

(t,k)m,i − α

2(t,k)m,i ) + 2 log2(P

(t,k)Rm ,pP

(t,k)(B+U )m ,i) + log2(|H1 |2 |H2 |2 |H3 |2 |H4 |2)

− log2

(α

(t,k)m,i P

(t,k)(B+U )m ,i |H2 |2 + (1− α

(t,k)m,i )P (t,k)

(B+U )m ,i |H4 |2 + P(t,k)Rm ,p |H3 |2

)− log2

(α

(t,k)m,i P

(t,k)(B+U )m ,i |H2 |2 + (1− α

(t,k)m,i )P (t,k)

(B+U )m ,i |H4 |2 + P(t,k)Rm ,p |H1 |2

)≥log2

⎛⎝ P(t,k)Rm ,pP

(t,k)(B+U )m ,i

P(t,k)Rm ,p + P

(t,k)(B+U )m ,i

⎞⎠+log2((α

(t,k)m,i − α

2(t,k)m,i )|H1 |2 |H2 |2 |H3 |2 |H4 |2)

2

− log2(|H1 |2). (10.38)

It is interesting to note that on the right hand side of (10.38),log2

(P

(t,k)Rm ,pP

(t,k)(B+U )m ,i/(P (t,k)

Rm ,p + P(t,k)(B+U )m ,i)

)is the only term related to the

power allocation variables and it is jointly concave w.r.t. P(t,k)Rm ,p and P

(t,k)(B+U )m ,i .

Therefore, for a given power P(t,k)m,i,p = P

(t,k)Rm ,p + P

(t,k)(B+U )m ,i and using standard

optimization techniques, the optimal values of P(t,k)Rm ,p and P

(t,k)(B+U )m ,i can be shown

to be identical and are given by P(t,k)m,i,p/2. On the other hand, using an approach

similar to that above, we can show that the obtained power allocation also max-imizes the cut set bound [14], i.e., log2(P

(t,k)Rm ,pP

(t,k)(B+U )m ,i), which is a capacity

upper bound for the relay channel.

Appendix 293

Proof of Lemma 10.3

We assume that the subcarrier pair (i, p) is used for transmission in the first andsecond time slots through relay m for user k. Then, the outage probability in C2for the UL data rate r

(t,k)U Lm ,i,p is given by

Pr

⎡⎣r(t,k)U Lm ,i,p >

12

log2

(1 + Λ(t,k)

ULm ,i,p

)|Ξm

⎤⎦= Pr

[|H(t,k)

U Rm ,i |2 ≤z(l(t)BRm

|H (t)BRm ,i |2 + l

(t)BRm|H (t)

BRm ,p |2)(l(t)BRm

|H (t)BRm ,p |2 − z)l(t,k)

U Rm

|Ξm

]

= F(t,k)U Rm ,i

(z(l(t)BRm

|H (t)BRm ,i |2 + l

(t)BRm|H (t)

BRm ,p |2)(l(t)BRm

|H (t)BRm ,p |2 − z)l(t,k)

U Rm

)(10.39)

where z = 2(22r(k )m , i , j − 1)/P

(t,k)m,i,p , and F

(t,k)U Rm ,i(·) denotes the CDF of a noncen-

tral chi-square random variable with two degrees of freedom and noncentralityparameter |H(t,k)

U Rm ,i |2/σ2e (t). Note that P

(t,k)Rm ,p l

(t)BRm|H (t)

BRm ,p |2 > z since r(k)m,i,j will

not exceed the channel capacity of the BS-to-relay links as the correspondingperfect CSI is available at the scheduler. Using the above result, the target out-age probability in constraint C2 in (10.18) is equivalent to

C2 ⇒ F(t,k)U Rm ,i

(z(l(t)BRm

|H (t)BRm ,i |2 + l

(t)BRm|H (t)

BRm ,p |2)(l(t)BRm

|H (t)BRm ,p |2 − z)l(t,k)

U Rm

)= ε (10.40)

⇒z(l(t)BRm

|H (t)BRm ,i |2 + l

(t)BRm|H (t)

BRm ,p |2)(l(t)BRm

|H (t)BRm ,p |2 − z)l(t,k)

U Rm

= F−1(t,k)U Rm ,i (ε)

⇒ r(t,k)U Lm ,i,p = log2

(1 + Λ(t,k)

ULm ,i,p

),

where F−1(t,k)U Rm ,i (·) represents the inverse function6 of F

(t,k)U Rm ,i(·). On the other

hand, in order to obtain the DL data rate r(t,k)DLm ,i,p which incorporates outage,

we need first to derive the PDF of the outage event. For the case of i = p,since there is only one random variable in the view of the scheduler, we canuse the same approach as for the UL to find the outage incorporated data rate.For the case of i = p, we first define random variables X

(t,k)m,p = |H (t,k)

U Rm ,p |2 and

Y(t,k)m,i = |H (t,k)

U Rm ,i |2 , which are noncentral chi-square distributed with two degrees

of freedom, noncentrality parameters s2x = |H (t,k)

U Rm ,p |2 and s2y = |H (t,k)

U Rm ,i |2 , andvariances σ2

x and σ2y , respectively. Conditional on the power allocation variables,

the CSI of the BS-to-relay link and the imperfect CSI of the relay-to-user link,upon rearranging terms, the outage probability of the DL transmission is given

6 The inverse of the noncentral chi-square CDF is commonly implemented as an inbuilt functionin software such as MATLAB.


by

Pr

⎛⎝√√√√

(t,k)m,i l

(t,k)U Rm

X(t,k)m,p

(t,k)m,i + θ

(t,k)m,i Y

(t,k)m,i

<

√√√√ (t,k)m,i η

(t,k)m,i,p

(t,k)m,i − η

(t,k)m,i,p

⎞⎠= Pr

⎛⎝A(t,k)m,i,p

B(t,k)m,i,p

<

√√√√ (t,k)m,i η

(t,k)m,i,p

(t,k)m,i − η

(t,k)m,i,p

⎞⎠ , (10.41)

where A(t,k)m,i,p =

√(t,k)m,i l

(t,k)U Rm

X(t,k)m,p , B

(t,k)m,i,p =

√(t,k)m,i + θ

(t,k)m,i Y

(t,k)m,i ,

(t,k)m,i = α

(t,k)m,i l

(t)BRm|H (t)

BRm ,i |2 , η(t,k)m,i,p = (22r

( t , k )D L m , i , p − 1)2/P

(t,k)m,i,p , and θ

(t,k)m,i =

(1− α(t,k)m,i )l(t,k)

U Rm. Note that in (10.41)

(t,k)m,i > η

(t,k)m,i,p as r

(t,k)DLm ,i,p will not exceed

the channel capacity of the BS-to-relay links since the corresponding perfectCSI is available at the schedulers. Let Z

(t,k)U Rm ,i,p = A

(t,k)m,i,p/B

(t,k)m,i,p , where A

(t,k)m,i,p

and B(t,k)m,i,p are Rician random variables with two degrees of freedom, noncen-

trality parameters s2a =

(t,k)m,i l

(t,k)U Rm

s2x and s2

b = (t,k)m,i + θ

(t,k)m,i s2

y , and variances

σ2a = ((t,k)

m,i l(t,k)U Rm

)2σ2x and σ2

b = (θ(t,k)m,i )2σ2

y , respectively. Thus, the CDF of

Z(t,k)U Rm ,i,p , which is the ratio of two independent nonidentical Rice distributed

random variables, is

F(t,k)U Rm ,i,p(z) = Q(c, d)− (σ2

ac2/s2b z

2) exp (−(c2 + d2)/2)I0(cd) (10.42)

for z ∈ R+, where c = (s2

b z2/(σ2

b z2 + σ2a))1/2 and d = (s2

a/(σ2b z2 + σ2

a))1/2 . Thus,when combining (10.41) and the constraint C1 in (10.18), we can solve forr

(t,k)DLm ,i,p , which yields

F(t,k)U Rm ,i,p

⎛⎝√√√√

(t,k)m,i η

(t,k)m,i,p

((t,k)m,i − η

(t,k)m,i,p)

⎞⎠ = ε

⇒ r(t,k)DLm ,i,p =

12

log2

(1 +

P(t,k)m,i,p

(t,k)m,i (F−1(t,k)

U Rm ,i,p(ε))2

2((t,k)m,i + (F−1(t,k)

U Rm ,i,p(ε))2)

). (10.43)

The inverse CDF F−1(t,k)U Rm ,i,p(ε) can be implemented as a look-up table or by using

the bisection method for practical implementation.

Asymptotic analysis

Here, we first show the asymptotic order growth of Rician and Rayleigh randomvariables, before we obtain the asymptotic order growth of the average systemgoodput for the PF scheduler. The order of growth of Rician fading coefficientswith perfect CSIT and Rayleigh fading coefficients with imperfect CSIT canbe derived by using Lemma 10.1. Suppose h1 , h2 , . . . , hM are M i.i.d. Ricianrandom variables with Rician factor κ. Let a = κ/(1 + κ), v = 1/(κ + 1), andxi = |hi |2 . Then the set x1 , x2 , . . . , xM of the magnitude squared of the Rician

Appendix 295

random variables with PDF f(·) and CDF F (·) is twice differentiable for all x.Therefore, the limit of the reciprocal hazard function is given by [31]

limx→∞

g(x) = limx→∞

1− F (x)f(x)

≈ 1v

(10.44)

which satisfies the sufficient condition in Lemma 10.1 and therefore xmax − lMconverges to a Gumbel distribution in the limiting case of M →∞. Then, solvingF (lM ) = 1− 1/M for lM , we obtain

lM =(√

v log M +√

a)2

+ O(log log M). (10.45)

Therefore, the growth of xmax is given by O((log M)/(κ + 1)) for sufficientlylarge M . On the other hand, we consider F

−1(t,k)U Rm ,i (ε), k ∈ 1, 2, . . . ,KN for

nondelay-sensitive users as defined in Section 10.5.1. By adopting a frameworksimilar to that in and applying Lemma 10.1, it can be shown that for CSITerror variance σ2

e (t) ∈ [0, 1), the growth of max1≤k≤KNF−1(t,k)U Rm ,i (ε) is given by

O((1− σ2

e (t)) log KN

)for sufficiently large KN and the term (1− σ2

e (t)) acts asa penalty on the multiuser diversity gain due to imperfect CSIT for σ2

e (t) ∈ [0, 1).

Remark 10.1 Since we are interested in the asymptotic performance of the PFscheduler with long-term fairness, the selection of the relay-to-user links will bebased on the i.i.d. small-scale fading coefficients only [29], and thus, the extremevalue theory for i.i.d. random variables is applicable.

Therefore, by considering only the first order growing terms, the asymptoticorder growth of the average weighted system goodput is given by

Ugoodput (P,R,S) =M∑

m =1

∑k∈Nm

F∑t=1

n F∑i=1

n F∑p=1

w(k )s(t ,k )m ,i,p

2Fn F

×

⎧⎨⎩O

⎛⎝log2

⎛⎝ P(t ,k )m ,i,p (1 − α

(t ,k )m ,i )l(t ,k )

U R m(1 − σ2

e (t))(log KN )l(t)B R m(log M/(κ + 1))

2((1 + α

(t ,k )m ,i )l(t)B R m

(log M/(κ + 1)) + (1 − α(t ,k )m ,i )l(t ,k )

U R m(1 − σ2

e (t)) log KN

)⎞⎠⎞⎠

+O

⎛⎝log2

⎛⎝ P(t ,k )m ,i,p α

(t ,k )m ,i l

(t)B R m

(log M/(κ + 1))l(t ,k )U R m

(1 − σ2e (t)) log KN

2(α

(t ,k )m ,i l

(t)B R m

(log M/(κ + 1)) + (2 − α(t ,k )m ,i )l(t ,k )

U R m(1 − σ2

e (t)) log KN

)⎞⎠⎞⎠

⎫⎬⎭(10.46)

where Nm = Um ∩N is the intersection of sets Um and N . We are now ready toderive the results of Case I and Case II.Case I (Asymptotic system goodput for a large number of non-delay-sensitiveusers KN and a growing number of relays M) In this case, we assume that thenumber of non-delay-sensitive users KN is always larger than the number ofrelays M and KN grows with M such that limKN ,M→∞KN /M →∞. By onlyconsidering the first order growing terms, the growth of the average system


goodput is given by

Ugoodput (P,R,S)

(a)≈

M∑m=1

∑k∈Nm

F∑t=1

nF∑i=1

nF∑p=1

w(k)s(t,k)m,i,p

2FnF

×O

(2 log2

(P

(t,k)m,i,p l

(t)BRm

(log M/(κ + 1))2

))(b)= O

(log2

(log M

κ + 1

)), (10.47)

where (a) is due to the assumption that limK,M→∞K/M →∞ and (b) is becausethe channel coefficients of the BS-to-relay links are identical distributed since thedistances between the BS and relays are assumed to be same.Case II (Asymptotic system goodput for a large number of relays M and agrowing number of non-delay-sensitive users KN ) In this case, we assume thatthe number of relays M is always larger than the number of users KN and M

grows with KN such that limKN ,M→∞M/KN →∞. By replacing the channelgain variables with the associated asymptotic growth expression, we obtain thegrowth of the average system goodput which is given by

Ugoodput(P,R,S)

(c)≈

M∑m=1

∑k∈Nm

F∑t=1

nF∑i=1

nF∑p=1

w(k)s(t,k)m,i,p

2FnF

×O

(2 log2

(P

(t,k)m,i,p l

(t,k)U Rm

((1− σ2e (t)) log KN )

2

))(d)≈ O

(log2

((1− σ2

e (F × τ)) log KN

)), (10.48)

where (c) is due to the assumption that limKN ,M→∞M/KN →∞ and (d) is dueto the fact that the growth of the system goodput is limited by the largest CSITestimation error variance.

It can be observed that in both Case I and Case II, the two-way relay compen-sates the loss of spectral efficiency due to half-duplexing, i.e., the prelog factor12 .

Derivation of feedback condition

Let Θth be the threshold representing the global subcarrier usage and replac-ing (γi + βi) in (10.30). Furthermore, assume that the SNR is high suchthat Λ(t,k)

ULm ,i,i/(1 + Λ(t,k)ULm ,i,i)+Λ(t,k)

DLm ,i,i/(1 + Λ(t,k)DLm ,i,p) ≈ 2 in (10.30). With these

assumptions and s(k)m,i,j = 1, based on (10.30), we can establish the following

upper bound for 0 < α(t,k)m,i < 1, which is given by

2 log2

(P

(t,k)m,i,p

2l(t,k)U Rm

F−1(t,k)U Rm ,i (ε)

)− 2 ≥ C

(t,k)m,i,i −

Λ(t,k)DLm ,i,i

1 + Λ(t,k)DLm ,i,i

−Λ(t,k)

ULm ,i,i

1 + Λ(t,k)ULm ,i,i

≥ 2Θth

(wk + δk )(1− ε). (10.49)

References 297

The above upper bound has the same asymptotic order growth as Case II inTheorem 10.2, which suggests that the adopted upper bound is an appropriatechoice. Furthermore, the user selection does not depend on the CSI of the BS-to-relay link. Therefore, based on (10.49), the proposed user feedback criterioncan be obtained as

l(t,k)U Rm

F−1(t,k)U Rm ,i (ε) ≥

(2

4 Θ th(w k + δ k ) ( 1−ε ) +4

)P

(t,k)m,i,p

2(a)≈(

24 Θ th

(w k + δ k ) ( 1−ε ) +4)

4nF

PT,

(10.50)

where (a) is due to the fact that the users do not know the final power allocationbefore the schedulers perform the resource allocation, and hence equal powerallocation is assumed for user selection.

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[3] V. K. N. Lau and Y. K. R. Kwok, Channel-Adaptive Technologies andCross-Layer Designs for Wireless Systems with Multiple Antennas: Theoryand Applications. 1st ed. Wiley-Interscience, 2006.

[4] A. Nosratinia, T. E. Hunter, and A. Hedayat, “Cooperative communicationin wireless networks,” IEEE Commun Magazine, 42 (2004),74–80.

[5] R. Pabst, B. H. Walke, D. C. Schultz, et al., “Relay-based deployment con-cepts for wireless and mobile broadband radio,” IEEE Commun Magazine,42 (2004), 80–89.

[6] M. A. Khojastepour, A. Sabharwal, and B. Aazhang, “On capacity of Gaus-sian ’cheap’ relay channel,” in Proc. of IEEE Global Telecommun. Conf.,2003, pp. 1776–1780. IEEE, 2003.

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[12] B. Rankov and A. Wittneben, “Spectral efficient protocols for half-duplexfading relay channels,” IEEE J. Select. Areas in Commun., 25 (2007), 379–389.

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[14] A. S. Avestimehr, A. Sezgin, and D. N. C. Tse, “Approximate capacity ofthe two-way relay channel: A deterministic approach,” in Proc. of IEEE 46thAnnual Allerton Commun., Control, and Computing, 2008, pp. 1582–1589.IEEE, 2008.

[15] B. Rankov and A. Wittneben, “Achievable rate regions for the two-wayrelay channel,” in Proc. of IEEE Int. Symp. on Inform. Theory, 2006,pp. 1668–1672. IEEE, 2006.

[16] D. W. K. Ng and R. Schober, “Cross-layer scheduling for OFDMA amplify-and-forward relay networks,” IEEE Trans. Vehi. Technology, to appear.

[17] G. D. Yu, Z. Y. Zhang, Y. Chen, S. Chen, and P. L. Qiu, “Power allocationfor non-regenerative OFDM relaying channels,” in Proc. of IEEE Int. Conf.on Wireless Commun., Networking and Mobile Computing, 2005, pp. 185–188. IEEE, 2005.

[18] Y. Li, W. Wang, J. Kong, W. Hong, X. Zhang, and M. Peng, “Powerallocation and subcarrier pairing in OFDM-based relaying networks,” inProc. of IEEE Int. Conf. on Commun., 2008, 2602–2606. IEEE, 2008.

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fairness in wireless communications: The single-cell case,” IEEE Trans.Inform. Theory, 53 (2007), 1366–1385.

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11 Green communications in cellularnetworks with fixed relay nodes

Peter Rost and Gerhard Fettweis

11.1 Introduction

Mobile communication systems have to provide exponentially increasing datarates for an increasing number of subscribers using ubiquitous data services.As the capacity per cell is limited by the available bandwidth, the same time–frequency resources must be spatially reused. Hence, the more the user densityincreases, the higher the spatial reuse must be to satisfy the demand for highdata rate services. This chapter discusses relaying as a candidate technology toincrease the spatial reuse and therefore to provide the required data rates whilereducing energy consumption in mobile communication systems.

11.1.1 Two motivating examples

A challenging property as well as an opportunity for exploiting the wirelesschannel is nonlinear signal attenuation (path-loss), which offers the possibility toconcentrate power at certain points in the network and spatially reuse resourceswithin a mobile communication network. Consider an additive white Gaussiannoise (AWGN) channel with a path-loss exponent α = 4, receiver noise powerN , and transmission power P . Given these qualities and assuming a downlinktransmission where a terminal can use the received signals from each radio accesspoint (RAP), the observed signal-to-noise ratio (SNR) at a normalized distanced is given by ρ(d) =

∑i P/N · |di − d|−α , where di is the position of the ith

RAP. Figure 11.1 compares the received SNR in two different configurations ofa one-dimensional wireless network:

A: RAPs are deployed at di = [0, 3, 6, . . . , i · 3] and each transmits with powerPA such that PA/N = 10

B: RAPs are deployed at di = [0, 2, 4, . . . , i · 2] and each transmits with powerPB such that PB/N = 2.

Configuration B increases the RAP density by a factor of 1.5 compared to con-figuration A but its RAPs transmit with only one-fifth the power PA. Therefore,



0

10

20

0 2 4 6 8 10Normalized distanced

ρ(d

)(d

B)

(a)

0

10

20

0 2 4 6 8 10Normalized distanced

ρ(d

)(d

B)

(b)

Figure 11.1. Spatial power distribution for two different deployment scenarios:(a) configuration A; (b) configuration B.

the total energy consumption in configuration B is less than half of the energyconsumption in configuration A, but both achieve the same minimum SNR. Inaddition to the lower energy consumption, configuration B provides a higher den-sity of RAPs and therefore also a higher spatial reuse, which potentially increasesthe overall system throughput.

Consider a similar setup with two RAPs, which are placed at distance d fromeach other, and one user terminal (UT), which is placed at distance ∆d, ∆ < 0.5,from its serving RAP. The signal-to-interference-and-noise ratio (SINR) experi-enced at the UT is given by

ρA =P (∆d)−α

N + P ((1−∆)d)−α . (11.1)

Let configuration B again use a higher RAP density, i. e., dA > dB , and let thesum power spent in both configurations be normalized, i. e., the transmissionpower per node in configuration B is given by P · dB /dA . The ratio of the SINRreceived at the user terminal in the configurations is given by

ρA

ρB=

(dA

dB

)1−α

+ P/N ((1−∆)dA )−α

1 + P/N ((1−∆)dA )−α < 1. (11.2)

The probability that a UT experiences a certain ∆ is the same for both scenarios,which implies that even though we move RAPs closer to each other and onlyexploit the signal received from the assigned RAP, we increase the SINR (inthis linear model). In next generation cellular systems not only will the distancebetween two RAPs decrease but also the carrier frequency will increase. There-fore, in the interference-limited regime (P N) let dA = dB and αA < αB in

302 Green communications in cellular networks with fixed relay nodes

order to account for the higher path-loss at higher carrier frequencies:

ρA

ρB=(

∆1−∆

)αB −αA

< 1. (11.3)

Hence, if we use a higher carrier frequency and move RAPs closer to each otherwe are able to improve the observed SINR and the spatial reuse of resources.

11.1.2 Scope and key problems

These examples illustrate that densely deployed networks potentially providehigher data rates while requiring less transmission energy. In addition, futurenetworks face the challenge of connecting RAPs through a backhaul using out-of-band resources in order to exploit interfering signals. Backhaul requirementssuch as the availability of a high-speed wired connection or microwave links toa central server diminish the deployment flexibility and raise necessary expendi-tures. Hence, deployment and transmission strategies in next generation networksshould be able to mitigate intercell interference and increased deployment costsdue to the higher RAP density.

In this chapter, we investigate relaying as an opportunity to increase the RAPdensity in a next generation mobile communication system operating at a car-rier frequency of about 4GHz. Future wireless networks are likely to use multi-cell multiple-input multiple-output (MIMO) where multiple RAPs cooperativelyserve UTs. More specifically, techniques introduced in the context of the MIMObroadcast channel (BC) [1, 2] and MIMO multiple access channel (MAC) [3, 4]are applied to an array of physically separated antennas. Multicell MIMO is ableto (partly) cancel interference and to provide an additional array gain. How-ever, in addition to high-quality channel state information (CSI), it requires theexchange of user data over a high-performance backhaul link. In this chapterdifferent aspects of a mobile communication system, which uses both multicellMIMO for interference cancelation and relaying in order to improve the spatialresource reuse, are analyzed and discussed.

Studies have shown that the energy consumption in cellular networks alreadyrepresents a major cost driver, which emphasizes that decreasing the system-wide energy consumption is not only of ecological but also economical inter-est. In a mobile communication system, we distinguish between the energyconsumed by the RF frontend (transmission power) and the energy requiredfor signal processing as well as encoding and decoding (computation power).It does not suffice to solely reduce the transmission power by using (almost)capacity-achieving codes and decoding algorithms, which imply that the addi-tional computation power required outweighs the reduced transmission power[5]. Our goal is to employ low-complexity approaches, which provide a higherthroughput while reducing the overall energy spent in the system. The scope ofthis chapter is the analysis of the cost–benefit tradeoff in relay networks as well


as the tradeoff between computation power, transmission power, and the systemperformance.

11.1.3 Outline and contributions

We explore system architectures based upon the transmission schemes introducedin [6] and apply these techniques to two major scenarios: the wide-area scenarioand the Manhattan-area scenario. While previous work considered either down-link or uplink performance, we analyze both jointly. As previously mentioned,the key to green communication is to use low-complexity algorithms as well as toreduce the overall consumed transmission energy. In order to show how conven-tional and relay-based systems perform with less complex encoding and decodingalgorithms, we provide results for different SNR gaps [7, p. 66]. The SNR-gapapproximation applies a constant SNR scaling under the assumption that forthe considered SNRs the difference between the employed encoding/decodingscheme and the maximum achievable rate is only an SNR shift.

Furthermore, we compare femto-cells with high data-rate infrastructure con-nection and relaying where only in-band connections are available. Each addi-tional relay node (RN) implies additional costs for the deployed system but alsoprovides a performance gain for its users. This relation is examined using a cost–benefit tradeoff analysis, which compares the system performance under a costconstraint.

In Section 11.2, we introduce the considered system model and we review themost important parameters of the physical layer. In Section 11.3 we discuss thesystem and protocol design, and summarize the approaches for the consideredmobile communication system. The main part is the discussion of numericalresults in Section 11.4. Section 11.5 concludes the chapter.

11.2 System model

11.2.1 Propagation scenarios

Our analysis in Section 11.4 is based on two propagation scenarios, which weredefined by the European research project WINNER: a macrocellular deploy-ment (referred to as wide-area) and a microcellular deployment (referred toas Manhattan-area) [8]1 . Figure 11.2(a) illustrates the wide-area scenario withuniformly deployed sites at an intersite distance dis,ref = 1000m. At each sitethree base stations (each indicated by “BS”) serve three adjacent sectors,each supported by two fixed RNs (indicated by triangles). Each BS uses adirected antenna (main lobe directions are indicated by arrows) with a down-tilt of 5 degrees and an antenna attenuation at an enclosed angle of ϕ given

1 All the WINNER documents referred to are publicly available on http://www.ist-winner.org.


BSBSBS

BSBSBS

BSBSBS

BSBSBS

BSBSBS

BSBS

(a)

BS

BSBSBS

200m

30m

BS

BS

BS

BS

BS

BS

BS

BSBS

BS

BS

BS

BS

BS

BS

(b)

Figure 11.2. The two reference scenarios considered in this chapter: (a) wide-area scenario with one tier of interfering sites. Triangles indicate relay nodesand arrows the main lobe direction in each cell; (b) Manhattan-area scenario asdefined in [9]. Triangles indicate outdoor relays and squares indoor relays.

by 12 (ϕ/70)2 dB. Throughout our analysis, we consider only the performanceresults for the central site, which is surrounded by 18 interfering sites. We ran-domly place users according to a uniform distribution and an average density of90 users per square kilometer [10]. Users are assigned to RAPs based on theirpath-loss to the respective base station (BS) or RN. Due to the path-loss-basedcell assignment, the actual instantaneous cell layout may differ from the regularlayout in Figure 11.2(a).

Figure 11.2(b) illustrates the second scenario and its regular street grid as orig-inally defined by the UMTS 30.03 recommendation [9]. In contrast to the wide-area scenario where BSs employ directed antennas, omni-directional antennasare used in the Manhattan scenario. Each BS is supported by four RNs of whichtwo are placed indoors (indicated by a square) and two are placed outdoors (indi-cated by a triangle). Both outdoor and indoor RNs are able to increase a user’sline-of-sight (LoS) probability with its assigned RAP and therefore promise, inparticular, to improve data rates indoors, which has been previously demon-strated using field trial results in [11]. The numerical results in Section 11.4 onlyinclude the inner three BSs, which are surrounded by 44 interfering cells. Userterminals are again randomly placed on streets and within buildings according toa uniform distribution with an average density of 250 users per square kilometer[10].

For each different link between user terminals and RAPs, an LoS probability,a path-loss model, and a power delay profile are defined in [12] for the small-scale


Table 11.1. Used channel models, which are defined in [12]

Link Manhattan-area Wide-area

BS to RN B5c B5aBS to indoor UT B4BS to outdoor UT B1 C2RN to indoor UT B4RN to outdoor UT B1 C2Indoor RN to indoor UT A1

fading process, where each tap is assumed to be Gaussian distributed. Table 11.1lists the channel models, which are used for the numerical evaluation.

11.2.2 Air interface and scheduling

Both the wide-area and the Manhattan-area scenario use orthogonal frequency-division multiple access (OFDMA) [13, 14] at a carrier frequency fc = 3.95GHz.The system resources are divided in resource blocks of 15 OFDM symbols and8 subcarriers. Uplink and downlink operate in time-division duplex (TDD) suchthat the whole bandwidth is alternately occupied by either uplink or down-link (which are separated by a duplex guard of 8.4µs). Two consecutive resourceblocks are assumed to be time-invariant, i.e., we model no Doppler spread result-ing from user mobility. Therefore, both uplink and downlink experience the samechannel realizations but use a separate radio resource management (RRM). Allindividual channel models for each link are listed in Table 11.2 and are describedin detail in [8]. In order to use the relevant capacity expressions defined in [6],we assume throughout our analysis Gaussian alphabets, perfect rate adaptation,and very large blocklengths. Nonetheless, in order to achieve realistic resultswe consider a rate clipping at 8 bits per channel use (bpcu) or (bits/symbol)enforced by a corresponding SNR clipping at 28 − 1. We assume that CSI is per-fectly available at the receiver as well as at the BS in the downlink. Furthermore,the system is perfectly synchronized.

Each transmitter is assumed to have a full queue, which implies that eachnode transmits at the maximum rate and exploits all available resources. Bothscenarios deploy half-duplex RNs, which are connected to their assigned BSusing an in-band feederlink operating on the same time–frequency resources asUTs. Furthermore, it might happen that in the downlink an unexpected highthroughput between the RN and UTs cannot be supported due to insufficientlyfilled relay buffers (and similarly in the uplink between the RN and BS). Hence,relay buffer management is an important part of the system in order to guarantee


Table 11.2. Parameters of the underlying WINNER system used for the numericalevaluation

User density 90 per km2 in wide-area,250 per km2 in Manhattan-area

Average no. users/cell 26 in wide/Manhattan-areaChannel models As defined inNumber of antennas BS/RN/UT 4 / 1 / 1BS transmit power 46 dBmRN transmit power 37 dBmRN transmit power 24 dBmUT noise figure 7 dBNoise power spectral density −174 dBm/HzFFT size 2048Carrier frequency 3.95GHzSystem bandwidth 100MHzOFDM symbol duration 20.48µsSuperframe duration 5.89msGuard interval 2.00µsUsed subcarriers [−920; 920] \ 0

Channel state information Assumed to be perfectly known attransmitter and receiver

that all resources are exploited while keeping the latency as low as possible. Dueto the assumption of perfect rate adaptation in our system, we do not considerany automatic repeat-request (ARQ) protocols.

11.3 System and protocol design

Assume that two BSs are connected by a high-performance backhaul that doesnot limit the data exchange between them. Both BSs can be regarded as onevirtual antenna array, which realizes an interpath cooperation based on the sameapproaches as introduced in the context of the BC. Since RNs are not connectedto the backhaul, they implement interpath coordination approaches as introducedin the context of the interference channel (IC) [15, 16]. The relay-interferencechannel combines both models and has been used in [6] to derive and evaluatestrategies for a relay-assisted cellular system. In this chapter, we briefly discussthese strategies and apply them to the presented scenarios. However, we do not

11.3 System and protocol design 307

consider intersubsystem cooperation where signals transmitted from the BS andthe RN are combined, i.e., cooperative relaying [17].

11.3.1 Non-relaying protocols

Conventional mobile communication systems such as GSM and UMTS do notprovide the possibility of interpath cooperation but solely coordinate theirresources. However, the spatial resource reuse can be improved if all BSs use thesame resources to serve UTs experiencing a high SINR (cell-center users) while allother UTs are served using orthogonal resources (cell-edge users) [18]. The actualassignment of users to the individual groups is based upon the expected long-term downlink SINR, which is assumed to be perfectly known. In our analysis,all users with an SINR below 10 dB [19] are assigned to the cell-edge group andall other users are regarded as cell-center users. Such a protocol requires inter-cell coordination because a change of the resource assignment at one BS directlyaffects the SINR experienced at UTs assigned to other BSs. As the density ofnodes increases, this resource coordination becomes even more complicated usingthe described conventional protocol.

One way to improve the SINR for users suffering from high intercell inter-ference is to employ multicell MIMO transmission approaches [20, 21], whichimprove the performance by investing in computation power instead of trans-mission power. The idea of multicell MIMO transmission is that multiple BSscan build one virtual antenna array and exploit interference using coherent trans-mission. It was shown in [1, 2] that dirty paper coding (DPC) [22] is the capacityapproaching strategy for the downlink scenario. In the uplink, multicell MIMOcan be regarded as a MIMO-MAC between UTs in different cells and the assignedBSs. For this scenario, the capacity is known [3, 4] and is achieved by successiveinterference cancelation (SIC), which assumes perfect rate adaptation in order tocancel interference. Furthermore, the application of SIC based on the (quantized)received signal of other BSs again requires a high data-rate backhaul.

If the channel is changing quickly, the CSI feedback delay causes a significantperformance loss [23] for downlink multicell MIMO transmission. Furthermore,using multicell MIMO requires a very-high-performance backhaul for both uplinkand downlink to exchange parts or complete user data in addition to the CSI [21,24]. In our analysis, we assume that all BSs are connected by an unconstrainedbackhaul link, which provides the means to exchange user data, unquantizedreceived signals, and perfect channel state information at the transmitter (CSIT).However, we show how the performance is affected in a scenario without intercellbackhaul links where only BSs at the same site cooperate.

11.3.2 Relay-only protocol

One key problem of nonrelaying protocols is a strongly nonuniform power dis-tribution. A more uniform power distribution is the requirement to lower the


system-wide spent transmission energy. Multicell MIMO improves the powerdistribution by exploiting interfering signals, which otherwise worsen the SINRparticularly at the cell edge. An alternative is to increase the RAP density whilestill keeping the computational overhead reasonably low, for instance using RNs,which aggregate data of multiple users and forward the data to the BSs. If RNsemploy low-complex algorithms, not only the transmission power but also thecomputation power can be decreased. Otherwise, the saved transmission poweris traded for computation power, which is then spatially distributed among theRNs.

Our analysis considers a protocol in which all users are served by RNs, whichemploy Han–Kobayashi (HK) coding [25] on the RN-to-UT links. In a half-duplex relay-based system, the in-band feederlink 2 represents the bottleneck, asit reduces the amount of available resources for the R−D links. Based on theresults in [6, 26], we assume that RNs are served using multicell MIMO. Incomparison to multicell MIMO between BSs and UTs, the signaling overhead isreduced as relays are stationary and can be placed such that they experience astrong LoS towards the base station. This implies a higher coherence bandwidthand coherence time, which allow less complex algorithms. Furthermore, the intro-duction of RNs might allow a lower density of BSs, which reduces the backhaulrequirements, initial deployment costs, and the system-wide spent computationenergy.

11.3.3 An integrated approach

Users in the cell center of their assigned BS are likely to experience an LoSlink towards the BS without strong multipath fading. Hence, for those users thefeedback overhead can be reduced by serving them without multicell MIMO orusing multicell MIMO involving only BSs at one site. Our analysis considers asimple protocol supporting both multicell MIMO and relaying in order to exploitthe benefits of both protocols and to reduce the signaling overhead for multicellMIMO. We constrain the system such that either multicell MIMO or relayingis used on the same time–frequency resource within one cell and the resourceassignment to the individual protocols is done adaptively using a fair scheduler.Such an approach is scalable as it exploits relaying for coverage extension andsupports multicell MIMO if only intercell interference cancelation is capable ofproviding the required data rates. Furthermore, since RNs can provide the samewireless interface as BSs, UTs need not implement relaying-specific functions,which reduces the required complexity at UTs and improves the legacy ability.

2 Note that we differentiate between the backhaul connecting multiple sites and in-band feed-erlinks, which connect BSs and RNs.

11.4 Numerical analysis 309

11.3.4 Simplifications

In [2], it has been shown that DPC is the capacity achieving approach for theMIMO BC. However, it requires time-sharing of multiple-user orderings in whichuser streams are encoded and it also requires the optimization of the precodingmatrix. In the case of per-antenna power constraints this is an extensive opti-mization with nondeterministic complexity [27, 28], which might not be realizablein a real-time system. In this work, we apply zero-forcing DPC (ZF-DPC) [29],which uses the LQ decomposition of the channel matrix. By precoding with theHermitian of Q, the channel becomes a triangular matrix. Afterwards, DPC isapplied such that individual interference-free links result and the power assign-ment is determined such that the antenna constraints are satisfied [30].

Similarly, at the BS the decoding process in the uplink is based on the QRdecomposition. By multiplying the received signal with the Hermitian of Q, theresulting channel matrix is again a triangular matrix. Then, beginning with thefirst interference-free user stream, the decoder applies SIC in order to obtaininterference-free links, which requires perfect rate adaptation in order to avoiderror propagation.

HK coding requires time-sharing of multiple power assignments, which aredifficult to determine in real time. Therefore, we apply Etkin–Tse–Wang (ETW)coding [31], which provides a rule for determining the power levels of commonand private messages, and guarantees rates within 1 bpcu of capacity. ApplyingETW coding based on the fast-fading information requires a recomputation ofthe power levels in every frame as well as a significant signaling overhead. Hence,instead of using the fast-fading information, we use the long-term SINR statisticsto determine the common and private message power level.

11.4 Numerical analysis

The previous sections introduced different approaches for the integrationof multicell MIMO transmission and relaying in a next generation mobilenetwork (NGMN). This section presents numerical results for the wide-area andManhattan-area scenarios in order to demonstrate how both approaches affectthe system performance. In particular, we discuss first the ability to counteractinter-cell and intracell interference and how the indoor service quality is affectedby relaying. We further evaluate the energy performance and cost–benefit trade-off of a relay-assisted system, where the provided performance gains are com-pared based on normalized energy consumption and normalized expenditures.

11.4.1 Simulation methodology

The previously presented protocols are analyzed using a snapshot-based system-level simulation. Instead of explicitly modeling the user mobility, it models the


Table 11.3. Numerical results for the wide-area scenario using in-band feederlinksand full inter-site cooperation

Scenario/protocol θ (MBit/s) σ (MBit/s) θ5% (MBit/s)

Downlink Conventional 1.3 2.4 2.3 · 10−2

Multi-cell MIMO 2.4 3.0 0.22 Relays, relay-only 3.4 3.1 5.9 · 10−2

2 Relays, mixed 4.9 3.9 0.7

Uplink Conventional 0.1 0.5 4.3 · 10−4

Multi-cell MIMO 0.2 0.6 3.7 · 10−3

2 Relays, relay-only 2.1 2.5 1.8 · 10−2

2 Relays, mixed 3.0 3.0 0.1

effects of user mobility on the experienced channel. For each placement of agroup of users and for each frame consisting of 16 OFDM symbols we randomlygenerate an independent channel realization and perform the resource assignmentas well as user scheduling. Block-fading models the situation in which usersexperience slowly varying channels but the connection spans multiple blockswith independent channel realizations.

Due to the fact that we do not explicitly consider user mobility, we also do nothave a continuous user context to which the scheduling can be applied. Hence,we partition the overall area into rectangles of equal size, i. e., in the wide-areascenario they are of size 30m× 30m and in the Manhattan-area scenario they areof size 10m× 10m. For each snapshot consisting of 16 frames, i. e., 256 OFDMsymbols, users are randomly placed according to a uniform distribution. Then, foreach individual user the corresponding spatial block (x, y) is determined. In orderto obtain sufficient statistics, we keep track of all results for all users, such as theaverage throughput θ(x, y) = Et θ(x, y, t), which is used by a fair scheduler todetermine the number of resources of a user placed in spatial block (x, y). Morespecifically, the number of resources is proportional to θ

−1(x, y). Alternatively,

we could use the 5% quantile of throughput θ5% , with Pr θ(x, y, t) ≤ θ5% ≤ 5%.In this case, a user with a highly varying performance would receive even moreresources at the expense of other users’ performance.

11.4.2 Throughput performance in the wide-area scenario

We analyze the ability of relaying and multi-cell MIMO to mitigate and can-cel intercell interference in the macrocellular wide-area scenario. Consider Fig-ure 11.3, which shows the cumulative distribution function (CDF) of θ(x, y, t)over all analyzed user snapshots. In addition, Table 11.3 lists the average


10-2

10-1

100

10-2 10-1 100 101 102

Throughput θ in MBit/s

Pr

θ(·,·

)≤

θ

+

+

++ + +

ConventionalVirtual MIMO+2 Relays, relay-only2 Relays, mixed

(a)

10-2

10-1

100

10-3 10-2 10-1 100 101


Pr

θ(·,·

)≤

θ

+

+

+

++ + + + +

ConventionalVirtual MIMO+2 Relays, relay-only2 Relays, mixed

(b)

Figure 11.3. Marginal throughput for the wide-area scenario using in-band feed-erlinks and full intersite cooperation: (a) downlink; (b) uplink.

throughput θ, the 5% quantile throughput θ5% , and the standard deviationσ =

√Varθ(x, y, t) for both uplink and downlink. Multicell MIMO doubles

the average throughput and improves the 5% quantile throughput by a factorof approximately 6. Due to the improved spatial reuse the cell throughput isincreased (average throughput), and in addition due to the additional intercellinterference cancelation as well as the array gain using coherent transmission theworst-user performance (5% quantile throughput) is significantly higher. Usingthe relay-only approach, the average throughput is further improved (by a factor


10-2

10-1

100

10-5 10-4 10-3 10-2 10-1 100 101 102


Pr

θ(·,·

)≤

θ

++

++

++

++

++

+ + + + + + + +

ConventionalMulticell MIMO+Relay-only, 2 RNsMixed, 2 RNsRelay-only, 4 RNsMixed, 4 RNs

Figure 11.4. Marginal uplink throughput for the Manhattan-area scenario usingin-band feederlinks.

of 3 in the uplink) but the 5% quantile throughput does not improve alike (iteven decreases in the downlink). Relay nodes only improve the path-loss andLoS conditions for cell-edge users and users close to a relay node. Users that arecloser to the BS now suffer from a high path-loss, which causes a worse servicequality for those users. By contrast, the mixed approach significantly improvesboth average and 5% quantile throughput and outperforms all other protocols.Users near a BS are directly served using multicell MIMO and users at the celledge or close to a RN are served by relay nodes. The improved spatial reuse ofresources using concurrently transmitting relays and the interference mitigationare able to outweigh the loss due to the half-duplex constraint. In this chapterwe consider downlink and uplink separately using the marginal CDF of bothalthough both directly affect each other. A joint uplink–downlink analysis tak-ing into account how the net and the gross rate of uplink and downlink influenceeach other was given in [32].

11.4.3 Throughput performance in the Manhattan-area scenario

The previous analysis showed that relaying improves both average throughputand worst-user throughput, in particular for those users at the cell edge. In amicrocellular scenario such as the Manhattan-area scenario, we face the problemof providing high data rates for indoor users. Consider Figure 11.4 and Table11.4, which show the uplink performance for the Manhattan-area scenario (the


Table 11.4. Numerical results for the Manhattan-area scenario using in-bandfeederlinks and full inter-site cooperation


Downlink Conventional 0.8 2.1 1.6× 10−4

Multi-cell MIMO 0.6 1.1 1.3× 10−3

Relay-only, 2 RNs 0.5 1.0 4.0× 10−4

Relay-only, 4 RNs 5.4 10.6 0.2Mixed, 2 RNs 1.2 2.5 2.1× 10−3

Mixed, 4 RNs 5.8 13.0 0.2

Uplink Conventional 0.2 0.8 4.4× 10−6

Multi-cell MIMO 0.2 0.8 3.0× 10−5

Relay-only, 2 RNs 0.4 1.0 2.0× 10−5

Relay-only, 4 RNs 5.3 10.4 0.1Mixed, 2 RNs 0.9 2.5 7.4× 10−5

Mixed, 4 RNs 5.7 12.0 0.2

downlink shows different quantitative but the same qualitative results as theuplink). Both conventional and multicell MIMO transmission are unable to pro-vide fair and sufficient throughput results, particularly for users that are indoors.In contrast, relaying is able to significantly improve the worst-user performanceand to deliver a sufficient service quality to indoor and outdoor users.

Table 11.4 further highlights that the required performance is only providedby four RNs per cell of which two are indoors and two are outdoors. Morespecifically, the average rate is improved by a factor of 10 and the 5% quantilethroughput by a factor of approximately 103 in the downlink and 104 in theuplink compared with the deployment without indoor relays. There is no signifi-cant difference between the performance of the relay-only and mixed approaches,which implies that the system could use only relays in a microcellular scenarioand apply multicell MIMO exclusively to the links between BSs and RNs. Sincefour relays consume less transmission power than one BS (a difference of 3 dBin our setup), the average downlink transmission power is reduced in the relay-only setup. Moreover, the improved performance offers the possibility to use lesscomplex algorithms, which require less computation power.

11.4.4 Femto-cells vs. relaying

Femto-cells [33] have attracted significant attention as they provide an efficientway of improving coverage and high data rates for indoor users. Femto-cells arehome-deployed by users and exploit the available wired network as the backhaul


Table 11.5. Numerical results for the Manhattan-area scenario and usingfemto-cells instead of in-band feederlinks



Multi-cell MIMO 0.5 1.0 1.2× 10−3

Femto-only, 2 RNs 0.5 1.0 5.0× 10−4

Femto-only, 4 RNs 13.4 27.5 0.7Mixed, 2 RNs 1.3 2.4 2.3× 10−3

Mixed, 4 RNs 13.7 31.1 0.7


Multi-cell MIMO 0.2 0.7 1.9× 10−5

Femto-only, 2 RNs 0.3 0.7 2.4× 10−5

Femto-only, 4 RNs 12.1 25.3 0.7Mixed, 2 RNs 0.7 2.0 6.9× 10−5

Mixed, 4 RNs 12.6 29.0 0.6

connection. Table 11.5 lists the numerical results for femto-cells using the sameparameters as for the previous relay setup except for a perfectly operating back-haul that provides very high data rates to each RN and a perfectly operatingrelay buffer.

The average throughput for the case of four RNs improves by a factor ofapproximately 2 due to the increased UT resources and the perfectly operatingrelay buffer. Furthermore, the 5% quantile throughput improves by a factor of3–5 as a major part of the additional resources are employed for indoor users.The similar uplink and downlink performances suggest that a majority of theSINR values are cut at 8 bpcu. Hence, the higher transmission power in thedownlink does not necessarily provide higher data rates, which implies that therelay-assisted network allows a lower RAP transmission power. Femto-cells donot improve the performance if only two outdoor RNs are deployed, which under-lines that the major bottleneck is the high path-loss from outdoor BSs to indoorUTs. This supports the field trial results presented in [11], which show significantperformance gains for a relay-based communication system in an LTE environ-ment. Femto-cells provide major performance improvements but the necessityto connect indoor RAPs to the data network makes the deployment less flexi-ble. Furthermore, the deployment of femto-cells is more expensive and it is notclear whether the backhaul resources require less computation and transmissionpower than a direct link between BS and RN. Nonetheless, the results prove theflexibility of the relaying concept as indoor relays could be equipped with both


10-3

10-2

10-1

100

101

0 2 4 6 8 10SNR-Gap Γ

Ave

rage

thro

ughp

utin

MB

it/s

+ + + + + +

Uncoded QAM [7]

Turbo Codes [7]

Trellis Codes + THP [35]

Virtual MIMO+Conventional2 Relays, relay-only2 Relays, mixed

(a)

10-3

10-2

10-1

100

101

0 2 4 6 8 10SNR-Gap Γ

Ave

rage

thro

ughp

utin

MB

it/s

+ + + + + +


(b)

Figure 11.5. Average uplink throughput performance for varying SNR-gap values:(a) Wide-area scenario; (b) Manhattan-area scenario.

a wireless interface to connect them directly to the BS and an interface to thewired broadband network.

11.4.5 Computation-transmission-power tradeoff

An energy-efficient mobile communication system must consider the trade-off between computation and transmission power, which differently affect theachieved performance. One way to examine this tradeoff is the SNR gap approx-imation [7, pp. 66]. This approximation defines an SNR gap Γ ≥ 1 between


practically possible modulation and coding schemes (MCS) and the theoreti-cally possible capacity [35, 36]. More formally, given an SNR gap Γ we apply themodified capacity expression

CMCS = log2

(1 +

SINRΓ

). (11.4)

Hence, the less efficient the MCS, the higher the SNR gap Γ. In particular, it isa useful means of approximating the effects of channel estimation errors, finiteblocklengths, and dirty RF effects.

In Figure 11.5, we see the average uplink throughput for both scenarios andvarying SNR-gaps. It further shows that for uncoded QAM Γgap = 8.8 dB for anerror probability of 10−6 . More complex MCS such as turbo codes [37] achievesmaller SNR gaps of about Γgap = 1dB [7]. In [34], the authors showed that theSNR gap for trellis coding and Tomlinson–Harashima precoding [38, 39], whichis a practical implementation of DPC, achieve Γgap = 1.5 dB and up to aboutΓgap = 5dB. Furthermore, in [40] Kannan derived the SNR gaps for differentblocklengths and MIMO algorithms such as D-BLAST.

The performance drop in Γ for both relaying approaches in the wide-areascenario has a slightly smaller slope than conventional and multicell MIMOtransmission. The reason for this behavior is the very high SINR values in arelay-based system and the resulting rate cut at 8 bpcu. For the same reasonthe slope in the Manhattan-area scenario is smaller than in the wide-area sce-nario. In order to achieve the same SINR after applying a practical MCS withSNR gap Γ, we had to spend at least additional transmission power Γ. If mostSINR values exceed 28 − 1, which occurred for both relaying approaches in theManhattan-area scenario, we do not need to increase the transmission power byΓ. Hence, the overall system-wide spent computation energy is reduced whileproviding almost the same performance. However, the optimal operating pointis still difficult to determine as the computation power for a specific approachcan only be approximated. Nonetheless, this analysis gives an indication thatrelaying is able to cope with less powerful MCS while still providing significantperformance gains over conventional nonrelaying-based approaches using morepowerful and more complex MCS. For instance, based on Figure 11.5, relayingwith uncoded QAM provides higher data rates than conventional and multicellMIMO transmission without an SNR gap.

11.4.6 Reduced backhaul requirements

In the relay-based system, multicell MIMO is particularly important for thearea between two cells served at the same site while the cell-edge area betweentwo different sites is covered by RNs. Due to the low intercell interference, thecell-center area in the main lobe direction of the BS could be served using conven-tional transmission. Since RAPs are uniformly distributed, the main interferersfor the BS-to-RN links are located at the same site instead of different sites. This


Table 11.6. Numerical results for the wide-area scenario using in-band feederlinksand limited inter-site cooperation. Full cooperation uses virtually infinite backhaulbetween multiple sites and limited cooperation only uses cooperation at the samesite



Multi-cell, full 2.4 3.0 0.2Multi-cell, limited 1.9 2.7 8.6 · 10−2

Mixed, full 4.9 3.9 0.7Mixed, limited 4.9 3.9 0.7


Multi-cell, full 2.39 3.03 0.16Multi-cell, limited 1.92 2.71 0.09

Mixed, full 4.95 3.91 0.66Mixed, limited 4.94 3.94 0.65

motivates the investigation of a system where only BSs at the same site cooper-ate. Such a system uses the same hardware for all BSs at one site and thereforedoes not increase the backhaul requirements compared to a conventional system.In this Table 11.6 system is compared with limited cooperation and a systemwith virtually infinite inter-site backhaul between two physically separated sites(full cooperation).

Only multicell MIMO transmission is affected by the limitation of the inter-site cooperation. More specifically, the average throughput is decreased by about20% and the 5% quantile throughput by approximately 50%. The decrease inthe worst-user performance is mainly caused by the cell edge between two siteswhere full cooperation enables interference cancelation. In a relay-based system,most of the cell-edge users between two sites are served by RNs and thereforefull and limited cooperation provide the same performance. Such a system usingRNs and limited intersite cooperation is more robust against multicell MIMOsynchronization errors, low coherence time/frequency, and the quality of theavailable CSI. In addition, it requires less resource-intensive backhaul network,which contributes a major part to the energy consumption of a mobile network.

11.4.7 Cost–benefit tradeoff

So far we have assumed that the additional performance gains from relaying areprovided for free, e. g., the increased costs have not been considered and thepossible influence on the computation and transmission power in our network


Table 11.7. Example for initial and operating costs for a relay node andsite with three base stations

Item of expenditure Relay node Site (with 3 BS)

Hardware 10 kEUR 80 kEURLoan 3 years at 8 % 8 years at 8 %Installation 5 kEUR 30 kEURRental costs 100 EUR per month 1000 EUR per monthEnergy costs(at 10 cent per kWh)

438 EUR p.a. (500W) 4.4 kEUR p.a. (5kW)

Life span 10a 10a

Cost ratio αRN, ref = CRelay/CSite = 0.1

has not yet been evaluated. In order to provide fair results considering amongthings the energy costs of RAPs, we have the following options:

(1) compare the performance for constant energy consumption per area element;(2) compare the required energy and costs for a constant performance measure;

and(3) compare the performance for constant costs (including energy costs).

In this chapter, we choose the third option and compare the performance fornormalized system costs.

Let CSite denote the capital and operational expenditures of a site (con-sisting of three BSs) including hardware, site rental, average costs for powerand backhaul supply. In addition, let CRelay denote the cost for a relay andαRN = CRelay /CSite the relative costs of an RN compared to a site. Table 11.7shows an example of the necessary costs of a BS and RN, which imply a relativecosts of αRN = 0.1. If we assume a regular grid of sites as shown in Figure 11.2(a)with NRelay = 6 RNs assigned to each site, the intersite distance dis (αRN ) nor-malizing the system expenditures is given by (dis,ref is the intersite distance ina system without relays):

dis (αRN ) = dis,ref

√1 + αRN NRelay . (11.5)

Figure 11.6 presents the 5% quantile uplink throughput depending on the rel-ative relay costs αRN . The mixed approach provides a significant performancegain for all plotted αRN and the relay-only approach for αRN < 0.2. Downlinkand uplink transmission show the same behavior (downlink performance resultsare not shown in this section) although the performance benefits of the down-link transmission are not as dominant. Our analysis uses in-band feederlinks,which still require significant resources for the BS-to-RN links. In the case of


10-4

10-3

10-2

10-1

100

0 0.05 0.10 0.15 0.20 0.25

RN-to-BS cost ratio αRN

5% q

uant

ilein

MB

it/s

+ + + + + +αRN, ref


Figure 11.6. Cost–benefit tradeoff for uplink transmission and 5% quantilethroughput.

femto-cells these resources are used by RNs and the shown performance advan-tage would be even higher.

Our cost–benefit analysis included among other things the energy costs, whichrepresent about 13% of the overall expenditure. However, assume that the targetis to normalize the system’s energy consumption and let the energy consumptionat the relay be ERN = βRN ESite . Then, Figure 11.6 illustrates the performancegain for a normalized energy consumption depending on the relative energy con-sumption βRN . Using the particular setup in Table 11.7, an energy normalizationimplies for βRN < 0.1 that the costs for the resulting relay-based system are alsoreduced. For βRN = 0.1 and αRN = 0.1 the system is both cost-normalized andenergy-normalized while providing significant performance gains over conven-tional transmission techniques.

A provider of mobile communication services is undoubtedly not exclusivelyinterested in the ecological aspects of green communication but also in the eco-nomical aspects. Hence, the cost–benefit tradeoff provides an interesting toolto analyze the tradeoff between the system expenditures, the performance, andthe energy consumption of the system. In our example we are able to normalizeboth costs and energy while providing an improved performance in the relay-assisted system. In addition, the computation energy can be reduced due to thehigher performance in a relay-based system and the much higher SINR values. Inthis chapter we have not quantitatively considered the fact that relaying allowsmore deployment flexibilities, very high data rates in otherwise shadowed areas,


and the reduced backhaul requirements. All three of these contribute to theenergy consumption of the system and further emphasize the ability of relay-ing to improve both the energy consumption in the system and to reduce theexpenditures.

11.5 Conclusion

We have introduced an approach to integrate relaying and multicell MIMO innext generation mobile communications systems. In particular, we have com-pared the achievable throughput performance, the energy saving potential, andhow relaying might reduce deployment costs. Relays provide a flexible way toimprove the spatial reuse, are less complex than BSs and therefore cheaper todeploy, and reduce both the computation and transmission power in the sys-tem. Hence, relays are an ecological and economic alternative to systems basedon direct transmission. These benefits result from the more homogeneous powerdistribution due to a denser RAP distribution and the interference mitigationat the relay nodes. Furthermore, the flexible and scalable deployment of RNsallows for a reuse of existing 2G and 3G sites, which further reduces deploymentcosts. In addition, a mixed approach using both relaying and on-site multicellMIMO significantly reduces the backhaul requirements, which otherwise increasethe deployment costs and require significant energy resources.

The probably most challenging problems in a relay-based mobile communica-tion system are the synchronization of all RAPs, the resource assignment andsynchronization of multiple cells, and the handover mechanisms. Furthermore,the optimization of the chosen MCS in order to exploit the available resourcesappears to be challenging. Practical results such as in [11] suggest that thepromising results in this chapter are realizable and allow significant performanceimprovements particularly for indoor users. Femto-cells already represent a wayto implement relaying using an existing infrastructure link, but are less flexibleand are not an option for those areas where the mobile communications systemis the only choice to provide broadband access.

Acknowledgments

Part of this work has been performed in the framework of the IST project IST-4-027756 WINNER II, which has been partly funded by the European Union,and the Celtic project CP5-026 WINNER+. The authors would like to acknowl-edge the contributions of their colleagues in WINNER II and WINNER+,although the views expressed are those of the authors and do not necessarilyrepresent the project.

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12 Network coding in relay-basednetworks

Hong Xu and Baochun Li

12.1 Introduction

Since its inception in information theory, network coding has attracted a sig-nificant amount of research attention. After theoretical explorations in wirednetworks, the use of network coding in wireless networks to improve throughputhas been widely recognized. In this chapter, we present a survey of advancesin relay-based cellular networks with network coding. We begin with an intro-duction to network coding theory with a focus on wireless networks. We discussvarious network coded cooperation schemes that apply network coding on digitalbits of packets or channel codes in terms of, for example, outage probability anddiversity–multiplexing tradeoff. We also consider physical-layer network codingwhich operates on the electromagnetic waves and its application in relay-basednetworks. Then we take a networking perspective, and present in detail somescheduling and resource allocation algorithms to improve throughput using net-work coding in relay-based networks with a cross-layer perspective. Finally, weconclude the chapter with an outlook into future developments.

Network coding was first proposed in [1] for noiseless wireline communicationnetworks to achieve the multicast capacity of the underlying network graph. Theessential idea of network coding is to allow coding capability at network nodes(routers, relays, etc.) in exchange for capacity gain, i.e., an alternative tradeoffbetween computation and communication. This can be understood by consider-ing the classic “butterfly” network example. In Figure 12.1, suppose the sourceS wants to multicast two bits a and b to two sinks D1 and D2 simultaneously.Each of the links in the network is assumed to have a unit capacity of 1 bit pertime slot (bps). With traditional routing, each relay node between S and the twosinks simply forwards a copy of what it receives. It is then impossible to achievethe theoretical multicast capacity of 2 bps for both sinks, since the thick linkin the middle can only transmit either a or b at a time. However, with networkcoding, the intermediate relay node (shaded in the figure) can perform coding,in this case a bitwise exclusive-or (XOR) operation, upon the two informationbits and generate a + b to multicast towards its two outgoing links. D1 receives



S

D1 D2 D1 D2

a b

b

b

ba

a b

a

a

b?a? a ba+b

a+b a+b

S

(a) (b)

Figure 12.1. The “butterfly” network example of network coding: (a) with tra-ditional routing, the link in the middle can only transmit either a or b at a time;(b) with network coding, the relay node can mix the bits together and transmita + b to achieve the multicast capacity of 2 bps.

a and a + b, and recovers b as b = a + (a + b). Similarly, D2 receives b and a + b

and can recover a. Both sinks are therefore able to receive at 2 bps, achievingthe multicast capacity.

In the above example, the network coding operation is bitwise XOR, which canbe viewed as linear coding over the finite field GF (2). Following the seminal workof [1], Li et al. [2] showed that a linear coding mechanism suffices to achieve themulticast capacity. Ho et al. [3, 4] further proposed a distributed random linearnetwork coding approach, in which nodes independently and randomly generatelinear coefficients from a finite field to apply over input symbols without a prioriknowledge of the network topology. They proved that receivers are able to decodewith high probability provided that the field size is sufficiently large. These workslay down a solid foundation for the practical use of network coding in a diverseset of applications.

After the initial theoretical studies in wire-line networks, the applicabilityand advantages of network coding in wireless networks were soon identified andinvestigated extensively [5]. Though the noiseless assumption no longer holds forwireless communications, the wireless medium does provide a unique character-istic conducive to network coding operations – the inherent broadcasting capa-bility. Again this can be best understood by a classic example of the “Alice andBob” topology as in Figure 12.2. Assume that Alice and Bob want to exchangetheir information represented by bits a and b, respectively, and each link has astatic capacity of 1 bps. It can readily be seen that under the traditional routingparadigm, four time slots are needed to exchange the bits through relay R, which

326 Network coding in relay-based networks

Figure 12.2. The benefits of network coding in wireless networks: (a) four timeslots are needed for Alice and Bob to exchange information bits through relay R

by plain routing; (b) with network coding, R can XOR the bits and broadcastthe coded bit to both parties simultaneously, reducing it to three time slots.

sequentially forwards one bit at a time. In contrast, with network coding, R canXOR the two bits together and transmit the coded bit. Because of the broad-cast nature of wireless medium, this transmission can be heard by both Aliceand Bob. Alice then receives a + b, and recovers Bob’s bit b as b = a + (a + b).Similarly Bob can recover a. Therefore only three time slots are needed in thiscase, which represents a 25% throughput improvement for both parties.

Inspired by the mathematical simplicity and practical potential of networkcoding, the communications and networking communities have devoted a sig-nificant amount of research to utilizing it in a number of wireless applications,ranging from opportunistic routing in mesh networks to distributed storage andlink inference in sensor networks. Our focus in this chapter is on relay-based net-works, which essentially generalizes the example above in various ways depend-ing on the network model. Here, the relays can refer to dedicated stations solelyproviding traffic relaying for others’ benefits, or to users relaying one another’ssignal, i.e., user cooperation. The purpose of relaying can be merely to extendthe coverage of a cellular network when the base station is too distant fromthe mobile station (multihopping), or to combat fading by providing additionalcooperative diversity with more advanced receiver hardware. Our discussion willassume that cooperative diversity is exploited whenever possible, i.e., wheneverthe receiver receives multiple transmissions that contain the same data, andrelaying amounts to mere multihopping only when the receiver obtains one copyof the data.

12.2 Network coded cooperation

In both wire-line and wireless networks, network coding usually operates overbits, or symbols. The general use of this conventional form of network coding in

12.2 Network coded cooperation 327

A BR

A BR

aa

b baa+b

(a) (b)

b

Figure 12.3. (a) Plain relaying without network coding; (b) network coded coop-eration with one dedicated relay.

cooperative diversity is usually termed network coded cooperation in the litera-ture. As was originally invented for wire-line networks, network coding can workat or above the MAC layer over the data bits of packets when applied to relay-based wireless networks, assuming the link layer delivers error-free data. In otherwords, it serves as an “add-on” component to the existing lower layer techniques.Alternatively, it can also be applied at the link layer, by a more dedicated jointdesign with channel coding/decoding.

12.2.1 Simple network coded cooperation

Consider a simple network model where there are two mobile stations transmit-ting on the uplink to the base station. The simplest and the most naive way toattain cooperative diversity, shown in Figure. 12.3(a), is to replicate the clas-sic three-terminal model in information theory by assigning a relay to users onorthogonal channels (this can be achieved by time, frequency, or code division).The cooperative transmission progresses in two phases [6]. In the first phase,each mobile station transmits its own data on orthogonal channels while itsrelay receives and decodes the data. In the second phase the relay forwards thedata to the base station, again on orthogonal channels. The base station receivesboth the original and relayed signals which results in a diversity order of 2 foreach user. If time-division is used to orthogonalize channels, a total of four timeslots is needed for two mobile stations, 2 for the first phase and 2 for the secondphase.

Chen et al. [7] were among the first to point out that the same diversitygain can be achieved with less spectrum cost by network coding as shown inFigure 12.3(b), where the relay assists both users at the same time by transmit-ting the XOR-ed version of information from both users in the second phase. If


any two of the three transmissions succeed, the base station can still recover botha and b, therefore the diversity order is 2 for both users. By a probabilistic anal-ysis, it can be shown [7] that the above network coded cooperation also providesa lower system outage probability at high SNR if the total power consumptionfor the system is fixed, since only three transmissions are required for a completeround of cooperative transmission.

The above network coded cooperation scheme allows the relay node to firstcombine information overheard from multiple sources with linear network cod-ing, and then forward the coded data to the destination. This provides diversityfor multiple sources with better spectral efficiency because the relaying band-width is suppressed. Though the analysis in [7] is fairly elementary, this key ideademonstrates the relevance of network coding in cooperative diversity, and islargely followed in the community.

Now consider the more general model of a cellular network with N ≥ 2 usersand M ≥ 1 relays communicating with the base station. Following [7], Peng et al.[8, 9] proposed an extended network coded cooperation for multiuser networks.Although their scheme was designed for multiple unicast sessions with N distinctdestinations, it can be readily applied to a multiuser cellular network, as outlinedabove, with one common destination, the base station. In their scheme, each userstill transmits its own data in the first phase on orthogonal channels achieved bytime-division. Then in the second phase, a single “best” relay is selected from theM candidates that maximizes the worst instantaneous channel conditions of linksfrom users to the relay and from the relay to the base station, and broadcaststhe XOR-ed version of data received from each user to the base station. The ideaof using a single best relay instead of all available ones is rooted in opportunisticrelaying, first proposed in [10].

Recall the conventional cooperation protocols mandate that a relay transmis-sion must be coupled with each source transmission, no matter whether the relaytransmission uses distributed space-time coding across multiple relays or oppor-tunistically utilizes a single best relay [10]. Thus with time-division, a total of2N time slots is needed with N time slots in the first phase and N time slots inthe second phase for N users. In contrast, the network coded cooperation in [9]takes only one time slot in the second phase to broadcast the XOR-ed messagefor all N users, and only N + 1 time slots are required. Therefore, intuitively, themultiplexing gain of the system can be improved by the proposed scheme. Thequestion is, however: can it also maintain the full diversity gain of M + 1 providedby the M + 1 possible paths to the base station as the conventional schemes?

A comprehensive diversity–multiplexing tradeoff analysis of the selection-based network coded cooperation was offered in [9]. Before we present the results,let us recall the definition of the diversity–multiplexing tradeoff.

Definition 12.1 A scheme is said to achieve spatial multiplexing gain Rnorm

and diversity gain D if the data rate R satisfies

limρ→∞

R(ρ)/ log ρ = Rnorm (12.1)


and the average error probability pe satisfies

− limρ→∞

log pe(ρ)/ log ρ = D (12.2)

where ρ denotes the signal-to-noise ratio (SNR).

We can see that essentially it is a fundamental tradeoff between error proba-bility and transmission rate, and has been widely recognized and adopted in theliterature.

Specifically, the following theorem was proved in [9].

Theorem 12.1 [9] In a single-cell network composed of N users and M relays,the above network coded cooperation scheme achieves a diversity–multiplexingtradeoff given as follows:

D(Rnorm) = 2(

1− N + 1N

Rnorm

), Rnorm ∈

(0,

N

N + 1

). (12.3)

As a comparison, conventional cooperation protocols for multi–user networks(distributed space-time coding or opportunistic relaying) achieve a diversity-multiplexing tradeoff of D(Rnorm ) = (M + 1) (1− 2Rnorm ) for Rnorm ∈

(0, 1

2

).

Therefore, only a diversity gain of 2 can be achieved at high SNR, while themultiplexing gain can indeed be improved from 1

2 to N/N + 1. In other words,the proposed network coded cooperation scheme achieves a different tradeoff.

The reason why XOR network coding does not help in attaining the full diver-sity gain in this case is that, although the coded message can be potentiallyhelpful for any user, it can only help at most one user provided that all the otherN − 1 users’ data are decoded correctly, no matter what the number of relays is.The end-to-end performance of one user is bottlenecked by all the other users,attributing to the diversity order1 of 2.

Interestingly, as a special case, when M = 1, i.e., only one relay exists inthe network, network coded cooperation achieves the full diversity order of 2and has a strictly better diversity–multiplexing tradeoff than the conventionalscheme 2 (1− 2Rnorm ) for Rnorm ∈

(0, 1

2

). It entails less loss in spectral effi-

ciency to achieve the same diversity gain, and offers larger diversity order at thesame spectral efficiency in this case. Finally, Figure 12.4 graphically summarizesthe above discussion and comparison of the diversity–multiplexing tradeoff fordifferent cooperative diversity schemes.

1 In the case of multiple unicast sessions, it can be shown that this net-work coded cooperation has a diversity–multiplexing tradeoff of D(Rn orm ) = (M +1) (1 −N + 1/NRn orm ) , Rn orm ∈ (0, N/N + 1), assuming that each distinct destination dj

can reliably overhear messages from other sources sj , j = i. This assumption, however, implic-itly requires enormous power consumption during sj s transmission and is strongly weakenedwhen the network scales. It may not be convincing to demonstrate the superiority of network-coded cooperation.


D(Rnorm)

Rnorm

M

M N N

Figure 12.4. Diversity–multiplexing tradeoff comparison.

Another user cooperation protocol, named adaptive network coded coopera-tion (ANCC), which essentially achieves the same diversity–multiplexing tradeoffas conventional cooperation protocols in the multiuser setting, was proposed in[11]. It also takes 2N time slots to complete one round of cooperation for N

users. The basic idea is that in the second phase, each user, acting now as arelay, takes turns to select (randomly) a subset of messages it correctly over-heard, and to transmit the binary checksum of them. From a coding perspective,the network coded cooperation can be viewed as matching network-on-graph, i.e.,instantaneous network topologies described in graphs, with the well-known classof code-on-graph, i.e., low-density parity-check (LDPC) codes, on the fly; hencethe term adaptive. Analysis of the achievable rate and outage rate coupled withnumerical evaluations shows that ANCC outperforms repetition-based coopera-tion and is on a par with space-time coded cooperation. This scheme, however,does introduce some level of overhead in transmitting a bitmap so the base sta-tion knows how the checksums are formed. Further, decoding also requires anadaptive architecture, and may not be practical in reality.

From the above discussion, we can see that in a multiuser cellular network,the superiority of network coded cooperation mainly lies in its adaptivity tothe lossy nature of the wireless media, and its operational simplicity. The per-user complexity, for both schemes in [9, 11], is invariant as the network grows,compared with space-time coded cooperation, whose complexity and overheadincreases linearly with the network size. We also note that, despite the factthat these proposals are available for combining network coding and cooperativerelaying and show the benefits of network coding in some scenarios, furtherresearch is required to unleash full potential of network coded cooperation andmake it practical in more general scenarios.


12.2.2 Joint network and channel coding/decoding

The discussion so far has focused on using network coding on packets producedby channel decoding. Network coding essentially works as an erasure–correctioncode that operates above the link layer and offers reliable communication throughredundant transmission of packets. Channel coding, on the other hand, is anerror-correction technique in a wireless environment. It is used in the link layerto recover erroneous bits through appending redundant parity-check bits to apacket. By treating them separately, a certain degree of performance loss isintroduced. Erasure–correction decoding cannot utilize the redundant informa-tion in those packets that fail the channel decoding, and hence are discardedat the link layer, while error-correction decoding cannot take advantage of theadditional redundancy provided in the erasure codes.

Indeed, in one early work on network coding [12] it was shown that, in general,capacity can only be achieved by a joint treatment of channel and network coding.A number of research efforts have directed at unifying the two techniques in orderto obtain further performance improvement. We survey some important ones inthe following.

(a) (b)2

1

3

3

4

x1x1

x3

x3x2

x2

Figure 12.5. (a) A multiple-access relay channel; (b) a two-way relay channel.

Let us first revisit the example of Figure 12.3 where two users share one relayon the uplink to the base station, which resembles the multiple-access relay chan-nel in coding and information theory as shown in Figure 12.5(a). Hausl et al.[13] first considered joint network-channel decoding in this model, assuming thatthe relay can reliably decode messages from both users. A distributed regularLDPC code is used for network-channel coding. Unlike in [7] in which the twomessages transmitted from the users with the network coded message transmit-ted from the relay are separately decoded, they proposed to decode the threemessages jointly on a single Tanner graph [14] with the iterative message-passingalgorithm.

More precisely, let ui denote the information bits of user i, i ∈ 1, 2, xi thenetwork-channel code, and Gij the generator matrix on the link from i to j.


Then the network encoder of [14] at the relay produces2

x3 = u1G31 + u2G32 . (12.4)

The encoding operations at the users and the relay can be jointly described as

x = [x1 x2 x3 ] = [u1 u2 ][G14 0 G31

0 G24 G32

]= uG. (12.5)

Then the parity-check matrix H of the network-channel code has 2N + NR

columns and 2(N −K) + NR rows and has to fulfill GHT = 0, where N andNR denote the channel code length and network code length, respectively andK denotes the length of information bits u1 ,u2 . The decoder at the base stationdecodes the LDPC code with parity-check matrix H on the Tanner graph andexploits the diversity provided by network coding.

In [13] the diversity and code length gain of network-channel code was shownby numerically comparing it with two references systems, one where the relayis shared without network coding, and another where no relay is employed. Thediversity and code length gain is not difficult to explain intuitively. For thecomparison to be fair, the numbers of code bits used in all systems, 2N + NR ,have to be equal. Consider the setup with K = 1500 and N = NR = 2000, whichcorresponds to a channel code rate of 0.75 in the first phase of cooperation.Network-channel code achieves the full diversity order of 2 since x4 containsboth u1 and u2 . For the system without network coding, the relay is shared andonly transmits 1000 code bits for each user, while there are 1500 information bits.Thus it is impossible to achieve full diversity. Now consider another setup withK = 1500 and N = NR = 4000. Without network coding, the relay transmits2000 code bits for each user and full diversity order can be achieved, with achannel code rate of 0.75 to the base station in the relaying phase. The network-channel code, in this case, provides a more robust code rate of 0.375 to the basestation for each user.

In [13] the LDPC-based network-channel coding was not compared with sepa-rate network and channel coding. In [15] the same idea was followed and turbo-code-based network-channel coding for the multiple-access relay channel wasproposed. Moreover, it was shown that even though full diversity order can beobtained with separate network-channel coding, joint network-channel codingbased on turbo codes is able to exploit the additional redundancy in the relaytransmission and exhibits strictly better bit error rate (BER) and frame errorrate (FER) performance.

Hausl further extended joint network-channel coding to a similar model, thetwo-way relay channel [16] as in Figure 12.5(b). It is essentially an abstractionof the “Alice and Bob” example shown in Figure 12.2. Note that simple network

2 Note that the scheme in [7] does not consider interleaving and produces x3 = (u1 + u2 )G3 ,which is slightly inferior in terms of bit error probability, though a diversity order of 2 isachievable.


coded cooperation proposed for the multiple-access relay channel as in [7] workswithout any change for the two-way relay channel, and full diversity order can beexploited. However, joint network-channel coding does call for a different design.The subtle difference is that in the two-way relay channel, each user exchangesinformation through a relay in the middle and decodes the other’s message,whereas in the multiple-access relay channel a common destination decodes bothmessages from each user. An example of the two-way relay channel is the uplinkand downlink transmissions between a mobile station and a base station witha relay. Thus the joint network-channel decoder at the mobile station takes asinputs the channel code from the base station and the network-channel code fromthe relay, and jointly decodes them to obtain the data from the base station. Itsown data are utilized during the decoding process, since the network-channelencoder at the relay is a convolutional encoder coding the interleaved bits fromboth the mobile station and the base station together. The network-channeldecoder at the base station works in a similar way. Again, joint network-channeldecoding is able to obtain the full diversity order of 2 here with better BERperformance.

The proposals in [13, 15, 16] rely on the key assumption that the relay is ableto reliably decode the messages from both ends, and utilize the simplest XORnetwork coding. Yang and Koelter [17] and Kang et al. [18] broke this assumptionand designed iterative network and channel decoding when the relay cannotperfectly recover packets. Guo et al. [19] took one step further and proposed apractical scheme, called nonbinary joint network-channel decoding, which couplesnon-binary LDPC channel coding and random linear network coding in a high-order Galois field. A joint network-channel coding scheme was also proposed in[20] for user cooperation that endows users with efficient use of resources bytransmitting the algebraic superposition of their locally generated informationand relayed information that originated at the other user.

Finally, we offer an information theoretic perspective regarding joint network-channel coding on the two-way relay channel in Figure 12.5(b) before we end thediscussion. The second phase of transmission involves the relay broadcasting totwo receivers at each end, and can be seen as the well-studied broadcast channel.Joint network-channel coding, as we discussed above, performs network codingacross channel codewords, i.e.,

x3 = π32(u1) + π31(u2), (12.6)

where πij (·) denotes the channel encoding function for link ij. In general, thecapacity-achieving code rate varies for different links, and by coding channelcodewords the capacity of each link involved in the broadcast is achieved as inthe single-link transmission.3 The only difference here is that for user i, certain

3 Note that all works we have described, including [13, 15, 17–20] which were not designedfor the two-way relay channel, assume that the code rate is the same for all channel codesinvolved on all links to ease the decoding design. These proposals will work for the more


bits in the channel code are flipped with a known pattern π3j (ui) at the relay asin (12.6), and they are flipped back after demodulation at i. If separate networkchannel coding is used, x3 = π3(u1 + u2). We can readily see that the rate of π3

has to be confined to the minimum rate of links 31 and 32 for both users to beable to decode, resulting in performance loss in terms of achieving the broadcastchannel capacity. This is referred to as the coding to the worst rate problem. Itis easy to verify that this problem does not exist in the multiple-access relaychannel.

12.3 Physical-layer network coding

The main distinguishing characteristic of wireless communications is its broad-cast nature. The radio signal transmitted from one node is often overheard bymany neighboring nodes, and causes interference to their reception. Conventionalwisdom treats interference as a nuisance and strives to avoid it by making thetransmissions orthogonal to each other in time, frequency, or by code, whichin effects disguises a wireless link as a wired one. In the preceding discussionsof network coded cooperation, network coding takes advantage of the broad-cast nature without changing this fundamental interference-avoiding structureof wireless transmissions.

Opposite to this line of thinking, a novel paradigm that embraces interferenceas a unique capacity-boosting advantage was developed in [21] and is gainingmomentum. The idea is to encourage interference from concurrent transmis-sions, and by smart physical-layer techniques transform the superposition of theelectromagnetic waves as an equivalent network coding operation that mixes theradio signals in the air. An apparatus of network coding is then created at thephysical layer, and works on the electromagnetic waves in the air rather thanon the digital bits of data packets or channel codes. Therefore, this is termedphysical-layer network coding (PNC), or analog network coding, while the termdigital network coding refers to its conventional counterpart.

More specifically, Figure 12.6(a) illustrates the working and power of PNC, onthe familiar two-way relay channel. Using PNC, only two time slots are neededfor each user to exchange information, as opposed to three using digital net-work coding and four using direct transmission. In the first time slot each userconcurrently transmits to the relay. For simplicity, assume that BPSK modu-lation is used, and symbol-level and carrier phase synchronization and channelpreequalization are done perfectly, so that the frames from users arrive at relaywith the same amplitude and phase. Then the baseband signal received by the

general case where code rate is different, with proper modification, mostly of the decodingalgorithm.

12.3 Physical-layer network coding 335

–1

Time

Time

2,–2

Figure 12.6. (a) The intuitive benefits of physical-layer network coding. The topgraph shows the transmission schedule using digital network coding, and thebottom graph shows that of physical-layer network coding. (b) BPSK modula-tion/demodulation mapping for physical-layer network coding.

relay is

r(t) = S1(t) + S2(t) = (a1 + a2) cos ωt, (12.7)

where Si(t) is the baseband signal from user i. The relay does not decode bothBPSK signals a1 and a2 from r(t). Instead it tries to decode and transmit thesignal a1 + a2 . The original BPSK scheme has only two signals, 1 and −1 corre-sponding to data bits of 1 and 0, respectively. However r(t) has three signals, −2,0, and 2. A modulation/demodulation mapping, shown in Figure 12.6(b), wasdeveloped for BPSK in [21] so that superposition of the analog signals a1 + a2

can be mapped to arithmetic addition of the digital bits they represent in GF (2).In theory, physical-layer network coding has the potential to improve through-

put performance greatly (by 100% compared with direct transmissions and by33.3% compared with digital network coding as in Figure 12.6(a)). This, however,does come with a nonnegligible price – the loss of diversity gain. Recall that thefull diversity order of 2 is achievable in a two-way relay channel for conventionaland network-coded cooperation as discussed in Section 12.2.2. Since PNC entailsconcurrent transmissions in the first time slot, both users only receive one trans-mission in the second slot when the relay broadcasts,4 whereas they receive adirect transmission and a relay transmission in conventional and network-codedcooperation. Hence, cooperative diversity cannot be exploited and only a diver-sity order of 1 can be obtained with PNC, and relaying here boils down to simplemultihopping. For this reason, to our knowledge almost all subsequent workson the subject compare PNC with multihopping and draw conclusions withoutconsidering cooperative diversity, even if it is possible. Hence unless otherwise

4 The standard assumption of half-duplex radio hardware is assumed.


specified, our discussion of PNC hereafter inherits this assumption from the lit-erature, the validity and fairness of which, however, remain disputable and leftto the judgment of readers.

Given its promising potential, the idea of physical-layer network coding hasgenerated a considerable amount of interest. Hao et al. [22] first analyzed theachievable rates of PNC, assuming the additive white Gaussian noise (AWGN)channel model. Through numerical analysis it was shown that PNC outperformsdigital network coding and direct transmission significantly, and approachesthe capacity limit of the two-way relay channel with appropriate modulationschemes. This is not unexpected as illustrated in the aforementioned example inFigure 12.6(a). Several estimation techniques were developed for PNC to dealwith noise in the decoding process in [23]. The rigid and unpractical require-ments of perfect synchronization and channel preequalization then became thefocal point of critics of PNC, as the detrimental effect of imperfect synchroniza-tion can be substantial (6 dB loss as shown in [22]).

General PNC schemes that relax the synchronization requirement while pre-serving the performance superiority are actively being pursued. An amplify-and-forward scheme, in which the relay directly amplifies and forwards the interferedsignal to both users as opposed to the decode-and-forward strategy in [21], wasproposed and studied in several works [22, 24–27]. It was generally found thatamplify-and-forward PNC is more robust and offers better performance whensynchronization is absent than decode-and-forward PNC [22], whereas when per-fect synchronization is provided amplify-and-forward PNC suffers from a loss ofoptimality in terms of achievable rate [25].

The robustness of amplify-and-forward PNC is more pronounced for generalscenarios because no channel preequalization is required. In [26, 27] the casein which there are M relays available for the two-way relay channel was con-sidered. To effectively utilize multiuser diversity offered by relays, a distributedrelay selection strategy was proposed with selection criteria specifically designedfor amplify-and-forward PNC. Two information theoretic metrics, outage andergodic capacities, closely related to the diversity and multiplexing gains of thesystem, were analytically and numerically evaluated to confirm its advantage.Indeed, the following theorem can be proved as in [27].

Theorem 12.2 [27] The amplify-and-forward PNC scheme in [27] achieves adiversity-multiplexing tradeoff of the following:

D(Rnorm) = M(1−Rnorm), Rnorm ∈ (0, 1]. (12.8)

Clearly, multiuser diversity is capitalized as the diversity order is M . Moreover,the same multiplexing gain of 1 as direct transmission can also be attained,echoing our remark on the benefit of network coding in suppressing bandwidthfor relaying in Section 12.2.1. On the other hand, decode-and-forward PNC isnot able to utilize multiuser diversity gain, due to the operational requirement

12.4 Scheduling and resource allocation: cross-layer issues 337

of channel preequalization before decoding in order to make sure both signalsare received with equal amplitude. One immediately realizes that, despite thetechnical difficulty, channel preequalization effectively inverses the fading effectof the channel, and results in loss of diversity gain.

Joint network-channel coding/decoding is also explored in the area of PNC.The main objective is to design a good coding/decoding scheme that maximizesthe amount of information that can be reliably exchanged through the two-wayrelay channel. More advanced coding that applies lattice code on the relay wasdiscussed in [28, 29].

We make a few comments about open issues and future directions of physical-layer network coding. First, several theoretic issues remain unsolved or unex-plored, as research in this area is still in its nascent stage. Most importantly,only the simplest XOR network coding on GF (2) is realized with signal super-position in the air, while linear network coding can work on a much larger Galoisfield. Note that in wireless communications, path-loss and channel fading effec-tively couple to the transmitted signal a complex coefficient, which, to someextent, resembles the multiplication operation in a finite field of complex num-bers, while signal superposition resembles the addition operation. It is thereforeinteresting, but certainly nontrivial, to investigate whether the complex channelcoefficient can be “transformed” to an equivalent network coding coefficient torealize an even larger improvement, in performance.

In addition, all the developed schemes remain fairly theoretical, and very fewresearchers have attempted to evaluate the true performance of PNC in a realhardware implementation. To the best of our knowledge, the only work in whichthe practical coding and decoding algorithms for MSK modulation based onamplify-and-forward PNC is sketched, and the system using software radiosimplemental is [24]. It is asserted that PNC is indeed practical, and achievessignificantly higher throughput than digital network coding. While this conveysan optimistic message, one should realize that physical-layer network codingmarks a significant departure from the conventional wisdom, and tremendousefforts have to be made across layers of the protocol stack which are designed toavoid interference before it can be implemented in general scenarios.

12.4 Scheduling and resource allocation: cross-layer issues

The discussion so far has largely focused on the lower layers of the protocolstack. From communications and information theory point of view, numerousschemes have been developed based on network coding to utilize a given budgetof resources to transmit information as efficiently as possible. In other words,they answer the question of how to transmit in a given scenario for individualnodes. From a networking point of view, provided with the lower-layer transmis-sion protocol, upper-layer protocols have to coordinate the transmissions betweennodes in the network, and allocate resources network-wise (such as channels) and


Figure 12.7. (a) A cellular network with multiple relays. Solid lines denote directtransmissions while dotted ones denote relay transmissions. All transmissionshappen on orthogonal OFDM subchannels. Note that one mobile station (MS)can be paired up with multiple relays (RSs), while one relay could help multiplemobile stations, complicating the scheduling and resource allocation. (b) XOR-assisted cooperative diversity as adapted from [31]. Here different line typesdenote different subchannels. (BS – base station).

node-wise (such as power) adequately to these competing sessions so as to opti-mize some network-wise metrics. In other words, we need to create scenariosamenable for network coding aided relay transmission protocols such that per-formance is maximized from a network perspective.

The use of network coding certainly calls for new designs of cross-layer schedul-ing and resource allocation protocols on existing cellular network architectures.To this end, there exist only a few publications in the literature. Zhang and Li[30] were arguably the first to venture into this area. They considered the use ofsimple network coded cooperation on the two-way relay channel, with the basestation serving as the relay to XOR the incoming packets and broadcast to twousers. They assumed an orthogonal frequency-division multiple-access (OFDMA)based cellular network model, and developed a coding aware dynamic subcar-rier assignment heuristic in a frequency-selective multipath fading environment.The idea is that in such an environment, different OFDM subcarriers have inde-pendent channel gains to the same mobile station (multichannel diversity), andeven the same subcarrier fades differently on different mobile stations (multiuserdiversity). By dynamically matching the subcarriers to the best mobile stationsfor network coded cooperation while taking fairness into account, a substantialthroughput improvement was reported in [30].

Another work, that of Xu and Li [31], represents an in-depth investigation inthis area, which is discussed in detail here. Consider the more general scenarioin Figure 12.7(a). Assume multiple relays are available for the OFDMA-basednetwork, and all transmissions happen on orthogonal OFDM subchannels. AnXOR-assisted cooperative diversity scheme, named XOR-CD, is employed byreplicating the two-way relay channel using bi-directional traffic of a given mobile

12.4 Scheduling and resource allocation: cross-layer issues 339

station as in Figure 12.7(b). Specifically, it works as follows. In the first phaseof cooperation, on the uplink MS sends packet A to the base station and onthe downlink base station sends packet B to mobile station, simultaneously onorthogonal subchannels. Transmissions are overheard by the relay. In the secondphase, the relay broadcasts A + B using another orthogonal subchannel. We canreadily see that cooperative diversity can still be exploited as in conventionalschemes, which require four subchannels and more power to complete the samejob.

Extending to the network scale, while XOR-CD shows promise, it seems pro-hibitive in terms of cost and complexity to design good scheduling and resourceallocation algorithms for the following reasons. First, one mobile station can bepaired up with multiple relays and one relay could help multiple mobile station,as can be illustrated in Figure 12.7(a). Second, for one mobile station, directtransmission, conventional cooperative diversity, and XOR-CD can be utilizedat the same time on different subchannels, depending on the dynamic channelconditions and resource availability. Third, there is an intricate interplay betweenthree of the problems, namely relay assignment, relay-strategy selection, and sub-channel assignment, further aggravating the problem. The contributions of [31] istwo-fold. First, a unifying optimization framework is developed that jointly con-siders relay assignment, relay-strategy selection, and subchannel assignment forboth mobile station and relays. Second, the joint optimization problem, referredto as a relay assignment, relay-strategy selection and subchannel assignment(RSS) XOR problem, is shown to be NP-hard, and an efficient approximationalgorithm is proposed based on set packing with a provable approximation ratio.

Specifically, the following theorem is shown to hold.

Theorem 12.3 [31] The RSS-XOR problem is equivalent to a maximumweighted three-set packing problem, and is NP-hard.

Proof. Construct a collection C of sets from a base set ζ ∪ ψ as shown in Fig-ure 12.8, where ζ is the set of data subchannels and ψ the set of relay subchannels.As we can see, there are three kinds of sets, representing three possible transmis-sion modes (ci), ci ∈ ζ, represents the direct transmission with data subchannelci : (ci, cr ), ci ∈ ζ, cr ∈ ψ; corresponds to the conventional cooperative diversitywith data subchannel ci and relay subchannel cr ; finally, (ci, cj , cr ), ci , cj ∈ ζ, cr ∈ψ, corresponds to XOR-CD with data subchannel pair (ci, cj ) and relay sub-channel cr . Sets intersect if they share at least one common channel, and areotherwise said to be disjoint. Each set has a corresponding weight, denoting themaximum marginal utility found across all possible assignments of this set todifferent combinations of relays and links.5 The utility function is defined suchthat proportional fairness is taken into account. For (ci, cj , cr ), its weight is found

5 One mobile station has two links, namely the uplink and the downlink.


Figure 12.8. Set construction and transformation into an intersection graph withtwo data subchannels and two relay subchannels. Vertices in GC correspond tosets in C. Edges are added between vertices whose corresponding sets intersect.

over all possible assignments of this set to combinations of relays and both linksof a MS.

The RSS-XOR problem is to find the optimal strategy to choose the transmis-sion mode and assign relays and channels to each link in order to maximize theaggregated throughput. The maximization is done across all links. Equivalently,we can also interpret it as finding the optimal strategy to select disjoint channelcombinations, and assign relays and links to them so as to maximize the objec-tive. In this alternative interpretation, the maximization is done over all possiblechannel sets by matching them to the best possible links and relays, withoutviolating the obvious constraint that each channel can only be used once. Thenumber of elements in a set is at most three; therefore, this problem is essentiallya weighted three-set packing problem [32], which is NP-complete.

To propose an approximation algorithm, we first construct an intersectiongraph GC , such that the a vertex in the vertex set VC corresponds to a setin the set system C, and there is an edge between two vertices in GC if thetwo corresponding sets intersect, as shown in Figure 12.8. Weighted set packingcan then be generalized as a weighted independent set problem, the objective ofwhich is to find a maximum weighted subset of mutually nonadjacent vertices inGC [33]. The size of sets is at most three, therefore GC is three-claw free. Here,a d-claw c is an induced subgraph that consists of an independent set Tc of d

nodes. The best-known approximation algorithm for the weighted independentset problem in a claw-free graph is proposed in [33] and then acknowledged in [32],which is then adopted in [31] as the solution algorithm with an approximationratio of 2

3 as proved in [33].As a side note, it was also shown in [31] that the joint optimization problem

that involves only conventional cooperative diversity and direct transmission canbe cast as a weighted bipartite matching problem, which admits polynomial-timealgorithms to obtain the optimal solution. This demonstrates the interestingpoint that, although network coding provides significant performance gains, itmay render the scheduling and resource allocation problems even more involvedat least in some cases. Moreover, this also reflects the importance of developing

12.5 Conclusion 341

cross-layer protocols to fully realize the benefits of network coding in relay-basednetworks.

While an attempt was made to address these upper-layer issues in [30, 31],the algorithms developed are still impractical for implementation in real-worldcellular networks. Full channel state information (CSI) is assumed to be availableat the base station, which may not be the case for fast fading environments. Thecomplexity of the algorithms is high for real-time scheduling at the time scaleof 5–10 ms, which is the common frame length. Therefore, substantial effortsin design, implementation, and evaluation of practical protocols are imperativeto further understand and to conquer the challenges network coding brings torelay-based networks.

12.5 Conclusion

Network coding, by allowing network nodes to mix information flows, representsa paradigm shift for communication networks. With the broadcast nature ofthe wireless medium, it can be naturally applied to wireless communications andbrings the promise of performance improvement in relay-based cellular networks.The question is: what is the most efficient way to utilize network coding in relay-based networks, and how practical is it to be adopted in the real world?

We have started with network-coded cooperation that applies network codingon digital bits of information, both without and with a joint consideration ofchannel codes. We have noted the operational simplicity and multiplexing gainof network-coded cooperation, and have shown that in general a joint designof network and channel coding/decoding is required to achieve the informationtheoretic capacity, at a cost of increased decoding complexity. Then we haveextended the discussion to physical-layer network coding, a radical yet interest-ing idea that treats the signal superposition in the air as the XOR network-coding operation. By embracing interference, physical-layer network coding hasthe potential dramatically to improve the throughput performance of relay-basednetworks.

From the communications and information theory perspective, the overall mes-sage appears to be very optimistic. From a networking perspective, althoughnetwork coding is mostly applied in the lower layers of the protocol stack, upperlayers have to be coding-aware and perform scheduling and resource allocationaccordingly. In other words, cross-layer efforts are needed to realize network cod-ing in a practical network setting. To this end, we have presented some initialcross-layer studies on cellular relay networks. An important lesson is that networkcoding may render the scheduling and resource allocation more complicated, atleast in some cases, because it mixes information flows from different sessions.

Despite a significant amount of research, the use of network coding in relay-based cellular networks remains largely theoretical. Substantial efforts on imple-mentation and evaluation of network-coding-aided transmissions in large-scale


relay networks are imperative at this stage. With the proliferation of wirelesstechnologies and devices, and the ever-growing bandwidth demand from data-intensive mobile applications, we envision that network coding could become apractical and important component in future wireless technologies, and play animportant role in the quest of high throughput and ubiquitous connectivity inwireless communications.

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Part IV

Game theoretic models forcooperative cellularwireless networks

13 Coalitional games for cooperativecellular wireless networks

Walid Saad, Zhu Han, and Are Hjørungnes

13.1 Introduction

Cooperation among wireless nodes has attracted significant attention as a novelnetworking paradigm for future wireless cellular networks. It has been demon-strated that, by using cooperation at different layers (physical layer, multipleaccess channel (MAC) layer, network layer), the performance of wireless systemssuch as cellular networks can be significantly improved. In fact, cooperation canyield significant performance improvement in terms of reduced bit error rate(BER), improved throughput, efficient packet forwarding, reduced energy, andso on. In order to reap the benefits of cooperation, efficient and distributed coop-eration strategies must be devised in future wireless networks. Designing suchcooperation protocols encounters many challenges. On the one hand, any coop-eration algorithm must take into account not only the gains but also the costsfrom cooperation which can both be challenging to model. On the other hand,the wireless network users tend to be selfish in nature and aim at improvingtheir own performance. Therefore, giving incentives for these users to cooperateis another major challenge. Hence, there is a strong need to design cooperativestrategies that can be implemented by the wireless nodes, in a distributed man-ner, while taking into account the selfish goals of each user as well as all thegains and losses from this cooperation.

This chapter describes analytical tools from game theory that can be usedto model the cooperative behavior in wireless cellular networks. In this context,the key tool that will be explored is the framework of game theory/coalitionalgame theory. For instance, coalitional game theory is the main branch of gametheory/cooperative game theory and it describes the formation of cooperatinggroups of players, referred to as coalitions [1, 2]. Coalitional games prove to be avery powerful tool for designing fair, robust, practical, and efficient cooperationstrategies, which can be used to model cooperative behavior in wireless networks.

The main goal in this chapter is to give the reader a good understanding ofhow cooperative behavior in a wireless system can be modeled through coali-tional game theory. In particular, the chapter gives a better understanding


348 Coalitional games for cooperative cellular wireless networks

of two main applications of coalitional games in wireless networks: (i) dis-tributed cooperation for virtual multiple-input multiple-output (MIMO) for-mation; and (ii) the impact of cooperative transmission and relaying on net-work formation in a wireless network. To achieve these goals, the chapter isorganized as follows. In Section 13.2, we provide a brief introduction to themain ideas of coalitional game theory. Then, in Section 13.3, we present acoalitional game model that allows single antenna users to benefit from theperformance advantage of MIMO systems, through cooperation. Further, in Sec-tion 13.4, we discuss how coalitional game theory can be used to study the struc-ture and dynamics of the wireless network architecture in the presence of relaystation nodes utilizing cooperative transmission. Finally, a chapter summary isprovided in Section 13.5.

13.2 A brief introduction to coalitional game theory

In general, coalitional game theory involves a set of players that are seeking toform cooperative entities, i.e., coalitions. Let N denote the set of these players.By forming any coalition S ⊆ N , the players can improve the utility they obtainin the game. Thus, another main concept of coalitional game theory is the valueor utility which describes the total benefit that the members of a coalition S

can obtain when acting cooperatively. The value of a coalitional game can havedifferent forms: characteristic form, partition form, or graph form. Briefly, acoalitional game is in a characteristic form if the utility of a coalition S dependssolely on the members of that coalition, with no dependence on the players inN \ S. In contrast, a game is in partition form if, for any coalition S ⊆ N , thecoalitional value depends on both the members of S as well as the coalitionsformed by the members in N \ S. In certain coalitional games, the differentplayers are connected to each other through a graph structure. Consequently, formodeling such coalitional games, the value is considered in graph form, i.e., foreach graph structure, a different utility can be assigned.

Independent of the form of the game, every coalitional game is uniquely definedby the pair (N , v), where N is the players’ set and v is the coalitional value. Inany coalitional game, it is always important to distinguish between two enti-ties: the value of a coalition and the payoff received by a player. The valueof a coalition represents the amount of utility that a coalition, as a whole,can obtain. In contrast, the payoff for a player represents the amount of util-ity that a player, the member of a certain coalition, will obtain. For instance,depending on how the value is mapped into payoffs, the coalitional game canbe either with transferable utility (TU) or with nontransferable utility (NTU). ATU game implies that the total utility received by any coalition S ⊆ N can beapportioned in any manner between the members of S. A prominent exampleof TU type games is when the value represents an amount of money, which canbe distributed in any way between coalition members. In contrast, in an NTU,

13.2 A brief introduction to coalitional game theory 349

the individual payoff obtained by any player within a coalition S is restrictedby some underlying structure of the game. In a TU environment, the utilityobtained by a coalition is characterized by a function over the real line, whilein an NTU framework, the utility of a coalition S is a set of payoff vectors ofsize 1× |S| (|S| represents the cardinality of set S), whereby each element of anyvector, represents the payoff that a particular player in S receives. Depend-ing on the metric being used as a utility, the game can be transferable ornon-transferable.

Consequently, depending on the form, type, and objectives of a coalitionalgame, three classes of games can be distinguished [3]: canonical coalitional games,coalition formation games, and coalitional graph games. Each class has its ownproperties, solutions, and challenges. For instance, the canonical coalitional gameclass can be used to model problems where: (i) the value is in characteristicform (or can be mapped to the characteristic form through some assumptions);(ii) cooperation is always beneficial, i.e., including more players in a coalitiondoes not decrease its value; and (iii) there is a need to study how payoffs canbe allocated in a fair manner that stabilizes the grand coalition, i.e., coalitionof all players. In wireless networks, such problems are of interest to study thelimits and fairness of cooperation, when no cost for forming coalitions exists. Forexample, using canonical coalitional games, the work in [4] focused on devisinga cooperative model for rate improvement through ideal receivers cooperation.Using canonical games, the authors of [4] showed that, for the receiver coalitiongame in a Gaussian interference channel and synchronous CDMA multiple accesschannel (MAC), a stable grand coalition of all receivers can be formed if no costfor cooperation is taken into account. In addition, using canonical games, the fairallocation of rate for cooperating users in an interference channel was studiedin [5] for the transmitters. Under some assumptions on the users’ behavior, theauthors showed that a unique rate allocation exists verifying certain well-definedfairness axioms from canonical coalitional games.

In canonical games, there is an implicit assumption that forming a coalitionis always beneficial. In contrast, coalition formation games consider cooperationproblems in the presence of both gains from and costs of cooperation. Thisis quite a useful class of games since, in several problems, forming a coalitionrequires a negotiation process or an information exchange process which can incura cost, thus reducing the gain from forming the coalition. In general, coalitionformation games are of two types: static coalition formation games and dynamiccoalition formation games [3]. On the one hand, for static coalition formationgames, a coalitional structure is imposed on the game through some externalfactor (e.g., a network owner), and, hence, the goal of static games is to studythe already formed structure. On the other hand, in dynamic coalition formationgames, the main objectives are to analyze the formation of a coalitional structure,through players’ interaction, as well as to study the properties of this structureand its adaptability to environmental variations or externalities. As a result, akey question that dynamic coalition formation games seek to answer is “which


coalitions will form in a given game?”.1 For instance, in any problem where thebenefit–cost tradeoff from cooperation is of interest, coalition formation gamesconstitute a well-suited analytical tool since they provide rules, concepts, andalgorithms for characterizing the coalitional structure that can emerge for a givencoalitional game. A coalition formation game can be in either characteristic orpartition form, as the network structure plays a key role in any solution. Inwireless systems, coalition formation games are quite a useful tool for studyingvarious problems such as virtual MIMO formation [6], cognitive radio networks[7, 8], or physical layer security [9, 10].

In both canonical and coalition formation games, the utility or value of a givencoalition has no dependence on how the players inside (and outside) the coalitioncommunicate. Nonetheless, in certain scenarios, the underlying communicationstructure, i.e., the graph that represents the connectivity between the players in acoalitional game can have a major impact on the utility and other characteristicsof the game [1, 3]. In such scenarios, coalitional graph games constitute a strongtool for studying the graph structures that can form based on the cooperativeincentives of the various players. In coalitional graph games, instead of focusingon forming or studying the properties of coalitions, one is interested in studyingthe properties of various graph structures. In this regard, coalitional graph gamescan be used in many wireless and communications applications such as routing,network formation, and vehicular networks.

In the remainder of this chapter, we will illustrate, in detail, the use of coalitionformation games and coalitional graph games in two main applications in coop-erative wireless cellular networks. On the one hand, we will discuss how coalitionformation games can be used for distributed virtual MIMO formation. On theother hand, we will formulate a coalitional graph game for studying the net-work architecture that will form in the uplink next-generation wireless systemswhen cooperative transmission is used. Finally, we note that, although canonicalcoalitional games also admit many interesting applications within cooperativewireless cellular networks (notably when cooperation has no costs), their treat-ment is outside the scope of the present chapter and the interested reader isreferred to [3–5].

13.3 A coalition formation game model for distributed cooperation

In this section, we investigate the use of coalition formation games for modelingcooperative behavior among the users of a wireless network. In particular, weemphasize the problem of the formation of multiple antenna systems throughcooperation among single-antenna transmitters. First, we motivate the problem

1 In the remainder of this chapter, the term “coalition formation game” refers to a dynamiccoalition formation game.

13.3 A coalition formation game model for distributed cooperation 351

and provide a suitable system model. Then, we formulate the problem usingcoalitional game theory, we describe the properties of the resulting game, andwe derive an algorithm for coalition formation.

13.3.1 Motivation and basic problem

An important application for cooperation in wireless cellular networks is the for-mation of virtual MIMO systems through cooperation among single-antennadevices. In this context, a number of single-antenna devices can form vir-tual multiple-antenna transmitters or receivers through cooperation, and conse-quently, benefit from the advantages of MIMO systems without the extra burdenof having multiple antennas physically present on each transmitter or receiver.Thus, the basic idea of virtual MIMO is to rely on cooperation among mobiledevices in order to benefit from the widely acclaimed performance gains of MIMOsystems.

An intensive research effort has been dedicated to information theoretic studiesof virtual MIMO systems. For instance, the authors of [11] showed the interestinggains in terms of outage capacity resulting from the cooperation of two single-antenna devices that are transmitting to a far away receiver in a Rayleigh fadingchannel. Further, the work in [12, 13] considered cooperation among multiplesingle-antenna transmitters as well as receivers in a broadcast channel. Differentcooperative scenarios were thus studied and the results showed the benefits ofcooperation from a sum-rate perspective. It is important also to note that virtualMIMO gains are not only limited to rate gains. For example, forming virtualMIMO clusters in sensor networks can yield gains in terms of energy conservation[14].

Implementing distributed cooperation algorithms that allow the wireless net-work to reap these capacity or energy benefits in a practical wireless network ischallenging and desirable. In this regard, using concepts from coalitional gametheory to design such distributed algorithms is quite appealing [3]. Thus, considerthe single cell of a wireless cellular network having N single-antenna transmitters(e.g., mobile users) sending data in the uplink to their serving base station (BS)which possesses K > 1 receive antennas. Let N = 1 . . . N denote the set of allN users in the network. For multiple access, we consider a TDMA transmissionin the network,2 thus, in a noncooperative manner, the N users require a timescale of N slots to transmit as every user occupies one time slot. In order toimprove their system performance, the users can cooperate. For instance, if theusers cooperate, each group, i.e., coalition S ⊆ N , of cooperating single-antennatransmitters can be seen as a single-user MIMO device (since the system alreadyhas multiple antennas at the receiving end, i.e., the BS). These cooperative

2 Note that the subsequent model and formulation can also be tailored for other multiple accessschemes such as OFDMA or CDMA.


Coalition 2

Coalition 1

Coalition 3

User 2

User 3

User 1

User 4 User 6

User 5

User 1

Time slot 1 Time slot 2 Time slot 3 Time slot 4 Time slot 5 Time slot 6

Time slot 1

Coal. 1 Coal. 1 Coal. 1 Coal. 2 Coal. 3 Coal. 2

Time slot 2 Time slot 3 Time slot 4 Time slot 5 Time slot 6

User 2 User 3 User 4 User 5 User 6

Base station with K antennas

Figure 13.1. An illustrative example of a single cell with N = 6 users cooperatingfor virtual MIMO formation.

coalitions subsequently transmit in a TDMA manner, i.e., one coalition per timeslot. Hence, during the time scale N , each coalition is able to transmit withinall the time slots previously held by its users. By doing so, there is a cooperativescheme within every cell in a wireless cellular network. An illustrative example ofthis network model is shown in Figure 13.1 for N = 6. The key issues that needto be tackled in this model are two-fold: (i) What are the benefits and costs fromcooperation? (ii) Given the benefit–cost tradeoff which groups of users shouldcooperate?

Given a coalition S ⊆ N with |S| users (| · | represents the cardinality of aset), we consider a block fading K × |S| channel matrix HS with a path-lossmodel between the users in S and the BS with each element of the matrixhi,k = ejΦ i , k

√κ/dµ

i,k with µ the path-loss exponent, κ the path-loss constant,Φi,k the phase of the signal from transmitter i to the BS receiver k, and di,k

the distance between transmitter i and the base BS’s receiver k. Further, for theconsidered TDMA system, we define a fixed transmit power constraint per timeslot, i.e., a power constraint per coalition P . This average power constraint isapplied to all the transmitters that are part of the coalition active in the slot. Inthe noncooperative scenario, this same power constraint per slot is simply thepower constraint per individual user active in the slot. In fact, due to ergodicity,for each time slot, the average long-term power constraint per individual userand the power constraint per slot (i.e., constraining all transmitters of a coalitionactive in a slot) are the same [12, 13]. Subsequently, each coalition transmits in aslot, hence, perceiving no interference from other coalitions during transmission.As a result, in a slot, the sum-rate capacity of the virtual MIMO formed by a


coalition S, under a power constraint PS with Gaussian signaling is given by [15]

CS = maxQS

I(xS ;yS ) = maxQS

(log det(IK + HS ·QS ·H†S ))

subject to: tr[QS ] ≤ PS , (13.1)

where xS and yS are, respectively, the transmitted and received signal vectorsof coalition S of size |S| × 1 and K × 1, QS = E [xS · x†S ] is the covariance of xS

and HS is the channel matrix with H†S its conjugate transpose.

The considered channel matrix HS is assumed perfectly known at the trans-mitter and receiver. Thus, the maximizing input signal covariance is given byQS = V S DS V †S [15], where V S is the unitary matrix given by the singularvalue decomposition of HS = USΣS V †S and DS is an |S| × |S| diagonal matrixgiven by DS = diag(D1 , . . . , DF , 0, . . . , 0). Here F ≤ min (K, |S|) is the num-ber of positive singular values of the channel HS (eigenmodes) and each Di

is given by Di = (µ− λ−1i )+ , where µ is determined by water-filling to satisfy

the coalition power constraint tr[QS ] = tr[DS ] =∑

i Di = PS , and λi is the itheigenvalue of H†

S HS . Using [15], the resulting capacity, in a slot, for a coalitionS is

CS =K∑

i=1

(log (µλi))+ . (13.2)

To form the considered virtual MIMO coalitions and benefit from the capac-ity gains, the users need to exchange their data information and their channel(user-BS) information. For this purpose, we will consider a cost for informationexchange in terms of transmit power. This transmit power cost mainly mod-els the data exchange penalty. As we consider block fading channels with a longcoherence time, the additional power penalty for exchanging the user-BS channelinformation can be deemed as negligible relative to the data exchange cost, sincethe considered channel varies slowly (for example, exchange of the channel infor-mation can be done only periodically). Consequently, the cost for informationexchange is taken as the sum of the powers required by each user in a coalitionS to broadcast to its corresponding farthest user inside S. Due to the broadcastnature of the wireless channel, once a coalition member broadcasts its informa-tion to the farthest user, all the other members can also receive this informationsimultaneously. The power needed for broadcast between a user i ∈ S and itscorresponding farthest user i ∈ S is

Pi,i =ν0 · σ2

h2i,i

, (13.3)

where ν0 is a target average SNR for information exchange, σ2 is the noisevariance, and hi,i =

√κ/dµ

i,iis the channel gain between users i and i with di,i

the distance between users i and i. In consequence, the total power cost for a


coalition S having |S| users is given by PS as follows:

PS =|S |∑i=1

Pi,i . (13.4)

It is interesting to note that the defined cost depends on the location of the usersand the size of the coalition; hence, a higher power cost is incurred whenever thedistance between the users increases or the coalition size increases. Thus, theactual power constraint PS per coalition S with cost is

PS = (P − PS )+ , (13.5)

where P is the average power constraint per coalition (per slot), PS is the coop-eration power cost given in (13.4), and a+ max (a, 0). In order to achieve thecapacity in (13.2), within a slot, each user of a coalition S adjusts its power valuebased on the water-filling solution, taking into account the available power con-straint PS . Note that, since the power constraint P applied over a coalition is thesame as the maximum power constraint per individual user in the coalition, thewater-filling solution always yields a power value per user that does not violatethe user’s available power after deducing the cost for cooperation in (13.3) fromits individual long-term power constraint.

The considered power cost does not take into account the interference duringexchange of information between users and can be considered as a lower boundof the penalty incurred by cooperation. In addition to this power cost, a fractionof time may be required for the data exchange between the users prior to coop-eration. However, due to the fact that the power cost given in (13.4) depends ondistance and coalition size, the formed coalitions will typically consist of smallclusters of nearby users, and thus the users can exchange information at highrates rendering the time for data exchange negligible relative to the transmissiontime slot (typically, the distance between the users of a coalition and the BS islarger than the distance between the coalition users themselves). Furthermore,in practice, cooperating to form a virtual MIMO formation can require a syn-chronization at the carrier frequency between the nodes, yielding some costs forpractical implementation. In this chapter, we will not account for these carriersynchronization costs; however, this could constitute quite an interesting futuredirection. The coalition formation results derived in this chapter could also beapplied for other cost functions without loss of generality. For example, the costof power can be replaced by the cost of bandwidth where one could quantify theuse of an additional band for information exchange, orthogonal to the band oftransmission.

Given this benefit–cost tradeoff, the following subsections mainly deal with:(i) formulating a coalitional game among the users by defining an appropriatevalue function, and (ii) classifying and studying the properties of the game.


13.3.2 Distributed virtual MIMO coalition formation game

Coalition formation game formulationBy investigating the illustrative example in Figure 13.1, one can easily see that toform a virtual MIMO system a coalitional game can be defined with the playersset being the set N of all users. The next step is to define an appropriate value forthe game. For instance, based on the capacity benefit and power cost defined,respectively, in (13.2) and (13.5), over the TDMA time scale of N , for everycoalition S ⊆ N , the utility (value) function in characteristic form is defined as

v(S) =

|S| · CS , if PS > 0,

0, otherwise,(13.6)

where PS is given by (13.5), CS is given by (13.2), and |S| is the number of usersin S. This utility represents the total capacity achieved by coalition S duringthe time scale N while accounting for the cost through the power constraint. Acoalition of |S| users will transmit with capacity CS during |S| time slots, thusachieving a total sum-rate of v(S) during the time scale N (e.g., in Figure 13.1,during N = 6 coalition 2 consisting of two users achieves C2 in slot 4 and C2

in slot 6; thus a total of 2 · C2 during N = 6 slots). The second case in (13.6)implies that if the power for information exchange is larger than (or equal to)the available power constraint the coalition cannot be formed due to a utilityof 0.

By a close inspection of (13.6), one can immediately make the followingremark.

Remark 13.1 The virtual MIMO formation game can be formulated as an(N , v) coalitional game in characteristic form with transferable utility (TU).

For instance, it is easily seen that the value function in (13.6) depends onlyon the users inside S and, thus, the game is in characteristic form. Moreover,the utility in (13.6) represents the sum-rate achieved by coalition S, therefore,this sum-rate can be divided in any manner between the coalition members inorder to obtain the individual user payoff achieved. This individual user payoff,denoted φv

i , represents the total rate achieved by user i during the transmissiontime scale N . Due to the TU property of the game, the payoff φv

i of each user i

in a coalition S can be computed by a fair division of the utility v(S) throughvarious criteria such as proportional fair division, Shapley value (SV) division,egalitarian fair division, or max–min fair division using the nucleolus. In thischapter, we restrict ourselves to the proportional fair and SV divisions definedbelow (interested readers can see [6] for information on the other rules).

Proportional fairnessIn practice, a network user experiencing a good channel might not be willing tocooperate with a user with bad channel conditions unless the payoff it receives


takes into account its contribution to the coalition. To account for the channeldifferences, one can use the proportional fairness criterion, in which the extrabenefit from forming a coalition is divided in weights according to the users’noncooperative utilities. Thus,

φvi = wi

⎛⎝v(S)−∑j∈S

v(j)

⎞⎠+ v(i), (13.7)

where∑

i∈S wi = 1 and within the coalition wi/wj = v(i)/v(j). Thus,within the coalition for proportional fair division, the users with good channelconditions deserve more extra benefits than the users with bad channel condi-tions.

Shapley value (SV) fairnessAnother measure of fairness for payoff division can be done using the SV [1],defined as follows.

Definition 13.1 An SV φv is a function that assigns to each possible charac-teristic function v a vector of real numbers, i.e., φv = (φv

1 , φv2 , . . . , φv

N ), whereφv

i represents the worth or value of user i in the game (N , v). There are fourShapley axioms that φv must satisfy:

(1) efficiency axiom:∑

i∈N φvi = v(N );

(2) symmetry axiom: if user i and user j are subject to v(S ∪ i) = v(S ∪ j)for every coalition S not containing user i and user j, then φv

i = φvj ;

(3) dummy axiom: if user i is subject to v(S) = v(S ∪ i) for every coalitionS not containing i, then φv

i = 0;(4) additivity axiom: if u and v are characteristic functions, then φu+v =

φv+u = φu + φv .

It is shown [1] that there exists a unique function φv satisfying the Shapleyaxioms given by

φvi =

∑S⊆N−i

(|S|)!(N − |S| − 1)!N !

[v(S ∪ i)− v(S)]. (13.8)

The SV provides a fair division which takes into account the randomlyordered joining of the users in the coalition. Under the assumption of randomlyordered joining, the Shapley function of each user is its expected marginalcontribution when it joins the coalition [1]. In general, the SV is used ingames where the grand coalition, i.e., the coalition of all users, will form(such as in canonical games). However, whenever independent coalitions canform in the network such as in the virtual MIMO game (as will be seen laterin this section), given any coalition S, one can consider the payoff divisionby SV by applying (13.8) on each restricted game (S, v) in the network.In fact, it is shown in [16] that, in a game where a coalitional structure is


present (not just a single grand coalition), the SV of the whole game (N , v) isfound by using the SV on the game restricted to each coalition S in the structure.

Given the formulated (N , v) TU coalitional game for virtual MIMO formation,we investigate some of the properties of this game in order to map it into asuitable class of coalitional game theory. First, we investigate the property ofsuperadditivity defined as follows:

Definition 13.2 A coalitional game (N , v) with transferable utility is said to besuperadditive if for any two disjoint coalitions S1 , S2 ⊂ N , v(S1 ∪ S2) ≥ v(S1) +v(S2).

Theorem 13.1 The virtual MIMO formation (N ,v) coalitional game is non-superadditive.

The proof of this theorem can be found in [6]. Theorem 13.1 implies that, forthe virtual MIMO formation game, due to the cost for cooperation implies, when-ever the coalition grows, the total utility, i.e., sum-rate, that it generates maydecrease (depending on the users’ channels). For instance, the cost for infor-mation exchange grows with the size of the coalition as well as the distancebetween these users. Further, we define the following concepts of coalitional gametheory [1].

Definition 13.3 A payoff vector φv = (φv1 , . . . , φv

N ) for dividing the value v ofa coalition is said to be group rational or efficient if

∑Ni=1 φv

i = v(N ). A payoffvector φv is said to be individually rational if the player can obtain a benefitno less than acting alone, i.e., φv

i ≥ v(i),∀ i. An imputation is a payoff vectorsatisfying the above two conditions.

Definition 13.4 An imputation φv is said to be unstable through a coalitionS if v(S)>

∑i∈S φv

i , i.e., the players have an incentive to form coalition S andreject the proposed φv . The set C of stable imputations is called the core, i.e.,

C =

φv :

∑i∈N

φvi = v(N ) and

∑i∈S

φvi ≥ v(S) ∀ S ⊆ N

. (13.9)

A nonempty core means that the players have an incentive to form the grandcoalition.

Remark 13.2 In general, the core of the (N ,v) virtual MIMO formation gameis empty.

In the discussed model, the costs of cooperation for a coalition S increaseas the number of users in a coalition increases as well as when the distancesbetween the users increase, hence affecting the topology. In particular, considerthe grand coalition N of all N users in the network. This coalition consists of


a large number of users who are randomly located at different distances. Hence,the grand coalition will often have a value of v(N ) = 0 due to the cooperationcosts and several coalitions S ⊂ N have an incentive to deviate from this grandcoalition and form independent disjoint coalitions. Consequently, an imputationthat lies in the core cannot be found, and, due to cost, the core of the virtualMIMO formation (N ,v) game is generally empty.

Hence, as seen in Figure 13.1 and corroborated by the nonsuperadditivy ofthe game and the emptiness of the core, in general, due to the cost for coalitionformation, the grand coalition will not form. Instead, independent and disjointcoalitions appear in the network as a result of the virtual MIMO formationprocess. In this regard, the game is classified as a coalition formation game [3],and the objective is to find the coalitional structure that will form in the network,instead of finding only a solution concept, such as the core. Further, note thatone implication of the nonsuperadditivity of the game is that the SV might notbe individually rational, hence, any coalition formation algorithm that will beconstructed must handle this property with an appropriate coalition formationdecision. In the next section, we will devise an algorithm for coalition formationthat can take into account all these properties of the virtual MIMO coalitionformation game and that allows to characterize the network structure in thepresence of the users’ cooperative behavior.

Coalition formation algorithmCoalition formation has been a topic of great interest in game theory [2, 3, 17,18]. By using mathematical tools from coalition formation games, one can buildalgorithms to form coalitions dynamically among a group of players, and, thusthese algorithms can be applied in a distributed manner, notably in a wirelessscenario. To devise a suitable algorithm for virtual MIMO formation, severalconcepts from coalition formation games need to be defined as follows.

Definition 13.5 A collection of coalitions, denoted by S, is defined as the setS = S1 , . . . , Sl of mutually disjoint coalitions Si ⊂ N . In other words, a collec-tion is any arbitrary group of disjoint coalitions Si of N , not necessarily spanningall players of N . If the collection spans all the players of N ; i.e.,

⋃lj=1 Sj = N ,

the collection is a partition of N .

Definition 13.6 A preference operator or comparison relation is an orderdefined for comparing two collections R = R1 , . . . , Rl and S = S1 , . . . , Spthat are partitions of the same subset A ⊆ N (i.e., same players in R and S).Therefore, R S implies that the way R partitions A is preferred to the way Spartitions A.

Various well-known orders can be used as comparison relations in differentscenarios [3]. For the virtual MIMO coalition formation game, we define thefollowing order.


Definition 13.7 Consider two collections R = R1 , . . . , Rl and S =S1 , . . . , Sm that are partitions of the same subset A ⊆ N (same players inR and S). For a collection R = R1 , . . . , Rl, let the utility of a player j in acoalition Rj ∈ R be denoted by φv

j (R). Then R is preferred over S by Paretoorder, written as R S, iff

R S ⇐⇒ φvj (R) ≥ φv

j (S) ∀ j ∈ R,Swith at least one strict inequality (>) for a player k. (13.10)

In other words, a collection is preferred by the players over another collection,if at least one player is able to improve its payoff without hurting the otherplayers. Subsequently, to perform autonomous coalition formation between theusers in the wireless network, we construct a distributed algorithm based on twosimple rules denoted as “merge” and “split” [17] defined as follows.

Definition 13.8 Merge rule Merge any set of coalitions S1 , . . . , Sl wheneverthe merged form is preferred by the players, i.e., where

l⋃

j=1

Sj S1 , . . . , Sl.

Therefore, S1 , . . . , Sl → ⋃l

j=1 Sj.

Definition 13.9 Split rule Split any coalition⋃l

j=1 Sj whenever a split formis preferred by the players, i.e., where

S1 , . . . , Sl l⋃

j=1

Sj.

Thus, ⋃l

j=1 Sj → S1 , . . . , Sl.

In brief, multiple coalitions will merge (split) if merging (splitting) yields apreferred collection based on the Pareto order. Thus, coalitions will merge onlyif at least one user can enhance its individual payoff through this merge withoutdecreasing the other users’ payoffs. Similarly, a coalition will split only if at leastone user in that coalition is able to strictly improve its individual payoff throughthe split without hurting other users. A decision to merge or split is thus tied tothe fact that all users must benefit from the merge or split, therefore any merged(or split) form is reached only if it allows all involved users to maintain theirpayoffs with at least one user improving. In summary, using merge and split onecan devise a coalition formation algorithm with partially reversible agreements[2], where the users sign a binding agreement to form a coalition through themerge operation (if all users are able to improve their individual payoffs fromthe previous state) and they can only split this coalition if splitting does notdecrease the payoff of any coalition member (partial reversibility).


For the virtual MIMO formation game, the coalition formation algorithm con-sists of two phases: adaptive coalition formation and transmission. In the adap-tive coalition formation phase, an iteration of sequential merge-and-split rulesis performed until a final network partition composed of independent disjointcoalitions is obtained. In the transmission phase, the formed coalitions trans-mit in their corresponding slots in a TDMA manner. The transmission phasemay occur several times prior to the repetition of the coalition formation phase,notably in a low-mobility environment where changes in the coalition structuredue to mobility seldomly occur.

Although any arbitrary merge process can be used, we consider a distributedcost-based merge procedure allowing the coalitions (users) to perform a localsearch for partners. Consequently, the decision to merge with neighboring coali-tions is taken based on the Pareto order proceeding from the partner that pro-vides the lowest cost. In order for coalition S1 to merge with another coali-tion S2 , the utility of the formed coalition through merge must be positive; i.e.,v(S1 ∪ S2) > 0 otherwise no benefits exist for the merge. Thus, based on thedefined power cost (13.4) and utility (13.6), coalitions can only merge when thecost for cooperation is less than P . Otherwise, when the cost is greater than orequal P , through (13.6) the utility of the merged coalition will be 0 and there isno mutual benefit. Thus, using (13.4) the merge is possible (nonzero utility) forS1 with S2 if PS1 ∪S2 < P , i.e.,

∑|S1 ∪S2 |i=1 Pi,i < P , which, by (13.3), yields

|S1 ∪S2 |∑i=1

1dµ

i,i

<P

ν0 · σ2 · κ. (13.11)

Thus, a coalition will only attempt to merge with other coalitions where (13.11)can be verified.

Each stage of the coalition formation algorithm starts from an initial networkpartition T = T1 , . . . , Tl of N . In this partition, any random coalition (user)can start with the merge process. For implementation purposes, assume that thecoalition Ti ∈ T which has the highest utility in the initial partition T starts themerge by attempting to cooperate with the coalition yielding the lowest cost.On one hand, if merging occurs, a new coalition Ti is formed and, in its turn,coalition Ti will attempt to merge with the lowest-cost partner. On the otherhand, if Ti were unable to merge with the lowest-cost coalition, it would try thenext lowest-cost partner, proceeding sequentially through the coalitions verifying(13.11). The search ends with a final merged coalition Tfinal

i composed of Ti andone or more of the coalitions in its vicinity (or just Ti , if no merge occurred).The algorithm is repeated for the remaining Ti ∈ T until all the coalitions havemade their local merge decisions, resulting in a final partition W. The coalitionsin the resulting partition W are next subject to split operations, if any are pos-sible. An iteration consisting of multiple successive merge-and-split operationsis repeated. As shown in [17], any arbitrary sequence of merge-and-split ruleswill terminate, and, thus, the convergence of the first phase of the algorithm is


Table 13.1. One stage of the merge-and-split coalition formation algorithm

Initial state

The network is partitioned by T = T1 , . . . , Tk (at the beginningof all time T = N = 1, . . . , N with non-cooperative users).

Coalition formation algorithm

Phase I Adaptive coalition formation:Coalition formation using merge-and-split occurs.

repeat

(a) Coalitions begin the local search merge operation:W = Merge(T ).

(b) Coalitions in W decide to split based on the Pareto order.T = Split(W).

until merge-and-split iteration terminates.Phase II Virtual MIMO transmission:

The coalitions transmit during the time scale N with 1 coalitionper slot with each coalition occupying all the time slotspreviously held by its members.

The algorithm is repeated periodically, enabling the users toautonomously self-organize and adapt the topology to environ-mental changes such as mobility.

always guaranteed. Table 13.1 shows a summary of one round of the coalitionformation algorithm. For networks where the environment is changing, e.g., dueto mobility, the algorithm in Table 13.1 can be repeated periodically in order toadapt the network structure to the environmental changes.

The result of the algorithm in Table 13.1 is a network partition composedof disjoint independent coalitions. First and foremost, one would note that, inthe final network structure, due to convergence, no coalition has an incentiveto pursue any further merge or split procedure. Thus, the resulting networkstructure is merge-and-split stable in the sense that no coalition has an incentiveto deviate from this structure through merge or split rules. This stability ofthe resulting network partition can be further investigated with respect to theconcept of a defection function D [17].

Definition 13.10 A defection function D is a function which associates witheach partition T of N a family (group) of collections in N . A partition T =T1 , . . . , Tl of N is D-stable if no group of players is interested in leaving Twhen the players who wish to leave can only form the collections allowed by D.


The most important defection function is the Dc(T ) function (denoted Dc)which associates with each partition T of N the family of all collections in N .This function allows any group of players to leave the partition T of N throughany operation and create an arbitrary collection in N . From the Dc function onecan define a strong stability concept.

Definition 13.11 A partition T of the players’ set N is said to be Dc -stable, ifno players in T are interested in leaving T to form other collections in N .

For instance, whenever a Dc -stable partition exists for a given coalitional game,this partition possesses the following properties:

(1) If it exists, a Dc -stable partition is the unique outcome of any arbitraryiteration of merge and split.

(2) A Dc -stable partition T is a unique -maximal partition, i.e., for all parti-tions T ′ = T of N , T T ′. In the case where represents the Pareto order,this implies that the Dc -stable partition T is the partition that presents aPareto optimal payoff distribution for all the players.

Clearly, a Dc -stable partition is an optimal partition that the wireless networkcan seek as it provides a payoff distribution that is Pareto optimal for all userswith respect to any other network partition. In addition, this partition is a uniqueoutcome of any arbitrary iteration of merge-and-split rules.

However, the existence of a Dc -stable partition is not always guaranteed [17].The Dc -stable partition T = T1 , . . . , Tl of the whole space N exists if a parti-tion of N verifies two necessary and sufficient conditions [17]:

(1) For each i ∈ 1, . . . , l and each pair of disjoint coalitions A and B suchthat A ∪B ⊆ Ti we have A ∪B A,B (referred to as cond. (A)hereafter).

(2) For the partition T = T1 , . . . , Tl a coalition S ⊂ N formed of playersbelonging to different Ti ∈ T is T -incompatible if for no i ∈ 1, . . . , l wehave S ⊂ Ti . Dc -stability requires that for all T -incompatible coalitionsS[T ] S, where S[T ] = S ∩ Ti ∀ i ∈ 1, . . . , l is the projection ofcoalition S in partition T (referred to as cond. (B) hereafter).

If no partition of N can satisfy these conditions, then no Dc -stable partitionof N exists. Since the Dc -stable partition is a unique outcome of any arbitrarymerge-and-split iteration, we have

Lemma 13.1 For the (N , v) virtual MIMO coalition formation game, the merge-and-split algorithm of Table 13.1 converges to the optimal Dc-stable partition, ifsuch a partition exists. Otherwise, the algorithm yields a final network partitionthat is merge-and-split proof.


In the transmitter cooperation game, the existence of a Dc -stable partitiondepends on various factors. For instance, cond. (A) states that, for a Dc -stablepartition T , every coalition Ti ∈ T must verify the Pareto order not only at thelevel of the whole coalition Ti but also at the level of all disjoint coalitions subsetsof Ti . Verifying the Pareto order requires that the utility of every union of anytwo disjoint coalitions subsets of a coalition Ti must yield an extra utility over thedisjoint case; i.e., v(A ∪B) > v(A) + v(B) ∀ A,B ⊂ Ti . In an ideal case with nocost, as the number of transmit antennas is increased for a fixed power constraint,the overall system diversity increases as the data pass through different channelvalues allowing, with adequate coding, the symbols to be recovered without errorat a higher rate [19]. In such a case, since A ∪B has a larger number of antennasthan A and B, ∀ A,B ⊂ Ti and for each Ti we have CA∪B > max (CA,CB ) andthus

|A ∪B| ·CA∪B>|A| ·max (CA,CB ) + |B| ·max (CA,CB ),(13.12)

|A ∪B| · CA∪B>|A| · CA+|B| · CB ⇔ v(A ∪B)>v(A)+v(B),

which is sufficient to verify cond. (A) for Dc -stability when adequate payoff divi-sions are done. However, due to the cost CA∪B ,CA and CB can have differentpower constraints and (13.12) may not be guaranteed ∀A,B ⊂ Ti . Guaranteeingthis condition is directly dependent on the cooperation cost within the coalitionsin T and, thus, on the users’ location. In practical networks, verifying cond. (A)for Dc -stability depends on the users’ random locations.

Cond. (B) for the existence of a Dc -stable partition T is that players formedfrom different Ti ∈ T have no incentive to form a coalition S outside of T . Inthe transmitter cooperation game, cond. (B) is also dependent on the location ofthe coalitions Ti ∈ T ; specifically on the distance between the users in differentcoalitions Ti ∈ T . Thus, cond. (B) is verified whenever two users belonging todifferent coalitions in a partition T are separated by a large distance. A sufficientcondition for verifying this second requirement can be derived.

Theorem 13.2 For a network partition T = T1 , . . . , Tl resulting from thecoalition formation algorithm, if the distance di,j between any two users i ∈ Ti

and j ∈ Tj with Ti = Tj verifies di,j >(κ · P /2 · ν0 · σ2

) 1µ

= d0 , then the secondcondition for Dc stability, cond. (B), is verified.

Proof. Since a Dc -stable partition is a unique outcome of any merge-and-splititeration, we will consider the partition T = T1 , . . . , Tl resulting from anymerge-and-split iteration in order to show when cond. (B) can be satisfied.A T -incompatible coalition is a coalition formed from users belonging to dif-ferent Ti ∈ T . Consider the T -incompatible coalition i, j that can poten-tially form between two users i ∈ Ti and j ∈ Tj with Ti = Tj . The total powercost for i, j is given by (13.3) as Pi,j = Pi,j + Pj,i = 2 · Pi,j . In the casewhere the total power cost is larger than the constraint, we have Pi,j ≥ P


and thus Pi,j ≥ P /2 which yields the required condition on distance di,j ≥(κ · P /2 · ν0 · σ2)

1µ = d0 . We have by (13.6) v(i, j) = 0, and, thus, φv

i (i, j) =φv

j (i, j) = 0. Or we have that i, j[T ] = i, j ∩ Tk ∀ k ∈ 1, . . . , l =i, j, and, thus, φv

i (i, j[T ]) = v(i) > φvi (i, j) = 0 and φv

j (i, j[T ]) =v(j) > φv

j (i, j) = 0. Consequently, i, j[T ] i, j and cond. (B) is verifiedfor any T -incompatible coalition formed of two users. Moreover, when any twousers i ∈ Ti and j ∈ Tj with Ti = Tj are separated by d0 , T -incompatible coali-tions S with |S| > 2 have a cost PS > Pi,j ≥ P and thus v(S) = 0; yieldingS[T ] S for all T -incompatible coalitions S. Hence, when any two users in thenetwork partition T resulting from merge and split are separated by a distancelarger than d0 , then cond. (B) for Dc stability existence is verified.

In summary, the existence of the Dc -stable partition is closely tied to the users’location, which is a random parameter in practical networks. However, whensuch a partition does exist, the network resulting from the coalition formationalgorithm will converge to that Dc -stable partition as per Lemma 13.1.

The algorithm in Table 13.1 can be implemented in a distributed way. As theuser can detect the strength of other users’ uplink signals (through techniquessimilar to those used in the ad-hoc routing discovery), nearby coalitions canbe discovered and the local merge algorithm performed. Each coalition surveysneighboring coalitions satisfying (13.11) and attempts to merge based on thePareto order. The users in a coalition need only to know the maximum distanceswith respect to the users in neighboring coalitions. Moreover, each formed coali-tion internally decides to split if its members find a split form by Pareto order.By using a control channel, the distributed users can exchange some channelinformation and then cooperate using our model (exchange data information ifneeded, form a coalition then transmit). Signaling for this handshaking can beminimal.

Numerical resultsTo assess the performance of coalition formation for distributed virtual MIMO,we set up a single-cell composed of a single BS with K = 3 equally spaced anten-nas located at the center of a square of 4 km× 4 km. Without loss of gener-ality, at the receiver, we consider antennas that are separated enough while3

Φi,k = 0 ∀i, k. The propagation loss is set to µ = 3 and the path-loss constantκ = 1. The power constraint per slot is P = 10 mW, the cost SNR target forinformation exchange is ν0 = 10 dB, and noise level is −90 dBm.

First, we set up a network with N = 10 users where the users are located ina way that a Dc -stable partition exists. Figure 13.2 shows that the coalition

3 This choice provides a lower bound on the performance gain of the coalition formationalgorithm (i.e., the gains mainly stemming from the transmitters cooperation which is themain objective of this section); considering different phases certainly yields an additionalmultiplexing gain and it does not affect the analysis or the results hereafter.


Figure 13.2. Convergence of the algorithm to a final Dc -stable partition.

formation algorithm converges to the final Dc -stable network partition T =T1 , . . . , T5 (valid for both proportional fair and SV fairness criteria). Cond.(A) for Dc -stability is easily verified for coalitions consisting of at most twousers since such coalitions do not form unless the Pareto order is internally ver-ified (definition of the merge rule). For the three-users coalition T2 = 7, 9, 10Table 13.2 shows the payoffs of the different subcoalitions for both fairness types.Table 13.2 shows that the Pareto order is internally verified for T2 , that is∀A,B ⊂ T2 ; A ∪B A,B for all fairness cases. In addition, by inspectingFigure 13.2 it is clear that any two users belonging to T -incompatible coali-tions are separated by a distance larger than the maximum distance, whichis d0 = 0.793 km, computed using Theorem 13.2 for the simulation parame-ters. Thus, Theorem 13.2 is satisfied and cond. (B) is verified. For example,for the T -incompatible coalition S = 4, 7 equation (13.6) yields v(S) = 0 andthus φv

4 (S) = φv7 (S) = 0 due to the distance between users 4 and 7. The projec-

tion of S in T is S[T ] = 4, 7 ∩ T1 , 4, 7 ∩ T2 , 4, 7 ∩ T3 , 4, 7 ∩ T4 , 4, 7 ∩T5 , 4, 7 ∩ T6 = 4, 7. In S[T ], the payoffs of users 4 and 7 are respec-tively φv

4 (S[T ]) = v(4) = 7.6069 and φv7 (S[T ]) = v(7) = 3.1077, by Pareto

order φv4 (S[T ]) > φv

4 (S) and φv7 (S[T ]) > φv

7 (S), thus, S[T ] S.In Figure 13.3, we show the average total individual user payoff (rate) improve-

ment achieved during the whole transmission time scale as a function of thenetwork size. This result is averaged over the random locations of the users.We compare the performance of the coalition formation algorithm to that of


Table 13.2. Payoffs for coalition T2 = 7, 9, 10 of Figure 13.2 and itssub-coalitions

Proportional fair Shapley

User 7 User 9 User 10 User 7 User 9 User 10

7 3.1077 3.10779 2.7173 2.717310 2.7345 2.73457, 9 4.0416 3.5338 3.9829 3.59257, 10 4.0648 3.5779 4.7863 4.44069, 10 3.6206 3.5967 3.5996 3.6177

T2 = 7, 9, 10 4.6431 4.0869 4.0598 4.5210 4.1558 4.1131

Figure 13.3. Cooperation gains in terms of the average individual user payoffachieved by the merge-and-split scheme during the whole transmission durationcompared with the noncooperative case and the centralized optimal solution fordifferent network sizes and different fairness criteria.

the noncooperative case as well as the optimal partition found by a centralizedentity through exhaustive search. For the cooperative case, the average user’spayoff increases with the number of users N since the possibility of finding coop-erating partners increases. In contrast, the noncooperative approach presents an


fairSV

Figure 13.4. Frequency of merge-and-split operations per minute for differentspeeds in a mobile network of Mt = 50 users.

almost constant performance with different network sizes. Cooperation presentsa significant advantage over the noncooperative case in terms of average individ-ual utility for all fairness types, and this advantage increases with the networksize. The proportional fair division presents the best performance, as it allowsan improvement of up to 40.42% over the noncooperative case at N = 100. Thisresult also highlights the tradeoff between fairness and cooperation gains. Forinstance, while the proportional fairness presents an advantage in terms of pay-off gain, since it allows larger coalitions to form (due to it being less strict infairness than the SV), the SV presents lower gains but more fairness in allocat-ing payoffs. Furthermore, compared to the optimal solution, the merge-and-splitalgorithm achieves a highly comparable performance with a performance loss notexceeding 1% at N = 20 users. This clearly shows that, by using the distributedmerge-and-split algorithm, the network can achieve a performance that is veryclose to optimal. Note that, for more than 20 users, finding the optimal partitionby exhaustive search is mathematically and computationally intractable.

To show how the coalition formation algorithm can handle mobility, we deploya network of N = 50 mobile users (random walk mobility model) for a period of5 minutes. For N = 50, each TDMA transmission requires 50× θ seconds with θ

the slot duration (we let θ = 10 ms). The results in terms of frequency of merge-and-split operations per minute are shown in Figure 13.4 for various speeds. Asthe speed increases, for both fairness types, the number of merge-and-split oper-ations increases due to the changes in the network structure incurred by mobil-ity. Fairness types that potentially yield large coalitions, such as proportional


fair, incur a higher frequency of merge and split since such coalitions requireadditional merge operations and are more prone to splitting due to mobility. Incontrast, strict fairness criteria, such as the SV, yield relatively lower frequencyof merge and split. In a nutshell, Figure 13.4 demonstrates that, by periodic runsof the coalition formation algorithm and through adequate merge-and-split deci-sions, the users can self-organize and adapt to the changes in the environment.

13.4 Coalitional graph game among relay stations

In this section the challenges of deploying relay stations in next generation wire-less systems are studied. For this purpose, we examine the use of coalitionalgraph games for modeling the interactions among the relay stations seeking tosend data in the uplink of a wireless system. First, we motivate the problem andprovide a suitable system model. Then, we formulate a network formation gameamong the relay stations, investigate the resulting graph structure, and studytheir properties.

13.4.1 Motivation and basic problem

In order to mitigate the fading effects of the wireless channel, several nodes orrelays can cooperate with a given source node in the transmission of its data toa far away destination, thereby, providing spatial diversity gains for the sourcenode. By doing so, one can significantly improve the performance of the sourcenode. This class of cooperation is commonly referred to as cooperative com-munications [20]. It has been shown that by using one or more relays [19–21]a significant improvement can be obtained in terms of BER, throughput, orother quality of service (QoS) parameters. Moreover, different aspects of coop-erative transmission have been discussed in the literature such as performanceanalysis and resource allocation [19–21]. Due to this proven advantage of cooper-ative communications, a key feature in next generation wireless systems, such as3GPP’s long-term evolution advanced (LTE-Advanced) [22], or the forthcomingIEEE 802.16j WiMAX standard [23], is the introduction of the relay station (RS)nodes which can enable relaying in the network.

Deploying RSs in a wireless system faces several challenging issues. Forinstance, as they are deployed in the network, the RSs need to route, amongthem, different packets received from external mobile stations using advancedtechniques such as cooperative transmission. Due to the presence of RSs, thearchitecture of next generation wireless networks is governed by a multihop net-work structure formed between the RSs and their serving BS. Consequently, oneprominent challenge is the design and study of the network multihop architecturethat will connect the BS to the RSs in its coverage area given the cooperativestrategies of the RSs and the existing network traffic.

Thus, consider the uplink of a wireless system with M RSs (fixed, mobile,or nomadic) under the coverage area of a single BS. The RSs transmit their

13.4 Coalitional graph game among relay stations 369

data in the uplink to the BS through multihop links, and, therefore, a treearchitecture needs to form, in the uplink, between the RSs and their servingBS. Once the uplink tree is formed, mobile stations (MSs) can hook up to thenetwork by selecting a serving RS (or directly connecting to the BS). Each MSis assigned to the closest RS. We consider that the MSs deposit their packets totheir serving RSs using direct transmission. In their turn, the serving RSs actas source nodes transmitting the received MS packets to the BS through one ormore hops in the formed tree, using cooperative transmission. This assumption ofdirect transmission between MS and RS allows the provision of a tree formationalgorithm that can be easily incorporated in a new or existing wireless networkwithout relying on external entities such as the MSs.

For cooperative transmission between the RSs and the BS, the decoded relay-ing multihop diversity channel of [21] is considered whereby each intermediatenode on the path between a transmitting RS and the BS combines, encodes,and reencodes the received signal from all preceding terminals before relaying(decode-and-forward relaying). Formally, each MS k in the network is consideredas a source of traffic following a Poisson distribution with an average arrival rateλk . With such Poisson streams at the entry points of the network (the MSs),we assume that for every RS incoming packets are stored and transmitted ina first-in first-out (FIFO) fashion and that we have Kleinrock’s independenceapproximation [24, Chap. 3] with each RS being an M/D/1 queueing system.With this approximation, the generation of the total traffic that RS i receivesfrom the MS that it is serving is a Poisson process with an average arrival rateof Λi =

∑Li

l=1 λl , where Li is the number of MSs served by RS i. Moreover, RS i

also receives packets from RSs that are connected to it with a total average rate∆i . For these ∆i packets, the sole role of RS i is to relay them to the next hop.In addition, any RS i that has no assigned MSs (Li = 0, Λi = 0, and ∆i = 0),transmits “HELLO” packets, generated with a Poisson arrival rate of η0 in orderto keep its link to the BS active during periods of no actual MS traffic. Anillustrative example of this model is shown in Figure 13.5.

The main objective in this section is to provide a distributed algorithm thatallows the RSs in a wireless system to autonomously form the uplink tree struc-ture such as in Figure 13.5, adapting it to environmental changes as the networkevolves. Further, another key goal is to model the gains in terms of coopera-tive transmission, while accounting for the costs in terms of the buffering andtransmission delay incurred by the multihop transmission. In this context, theremainder of this section is dedicated to providing an accurate model for theuplink tree formation problem.

13.4.2 A network formation game among relay stations

Game formulationTo model the interactions among the RSs seeking to form the uplink networkstructure, we refer to coalitional graph games [3] which is a class of coalitional


Figure 13.5. A prototype of the uplink tree model that governs the networkarchitecture of next generation wireless systems.

game theory that deals with the formation of network graphs among a numberof nodes seeking to cooperate. In particular, for the RSs game, we utilize asubclass of coalitional graph games known as network formation games. Forinstance, network formation games are a hybrid class of games that combineconcepts from both cooperative and noncooperative game theory [3, 18, 25]. Insuch games, several independent decision makers (players) interact in order toform a network graph among them. Depending on the goals of each player, afinal network graph G, resulting from individual players’ decisions, forms. Wemodel the uplink tree formation problem among the RSs as a network formationgame with the RSs being the players. The result of the interactions among theRSs is a directed graph G(V, E) with V = 1, . . . , M + 1 denoting the set of allvertices (M RSs and the BS) and E denoting the set of all edges (links) betweenpairs of RSs. Each link between two RSs i and j, denoted (i, j) ∈ E , correspondsto an uplink traffic flow between RS i and RS j. First and foremost, we definethe notion of a path:

Definition 13.12 A path between two nodes i and j in the graph G is definedas a sequence of nodes i1 , . . . , iK such that i1 = i, iK = j and each directed link(ik , ik+1) ∈ G for each k ∈ 1, . . . ,K − 1.

This section considers solely multihop tree (or forest, if some parts of the graphare disconnected) architectures, since such architectures are ubiquitous in next


generation networks [22, 23]. In this regard, throughout the remainder of thissection we adopt the following convention.

Remark 13.3 Each RS i is connected to the BS through at most one path,and, thus, we denote by qi the path between any RS i and the BS whenever thispath exists.

Further, we delineate the possible actions or strategies that each RS can takein the network formation game. The strategy space of each RS i consists of theRSs (or the BS) to which i wants to connect. Consequently, the strategy of RS i

is to select the link that it wants to form from the available strategy space. Wenote that RS i cannot connect to RS j, which is already connected to i, in thesense that if (j, i) ∈ G, then (i, j) /∈ G. Formally, for a current network graph G,let Ai = j ∈ V \ i|(j, i) ∈ G be the set of RSs from which RS i accepted alink (j, i), and Si = (i, j)|j ∈ V \ (i

⋃Ai) as the set of links corresponding

to the nodes (RSs or the BS) with whom i wants to connect (note that i cannotconnect to RSs that are already connected to it, i.e., RSs in Ai .). Consequently,the strategy of RS i is to select the link si ∈ Si that it wants to form, i.e., choosethe RS to which it will connect. Based on Remark 13.3, an RS can be connectedto at most one other node in our game so choosing to form a link si implicitlyimplies that RS i will replace its previously connected link (if any) with the newlink si .

Having modeled the tree formation problem as a network formation game,we introduce a utility function that takes into account the QoS in terms of thepacket success rate (PSR) as well as the delay incurred by multihop transmission.Consider an actual network tree graph G where each RS extracts a positiveutility from the packets successfully transmitted to the BS out of the packetsreceived from the MSs. Each transmitted packet is subject to a BER due tothe transmission over the wireless channel using one or more hops. For example,for a transmission between RS V1 ∈ V and destination Vn+1 (the destinaton isalways the BS) going through n− 1 intermediate relays V2 , . . . , Vn ⊂ V , letNr be the set of all receiving terminals, i.e., Nr = V2 . . . Vn+1 and Nr(i) bethe set of terminals that transmit a signal received by a node Vi . Hence, for arelay Vi on the path from the source V1 to the destination Vn+1, we have Nr(i) =V1 , . . . , Vi−1. Given this notation, the BER between a source RS V1 ∈ V andthe destination Vn+1 = BS is computed along the path qV1 = V1 , . . . , BS usingthe tight upper bound given in [21, Eq. (10)] for the decoded relaying multihopdiversity channel with BPSK modulation and Rayleigh fading as follows:

PeqV 1≤

∑Ni ∈Nr

12

⎛⎜⎜⎝ ∑Nk ∈Nr ( i )

⎡⎢⎢⎣ ∏Nj ∈Nr ( i )

N j = N k

γk,i

γk,i − γj,i×(

1−√

γk,i

γk,i + 2

)⎤⎥⎥⎦⎞⎟⎟⎠ .

(13.13)


Here, γi,j = Pi · gi,j /σ2 is the average received SNR at node j from node i,where Pi is the transmit power of node i, σ2 the noise variance, and gi,j =1/dµ

i,j is the path-loss with di,j the distance between i and j and µ the path-lossexponent. Without loss of generality, we assume that all the RSs transmit withequal power Pi = P , ∀i. Finally, for RS i which is connected to the BS througha direct transmission path qd

i ∈ Qi with no intermediate hops, the BER is givenby Pe

qdi

= 12

(1−√

γi,BS /(1 + γi,BS ))

[21], where γi,BS is the SNR at the BSfor transmission from RS i. Using the BER expression in (13.13) and with nochannel coding, the PSR ρi,qi

perceived by RS i over a path qi is defined asfollows:

ρi,qi(G) = (1− Pe

qi)B , (13.14)

where B is the number of bits per packet. The PSR is a function of the networkgraph G as the path qi varies depending on how RS i is connected to the BS inthe formed network tree structure.

Transmitting over multihop links incurs a significant delay due to bufferingand multiple transmissions. For this purpose, we consider the average delay τi,qi

along the path qi = i1 , . . . , ik from RS i1 = i to the BS. A measure of theaverage delay over qi in a network with Poisson arrivals at the entry points andconsidering the Kleinrock approximation as in the previous section (each RS isan M/D/1 queueing system) is given by [24, Chap. 3, eqs. (3.42), (3.45), and(3.93)]

τi,qi(G)=

∑(ik ,ik + 1 )∈qi

(Ψik ,ik + 1

2µik ,ik + 1 (µik ,ik + 1 −Ψik ,ik + 1 )+

1µik ,ik + 1

), (13.15)

where Ψik ,ik + 1 = Λik+ ∆ik

is the total traffic (packets/s) originating from MSs(Λik

) and from RSs (∆ik) traversing link (ik , ik+1) ∈ qi between RS ik and RS

ik+1. The ratio 1/µik ,ik + 1 represents the average transmission time (service time)on link (ik , ik+1) ∈ qi with µik ,ik + 1 being the service rate on link (ik , ik+1). Thisservice rate is given by µik ,ik + 1 = Cik ,ik + 1 /B where

Cik ,ik + 1 = W log (1 + νik ,ik + 1 ) (13.16)

is the capacity of the direct transmission between RS ik and RS ik+1, νik ,ik + 1 =P gik ,ik + 1 /σ2 is the received SNR from RS ik at RS ik+1, and W is the bandwidthavailable for RS ik which is assumed the same for all RSs in the set of vertices V,without loss of generality. Similarly to the PSR, the delay depends on the pathsfrom the RSs to the BS, hence is a function of the network graph G.

For VoIP services, given the delay and the PSR, an appropriate utility func-tion can be defined through the concept of the R-factor [26]. The R-factoris an expression that links the delay and packet loss to the voice quality as


follows [26]:

Ui(G) = Ωa − ε1τi,qi(G)− ε2(τi,qi

(G)− ε3)H − υ1

−υ2 ln (1 + 100υ3(1− ρi,qi(G))), (13.17)

where τi,qiis the delay given by (13.15) expressed in milliseconds, 100(1− ρi,qi

)represents the packet-loss percentage (we consider only the packet loss due toerrors through ρi,qi

in (13.14), ignoring packet loss due to overloaded links). Theremaining parameters are constants defined as follows: Ωa = 94.2, ε1 = 0.024,ε2 = 0.11, ε3 = 177.3, H = 0 if τi,qi

< ε3 , H = 1 otherwise. The parameters υ1 ,υ2 , and υ3 depend on the voice speech codec. The relationship between theR-factor and the VoIP service quality is such that as the R-factor increases,the voice quality improves. For different voice codecs, different R-factor rangesprovide an indication of the voice quality varying through poor, low, medium,high to best as the R-factor increases [26]. For example, for certain speech codecsas the R-factor increases in steps of 10 from 50 to 100, the voice quality is poor,low, medium, high and best, respectively [26].

Although the RSs are the players of the game, in the final results the perfor-mance of the MSs must be assessed in terms of the R-factor achieved (consideredas MS utility). To compute the R-factor of the MSs, the PSR, and the delay forthe whole transmission from MS to BS must be considered. For instance, thePSR perceived by each MS i served by RS j is given by

ζi,j (G) = ρi,ij · ρj,qj(G), (13.18)

where ρi,ij is the PSR on the direct transmission between MS i and RS j (inde-pendent of network graph G) and ρj,qj

(G) is the PSR from RS j to the BSalong path qj given by (13.14) (which can be either a multihop transmission ora direct transmission depending on how RS j is connected in the tree graph G).Moreover, the delay perceived by an MS i served by RS j is given by (13.15) bytaking into account, in addition to the delay on the path qj , the traffic on thelink (i, j) between the MS and the RS, i.e., the buffering and transmission delayat the MS level. Having the PSR given by (13.18) and the delay, the utilities ofthe MSs can be computed for performance assessment.

Network formation algorithmHaving formulated a network formation game between the RSs, the next stepis to define an algorithm of interaction between the RSs in order to form thedesired network graph. For the RSs game, prior to providing a network formationalgorithm, we first highlight that any such algorithm will result in a connectedtree structure, as follows:

Proposition 13.1 Any network graph G resulting from a network formationalgorithm applied to the RSs network formation game is a connected directedtree structure rooted at the BS.


The proof of this property can be found in [27]. Briefly, due to the high discon-nection cost, if an RS is unable to find any partner suitable for forming a link, itwill connect to the BS through direct transmission. Thus, the network initiallystarts with all the RSs connected to the BS (star topology), before engaging inthe network formation game.

Let Gsi ,s−idenote the graph G formed when RS i plays a strategy si ∈ Si while

all other RSs maintain their vector of strategies s−i = [s1 , . . . , si−1 , si+1 , . . . , sM ].We define the best response for an RS as follows [25].

Definition 13.13 A strategy s∗i ∈ Si is a best response for RS i ∈ V ifUi(Gs∗i ,s−i

) ≥ Ui(Gsi ,s−i), ∀si ∈ Si . Thus, the best response for RS i is to make

the selection of the link that maximizes its utility given that the other RSsmaintain their vector of strategies.

By using the different properties of the RS network formation game, one canbuild a best response-based algorithm that allows a distributed formation of thenetwork graph. In this algorithm, the RSs are assumed to be myopic in the sensethat the RSs aim at improving their payoff considering only the current stateof the network without taking into account the future evolution of the network.Finding an optimal network formation algorithm is a very complex problem,and no strict rules exist for doing so in the literature [18, 25]. Therefore, for eachnetwork formation game model, different operations must be applied suited tothe model considered. Network formation literature encompasses several myopicdynamics for various game models with directed and undirected graphs [18, 25].Inspired by [18] and [25], an algorithm composed of several rounds is constructed.In this algorithm, each round consists mainly of two phases: a fair prioritizationphase and a myopic network formation phase. In the fair prioritization phase,we consider a priority function that assigns a priority to each RS. In the myopicnetwork formation phase, by increasing priority, the RSs are allowed to interact.

Therefore, each round of the network formation algorithm begins with thefair prioritization phase where each RS is assigned a priority depending on itsactual perceived BER: RSs with a higher BER are assigned a higher priority.The motivation behind this procedure is to allow RSs that are perceiving a badchannel fairly to possess an advantage in selecting their partners for the purposeof improving their BER. Thus, the RSs experiencing a high BER can select theirpartners out of a larger space of strategies during the dynamics phase. Otherpriority functions can also be used, and in a general case, a random priorityfunction can be defined. Following prioritization, the RSs start selecting theirstrategies sequentially in order of priority. During its turn, each RS i choosesto play its best response s∗i ∈ Si in order to maximize its utility at each roundgiven the current network graph resulting from the strategies of the other RSs.The best response of each RS can be seen as a replace operation, whereby theRS will replace its current link to the BS with another link that maximizes itsutility (if such a link is available).


Table 13.3. One round of the RSs network formation algorithm

Initial state

All the RSs start by directly connecting to the BS in a star topology.Two phases in each round of network formation

Phase 1 Fair prioritization:Prioritize the RSs from the highest to the lowest current BER.

Phase 2 Myopic network formation:The RSs take action sequentially by priority.

Each RS i plays its best response s∗i , maximizing itsutility (R-factor).The best response s∗i of each RS is a replace link operationthrough which a RS i splits from its current parent RS andreplaces it with a new RS that maximizes its utility.

Multiple rounds are run until convergence to the final Nashtree G† after which no RS can improve its utility by a unilateralchange of strategy.

Multiple rounds consisting of the above two phases are run until convergence tothe final tree structure G† after which the RSs can no longer improve their utilitythrough best responses. A summary of this algorithm is shown in Table 13.3.

The stability of the final graph G† is given using the concept of Nash equilib-rium applied to network formation games [25].

Definition 13.14 A network graph G in which no node i can improve its utilityby a unilateral change in its strategy si ∈ Si is a Nash network.

Therefore, a Nash network is a network where the links chosen by each node arethe best responses. Hence, in such a network, the nodes are in a Nash equilibriumwith no node able to improve its utility by unilaterally changing its currentstrategy. When our dynamics converge, and as an immediate consequence ofplaying a best response dynamics, we have:

Lemma 13.2 The final tree structure G† resulting from the RSs network for-mation algorithm is a Nash network.

Numerical resultsIn order to highlight the properties and performance of the network formationgame among the RSs, we consider a square area of 4 km × 4 km with the BS atthe center. We deploy the RSs and the MSs within this area. Further, we set the


Figure 13.6. Snapshot of a tree topology formed using the RSs network formationalgorithm with 10 RSs before (solid line) and after (dashed line) the randomdeployment of 50 MSs (MS positions not shown for clarity).

transmit power to P = 50 mW (RSs and MSs), the noise level to −110 dBm, andthe bandwidth per RS to W = 100 kHz. For path-loss, we set the propagationloss to µ = 3. For the VoIP traffic, we consider a traffic of 64 kbps, divided intopackets of length B = 200 bits with an arrival rate of 320 packets/s. For theHELLO packets we set η0 = 1 packet/s with the same packet length of B = 200bits. For voice, we select the G.729 codec, hence υ1 = 12, υ2 = 15 and υ3 = 0.6[26].

In Figure 13.6 we randomly deploy M = 10 RSs within the BS area. The net-work formation game starts with the star topology where all RSs are connecteddirectly to the BS. Prior to the presence of the MSs in the network (only HELLOpackets present), the RSs interact and converge to a final Nash tree structureshown by the solid lines in the figure. This figure clearly shows how the RSs con-nect to their nearby partners, forming the tree structure. Furthermore, we ran-domly deploy 50 MSs in the area, and show how the RSs autonomously adapt thetopology to this incoming traffic. The resulting network structure upon deploy-ment of MSs is shown in Figure 13.6 in dashed lines. The RSs autonomouslyself-organize and adapt to the deployed traffic. For instance, RS 3 can no longeraccommodate the traffic generated by RS 2 as it drastically decreases its utility.As a result, RS 2 takes the decision to disconnect from RS 3 and improve its R-factor by directly connecting to the BS. Similarly, RS 7 disconnects from RS 10and connects directly to the BS. Moreover, RS 9 finds it beneficial to replace itslink with RS 5 with a link with the less loaded RS 6.


Figure 13.7. Self-adaptation of the network’s tree topology to mobility shownthrough the variation of the utility of RS 5 as it moves upwards on the y-axisprior to any MS presence.

Furthermore, we assess the effect of mobility on the network structure. Weconsider the network of Figure 13.6 prior to the deployment of the MSs and weassume that RS 5 is moving upwards on the positive y-axis while the other RSsremain fixed. The changes in utility of the concerned RSs during the movementof RS 5 are shown in Figure 13.7. As RS 5 moves upwards, its utility starts bydropping since the distance to its serving RS (RS 6) increases. Upon moving0.3 km, RS 5 finds it beneficial to replace its link with RS 6 with a direct linkto the BS, adapting the topology. Meanwhile, RS 9 decides to remain connectedto RS 5 since it cannot improve its utility elsewhere. However, when RS 5 hasmoved 0.4 km, RS 9 decides to disconnect from RS 5 and connect directly toRS 6 improving its utility. This decreases the traffic on RS 5 which is now closerto RS 3 and can maximize its utility by connecting to RS 3. As RS 5 moves closerto RS 3, its utility continues to improve. After moving 1.2 km, RS 5 approachesRS 8 which finds it beneficial to disconnect its link with RS 3 and connect toRS 5. At this point the utility of RS 5 drops due to the newly accepted traffic;moreover, this utility drops further as RS 5 distances itself from its serving RS(RS 3). Meanwhile, the utility of RS 8 continues to improve as RS 5 moves closerto it. Through these results, we clearly illustrate how the RSs can autonomouslyself-organize adapting the topology to mobility. Similar results can be shownwhen new RSs enter the network or RSs leave the network with or without thepresence of MSs.

In Figure 13.8, we show the average achieved utility per MS as the number ofRSs, M , in the network increases. The results are averaged over random positions


Figure 13.8. Performance assessment of the distributed tree formation algorithmfor a network with 40 MSs shown through the average achieved MS utility vs.number of RSs M in the network (average over random positions of MSs andRSs).

of the MSs and the RSs in a network having 40 MSs. We compare the performanceof the network formation algorithm with the star topology whereby each RS isdirectly connected to the BS as well as the scenario where there are no RSs in thenetwork. In this figure, we clearly see that as the number of RSs in the networkincreases the performance of the network formation algorithm as well as of thestar topology improves. However, for the star topology the slope of increaseis much lower than that of the network formation algorithm. In addition, thenetwork formation algorithm presents a clear performance advantage, increasingwith the number of the RSs, and reaching 40.3% and 42.75% (at M = 25 RSs)relative to the star topology and the no RSs case, respectively.

13.5 Conclusion

Coalitional game theory presents a rich framework that can be used to modelvarious aspects of cooperative behavior in wireless cellular networks. On theone hand, for ideal cooperation, one can utilize the various solution conceptsof canonical coalitional games to study the stability and fairness of allocatingutilities when all the users in the network cooperate. Although in this chaptercanonical games have not been explored, their applications are numerous andthey provide useful analytical tools for studying the limits of cooperation and the

13.5 Conclusion 379

feasibility of providing incentives for the wireless users to maintain a cooperativebehavior, when cooperation is ideal.

On the other hand, whenever there is a benefit–cost tradeoff for cooperation,one can revert to a class of coalitional games, known as coalition formation games,to derive models and algorithms that can help in analyzing the cooperatinggroups that will emerge in a given wireless network. For example, using simpleconcepts from coalition formation game theory such as the merge-and-split rules,single-antenna users can cooperate to form virtual MIMO coalitions and, thus,benefit from the advantages of multiple-antenna systems. Using merge and splitfor cooperation is not limited to the single cell of a wireless cellular systemnor to the virtual MIMO application. In fact, cooperative approaches based oncoalition formation games can extend to multicell systems and can model avariety of scenarios. For example, in a wireless cellular network, one can adopta merge-and-split algorithm for cooperation among the BSs in order to benefitfrom receive diversity, receive or transmit beamforming, interference cancelation,and other advanced communication techniques. In brief, the coalition formationgame class constitutes an appropriate framework for modeling the cooperativebehavior in wireless systems, and, thus, it will admit numerous applications inthe future.

Further, for analyzing routing problems, network structure formation, andgraph interconnection, coalitional graph games provide several algorithms andsolutions, notably through the framework of network formation games. Asdemonstrated in this chapter, network formation games are quite useful for mod-eling the interactions among the relay stations that are bound to be deployedin next generation cooperative wireless systems. In this context, one can designefficient and robust strategies for forming the network structure that will governthe architecture of wireless systems. The application of network formation gamesis not limited to the RSs problem studied in this chapter. In fact, this frameworkadmits numerous uses in wireless systems such as modeling the downlink trans-mission path in multihop systems, studying network routing in cooperative wire-less cellular systems, identifying the hierarchy that can govern the architecture ofwireless systems, modeling wireless peer-to-peer interaction. Also, an interestingaspect of network formation is to study the cooperative behavior of the nodeswhenever they are far sighted, i.e., they make decisions based on future rewards.

In a nutshell, using coalitional game theory one can design efficient, robust,and fair models for cooperative wireless cellular networks. Consequently, the useof these games and models is bound to be prevalent in the design and analysisof cooperative behavior in future wireless communication networks.

Acknowledgments

This research is supported by the Research Council of Norway through projects183311/510, 176773/510, 18778/VII.


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14 Modeling malicious behavior incooperative cellular wirelessnetworks

Ninoslav Marina, Walid Saad, Zhu Han, and Are Hjørungnes

14.1 Introduction

Future communication systems will be decentralized and ad-hoc, hence allow-ing various types of network mobile terminals to join and leave. This makes thewhole system vulnerable and susceptible to attacks. Anyone within communi-cation range can listen to and possibly extract information. While these dayswe have numerous cryptographic methods to ensure high-level security, thereis no system with perfect security on the physical layer. Therefore, the physi-cal layer security is attracting renewed attention. Of special interest is so-calledinformation-theoretic security since it concerns the ability of the physical layerto provide perfect secrecy of the transmitted data.

In this chapter, we present different scenarios of a decentralized system thatprotects the broadcasted data on the physical layer and makes it impossible forthe eavesdropper to receive the packets no matter how computationally pow-erful the eavesdropper is. In approaches where information-theoretic security isapplied, the main objective is to maximize the rate of reliable information fromthe source to the intended destination, while all malicious nodes are kept igno-rant of that information. This maximum reliable rate under which a perfectlysecret communication is possible is known as the secrecy capacity.

This line of work was pioneered by Aaron Wyner, who defined the wiretapchannel and established the possibility of secure communication links withoutrelying on private (secret) keys [1]. Wyner showed that when the eavesdrop-per channel is a degraded version of the main channel, the source and the des-tination can exchange perfectly secure messages at a nonzero rate. The mainidea proposed by him is to exploit the additive noise impairing the eavesdrop-per by using a stochastic encoder that maps each message to many codewordsaccording to an appropriate probability distribution. With this scheme, a max-imal equivocation (i.e., uncertainty) is induced at the eavesdropper. In otherwords, a maximal level of secrecy is obtained. By ensuring that the equivoca-tion rate is arbitrarily close to the message rate, one can achieve perfect secrecyin the sense that the eavesdropper is limited to learning almost nothing about



S D

E

C

Cm

Figure 14.1. The eavesdropper channel.

the source–destination messages from its observations. Follow-up work by Leung-Yan-Cheong and Hellman characterized the secrecy capacity of the additive whiteGaussian noise (AWGN) wiretap channel [2]. In their landmark paper, Csiszarand Korner generalized Wyner’s approach by considering the transmission ofconfidential messages over broadcast channels [3]. There have been considerableefforts to generalize these studies to the wireless channel and multiuser scenarios([2, 4–11]).

The basic scenario, called the eavesdropper channel, is shown in Figure 14.1.There is a source S that is transmitting a message to a destination D, while aneavesdropper E is trying to listen to the communication between S and D. In thefollowing text we shall also use the term malicious node for the eavesdropper.

A perfect information-theoretically secret system is a system with positivesecrecy capacity. In addition to the secrecy capacity being positive it is bene-ficial for the source to have it as large as possible to enable higher-rate secretcommunication. For the class of channels of interest here, the secrecy capacity isdefined as

Cs = max(C − Cm , 0), (14.1)

where C is the capacity of the direct point-to-point channel between the sourceand the destination and Cm is the capacity of the channel between the source andthe eavesdropper. Having a positive secrecy capacity guarantees perfect secrecy.Note that it is in the interest of the system designer to make Cs as large aspossible. To increase Cs , it is obvious from (14.1) that one has to either increaseC or decrease Cm or both.

In the rest of this chapter we describe three different scenarios for how thesecrecy capacity could be changed by cooperation. First in Section 14.2 wedescribe how cooperation with some friendly jamming nodes can decrease Cm ,which results in increasing Cs . In order to study what the incentive is for thefriendly jammer to help the source, we analyze the system by using the Stock-holder game. In Section 14.3 we study how the cooperating nodes can helpthe source by relaying the useful information to the destination while at thesame time jamming the eavesdropper. Here we realize that for such a model

384 Modeling malicious behavior in cooperative cellular wireless networks

there is an area that the eavesdropper must not be allowed to enter in order toensure a positive secrecy capacity. We call this region the vulnerability regionand we study its size as the number of cooperative relaying nodes increases.Finally, in Section 14.4 we warn that as well as the “good guys”, the eaves-droppers can also organize themselves, making the secrecy capacity lower. Westudy a scenario in which eavesdroppers form coalitions, thereby decreasing thesecrecy capacity acted much more than if the eavesdroppers act individually.The cooperative behavior of the eavesdroppers is studied by using coalitiongames.

14.2 Cooperating jammers

In this section, we investigate the interaction between the source and friendlyjammers, who help the source by jamming the eavesdropper. Although thefriendly jammers help the source by reducing the data rate that is “leaking”from the source to the malicious node, at the same time they also reduce theuseful data rate from the source to the destination. Using well-chosen amounts ofpower from the friendly jammers, the secrecy capacity can be maximized. In thegame that we define here, the source pays jammers to interfere with the mali-cious eavesdropper and therefore to increase the secrecy capacity. The jammerscharge the source a certain price for jamming the eavesdropper. It can be seenthat there is a tradeoff when deciding the price: If the price of a certain jammeris too low, its profit is also low; if its price is too high, the source will buy fromanother jammer. In modeling the outcome of the above games our analysis usesthe Stockholder type of game. Initially, the existence of equilibrium will be stud-ied. Then, a distributed algorithm will be proposed and its convergence will beinvestigated. The outcome of the distributed algorithm will be compared withthe centralized genie-aided solution. Some implementation concerns are also dis-cussed. From the simulation results, we can see the efficiency of friendly jammingand the tradeoff for setting the price; the source prefers buying service from onlyone jammer, and the centralized scheme and the proposed game scheme havesimilar performances.

Jamming [12–14] has been studied for a long time to analyze the hostile behav-iors of malicious nodes. Jamming has been employed as a physical layer securitymethod to reduce the eavesdropper’s ability to decode the source’s informa-tion [15]. In other words, the jamming is friendly in this context. Moreover, thefriendly helper can assist the secrecy by sending codewords, and bring furthergains relative to unstructured Gaussian noise [15–17].

Game theory [18] is a formal framework with a set of mathematical toolsto study some complex interactions among interdependent rational players.There has been a surge in research activity that employs game theory tomodel and analyze modern distributed communication systems. Most of this

14.2 Cooperating jammers 385

S D

M

Cm

C

J1

J2

JJ

S – SourceD – DestinationM – Malicious node (Eavesdropper)J1,…,JJ – J Friendly jammers

Useful dataInterferencePayment

Figure 14.2. System model for the proposed information-theoretic security game.

research [19–22] concentrated on the distributed resource allocation for wirelessnetworks.

14.2.1 System model

We consider a network with a source, a destination, a malicious eavesdroppernode, and J friendly jammer nodes as shown in Figure 14.2. The malicious nodetries to eavesdrop the transmitted data coming from the source node. When theeavesdropper channel from the source to the malicious node is a degraded versionof the main source–destination channel, the source and destination can exchangeperfectly secure messages at a nonzero rate. By transmitting a message at a ratehigher than the rate of the malicious node, the malicious node can learn almostnothing about the messages from its observations. The maximum rate of secrecyinformation from the source to its intended destination is defined by the termsecrecy capacity.

Suppose the source transmits with power P0 . The channel gains from thesource to the destination and from the source to the malicious node are Gsd andGsm , respectively. Each friendly jammer i, i = 1, . . . , J , transmits with powerPi and the channel gains from it to the destination and the malicious node areGid and Gim , respectively. We denote by J the set of indices 1, 2, . . . , J. Ifthe path-loss model is used, the channel gain is given by the distance to thenegative power of the path-loss coefficient. The thermal noise for each chan-nel is σ2 and the bandwidth is W . The channel capacity for the source to thedestination is

C = W log2

(1 +

P0Gsd

σ2 +∑

i∈J PiGid

). (14.2)


The channel capacity from the source to the malicious node is

Cm = W log2

(1 +

P0Gsm

σ2 +∑

i∈J PiGim

). (14.3)

As we know from (14.1), the secrecy capacity is Cs = max(C − Cm , 0). Both C

and Cm are decreasing and convex functions of the jamming powers Pi . However,Cs = C − Cm is not a monotonous and convex function. This is because thejamming power might decrease C faster than Cm . As a result, Cs might increasefor some values of Pi . So, the questions to be considered are whether or not Cs

can be increased, and how the jamming power can be controlled in a distributedmanner. We will solve the problems in the following text using a game theoreticalapproach.

14.2.2 The game

Next we describe how game theory can be used to analyze information-theoreticsecurity in a cooperative network. First, we define the game between the sourceand the friendly jammers. We optimize the source side and the jammer side,respectively. Then, we prove some properties of the proposed game. Furthermore,a comparison is made with the centralized scheme. Finally, we discuss someimplementation concerns. The source can be modeled as a buyer who wants tooptimize its secrecy capacity minus cost by modifying the “service” (jammingpower Pi) from the friendly jammer, i.e.,

source’s game: max Us = max(aCs −M),

subject to : Pi ≤ Pmax, (14.4)

where a is the gain per unit capacity, Pmax is the maximal power that a jammercan provide, and M is the cost to pay for the other friendly jamming nodes. Here

M =∑i∈J

piPi, (14.5)

where pi is the price per unit power for the friendly jammer, Pi is the friendlyjammer’s power, and J is the set of friendly jammers. From (14.4) we note thatthe source will not participate in the game if C < Cm , or, in other words, thesecrecy capacity is zero. For each jammer, Ui(pi, Pi(pi)), is the utility functionof the price and power bought by the source. For the jammer’s (seller’s) utility,we define the following utility

Ui = piPcii , (14.6)

where ci ≥ 1 is a constant to balance the payment piPi from the source and thetransmission cost Pi . Notice that Pi is also a function of the vector of prices(p1 , . . . pN ), since the power that the source will buy also depends on the pricethat the friendly jammers ask. Hence, for each friendly jammer, the optimization


problem is

friendly jammer’s game: maxpi

Ui. (14.7)

In the following text, we analyze the optimal strategies for the source andfriendly jammers to maximize their own utilities.

Introducing A = P0Gsd/σ2 , B = P0Gsm /σ2 , ui = Gid/σ2 , and vi = Gim /σ2 ,i ∈ J , we have

Us = aW

⎛⎜⎜⎝log

⎛⎜⎜⎝1 +A

1 +∑j∈J

ujPj

⎞⎟⎟⎠− log

⎛⎜⎜⎝1 +B

1 +∑j∈J

vjPj

⎞⎟⎟⎠⎞⎟⎟⎠

+

−∑j∈J

pjPj .

(14.8)

For the source (buyer) side, we analyze the case C > Cm . By differentiating(14.4), we have

∂Us

∂Pi= − aWAui/ ln 2

(1 + A +∑

j∈J ujPj )(1 +∑

j∈J ujPj )

+aWBvi/ ln 2

(1 + B +∑

j∈J vjPj )(1 +∑

j∈J vjPj )− pi = 0. (14.9)

Rearranging the above equation, we have

P 4i + Fi,3P

3i + Fi,2(pi)P 2

i + Fi,1(pi)Pi + Fi,0(pi) = 0, (14.10)

where

Fi,3 = (2 + 2αi + A)2 + (2 + 2βi + B)2 ,

Fi,2(pi) =(2 + 2αi + A)(2 + 2βi + B)

uivi+

Li

v2i

+Ki

u2i

− aW

piuivi

(B

vi− A

ui

),

Fi,1(pi) =LiCi + KiDi

u2i v

2i

+aW (ADi −BCi)

piu2i v

2i

, (14.11)

Fi,0(pi) =KiLi

u2i v

2i

+aW (AuiLi −BviKi)

piu2i v

2i

,

and

αi =∑j =i

GjdPj , βi =∑j =i

Gjm Pj , (14.12)

Ki = (1 + αi)(1 + αi + A), (14.13)

Li = (1 + βi)(1 + βi + B), (14.14)

Ci = ui(2 + 2αi + A), (14.15)

Di = vi(2 + 2βi + B). (14.16)

The solutions of the quartic equation (14.10) can be expressed in a closed formbut this is not the primary goal here. It is important that the solution we are


interested in is given by the following function:

P ∗i = P ∗i (pi, A,B, uj, vj, Pjj =i). (14.17)

Note that 0 ≤ Pi ≤ Pmax . Since Pi satisfies the polynomial function, we canhave the optimal strategy as

P ∗i = min[max(Pi, 0), Pmax ]. (14.18)

Because of the complexity of the closed-form solution of the quartic equationin (14.18), we also consider two special cases: the low interference case and thehigh interference case.

(a) Interference at the destination is much smaller than the noise (low inter-ference case) Remember the definitions: A = P0Gsd/σ2 , B = P0Gsm /σ2 ,ui = Gid/σ2 , and vi = Gim /σ2 . Imagine a situation in which all jammersare close to the malicious node and far from the destination node. In thatcase the interference from the jammer to the destination is very small incomparison with the additive noise and therefore

Us ≈ aW

(log (1 + A)− log

(1 +

B

1 +∑

j∈J vjPj

))+

−∑j∈J

pjPj .(14.19)

Then

∂Us

∂Pi=

aWBvi/ ln 2(1 + B +

∑j∈J vjPj )(1 +

∑j∈J vjPj )

− pi = 0. (14.20)

Rearranging we get

P 2i +

2 + 2βi + B

viPi +

(1 + βi)(1 + B + βi)v2

i

− aWB

pivi ln 2= 0. (14.21)

Solving the above equation we obtain a closed-form solution

P ∗i = −2 + 2βi + B

2vi+

√(2 + 2βi + B)2

4v2i

− (1 + βi)(1 + B + βi)v2

i

+aWB

pivi ln 2

= qi +√

wi +zi

pi, (14.22)

where

qi = −2 + 2βi + B

2vi, (14.23)

wi =(2 + 2βi + B)2

4v2i

− (1 + βi)(1 + B + βi)v2

i

, (14.24)

zi =aWB

vi ln 2. (14.25)


Finally, by comparing P ∗i with the power under the boundary conditions(Pi = 0, Pi = Pmax , and Cs = 0), the optimal P ∗i in the low-SNR region canbe obtained.

(b) One jammer with interference that is much higher than the noise but muchsmaller than the received power at the destination and the malicious nodeIn this case the interference from the jammer is much higher than the addi-tive noise but much smaller than the power of the received signal at thedestination and the malicious node. In other words, 1 << u1P1 << A and1 << v1P1 << B. Therefore, the utility function of the source is given by

Us ≈ aW

(log(

1 +A

u1P1

)− log

(1 +

B

v1P1

))+

− p1P1

≈(

aWA

u1P1− aWB

v1P1

)+

− p1P1 . (14.26)

If (B/v1)− (A/u1) ≤ 0, Us is a decreasing function of P1 . As a result, Ps isoptimized when P1 = 0, i.e., the jammer would not participate in the game.On the other hand, if (B/v1)− (A/u1) > 0, then the secrecy capacity is zero.

Next we study how the friendly jammer can set the optimal price to maximizeits utility. By differentiating the utility in (14.6) and setting it to zero, we have

∂Ui

∂pi= (P ∗i )ci + pici(P ∗i )ci−1 ∂P ∗i

∂pi= 0. (14.27)

This is equivalent to

(P ∗i )ci−1(

P ∗i + pici ·∂P ∗i∂pi

)= 0. (14.28)

This happens either if P ∗i = 0 or if

P ∗i + pici ·∂P ∗i∂pi

= 0. (14.29)

From the closed-form solution of P ∗i the solution of p∗i will be a function givenas

p∗i = p∗i (σ2 , Gsd ,Gsm , Gid, Gim). (14.30)

Notice that p∗i should be positive. Otherwise, the friendly jammer would notplay.

In the following text, we prove some properties of the proposed game. First,we prove that the power is a monotonous function of the price under the twoextreme cases. The properties can help the proof of equilibrium existence laterin the chapter.

Property 1 Under the low-interference special case, the optimal power con-sumption P ∗i for friendly jammer i is monotonous with its price pi , when the otherfriendly jammers’ prices are fixed. The proof is straightforward from (14.22).


We investigate the following analysis of the relation between the price andthe power. We find that the price Pi of the friendly jammer’s power Pi boughtfrom the source is convex under some conditions. To prove this we need to checkwhether the second derivative ∂2Pi/∂p2

i < 0.In the first special case, in which the interference is small,

∂P ∗i∂pi

= − zi

2p2i

√wi +

zi

pi

(14.31)

and

∂2P ∗i∂p2

i

=zi

p3i

(wi +

zi

pi

)1/2

⎛⎜⎜⎝1− 1

4(

piwi

zi+ 1)⎞⎟⎟⎠ . (14.32)

The above equation is greater than zero when pi is small. This means when theinterference is small and the price is small, the power is convex as a function ofthe price.

In the second special case, in which the interference is severe,

∂P ∗i∂pi

= −12

√D1p

−3/21 (14.33)

and

∂2P ∗i∂p2

i

=34

√D1p

−5/21 > 0. (14.34)

This means when the interference is severe, the power is a convex function of theprice.

Next, we investigate the equilibrium of the proposed game. At the equilibrium,no user can improve its utility by changing its own strategy only. We first definethe Stockholder equilibrium as follows.

Definition 14.1 PSEi and pSE

i are the Stockholder equilibrium of the proposedgame if when pi is fixed,

Us(PSEi ) = sup

Pm a x≥P S Ei ≥0,∀i

Us(Pi), ∀i ∈ J (14.35)

and when Pi is fixed

Ui(pSEi ) = sup

pi

Ui(pi), ∀i ∈ J . (14.36)

Finally, from the previous analysis, we can show the following property for theproposed game.

Property 2 The pair of P ∗i Ni=1 in (14.18) and p∗i Ni=1 in (14.30) is the Stock-holder equilibrium for the proposed game.


Notice that there might be multiple roots in (14.10), and as a result, theremight be multiple Stockholder equilibria. In the simulation results shown laterin this section, we will demonstrate that the proposed scheme can still achievethe equilibria with better performances than those of the no-jammer case.

Next we study how the distributed game can converge to the Stockholderequilibrium defined earlier. After rearranging (14.27), we have

pi = Ii(p) = − (P ∗i )

ci∂P ∗i∂pi

(14.37)

where p = [p1 , . . . , pN ]T and Ii(p) is the price update function. Notice that P ∗iis a function of p.

The information for the update can be obtained from the source node. This issimilar to the distributed power control [23]. The update of the friendly jammers’prices can be written in a vector form as

distributed algorithm: p(t + 1) = I(p(t)), (14.38)

where I = [I1 , . . . , IN ]T , and the iteration is from time t to time t + 1. Next weshow the convergence of the proposed scheme by proving that the price updatefunction in (14.38) is a standard function [24] defined as follows.

Definition 14.2 A function I(p) is standard, if for all p ≥ 0, the followingproperties are satisfied:

(1) positivity: p > 0;(2) monotonicity: p ≥ p′, then I(p) ≥ I(p′), or I(p) ≤ I(p′);(3) scalability: for all η > 1, ηI(p) ≥ I(ηp).

In [24], it has been proved that the price will converge to the fixed point (i.e.,the Stockholder equilibrium in our case) from any feasible initial price vector.The positivity is very easy to prove. If the price pi goes up, the source will buyless from the ith friendly jammer. As a result, ∂P ∗i /∂pi in (14.27) is negative,and we prove positivity pi = Ii(p) > 0.

We prove the monotonicity and scalability only for the low-interference case.In this case, from (14.22) it is obvious that

Ii(p) = − (P ∗i )

ci∂P ∗i∂pi

=2√

wip2i + zipi(qipi +

√wip2

i + zipi)cizi

, (14.39)

which is monotonically increasing in pi . For scalability, we have

Ii(ηp)ηIi(p)

=

√wip2

i + zipi/η(qipi +√

wip2i + zipi/η)√

wip2i + zipi(qipi +

√wip2

i + zipi)< 1 (14.40)

since η > 1.


For more general cases, the analysis is not tractable. In our simulations, weemploy general simulation setups. The simulation results show that the proposedscheme can converge and outperform the no-jammer case.

Traditionally, the centralized scheme is employed assuming all channel infor-mation is known. The objective is to optimize the secrecy capacity under theconstraints of maximal jamming power:

maxPi

Cs = max

⎡⎢⎢⎣W log2

⎛⎜⎜⎝ 1 + P0 Gs d

σ 2 +∑

i∈J Pi Gi d

1 +P0Gsm

σ2 +∑

i∈J PiGim

⎞⎟⎟⎠ , 0

⎤⎥⎥⎦subject to 0 ≤ Pi ≤ Pmax,∀i. (14.41)

The centralized solution is found by maximizing the secrecy capacity only. Ifwe do not consider the constraint, we have

∂Cs

∂Pi=

−AWui

(1 + αi + uiPi)(1 + A + αi + uiPi)

+BWvi

(1 + βi + uiPi)(1 + B + βi + uiPi)= 0. (14.42)

Rearranging we get

P 2i +

Au2i (2 + B + 2βi)−Bv2

i (2 + A + 2αi)Au3

i −Bv3i

Pi

+Aui(1 + βi)(1 + B + βi)−Bvi(1 + αi)(1 + A + αi)

Au3i −Bv3

i

= 0. (14.43)

Using the Karush–Kuhn–Tucker (KKT) condition [25], the final solution wouldbe obtained by comparing the boundary conditions (i.e., Pi = 0, Pi = Pmax , andCs = 0).

Notice that our proposed algorithm is distributive, in the sense that only thepricing information needs to be exchanged. In the simulation results, we comparethe proposed game-theoretical approach with this centralized scheme.

There are several implementation concerns for the proposed scheme. First, thechannel information from the source to the malicious eavesdropper might not beaccurately known. Under this condition, the secrecy capacity formula should berewritten considering the uncertainty. If the direction of arrival is known, mul-tiple antenna techniques can be employed such as in [11]. Second, the proposedscheme needs to update the price and power information iteratively. A naturalquestion arises if the distributed scheme has less signalling than the centralizedscheme. The comparison is similar to distributed and centralized power controlin the literature [23, 24]. Since the channel condition is continuously changing,the distributed solution only needs to update the difference of the parameterssuch as power and price to be adaptive, while the centralized scheme requires


0 0.005 0.01 0.015 0.020

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Jamming power

Sec

recy

cap

acity

Cs

Jammer location (50,75)Jammer location (10,75)

Figure 14.3. Secrecy capacity vs. the power of the single jammer.

all channel information in each time period. As a result, the distributed solu-tion has a clear advantage and dominates current and future wireless networkdesign. For example, in the power control for cellular networks, the open-looppower control is done only once during the link initialization, while the closed-loop power control (distributed power allocation such as [24]) is performed 1500times for UMTS and 800 times for CDMA2000. Finally, for the multisource mul-tidestination case, there are two possible choices to solve the problem. First,we can use a clustering method to divide the network into subnetworks, andthen employ the single-source–destination pair and multiple-friendly-jammerssolution proposed in this section. If we believe that the jamming power can beuseful for multiple eavesdroppers, techniques such as double auction could beinvestigated.


The simulation was set up as follows. The source and friendly jammers havepower of 0.02, the bandwidth is 1, the noise level is 10−8 , the propagation lossfactor is 3, and an additive white Gaussian noise (AWGN) channel is assumed.The source, destination, and eavesdropper are located at the coordinates (0,0),(100,0), and (50,50), respectively. Here we select a = 2 for the friendly jammer’sutility in (14.6).

For the single-friendly-jammer case, we show the simulation with the friendlyjammer at a location of (50,75) and (10,75). In Figure 14.3, we show the secrecy


0 50 100 150 2000

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

Jammer price

Am

ount

of p

ower

bou

ght

Jammer location (50,75)Jammer location (10,75)

Figure 14.4. How much power the source buys as a function of the price.

capacity as a function of the jamming power. We can see that with the increaseof the jamming power, the secrecy capacity first increases and then decreases.This is because the jamming power has different effects on C and Cm . There isan optimal point for the jamming power. Also the optimal point depends on thelocation of the friendly jammer, and a friendly jammer close to the eavesdropperis more effective in improving the secrecy capacity. Moreover, notice that thecurve is neither convex nor concave. Figure 14.4 shows how the amount of thepower bought by the source from the jammer depends on the requested price.We can see that the power is reduced if the price is high. At some point, thesource would stop buying the power. So there is a tradeoff for setting the price,i.e., if the price is too high, the source will buy less power or even stop buyingit.

For the two-jammer case, we set up the following simulations. The maliciousnode is located at (50,90), the first friendly jammer is located at (50,50), andthe second friendly jammer is located at (50,75). Figures 14.5, 14.6, and 14.7show, respectively, the source’s utility Us , the first jammer’s utility U1 , and thesecond jammer’s utility U2 as a function of both users’ price. We can see thatthe source will buy service from only one of the friendly jammer. If the friendlyjammer asks too low a price, the jammer’s utility is very low. On the other hand,if the jammer asks too high a price, it risks the situation in which the sourcewill buy the service from another friendly jammer. There is an optimal price foreach friendly jammer to ask, and the source will always select the one that canprovide the best performance improvement.

Next, we set up a simulation of mobility. The first friendly jammer is fixedat (50,50), while the second friendly jammer moves from (−50,75) to (100,75).


0

50

100

150

0

100

200

300

0.2

0.4

0.6

0.8

1

User 2 Price p1

User 1 Price p2

Sou

rce

Us

Figure 14.5. Us vs. the prices of both users. (Source (0,0), destination (100,0)malicious node (50,90), user 1(50,50), user 2(50,75).)

'

Figure 14.6. U1 vs. the prices of both users. (source (0,0), destination (100,0)malicious node (50,90), user 1(50,50), user 2(50,75).)

In Figure 14.8, we show the source utilities for the centralized scheme and theproposed game. The centralized scheme serves as a performance upper bound.We observe that the game result is not far away from the upper bound, while thegame solution can be implemented in a distributed manner. The performancedifference is insignificant when friendly jammer 2 is close to the malicious eaves-dropper (e.g., the friendly jammer is at locations from (20, 75) to (70, 75)). In


Figure 14.7. U2 vs. the prices of both users. (Source (0,0), destination (100,0)malicious node (50,90), user 1(50,50), user 2(50,75).)

Figure 14.8. Us vs. the location of the second jammer.

Figure 14.9, we show the jammer power as a function of the location of jammer2. We can see that depending on the jammers’ locations, the source switchesbetween the two jammers for the best performance. Moreover, the source alsobuys the optimal amount of jamming power: when the jammer is close to themalicious eavesdropper, the source buys less power since the jammer is more


Figure 14.9. Power vs. the location of the second jammer.

utili

ty

location

utilityutility

Figure 14.10. Utility vs. the location of the second jammer.

effective at improving the secrecy capacity. In Figure 14.10, we show the corre-sponding friendly jammers’ utilities of the proposed game.

Finally, we show the effect of parameter a on the friendly jammer’s utilityin (14.6). When a is large, the friendly jammer’s utility reduces quickly if thesource does not buy the service. As a result, the friendly jammer would not askan arbitrary price, and the performance gap to the optimal solution is small. In


2 2.5 3 3.5 4 4.5 5

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

Factor a

Sec

recy

cap

acity

Optimal solutionGame result

Figure 14.11. Effect of the parameter a on the game.

Figure 14.11, we show the secrecy capacity as a function of a when the secondjammer is located at (0,75). We can see that the performance gap shrinks whena increases.

To summarize, if the source pays friendly jammers to interfere with the mali-cious eavesdropper, the secrecy capacity, and therefore the security of the networkis increased. The friendly jammers charge the source a price for the jamming.To analyze the game outcome, we investigated the Stockholder game and con-structed a distributed algorithm. Some properties such as equilibrium and con-vergence were analyzed. From the simulation results, we conclude the following.First, there is a tradeoff for the price: if the price is too low, the profit is low;and if the price is too high, the source will not buy or buy from another jam-mer. Second, for the multiple-jammer case, the source will buy service from onlyone jammer. Third, the centralized scheme and distributed scheme have simi-lar performances, especially when a is sufficiently large. Overall, the proposedgame theoretical scheme can achieve a comparable performance with distributedimplementation.

14.3 Cooperating relays

In this section, we observe how node cooperation improves the information-theoretic security of a simple wireless network by reducing the surface ofthe geographical area in which the malicious nodes can listen to the datatransmitted from the source to the destination. Our analysis and simulation

14.3 Cooperating relays 399

Destinationnode

Sourcenode

Relay 1

Relay 2

Relay 3

Relay M

Figure 14.12. Cooperative network with a source, a destination, M cooperativerelays, and a malicious node.

results show a dramatic improvement even for cooperation with only one relaynode. Adding more cooperating nodes gives greater improvement. We alsoobserve that when cooperating nodes are closer to the line that connects thesource and the destination node, the region in which the malicious node canprofit from the eavesdropping is smaller.

14.3.1 System model

We analyze the Gaussian parallel multiple-relay network. Although the capacityof this network is not known, we use its upper and lower bounds, with a hopethat our results will initiate further thought in this interesting and importantresearch area. Observe the network in Figure 14.12. There is a source node thattransmits data to a destination node, while a malicious node “listens” to thetransmitted information. There are several relay nodes that help the source byrelaying the transmitted data.

We consider the additive complex white Gaussian noise model. A message atthe source node is encoded into a codeword X[j]nj=1 of length n. The compo-nents X[j] are complex numbers that satisfy the power constraint

n−1n∑

j=1

E[|X[j]|2 ] ≤ P. (14.44)

At time j each of the M relays observes an attenuated and noisy version of theinput, i.e.,

Yi [j] = hi,sX[j] + Zi [j], i = 1, 2, . . . ,M,


where Zi [j] is an independent and identically distributed (i.i.d.) circularly sym-metric complex Gaussian random variable of zero mean and (without loss ofgenerality) variance σ2 . Moreover, Zi and Z are independent for i = . Thecoefficients hi,s , i = 1, 2, . . . ,M , are fixed real-valued constants, assumed to beknown throughout the network. For that reason we may assume that all noiseprocesses Zi are of same variance σ2 without loss of generality. ObservingYi [j]nj=1 at each relay i produces a sequence Xi [j]nj=1 that must be causal,i.e.,

Xi [j] = fi,j (Yi [j − 1], Yi [j − 2], . . . , Yi [1]),

and satisfies the individual power constraint

n−1n∑

j=1

E[|Xi [j]|2 ] ≤ Pi. (14.45)

The received signal at the destination node is

Y [j] = hd,sX[j] +M∑i=1

hd,iXi [j] + Zd [j],

where Zd [j] is a sequence of i.i.d. zero-mean circularly symmetric complex Gaus-sian random variables of variance σ2 . The coefficients hd,s and hd,i , wherei = 1, 2, . . . ,M , are fixed and assumed to be known throughout the network.We assume that the coefficient ha,b between two nodes a and b is

ha,b = d−β/2a,b , (14.46)

where β is the path-loss exponent and da,b is the distance between the nodesa and b. In this case, the distance between the source and the destination isdenoted by dd,s , that between the source and relay i, by di,s , i = 1, 2, . . . ,M ,and that between relay i and the destination, by dd,i , where i = 1, 2, . . . ,M .

14.3.2 Secrecy capacity

Here we develop expressions for the secrecy capacity of the cooperative systemdescribed in Figure 14.12. It is assumed that the malicious node may eavesdropon the source as well as on the cooperating relay nodes. Note, however, that inorder to get full use of the signals transmitted from the source and the relaynodes, the source must be fully synchronized with all of them. To capture theeffect of synchronization, we model the received signal at the malicious node asfollows:

Ym [j] = hm,s√

qX[j] +M∑i=1

hm,i

√kiXi [j] + Zm [j],


Zm ∼ CN(

0, σ2 + (1− q)Pd−βm,s +

M∑i=1

(1− ki)Pid−βm,i

), (14.47)

where Zm [j] is a sequence of i.i.d. circularly symmetric complex Gaussian ran-dom variables of zero mean and variance σ2 + (1− q)P +

∑Mi=1 hm,i

√1− kiPi ,

hm,s = d−β/2m,s , and hm,i = d

−β/2m,i , i = 1, 2, . . . ,M . How well the malicious node

is synchronized with the source is modeled by q ∈ [0, 1], while how well it issynchronized with the relay node i is modeled by ki ∈ [0, 1] for i = 1, 2, . . . ,M .More precisely, q is the fraction of the source transmitting power that will bereceived by the malicious node as useful signal for itself, while (1− q) is thefraction of the source power that makes interference at the malicious node. Ifq = 1, then the malicious node is perfectly synchronized with the source node,while if q = 0 there is no synchronization and the malicious node receives onlynoise from the source. Similarly, ki is the fraction of the transmitting power ofrelay node i that will be received by the malicious node as useful signal for itself,while (1− ki) is the fraction of the power of relay node i that makes interferenceat the malicious node. The same explanation is valid for the parameters ki . Thatmeans, an omnipotent eavesdropper will have q = ki = 1 for all i = 1, 2, . . . ,M

and a “dummy” eavesdropper will have q = ki = 0 for all i = 1, 2, . . . ,M . Inthe former case, the vulnerability region will be maximal, while in the latter,it vanishes, i.e., we have a perfect secrecy system. In order to make the eaves-dropper capabilities closer to reality, we introduce two models to describe thesynchronization parameters as a function of the distance between the eaves-dropper and the eavesdropped node. Model 1 is the exponential model, definedas

q = e−dm , s ,(14.48)

ki = e−dm , i .

Model 2 is the squared exponential model (Gaussian model), defined as

q = e−d2m , s ,

(14.49)ki = e−d2

m , i .

For notational convenience, we use definitions similar to those in, i.e.,

aM = d−βd,s +

M∑i=1

d−βi,s ,

bM =M∑i=1

d−βi,s P + σ2

dβi,sd

−βd,i

,

dM = d−βd,s +

M∑i=1

d−βd,i .


With all these assumptions we will be able to determine the bounds on thesecrecy capacity, since the capacity of a general nondegraded relay channel isnot known in general. First, the capacity of the main channel (the parallel relaychannel between the source and the destination) is upper bounded by

C ≤ log2

(1 +

minaM P, (P +∑M

i=1 Pi)dM σ2

). (14.50)

The lower bound of the capacity of the main channel is given by

C ≥ log2

⎛⎜⎜⎜⎜⎝1 +(aM − d−β

d,s) + 2√

bM d−βd,s/

∑Mi=1 Pi

σ2 +bM (d−β

d,sP + σ2)

(aM − d−βd,s)∑M

i=1 Pi

P

⎞⎟⎟⎟⎟⎠ . (14.51)

The capacity of the eavesdropper channel (the maximum rate that can beachieved by the malicious node) is given by

Cm = log2

⎛⎜⎜⎜⎜⎝1 +

qP

dβm,s

+M∑i=1

kiPi

dβm,i

(1− q)P

dβm,s

+M∑i=1

(1− ki)Pi

dβm,i

+ σ2

⎞⎟⎟⎟⎟⎠ (14.52)

where Pi is the transmit power of relay i. Note that it might be obtained aftersome allocation process since we have the total power constraint applied to allrelays, given by (14.45).

The secrecy capacity is then defined as [2]

Cs = maxC − Cm , 0. (14.53)

In other words, the secrecy capacity is positive only if C > Cm . In order toanalyze how cooperation improves the secrecy, we introduce the following twodefinitions.

Definition 14.3 The geometrical area (region) in which the secrecy capacity ispositive is called the secrecy region.

Definition 14.4 The geometrical area (region) in which the secrecy capacityvanishes is called the vulnerability region.

Obviously, we want to keep all malicious nodes away from the vulnerabilityregion. In other words, the system is more secure if its vulnerability region isminimized, or, equivalently, if its secrecy region is maximized. Note that if thereare no cooperating relay nodes (M = 0), it can be shown that the vulnerabilityregion is a circle (disk) since in that case the capacity of the main channel isthe capacity of the point-to-point Gaussian channel between the source and the


destination. More precisely the region is determined from

C = log2

(1 +

Pd−βd,s

σ2

)

< log2

(1 +

qPd−βm,s

(1− q)Pd−βm,s + σ2

)= Cm . (14.54)

Solving (14.54), we get that the vulnerability region is a disk centered at thesource with radius

d∗m,s = dd,s (max 0, q(1 + γ)− γ)1/β , (14.55)

where γ = Pd−βd,s/σ2 . In other words,

d∗m,s =

⎧⎨⎩0, for 0 ≤ q ≤ γ

1 + γ,

dd,s (q(1 + γ)− γ)1/β , forγ

1 + γ≤ q ≤ 1.

This means that for a high SNR, it is easier to get a perfectly secure system ifq ≤ γ/(1 + γ). If q = 1,

d∗s,m = dd,s ,

while for 0 ≤ q ≤ γ/(1 + γ) the vulnerability region vanishes, which is a desiredsituation.

In order to compare the vulnerability region to some reference region we intro-duce the normalized vulnerability region.

Definition 14.5 The normalized vulnerability region is the ratio of the vulner-ability region to the surface of the disk with radius dd,s .

The definition tells us that if the normalized vulnerability region of a coop-erative system is less than 1, we get a smaller vulnerability region than for anoncooperative system, or in other words, cooperation increases network secu-rity.

In our numerical analysis we observe the following bounds on the secrecycapacity:

CU Bs = max(CU B − Cm , 0),

CL Bs = max(CL B − Cm , 0).

In a cooperative system, where M ≥ 1, we can determine numerically thelower and the upper bound of the normalized vulnerability region. It is naturalthat they depend heavily on the position of the cooperating relays, and that thelower bound of the vulnerability region is determined by the upper bound of thecapacity of the main channel (14.50), while the upper bound of the vulnerabilityregion is determined by the lower bound on the capacity of the main channel(14.51).


LB UB

LB UB

LB UB

Figure 14.13. Examples of the lower bound (LB) and upper bound (UB) on theshape of a typical vulnerability region for M = 1 (upper), M = 3 (middle), andM = 5 (lower).


In this subsection, we show several examples of the shape of the secrecy regionin a cooperative system. We also observe how the average surface depends onthe number of relays.

We fix the parameters as follows: σ2 = 1, P = Pi = 1, i = 1, 2, . . . ,M , andβ = 2. For these parameters, typical vulnerability regions are described in Fig-ure 14.13 for M = 1, M = 3, and M = 5, using model 2. The source node is repre-sented by a centrally positioned star, the destination node by a square positionedto the right of the source, and the randomly placed relay nodes by diamonds.When the malicious node is positioned in a dark area, perfectly secure communi-cation is possible (i.e., the secrecy capacity is positive). The white areas (islands)represent the vulnerability regions. It is easily noticeable that an increased num-ber of cooperating relays reduces the vulnerability region, hence, increasing thesystem secrecy.


1 2 3 4(a)

5 60

0.1

0.2

0.3

0.4

0.5

0.6

M

Bou

nds

LB

UB

(b)1 2 3 4

M5 6

0

0.1

0.2

0.3

0.4

0.5

0.6

Bou

nds

LB

UB

Figure 14.14. Lower bound (LB) and upper bound (UB) of the normalized vul-nerability region for β = 2 and (a) correlation model 1 and (b) correlation model2 as a function of the number of cooperating relays M .

In order to understand the importance of the cooperation in increasing thesecrecy capacity or, equivalently, the secrecy region of a certain network, wecharacterize the surface of the vulnerability region. To that end, we analyze howthe normalized vulnerability region depends on the number of cooperative relays.The dependence of the lower and upper bounds of the normalized vulnerabilityregion on the number of relay nodes, for β = 2, for both correlation models isshown in Figure 14.14.

Our simulations indicate that choosing cooperation relays that are closer tothe line that connects the source and the destination, minimizes the vulnerabilityregion. In Figure 14.15 we observe the dependence of the normalized vulnerabilityregion bounds on the number of relay nodes, for β = 2, for both correlationmodels (model 1 and model 2) when the relays are placed on the line connectingthe source and the destination. Note that for both models the secrecy region issmaller in this case. This indicates that the source should choose relays that arecloser to the line in order to minimize the secrecy region. This is not surprising


1 2 3 4 5 60

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

M

Bou

nds

UB

LB

(a)

1 2 3 4 5 60

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

M

Bou

nds

LB

UB

(b)

Figure 14.15. Lower bound (LB) and upper bound (UB) of the normalized vul-nerability region for β = 2 and (a) correlation model 1 and (b) correlation model2 as a function of the number of cooperating relays M that are placed on theline between the source and the destination.

since the relaying is the most efficient when the relay node lies on the line betweenthe source and the destination. For M = 1, we notice in Figure 14.16 a minimumof the lower and upper bounds on the normalized vulnerability region if therelay is placed between the source and the destination. The minimum dependson β, P, Pi as well as on the model chosen. It is very intuitive that choosinga larger transmit power for either the source or the relays makes the systemmore vulnerable, and, hence, the secrecy region larger. Finally, we would like tocomment that correlation model 2 is worse than correlation model 1. This comesfrom the properties of the exponential and the Gaussian function and how theyaffect the secrecy capacity.

We have demonstrated that the information-theoretic security of a networkcan be increased by cooperation. Depending on the capabilities of the maliciousnode, one could improve the security a great deal, by minimizing the vulnerabil-ity region. As we include more and more relays, the increase in the improvement

14.4 Eavesdroppers’ cooperative model 407

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

UB

LB

d1,s

Bou

nds

Figure 14.16. Lower (LB) and upper bound (UB) of the normalized vulnerabilityregion for β = 2 and correlation model 1 as a function of the distance betweenrelay 1 in the cooperative system with one relay (M = 1) which is placed alongthe line between the source and the destination.

is less and less. The most dramatic improvement is obtained by cooperationwith one relay and for each additional relay the improvement that is obtaineddecreases. From the simulation results, we see that depending on the correlationmodel of the eavesdropper, we have a different size vulnerability region. In addi-tion, the source should choose relays that stay close to the line that connects thesource and the destination in order to minimize the secrecy region. Depending onthe system parameters there is a distance between the source and the relay nodethat results in the region being minimal. By a simple analysis we have shownthat cooperation can dramatically improve the information-theoretic securityin a given wireless network. One has to be aware, however, that the securityimprovement is not simply because of the reduction of the transmission rangebetween the hops in a multihop communication setting. It actually comes fromthe fact that cooperation increases the capacity of the main channel for morethan the eavesdropper channel can benefit from eavesdropping on the sourcesplus multiple relay nodes.

14.4 Eavesdroppers cooperative model

While there has been increased attention paid to physical layer security, a sig-nificant amount of the research has been devoted to studying methods andtechniques for improving the secrecy rate of wireless nodes in the presence ofeavesdroppers. However, in order to understand better the defense mechanismsthat wireless users can adopt protect their transmission from eavesdroppers it isnecessary to understand how the eavesdroppers themselves operate in the net-work. In this context, it is of interest to study how the malicious nodes, i.e., the


eavesdroppers, can use different strategies to increase the amount of damage theycan cause on the network’s nodes. For instance, with the emergence of coopera-tion as a new communication paradigm, the eavesdroppers in a wireless networkcan benefit from various cooperative techniques for improving their reception ofthe signal that they are interested in tapping.

Hence, while most literature is focused mainly on the users’ side in physicallayer security problems, this section aims to provide cooperation models for theeavesdroppers. In this regard, the main objectives of this section are to propose:(i) a cooperation protocol that allows a network of eavesdroppers to interactto improve their eavesdropping performance; (ii) an adequate utility functionfor the eavesdroppers that accounts for the cooperation gains and cost; and(iii) a coalitional game-based model for forming cooperative groups among theeavesdroppers. Using the proposed coalitional game model, the eavesdroppers cantake distributed decisions to form or break up a cooperative group dependingon their gains from and costs of cooperation. Consequently, by allowing theeavesdroppers to cooperate, independent disjoint eavesdroppers’ coalitions willbe formed in the network.

Consider a network having K single-antenna eavesdroppers (static or mobile)that intend to tap into the transmissions of N wireless transmitters which arecommunicating with a central base station (BS). Let us denote by K and Nthe sets of eavesdroppers and users, respectively. In a noncooperative approach,consider a time-slotted system whereby during a single slot of duration θslot

all K eavesdroppers, each acting on its own (noncooperatively), are interestedin tapping into the transmission of one of the N users in the network.1 Theeavesdroppers can attack the users in any arbitrary manner over the slots but,for convenience (and due to the ergodicity of the attacks over time), in slot 1,it is assumed that all eavesdroppers are noncooperatively attacking user 1, inslot 2, all eavesdroppers are non-cooperatively attacking user 2, and so on untilall N users have been attacked once by the eavesdroppers. Consequently, a totalof N slots is required to complete one round of eavesdropping on all N users.Every block of N slots will be referred to as the eavesdropping cycle and theeavesdroppers engage in multiple eavesdropping cycles over time.

During a single eavesdropping cycle (N slots), the objective of every eaves-dropper is to maximize the damage caused on the users, which translates intominimizing the secrecy capacities of all N users (during one cycle). Thus, thetotal damage that an eavesdropper k ∈ K can cause to the transmitters througha single eavesdropping cycle is given by overall reduction of the secrecy capacitiesthat k yielded, as follows:

u(k) = −∑i∈N

(Cd

i − Cek,i

)+, (14.56)

1 This model is selected for simplicity; however, the case where each eavesdropper may selecta different user to tap into within a slot can also be treated using the proposed coalitionalgame model.


where Cdi = W · log2 (1 + g2

i,BS · P /σ2) is the capacity of user i ∈ N achievedat the BS with gi,BS being the channel gain between i and the BS, W beingthe available bandwidth, P being the transmit power of user i (assumed tobe the same for all users in N ), and σ2 the variance of the Gaussian noise.Further, Ce

k,i = W · log2 (1 + g2i,k · P /σ2) is the capacity of the point-to-point

channel between user i and eavesdropper k. A quasi-static channel model isconsidered whereby the channel gain gi,j between any two nodes (users–BS,eavesdropper–user, or eavesdropper–eavesdropper) is given by

gi,j = ai,j ·√

d−µi,j , (14.57)

where di,j is the distance between nodes i and j, µ is the path-loss exponent, andai,j is a Rayleigh distributed fading amplitude with variance 1 which is stableover the duration θslot of a slot but changes from one slot to the another (quasi-static channel). Note that the minus sign is inserted in (14.56) for convenience,in order to turn the problem into a maximization problem.

In (14.56), each element of the summation quantifies the damage that eaves-dropper k is able to cause on the secrecy capacity of user i when tappinginto its signal during the corresponding time slot. The eavesdroppers aim tominimize the summation in (14.56) in every eavesdropping cycle by maximizingthe damage caused through the eavesdropping capacities Ce

k,i ,∀k ∈ K, i ∈ N .Due to the fading and path-loss between the eavesdropper and the user, theseeavesdropping capacities may be small, thus, reducing the overall effectivenessof the eavesdropping process of all eavesdroppers. Hence, efficient techniquesfor combatting this fading are needed by the eavesdroppers in order to improvetheir performance. For example, the eavesdroppers can engage in distributedcollaborative receive beamforming [26–28], whereby the radio signals receivedby a group of single-antenna eavesdroppers with nondirectional antennas can becombined using advanced signal processing techniques to improve the capacitiesCe

k,i ,∀k ∈ K, i ∈ N .Therefore, to improve their performance in terms of eavesdropping capacities,

the eavesdroppers in our model can cooperate by forming groups of eavesdrop-pers, i.e., coalitions. Every coalition of eavesdroppers, S ⊆ K, can be regardedas a single eavesdropper with multiple receive antennas and, within a single slot,this coalition can use collaborative receive beamforming to tap into the signal ofone of the transmitters. For every coalition S, a two-stage cooperation protocolis defined whereby the coalition divides its slot into two phases as follows (thisprotocol is used every slot to eavesdrop on a particular user i ∈ N ):

(1) The first phase of the slot is dedicated to information exchange betweeneavesdroppers. Hence, sequentially, each eavesdropper k ∈ S broadcasts itsinformation (channel, control, etc.) to the other members of coalition S inthis duration of the slot.


(2) In the remainder of the slot, the members of coalition S perform collaborativereceive beamforming, i.e., the coalition directs its beam towards the user thatits members are currently interested in attacking.

Once the coalitions in the network are formed, during each time slot in an eaves-dropping cycle all the coalitions (each coalition acting on its own) eavesdrop onone user i ∈ N in a round-robin manner.

During the information exchange phase, the users are able to transmit withoutbeing tapped into since the eavesdroppers are communicating with each otherto exchange their channel and control information. Further, during this firstphase, the users can overhear the information exchange between the eavesdrop-pers (act as eavesdroppers on the eavesdroppers!) and, thus, detect the presenceof the eavesdropping threat. Consequently, while in the second phase the eaves-droppers improve their eavesdropping capacity using receive beamforming, thisperformance improvement is hindered by the time and security costs during theinformation exchange phase. Given this benefit–cost tradeoff, for any coalitionS ⊆ K of eavesdroppers, the total secrecy capacity reduction that a coalitionS can cause for the users during an eavesdropping cycle can be given by thefollowing utility function:

u(S) = −∑i∈N

(θS,i · Cd

i + (1− θS,i)(Cd

i − CeS,i

)+), (14.58)

where CeS,i is the receive beamforming eavesdropping capacity, which is given by

CeS,i = W · log2

(1 +

P · ‖h‖2σ2

), (14.59)

where h is the |S| × 1 channel vector and each row element hk = gi,k with gi,k

the channel gain between user i and eavesdropper k ∈ S as given by (14.57).The eavesdropping capacity in (14.59) is achieved by the eavesdroppers throughmaximal ratio combining which is well known as the optimal SNR maximizingtechnique for combining the received signals and directing the beam towardsa particular direction [26]. Moreover, θS,i is a time cost that accounts for twotypes of cost for cooperation: (i) the time required for information exchangeduring which users are transmitting securely; (ii) the possibility that the usersmay overhear the transmission (and act as eavesdroppers on the eavesdroppers!)between the eavesdroppers during the information exchange phase. This fractionof time is given by

θS,i =

(∑k∈S

θik

)−, (14.60)

with b− min (b, 1) and θik the fraction of time required for exchanging infor-

mation between an eavesdropper k ∈ S and the other members of coalition S

without being tapped into by transmitter i ∈ N (in the slot when the coalition’s


beam is directed towards user i). In the first phase of the slot, every eavesdropperk ∈ S exchanges its information with the members of S by sending its data tothe farthest member k = arg maxl∈S (dk,l) in S as the other members of S simul-taneously receive this information due to the broadcast nature of the wirelesschannel. Consequently, θi

k =(θi

k,k/θslot

)with

θik,k

=L

Cexchk,k ,i

, (14.61)

where Cexchk,k ,i

= (Cdk,k− Ce

i,k )+ represents the secrecy capacity for exchange of

information between eavesdropper k and the farthest eavesdropper k ∈ S whenbeing eavesdropped on by user i and L is the size (in bits) of the packet con-taining control and channel information.

Every element in the summation of (14.58) represents the secrecy capacityreduction for the slot where coalition S was eavesdropping on a user i ∈ Nusing the two-stage cooperative protocol proposed. For instance, during theeavesdroppers information exchange period θS,i , user i is able to transmitfreely with no eavesdropping, hence the term θS,i · Cd

i . For the rest of the slot(1− θS,i), coalition S is able to eavesdrop on user i with an improved perfor-mance due to the receive beamforming gain as exhibited by Ce

S,i in the term

(1− θS,i)(Cd

i − CeS,i

)+. The objective of the eavesdroppers (coalitions) is tomaximize the damage on the users as captured by (14.58).

For a better understanding of (14.58) one can consider some extreme cases.For example, when the eavesdroppers in coalition S, who are eavesdropping onuser i, (θS,i = 1,), spend the whole time slot θc exchanging information, user i

will have transmitted all of its data without any tapping and, cooperation isnot beneficial for attacking i (although it may be beneficial for eavesdroppingon another user j = i in another time slot). On the other hand, if θS,i = 0, thencoalition S spends no time for information exchange, and, hence, the attack onuser i is most efficient as coalition S is able to perform receive beamforming onuser i during the whole slot θc . Finally, whenever S is a singleton, then u(S) in(14.58) reduces to the expression given in (14.56) (for a singleton coalition ofsize 1 there is no information exchange, i.e., θS,i = 0).

Given this cooperative model for eavesdropping, the key question that remainsto be answered is: how can a network of eavesdroppers form cooperative coalitionsin a distributed manner taking into account the benefit–cost tradeoff for coop-eration previously described. The following subsection is dedicated to answeringthis question using coalitional game theory.

14.4.1 Coalition formation games for distributed eavesdroppers cooperation

To model the eavesdroppers cooperation problem mathematically, coalitionalgame theory [29, 30] provides a set of suitable analytical tools. In fact, the


eavesdroppers cooperation problem can be modeled as a coalitional game witha nontransferable utility which is defined as follows [29, Chap. 9].

Definition 14.6 A coalitional game with nontransferable utility is defined bya pair (K, V ), where K is the set of players and V is a mapping such that forevery coalition S ⊆ K, V (S) is a closed convex subset of R

|S | that contains thepayoff vectors that players in S can achieve.

In other words, a coalitional game has a nontransferable utility whenever thetotal utility achieved by any coalition S cannot be arbitrarily apportioned amongthe members of S, hence there is a need for a set of payoff vectors, i.e., a map-ping V to describe the utilities achieved by the players in a coalition S. In theeavesdroppers cooperation model, the set of eavesdroppers K is the set of playersin the coalitional game. In addition, given a coalition S and denoting by φk (S)the payoff of eavesdropper k ∈ S achieved during an eavesdropping cycle, thefollowing property is highlighted.

Property 3 The proposed cooperative eavesdropping game has a non-transferable utility where the payoff φk (S) received by any eavesdropper k ∈ S

during one eavesdropping cycle, i.e., the overall secrecy capacity reduction causedduring one cycle by eavesdropper k when acting as part of S, is equal to theoverall secrecy capacity reduction u(S) achieved by the coalition S as given by(14.58).

Given Property 3, the mapping V for the eavesdroppers coalitional game canbe defined as follows:

V (S) = φ(S) ∈ R|S || φk (S) = u(S), ∀k ∈ S, (14.62)

where φ(S) is a vector of payoffs achieved during one eavesdropping cycle by theeavesdroppers when acting in coalition S, u(S) is the overall secrecy capacityreduction incurred on the users in N as given by (14.58). Clearly, the set V (S)in the proposed game is a singleton since a coalition S can only achieve a singleutility value as dictated by (14.58). Consequently, this set is closed and con-vex, and the eavesdroppers cooperation problem is cast into a (K, V ) coalitionalgame with nontransferable utility, where the eavesdroppers aim to maximizetheir payoffs and hence minimize the overall secrecy capacity achieved by theusers (achieve maximum damage to the users) by forming coalitions.

Moreover, as explained in the previous section, the damage achieved by anycoalition as per (14.58) takes into account the cost for cooperation. Consequently,given the cost of information exchange, the eavesdroppers coalitional game forcooperation satisfies the following property.


Remark 14.1 For the (K, V ) eavesdroppers coalitional game, due to the cost ofcooperation, the grand coalition of all users seldom forms. Instead, independentdisjoint coalitions will appear in the network.

This can be easily seen by noting that the cost of cooperation grows as:(i) the number of eavesdroppers in the coalition increases as seen in (14.60)and (ii) the channel (distance) between the eavesdroppers in the coalition,as well as the channel (distance) between the eavesdroppers and the users variesas seen from (14.61). For example, by considering a network of two eavesdroppersseparated by a very large distance, the time required for information exchangeas seen from (14.60) can be close to 1, hence yielding no benefit for cooperationas per (14.58). Therefore, due to the various cooperation costs, the grand coali-tion of all users forms only in very favorable conditions which can be quite unre-alistic for a large-scale wireless network. Hence, the network structure consistsof disjoint independent coalitions.

Therefore, the proposed game for eavesdroppers cooperation is classified as acoalition formation game due to the presence of cooperation costs and the factthat the grand coalition is not always the optimal solution [30, Sec. IV]. In thisregard, coalition formation games have been a topic of great interest in game the-ory [30, 31, 33] and have also attracted attention in wireless and communicationnetworks [30]. The goal is to find algorithms for characterizing the coalitionalstructures that form in a network where the grand coalition is not optimal. Byusing game-theoretical concepts from coalition formation games, a distributedcoalition formation algorithm is devised for the proposed (K, V ) eavesdropperscooperation game. For this purpose, an algorithm can be built based on two sim-ples operations, called “merge” and “split” borrowed from coalition formationgames [32] and defined as follows.

Definition 14.7 Merge rule. Merge any set of coalitions S1 , . . . , Sl wheneverthe merged form is preferred by the players, i.e., where

⋃lj=1 Sj S1 , . . . , Sl.

Therefore S1 , . . . , Sl → ⋃l

j=1 Sj.

Definition 14.8 Split rule. Split any coalition⋃l

j=1 Sj whenever a splitform is preferred by the players, i.e., where S1 , . . . , Sl

⋃lj=1 Sj. Thus,

⋃l

j=1 Sj → S1 , . . . , Sl.

In these definitions, the operator represents a comparison relation, i.e., anoperator that allows the players to quantify their preferences over the differentcoalitional structure. For instance, for the proposed eavesdroppers coalitionalgames, the Pareto order is selected as a comparison relation , and is definedas follows:


Definition 14.9 Consider two collections of coalitions R = R1 , . . . , Rl andS = S1 , . . . , Sm that are partitions of the same subset A ⊆ K (same players inR and S). For a collection R = R1 , . . . , Rl, let the utility of a player j in acoalition Rj ∈ R be denoted by Φj (R) = φj (Rj ) ∈ V (Rj ). R is preferred over Sby Pareto order, written as R S, iff

R S ⇐⇒ Φj (R) ≥ Φj (S) ∀ j ∈ R,Swith at least one strict inequality (>) for a player k. (14.63)

Using the Pareto order, the merge and split rules are interpreted as follows.On the one hand, using the merge rule, a number of coalitions can cooperateand form a larger coalition if this merge yields a preferred collection based onthe Pareto order. This implies that a group of players can agree to form a largercoalition, if at least one of the players improves its payoff without decreasing theutilities of any of the other players. On the other hand, any formed coalition candecide to break up into smaller coalitions, using the split rule, if splitting yieldsa preferred collection by Pareto order. The idea of merge and split is based ona family of coalition formation games, known as games with partially reversibleagreements. In such games, once the players agree to sign an agreement to form acoalition (e.g., using merge), this agreement can only be broken if all the playersapprove (e.g., using split).

In the proposed eavesdroppers game, performing merge or split using thePareto order defined in (14.63) requires that the eavesdroppers have full knowl-edge of the instantaneous channel gain, including the fading amplitude as per(14.57). As the fading amplitude varies from one slot to another, utilizing thePareto order as per (14.63) can require a continuous estimation of the instan-taneous fading amplitude of the channel, which can be quite a complex processfor the eavesdroppers. Thus, in order to avoid this complexity, the eavesdrop-pers can use a far sighted approach to the merge and split rules whereby theeavesdroppers use the Pareto order in (14.63) based on their long-term payoffφk (S) = u(S).

This long-term payoff is defined as the utility that the eavesdroppers receiveduring an eavesdropping cycle averaged over the fading amplitude realizations.Using the quasi-static channel mode, one can easily note from (14.57) and(14.58) that the secrecy capacities, and payoffs φk (S) averaged over the chan-nel realizations depend mainly on the path-loss (distance) between the nodes(eavesdropper–eavesdropper, eavesdropper–user, or user–BS). As a result, toform coalitions, the eavesdroppers can use the far sighted merge and split rules.Then, any coalition formation algorithm based on the far sighted merge and splitrules no longer requires a knowledge of the instantaneous fading amplitude asthe decisions are based on long-term utilities averaged over the fading amplitude.

Using the far sighted merge and split rules, one can devise a coalition forma-tion algorithm based on three phases: neighbor discovery, adaptive far sightedcoalition formation, and cooperative eavesdropping. In the neighbor discovery


phase (phase 1), each coalition (or eavesdropper) surveys its neighborhood tolocate nearby eavesdroppers with whom cooperation is possible. At the end ofthis phase, each coalition constructs a list of its neighboring partners and pro-ceeds to the next phase of the algorithm.

In the second phase, the coalitions (or individual eavesdroppers) interact withtheir neighbors to assess whether to form new coalitions or whether to breakuptheir current coalition. For this purpose, an iteration of sequential far sightedmerge and split rules occurs in the network, whereby each coalition decides tomerge (or split) depending on the long-term utility improvement that merging(or splitting) yields. This phase starts with an initial network partition T =T1 , . . . , Tl of K. Subsequently, any random coalition (individual eavesdropper)can start with the merge process. For practicality purposes, consider that thecoalition Ti ∈ T which has the highest long-term utility in the initial partitionT starts by attempting to merge with a nearby coalition. On the one hand, ifmerging occurs, a new coalition of eavesdroppers Ti is formed and, in its turn,Ti will attempt to merge with nearby eavesdroppers (coalitions), if possible. Onthe other hand, if Ti is unable to merge with the first neighbor it finds, it triesto find other coalitions that have a mutual benefit in merging. The search endswith a final merged coalition T f inal

i composed of the eavesdroppers in Ti andone or several of coalitions in its vicinity (Tf inal

i = Ti , if no merge occurred).The algorithm is repeated for the remaining Ti ∈ T until all the coalitions havemade their merge decisions, resulting in a final partition F .

Following the merge process, the coalitions in the resulting partition F cannext perform split operations, if any are possible. An iteration consisting of mul-tiple successive merge and split operations is repeated until there is convergence.Note that the decisions on whether to merge or split can be taken in a dis-tributed way by the eavesdroppers without relying on a centralized entity. Theconvergence of an iteration of merge and split rules is guaranteed [32]. Further,as shown in [33], this convergence always leads to a partition that is stable inthe sense that no coalition has any further incentive to perform merge and split.Also, under certain conditions, as per [33], the network partition can be bothstable and Pareto optimal, in terms of the eavesdroppers payoffs.

In the cooperative eavesdropping phase (phase 3), within every slot of aneavesdropping cycle, the coalitions exchange their information and begin theircooperative eavesdropping process, in a time-slotted manner, one coalition perslot. Hence, in this phase, the eavesdropper coalitions perform the actual receivebeamforming, to efficiently tap into the signal of the network’s users within thecorresponding slot. For a stationary network, the last phase of the algorithm,i.e., the cooperative eavesdropping phase, is performed continuously over a largenumber of eavesdropping cycles. On the other hand, in a network where theeavesdroppers and/or the users are mobile, periodic runs of the first two phasesof the proposed algorithms are performed which allows the eavesdroppers toautonomously self-organize and adapt the network’s topology through appropri-ate merge-and-split decisions during phase 2. This adaptation to environmental


changes is performed in mobile networks periodically every M eavesdroppingcycles. In general, the number M of cycles can be chosen arbitrarily but, toadapt to mobility, M must be small as mobility increases in order to allow ade-quate adaptation of the network.

The proposed coalition formation algorithm can be implemented in a dis-tributed manner. At the beginning, the eavesdroppers can detect the strengthof the users’ uplink signals, and, thus, estimate the location of these users. Notethat, due to the far sighted merge and split rules considered, the eavesdroppersare not required to estimate the instantaneous fading amplitude of the chan-nel (only estimates of the users’ locations are needed to evaluate the long-termpayoffs needed for coalition formation). Further, nearby coalitions (eavesdrop-pers) can be discovered in phase 1 through techniques similar to those used inthe ad-hoc routing discovery process. Once the neighbors are discovered and theusers’ locations are estimated, the coalitions can perform merge operations inphase 2. Moreover, each coalition formed can also internally decide to split if itsmembers find a preferred split structure. During phase 3, in every slot, the dis-tributed eavesdroppers exchange their information (channels, control, etc.) andthen cooperate to perform receive beamforming using the cooperative protocolpreviously described.


The performance of the coalition formation algorithm for the eavesdroppers wasassessed by simulations. Thus, given a square network of 4 km × 4 km with theBS located at the center, the eavesdroppers were randomly placed in the upper4× 2 rectangle while the users were randomly deployed within the lower 4× 2rectangle. The simulation parameters used were as follows: the number of bitsfor information exchange was taken as L = 128 bits, the power constraint pereavesdropper/user was P = 10 mW, the noise level was −90 dBm, the channelpropagation loss was set to α = 3, and the bandwidth was W = 100 kHz. Thetime slot duration was taken as θc = 42.3 ms which corresponds to the coherencetime of a network with very low mobility (e.g., Doppler frequency of around10 Hz).

Figure 14.17 shows a snapshot of the network structure resulting from theproposed coalition formation algorithm for a randomly deployed network withK = 10 eavesdroppers, and N = 10 users. In this figure, one can see how theeavesdroppers were able to self-organize into four coalitions, hence forming thenetwork structure T = T1 , T2 , T3 , T4. This structure is a direct result of the farsighted merge-and-split coalition formation algorithm. For example, eavesdrop-per 2 is unable to find nearby partner to improve his payoff and hence decidesto act alone. In contrast, eavesdroppers 5 and 9 merge into a single coalitionT1 = 5, 9 due to the fact that V (5, 9) = φ(5, 9) = [−135× 104 , −135×104] which is a clear improvement on the noncooperative utilities which wereφ5(5) = −177.32× 104 and φ9(9) = −174.44× 104. Similar results can also


y

T

T

T

T

x

Figure 14.17. A snapshot of a coalitional structure resulting from our proposedcoalition formation algorithm for a network with K = 10 eavesdroppers, andN = 10 users (circles).

be seen for the formation of coalitions T3 and T4 . In summary, Figure 14.17 showshow the eavesdroppers can self-organize into disjoint independent coalitions toperform cooperative eavesdropping through receive beamforming.

In Figure 14.18, for a network having N = 10 users, the payoff (secrecy capac-ity reduction) per eavesdropper achieved per eavesdropping cycle is shown duringa period of about 4.2 minutes, i.e., M = 600 eavesdropping cycles (each eaves-dropping cycle consists of N = 10 slots) averaged over the random locations ofthe eavesdroppers and the users as a function of the eavesdroppers network sizeK. The payoff shown is the actual payoff achieved by the eavesdroppers overthis period given the instantaneous fading amplitudes of the channel followingthe coalition formation process. The performance of the proposed eavesdroppercoalition formation algorithm is compared to that of the noncooperative case.For the cooperative case, the average eavesdropper’s payoff increases with thenumber of eavesdroppers since the possibility of finding cooperating partnersincreases. Moreover, this increase is interpreted that, as more eavesdroppers areavailable, the efficiency of attacking several users also improves. In contrast, thenoncooperative approach presents an almost constant performance with differ-ent network sizes. Clearly, Figure 14.18 demonstrates that cooperation presents asignificant advantage over the noncooperating case in terms of average payoff pereavesdropper per eavesdropping cycle for all network sizes, and this advantage


K

Figure 14.18. Payoff per eavesdropper per eavesdropping cycle (averagedover random locations of the eavesdroppers and users) achieved during M =600 eavesdropping cycles (around 4 minutes) in a network with N = 10 users asthe number of eavesdroppers K varies.

increases with K, reaching 27.6% of improvement relative to the noncooperatingcase at K = 40 eavesdroppers.

14.4.3 Conclusion

We have introduced a model for cooperation among the eavesdroppers in a wire-less network. Using a coalition formation game model, a number of single-antennaeavesdroppers interact to form cooperative coalitions that can utilize receivebeamforming techniques to improve their attacks on the wireless users. For form-ing coalitions, a distributed algorithm has been devised based two simple rulesof merge and split that allow the eavesdroppers to take autonomous decisions toform or breakup a coalition depending on their utility improvement. The utilityof every coalition corresponds to the overall secrecy capacity reduction that thecoalition can inflict on the network’s users over the duration of an eavesdrop-ping cycle. For the derived model, we have highlighted the key properties andcharacterized the resulting network structures. By simulations, it has been shownthat, using coalition formation, the eavesdroppers can self-organize while improv-ing the average payoff per eavesdropper up to 27.6% per eavesdropping cycle

References 419

relative to the noncooperating case. For future work in this area, one could con-sider cooperative defense mechanisms (against the eavesdroppers’ cooperation)for the users and examine any possible equilibria, in terms of network partitions(at both the eavesdroppers and users sides) that can result when the eavesdrop-pers and the users engage in coalition formation simultaneously.

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Part V

Standardization activities

15 Cooperative communications in3GPP LTE-Advanced standard

Hichan Moon, Bruno Clerckx, and Farooq Khan

15.1 Introduction

A cellular communication system is designed based on the concept of frequencyreuse, in which the same frequency resources are reused at a certain distancefrom a cell site [1, 2]. Traditionally, a cellular system has been composed of cellsites operating independently except in some inevitable scenarios like handover.Independent operation of each cell site makes it possible to deploy a wirelesssystem at a low cost, while maintaining the quality of the voice service. However,due to the large amount of interference from neighboring cell sites, cell-edgeusers experience bad channel conditions. Furthermore, the cell-edge interferencebecomes more severe, when the frequency reuse factor is 1, which is a commonassumption for cellular systems designed for high capacity. Therefore, with theconventional cellular designs, it is difficult to achieve high data throughput forusers located at cell edges.

However, as the need for high-speed data communication increases, coopera-tive communications between the neighboring cell sites and UEs1 are being moreintensively studied not only in academia but also in industry. One of the mainfocuses of these studies is to increase the data throughput for the cell-edge UEs.To increase the throughput of the cell-edge UEs, neighboring eNodeBs2 cooper-ate to enhance the signal quality and/or decrease the interference level. Cover-age extension through a wireless relay is another research focus of cooperativecommunication. Interference management and cooperation between eNodeBs areimportant issues in a heterogeneous network.

The third generation partnership project (3GPP) long-term evolution (LTE)-Advanced is one of the most promising standards for the next generation wire-less communications systems. LTE-Advanced is a candidate for the Interna-tional Mobile Telecommunication Advanced (IMT-Advanced) of Internation-Telecommunications-Union-R (ITU-R) and is being designed based on the 3GPP

1 The UE is the common terminology used to denote mobile terminal in LTE.2 Note that eNodeB is the terminology used in LTE to denote (or eNB) the base station.


426 Cooperative communications in 3GPP LTE-Advanced standard

Table 15.1. LTE system attributes

Bandwidth 1.25 ∼ 20 MHzDuplexing FDD, TDD, half-duplex FDDMobility 350 Km/Hr

Multiple access Downlink OFDMAUplink SC-FDMA

MIMO Downlink 2×2, 4×2, 4×4Uplink 1×2, 1×4

Peak data rate Downlink 173 and 326 Mbps for 2×2 and 4×4 MIMOin 20 MHz Uplink 86 Mbps with 1x2 antenna configuration

Modulation QPSK, 16-QAM and 64-QAMChannel coding Turbo codeOther techniques Channel sensitive scheduling, link adaptation,

power control, ICIC and hybrid ARQ

LTE system, which utilizes orthogonal frequency-division multiplexing (OFDM)technology in the air interface [3]. In this chapter, standardization trends incooperative wireless communications are presented for the 3GPP LTE-Advancedsystem.

The rest of this chapter is organized as follows. Section 15.2 introduces the3GPP LTE and LTE-Advanced systems. Cooperative multipoint (CoMP) trans-mission techniques are investigated in Section 15.3. Sections 15.4 and 15.5present the wireless relay and the heterogeneous networks considered in the LTE-Advanced standard, respectively.

15.2 LTE and LTE-Advanced

The 3GPP LTE standard was developed between 2004 and 2009 with the goal ofproviding a high-data-rate, low-latency and packet-optimized radio-access tech-nology supporting flexible bandwidth deployments. In parallel, a new networkarchitecture was designed with the objective of supporting packet-switched traf-fic with seamless mobility, quality of service (QoS) and minimal latency.

The air-interface-related attributes of the LTE system are summarized in Table15.1. The system supports flexible bandwidths thanks to OFDMA and singlecarrier frequency division multiple access (SC-FDMA) schemes. In addition tofrequency-division duplexing (FDD) and time-division duplexing (TDD), half-duplex FDD is allowed to support low-cost UEs. Unlike FDD, in half-duplexFDD operation, a UE is not required to transmit and receive at the same time.This avoids the need for a costly duplexer in the UE. The system is primarily

15.2 LTE and LTE-Advanced 427

optimized for low speeds, up to 15 km/h. However, the system specifications allowmobility support in excess of 350 km/h with some performance degradation. Theuplink access is based on SC-FDMA, which promises increased uplink coveragedue to low peak-to-average power ratio (PAPR) relative to OFDMA [4].

The system supports a downlink peak data rate of 326 Mbps with 4× 4 MIMOwithin 20 MHz bandwidth. Since uplink MIMO is not employed in the firstrelease of the LTE standard, the uplink peak data rate is limited to 86 Mbpswithin 20 MHz bandwidth. In addition to the peak data rate improvements, theLTE system provides 2–4 times higher cell spectral efficiency than the Release6 high-speed packet access (HSPA) system. Similar improvements are observedin cell-edge throughput while maintaining the same site locations as deployedfor HSPA. In terms of latency, LTE radio-interface and network are capable ofdelivering a packet from the network to the UE in less than 10 ms. We refer thereaders to [3] for a detailed description of the LTE system.

The LTE standard was completed in 2009 and some initial commercial LTEdeployments are already underway in the USA, Japan, and Europe to accommo-date the growing data traffic demands. The mobile data traffic continues to growand is expected to grow at a compound annual growth rate (CAGR) of 131%[5] over the next years, increasing more than 65 fold in 5 years. In order to meetthis spectacular growth in data traffic, continuous improvements in air-interfaceefficiency as well as allocation of new spectrum are of paramount importance.

The decisions on IMT spectrum allocation at the World RadiocommunicationConference 2007 (WRC-07) have set the stage for the future evolution of radiotechnologies towards IMT-Advanced. IMT-Advanced is an ITU-R initiative fordeveloping the fourth generation global mobile broadband wireless standard.A major effort is underway by the 3GPP and IEEE 802.16 standard bodiesto develop the IMT-Advanced compliant fourth generation mobile broadbandstandards. With only two candidate technologies proposed for IMT-Advanced,it is expected that the fourth generation mobile broadband market will be lessfragmented compared with the previous generations of cellular technologies.

At WRC-07, the bands identified for IMT in addition to the existing IMT-2000 bands include: 450-470 MHz, 698-862 MHz, 790-862 MHz, 2.3-2.4 GHz,3.4-4.2 GHz, and 4.4-4.99 GHz, as shown in Figure 15.1. A maximum of428 MHz new spectrum has been identified for IMT-2000/IMT-Advanced(including TV bands).

The IMT-Advanced set peak data rate targets are 1 Gbps in nomadic envi-ronments and 100 Mbps in high mobility scenarios. Also, the cell throughput orspectral efficiency target is set at around two times higher than existing LTE[3] and WiMAX [6] systems. In order to meet the peak data rate and spectralefficiency targets set by IMT-Advanced, the air interface needs to be evolved byincorporating new radio technologies as well as improving performance of theexisting techniques.

In April 2008, 3GPP started LTE-Advanced standardization activities as partof Release 9 work. The LTE-Advanced study item was completed in 2009 forming


100 200 300 400 500 600 700 800 900 1000 1100 1200

470-806/862 MHz

1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900

2700-2900

MHz

3300 3400 3500 3600 3700 3800 3900 4000 4100 4200 4300 4400 4500 4600 4700 4800 4900 5000

3400–4200 MHz 4400–4900 MHz

2300–2400 MHz

410–430 MHz 450–470 MHz806–960 MHz

1710–2025 MHz

2110–2200 MHz2500-2690MHz

IMT-2000 bands Candidate bands for IMT-Advanced

Figure 15.1. Candidate bands for the IMT-Advanced spectrum.

the basis for LTE-Advanced standardization in Release 10. The Release 10 LTE-Advanced standard, with expected completion in 2011, incorporates the followingnew features [7, 8]:

carrier aggregation, latency reductions, enhanced downlink multiple-antenna transmission, uplink multiple-antenna transmission.

Additionally, a work item on LTE-Advanced relays targeted to improve cov-erage and cell edge throughput was approved separately.

15.2.1 Carrier aggregation

LTE-Advanced is expected to operate in spectrum allocations of different sizesincluding wider spectrum allocations of up to 100 MHz to achieve the target peakdata rate of 1 Gbps. The main focus for a wider bandwidth than the 20 MHz usedfor LTE is on a consecutive spectrum. However, carrier aggregation over non-contiguous component carriers is also permitted. Another requirement is that theLTE-Advanced system should be backwardly compatible with the earlier releasesof the LTE system in the sense that for an LTE terminal, an LTE-Advancednetwork should appear as an LTE network. One way of achieving such backwardcompatibility while supporting larger bandwidths for LTE-Advanced is to usecarrier aggregation where multiple component carriers are aggregated on thephysical layer as shown in Figure 15.2. When an LTE-Advanced system supportsmultiple component carriers, not all component carriers may necessarily be LTE

15.2 LTE and LTE-Advanced 429

Componentcarriers

20 MHz 20 MHz 20 MHz 20 MHz 20 MHz

100 MHz

Figure 15.2. An example of carrier aggregation with 20 MHz component carriersto provide 100 MHz bandwidth for LTE-Advanced terminals.

Release 8 compatible. This means that as long as there is a single carrier that isLTE Release 8 compatible, LTE terminals can use this carrier for communication.

A terminal may simultaneously receive or transmit signals over one or multiplecomponent carriers depending on its capabilities:

An LTE-Advanced terminal with reception and/or transmission capabilitiesfor carrier aggregation can simultaneously receive and/or transmit on multiplecomponent carriers.

An LTE Release 8 terminal can receive and transmit on a single componentcarrier only, provided that the structure of the component carrier follows theRelease 8 specifications.

Carrier aggregation is supported for both contiguous and noncontiguous com-ponent carriers with each component carrier limited to a maximum of 110resource blocks in the frequency domain using the LTE Release 8 numerology.It is possible to configure a UE to aggregate a different number of componentcarriers originating from the same eNodeB and possibly different bandwidthsin the uplink (UL) and the downlink (DL). In typical TDD deployments, thenumber of component carriers and the bandwidth of each component carrier inthe UL and DL will be the same. The spacing between the center frequencies ofcontiguously aggregated component carriers is a multiple of 300 kHz. This is inorder to be compatible with the 100 kHz frequency raster of LTE Release 8 andat the same time preserve orthogonality of the subcarriers with 15 kHz spacing.

15.2.2 Latency improvements

The LTE-Advanced target is to further reduce the latency to improve the userexperience for Internet applications. The target for the transition time from Idlemode (with the IP address allocated) to Connected mode is for it to be less than50 ms including the establishment of the user plane. The target for the transitiontime from the “Dormant state” in Connected mode to the “Active state” is lessthan 10 ms as depicted in Figure 15.3. Several mechanisms are being consid-ered to further reduce the latency in the LTE-Advanced system including thefollowing:


50 ms

Connected

Idle

Dormant

Active

10 ms

Figure 15.3. State transitions time in the LTE-advanced system.

Combined RRC connection request and nonaccess stratum (NAS) servicerequest Combining allows those two messages to be processed in parallel atthe eNodeB and mobility management entity (MME), respectively, reducingoverall latency from Idle mode to Connected mode by approximately 20 ms.

Reduced processing delays The processing delays in different nodes form themajor part of the delay (around 75% for the transition from Idle mode to Con-nected mode assuming a combined request). Therefore, reducing processingdelays will have a large impact on the overall latency.

Reduced random access channel (RACH) scheduling period Decreasing theRACH scheduling period from 10 ms to 5 ms results in decreasing the averagewaiting time for the UE to initiate the procedure to transit from Idle modeto Connected mode by 2.5 ms.

In order to reduce the transition time from the “Dormant state” in Connectedmode to the “Active state,” the following mechanisms are considered for LTE-Advanced:

Shorter physical uplink control channel (PUCCH) cycle A shorter cycle ofPUCCH would reduce the average waiting time for a synchronized UE torequest resources in Connected mode.

Contention-based uplink Contention-based uplink allows UEs to transmituplink data without having to first transmit a scheduling request on PUCCH,thus reducing the access time for synchronized UEs in Connected mode.

15.2.3 DL multiantenna transmission

The current LTE system supports a maximum of four MIMO layers in the DL.LTE-Advanced extends DL spatial multiplexing with support for up to eight-layer spatial multiplexing. In the DL, up to 8× 8 single-user spatial multiplexingper DL component carrier is supported. A maximum of two transport blocks canbe transmitted to a scheduled UE in a subframe per DL component carrier. Each

15.3 Cooperative multipoint transmission 431

transport block is assigned its own modulation and coding scheme and codedseparately using Turbo coding and the coded bits from each transport block arescrambled. For hybrid automatic repeat request (HARQ) ACK/NAK feedbackon the UL, one bit is used for each transport block separately.

Two types of DL reference signals are considered for LTE-Advanced, namelyreference signals for data demodulation and reference signals targeting channelstate indication (CSI) estimation for reporting channel quality indicator (CQI),precoding matrix index (PMI), and rank information. These reference signalscan be used to support multiple LTE-Advanced features, e.g., CoMP and spatialmultiplexing. These reference signals introduced in LTE-Advanced are differentfrom the common reference signals in the LTE system, where the same referencesignals are used for demodulation and CSI estimation.

15.2.4 UL multiantenna transmission

The UL in the current LTE system does not support spatial multiplexing. LTE-Advanced extends LTE Release 8 with support for UL spatial multiplexing of upto four MIMO layers. In the case of UL single-user spatial multiplexing, up totwo transport blocks can be transmitted from a scheduled UE in a subframe perUL component carrier. The rate can be adapted independently for each transportblock with each transport block having its own modulation and coding scheme(MCS) level. The uplink MIMO transmission chain is similar to the downlinktransmission chain with the differences that the maximum number of layers (andantennas ports) in the UL is limited to four and that SC-FDMA is used as themultiple access scheme in the UL. The MIMO transmission rank can be adapteddynamically.

15.3 Cooperative multipoint transmission

A wireless system is commonly evaluated based on its average cell throughputand its cell-edge throughput [9, 10]. Improving both the cell average and celledge performance is the target in the standardization of wireless systems. Whilethe average cell performance can be improved by increasing the received signalstrength using power boosting techniques, cell-edge users experience low receivedsignal strength and the cell-edge performance is therefore primarily affected bythe intercell interference (ICI). This is especially true for systems designed tooperate with a frequency reuse factor of 1 or close to 1, which is a key objectiveof OFDM-based fourth generation networks. Such frequency reuse implies thatsystems become primarily interference limited as all cells transmit on all timeand frequency resources simultaneously. Unfortunately, power boosting does notimprove-cell-edge performance as both the serving cell signal and the interferingsignal strengths would be increased. This motivates the development of othertechniques that particularly target improving cell-edge performance.


System level simulations of a frequency reuse 1 network composed of 57 sec-tors with an inter-site distance of 100 m indicate that around 5% of the usershave a wideband carrier-to-interference-plus-noise ratio (CINR) lower than -4 dBwith a two-dimensional antenna pattern at the eNodeB and lower than −2 dBwith a three-dimensional antenna pattern at the eNodeB (the three-dimensionalradiation pattern includes 15 degrees down-tilting of the antenna array). 30% ofthe users have a wideband CINR lower than 0 dB with a two-dimensional pat-tern and lower than 2.5 dB with a three-dimensional pattern. Hence, especiallywith a two-dimensional antenna pattern, a large proportion of users in the cellexperience very low CINR and therefore unsatisfactory throughput performance.

The goals of LTE-Advanced are to improve the peak throughput (or spectrumefficiency) by increasing the numbers of transmit and receive antennas and tofurther boost the average cell throughput by enhancing DL multiuser MIMO [9].In addition, a particularly challenging task of standardization organizations like3GPP LTE-Advanced is to improve the cell-edge performance further [9] usingnovel interference mitigation technologies that are expected to outperform theclassical mitigation techniques originally introduced in LTE Release 8. Thosetechniques have received a lot of attention in the standards community as wellas in academia [7, 8, 10, 11] and are commonly referred to as CoMP in theLTE-Advanced community.

CoMP stands for coordinated multiple point transmission/reception and is acandidate technology for cooperative communications where antennas of multiplecell sites are utilized in such a way that the serving cell as well as the neighbor-ing cells can contribute to improving the received signal quality at the mobileterminal, as well as to reducing the co-channel interferences from neighboringcells.

15.3.1 Interference mitigation techniques in previous releases of LTE

ICI mitigation is not new in cellular systems. Universal terrestrial radio access(UTRA) Release 7 classified these mitigation techniques into three types [11].

The ICI randomization techniques apply random scrambling or frequency hop-ping to randomize the interference.

The ICI cancellation techniques suppress interference through the use of mul-tiple receive antennas at the UE and cancel interference by detecting and sub-tracting the inter-cell interference.

The ICI coordination/avoidance techniques apply restrictions (on the availabletime/frequency resources and on the transmit power applied to those resources)to the DL resource management using coordination between cells in order toimprove the signal-to-interference ratio (SIR) and cell-edge throughput and cov-erage. Such coordination may require some additional measurement and feedbackon top of the usual CQI reports. For instance, the average path-loss of servingand interfering cells can be reported every 100 ms. In static interference coordina-tion, the reconfiguration of the scheduler restriction is rare, occurring only with


a rate of the order of days, therefore avoiding internode signaling (over the X2interface). In semistatic interference coordination, reconfigurations are carriedout much more frequently, with a rate of the order of seconds. Internode signal-ing (over the X2 interface) contains the necessary information to reconfigure thescheduler restrictions.

Those techniques require a low feedback overhead on the UL control channelsas well as over the internode (e.g., X2) interface. Moreover, the coordinationbetween cells is done at a relatively low pace. CoMP can be seen as an extensionof the ICI coordination techniques with faster decisions, faster backhaul, andhigher overhead in order to share CSI and data information among cells.

In the following subsection, we provide an overview of the CoMP techniquesdiscussed in the literature and by the 3GPP LTE-Advanced standardizationbody.

15.3.2 Overview of CoMP techniques

CoMP categoriesIn order to categorize the techniques, two major kinds of CoMP transmission forapplication in the DL are identified in LTE-Advanced [7].

Coordinated beamforming/coordinated scheduling [7] (denoted as CB/CS) ischaracterized by the fact that it does not require data sharing between cells.The data are only available at the serving cell and are transmitted from thatcell. However, the user scheduling and beamforming decisions are made withcoordination among the cells in the set of cooperating cells (denoted as the CoMPcooperating set). CB/CS can operate with and without sharing CSI among cells.The ICI coordination/avoidance techniques first introduced in UTRA Release 7and discussed in the previous subsection can be thought of as a subset of theCB/CS techniques as data are not shared between cells. CB/CS techniques aremotivated by the interference channel in information theory.

Joint processing [7] (denoted as JP) is characterized by the fact that data areshared between eNodeBs and are available at each cooperating cell. JP is furthercategorized into dynamic cell selection and joint transmission (JT). If at a giventime instant, data (more rigorously the physical DL shared channel (PDSCH))are transmitted from a single cell in the CoMP cooperating set, JP is referredto as dynamic cell selection. However, if the data (i.e., PDSCH) to a single UEare transmitted simultaneously from multiple points in the CoMP cooperatingset, by performing coherent or noncoherent beamforming, JP is referred to asJT. Like CB/CS, JP can also operate with and without CSI exchange. JP withCSI exchange is aimed at increasing the beamforming gain on top of interferencemitigation. JP techniques are motivated by the MIMO broadcast channel forwhich cooperation between transmitters is possible.

CoMP reception coordinates multiple cells to perform joint reception (JR)of the transmitted signal at multiple receiving eNodeBs and/or coordinatedscheduling (CS) decisions among cells to control interference. UL CoMP


Table 15.2. Categories of CoMP schemes

No CSI sharing CSI sharing

No datasharing(CB/CS)

Frequency reuseStatic FFR

Adaptive FFRRate splittingCoordinated beam patternsPMIa -coordinationCoordinated beamformingInterference alignmentCoordinated scheduling

Datasharing(JP)

Distributed OL MIMO Dynamic cell selectionJoint transmission(Network MIMO)

a PMT – precoding matrix indication.

techniques are motivated by the multiple access channel for which receivers cancooperate. UL CoMP has less impact on the standard specifications from a phys-ical layer perspective. Therefore, we will mainly focus on DL CoMP.

In Table 15.2, we summarize the potential DL CoMP techniques based ontheir requirements in terms of data and CSI sharing. Each technique mentionedin Table 15.2 will be discussed in the following subsections.

CoMP setsLTE-Advanced has defined various kinds of CoMP sets [7].

The CoMP measurement set Mk of the user k is defined in LTE-Advanced [7]as the set of cells about which CSI/statistical information related to their linkto the UE k is reported. The actual UE may downselect cells for which actualfeedback information is reported.

The CoMP-requested user set of cell i is the set of users that have cell i intheir measurement set, i.e., Ri = l| i ∈Ml ,∀l. Note that the CoMP-requesteduser set can also be viewed as the victim user set of cell i as it is the set of userswho could be impacted by cell i if cooperation is not performed.

The CoMP cooperating set is defined in LTE-Advanced [7] as the set of(geographically separated) points directly or indirectly participating in PDSCHtransmission to the UE. Ck ⊂ j| k ∈ Rj ,∀j = i denotes the CoMP cooperat-ing set of user k whose serving cell is i. As defined, the CoMP cooperating setdoes not include the serving cell i. The CoMP cooperating set is a subset of theCoMP measurement set. The CoMP measurement set may be the same as theCoMP cooperating set. In order to avoid feeding back CSI that is not used bythe eNodeB, it is preferable for the CoMP measurement set and the cooperatingset to be as similar as possible.


Two types of cooperating set are frequently mentioned: one is the net-work predefined cooperating set, and the other is the user-centric cooperat-ing set. With a network predefined cooperating set, a fixed set of eNodeBsis cooperating. This is a simple approach. However, due to shadowing, thestrongest interference to a certain UE may not always come from the cells in thecooperation set.

The CoMP transmission point(s) as defined in LTE-Advanced [7] is a subsetof the CoMP cooperating set given by the points or set of points actively trans-mitting PDSCH to UE. For JT, the CoMP transmission points are the points inthe CoMP cooperating set. For dynamic cell selection, a single point is the trans-mission point at each subframe. This transmission point can change dynamicallywithin the CoMP cooperating set. For coordinated scheduling/beamforming, theCoMP transmission point corresponds to the serving cell.

CS/CB with no CSI sharingCS/CB with no CSI sharing covers the static interference coordination intro-duced in the previous subsection.

(1) Frequency reuse partitioningFrequency reuse partitioning involves dividing the available spectrum into multi-ple frequency partitions and assigning a given partition to a given cell (sector) insuch a way that ICI is minimized. A pure three-reuse is achieved by dividing thefrequencies into three parts f1 , f2 , and f3 and by setting the maximum power ineach frequency f as Pmax (f) = P (> 0) for f ∈ fn , and Pmax (f) = 0 for f /∈ fn

for each cell. In a three-sector cell plan, each sector can be allocated one fre-quency partition. Unfortunately, such frequency reuse partitioning based on, forexample, three-reuse only slightly improves the performance of cell-edge usersby decreasing the interference. However, the average cell throughput is degraded[12]. The complexity of such a scheme is minimal since a fixed assignment ispredefined.

(2) Static fractional frequency reuse (static FFR)Static FFR is a resource partitioning scheme that applies different reuse factorsfor cell-center users and cell-edge users in the serving cell. Interference is miti-gated by assigning resources for cell-edge users with high frequency reuse suchthat they do not overlap with neighboring cells. Resources for cell-center usersare allocated in a frequency reuse 1 (or close to 1) fashion. Power transmittedto the cell-center region on frequency resources not used by cell-edge users islower than the power allocated to the cell-edge region. In such a way cell-centerusers interfere with users in an adjacent cell but with a lower transmit power.The SINR of a cell edge user is improved. Therefore, the cell-edge throughputis expected to increase. However, the use of large frequency reuse factors forcell-edge users also induces some loss in throughput as only a small portion ofthe bandwidth is available. The performance ultimately depends essentially on


whether the eNodeB decides to allocate a user in the frequency reuse 1 regionor in a higher frequency reuse region.

There are several ways to assign the frequency resources. In one approachusers close to eNB operate in all frequency partitions (e.g., F = f1 + f2 + f3)available, while for the edge users, each cell operates only in a specific frequencypartition (e.g., f1 only). Another approach is to allocate f1 , f2 , f3 to the cell-edgeregion in each cell, and F − f1 , F − f2 , F − f3 to the corresponding cell-centerregion of each cell.

Static FFR has been shown to provide additional gain in terms of sectorthroughput compared to the frequency reuse partitioning scheme based on afrequency reuse factor of 3. However, FFR can decrease the sector throughputcompared to a full reuse 1 system due to the efficiency loss induced by thehigher reuse factor. Therefore, the gain obtained in terms of SINR for cell-edgeusers does not compensate for the loss due to spectral efficiency. Despite such aloss, FFR is known to expand the coverage significantly compared to a frequencyreuse 1 system and can actually achieve a coverage similar to a frequency reuse-3system [12, 13].

LTE Release 8 supports ICI coordination with limited interaction betweenneighboring sites via the internode interface X2. In the DL, the exchange of rela-tive narrowband Tx power (RNTP) messages [14] over X2 enables static FFR-likeinter-cell interference coordination (ICIC) techniques with slow coordination inthe frequency domain.

CS/CB with CSI sharingWhile frequency reuse partitioning and static FFR can help to reduce the ICI,their contribution to increasing the spectral efficiency is relatively limited. Itis preferable to use more advanced techniques that use a reuse factor of 1 andprovide faster interference coordination based on multipoint transmission.

In this scenario where no data are shared but CSI is shared, many differentkinds of processing can be undertaken. The ICI is mitigated with the aid ofsome form of CSI exchange such that the beamforming vectors, the schedulingdecisions, or the transmit powers can be adequately chosen in a dynamic way.This scenario is closely related with the multiuser MIMO interference channels(IC).

(1) Adaptive FFR In an adaptive FFR scheme, the same resources are sharedamong cell-centered users and cell-edge users. By performing frequency selec-tive scheduling (based on CQI feedback), by adapting the frequency partitionassignment (based on interference measurements and cell loading), and by usingtransmit power control, the performance and efficiency of cell-edge users can beincreased while maintaining the performance of cell-center users.

The complexity of adaptive FFR is proportional to the number of UEs servedby an eNodeB. Moreover, adaptive FFR requires exchange of information relatedto transmit power among eNodeB. To operate adaptive FFR, the serving eNodeB


can instruct the UEs to perform some interference measurement over specificfrequency partitions and to report the interference information to the servingeNodeB as well as the preferred frequency partition. Adaptive FFR is a popularinterference mitigation technique in IEEE 802.16m [10].

(2) Han–Kobayashi (HK) rate splitting Unlike in FFR, which uses power con-trol to mitigate interference, in the Han–Kobayashi (HK) scheme [15, 16], orig-inally proposed for a two-cell two-user scenario, the interference is mitigatedby choosing appropriately the transmission rate of a part of the data (denotedas the common message) to be transmitted in the serving cell such that it isdecodable to a cell-edge user located in a neighboring cell. By canceling theinterference created by the common message, the interference to the cell-edgeuser can be mitigated without reducing the transmission power. The operationof such a scheme is presented below and more details can be found in [17].

Assume a serving cell communicating with a user and a neighboring cell com-municating with a cell-edge user subject to interference from the serving cell.The serving cell splits the transmit information ds into two parts: a commonds,c and a private ds,p message. The common message ds,c is transmitted witha transmission power fraction α and the private message with a fraction 1− α.The neighboring cell transmits message dn to the cell-edge user.

The parameter α is computed by the cell-edge user and reported to the neigh-boring cell along with two CQIs. The first CQI, CQIn , is the CQI that the cell-edge user would experience while decoding its message dn if the interferencefrom the common message with power fraction α were removed, i.e., the cell-edge user only experiences interference from the private message ds,p . Parameterα could be computed by the cell-edge user in such a way that the interferencelevel caused by the private message has the same level as the noise level [16]. Thesecond CQI, CQIn,c , corresponds to the CQI measured by the cell-edge user whendecoding the common message ds,c sent by the serving cell and experiencing theinterference from its own message dn transmitted from the neighboring cell andthe private message ds,p sent by the serving cell.

The serving cell is informed of parameter α. The serving cell indicates α to theserving cell user such that this user can compute two CQI. The first CQI is theCQI of the common message in the serving cell, denoted as CQIs,c , while expe-riencing the interference from the private message ds,p and from dn transmittedfrom the neighboring cell. The second CQI is that of the private message, CQIs,p ,assuming that the common message has been correctly decoded and thereforeexperiencing only the interference from message dn .

Given CQIn,c and CQIs,c , it is possible to compute the rate of the commonmessage ds,c decodable by both users. The rate of the private message ds,p canbe computed based on CQIs,p and the rate of message dn is computed based onCQIn .

The cell-edge user decodes the common part first and subtracts the commonmessage from the received signal to decode message dn . The common message


ds,c is discarded by the cell-edge user. The serving cell user decodes both theprivate and common messages and the total rate experienced by the serving celluser is the sum of the rates of the common message and the private message.

While the operation of the HK scheme for the two-cell two-user case is rela-tively well understood, the extension to multicell operations and multiple usersis far from clear. Given that in the two-user case, the HK scheme gets only adegree of freedom of 1/2 in the medium interference range [16] (i.e., the capacityper user would scale as 0.5 log(SNR)), it was conjectured that in the K-usercase, the degree of freedom would be of the order of 1/K. However, interferencealignment techniques, which are discussed later, have provided some refreshingviews on this conjecture.

Overall, the HK scheme has the advantage of requiring a relatively smallamount of information to be shared among cells, since only scheduling infor-mation, CQI, the power fraction for common, and private messages need to becommunicated over the X2 interface. However, the HK scheme requires a moreadvanced receiver enabling successive interference cancellation and increases theDL overhead to indicate the modulation and coding scheme (MCS) of the com-mon message in order to be decoded correctly. Its biggest drawback is that itsextension to a more general setting with more than two users is not straightfor-ward.

(3) Coordinated beam patterns – opportunistic beamforming To benefit fromHARQ and adaptive coding and modulation, wireless communication systemssignificantly rely on fast link adaptation which requires accurate CQI estimation.However, in a beamformed multiantenna system, interference fluctuates veryseverely between the time of UE measurement and the time of UE demodulationas the beamformers in interfering cells change in a very dynamic way. Such asituation occurs frequently if there is no coordination between cells. The dynamicinterference is sometimes referred as the flashlight effect.

In IEEE 802.16m, an open-loop region was defined [10]. The open-loop regionis a resource in the frequency partition with a reuse factor 1 where open-looptransmission with one or two streams is performed. This resource is alignedfor all cells and sectors which apply a fixed and predefined precoder to preventdynamic interference and guarantee small CQI mismatch (and therefore accuratelink adaptation). To do so, rank adaptation is prohibited in the open-loop region.The UE is requested to feedback its preferred subbands and best streams. Giventhat the precoders are predefined, the CQI(s) can be estimated accurately.

In [18, 19], a somewhat similar but more flexible approach was proposed. EacheNodeB in the CoMP cooperating set determines its own beam cycling pattern (itcan be predefined or can be defined based on the cell load and user distribution).The central controller that calculates the optimal cycling period (in time and/orfrequency domain) is informed of the pattern and reports the optimal period toall eNodeB in the CoMP cooperating set. Given the cycling period and beam pat-tern, the eNodeBs cycle through the fixed set of beams. The UE is requested to


feedback its best CQI per cycling period and the subframes/frequency subbandswhere the maximum CQI is experienced during that cycling period.

Unlike in closed-loop operations, the UE does not have to report a preferredPMI nor a restricted/recommended PMI as in PMI coordination schemes. More-over, the UE does not have to estimate the channel of an interfering cell. TheCQI is measured based on the demodulation reference signal (DM-RS) as theUE is not aware of the beam pattern. Therefore, the CQI is calculated as afunction of the complete interference that the UE will experience at the timeof demodulation and is not based only on the dominant interference as in PMIcoordination. The UE is informed about the cycling period in order to keep theCQI report synchronized with the beam cycling period. Based on the report, theeNodeB will decide the best beam subframes/frequency subbands on which toschedule a particular beam for the UE. Examples are provided in [19].

Like all opportunistic beamforming schemes, the major drawback of such ascheme is that its performance gains are expected only when the number of UEsis relatively large (i.e., larger than the ten users commonly assumed in a cell). Fora limited number of UEs, a more accurate coordination based on CSI feedbackis desirable to achieve performance gains.

(4) PMI coordination PMI coordination [20–22] is a relatively simple conceptthat uses the multiple antennas at the eNodeB to mitigate the ICI. Two variantsexist, namely PMI restriction and PMI recommendation.

Assuming that the users and the eNodeB have knowledge of a codebook Ccomposed of codewords, PMI restriction and PMI recommendation techniquesaim to improve cell-edge user throughput by constraining the interfering cells touse only a subset of the codebook C.

In the case of PMI restriction, the cell-edge users in each cell measure thechannel of the interfering cells belonging to the CoMP measurement setMk andcalculate the worst PMI or the set of bad PMIs that would create the highestinterference if used as the precoder in the interfering cells. The restricted PMIset can be calculated as the set of codewords in the codebook whose correlationwith the dominant eigenvector of the interfering cell channel is larger than acertain predefined value. Let us denote that PMI restricted set as Rrestr. .

Alternatively, in the case of PMI recommendation, the cell-edge users calculatethe best PMI or the set of good PMIs that would generate low interference if usedas precoders in the interfering cells. The recommended PMI set can be calculatedas the set of codewords in the codebook whose correlation with the dominanteigenvector of the interfering cell channel is lower than a certain predefined value.Let us denote that PMI restricted set as Rrec. .

In order to help the interfering cell make appropriate decisions on whether toaccept or reject the request of PMI restriction/recommendation and to resolvepotential PMI conflict between different requests, additional quantities, e.g., dif-ferential CQI (difference between CQIs with and without PMI coordination), canprovide information about the gain achievable if the restriction/recommendation


is accepted. UEs feed back to the serving eNodeB the cell and sector IDs, alongwith the restricted/recommended PMI or PMI set and the differential CQIs. Thenecessary information is forwarded to the interfering eNodeBs in order for themto accept or reject the coordination request.

If an interfering eNodeB decides to accept the request of PMI restriction,this eNodeB restricts the precoders in Rrestr. from being used by the inner-cellusers that it serves. To do so, the eNodeB broadcasts information about therestricted set to the users in the cell (using, e.g., bitmap [10]). After receptionof such information, the inner-cell users are forced to use and feedback onlyPMI included in the reduced codebook set C\Rrestr. (i.e., the set defined as thedifference between C and Rrestr.). Cell-edge users on the other hand are allowedto use the full codebook C.

If the request of PMI recommendation is accepted, the interfering cell indicatesto its inner-cell users to feedback only PMI included in Rrec. . Cell-edge users onthe other hand are allowed to use the full codebook C.

Such an approach targets a practical scenario where the UL feedback overheadwould be too large to accommodate the feedback of full CSI of many interfer-ing cells. It primarily targets rank-1 PMI feedback in highly correlated channelsenabling the feedback of a single wideband restricted/recommended PMI to fur-ther decrease the uplink overhead.

(5) Coordinated beamforming Coordinated beamforming refers to the use of acoordinated design of the transmit precoders in each cell to eliminate or reducethe effect of ICI. In contrast to PMI coordination, the eNodeB computes a newtransmit filter based on the CSI/PMI feedback from cells in the CoMP measure-ment set.

Zero-forcing beamforming (ZFBF) based coordinated beamforming [23, 24] isone of the most popular schemes in standardization communities such as theLTE-Advanced and in the literature. In the presence of multiple antennas at theeNodeBs, such an approach consists in forcing the interference to zero.

The number of interfering links that can be eliminated depends on the numberof transmit antennas at the eNodeB. There is no coordinated scheduling amongcells in such an approach. This means that each eNodeB must first decide whichuser will be scheduled in each cell. Once this is decided, the transmit beamform-ing can be accommodated in order to avoid creating interference to other cells.Such an approach requires CSI feedback of both the interfering cell in the CoMPmeasurement set and the serving cell, i.e., a given UE feeds back to the serv-ing eNodeB not only its serving cell channel (between the UE and the servingeNodeB) but also the interfering cells channels (between the UE and the inter-fering cells in the CoMP measurement set). Note that it would also work if theUE did not feedback its serving cell channel. However, this is not the commonscenario under investigation. The information required to be communicated overthe backhaul (e.g., X2 interface) consists of the interfering cell CSI and the infor-mation related to which users will be scheduled simultaneously by the eNodeBs


in the CoMP cooperating set. ZFBF filter design has the advantage of being rel-atively simple to implement as it does not require any iteration. Unfortunately,such an approach is very sensitive to the accuracy of the CSI feedback. Perfor-mance is significantly impacted by the quantization error induced by the limitedfeedback based on a codebook.

Another popular scheme in LTE-Advanced is a joint leakage suppression (JLS)scheme [24–26]. Such a filter design does not maximize the SINR or the sum-ratebut does maximize the SLNR which is the signal-to-leakage-plus-noise ratio.

Compared with the zero-forcing solutions, SLNR does not impose a conditionon the number of degrees of freedom as there is no pure suppression (hence thereis no constraint on the relation between the number of transmit antennas, thenumber of receive antennas, and the number of users to mitigate interference),and it also avoids noise enhancement. However, one issue is that the leakagesignal power has to be relatively small compared with the received signal powerof the scheduled user in the interfering cell. Otherwise, a ZFBF-like solutionwould be more appropriate as it fully cancels the interference. As in ZFBF, suchschemes require both serving cell and interfering cell CSI as well as the informa-tion related to which users will be scheduled simultaneously by the eNodeBs inthe CoMP cooperating set. The interfering cell CSI is shared with other cells overthe backhaul. The beamforming design does not require iterations since the filterdesign is obtained as a solution of a generalized eigenvalue problem. Therefore,the complexity is similar to that of ZFBF.

It is important to note that ZFBF and JLS may have different requirements orpreferences in terms of feedback. The JLS solution typically requires the channelcovariance matrices, while the ZFBF filter is a function of the channel matrixitself.

(6) Interference alignment (IA) Interference alignment (IA), originally intro-duced in [27, 28], is a single-user MIMO (SU-MIMO) coordinated beamformingscheme that has attracted a lot of attention in the literature but not much inthe standards community. Regarding the degrees of freedom of a K-users inter-ference channel, it has been shown [29] that it is possible to achieve 1/2 degreeof freedom (i.e., in the limit of high SNR, the capacity per user would scale as0.5 log(SNR)) despite the presence of K interfering users. In other words, as thetransmit power of each eNodeB increases, every user will be able simultaneouslyto achieve half of the capacity it could achieve in the absence of the interferencefrom other users.

Assume a K-user, K-cell network with Nt transmit antennas at each eNodeBand Nr ≤ Nt receive antennas at each mobile where each mobile receives d < Nr

data streams from its serving cell in a closed-loop SU-MIMO mode. The IAscheme consists of dividing the Nr -dimensional observation space at the receiverinto a d-dimensional signal space and a (Nr − d)-dimensional interference spaceand designing jointly the transmit and receive filters such that every interferenceis aligned into the (Nr − d)-dimensional interference space. Unlike coordinated


beamforming schemes, which optimize the transmit filter based on the feedback,IA jointly optimizes the transmit and receive filters.

The necessary and sufficient condition for interference alignment is that thecolumn space of each interference to a given user should be aligned. Interfer-ence is aligned before receive shaping in such a way that after receive shaping,it is completely canceled out and the received signal after filtering lies in thed-dimensional signal space.

Such a scheme requires the global CSI to design the transmit and receive filtersand is very computationally demanding.

(7) Coordinated scheduling The aforementioned techniques such as coordinatedbeamforming and IA rely on only transmit and/or receive filter design to miti-gate interference. However, as is well known in single-cell multiuser MIMO (MU-MIMO), an appropriate scheduler is highly beneficial to reduce further the mul-tiuser interference. Similarly, in a multicell scenario, a coordinated scheduler hasa significant impact on the performance. The scheduler design is not standardizedas it is left as an implementation issue for the vendors and operators. Depend-ing on the network architecture, centralized and distributed schedulers can beidentified.

In the centralized scheduler, a central controller collects all CSI from all cells inthe network and makes all scheduling decisions for all cells before passing thosescheduling decisions onto each individual eNodeB. The central scheduler may beimplemented at one of the eNodeBs in the network.

In the distributed scheduler of [30], cells make scheduling decisions (e.g., UEdecision and transmit precoding) one after the other for their own users basedon the scheduling decisions made by other cells (belonging to the CoMP coop-erating set) and then broadcast those decisions so that other cells (belongingto the CoMP cooperating set) can make their own decisions. As an example,cell 1 makes the scheduling decisions assuming no cooperation between cells andbroadcasts those decisions. Cell 2 can make decisions based on cell 1 schedulingknowledge and then broadcasts the decisions. Cell 3 makes decisions based onthose of cells 1 and 2. Such procedure is completed when all cells have made theirdecisions. In the distributed schedulers of [25, 31], scheduling decisions at eachcell are reconsidered and updated in an iterative way prior to scheduling a UEin a given subframe based on decisions taken by all other cells at the previousiteration.

Note that in its general form, the coordinated scheduler is actually a coor-dinated beamformer and scheduler and all techniques described in the previoussubsections (e.g., coordinated beamforming, IA) are performed in each iterationof the iterative scheduler. Hence, at each iteration, each cell makes decision onthe beamformer and on the UE to schedule.

For both centralized and distributed schedulers, the importance of defining anetwork utility metric is stressed in [31, 32]. The goal of the scheduler is to max-imize the utility metric through coordination. In its most advanced form, the


network utility metric should account for the spectral efficiency associated witha particular cooperative transmission scheme (i.e., the exact type of coopera-tive scheme), the transmission modes (e.g., SU-MIMO, MU-MIMO), the relativepriorities of the UEs (to account for fairness/QoS requirements), the backhaulconstraints, the CSI accuracy as well as certain UE/network capabilities (e.g.,centralized or distributed).

A typical procedure of an iterative coordinated scheduler (and beamformer)can be summarized as follows [25, 31]:

Initialization step Each cell decides upon which UEs to schedule in the SU-or MU-MIMO mode and the corresponding transmit precoding, assuming nocoordination between cells (i.e., single-cell processing). The decision is takenbased on some priority metric according to, e.g., proportional fairness andthe most recent CSI available at the eNodeB. In SU-MIMO, precoding wouldbe chosen, e.g., as the dominant eigenvector(s) of the short-term covariancematrix, the number of eigenvectors being determined by the rank of the trans-mission. Such an approach is generally referred as singular value decomposi-tion (SVD) precoding. In MU-MIMO, precoding is computed based on, e.g.,ZFBF or JLS criteria, similarly to single-cell MU-MIMO precoding designs.

Iteration-n Each cell revisits its decision on the UEs to schedule and theirtransmit precoding based on decisions taken by other cells in iteration n− 1.In order for each cell to maximize a network-wide utility metric (and thereforeguarantee some convergence of the iterative scheduler), the scheduling decisionin a given cell i is a function of not only the utility metric of users scheduled bythat cell but also the utility metric of victim users that have been tentativelyscheduled by other cells in iteration n− 1.

Interestingly, the results in [33] show that performing coordinated schedulingwith SVD precoding and with JLS precoding both provide the same performance,suggesting that the scheduler itself is much more critical than the beamformingdesign.

JP with no CSI sharing

Distributed open-loop MIMO The joint transmission based on distributed open-loop (OL) MIMO can be seen as a direct extension of the single-cell OL MIMOwhere space-time encoding is done over multiple antennas of all eNodeBs in theCoMP cooperating set rather than just on the multiple antennas of the servingcell. It is sometimes referred to as macrodiversity. As an example, assuming twosingle-antenna eNodeBs, orthogonal space-time coding is obtained by encodingdata over those two antennas as if they belong to a single eNodeB. Such schemesnaturally require data sharing between cells but no CSI sharing. A simple sce-nario of this scheme is the intra-eNodeB (intrasite) transmission where there iscooperation between multiple sectors of the same cell.


JP with CSI sharing

(1) Dynamic cell selection Dynamic cell selection refers to the coordinatedscheduling technique in which instantaneous single-point (i.e., from a singleeNodeB) transmission is performed to a single user. Based on the instantaneouschannel condition of a UE, fast selection of the most appropriate eNodeB is per-formed. eNodeBs in the CoMP cooperating set share the data in order to enablethe fast switching.

An example of the fast cell selection is provided in [34]. Once a cell-edge useris identified based on its average received power from multiple cells, a centralscheduler allocates frequency resources to that cell-edge user in such a way thatthe cell with the highest interfering power to that cell-edge user is muted andthe power allocated to that frequency resource in the serving cell is boosted bya factor of 2. Resource allocation is ended once the transmission power for eachcell reaches its maximum value.

(2) JT with CSI sharing Joint transmission with CSI sharing is commonlycalled network MIMO in the literature. In this scheme, all cells in the CoMPcooperating set effectively form a super eNodeB whose effective number of trans-mit antennas is equal to the sum of the numbers of transmit antennas of the cellsin the CoMP cooperating set. Transmission to a UE is performed from multiplecells simultaneously. In such scenarios, it is typically assumed that multiple cellsin a cellular network are connected to a central processing unit, which has knowl-edge of the transmit messages for all the users and the channels from differentcells to all the users. In these fully cooperative multicell systems, the optimiza-tion problem reduces to a MIMO broadcast channel with the number of transmitantennas equal to the sum of those of all cells in the CoMP cooperating set. Amajor difference from the single-cell MIMO broadcast channel is that the trans-mit signals are subject to a per-cell power constraint rather than a sum-powerconstraint.

Such a technique is expected to provide significant performance gain oversingle-cell operation as it provides beamforming gain and interference mitigation.Unlike CB techniques, JP is very beneficial even for single transmit antennacells as it enables spatial interference nulling as well as transmit channel gaincombining across multiple cells. Unfortunately, the complexity of such a systemincreases exponentially with the number of cells and the number of links, makingthe task of the scheduler extremely complicated if it has to be centralized.

To provide sufficient beamforming gains from multiple cells, coherent trans-mission is recommended, i.e., the UE needs to feedback the aggregated channelcontaining the phase shift between the channels of the cells. It is quite demandingin terms of feedback overhead. Another form of JT is non-coherent JT, wherethe phase shift between the channels of the cells is not fed back. In such a sce-nario, feedback overhead is decreased but coherent combining is not achievedand therefore beamforming gain is decreased compared with the coherent trans-mission.


Like single-cell MU-MIMO (single-cell broadcast channels), transmissionstrategies can be classified into linear and nonlinear precoding schemes. Linear fil-ters based on ZFBF and JLS are far more popular than nonlinear schemes due totheir lower complexity [24]. Popular nonlinear schemes include dirty paper coding(DPC) and Tomlinson–Harashima precoding (THP). Note that while comput-ing those transmit filters, a per eNodeB power constraint should be taken intoaccount.

The original paper [35] dealing with JTs assumed a ZF-DPC approach basedon a sum power constraint, i.e., the power is shared among all eNodeBs in theCoMP cooperating set. Later, filter design with per-eNodeB power constraintswas considered [36–39]. Theoretical limits (DPC) with per-eNodeB power con-straints were derived in [40].

Some practical considerationsSome important factors should be taken into account in the design of CoMPschemes.

(1) Scheduler architecture and complexity The overall complexity of CoMPdepends on the scheduler architecture and the size of the CoMP cooperatingset. To reduce the complexity, cell clustering has been investigated. Two popularclustering methods for identifying the CoMP cooperating sets are the user-centriccooperating set and the network predefined cooperating set [33, 41, 42]. Theformer has the advantage of efficiently suppressing the interference by allowingeach UE to have its own cooperating set. However, it is extremely complex andchallenging as the cooperating sets are selected dynamically and could overlapwith each other. If the scheduling is performed in a centralized way, the numberof cells to manage is very large in order to cover the cooperating sets of allusers and avoid performance degradation for boundary UEs. In the network-centric cooperating sets, cells are clustered in a more static way and UEs areserved only by one of the clusters. Hence, clusters do not overlap with eachother. Unfortunately, users at the boundary of the clusters are subject to poorperformance. A hybrid approach enabling partial overlap of the clusters has alsobeen proposed [41].

(2) Intra-eNodeB vs. inter-eNodeB CoMP There are two important CoMPdeployment scenarios: intra-eNodeB and inter-eNodeB CoMP.

Intra-eNodeB (intrasite) CoMP performs cooperation between the cellsbelonging to the same eNodeB. Intra-eNodeB CoMP does not require any X2interface, therefore reducing the impact of CoMP on the standard. Efficient JPrelies on a low latency and large bandwidth backhaul to convey data to cellsthat jointly serve a UE as well as to provide fast CSI and HARQ feedback tothe scheduler and scheduling decisions, MCS level, and HARQ information tothe transmitters. This makes JP more suitable to intercell intra-eNodeB coop-eration as well as cooperative transmission within a set of remote radio heads


(RRHs) or distributed antennas (DAs) interconnected by high-speed broadbandlinks [32].

Inter-eNodeB (intersite) CoMP performs cooperation between cells belongingto different eNodeBs and linked through the X2 interface. Inter-eNodeB CoMPrelies on the backhaul link to support the CSI and/or scheduling informationexchange among eNodeBs. The backhaul latency and limited capacity is a com-mon issue for all inter-eNodeB CoMP schemes. However, the backhaul require-ments are different for JP and CB/CS. Since JP requires data sharing amongeNodeBs, its requirements in terms of backhaul capacity are higher than thosefor CB/CS which only require CSI sharing and scheduling decisions. Such consid-erations makes CB/CS more for attractive inter-eNodeB with limited backhaulcapacity.

(3) Backhaul capacity and latency X2 defines the logical interface between twoeNodeBs. A typical maximum backhaul delay over the X2 interface is expectedto be in the order of 20 ms [43]. However, larger delays can be found in somespecific scenarios. A median delay over the X2 interface would be around 10 ms.It is important to note though that the physical realization of the X2 interfacecan be implemented in many ways, including fiber, copper, and microwave. Suchimplementation highly impacts network performance. A comprehensive analysisof different types of (current and future) backhaul was provided in [44].

While studies of CoMP with limited backhaul are scarce, some results are avail-able. CoMP has been shown to present a graceful degradation as the backhaulcapacity decreases [45].

(4) Impact of delay and mobility on CoMP CoMP schemes experience differentdelays depending on, e.g., the kind of CSI sharing, scheduler, and transmit fil-ter. Users scheduled based on a scheme like coordinated beam patterns requiringlong-term CSI sharing and no iterative scheduler are less sensitive to the back-haul delay than users scheduled based on CoMP using an iterative distributedcoordinated scheduler and beamformer.

CoMP performance depends on the total delay, which is a function of theCSI/CQI delay (typically of the order of 4–6 ms), the backhaul delay (10 ms one-way on average based on current technology), the delay of periodic exchange ofinformation as long-term CSI (e.g., 50 ms), eNodeB processing time (of the orderof milliseconds), and the number of iterations required by an iterative scheduler.

In [30], it was shown that the CoMP scheme based on the coordinated beampattern scheme relying on long-term information exchange would experience atotal delay of the order of 5 ms for serving cells’ UEs and 65 ms for UEs incooperating cells. The CoMP scheme based on short-term CSI sharing and acentralized scheduler (e.g., intrasite CB/CS, JP) would experience a total delayof 5 and 7 ms (for one and three iterations in the centralized scheduler respec-tively). The CoMP scheme based on short-term CSI sharing and a distributednoniterative scheduler (e.g., intersite CB) would experience about 16 ms total


delay in cooperating cells and 5 ms total delay in the serving cell. Finally, aCoMP scheme based on short-term CSI sharing and distributed iterative sched-uler (e.g., intersite iterative CB/CS) experiences about 16 ms total delay forone iteration and 70 ms total delay for three iterations. Therefore, the CoMPschemes relying on iterative and distributed schedulers would not operate on theclassical backhaul but would require a high-speed backhaul.

Note, however, that CoMP schemes have different sensitivities to those delaysdepending on the deployment scenarios. A distributed iterative scheduler expe-riences a delay that is proportional to the number of iterations and the backhauldelay but users may or may not be impacted by such a delay depending onwhether closely spaced antennas are deployed or not at the eNB. Such a configu-ration leads to spatially correlated channels whose channel directions are stablein the frequency and time domain. In such closely spaced antenna configurations,CB is also believed to be more robust to UE mobility and delay than JP [32].JP based on JT techniques is mainly limited to only low mobility UEs.

CS can also be used to handle high mobility UEs when efficient cooperationthrough spatial interference nulling is not possible.

(5) Downlink reference signals CoMP operations rely on accurate measurementof the channels in the CoMP measurement set. For channel measurement, ref-erence signals (RS), denoted CSI-RS, are introduced in LTE-Advanced. Unlikethe common reference signals (CRS) in Release 8 used for measurement anddemodulation, CSI-RS is only used for measurement and therefore requires alower density in the frequency and time domains than CRS. Any CSI-RS designthat did not consider multicell operations would result in dramatic CoMP per-formance losses. Hence, one of the priorities of the CoMP design is CSI-RSdesign [46, 47]. The goal of CSI-RS design is to guarantee good performancewith low overhead by benefiting from power boosting and avoiding RS collisions.The larger the CoMP measurement set is, the more difficult is the design. Typ-ical approaches to design CSI-RS in a multicell environment introduce orthog-onal CSI-RS patterns. Methods to introduce orthogonal patterns include shift-ing in the time domain and/or frequency domain by a certain time/frequencyoffset or using CSI-RS patterns that are orthogonal to each other ineach RB.

Note that CSI-RS also depends on the CoMP architecture. For a user-centriccooperating set, the overall number of involved cells for cooperation is muchlarger than that for a network predefined cooperating set. CSI-RS design for aCoMP architecture-based user-centric cooperating set is more difficult than forCoMP architecture relying on a network predefined cooperating set [33].

The user-specific reference signal (DM-RS) is primarily used as a demodu-lation signal and is one of the key features of LTE-Advanced (and standardslike IEEE 802.16m) to improve system capacity. The use of DM-RS allows formore advanced transmit filtering at the eNodeB (for single-cell and CoMP oper-ations) and more advanced feedback mechanisms at the UE side compared with


the Release 8 codebook-based precoding approach using CRSs. With the DM-RS, the eNodeB transmit filter design becomes an implementation issue and istherefore not standardized.

(6) CSI feedback CSI feedback is related to the report of the dynamic channelconditions between the multiple points included in the CoMP measurement setand the UE. It can also include reports that could facilitate the decision on theset of participating transmission points [7].

In FDD, CoMP based on short-term feedback naturally requires higher feed-back overhead than single-cell operations, since the channels from the CoMPmeasurement set need to be reported to the serving cell. Depending on theCoMP transmission scheme, the feedback accuracy requirement might differ.Very accurate feedback is required for techniques based on interference nullingsuch as JT, CB, or IA. Inaccurate feedback would significantly reduce the inter-ference nulling capability as in single-cell MU-MIMO. Moreover, JP based on JTand coherent combining typically also requires more feedback than CB schemesor noncoherent combining beamformers [48]. To provide the expected gains, JTrequires an individual per-cell feedback and an intercell feedback that containsinformation about the phase shift between individual per-cell feedback informa-tion. As in single-cell MU-MIMO, advanced feedback mechanisms (in the formof adaptive codebooks, differential codebooks, hierarchical codebooks, etc.) areessential to support and fully benefit from the advanced CoMP deployed withhigh-speed backhaul.

In TDD, channel reciprocity can provide some advantages. The transmissionof a single sounding sequence on the UL can be received simultaneously frommultiple cells. LTE-Advanced supports both a FDD mode and a TDD mode forwhich channel reciprocity may be exploited [7].

Another important design principle of the feedback mechanisms is to developa universal and scalable structure supporting various downlink transmissionschemes including single-cell SU-MIMO, single-cell MU-MIMO, CoMP CB/CS,and CoMP JP [48, 49]. Feedback scalability was defined such that the feedbackin support of CoMP JP is a superset of the feedback in support of CoMP CB/CS.Such feedback structure can easily and dynamically switch from one transmissionscheme to another and avoids standardizing multiple feedback and transmissionmodes.

LTE-Advanced has identified three main categories of CoMP feedback mech-anisms [7]:

Explicit feedback of the channel state/statistical information consists in feed-ing back the channel as it is observed by the receiver without assuming anyhypothetical transmission scheme or any receiver processing.

Explicit feedback information may include the short-term channel matrix,the instantaneous transmit covariance matrix, or its average in time or fre-quency [25]. For both the channel matrix and the covariance matrix, the full


information or just its dominant eigencomponents may be reported. Addition-ally, any intercell channel properties can be reported.

As well as the information originating from the CoMP measurement set,additional information related to the interference outside the CoMP measure-ment set can be reported, e.g., the full matrix or the dominant eigencompo-nents of the noise-plus-interference covariance matrix.

Implicit feedback of the channel state/statistical information is the feedbackmechanism used in Release 8. It makes some hypotheses on the transmissionand/or reception processing at the time of feedback. Typical contents of theimplicit feedback are the well-known CQI, PMI, and rank indicater (RI). Asexamples of the hypotheses, the UE could assume at the time of feedback thatit will be scheduled in SU-MIMO or MU-MIMO mode, in single or coordinatedtransmission using single- or multi-point transmission [50, 51]. It could alsomake assumptions on the receiver processing (e.g., MMSE, ML), or on theway the interference is processed given the transmit and receive processing.

Sounding reference signals (SRSs) transmitted by a UE can be used for CSIestimation at an eNB exploiting channel reciprocity.

A key issue of CoMP design is to identify the UL overhead vs. DL perfor-mance tradeoff achievable with each feedback mechanism. To support CoMP, theUL overhead will necessarily be increased compared to Release 8. This calls forenhanced UL control channels that can carry this increased traffic. Two optionscan be considered in LTE-Advanced [7]: either expand the physical uplink con-trol channel (PUCCH) payload sizes or use periodic/aperiodic reports on thephysical uplink shared channel (PUSCH).

(7) Time and frequency synchronization Time and frequency synchronizationerrors can have a severe impact on the performance of CoMP if appropriaterequirements are not satisfied.

To illustrate the issue, assume two single-antenna cells are communicating witha single UE. Assume cell 1 transmits the passband signal over carrier frequencyf1 and cell 2 transmits the passband signal over carrier frequency f2 . The idealcentral frequency is denoted as f0 . The difference ∆f = f2 − f1 is the frequencyoffset between the cell 1 and cell 2 carrier frequencies. The differences f1 − f0

and f2 − f0 are the frequency errors of cell 1 and cell 2, respectively. Assumealso narrowband and static channels such that the channel from cell 1 to the UEis modeled as 1 and the channel from cell 2 to the UE is modeled as a complexscalar h. The UE receives the signals from cell 2 with a delay τ compared withthe signals from cell 1.

Assuming the UE locks its receiver on frequency f1 , we can easily showthat the equivalent baseband channel h′ from cell 2 to the UE becomes h′ =hej2π (−f1 τ +∆f (t−τ )) . Hence, the phase of the channel is affected by two factors:the phase shift due to the time delay τ and the phase shift due to the phaseoffset ∆f .


The quantity 2πf1τ represents the phase shift due to the time delay τ . Thetime delay creates a frequency selective channel. Due to the increased frequencyselectivity of the channel, multiple PMI feedback is required over the wholebandwidth in order to reasonably limit the losses due to the mismatched beam-forming [52]. This significantly increases the signaling overhead. Such a situationwould be even more critical in a CoMP scenario. Inter-eNodeB CoMP coherentJT is more sensitive to time synchronization errors than other CoMP schemes.A maximum delay of 0.5 µs for JT schemes is recommended in [53], while themaximum delay should be smaller than the cyclic prefix for other types of CoMPtransmission schemes.

The quantity 2π∆f (t− τ) represents the phase shift due to the frequencyoffset ∆f . Such a phase offset induces a time varying channel due to the prod-uct ∆ft. Requirements for the frequency errors are provided in [54] for differentclasses of eNodeBs. The minimum requirement allows the frequency error to besmaller than ±0.05 ppm for wide-area eNodeBs, ±0.1 ppm for medium rangeeNodeBs, ±0.1 ppm for local area eNodeBs and ±0.25 ppm for home eNodeBs.An error of ±0.05 ppm corresponds to ±2GHz ∗ 0.05/1e6 = ±100 Hz for a car-rier frequency of 2 GHz. Assuming a 5 ms backhaul delay and ∆f = 100 Hz, thechannel phase can change by π between the measurement time and the trans-mission time. Both backhaul delay and frequency synchronization errors have tobe significantly decreased in order to avoid such phase mismatch.

Time and frequency synchronization issues are much more serious for JT tech-niques than for CB/CS, since two signals from multi-eNodeBs are coherentlycombined in JT. Requirements on the frequency synchronization accuracy arehigher for the JT technique. Considering frequency offset of the order of ±0.005ppm for inter-eNodeB CoMP JT is suggested in [53]. A maximum frequencyoffset of one order of magnitude smaller than current requirements used in acommercial eNodeBs is suggested in [55]. For intra-eNodeBs CoMP JT, it ispossible to achieve a much better accuracy, since the same reference clock canbe used to calibrate the clocks of the cells attached to the same eNB. For CoMPCB/CS, accuracies similar to that required by Release 8 would be sufficient, sinceCB/CS is less sensitive to the frequency offset.

Higher frequency and time synchronization accuracies can be obtained usingGPS assistance or network-based synchronization [53, 55, 56].

15.3.3 Release 10 of LTE-Advanced

CoMP has been heavily discussed for Release 10 of LTE-Advanced. The systemhas been designed and built in such a way that even if only some types ofCoMP are supported in Release 10, more advanced features can be supported infuture releases of LTE-Advanced. As discussed previously, the CSI-RS design foraccurate measurement of multicell channels is a fundamental issue in the designof CoMP and is under investigation. Feedback mechanisms and the performancevs. overhead tradeoff are other core problems under discussion.

15.4 Wireless relay 451

Below is a summary of the major decisions on CoMP for Release 10 [7]: As the baseline of CoMP design in LTE-Advanced, the UE is not explic-

itly informed of the CoMP transmission point(s) and the UE reception anddemodulation of CoMP transmissions (CS/CB, or JP) are the same as thosefor non-CoMP (SU/MU-MIMO).

For CoMP schemes that require feedback, individual per-cell feedback is con-sidered as the baseline. Complementary intercell feedback may be supported.As the baseline, the feedback information is reported to the serving cell whenthe X2 interface is available and suitable enough in terms of latency andcapacity to support CoMP operations. For other scenarios (X2 interface notavailable or not suitable due to latency and/or limited capacity), more dis-cussions are required.

For Release 10, any DL CoMP scheme will not include a new standardizedX2 interface communication to support multivendor inter-eNodeB CoMP. Inother words, CoMP will assume only intra-eNodeB techniques.

CSI RS design should take the potential needs of DL CoMP into account andshould allow for accurate intercell measurements.

No additional features are specified in Release 10 to support DL CoMP.

Companies recommend considering further studies on DL-CoMP within theRelease 10 timeframe in the framework of a new study item [57]. A new studyitem on CoMP has been introduced with the objectives of evaluating the perfor-mance benefits of CoMP and the required specification support in the physicaland higher layers [67].

LTE and LTE-Advanced have been submitted to ITU as IMT-Advanced can-didates. Extensive simulation results were provided at that time to assess theperformance of LTE-Advanced vs. ITU requirements [8]. Generally speaking,it appeared that MU-MIMO based on DM-RS provides significant gains overSU-MIMO relying on Release 8. CB/CS provides negligible gains over advancedMU-MIMO. JP outperforms MU-MIMO significantly in some specific scenar-ios like Urban Micro. Note that these results and conclusions that could bedrawn should be considered with caution as they greatly depend on the simula-tion assumptions. Hence, careful investigation of the simulation assumptions isrequired before drawing any meaningful conclusions [8].

15.4 Wireless relay

Wireless relay is one of the most important features of the 3GPP LTE-Advancedstandard. In a conventional cellular system, a wired backhaul is one of the majorsources of the maintenance cost of a cellular network. Wireless relay is introducedto reduce the cost of the wired backhaul.

A wireless relay can forward user data between a neighboring macro-eNodeBand UEs. Therefore, it can be regarded as a kind of cooperative communication.There has been a lot of research on several types of wireless relays including the


Table 15.3. Comparison of two types of wireless relay

Type 1 relay Type 2 relay

Cell ID Relay has a unique cellID (relay operates as anindependent cell)

Cannot have a uniquecell ID

Data transmission Transmits all DL datachannel

Retransmits PDSCHHARQ

SYNC, CRS transmission Transmits Does not transmitNotes Major work item for

Release 10

decode-and-forward relay, and the amplify-and-forward relay. The 3GPP LTE-Advanced standard considers only decode-and-forward wireless relays, which canforward the user data after successfully decoding the corresponding data packet.

15.4.1 Key technologies

Types of wireless relays

Two different types of wireless relays are discussed in the LTE-Advanced stan-dard. Table 15.3 compares these two different types of wireless relays.

A type 1 relay node has an independent cell ID and operates as an independenteNodeB. The only difference from the conventional macrocell is that a type 1relay has a wireless backhaul link instead of wired one. Therefore, a type 1 relaynode has all the scheduling and resource allocation functionalities in addition tothe physical layer functionalities.

Unlike a type 1 relay, which has an independent cell ID, a type 2 relay can-not have an independent cell ID. Hence, it is not possible for it to operate asan independent eNodeB. A type 2 relay is used to retransmit HARQ packetsafter the relay node has successfully received the PDSCH packets sent to UEs.Therefore, a type 2 relay can send only the retransmissions of PDSCH and therelated reference signals for demodulation. A type 2 relay node is not allowed totransmit SCH, RSs, or PDCCH. Therefore, it is difficult to consider the signalquality from a type 2 relay in computing the CQI used for adaptive modulationand coding.

Operation of wireless relayThere are several design issues for the backhaul link between a macro-eNodeBand a relay node. Depending on the frequency band used for the wireless back-haul, the wireless backhaul link is categorized as [7]:

15.4 Wireless relay 453

(1) Inband The macro-eNodeB to relay link uses the same frequency band usedfor the macro-eNodeB to UE links.

(2) Outband The macro-eNodeB to relay link uses a different frequency bandfrom the macro-eNodeB to UE links.

The macro eNodeB is required to support both UEs in the cell and the wirelessbackhaul link. For a relay node operating as an inband relay, it is difficult toreceive data from the macro-eNodeB, while transmitting a DL signal at the samefrequency band. This may result in discontinuity in the DL signal sent from arelay node, during the subframes when the relay receives data from the macro-eNodeB. The solution used for the inband relay is not to transmit any signal inthe DL by creating “gaps” in these subframes. Therefore, timing alignment isone of the important issues in designing the wireless backhaul link. As describedin [7], the DL subframe boundary from a macro-eNodeB should be aligned withthe backhaul downlink subframe boundary at the relay node, although therecould be some adjustment to allow for the relay node transmitting/receivingtime switching.

A wireless relay node should also support LTE Release 8 UEs. Since LTERelease 8 UEs are not designed for the wireless relay operation and do not knowthe subframes when a wireless relay node switches to the DL reception mode,they may experience problems from these subframes configured as the gaps.To the LTE Release 8 UEs located in a relay cell, the relay node declares thesesubframe as the multimedia broadcast over a single-frequency network (MBSFN)subframe, which the UEs do not have to receive. The MBSFN subframes areused for broadcasting services in an LTE system. With this information, theLTE Release 8 UEs can discard the DL PDSCH of these subframes configuredas the gaps.

Figure 15.4 shows an example of the timings of a macro-eNodeB and a relaynode. The figure shows only two subframes. It can be observed that the sub-frame boundaries are aligned between the macro and the relay. The first sub-frame is not used for the backhaul link. Therefore, the macro-eNodeB andrelay node transmits data to the UEs in each cell. The second subframe isused for the backhaul link and the macro-eNodeB can send data to the relaynode. The macro-eNodeB sends data to the relay node (and to the UEs inthe macrocell if necessary). Therefore, the relay node stops DL transmissionafter the transmission of PDCCH in the second subframe and switches itsmode to receive the data sent over the wireless backhaul link. The secondsubframe is noticed as an MBSFN subframe to the UEs in the cell servedby the relay node. UEs in a relay cell can decode only the data from therelay node.

Since a wireless relay node should transmit the PDCCH even in the gap sub-frame shown in Figure 15.4, it may not demodulate the PDCCH sent fromthe macro-eNodeB. Therefore, new physical channels need to be designed thatinclude R-PDCCH and R-PDSCH for the inband type 1 relays, where R-PDCCH


Macro-eNB

Relay

Control

Control

Control

Control

Data

Data Transmission gap(MBSFN subframe)

Data

Subframe

Figure 15.4. Downlink subframes of macro eNB and relay node.

and R-PDSCH are the channels to send the control information and data to therelay nodes, respectively. In addition to R-PDCCH and R-PDSCH, other chan-nels are being considered and will be defined if they are necessary for efficientoperation of the wireless relay.

15.4.2 Standard trends on Release 10 and future works

Even though the concept of a wireless relay was introduced in the LTE-Advancedstandard to reduce the backhaul cost, only the most fundamental and simplestdesigns will be embodied in the Release 10 standard. There are some technicalconcerns with the type 2 relay and its benefit is not clear. Hence, it was decidedthat the standardization of LTE-Advanced Release 10 will be based on the type1 relay only [58].

It is expected that more complicated and efficient PHY/MAC designs andprocedures will be added after the Release 10. These may include the issuesthat are actively being discussed in the heterogenous network, which will beintroduced in the next section. In addition to these issues, more efficient air-interface designs may be included in the standards after Release 10.

15.5 Heterogeneous network

One of the research topics in the LTE-Advanced standard is the heterogeneousnetwork. The purpose of the heterogeneous network is to ensure reliable commu-nication links and to increase system capacity, when the network is configuredwith different types of eNodeBs in addition to the conventional eNodeBs. Inthis section, the standardization trends for the heterogeneous network will beinvestigated.

15.5.1 Key technologies

Heterogeneous network scenarios

The heterogeneous network issue concerns the deployment environments, wheremany low-power nodes are placed in a macro-cell layout. The configurations

15.5 Heterogeneous network 455

Table 15.4. Summary of heterogeneous network scenarios

Backhaul Access Notes

RRH Several µs latencyto macro

Open to all UEs Placed indoor oroutdoors

Pico-eNodeB(nodes forfemto-cells)

X2 interface Open to all UEs Placed indoor oroutdoors

HomeeNodeB(nodes forfemto-cells)

For further study Closed subscribergroup (CSG)

Placed indoors

Relay nodes Throughair-interface witha macro-cell

Open to all UEs Placed outdoors

that are currently considered for the heterogeneous network are (Table 15.4)[7]:

(1) Macro-eNodeB + RRH;(2) Macro-eNodeB + pico-eNodeB;(3) Macro eNodeB + home eNodeB;(4) Macro-eNodeB + relay nodes.

The RRH is one of the promising solutions for implementing a distributednetwork. It can geometrically separate the radio frequency (RF) modules fromthe baseband signal processing module using fibers. With RRH, the locations ofthe baseband processes are concentrated and the RF modules are placed in thegeometrically separated nodes. The backhaul to the macrocell uses optical fibersand its latency can be assumed to be several microseconds. With this low delaybackhaul, it is possible to coordinate resources among geometrically separatednodes in real time. Therefore, RRH is one of the widely studied frameworks forimplementing CoMP technology.

The pico-eNodeB is used for hotzone cells, which are intended for areas witha small cell radius and densely located UEs. The maximum transmission powerof a pico-eNodeB is typically about 30 dBm. Basically, a pico-eNodeB is locatedwith planned deployment as normal cellular eNodeBs and open to all UEs. Thebackhaul is assumed to be the X2 interface, which is the same as the conventionalcellular networks.

Wireless relay is used to extend coverage of a cellular system. The backhaulis the wireless one as explained in Section 15.4. Performance enhancement isan important issue in the environments, where UEs are located between themacro-eNodeB and the wireless relay node.


The home eNodeB is used for femto-cells, which are targeted for an indepen-dently operated node by a personal user (customer deployed). The backhaul fora home eNodeB is another item for study. While the other three heterogeneousnetwork scenarios are designed to be open to all users, the home eNodeB istargeted for a closed subscriber group (CSG). Therefore, only limited UEs areallowed to access the home eNodeB.

Performance requirementsWhen standardizing LTE-Advanced, the performance of several heterogeneousnetworks is evaluated. To evaluate the benefit of adding low-power nodes to themacrocell only network, several performance metrics are considered. In additionto the existing traffic performance metrics, some additional important perfor-mance metrics are considered for the heterogenous network:

the macrocell area throughput, the fraction of throughput over low-power nodes, the UE throughput ratio between the macro- and the low-power node.

For the performance simulation, there are several key assumptions includ-ing the channel model, traffic model, and operation scenarios. Details of theseassumptions can be found in [7].

Important technical issuesIn deploying a heterogeneous network, there are several technical issues to beconsidered.

The interference problem is one of the main issues of a heterogeneous net-work. Due to the interference between the neighboring macro-eNodeBs and newlydeployed nodes (pico, femto, and wireless relay nodes), it is difficult to establisha stable communication link with high data throughput. In particular, interfer-ence on the control channel can make a serious impact on maintaining a reliablecommunication link. The interference on the data channel region can reduce thedata throughput drastically. Therefore, it is essential to mitigate and coordinatethe interferences in a heterogeneous network.

One of the most interference-dominated areas is the boundary between amacro-eNodeB and a femto-eNodeB. Since a femto-cell is custom deployed andtargeted for CSG, it may be difficult to control the interference from a femto-cell. In particular, when a UE is located near a femto-cell, it may be difficult toacquire the signal from a macro-eNodeB. If the UE can acquire the signal fromthe macro-eNodeB and make a communication link, the transmitted signal fromthe UE can be a large interference to the femto-receiver. Therefore, it is veryimportant to measure and coordinate the interference generated by the femto-eNodeBs and UEs. This becomes more difficult to do in a femto-cell scenario,since all UEs are not allowed to access the femto-cell.

15.6 Conclusion 457

There are many technical contributions to coordinate the interference gen-erated from neighboring eNodeBs and UEs [59–63]. For further reduction ofinterference, ICI cancelation is considered as a receiver technology [64].

Efficient serving eNodeB selection is another important technical issue [65,66]. Unlike in conventional cell selection in a homogeneous network, the servicecapability and delay are different depending on the type of eNodeBs. Therefore,selecting a proper serving eNodeB can be an important issue determining thedata throughput and service quality in a heterogenous network.

Measurement is also an important issue. For both interference coordinationand cell selection, it is essential to detect and measure the neighboring andinterfering sources. Without proper measurement, it is impossible to make an effi-cient decision about interference coordination and cell selection. Specific eNodeBsignals should be designed with measurement in mind. The candidates for themeasurement signals are the CSR and the CSI-RS. Measurement based on thesechannels is being discussed for heterogeneous networks.

15.5.2 Standard trends on Release 10 and future work

The heterogeneous network issue was adopted as a study item in the fourthquarter of 2009 and added to the work items in the first quarter of 2010. Itis premature to say that a separate section for the heterogenous network willbe included in Release 10 of LTE-Advanced standard. This is because someessential techniques can be included in other work items, such as the wirelessrelay, feedback and measurement issues, if they are necessary for heterogeneousnetwork operation.

It is widely believed that the heterogeneous network is important from bothtechnical and business perspectives. Therefore, many companies will focus on theheterogeneous network issue. It is expected that heterogeneous-network-relatedissues will be one of the major work items in the later versions of the LTE-Advanced standard and future wireless systems. The heterogenous network sce-narios will be the baseline for the cooperative communication technologies ofwireless cellular systems.

15.6 Conclusion

The standard trends in cooperative wireless communication are investigated inthe 3GPP LTE-Advanced system. In particular, CoMP transmission, wirelessrelay, and heterogeneous network issues are presented in addition to the generalLTE-Advanced concepts.

CoMP is being intensively discussed as a means to enhance the throughput ofcell-edge users. Wireless relay links between a donor eNodeB and a relay nodeare also being designed. Heterogenous networks are being investigated for thescenarios where different kinds of eNodeB are deployed.


It is expected that only simple concepts will be included in the Release 10 ver-sion of the LTE-Advanced standard. However, more complicated and advancedcooperative communication techniques will be considered for the later versionsof LTE-Advanced and other future wireless systems.

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16 Partial information relaying andrelaying in 3GPP LTE

Dong In Kim, Wan Choi, Hanbyul Seo, and Byoung-Hoon Kim

16.1 Introduction

Direct transmission from source to destination often faces weaker channel con-ditions when a mobile is moving across the cell border, because of the largepropagation loss due to path-loss and shadowing, and the power limitation notto cause undue interference. For this reason, attention has been given to the useof cooperative relaying to mitigate intercell interference to abtain an increasedrate and extended coverage at cell edge.

There have been many proposals for cooperative relaying, such as amplify-and-forward (AF), decode-and-forward (DF), and compress-and-forward (CF), someof which were developed in [1–4]. Such relaying schemes are mainly designedto exploit the multipath diversity for a power gain (or increased rate) thatresults from combining direct and relayed signals. However, these schemes donot fully utilize the asymmetric link capacity in direct (source–destination) andrelay (source–relay) links, e.g., where the latter gives better results in the down-link if line-of-sight (LoS) transmission is realized in the link between the basestation and a fixed relay.

A partial DF protocol has been proposed in [5] that aims to exploit the asym-metric link capacity more efficiently by forwarding a part of the decoded infor-mation to the destination using superposition coding. Further, Popovski andde Carvalho [6] investigated a power division between the basic data and thesuperposed data that result from superposition coding, for a maximum overallrate capacity. However, the multiple-antenna configurations that cause additionalinterstream interference due to spatial multiplexing were not considered, and alsothe partial DF relaying can be designed more efficiently using multiple antennas,which is a crucial issue in realizing next generation cellular systems.

The concept of partial DF relaying can be translated into multiple-antennaconfigurations by applying superposition coding per antenna, termed per-antenna superposition coding (PASC), and across antennas, termed multilayersuperposition coding (MLSC). However, the extension is not straightforwardbecause the power should be divided not only between the basic and superposed


16.2 Partial information relaying with multiple antennas 463

layers but also across the spatial layers under multiple-antenna configurations.Furthermore, the power division here interacts with spatial interference.

In this context, we describe how to form the partial information to be for-warded, find a proper power division strategy for partial DF relaying with PASCand MLSC, and eventually show how another form of relaying based on PASCand MLSC, termed partial information relaying can be effective in increasing anoverall data rate at the cell edge when multiple antennas are employed.

In addition, multinode cooperation is introduced for partial information relay-ing that realizes two-stage superposition coding at the source and relay, in con-junction with relay selection, when multiple relays and destinations exist. Thismultinode cooperative relaying more effectively increases the overall rate capac-ity by fast forwarding the partial information in the second cooperating phase,considering asymmetric link conditions.

Finally, we summarize the LTE-Advanced standard issues, discussions, andcurrent conclusions on relay, while detailing the functionalities of relay nodes.We also highlight the self-interference issue which is the key point of multiplex-ing the source-to-relay link and the relay-to-destination link, and provide somediscussion on how to resolve it.

The rest of this chapter is organized as follows. Section 16.2 describes howto form partial information in multiple-antenna configurations, using PASC andMLSC, where the relaying protocols with PASC and MLSC are given along withtheir performance comparison. In Section 16.3, the PASC with zero-forcing decor-relation is analyzed to find a proper power division strategy for partial informa-tion relaying, leading to an overall rate capacity. Multinode partial informationrelaying is introduced in Section 16.4, along with two-stage superposition cod-ing, in order to increase further the overall rate capacity, and this is followed byconcluding remarks on partial information relaying in Section 16.5. Section 16.6provides an overview of relaying in 3GPP LTE-Advanced.

16.2 Partial information relaying with multiple antennas

Due to the broadcast nature of the wireless channel, an intermediate node canrelay the signal from source to destination using either the AF or the DF relay-ing protocol. When orthogonal channels are used for simple relaying, informationloss cannot be avoided because receiving and forwarding at the relays are dividedinto two hops to avoid the self-interference, resulting in a half-duplex operation.It is also reported in the literature that non-orthogonal AF (NAF) [7] can adoptjoint maximum-likelihood (ML) detection for the intersymbol interference chan-nel caused by duplicate relaying, where a new symbol from the source overlapswith the prior symbol from the relay under time-division multiplexing (TDM).This approach attempts to avoid the information loss by virtue of nonorthogonalchannelization through joint ML detection.

464 Partial information relaying and relaying in 3GPP LTE

P

P

P

R

R

R P RiLiL

Pi2 i2R

P Ri1i1

X1

X1

Xi1

Xi1

Xi2

Xi2

XiLXiL

M

M

M

Pm= P

L M

Rm= R

m

m

X2

XM

XM

X2

MM

Figure 16.1. Partial information relaying with multiple antennas.

Unlike in the existing approach, we develop a partial information relayingmethod in which multiple antennas are available at the source (S), the relay (R),and the destination (D), as shown in Figure 16.1, where Pm and Rm denote thepower and rate allocated to antenna m, m = 1, 2, . . . ,M .

This relaying method realizes transmission of multiple parallel data streamswhich carry two types of information: (1) basic data streams, (2) superpositioncoded (SC) data streams, on the condition that the relay forwards only theSC streams, i.e., partial information rather than full information as received inconventional AF and DF protocols.

The key idea behind partial information relaying is to exploit the asymmetriclink conditions often observed in a cellular environment, where the relay (source–relay) link and the access (relay–destination) link are relatively better than thedirect (source–destination) link. Considering this with half-duplexing mode forrelaying, the source sends M multiple (basic and SC) streams in the first hop, asshown in Figure 16.1. Then, the relay forwards only L (≤M) SC streams in thesecond hop to the destination. Finally, the destination decodes the SC streamsreceived in the second hop after which the basic streams are decoded by cancelingout the SC streams from the original signal received in the first hop. Here, weassume adaptive TDM so that the relatively better access link will forward theSC streams/partial information in the second hop whose duration can be mademuch shorter than that of the first hop. This leads to an increase in overallrate capacity because of the fast forwarding of partial information/SC streams,thereby reducing the information loss caused by half-duplexing operation.

To realize the partial information relaying method, it is a prerequisite to formthe partial information to be forwarded in multiple-antenna configurations, basedon the superposition coding. Here, the superposition coding refers to a simple


linear combining of basic data streams and SC data streams. For this we considertwo possible realizations below when M antennas are employed.

16.2.1 Per-antenna superposition coding (PASC)

Figure 16.2 shows the structure of PASC where the basic and SC streams (orlayers) are serially formed at each antenna, and the per-antenna power Pm isdivided between the two layers according to the power division factor αm , m =1, 2, . . . ,M , which considers the asymmetric link conditions.

x [(1- ) ]b,M M MP

... .x [(1- ) ]b,2 2 2P

x [(1- ) ]b,1 1 1P

x [ ]s,M M MP

x [ ]s,2 2 2P

x [ ]s,1 1 1P

... .

ANT #1

ANT #2

....

ANT #M

R = R + R1 b,1 s,1

R = R + R2 b,2 s,2

....

R = R + RM b,M s,M

Basic layers SC layers

Figure 16.2. PASC with M antennas.

In the multiple parallel transmission under PASC as shown in Figure 16.3, itis necessary to optimally determine the set of power division factors αm ,m =1, 2, . . . ,M such that an overall rate capacity can be maximized. In fact, todetermine the power division factors, we need to acquire the information aboutasymmetric link conditions for direct and relay links, in terms of the per-antennasignal-to-interference-plus-noise ratio (SINR) after a proper decorrelation process(to minimize the interstream interference), e.g., the minimum mean-square-errorsuccessive interference cancelation (MMSE-SIC) algorithm [8]. It is assumed thata low-rate feedback channel is available to report the post-processing per-antennaSINR to the source so as to allow joint power and rate allocation.

Basic layer

SC layer

RS RD

RR

Figure 16.3. Partial information relaying via PASC with M = 2.


Figure 16.3 shows that two parallel data streams carry both basic and SC layersper stream from each antenna, of which the SC layers only are being forwardedin the second cooperating phase using two antennas at the relay. This allows thefast forwarding of the partial information/SC layers using the relatively betteraccess link, leading to a gain in the overall rate capacity, as anticipated.

Description of the PASC (2 × 2 × 2):

♦ Phase 1• S broadcasts two streams:stream 1 :

√1− α1 xb,1 +

√α1 xs,1 ,

stream 2 :√

1− α2 xb,2 +√

α2 xs,2 ;• αi denotes the power division factor between basic data xb,i

and SC data xs,i of ith stream;• R decodes the received signal from S, in the order of basic and SC,stream-by-stream, while D keeps the received signal in its memory.

♦ Phase 2• R forwards only the SC data streams xs,1 and xs,2 from phase 1after re-encoding;• D decodes the received SC data streams to estimate xs,1 and xs,2

using MMSE-SIC;• Based on the decoded xs,1 and xs,2 , D performs SIC to decode xb,1

and xb,2 from phase 1.

Figure 16.4 shows a flow diagram of partial information relaying via PASCin two phases (hops) under adaptive TDM when two antennas are used at thesource, relay, and destination, assuming half-duplexing operation.

16.2.2 Multilayer superposition coding (MLSC)

Figure 16.5 shows the structure of MLSC where the basic and SC streamsare formed in parallel across antennas, and a specific configuration of L SCstreams and (M − L) basic streams with per-antenna power allocation Pm ,m =1, 2, . . . ,M is determined according to the asymmetric link conditions.

In the multiple parallel transmission under MLSC as shown in Figure 16.6, itis necessary to optimally determine the subset of SC streams to be forwardedpartially, i.e., the adaptation parameter L such that an overall rate capacity canbe maximized. As mentioned above, how to set the parameter L depends onthe information about asymmetric link conditions for direct and relay links, interms of the per-antenna SINR after proper decorrelation process (to minimizethe interstream interference), e.g., MMSE-SIC.


Broadcasts data streams

Decodes received signals

Transmits only SC layers

1. Decodes SC layers first2. Decodes basic layers after SIC

(b)

RS RD

RR

RS RD

RR

(a)

Figure 16.4. Flow diagram of partial information relaying via PASC with M = 2:(a) phase 1; (b) phase 2.

xb,M-L (PM, RM)ANT #M

... L SC layers

xb,1(PL+1, RL+1)ANT #L+1

xs,L (PL, RL)ANT #L

xs,1 (P1, R1)ANT #1

... (M – L) basic layers

Figure 16.5. MLSC with M antennas.

Basic layer

SC layer

RS RD

RR

Figure 16.6. Partial information relaying via MLSC with M = 2 and L = 1.

Figure 16.6 shows the two parallel data streams carrying basic and SC layers,respectively, from each antenna, of which the SC layer only is being forwardedin the second cooperating phase using two antennas at relay. By exploiting therelatively better access link, this partial information relaying can provide a gainin the overall rate capacity.


Description of the MLSC (2× 2× 2, assume L=1):

♦ Phase 1• After L is selected to maximize rate, S broadcasts two streamsstream 1 : xb,1 , stream 2 : xs,1 ;• R decodes only SC streams xs using MMSE-SIC;• D keeps both SC and basic streams in its memory.

♦ Phase 2• R forwards only SC streams xs using all antennas;• D decodes xs first, and then decodes xb after SIC;• If L = M , it realizes two-hop transmission with no basic stream;• If L = 0, it reduces to direct transmission with no SC stream.

Broadcasts data streams

Decodes only SC streams

Transmits only SC streams

1. Decodes SC streams first2. Decodes basic streams after SIC

(b)

RS RD

RR

RS RD

RR

(a)

Figure 16.7. Flow diagram of partial information relaying via MLSC with M = 2and L = 1: (a) phase 1, (b) phase 2.

Figure 16.7 Shows a flow diagram of partial information relaying via MLSCwith L = 1 in two phases (hops) under adaptive TDM when two antennas areused at the source, relay, and destination, assuming half-duplexing operation.

16.2.3 Rate matching for superposition coding

Based on the post-processing per antenna SINRs ρ0,m ,m = 1, 2, . . . ,M of thedirect link and per-antenna SINRs ρ1,m ,m = 1, 2, . . . ,M of the relay link,where αm is initially set to zero in order to measure the degree of asymmetry in


both links, the power division factor αm at the mth stream for partial informationrelaying via PASC is set by the following formula:

αm =(

1ρ0,m

− 1ρ1,m

)+

for m = 1, 2, . . . ,M (16.1)

where (x)+ = max(0, x). Here, αm is adjusted to balance between the unevendirect and relay links in terms of the rate capacity, which is discussed in Sec-tion 16.3, and the per-antenna power allocations Pm ,m = 1, 2, . . . ,M havebeen assumed to be performed through the water-filling algorithm as

Pm

P=(

1λ− 1

λ1,m

)+

for m = 1, 2, . . . , M, (16.2)

where λ1,m denotes the per-antenna SINR of the relay link at the mth stream ifthe total power P is allocated to the mth stream, whereas ρ1,m is the pre-antennaSINR if the power Pm is allocated to the mth stream. Here, λ is determined tomeet the total power constraint

∑m Pm ≤ P .

Based on the post-processing per-antenna SINRs ρ0,m ,m = 1, 2, . . . ,M ofthe direct link and per-antenna SINRs ρ1,m ,m = 1, 2, . . . , M of the relay link,the adaptation parameter L for partial information relaying via MLSC is set bythe following formula:

L =M∑

m=1

u(ρ1,m − ρ0,m

), (16.3)

where u(x) = 1 if x > δ (some threshold to be tuned) and zero otherwise. Notethat the threshold δ is selected properly such that an overall rate capacity canbe maximized, since the better condition of the access link can be utilized to fastforward arbitrary L partial SC streams in the second cooperating phase.

16.2.4 Overall rate capacity

The overall rate capacity of the partial information relaying via PASC and MLSCis compared with those of existing relaying protocols. First, the rate capacity asa function of αm ,m = 1, 2, . . . ,M and L for PASC and MLSC, respectively,can be evaluated as:

RP ASC =

∑Mm=1

[log(1 + (1− αm )ρ0,m ) + log(1 + αm ρ1,m )

]1 +∑M

m=1 log(1 + αm ρ1,m )/R2, (16.4)

RM LSC =∑L

m=1 log(1 + ρ1,m ) +∑M

m=L+1 log(1 + ρ0,m )

1 +∑L

m=1 log(1 + ρ1,m )/R2, (16.5)

where R2 denotes the rate capacity (bits/symbol) of the access link between therelay and the destination. In the above, the overall rate capacity is due to thebasic layers of direct transmission after the successive interference cancelation(SIC) at the destination and the SC layers after the SIC at the relay, normalized


by the average time spent over two-hop transmission. Here, the average secondhop time can be made shorter than the normalized first hop time of 1 becauseof the better access link, or equivalently the larger R2 , than the rate capacity ofthe SC layers to be forwarded.

For comparison, the average rate capacity (or throughput) of conventionalrelaying protocols is evaluated as follows:

1. direct transmission (DT):

RDT = log(1 + ρ0,m ); (16.6)

2. two-hop transmission (2H):

R2H =∑M

m=1 log(1 + ρ1,m )

1 +∑M

m=1 log(1 + ρ1,m )/∑M

m=1 log(1 + ρ0,m + ρ2,m ); (16.7)

3. DF:

RDF =12

min

M∑

m=1

log(1 + ρ1,m ),M∑

m=1

log(1 + ρ0,m + ρ2,m )

, (16.8)

where the maximal-ratio combining (MRC) of direct and access links is assumed,whereas the access link only yields R2 =

∑Mm=1 log(1 + ρ2,m ) for its own per-

antenna SINR ρ2,m at the mth stream.Figure 16.8 shows the average throughput of two partial information relaying

methods and conventional relaying protocols, where the direct, relay, and accesslink SNRs are γi = |hi |2P/σ2 , i = 0, 1, 2.

16.2.5 Features of partial information relaying

The notable features offered by the partial information relaying developed hereare described as follows. First, the asymmetric link conditions are fully exploitedin implementing a practical MMSE-SIC receiver rather than the ML receiverwith complexity. Second, the near-optimal rate capacity via ML detection can beachieved by the cascaded operation of partial information relaying and SIC withmanageable complexity, in conjunction with a low-rate feedback on SINR. Third,the multidimensional rate adaptation via PASC and MLSC in multiple-antennaconfigurations will give rise to a new adaptive modulation coding (AMC), espe-cially when the relay is adopted for extended coverage and to mitigate intercellinterference. The latter is of great interest in that cell-edge users can benefitmostly from this for various quality-of-service (QoS) demands in wireless multi-media communications.

16.3 Analysis of PASC with zero-forcing decorrelation

A multiple-antenna configuration is considered with M transmit antennas atthe source and N receive antennas at the destination. A half-duplexing mode is

16.3 Analysis of PASC with zero-forcing decorrelation 471

Figure 16.8. Achievable rate capacity (bits/symbol) when M = 4.

assumed at relay with N receive and N transmit antennas. It is assumed thatthe slot length in the first and second hops varies depending on the amount ofinformation to be transferred and the link conditions for efficient link utilization.The transmit signal vector at the source is

x = [x1 , x2 , . . . , xM ]T , (16.9)

where xm =√

1− αm xb,m +√

αm xs,m , αm represents the power division fac-tors between the basic and superposed layers of each data stream per antenna,the power allocation to antenna m is Pm = E[|xb,m |2 ] = E[|xs,m |2 ], and (·)T andE[·] denote the transpose and expectation, respectively. Note that the subscriptb denotes the basic layer while s indicates the superposed layer on top of basiclayer.

With path-loss and fading accounted for, the N × 1 received signal vector atdestination is of the form

y0 =√

µ0 H0 x + n0 , (16.10)

where µ0 is the channel attenuation due to path-loss, the N ×M channel matrixof the direct link H0 is composed of independent zero-mean complex Gaussianrandom variables (flat fading), n0 denotes the zero-mean additive white Gaussiannoise (AWGN) vector with E[n0nH

0 ] = σ2IN , (·)H and IN denotes the Hermitiantranspose and the identity matrix of size N ×N .

Likewise, the N × 1 received signal vector at relay can be formulated as

y1 =√

µ1 H1 x + n1 , (16.11)


where the channel and noise statistics associated with different links and anten-nas are assumed statistically independent. Note that no precoding across multipletransmit antennas is considered at the transmitter because we assume feedbackabout per-antenna SINR instead of full channel state information (CSI).

Zero-forcing (ZF) V-BLAST [9] is employed at relay for successive interferencecancelation and spatial decorrelation of the interstream interference. The ZF-nulling vector for the stream to be decoded in the jth order is given by

w1,lj =(H+

1,lj −1

)T

lj, (16.12)

where lj is the index of the stream to be decoded in the jth order, H1,lj −1is

the matrix obtained by zeroing columns l1 , l2 , . . . , lj−1 of H1 , (·)+ denotes theMoore–Penrose pseudoinverse [10], and (·)lj denotes the lj th row of the givenmatrix. Note that the jth decoding order is determined by

lj = argminn /∈l1 ,...,lj −1||(H+

1,lj −1)n ||2 .

After spatial decorrelation by the ZF-nulling vector, the basic data are decodedfirst and then the superposed data are decoded by subtracting the effects of thebasic data. Assuming that the data stream through antenna m is decoded atrelay in the jth order, the SINRs of the basic and superposed data on the mthantenna are given, respectively, by

ρ1b,m =

(1− αm )γ1,m

||w1,lj ||2 + αm γ1,m, (16.13)

ρ1s,m =

αm γ1,m

||w1,lj ||2, (16.14)

where the superscript 1 denotes the relay and γ1,m is the per-antenna link SNRfrom the source to the relay and is given by γ1,m = µ1Pm /σ2 .

The relay forwards only the superposed layers in the second hop. In the adap-tive slot length protocol, the duration of the second hop can be much shorterthan that of the first hop since only partial information needs to be transferredover the relatively better link. This might contribute to an increase in the overallrate owing to the fast forwarding of partial information. Once the destinationsuccessfully decodes the superposed layers,1 the effects of the superposed lay-ers are canceled out from the signal received in the first hop. Consequently, thebasic layers become free from interference by superposed layers. Applying ZFV-BLAST, the ZF-nulling vector for the stream to be decoded in the ith orderis given by

w0,ki=(H+

0,k i−1

)T

ki

, (16.15)

1 Sufficient energy for successful decoding can be accumulated by the variable duration in thesecond hop.

16.3 Analysis of PASC with zero-forcing decorrelation 473

where ki is the index of the stream to be decoded in the ith order and determinedby

ki = argminn /∈k1 ,...,ki−1||(H+

0,k i−1)n ||2 .

The data stream through antenna m is assumed to be decoded at the desti-nation in the ith order; the SINR of the basic layer on the mth antenna is givenby

ρ0b,m =

(1− αm )γ0,m

||w0,ki||2 , (16.16)

where the superscript 0 denotes the destination and γ0,m is the per-antenna linkSNR from the source to the destination and given by γ0,m = µ0Pm /σ2 .

Then, the achievable rates for the basic layer and the SC layer through antennam are determined, respectively, by

Rb,m = log(1 + ρb,m ), (16.17)

Rs,m = log(1 + ρs,m ), (16.18)

where ρb,m = min(ρ0b,m , ρ1

b,m ). Based on the feedback from the destination andthe relay to the source about per-antenna SINRs, the optimal power and rateallocation between the basic and superposed layers and across antennas is per-fermed to maximize an overall data rate. That is, the overall rate offered bypartial information relaying with multiple antennas, denoted by Rsc(M,N), ismaximized by finding optimum combinations of power division factors αm andper-antenna power allocation Pm.

Considering the adaptive slot length protocol, the problem for optimizing thepower allocations above can be formulated as(

αm, Pm)

= argmax α m , P m ∑M

m = 1P m ≤P T

Rsc(M,N) = (16.19)

∑Mm=1 Rb,m (αm , Pm ) + Rs,m (αm , Pm )

1 +∑M

m=1 Rs,m (αm , Pm )/R2(N)

, (16.20)

where (αm , Pm ) denote explicitly the dependence of Rb,m and Rs,m on theseparameters. Here, the capacity of the relay-to-destination link (the R–D link)R2(N) is evaluated as

R2(N) =N∑

n=1

R2,n =N∑

n=1

log(1 + ρ2,n ), (16.21)

where the post-detection SINR at the nth receive antenna of the R–D link is

ρ2,n =γ2,n

||w2,lj||2 . (16.22)

Here, γ2,n = µ2 Pn/σ2 is the R–D link SNR at the nth antenna, and Pn denotesthe power allocation to nth antenna of the R–D link. Note that the ZF-nulling


vector of the R–D link w2,ljcan be obtained similarly as in (16.12) with H1

replaced by the N ×N channel matrix of the R–D link H2 .Given Pm, the overall rate Rsc(M,N) is maximized if the rates are matched

as ρ0b,m = ρ1

b,m because of decorrelation after the projection by each ZF-nullingvector. To achieve the rate matching, i.e., ρ0

b,m = ρ1b,m , the power division factors

should be set to

αm =(||w0,ki

||2γ0,m

−||w1,lj ||2

γ1,m

)+

for m = 1, 2, . . . ,M . (16.23)

Now, the overall capacity offered by partial information relaying with PASC issimplified to

Rsc(M,N) =

∑Mm=1 log

(1 +

γ1,m

||w1,lj ||2)

1 +∑M

m=1 θ(αm ) log(µ1 ||w0,ki

||2µ0 ||w1,lj ||2

)Big/R2(N)

(16.24)

for 0 ≤ αm < 1, where θ(αm ) = 0 if αm = 0 and otherwise is 1.

16.4 Multinode partial information relaying

In a single-node scenario as shown in Figure 16.1, the superposition coding forpartial information relaying is performed at the source using the per-antennaSINRs of the direct and relay links, for which the rate matching is achieved tobalance the two links by adjusting the power division factors αm and adapta-tion parameter L for PASC and MLSC, respectively. In this method the aim isto fast forward the partial information, i.e., SC layers, through the rate match-ing, which helps to reduce the average time for the second hop, provided relayand access links are in a better condition than the direct link. It is noted thatadaptive TDM is a prerequisite for enabling this method, which may not be fea-sible in the channel structure designed for current and next-generation cellularsystems.

To circumvent this limitation, we consider a generalized partial informationrelaying in multinode configurations, as shown in Figure 16.9, where two-stagesuperposition coding is performed at the source and relay, and the SC layersintended for multiple destinations are superposed again at the relay. A fixedTDM can be implemented by superposing multiple SC layers at the relay andforwarding them in the second cooperating phase.

Figure 16.10 illustrates the resulting partial information relaying method inmultinode configurations with M relays, N destinations, and L (≤ N) SC layersto be superposed at a relay, where a single antenna is assumed (although it caneasily be generalized to multiple-antenna configurations), resulting in a specific(M,N,L) multinode configuration. Here, the best relay is selected to performthe second-stage superposition coding when multiple relays M > 1 are available.

16.4 Multinode partial information relaying 475

RS

R2

R1

RM

D1

D2

DN

Figure 16.9. Multinode configurations with M relays and N destinations.

Listening phaseTime

Cooperating phaseTime

xb,1 xs,1 xb,N xs,Nxb,2 xs,2

1st 2nd N th

(N+1)th (N+2)th (N+N/L)th

xs,1 xs,2 xs,L xs,Nxc,L+1xc,L+2 xs,N-L+1xs,N-L+2xs,2L

Figure 16.10. Multinode patial information relaying with (M,N,L) configura-tion.

16.4.1 Two-stage superposition coding

With multiple relays and destinations, all SC layers decoded correctly in thefirst listening phase are superposed at a relay before forwarding them in thesecond cooperating phase, and the best relay is selected to maximize the overallrate capacity. It is also possible to superpose the SC layers at multiple relays toexploit the heterogeneous path-losses between multiple relays and destinations,but this requires undue information exchange to share the total available poweramong multiple relays. Hence, the latter case is not dealt with, instead the bestrelay is involved in the second-stage superposition coding.

The procedure and related signaling for multinode partial information relay-ing is illustrated in Figure 16.11 where N = L = 2 is assumed. Here, the powerdivision factors αi, i = 1, 2, 3 are determined to achieve the rate matching fortwo-stage superposition coding at the source and relay, which interact with eachother in view of the overall rate capacity derived in the sequel.


Description of the scheme (e.g., M = 1, N = L = 2):

♦ Phase 1, 2 (listening phase)• S broadcasts x1 and x2 to D1 and D2 , respectively and Rphase 1 :

√1− α1 xb,1 +

√α1 xs,1

phase 2 :√

1− α2 xb,2 +√

α2 xs,2

♦ Phase 3 (cooperating phase)• R forwards superposed SC layers xs,1 and xs,2 simultaneouslyphase 3 :

√1− α3 xs,1 +

√α3 xs,2

where α3 is the power division factor between the two SC layers.

(a) (b)

RS

D

RD

RRxb,1

xb,2

xs,1

xs,2

x b,1

x s,1

xb,2

xs,2

RS

D

D

RR

x s,2

x s,1

xs,2

xs,1

1

2

1

2

Figure 16.11. Flow diagram of multinode partial information relaying with N =L = 2: (a) listening phase; (b) cooperating phase.

To achieve the rate matching for the first-stage superposition coding, the powerdivision factors αi, i = 1, 2 are set to

αi =[

1γsd,i

− 1γsr

]+

, (16.25)

where γsr and γsd,i denote the link SNRs associated with the relay link and thedirect link intended for destination i, respectively. The above power division isnot strictly optimal, but it is an attempt to increase the overall rate capacity asderived in (16.35) by balancing the asymmetric link capacities over direct andrelay links. The latter can be found in balancing the rate capacities of basic layeri over both links, since their minimum rate should be allocated at both ends forsuccessful decoding, as derived in (16.36).

16.4 Multinode partial information relaying 477

16.4.2 Successive decoding in cooperating phase

L superposed SC layers at a relay are forwarded in the second cooperating phaseand then decoded at N multiple destinations, one-by-one, using the SIC, wherethe order of decoding will largely affect the overall rate capacity.

To illustrate the decoding procedure, we consider a practical scenario withN = L = 2 for which the forwarded signal is represented by

sr (t) =√

1− α3 xs,1(t) +√

α3 xs,2(t). (16.26)

Here, xs,i denotes the transmitted signal associated with SC layer i = 1, 2, whereP = E[|xs,i |2 ], and 0 ≤ α3 ≤ 1 is the corresponding power division factor. Then,the received signal at destination j can be expressed by

yrd,j (t) = hrd,j sr (t) + nj (t), (16.27)

where hrd,j is the channel gain of the complex Gaussian with variance normalizedto 1 for the access link from the relay to the destination j and nj (t) is the AWGNwith variance σ2 .

Suppose |hrd,1 | > |hrd,2 |, then SC layer 2 directed to destination 2 should bedecoded at both ends to utilize the better link condition when SC layer 1 isdecoded at destination 1 after canceling out SC layer 2. Therefore, it turns outthat the link capacities for carrying SC layer i are

Rrd,1 = C((1− α3)γrd,1), (16.28)

Rrd,2 = C

(α3γrd,2

1 + (1− α3)γrd,2

), (16.29)

where C(x) = log2(1 + x) and γrd,i = |hrd,i |2P/σ2 , i = 0, 1, 2. Likewise, if|hrd,1 | < |hrd,2 |, SC layer 1 is first decoded at both ends, and SC layer 2 isthen decoded at destination 2 after canceling out SC layer 1. In this case, theabove link capacities are rewritten as

Rrd,1 = C

((1− α3)γrd,1

1 + α3γrd,1

), (16.30)

Rrd,2 = C(α3γrd,2). (16.31)

Figure 16.12 shows the decoding procedure at both ends depending on the linkconditions when M > 1 and N = L = 2.

16.4.3 Relay selection for maximum capacity

In (M,N,L) multinode configurations with M > 1, the best relay is selected tomaximize an overall rate capacity when adaptive TDM is assumed for optimumperformance. In practice, the second-stage superposition coding is likely to beperformed with the configuration of M > 1 and N = L = 2 because of the suc-cessive decoding at a mobile handset with limited complexity. In this case, theframe messages i = 1, 2 intended for destination i are sent in time slots i = 1, 2


RS

RD1

RD2

RD1

RD2

RD1

RD2

xs,1 xs,2

xs,1 xs,2

xs,2xs,1

xs,2xs,1

SIC

SIC

RD1 xs,1

RD2 xs,2

xs, 2Decode

xs, 1Decode

xs,1Decodeafter SIC xs,2

xs,2Decodeafter SIC xs,1

Case 1: Relay to D1channel gain is better

Case 2: Relay to D2channel gain is better

Figure 16.12. Successive decoding of superposed SC layers when M > 1 andN = L = 2.

whose length is normalized to 1 (i.e., Ti = 1), and the superposed SC layersi = 1, 2 are then forwarded to destinations i = 1, 2 in time slot 3 with variablelength, determined by their maximum transmission time

T3 = max(

Rs,1

Rrd,1,

Rs,2

Rrd,2

). (16.32)

Here, Rs,i denotes the rate capacity of SC layer i over the relay link, given thatthe basic layer i is removed after the SIC at a relay, which is evaluated as

Rs,i = C(αiγsr ) (16.33)

for the power division factor αi between the basic layer and the SC layer i.Finally, the overall rate capacity can be derived as

Rtot =Rb,1 + Rs,1 + Rb,2 + Rs,2

T1 + T2 + T3(16.34)

=Rb,1 + Rs,1 + Rb,2 + Rs,2

1 + 1 + max(

Rs,1

Rrd,1,

Rs,2

Rrd,2

) , (16.35)

where Rb,i denotes the rate capacity of basic layer i over direct and relay links.Note that basic layer i over the direct link is decoded at destination i after theSIC to remove SC layer i, whereas it is decoded at a relay in the presence of SClayer i as interlayer interference. To allow successful decoding at both ends, therate selection should be made by choosing the minimum, which is evaluated as

Rb,i = C

(min

[(1− αi)γsr

1 + αiγsr, (1− αi)γsd,i

]). (16.36)

In Figure 16.13, the overall rate capacity in (16.35) is plotted as a functionof direct link SNR γsd,i (dB) when other link SNRs are set to γsr = γrd,i = 20dB, M = 1, 2, 3, and N = L = 2. It is observed that the overall rate increaseswith increased M because of the increased diversity order, and most of this gain

16.5 Concluding remarks on partial information relaying 479

Figure 16.13. Overall rate capacity with increased diversity order when M =1, 2, 3 and N = L = 2.

is achieved when M = 2, thereby suggesting two-relay cooperation for multi-node partial information relaying. To see the rate increase with multinode partialinformation relaying, the rate capacity for the partial information relaying witha dedicated single relay without second-stage superposition coding is comparedwith the former in Figure 16.14 when M = 2. Here, we assume that the relay and(dedicated) access link SNRs are γsr = γrd,i,i = 20 dB (i = 1, 2) from relay i todestination i, whereas the cross-access link SNRs are γrd,1,2 = γrd,2,1 = 15 dB.We see that the multinode cooperation with second-stage superposition codingoutperforms the partial information relaying without it, which validates the use-fulness of second-stage superposition coding at a relay, along with relay selectionfor increased diversity. Moreover, if the power allocation between the source andthe relay is jointly performed subject to a fixed total power (i.e., 2P ), the ratecapacity is further increased because the rate matching can be more effective inmaximizing the overall rate capacity.

16.5 Concluding remarks on partial information relaying

We have shown that partial information relaying via PASC and MLSC allowsperfect rate matching among the asymmetric links often observed at the cell edge,resulting in significant capacity gain over full information relaying. In additon,PASC with ZF decorrelation has been analyzed to show how to achieve therate matching while maximizing the overall rate capacity, thereby balancing theasymmetric link capacities through a proper power division between the basic


Figure 16.14. Comparison of overall rate capacity without and with second-stagesuperposition coding when M = N = L = 2.

and SC layers. Furthermore, the extension to multinode cooperation with two-stage superposition coding has shown that the overall rate capacity can be signif-icantly increased by making the cooperating phase more effective in forwardingthe partial information through second-stage superposition coding at a relay. Inparticular, relay selection to achieve the diversity gain has been shown to beeffective in increasing the overall rate capacity, in conjunction with the second-stage superposition coding, which can be generalized to distributed superpositioncoding using multiple relays under the multinode cooperation.

16.6 Relaying in 3GPP LTE-Advanced

The 3GPP has been considering the wireless relaying operation for long-term evo-lution advanced (LTE-Advanced). The relay node (RN) is wirelessly connected toradio access network via a donor eNodeB2 and serves the user equipment (UEs)under its coverage as illustrated in Figure 16.15. The wireless link between adonor eNodeB and an RN is called the backhaul link and the link between anRN and UEs associated with the RN is called the access link. The link betweenan eNodeB and a UE directly associated to the eNodeB is called the direct linkto differentiate from the links in which an RN is involved.

2 eNodeB means evolved NodeB, the base station of 3GPP LTE systems.

16.6 Relaying in 3GPP LTE-Advanced 481

Figure 16.15. Illustration of a relay network.

The relaying operation can have various uses. First, an RN can be deployedto enhance the system throughput and improve the coverage of high data ratetransmissions. By locating an RN in a crowded hotspot area, the direct link canbe replaced by the backhaul and access links in which the channel conditions aremore favorable and high rate transmissions are allowed more frequently. Second,an RN can improve the user experience at the cell edge where the signal strengthfrom the network is weak. In this case, the RN can be a cost-effective solution forproviding service coverage in new areas as no additional cost is required to deploythe wireline backhaul link to connect the RN to radio access network. Third, anRN deployed in a bus or train can support the group mobility efficiently. UEsunder the RN coverage do not need to perform handover as the “mobile” RNon their behalf takes care of the group mobility which requires the individualUE handover procedure when such a mobile RN does not exist. Fourth, an RNcan be used for temporary network deployment (also known as a portable ornomadic RN) in cases such as concerts, exhibitions, and sports events.

The issues, discussions, and current conclusions on the relaying agenda of3GPP LTE-Advanced will be described in the following sections.3 Section 16.6.1is about the functionalities of an RN in view of the protocol layer. Section 16.6.2describes how to separate the backhaul and access links in a single RN.

16.6.1 Functionality of RNs

One topic discussed in 3GPP is with what functionality should an RN beequipped (e.g., [12–14]). The decision on this topic determines the “function-alities” of the relaying operation of the RN in view of the protocol stack, i.e.,at which protocol layer the relaying operation is performed. Depending on thefunctionalities of the RN, control/data signals of some lower layers are managedand forwarded by the RN while signals of the remaining higher layers are directlyexchanged between the UE and eNodeB bypassing the RN. Also, this topic is

3 The content of this chapter is based on [11].


related to how the RN appears to the UEs – as a part of the donor cell or asa separate cell. In the following, RNs are classified in three categories based onthe layer in which the user data are relayed.

Layer 1 relay – repeaterLayer 1 (L1) RNs simply act as repeaters, amplifying the input signal whilethey do not carry out any decode/reencode processing. Figure 16.16 depicts theprotocol layers of this type of RN. As an L1 RN simply amplifies and forwardsthe input signal, the RF layer is the only protocol layer with which it is equipped.The operation of each layer in this figure can be summarized as follows:

RF layer: passband signal processing including filtering and amplification; PHY layer: baseband signal processing including modulation/demodulation

and channel coding/decoding; MAC+ layer: operation of high-layer radio resource management from the

viewpoint of the PHY layer. This includes the medium access control (MAC)layer performing operations such as scheduling and hybrid automatic repeatrequest (HARQ), the radio link control (RLC) layer performing operationssuch as segmentation/reassembly, high-level ARQ, and flow control, and thepacket data convergence protocol (PDCP) layer performing operations suchas IP header compression and sequence number maintenance;

IP layer: management of IP packets.

RF

eNodeB

PHY

MAC+

IP

RF

Relay node

RF

UE

PHY

MAC+

IP

Figure 16.16. Protocol stack of an L1 RN.

One benefit of an L1 RN is that it incurs very little delay (typically less thana microsecond), which is mainly due to filtering carried out within the repeater.Another benefit is the possibility for operation without “duplex” loss, i.e., it maybe possible to operate the backhaul and access links simultaneously on the samefrequency. As the latency incurred by the relaying operation is significantly lessthan the length of the cyclic prefix of a typical OFDM system, the two signalcomponents – one directly from/to the eNodeB and the other forwarded by theRN – are seen as nothing but two different multipath components of the samesignal which can be resolved by the corresponding OFDM processing.


The drawback with an L1 RN is that, due to the absence of decoding/re-encoding, the noise added in the receiver side of the RN is amplified and for-warded together with the desired signals. As a result, the SINR cannot beimproved between the repeater input and the repeater output, i.e., the SINRat the input of an L1 RN is an upper limit on the SINR experienced by theUE. It is also possible to consider an enhancement of the L1 RN (i.e., “advancedrepeater” or “smart repeater”) by adding some further capability to the RN. Onepossibility is a power control capability which enables the L1 RN to limit anyunnecessary interference to the other transmissions and reduce the RN powerconsumption. Another possibility is time/frequency-selective repetition whichimplies that the RN repeats only a part of the input signal which corresponds tosome specific frequency/time resources. This selective repetition enables the RNto forward the relevant part (e.g., the signal of the UEs that require the RN’sassistance) only, thereby limiting the unnecessary interference caused by the RNand allowing for more efficient utilization of the available RN power.

Layer 2 relay – decode and forwardLayer 2 (L2) RNs are also known as decode-and-forward RNs: they decode thephysical layer signal, and may also decode some MAC parameters by decodingcontrol signals and so on. After successfully decoding the received signal, an L2RN reencodes the data and then forwards them to the destination (e.g., UEsassociated with it in the downlink). Figure 16.17 depicts the protocol stack of aL2 RN.

PHY

RF

eNodeB

PHY

MAC+

RF

Relay node

RF

UE

PHY

MAC+

IP IP


As an L2 RN carries out a decode–reencode operation, the noise added inthe receiver side of the RN can be removed during the decoding process and,as a result, the output signal SINR can be improved. In addition, it becomespossible to change the modulation and coding scheme and the amount/locationof resources allocated to each packet during the relaying operation, which impliesthat for an L2 RN it is allowed to separate the link adaption and optimizationin the backhaul and access links.


MAC+

PHY

RF

eNodeB

PHY

MAC+

RF

Relay node

RF

UE

PHY

MAC+

IP IP


One drawback of an L2 RN is that a substantial delay (typically a couple ofmilliseconds) occurs during the relaying operation (especially during the decod-ing process). This implies that, at a given time, the signal directly from/to theeNodeB and the signal forwarded by RN can no longer be seen as multipathcomponents of the same signal as they are in an L1 RN. As a result, the inputsignal and the output signal of an L2 RN interfere with each other, and this maycause a duplex loss which has to be known in order to separate the input andoutput signals.

An L2 RN is not involved in controlling the operation of the layers higherthan the PHY layer. In other words, it does not issue scheduling informationor a control signal about HARQ and channel feedback. The control signalingis handled by the donor eNodeB. Thus, an L2 RN cannot generate a completecell and is only a part of the donor cell from the UE’s perspective. As a result,an L2 RN has to intervene in the MAC or higher-layer operation (e.g., deliveryof the scheduling message, HARQ ACK/NACK transmission/reception, retrans-mission of error packets, channel quality measurement/feedback, etc.) performedbetween the donor eNodeB and the relay–UE. This intervention may require asophisticated operation protocol among the eNodeB, RN, and UE.

Layer 3 relay – self-backhaulingLayer 3 (L3) RNs perform the same operation as eNodeBs, so they are equivalentto new eNodeBs with their own cell identity from a PHY and MAC viewpoint.4

Here, “self-backhauling” means that an L3 RN is provided with the backhaullink (connecting it to the other eNodeBs) by itself, not relying on the interfacesother than the operating radio spectrum. Figure 16.18 depicts the protocol stackof an L3 RN.

4 It is possible to consider RNs in which the relaying operation is performed within the MAC+layer in Figure 16.18, i.e., at MAC, RLC, or PDCP layer. But they are not very feasible andefficient because one part of radio resource management (RRM) function is located in thedonor eNode while the rest is in the RN.


One advantage of an L3 RN is that the mechanisms designed for the linkbetween the eNodeB and the UE (e.g., scheduling, HARQ, handover) can beapplied to the access link (the link between the RN and the UE) with no change,which is helpful in reducing the UE implementation complexity. However, thissimplicity comes with the cost that an RN should be equipped with all theeNodeB’s functionalities which may increase the RN’s implementation cost.

Type 1 vs. type 2 relayAfter discussions about the different types of RNs described in the previoussubsections, 3GPP has specified two different types of RNs – type 1 relay andtype 2 relay – for more detailed discussion and description.

A type 1 relay is an L3 RN which is characterized by the following:

It controls cell(s), each of which appears to a UE as a separate cell distinctfrom the donor cell.

The cell has its own cell identity which can be recognized by legacy LTE LEs;the RN transmits its own control signals such as synchronization channelsand reference signals. This means that the RN appears as a legacy eNodeBto legacy LTE UEs (i.e., it is backward compatible).

In the context of single-cell operation, the UE receives scheduling informationand HARQ feedback directly from the RN and sends its control channels tothe RN.

To LTE-Advanced UEs, a type 1 RN should appear different from a legacyeNodeB to allow for further performance enhancement.

It has been agreed that type 1 relay will be supported as a part of LTE-Advancedand the corresponding specification work is ongoing.

A type 2 RN is an L2 RN which is characterized by the following:

It does not have a separate cell identity and thus does not create any newcells.

It is transparent to legacy LTE UEs; a legacy LTE UE is not aware of thepresence of a type 2 RN.

It can transmit the downlink physical data channel but it does not transmitthe downlink physical control channel and cell-specific reference signal whichis used for the demodulation of the downlink control channel and the legacyUE’s channel measurement.

One important feature of a type 2 RN is that the UEs facilitated by the RNrely on the downlink physical control channel and cell-specific reference signaltransmitted from the donor eNodeB. No agreement on the support of the type2 relay for 3GPP has been reached as a conclusion has not yet been made aboutits features and advantages. This topic is still under the study item of 3GPP.

It is widely understood that the type 1 relay may be a solution for coverageextension while the type 2 relay may be more suitable for throughput enhance-ment. A type 2 relay cannot be an effective solution for coverage extension as


Donor eNodeB

Type 1 RNUE1 UE2 Cell created by the

donor eNode B

Cell created by theRN

(a)

(b)

Donor eNodeB

Type 2 RNUE1 UE2

A single cell is created by thedonor eNodeB and RN

Figure 16.19. Illustration of cell creation in case of: (a) type 1 relay and (b) type2 relay.

it does not transmit the downlink control channel to the UEs which the donoreNodeB’s control signal cannot reach (e.g., UE1 in Figure 16.19). On the otherhand, a type 1 RN can provide strong control channels to these UEs, therebyimproving the control channel coverage of the radio access network, i.e., the rangeof the “connectivity.”

Figure 16.19 compares the cell coverages of type 1 and type 2 RNs. A type 2relay has the potential to improve the UE throughput (especially when locatedbetween the donor eNodeB and the RN such as UE2 in Figure 16.19) by exploit-ing the tight coordination between the donor eNodeB and the RN, which isnot possible in a type 1 relay. In a type 1 relay, the transmission between thedonor eNodeB and the RN is a kind of inter-eNodeB communication which is notusable in view of a UE. Thus, even though this backhaul transmission containsinformation to be forwarded to a UE, it is impossible for that UE to utilize thistransmission and the backhaul link transmission appears as intercell interferenceto that UE as shown in phase 1 of Figure 16.20(a).

However, as a type 2 RN is invisible to UEs, the transmission from an eNodeBto an RN for the purpose of data forwarding to a UE can be seen as the directtransmission to that UE which is overheard by the RN as depicted in phase 1


Donor eNodeB

Type 1 RN

UE

Phase 1

Notreceived

Donor eNodeB

Type 1 RN

UE

Phase 2

Transmission fromeNodeB to RN

Transmission fromRN to UE

(a)

Donor eNodeB

Type 2 RN

UE

Phase 1

Donor eNodeB

Type 2 RN

UE

Phase 2

Transmission fromeNodeB to UE

Transmission fromRN to UE if needed

(b)

Overhearing

Figure 16.20. Examples of downlink data relaying: (a) a type 1 relay and(b) a type 2 relay.

of Figure 16.20(b). Consequently, it becomes possible to reduce the probabilityof the decoding error remaining after the RN-to-UE transmission in phase 2 byproperly combining the signals received in phases 1 and 2. The operation inFigure 16.20(b) can be interpreted as a kind of intervention of a type 2 RN inorder to assist the HARQ procedure between the donor eNodeB and the UE.In other words, the RN overhears the transmission from the donor eNodeB (theinitial transmission) to UE in phase 1 and participates in the retransmission inphase 2 for more robust error recovery as shown in Figure 16.20(b).


16.6.2 Separation of the backhaul and access links

Another important topic in the 3GPP relaying discussions is how to separatethe backhaul and access links. This link separation is necessary in order to avoidthe self-interference shown in Figure 16.21. In this figure the RN is receiving abackhaul link signal from the donor eNodeB while transmitting an access linksignal to the UEs at the same time. Therefore, from the perspective of the RN’sreceiver, the RN’s transmission signal is an interference which may corrupt thesignal reception especially for L2 and L3 RNs where the transmitting access linksignal is different from the receiving backhaul link signal. This self-interferencecan be much stronger than the desired signal when the distance between thetransmission antenna and the reception antenna is small, for example, when thetransmission/reception antennas are co-located.

RN

eNodeB UE

Self-interference

Figure 16.21. Example of self-interference in a relay node.

There are two approaches that have been discussed to avoid this self-interference: One is to separate the backhaul and access links in the time domainwhile operating the two links within a single frequency band. This kind of relayingis called inband relaying. The other is to separate the two links in the frequencydomain, which implies that there are at least two different frequency bands, oneis used for the backhaul link and another is used for the access link. This kindof relaying is called outband relaying.

To be precise, the inband relaying explained above corresponds to inband half-duplex relaying which implies that either the backhaul or the access link is acti-vated at a given time. 3GPP also discussed the possibility of inband full-duplexrelaying in which both backhaul and access links are activated simultaneouslywithin a single frequency band. To support this inband full-duplex relaying, someother type of link separation is needed, such as separate transmission/receptionantennas. This scenario is considered as one possibility in the indoor relay casewhere the backhaul link antenna is located out of a building and the accesslink antenna is located inside a building (or even underground). It was decidedthat further study is needed to determine the feasibility and detailed uses ofinband full-duplex relaying, so inband half-duplex relaying and outband relayingoperations are in the current specification work.


Inband relay

This subsection discusses the time-domain link separation of inband half-duplexrelaying. Inband relaying hereinafter means inband half-duplex relaying.

In order to allow inband backhauling, some resources in the time-frequencyspace are set aside for the backhaul link and cannot be used for the access linkon the respective node. The general principles for resource partitioning at theRN are:

eNodeB-to-RN and RN-to-UE links are time division multiplexed in a singlefrequency band (only one is active at any time).

RN-to-eNodeB and UE-to-RN links are time division multiplexed in a singlefrequency band (only one is active at any time).

The basic rule agreed for the backhaul link transmission is quite straight-forward: eNodeB-to-RN transmissions are done in the downlink resource whileRN-to-eNodeB transmissions are done in the uplink resource.5 In the case of atype 1 relay, this operation seen as a noncontinuous existence of the serving cellfrom the viewpoint of a UE associated with the RN because the RN sometimesdoes not transmit any signal to the UE. This implies that the RN creates “gaps”in the RN-to-UE transmission when it receives the eNodeB-to-RN transmission.

Since a legacy LTE UE expects a cell-specific reference signal in every subframefor the purpose of channel measurement, the relay-UEs should be informed of thelocation of these “gaps” in order to prevent the UEs from unnecessarily trying tomeasure the cell-specific reference signal during the gaps when there is only noise.In a type 1 RN, a “partial blanking” method is used for a downlink subframewhich is allocated to the eNode-to-RN transmission as shown in Figure 16.22.Here, “partial blanking” means that the RN transmits a few OFDM symbolsat the beginning of a subframe to transmit the downlink control channel tothe relay-UEs, and it does not transmit any signal in the remaining symbols.6

A relay-UE does not try to measure the cell-specific reference signal during the

5 Here, downlink (uplink) resource means downlink (uplink) frequency band in a frequencydomain duplex system (FDD) where downlink and uplink transmissions are separated infrequency. Downlink (uplink) resource means and downlink (uplink) subframe in a timedomain duplex (TDD) system, where downlink and uplink transmissions are separated intime.

6 This “partially blank” subframe appears as multicast broadcast multimedia service (MBMS)single-frequency network (MBSFN) subframe to the relay-UEs. The original purpose ofthe MBSFN subframe was to support the simultaneous transmissions (usually multicastor broadcast traffic) from the serving eNodeB and all the neighboring eNodeBs within apredefined area. In an MBSFN subframe, a few downlink control symbols are transmitted ina cell-specific manner at the beginning of the subframe but, after those control symbols, nocell-specific transmission (including cell-specific reference signals) occurs to send the multi-cast/broadcast traffic. Consequently, a relay-UE does not perform the measurement of thecell-specific reference signal of the associated RN in this partially blank subframe and theRN is allowed to halt the downlink signal transmission to receive the backhaul signal withoutcausing performance degradation in the relay-UE’s measurement.


transmission gap of a partially blank subframe, and its measurement performanceis not affected by the RN’s half-duplex operation.

Control Data

One subframe

UE

Control

eNodeB

Partially blank subframe

Transmission gap(no RN-to-UE signal)

UE UE

Figure 16.22. Example of RN-to-UE communication using a normal subframe(left) and eNodeB-to-RN communication using a partially blank subframe(right).

Figure 16.23 illustrates the basic rule of the backhaul and access link separationin a half-duplex relaying system. Downlink (uplink) resource activation in thebackhaul and access links is separated in time from the perspective of the RN.

eNodeB

Relay node

UE

DL resource

UL resource

UL resource

DL resource

UE

UL resource

DL resource

Separated intime

Separated intime

Figure 16.23. Illustration of the backhaul transmission multiplexing methodsbased on the basic multiplexing rule (DL – downlink; UL – uplink).

Outband relayIf backhaul and access links are isolated enough in frequency, then there is nointerference when activating both links simultaneously. Figure 16.24 shows anexample of an outband relaying operation where the RN uses frequency band1 for the backhaul link and frequency band 2 for the access link. In general, aguard band is required to avoid self-interference across the frequency band and


it is also possible to assist the link separation by an additional means such asantenna separation which can be used for inband full-duplex relay. As the twolinks are completely separated, there is no correlation between the operationsin the two frequency bands. Thus, it is possible for an RN to operate as anormal UE in frequency band 1 while operating as a normal eNodeB in frequencyband 2.

FrequencyBand 1 Band 2

Guardband

eNodeB

UE

Figure 16.24. An example of outband relaying operation.

Hybrid of inband and outband relayIn most cases, the backhaul link capacity becomes the bottleneck in the perfor-mance of a relaying system. As shown in Figure 16.15, all the transmissions forthe backhaul link and direct link share the same resource of the donor cell. Thus,with only the inband or outband relaying operation discussed in the above sub-sections, a relaying system usually suffers from backhaul resource shortage, sothat the amount of the backhaul link resource is not enough to achieve satisfac-tory performance improvement. To be specific, in inband relaying, half-duplexoperation requires frequent switching between the transmission and receptionmodes of an RN. As this mode switching typically requires around 20 microsec-onds which is larger than the length of the cyclic prefix, an OFDM symbolcannot be used if an RN switches its operation mode during that symbol time.This OFDM symbol loss degrades the throughput of the backhaul link which isthe bottleneck in the system. In outband relaying, a guard band is required toseparate the two frequency bands (typically more than 10 MHz separation) asshown in Figure 16.24, thereby wasting some frequency resource. In addition, theoutband relaying operation cannot provide flexible resource allocation betweenthe backhaul and access links as the bandwidth of each frequency spectrum isusually predefined to a fixed value.

One solution that can resolve the above-mentioned backhaul resource short-age is to use additional frequency resource (i.e., frequency spectrum or frequencyband) in the backhaul link. Let us assume that an inband RN suffers from back-haul resource shortage and it is decided to use an additional frequency band to


resolve the shortage problem.7 In this case, the RN does not necessarily open theaccess link in the newly added spectrum as the access link does not require addi-tional resources in most case. Therefore, as long as the two frequency bands arewell separated, it is desirable to use one frequency band solely for the backhaullink while performing the half-duplex operation in the other frequency band.In other words, if an RN is provided with two well-separated frequency bands,a hybrid RN which uses both bands for the backhaul link but uses only oneband for the access link can be considered as an attractive solution. Figure 16.25illustrates the operation of this hybrid RN in comparison with Figure 16.24. Ahybrid of inband and outband relaying provides more flexible resource allocationbetween the backhaul and access links when compared with the pure outbandrelaying, while it can reduce the OFDM symbol waste caused by the RN’s modeswitching when compared with the pure inband relaying. Outband relaying canbe regarded as a special case of the hybrid relaying in which all the time resourcesare used only for the access link in a frequency band.

FrequencyBand 1 Band 2

Guardband

eNodeB

UE

eNodeB

Separated in time

Figure 16.25. An example of hybrid of inband and outband relayingoperation.

As a special example of the hybrid of inband and outband relaying, hybridrelaying operation across downlink and uplink frequency bands can be consid-ered in an FDD relaying system. As downlink traffic is much heavier than uplinktraffic in most data communication scenarios, the uplink frequency band cansometimes be borrowed for the purpose of eNodeB-to-RN communication ontop of the basic rule discussed above [15]. This operation falls within the cate-gory of hybrid relaying as, from the perspective of the transmissions in down-link frequency band (i.e., eNodeB-to-RN and RN-to-UE link), there is no accesslink (i.e., RN-to-UE link) in the uplink frequency band and thus eNodeB-to-RNtransmission in the uplink frequency band can be regarded as a kind of out-band relaying operation. The donor eNodeB sometimes uses the uplink resource

7 Communication over multiple frequency carriers can be achieved by “carrier aggregation”which is in development in 3GPP as a work item of LTE-Advanced.


Table 16.1. Types of relay nodes defined in 3GPP LTE-Advanced

L3 relay L2 relay

Inband Half duplex Type 1a Type 2Full duplex Type 1b Not defined

Outband Type 1aa Not defined

a It has been agreed that this will be supported as a part of LTE-Advanced and

the specification work is currently ongoing.

eNodeB

Relay node

UE

DL resource

UL resource

UL resource

DL resource

UE

UL resource

DL resource

Separated intime

Separated intime

UL resource

Separated intime

Figure 16.26. Illustration of the backhaul transmission multiplexing methodsbased on the uplink resource borrowing for eNodeB-to-RN communication.(DL – downlink; UL – uplink.)

for the backhaul link transmission to the RN while stopping all the uplinktransmission of the direct link. Figure 16.26 illustrates this multiplexing methodbased on this uplink resource borrowing.

Table 16.1 summarizes the “types” of RN defined so far in 3GPP. As has beendiscussed before, there are two types of RN according to the RN’s functional-ity: type 1 and type 2 RNs. In view of the separation between the backhaul andaccess links, both type 1 and type 2 RNs fall within the category of inband relay-ing (specifically, inband half-duplex relaying). Two more RN types are definedin the type 1 family: type 1a and type 1b RNs. A type 1a RN has the samecharacteristics as a type 1 RN except that it operates as an outband RN. Theonly difference for a type 1b RN is that it is an inband full-duplex RN.


References

[1] J. Laneman, D. Tse, and G. Wornell, “Cooperative diversity in wireless net-works: Efficient protocols and outage behavior,” IEEE Trans. Info. Theory,vol. 50, no. 12, pp. 3062–3080, Dec. 2004.

[2] A. Nosratinia and A. Hedayat, “Cooperative communication in wireless net-works,” IEEE Commun. Mag., vol. 42, no. 10, pp. 74–80, Oct. 2004.

[3] R. Nabar, H. Bolcskei, and F. Kneubuhler, “Fading relay channels: Per-formance limits and space-time signal design,” IEEE Journal Sel. AreasCommun., vol. 22, no. 6, pp. 1099–1109, Aug. 2004

[4] T. Cover and A. El Gamal, “Capacity theorems for the relay channel,” IEEETrans. Info. Theory, vol. IT-25, no. 5, pp. 572–584, Sept. 1979.

[5] M. Yuksel and E. Erkip, “Broadcast strategies for the fading relay channel,”in Proc. of IEEE MILCOM 2004, vol. 2, pp. 1060–1065, Oct. 2004. IEEE,2004.

[6] P. Popovski and E. de Carvalho, “Improving the rates in wireless relaysystems through superposition coding,” IEEE Trans. Wireless Commun.,vol. 7, pp. 4831–4836, Dec. 2008.

[7] K. Azarian, H. Gamal, and P. Schniter, “On the achievable diversity-multiplexing tradeoff in half-duplex cooperative channels,” IEEE Trans.Info. Theory, vol. 51, pp. 4152–4172, Dec. 2005.

[8] S. T. Chung, A. Lozano, H. C. Huang et. al., “Approaching the MIMOcapacity with a low-rate feedback channel in V-BLAST,” EURASIP J. Appl.Signal. Proc., pp. 762–771, May 2004.

[9] P. W. Wolniansky, G. J. Foscini, G. D. Golden, and R. A. Valenzuelar,“V-BLAST: an architecture for realizing very high data rates over the rich-scattering wireless channel,” in Proc. of URSI International Symposium onSignals, Systems, and Electronics (ISSSE ’98), pp. 295–300, Pisa, Italy,Sept. 1998. IEEE, 2008.

[10] G. H. Golub and C. F. Van Loan, Matrix Computations. Johns HopkinsUniversity Press, 1983.

[11] 3GPP TR 36.814 V9.0.0, 3rd Generation Partnership Project; TechnicalSpecification Group Radio Access Network; Further Advancements for E-UTRA; Physical Layer Aspects (Release 9).

[12] Technical document R1-083533, Decode and Forward Relays for E-UTRAenhancements, Texas Instruments, 3GPP TSG RAN WG1 #54bis.

[13] Technical document R1-083752, Wireless Relaying for the LTE Evolution,Ericsson, 3GPP TSG RAN WG1 #54bis.

[14] Technical document R1-083568, Discussion on L3 Relay for LTE-A, Sam-sung, 3GPP TSG RAN WG1 meeting #54bis.

[15] Technical document R1-084206, UL/DL Band Swapping for Efficient Sup-port of Relays in FDD Mode, LG Electronics, 3GPP TSG RAN WG1 Meet-ing #55.

17 Coordinated multipointtransmission in LTE-Advanced

Sung-Rae Cho, Wan Choi, Young-Jo Ko, and Jae-Young Ahn

17.1 Introduction

Coordinated multipoint (CoMP) transmission is considered as a promisingmultiple-input multiple-output (MIMO) technique that can be a primary ele-ment for better intercell interference (ICI) control in the next generation cellularnetworks. The classical MIMO technique uses a colocated antenna array forbeamforming to the direction of an intended user while trying to reduce inter-stream and interuser interference. However, such single-cell MIMO transmissionscause intensified narrow beams and can interfere with other cells’ users. In mul-ticell simulations, interference from adjacent cells is even more detrimental. It isfound that, depending on the scenario, no less than 30% of the user equipment(UEs) in a cell will have a wideband signal-to-interference-and-noise ratio (SINR)below 0 dB. Various techniques to combat this problem have been proposed bystandardization organizations such as 3GPP LTE and IEEE 802.16e/m. Typ-ical examples [1] include sectorization using directional antenna, ICI random-ization with interference cancelation at the receiver, and ICI avoidance tech-niques, such as ICI-aware power control, fractional frequency reuse (FFR), andintercell scheduling. These techniques can be deployed in addition to MIMObut often lead to either loss of average sector throughput or increased receivercomplexity. CoMP transmission has been proposed and supported by manycompanies, including Ericsson, Motorola, Alcatel-Lucent, Huawei, Qualcomm,Samsung, LGE, ETRI, DoCoMO, Nortel, and is believed to be a promising ICImitigation solution that can improve cell-edge throughput as well as averagesector throughput with little complexity increase at the receiver side.

The basic idea behind CoMP is to extend the conventional single-cell-to-multiple-UEs transmission to a multiple-cell-to-multiple-UEs transmission bybase station cooperation [2]. Similar concepts have also been discussed in IEEE802.16m and the advantages especially for cell-edge users have been evaluatedby many companies. To enhance competitiveness with regard to other standards,the CoMP agenda has been discussed since July 2008. Preliminary studies on


496 Coordinated multipoint transmission in LTE-advanced

the requirements of LTE-Advanced [3] have been undertaken as 3GPP RAN 1study items in LTE Release 9.

The proposals and current conclusions regarding the CoMP program for LTE-Advanced will be outlined as follows: Section 17.2 gives an overview of thearchitecture of the CoMP transmission scheme. Section 17.3 describes the neces-sary CoMP design parameters. Section 17.4 outlines the performance evaluationmethodologies related to link level and system level simulations.

17.2 CoMP architecture

In a universal frequency reuse system, it is well known that interference fromneighboring cells substantially degrades performance compared to what can beachieved in a single-cell scenario and it is also recognized that reducing the inter-ference from only one neighboring cell can significantly improve the performance,e.g., 8.12% (5 percentile) cell-edge gain was obtained in [4] and about 20% gainwas obtained in [5]. Two categories of CoMP are used to reduce the ICI: coor-dinated scheduling and beamforming (CS/CB) and joint processing (JP). JPis further divided into (noncoherent and coherent) joint transmission (JT) anddynamic cell selection (DCS).

For JT, data are shared among multiple eNodeBs1 that belong to a CoMPcooperating set and the physical downlink shared channel2 (PDSCH) is con-structed from multiple eNodeBs of the entire CoMP cooperating set, but forDCS there is a single-transmission eNodeB at every subframe time and thistransmission eNodeB can dynamically change within the CoMP cooperating set.For CS/CB, data are transmitted from the serving cell but user scheduling andbeamforming decisions are made with coordination among the eNodeBs in theCoMP cooperating set. Some terminologies to facilitate discussions for CoMPproposals were agreed in [6], despite being revisited in work items for specifica-tion impact:

A CoMP cooperating set is a set of eNodeBs participating in transmittingover the PDSCH to the UE.

A CoMP transmission set is a set of eNodeBs actively transmitting data tothe UE over the PDSCH. This is a subset of the CoMP cooperating set.

Different CoMP categories require different levels of coordination in terms ofchannel state information (CSI) and data sharing, e.g., sharing both CSI anddata, either or neither of them where each entails different CoMP operationcosts, such as the backhaul limit, thus providing different performance gains[4, 7].

1 eNodeB denotes the base station of 3GPP LTE systems.2 The PDSCH is a shared data channel that can be multiplexed over frequency and time by a

number of UEs.

17.2 CoMP architecture 497

17.2.1 Joint processing and transmission (JPT)

Joint processing and transmission (JPT) basically changes interference signalsinto desired signals with a cooperation gain by combining the signals as construc-tively as possible over the same radio resources. Many companies have discussedmany different ways to find a realistic balance between performance gains andeffort; and have built scalable design parameters to decide the level of cooper-ation. Three main topics have been addressed in this context [8]: (1) referencesignal design for multicell channel estimation; (2) an uplink control overheadincrease for channel knowledge at the transmitter; and (3) the choice of precod-ing techniques to combine the signals from multiple cells effectively. Details aregiven in Section 17.3.

17.2.2 Coordinated scheduling and beamforming (CS/CB)

CS/CB is a kind of beam coordination among coordinated cells that dynami-cally reduces the dominant interference from interfering cells. Beam coordina-tion tunes the interfering beam toward a null space of the desired signal, therebynullifying the interference to the UE, and otherwise avoids pointing the beamtoward the direction that has high correlation, which can be done by reportinga recommended precoding matrix index (PMI) and a restricted PMI, respec-tively. A subset of most efficient PMIs is chosen and exchanged to reduce back-haul overheads. As discussed in [9], multibeam coordination can be improvedby enhanced UE feedback, additional reports that indicate how the interferencelevel can be reduced (in the form of Delta-CQI [10]). The UEs can report (say)best-companion or worst-companion PMIs for a number of interfering cells andthen serving cells can schedule the UEs in such a way that they experiencelower interference by improved user pairing. For better beam coordination, thecoordination can be updated according to channel variation and also schedulinginformation can be exchanged. The reported PMIs may be statistically processedin terms of time, frequency, and user domain so that the most efficient beam canbe found from the beam selection pool. When the serving cell wants not to final-ize UE scheduling prior to beam information exchange but to maintain a pluralnumber of UE candidates, the multiple PMIs collected can be delivered to theinterfering cell and then the interfering beam can be tuned toward the null spaceof all the beams [11].

17.2.3 Cell clustering

In cellular networks, all users are potentially coupled by interference and theperformance of one link depends on the other links. In general, a joint optimiza-tion approach is desirable but full cooperation between the users over a large


network is in practice infeasible. Dynamic cell clustering to identify dominantinterfering cells according to UE position is a reasonable choice and hence a lim-ited number of cooperation cells are determined in a geographical sense to form acooperation area [12]. To identify candidate cooperation cells, post-CoMP SINR(SINR after CoMP), as a measure of ICI mitigation, is calculated by turning (oneor two) interfering signals into the desired signal. As was observed in [13], thegain of the coordination saturates when the number of coordinating eNodeBsgoes beyond some threshold value; therefore further study is required to findan exact threshold to be incorporated with UE geometry and interference levelinformation.

The complexity dramatically increases with the number of coordinatingeNodeBs. Furthermore, backhaul latency is also a limiting factor for cell cluster-ing. Cluster can be formed in a UE-centric, network-centric, or a hybrid fashion.In UE-centric clustering, each UE chooses a small number of cells that give thegreatest cooperation gain. In general, UE-centric clustering is, however, verycomplex from a scheduling point of view. Coordinated clusters corresponding todifferent UEs may overlap and coordination among all overlapping clusters canspan the whole network. Arguing that pure UE-centric dynamic clustering wasimpractical for real implementation, a UE-centric clustering was proposed in [14]in which the cluster serving a particular UE is a subset of a larger fixed clusterrather than the whole network and the subset can change in different frequencysubbands and different times. A semi-fixed cell clustering (SFCC) was proposedin [15] in which the clustering of the cells is fixed during a certain time period butvaries over frequency and/or time in order to dynamically adapt to the changingenvironment.

When the network predefines a set of cooperation cells, the cooperation areacan be determined by network-centric clustering or in a hybrid fashion [16].In network-centric clustering the clustering is done in a static way and hencethe performance of boundary UEs can be compromised, whereas in a hybridapproach multiple clusters that possibly overlap are formed but this alleviatesthe boundary problems among clusters by having flexibility in resource allocationbetween the clusters [17].

Comparing rate geometries with and without CoMP transmission, the choiceof a better UE is considered important to enhance the CoMP gain. In [18] acriterion for deciding which UEs should be served by comparing pre-CoMPand post-CoMP rates under given cluster was proposed. The geometry view-point shows that most gain achieved by CoMP transmission is in the 5%throughput regime (cell edge). Confining CoMP to cell-edge UEs is justifiedby less arrival timing mismatch because obviously cell-centric UEs are far fromtransmission points of other cells. It has also been realized that if the trans-mission delay from cooperating cells is significant, the CoMP transmissiongain is drastically diminished and clustering is forbidden at points far froma UE [19, 20].

17.3 CoMP design parameters 499

17.2.4 Inter-eNodeB and intra-eNodeB coordination

Coordination among eNodeBs carried out through the X2 interface,3 so thatusers can be served by different eNodeBs, is called inter-eNodeB coordination,whereas coordination within the eNodeB, so that users can be served by a num-ber of co-located or distributed antenna system (DAS) connected to the sameeNodeB by a physical connection, e.g., fiber, is called intra-eNodeB coordina-tion. While the latency of the X2 interface is specified to be about 20 ms [21],some companies are inclined to skepticism about whether inter-eNodeB coor-dination is feasible because of the functionalities limited by the X2 interface,and hence they consider the intra-eNodeB coordination scheme more realizablein practice [22]. Scheduling information, dynamic channel knowledge, and userdata may not be reflected promptly by cooperating cells so that the performancegain of inter-eNodeB coordination scheme is restricted [17]. Nevertheless, somecompanies [23–25] have expressed strong interest in the scheme. JPT schemesare considered feasible in practice for intra-eNodeB scenarios due to the factthat the cooperating sectors are geographically colocated and communicationbetween the sectors is assumed to be fast enough, whereas CS/CB schemes haveno severe backhaul constraints since data packets are not shared among cells andthus seem more practical for inter-eNodeB cooperation scenarios.

17.3 CoMP design parameters

17.3.1 Reference signal (RS)

A reference signal (RS) is defined at each individual antenna port4 as the pilotsymbols needed at the UE for CSI estimation and data demodulation. The cell-specific RS (CRS) was designed for both purposes. LTE Release 8 provides CRSfor at most four antenna ports with an overhead of 14.3% that can support up to1, 2, and 4 streams for single-user MIMO and up to four users with each beingwith a single stream for multi-user MIMO. Since CRSs from different cells havedifferent shifts in either frequency or time,5 most companies realize that addingmore CRS patterns across the full band in LTE-Advanced introduces too muchoverhead [27] and that it is better to utilize the current CRS structure thanto introduce new CRS patterns for backward compatibility; like CRS, CSI-RSis additionally defined to provide a low-density RS with a different density inthe frequency and a different periodicity in time, and is aimed at obtaining CSIespecially for CoMP UEs [28].

3 It is a direct physical connection for interfacing between neighboring eNodeBs.4 Each physical antenna is called an antenna port and has a distinguishable RS pattern.

Orthogonal reference symbols among coordinating eNodeBs may need to be designed forestimating channels accurately for neighboring eNodeBs.

5 An overhead analysis of different RS patterns is given in [26].


An existing CRS may interfere with data transmission by other active cellssuch that the actual channel is affected by the data symbol [29] and hence thequality of channel measurement is likely to be poorer, resulting in a modulationand coding scheme (MCS) level mismatch and precoding performance degrada-tion. A slightly different CRS design should be considered in which the weakercells do not suffer from interference from the stronger cells. Interference causedby the stronger cells can be removed by making such cells puncture resource ele-ments (REs) that overlap with the CRS of other cells. Such puncturing is usefulonly in the presence of UEs that benefit from the cooperation of weak neighbors.It could be enabled based on the assessment of cooperation gains and overheadassociated with RE puncturing. This clearly results in an additional waste ofREs and the total overhead increases, but the expected performance gain maycompensate for the additional overhead.

Leaving aside the CRS–data collision issue, the expected CoMP gain can alsobe degraded due to channel quality indicator (CQI) mismatch with the actualpost-processing SINR from existing PMI and CQI feedback. Interference condi-tions may change significantly across resource blocks (RBs) and subframes andalso depend on the beams and transmit power densities used by different cellson each RB. Therefore, periodic CQI feedback that estimates the channel andinterference over a larger time–frequency resource6 (potentially the entire band-width) would not accurately capture the exact CQI. This, in turn, would impactthe ability of the eNodeB to choose the MCS accurately, thereby resulting in asignificant throughput loss. In [31] a challenge to investigate whether a new typeof CQI would be beneficial was posed, and a resource (channel) quality indicator(RQI) was proposed that would accurately reflect the channel quality, therebyenabling the eNodeB to choose the MCS correctly. Furthermore, in [13] it wasproposed that when CoMP is used the UE should report a new type of CQIcorresponding to different CoMP transmission schemes and a number of CQIsin order to support a dynamic switch between the transmission schemes. SinceCoMP transmission can be transparent to CoMP UEs, a transmission pointsconfiguration for CoMP (TPCC) is proposed in [32] so that UE can provide aset of CQI values according to different CoMP configurations and the networkcan then decide the link adaptation appropriately.

It has been agreed [33] that in CoMP a dedicated RS will be used for demod-ulation and a UE-specific demodulation RS (DM-RS) has been considered forCoMP transmission because weighting of the reference signal from multiple cellscan help improve the quality of channel estimation. The operation at the networkside is transparent to UEs and whether the signal is emitted from a single cellor from multiple cells is irrelevant. Such overlapping DM-RS is transmitted onlyin scheduled RBs [28] and can save downlink signaling.

6 The granularity of CQI report defined in LTE Release 8 [30] is divided into three levels, wide-band, selected subband, and higher layer configured subband, according to the transmissionmodes.


An extension of the current DM-RS is needed to support more streams forCoMP UEs. There are two basic DM-RS structures to add more DM-RS pat-terns, i.e., FDM-based and CDM-based. In FDM-based multiplexing, additionalDM-RS symbols are transmitted on different REs, while in CDM-based multi-plexing they are transmitted on the same REs but are distinguished by differ-ent orthogonal codes. Several FDM and CDM DM-RS patterns with differentinterpolation spacings in time and frequency are evaluated in [34]. In general,FDM-based DM-RS performs better than CDM-based DM–RS but may resultin an unacceptable overhead. For instance, if two exclusive FDM-based DM-RSports are supported, the total overhead including the current four CRS ports willbe 28.6% [26]. Indeed, CDM-based DM-RS multiplexing to differentiate multi-ple streams per UE or multiple UEs could exploit the commonality betweenRS designs for single-user and multiuser transmissions, but it entails eNodeBcoordination to switch between the modes [35]. Although many companies putemphasis on MU-CoMP operation outperforming SU-CoMP operation in the sys-tem level perspective (despite the restrictive user pairing problem [36]), employ-ing additional DM-RS patterns needs careful investigation in terms of increasedoverhead of RS and expected performance gain.

17.3.2 Precoding

To change a dominant interference signal into desired signal requires data andCSI sharing between the cooperating cells and can thus cause high backhaulcapacity and complexity. To reduce the complexity, several CoMP transmis-sion modes have been defined and are classified primarily into noncoherent andcoherent transmissions. Noncoherent transmission does not coherently combinethe signals arriving at the UE but does obtain an cooperation gain, approxi-mately 3 dB for the case of two-cell cooperation from the doubled transmissionpower [19]. In coherent transmission, the signals from multiple cells are combinedcoherently by adjusting the phase of locally precoded signals and by global pre-coding of a composite channel among the cooperating cells, with the networkobtaining the CSIs of all the cooperating cells. Various precoding techniques arewell categorized in [19, 37, 38].

Although CoMP is carried out in synchronized networks, the received signalfrom several different cells may arrive at the UE at different times due to the dif-ferent distances between the UE and the cell sites. A mismatch greater than theintersymbol interference (ISI) leads to a diminishing cooperation gain, resultingin a linear phase rotation in the frequency domain. Once the mismatch exceedsa certain threshold associated with a cyclic prefix (CP), the cell is excludedfrom the CoMP cooperation set, otherwise some timing calibration has to beintroduced to compensate for the mismatch. Similar concerns about the arrivaltiming mismatch problem as well as feedback aging and power mismatch wereaddressed in [37] and with more elaborate work in [39] including the effect offrequency selective scheduling, codebook quantization, and spatial correlation.


The impact of the residual timing mismatch even after the compensationdepends on the applied CoMP scheme. Transmitted data separated by the space-frequency block code (SFBC) mechanism between cooperation cells are robustagainst the arrival timing mismatch since the channels from cooperating cellsare distinguishable, whereas coherent precoding schemes such as local precodingwith phase correction, as well as global precoding suffer a performance loss ofabout 1–2 dB, since linear phase distortion over a span of consecutive subcarrierscannot be recovered by a single phase correction factor [19]. Interestingly, how-ever, arrival mismatch may benefit noncoherent precoding schemes such that sin-gle frequency network (SFN) precoding can give extra frequency diversity. Cyclicdelay diversity (CDD) based on precoding, in which the signals from cooperatingcells are cyclically delayed, may also be affected (if the CDD delay is shortened,the performance is degraded and otherwise improved). In the context of suchpotential benefit, some companies [19, 40] argue that noncoherent transmissionmay be a promising multicell precoding method with respect to low realizationcomplexity and backhaul capacity and particularly for the case of TDD systems[38, 41]. Moreover, simple SFN precoding can be enhanced by antenna selectionsuch that only a subset of transmit antennas is used from each of the cooperatingcells [42]. Thanks to better resource utilization of the number of transmit anten-nas and power, it even outperforms codebook-based global precoding, therebyhighlighting the importance of antenna selection for CoMP operation. However,it may entail increased complexity with regard to fast antenna selection.

17.3.3 Feedback

Once the UE obtains channel knowledge of the serving cell as well as the inter-fering cells when CoMP is used, this information needs to be transferred to theserving cell. Agreements in CoMP feedback schemes were made on the principlesof feedback signal design [6, 43, 44], and since then discussion on CoMP feedbackhas been focused on feedback types, including the following categories:

Explicit channel state/statistical information feedback Direct channelfeedback as observed by the receiver, without assuming any transmission orreceiver processing,7 is aimed at providing complete channel knowledge of aset of subcarriers (corresponding to a subband or the entire band from CRS)for optimal beamforming. Explicit channel state/statistical information is fedback based on aperiodic or periodic reporting mechanisms [46]. If this infor-mation is accumulated over a long period of time, it converges to a statisticalcorrelation and it was shown in [47–50] that significant gains can be obtainedfor MU-MIMO and CoMP schemes. Possible examples of spatial covariancefeedback (SCF) using the statistical correlation were discussed in [48, 51].

7 A compression technique [45] may be applied to reduce feedback overhead.


Each entry of the spatial covariance matrix can be fed back by a direct mod-ulation technique, e.g., by mapping the entries to QPSK/QAM modulationsymbols carried in enhanced uplink control channels, i.e., physical uplink con-trol channel (PUCCH) and physical uplink shared channel (PUSCH), or bya generalized quantized codebook by minimizing a combination of entry-wisedistance. However, spatial channel feedback with a limited number of bitswould be a limiting factor [52].

Implicit channel state/statistical information feedback A transmissionformat is fed back by using different types of transmission and/or recep-tion processing, e.g., direct extension of LTE Release 8 MIMO feedback,CQI/PMI/RI. In fact, optimal precoding requires the eNodeB to acquire com-plete channel knowledge on each subcarrier and thus increases feedback over-head. On the other hand, one PMI for full frequency band fed back to theeNodeB results in a simpler implementation but in very small performancegain due to inaccuracy to frequency selective channel [53]. Interestingly, it hasbeen shown that under the assumption of fixed feedback overhead, PMI-basedimplicit feedback is superior to explicit channel feedback since averaging thetransmit covariance matrix over a wideband basis may result in increasedmismatch due to quantization errors in a frequency-selective channel [54].

Uplink sounding reference signal (SRS) CSI is estimated at the eNodeBby exploiting channel reciprocity. Due to channel reciprocity, direction ofarrival (DOA) information can be obtained through uplink SRS. By shar-ing DOA and scheduling information of cell-edge UEs, each cell constructs aset of directions that are forbidden while forming beams, and schedules usersto maximize the cell throughput [55].

A suitable feedback scheme may well depend on the CoMP scheme used. Thereis a tradeoff between performance gain and overhead [53]; noncoherent per-cellbased precoding can further be improved by adding additional beam-phase cor-rection feedback and explicit channel feedback8 as well as MU-MIMO can also beused to further improve the performance of CoMP UEs [51]. A common feedbackframework for single-cell MIMO and different CoMP schemes has been discussedextensively [57, 58] and hierarchical and self-contained feedback structure wasproposed to give scalability and flexibility [50, 59, 60]. It has also been agreed thatdynamic switching between different CoMP schemes can be supported and thatfeedback for single-cell MIMO should be a subset of feedback for CoMP opera-tion. For commonality between different CoMP schemes [44], the same feedbackcan be used for CS/CB and noncoherent JPT operations. UE PMI feedback isused for intercell coordination by interference avoidance and user paring.

8 The performance of the CoMP precoding schemes based on explicit channel feedback issummarized in [56].


17.4 CoMP performance evaluation methodologies

The performance of CoMP schemes has been evaluated by a number of companiesunder reasonable but not identical simulation assumptions, such as scheduler,frequency granularity of resource allocation, and MCS determination. Hence, itis difficult to fairly compare the results directly from the work done by differentcompanies and research groups. TR36.814 provides some guidelines for systemlevel evaluations and related simulation results from some typical LTE-Advancedconfigurations which have been conducted by a number of companies [61]. In thissection, we outline the evaluation methodologies especially for CoMP operationin link level and system level simulations.

17.4.1 Link level simulation

The link level model implemented for the LTE downlink conforms to LTE Release8 [62, 63] and employs CoMP JT. As illustrated in Figure 17.1, frequency selec-tive channel coefficients are first generated in the frequency domain and kept tobe later convolved in the time domain with generated time-domain OFDM sym-bols. Modulation symbols are then generated through the modulation symbolgeneration block [63] and are mapped onto one or several transmission layers.After the layer mapper, the complex-valued modulation symbols are each pre-coded by PMI fed back from the CoMP precoding block and then mapped foreach antenna port to resource elements. Finally a complex-valued time-domainOFDM signal is generated for each antenna port.

For the CoMP precoding block, we can consider the following precoding meth-ods, codebook-based precoding schemes proposed in [64] and eigenbeamformingschemes using explicit channel feedback [56].

Multiple single-cell precoding with identical precoding across cells – SFN trans-mission All cooperating cells employ the same precoding to the UE. The UEselects the best precoding assuming the same precoding across different coop-erating cells. The UE feedback format defined in LTE Release 8 can be reused.

Multiple single-cell precoding allowing different single-cell precoding across cellsDifferent cells can employ different precoding. UE feedback includes the bestcombination of precoding vectors for a combined multicell channel. The PMIfeedback overhead scales with the number of cooperating cells.

Multiple single-cell precoding with additional beam-phase correction The UEfirst finds the best precoder for each of the cooperating cells, assuming single-cell transmission, and then chooses the best beam-phase factors for coherentcombining of beams from different cells. The PMI feedback overhead scaleswith the number of cooperating cells.

Multiple single-cell precoding with a single eigenbeam vector precoding acrosscells The UE selects the best common eigenbeam vector, assuming the sameprecoding across different cooperating cells.

17.4 CoMP performance evaluation methodologies 505

Modulation symbolgeneration

MCS report

Sourcegeneration

CRC encoding

Layer mapping PrecodingResource element

mapping

PMI report

From CRS

Resource elementdemapping

OFDMdemodulation

Channeldecoding

Channelestimation

MCS level

HARQ

CRC checkBLER

calculation

Y

Simulationend?

Simulation result

LLR accumulation forHARQ retransmission

Retains transmitted datawhen CRC checksum fails

For ideal channel estimation

From DM-RS

Time-domainsignal

MultipathchannelCoMP

precoding

OFDMmodulation

RS generation

PMI forprecodedDM-RS

CRS and DM-RSChannel coding

Interleaver

Rate matching

Modulationsymbol mapper

Channelgeneration

Figure 17.1. Link level simulator block diagram of CoMP transmission whereshaded blocks incorporate multicell processing.

Multiple single-cell precoding with additional beam-phase correction using aneigenbeam matrix The precoding at joint transmission eNodeBs is chosenlocally, with each based on the eigendecomposition of its own channel. Forcoherent combining, a phase-correction is additionally computed.

The CoMP precoding block for computing either PMIs or eigenbeamformingvectors can directly use the channel coefficients generated in the channel gener-ation block for ideal channel estimation case.

The receiver performs the reverse processes to those performed by the trans-mitter in order to detect the transmitted symbols and to decode them to recoverthe original bit streams, for which the receiver has to estimate the MIMO chan-nel and the instantaneous effective SINR, feedback CQI to the transmitter andgenerate the soft bit information, called the log likelihood ratio (LLR), that isthe input for the turbo decoder. In the simulation, the LLR that reflects thelink reliability is calculated per subframe after the channel decoding block thatincludes the reverse processes of the modulation symbol generation block. Whileperforming the hybrid automatic repeat request (HARQ) process, to increaseredundancy the LLR can be accumulated up to (say) four retransmissions in thecase of a block error. Generation of ACK/NACK is based on the CRC check sumerror. Whether to generate a new source message is incorporated with the HARQprocess. The HARQ protocol enables block error rate (BLER) to be reduced


UE distribution

Simulation resultY Y

UE

Compute CSIGenerate

ACK/NACKAccumulate SINRby HARQ process

End of drops? End of TTIs?

Large-scalechannel generation

Small-scalechannel generation

eNodeB

CoMP schedulingCoMP precoding

for scheduled UEsRate update afterretransmissions

Report assignedMCS to UEs

Report ACK/NACKfor retransmission

Report CSI forscheduling

2 TTI roundtrip delay

Figure 17.2. System level simulator block diagram of CoMP transmission wheredashed line blocks are invoked every three TTIs and rate update is done afterthree retransmissions in this case. CSI feedback includes computed PMIs andphase corrector, MCS values and SINR values for the non-CoMP and CoMPcases, all in per-RB basis, for CoMP scheduling.

so that when an ACK is obtained, a new transmission is made and otherwisea retransmission is enqueued. Adaptive modulation and coding (AMC) is alsoused to maximize throughput while maintaining the BLER below a predefinedtarget value. There are several different MCS options for adapting to varyingchannel conditions. To find an optimum MCS level, the MMSE post-processingeffective SINR obtained from DM-RS is calculated and the best MCS is selected,satisfying a required BLER of about 0.1.

17.4.2 System level simulation

Figure 17.2 shows system level simulator that performs CoMP JT. Path-lossand shadow fading are position-dependent and time-invariant (per-drop based)according to the given UE distribution. Small-scale fading is modeled as a time-dependent process (per-TTI9 based). The number of drops and TTIs are definedso that the performance of the employed scheme represents statistically converg-ing results. The spatial channel model (SCM) or the SCM extended (SCME) fora larger bandwidth is employed for generating small-scale fading channels. It isa ray-based model using stochastic modeling of scatterers. Six paths formed andeach path is made up with 20 spatially separated sub-paths by summing up sinu-soidal waves. In general, there are 19 cell-sites with three sectors each where eachcell-site receives interference from up to two-tier rings with a wrap-around celllayout that ensures that all cells experience the same interference characteristics,and statistics are gathered from all the 19 cell-sites.

9 Transmission time interval.

17.4 CoMP performance evaluation methodologies 507

Either intersector cooperation within each cell-site (up to two-cell JT) or inter-cell cooperation between different cell-sites can occur. From a practical point ofview, intra-eNodeB CoMP operation has a scheduling algorithm that can beexplicitly modeled in each cell-site coordinating only three sectors. The FFR ofreuse 3 is typically used for cell-edge users [65] to mitigate intercell interferencebetween the CoMP clusters.

Some conditions made for CoMP operation, which comply with typical CoMPoperation steps [66] are:

Decision on CoMP UEs Once UEs are considered as cell-edge UEs based onthe downlink average received signal power, CoMP UE is decided by the ref-erence signal received power (RSRP) difference between the received signalsfrom the CoMP cooperation set. In the simulation, a UE is considered to be acell-edge UE when the SINR averaged over the entire band goes below 0 dB,and a cell-edge UE is considered as a candidate CoMP UE when the largestinterfering signal power is within a threshold from the received signal power ofthe serving cell, in order to facilitate UE-centric cell clustering. The thresholdvalue is set to −3 dB for two-cell cooperation:

η =mini∈C RSRPi

maxj∈C RSRPj, (17.1)

where C is the CoMP cooperation set.

The UE reports a candidate set of interfering cells based on the RSRP mea-surement. The eNodeB first broadcasts a threshold and the UE reports thecells whose RSRP difference relative to that of the serving cell is within thethreshold (Figures 17.3 and 17.4).

Selection of precoding vector for the cell-edge UE Precoding vectors are selectedso that the instantaneous received signal power is maximized as proposed in[64]. We assume error-free feedback signaling in the simulation and that thetotal number of signaling bits required for the PMI feedback is seven, i.e., twobits for each cell and three bits for the eight-different phase correction factor tolet the signals from the two cells coherently combine. In general, the precodingvector is updated every three TTIs.

CoMP UE MCS selection In practice, the eNodeB may request the CoMP UEto make a certain CoMP feedback related to the full or a subset of the dominantinterfering cells in order to choose the MCS accurately. In the simulation,the CoMP UE calculate the received SINR to be improved by the expectedprecoding vectors, i.e., combined CQIs [13], and correspondingly fed back everythree TTIs per-RB MCS selection for the entire band to the serving cell, wherethe MCS table is obtained from the link level simulation in advance. Givena MCS table, exponential effective SINR mapping (EESM) [67] is used toselect an MCS option. It translates the SINR obtained by a linear minimum


Figure 17.3. Geometry of candidate CoMP UEs in intra-eNodeB cooperation(two-cell): the darker spot represents greater likelihood of being a candidateCoMP (target center cell).

Figure 17.4. Geometry of candidate CoMP UEs in inter-eNodeB cooperation(two-cell): the darker spot represents greater likelihood of being a candidateCoMP (target center cell).

mean square error (MMSE) receiver [68] to effective SINR values in associationwith available MCS options [69]. The MCS with the largest data rate thatsimultaneously satisfies the target BLER, is selected. We assume error-freefeedback signaling for the MCS report.

Scheduling algorithm Based on the UE’s CSI feedback, the scheduling algo-rithm will decide the CoMP type (JPT or CS/CB) and the cooperating cells,UE pairing, and link adaptation. The scheduler performs user selection andlink adaptation using parameters, including precoding vectors and MCSs. User

17.5 Conclusion 509

selection is based on the scheduling metric determined by a proportional fair-ness (PF) criterion for all the UEs served by the cell-site. The scheduler thenassigns the RBs of the cells to the UEs in descending order of the schedulingmetric, where the scheduling metric is normalized by the number of cooperatingcells for the UE. When there is intra-eNodeB operation and JPT is performed,19 master schedulers are formed so that each can manage the resources avail-able at one three-sector cell site and when an RB is available for the two sectorsthat perform JT, the scheduler is allowed to assign the RB to the UE. If noCoMP UE is available, the RB is allocated to cell-edge UE that performs asingle-cell transmission. In general, cell-centric UEs whose SINRs are above 0dB operate with all subcarriers of reuse 1.

ACK/NACK generation The PDSCHs are constructed from multiple cellsapplying the selected precoding vectors of each with RB-based frequency gran-ularity, and the UE is supposed to decode the data over PDSCH with DM-RSso that the multiple signals are coherently combined at the UE. The SINRobtained by a linear MMSE receiver that accounts for the combined desiredsignal and interference of precoded beams is translated to the effective SINRin association with the selected MCS. The effective SINR computed per RBbasis and averaged over the number of assigned RBs is then used to generatean ACK or NACK according to the BLER.

17.5 Conclusion

We have outlined the issues and agreements regarding CoMP. A number of com-panies have expressed strong interest in CoMP systems and put forth great effortsto determine the necessary design parameters, such as RS design, feedback sig-naling, and precoding strategies, required for the CoMP operation. Dependingon the CoMP schemes used, CoMP operation entails different costs and providesdifferent performance gains. Non-coherent precoding can be improved by addinga beam-phase factor and explicit channel feedback is also employed to improvethe CoMP gain further. A scalable control framework for resilient deploymentthat takes into account the tradeoff between complexity and performance shouldbe carefully investigated as part of the work item phase. Then, some form ofeNodeB cooperation can be finalized and this is expected to appear in futurestandards.

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[54] R1-092938, Implicit Feedback in Support of Downlink MU-MIMO Beam-forming, Texas Instruments, 3GPP TSG RAN WG1, #57bis, June 2009.

[55] R1-084290, Proposal of Multiple Sites Coordination for LTE-A TDD,CATT, 3GPP TSG RAN WG1, #55, Nov. 2008.

[56] R1-092304, UE Feedback for Downlink CoMP Schemes, ETRI, 3GPP TSGRAN WG1, #57bis, June 2009.

[57] R1-093720, CoMP E-mail Discussion Summary, Qualcomm Europe, 3GPPTSG RAN WG1, #58, Aug. 2009.

[58] R1-093912, Downlink Feedback Framework for LTE-Advanced, Nokia,3GPP TSG RAN WG1, #58bis, Oct. 2009.

[59] R1-092056, Hierarchical Feedback in Support of Downlink CoMP operation,Qualcomm Europe, 3GPP TSG RAN WG1, #57, May 2009.

[60] R1-094217, Feedback in Support of Downlink CoMP: General Views, Qual-comm Europe, 3GPP TSG RAN WG1, #58bis, Oct. 2009.

[61] 3GPP TR 36.814, Further Advancements for E-UTRA Physical LayerAspects, Release-9, V9.0.0, March 2010.

[62] 3GPP TS 36.211, Evolved Universal Terrestrial Radio Access (E-UTRA);Physical Channels and Modulation.

References 513

[63] 3GPP TS 36.212, Evolved Universal Terrestrial Radio Access (E-UTRA);Multiplexing and Channel Coding.

[64] R1-083546, Per-cell Precoding Methods for Downlink Joint ProcessingCoMP ETRI, 3GPP TSG RAN WG1, #54bis, Sept. 2008.

[65] R1-091490, Multi-cell PMI Coordination for Downlink CoMP, ETRI, 3GPPTSG RAN WG1, #56bis, March 2009.

[66] R1-091484, Evaluation of DL CoMP Gain Considering RS Overhead forLTE-Advanced, NTT DOCOMO, 3GPP TSG RAN WG1, #56bis, Mar2009.

[67] R1-031303, System-level Evaluation of OFDM – Further Considerations,Ericsson, 3GPP TSG RAN WG1, #35, Nov. 2003.

[68] R1-092429, Different Types of DL CoMP Transmission for LTE-A, Fujitsu,3GPP TSG RAN WG1, #57bis, Jun. 2009.

[69] R1-062050, Initial Characterization of E-UTRA UL VoIP Capacity, Qual-comm Europe, 3GPP TSG RAN LTE, Sep. 2006.

Index

3GPP, 480802.16j, 7

adaptive precoding order (APO), 48, 50, 60

backhaul, 3, 302, 306, 313BC, see broadcast channelBCJR algorithm, 80, 86, 89, 90beamforming, 4best-effort resource allocation, 261broadcast channel, 110, 302, 309

capacity achieving codelow-density parity-check code, 163, 266turbo codes, 266

carrier aggregation, 428cell clustering, 497, 498cell grouping, 138cell-specific reference signal (CSR), 457cellular network, 233

multicell network, 244relay network, 251

channel capacity, 208, 237channel state information (CSI), 6, 261

global, 261local, 281

channel state information reference signal(CSI-RS), 457

classification, 349clover-leaf-shaped cells, 143coded cooperation, 205collaborative power addition, 179, 184collaborative spatial multiplexing, 9combinatorial, 276

brute force, 276common rate, 179, 180, 189–192, 195,

197–199, 201computation power, 302, 315convergence, 102convex optimization, 214, 278

dual decompositionmaster problem, 279subproblem, 279

duality gap, 243, 254ellipsoid, 243, 246first-order condition, 246gradient method, 280Hessian matrix, 279; negative

semi-definite, 279Karush–Kuhn–Tucker (KKT) condition,

214, 280Lagrange dual method, 214Lagrange multiplier, 210, 279Lagrangian, 279Lagrangian duality, 238, 242, 243, 246subgradient, 243, 246subgradient method, 214

cooperating jammers, 384cooperative communication, 205, 259cooperative network, 233

base station cooperation, 4, 234, 244, 249,259

cooperative base station, 47cooperative base station complexity, 61cooperative transmission algorithm, 60cooperative transmitter, 49relay cooperation, 250relaying, 259

amplify-and-forward (AF), 18, 154, 168,205, 250, 260

compress-and-forward (CF), 19, 250decode-and-forward (DF), 18, 154, 162,

205, 260, 470full-duplex relaying, 259inband relay, 488, 489layer 1 relay, 482layer 2 relay, 483layer 3 relay, 484one-way half-duplex relaying, 259outband relay, 490relay cooperation, 234, 255relay selection, 206selective relaying, 218two-way half-duplex relaying, 259type 1 relay, 485type 2 relay, 485

514

Index 515

turbo base station cooperation, 110user cooperation, 259

coordinated beamforming, 433, 440, 496, 497coordinated multipoint transmission

(CoMP), 426, 431, 495CoMP feedback, 502CoMP set, 434direct channel feedback, 502explicit channel feedback, 503reference signal, 499uplink sounding reference signal (SRS),

503coordinated scheduling, 433, 434, 442, 496,

497cost–benefit tradeoff, 317

decode-and-forward (DF), 250decomposed factor graph, 102defection function, 361degraded BC, see degraded broadcast

channeldegraded broadcast channel, 111diamond-shaped cells, 143dirty paper coding (DPC), 48, 111, 133, 307,

309, 445distributed beamforming, 4distributed optimization, 206diversity, 160

delay, 154, 171diversity-multiplexing tradeoff, 328, 336dynamic cell selection (DCS), 496

ergodic capacity, 259extreme value distribution, 267

Frechet distribution, 268Gumbel distribution, 268Weibull distribution, 268

factor graph, 82, 83, 85femto-cells, 313flow conservation, 253forward–backward algorithm, see BCJR

algorithmfractional frequency reuse (FFR), 128, 136frequency reuse, 3, 77, 233frequency reuse partitioning , 435frequency-division multiple access (FDMA),

49front-channel interference, 51, 55

game theory, 385canonical coalitional game, 349coalition formation game, 349, 350,

411coalitional value, 348core, 357

merge-and-split, 359Shapley value, 356

coalitional game model, 408coalitional game theory, 348

characteristic form, 348graph form, 348partition form, 348

coalitional graph game, 350cooperative eavesdropping game, 412Pareto order, 414Stockholder equilibrium, 391Stockholder game, 398

Gaussian parallel multiple relay network, 399geometric mean decomposition (GMD), 59,

60goodput, 274

Han–Kobayashi coding, 308Etkin–Tse–Wang coding, 309

hexagonal cellular array, 110hidden Markov model, 85, 89

information-theoretic security, 382intercell interference, 3, 107, 233intercell interference coordination (ICIC),

436interference alignment, 441interference channel, 87, 114interference management, 4intergroup interference (IGI), 130, 134interlink interference, 51interstream interference, 51intracell interference, 3iterative transmit–receive antenna weights

optimization, 53

joint leakage suppression (JLS), 441, 445joint network channel coding, 331joint processing, 433, 496, 497

Kalman smoother, 80, 92

learning phase, 188linear cellular array, see one-dimensional

cellular arraylinear minimum mean squared error filter, 80linear program (LP), 194Lloyd–Max algorithm, 284LMMSE filter, see linear minimum mean

squared error filterLQ precoding, 309LTE, 8, 176, 451

eNodeB, 425inter-eNodeB coordination scheme, 499intra-eNodeB coordination scheme, 499

UE, 425

516 Index

LTE-Advanced, 8, 450, 451, 480Release 10, 450

Manhattan scenario, 304, 312MAP detector, see maximum a posteriori

detectormargin adaptive (MA) scheme, 23matched filter (MF), 59maximum a posteriori detector, 80, 91MCP, see multicell processingMIMO broadcast channel, see vector

broadcast channelminimum variance distortionless response

(MVDR), 56modulo operation, 52multicell MIMO transmission, 307multicell processing, 79–81multichannel diversity, 338multilayer superposition coding (MLSC),

462, 466multinode partial information relaying, 474multiple access channel, 302, 307multiple access relay channel, 331multiple-input multiple-output (MIMO), 8,

205, 259, 351distributed, 6virtual, 259

multiple-input single-output (MISO), 47, 48,55

multiuser diversity, 261, 266, 267, 338diversity gain, 210

multiuser MIMO system, 49myopic optimization, 61myopic policy, 187

Nash bargaining solution (NBS), 29network coded cooperation, 326network coding, 324network formation, 370, 373network MIMO, 77, 129, 235network utility maximization, 240NP-hard problem, 228

one-dimensional cellular array, 78, 79, 88open system interconnection, 263

media access control layer, 263physical layer, 263

orthogonal frequency-division multiple access(OFDMA), 14, 49, 236, 260

subcarrier mapping, 272orthogonal frequency-division multiplexing

(OFDM), 235, 426orthogonal relaying, 200, 202outage, 187–191, 197–201

information-outage probability, 163outage probability, 208

P-CPA, 179, 186pair-wise error probability (PEP), 36, 161parallel relay channel, 402parallel relay network, 213partial information relaying, 463partner selection, 138path-loss, 234, 250PC-CPA, 179, 186, 192per-antenna superposition coding (PASC),

462, 465physical-layer network coding, 334PMI coordination, 434power allocation, 57, 245, 254power control, 192, 194, 201precoding, 501precoding matrix index (PMI), 431preference operator, 358

QR decomposition, 55, 56, 309quality-of-service (QoS), 266

bit error rate (BER), 266channel outage probability, 276delay-sensitive, 266frame error rate (FER), 266minimum data rate requirement, 266nondelay-sensitive, 266

R-factor, 372random linear network coding, 325rate adaptive (RA) scheme, 23rate region, 242rear-channel interference, 51recommended PMI, 497rectangular cellular array, 96regularized channel inversion beamforming,

113relay channel, 16, 205relay station, 368relay-interference channel, 306remote radio head (RRH), 446, 455resource allocation, 233, 337restricted PMI, 497reuse partition, 136routing, 254

scheduling, 245cross-layer scheduling, 265max–min fairness, 220maximum throughput scheduler, 265proportional fair, 241, 282proportional fair scheduler, 265round-robin scheduler, 267weighted-sum fairness, 220

SCP, see single cell processingsecrecy capacity, 382secrecy region, 402

Index 517

self-interference, 272signal-to-interference-plus-noise-ratio

(SINR), 48, 237SINR equalization, 48SINR maximization, 56SINR gap, 237, 315single carrier frequency division multiple

access (SC-FDMA), 426single-cell processing, 79singular value decomposition (SVD), 55space-division multiple access (SDMA), 9space-time block codes, 157

Alamouti, 158distributed, 153

delay tolerant, 171linear dispersion, 157orthogonal, 159quasi-orthogonal, 159

space-time spreading, 172spatial diversity, 13spectral/eigenvalue decomposition, 56state-based factor graph, 98suboptimal solution, 229successive decoding, 477sum-product algorithm, 83synchronization, 170

time-sharing, 278Tomlinson–Harashima precoding (THP), 48,

50–53, 445transferable utility, 348

two-dimensional cellular array, 96two-stage superposition coding, 463, 475two-way relay channel, 331, 334

uplink–downlink duality, 116, 118utility function, 265

vector broadcast channel, 110virtual antenna array (VAA), 14, 20virtual LMMSE estimation, 117vulnerability region, 402

water-filling, 215, 238, 239iterative, 240modified, 247multilevel water-filling, 280

wide-area scenario, 303, 310WiMAX, 7WINNER system model, 303wireless relay, 451

XOR-CD, 338

zero-forcing (ZF) transmission, 48, 53, 133zero-forcing beamforming, 4, 113, 445zero-forcing decorrelation, 470zero-forcing dirty paper coding (ZF-DPC),

133zero-forcing DPC, 309ZF beamforming, see zero-forcing

beamforming

cooperative cellular wireless networks

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