resource allocation in ofdm-based relay and cognitive

RESOURCE ALLOCATION IN

OFDM-BASED

RELAY AND COGNITIVE RADIO NETWORKS

Shashika Lakmali Biyanwilage

A thesis submitted for the degree of

Doctor of Philosophy in Engineering

SCHOOL OF COMPUTING, ENGINEERING AND MATHEMATICS

UNIVERSITY OF WESTERN SYDNEY

AUSTRALIA

NOVEMBER 2013

c⃝ Shashika Lakmali Biyanwilage, 2013

To my Parents and my beloved Husband

DECLARATION

Date: NOVEMBER 2013

Author: Shashika Lakmali Biyanwilage

Title: RESOURCE ALLOCATION IN OFDM-BASED RELAY AND

COGNITIVE RADIO NETWORKS

Degree: PhD

I certify that the work presented in this thesis is, to the best of my knowledge

and belief, original, except as acknowledged in the text, and that the material has not

been submitted, either in full or in part, for a degree at this or any other institution.

I certify that I have complied with the rules, requirements, procedures and policy

relating to my higher degree research award of the University of Western Sydney.

Author's Signature

Acknowledgements

First and foremost, I would like to express my sincere gratitude to my prin-

cipal supervisor, Dr. Ranjith Liyanapathirana, for providing me the invaluable

opportunity to pursue my PhD under his supervision. Successful completion of

this thesis would not have been possible without his expertise, guidance, and

feedback.

I extend my deepest gratitude to my co-supervisor, Dr. Upul Gunawardana,

for his excellent supervision and mentorship throughout my candidature. His

persistent support, motivation and indispensable feedback have been the key for

my research achievements.

I am grateful to the University of Western Sydney for granting me an In-

ternational Postgraduate Research Scholarship and an Australian Postgraduate

Award, without which this research study would not have been possible. I am

also thankful to the School of Computing, Engineering, and Mathematics for

providing travel assistance to attend national and international conferences.

I would like to thank all the technical sta, general sta and academics of

School of Computing, Engineering, and Mathematics who directly or indirectly

helped me during my candidature. My gratitude also goes to all my colleagues for

their support, friendship and useful discussions. I specially thank Mr. Prasanna

Herath and Ms. Madhuka Jayawardhana for allowing me to access their PCs to

run my simulations.

I gratefully remember my Honours and Masters Degree Supervisor, Professor

Dileeka Dias of University of Moratuwa, Sri Lanka, for providing me with the

initiation towards pursuing a research career. I am also grateful to all my teachers

and lecturers for their guidance which is the reason behind my success.

My sincere and heartfelt gratitude is deserved by my parents for their love,

encouragement and inspiration throughout my life. I owe all my achievements

to their unconditional support. I am also greatly indebted to my two sisters for

being supportive and caring whenever required.

Finally, and most importantly, I would like to thank my loving husband,

Lokitha Amarasena, who has been a shadow behind all my successes during the

last several years. Words fail me to express my appreciation for his understanding,

patience and support throughout this period.

v

Abstract

Resource allocation methods are highly system dependent and specic re-

source allocation methods should be tailored according to the respective system

specications and requirements. This thesis investigates new resource allocation

methods for OFDM-based relay and cognitive radio (CR) networks. Performance

of the proposed methods is veried through computer simulations. Firstly, re-

source allocation in multi-relay assisted cooperative OFDM networks is consid-

ered. Resource allocation problem is mathematically formulated to maximize the

instantaneous capacity. As an alternative for more complex jointly optimal re-

source allocation methods, less-complex yet eective resource allocation methods

are proposed. Secondly, power allocation in OFDM-based two-hop relay networks

is studied in the presence of outdated channel knowledge. Two new power allo-

cation methods are discussed to maximize the expected rate and the outage rate.

Thirdly, relay selection and power allocation in OFDM-based CR relay networks

is studied to maximize the instantaneous capacity of the CR transmission. Subop-

timal resource allocation methods are presented for multi-relay assisted OFDM

CR networks and their performance is compared with jointly optimal resource

allocation method. Next, new resource allocation methods are presented to max-

imize the instantaneous capacity of CR relay networks when only the statistical

channel information between the CR network and the legacy network is known.

Optimal power allocation methods to maximize the instantaneous capacity of the

CR transmission are derived and low complexity suboptimal power allocation al-

gorithms are also proposed. Finally, a practical scenario of operating CR networks

in TV white spaces is considered. An interference minimization based power al-

location method is developed for OFDM-based single-hop CR transmission. Nu-

merical results conrm that the proposed power allocation scheme produces less

interference to TV receivers compared to other classical power allocation methods

while guaranteeing an acceptable quality of service for secondary transmission.

Contents

Abstract v

Contents vi

Abbreviations xi

Notation xiii

List of Figures xiv

List of Publications xviii

1 Introduction 1

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Major Contributions . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3 Thesis organization . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Literature Review 10

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2 Relay Communication . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3 Diversity Reception . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.4 Cooperative Communication . . . . . . . . . . . . . . . . . . . . . 12

2.5 Protocols for Cooperative Communication . . . . . . . . . . . . . 15

2.5.1 Amplify-and-Forward Method . . . . . . . . . . . . . . . . 15

CONTENTS vii

2.5.2 Decode-and-Forward Method . . . . . . . . . . . . . . . . 17

2.6 Fixed and Adaptive Relaying . . . . . . . . . . . . . . . . . . . . 17

2.6.1 Selection Relaying . . . . . . . . . . . . . . . . . . . . . . 18

2.6.2 Incremental Relaying . . . . . . . . . . . . . . . . . . . . . 19

2.7 Orthogonal Frequency Division Multiplexing . . . . . . . . . . . . 19

2.8 Orthogonal Frequency Division Multiple Access . . . . . . . . . . 22

2.9 Cooperative OFDM Networks . . . . . . . . . . . . . . . . . . . . 24

2.10 Cognitive Radio . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.10.1 OFDM for Cognitive Radio . . . . . . . . . . . . . . . . . 30

2.11 Cooperative Relaying in OFDM-Based Cognitive Radio Networks 30

2.11.1 OFDM Cognitive Wireless Relay Networks . . . . . . . . . 31

2.12 Resource Allocation in Wireless Networks . . . . . . . . . . . . . 33

2.12.1 Resource Allocation in Cooperative OFDM Networks . . . 34

2.12.2 Resource Allocation in OFDM Cognitive Wireless Relay

Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.12.3 Resource Allocation for Rate Maximization . . . . . . . . . 37

2.13 Optimization Techniques for Resource Allocation . . . . . . . . . 39

2.14 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3 Resource Allocation in Cooperative OFDM Networks 44

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.2 System and Channel Model . . . . . . . . . . . . . . . . . . . . . 46

3.3 All Subcarrier Relaying . . . . . . . . . . . . . . . . . . . . . . . . 50

3.3.1 Relay Selection . . . . . . . . . . . . . . . . . . . . . . . . 51

3.3.2 Power Allocation . . . . . . . . . . . . . . . . . . . . . . . 51

3.4 Selective Subcarrier Relaying . . . . . . . . . . . . . . . . . . . . 55

3.4.1 Subcarrier and Relay Selection . . . . . . . . . . . . . . . . 56

3.4.2 Power Allocation . . . . . . . . . . . . . . . . . . . . . . . 58

3.4.3 Resource Allocation Algorithm . . . . . . . . . . . . . . . 61

CONTENTS viii

3.5 Numerical Results and Discussion . . . . . . . . . . . . . . . . . . 63

3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

4 Power Allocation in OFDM Relay Networks with Outdated CSI 69

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69


4.3 Maximizing Instantaneous Rate . . . . . . . . . . . . . . . . . . . 74

4.4 Maximizing Expected Rate . . . . . . . . . . . . . . . . . . . . . . 77

4.4.1 Numerical Results and Discussion . . . . . . . . . . . . . . 80

4.5 Maximizing Outage Rate . . . . . . . . . . . . . . . . . . . . . . . 82

4.5.1 Numerical Results and Discussion . . . . . . . . . . . . . . 86

4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

5 Resource Allocation in OFDM Cognitive Radio Relay Networks 91

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91


5.3 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . 97

5.4 Proposed Resource Allocation Methods . . . . . . . . . . . . . . . 100

5.4.1 Resource Allocation Method A . . . . . . . . . . . . . . . 100

5.4.1.1 Simplied Relay Selection . . . . . . . . . . . . . 101

5.4.1.2 Optimal Power Allocation . . . . . . . . . . . . . 102

5.4.2 Resource Allocation Method B . . . . . . . . . . . . . . . 105

5.5 Joint Optimal Resource Allocation . . . . . . . . . . . . . . . . . 106


5.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

6 Power Allocation in OFDM CR Relay Networks with Knowledge

of Statistical CSI 115

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115


CONTENTS ix

6.3 Power Allocation for DF Relay Assisted CR Networks . . . . . . . 123

6.3.1 Optimal Power Allocation Method . . . . . . . . . . . . . 124

6.3.2 Suboptimal Power Allocation Method . . . . . . . . . . . . 125

6.4 Power Allocation for AF Relay Assisted CR Networks . . . . . . . 129

6.4.1 Optimal Power Allocation Method . . . . . . . . . . . . . 130

6.4.2 Suboptimal Power Allocation Method . . . . . . . . . . . . 132

6.5 Uniform Power Allocation Method . . . . . . . . . . . . . . . . . 134


6.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

7 Power Allocation in OFDM Cognitive Radio Networks Operat-

ing in TV White Space 147

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

7.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150


7.4 Power Allocation for Interference Minimization . . . . . . . . . . . 155

7.4.1 Simplied Power Allocation Algorithm . . . . . . . . . . . 158

7.5 Comparison with Other Power Allocation Methods . . . . . . . . 160

7.5.1 Water Filling Power Allocation . . . . . . . . . . . . . . . 160

7.5.2 Capacity Threshold Based Power Allocation . . . . . . . . 161


7.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

8 Conclusion 167

8.1 Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . . 168

8.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

References 173

Appendices 188

CONTENTS x

A Optimal Relay and Source Transmit Powers in Cooperative OFDM

Transmission 188

A.1 Derivation of Optimal Relay Transmit Power . . . . . . . . . . . . 188

A.2 Derivation of Optimal Source Transmit Power . . . . . . . . . . . 190

B Optimal Relay Transmit Power in OFDM CR Relay Transmis-

sion with Total Interference Constraint 193

C Optimal Transmit Powers in OFDMCR Relay Transmission with

Average Interference Constraints 196

C.1 Derivation of Optimal Source Transmit Power in DF Relay As-

sisted CR Transmission . . . . . . . . . . . . . . . . . . . . . . . . 196

C.2 Derivation of Optimal Relay Transmit Power in AF Relay Assisted

CR Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . 198

D Optimal Transmit Power for Interference Minimization in OFDM

CR Networks 200

Abbreviations

AF amplify-and-forward

AWGN additive white Gaussian noise

BER bit-error-rate

CDMA code division multiple access

CNR channel-to-noise ratio

CR cognitive radio

CSI channel state information

DF decode-and-forward

DFT discrete Fourier transform

EGC equal-gain combining

FDD frequency division duplex

FFT fast Fourier transform

IFFT inverse fast Fourier transform

KKT Karush-Kuhn-Tucker

MIMO multiple-input multiple-output

MRC maximal-ratio combining

NP nondeterministic-polynomial

OFDM orthogonal frequency division multiplexing

OFDMA orthogonal frequency division multiple access

ABBREVIATIONS xii

OSP ordered subcarrier pairing

PDF probability density function

PU primary user

QoS quality of service

SC selection combining

SNR signal-to-noise ratio

ST space-time

SU secondary user

TDD time division duplex

TDMA time division multiple access

TVWS TV white space

TVBD TV band device

WRAN wireless regional area network

Notation

E [ · ] Expectation operation

J0(·) Zero-order Bessel function of the rst kind

I0(·) Zero-order modied Bessel function of the rst kind

Γ (x) Gamma function

Γ (a, x) Incomplete gamma function

Q(·) Complementary Gaussian cumulative distribution function

CN(0, σ2) Circularly-symmetric complex Gaussian random variable

having zero-mean and variance σ2

max Maximum of the elements

min Minimum of the elements

2F1(a, b; c; z) Gauss' Hypergeometric function

fγ(γ) Probability density function of the random variable γ

fγ|γ(γ, γ) Conditional probability density function of the random vari-

able γ given the random variable γ

hmn Channel impulse response of link between terminals m and n

Hmn N-point FFT of channel impulse response of link between

terminals m and n

ρ Correlation coecient

List of Figures

2.1 Two-hop relay communication . . . . . . . . . . . . . . . . . . . . 11

2.2 Cooperative communication system with multiple relays . . . . . 13

2.3 Two-user cooperative communication model . . . . . . . . . . . . 14

2.4 TDMA channel model for cooperative transmission . . . . . . . . 14

2.5 Block diagram of (a) OFDM transmitter (b) OFDM receiver . . . 21

2.6 Multiple access with OFDMA . . . . . . . . . . . . . . . . . . . . 22

2.7 Block diagram of OFDMA system . . . . . . . . . . . . . . . . . . 23

2.8 Multi-relay assisted cooperative OFDM system model. . . . . . . 25

2.9 Shared subcarrier cooperation with two-user cooperative OFDM

system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.10 Subcarrier allocation in OFDM-based cognitive radio system . . . 31

2.11 Cognitive wireless relay network . . . . . . . . . . . . . . . . . . . 32

3.1 Cooperative OFDM system model . . . . . . . . . . . . . . . . . . 47

3.2 Flowchart of two-step iterative power allocation . . . . . . . . . . 52

3.3 Flowchart of selective subcarrier relaying based resource allocation 62

3.4 Relay node distribution. . . . . . . . . . . . . . . . . . . . . . . . 64

3.5 Normalized capacity variation with source-relay distance for dif-

ferent resource allocation methods, K = 8 relays, r = 100m. . . . 65

3.6 Normalized capacity variation with source-relay distance with Se-

lective relaying-B method for dierent relay cluster sizes, K = 16

relays. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

LIST OF FIGURES xv

3.7 Normalized capacity variation with source-relay distance with Se-

lective relaying-B method for dierent number of relays, r = 100m. 67

3.8 Histogram of number of participating relays with Selective relaying-

B method, K = 16 relays, r = 100m. . . . . . . . . . . . . . . . . 67

3.9 Histogram of number of participating relays with Selective relaying-

B method, K = 32 relays, r = 100m. . . . . . . . . . . . . . . . . 68

4.1 Two-hop OFDM relay link. . . . . . . . . . . . . . . . . . . . . . . 71

4.2 Expected rate variation with transmit power, dsr = 500m, ρ = 0.5. 80

4.3 Expected rate variation with source-relay distance, ρ = 0.2. . . . . 81

4.4 Expected rate variation with source-relay distance, ρ = 0.8. . . . . 82

4.5 Outage rate variation with transmit power, dsr = 200m, ρ = 0.98,

Pout = 0.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

4.6 Outage rate variation with source-relay distance, Pout = 0.1. . . . 87

4.7 Outage rate variation with source-relay distance, Pout = 0.01. . . . 88

4.8 Outage rate variation with source-relay distance, ρ = 0.98 and

Pout = 0.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

5.1 Multi-relay assisted CR system model . . . . . . . . . . . . . . . . 95

5.2 Spectrum allocation for OFDM-based CR system . . . . . . . . . 96

5.3 Primary user (PU) and CR distribution - Simulation setup 1 . . . 107

5.4 Spectrum allocation - Simulation setup 1 . . . . . . . . . . . . . . 108

5.5 Instantaneous capacity variation with interference threshold - Sim-

ulation setup 1, K = 3, dsr = 300m . . . . . . . . . . . . . . . . . 108

5.6 Instantaneous capacity variation with number of relays - Simula-

tion setup 1, Ith = 5× 10−15W, dsr = 300m . . . . . . . . . . . . 109

5.7 Instantaneous capacity variation with relay location - Simulation

setup 1, K = 3, Ith = 5× 10−15W . . . . . . . . . . . . . . . . . . 110

5.8 Primary user (PU) and CR distribution - Simulation setup 2 . . . 110

5.9 Spectrum allocation - Simulation setup 2 . . . . . . . . . . . . . . 111

LIST OF FIGURES xvi

5.10 Instantaneous capacity variation with relay location - Simulation

setup 2, K = 3, Ith = 5× 10−15W . . . . . . . . . . . . . . . . . . 111

5.11 Instantaneous capacity variation with interference threshold - Sim-

ulation setup 2, K = 3, dsr = 400m . . . . . . . . . . . . . . . . . 112

5.12 Instantaneous capacity variation with number of relays - Simula-

tion setup 2, Ith = 5× 10−15W, dsr = 400m . . . . . . . . . . . . 113

6.1 Co-existence of CR relay link and PU system . . . . . . . . . . . . 118

6.2 Primary user (PU) and CR distribution . . . . . . . . . . . . . . . 135

6.3 Spectrum allocation used in computer simulation . . . . . . . . . 136

6.4 Instantaneous capacity variation with relay location - DF relay (a)

with outdated CSI (b) with fading statistics, Ith = 5 × 10−6W,

P = 0.01W . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

6.5 Instantaneous capacity variation with relay location - AF relay (a)

with outdated CSI (b) with fading statistics, Ith = 5 × 10−6W,

P = 0.01W . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

6.6 Instantaneous capacity variation with interference threshold - DF

relay (a) with outdated CSI (b) with fading statistics, dsr = 500m,

P = 0.01W . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

6.7 Instantaneous capacity variation with interference threshold - AF

relay (a) with outdated CSI (b) with fading statistics, dsr = 500m,

P = 0.01W . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

6.8 Instantaneous capacity variation with relay location and interfer-

ence threshold with optimal power allocation method (DF relay),

P = 0.01W, ρ = 0.8 . . . . . . . . . . . . . . . . . . . . . . . . . 143

6.9 Instantaneous capacity variation with transmit power - DF relay

(a) with outdated CSI, ρ = 0.9 (b) with fading statistics, dsr =

500m, Ith = 10−3W . . . . . . . . . . . . . . . . . . . . . . . . . . 144

LIST OF FIGURES xvii

6.10 Instantaneous capacity variation with transmit power - AF relay

(a) with outdated CSI, ρ = 0.9 (b) with fading statistics, dsr =

500m, Ith = 10−3W . . . . . . . . . . . . . . . . . . . . . . . . . . 145

7.1 Co-existence of secondary network within TV coverage area . . . 153

7.2 General model of spectrum allocation for CRs in TVWS . . . . . 154

7.3 Flowchart of the simplied power allocation algorithm . . . . . . . 159

7.4 TV receivers, and CR transmitter and receiver distribution . . . . 162

7.5 Total interference variation with capacity threshold, M = 4 TV

receivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

7.6 Interference variation at each TV receiver with capacity threshold 164

7.7 Total interference variation with distance between the CR trans-

mitter and TV receiver, M = 1 TV receiver, Cth = 50b/s/Hz . . . 165

7.8 Total interference variation with distance between the CR trans-

mitter and TV receiver, and capacity threshold with interference

minimization based power allocation, M = 1 TV receiver . . . . . 165

List of Publications

1. S. Biyanwilage, U. Gunawardana, and R. Liyanapathirana, Power Alloca-

tion in OFDM Cognitive Radio Relay Networks with Outdated CSI, Ac-

cepted for publication in International Journal of Communication Systems,

Available online doi: 10.1002/dac.2755

2. S. Biyanwilage, U. Gunawardana, and R. Liyanapathirana, Resource Allo-

cation in Multiple DF Relay Assisted OFDM Cognitive Radio Relay Net-

works with the Knowledge of Fading Statistics, in Proceedings of IEEE

TENCON Spring, pp. 436 − 440, Apr. 2013, Sydney, Australia. doi:

10.1109/TENCONSpring.2013.6584480

3. S. Biyanwilage, U. Gunawardana, and R. Liyanapathirana, Power Allo-

cation in OFDM Cognitive Radio Relay Networks with Average Interfer-

ence Constraints, in Proceedings of Australian Communications Theory

Workshop (AusCTW), pp. 81 − 86, Jan. 2013, Adelaide, Australia. doi:

10.1109/AusCTW.2013.6510049 (Chapter 6)

4. S. Biyanwilage, U. Gunawardana, and R. Liyanapathirana, New Power Al-

location Methods for AF Relay Assisted OFDM Cognitive Radio Networks

with Outdated CSI, in Proceedings of International Symposium on Com-

munications and Information Technologies (ISCIT), pp. 404 − 409, Oct.

2012, Gold Coast, Australia. doi: 10.1109/ISCIT.2012.6380930 (Chapter

6)

LIST OF PUBLICATIONS xix


tion in DF Relay Assisted OFDM Cognitive Radio Networks with Outdated

CSI, in Proceedings of International Symposium on Communications and

Information Technologies (ISCIT), pp. 561− 566, Oct. 2012, Gold Coast,

Australia. doi: 10.1109/ISCIT.2012.6380962 (Chapter 6)


tion for Outage Rate Maximization in OFDM Relay Links, in Proceedings

of International Symposium on Personal, Indoor, and Mobile Communi-

cations (PIMRC), pp. 1863 − 1867, Sep. 2012, Sydney, Australia. doi:

10.1109/PIMRC.2012.6362655 (Chapter 4)

7. S. Biyanwilage, U. Gunawardana, and R. Liyanapathirana, Power Allo-

cation for Nonregenerative OFDM Relay Links with Outdated Channel

Knowledge, in Proceedings of International Symposium on Communica-

tions and Information Technologies (ISCIT), pp. 428 − 432, Oct. 2011,

Hangzhou, China. doi: 10.1109/ISCIT.2011.6089964 (Chapter 4)

8. S. Biyanwilage, U. Gunawardana, and R. Liyanapathirana, Selective Sub-

Carrier Relaying and Power Allocation for Multi-Relay-Assisted Coopera-

tive OFDM Systems with Outdated CSI, in Proceedings of International

Conference on Telecommunications, pp. 528− 533, May 2011, Ayia Napa,

Cyprus. doi: 10.1109/CTS.2011.5898982,

9. S. Biyanwilage, U. Gunawardana, and R. Liyanapathirana, Selective Sub-

Carrier Relaying and Power Allocation for Multi-Relay-Assisted Coopera-

tive OFDM Systems, in Proceedings of Australian Communications Theory

Workshop (AusCTW), pp. 164−169, Jan. 2011, Melbourne, Australia. doi:

10.1109/AUSCTW.2011.5728756 (Chapter 3)

Chapter 1

Introduction

Wireless communication has become the fastest growing and most popular form

of communication technology. Among the current wireless standards, cellular sys-

tems (e.g., 3GPP LTE, WCDMA/UMTS, CDMA2000), WiMAX (IEEE 802.16)

and WiFi (IEEE 802.11) are widely used to provide voice and data services to

subscribers. Also many new wireless applications such as wireless sensor networks

and smart home appliances are emerging as practical systems. However, achiev-

ing reliable multi-user communication through a wireless channel is a challenging

task since it is subject to noise, interference and other channel impairments in

addition to being limited in power and bandwidth.

Path loss, shadowing and multipath fading are some of the main channel im-

pediments in a wireless channel. Depending on the relation between the signal

parameters and the channel propagation characteristics, multipath fading can be

classied as at fading and frequency selective fading [1]. The coherence band-

width of a channel is a measure of the width of the frequencies that are aected

by the channel response [2]. Flat fading or frequency non-selective fading occurs

when the signal bandwidth is smaller than the channel coherence bandwidth. On

the other hand, when the signal bandwidth is larger than the channel coherence

bandwidth the signal experiences frequency selective fading. The signal can be a

singlecarrier or multicarrier signal.

1. INTRODUCTION 2

Relay communication and cooperative communication are two key technolo-

gies that can be used to overcome the eects of shadowing and frequency at

fading. With relay communication, the wireless transmission path is split into

multiple shorter paths with the introduction of intermediate nodes called relays.

This approach can be used to improve the coverage in heavily shadowed areas.

In at fading situations, diversity methods can be used to combat the eects

of fading. The basic idea of diversity is to create multiple independently fad-

ing communication paths between the source and the destination [3]. Spatial

diversity is a common method of generating multiple communication paths by

using more than one transmit and/or receive antennas. However, due to cost,

size, and hardware limitations, mobile and handheld wireless devices may not

be able to support multiple transmit antennas. Cooperative communication is

a promising technology which provides spatial diversity without having multiple

transmit/receive antennas. The basic principle here is to share multiple users'

antennas to create a virtual antenna array. Due to the broadcast nature of radio

signals, the signals transmitted from a source can also be received by other users

which are often known as relays or partners. These partners can then retransmit

the received signals to the destination, thereby creating a virtual antenna array.

In wireless broadband applications, where the signal bandwidth is much larger

than the channel coherence bandwidth, multicarrier modulation techniques such

as orthogonal frequency division multiplexing (OFDM) can be used to mitigate

the eect of frequency selective fading. In multicarrier modulation, a high band-

width signal is transmitted over multiple orthogonal subcarriers of a bandwidth

much smaller than the coherence bandwidth of the channel. Then the channel

can be approximated to behave like frequency non-selective. The individual sub-

carriers may still suer from pathloss, shadowing and at fading. Hence, relay

and cooperative communication technologies can be used to improve coverage

and to reduce the eect of subcarrier fading in OFDM systems.

1. INTRODUCTION 3

With the ever increasing demand for high bit rate voice and data services,

and the emergence of numerous wireless communication technologies and devices,

the electromagnetic radio spectrum has become a scarce resource. Almost all

wireless devices depend on access to the radio spectrum and it is controlled by

radio communication regulations. It has been identied that the allocated radio

spectrum is not fully utilized all the time [4]. Therefore, an interesting wireless

communication paradigm called cognitive radio (CR) [5, 6, 7] has been introduced

as a key to improve the current spectrum utilization. CRs have the ability to

dynamically adapt their transmission parameters according to the information

gathered from their radio environment. This allows CRs to access the frequency

bands unoccupied by the respective licensed user in an opportunistic manner.

Furthermore, OFDM has been identied as a candidate modulation technique for

CR based services. Relay transmission technologies can be used in OFDM-based

CR networks to reduce the eect of multipath fading and to enhance the coverage

area. This has led to the concept of cognitive wireless relay networks, which has

gained rapidly increasing interest in wireless communication research.

1.1 Motivation

In wireless communication networks, system resources can be allocated adaptively

to meet varying channel conditions and to enhance the system performance. This

encourages studies on resource allocation in relay assisted OFDM networks and

OFDM-based CR relay networks. Relay nodes, subcarriers, and transmit signal

power are the main resources in a relay assisted OFDM network. These system

resources can be allocated to achieve a predened target within the given sys-

tem limitations. The resource allocation objective or the target can be capacity

maximization, bit-error-rate (BER) minimization, outage rate minimization, or

transmit power minimization. One of the most common system limitations is the

limited transmit power available at transmitters. Despite the large amount of

1. INTRODUCTION 4

research that has been carried out in this eld of study, there are still gaps in

knowledge due to the system specic nature of resource allocation problems.

A rich literature is available on adaptive power allocation methods in single-

relay assisted OFDM networks in both non-cognitive and cognitive environments.

However, multi-relay assisted transmission is preferred for multicarrier systems

such as OFDM networks to gain the advantage of available multiple subcarriers.

It provides the exibility to select the best relay for each subcarrier [8, 9]. Some

of the reported work in the literature has considered resource allocation in multi-

relay assisted OFDM networks as a joint allocation of transmit power, subcarriers

and relay nodes [10, 11, 12, 13]. The overall resource allocation problem is de-

veloped as a joint optimization problem of multiple system resources. Such joint

optimization methods may provide an optimal resource allocation but involves

higher computational complexity. It makes them less attractive for practical im-

plementation. This motivates the development of less-complex but still eective

resource allocation methods for multi-relay assisted OFDM networks.

In general, resource allocation decisions are made at the transmitter, and it

requires some knowledge of the wireless channel condition or the channel state

information (CSI) to perform adaptive resource allocation. Wireless channels are

time varying in nature, and the transmitter should obtain the CSI in timely man-

ner in order to adaptively allocate the system resources to suit varying channel

conditions. In frequency division duplex (FDD) systems, receiver estimates the

CSI and sends that information to the transmitter via a feedback channel. In

time division duplex (TDD) systems, the transmitter can obtain the CSI directly

by channel estimation. However, in practice, the available CSI at the transmitter

is rarely perfect due to the channel estimation errors and feedback delay. There-

fore, these issues should be taken into consideration when developing resource

allocation methods. Nevertheless, power allocation in OFDM relay networks in

the presence of imperfect/outdated CSI is barely covered in the current litera-

ture. This highlights the need to study adaptive resource allocation in OFDM

1. INTRODUCTION 5

relay networks when the perfect knowledge of the actual instantaneous CSI is not

available.

In OFDM-based CR relay networks, the CR transmission should not produce

unacceptable levels of interference to licensed (primary) users. To estimate the

level of interference, a CR transmitter needs to obtain the CSI between itself and

the licensed users. In general, the CSI is obtained via a central controller operat-

ing between the secondary and primary networks or else by directly observing the

pilot signal transmitted by primary users. As mentioned before, in practice, it is

dicult or infeasible to obtain perfect CSI between CR transmitters and licensed

users due to the channel estimation errors and feedback delay. Nevertheless,

statistical channel information can be obtained via long-term averaging of the

available CSI. Power allocation in OFDM CR relay networks with statistical CSI

is not covered in detail in the existing studies. This motivates the investigation

of power allocation methods for CR relay networks in the presence of statistical

CSI between the CR network and the licensed network.

Cognitive radio networks are currently being evaluated to be implemented

as practical systems, and several international standards have already been de-

veloped to standardize the cognitive access to licensed radio spectrum. Unused

spectrum of TV broadcasting bands, which is known as TV white space (TVWS),

has been identied as an initial candidate for CR based services [14, 15]. CR net-

works in TVWS is one of the main practical applications of CR concept and it

provides the platform for researchers to test and verify their research outcomes.

This can be used to test dierent power allocation algorithms that have already

been proposed for CR networks. Moreover, new resource allocation methods can

be designed specically for this particular application.

Driven by the aforementioned motivations, the major objective of this re-

search is to investigate resource allocation methods for OFDM relay networks and

OFDM-based CR relay networks with a more practical insight. Two main aspects

are taken into consideration: higher computational complexity and ineciency of

1. INTRODUCTION 6

joint optimal resource allocation methods in multi-relay assisted networks, and

the infeasibility to obtain perfect instantaneous CSI in practical situations.

1.2 Major Contributions

This thesis has resulted in several contributions towards resource allocation stud-

ies in OFDM relay networks. The major contributions are as follows:

• Resource allocation methods for multi-relay assisted cooperative OFDM

networks and OFDM-based CR relay networks are investigated. Two-step

suboptimal resource allocation method with much less computational com-

plexity is introduced as a more practical alternative for complex joint opti-

mal resource allocation methods. Further, analytical expressions for source

and relay transmit powers are derived and the performance evaluation of

the proposed methods is presented.

• Two power allocation methods are introduced for OFDM relay networks in

the presence of imperfect CSI at the source. In particular, outdated CSI

due to feedback delay is considered. However, it is infeasible to solve the

resulting power allocation problems analytically to obtain closed-form ex-

pressions for source and relay transmit powers. Performance of the proposed

power allocation methods is analyzed using computer simulation results.

• A comprehensive study of power allocation methods for OFDM-based CR

relay networks is carried out when the statistical CSI between the CR net-

work and the licensed network is known by the CR transmitters. More

specically, the availability of outdated CSI and the availability of only the

fading statistics are considered. New power allocation methods are devel-

oped and analytical expressions for source and relay transmit powers are

derived. Performance of the proposed methods is evaluated using computer

simulations.

1. INTRODUCTION 7

• Application of CR networks in TVWS is discussed along with adaptive re-

source allocation. Among the dierent aspects related to CR operation

in TVWS, this thesis is focused on adaptive resource allocation in such

systems. Power allocation in single-hop OFDM-based CR networks oper-

ating in TVWS is studied as an initial step towards this broad research

context. A new power allocation method that minimizes the interference

to TV receivers is proposed for CR networks operating in TVWS and its

performance is compared with other classical power allocation methods.

1.3 Thesis organization

The remainder of this thesis is organized as follows:

Chapter 2 presents a detailed literature review which introduces relay com-

munication, cooperative communication, OFDM and cognitive radio concepts.

Dierent methods of applying relay communication in OFDM networks are dis-

cussed in detail followed by a review of OFDM-based CR networks and OFDM-

based cognitive wireless relay networks. A review of resource allocation methods

in cooperative OFDM networks and OFDM-based CR relay networks is given and

an overview of optimization techniques used for resource allocation is provided.

In Chapter 3, resource allocation methods for multi-relay assisted cooperative

OFDM networks are presented. The resource allocation problem is formulated to

maximize the instantaneous capacity of the cooperative OFDM network subject

to transmit power constraints at source and the relays. There are three resources

to be allocated: relays, subcarriers, and transmit power. In order to obtain a

feasible solution, a two-step approach is proposed where resource allocation is

performed in two steps: relay and/or subcarrier selection, and power allocation.

Resource allocation methods are presented for two scenarios: all subcarrier re-

laying and selective subcarrier relaying. Analytical expressions for source and

1. INTRODUCTION 8

relay transmit powers are derived and the performance of the proposed methods

is evaluated using computer simulations.

Chapter 4 investigates adaptive power allocation methods in OFDM-based

two-hop relay links with the knowledge of outdated CSI. It is assumed that the

available CSI of source-relay and relay-destination channels at the source is out-

dated due to feedback delay. Two power allocation methods are developed con-

sidering two dierent objectives: expected rate maximization and outage rate

maximization. Computer simulation results are presented to compare the perfor-

mance of the proposed methods.

In Chapter 5, resource allocation methods are studied for OFDM-based CR

relay networks with multiple relays. The resource allocation problem is formu-

lated to maximize the instantaneous capacity of the CR transmission subject to

total interference constraint at primary receivers and transmit power constraints

at CR transmitters. Joint optimization of relay selection and subcarrier power

allocation is a mixed binary integer programming problem, and hence it is hard to

nd an analytical solution. Thus, the resource allocation problem is simplied by

dividing it into two subproblems and suboptimal yet ecient resource allocation

methods are investigated. Two new resource allocation methods are developed

and their performance is evaluated using computer simulations.

Chapter 6 investigates power allocation methods for two-hop OFDM-based

CR networks when only the statistical CSI between CR network and primary

network is known at the CR source. Statistical CSI is obtained under two scenar-

ios: when the available CSI is outdated, and when only the fading statistics are

available. New power allocation methods are derived with average interference

constraints at each primary receiver. A comprehensive study is presented consid-

ering two dierent relaying protocols, namely, amplify-and-forward and decode-

and-forward. Optimal power allocation methods to maximize the instantaneous

capacity of the CR transmission are developed and less-complex suboptimal power

allocation methods are also proposed.

1. INTRODUCTION 9

In Chapter 7, power allocation methods are investigated for CR networks

operating in TVWS. A new power allocation method is developed for single-hop

OFDM-based CR networks operating in TVWS. Power allocation is performed

to minimize interference at the TV receivers while guaranteeing quality of service

(QoS) for CR transmission. The QoS is measured in terms of the minimum

transmission capacity required by the secondary network. Analytical expression

for optimal CR transmit power is derived and the performance of the proposed

method is evaluated using computer simulation results. The proposed approach

achieves substantial interference reduction compared to other power allocation

methods while satisfying the necessary capacity requirement for CR transmission.

Chapter 8 concludes the thesis by providing a summary of the research work,

its outcomes, and possible directions for future research.

Chapter 2

Literature Review

2.1 Introduction

This chapter provides the necessary background information for the research con-

text addressed in this thesis. Firstly, relay communication, cooperative commu-

nication, orthogonal frequency division multiplexing (OFDM) and cognitive ra-

dio (CR) concepts are introduced and the dierent methods of combining the

aforementioned technologies are discussed. Next, a review of adaptive resource

allocation in cooperative OFDM networks and OFDM-based CR relay networks

is provided and unexplored gaps in knowledge are identied. Finally, an overview

of optimization techniques for wireless resource allocation is given.

2.2 Relay Communication

Relay communication [16] is used to achieve coverage and capacity enhancements

in wireless networks. When the destination cannot receive the source trans-

mitted signal properly due to heavy path loss or shadowing, relay transmission

splits the channel between the source and the destination into multiple shorter

hops by using intermediate nodes called relays. The simplest form of a two-hop

(dual-hop) transmission is focused in this thesis since it has gained an increasing

2. LITERATURE REVIEW 11

interest in the context of cooperative communication [17, 18, 19]. A two-hop

relay transmission which involves one intermediate relay is illustrated in Figure

2.1. The dual-hop communication involves two transmission phases. During the

rst phase, the source transmits the data and it is received by the relay station.

In the second phase, the relay simply forwards the received information to the

destination. These two phases are generally implemented in time domain where

two time slots are assigned for source-relay and relay-destination transmissions

[20].

Source Destination

Relay

Figure 2.1: Two-hop relay communication

Relay communication can be used to improve radio coverage in scenarios with

heavy shadowing [21]. Also, the relay concept can be used to extend the radio

coverage of a transmitter to non-shadowed areas with comparatively less transmit

power than the conventional single-hop transmission [20]. Furthermore, the relay

communication provides the possibility of installing temporary coverage in areas

where permanent coverage is not needed or where a fast initial network roll-out

has to be performed [21].

2.3 Diversity Reception

Diversity methods are used to reduce the eect of multipath fading by using two

or more communication channels with dierent characteristics. It is based on the

fact that individual communication channels experience independent fading. Spa-

tial diversity is a common method of generating multiple communication paths

by using multiple transmitter and/or receiver antennas [3]. In addition, there are


number of other diversity schemes including angle diversity, frequency diversity,

polarization diversity, time diversity and multipath diversity [3].

Performance of a diversity scheme is measured in terms of diversity gain,

which provides a measure of the advantage due to some diversity scheme. For an

example, in a slow Rayleigh fading environment with one transmit and n receive

antennas, a full diversity gain of n can be achieved. It implies that in the high

signal-to-noise ratio (SNR) region, the average error probability decays at a rate

of 1/SNRn as opposed to 1/SNR in single-antenna fading channels [22].

2.4 Cooperative Communication

Emerging from the idea of user cooperation diversity introduced in [17], cooper-

ative relaying which is also known as cooperative communication, is a powerful

solution that can be used to mitigate the eect of multipath fading. Coopera-

tive communication allows single antenna mobiles in a multi-user environment to

achieve some of the benets of multiple-input multiple-output (MIMO) systems

by sharing their antennas in a manner that creates a virtual antenna array. Al-

though the basic idea behind cooperative communication is the relay concept, in

many aspects cooperative communication is dierent from a conventional relay

transmission [23]. Here, each wireless node or user can cooperatively act as a

relay for its partner while transmitting its own information. So users can behave

as both information sources as well as relays. The idea of cooperation can be

applied to dierent wireless systems such as cellular networks, wireless ad hoc

networks and wireless sensor networks.

Cooperative relaying concept exploits two fundamental features of the wireless

medium: its broadcast nature and its ability to achieve diversity through inde-

pendent channels [20]. Due to its broadcast nature, the signal transmitted by a

source to a destination can also be received by other terminals, which are often

referred to as relays or partners. With the help of these relays, multiple inde-


pendent paths can be generated between the source and the destination, thereby

creating spatial diversity. This form of diversity is also known as cooperative di-

versity. Figure 2.2 illustrates a cooperative communication system model where

the source transmission is assisted by multiple relays.

Source

Relay 1

Destination

Direct transmission

Relayed transmission

Relay 2

Relay k

Relay K

.

.

.

Figure 2.2: Cooperative communication system with multiple relays

Cooperative communication assumes that the destination can separately re-

ceive the original and the relayed transmissions. Therefore, they should be or-

thogonal to each other. This is accomplished by transmitting the direct and

relayed signals via orthogonal channels such as non-overlapping time slots [19],

orthogonal frequencies or spreading codes [24, 25].

With time division multiple access (TDMA) implementation, non-overlapping

time periods are used to transmit each user's information. Figure 2.3 illustrates

a two-user cooperation system where, User 2 acts as a relay for User 1. To

enable cooperation, the time period allocated for User 1 is further divided into

two orthogonal time slots as shown in Figure 2.4. The rst time slot is used for

direct transmission and the next time slot is used for relayed transmission.


User 1

(s)

User 2

(r)

Destination

(d)

Direct transmission

Relayed transmission

hsr

hsd

hrd

Figure 2.3: Two-user cooperative communication model

S R,D R D

Time slot t Time slot t+1

Time

Figure 2.4: TDMA channel model for cooperative transmission

During the rst time slot, the User 1 transmits and it is received by both the

User 2 (relay in this case) and the destination. The received signal at the relay,

Yr[t], and at the destination, Yd[t], can be given as,

Yr[t] =√Es hsrXs[t] + nr[t] (2.1)

and

Yd[t] =√Es hsdXs[t] + nd[t], (2.2)

respectively. Here, Xs[t] is the unit energy transmitted signal and Es is the

average energy per symbol transmitted by the source. During the second time

slot, the relay (User 2) transmits the cooperating signal to the destination. The

signal received at the destination during the second time slot can be expressed

as,

Yd[t+ 1] = hrdXr[t+ 1] + nd[t+ 1] (2.3)


where, Xr[t+1] is the relay transmitted signal. In (2.1)-(2.3), the channel coe-

cient, hij (i ∈ s, r , j ∈ r, d), captures the eect of path loss, shadowing, and

frequency at fading. nj[t] captures the eects of additive white Gaussian noise

(AWGN) with variance Nj.

The destination combines the two received signals given by (2.2) and (2.3)

to estimate the source transmitted signal Xs[t]. A diversity combining technique

such as maximal-ratio combining (MRC), equal-gain combining (EGC) or selec-

tion combining (SC) [3] can be implemented at the destination receiver to combine

the multiple received signals. The TDMA model described in this section is used

throughout this thesis unless otherwise stated.

2.5 Protocols for Cooperative Communication

There are dierent strategies (protocols) employed by relays to process and for-

ward the received signal. Depending on the nature and the complexity of the relay

operation there are two main relaying protocols, namely, amplify-and-forward

(AF) and decode-and-forward (DF). This section outlines these two protocols

used for relay transmission.

2.5.1 Amplify-and-Forward Method

With AF method, the relaying partner amplies the received signal and then

retransmits it to the destination. This method is also referred as nonregenerative

relaying [26] or analog relaying [27]. Although the noise also gets amplied by the

cooperating partner, the destination receives two independently faded versions of

the source signal. If an AF relay is employed in the single-relay assisted coop-

erative communication system model shown in Figure 2.3, the relay transmitted

signal could be given as,

Xr[t] = βYr[t− 1] (2.4)


where, β is the relay amplifying factor or the relay gain.

One method of calculating the relay gain is given in [28] as,

β =

√Er

| hsr |2 Es +Nr

(2.5)

where, Er is the average energy per symbol transmitted at the relay. This choice

of the gain inverts the fading eect of the source-relay channel while maintaining

the output power of the relay within its power limits when hsr is very low. The

end-to-end SNR of the relaying path, γsrd, can be obtained as [29, 30],

γsrd =Es | hsr β hrd |2

Nd +Nr | β hrd |2

=γsr γrd

γsr + γrd + 1(2.6)

where, γsr =Es |hsr|2Nr

and γrd =Er |hrd|2

Ndare the instantaneous SNR of source-relay

and relay-destination channels, respectively.

Another choice for the relay gain, which ignores the noise at the relay can be

expressed as [29],

β =

√Er

| hsr |2 Es. (2.7)

With this approach γsrd can be calculated as,

γsrd =γsr γrdγsr + γrd

. (2.8)

In both these methods, the relay uses the instantaneous CSI of the rst hop

for signal amplication. These type of relays are called CSI-assisted relays [26].

On the other hand, blind relays [26] amplify the signal with a xed gain regardless

of the rst hop channel condition.

Among the dierent available relaying protocols, AF relaying is considered

as the simplest relaying mechanism. However, at the relay, the noise component


also gets amplied along with the received signal and forwarded to the destina-

tion. This can diminish the system performance in situations where the rst hop

channel SNR is very poor and the communication involves multiple hops.

2.5.2 Decode-and-Forward Method

With DF method, the relay attempts to decode or detect the received signal and

then retransmits the decoded signal. This method is also known as regenerative

relaying [26] or digital relaying [27]. With the TDMA channel model shown in

Figure 2.4, during the second time slot, the relay decodes the received signal

Yr[t] and makes an estimate Xs[t] of the source transmitted signal. The relay

transmitted signal with DF relaying can be expressed as [19],

Xr[t+ 1] =√Er Xs[t]. (2.9)

The end-to-end SNR of a two-hop DF relay system can be computed as [30],

γsrd = γsr + γrd. (2.10)

The regenerative relaying has the advantage over nonregenerative (AF) relay-

ing in reducing the eect of additive noise at the relay. However, if the decoded

signal at the relay is incorrect there is the possibility of forwarding an erroneously

detected signal to the destination and eventually reduces the system performance

[30]. Also compared to AF relays, the DF systems require more complex relays

to fully decode and re-encode the signal.

2.6 Fixed and Adaptive Relaying

In cooperative relaying, relays may always cooperate with their partners or they

may choose to cooperate only when necessary. This leads to two dierent co-


operative relaying strategies namely, xed relaying and adaptive relaying [30].

In xed relaying, the relay always cooperates with the source, using either AF

or DF protocol, regardless of the interuser (source-relay) channel condition. On

the other hand, in adaptive relaying, the relay judiciously selects its operation

depending on the instantaneous channel conditions and user requirements. It is

shown in [19] that the xed AF relaying achieves full diversity gain. However

xed DF scheme does not oer full diversity gain. The need for the relay to fully

decode the received signal limits diversity gain of the xed DF method to that of

the direct transmission between the source and destination.

When the source-destination link is good and when the interuser channel is

very poor, relay transmission would be useless for signal detection at the desti-

nation. In such situations, relay's transmission would be wasted and ultimately

the overall spectral eciency will be reduced [19]. As a solution to this prob-

lem, adaptive relaying protocols can be employed such that, the relays transmit

only when necessary. This section presents two such adaptive relaying protocols:

selection relaying and incremental relaying.

2.6.1 Selection Relaying

With selection relaying (also known as selective relaying [30]), users cooperate

only when the SNR of the signal received at the relay, γsr, exceeds a predened

threshold γth. If the interuser channel between the source and the relay suers

from severe fading such that γsr falls below γth, the users revert to non cooperative

mode [19]. If the CSI of the source-relay link is available at the appropriate

receivers, γsr can be measured to high accuracy by the cooperating relays. Thus

they can adapt their transmission format according to the realized value of γsr

[30]. If the measured γsr < γth, the source simply continues its transmission to

the destination in the form of repetition codes or more sophisticated single-user

coding schemes to justify cooperation, and the relay stays idle. On the other


hand, if the measured γsr > γth, the relay forwards what it received from the

source, using either AF or DF methods [19]. The results in [19] show that the

selection DF protocol achieves full diversity gain. This is in contrast to the xed

DF protocol which does not oer full diversity gain.

2.6.2 Incremental Relaying

With incremental relaying, users cooperate only when the destination requires

cooperation from the relay. It is assumed that there is a feedback channel from

the destination to the relay. Then the destination sends an acknowledgement to

the relay if it was able to receive the source message correctly in the rst trans-

mission phase, so the relay does not need to transmit. If the source transmission

in the rst phase is successful, then there is no second phase and the source trans-

mits new information in the next time slot. As explained in [19] and [31], this

protocol has the best spectral eciency among the other protocols since the relay

transmission becomes opportunistic depending on the feedback. Also [19] shows

that the incremental relaying with AF method achieves full diversity gain.

2.7 Orthogonal Frequency Division Multiplexing

Orthogonal frequency division multiplexing (OFDM) is used for high bandwidth

data transmission to avoid frequency selective fading and inter symbol interfer-

ence (ISI). The basic idea here is to divide the transmitted bit stream into many

dierent substreams and send them over dierent orthogonal subchannels (sub-

carriers) [32]. The bandwidth of each subcarrier is much less than the coherence

bandwidth of the channel, so the subcarriers do not experience frequency selec-

tive fading. Also the data rate of each subcarrier is much less than the total data

rate. OFDM is currently used in many wireless systems including digital sub-

scriber lines (DSL), Wireless LANs (IEEE 802.11), WiMAX (IEEE 802.16), next

generation cellular systems (4G-LTE) and Digital Video Broadcasting (DVB).


The major advantage of OFDM is that, it can be eciently implemented

digitally with discrete Fourier transform (DFT) technique [32]. The DFT of a

N-dimensional input symbol x is,

X =

X0

X1

...

XN−2

XN−1

(2.11)

where,

Xn =1√N

N−1∑k=0

xke−j 2π

Nkn, ∀n ∈ [0 : N − 1] (2.12)

and

x =

x0

x1...

xN−2

xN−1

. (2.13)

The corresponding inverse DFT is given by,

xk =1√N

N−1∑n=0

Xnej 2πNkn, ∀ k ∈ [0 : N − 1]. (2.14)

The DFT and inverse DFT are generally implemented using the fast Fourier

transform (FFT) and inverse fast Fourier transform (IFFT) algorithms. Figure

2.5 illustrates a typical implementation of the baseband OFDM transmitter and

receiver using FFT and IFFT modules. At the transmitter, the incoming bit

stream is rst forward error-correction (FEC) encoded, followed by the modula-

tor. Then the data is passed through a serial-to-parallel converter to create the

multiple independent bit streams. The number of bit streams should be equal


to the number of subcarriers in the OFDM system. Next, these bit streams are

combined by an IFFT block. The input to the IFFT block are the discrete fre-

quency domain samples and the corresponding output is the discrete time domain

samples of the signal to be transmitted. These samples are then sent through

a parallel-to-serial converter and a digital-to-analog converter to generate the

transmitted signal. The reverse operation is carried out at the OFDM receiver.

FEC

encoder

Modulat

-or

Serial

to

Parallel

converter

Inverse

FFT

Parallel

to

Serial

converter

D/A

converter

.

.

.

.

Input bit

stream

Transmitted

signal

A/D

converter

Serial

to

Parallel

converter

FFT

Parallel

to

Serial

converter

Demodul-

ator

FEC

decoder

Received

signal.

.

.

.

output bit

stream

(a)

(b)

Figure 2.5: Block diagram of (a) OFDM transmitter (b) OFDM receiver

When using high data rate transmissions, OFDM is considered as a better al-

ternative for time domain equalizers to mitigate ISI [33]. But the system design-

ers have to face challenges such as frequency and timing oset, peak-to-average

power ratio (PAPR) and at fading experienced by individual subcarriers [33].

This thesis concerns on resource allocation in relay assisted OFDM networks.

Hence, addressing the above mentioned challenges inherent in OFDM systems is

out of the scope of this research.


2.8 Orthogonal Frequency Division Multiple

Access

Orthogonal frequency division multiple access (OFDMA) is the multiple access

version of OFDM. OFDM transmissions can also be combined with other multiple

access techniques such as TDMA (OFDM-TDMA) and CDMA(OFDM-CDMA).

As an example, in OFDM-TDMA, time slots in multiples of OFDM symbols are

allocated for dierent users, i.e., all the subcarriers in the OFDM symbol are

allocated to one user during a particular time period.

User 1

Destination

User 2 User k

User K

. . . . . . . . . .

User 1 User 2 User k User K

Frequency

. . . . . . . .

1 2 3 4 5 6 7 8 910 1112 13 14 . . . . . . . . . . . N

Figure 2.6: Multiple access with OFDMA

In OFDMA, multiple user signals are separated in both time and/or frequency

[34]. As a result of this, groups of OFDM symbols and/or groups of OFDM sub-

carriers are the units used to separate transmissions of dierent users. Figure 2.6

illustrates a typical multiple access system where K user terminals communicate

with a common destination using OFDMA. The total number of subcarriers is

considered to be N . Dierent users are allocated dierent orthogonal subcarriers

such that, at a given time, one subcarrier is allocated to only one user. This

allows all the users to transmit at the same time.


The block diagram of the considered multiple access system is shown in Figure

2.7. Xk,i is the data symbol transmitted by the user k using the subcarrier i. Xk,i

is non-zero if and only if the subcarrier i is assigned to user k [35]. The subcarriers

which are not assigned to the kth user are fed with zeros. The OFDM transmitter

and receiver operation can be replaced by the respective block diagrams shown

in Figure 2.5.

OFDM

Transmitter

.

.

.

.

.

.

X1,1X1,2

X1,N

OFDM

Transmitter

Xk,1Xk,2

Xk,N

OFDM

Transmitter

XK,1XK,2

XK,N

h1

hk

hK

OFDM

Receiver

Y1Y2

YN

n

.

.

.

.

.

.

.

.

Figure 2.7: Block diagram of OFDMA system

Each user constructs and transmits the corresponding OFDM symbols simul-

taneously. The received signal at the destination is the superposition of all the

signals transmitted by the K users. After inverting the transmitter operation at

the receiver, the ith subcarrier signal received at the destination can be expressed

by,

Yi =K∑k=1

Ak,iXk,iHk,i + n (2.15)

where, k ∈ [1 : K], and i ∈ [1 : N ] indicate the kth user and ith subcarrier,

respectively. The element Ak,i indicates the subcarrier allocation and Ak,i = 1 if

and only if the subcarrier i is allocated to user k. Otherwise Ak,i = 0. Hk is the


N-point FFT of the channel impulse response hk. n denotes the AWGN at the

destination.

2.9 Cooperative OFDM Networks

As mentioned in Section 2.7, OFDM is used in broadband communications as an

eective method to mitigate frequency selective fading and ISI. However, sub-

carriers of a properly designed OFDM network may experience at fading with

dierent amplitudes [36]. Thus cooperative diversity schemes can be used at

each subcarrier to reduce the eect of at fading. Nevertheless, special coopera-

tion strategies are needed to eciently exploit the available multiple subcarriers.

This section describes dierent means of applying cooperative relaying in OFDM

networks.

The basic idea in cooperative OFDM is to treat each available subcarrier as

an independent channel for cooperation. This provides the freedom to select

the best relaying protocol for each subcarrier. Since there are independently

fading subcarriers, it would be benecial for the relay terminal to use the best

cooperative strategy for each subcarrier. A hybrid forwarding scheme is proposed

in [37], which adaptively chooses to switch between AF, DF, or `no relay' modes

according to the channel condition between the source-relay and relay-destination

links. The decision is made on per subcarrier basis. The results show that

the hybrid forwarding scheme of [37] achieves lower bit-error-rate than the xed

relaying method, where the same relaying protocol (AF or DF) is applied on all

the subcarriers.

Since subcarriers are treated as independent channels, there is the exibility to

transmit dierent subcarriers via dierent relays [8]. Figure 2.8 illustrates a multi-

relay cooperative OFDM system, where dierent subcarriers are traversed via

dierent relays. Hence, relays use OFDMA to transmit data to the destination.

Furthermore, multicarrier transmission provides the opportunity for subcarrier


rearrangement or subcarrier pairing [38] at the relay, where the data received on

one subcarrier is forwarded via a dierent subcarrier.

Source

R1

Destination

Time slot n

Time slot n+1

R2

Rk

RK

1

2

3

4

5

N

2

4

1

5

N

.

.

.

.

.

.

.

.

Subcarriers 3

6

7

Figure 2.8: Multi-relay assisted cooperative OFDM system model.

Duval et al. in [39] propose a selective subcarrier relaying method where only a

selected set of subcarriers is retransmitted by the relay. In the rst transmission

phase, the source transmits the OFDM signal, and it is received by the relay

and the destination. During the second phase, the relay transmits the selected

subcarriers, while the source retransmits the other nonrelaying subcarriers. It

has been shown in [39] that, by carefully selecting the required subcarriers to be

relayed, this approach results in better performance than relaying all the available

subcarriers.

Siriwongpairat et al. in [40] propose a cooperative protocol for multiuser

OFDM networks, where multiple users are helped by a single xed relay. All the

users communicate with a central node. The proposed protocol is based on incre-

mental relaying [19], and improves spectral eciency over xed relaying protocols


while achieving the full diversity gain. This method involves two communication

phases. During the rst phase, each user transmits data to the relay and the

central node, which is considered as the destination. Then the destination speci-

es the subcarriers that are not successfully received, by broadcasting the indices

of those unsuccessfully received subcarriers. During the second phase, the relay

retransmits information on the subcarriers which are specied by the destination.

Since the relay does not transmit on all the subcarriers, one relay can send infor-

mation of more than one user in a single OFDM symbol making ecient use of

the available bandwidth.

User j

User i

Destination

Time slot n

Time slot n+1

1

2

3

4

5

N

.

.

.

Subcarriers

12345

N

.

.

.

Time slot n

User j’s dataUser i’s data

Subcarriers

Figure 2.9: Shared subcarrier cooperation with two-user cooperative OFDM sys-tem.

In order to take the advantage of available multiple subcarriers in a multiuser

cooperative OFDM network, a shared subcarrier cooperation method is proposed

in [41]. Unlike conventional cooperative communication, there are no dedicated

stages for direct transmission and relayed transmission. Rather, the users trans-

mit their own information and partner's information together in their allocated

time slot. As depicted in Figure 2.9, the users try to help each other by using a

portion of its subcarriers to transmit other user's data on its allocated time slot,


i.e., the users simultaneously transmit their own data and their partners' data in

the same OFDM symbol. In this way, the spectral eciency of the cooperative

OFDM system can be improved.

Space-time (ST) coding techniques [42] also have been studied with coopera-

tive OFDM networks. The work in [43] presents a space time coding technique for

a single-relay assisted cooperative OFDM network. The proposed method divides

the transmit data frame into two subframes, listening subframe and cooperation

subframe. Each subframe comprises the same signal components. During the

rst phase, the source transmits the listening subframe, which is received by the

destination and the relay. If the destination succeeds in decoding the listening

subframe, the following cooperation phase is ignored at the destination. Other-

wise, the destination attempts to decode the cooperation subframe. During the

cooperation phase, both the source and the relay construct the corresponding

cooperation subframes, which together construct the complete ST coded signal.

Since the destination receives a ST coded signal in the cooperation phase, it can

decode the cooperation subframe more reliably than the listening subframe. It

has been shown in [43] that this protocol achieves signicant performance gain

over single antenna OFDM with a diversity gain equivalent to double antenna

OFDM systems.

2.10 Cognitive Radio

In recent years, dynamic spectrum access techniques [44] have gained wide at-

tention due to the scarcity of radio spectrum and the inecient utilization of

xed (licensed) spectrum allocation. Regulatory bodies in dierent parts of the

world assign the available radio spectrum to licensed users, also known as pri-

mary users (PUs), on a long-term basis to be used over large geographical areas.

However, according to a report published by the Federal Communications Com-

mission (FCC) in November 2002 [4], none of these assigned frequency bands


are perfectly utilized at all the time. Some frequency bands in the spectrum are

largely unoccupied most of the time while some others are heavily used. The

inecient usage of the limited radio spectrum necessitates the development of

dynamic spectrum access techniques, where the unlicensed users, also known as

secondary users (SUs), are allowed to use the unused frequency bands in an op-

portunistic manner [45].

Cognitive radio (CR) [5, 6, 7] has been identied as a promising technology

to realize the dynamic or opportunistic access to the underutilized radio spec-

trum. A cognitive radio is a radio that has the ability to dynamically change

its transmission parameters according to the information gathered from its sur-

rounding environment [45]. CRs have two main characteristics, namely, cognitive

capability and recongurability [44, 45]. The cognitive capability refers to the abil-

ity to capture or sense the information from the surrounding radio environment.

The recongurability denes the ability to dynamically adjust transmission pa-

rameters, such as operating frequency, modulation technique, and transmission

power according to the information gathered from the radio environment. In

CR perspective, a band of frequencies unoccupied by the respective PUs at a

given time and a specic geographic location is referred as a spectrum hole or a

white space [6]. With CR technology, the unlicensed SUs are designed to have

CR capabilities, so they can detect the available spectrum holes and adjust their

transmission frequencies accordingly to make use of these spectral opportunities.

Therefore, CR technology brings better spectrum utilization by allowing SUs to

use or share the underutilized licensed frequency bands when they would not

introduce unacceptable level of interference to the PUs.

There are three main functionalities of CR: spectrum sensing, spectrum man-

agement and hando, and spectrum sharing.

• Spectrum sensing : CR monitors the available spectrum bands to detect

the spectrum holes. Also, when PUs start transmission on these licensed


frequency bands, CR detects their activity through sensing, so that it can

release those specic frequency bands.

• Spectrum management and hando : CR may also require to change the

transmission frequencies according to time varying characteristics of the ra-

dio environment and the presence of the PU activity on the identied spec-

trum holes. When a PU activity is sensed on a particular frequency band,

the CR may need to release that frequency band and direct its transmission

on another available spectrum hole to ensure continuous transmission [45].

• Spectrum sharing : Spectrum sharing is also known as transmission oppor-

tunity exploitation [46]. In dynamic spectrum access environment, a CR

may share the spectrum resources with PUs, other SUs, or both [45]. There

are two main approaches for SUs to access the shared licensed spectrum:

spectrum underlay and spectrum overlay [44, 45]. In spectrum underlay

method, SUs are allowed to simultaneously transmit on the licensed fre-

quencies when PUs are also transmitting. In order to enable simultaneous

transmission, SUs should properly control their transmit power to avoid

harmful interference to the PU receivers. Alternately, in spectrum overlay

approach, SUs use the licensed spectrum only when PUs are not transmit-

ting on those frequencies. This approach is also known as opportunistic

spectrum access [45, 47].

CR technology is currently being evaluated by regulators as the technology

that would enable better spectrum utilization by allowing unlicensed devices to

access the available frequency white spaces. In particular, cognitive access to

unused portions of TV spectrum, known as TV white space (TVWS), has al-

ready gained an upsurge of attention in many parts of the world including United

States, United Kingdom and Europe [14, 15, 48, 49, 50]. Furthermore, several in-

ternational standardization activities can be found on cognitive access in TVWS

[51, 52, 53, 54]. One such standard is the IEEE 802.22 wireless regional area


network [54] which is designed to provide xed broadband access in rural ar-

eas. ECMA 392 [55, 56] is another standard which has been developed to enable

personal/portable devices to access the TVWS. In addition, the IEEE 802.11af

standard [56], which attempts to dene a WiFi like protocol for portable devices

operating in TVWS is also under development.

2.10.1 OFDM for Cognitive Radio

OFDM has been identied as a potential transmission technology for CR systems

due to its underlying sensing and spectrum shaping capabilities, exibility, and

adaptability [57, 58, 59]. A CR system needs to be highly exible in terms

of spectrum allocation, and requires to eciently ll the spectral holes left by

the licensed users. OFDM is a candidate for such exible CR systems as it is

possible to leave a set of subcarriers unused providing an adaptive transmit lter

[59]. The basic idea of OFDM-based CR networks is to match the bandwidth

of one subband of the licensed system with an integer multiple of the carrier

spacing used in the OFDM-based CR network [57]. As shown in Figure 2.10

[57], the subcarriers which are not allowed to be used by the CRs can be fed

with zeros, thus sparing these subcarriers from the emission of radio power. This

allows spectral coexistence of both licensed and cognitive systems with very low

mutual interference. Another advantage of OFDM is that, the FFT operation in

the OFDM receiver can be used for the analysis of the spectral activity of the

licensed users.

2.11 Cooperative Relaying in OFDM-Based Cog-

nitive Radio Networks

Spectrum sensing and transmission opportunity exploitation are the main chal-

lenges faced by CRs. In the context of a CR network, cooperative transmission


Frequency bands used by licensed users (PUs)

Deactivated subcarriers due to PU access OFDM subcarriers used by

secondary users (SUs)

0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1

frequency

Figure 2.10: Subcarrier allocation in OFDM-based cognitive radio system

can be used to improve both spectrum sensing and transmission opportunity ex-

ploitation [60, 61]. This leads to two dierent scenarios for cooperative relaying

in CR networks : cooperative spectrum sensing and cooperative spectrum sharing

[60]. This thesis is focused on cooperative spectrum sharing, which is also known

as cognitive wireless relay networks [60, 62], where one or more CRs act as relay/s

to help the transmission between a source node and a destination node.

2.11.1 OFDM Cognitive Wireless Relay Networks

Cooperative spectrum sharing can give rise to two basic scenarios: cooperative

transmission between SUs, and cooperative transmission between primary and

secondary users [46]. In the rst case, a secondary user/s acts as a relay/s for

another secondary user and aims to increase the secondary throughput for a

given frequency white space [46, 60, 63]. In the latter scenario, the secondary

users relay the trac of a primary user [64, 65]. Helping primary users to nish

their transmissions as quickly as possible will, in turn, generate more transmission

opportunities for secondary users.

A model of a cognitive wireless relay network is shown in Figure 2.11. The

relay nodes are CRs distributed over a large geographic area, and several PUs are


operating in the proximity of the CR network. The source and the destination can

be either SUs or PUs. Same as the conventional relay networks, cognitive relay

networks also operate in two phases. In the rst phase, the source broadcasts

its data and it is received by the destination and all the intermediate CR relays.

In the second phase, depending on the relaying protocol used, the CR relays

retransmit the received data to the destination.

S

D

CR

CR

CR

CRPU

PU

CR network

Phase 1

Phase 2

Figure 2.11: Cognitive wireless relay network

Cognitive wireless relay networks can be used to achieve spatial diversity

and/or coverage expansion [63]. As shown in Figure 2.11, if the source trans-

mitted data is received by the destination through the direct path and other

multiple paths created by the relays, spatial diversity can be achieved via coop-

erative relaying. However, in some situations, the direct path between the source

and the destination may be blocked by shadowing and it may not be possible to

achieve direct transmission. It may also happen that the secondary source has to

transmit high power in order to directly communicate with the secondary desti-

nation. This might create signicant interference to primary receivers. Hence, it

may not be possible for the secondary source to directly communicate with the

destination. In these circumstances, an intermediate cognitive relay can be used

to achieve the end-to-end communication by creating a dual-hop channel between


the source and the destination. This may extend coverage, reduce interference

and increase throughput. Further, it may also happen that there is no common

frequency band available at the secondary source and the secondary destination

to communicate. Under such circumstances, a relay node which has available

common frequency bands with both the source and the destination can be used

to assist the communication [63, 66].

When an OFDM-based CR relay network is considered, each PU operates in

a wide band channel consisting of a number of nonoverlapping frequency bands

[60]. The PUs may occupy all or some of the frequency bands when in opera-

tion. The CRs rst get the spectrum map of its radio environment by spectrum

sensing. The spectrum map implies the available spectrum opportunities in the

CR environment. Compared to conventional OFDM relay networks, the available

frequency white spaces may or may not be dierent from one relay to another

in cognitive relay networks. The CR relays with one or more available spectrum

holes, can use those frequency bands to relay the source data.

2.12 Resource Allocation in Wireless Networks

In this research, adaptive resource allocation methods for OFDM relay networks

are investigated in both non-cognitive and cognitive environments. Adaptive re-

source allocation is used to enhance the network performance and it is one of

the prominent aspects in designing wireless networks [67]. Resource allocation

techniques depend on the resource allocation objective, system limitations, relay-

ing protocol and the system architecture [12]. The resource allocation objective

could be transmission rate maximization, outage probability minimization, bit-

error-rate (BER) minimization, or transmit power minimization. Some systems

are subjected to total network power constraint while some other networks are

limited by individual power constraint at each transmitter. Also the cooperative

network may use either AF or DF protocol for relaying. The system architecture


can be two-hop single-relay, two-hop multi-relay, multi-hop single-relay or multi-

hop multi-relay. Thus, all these factors need to be considered when developing a

resource allocation method for a wireless network.

The following subsections provide an overview of adaptive resource alloca-

tion in cooperative OFDM networks and OFDM-based cognitive wireless relay

networks.

2.12.1 Resource Allocation in Cooperative OFDMNetworks

In cooperative OFDM networks, adaptive subcarrier, bit and power allocation

is essential to obtain optimum system performance. In particular, subcarriers

with large channel gains can employ higher order modulations to carry more

bits per OFDM symbol, while subcarriers with deep fade carry one or even zero

bits per OFDM symbol. As dierent subcarriers experience dierent fades and

carry dierent number of bits, subcarrier power allocation should be performed

accordingly [68]. Even without adaptive bit allocation, transmit power of each

subcarrier can be adjusted to meet their fading conditions [12, 39, 41].

In a singlecarrier, single-relay system, the power allocation problem is to as-

sign the optimum power for each node (i.e., source and relay/s) such that the

resource allocation objective is achieved. In multicarrier systems such as coop-

erative OFDM networks, power allocation implies the adaptive subcarrier power

allocation at source and relay/s subject to a sum power constraint or individ-

ual power constraints. This can be treated as a power optimization problem to

achieve a given optimization objective within a given transmit power constraint.

Substantial amount of studies is available on power allocation in cooperative

OFDM systems with both AF [41, 69, 70, 71] and DF [11, 72, 73] relays taking

capacity maximization as the optimization objective.

Subcarrier power allocation can also be combined with subcarrier pairing [12,

69, 71, 72, 74]. In conventional relaying, the relay forwards the data received


in one subcarrier on the same subcarrier. With subcarrier pairing, data in the

incoming subcarriers at the relay/s is paired with dierent outgoing subcarriers

such that the system performance is improved. It is proved in [74] that ordered

subcarrier pairing (OSP), where the data in the best (with highest SNR) incoming

subcarrier is paired with the best outgoing subcarrier, is optimal for both AF and

DF relay links when optimal power allocation is applied. The conventional OSP

consider only source-relay and relay-destination links, and is optimal for two-hop

communication systems without diversity [71]. For systems with diversity (such as

cooperative OFDM networks), all the three links, source-relay, relay-destination

and source-destination, have to be considered when pairing the subcarriers [71].

Similar strategies can be adapted for multi-relay assisted communication with

relay selection as another dimension of the optimization problem. To fully utilize

the dierent channel conditions of dierent subcarriers, subcarrier based relay

selection can be employed with optimal subcarrier power allocation. Power allo-

cation, subcarrier pairing and relay selection in multi-relay assisted cooperative

OFDM systems can be considered as a joint optimization problem of the three

resources: power, subcarriers, and relay nodes [10, 11, 12]. Such joint opti-

mization methods may provide an optimal solution for resource allocation but

with the expense of higher system complexity. Hence, less-complex but eec-

tive resource allocation methods need to be developed for multi-relay assisted

cooperative OFDM networks. However, such resource allocation methods are not

comprehensively studied in the existing literature.

In relay networks, resource allocation decisions can be made at the source

[75, 76], or a central unit can be employed to make the necessary resource allo-

cation decisions [77]. In general, some knowledge of the source-relay, and relay-

destination channel conditions is required to dynamically allocate the available

resources according to varying channel quality. Most of the prevailing work on

resource allocation in OFDM dual-hop relay links assume that the perfect knowl-

edge of the instantaneous CSI of rst and second hop is available at the time of


resource allocation. In practice, this assumption is hardly realistic. The available

CSI can be outdated due to feedback delay or they can be imperfect due to chan-

nel estimation errors [77, 78, 79]. It is therefore important to investigate resource

allocation methods with practically available imperfect or outdated CSI, which

is barely covered in the current studies.

2.12.2 Resource Allocation in OFDM Cognitive Wireless

Relay Networks

Unlike in non-cognitive relay networks, in cognitive relay networks resource allo-

cation is limited by the interference introduced to the PU receivers. Hence, inter-

ference generated by secondary transmissions should be taken into consideration

when developing resource allocation methods for cognitive wireless relay networks.

The most existing work on spectrum sharing has concentrated on the scenario

where the primary system is capable of tolerating some amount of interference

from the secondary transmission [65]. As a result, a total interference threshold

for the PU system or individual interference thresholds for PU receivers can be

specied. Secondary transmission is then subject to this interference threshold

constraint in addition to the transmit power constraint/s.

Resource allocation in the scenario where SUs act as relays to help the pri-

mary transmission is studied in [64] and [65]. During the cooperating phase, the

primary transmitter allows the secondary relays to use a fraction of the subcar-

riers in the licensed frequency band to transmit primary data. These required

subcarriers are specied by the primary receiver. Since the cognitive relays may

not need to transmit on all the subcarriers of the licensed frequency band, they

can use the remaining subcarriers to transmit their own data.

Most of the existing work investigates resource allocation methods for the

scenario where cognitive relays help the secondary transmission. Considerable

amount of work is available on resource allocation in singlecarrier CR relay net-


works (e.g., [63, 80, 81, 82] and reference therein). The work reported in [83], [84],

[85] and [86] presents subcarrier pairing and power allocation methods for single-

relay assisted OFDM-based secondary transmission. Power allocation methods

are proposed with transmit power constraints at secondary transmitters and in-

terference constraints at primary receivers. Relay selection, power allocation

and subcarrier pairing in multi-relay assisted OFDM cognitive wireless relay net-

works is considered in [13], [87], [88], and [89]. Capacity maximization of the

secondary transmission is taken as the optimization objective. The resource allo-

cation problem is formulated as a joint optimization problem of relays, subcarriers

and transmit powers. An asymptotically optimal solution for joint optimal re-

source allocation is presented and low complexity suboptimal resource allocation

methods are also proposed.

CR transmitters need some information of the CSI between itself and PU

receivers to estimate or predict the amount of interference produced by secondary

transmission. However, in practice, it is infeasible to obtain perfect instantaneous

CSI between primary and secondary networks [90, 91, 92, 93]. Most of the time

the available CSI is outdated due to feedback delay or only the fading statistics

are known at the CR transmitters. Although the availability of outdated or

statistical CSI corresponds to several practical scenarios, it has not been well

investigated when developing resource allocation methods for CR relay networks.

2.12.3 Resource Allocation for Rate Maximization

In this thesis, resource allocation problems are formulated as rate maximization

problems, where the objective of resource allocation is to maximize the end-to-

end transmission rate or the capacity. Transmission rate or capacity is calculated

using Shannon-Hartley theorem [94], which states the maximum information rate

that can be transmitted over a communication channel of a specied bandwidth

in the presence of AWGN. Shannon-Hartley theorem states the channel capac-


ity Cshannon, which is the theoretical tightest upper bound on the end-to-end

transmission rate, of a channel with a bandwidth B is:

Cshannon = B log2

(1 +

S

N

)b/s (2.16)

where S is the average received signal power over the bandwidth and N is the

average noise and/or interference power over the bandwidth. The term S/N is

the end-to-end SNR of the communication signal. The capacity given by (2.16)

can be normalized by the bandwidth and the normalized capacity,

CshannonB

= log2

(1 +

S

N

)b/s/Hz (2.17)

is used in the remainder of this thesis, unless otherwise stated. The terms trans-

mission rate (or simply rate) and capacity are used interchangeably throughout

this thesis to denote the quantity obtained using (2.17).

When an OFDM-based two-hop relay network withN number of subcarriers is

considered, the capacity of one subcarrier (ith subcarrier), Ci, with an end-to-end

SNR γi can be expressed as,

Ci =1

2log2 (1 + γi) b/s/Hz (2.18)

where, the factor 1/2 is due to half-duplex operation. Then the summation over

all the N subcarriers is taken to calculate the capacity of the entire OFDM signal

as,

C =1

2

N∑i=1

log2 (1 + γi) b/s/Hz. (2.19)

If the SNR γi is calculated using actual instantaneous CSI, the resulting capacity

is referred as instantaneous rate or instantaneous capacity.


2.13 Optimization Techniques for Resource Allo-

cation

Many resource allocation problems in wireless networks can be formulated as

constrained optimization problems. There are dierent types of constrained op-

timization problems: linear programs, nonlinear programs, convex optimization

problems and integer programs. This section provides an overview of constrained

optimization problems in the context of wireless resource allocation.

The general formulation of a constrained optimization problem can be written

as [67],

minimize f(x)

subject to gi(x) ≤ 0, for i = 1, . . . ,m

hj(x) = 0, for j = 1, . . . , n

(2.20)

where, x is the set of parameters to be optimized, f(x) is the optimization objec-

tive, gi(x), ∀i, represent the inequality constraints, and hj(x), ∀j, represent the

equality constraints. The optimization process nds the optimal solution x∗ ∈ Ω

which satises all inequality and equality constraints. Here, Ω is the feasible set

for the parameter vector x.

If the optimization goal and all the inequality and equality constraints are

linear functions of x, the optimization problem is a linear program. If either the

optimization objective or the constraints are nonlinear functions of x, the problem

becomes a nonlinear program. If the feasible set Ω contains some integer sets,

the optimization problem is called an integer program. Most integer programs

are nondeterministic-polynomial-hard (NP-hard) problems and dicult to solve

in polynomial time [67].

If the feasible set Ω is a convex set and the optimization goal and the constraint

functions are convex/concave/linear functions of x, the optimization problem is a


convex optimization problem [67, 95]. Convex optimization problems are a special

kind of nonlinear programs. Most of the wireless resource allocation problems can

be formulated as convex optimization problems and they are more mathematically

tractable than other nonlinear programs. In convex optimization problems, any

local optimum is necessary a global optimum, and number of ecient numerical

solution methods are available to solve such problems [95].

The Lagrangian

The Lagrangian associated with the problem (2.20) can be written as,

L(x,λ,υ) = f(x) +m∑i=1

λi gi(x) +n∑j=1

υj hj(x). (2.21)

The parameters λi (λi ≥ 0) and υj are referred as Lagrange multipliers associated

with inequality constraints and Lagrange multipliers associated with equality

constraints, respectively.

The Lagrange dual function

The corresponding Lagrange dual function of the problem (2.20) is dened as the

minimum value of the Lagrangian over x. The dual function can be expressed as,

g(λ,υ) = infx∈Ω

(f(x) +

m∑i=1

λi gi(x) +n∑j=1

υj hj(x)

). (2.22)

The dual function in (2.22) is concave even when the respective optimization

problem (2.20) is not convex [95].


Lagrange dual problem

The Lagrange dual problem associated with the optimization problem in (2.20)

can be written as,

maximize g(λ,υ)

subject to λ ≥ 0.(2.23)

In this context, the original problem in (2.20) is referred as the primal problem.

The Lagrange dual problem in (2.23) is a convex optimization problem regardless

of the convexity of the primal problem [67]. When the primal problem is convex,

both the primal problem (2.20) and the dual problem (2.23) has the same solu-

tion [95]. When the primal problem is nonconvex, the dual problem provides a

solution, which is a lower bound to the solution of (2.20). The dierence between

the lower bound and the true optimum is called the duality gap [95].

When the duality gap is zero, the primal problem can be solved via the dual

problem. This approach is widely used in nonconvex optimization problems as-

sociated with OFDM systems. It is shown in [96], that nonconvex optimization

problems in multicarrier systems has zero duality gap owing to the time-sharing

property of multicarrier systems. This time-sharing condition is satised for many

practical problems with suciently large number of subcarriers.

Karush-Kuhn-Tucker (KKT) optimality conditions

For any optimization problem with zero duality gap, and dierentiable objective

and constraint functions, any pair of primal and dual optimal points must satisfy

the Karush-Kuhn-Tucker (KKT) conditions. If x∗ and (λ∗,υ∗) are the respective

primal and dual optimal points associated with (2.20), the KKT conditions can


be written as follows:

∂L(x,λ∗,υ∗)∂x

∣∣∣x=x∗

= 0

gi(x∗) ≤ 0, i = 1, . . . ,m

hj(x∗) = 0, j = 1, . . . , n

λ∗i ≥ 0, i = 1, . . . ,m

λ∗i gi(x∗) = 0, i = 1, . . . ,m

(2.24)

When the primal problem is convex, the KKT conditions are sucient for the

points to be primal and dual optimal [95]. Hence, the optimal points can be

obtained by solving the KKT conditions. In some cases, the KKT conditions can

be solved analytically to derive closed-form expressions for the optimal solution.

In general, optimization algorithms can be interpreted as methods for numerically

solving the KKT system of equations. Interior-point method/barrier method

[95, 97] is a certain class of algorithms that is widely used to solve the KKT

conditions associated with linear and nonlinear convex optimization problems.

Majority of the resource allocation problems presented in this thesis are for-

mulated as convex optimization problems, and hence can be solved using KKT

conditions. Furthermore, MATLAB optimization toolbox is used to numerically

solve the respective KKT conditions using interior-point method. Detailed anal-

ysis of interior-point method or any other optimization algorithm is out of the

scope of this thesis.

2.14 Conclusion

Frequency selective fading and ISI are two major channel impairments involved

with broadband transmissions. OFDM has been identied as a candidate modu-

lation technique to reduce the eect of frequency selective fading and ISI and is

used with most of the existing broadband wireless systems. On the other hand,

CR concept has been introduced as a method of optimizing the usage of scarce


radio resources, by allowing SUs to transmit on the unused spectrum bands in an

opportunistic manner. OFDM has also been identied as a potential transmission

technology for CR networks.

Cooperative communication and relay transmission is used in OFDM net-

works to reduce the eect of multipath fading, to enhance the coverage and to

improve the throughput. In wireless communication networks, adaptive resource

allocation can be used to improve the network performance. This motivates the

development of resource allocation methods for OFDM relay networks in cogni-

tive and non-cognitive environments. However, resource allocation in multi-relay

assisted cooperative OFDM networks is not comprehensively covered in the cur-

rent studies. Furthermore, resource allocation in OFDM relay and OFDM-based

CR relay networks with practically available imperfect or outdated CSI is barely

addressed in the existing literature. In addition, CR networks in TVWS is gaining

an increasing interest as a prominent application of CR based services. Resource

allocation methods for this practical application is still in its early stage and is

not investigated in detail in the prevailing studies. This thesis aims to address

the aforementioned gaps related to resource allocation studies in OFDM-based

relay and CR networks.

Chapter 3

Resource Allocation in Cooperative

OFDM Networks

3.1 Introduction

Adaptive resource allocation has long been considered as a critical aspect in wire-

less communication. It is equally important in cooperative OFDM networks to

allocate its system resources optimally to reap the maximum benet of coopera-

tion. In cooperative OFDM networks, subcarriers, relays and transmit power are

the resources that can be adaptively allocated to improve the system performance.

Adaptive power allocation in single-relay assisted cooperative OFDM networks

is well investigated in the existing literature [41, 69, 70, 71, 11, 72, 73]. Such

methods involve adaptive subcarrier power allocation at the source and the relay

to achieve a predened target within the limited transmit power available at

source and relay. In cooperative OFDM networks, the power allocation problem

can be further rened with subcarrier selection, where the relay forwards only a

selected set of subcarriers. This selective subcarrier relaying approach improves

the system performance compared with the nonselective case, where the relay

forwards all the subcarriers [39, 72]. The relay node also has the opportunity to

3. COOPERATIVE OFDM NETWORKS 45

forward the signal on the same subcarrier or it can judiciously pair incoming and

outgoing subcarriers to forward the signal in the best available channel [71, 72].

This chapter investigates resource allocation methods for multi-relay assisted

cooperative OFDM networks. With multiple relays, dierent subcarriers can

be transmitted by dierent relays as long as the subcarriers are orthogonal to

each other. As a result, subcarrier based relay selection can be introduced as

another dimension of the resource allocation problem. Recent research work

[10, 11, 12] has considered power allocation and relay selection in multi-relay

assisted cooperative OFDM networks as a joint optimization problem of transmit

power, subcarriers and relay nodes. Such joint optimization methods may provide

an optimal resource allocation, but involves higher computational complexity.

Also these methods may not be feasible to extend for a more realistic scenario

with imperfect channel state information, latency and interference.

This chapter investigates less-complex but eective resource allocation meth-

ods for multiple amplify-and-forward (AF) relay assisted cooperative OFDM net-

works. The selective subcarrier relaying method proposed in [39] for a single-relay

assisted system is adapted for a multi-relay assisted scenario. With selective sub-

carrier relaying, only the subcarriers which have the potential to improve the ca-

pacity via relaying is selected to be retransmitted by the relays [39]. This method

has proven to improve the capacity in single-relay assisted OFDM transmission

with both AF [39] and DF [98, 99] relays. Performance of the subcarrier selection

based resource allocation method is compared with all subcarrier relaying based

method, where the relays collectively forward all the available subcarriers. All

subcarrier relaying in single-relay assisted cooperative OFDM transmission has

been shown to improve the capacity compared with the non-cooperative trans-

mission [69].

Resource allocation methods are proposed for selective subcarrier relaying and

all subcarrier relaying scenarios. For analytical feasibility, the optimization prob-

lem in each case is divided into two subproblems: relay and/or subcarrier selec-


tion, and subcarrier power allocation. Rather than providing a less feasible joint

optimization strategy, the proposed resource allocation methods investigate the

solutions for each subproblem in an optimal manner.

The rest of this chapter is organized as follows. The system and channel model

is presented in Section 3.2. All subcarrier relaying based resource allocation is de-

scribed in Section 3.3, and selective subcarrier relaying based resource allocation

is presented in Section 3.4. Performance of the proposed methods is analyzed in

Section 3.5 along with numerical results.

3.2 System and Channel Model

The cooperative OFDM system considered in this chapter is shown in Figure 3.1.

Here, the source node (s) communicates with the destination (d) through the

help of K number of relays. The destination receives the signals from K + 1 in-

dependent channels and combines them using a maximal-ratio combiner (MRC).

Number of subcarriers in the OFDM transmission is taken as N . It is assumed

that all the K relays operate in AF mode. Further, it is also assumed that the

source and relay nodes support only half-duplex operation. For the simplicity

of presentation, let s denote the source, k denote the kth relay, d denote the

destination and i denote the ith subcarrier.

A TDMA communication model is assumed where each user is allocated a

dedicated time period for its data transmission. For relay assisted communication,

this time period is further divided into two time slots and the communication is

carried out in two orthogonal phases. During the rst phase, the source terminal

transmits a message in the rst time slot and it is received by the destination and

all the K relays in its vicinity. Then in the second time slot, the relays forward

the received signal to the destination according to a subcarrier assignment matrix

A, which determines the subcarriers helped by each relay. A is a K ×N matrix


and its elements are given by,

Ak,i =

1, if kth relay helps ith subcarrier;

0, otherwise.(3.1)

Source

(s)

r1

Destination

(d)

Time slot n

Time slot n+1

r2

rk

rK

1

2

3

4

5

N

2

4

1

5

N

.

.

.

.

.

.

.

.

.

.

Subcarriers3

6

7

Relays

Figure 3.1: Cooperative OFDM system model

Unlike in singlecarrier systems, with multiple subcarriers, there is the ad-

vantage of allocating one time slot for all the relay transmissions if orthogonal

subcarriers are transmitted by each relay. Then, increasing the number of re-

lays will not reduce the spectral eciency of the system. This introduces the

constraint∑K

k=1Ak,i = 1 for all the relaying subcarriers, i.e., only one relay is

assigned for each relaying subcarrier.

In selective subcarrier relaying, relays forward only the selected subcarriers.

Thus, another decision vector µ can be introduced as the subcarrier selection

decision. If ith subcarrier is relayed by one of theK relays then, µi = 1. Otherwise


µi = 0, i.e.,

µi =

1, if∑K

k=1Ak,i = 1 ;

0, otherwise.(3.2)

It is assumed that the fading channel coecients are constant during both

transmission phases. Frequency selective Rayleigh fading channels are considered

for this study. The frequency selective channel, hmn, between nodes m and n;

m ∈ s, k and n ∈ k, d, can be dened in the time domain by,

hmn(t) =L∑l=1

hmn,l δ(t− lT ) (3.3)

where hmn,l is the impulse response of the lth fading path between nodes m and

n, and L is the number of channel taps. In order to take the path loss into

consideration, hmn,l is taken from a complex normal distribution [69],

hmn,l ∼ CN

(0,

1

L(1 + dmn)α

), ∀ l ∈ [1 : L]. (3.4)

Here, dmn is the distance between nodesm and n, and α is the path loss exponent.

The L-dimensional channel impulse response vector hmn represents the eect due

to both the path loss and fading. The N -dimensional frequency response vector of

the channel, Hmn, is given by the N -point FFT of the channel impulse response

hmn.

It is assumed that the source sends data with power Ps,i on the ith subcarrier,

and the kth relay amplies the signal by a factor βk,i using power Pk,i on the same

subcarrier. Then βk,i is given by [19, 39],

βk,i =

√Pk,i

| Hsk,i |2 Ps,i + σ2k

(3.5)

where, σ2k is the noise variance at kth relay. It is assumed that the destination

employs MRC to combine the signals received by relay transmission and source


transmission. When MRC is employed at the destination, the signal-to-noise ratio

(SNR) at the output of the MRC receiver, Γk,i, for all the relaying subcarriers

can be written as the summation of the SNRs of the relayed path and the direct

path as shown in (3.6).

Γk,i =Ps,i | Hkd,iβk,iHsk,i |2

σ2d + σ2

k | βk,iHkd,i |2+Ps,i | Hsd,i |2

σ2d

=Ps,iγsk,iPk,iγkd,i

1 + Ps,iγsk,i + Pk,iγkd,i+ Ps,iγsd,i (3.6)

The rst term of (3.6) represents the SNR of the relayed path and the second

term represents the SNR of the direct path. Here, γsk,i =|Hsk,i|2σ2k

, γkd,i =|Hkd,i|2σ2d

and γsd,i =|Hsd,i|2σ2d

. σ2d is the noise variance at the destination.

If the ith subcarrier is helped by one of the K relays, then the instantaneous

rate of the relaying subcarrier, CR,i, can be written as,

CR,i = µi

K∑k=1

Ak,i1

2log2(1 + Γk,i) b/s/Hz. (3.7)

The factor 1/2 is due to the half-duplex operation. For those subcarriers which

are not helped by any of the K relays, the instantaneous capacity can be given

by (3.8) assuming that the source retransmits these subcarriers during the second

phase.

CS,i = (1− µi) log2(1 + Ps,iγsd,i) b/s/Hz (3.8)

Combining (3.7) and (3.8), the instantaneous rate Ci for the ith subcarrier can

be expressed as,

Ci = µi

K∑k=1

Ak,i1

2log2(1 + Γk,i) + (1− µi) log2(1 + Ps,iγsd,i). (3.9)


Then the instantaneous rate over the entire OFDM symbol with N subcarriers

can be written as,

C =N∑i=1

Ci. (3.10)

The objective of resource allocation is to determine the relay selection, and

subcarrier power allocation to maximize the end-to-end capacity of the OFDM

transmission. Resource allocation methods are proposed for two cases:

• All subcarrier relaying: All the participating relays collectively forward all

the subcarriers of the original OFDM symbol.

• Selective subcarrier relaying: All the participating relays collectively for-

ward only a selected set of subcarriers of the transmitted OFDM symbol.

Resource allocation methods for these two scenarios are described in the subse-

quent sections.

3.3 All Subcarrier Relaying

With all subcarrier relaying approach, which is also known as nonselective relay-

ing, relay nodes collectively forward all the subcarriers in the transmitted OFDM

symbol, i.e., µi = 1, ∀ i. The capacity expression for all subcarrier relaying sce-

nario can be written as,

C =N∑i=1

K∑k=1

Ak,i1

2log2(1 + Γk,i). (3.11)

The objective of resource allocation in this scenario is to maximize the capacity

given by (3.11). The resource allocation problem is divided into two subproblems,

namely, relay selection and power allocation. Each subproblem is then solved in

an optimal manner as described in the following subsections.


3.3.1 Relay Selection

With relay selection, a single relay among the set of K relays is selected for each

subcarrier, depending on which relay provides the `best' end-to-end path between

the source and destination [100]. At this stage, equal transmit power is assumed

for all the subcarriers at the source and the relays to focus only on the idea of

relay selection. Then the relay which provides the best end-to-end SNR is selected

for the respective subcarriers. The end-to-end SNR for relay transmission,

γskd,i =Ps,iγsk,iPk,iγkd,i

1 + Ps,iγsk,i + Pk,iγkd,i. (3.12)

This relay selection method is known as the best end-to-end SNR based relay

selection and is proved to be the optimum single relay selection strategy [101].

With this relay selection approach, the subcarrier assignment matrix A can be

expressed as,

Ak,i =

1, if k = argmax

kγskd,i;

0, otherwise.(3.13)

3.3.2 Power Allocation

With power allocation, the subcarrier transmit power for the given subcarrier

assignment matrix A is optimized to maximize the end-to-end capacity given

in (3.11). It is assumed that the individual transmitters have their own trans-

mit power limitations. Hence, the power optimization is subject to individual

transmit power constraints at source and relays.

With AF relay, power optimization can be performed in two steps: relay

power optimization and source power optimization. The alternate optimization

of source and relay transmit power is widely used with AF relays, and it is proved

to converge to the optimal solution using only a few iterations [69]. Figure 3.2

illustrates this iterative optimization process. First, the source transmit power is


initialized such that uniform transmit power is assigned for all the subcarriers at

the source. The iterative optimization process is started with this initial source

power allocation, and the subcarrier transmit powers at the relays are optimized

such that the total capacity is maximized. Then, for this optimized relay power

allocation, the subcarrier transmit power at the source is optimized. These two

steps are alternately carried out such that the output of the previous optimization

is the input to the next optimization until convergence has been achieved.

Initialize

Initialize source power

(Ps,i=PS/N)

Power optimization at

Relays

Power optimization at

Source

PS

Does capacity

increase?

Return results

Does capacity

increase?

Yes

No

Yes No

Figure 3.2: Flowchart of two-step iterative power allocation

The relay and source power optimizations can be described as follows.


A. Power Allocation at Relays

For a given source power allocation, the subcarrier transmit powers at all the

participating relays can be jointly optimized such that the capacity is maxi-

mized. When the relay selection is known and the N -dimensional source transmit

power vector Ps is known for all the subcarriers, the relay transmit power vector

Pk, ∀ k ∈ [1 : K] is optimized such that the instantaneous rate C in (3.11) is

maximized. Since each node has individual power limitations, the constraints for

relay power optimization can be expressed as,

N∑i=1

Ak,iPk,i = Pk, ∀ k ∈ [1 : K] (3.14)

where Pk is the maximum transmit power of the kth relay. The joint optimization

problem of relay transmit powers can be formulated as,

MaximizeN∑i=1

K∑k=1

Ak,i1

2log2 (1 + Γk,i) (3.15)

subject to,

∑Ni=1Ak,iPk,i ≤ Pk, ∀ k

Pk,i ≥ 0, ∀ k, i(3.16)

The objective function in (3.15) is a maximization of a concave function of

Pk,i and the constraints in (3.16) are linear functions of Pk,i. Hence this is a con-

vex optimization problem, and can be solved using Karush-Kuhn-Tucker (KKT)

conditions [95]. The solution for the optimal relay transmit power P ∗k,i can be

obtained as,

P ∗k,i =

Ak,i (1 + Ps,iγsk,i)

2γkd,i (1 + Ps,iγsk,i + Ps,iγsd,i)

[Ps,iγsk,i

√1 + [·]

]+[·] =

4γkd,i (1 + Ps,iγsk,i + Ps,iγsd, i)

υk ln(2)Ps,iγsk,i(1 + Ps,iγsk,i)(3.17)


where, [x]+ = max(0, x), and the constants υk, k ∈ [1 : K] are non-negative

Lagrange parameters which are selected such that the sum power constraints in

(3.16) are satised.

B. Power Allocation at Source

After optimizing the transmit powers at relays, the source transmit power Ps can

be optimized such that the instantaneous capacity is maximized within a given

maximum transmit power at the source. The power constraint for source power

optimization can be expressed as,

N∑i=1

Ps,i = Ps (3.18)

where Ps is the maximum source transmit power.

Then the optimization problem can be formulated as,

MaximizeN∑i=1

K∑k=1

Ak,i1

2log2 (1 + Γk,i) (3.19)

subject to,

∑Ni=1 Ps,i ≤ Ps

Ps,i ≥ 0(3.20)

In order to get a mathematically tractable solution for source power allocation,

it is assumed that |Hsd,i| ≪ 1, so the SNR in (3.6) can be approximated as [39],

Γk,i ≈Ps,iγsk,iPk,iγkd,i

1 + Ps,iγsk,i + Pk,iγkd,i.

With the above approximation, it is possible to solve the optimization problem

in (3.19)-(3.20) using KKT conditions. A marginally optimal solution for source


power allocation P ∗s,i can be obtained as,

P ∗s,i =

Ak,iγsk,i

[−1 +

Pk,iγkd,i2

(−1 +

√1 +

2γsk,iλ ln(2)γkd,iPk,i

)]+. (3.21)

The non-negative Lagrange parameter λ is selected such that the source power

constraint in (3.20) is satised.

A detailed derivation of the solutions of relay and source power optimization

problems is given in Appendix A. These optimizations can be solved numerically

using interior-point method with a complexity of O(N3) [95].

3.4 Selective Subcarrier Relaying

With selective subcarrier relaying, only a selected set of subcarriers, which has

the potential to improve the system performance via relaying, is retransmitted

by the relay/s. Duval et al. in [39] propose a selective subcarrier relaying based

power allocation method for a single-relay system which achieves higher capacity

than the nonselective relaying scheme. The proposed method in [39] selects the

subcarriers to be relayed such that the overall capacity is maximized through

relaying. In this section, the selective subcarrier relaying concept presented in

[39] is applied for multi-relay assisted cooperative OFDM transmission. If the ith

subcarrier is relayed by kth relay (i.e., Ak,i = 1), the capacity expression for ith

subcarrier in (3.9) can be rewritten as [39],

Ci =1

2log2

[(1 + Γk,i

(1 + Ps,iγsd,i)2

)µi]+ log2(1 + Ps,iγsd,i). (3.22)

The rst term of the above expression represents the capacity improvement

achieved by relaying ith subcarrier through kth relay. Accordingly, a capacity


improvement factor Ξ(Pk,i, Ps,i) can be dened as,

Ξ(Pk,i, Ps,i) =

(1 + Γk,i

(1 + Ps,iγsd,i)2

). (3.23)

To improve the capacity through relaying the capacity improvement factor should

be greater than 1 (i.e., Ξ(Pk,i, Ps,i) > 1) for all the relaying subcarriers. Based on

this condition a subcarrier selection criterion can be derived as [39],

γsk,i > γsd,i(Ps,iγsd,i + 1). (3.24)

Then, all the subcarriers which do not satisfy the condition (3.24) for any of the

K relays will not be relayed and they will be retransmitted by the source during

the relaying phase.

Duval et al. in [39] derive an expression for the minimum relay power required

for capacity improvement of each subcarrier. In multi-relay environment, the

same expression can be considered as the minimum power required by the kth

relay to improve the capacity of the ith subcarrier, Pmink,i . Pmin

k,i can be expressed

as [39],

Pmink,i =

γsd,i(Ps,iγsk,i + 1)(Ps,iγsd,i + 1)

γkd,i(γsk,i − γsd,i(Ps,iγsd,i + 1)). (3.25)

When selective subcarrier relaying is applied in a multi-relay environment, it

is necessary to perform a joint selection of subcarriers and relay nodes such that

the end-to-end capacity is maximized. Thus the optimization problem can be

studied under two subproblems as elaborated in the following subsections.

3.4.1 Subcarrier and Relay Selection

First, it is necessary to select the subcarriers to be retransmitted by the relays.

For this, the condition (3.24) is checked for all the subcarrier-relay pairs and the

subcarriers which satisfy (3.24) for one or more relays is selected for relaying. A


K ×N subcarrier selection matrix B can be dened as,

Bk,i =

1, if γsk,i > γsd,i(Ps,iγsd,i + 1) ;

0, otherwise,(3.26)

Then, the subcarrier selection decision µi can be obtained as,

µi =

1, if∑K

k=1Bk,i ≥ 1 ;

0, otherwise,(3.27)

Since more than one relay can satisfy the condition (3.24) for one subcarrier, it

is necessary to select the `best' relay for each selected subcarrier. Hence, two

relay selection methods are presented in this subsection and their performance is

investigated in Section 3.5.

Relay Selection: Method A

The rst relay selection method is based on the minimum relay power required for

capacity improvement, Pmink,i . Pmin

k,i is calculated for all the subcarrier-relay pairs

which satisfy condition (3.24). Then the relay with the minimum Pmink,i is selected

for the ith relaying subcarrier. This relay selection criterion can be expressed as,

Ak,i =

1, if k = argmin

kBk,i P

mink,i ;

0, otherwise.(3.28)

After selecting the best relay for each subcarrier, the power constraint (3.14)

for each participating relay needs to be veried. Thus for each relay, the subcarri-

ers which utilize the highest power for capacity enhancement is removed until the

relay power limitation is satised, i.e., Ak,i and µi is set as 0 for subcarriers with

the largest Ak,iPmink,i value until

∑Ni=1Ak,iP

mink,i ≤ Pk. This method is referred as

Selective relaying-A throughout the rest of this chapter.


Relay Selection: Method B

The second relay selection method is based on the best end-to-end SNR based

relay selection method described in Section 3.3.1. The intention here is to se-

lect the relay which provides the best end-to-end channel gain for the respective

subcarriers. For this purpose, γskd,i is calculated as shown in (3.12) for all the

subcarrier-relay pairs that satisfy condition (3.24). For each relaying subcarrier,

the relay with the maximum γskd,i is selected, i.e.,

Ak,i =

1, if k = argmax

kBk,i γskd,i;

0, otherwise.(3.29)

Then for each relay, the power constraint (3.14) is veried and those subcar-

riers with the highest Pmink,i values are removed until the relay power constraint

is satised. This approach is referred as Selective relaying-B in the remainder of

this chapter.

3.4.2 Power Allocation

Once the subcarrier selection decision µ and the subcarrier-relay assignment ma-

trixA are known, the relay and source transmit powers are optimized to maximize

the capacity given in (3.10). This power optimization is subject to separate power

constraints at the source and the relays. As explained in Section 3.3.2, with AF

relays, two-step iterative power optimization can be used to nd the optimum

relay and source transmit powers. These two optimization steps with selective

subcarrier relaying can be described as below.

A. Power Allocation at Relays

When the source transmit power Ps is known, the subcarrier transmit power at

each participating relay can be jointly optimized. The objective here is to max-


imize the total capacity improvement∑N

i=1

∑Kk=1Ak,i log2 Ξ(Pk,i, Ps,i) subject to

the power constraints (3.14) [39]. Here, Ξ(Pk,i, Ps,i) can be calculated as given

in (3.23). Once the capacity improvement is maximized it will inherently maxi-

mize the total capacity achieved via relaying. This optimization problem can be

formulated as,

MaximizeN∑i=1

K∑k=1

Ak,i log2 Ξ(Pk,i, Ps,i) (3.30)

subject to,


Pk,i ≥ Pmink,i , ∀ k, i

(3.31)

This is a convex optimization problem and the solution for the optimal relay

transmit power P ∗k,i can be obtained as,

P ∗k,i = max

Pmink,i ,

Ak,i (1 + Ps,iγsk,i)

2γkd,i (1 + Ps,iγsk,i + Ps,iγsd,i)[·]

[·] = Ps,iγsk,i

√1 +


νk ln(2)Ps,iγsk,i(1 + Ps,iγsk,i)(3.32)

The constants νk, k ∈ [1 : K] are non-negative Lagrange parameters which are

selected such that the sum power constraints in (3.31) are satised. The derivation

of this solution follows the same procedure as for the solution for relay power

optimization in Appendix A.

B. Power Allocation at Source

When the relay transmit powers Pk, ∀k ∈ [1 : K], and the subcarrier assignment

matrix A are given, the source transmit powers for all the N subcarriers, Ps, can

be optimized such that the instantaneous rate C in (3.10) is maximized. This

power optimization problem can be solved in a similar fashion as described in

[39]. The optimization is subject to the source power constraint. Further, for


all the relaying subcarriers, the optimized source transmit power should satisfy

the capacity improvement requirement∑K

k=1Ak,i Ξ(Pk,i, Ps,i) > 1. After some

mathematical manipulations this condition can be reformulated as [39],

Ps,i < Pmaxs,i (3.33)

where,

Pmaxs,i =

∑Kk=1Ak,i

√[·]−(γsk,i+γsd,i(Pk,iγkd,i+1))

2γsk,iγsd,i, for γsk,i > γsd,i

[·] = (γsk,i + γsd,i (Pk,iγkd,i + 1))2 − 4γsk,i (Pk,iγkd,i (γsd,i − γsk,i) + γsd,i) .

(3.34)

The source power optimization problem can be expressed as below.

MaximizeN∑i=1

Ci (3.35)

subject to,

∑Ni=1 Ps,i ≤ Ps

µi Ps,i < Pmaxs,i , ∀ i

Ps,i ≥ 0

(3.36)

This optimization problem can be solved for two cases, i.e., µi = 1 and µi = 0.

For the relaying subcarriers with µi = 1, the capacity expression reduces to (3.7).

Assuming |Hsd,i| ≪ 1 for the relaying subcarriers, a similar approach can be

used as described in Section 3.3.2 to obtain a marginally optimal source transmit

power. For the nonrelaying subcarriers (i.e., µi = 0), the capacity expression can

be given as (3.8) and the optimization reduces to a traditional water lling power

allocation problem [102, 103]. The combined solution for the source transmit


power Ps,i can be obtained as,

P ∗s,i =

minPmaxs,i ,

Ak,i

γsk,i

(−1 +

γkd,iPk,i

2[·])

, if µi = 1;

1δ ln(2)

− 1γsd,i

, if µi = 0.(3.37)

where [·] = −1 +√1 +

2γsk,iδ ln(2)γkd,iPk,i

. The Lagrange parameter δ is chosen such

that the maximum source transmit power is satised.

3.4.3 Resource Allocation Algorithm

Figure 3.3 illustrates the algorithm used for selective subcarrier relaying based

resource allocation scheme. Here, the N -dimensional vectors Pr and P∗r represent

the relay transmit power vector and the optimum relay transmit power vector for

all the subcarriers, respectively. If ith subcarrier is transmitted by kth relay,

Pr,i = Pk,i and if ith subcarrier is not relayed by any of the K relays, Pr,i = 0.

The resource allocation algorithm involves two steps: subcarrier and relay

selection, and iterative power optimization. Resource allocation is started with

an initial source and relay transmit power. Then, the relaying subcarriers are

selected and the subcarrier-relay assignment is obtained for this initial power

allocation. Once the subcarrier and relay selection is completed, for each par-

ticipating relay, the relay power constraint is checked with Pmink,i values of the

respective subcarriers. If the power constraint is violated for any of the par-

ticipating relays, then the subcarriers with highest Pmink,i value is removed until

the transmit power limitation is satised. After nalizing the subcarrier and re-

lay selection, source and relay power optimization is carried out iteratively for

the given subcarrier selection vector µ and the relay selection matrix A. The

two-step iterative power optimization is continued until the capacity reaches its

convergence.


Calculate optimum relay transmit

power and capacity CR

- Set Cmax = CR

- Pr=

Ps0, Pr0

CR > Cmax ?

Return Pr, Ps, and Cmax

Yes

No

Yes No

Initialize

Initialize source and relay power (Ps0,i=PS/N, Pr0,i=Ps0,i)

Set,

- Subcarrier selection decision Bk,i=0, µi=0 for all k,i

- Relay selection decision Ak,i=0, for all k,i

Subcarrier and relay selection

For all the subcarriers

- Set Bk,i=1, for all k that satisfy (3.24)

- Set µi according to (3.27)

For all relaying subcarriers

- Set Ak,i=1, for k that satisfy (3.28) or (3.29)

For each participating relay,

If

Set Ak,i=0, µi=0 for the subcarriers with highest until

∑=

>N

i

kikikPPA

1

min

,,

min

,ikP∑=

≤N

i

kikikPPA

1

min

,,

Set Cmax=0, Pr=Pr0, Ps=Ps0

*

rP

Calculate optimum source transmit

power and capacity CS*

sP

CS > Cmax ?

*

rP

- Set Cmax = CS

- Ps=*

sP

Ps

Pr

Ps

Figure 3.3: Flowchart of selective subcarrier relaying based resource allocation


3.5 Numerical Results and Discussion

This section presents numerical results to evaluate the performance of all sub-

carrier relaying and selective subcarrier relaying based resource allocation algo-

rithms in a multi-relay scenario. Performance of the proposed resource allocation

schemes are studied by means of Monte-Carlo simulations. Computer simulations

were carried out using MATLAB, and MATLAB optimization toolbox was used

to numerically solve the optimization problems using interior-point method.

For all evaluations, maximum source transmit power Ps was adjusted to obtain

an average SNR γ0 = 0dB with the direct transmission. γ0 can be expressed as

[69],

γ0 =Ps

Nσ2d (1 + dsd)

α . (3.38)

The expression (3.38) is used only to determine Ps. Maximum allowable relay

transmit powers were taken as Pk = Ps, ∀k ∈ [1 : K] unless otherwise stated.

Fading channel gains in (3.4) were generated with α = 3 and L = 4. The

distance between the source and the destination, dsd, was taken as 1000m. The

noise variances at the relays and the destination were set to 4.14 × 10−17W.

This corresponds to a 10KHz subcarrier bandwidth with a noise power spectrum

density of 4.14 × 10−21W/Hz [12]. An OFDM system with N = 32 subcarriers

was used for all evaluations. Results were averaged over 1000 dierent fading

channel realizations, unless otherwise stated.

Figure 3.4 illustrates the relay distribution used for this analysis. Relays are

uniformly distributed within a circular area of radius r. d is the distance from

the source to the center of the relay distribution, which is located on the line

connecting the source and the destination. All the distances are expressed in

meters unless otherwise stated. According to this relay distribution, source-to-

relay and relay-to-destination distances are dierent for each relay. Thus the

fading statistics in (3.4) are dierent for each relay depending on the respective

path gain.


d (m)

r (m)

Relay Cluster

Source Destination

Figure 3.4: Relay node distribution.

Figure 3.5 plots the capacity variation with relay cluster location for Selective

relaying-A, Selective relaying-B, and All subcarrier relaying methods. Capac-

ity values are normalized to the number of OFDM subcarriers. For this anal-

ysis, K = 8 relays were uniformly distributed within a circular area of 100m

radius. For comparison, the results obtained with No relaying scheme is also

presented. Selective relaying-A method improves capacity over All subcarrier re-

laying method when the relays are located close to the source. However, when

the distance to the relay cluster, d is increased beyond about 300m, All sub-

carrier relaying method outperforms Selective relaying-A scheme. But Selective

relaying-B approach improves the system capacity for all the relay locations over

the nonselective relaying scheme. This conrms that relay selection Method-B

performs better than relay selection Method-A with selective relaying.

According to the results in Figure 3.5, maximum capacity is achieved with

selective relaying based resource allocation schemes when the relay cluster is lo-

cated d = 200m away from the source. With All subcarrier relaying, maximum

capacity is achieved when the relay cluster is located d = 300m away from the

source. In general, the channel-to-noise ratios (CNRs) of source-to-relay link,

γsk,i, decreases and CNR of relay-to-destination link, γkd,i, increases as the relay

cluster moves away from the source towards the destination. According to the ca-

pacity expression (3.7), maximum capacity is achieved when the SNRs of the two

hops (Ps,iγsk,i and Pk,iγkd,i) balance with each other. In this particular simulation

scenario, maximum relay transmit power is taken to be as same as the maximum


100 200 300 400 500 600 700 800 9001

1.2

1.4

1.6

1.8

2

2.2

d (m)

Norm

aliz

ed c

apac

ity p

er s

ubca

rrie

r (b

/s/H

z)

Selective relaying-A

Selective relaying-B

All sub-carrier relaying

No relaying

Figure 3.5: Normalized capacity variation with source-relay distance for dierentresource allocation methods, K = 8 relays, r = 100m.

source transmit power, and in general, more than one relay participate for the

relaying process. Thus the cumulative relay transmit power is higher than the

source power. This results in higher relay transmit power for each relaying sub-

carrier than the source transmit power. Thus, the SNR of the relay-to-destination

path increases at a much higher rate than the SNR of the source-to-relay path.

Hence, the SNRs of the two hops balance before the relay cluster reaches the

midpoint between the source and the destination, and the maximum capacity is

achieved.

Figure 3.6 illustrates the capacity variation when the radius of the relay cluster

is increased. Results were obtained for Selective relaying-B method and the

number of relays were taken as K = 16. It can be observed that when the relay

cluster locates close to the source, smaller relay clusters provide higher capacity.

On the other hand, when the relay cluster locates close to the destination, larger

relay clusters result in higher capacity. When the relay cluster locates close to the

source, smaller relay clusters provide higher capacity since almost all the relays

are positioned closer to the source. Larger relay clusters result in lower capacity


100 200 300 400 500 600 700 800 9001.4

1.6

1.8

2

2.2

2.4

d(m)

Norm

aliz

ed c

apac

ity p

er s

ubca

rrie

r (b

/s/H

z)

r=100m

r=200m

r=300m

Figure 3.6: Normalized capacity variation with source-relay distance with Selec-tive relaying-B method for dierent relay cluster sizes, K = 16 relays.

due to the negative eect of the relays that locates further away from the source.

The opposite happens when the relay cluster is located close to the destination.

In that case, larger relay clusters result in higher capacity since more relays might

locate biased to the source direction.

Figure 3.7 shows the results obtained with dierent number of relays for Selec-

tive relaying-B method when the relays are distributed within an area of radius

r = 100m. Accordingly, signicant capacity gain could not be achieved when

the number of relays increases beyond 24 for a system with N = 32 subcarriers.

For all these scenarios, Selective relaying-B method converges to the maximum

capacity in less than 5 iterations.

In a multi-relay scenario, it would be interesting to investigate the actual

number of relays that eectively participate for communication. The results

in Figure 3.8 and Figure 3.9 show the histograms of the number of eectively

participating relays when K = 16 and K = 32 relays are employed, respectively.

This histograms are based on 100 realizations of the channel coecients and the

number of participating relays is analyzed for a range of relay cluster locations.


100 200 300 400 500 600 700 800 9001

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

d (m)

Norm

aliz

ed c

apac

ity p

er s

ubca

rrie

r (b

/s/H

z)

K=2

K=4

K=8

K=16

K=24

K=32

Figure 3.7: Normalized capacity variation with source-relay distance with Selec-tive relaying-B method for dierent number of relays, r = 100m.

Figure 3.8: Histogram of number of participating relays with Selective relaying-Bmethod, K = 16 relays, r = 100m.

Accordingly, a maximum of 12 relays participate in the relaying process when

there are total of 16 relays are present. In the case where there are K = 32 relays,


no more than 13 relays are occupied at a time. Thus, regardless of the number

of relays employed in the system, only the best few relays actively participate in

the communication process.

Figure 3.9: Histogram of number of participating relays with Selective relaying-Bmethod, K = 32 relays, r = 100m.

3.6 Conclusion

In this chapter, relay selection and subcarrier power allocation was studied for a

multi-relay assisted cooperative OFDM system. A two-step resource allocation

approach was proposed as a more feasible and eective alternative for complex

joint optimal resource allocation methods. With the proposed approach, resource

allocation is carried out in two steps: relay and/or subcarrier selection, and power

allocation. Resource allocation methods were developed for two scenarios: all

subcarrier relaying, and selective subcarrier relaying. Numerical results conrm

that the proposed selective subcarrier relaying based resource allocation method,

which involves best end-to-end SNR based relay selection and optimal power

allocation, outperforms the baseline nonselective relaying method for a range of

relay cluster locations.

Chapter 4

Power Allocation in OFDM Relay

Networks with Outdated CSI

4.1 Introduction

In OFDM relay networks, power allocation can be performed at the source and

the relay/s to enhance the network performance. For adaptive power alloca-

tion, transmitter requires some knowledge of the wireless channel condition or

the channel state information (CSI). In FDD systems, CSI is estimated at the

receiver and is usually fed back to the transmitter. A signicant amount of stud-

ies on power allocation in OFDM relay networks with the assumption of perfect

instantaneous CSI is available in the current literature ([12],[39],[69] and refer-

ences therein). However, the available CSI at the transmitter is rarely perfect in

practice due to channel estimation errors and feedback delay. Thus the eect of

imperfect CSI should be considered for power allocation to gain a more accurate

insight of practical scenarios.

Power allocation of single-hop OFDM networks with imperfect channel knowl-

edge is considered in [104],[105],[106] [107] and [108]. Yao and Giannakis in [104]

study power allocation methods for ergodic and outage capacity maximization

4. POWER ALLOCATION WITH OUTDATED CSI 70

in OFDM networks assuming that partial (imperfect) channel distribution is

available at the transmitter. Ian and Brian in [105] study resource allocation

for multiuser OFDMA networks for ergodic capacity maximization under the

assumption of imperfect CSI at the transmitter. When a feedback channel is

employed in FDD systems to obtain the wireless channel information, the avail-

able CSI at the transmitter can be outdated due to channel feedback delay. The

work in [108] presents resource allocation methods to minimize the total trans-

mit power in OFDMA downlink transmission in the presence of outdated CSI. In

[106], authors propose power allocation methods to minimize the bit-error-rate

(BER) when the available CSI at the transmitter is outdated. Awad et al. in

[107] study resource allocation in OFDMA based networks under imperfect CSI

for the case where the OFDMA network serves multiple classes of services with

dierent quality of service requirements.

However, power allocation in OFDM relay networks with imperfect channel

knowledge is hardly addressed in the existing studies. Ahmad and Assaad in

[109] consider joint optimization of resource allocation and relay selection in a

downlink OFDMA cooperative network with DF relays under the assumption of

imperfect CSI at the base station. This method considers resource allocation to

minimize the total transmit power of the system.

This chapter addresses the power allocation problem in OFDM-based two-

hop relay networks when the available CSI at the transmitter is outdated due

to feedback delay. Two power allocation methods are proposed considering two

dierent objectives: expected rate maximization and outage rate maximization.

The rest of this chapter is organized as follows. The system and channel model

is given in Section 4.2. A baseline power allocation method that maximizes

the instantaneous rate assuming that the available outdated CSI is perfect is

presented in Section 4.3. Power allocation method to maximize the expected rate

is described in Section 4.4 along with the numerical results. The second power

allocation scenario to maximize the outage rate is presented in Section 4.5.



A two-hop relay link with one source-destination pair and one amplify-and-

forward (AF) relay is considered for this study. The system model is as shown

in Figure 4.1. It is assumed that the direct path between the source and the

destination does not exist due to heavy path loss or shadowing. It is further as-

sumed that the relay supports only half duplex operation and the system employs

TDMA, where each user is allocated a dedicated time period for data transmis-

sion. To enable relay communication, this time period is further divided into two

time slots.

Source

(s)Destination

(d)

Time slot t

Time slot t+1

Relay

(r)

1

2

3

4

5

N

.

.

.

Figure 4.1: Two-hop OFDM relay link.

The number of subcarriers in the OFDM system is taken as N . Frequency

selective channels are considered and it is assumed that all the channel taps are

subject to Rayleigh fading and path loss. The frequency response of the channel

between nodes m and n: m ∈ s, r and n ∈ r, d, Hmn, is given by the N -

point FFT of the channel impulse response. Hmn is a N -dimensional vector that

represents the frequency domain fading coecients. The N -dimensional channel

coecient vector Gmn represents the eect due to both the path loss and the

fading gain. Then,

Gmn =√Kd−αmn Hmn (4.1)


where, dmn is the distance between the nodes m and n, K is a constant that

depends on the antenna design and α is the path loss exponent [110, 111]. K and

α are assumed to be the same for all the channels.

It is assumed that the source sends data with power Ps,i on the ith subcarrier.

With AF relay, the relay amplies the signal by a factor of βi using power Pr,i on

the same subcarrier. βi is given by [69],

βi =

√Pr,i

| Gsr,i |2 Ps,i + σ2r

(4.2)

where σ2r is the noise variance at the relay. If the destination receives signal from

the relay in the second time slot, the signal-to-noise ratio (SNR) γi of the ith

subcarrier can be written as [69],

γi =Ps,i | Grd,iβiGsr,i |2

σ2d + σ2

r | βiGrd,i |2

=Ps,iγsr,iPr,iγrd,i

1 + Ps,iγsr,i + Pr,iγrd,i(4.3)

where, γsr,i =|Gsr,i|2σ2r

and γrd,i =|Grd,i|2σ2d

are the instantaneous channel-to-noise

ratios (CNRs) of source-to-relay and relay-to-destination links, respectively. σ2d

is the noise variance at the destination. At high SNR, γi can be approximated

as,

γi ≃Ps,iγsr,iPr,iγrd,iPs,iγsr,i + Pr,iγrd,i

. (4.4)

This approximation has been commonly used in the literature to approximate

the SNR at high SNR regime [12, 112, 113]. Although the standard form in (4.3)

is commonly used in moderate to low SNR regime, it is shown in [113] that in

some cases the approximation (4.4) can also be applied at moderate to low SNR

regime.

It is assumed that the available CSI at the transmitter is an outdated but

correlated version of the actual instantaneous CSI. For the ith subcarrier, the


available outdated CSI of the channel between nodes m and n is denoted by

Hmn,i. Assuming that both the instantaneous CSI, Hmn,i, and the outdated CSI,

Hmn,i, are complex Gaussian with zero mean and unit variance, the distribution

of Hmn,i conditioned on Hmn,i can be expressed as [114],

Hmn,i | Hmn,i ∼ CN (ρ Hmn,i, 1− ρ2) (4.5)

where, ρ is the correlation coecient between the two envelopes of instantaneous

and outdated CSI. If Jake's model is considered, the correlation coecient takes

the value ρ = J0(2πfDτD) where, fD is the Doppler frequency, τD is the feed-

back delay and J0(·) denotes the zero-order Bessel function of the rst kind [114].

Without loss of generality, it is assumed that ρ is the same for all the subcar-

riers. Gmn,i and γmn,i represent the corresponding outdated channel gain and

the outdated CNR, respectively. The conditional pdf of the instantaneous CNR,

γmn,i =|Gmn,i|2σ2n

can be expressed as a non-central Chi-squared distribution with

two degrees of freedom as shown in (4.6) [115] (subscript i has been omitted for

simplicity of presentation).

fγmn|γmn =1

γmn(1− ρ2)e− 1

γmn(1−ρ2)(ρ2γmn+γmn)

I0 ([·])

[·] =2

γmn(1− ρ2)

√ρ2γmnγmn (4.6)

Here, I0(·) is the zero-order modied Bessel function of the rst kind, γmn =

|Gmn,i|2σ2n

is the outdated CNR and γmn is the long-term average CNR.

The objective of power allocation is to maximize the end-to-end capacity of

the OFDM relay transmission. The instantaneous rate Ci of the ith subcarrier

assuming perfect instantaneous CSI can be expressed as [69],

Ci =1

2log2(1 + γi) b/s/Hz (4.7)


where, factor 1/2 represents the half-duplex relaying process.

Then the instantaneous rate over the entire OFDM symbol with N subcarriers

can be given by,

C =N∑i=1

1

2log2(1 + γi) b/s/Hz. (4.8)

However, when the available CSI is outdated it is impossible to know the actual

instantaneous rate. Hence, two cases are studied assuming that outdated CSI

and outdatedness (correlation coecient) is known at the transmitter:

• Power allocation to maximize expected rate

• Power allocation to maximize outage rate

To compare the performance of the above two scenarios, a baseline power alloca-

tion method is introduced assuming that only the outdated CSI is known. In that

case, power allocation is performed to maximize the instantaneous rate calculated

for available outdated CSI.

It is also considered that both the source and the relay are subject to individual

transmit power constraints. Then each node (source and relay) optimizes its

transmit power among all the subcarriers such that the following constraints are

satised:N∑i=0

Ps,i = 1TPs = PS (4.9)

N∑i=0

Pr,i = 1TPr = PR (4.10)

PS and PR are maximum source and relay transmit powers, respectively.

4.3 Maximizing Instantaneous Rate

As a baseline approach, a power allocation method is proposed considering that

only the outdated CSI is available for decision making. In this scenario, power


allocation is performed assuming that the available CSI is perfect, and the in-

stantaneous rate is calculated for the available outdated channel coecients. The

objective function for power optimization can be expressed as,

C =N∑i=1

1

2log2(1 + γi) (4.11)

where,

γi =Ps,iγsr,iPr,iγrd,i

1 + Ps,iγsr,i + Pr,iγrd,i. (4.12)

Source and relay transmit powers need to be determined to maximize the total

capacity given by (4.11). As described in Section 3.3.2, with AF relay, two-step

iterative power optimization is used to nd the source and relay power allocations.

The iterative power allocation is started with an initial source transmit power and

the relay transmit powers are optimized for this initial source power allocation.

Next, the source transmit power is optimized for the given optimized relay power

allocation. These two steps are repeated alternately until the convergence is

achieved. Relay and source power optimizations for this baseline power allocation

method can be described as follows.

A. Relay power optimization

For a given source power allocation vector Ps, the relay power optimization prob-

lem can be formulated as,

MaximizeN∑i=1

1

2log2 (1 + γi) (4.13)

subject to,

∑Ni=1 Pr,i ≤ PR,

Pr,i ≥ 0, ∀ i(4.14)


This is a convex optimization problem and the optimal relay transmit power

can be calculated using Karush-Kuhn-Tucker (KKT) conditions [95]. The solu-

tion for the optimal relay transmit power P ∗r,i can be obtained as,

P ∗r,i =

1

γrd,i

[Ps,iγsr,i

2

(√1 +

4γrd,iPs,iγsr,i λ

− 1

)− 1

]+(4.15)

where [x]+ = max(0, x). The constant λ is chosen such that the sum power

constraint in (4.14) is satised.

B. Source power optimization

Once the relay power allocation vector Pr is given, the source power optimization

problem can be formulated as follows:

MaximizeN∑i=1

1

2log2 (1 + γi) (4.16)

subject to,

∑Ni=1 Ps,i ≤ PS,

Ps,i ≥ 0, ∀ i(4.17)

The solution for source power optimization can be obtained by solving the

KKT system of equations. The optimal source transmit power can be obtained

as,

P ∗s,i =

1

γsr,i

[Pr,iγrd,i

2

(√1 +

4γsr,iPr,iγrd,i ν

− 1

)− 1

]+(4.18)

where the constant ν is chosen such that the sum power constraint in (4.17) is

satised.


4.4 Maximizing Expected Rate

The expected value of the instantaneous rate is taken as the performance mea-

sure in most of the existing works on resource allocation with imperfect CSI

([105],[107],[108] and references therein). In order to calculate the expected rate,

it is assumed that the knowledge of the correlation coecient ρ is also available

at the time of decision making. Then it is possible to obtain the marginal dis-

tributions of the actual CNRs, γsr,i and γrd,i as given in (4.6). The conditional

pdfs of γsr,i and γrd,i can be used to calculate the expected value of the actual

instantaneous rate,

E [Ci] =1

2E [log2(1 + γi)] . (4.19)

Here, E [·] represents the expectation with respect to fγsr,i|γsr,i and fγrd,i|γrd,i . Find-

ing a closed form solution for (4.19) analytically is very hard (if not infeasible).

Hence, the Jensen's inequality [102] is applied to obtain the following upper bound

for the expected capacity.

E [Ci] ≤1

2log2(1 + E [γi]) (4.20)

Using the high SNR approximation (4.4) for γi,

E [γi] ≃ E

[Ps,iγsr,iPr,iγrd,iPs,iγsr,i + Pr,iγrd,i

]. (4.21)

It is dicult to nd a closed form solution for the expectation in (4.21) with

the Chi-squared pdf (4.6). However, it is possible to approximate the Chi-squared

distribution using the Gamma distribution as shown in [3] and [105]. Then the

conditional pdf of γmn,i given γmn,i can be approximated as (subscript i has been

omitted for notational brevity),

fγmn|γmn ≃ Ωθmnmn

Γ(θmn)γθmn−1mn e−Ωmnγmn (4.22)


where θmn = (Kmn+1)2

2Kmn+1is the Gamma pdf shape parameter with Kmn = ρ2γmn

γmn(1−ρ2),

and Ωmn = θmn

ρ2γmn+γmn(1−ρ2)is the Gamma pdf rate parameter : m ∈ s, r,

n ∈ r, d. Γ(x) is the Gamma function.

By using this approximation, the conditional expectation in (4.21) can be

solved as follows:

E [γi] ≃∫ ∞

0

∫ ∞

0

Ps,iγsr,iPr,iγrd,iPs,iγsr,i + Pr,iγrd,i

fγsr,i|γsr,i fγrd,i|γrd,i dγsr,i dγrd,i (4.23)

First, the inner integral (i.e., integration with respect to γsr,i) is solved using the

result [116, Eq. 3.383.10] to arrive at,

E [γi] ≃ P θsr+1r,i Ωθsr

sr Ωθrdrd Γ(θsr+1)

P θsrs,i Γ(θsr) Γ(θrd)

∫∞0

[·] dγrd,i

[·] = γθsr+θrdrd,i e−(Ωrd−

ΩsrPr,iPs,i

)γrd,i

Γ(−θsr, ΩsrPr,i

Ps,iγrd,i

).

(4.24)

Here, Γ(a, x) is the incomplete gamma function. Solution for above integration

can be obtained using [116, Eq. 6.455.1], and the nal closed-form expression for

the expected value of γi can be obtained as,

E [γi] ≃Pr,iθsrθrd

Ωrd(θsr + θrd + 1)2F1 (1, c1; c2; c3) (4.25)

where, c1 = θrd + 1, c2 = θsr + θrd + 2, and c3 = 1 − ΩsrPr,i

ΩrdPs,i. 2F1(a, b; c; z) is the

Gauss' Hypergeometric function [116, Sec. 9.1].

By substituting (4.25) in (4.20), an approximate upper bound for the expected

rate can be obtained as,

E [Ci] ≤1

2log2

(1 +

Pr,iθsrθrd 2F1 (1, c1; c2; c3)

Ωrd(θsr + θrd + 1)

). (4.26)


The summation of (4.26) over all the N subcarriers is taken to approximate the

total expected capacity as,

E [C] =N∑i=1

E [Ci]

≤N∑i=1

1

2log2

(1 +

Pr,iθsrθrd 2F1 (1, c1; c2; c3)

Ωrd(θsr + θrd + 1)

). (4.27)

After formulating the objective function (4.27), power optimization is carried

out iteratively in two steps as described in Section 3.3.2. The relay and source

power optimizations for expected rate maximization can be described as follows:


When the source power vector Ps is given, the relay power optimization problem

to maximize the expected capacity can be stated as,

Maximize∑N

i=1E [Ci]

subject to∑N

i=1 Pr,i ≤ PR and Pr,i ≥ 0, ∀ i(4.28)

B. Source power optimization

For a given relay power vector Pr, the source power optimization problem to

maximize the expected capacity can be given as,

Maximize∑N

i=1E [Ci]

subject to∑N

i=1 Ps,i ≤ PS and Ps,i ≥ 0, ∀ i(4.29)

It is mathematically infeasible to nd closed-form solutions for (4.28) and

(4.29) with the objective function given in (4.27). Hence, these two optimization

problems are numerically solved using MATLAB optimization toolbox.


4.4.1 Numerical Results and Discussion

This section evaluates the performance of the expected rate maximization based

power allocation in the presence of outdated CSI. Monte-Carlo simulations were

carried out using MATLAB to obtain the necessary performance results.

Frequency selective channels with 4 multipath taps and unit fading power

were used for this analysis. Distance between the source and the destination was

taken as 1000m and the path loss exponent α was xed at 3. The noise variances

at the relay and the destination were set to σ2r = σ2

d = 4.14 × 10−17W/Hz. The

given noise variances correspond to a 10KHz subcarrier bandwidth with a noise

power spectrum density of 4.14× 10−21W/Hz [12]. Performance evaluation was

carried out for an OFDM system with N = 16 subcarriers. Maximum source and

relay transmit powers were taken to be same for all evaluations, i.e., PR = PS.

-10 -5 0 5 10 15 20 25 300

1

2

3

4

5

6

Transmit power (dBm)

Expected rate per subcarrier (b/s/Hz)

Theoretical upper bound

Simulated expected rate

Figure 4.2: Expected rate variation with transmit power, dsr = 500m, ρ = 0.5.

First, the expected rate given by (4.27) is compared with the actual expected

capacity to conrm the validity of the approximations used. The results are shown

in Figure 4.2. For a given sample of outdated CSI, the expected rate is calculated


using (4.27), which is the theoretical upper bound of the expected capacity. In

order to calculate the actual expected rate, 1000 dierent instantaneous channel

realizations were generated using the given outdated CSI and channel correlation

information. Then, the average of the corresponding instantaneous capacities

was calculated. As expected, the capacity given by expression (4.27) is an upper

bound for the actual expected rate. This conrms the validity of the approxi-

mations in (4.20). The results shown in Figure 4.2 are obtained when ρ = 0.5.

However, the approximation is valid for other correlation coecient values as

well. Hence, the proposed method is valid for any correlation coecient value.

100 200 300 400 500 600 700 800 9002.8

3

3.2

3.4

3.6

3.8

dsr (m)


Maximize expected rate

Maximize instantaneous rate

Figure 4.3: Expected rate variation with source-relay distance, ρ = 0.2.

Figure 4.3 and Figure 4.4 compare the expected capacities achieved with the

proposed expected rate maximization based power allocation scheme and the in-

stantaneous rate maximization based power allocation scheme described in Sec-

tion 4.3. The gures show the expected capacities achieved with these two meth-

ods for ρ = 0.2 and ρ = 0.8, respectively. For this analysis, PR and PS were xed

to be 20dBm. When ρ = 0.2, expected rate maximization achieves much higher


capacity than the instantaneous rate maximization. On the other hand, when

ρ = 0.8, a signicant capacity improvement cannot be observed with expected

rate maximization. Accordingly, the proposed expected rate maximization based

power allocation method outperforms the baseline power allocation method when

the available CSI is increasingly outdated. When the correlation is high, a signif-

icant dierence cannot be observed between the two methods. Also the proposed

expected rate maximization based power allocation method achieves the highest

capacity gain over the baseline method when the relay is located close to the

midpoint of the line connecting the source and the destination.

100 200 300 400 500 600 700 800 9002.8

3

3.2

3.4

3.6

3.8

dsr (m)


Maximize expected rate


Figure 4.4: Expected rate variation with source-relay distance, ρ = 0.8.

4.5 Maximizing Outage Rate

Expected rate closely bounds the rate of an OFDM system when the channel

uncertainty can be modeled as an ergodic process. When the available CSI is

imperfect due to feedback delay, the channel uncertainty cannot be modeled as

an ergodic process [117]. Hence, outage rate is a more suitable gure of merit


for situations where the available CSI is outdated [104], [117]. Outage rate is the

maximum rate that can be sent over a channel with a given outage probability.

When the available CSI is outdated, this section presents a power allocation

scheme for a two-hop OFDM relay communication to maximize the outage rate

for a given outage probability.

The instantaneous rate of one subcarrier can be rewritten as Ci ≃ 12ln(1+γi)

where γi is as dened in (4.4). If the conditional pdf of the instantaneous rate,

fCi|γi is known, the outage rate Ri for a given outage probability, Pout, can be

calculated such that, ∫ Ri

0

fCi|γi dCi = Pout. (4.30)

In order to get a mathematically tractable expression for the conditional pdf

fCi|γi , the following approximation is used to obtain an upper bound for γi as

shown in [78].

Ps,i γsr,i Pr,i γrd,iPs,iγsr,i + Pr,iγrd,i

≤ min(Ps,i γsr,i, Pr,i γrd,i) = γup,i. (4.31)

Then the conditional pdf of γup,i can be expressed as (subscript i has been omitted

for simplicity of presentation) [78],

fγup|γup =1

γup(1− ρ2)e− 1

γup(1−ρ2)(ρ2γup+γup)

I0 ([·])

[·] =2

γup(1− ρ2)

√ρ2γupγup (4.32)

where, γup =Ps,i γsr,i Pr,i γrd,iPs,i γsr,i+Pr,i γrd,i

. Once the conditional pdf of γup,i is available, a

simple transformation of random variables can be used to obtain the conditional

pdf of the rate Ci ≃ 12ln(1 + γup,i) as,

fCi|γup,i = 2bi e2Ci−ai−bi(e2Ci−1) I0

(2√aibi(e2Ci − 1)

)(4.33)


where, ai =ρ2γup,i

(1−ρ2)γup,iand bi =

1(1−ρ2)γup,i

. If ai is very large, a similar approach

as in [104] can be adopted to approximate the above pdf by the Gaussian distri-

bution,

fCi|γup,i ∼ N

(ln

(1 +

aibi

),

ai2 (ai + bi)2

). (4.34)

With the use of the above Gaussian pdf approximation, (4.30) can be solved for

Ri and the solution can be obtained as,

Ri = 12ln(1 + ai

bi

)−

√ai/2

(ai+bi)Q−1(Pout)

= 12ln (1 + ρ2γup,i)−

√ρ2(1−ρ2)γup,iγup,iQ−1(Pout)√

2(ρ2γup,i+1)

(4.35)

where, Q(·) is the complementary Gaussian cumulative distribution function.

It should be noted that, for the given system model, the large ai assumption

can be utilized in very limited cases where the CSI is highly correlated (i.e.,

ρ > 0.9). Figure 4.5 compares the outage rate approximation with the simulated

outage rate when ρ = 0.98 and dsr = 200m. Average outage rate, Rout, is plotted,

which is calculated as shown in (4.39).

When ai is not large enough, in order to get a closed-form expression for

(4.30), the Chi-squared distribution (4.32) is approximated using the Gamma

pdf as shown in [105]. Then the conditional pdf of γup,i can be expressed as,

fγup,i|γup,i ≃Ωθii

Γ(θi)γθi−1up,i e

−Ωiγup,i (4.36)

where θi =(Ki+1)2

2Ki+1is the Gamma pdf shape parameter with Ki =

ρ2γup,iγup,i(1−ρ2)

and

Ωi =θi

ρ2γup,i+γup,i(1−ρ2)is the Gamma pdf rate parameter. With the above result,

the conditional pdf of the rate can be obtained as,

fCi|γup,i =2Ωi

Γ(θi)(e2Ci − 1)θi−1 e2Ci−Ωi(e

2Ci−1). (4.37)


0 5 10 15 20 25 300

1

2

3

4

5

Transmit power (dBm)

Outa

ge

rate

Rout (

b/s

/Hz)

Outage rate - Simulated

Outage rate - Approximation

Figure 4.5: Outage rate variation with transmit power, dsr = 200m, ρ = 0.98,Pout = 0.1.

Substituting (4.37) in (4.30) and using the result [116, Eq. 3.462.14], Pout can be

obtained as,

Pout = 1− Γ[θi,Ω(e2Ri − 1)]

Γ[θi]. (4.38)

It is not feasible to solve the above equation analytically to obtain a closed-form

expression for outage rate. Thus the equation (4.38) is solved numerically to nd

Ri.

After calculating Ri for each subcarrier, the subcarrier transmit power is al-

located to maximize the average outage rate,

Rout =1

N

N∑i=1

Ri. (4.39)

The two-step iteratively power optimization for outage rate maximization can be

described as follows:



When the source power vector Ps is given, the relay power optimization problem

to maximize the outage rate can be state as,

Maximize Rout

subject to∑N

i=1 Pr,i ≤ PR and Pr,i ≥ 0, ∀ i(4.40)

where PR is the maximum allowable relay transmit power.

A. Source power optimization

For a given relay power vector Pr, the source power optimization problem to

maximize the outage rate can be given as,

Maximize Rout

subject to∑N

i=1 Ps,i ≤ PS and Ps,i ≥ 0, ∀ i.(4.41)

Here, PS is the maximum transmit power of the source.

When ai is not large (i.e., when ρ <= 0.9), there is no closed-form expression

for outage rate and (4.38) has to be solved numerically to obtain Ri. Thus it is

impossible to nd closed-form solutions for the above two optimization problems.

When ai is large, it is still dicult to obtain an analytical expression for the

optimum relay and source power allocation with the outage rate approximation

(4.35). Thus for all the cases (4.40) and (4.41) are solved numerically to nd the

relay and source transmit powers.

4.5.1 Numerical Results and Discussion

Monte-Carlo simulation results are presented in this section to assess the perfor-

mance of outage rate maximization based power allocation. Computer simula-

tions were performed using MATLAB. Simulations were carried out for frequency


selective Rayleigh fading channels with 2 multipath taps and unit fading power.

Other simulation parameters were taken to be same as that mentioned in Section

4.4.1.

Figure 4.6 and Figure 4.7 compare the outage rate obtained with dierent

power allocation methods when Pout = 0.1 and Pout = 0.01, respectively. Outage

rate variation with relay location is shown for dierent correlation coecients.

For comparison, results obtained with uniform power allocation and instantaneous

rate maximization described in Section 4.3 are also provided.

100 200 300 400 500 600 700 800 9001

1.5

2

2.5

3

3.5

dsr (m)

Outage Rate Rout (b/s/Hz)

Uniform power allocation

Maximize outage rate


ρ = 0.9

ρ = 0.7

ρ = 0.5

Figure 4.6: Outage rate variation with source-relay distance, Pout = 0.1.

It can be clearly observed in Figure 4.6 and Figure 4.7 that the outage rate

increases with the increase of correlation coecient. Moreover, outage rate maxi-

mization brings substantial gain over uniform power allocation and instantaneous

rate maximization. The highest outage rate as well as the highest outage rate

improvement over uniform power allocation is achieved when the relay is located

at the midpoint of the source and the destination. Additionally, it is also evident

that much higher outage rate improvement can be obtained with outage rate


maximization when Pout is set at a lower value. As an example, when Pout = 0.01

and ρ = 0.9, outage rate maximization achieves 12% improvement in outage rate

over uniform power allocation when the relay is located at the midpoint. When

Pout = 0.1, the respective outage rate improvement is about 6% at the midpoint.

100 200 300 400 500 600 700 800 9000

0.5

1

1.5

2

2.5

3

3.5

dsr (m)

Outage rate R

out (b/s/Hz)

Uniform Power allocation

Maximize outage rate


ρ = 0.9

ρ = 0.7

ρ = 0.5

Figure 4.7: Outage rate variation with source-relay distance, Pout = 0.01.


100 200 300 400 500 600 700 800 9002.2

2.4

2.6

2.8

3

3.2

3.4

dsr

(m)

Outa

ge

rate

Rout (

b/s

/Hz)

Simulation

Approximation


Outage ratemaximization

Figure 4.8: Outage rate variation with source-relay distance, ρ = 0.98 and Pout =0.1.

Figure 4.8 shows the outage rate Rout achieved with outage rate maximization

and uniform power allocation when ρ = 0.98 and Pout = 0.1. In order to eval-

uate the validity of the outage rate approximation given in (4.35), results were

obtained with two methods: numerical outage rate calculation (Simulation) and

the approximation (4.35) (Approximation). It can be observed that the outage

rate approximation becomes tighter when the relay is located close to the source

or the destination.

4.6 Conclusion

This chapter investigated power allocation in OFDM two-hop relay links in the

presence of outdated CSI. Two scenarios were considered assuming that the out-

dated CSI and the outdatedness are known at the time of power allocation: max-

imizing expected rate and maximizing outage rate. Several approximations were

used to obtain mathematically tractable power allocation problems for these two


scenarios. Still, it was infeasible to solve the optimization problems analytically

to obtain closed-form expressions for the optimal source and relay transmit pow-

ers. Thus, optimization problems were solved numerically and the results were

analyzed to assess the performance of expected rate maximization and outage

rate maximization based power allocation schemes. Performance of the proposed

power allocation methods was compared with a baseline method which maximizes

the instantaneous rate assuming that the available outdated CSI is perfect.

According to simulation results, outage rate maximization based power al-

location is favored over expected rate maximization when the available CSI is

imperfect due to feedback delay. Outage rate maximization shows better perfor-

mance than instantaneous rate maximization and uniform power allocation for

a range of relay locations and correlation coecient values. On the other hand,

expected rate maximization displays slightly improved performance over the base-

line method only when the CSI is poorly correlated (i.e., highly outdated).

Chapter 5

Resource Allocation in OFDM

Cognitive Radio Relay Networks

5.1 Introduction

The cognitive radio (CR) concept [5] has been identied as a method to improve

the spectrum utilization by allowing secondary users (SUs) to cooperatively trans-

mit on the unutilized frequency bands left by licensed users/primary users (PUs).

SUs have CR capability which allows them to detect the available spectrum holes

and to adapt their transmission parameters accordingly. SUs should use the avail-

able unoccupied licensed frequency bands without causing intolerable interference

to the incumbent PUs. For situations where there is a weak channel between the

CR source and CR destination, reliable communication can be achieved by intro-

ducing a set of cooperative relays between the source and the destination [60].

Using these intermediate CR relays, data can be transmitted using relatively low

power and possibly with lower interference to the PUs.

OFDM is a key modulation technique for realizing the CR concept due to its

exibility for spectrum allocation [57, 58]. In spectrum sharing environment, CR

users and PUs may exist in side-by-side bands and the PU network might not use

5. RESOURCE ALLOCATION IN OFDM CR RELAY NETWORKS 92

OFDM. Hence, CR transmissions are not orthogonal to PU transmissions, and

may introduce interference in PU band and vice-a-versa [118, 119]. The mutual

interference is the limiting factor for the performance of both networks. Weiss et

al. in [120] have shown that using OFDM for CR transmission generates mutual

interference between PU and CR bands due to the non-orthogonality of the trans-

mitted signals. The amount of interference produced at the PU frequency band

by the CR transmission depends on the transmit power of each OFDM subcarrier

and the spectral distance between the OFDM subcarriers and the PU band.

Contrary to non-cognitive networks, in CR networks resource allocation should

be performed such that the CR transmission does not create harmful interference

to PUs. Generally, this is achieved by introducing a tolerable interference limit

to the PU network. Then the resources in the CR network can be adaptively

allocated to improve the performance of the CR transmission while ensuring that

the specied interference threshold is not violated. The interference threshold

can be specied as a total interference threshold for the PU system or as an in-

dividual interference threshold for each PU receiver. A rich literature is available

on resource allocation in OFDM-based single-hop CR networks. As an exam-

ple, the work in [118] and [119] present subcarrier power allocation schemes to

maximize the capacity of the CR transmission. The power allocation problem

in [118] is subject to a total interference threshold and the problem addressed in

[119] is subject to individual interference thresholds at each PU receiver. The

work in [121] presents resource allocation schemes for multiuser cognitive OFDM

networks to maximize the capacity under individual interference constraints at

each PU receiver. In [122], authors investigate uplink resource allocation schemes

for OFDMA-based CR networks, and propose subcarrier and power allocation

schemes under total interference constraint to maximize the total throughput of

the CR uplink transmission.

In recent years, there has been a signicant interest on resource allocation

in CR relay networks. Number of studies can be found on resource allocation


in singlecarrier CR relay networks (e.g., [63, 80, 81, 82]). Similarly, consider-

able amount of work is available on resource allocation in OFDM-based CR relay

networks (e.g., [13, 84, 86, 87, 88, 85, 89, 123, 124]). In [13], Shaat and Bader

study joint optimization of relay selection, subcarrier pairing and power alloca-

tion in OFDM-based CR networks with multiple DF relays. The authors derive

an asymptotically optimal solution using dual-decomposition method and also

propose a suboptimal algorithm with less complexity. The work in [87] presents

suboptimal relay selection and power allocation schemes for OFDM-based CR

systems with multiple DF relays. Subcarrier power allocation in OFDM-based

CR networks with an AF relay is studied in [123], without considering diversity.

Only the interference constraint has been considered. An AF relay assisted CR

network with diversity is studied in [124] and the authors propose optimal power

allocation schemes under peak and average interference constraints. In [86], au-

thors propose joint subcarrier pairing and power loading method for AF relay

assisted CR networks considering interference and transmit power constraints.

Furthermore, power allocation in OFDM CR relay networks using adaptive relay-

ing strategy is studied in [85]. With adaptive relaying, the forwarding technique

at the relay is adaptively selected between AF and DF protocols based on the

quality of the signal. The reported work in [85] presents a near optimal power

allocation scheme that maximizes the capacity of the CR system while ensuring

that the interference introduced to the PU receiver is maintained below a specied

threshold.

However, relay selection and power allocation problem in multiple AF relay

assisted OFDM-based CR networks is not comprehensively investigated in the

existing literature. This chapter addresses joint optimization of relay selection

and power allocation in OFDM-based CR networks with multiple AF relays. This

study considers a more general system model with multiple PU bands and the

resource allocation problem is developed to maximize the capacity of the CR

transmission. Both interference and transmit power constraints are taken into


consideration. Suboptimal resource allocation schemes are proposed to maximize

the instantaneous capacity of the CR transmission. The performance of the

proposed methods is compared with the optimal resource allocation, which jointly

optimizes the relay selection and power allocation.

The remainder of this chapter is organized as follows: The system and the

channel model is described in Section 5.2. The joint resource allocation prob-

lem is formulated in Section 5.3, and the proposed resource allocation methods

are presented Section 5.4. Section 5.5 describes the joint optimal resource allo-

cation method. Numerical results are presented in Section 5.6 to evaluate the

performance of the proposed methods.


A two-hop OFDM-based CR system co-existing with a PU system is considered

for this study. The system model is shown in Figure 5.1. There are L PU

transmitter and receiver pairs in the vicinity of the CR system and K AF relays

to assist the communication between the CR source (s) and the CR destination

(d). For clarity of presentation only one PU transmitter and receiver pair is

shown in Figure 5.1. The direct link between the source and the destination is

assumed to be blocked by obstacles and does not exist. It is assumed that the

spectrum sensing has been performed and the source and the relays have the full

knowledge of the frequency bands available for transmission. CR network uses

OFDM modulation with N number of subcarriers. For simplicity of presentation,

let k denote the kth relay: k ∈ [1 : K], l denote the lth PU: l ∈ [1 : L], and i

denote the ith subcarrier: i ∈ [1 : N ].

Frequency selective Rayleigh fading channels are considered and the N - di-

mensional channel coecient vector between nodes m and n, Hmn, m ∈ s, k

and n ∈ k, d, l, represents the eect due to both the path loss and the fading

gain. Then, Hsk,i and Hkd,i represent the instantaneous channel coecients of


lth

band

PU

receiver

Cognitive

Radio

Source (s)

R1

Cognitive

Radio

Destination (d)

R2

RK

.

.

.

.

.

.

Cognitive

Radio Relays

lth

band

PU

transmitter

Interference

to PU

receiver

Interference

from PU

transmitter

Direct path

blocked by

obstacle

Figure 5.1: Multi-relay assisted CR system model

the ith subcarrier between source and kth relay, and kth relay and destination, re-

spectively. Hsl,i and Hkl,i denote the instantaneous channel coeecients between

source and lth PU, and kth relay and lth PU, respectively. In general, the resource

allocation decisions are made at the CR source and it is assumed that the knowl-

edge of instantaneous channel information, Hsk and Hkd, is available at the time

of decision making. Further it is also assumed that the CR network has perfect

knowledge of the instantaneous channel information Hsl and Hkl between itself

and the PU receivers.

In the frequency domain, a side-by-side access model is considered as shown

in Figure 5.2 [118, 120]. There are L PU bands with the lth PU band having a

bandwidth of Bl. A selected set of frequency bands from the remaining unused

spectrum is divided into N subcarriers each having a bandwidth of ∆f to be used

by the CR network.


B2∆f

2nd

PU

band

1st

PU

band

Lth

PU

band

Secondary users

B1 BL

1 2 3 4 5 N

Figure 5.2: Spectrum allocation for OFDM-based CR system

There are two types of interferences in an OFDM-based CR system: interfer-

ence introduced by PU transmitters to CR receivers, and interference introduced

by CR transmitters to PU receivers.

A. Interference introduced by primary user's signal

The interference introduced by the lth PU's signal at nth CR receiver on ith

subcarrier, Jln,i, can be expressed as [118],

Jln,i = |Hln,i|2∫ di,l+

∆f2

di,l−∆f2

Υ(ejw) dw (5.1)

where, Υ(ejw) is the power density spectrum of the PU signal after N-point

fast Fourier transform and Hln,i is the CSI of the ith subcarrier between lth PU

transmitter and nth CR receiver. di,l is the spectral distance between the ith

subcarrier and the lth PU band, and ∆f is the subcarrier bandwidth. Υ(ejw) can

be expressed as [120],

Υ(ejw) =1

2πN

∫ π

−πϕPU(e

jω)

(sin(ω − ψ)N/2

sin(ω − ψ)/2

)2

dψ (5.2)

where ω is the frequency normalized to the sampling frequency and ϕPU(ejω) is

the power spectrum density of the PU signal. PU signal can be taken as an

elliptically ltered white noise process [120].


B. Interference introduced by CR user's signal

The power density spectrum of the ith subcarrier in CR frequency band can be

written as [120],

ϕi(f) = PiTs

(sin(πfTs)

πfTs

)2

(5.3)

where, Pi is the transmit power of the ith subcarrier and Ts is the symbol duration.

Then the interference introduced by the mth CR transmitter at lth PU band on ith

CR subcarrier, Iml,i, can be expressed as the integration of the power spectrum

density over the primary user band and can be given as [118],

Iml,i = Pi |Hml,i|2 Ts∫ di,l+Bl/2

di,l−Bl/2

(sin (πfTs)πfTs

)2df,

= Pi |Hml,i|2Ωl,i.(5.4)

Here, Bl is the lth PU bandwidth. Ωl,i = Ts

∫ di,l+Bl/2

di,l−Bl/2

(sin(πfTs)πfTs

)2df and it depends

on the spectral distance between the CR subcarrier and the PU band. Hml,i is the

CSI of the ith subcarrier between the mth CR transmitter and lth PU receiver.

Accordingly, the interference generated from CR transmission depends on the

transmit power of ith subcarrier, channel gain between the CR transmitter and

PU receiver, and the spectral distance between the ith subcarrier and the PU

band.

5.3 Problem Formulation

The objective of resource allocation is to maximize the capacity of the CR trans-

mission. It is assumed that the CR relays support only half-duplex operations

and two orthogonal time slots are used for source-to-relay communication and

relay-to-destination communication. In the rst time slot, the source sends data

to the kth relay, with power Psk,i on the ith subcarrier. Then in the second time

slot, the kth relay amplies the signal by a factor of βk,i using power Pkd,i on


the same subcarrier and transmits the amplied signal to the destination. To

ensure that the CR relay transmit power is Pkd,i, the relay amplifying factor can

be obtained for CR transmission as,

βk,i =

√Pkd,i

| Hsk,i |2 Psk,i + σ2k +

∑Ll=1 Jlk,i

. (5.5)

Here, σ2k is the noise variance at the k

th relay, and Jlk,i is the interference intro-

duced by the lth PU at the kth relay. If the destination receives the signal from

the relay during the second time slot, the signal-to-noise ratio (SNR), γk,i, of the

ith subcarrier can be expressed as,

γk,i =Psk,i | Hkd,iβk,iHsk,i |2

σ2d +

∑Ll=1 Jld,i + (σ2

k +∑L

l=1 Jlk,i) | βk,iHkd,i |2

=Psk,iγsk,iPkd,iγkd,i

1 + Psk,iγsk,i + Pkd,iγkd,i(5.6)

where, γsk,i =|Hsk,i|2

σ2k+

∑Ll=1 Jlk,i

and γkd,i =|Hkd,i|2

σ2d+

∑Ll=1 Jld,i

are the instantaneous channel-

to-noise ratios (CNRs) at the kth relay and the destination, respectively. σ2d is the

noise variance at the destination, and Jld,i is the interference introduced by the

lth PU at the destination. Following [118], it is assumed that the CR receivers

can perfectly estimate the interferences Jlk,i and Jld,i.

In order to formulate the joint resource allocation problem, the relay selection

decision is taken as Ak,i = 0, 1. If the subcarrier i in the second hop is trans-

mitted by relay k, Ak,i = 1, otherwise, it is 0. Then the instantaneous rate of one

subcarrier can be expressed as,

Ci =K∑k=1

Ak,i1

2log2(1 + γk,i) b/s/Hz. (5.7)


With resource allocation, the relay selection and subcarrier power allocation is

determined to maximize the total instantaneous capacity, C =∑N

i=1Ci, of the

CR system. The resource allocation problem is subject to following constraints:

• Individual transmit power constraints at each CR transmitter (source and

relays)

• Total interference constraint at PU receivers

Total interferences introduced by CR source and relay transmissions can be ex-

pressed as,

Isp =L∑l=1

K∑k=1

N∑i=1

Ak,i |Hsl,i|2 Psk,iΩl,i (5.8)

and

Irp =L∑l=1

K∑k=1

N∑i=1

Ak,i |Hkl,i|2 Pkd,iΩl,i, (5.9)

respectively. The joint relay selection and power allocation problem can be stated

as follows:

MaximizeN∑i=1

K∑k=1

Ak,i1

2log2(1 + γk,i) (5.10)

subject to,

C1 :∑N

i=1

∑Kk=1Ak,iPsk,i ≤ PS

C2 :∑N

i=1Ak,iPkd,i ≤ PK , ∀ k

C3 : Isp ≤ Ith

C4 : Irp ≤ Ith

C5 :∑K

k=1Ak,i = 1, ∀ i

C6 : Ak,i ∈ 0, 1, ∀ k, i

C7 : Psk,i ≥ 0, ∀ k, i

C8 : Pkd,i ≥ 0, ∀ k, i

(5.11)

Here, PS and PK are the maximum allowable transmit powers at the source and

the kth relay, respectively. Ith is the maximum permissible interference to the PU


receivers. Constraints C1 and C2 are independent transmit power constraints at

source and relays, respectively. Constraints C3 and C4 correspond to the total

interference threshold for source and relay transmission, respectively. Since all

the subcarriers are transmitted simultaneously during the relaying phase, only

one relay can be allocated for a given subcarrier i. This imposes the constraint

C5.

Due to the constraint C6, the optimization problem given in (5.10) - (5.11) is a

mixed binary integer programming problem and is NP-hard. Hence, it is dicult

to nd an analytical solution for the joint optimal relay selection and power

allocation. An asymptotically optimum solution can be obtained using the dual-

decomposition method but with a much higher computational complexity [12, 13].

Thus, the following section proposes less-complex suboptimal relay selection and

power allocation methods.

5.4 Proposed Resource Allocation Methods

The joint optimal relay selection and power allocation problem can be simplied

by dividing it into two subproblems: relay selection, and power allocation. Then

the original resource allocation problem can be solved suboptimally, but with less

complexity. The subsequent sections present two suboptimal resource allocation

methods based on this two-step resource allocation approach.

5.4.1 Resource Allocation Method A

First, subcarrier-relay assignment is determined for a xed transmit power al-

location at the source and the relays. Once the subcarrier-relay assignment is

obtained, transmit power at the source and the relays is optimized such that

the capacity is maximized within the given constraints. This two-step resource

allocation can be described as follows:


5.4.1.1 Simplied Relay Selection

With this simplied relay selection method, the subcarrier-relay assignment is

obtained for an initial source and relay power allocation. For non-cognitive relay

networks, the general practice is to assume uniform transmit power for all the

subcarriers and then nd the best relay assignment for this initial power allocation

[12]. The best end-to-end SNR based relay selection has been identied as the

optimum relay selection method that maximizes the capacity for a given transmit

power allocation [100].

However, in CR relay networks, interference should be taken into consideration

while allocating a subcarrier to a specic relay. For a given subcarrier, the relay

which provides the highest end-to-end SNR while generating lower interference

should be selected. The eect of interference can be linked to the relay selection

decision by appropriately selecting the initial transmit power values. In order

to achieve this, it is assumed that all the subcarriers generate the same amount

of interference (i.e., Ith/N) to the PUs during source and relay transmissions.

P ints,i and P int

k,i are the source and kth relay transmit powers of ith subcarrier that

is required to generate Ith/N interference, respectively. P ints,i and P int

k,i can be

expressed as,

P ints,i =

Ith/N∑Ll=1 |Hsl,i|2Ωl,i

(5.12)

and

P intk,i =

Ith/N∑Ll=1 |Hkl,i|2Ωl,i

, (5.13)

respectively. Here,∑L

l=1 |Hsl,i|2 Ωl,i and∑L

l=1 |Hkl,i|2Ωl,i can be considered as nor-

malized interferences generated by transmitting subcarrier i from source and kth

relay, respectively. According to this power allocation, P intk,i is inversely propor-

tional to the normalized interference. Hence, higher the normalized interference

lesser power is allocated resulting in lower end-to-end SNR. With this approach,


relays with higher normalized interference for a given subcarrier i are disfavored

for transmitting the subcarrier i.

In this simplied relay selection method, for each subcarrier, the relay which

gives the highest end-to-end SNR is selected. For the xed source and relay

transmit powers given in (5.12) and (5.13), the end-to-end SNR, γk,i, is calculated

using (5.6) for all the subcarrier-relay pairs. Then, for each subcarrier, the relay

which gives the maximum end-to-end SNR is selected, i.e.,

Ak,i =

1, if argmax

kγk,i ;

0, otherwise.(5.14)

The computational complexity of this simplied relay selection is O(KN).

5.4.1.2 Optimal Power Allocation

When the subcarrier-relay assignment is known, the source and relay transmit

powers can be allocated optimally to maximize the capacity while not violating

the transmit power and interference threshold constraints. As described in Section

3.3.2, with AF relays, an alternate, separate optimization of source and relay

transmit powers is used as the optimal power allocation method. First, the source

transmit power is initialized such that both the interference constraint and the

power constraints are satised. The iterative optimization process is started with

this initial source power allocation, and the transmit powers at relays is jointly

optimized such that the total capacity is maximized. Then for this optimized

relay power allocation, the subcarrier transmit power at the source is optimized.

These two steps are alternately carried out such that the output of the previous

optimization is the input to the next optimization until convergence has been

achieved.


Relay Power Optimization

For a given subcarrier-relay assignment and source power allocation, the relay

power optimization problem can be stated as follows:

MaximizeK∑k=1

N∑i=1

Ak,i1

2log2(1 + γk,i) (5.15)

subject to,

C1 :∑N

i=1Ak,i Pkd,i ≤ PK , ∀ k

C2 :∑L

l=1

∑Kk=1

∑Ni=1Ak,i |Hkl,i|2 Pkd,iΩl,i ≤ Ith

C3 : Pkd,i ≥ 0, ∀ k, i

(5.16)

Here, constraint C1 represents the transmit power constraint for each relay and

constraint C2 corresponds to the total interference generated by relay transmis-

sion. This is a convex optimization problem and, can be solved using Karush-

Kuhn-Tucker (KKT) conditions [95]. The solution for the optimal relay transmit

power P ∗kd,i can be obtained as,

P ∗kd,i =

Ak,iγkd,i

[Psk,iγsk,i

2

(√1 + [·]− 1

)− 1

]+[·] =

2γkd,i

ln(2)Psk,i γsk,i (υk + µ∑L

l=1 |Hkl,i|2 Ωl,i)(5.17)

where, the constants υk and µ are non-negative Lagrange parameters which are se-

lected such that the sum power constraints C1 and the sum interference constraint

C2 in (5.16) are satised, respectively. A detailed derivation of this solution is

given in Appendix B.


Source Power Optimization

For a given relay power allocation, the source power optimization problem can

be expressed as follows:

MaximizeN∑i=1

Ak,i1

2log2(1 + γk,i) (5.18)

subject to,

C1 :∑N

i=1

∑Kk=1Ak,i Psk,i ≤ PS

C2 :∑L

l=1

∑Kk=1

∑Ni=1Ak,i |Hsl,i|2 Psk,iΩl,i ≤ Ith

C3 : Psk,i ≥ 0, ∀ k, i

(5.19)

The expression of SNR γk,i at the destination in (5.6) is symmetric with respect

to the transmit power of the source or the relay. Therefore, above constrained

optimization problem can be solved in a similar manner to that of the relay power

optimization. The solution for the optimal source transmit power P ∗sk,i can be

obtained as,

P ∗sk,i =

Ak,iγsk,i

[Pkd,iγkd,i

2

(√1 + [·]

)− 1

]+[·] =

2γsk,i

ln(2)Pkd,i γkd,i (δ + λ∑L

l=1 |Hsl,i|2 Ωl,i)(5.20)

where, δ and λ are non-negative Lagrange parameters that should be chosen

such that the sum power constraint and the sum interference constraint in (5.19)

are satised. The derivation of this solution follows the same procedure as for

the solution for relay power optimization in Appendix B. The two optimization

problems given in (5.15)-(5.16) and (5.18)-(5.19) can be solved numerically using

interior-point method with a complexity of O(N3) [95].


Resource Allocation Method A has a computational complexity of O(KN +

N3). Numerical results show that this suboptimal resource allocation method

achieves near optimal performance in many situations.

5.4.2 Resource Allocation Method B

The optimal power allocation described in Section 5.4.1.2 is still computationally

intensive since it is required to solve for multiple Lagrange multipliers during each

iteration. Thus, this subsection proposes a much simpler method which replaces

the optimal power allocation in Section 5.4.1.2 with a more simple power allo-

cation method. First, the subcarrier-relay assignment is obtained as described

in Section 5.4.1.1. Next, transmit power is allocated in a way such that both

interference and power constraints are satised during source and relay transmis-

sions. Capacity maximization is not considered. Ps,i and Pk,i are taken as the

ith subcarrier transmit power at the source and the kth relay, respectively. It is

assumed that all the subcarriers generate same amount of interference and assign

subcarrier transmit powers such that each subcarrier generates Ith/N interfer-

ence. Since this power allocation might violate the maximum transmit power

constraint, the source transmit powers are allocated as,

Ps,i =

P ints,i , if

∑Ni=1 P

ints,i ≤ PS ;

min(P ints,i ,

PS

N

), otherwise.

(5.21)

Similarly, at each relay, the relay power is allocated among the respective sub-

carriers (subcarriers with Ak,i = 1) as,

Pk,i =

P intk,i , if

∑i∈Dk

P intk,i ≤ PK ;

min(P intk,i ,

PK

nk

), otherwise.

(5.22)


Here, Dk is the set of subcarriers relayed by the kth relay, and nk is the number

of subcarriers in the set Dk. Pints,i and P int

k,i are as dened in (5.12) and (5.13),

respectively.

The computational complexity of this resource allocation method is O((K +

2)N). The relay selection process requires KN number of evaluations and the

power allocation requires N number of calculations for source and relay power

allocation, each. This results in total of (K + 2)N number of calculations.

5.5 Joint Optimal Resource Allocation

With joint optimal resource allocation, all possible subcarrier-relay assignments

are considered, and for each subcarrier-relay assignment the power is allocated in

an optimal manner as described in Section 5.4.1.2. Then the relay selection and

power allocation which results in the maximum capacity is chosen as the optimal

solution. There areKN possible subcarrier-relay assignment combinations and for

each possible subcarrier-relay assignment, optimal power allocation is performed

with O(N3) computational complexity (with interior-point method). This results

in a total computational complexity of O(KN N3) for the joint optimal resource

allocation method.


This section presents numerical results to evaluate the performance of the pro-

posed resource allocation methods. A multi-relay assisted OFDM-based CR sys-

tem was implemented in MATLAB and the performance of the dierent resource

allocation methods was studied by means of Monte-Carlo simulations. Results

were obtained for two dierent simulation scenarios.

Figure 5.3 illustrates the PU and CR distribution for the rst simulation

scenario. The PUs are located at (0, 0) and (1800, 0). The CR source and the


CR destination are located at (400, 0) and (1400, 0), respectively. The CR relays

are assumed to be uniformly distributed within a circular area with a radius

r = 100m. The center of the relay cluster is located between the source and the

destination, dsr (m) away from the source.

dsr (m)

r (m)

CR Relay

Cluster

CR Source CR DestinationPU 1 PU 2

(400,0) (1400,0) (1800,0)(0,0)

Figure 5.3: Primary user (PU) and CR distribution - Simulation setup 1

In order to obtain the results with the joint optimal resource allocation method,

number of subcarriers in the OFDM system was taken as N = 6. The joint

optimal resource allocation involves higher computational complexity for large

number of subcarriers and relays. Further it requires longer simulation run time.

Thus, the number of subcarriers was limited to N = 6. Figure 5.4 shows the cor-

responding spectrum allocation, which was adapted from [87]. The values of ∆f ,

B1, and B2 were 0.3125MHz, 1MHz, and 2MHz, respectively [87, 125]. The noise

variances at the relays and the destination were set to σ2k = σ2

d = 4.14× 10−16W.

This corresponds to a noise power spectrum density of 4.14 × 10−21W/Hz [12].

The values of interferences Jlk,i and Jld,i were taken as 1× 10−17W. Ts was cho-

sen to be 4µs [125]. Simulations were carried out for frequency selective Rayleigh

fading channels with two multipath taps and unit fading power. The path loss

exponent was taken as 4. PS and PK were set to be 20dBm.

Figure 5.5 illustrates capacity variation with the interference threshold for

proposed resource allocation methods. The number of relays is taken as K = 3,

and the distance from the CR source to the relay cluster is xed to be dsr = 300m.

Figure 5.5 also shows the capacity obtained with the joint optimal resource alloca-


B2=2 MHz ∆f

2nd

PU

band

1st

PU

band

Secondary users

B1=1 MHz

1 2 3 4 5 6

Figure 5.4: Spectrum allocation - Simulation setup 1

tion. It can be observed that the Resource Allocation Method B has relatively poor

performance than the Resource Allocation Method A. The performance degrada-

tion can be compensated by the simple power allocation strategy used in Resource

Allocation Method B. Further, the Resource Allocation Method A shows near op-

timal performance at low interference thresholds. It can be observed that at

low Ith values capacity increases with interference. But at higher Ith values maxi-

mum transmit power becomes the limiting constraint and capacity saturates with

increase in Ith.

1 3 5 7 9 11 13 152

2.5

3

3.5

4

4.5

Ith (in 10

-15 W)

Instan

taneo

us ca

pac

ity per subca

rrier (b/s/H

z)

Joint Optimization

Resource Allocation Method A

Resource Allocation Method B

Figure 5.5: Instantaneous capacity variation with interference threshold - Simu-lation setup 1, K = 3, dsr = 300m


Figure 5.6 compares the capacity variation of dierent resource allocation

methods with varying number of relays. The interference threshold is xed at

Ith = 5 × 10−15 W. Accordingly, as the number of relays increases, performance

of the Resource Allocation Method A degrades as compared to the joint optimal

resource allocation.

2 3 4 53

3.1

3.2

3.3

3.4

3.5

3.6

3.7

3.8

Number of relays

Instan

taneo

us ca

pac

ity per subca

rrier (b/s/H

z)

Joint Optimization



Figure 5.6: Instantaneous capacity variation with number of relays - Simulationsetup 1, Ith = 5× 10−15W, dsr = 300m

In Figure 5.7, capacity versus relay location is plotted for dierent resource

allocation methods with K = 3 relays and Ith = 5 × 10−15W. For the given

PU and CR distribution in Figure 5.3, the maximum capacity is achieved when

the relay cluster is located dsr = 300m away from the source. Also the Resource

Allocation Method A achieves close to optimal performance when the relay cluster

is located close to the source or the destination.

In order to further analyze the performance of the proposed resource alloca-

tion methods, an OFDM-based CR relay network with N = 16 subcarriers was

implemented in MATLAB. The number of PUs was taken as L = 4. Figure 5.8


100 200 300 400 500 600 700 800 9002

2.2

2.4

2.6

2.8

3

3.2

3.4

3.6

dsr (m)

Instantaneous capacity per subcarrier (b/s/Hz)

Joint Optimization



Figure 5.7: Instantaneous capacity variation with relay location - Simulationsetup 1, K = 3, Ith = 5× 10−15W

and Figure 5.9 illustrate the respective CR and PU distribution, and the spectrum

allocation.

dsr (m)

r (m)

CR Relay

Cluster

CR Source CR DestinationPU 1 PU 4

(400,0) (1400,0) (1800,0)(0,0)

(700, 500)

PU 2

(1100, -500)

PU 3

Figure 5.8: Primary user (PU) and CR distribution - Simulation setup 2

Figure 5.10 shows the capacity variation with the location of the relay cluster

for Resource Allocation Method A and Resource Allocation Method B with the

second simulation scenario. For the CR and PU distribution given in Figure 5.8,

the maximum capacity is achieved when the relay cluster is located dsr = 400m


B2=2 MHz∆f

2nd

PU

band

1st

PU

band

Secondary users

B1=1 MHz

1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16

3rd

PU

band

4th

PU

band

B3=3 MHz B4=5 MHz

Figure 5.9: Spectrum allocation - Simulation setup 2

away from the CR source. At the maximum capacity relay location, Resource

Allocation Method A achieves, on average, 4% capacity improvement compared

to Resource Allocation Method B.

100 200 300 400 500 600 700 800 9001.6

1.8

2

2.2

2.4

2.6

dsr (m)




Figure 5.10: Instantaneous capacity variation with relay location - Simulationsetup 2, K = 3, Ith = 5× 10−15W

In Figure 5.11, capacity variation with the interference threshold is plotted

for the proposed two resource allocation methods. The relay location is xed

at dsr = 400m and the number of relays is set as K = 3. Even for the second

simulation scenario, the Resource Allocation Method A results in higher capacity

than the Resource Allocation Method B. Figure 5.12 illustrates capacity variation


with number of relays for Resource Allocation Method A and Resource Allocation

Method B. The relay location is xed at dsr = 400m and the interference threshold

is taken as Ith = 5 × 10−15 W. Performance results in Figure 5.12 conrm the

behavior observed in Figure 5.6 for the simulation setup 1.

1 3 5 7 9 11 13 151

1.5

2

2.5

3

3.5

Ith

(W)

Inst

anta

neo

us

capac

ity p

er s

ubca

rrie

r (b

/s/H

z)



Figure 5.11: Instantaneous capacity variation with interference threshold - Sim-ulation setup 2, K = 3, dsr = 400m

It can be observed that the overall capacities achieved with simulation setup 2

is much lower than the capacities obtained for simulation setup 1. In simulation

setup 2, the CR transmission is limited by the interference introduced to four PU

receivers. In both simulation scenarios, the CR source transmit power is limited

by the interference generated at PU 1 which is located closest to the source. In

the rst simulation setup in Figure 5.3, the CR relay transmit power increases

when the relay cluster moves away from PU 1 and again decreases when the relay

cluster moves closer to PU 2. In the second simulation scenario in Figure 5.8,

the CR relay transmit power is further limited by the interference produced at

PU 2 and PU 3, which are located between the CR source and destination. As


2 3 4 5 6 72

2.2

2.4

2.6

2.8

Number of Relays

Instan

taneo

us ca

pac

ity per subca

rrier (b/s/H

z)



Figure 5.12: Instantaneous capacity variation with number of relays - Simulationsetup 2, Ith = 5× 10−15W, dsr = 400m

a result, CR relays transmit less power and eventually results in lesser capacity

compared to scenario 1.

5.7 Conclusion

This chapter addressed the relay selection and power allocation problems in

OFDM-based CR systems with multiple AF relays. The resource allocation

problem was formulated to maximize the total instantaneous capacity of the

CR system. Both individual power constraints and total interference constraints

were taken into consideration. The joint optimization problem is a mixed bi-

nary integer programming problem and hence, it is hard to nd an analytical

solution. Thus, two suboptimal resource allocation methods, Resource Allocation

Method A and Resource Allocation Method B, were proposed. In these subopti-

mal resource allocation methods, the relay selection is performed suboptimally,

assuming xed power allocation at source and relays. For this relay selection, the


Resource Allocation Method A allocates subcarrier transmit power in an optimal

manner and the Resource Allocation Method B allocates transmit power in a sub-

optimal manner. Results conrm that the proposed Resource Allocation Method

A outperforms the Resource Allocation Method B. Moreover, Resource Allocation

Method A achieves near optimal performance in many situations with much less

computational complexity than the joint optimal resource allocation.

Chapter 6

Power Allocation in OFDM CR

Relay Networks with Knowledge of

Statistical CSI

6.1 Introduction

The increasing demand for the currently deployed spectrum and the underuti-

lization of the current spectrum allocation motivate the development of cogni-

tive radio (CR) communications. With CR technology, secondary users (SUs)

are allowed to access and share the available spectrum holes which are origi-

nally licensed to primary users (PUs). The coexistence of secondary and primary

transmissions is allowed as long as the secondary transmission does not generate

unacceptable level of interference to the primary transmissions.

As mentioned in Chapter 5, substantial amount of studies has been carried

out on resource allocation in OFDM-based CR relay networks (e.g., [13, 84, 86,

87, 88, 85, 89, 123, 124]). Almost all of the available studies on resource allo-

cation in OFDM-based CR relay networks assume that a perfect knowledge of

the instantaneous channel state information (CSI) between CR transmitters and

6. OFDM CR RELAY NETWORKS WITH STATISTICAL CSI 116

PU receivers is available at the CR transmitters. However, it may not be rea-

sonable to assume that the CR transmitters can obtain the CSI between itself

and the PUs in an instantaneous manner. In particular, the CSI between the CR

transmitter and its receiver can be known at the CR transmitter via a feedback

channel. But it is dicult, if not possible, to estimate the instantaneous CSI be-

tween the CR transmitter and the PU receivers. In general, the CR transmitter

can obtain the channel fading gains between itself and the PU receivers from a

band manager mediating between the primary and secondary systems [126] or

from the pilot signals transmitted by the PU receivers [127, 128]. But there is no

guarantee that these methods can provide the channel fading gain information

instantaneously. If the SU transmitter or PU receiver has mobility, the resulting

CSI can be outdated due to the delay in feedback [90]. Nevertheless, the infor-

mation received in these methods can be used to predict the long-term fading

statistics (channel mean and channel correlation) instead of instantaneous fading

gains between the CR transmitter and PU receiver. As an example, the mean

value of the random channel fading gains between a PU receiver and a CR trans-

mitter can be estimated from the pilot signals transmitted by the PU receiver

[127]. When the knowledge of the channel correlation and/or channel mean is

available, the CSI can be expressed in a statistical manner.

This chapter investigates power allocation in OFDM-based CR relay networks

in the presence of statistical CSI between the CR transmitter and PU receivers.

Power allocation in CR relay networks with statistical CSI is not comprehensively

studied in the prevailing literature. In [129], authors study power allocation in

single-hop OFDM-based CR networks assuming only the fading statistics between

the CR and the PUs is available at the CR transmitter. Authors propose power

allocation methods with dierent statistical interference constraints imposed by

dierent PUs. This chapter presents power allocation methods to maximize the

instantaneous capacity of CR relay networks assuming average interference con-

straints at each PU receiver. In particular, two scenarios are considered:


• Available CSI at the CR transmitter is outdated

• Only the channel fading statistics are known at the CR transmitter

Optimal power allocation schemes for both decode-and-forward (DF) and amplify-

and-forward (AF) relay assisted OFDM CR transmissions are derived. Further-

more, less-complex suboptimal power allocation schemes are also proposed as

simpler alternatives for optimal power allocation methods.

The rest of this chapter is organized as follows: The system and channel model

is described in Section 6.2. Power allocation schemes for DF and AF relay assisted

CR networks is presented in Section 6.3 and Section 6.4, respectively. In Section

6.5, uniform power allocation method is presented as a baseline power allocation

strategy. Section 6.6 illustrates the performance of the proposed methods through

computer simulations.


A scenario where an OFDM-based CR relay network co-existing with a PU net-

work is considered for this analysis. It is assumed that the direct link between

the CR source (s) and the CR destination (d) is blocked by obstacles and there

is no direct path between source and destination. Thus, the CR source tries to

communicate with the destination through an intermediate relay (r). In spatial

domain, the CR network co-exists with the primary network as shown in Fig-

ure 6.1. For clarity of presentation only one PU transmitter and receiver pair is

shown in Figure 6.1. In general, there are L PU transmitter and receiver pairs in

the proximity of the CR system. In the frequency domain, CRs and PUs co-exist

in side-by-side bands as shown in Figure 5.2. There are L PU bands with the lth

PU band having a bandwidth of Bl. A selected set of available unused frequency

bands are divided into N subcarriers each having a bandwidth of ∆f . These N

subcarriers are used for OFDM transmission of the CR network. It is assumed


that the spectrum sensing has been performed and the source and the relay have

a complete knowledge of the frequency bands available for transmission. Let l

denote the lth PU: l ∈ [1 : L], and i denote the ith subcarrier: i ∈ [1 : N ].

lthband

PU

receiver

CR Source

(s)

CR

Destination

(d)

CR Relay

(r)

lthband

PU

transmitter

Interference

to PU

receiver

Interference

from PU

transmitter

Direct path blocked

by obstacle

Figure 6.1: Co-existence of CR relay link and PU system

It is assumed that the CR relays support only half-duplex operations. As in

any conventional relay communication, two orthogonal time slots are used to im-

plement source-to-relay communication and relay-to-destination communication.

In the rst time slot, the source transmits data with power Ps,i on the ith subcar-

rier and it is received by the relay; in the second time slot, the relay retransmits

the received information to the destination. In the case of a DF relay, the relay

decodes and retransmits the received data on the same subcarrier using power

Pr,i. Then the instantaneous rate of the ith subcarrier, CDF,i can be expressed as

[19, 87],

CDF,i = min

(1

2log2(1 + Ps,iγsr,i),

1

2log2(1 + Pr,iγrd,i)

)b/s/Hz. (6.1)

With AF relay, the relay amplies the signal using power Pr,i on the same sub-

carrier and transmits the amplied signal to the destination. Following a similar

approach as in Section 5.3, the instantaneous rate of one subcarrier with AF relay,


CAF,i, can be written as,

CAF,i =1

2log2

(1 +

Ps,iγsr,iPr,iγrd,i1 + Ps,iγsr,i + Pr,iγrd,i

)b/s/Hz. (6.2)

Here, γsr,i =|Hsr,i|2

σ2r+

∑Ll=1 Jlr,i

, and γrd,i =|Hrd,i|2

σ2d+

∑Ll=1 Jld,i

are the instantaneous channel-

to-noise ratios (CNRs) at the relay and the destination, respectively. The CSI

of the ith subcarrier between nodes m and n, Hmn,i (m ∈ s, r andn ∈ r, d, l),

represents the eect due to both the path loss and the fading gain. σ2r and σ2

d

are the noise variances at the relay and destination, respectively. Jlr,i is the

interference introduced by the lth PU at the relay and Jld,i is the interference

introduced by the lth PU at the destination. Following [118] and [129], it is

assumed that the CR receivers can perfectly estimate the total interference from

PUs (∑L

i=1 Jlr,i and∑L

i=1 Jld,i) and these estimated values are fed back to CR

transmitters via a feedback channel.

When a CR system co-exists with a PU system, the interference introduced

by mth CR transmitter (m ∈ s, r) at lth PU band on ith CR subcarrier, Iml,i,

can be expressed as [87, 120],

Iml,i = Pm,i |Hml,i|2 Ωl,i

= Pm,i gml,iΩl,i (6.3)

where, Pm,i is the transmit power of the ith subcarrier, Ts is the symbol duration,

and Bl is the lth PU bandwidth. Hml,i is the CSI of the i

th subcarrier between the

CR transmitter m and lth PU receiver, and gml,i = |Hml,i|2 is the corresponding

channel gain. di,l is the spectral distance between the ith subcarrier and the lth

PU band, and Ωl,i = Ts∫ di,l+Bl/2

di,l−Bl/2

(sin (πfTs)πfTs

)2df .

It is assumed that the resource allocation decisions are made at the CR source

and a perfect knowledge of instantaneous CSI, Hsr and Hrd, between CR trans-

mitters and CR receivers are available at the time of decision making. However,


it is assumed that obtaining the CSI between the secondary and primary users in

an instantaneous manner is not possible. Thus, it is not possible to calculate the

instantaneous interference in (6.3). Nevertheless, if the probability distribution

of the CSI between CR transmitters and PU receivers is known, then the average

interference can be calculated using the knowledge of the probability distribution

of gml,i. Following two scenarios are considered in this study:

• Available CSI is outdated and the knowledge of channel correlation and

channel mean is available at the CR transmitter

• Only the channel fading statistics (mean value of the channel fading gains)

are known at the CR transmitter

Case 1: Average Interference with Outdated CSI

It is assumed that the available CSI at the CR transmitter is an outdated, but

correlated version of the actual instantaneous CSI with a correlation coecient ρ.

Assuming that both the instantaneous and outdated CSI are complex Gaussian

with zero mean and unit variance, the distribution of instantaneous CSI, Hml,i,

conditioned on available outdated CSI, Hml,i, can be expressed as [114],

Hml,i | Hml,i ∼ CN (ρ Hml,i, 1− ρ2) (6.4)

Without loss of generality ρ is assumed to be same for all the subcarriers. As-

suming that CR source knows not only the outdated CSI, but also the correlation

coecient ρ, the conditional pdf of the instantaneous channel gain, gml,i, can be

expressed as a non-central Chi-squared distribution with two degrees of freedom

as shown in (6.5) (subscript i has been omitted for simplicity of presentation)[114].

fgml|gml=

1

gml(1− ρ2)e− 1

gml(1−ρ2)(ρ2gml+gml)

I0 ([·])

[·] =2

gml(1− ρ2)

√ρ2gmlgml (6.5)


Here, I0 is the zero-order modied Bessel function of the rst kind, gml = |Hml|2

is the outdated channel gain, and gml is the long-term average. To evaluate the

average interference in closed-form, the Chi-squared pdf (6.5) can be approxi-

mated with the Gamma pdf as shown in [105]. Then the conditional pdf of gml,i

can be expressed as (subcarrier index i has been omitted for notational brevity),

fgml|gml≃ βθml

ml

Γ(θml)gθml−1ml e−βmlgml (6.6)

where, θml =(Kml+1)2

2Kml+1is the Gamma pdf shape parameter with Kml =

ρ2gml

gml(1−ρ2),

and βml =θml

ρ2gml+gml(1−ρ2)is the Gamma pdf rate parameter.

With the conditional pdf (6.6), the average interference introduced by ith

subcarrier during CR source transmission can be written as,

E [Isl,i] = Egsl,i|gsl,i [Ps,igsl,iΩl,i]

= Ps,iΩl,i

∫ ∞

0

gsl,i fgsl,i|gsl,i d gsl,i

= Ps,iΩl,i

βθsl,isl,i

Γ(θsl,i)

∫ ∞

0

gθsl,isl,i e

−βsl,igsl,i d gsl,i (6.7)

where, E[·] denote the expectation operator. Above integration can be solved

using the result [116, Eq. 3.351.3], and the closed-form expression for E [Isl,i] can

be obtained as,

E [Isl,i] =Ps,iΩl,i θsl,i

βsl,i

= Ps,iΩl,i

[ρ2gsl,i + gsl,i(1− ρ2)

]. (6.8)

Similarly, the average interference generated by ith subcarrier during CR relay

transmission can be derived as,

E [Irl,i] = Egrl,i|grl,i [Pr,igrl,iΩl,i]

= Pr,iΩl,i

[ρ2grl,i + grl,i(1− ρ2)

]. (6.9)


Case 2: Average Interference with Fading Statistics

In this scenario, it is assumed that only the mean value of the fading gains is

known at the CR transmitter. As an example, if Rayleigh fading with known

variance σ2ml is considered between CR transmitters m and lth PU receiver, the

pdf of gml,i can be expressed as an exponential distribution with parameter λml

as shown in (6.10).

fgml,i= λmle

−λmlgml,i (6.10)

Here, λml =ψml

2σ2ml, where ψml is a factor that depends on the path loss experienced

between the CR transmitter and PU receiver.

With the help of the pdf (6.10) and the result [116, Eq. 3.351.3], the av-

erage interferences introduced by ith subcarrier during the CR source and relay

transmissions can be expressed as,

E [Isl,i] = Egsl,i [Ps,igsl,iΩl,i] = Ps,iΩl,i

λsl(6.11)

and

E [Irl,i] = Egrl,i [Pr,igrl,iΩl,i] = Pr,iΩl,i

λrl, (6.12)

respectively.

For ease of presentation and explanation, the average interference expressions

derived in above two cases can be combined as follows:

E [Isl,i] = Ps,i al,i (6.13)

and

E [Irl,i] = Pr,i bl,i (6.14)

where, al,i = Ωl,i

[ρ2gsl,i + gsl,i(1− ρ2)

]and bl,i = Ωl,i

[ρ2grl,i + grl,i(1− ρ2)

]for

case 1, and al,i =Ωl,i

λsland bl,i =

Ωl,i

λrlfor case 2.


6.3 Power Allocation for DF Relay Assisted CR

Networks

This section presents power allocation methods for DF relay assisted CR transmis-

sion when only the statistical CSI between the CR transmitter and PU receivers

is known at the CR transmitter. Knowledge of statistical CSI between secondary

and primary networks imposes average interference constraints at each PU re-

ceiver. The power allocation problem is formulated to maximize the capacity of

the CR transmission while the individual transmit power constraints and average

interference constraints are satised. Then the power allocation problem can be

written as follows:

MaximizeN∑i=1

min

(1

2log2(1 + Ps,iγsr,i),

1

2log2(1 + Pr,iγrd,i)

)(6.15)

subject to,

C1 :∑N

i=1 Ps,i ≤ PS

C2 :∑N

i=1 Pr,i ≤ PR

C3 :∑N

i=1E [Isl,i] ≤ I lth, ∀ l

C4 :∑N

i=1E [Irl,i] ≤ I lth, ∀ l

C5 : Ps,i ≥ 0, ∀ i

C6 : Pr,i ≥ 0, ∀ i

(6.16)

where, PS and PR are the maximum source and the relay transmit powers, re-

spectively. I lth is the maximum permissible average interference to the lth PU

receiver. The constraints C1 and C2 are the total transmit power constraints for

CR source and relay transmission, respectively. The constraints C3 and C4 rep-

resent the average interference introduced by CR source and relay transmission,

respectively. The average interferences E [Isl,i] and E [Irl,i] can be calculated as

shown in (6.13) and (6.14), respectively.


It has been shown in [87] and [130], that the minimum of the capacities in

(6.15) is maximized when the signal-to-noise ratios (SNRs) at the relay and the

destination are equal, i.e., when

γrd,i Pr,i = γsr,i Ps,i

Pr,i = ηi Ps,i (6.17)

where, ηi =γsr,iγrd,i

. With the result in (6.17), the optimization problem can now be

reformulated as,

MaximizeN∑i=1

1

2log2 (1 + Ps,i γsr,i) (6.18)

subject to,

C1 :∑N

i=1 Ps,i ≤ PS

C2 :∑N

i=1 ηi Ps,i ≤ PR

C3 :∑N

i=1 Ps,i al,i ≤ I lth, ∀ l

C4 :∑N

i=1 Ps,i ηi bl,i ≤ I lth, ∀ l

C5 : Ps,i ≥ 0, ∀ i

(6.19)

6.3.1 Optimal Power Allocation Method

The objective function (6.18) is a maximization of a concave function of Ps,i

and the constraints in (6.19) are linear functions of Ps,i. Hence it is a convex

optimization problem can be solved using Karush-Kuhn-Tucker (KKT) optimality

conditions [95]. The solution for the optimal source transmit power P ∗s,i can be

obtained as,

P ∗s,i =

1

2 ln(2)[ν1 + ν2ηi +

∑Ll=1 (µlal,i + δlηibl,i)

] − 1

γsr,i

+

(6.20)


where, [x]+ = max(0, x). The constants ν1 and ν2 are non-negative Lagrange

parameters which are selected such that the sum power constraints C1 and C2 in

(6.19) are satised, respectively. The Lagrange parameters µl and δl are chosen

such that the sum interference constraints C3 and C4 in (6.19) are satised,

respectively. A detailed derivation of this solution is provided in Appendix C.

The optimal power allocation problem can be solved numerically using interior-

point method with a complexity of O(N3) [95]. Once the optimal source transmit

powers are calculated, the respective relay transmit powers can be obtained using

(6.17).

6.3.2 Suboptimal Power Allocation Method

The optimal power allocation scheme has higher computational complexity for

large number of subcarriers. Hence, this section presents a suboptimal power

allocation scheme with reduced complexity. The proposed method can be used

in situations where ecient power allocation schemes with some capacity degra-

dation are preferred over complex optimal power allocation algorithms.

The suboptimal method takes one constraint at a time and nd a set of power

values corresponding for each constraint. For the lth PU interference constraint,

two power values can be obtained considering the interference generated at each

time slot independently. First, ignoring the interference generated during relay

transmission, the following optimization problem can be formulated.

MaximizeN∑i=1

1

2log2 (1 + Ps,i γsr,i) (6.21)

subject to,

∑Ni=1 Ps,i al,i ≤ I lth

Ps,i ≥ 0, ∀ i(6.22)


This constrained optimization problem can be solved using KKT optimality con-

ditions and the solution can be obtained as shown in (6.23).

P ls,i(T1) =

[1

2 ln(2)υl1 al,i− 1

γsr,i

]+υl1 =

N

2 ln(2)(I lth +

∑Ni=1

al,iγsr,i

) (6.23)

Similarly, ignoring the interference in the rst time slot, the optimization problem

can be written as,

MaximizeN∑i=1

1

2log2 (1 + Ps,i γsr,i) (6.24)

subject to,

∑Ni=1 Ps,i ηi bl,i ≤ I lth

Ps,i ≥ 0, ∀ i(6.25)

Then the solution can be calculated as,

P ls,i(T2) =

[1

2 ln(2)υl2 ηi bl,i− 1

γsr,i

]+υl2 =

N

2 ln(2)(I lth +

∑Ni=1

ηi bl,iγsr,i

) (6.26)

A similar approach is used to get the respective power values for the maximum

transmit power constraints. These can be expressed as given in (6.27) and (6.28).

PL+1s,i (T1) =

[1

2 ln(2)ω1

− 1

γsr,i

]+ω1 =

N

2 ln(2)(PS +

∑Ni=1

1γsr,i

) (6.27)


PL+1s,i (T2) =

[1

2 ln(2)ω2 ηi− 1

γsr,i

]+ω2 =

N

2 ln(2)(PR +

∑Ni=1

ηiγsr,i

) (6.28)

The power allocation procedure for the suboptimal algorithm is as follows:

1. For the lth interference constraint calculate P ls,i(T1) and P l

s,i(T2) using

(6.23) and (6.26), respectively.

2. Find the power P ls,i that satises the l

th interference constraint during both

source and relay transmission. If the set of subcarrier transmit power values

P ls,i(T1) satisfy the interference constraint for the second time slot (i.e.,∑Ni=1 P

ls,i(T1) ηi bl,i ≤ I lth), set P

ls,i to be P l

s,i(T1),∀i. Otherwise, assign P ls,i

as P ls,i = min

(P ls,i(T1), P

ls,i(T2)

).

3. Repeat above procedure for all the L interference constraints.

4. For the maximum transmit power constraints, calculate PL+1s,i (T1) and

PL+1s,i (T2) using (6.27) and (6.28), respectively.

5. If the set of subcarrier transmit power values PL+1s,i (T1) satisfy the relay

transmit power limitation (i.e.,∑N

i=1 PL+1s,i (T1)ηi ≤ PR), set P

L+1s,i to be

PL+1s,i (T1), ∀i. Otherwise, assign PL+1

s,i as PL+1s,i = min

(PL+1s,i (T1), PL+1

s,i (T2)).

6. This procedure leads to a set of L + 1 power values for each subcarrier.

Then, for each subcarrier, the source transmit power is set as the minimum

of the available power values, i.e.,

Ps,i = min(P 1s,i, P

2s,i, ...., P

Ls,i, P

L+1s,i

), ∀ i. (6.29)

Hence, all the constraints are satised by the assigned subcarrier transmit

powers.


But it may happen that above power allocation might not meet any of the con-

straints with strict equality. Thus subcarrier transmit power may be increased to

meet at least one of the constraints with equality and the capacity can be further

increased. Let ∆Il(T1) and ∆Il(T2) be the residual interferences related to the

source and relay transmission, respectively. These residual interferences can be

expressed as below:

∆Il(T1) = I lth −N∑i=1

Ps,i al,i, ∀ l (6.30)

∆Il(T2) = I lth −N∑i=1

Ps,i ηi bl,i, ∀ l (6.31)

The source transmit power can be updated such that the minimum of the residual

interferences is distributed among the subcarriers according to the ratio of the

interference each subcarrier generates to the respective PU receiver. Let ∆I be

the minimum residual interference. Then the power values can be updated as,

P updates,i =

Ps,i +∆I Ps,i∑Ni=1 Ps,ial,i

, if ∆I = ∆Il(T1) ;

Ps,i +∆I Ps,i∑N

i=1 Ps,i ηi bl,i, if ∆I = ∆Il(T2) .

(6.32)

Similarly, let ∆P (T1) and ∆P (T2) be the residual powers related to source and

relay power constraints, respectively. These residual powers can be expressed as,

∆P (T1) = PS −N∑i=1

Ps,i (6.33)

and,

∆P (T2) = PR −N∑i=1

ηiPs,i. (6.34)

If the system is power limited, Ps,i can be updated such that the minimum of

the residual powers is distributed among the subcarriers according to the ratio of

the current power allocation. Let ∆P be the minimum residual power. Then the


updated power values can be given as,

P updates,i =

Ps,i +∆P Ps,i∑Ni=1 Ps,i

, if ∆P = ∆P (T1) ;

Ps,i +∆P Ps,i∑Ni=1 Ps,iηi

, if ∆P = ∆P (T2) .(6.35)

This power update procedure can be expressed as follows:

1. Calculate ∆Il(T1) and ∆Il(T2) for all the l ∈ [1 : L] interference con-

straints. Find the minimum residual interference ∆I and update the power

values using (6.32).

2. If the power constraints are violated by the above updated power values,

(a) Calculate ∆P (T1) and ∆P (T2). Find the minimum residual power

∆P and update Ps,i using (6.35).

(b) If at least one of the interference constraints is violated by the above

updated power values switch back to the power allocation given by

(6.29).

The computational complexity of the proposed suboptimal power allocation method

is O(LN).

6.4 Power Allocation for AF Relay Assisted CR

Networks

This section discusses power allocation schemes for AF relay assisted CR trans-

mission. The objective of power allocation is to maximize the total instantaneous

capacity of the CR transmission while the transmit power and average interfer-

ence introduced to PU receivers do not exceed the given thresholds. The Power

allocation problem for AF relay assisted CR relay transmission can be stated as


follows:

MaximizeN∑i=1

1

2log2

(1 +


)(6.36)

subject to,

C1 :∑N

i=1 Ps,i ≤ PS

C2 :∑N

i=1 Pr,i ≤ PR

C3 :∑N

i=1E [Isl,i] ≤ I lth, ∀ l

C4 :∑N

i=1E [Irl,i] ≤ I lth, ∀ l

C5 : Ps,i ≥ 0, ∀ i

C6 : Pr,i ≥ 0, ∀ i

(6.37)

The constraints C1 and C2 are individual power constraints for source and

relay transmission, respectively. The constraints C3 and C4 represent the average

interference constraints for source and relay transmissions and can be replaced

by the closed form expressions (6.13) and (6.14), respectively.

6.4.1 Optimal Power Allocation Method

With AF relays, transmit power optimization is performed in two steps: relay

power optimization and source power optimization. As described in Section 3.3.2,

the power allocation process is started with an initial source power allocation.

First, the optimal relay transmit powers are calculated for this initial source power

allocation. Then, the source transmit powers are optimized for this optimal relay

power allocation. This process is continued until the capacity approaches to its

maximum value and further capacity improvement is not possible. The relay and

source power optimizations for the power allocation problem in (6.36)-(6.37) can

be explained as follows:


Relay Power Optimization

For a given source power allocation, the relay power optimization problem can

be stated as,

MaximizeN∑i=1

1

2log2

(1 +


)(6.38)

subject to,

∑Ni=1 Pr,i ≤ PR∑N

i=1 Pr,i bl,i ≤ I lth, ∀ l

Pr,i ≥ 0, ∀ i

(6.39)

This is a convex optimization problem and can be solved using the respective

KKT system of equations. The solution for the optimal relay transmit power P ∗r,i

can be obtained as,

P ∗r,i =

1

γrd,i

[Ps,iγsr,i

2

(√[·]− 1

)− 1

]+[·] = 1 +

2γrd,i

ln(2)Ps,i γsr,i (α+∑L

l=1 ϕl bl,i)(6.40)

where, [x]+ = max(0, x). The constants α and ϕl are selected such that the sum

power constraint and the sum interference constraints in (6.39) are satised. A

detailed derivation of this solution is given in Appendix C.

Source Power Optimization

When the relay power allocation is known, the source power optimization problem

can be expressed as follows:

MaximizeN∑i=1

1

2log2

(1 +


)(6.41)


subject to,

∑Ni=1 Ps,i ≤ PS∑N


Ps,i ≥ 0, ∀ i

(6.42)

Solution for above optimization problem follows the same process to that of relay

power optimization in Appendix C, and the optimal source transmit power P ∗s,i

can be obtained as,

P ∗s,i =

1

γsr,i

[Pr,iγrd,i

2

(√[·])− 1

]+[·] = 1 +

2γsr,i

ln(2)Pr,i γrd,i (ϵ+∑L

l=1 ζl al,i). (6.43)

The non-negative Lagrange parameters ϵ and ζl should be chosen such that the

sum power constraint and the sum interference constraints in (6.42) are satised.

The optimal power allocation scheme involves a computational complexity of

O(N3) when interior-point method is used to solve the relay and source power

optimization problems.

6.4.2 Suboptimal Power Allocation Method

Optimal power allocation requires to solve for L+ 1 Lagrange multipliers at the

relay and source power optimizations and the computational complexity is very

high for systems with large number of subcarriers. Thus, this section presents

a suboptimal power allocation scheme with less computational complexity. The

suboptimal method allocates subcarrier transmit power such that the average

interference constraint at the PU receivers and the maximum transmit power

constraint at the CR transmitters are satised.

In this suboptimal scheme, the subcarrier transmit powers are allocated such

that each subcarrier generates uniform interference to the PUs during source and


relay transmissions. It is assumed that each subcarrier generates same amount

of interference (I lth/N) to the lth PU. If P ls,i and P

lr,i are the required amount of

source and relay transmit power to generate I lth/N interference at the lth PU,

then P ls,i and P

lr,i can be expressed as,

P ls,i =

I lth/N

al,i(6.44)

and

P lr,i =

I lth/N

bl,i, (6.45)

respectively. Since there are maximum transmit power limitations at the CR

source and relay, two other power values PL+1s,i = PS/N and PL+1

r,i = PR/N are

dened as uniform transmit powers at the source and the relay to satisfy the

maximum transmit power constraints.

For CR source transmission, P ls,i (l ∈ [1 : L]) together with PL+1

s,i provide a set

of L + 1 power values for each subcarrier. Thus, the source transmit power Ps,i

is set as the minimum of the available power values, i.e.,

Ps,i = min(P 1s,i, P

2s,i, ...., P

Ls,i, P

L+1s,i

), ∀ i. (6.46)

Similarly at the relay, the relay transmit powers are assigned as,

Pr,i = min(P 1r,i, P

2r,i, ...., P

Lr,i, P

L+1r,i

), ∀ i. (6.47)

Hence, all the constraints are satised. But it may happen that none of the

constraints are satised with strict equality. Thus subcarrier transmit power

may be increased to meet at least one of the constraints with equality and the

capacity can be further increased.

In order to update source transit powers, the interference constraints are taken

rst and the respective residual interferences, ∆Il, ∀l ∈ [1 : L] are calculate as


below:

∆Il = I lth −N∑i=1

Ps,i al,i, ∀ l. (6.48)

Then the source transmit power is updated such that the minimum of these

residual interferences is distributed among the subcarriers according to the ratio

of the interference each subcarrier generates to the respective PU receiver. If the

source power constraint is violated by this updated power allocation, the system

is power limited and the transmit power is updated using the residual power,

∆Ps = PS −∑N

i=1 Ps,i. This residual power is distributed among the subcarriers

according to the ratio of the current power allocation. Similarly, the relay power

allocation is also updated to meet at least one of the constraints with equality.

The proposed suboptimal power allocation scheme has a computational com-

plexity of O(LN).

6.5 Uniform Power Allocation Method

With uniform power allocation, the transmit power is allocated equally among

the subcarriers such that the interference and transmit power constraints are

satised. Since each CR transmission is subject to L interference constraints and

a maximum transmit power constraint, the assigned uniform power should satisfy

all the L + 1 constraints during source and relay transmission, respectively. Let

P ls,uni =

Ilth∑Ni=1 al,i

and P lr,uni =

Ilth∑Ni=1 bl,i

be the required uniform transmit power at

the source and the relay to generate I lth interference at the lth PU. Also PL+1

s,uni =

PS/N and PL+1r,uni = PR/N are the respective uniform transmit powers due to

the maximum transmit power constraints. Then the uniform source and relay

transmit powers, Ps,uni and Pr,uni are assigned as follows:

Ps,uni = min(P 1s,uni, P

2s,uni, ...., P

Ls,uni, P

L+1s,uni

)(6.49)

Pr,uni = min(P 1r,uni, P

2r,uni, ...., P

Lr,uni, P

L+1r,uni

)(6.50)


Hence, the selected uniform transmit power would satisfy all the constraints dur-

ing both source and relay transmission.


Monte-Carlo simulation results are presented in this section to assess the perfor-

mance of the proposed power allocation methods.

A CR relay network co-existing with a PU system as shown in Figure 6.2 was

simulated in MATLAB. The number of PUs was taken as L = 3 and the CR

relay was assumed to be located between the source and the destination. The

distance between the source and the relay were taken as dsr. All the distances

were taken in meters unless otherwise stated. The number of subcarriers in

the OFDM network was taken as N = 12. Figure 6.3 illustrates the spectrum

allocation used for the simulations. The values of B1, B2, and B3 were 1MHz,

2MHz and 5MHz, respectively. ∆f and Ts was chosen to be 0.3125MHz and

4µs, respectively [125]. The noise variances at the relays and the destination

were taken as σ2r = σ2

d = 1× 10−8W, and the values of interference Jlr,i and Jld,i

were set to be 1× 10−6W [87].

dsr (m)

CR

Relay

CR

SourceCR

Destination

PU 2

PU 3

(500,0) (1500,0) (2000,0)

PU 1

(0,0)

(1000,500)

Figure 6.2: Primary user (PU) and CR distribution

Frequency selective Rayleigh fading channels with two multipath taps and unit

fading power were assumed for this analysis. The path loss exponent was taken

as 3. Maximum allowable transmit powers at source and relay were considered

to be same at a value of P . Similarly, interference threshold at PU receivers were


B2=2 MHz∆f

2nd

PU

band

1st

PU

band

Secondary users

B1=1 MHz

3rd

PU

band

B3=5 MHz

1 2 3 4 5 6 7 8 9 101112

Figure 6.3: Spectrum allocation used in computer simulation

considered to be same for all the PUs and it was taken as Ith. All the results were

averaged over 1000 dierent fading channel realizations.

Capacity Variation with Relay Location

Figure 6.4 and Figure 6.5 illustrate the capacity variation with the relay location

for DF and AF relay assisted CR transmission, respectively. The results are

obtained for two cases:

• When the available CSI between CR transmitters and PU receivers is out-

dated

• When only the fading statistics between CR transmitters and PU receivers

are known

The gures compare the results obtained with the proposed optimal, suboptimal

and uniform power allocation methods. The interference threshold of each PU

is taken as 5 × 10−6W. For the given SU and PU distribution, for majority of

the situations, the maximum capacity is achieved when the source-relay distance,

dsr = 400m. In general, the CNR of source-to-relay hop, γsr,i, decreases and

CNR of relay-to-destination hop, γrd,i, increases as the relay moves away from

the source towards the destination. If the same amount of power is transmitted

by the source and the relay, the SNRs of the two hops (Ps,iγsr,i and Pr,iγrd,i)

balance at the middle of the source and the destination. This is generally where

the maximum capacity is achieved in non-cognitive networks if same amount of


100 200 300 400 500 600 700 800 9000.5

1

1.5

2

2.5

3

dsr (m)


ρ=0.7

ρ=0.8

ρ=0.9

ρ=0.99

Optimal powerallocation

Suboptimal powerallocation

Uniform powerallocation

(a)

100 200 300 400 500 600 700 800 9000.5

1

1.5

2

2.5

3

dsr (m)


Optimal power allocation

Suboptimal power allocation


(b)

Figure 6.4: Instantaneous capacity variation with relay location - DF relay (a)with outdated CSI (b) with fading statistics, Ith = 5× 10−6W, P = 0.01W


100 200 300 400 500 600 700 800 9000.5

1

1.5

2

2.5

3

dsr (m)


ρ=0.7

ρ=0.8

ρ=0.9

ρ=0.99




(a)

100 200 300 400 500 600 700 800 9000.5

1

1.5

2

2.5

3

dsr (m)





(b)

Figure 6.5: Instantaneous capacity variation with relay location - AF relay (a)with outdated CSI (b) with fading statistics, Ith = 5× 10−6W, P = 0.01W


power is transmitted by source and relay. In a CR environment, when the CR

network is interference limited, the transmit power of each CR transmitter is

mainly determined by the interference introduced to the closest PU receiver. For

the CR and PU distribution shown in Figure 6.2, the CR source transmit power

is determined by the interference introduced to PU 1, and on average, does not

vary with the relay location. On the other hand, the CR relay power increases

when the relay moves away from PU 1 and PU 2 and again decreases when it gets

closer to PU 3. Thus the SNR of the second hop increases at a rate much higher

than the rate that the SNR of the rst hop decreases. As a result, the SNRs of

the two hops balance before the relay reaches the midpoint of the source and the

destination, and the maximum capacity is achieved.

It can be clearly observed in Figure 6.4 and Figure 6.5 that the proposed

optimal and suboptimal power allocation schemes achieve signicant capacity

improvement over uniform power allocation. Table 6.1 summarizes the average

capacity improvement achieved with optimal and suboptimal power allocation

schemes over uniform power allocation at the peak capacity relay location. Also

it is evident from the results that the capacity achieved with the knowledge

of fading statistics is much less than the capacity achieved with outdated CSI,

specially when the available outdated CSI is highly correlated. According to

Figure 6.4a and Figure 6.5a, the achieved capacity degrades slightly with the

decrease of correlation coecient.


Suboptimalpower allocation

DF relay- Outdated CSI 32% 20%DF relay- Fading statistics 33% 17%AF relay- Outdated CSI 34% 22%AF relay- Fading statistics 36% 31%

Table 6.1: Average capacity improvement over uniform power allocation whendsr = 400m


Capacity Variation with Interference Threshold

1 3 5 7 9

x 10-6

0.5

1

1.5

2

2.5

3

3.5

Ith (W)


ρ=0.7

ρ=0.8

ρ=0.9

ρ=0.99




(a)

1 3 5 7 9

x 10-6

0.5

1

1.5

2

2.5

3

3.5

Ith (W)





(b)

Figure 6.6: Instantaneous capacity variation with interference threshold - DFrelay (a) with outdated CSI (b) with fading statistics, dsr = 500m, P = 0.01W


1 3 5 7 9

x 10-6

0.5

1

1.5

2

2.5

3

3.5

Ith (W)


ρ=0.7

ρ=0.8

ρ=0.9

ρ=0.99




(a)

1 3 5 7 9

x 10-6

0.5

1

1.5

2

2.5

3

3.5

Ith (W)





(b)

Figure 6.7: Instantaneous capacity variation with interference threshold - AFrelay (a) with outdated CSI (b) with fading statistics, dsr = 500m, P = 0.01W


Figure 6.6 and Figure 6.7 show the capacity variation with the interference thresh-

old for DF and AF relaying protocols, respectively. Results are obtained when

the relay is located dsr = 500m away from the source. The gures illustrate

capacity variation at low interference thresholds, i.e., when the CR transmission

is interference limited. Accordingly, the capacity increases with the increase of

interference threshold as the CR transmitters gain more freedom to allocate more

power on the dierent subcarriers. But at much higher interference thresholds,

transmit power constraint becomes the limiting factor and the capacity does not

vary with the interference threshold.

In order to further analyze the capacity behavior of CR relay networks with

respect to both the relay location and the interference threshold, Figure 6.8 plots

the capacity achieved with optimal power allocation for a range of source-relay

distances and interference threshold values. The results are obtained with DF

relay and when the correlation coecient is 0.8. It can be observed that for all

the interference threshold values the maximum capacity is achieved at the same

relay location.

Capacity Variation with Transmit Power

Figure 6.9 and Figure 6.10 plot the capacity variation with transmit power for DF

and AF relay assisted CR transmission, respectively. Results are obtained when

dsr = 500m and Ith = 1mW. The values for P and Ith were selected such that the

CR transmission becomes power limited, where the network can be approximated

to be performed in a non-cognitive manner and the power allocation problem

is mainly governed by the transmit power constraints, not by the interference

constraints. Hence, the average interference constraints appear to have very little

impact on the allocated powers. It can be observed that the results obtained with

outdated CSI and fading statistics are very close to each other in both the DF

and the AF relay cases. Also when the available CSI is outdated, the correlation


0.10.3

0.50.7

0.90.9

x 10-5

200400

600800

1

2

3

4

Ith

(W)d

sr (m)

Inst

anta

neo

us

capac

ity p

er s

ubca

rrie

r (b

/s/H

z)

Figure 6.8: Instantaneous capacity variation with relay location and interferencethreshold with optimal power allocation method (DF relay), P = 0.01W, ρ = 0.8

coecient only eects the average interference. Hence, the correlation coecient

does not have a noticeable impact on the capacity in the power limited situation.

Thus in Figure 6.9a and Figure 6.10a, the results are shown only for ρ = 0.9 case.

Furthermore, with AF relay, the proposed suboptimal power allocation scheme

reduces to uniform power allocation when the CR transmission is power limited.

With DF relay, both optimal and suboptimal power allocation methods perform

better than the uniform power allocation but with less capacity improvement

compared to the interference limited situation. As expected, at low transmit

powers, the capacity increases with the increase of P as the CR source and relay

become able to distribute the total available transmit power among the dierent

subcarriers without violating the interference constraints.


1 3 5 7 9 11 13 15

x 10-3

2

2.5

3

3.5

4

4.5

P (W)





(a)

1 3 5 7 9 11 13 15

x 10-3

2

2.5

3

3.5

4

4.5

P (W)





(b)

Figure 6.9: Instantaneous capacity variation with transmit power - DF relay (a)with outdated CSI, ρ = 0.9 (b) with fading statistics, dsr = 500m, Ith = 10−3W


1 3 5 7 9 11 13 15

x 10-3

1.5

2

2.5

3

3.5

4

P (W)





(a)

1 3 5 7 9 11 13 15

x 10-3

1.5

2

2.5

3

3.5

4

P(W)





(b)

Figure 6.10: Instantaneous capacity variation with transmit power - AF relay (a)with outdated CSI, ρ = 0.9 (b) with fading statistics, dsr = 500m, Ith = 10−3W


6.7 Conclusion

This chapter investigated the power allocation problem in relay assisted OFDM-

based CR networks when the statistical CSI between CR and PU networks are

known at the CR transmitter. In particular, two statistical CSI cases were con-

sidered: when the available CSI is outdated, and when only the fading statistics

are known. Since it is impossible to obtain the actual instantaneous interference

with the knowledge of statistical CSI between the CRs and PUs, the interfer-

ence constraints were satised in an average manner. Optimal power allocation

schemes to maximize the instantaneous capacity of the CR transmission were

presented for both DF and AF relay assisted scenarios. Additionally, suboptimal

power allocation schemes with reduced complexity were also proposed for both

DF and AF relay assisted CR transmissions. Performance of the proposed power

allocation methods was compared with uniform power allocation. Accordingly,

proposed optimal and suboptimal power allocation schemes achieve signicantly

higher capacity than uniform power allocation method when the CR transmission

is interference limited. However, the respective capacity improvement in power

limited situation is much less than the interference limited situation.

Chapter 7

Power Allocation in OFDM

Cognitive Radio Networks

Operating in TV White Space

7.1 Introduction

Cognitive radio (CR) [5] has been identied and researched as the enabling tech-

nology that would allow dynamic reuse of already licensed but spatially or tem-

porally unused frequency bands. This would improve the spectrum utilization

and increase the spectrum availability for new applications. Due to the explosive

growth of wireless and mobile services and the underutilization of the licensed

spectrum, regulators around the world are paying more attention towards al-

lowing unlicensed access to the unused or underutilized portions of the licensed

spectrum. In particular, the Federal Communications Commission (FCC) in the

United States, Ofcom in the United Kingdom (UK), and the Electronic Commu-

nications Committee (ECC) of the Conference of European Post and Telecom-

munications (CEPT) in Europe have identied the unused portions of the TV

spectrum as the initial home for CR based services [14, 15]. This portion of the

7. CR IN TV WHITE SPACE 148

TV spectrum that is becoming available for sharing is known as TV white space

(TVWS).

TVWS is a result of the switchover from analog to digital television transmis-

sion. Television broadcasters around the world are moving from analog television

broadcasting to digital television broadcasting. As an example, the United States

and United Kingdom have already completed their digital television switchover

while Australia is expecting to complete the full region-by-region transition by

December 2013 [131]. Upon completion of the digital switchover from analog to

digital TV, a large portion of the spectrum currently allocated for TV broadcast-

ing will be cleared and available for other services. These frequencies are known

as the digital dividend and is not available for CR access. The retained spectrum

for digital TV broadcasting is the frequency band that may be used by CR de-

vices on a geographical basis depending on their availability. Any TV frequency

band which is available for CR access in geotemporal basis is known as a TVWS.

The major worldwide regulatory agencies are currently involved in developing

rules and regulations for the unlicensed use of TVWS [132, 133]. As an exam-

ple, the secondary operation of CRs in TV bands is controlled by regulators on

the ability of these devices to avoid harmful interference to the incumbent ser-

vices. These incumbent services include TV broadcasting as well as program

making and special event (PMSE) users such as wireless microphones. In ad-

dition, the CR devices should be able to reliably detect and use the available

TVWS. Two main approaches have been proposed by the regulators to achieve

the aforementioned tasks: the use of geolocation database, and spectrum sensing

[15, 134]. With geolocation database, there is a central database which stores

information such as location, transmit power, frequencies and antenna radiation

patterns of all the TV transmitters in a specic region. The CR device usually

queries this database with its location and other device specications when re-

quired. The database then uses this information and its stored information of

the TV transmitters to calculate the available TVWS channels for the requesting


device [135, 136]. With spectrum sensing, the CR devices are built with spectrum

sensing capabilities which allows these devices to autonomously detect the pres-

ence of TV channel signals [137]. Furthermore, the FCC has already published a

series of regulations and specications related to CR devices operating in TVWS

[132]. These include maximum transmit power limit, out-of-band emission levels,

and incumbent protection mechanisms. The UK regulator Ofcom also published

their set of proposed parameters and specications for cognitive access in 2009

[133].

The CR devices operating on TVWS are also known as TV band devices

(TVBDs). However, in this thesis, the TVBDs are referred as TVWS devices. The

TVWS devices are divided into two categories, namely, xed and personal/portable

devices [15, 49]. The xed devices operate from a known, xed location and

have a maximum transmit power limit of 4W, according to FCC specications

[132]. The personal/portable devices are allowed to transmit up to 100mW on

non-adjacent channels and up to 40mW on adjacent channels [132]. In order to

protect the primary television services, CR network operating on co-channel or

adjacent channels must be located outside the respective TV transmitter coverage

area [138]. The CR network should maintain an additional separation distance

called keep-out distance from the coverage edge of the TV transmitter. However,

personal/portable devices operating on TVWS channels adjacent to an active

TV channel can be operated within the TV coverage area if its transmit power

is suciently low to avoid harmful interference to the TV receivers within its

vicinity.

There are several emerging international standards to utilize TVWS using

CR technology. IEEE 802.22 wireless regional area network (WRAN) is the

rst international CR standard [51, 54]. It is designed for last-mile services in

rural areas for xed CR devices including the base station and end customer

devices. ECMA 392 [51, 55] is the rst standard for personal/portable devices to

exploit TVWS, and IEEE 802.11af denes a WiFi like protocol for CR devices


operating over the TVWS [51, 56]. In addition, there has been signicant interest

on operating LTE within the TVWS [139, 140]. Almost all of these standards

use OFDM as the underlying modulation technique.

Secondary access to TVWS can be considered as a new and interesting avenue

for future research with a signicant practical value. There are several aspects to

be examined when the secondary access to TVWS is considered. These include,

but not limited to incumbent protection techniques, database access, power al-

location, and spectrum sensing. However, this chapter is focused on the power

allocation problem. The rest of this chapter is organized as follows: A review of

power allocation studies in CR networks operating in TVWS is given in Section

7.2. The system and channel model is described in Section 7.3. An interference

minimization based power allocation method for CR transmission is proposed in

Section 7.4 and two other power allocation schemes to compare the performance

of the proposed power allocation method is presented in Section 7.5. Simulation

results are presented in Section 7.6 to illustrate the performance of the dierent

power allocation methods.

7.2 Related Work

As mentioned before, secondary access to TVWS has gained enormous attention

in both industry and academia. However, there are only a few studies reported

in the existing literature on power allocation in secondary systems which are op-

erating in TVWS. In a CR point of view, adaptive power allocation algorithms

can be used to improve the performance of the CR transmission while maintain-

ing the interference to the incumbent receivers below a given threshold. A rich

literature is available on such power loading algorithms for OFDM-based CR net-

works. Although these existing studies on resource allocation in CR networks can

be adapted for this scenario, the specic features of the television transmission


and the current regulatory requirements for TVWS devices should be taken into

consideration when developing power allocation methods for such systems.

The work in [141] investigates transmit power control algorithm that maxi-

mizes the spectral eciency of TVWS wireless systems. It is assumed that the

secondary network is located outside the TV coverage area and transmits on the

same TV channel. The proposed algorithm tries to maintain the interference at

TV service contour to minimum level. In [142], authors propose a power allo-

cation scheme for a cellular like CR network operating in TVWS. The proposed

method aims to maximize the cell border data rate of the CR system while not

violating the protection criteria of TV and CR systems. In [143], the authors

study an interference control algorithm for multiple secondary systems at TV cell

border. In the proposed scheme, a central controller allocates transmit power to

dierent secondary systems such that the aggregate interference to TV receivers

is maintained within a given protection margin. The optimization objective is to

maximize the sum of the transmission power levels allocated to each secondary

system which would ultimately increases the secondary system's capacity. The

work in [144] presents a proportional fair power allocation scheme for multiple

secondary transmitters operating in TVWS. Selen, and Kronander in [145] pro-

pose a method to optimize the transmit power limits for white space devices to

maximize the sum capacity of all the secondary transmitters under a probabilistic

interference constraint. The proposed method set optimal power limits for each

secondary transmitter such that the probability of harmful aggregate interference

is below a given threshold. All of the above mentioned work investigate trans-

mit power control algorithms that maximize the performance of the single-carrier

secondary networks in TVWS.

When the incumbent TV transmission (primary users) is considered, it is

crucial to minimize the interference introduced by the secondary transmission.

Hence, interference minimization based power allocation schemes can be intro-

duced to the secondary network to protect the television services while guarantee-


ing the necessary quality of service (QoS) requirements of the secondary system.

It is assumed that there are vacant TV channels available for secondary access so

that the QoS requirement of the secondary network can be guaranteed. Tao et al.

in [146] study interference control based power allocation scheme for IEEE 802.22

like OFDM-based CR system operating in TVWS. Similar to [141], they assume

that the CR system is located adjacent to the TV service contour with a keep-out

distance. The secondary network is assumed to be operating on either the same

TV channel or an adjacent TV channel. The authors present a power loading

method that minimizes the interference to a TV receiver at the TV coverage edge

while maintaining the data rate of the CR transmission above a given threshold.

The work presented in this chapter considers a secondary network located

inside the TV coverage area. A more general system model is studied where

multiple TV transmitters are broadcasting on multiple TV channels and the sec-

ondary network has access to multiple TV white spaces. Power allocation scheme

for CR transmission is proposed which minimize the total interference to the

incumbent TV receivers located within the secondary transmitter coverage area.


A short-range OFDM-based CR network deployed within a TV coverage area

is considered for this study. The short-range CR network can be a system like

IEEE 802.11af. Figure 7.1 illustrates the co-existence scenario of primary and CR

networks. The TV receivers within the coverage area of the secondary transmitter

is interfered by the secondary transmission. The eect of downlink transmission of

the secondary network with multiple TV receivers within the secondary coverage

area is considered. In general, there are M TV receivers in the vicinity of the

secondary transmitter. To make the analysis more clear, only one secondary

receiver is considered here.


Television

Tower

CR network

TV coverage

area

CR transmission

Interference to

TV receivers

Secondary

transmitter

Secondary

mobile

devices

TV

receivers

Figure 7.1: Co-existence of secondary network within TV coverage area

Usually, number of TV channels are available within a given TV coverage area.

Hence, it is assumed that the television tower serves number of TV transmitters

and they are broadcasting on a set of TV channels, X. The secondary network

can transmit on the unoccupied channels, y ∈ Y : Y = Xc, where Xc is the

complement of the set of TV channelsX, with all the TV channels as the universal

set. In practice, the secondary network can choose either one TVWS channel or a

number of adjacent TVWS channels from the available unoccupied channels in set

Y . It is also assumed that the secondary transmitter can obtain the information

regarding the available TV channels via a method like database access [15]. In

the spectrum domain, there are L TV bands with a bandwidth BTV in the set

X. Each available TV white space is divided into N subcarriers each having

a bandwidth of ∆f to be used by the secondary network. A general spectrum

allocation model is shown in Figure 7.2. Let m denote the mth TV receiver, i

denote the ith subcarrier and l denote the lth occupied TV channel: m ∈ [1 :M ],

i ∈ [1 : Ntot] where Ntot = N × Number of TVWS channels used for secondary

transmission, and l ∈ [1 : L].


∆f

TV white spaces

BTV

1 2 ............N

Occupied TV

channels

Figure 7.2: General model of spectrum allocation for CRs in TVWS

When a CR system co-exists with a primary television system, the interference

introduced by the CR transmission at the mth TV receiver on the lth TV channel

can be expressed as [87, 120],

Iml,i = Pi |Hm,i|2 Ts∫ di,l+BTV /2

di,l−BTV /2

(sin (πfTs)

πfTs

)2

df

= Pi gm,iΩl,i (7.1)

where Pi is the transmit power of the ith subcarrier, Ts is the symbol duration,

and BTV is the TV channel bandwidth. Hm,i is the CSI of the ith subcarrier

between the CR transmitter and mth TV receiver and gm,i = |Hm,i|2. The CSI

Hm,i represent the eect due to both the path loss and the fading gain. di,l is the

spectral distance between the ith subcarrier and the lth TV band. The interference

factor Ωl,i = Ts∫ di,l+BTV /2

di,l−BTV /2

(sin (πfTs)πfTs

)2df .

It is generally assumed that the resource allocation decisions in a CR net-

work are made at the CR transmitter and the perfect knowledge of instantaneous

CSI between CR transmitter and CR receivers is available at the time of power

allocation. However, it is not reasonable to assume that the CR transmitter

can instantaneously obtain the actual CSI between itself and the TV receivers.

Therefore this work assumes that only the fading statistics between the CR trans-

mitter and PU receivers are known at the CR transmitter. Thus it is not possible

to calculate the instantaneous interference in (7.1). Nevertheless, if the more


readily available fading statistics between CR transmitters and TV receivers are

used, the average interference E [Iml,i] = PiΩl,iE [gm,i] can be calculated using the

knowledge of the probability distribution of gm,i.

As an example, if Rayleigh fading with known variance σ2m is assumed between

the CR transmitter and mth TV receiver, the pdf of gm,i can be expressed as an

exponential distribution with parameter λm as shown in (6.10). The parameter

λm can be expressed as, λm = ψm

2σ2m, where ψm is a factor that depends on the path

loss experienced between the CR transmitter and TV receiver. With the help of

the exponential pdf and the result [116, Eq. 3.351.3] the average interference

introduced during the CR transmission can be calculated for Rayleigh fading

case as, E [Iml,i] = PiΩl,i

λm.

The objective of power allocation is to minimize the total average interference

to the TV receivers. In order to guarantee QoS to the secondary transmission, a

capacity threshold is introduced for the secondary transmission. The sum capac-

ity of the OFDM transmission can be expressed as,

C =Ntot∑i=1

log2(1 + Piγi) b/s/Hz (7.2)

Here, γi =|Hi|2

σ2+∑L

l=1 Jl,iis the instantaneous channel-to-noise ratios (CNR) of CR

source-destination link. Hi is the CSI between CR transmitter and receiver, σ2

is the noise variance at the CR receiver and Jl,i is the interference produced at

the CR receiver by the lth TV channel.

7.4 Power Allocation for Interference Minimiza-

tion

This section presents a power allocation scheme to minimize the total average

interference to the TV receivers while maintaining the total capacity of the CR


transmission above or equal to a given capacity threshold. However, this may

result in an interference level that is unacceptable to the primary TV receivers.

Hence, individual interference thresholds can be imposed to protect each TV re-

ceiver. The power allocation problem can be mathematically expressed as follows:

MinimizeM∑m=1

Ntot∑i=1

L∑l=1

PiΩl,iE [gm,i] (7.3)

subject to,

Ntot∑i=1

log2(1 + Piγi) ≥ Cth (7.4)

Ntot∑i=1

L∑l=1

PiΩl,iE [gm,i] ≤ Imth , ∀m (7.5)

Ntot∑i=1

Pi ≤ P (7.6)

Pi ≥ 0, ∀ i (7.7)

Here, Cth is the capacity threshold for CR transmission, Imth is the maximum

interference threshold for mth TV receiver, and P is the maximum allowable

transmit power for secondary transmitter. It can be shown that the objective

function (7.3) is a minimization of a convex function of Pi and the constraints (7.4)

- (7.7) are concave or linear functions of Pi. Hence this is a convex optimization

problem and, can be solved using Karush-Kuhn-Tucker (KKT) conditions [95].

The solution for the optimal transmit power P ∗i can be obtained as,

P ∗i =

δ[(∑Ll=1 Ωl,i

∑Mm=1E [gm,i]

) (1 +

∑Mm=1 βm

)+ υ]ln(2)

− 1

γi

+

(7.8)

where [x]+ = max(0, x). The constants δ, βm, and υ are non-negative Lagrange

parameters which are selected such that the sum capacity constraint (7.4), inter-


ference constraints (7.5) and sum power constraint (7.6) are satised, respectively.

A detailed derivation of this solution is given in Appendix D. The computational

complexity of assigning transmit power to the subcarriers using interior-point

method is O(N3) [95].

Above power allocation involves solving for (M +2) Lagrange multipliers and

has a higher computational complexity for large number of subcarriers in the

secondary network. The power allocation problem can be simplied by not con-

sidering the interference thresholds (7.5) during power allocation. In order to

make sure that the CR transmission does not result in an unacceptable level of

interference to the TV receivers, the capacity threshold can be appropriately se-

lected. It is shown in Section 7.6 that a suitable capacity threshold can be selected

to meet a given maximum permissible interference threshold limit. Thus, it is

assumed in the remainder of this chapter that an appropriate capacity threshold

is selected for secondary transmission and the power allocation does not result in

an unacceptable level of interference to the TV receivers.

The simplied power allocation problem can be stated as follows:

MinimizeM∑m=1

Ntot∑i=1

L∑l=1


subject to,

∑Ntot

i=1 log2(1 + Piγi) ≥ Cth∑Ntot

i=1 Pi ≤ P

Pi ≥ 0, ∀ i

(7.10)

Using a similar approach to that in Appendix D, the optimal transmit powers for

above optimization problem can be calculated as,

P ∗i =

δ(∑Ll=1 Ωl,i

∑Mm=1E [gm,i] + υ

)ln(2)

− 1

γi

+

. (7.11)


Still (7.11) requires to solve for the two Lagrange constants δ and υ, and has a

computational complexity of O(N3).

7.4.1 Simplied Power Allocation Algorithm

If only the capacity constraint is considered, then the power allocation problem

can be solved using direct calculation. If the transmit power constraint is relaxed,

the power allocation problem can be further reduced as,

MinimizeM∑m=1

Ntot∑i=1

L∑l=1


subject to,

Ntot∑i=1

log2(1 + Piγi) ≥ Cth (7.13)

Pi ≥ 0, ∀ i (7.14)

Using KKT optimality conditions, the solution for this simplied power allocation

problem can be obtained as,

P ∗i =

δ(∑Ll=1 Ωl,i

∑Mm=1E [gm,i]

)ln(2)

− 1

γi

+

. (7.15)

The value of δ can be calculated by substituting (7.15) in to (7.13) and its value

can be obtained as,

δ = ln(2)

[2Cth

Ntot∏i=1

(∑Ll=1 Ωl,i

∑Mm=1E [gm,i]

γi

)](1/Ntot)

. (7.16)

If the transmit power constraint is violated by the above power values, these

can be rened until the sum of the transmit powers is equal to the total available


power. Flowchart for the simplied power allocation algorithm is shown in Figure

7.3.

Calculate using (7.15)

and (7.16)

Calculate the residual power,

Yes

No

*

iP

?1

* PPtotN

i

i >∑=

PPPtotN

i

i −=∆ ∑=1

*

Refine the power values

∆−=

∑=

totN

i

i

iirefinei

P

PPPP

1

*

**

, ,0max

Return refineiP ,

Return *

iP

Figure 7.3: Flowchart of the simplied power allocation algorithm

This simplied power allocation algorithm provides close to optimal results

when the CR system is not power limited.


7.5 Comparison with Other Power Allocation Meth-

ods

Performance of the proposed interference minimization based power allocation

scheme is compared with two other power allocation methods. The following two

subsections describe those two power allocation methods.

7.5.1 Water Filling Power Allocation

Water lling power allocation has been identied as the optimum power allocation

mechanism that maximizes the capacity for a single-hop transmission under a

maximum transmit power constraint [102, 103]. The transmit power allocation

for the water lling scheme can be given as,

Pi = max

(0,

[1

λ− 1

γi

])(7.17)

where, λ denes the water level. For the power allocation scenario considered

in this chapter, λ can be determined such that the sum capacity threshold is

satised, i.e.,Ntot∑i=1

log2 (1 + Pi γi) = Cth (7.18)

with Pi as dened in (7.17). After some mathematical manipulations, λ can be

obtained as,

λ =

[∏Ntot

i=1 γi2Cth

]1/Ntot

. (7.19)

Once the transmit power values are obtained using (7.17) and (7.19), the trans-

mit power constraint is checked for the assigned power values. If the maximum

transmit power constraint is violated, then uniform transmit power is allocated

among all the subcarriers, i.e., Pi = P/N .


7.5.2 Capacity Threshold Based Power Allocation

This method tries to meet the QoS requirement of the CR transmission without

trying to minimize the interference to TV receivers. First, the capacity is dis-

tributed among the subcarriers according to the ratio of the CNR of the dierent

subcarriers. With this approach, the subcarriers with the highest CNR (i.e., good

channel quality) carry more bits than the others. The capacity assigned for each

subcarrier can be given as,

Ci =Cthγi∑Ntot

i=1 γi(7.20)

Since Ci = log2(1 + Piγi), the power required to achieve the target capacity of

each subcarrier can then be obtained as,

Pi =2Ci − 1

γi. (7.21)

If the above transmit power allocation violates the transmit power constraint of

the CR transmitter, uniform transmit power is allocated to each subcarrier.


Monte-Carlo simulation results are presented in this section to evaluate the perfor-

mance of the proposed interference minimization based power allocation method.

A CR network operating in TVWS as described in Section 7.3 was imple-

mented in MATLAB. A co-existence scenario with L = 5 occupied TV channels

and two TV white space channels was used for this evaluation. Each TVWS

channel was divided in to N = 16 subcarriers resulting in total of Ntot = 32

subcarriers for secondary transmission. The values of ∆f , BTV , σ2 and Jl,i were

taken as 0.3125MHz, 6MHz, 1× 10−8W and 1× 10−6W, respectively [125, 87].

Ts was set to be 4µs [125]. Frequency selective Rayleigh fading channels with two

multipath taps and unit fading power were assumed between transmitters and re-


ceivers. The path loss exponent was taken as 3 and the results were averaged over

1000 dierent fading channel realizations. Maximum allowable transmit power of

the CR transmitter was taken as 100mW according to FCC specications [132].

First, the performance of the proposed power allocation methods is assessed

with multiple TV receivers. Number of TV receivers was taken asM = 4. For this

analysis, the TV receivers and the CR transmitter and receiver were distributed

as illustrated in Figure 7.4.

(0,0)

CR

transmitter

(100,100)

CR receiver

(-40, 40)

TV 1 (70, -70)

TV 2

(100, 110)

TV 3

(-150, 150)

TV 4

X (m)

Y (m)

Figure 7.4: TV receivers, and CR transmitter and receiver distribution

Figure 7.5 illustrates the variation of the total average interference at TV re-

ceivers with the capacity threshold for dierent power allocation schemes. It can

be clearly observed that the interference increases with the capacity threshold.

As higher transmit powers are used to achieve higher capacities more interference

is produced at the TV receivers. It should be noted that in this situation, the CR

transmission is not limited by the transmit power constraint. It is also evident

that the interference minimization based power allocation produces signicantly

less interference compared to other two methods. As an example, it produces on

average, 2.2 dB less interference compared to water lling power allocation. When

the percentage of interference reduction is considered, the interference minimiza-


tion based approach achieves, on average, 40% interference reduction compared

to water lling power allocation.

5 10 15 20 25 30 35 40 45 50-74

-72

-70

-68

-66

-64

-62

-60

-58

-56

Normalized capacity threshold (b/s/Hz)

Tota

l av

erag

e in

terf

eren

ce (dB

)

Capacity threshold based power allocation

Water filling power allocation

Interference minimization based power allocation

Figure 7.5: Total interference variation with capacity threshold, M = 4 TVreceivers

Figure 7.6 shows the individual interferences produced at each TV receiver.

Accordingly, TV 1, which is located closer to the CR transmitter, suerers from

the highest interference. Furthermore, it can also be observed that the interfer-

ence minimization based power allocation has reduced the individual interferences

at each TV receiver compared to the other two power allocation schemes.

If the TV receivers are protected by a maximum permissible interference

threshold specication, the behavior in Figure 7.5 can be used to obtain a suitable

capacity threshold for secondary transmission. As an example, if −64dB is se-

lected as the interference threshold, the secondary network can use 18b/s/Hz as

the target normalized data rate with water lling method. However, with interfer-

ence minimization based power allocation this can be increased up to 27b/s/Hz.

Hence, it is evident that interference minimization based power allocation scheme

allows the secondary network to achieve a higher data rate for a given interference


5 10 15 20 25 30 35 40 45 50-100

-95

-90

-85

-80

-75

-70

-65

-60

-55

Normalized capacity threshold (b/s/Hz)

Aggregate interference at each TV receiver (dB)




TV 1

TV 2

TV 3

TV 4

Figure 7.6: Interference variation at each TV receiver with capacity threshold

threshold. Similarly, the behavior in Figure 7.6 can be used to specify a maximum

possible data rate for the secondary transmission, if the incumbent receivers are

protected by an individual interference threshold. As an example, if −65dB is

selected as the interference threshold at each TV receiver, secondary network is

able to achieve up to 27b/s/Hz date rate. In this situation, the maximum data

rate is governed by the interference introduced to TV1 which is located closest

to the CR transmitter.

Next, the total average interference variation with the TV receiver location

is studied with only one TV receiver. Figure 7.7 illustrates the variation of the

aggregate interference at a given TV receiver with the distance between the TV

receiver and CR transmitter. As that can be predicted, the interference at the TV

receiver decreases as it moves away from the CR transmitter. However, the inter-

ference minimization based power allocation always results in lesser interference

than the other methods.


20 40 60 80 100 120 140 160 180 200-60

-55

-50

-45

-40

-35

-30

-25

Distance between CR transmitter and TV receiver (m)

Tota

l av

erag

e in

terf

eren

ce (

dB

)




Figure 7.7: Total interference variation with distance between the CR transmitterand TV receiver, M = 1 TV receiver, Cth = 50b/s/Hz

0 20 40 60 80 100 120 140 160 180 200010

2030

4050-80

-70

-60

-50

-40

-30

-20

Distance between CR transmitter and TV receiver (m)

Cth (b/s/Hz)

Total average interference (dB)

-70

-65

-60

-55

-50

-45

-40

-35

-30

Figure 7.8: Total interference variation with distance between the CR transmitterand TV receiver, and capacity threshold with interference minimization basedpower allocation, M = 1 TV receiver


Figure 7.8 plots the variation of total average interference for a range of TV

locations and secondary network capacity threshold values. The results are ob-

tained with interference minimization based power allocation. Accordingly, the

amount of interference can be predicted based on the location of the TV receiver

and the secondary network's target data rate. On the other hand, this result can

also be used to predict the achievable data rate for the secondary network for a

given interference and a TV receiver location.

7.7 Conclusion

This chapter addressed the power allocation problem in OFDM-based CR net-

works operating within the TV coverage area using TVWS channels. Power allo-

cation scheme was studied to minimize the total average interference to the TV

receivers while satisfying a minimum capacity requirement for secondary trans-

mission. Optimal power allocation method has been derived and a simplied

power allocation scheme has also been proposed which achieves near optimal per-

formance when the CR system is not power limited. Performance of the proposed

power allocation scheme was compared with water lling power allocation and

capacity threshold based power allocation methods. According to the numerical

results, the proposed interference minimization based power allocation produces

signicantly less interference than the other two methods while not violating the

capacity requirement of the secondary transmission.

Chapter 8

Conclusion

Adaptive resource allocation is used in wireless networks to dynamically assign

the system resources according to varying channel conditions. It is a prominent

factor in improving network performance. The work presented in this thesis

studied and proposed resource allocation methods for OFDM-based relay and

CR networks considering several practical aspects.

Most of the reported work on power allocation in OFDM relay networks as-

sume that perfect knowledge of the instantaneous CSI between transmitters and

receivers is available at the time of power allocation. However, available CSI

is rarely perfect in practice. Hence, this thesis investigated resource allocation

methods with practically available outdated CSI, which is barely addressed in the

current literature. In CR networks, one common assumption is to consider that

perfect instantaneous CSI between primary and secondary networks is known by

the secondary transmitters. Almost all the existing studies on resource alloca-

tion in OFDM-based CR relay networks are based on this assumption, which is

hardly realistic. Therefore, new power allocation methods were developed for

OFDM-based CR relay networks considering the practically available statistical

CSI between primary and secondary networks. Furthermore, low complexity re-

source allocation methods for multi-relay assisted OFDM relay networks were

proposed as alternatives for hard to implement complex joint optimal resource

8. CONCLUSION 168

allocation methods. In addition, operating CR networks in TVWS, which is a

promising application of CR concept, was also investigated along with adaptive

power allocation.

8.1 Summary and Conclusion

Adaptive resource allocation methods for multi-relay assisted cooperative OFDM

networks were investigated in Chapter 3. The objective of resource allocation was

to maximize the instantaneous capacity of the cooperative OFDM network and

the resource allocation was subject to transmit power constraints at source and

relays. Joint allocation of relays, subcarriers and transmit power is computation-

ally intensive. As an alternative, a two-step resource allocation method which

involves relay and/or subcarrier selection, and power allocation was proposed.

Two scenarios were considered: all subcarrier relaying and selective subcarrier

relaying. Closed-form expressions were derived for source and relay transmit

powers and the performance of the proposed resource allocation methods was

compared using computer simulations. It was observed that the subcarrier selec-

tion based resource allocation results in higher capacity than the non-selective or

all subcarrier relaying based approach.

In Chapter 4, power allocation in OFDM-based two-hop relay networks was

studied in the presence of outdated CSI. Available CSI of the both hops at the

transmitter was considered as an outdated but correlated version of the actual

instantaneous CSI. The objective of power allocation was taken as expected rate

maximization or outage rate maximization. Expected rate and outage rate can

be calculated with the knowledge of the outdated CSI and the outdatedness. Two

power allocation methods were presented based on the two objectives. It was hard

to solve the resulting power allocation problems analytically to obtain closed-form

expressions for source and relay transmit powers. However, performance of the

proposed methods was assessed using numerical calculation and it was found that

8. CONCLUSION 169

outage rate maximization based power allocation makes better use of the available

outdated channel knowledge compared to expected rate maximization.

Work presented in Chapter 5 proposed resource allocation methods for multi-

relay assisted OFDM-based CR relay networks to maximize the instantaneous

capacity of the CR transmission. The resource allocation problem was subject to

interference constraint at primary network, and the transmit power constraints at

the CR source and the relays. Two suboptimal resource allocation methods were

proposed based on the two-step resource allocation approach. First, the relay

selection was performed for each subcarrier in a suboptimal manner. Next, the

transmit power at the source and the relays were allocated for this subcarrier-

relay assignment. Performance of the proposed methods was evaluated using

computer simulation results and a comparison with joint optimal resource allo-

cation was also given. It was concluded that the two-step resource allocation

method, which involves simplied relay selection and optimal power allocation, is

able to achieve near optimal performance in many situations with comparatively

less computational complexity.

In Chapter 6, power allocation methods were investigated for OFDM CR re-

lay networks when only the statistical CSI between the secondary and primary

networks are known at the CR transmitters. New power allocation methods were

proposed considering average interference constraints at each PU receiver. Op-

timal power allocation methods were developed to maximize the instantaneous

capacity of the CR transmission and less-complex suboptimal power allocation

methods were also proposed. Analytical expressions were derived for source and

relay transmit powers and the performance of the proposed methods was assessed

using computer simulation results. Statistical CSI due to outdated channel knowl-

edge and channel fading statistics were considered for performance evaluation.

It was observed that the optimal power allocation methods result in substantial

capacity improvement over other classical and suboptimal power allocation meth-

ods. Nevertheless, the proposed suboptimal power allocation methods are well

8. CONCLUSION 170

applicable for situations where ecient power allocation methods with certain

amount of capacity degradation are preferred over optimal power allocation.

A practical application of operating CR networks in TV white space was

considered in Chapter 7 from an adaptive power allocation point of view. A new

power allocation method was proposed for OFDM-based single-hop CR networks

to minimize the total average interference at the incumbent TV receivers while

satisfying a minimum capacity threshold for CR transmission. The proposed

method is well suited for CR networks when the protection of TV receivers is

more important than capacity maximization of secondary transmissions.

8.2 Future Work

This section provides recommendations for possible directions for future research

based on the outcomes of this thesis.

• This thesis investigated power allocation methods in the presence of out-

dated CSI. A natural extension for this work is to consider imperfect CSI

due to channel estimation errors.

• Power allocation in OFDM-based two-hop relay networks with outdated CSI

was studied in Chapter 4. It was assumed that outdated CSI is available for

both the source-relay and the relay-destination channels. It was dicult to

solve the resulting power allocation problems owing to the mathematically

intractable expressions obtained for expected rate and outage rate. A more

feasible extension for this work should include an investigation of power

allocation methods considering only the outdated relay-destination channel

information.

• Work presented in this thesis considered resource allocation methods for

single-antenna OFDM-based CR relay networks. This study could be fur-

8. CONCLUSION 171

ther extended for dual-hop multiple-input multiple-output (MIMO) OFDM

CR networks.

• Power allocation in CR networks was investigated in Chapter 6 considering

statistical CSI between primary and secondary networks. The knowledge

of perfect instantaneous CSI between CR transmitters and receivers was

assumed. However, more practical result could be obtained by considering

outdated/imperfect CSI between CR transmitters and receivers in addition

to statistical CSI between primary and secondary networks.

• Power allocation in OFDM-based CR relay networks is studied in Chapter

5 and Chapter 6 assuming that the direct path between the source and the

destination is not available. Power allocation in OFDM-based CR relay

networks with the direct path can be considered as a possible extension for

this work.

• Work presented in this thesis proposed power allocation methods for OFDM-

based relay and CR networks. Any particular practical system is not con-

sidered in these studies. However, more practical insight of the proposed

methods could be obtained considering currently deployed cellular systems

such as LTE. Furthermore, application of these methods in a typical multi-

cell multi-user MIMO conguration could be another avenue for future re-

search.

• This thesis presented resource allocation methods to maximize the end-to-

end capacity of the relay transmission and the performance of the proposed

methods is evaluated in terms of the capacity. However, it would be inter-

esting to analyze the BER performances of the scenarios considered. This

would provide an overall understanding of the dierent resource allocation

methods.

8. CONCLUSION 172

• This thesis provided a foundation study for power allocation in CR networks

operating in TV white space. A wider range of power allocation algorithms

are yet to be investigated for such systems. One interesting study could be

the investigation of power allocation methods for relay assisted CR networks

operating in TVWS.

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Appendix A

Optimal Relay and Source Transmit

Powers in Cooperative OFDM

Transmission

A.1 Derivation of Optimal Relay Transmit Power

The objective function in (3.15) is a maximization of a concave function and theconstraints in (3.16) are linear functions of the optimization variable Pk,i. Thusthe optimization problem can be converted in to a convex optimization problemby rewriting the objective function as a minimization of the negative value of theconcave function as follows:

Minimize −N∑i=1

K∑k=1

Ak,i1

2log2

(1 +

Ps,iγsk,iPk,iγkd,i1 + Ps,iγsk,i + Pk,iγkd,i

+ Ps,iγsd,i

)(A.1)

subject to,


Pk,i ≥ 0, ∀ k, i(A.2)

This convex optimization problem can be solved using Karush-Kuhn-Tucker (KKT)conditions [95] as described below.

APPENDIX 189

First, the Lagrangian function for the above convex optimization problem isobtained as,

L(Pk,i, δi, υk)

= −N∑i=1

K∑k=1

Ak,i1

2log2

(d1Pk,i + d2d3Pk,i + d4

)−

N∑i=1

δiPk,i

+K∑k=1

[υk

(N∑i=1

Ak,iPk,i − Pk

)](A.3)

where, d1 = γkd,i (1 + Ps,iγsd,i) + Ps,iγsk,iγkd,i, d2 = (1 + Ps,iγsk,i) (1 + Ps,iγsd,i),d3 = γkd,i, and d4 = 1 + Ps,iγsk,i. Here, δi and υk are non-negative Lagrangeparameters which are related to the constraints in (A.2).

In order to solve the relay power optimization problem, two cases are consid-ered dependent on the relay selection decision, Ak,i.

Case 1: Ak,i = 1

When Ak,i = 1, the derivative of the Lagrangian with respect to Pk,i can be givenas,

∂L(Pk,i, δi, υk)

∂Pk,i=

d1d2 − d2d32 ln(2)(d1Pk,i + d2)(d3Pk,i + d4)

− δi + υk (A.4)

Then, the KKT optimality conditions for the relay power optimization problemcan be written as follows:

∂L(Pk,i, δi, υk)

∂Pk,i= 0

δi = υk −d1d2 − d2d3

2 ln(2)(d1Pk,i + d2)(d3Pk,i + d4)(A.5)

δi ≥ 0

υk ≥ d1d2 − d2d32 ln(2)(d1Pk,i + d2)(d3Pk,i + d4)

(A.6)

APPENDIX 190

δi Pk,i = 0[υk −

d1d2 − d2d32 ln(2)(d1Pk,i + d2)(d3Pk,i + d4)

]Pk,i = 0 (A.7)

If υk <d1d2−d2d32 ln(2)d2d4

, condition (A.6) can only be satised if Pk,i > 0. Then from

(A.7),

υk −1

2 ln(2)

d1d2 − d2d3(d1Pk,i + d2)(d3Pk,i + d4)

= 0. (A.8)

If υk >d1d2−d2d32 ln(2)d2d4

with Pk,i > 0, it is impossible to satisfy the condition (A.7).

Therefore, (A.7) implies that Pk,i = 0. Solving (A.8) with respect to Pk,i and aftersome mathematical manipulations the solution for the optimal relay transmitpower can be obtained as,

P ∗k,i =

(1 + Ps,iγsk,i)


[Ps,iγsk,i

√1 + [·]

]+[·] =


υk ln(2)Ps,iγsk,i(1 + Ps,iγsk,i)(A.9)

where [x]+ = max(0, x).

Case 2: Ak,i = 0

Ak,i = 0 implies that the ith subcarrier is not transmitted by the kth relay. Thusit is obvious that P ∗

k,i = 0 when Ak,i = 0.Combining the above two cases, the solution for optimal relay transmit power

can be obtained as given in (A.9).

A.2 Derivation of Optimal Source Transmit Power

The source power optimization problem can be rewritten as,

Minimize −N∑i=1

K∑k=1

Ak,i1

2log2

(1 +


)(A.10)

APPENDIX 191

subject to,

∑Ni=1 Ps,i ≤ Ps, ∀ k

Ps,i ≥ 0, ∀ k, i(A.11)

This is a convex optimization problem and the respective Lagrangian functioncan be written as,

L(Ps,i, µi, λ)

= −N∑i=1

K∑k=1

Ak,i1

2log2

(1 +


)

−N∑i=1

µiPs,i + λ

(N∑i=1

Ps,i − Ps

)(A.12)

where µi and λ are non-negative Lagrange parameters. The KKT conditions forthe source power optimization problem can be written as follows:

∂L(Ps,i, µi, λ)

∂Ps,i= 0

µi = λ− Ak,iγsk,iPk,iγkd,i

2 ln(2)(1 + Ps,iγsk,i)(1 + Ps,iγsk,i + Pk,iγkd,i)

(A.13)

µi ≥ 0

λ ≥ Ak,iγsk,iPk,iγkd,i

2 ln(2)(1 + Ps,iγsk,i)(1 + Ps,iγsk,i + Pk,iγkd,i)(A.14)

µi Ps,i = 0[λ− Ak,i

γsk,iPk,iγkd,i2 ln(2)(1 + Ps,iγsk,i)(1 + Ps,iγsk,i + Pk,iγkd,i)

]Ps,i = 0 (A.15)

APPENDIX 192

If λ < Ak,iγsk,iPk,iγkd,i

2 ln(2)(1+Pk,iγkd,i), condition (A.14) can only be satised if Ps,i > 0.

Then condition (A.15) implies that,

λ− Ak,iγsk,iPk,iγkd,i

2 ln(2)(1 + Ps,iγsk,i)(1 + Ps,iγsk,i + Pk,iγkd,i)= 0 (A.16)

If λ > Ak,iγsk,iPk,iγkd,i

2 ln(2)(1+Pk,iγkd,i)with Ps,i > 0, it is impossible to satisfy the condition

(A.15). Thus Ps,i should be equal to 0. Then (A.16) can be solved to obtainthe optimal source transmit power. After some mathematical manipulations thesolution for the optimal source transmit power can be expressed as given in (3.21).

Appendix B

Optimal Relay Transmit Power in

OFDM CR Relay Transmission

with Total Interference Constraint

The objective function in (5.15) is a maximization of a concave function and theconstraints in (5.16) are linear functions of the optimization variable Pkd,i. Thus,the optimization problem can be converted in to a convex optimization problemby rewriting the objective function as a minimization of the negative value of theconcave function as follows:

Minimize −K∑k=1

N∑i=1

Ak,i1

2log2(1 + γk,i) (B.1)

subject to,

∑Ni=1Ak,iPkd,i ≤ PK , ∀ k∑L

l=1

∑Kk=1

∑Ni=1Ak,i |Hkl,i|2 Pkd,iΩl,i ≤ Ith

Pkd,i ≥ 0, ∀ k, i

(B.2)

This convex optimization problem can be solved using Karush-Kuhn-Tucker (KKT)conditions [95] as described below.

APPENDIX 194

The corresponding Lagrangian function can be written as,

L(Pkd,i, υk, µ, δi)

= −K∑k=1

N∑i=1

Ak,i1

2log2(1 + γk,i) +

K∑k=1

υk

(N∑i=1

Ak,iPkd,i − PK

)

+µ

(L∑l=1

K∑k=1

N∑i=1

Ak,i|Hkl,i|2Pkd,iΩl,i − Ith

)−

N∑i−1

δiPkd,i (B.3)

where, υk, µ, and δi are non-negative Lagrange parameters.The optimization problem is solved for two cases dependent on the relay se-

lection decision.

Case 1: Ak,i = 1

The derivative of the Lagrangian with respect to Pkd,i can be given as,

∂L(Pkd,i, υk, µ, δi)

∂Pkd,i= − d1

(1 + Pkd,iγkd,i)(d2 + Pkd,iγkd,i)+ υk

+µL∑l=1

|Hkl,i|2Ωl,i − δi (B.4)

where, d1 =Psk,iγsk,iγkd,i

2 ln(2)and d2 = 1 + Psk,iγsk,i.

The KKT optimality conditions for the relay power optimization can be writ-ten as follows:

∂L(Pkd,i, υk, µ, δi)

∂Pkd,i= 0

δi = υk + µL∑l=1

|Hkl,i|2Ωl,i −d1

(1 + Pkd,iγkd,i)(d2 + Pkd,iγkd,i)

(B.5)

δi ≥ 0

υk ≥ d1(1 + Pkd,iγkd,i)(d2 + Pkd,iγkd,i)

− µL∑l=1

|Hkl,i|2Ωl,i (B.6)

APPENDIX 195

δi Pkd,i = 0[υk + µ

L∑l=1

|Hkl,i|2Ωl,i −d1

(1 + Pkd,iγkd,i)(d2 + Pkd,iγkd,i)

]Pkd,i = 0

(B.7)

If υk <d1d2−µ

(∑Ll=1|Hkl,i|2Ωl,i

), condition (B.6) can only be satised if P ∗

kd,i >

0. Then from (B.7),

υk + µ

L∑l=1

|Hkl,i|2Ωl,i −d1

(1 + Pkd,iγkd,i)(d2 + Pkd,iγkd,i)= 0 (B.8)

If υk >d1d2

− µ(∑L

l=1|Hkl,i|2Ωl,i

)with P ∗

kd,i > 0, it is impossible to satisfy the

condition (B.7). Therefore, (B.7) implies that P ∗kd,i = 0. Solving (B.8) with

respect to Pkd,i and after some mathematical manipulations, the solution foroptimal relay transmit power can be obtained as,

P ∗kd,i =

1

γkd,i

[Psk,iγsk,i

2

(√1 + [·]− 1

)− 1

]+[·] =

2γkd,i

ln(2)Psk,i γsk,i (υk + µ∑L

l=1 |Hkl,i|2 Ωl,i)(B.9)

where [x]+ = max(0, x).

Case 2: Ak,i = 0

Ak,i = 0 implies that the ith subcarrier is not transmitted by the kth relay. Thusit is obvious that P ∗

kd,i = 0 when Ak,i = 0.Combining the results obtained for above two cases, the solution for optimal

relay transmit power can be expressed as given in (5.17).

Appendix C

Optimal Transmit Powers in OFDM

CR Relay Transmission with

Average Interference Constraints

C.1 Derivation of Optimal Source Transmit Power

in DF Relay Assisted CR Transmission

the optimization problem in (6.18)-(6.19) can be converted in to a convex opti-mization problem by rewriting the objective function as a minimization of thenegative value of the concave function

∑Ni=1

12log2 (1 + Ps,iγsr,i) as follows:

Minimize−N∑i=1

1

2log2 (1 + Ps,i γsr,i) (C.1)

APPENDIX 197

subject to,

C1 :∑N

i=1 Ps,i ≤ PS

C2 :∑N

i=1 ηi Ps,i ≤ PR

C3 :∑N


C4 :∑N

i=1 Ps,i ηi bl,i ≤ I lth, ∀ l

C5 : Ps,i ≥ 0, ∀ i

(C.2)

The corresponding Lagrangian function for above optimization problem canbe written as,

L(Ps,i, ν1, ν2, µl, δl, υi)

= −N∑i=1

1

2log2 (1 + Ps,i γsr,i) + ν1

[N∑i=1

Ps,i − PS

]+ ν2

[N∑i=1

ηiPs,i − PR

]

+L∑l=1

µl

[N∑i=1

Ps,ial,i

]+

L∑l=1

δl

[N∑i=1

ηiPs,ibl,i

]−

N∑i=1

υiPs,i.

(C.3)

The non-negative Lagrange parameters ν1, ν2, µl, δl, and υi represent the con-straints C1−C5, respectively. The respective KKT optimality conditions for theoptimization problem in (C.1)-(C.2) can be given as follows:

∂L(Ps,i, ν1, ν2, µl, δl, υi)

∂Ps,i= 0

υi = ν1 + ν2ηi +L∑l=1

µlal,i

+L∑l=1

δlηibl,i −γsr,i

2 ln(2)(1 + γsr,iPs,i)(C.4)

υi ≥ 0

ν1 + ν2ηi +L∑l=1

µlal,i +L∑l=1

δlηibl,i ≥ γsr,i2 ln(2)(1 + γsr,iPs,i)

(C.5)

APPENDIX 198

υi Ps,i = 0[ν1 + ν2ηi +

L∑l=1

µlal,i +L∑l=1


2 ln(2)(1 + γsr,iPs,i)

]Ps,i = 0

(C.6)

If ν1+ν2ηi+∑L

l=1 µlal,i+∑L

l=1 δlηibl,i <γsr,i2 ln(2)

, condition (C.5) can be satised

only if P ∗s,i > 0. Then from (C.6),

ν1 + ν2ηi +L∑l=1

µlal,i +L∑l=1


2 ln(2)(1 + γsr,iPs,i)= 0 (C.7)

If ν1 + ν2ηi +∑L

l=1 µlal,i +∑L

l=1 δlηibl,i >γsr,i2 ln(2)

with P ∗s,i > 0, it is impossible to

meet the condition (C.6). Therefore, (C.6) implies that P ∗s,i = 0. Solving (C.7)

with respect to Ps,i and after some mathematical manipulations the solution foroptimal source transmit power can be obtained as,

P ∗s,i =

1

2 ln(2)[ν1 + ν2ηi +

∑Ll=1 (µlal,i + δlηibl,i)

] − 1

γsr,i

+

(C.8)

where, [x]+ = max(0, x).

C.2 Derivation of Optimal Relay Transmit Power

in AF Relay Assisted CR Transmission

The Lagrangian function for the relay power optimization problem in (6.38)-(6.39)can be expressed as,

L(Pr,i, α, ϕl, δi)

= −N∑i=1

1

2log2

(1 +


)+ α

[N∑i=1

Pr,i − PR

]

+L∑l=1

ϕl

[N∑i=1

Pr,ibl,i

]−

N∑i=1

δiPr,i. (C.9)

APPENDIX 199

where, α, ϕl, and δi are non-negative Lagrange parameters correspond to theconstraints in (6.39). The KKT conditions for this optimization problem can begiven as follows:

∂L(Pr,i, α, ϕl, δi)

∂Pr,i= 0

δi = α+ ϕl bl,i −Ps,iγsr,iγrd,i

2 ln(2)(1 + Pr,iγrd,i)(1 + Ps,iγsr,i + Pr,iγrd,i)

(C.10)

δi ≥ 0

α ≥ Ps,iγsr,iγrd,i2 ln(2)(1 + Pr,iγrd,i)(1 + Ps,iγsr,i + Pr,iγrd,i)

− ϕl bl,i (C.11)

δiPr,i = 0[α+ ϕl bl,i −

Ps,iγsr,iγrd,i2 ln(2)(1 + Pr,iγrd,i)(1 + Ps,iγsr,i + Pr,iγrd,i)

]Pr,i = 0

(C.12)

If α >Ps,iγsr,iγrd,i

2 ln(2)(1+Ps,iγsr,i)− ϕl bl,i with P ∗

r,i > 0, condition (C.12) cannot be

satised. Hence, (C.12) implies that P ∗r,i = 0. However, if α <

Ps,iγsr,iγrd,i2 ln(2)(1+Ps,iγsr,i)

−ϕl bl,i, condition (C.11) can only be satised if P ∗

r,i > 0. Then, (C.12) impliesthat,

α+ ϕl bl,i −Ps,iγsr,iγrd,i

2 ln(2)(1 + Pr,iγrd,i)(1 + Ps,iγsr,i + Pr,iγrd,i)= 0 (C.13)

By solving (C.13) with respect to Pr,i the solution for optimal relay transmitpower can be obtained as,

P ∗r,i =

1

γrd,i

[Ps,iγsr,i

2

(√[·]− 1

)− 1

]+[·] = 1 +

2γrd,i

ln(2)Ps,i γsr,i (α+∑L

l=1 ϕl bl,i)(C.14)

where, [x]+ = max(0, x).

Appendix D

Optimal Transmit Power for

Interference Minimization in

OFDM CR Networks

The Lagrangian for the given optimization problem in (7.3)-(7.7) can be writtenas,

L(Pi, δ, υ, βm, µi)

=Ntot∑i=1

L∑l=1

M∑m=1

PiΩl,iE[gm,i] + δ

[Cth −

Ntot∑i=1

log2(1 + Piγi)

]+ υ

[Ntot∑i=1

Pi − P

]

+M∑m=1

βm

[Ntot∑i=1

L∑l=1

PiΩl,iE[gm,i]− Imth

]−

N∑i=1

µiPi (D.1)

where, δ,υ, βm, and µi are the Lagrange multipliers.The corresponding Karush-Kuhn-Tucker (KKT) conditions can be expressed

as follows:

APPENDIX 201

∂L(Pi, δ, υ, βm, µi)

∂Pi= 0

µi =L∑l=1

Ωl,i

M∑m=1

E[gm,i]−δγi

ln(2)(1 + Piγi)+ υ

+M∑m=1

βm

[L∑l=1

Ωl,i

M∑m=1

E[gm,i]

](D.2)

µi ≥ 0

υ ≥ δγiln(2)(1 + Piγi)

−L∑l=1

Ωl,i

M∑m=1

E[gm,i]

−M∑m=1

βm

[L∑l=1

Ωl,i

M∑m=1

E[gm,i]

](D.3)

µi Pi = 0[(L∑l=1

Ωl,i

M∑m=1

E[gm,i]

)(1 +

M∑m=1

βm

)− δγi

ln(2)(1 + Piγi)+ υ

]Pi = 0

(D.4)

If υ < δγiln(2)

−(∑L

l=1 Ωl,i

∑Mm=1E[gm,i]

)(1 +

∑Mm=1 βm

), condition (D.3) can

be satised if and only if P ∗i > 0. Then from (D.4),

(L∑l=1

Ωl,i

M∑m=1

E[gm,i]

)(1 +

M∑m=1

βm

)− δγi

ln(2)(1 + Piγi)+ υ = 0

P ∗i =

δ[(∑Ll=1 Ωl,i

∑Mm=1E [gm,i]

) (1 +

∑Mm=1 βm

)+ υ]ln(2)

− 1

γi

(D.5)

Otherwise, if υ > δγiln(2)

−(∑L

l=1 Ωl,i

∑Mm=1E[gm,i]

)(1 +

∑Mm=1 βm

)with P ∗

i > 0,

it is impossible to meet the condition (D.4). Therefore, (D.4) implies that P ∗i = 0.

Combining the above solutions achieves the result in (7.8).

resource allocation in ofdm-based relay and cognitive

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