cognitive radio ad hoc networks: a local control approach

Cognitive Radio Ad Hoc Networks:

A Local Control Approach

by

Peng Hu

A thesis submitted to the

Department of Electrical and Computer Engineering

in conformity with the requirements for

the degree of Doctor of Philosophy

Queen’s University

Kingston, Ontario, Canada

February 2013

Copyright c© Peng Hu, 2013

Abstract

Cognitive radio is an important technology which aims to improve the spectrum

resource utilization and allows a cognitive radio transceiver to detect and sense spec-

trum holes without causing interference to the primary users (PUs). As a result of

the development of cognitive radio technology, the concept of cognitive radio ad hoc

networks (CRAHNs) has recently been proposed in the literature, which aims to ap-

ply the cognitive radio to traditional ad hoc networks. However, this new network

paradigm creates more research challenges than those in classical cognitive radio net-

works (CRNs). These research challenges in CRAHNs are due to the variable radio

environments caused by spectrum-dependent communication links, hop-by-hop trans-

mission, and changing topology. This study will focus on important research topics in

spectrum management in scalable CRAHNs driven by local control, such as spectrum

sharing, allocation, and mobility. To conduct this study, a local control approach is

proposed to enable system-level analysis and protocol-level design with distributed

protocols for spectrum sharing. In the local control approach, we can evaluate the

system dynamics caused by either protocol-specific parameters or application-specific

parameters in CRAHNs, which is hard to explore using existing methods. Moreover,

combining the previous evaluations and scaling law analysis based on local control

i

concept, we can design new distributed protocols based on the features of the medi-

um access control (MAC) layer and the physical layer. In this study, the proposed

research themes and related research issues surrounding spectrum sharing are dis-

cussed. Moreover, justification of the research has been made by experimental and

analytical results.

ii

Acknowledgments

I would like to express my sincere gratitude in the support and help to Dr. Mohamed

Ibnkahla. He encouraged me greatly to work in this topic. His willingness to motivate

us contributed tremendously to my research. He offered invaluable assistance, support

and guidance.

I am indebted to my colleagues for providing a stimulating environment in which

to learn and grow, especially grateful to our group members and friends: Vivien

Kan, Amr El Mougy, Basel Nabulsi, Zouheir El-Jabi, Gayathri Vijay, Parisa Abedi

Khoozani, Abdallah Alma’Aitah, Ala Abu Alkheir, Ayman Sabbah, and Yang Li,

just to name a few.

I wish to thank my entire extended family for providing a loving environment for

me. And most importantly, I wish to thank my parents. To them I dedicate this

thesis.

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Contents

Abstract i

Acknowledgments iii

Contents iv

List of Tables vii

List of Figures viii

Chapter 1: Introduction 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.4 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.4.1 Distributed Local Control Schemes & Dynamics . . . . . . . . 61.4.2 Emergent Behavior of CRAHNs . . . . . . . . . . . . . . . . . 71.4.3 Local Control Driven MAC Protocol Design . . . . . . . . . . 71.4.4 Scaling Law Based on Local Control . . . . . . . . . . . . . . 8

1.5 Organization of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Chapter 2: Background & Related Work 102.1 Cognitive Radio Ad Hoc Networks . . . . . . . . . . . . . . . . . . . 102.2 Cognitive Radio Networks Vs. Cognitive Radio Ad Hoc Networks . . 122.3 Spectrum Sharing in CRAHNs . . . . . . . . . . . . . . . . . . . . . . 12

2.3.1 Spectrum Allocation . . . . . . . . . . . . . . . . . . . . . . . 132.3.2 Spectrum Access Model . . . . . . . . . . . . . . . . . . . . . 152.3.3 Spectrum Sensing . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.4 Cognitive MAC Protocols . . . . . . . . . . . . . . . . . . . . . . . . 162.5 Scaling Law of CRAHNs . . . . . . . . . . . . . . . . . . . . . . . . . 19

Chapter 3: System Model and Approach 22

iv

3.1 Spectrum Availability Map . . . . . . . . . . . . . . . . . . . . . . . . 223.1.1 Cell-Based Spectrum Availability Map . . . . . . . . . . . . . 233.1.2 Radio Environment Map . . . . . . . . . . . . . . . . . . . . . 24

3.2 Spectrum Availability Probability . . . . . . . . . . . . . . . . . . . . 253.3 Variable Size of Spectrum Bands . . . . . . . . . . . . . . . . . . . . 263.4 Multi-Channel Multi-Radio Support . . . . . . . . . . . . . . . . . . . 273.5 Resultant Channel Model . . . . . . . . . . . . . . . . . . . . . . . . 273.6 Local and Global Information . . . . . . . . . . . . . . . . . . . . . . 303.7 Local Control in Spectrum Management . . . . . . . . . . . . . . . . 313.8 Game Theoretic Approach . . . . . . . . . . . . . . . . . . . . . . . . 323.9 Graph Coloring Based Algorithms . . . . . . . . . . . . . . . . . . . . 353.10 Partial Observable Markov Decision Process . . . . . . . . . . . . . . 363.11 Bio-Inspired Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.12 Conclusive Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Chapter 4: Local Control Schemes for Spectrum Sharing 394.1 Applicability of A Local Control Scheme to CRAHNs, CRSNs, And

Sensor Networks for CRAHNs . . . . . . . . . . . . . . . . . . . . . . 394.2 Revisit of Spectrum Sharing in the Perspective of Local Control Schemes 414.3 Framework of Local Control Schemes . . . . . . . . . . . . . . . . . . 424.4 Fairness in Spectrum Sharing . . . . . . . . . . . . . . . . . . . . . . 434.5 Protocol Design And Experimental Results . . . . . . . . . . . . . . . 49

4.5.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.5.2 Protocol Design . . . . . . . . . . . . . . . . . . . . . . . . . . 524.5.3 Computer Simulation Results . . . . . . . . . . . . . . . . . . 554.5.4 Convergence Performance And Feedback Quality . . . . . . . 564.5.5 Fairness Performance in Various Network Sizes . . . . . . . . . 60

4.6 Conclusive Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

Chapter 5: Local Control Driven Medium Access Control Protocol 685.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685.2 Primary Exclusive Regions . . . . . . . . . . . . . . . . . . . . . . . . 705.3 Proposed CM-MAC Protocol . . . . . . . . . . . . . . . . . . . . . . . 75

5.3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 755.3.2 Channel Aggregation Technique . . . . . . . . . . . . . . . . . 775.3.3 Spectrum Access and Sharing . . . . . . . . . . . . . . . . . . 785.3.4 Mobility Support Algorithm . . . . . . . . . . . . . . . . . . . 79

5.4 Throughput Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 825.4.1 Average Time Spent on Mobility . . . . . . . . . . . . . . . . 835.4.2 Link Throughput Performance . . . . . . . . . . . . . . . . . 85

v

5.4.3 Upper Bound of Spectrum Utilization . . . . . . . . . . . . . 885.4.4 A Special Case of the Proposed CM-MAC Protocol . . . . . . 89

5.5 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 905.6 Conclusive Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

Chapter 6: Scaling Law of CRAHNs Based on Local Control 1016.1 PU Interference Region . . . . . . . . . . . . . . . . . . . . . . . . . . 1016.2 Network Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

6.2.1 Virtual PU in the Resultant Spectrum Band . . . . . . . . . . 1056.2.2 Medium Access Probability . . . . . . . . . . . . . . . . . . . 107

6.3 Network Divisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1096.4 Multi-Hop Data Transmission Scenario . . . . . . . . . . . . . . . . . 111

6.4.1 Probability of A Transmission over Multiple Hops . . . . . . 1136.4.2 Packet Reception Probability . . . . . . . . . . . . . . . . . . 114

6.5 Scaling Law of CRAHNs . . . . . . . . . . . . . . . . . . . . . . . . . 1146.6 Discussion on IEEE 802.22 Based CRAHNs & IEEE 802.11 Based

CRAHNs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1196.7 Conclusive Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

Chapter 7: Conclusion 1217.1 Summary of Contributions . . . . . . . . . . . . . . . . . . . . . . . . 1217.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

vi

List of Tables

3.1 Local information associated with cost values . . . . . . . . . . . . . 30

5.1 Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

6.1 Common parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

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List of Figures

1.1 An example of a CRAHN . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Spectrum management framework . . . . . . . . . . . . . . . . . . . . 3

2.1 An example of (a) a CRAHN and (b) a CRSN . . . . . . . . . . . . . 11

3.1 An example of C-SAM in a CRAHN with 3 spectrum band indexes for

each CR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.2 The architecture of a CRAHN with REM servers . . . . . . . . . . . 25

3.3 Throughput performance in a CRAHN with multi-channel multi-radio

support in different settings. The network has 10 CRs and the com-

munication range per node is 250m in 2GHz band. . . . . . . . . . . . 28

3.4 Example of the resultant channel model . . . . . . . . . . . . . . . . 29

4.1 A CRAHN deployed in a radio environment . . . . . . . . . . . . . . 41

4.2 Framework of a local control scheme . . . . . . . . . . . . . . . . . . 42

4.3 Analytical results for stability when using the consensus-based feed-

back. Nyquist plots with different time delays τ and with maximum

degree of three in the CRAHN . . . . . . . . . . . . . . . . . . . . . . 48

4.4 Results of the proposed open-loop local control scheme for spectrum

allocation in a CRAHN . . . . . . . . . . . . . . . . . . . . . . . . . . 51

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4.5 Pseudo code of consensus-based spectrum allocation protocol . . . . . 53

4.6 A randomly distributed CRAHN with 350 CRs and initially allocated

spectrum bands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.7 Convergence performance of the proposed consensus-based protocol,

Rule-A, and Rule-A (P) . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.8 Convergence performance of the consensus-based protocol and Rule-A

in multiple iterations . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

4.9 An example of the ZigZag network. In (a), there is only one shaded

region of PU activity L, while in (b), there are two shaded regions of

PU activities, denoted by L(1) and L(2), respectively. We will show

that the feedback adopted in Rule-A is overestimated in both cases. . 59

4.10 The value of L versus the maximum number of spectrum bands with

the different number of CR nodes M . . . . . . . . . . . . . . . . . . 61

4.11 Fairness performance versus different network sizes when (a) M=100,

(b) M=150, (c) M=200, and (d) M=350 . . . . . . . . . . . . . . . . 62

4.12 Intermediate spectrum sharing results in CRAHN when (a) FG=1, (b)

FG=2, and (c) FG=3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

4.13 Convergence performance with different number of FGs . . . . . . . . 64

4.14 Fairness performance in a network when (a) FG=2 (b) FG=3 . . . . 65

5.1 A CRAHN with a PER and multiple CRs . . . . . . . . . . . . . . . 69

5.2 An example of the necessity of a CRAHN MAC protocol in a CRAHN.

The available spectrum bands for the nodes covered by a PU are shown

in brackets. The links are broken (shown in dashed arrows) when the

data transmission from S to D is operated on channel 3. . . . . . . . 71

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5.3 The normalized throughput of a PU and CRs versus PCR and R/R0,

when (a) v = 0.3 and (b) v = 0.7 . . . . . . . . . . . . . . . . . . . . 74

5.4 Frame structures of (a) the traditional CSMA/CA-based MAC proto-

col and (b) the proposed CM-MAC protocol . . . . . . . . . . . . . . 75

5.5 An example of channel aggregation in the view of (a) the MAC frame

and (b) the sequence diagram . . . . . . . . . . . . . . . . . . . . . . 77

5.6 An example of intermediate results of the spectrum sharing procedure

after (a) a RTS transmission, (b) a CTS transmission, and (c) an ACTS

transmission. The dotted lines are transmission ranges of CR node 1

and CR node 6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

5.7 Description of the mobility support algorithm (MSA) . . . . . . . . . 81

5.8 An example of a CRAHN with PUs and CRs . . . . . . . . . . . . . . 82

5.9 Description of a successful data transmission . . . . . . . . . . . . . . 86

5.10 Description of a successful data transmission . . . . . . . . . . . . . . 92

5.11 CR link throughput versus N and λ′ . . . . . . . . . . . . . . . . . . 94

5.12 CR link throughput versus N and λ . . . . . . . . . . . . . . . . . . . 95

5.13 CR link throughput performance with different values of Kp in the (a)

saturated mode, and (b)-(c) non-saturated mode . . . . . . . . . . . . 97

5.14 CR link throughput performance versus P0, where CR traffic is in the

(a) saturated mode and (b)-(c) non-saturated mode with PU traffic . 98

5.15 Simulation results. (a) Response time and (b) throughout performance 99

6.1 Network layout of a CRAHN . . . . . . . . . . . . . . . . . . . . . . . 103

6.2 Toff and Ton based on resultant channel model . . . . . . . . . . . . . 107

6.3 MAP results based on the resultant channel model . . . . . . . . . . 110

x

6.4 Multi-hop data transmission from CR 1 to CR n. . . . . . . . . . . . 111

6.5 Throughput results of a single-hop scenario. (a) The whole network

within an area S is considered; (b) the throughput performance in a

subarea of S is considered. . . . . . . . . . . . . . . . . . . . . . . . . 116

6.6 Normalized throughput results when hop counts are 2, 3, and 4 in a

bounded circular area. . . . . . . . . . . . . . . . . . . . . . . . . . . 117

6.7 Normalized throughput results of a multi-hop scenario with different

hop counts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

xi

1

Chapter 1

Introduction

Radio spectrum is a precious resource for wireless communications. However, for

decades, this resource has been underutilized. From the Federal Communications

Commission (FCC) report in 2003 [1], the variation of spectrum utilization ranges

from 15% to 85%, which means that a large portion of the radio spectrum is not effi-

ciently used most of the time. A recent long-term study for a wideband (30 MHz to

3 GHz) spectrum observatory system [2] in downtown Chicago indicates the spectral

capacity is underutilized over the entire range. In order to use the radio spectrum

more efficiently, the concept of cognitive radio (CR) [3, 4] has been introduced. D-

ifferent from the traditional radio frequency (RF) system, cognitive radio enables

real-time interaction and adaptation to the surrounding radio environment in order

to determine the communication parameters, such as data rate, modulation scheme,

and transmission power. The ultimate objective of cognitive radio is to obtain the

best available spectrum resource through cognitive capability and reconfigurability

[5]. To achieve this objective, cognitive radio needs to have certain capabilities, such

as spectrum sensing, spectrum analysis, and spectrum decision [6].

As a result of the development of CR technology, the concept of cognitive radio

1.1. MOTIVATION 2

ad hoc networks (CRAHNs) has been proposed in 2009 [5]. A CRAHN is an ad hoc

network composed by CR nodes (a.k.a. secondary users or CRs) and primary users

(PUs) applying the cognitive radio technology on CR transceivers. As such, the CRs

in CRAHNs do not favor central coordination when performing spectrum sharing

processes. Instead, CRs have to perform local observation most of the time. An

example of a CRAHN that can work in different spectrum bands can be seen in Fig.

1.1. Similar to CRAHNs, the concept of cognitive radio sensor networks (CRSNs) [7]

was coined in 2009, where each sensor node in a CRSN can be considered as a CR

with limited hardware and capability to obtain surrounding information.

1.1 Motivation

Due to the lack of central network entities in CRAHNs [8], each CR node necessi-

tates that all the spectrum-related CR capabilities and distributed operations must be

mostly based on local observations. As such, the new features introduced by CRAHNs

mean that spectrum management in CRAHN opens a range of new research topics

that differ from traditional cognitive radio or cognitive radio networks (CRNs). Based

on the cognitive cycle proposed in [6], Akyildiz et al. [8] defined the spectrum man-

agement problems in CRAHNs, where the authors specified several essential topics

of spectrum management, including spectrum sensing, spectrum sharing, spectrum

mobility, and spectrum decision.

As an important research topic in cognitive radio and CRAHNs, spectrum man-

agement in CR has been an intensive research area but the spectrum management for

CRAHNs is open to be answered. Spectrum management in CR research is mainly

1.1. MOTIVATION 3

CR

PU

CR

PU

PU

CRCR

CR

CR

CR

PU

PU

PU

CR

Figure 1.1: An example of a CRAHN

Link Layer Protocol

Spectrum Sharing

PHY Layer

NWK Layer ProtocolSpectrumMobility

Spectrum Sensing

Cooperation

Upper Layers

SpectrumDecision

Figure 1.2: Spectrum management framework

focused on physical layer (PHY) issues. Haykin in [6] defined the objective of the spec-

trum management algorithm for CR mostly in the PHY layer, which is to “build on

the spectrum holes detected by the radio-scene analyzer and the output of transmit-

power controller, select a modulation strategy that adapts to the time-varying con-

ditions of the radio environment, all the time assuring reliable communication across

the channel”. However, spectrum management in CRAHNs has to deal with issues

not only in the PHY layer but also in the medium access control (MAC) layer and

the network (NWK) layer. As such, spectrum management in CRAHNs should solve

1.2. PROBLEM 4

spectrum management issues by taking advantage of functions across layers. Further-

more, spectrum management in CRAHNs can address the application-specific quality

of service (QoS) requirements [5]. As the spectrum availability fluctuates over time

and location [9], a CR should be intelligent enough to make a spectrum decision.

Spectrum sharing shown in Fig. 1.2 [8] plays a key role in the whole spectrum man-

agement module, where it requires cross-layer support from the PHY layer to the

NWK layer. This cross-layer nature of a spectrum sharing function requires us to

propose a new approach to distributed operations for the local information driven

CRAHNs.

1.2 Problem

CRAHNs have recently attracted intensive research interest, but some key theoretical

questions have yet to be answered. The previously proposed algorithms and tech-

niques for solving spectrum management problems are not suited to CRAHNs. For

the CRs relying on the local control with local observation and limited local informa-

tion, we need to design the local control schemes for the spectrum sharing function.

Moreover, with the features brought by CRAHNs, MAC protocols for traditional

CRNs or ad hoc networks need to be re-designed because they need to address the

spectrum availability, interference, as well as mobility issues. For example, mobility

issues that can cause spectrum mobility will result in the negative effects to the data

transmissions in CRAHNs, such as interference to PU communications and spectrum

variations. More importantly, when we consider a CRAHN as a complex system, a

change of a parameter value in initial conditions may cause unexpected results to the

CRAHN. In this sense, we propose to study the system stability condition in order to

1.3. OBJECTIVE 5

explore system-level properties and behaviors for spectrum management problems in

CRAHNs. Because the system-level properties are related to the protocols or algo-

rithms used in a certain layer of the CRAHN, we must study protocols or algorithms

used for spectrum management problems. Subsequently, the scaling law should be

considered because a change in system-level parameters or protocol-level parameters

may result in a new scaling law for PUs and CRs data transmissions in CRAHNs. In

addition, because the protocols/algorithms in CRAHNs are mostly based on the local

sensing, an important problem is to determine how the local information acquired by

local sensing can be used in the protocols/algorithms and how the local information

can affect the performance of these protocols/algorithms.

Furthermore, the throughput performance in a CRAHN based on the local control

approach together with the MAC and PHY features needs to be addressed. For

example, an accurate channel profile can be considered when analyzing the scaling

law. Furthermore, after a successful dynamic spectrum access, CRs must be able to

relay packets to the destination node with the available CRs in the CRAHN. In this

sense, how the cognitive environment can affect the performance degradation for CRs

is a challenge. The analysis in multi-hop data transmission scenarios can provide

some insights to this issue.

1.3 Objective

Fundamental problems of spectrum sharing in CRAHNs need to be investigated.

A light-wight and effective scheme for spectrum sharing of CRAHN needs to be

investigated, not only because it utilizes the cross-layer information but also because

it can take advantage of the main features introduced by scalable CRAHNs. These

1.4. CONTRIBUTIONS 6

features can provide opportunities for solving spectrum sharing problems in local

control approach with radio environment information, including global information

and local information. In this way, we are required to propose a local control approach

to address the spectrum sharing related problems. This study defines and develops

the local control approach concept. In the local control approach, we need to consider

the distributed operations for CRs, where a CR or a PU can perform a local control

scheme with sensing inputs and decision outputs. We also need to address the mobility

and interference issues in the MAC layer and perform the system-level analysis for the

local control driven CRAHNs. By studying some fundamental problems regarding

spectrum sharing in local control approach, we can model, analyze, and evaluate

essential system and protocol-specific performance for CRAHNs.

1.4 Contributions

1.4.1 Distributed Local Control Schemes & Dynamics

We propose a local control framework for the distributed protocols for spectrum

sharing. We address the time delay in the transmission delay for the proposed local

control scheme. For example, the delay may be significant if an energy-detection-

based spectrum sensing scheme [10] is used. Therefore, the issue of how the delay

variation can affect the spectrum decision and sensing control should be explored.

To address this issue, together with the system-level analytic results of local control

schemes, we propose a cross-layer local control scheme.

Considering the scalable deployment of a CRAHN, we should exploit the system

dynamics of local control schemes. As such, we aim to prove the applicability and

conditions of using consensus-based protocols in local control schemes in spectrum

1.4. CONTRIBUTIONS 7

sharing problems in CRAHNs. The main goals of our research based on consensus

protocols are the following:

• We analyze and evaluate the algorithmic performance in a scalable CRAHN;

• We investigate how the collective intelligence will occur and how it helps to

solve spectrum sharing problems;

• We explore the system dynamics by employing a consensus protocol in local con-

trol schemes. For example, the analytic results from system dynamics analysis

can tell us the equilibrium condition when using a local control scheme.

1.4.2 Emergent Behavior of CRAHNs

Because of the existence of “emergent behavior” in a large-scale CRAHN, a cognitive

protocol or algorithm that works well in an individual cognitive radio may behave

differently in a large scale. On the one hand, this phenomenon can be examined before

the protocol design. On the other hand, it is not clear what emergent behaviors might

arise when the CR interacts with legacy radios or with other heterogeneous systems,

and whether these behaviors can inadvertently lead to communication failures in

critical applications. Without investigating the CRAHN at the system level, it is

not possible to justify the effectiveness and robustness of spectrum policy changes

for spectrum management. We have addressed this topic in the local control scheme

design.

1.4.3 Local Control Driven MAC Protocol Design

The protocols in the MAC sub layer has the scope of only exchanging the informa-

tion with neighbouring CRs. Therefore, it is an ideal place for applying the local

1.5. ORGANIZATION OF THESIS 8

control approach for CRAHNs. With local control concept, a MAC protocol needs to

solve the issues including mobility and PU interference with cognitive radio capability

without inducing significant communication efforts. In this research theme, in order

to address these issues, we propose a cognitive MAC protocol called CM-MAC. The

main contributions are listed as follows:

• We propose a CM-MAC protocol that addresses CR mobility and PER issues;

• We analyze the throughput and spectrum utilization of CM-MAC protocol as-

suming that the PU traffic follows a Poisson process;

• We show that the throughput and spectrum utilization are improved by CM-

MAC compared to classical MAC protocols.

1.4.4 Scaling Law Based on Local Control

As a main goal of CRAHNs, throughput performance needs to be investigated and

analyzed in single-hop and multi-hop scenarios. The state-of-the-art research in the

literature has addressed throughput analysis in CRNs, but several key factors in

CRAHNs have not been comprehensively addressed. As a result, we develop a model

for throughput analysis because in this way some key factors such as the route selec-

tion, local observation & control, spectrum sharing, and multi-hop data transmission

scenarios can be addressed.

1.5 Organization of Thesis

We proceed by introducing the CRAHN and spectrum sharing functions and dis-

cussing related work in Chapter 2. The related system models and approaches are

1.5. ORGANIZATION OF THESIS 9

presented in Chapter 3. We discuss the local control framework for the spectrum

sharing fairness problem with experimental results in Chapter 4. Chapter 5 discusses

the mobility supported MAC which further shows the local control concept. The s-

caling law analysis is discussed in Chapter 6. Chapter 7 concludes and outlines future

work.

10

Chapter 2

Background & Related Work

In this chapter, we briefly introduce the background knowledge about CRAHNs and

discuss the related work regarding the thesis research topics.

2.1 Cognitive Radio Ad Hoc Networks

A CRANH is a network composed by CRs nodes and PUs in an ad hoc manner in

a changing radio environment induced by the time and location and PU activities.

In order to ensure the successful data transmissions, accessing the spectrum resource

needs to be coordinated to prevent collisions. As such, with a spectrum sharing

module, a CR is able to share spectrum resources among CRs [5]. As an example of

a CRAHN shown in Fig. 2.1(a), the CRs are co-located with PUs, where PUs and

CRs are able to move. In order to make CRs aware of the available spectrum bands,

the spectrum sharing module in each CR is required to ensure changing spectrum

resources in a region can be fairly shared with CRs. Similarly, the CRSN needs the

spectrum sharing module to ensure spectrum resources available to sensor nodes (SNs)

as shown in Fig. 2.1(b). Besides, if we consider a spectrum sharing scheme, we need

to choose a spectrum sharing model. There are two competing models of spectrum

2.1. COGNITIVE RADIO AD HOC NETWORKS 11

sharing [11]: (1) sharing among equals and (2) sharing between licensed primary

and secondary, where the former can be considered as the underlay technique and

the latter can be considered as the overlay technique (i.e., a CR does not use the

spectrum bands occupied by the PUs).

(a)

(b)

Figure 2.1: An example of (a) a CRAHN and (b) a CRSN

2.2. COGNITIVE RADIO NETWORKS VS. COGNITIVE RADIO ADHOC NETWORKS 12

2.2 Cognitive Radio Networks Vs. Cognitive Radio Ad Hoc Networks

The concept of cognitive radio networks is defined as the wireless networks that

consist of primary and secondary users [12]. The traditional CRNs are often modeled

as small networks in licensed bands with one PU and multiple SUs as seen in the

current IEEE 802.22 networks. However, the CRN paradigm can be extended to

the unlicensed industrial, scientific and medical (ISM) radio bands and therefore can

be used in the current ad hoc networks and wireless sensor networks. Some current

research topics of CRNs can be found in the recent survey papers [13, 14].

The CRAHN has different specific research foci compared with CRNs. Inherited

from the features in traditional ad hoc networks, nodes in a CRAHN can communicate

with each other without a fixed infrastructure [15]. The ad hoc topology and data

transmissions of ad hoc networks as well as the cognitive capabilities of CRNs bring

the new features and new challenges to CRAHNs. With the new features, the research

of CRAHN is expected to shed light on some current and future wireless networks.

2.3 Spectrum Sharing in CRAHNs

Spectrum sharing is a important function of spectrum management in CRAHNs. In

[5], spectrum sharing is defined to provide the capability of sharing the spectrum

resource opportunistically with multiple CRs while avoiding interference caused to

the primary network. Basically, spectrum sharing involves spectrum access, spectrum

allocation, and spectrum sensing with cross-layer information. In this sense, in the

protocol architecture point of view, it has to collaborate with PHY, MAC, and NWK

layers.

2.3. SPECTRUM SHARING IN CRAHNS 13

2.3.1 Spectrum Allocation

In order to ensure the data communications, CRs need to maximize their own share of

spectrum resources for data transmission sessions. Furthermore, CRs need to perform

channel selection and power allocation while choosing the best channel. Cooperation

among neighbors can help enhance the performance of spectrum sharing. However,

with the local observation to radio environment, CRs have limited radio information

from their neighbors by cooperation, and this constraint is expected to be able to affect

the performance of the network in terms of throughput and spectrum utilization.

Several distributed schemes or algorithms have been proposed in the literature

to solve the spectrum sharing problems. A single-channel asynchronous distributed

pricing scheme for spectrum selection and power control was proposed in [16], where

each CR determines the transmit power by maximizing the received utility minus the

total cost of the associated interference. A graph coloring based scheme was proposed

in [17], which is essentially a global optimization algorithm. This global optimiza-

tion algorithm is centralized in nature and is required to be recomputed whenever

there is a change in CRAHNs. Compared to a centralized scheme, a distributed

scheme is more suitable for the CRAHN due to its robustness in varying radio en-

vironments (e.g., topology and spectrum availability, etc.). A distributed spectrum

allocation scheme, referred as local bargaining, was proposed in [18], where CRs can

self-organize and form a local group to improve system utility. Results in [18] show

that the communication overhead using local bargaining can be significantly reduced

compared to a greedy coloring algorithm. A device-centric spectrum access approach

for spectrum allocation problem was introduced in [9], where five different rules are

applied to individual CRs. Although these rules have a slightly worse performance


than local bargaining [9], they have lower computational complexity and communica-

tion overhead. Furthermore, learning algorithms like reinforcement learning [19, 20]

can be involved in the spectrum sharing problems, but they may need much more in-

formation and collaboration efforts across the layers and hops, and a new architecture

is required.

Another type of algorithm, known as swarm intelligence algorithms, has been

proposed in the literature to solve spectrum sharing problems. In [21], the spectrum

sharing problem is solved by an insect colony based algorithm. In [22], an algorithm

based on the schooling mechanism of fish is studied to solve the spectrum sharing

problem. However, both papers do not give a formal proof for the convergence condi-

tion, which is important when applying the swarm intelligence algorithms to spectrum

management. Moreover, the swarm intelligence algorithms belong to a more general

type of protocols, called the consensus protocol, which is inspired by observing the

flocking or schooling phenomenon in nature. Moreover, we found that consensus pro-

tocols can be used to analyze some non-swarm-intelligence algorithms, such as local

bargaining and device-centric algorithms. The consensus protocols have been used for

the data fusion problems in sensor networks, robotic control, and multi-agent system-

s (MASs). Recently, Li et al. [23] have applied the consensus protocol to spectrum

sensing in order to control the fusion of sensing data. Yu et al. [24] have proposed a

distributed and scalable scheme for spectrum sensing based on consensus algorithms.

The above references have given hints of how to use consensus protocols in CRNs,

but they hardly address spectrum sharing fairness in CRAHNs and CRSNs. In this

study, we will formulate the convergence condition when applying a general consen-

sus protocol, which is necessary to theoretically show the applicability of consensus


protocols in spectrum sharing for CRAHNs and CRSNs. Moreover, we will discuss

how to use the consensus protocol for the spectrum sharing fairness.

2.3.2 Spectrum Access Model

Spectrum access techniques aim to make sure CRs can access the spectrum bands

without causing harmful interference to PUs, SUs need opportunistic or negotiation-

based spectrum access techniques [25]. There are three techniques (i.e., overlay, under-

lay or interweave) that aim to ensure the concurrent PU and SU data transmissions.

With the underlay technique, simultaneous PU and CR are allowed as in ultra-

wideband (UWB) systems. A CR spreads signal over a bandwidth large enough

to ensure that the amount of interference caused by the PUs is within a desired

threshold. With the overlay technique, PU messages sensed at the CR transmitter

are used to perform dirty paper coding in order to mitigate the interference seen by

the CR. With the interweave technique, CRs monitor the available channels absent

of PUs, and interweave the secondary signal through the gaps that arise in frequency

and time. The spectrum detection is critical in this interweave technique.

Spectrum overlay and spectrum underlay are considered as hierarchical access

models [26]. The overlay approach under the hierarchical access model is discussed in

[26] referred as opportunistic spectrum access, which includes spectrum opportunity

identification, spectrum opportunity exploitation, and regulatory policy.

In this thesis, we will consider the underlay and overlay techniques in the spectrum

sharing and the terms underlay spectrum sharing and overlay spectrum sharing will

be used correspondingly.

2.4. COGNITIVE MAC PROTOCOLS 16

2.3.3 Spectrum Sensing

The spectrum sensing function is closely related to the spectrum sharing as a under-

lying technology. There are two technologies to perform spectrum sensing: energy

detection and feature detection [27].

Time delay in sensing is an important factor to consider. The current sensing

technologies require us to consider the time delay caused to either PHY or upper-

layer schemes. For example, when cooperation is used for spectrum sensing, the

combination of the results from various users may have different sensitivities and

sensing times [28]. How to make the quickest detection is one of the current open

problems in spectrum sensing [27, 29, 30, 31], where it aims to detect the beginning

of a PUs transmission as quickly as possible after it happens. In fact, the well-known

sensing technology shows that sensing task takes up to several tens of milliseconds

per channel. Due to the out-of-band interference, a channel considered to be free

needs the additional sensing efforts from the adjacent channel. Moreover, a multi-

band detection technique was introduced in [32], and the sensing optimization with

MAC protocols were discussed in [33].

In the thesis, we will assume the existence of the spectrum sensing module and

consider the time delay in the spectrum sensing.

2.4 Cognitive MAC Protocols

The objectives of the CRAHN MAC protocol not only include the improvement of

channel utilization and throughput without degrading PU communications, but also

include the control of spectrum management modules such as spectrum access and

spectrum sharing functions to determine the timing for data transmissions [5].


The use of multiple channels for throughput improvement has been addressed

in several MAC protocols. A feasible solution for throughput improvement is to

find a set of good-quality channels. A dual-channel MAC protocol (DUCHA) was

proposed in [34] which can improve the one-hop throughput up to 1.2 times and

multi-hop throughput up to five times compared to the IEEE 802.11 MAC protocol.

An opportunistic multi-radio MAC (OMMAC) was proposed in [35], where a multi-

channel-based packet scheduling algorithm was employed and packets were sent on a

channel having best spectral efficiency (i.e., the channel with the highest bit rate). A

CSMA/CA-based multichannel cognitive radio medium access control (MCR-MAC)

protocol was proposed in [36].

In a CRN, the spectrum utilization can be improved if we choose the appropriate

set of channels that meet the transmission rate requirement. A MAC protocol based

on statistical channel allocation (SCA) was proposed in [37] which uses a channel ag-

gregation approach to improve the throughput and dynamic operating range to reduce

the computational complexity. Results of [37] show that SCA-MAC can use spectrum

holes effectively to improve spectrum efficiency while keeping the performance of co-

existing PUs. In order to meet data rate requirement for data transmissions, a MAC

with a so-called multi-channel parallel transmission protocol was proposed in [38],

where the minimum number of channels were selected to meet a certain data rate.

The results of [38] show that the proposed MAC protocol has better spectrum uti-

lization and system throughput than the results shown in [39], which only selected

the channels by the best signal-to-interference-plus-noise ratio (SINR) value. In [40],

an opportunistic auto-rate MAC protocol is used to maximize the utilization on in-

dividual channels.


Spectrum sharing and spectrum access functions are explicitly addressed in [41],

where spectrum access and spectrum allocation schemes are introduced into the pro-

posed cognitive radio MAC (COMAC) protocol. Specifically, the spectrum utilization

is improved by providing enough channels instead of assigning all the possible chan-

nels to a CR node, so that the other available channels could be reserved for other

CR transmissions. In [42], the authors employed a distance-dependent channel as-

signment scheme in a proposed distance-dependent MAC (DDMAC).

In fact, the aforementioned works do not comprehensively consider several impor-

tant factors. Firstly, although the spectrum sensing can be simultaneously performed

in one shot [43], the sensing time cannot be ignored, as it may be relatively large

and lead to end-to-end throughput degradation [44]. Secondly, with the existence of

the primary exclusive region (PER) where CR communications will interfere with PU

communications, the CR should keep silent when moving into this region if maintain-

ing PU communication is a priority.

As CRAHN MAC protocols favor distributed solutions, a distributed function

like distributed coordination function (DCF) is a good option for protocol design.

In fact, most of the aforementioned MAC protocols [35, 36, 38, 39, 40, 41, 42] are

DCF-based with request-to-send (RTS)/clear-to-send (CTS) handshaking procedures,

which intrinsically deal with the hidden terminal problem. Other non-CSMA/CA-

based MAC protocols like multi-channel MAC (MMAC) [45] and cognitive MAC

(C-MAC) [46] can also solve the hidden terminal problem, but they need a periodic

synchronization which can hardly be applied to large-scale CRAHNs.

2.5. SCALING LAW OF CRAHNS 19

Carrier sense multiple access/collision avoidance (CSMA/CA) based MAC pro-

tocols have the advantage of dealing with hidden terminal problems and having dis-

tributed operations (e.g., distributed coordination function in IEEE 802.11 MAC).

Thus, some state-of-the-art MAC protocols [36, 37, 38, 39, 40, 41, 42, 47] for CRNs

have been proposed. However, PER, PU activity and CR mobility have not been

comprehensively addressed in the literature.

2.5 Scaling Law of CRAHNs

The scaling law analysis for wireless networks can give hints to the theoretical bound-

s of throughput performance. Guptar and Kumar [48] firstly give the throughput

bounds for a general wireless network. They show that the throughput will decrease

with an increase of the number of nodes. However, the bounds given by Gupta and

Kumar [48] are loose for the CR network in CRAHNs, because, in CRAHNs, com-

munications between CR nodes can be affected by the PU activities. By utilizing

the multiple spectrum bands for data communications, system capacity, multi-path

diversity, and data rate can be improved [49]. However, how to comprehensively ad-

dress the design parameters across different layers in the randomly deployed CRAHN

is a challenge. Vu et al. [50] have analyzed the throughput for cognitive networks,

where the authors merely discussed the network model with one PU transmitter. This

analysis is suitable for some cognitive networks, such as the cognitive network with

one TV tower and multiple CRs. However, the analysis in [48, 50] is not suitable

for CRAHNs, as more than one PU transmitters can be present with CRs. More-

over, considering the possible flexible deployment of CRAHNs, we should analyze the

scaling law of throughput in different transmission scenarios.


Some research work has been done regarding the throughput scaling law for

CRAHNs. Shi et al. [51] have recently given lower and upper bounds for the through-

put in a randomly distributed CRAHN by using two auxiliary networks. The authors

show that the lower and upper bounds for the throughput are Ω(Cα/√n lnn) and

O(Cζ/√n lnn) respectively, where the number of CR nodes is n. However, PU activ-

ities and multi-hop transmission scenarios have not been considered in the discussion.

When the primary exclusive region (PER) was addressed in [52], where interference

and outage probability was derived for bipolar and nearest-neighbor network models.

When employing underlay transmissions with PUs, CRs will experience transmission

delay because of the reduced transmission range from increased interference. The op-

portunistic multi-channel MAC protocols for CRAHNs were analyzed in [53], where

a Markov model is used to estimate the number of sensed channels. The relation-

ship of delay, connectivity, and interference were analyzed in [54]. Besides, with new

features brought to CRAHNs, different spectrum management schemes can result in

new scaling laws in the CRAHN. Moreover, although some recently proposed physical

layer techniques, such as physical-layer network coding (PLNC) [55, 56] or interfer-

ence based network, may help to derive new scaling laws in CRAHNs, we need to

explore the essential factors that affect the CRAHN throughput performance. S-

tochastic geometry has been employed as an analytical tool for fundamental limits of

wireless networks [57] which is able to include many essential factors and transmission

scenarios [58] in the analysis.

In this thesis, we mainly explore the CRAHN with essential cognitive capabili-

ties instead of reiterating the use of new PHY technologies. We will start with our

throughput analysis by constructing the network model with the consideration of


PER, deployment of PUs and CRs, spectrum access scheme, and spectrum sharing

scheme.

22

Chapter 3

System Model and Approach

In this chapter, we discuss the essential modelling techniques and approaches re-

garding the thesis research. We compare the existing approaches and introduce the

research approach for our study.

3.1 Spectrum Availability Map

Spectrum availability varies from node to node and from link to link in CRAHNs. In

the same radio environment, node spectrum availability and link spectrum availability

can be converted to each other. It is known that spectrum availability in a CRN is

usually modelled as conflict graph [18, 59]. However, in this study, we model the

spectrum availability in the perspective of PUs. In this sense, we can start from the

introduction of spectrum availability map in a CRAHN with grid topology.

Spectrum availability map (SAM) is defined against time and it is the probability

of using some available spectrum bands for data transmissions in a time slot ∆t.

Although in a time slot, a CR can do the spectrum hopping from one spectrum band

to another, here we start with considering an example that, in a time slot ∆t, there

are only two available spectrum bands for data communication. It is worth noting

3.1. SPECTRUM AVAILABILITY MAP 23

that the correlation between two SAMs are based on the previous time slot ∆(t− 1)

and the immediate next time slot ∆t. The value of SAM for a data communication

using two spectrum bands in a time slot ∆t for the ith CR and jth CR with k available

spectrum bands on the two CRs is:(

2k

)(2

k−2

), k ≥ 2.

The knowledge of SAM known a priori can be considered as global information;

the knowledge of local SAM known a priori is considered as local information.

For a CR in a CRAHN, the local SAM is enough and this local SAM can be

constructed by: (1) sensing the available spectrum bands; and (2) capturing the

available spectrum bands from different PUs and store them into the internal memory.

3.1.1 Cell-Based Spectrum Availability Map

A cellular automaton (CA) is a discrete model that has been broadly studied in dif-

ferent disciplines including computer science [60]. A cellular automaton is composed

by a regular grid of cells with a finite number of states in each cell.

The spectrum availability of a CRAHN can be modeled as a map by the concept

of CA and we name it cell-based spectrum availability map (C-SAM). Suppose each

CR has different spectra at a time t, we can explore the dynamics of the available

spectrums in a large-scale CRAHN. With this model , the dynamics of the CRAHN’s

system behaviour can be evaluated by this 2-D CA model. In Fig. 3.1, assumptions

regarding the CA based model are:

1. Available spectrums at a time t are identical to all CRs;

2. Each CR can only communicate the immediate neighbors, which states decide

the availability of the spectrums of CR i;

3. Numbers in the following figure represent the different spectrum indexes.

3.1. SPECTRUM AVAILABILITY MAP 24

1 2 3 1 2 3 1 2 3

1 2 3 1 2 3 1 2 3

1 2 3 1 2 3 1 2 3

Figure 3.1: An example of C-SAM in a CRAHN with 3 spectrum band indexes foreach CR

3.1.2 Radio Environment Map

Instead of obtaining the radio environment parameters at CR nodes, the radio envi-

ronment map (REM) proposed in [61] can be used to store environmental and opera-

tional information. A REM can provide many kinds of radio environment information

over a CRN, such as geographical features, available services, spectral regulations, lo-

cation and radio activities, and experience. The REM can be classified as global

REM and local REM [62].These two classes of REMs can be used by cognitive ra-

dio regional area networks (e.g., IEEE 802.22 networks) or cognitive radio local area

networks (e.g., CRAHNs). According to the link-level and network-level analysis

in [63], using the REM can significantly improve the network performance in terms

of reduced adaptation time, average packet delay, and the mitigation of the hidden

terminal problem.

3.2. SPECTRUM AVAILABILITY PROBABILITY 25

Global REM Server

Local REM Server

CR

CR

CR

CH

CR

Local REM Server CR

CR

CR

CH

CR

Local REM Server

CR

CR

CR

CH

CR PU

PU

Figure 3.2: The architecture of a CRAHN with REM servers

The REM is a practical solution when reliable information (e.g., a certain amount

of local information and global information) regarding radio environment is needed in

CRAHNs. As an example of the REM-based architecture, in Fig. 3.2, the CH is the

cluster head which is responsible of exchanging information to the local REM server.

The local REM server contains the information collected from CRs in each cluster.

The data in local REMs will be sent to the global REM server.

3.2 Spectrum Availability Probability

For the spectrum sharing protocols, it is natural to see the relationship between the

spectrum availability map and the CRs. In fact, we propose that the two models

can be converted from one to another. With the proposed spectrum availability

probability (SAP), we can divide a CRAHN into different sub areas. In this sense,

the data transmission scenario can be converted to the probability of a CR transmitter

at the center of a sub area and the SAP of this transmitter at a location.

Definition 1. (Spectrum availability probability): SAP, %(∆t, k, s), is defined as the

3.3. VARIABLE SIZE OF SPECTRUM BANDS 26

probability of when a CR is able to access a spectrum band k in a time period ∆t in

an area s.

With a Poisson traffic flow of PUs deployed in an area S, we know that in an area

s ∈ S, SAP can be determined by three parameters ∆t, k, and S.

If we consider the flow of fairness, i.e., each data transmission flow needs differ-

ent bandwidths, we have to improve the aforementioned SAP and SAM. With an

application-specific QoS requirement, if the speed cannot be met by the available

spectrum band, the spectrum band is considered not available.

3.3 Variable Size of Spectrum Bands

From the results we discussed about SAP, we assume that the size of the spectrum

bands is identical in terms of same traffic model. The problem is more complicated

when we consider a more general case that the spectrum bands have variable sizes.

This means that a large chunk of spectrum can be split into two or more smaller

chunks of spectrum, or a smaller chunks of spectrum can be combined into a larger

chunk. We consider this variation occurs only when the current available spectrum

bands cannot meet the flow bandwidth requirement.

In fact, multiple available spectrum bands can be virtually combined as one when

we use the channel aggregation technique to boost the throughput, where, for exam-

ple, a large packet can be split into two and transmitted in the two channels in a

faster speed. With these assumptions, we can convert this case into a case similar to

SAP that spectrum bands have identical sizes. We are able to calculate the bound of

probability of the presence of variable spectrum bands.

3.4. MULTI-CHANNEL MULTI-RADIO SUPPORT 27

3.4 Multi-Channel Multi-Radio Support

The CRAHN can be considered a network paradigm with multi-channel multi-radio

support. The network throughput performance can be boosted by multi-channel

multi-radio capability in CRs. It is readily to see the NWK layer schemes can take

advantage of that capability in CRs, because the multiple routes brought by the CR

capability can increase the data transmitted per unit time. To see this, we plot Fig.

3.3 showing the throughput performance of a CRAHN based on different routing

protocols with K spectrum bands and R multiple radios. We can see from Fig.

3.3 that, when more channels and radios are available, the routing protocol metric,

i.e., weighted cumulative expected transmission time (WCETT) [64], which can take

advantage of multi-channel multi-radio capability, has better performance than the

network with the ad hoc on-demand distance vector (AODV) routing protocol. More

cognitive routing protocols have been discussed in [65, 66, 67, 68].

In the subsequent chapters, we will address the multi-channel multi-radio capa-

bility for the MAC protocol design.

3.5 Resultant Channel Model

With the proposed concept of SAM, we are able to visualize spectrum availability at

a time t. It will be more useful if we can map spectrum availability in different bands

into one spectrum band at a time t. This can be achieved by using the resultant

channel model [69].

The resultant channel model can be seen in Fig. 3.4, where for the ith PU the

time spent in “busy” and “idle” states are exponentially distributed with mean αi and

βi, respectively. In this model, the PU activity is determined by a ON-OFF model,

3.5. RESULTANT CHANNEL MODEL 28

0 50 100 150 200 250 300 350 400 4500

50

100

150

200

250

300

350

400

4501

2 3

45

6

7

8

9

10

X (m)

Y (

m)

(a)

0 5 10 15 20 25 30 35 40 45 500

2

4

6

8

10

12

14x 10

4

Time (s)

Ave

rag

e T

hro

ug

hp

ut (

B/s

)

WiFi Network (AODV, K=1, R=1)

ZigBee Network (AODV, K=1, R=1)

WiFi Network (AODV, K=2, R=2)

WiFi Network (WCETT, K=2, R=2)

(b)

Figure 3.3: Throughput performance in a CRAHN with multi-channel multi-radiosupport in different settings. The network has 10 CRs and the communi-cation range per node is 250m in 2GHz band.

3.5. RESULTANT CHANNEL MODEL 29

Channels 1 to Kwith PU activities

“OFF” state

“ON” state

E[Ton]

Ch 1

Ch 2

Ch K...

E[Toff] Resultant Channel

Figure 3.4: Example of the resultant channel model

where ON or ‘1’ means PU is busy and is occupying a channel; OFF or ‘0’ means

PU is not transmitting and is not occupying a channel. It is worth noting that by

using the resultant channel model, multiple PU transmitters can be modelled as one

virtual PU transmitter.

From [69], the expected number of idle and busy channels can be estimated as:

ω0,i =αi

αi + βiω1,i =

βiαi + βi

(3.1)

The expected length of the resultant idle period and busy period are:

E[Toff ] =

1−K∏i=1

ω1,i

K∏i=1

ω1,i

K∑i=1

βi−1

E[Ton] =1

K∑i=1

βi−1

(3.2)

The expected number of idle channels can be estimated as

L =K∑m=1

mπoffch (m) =πch(m)

1−K∏j=1

1− ω0,j

(3.3)

3.6. LOCAL AND GLOBAL INFORMATION 30

Local InformationChannelstate (i-dle/busy)

Numberof neigh-bors

Immediateneighborsspectrumusage

Spectrumutiliza-tion

OverheardMAC in-fo

Signalstrength

Cost C1 C2 C2 C3 0 0

Table 3.1: Local information associated with cost values

3.6 Local and Global Information

Local information is the information that can be acquired by local observation (e.g.,

local sensing) or communications with neighbors. We can refer to the categorization

for local information in IEEE 1900.4 standard [70], where information is categorized

into terminal class and network class. The former can be used for classifying the local

information and the latter can be used for classifying the global information. Terminal

class includes application information and device information. Application informa-

tion contains information about measurements supported by applications, such as

delay, packet loss, and bandwidth. Device information contains information about

the current active links and channels. Information about links includes block er-

ror rate, power, signal-to-interference-plus-noise ratio, etc., while information about

channels includes channel ID, frequency range, etc.

When obtaining local information, we should consider the communication cost

of obtaining the information. Due to the changing radio environments in CRAHNs,

some cost values may be dynamic, while others are not. Moreover, the cost values

can be considered in the metrics for distributed protocol design. As an example, we

show some pieces of local information with cost values in Table 3.1.

In Table 3.1, we can see the cost of obtaining the channel state and the cost

3.7. LOCAL CONTROL IN SPECTRUM MANAGEMENT 31

of obtaining channel utilization are C1 and C3, respectively. The cost of obtaining

the number of neighbors and the cost of obtaining the neighboring spectrum usage

are the same, i.e., C2. This is true when some information such as the number of

neighbors can be estimated from overheard incoming packets, which contain MAC

address fields and data fields with spectrum utilization of neighbors. Therefore, we

can assume MAC information needs no cost to obtain. For the signal strength that

can be easily estimated by most receivers, we assume the cost of obtaining it is zero.

If we initiate a particular communication process to obtain channel state and channel

utilization, the values of C1 or C3 would be larger than C2.

The global information refers to information over the network. For example, from

the IEEE 1900.4 standard [70], the network information includes channel information,

cell information, and base station information. Channel information is mainly about

the frequency channel, including frequency channel ID, frequency range, etc. Cell

information is the general information about a cell configuration, including cell ID,

location, coverage area, etc. Base station information contains the general information

about the current base station configuration, including transmission power, load, etc.

3.7 Local Control in Spectrum Management

The local control can be considered as a distributed control of individual CRs in

CRAHNs. Because of the lack of a central controller and changing radio conditions, a

centralized control is not suitable. Moreover, the cooperation between CRs can help

create and distribute radio environment information, which makes an individual node

have a macroscopic view of the network status. It has been proven that cooperation

between CRs can help improve the spectrum sharing process. However, cooperation

3.8. GAME THEORETIC APPROACH 32

can lead to increasing communication overhead and underlying interference. As such,

the approach of spectrum management based on global information would be costly.

Here we discuss the different between local control schemes and spectrum etiquette

[71]. The former may include a set of protocols, rules, or schemes, enabling system-

level and protocol-level modeling and analysis for spectrum management problems,

such as spectrum sharing, spectrum mobility, and spectrum decision. The latter may

be considered as a mere set of rules, which regulate access to spectrum and its usage

[71] (i.e., a set of rules dictating when, where and how may devices transmit [72]).

Therefore, the two concepts may overlap to some extent, but, in fact, they focus on

different problems.

3.8 Game Theoretic Approach

Due to the features of the CRAHN, a non-cooperative scheme is desirable for spectrum

sharing and allocation as it can reduce the communication overhead and underlying

interference. In game theoretic approach, Nash equilibrium is an important tool to

measure the outcome of a non-cooperative game [25, 73, 74, 75, 76] in the spectrum

management problems.

A game theoretic approach for spectrum allocation is proposed in [77], where the

CR nodes (i.e., players) make decision based on the utility function to select a channel

without causing interference to other nodes. In [78], a spectrum sharing solution based

on game theoretic approach for the primary-secondary model is proposed, where

an oligopoly market model is used to maximize the profit of all CRs based on the

equilibrium adopted by all CRs.


The game theory is used for multi-player optimization to achieve individual opti-

mal solution. Mathematically, the game can be defined as Γ = N, Si(i∈N), Ui(i∈N)

, where N is the finite set of players, and Si is the set of strategies associated with

player i. For every player in game Γ, the utility function Ui is a function of si, (the

strategy selected by player i) and s−i (the current strategy profile of its opponents).

All the players make decisions independently and have to converge into equilibrium.

For Nash equilibrium, a strategy profile for players should meet

Ui(S) ≥ Ui(s′i, s−i), ∀i ∈ N, s′i ∈ Si (3.4)

In order to select a channel without interfering other CRs, the authors of [77]

define two utility functions. One utility function is a selfish scheme that a user values

a channel based on its own perception of interference on a particular channel. The

other is less selfish as a user will measure the interference perceived by its neighbor.

A selfish utility function is useful to some extent because it uses less information

than a less selfish utility function. In order to achieve convergence, both utility

functions have to be a potential function, P , which is defined as:

P : S → R, if ∀i and si, s′i ∈ Si

Ui(si, s−i)− Ui(s′i, s−i) = P (si, s−i)− P (s′i, s−i)

(3.5)

where S = ×Si is the strategy space.

However, to model a spectrum sharing problem in game theoretic approach, the

players have to make decisions sequentially, i.e., a coordinator to control the playing

order is required. To transform the game theoretic scheme into a distributed ver-

sion, a Bernoulli trial is used to make the sequential decision-making process happen


at players by probability. In other words, at the beginning of every iteration, the

decision-making process is performed at players who win a Bernoulli trial.

From the above discussion, the game theoretic approach can model strategic inter-

actions among agents using formalized incentive structures [25]. The general method-

ology in game theoretic approach is to: (1) find a suitable game model for a problem,

(2) formulate a utilization function, and (3) prove the equilibrium condition. Due to

the autonomous and learning properties of CRs, the game theoretic approach maybe

a suitable way to solve problems in CRAHNs.

However, we should note that modeling a problem as a game cannot always get

an optimal solution. For example, the authors of [79] show that when the nodes have

complete information about the network, the steady-state topologies are suboptimal.

In order to make a game have a convergence property, the utility function also has to

meet some conditions.

In [6], Haykin indicated that Nash equilibrium assumes the players are rational,

meaning each player has a view of the world. Haykin also argues that the Nash equi-

librium has two practical limitations: (1) best-response strategy required to achieve

Nash equilibrium does not always hold. For example, in a two-player game, if on-

ly one player adopts a non-equilibrium strategy, the optimal response of the other

player is of a non-equilibrium kind too. (2) Description of a non-cooperative game is

essentially confined to an equilibrium condition, which is not enough to be used in

cognitive radio with underlying dynamics.

In the state-of-the-art research work, although the game theoretic approach is

popular for decision-making in spectrum allocation and spectrum sharing, the real-

ization in this approach is dependent on a certain centralized flow control protocol

3.9. GRAPH COLORING BASED ALGORITHMS 35

in the MAC or NWK layer. A zero-player game may be included in a local control

scheme to show the system-level characteristics. In this thesis, the further discussion

on game theoretic based local control schemes is out of the scope of this study.

3.9 Graph Coloring Based Algorithms

Graph coloring based algorithms can be directly used to solve the spectrum allocation

problem. As soon as the available spectrum bands for each CR are transformed to the

colors of a map, the objective of the graph coloring algorithm for spectrum allocation

is to minimize the use of colors.

Here we show the classical graph coloring algorithm proposed in [17]. In a undi-

rected graph G = (V,E), the number of users is N = |V |, and E = eij, where eij = 1

if there is an edge between vertices i and j and eij = 0 if i and j use the same spec-

trum bands. The availability of spectrum bands at vertices of G is represented by a

N ×K matrix L = lik, referred to as a coloring matrix. For example, lik=1 means a

color (spectrum band) k is available at vertex i.

A channel assignment policy is denoted by N×K matrix S = sik, where sik = 0, 1.

If sik=0, channel k is assigned to the node i and 0 otherwise. S is a feasible assign-

ment if the assignments satisfy the interference constraint and the color availability

constraint, which can be denoted by siksjkeij = 0,∀i, j = 1, . . . , N, k = 1, . . . , K.

The above constraint means that two connected nodes cannot be assigned to the same

colors (channels).

The objective of the resource allocation is to maximize the spectrum utilization.

3.10. PARTIAL OBSERVABLE MARKOV DECISION PROCESS 36

The formal representation of the spectrum allocation problem is

MaximizeN∑i=1

K∑k=1

sik

Subject to sik ≤ lik

siksjkeij = 0,

sik = 0, 1

∀i, j = 1, . . . , N, k = 1, . . . , K.

(3.6)

If a time slotted communication between the network nodes is considered, at each

time unit, the optimization problem in (3.6) needs to be recomputed.

We can see from (3.6) that, in the varying radio environment in CRAHNs, the

optimization problem has to be executed many times, which make the graph coloring

algorithm inefficient. Moreover, the graph coloring algorithm is an innate central-

ized algorithm, so it is not suitable for the CRAHN. However, it can be used as a

benchmark to compare with distributed algorithms.

3.10 Partial Observable Markov Decision Process

The partial observable Markov decision process (POMDP) is a generalization of a

Markov decision process (MDP). A POMDP models a decision process of a CR where

the system dynamics is determined by an MDP, but the CR cannot directly observe

the underlying state of a channel. Therefore, the POMDP is more practical than an

MDP model when solving spectrum access problems.

For example, if the channel is modeled as a Markov channel with two states“good”

and “bad”and four transition probabilities given by pij, i, j = 0, 1, a transmitter can

3.11. BIO-INSPIRED SCHEMES 37

select one of the channels to sense based on its prior observations, and the selected

channels obtain some fixed award if it is in the good state. This problem can be

described as a POMDP, as the states of the Markov chains are not fully observable.

In [80], the myopic policy (i.e., a policy that maximizes one-step reward) is examined

that, when p11 ≥ p01, it is optimal for any number of channels; when p11 < p01, it is

optimal when the number of channels n = 3.

As we can see that, a POMDP is suitable for modeling a channel access problem,

as the channel states are not fully observable to a CR. However, there are some

limitations of a POMDP. One limitation is that a POMDP is often computationally

intractable to be solved. Another problem is that a POMDP is suited to the single

player with multiple states. As an MDP is in fact a special case of stochastic game

[6], in spectrum management, a POMDP may be suitable for spectrum sensing in

individual CRs but not the spectrum sharing based on local observation.

3.11 Bio-Inspired Schemes

There are some swarm intelligence algorithms which have been proposed recently.

Atakan and Akan [21] propose a spectrum sharing algorithm called BIOSS (BIOlogically-

inspired Spectrum Sharing) based on the task allocation model of an insect colony.

This algorithm does not need any coordination among the CRs compared to non-bio-

inspired ones. Another swarm intelligence algorithm is proposed by Doerr et al. [22],

which is inspired by the emergent behavior of a school of fish. In [22], CRs’ behavior

can be analogous to a school of fish, where CRs can sense the radio environment by

local observation and react to the changing radio environment. Each CR has lim-

ited intelligence but in the entire network they have better overall intelligence than

3.12. CONCLUSIVE REMARKS 38

individual intelligence for a certain task.

The existing work in the literature prove the idea of applying swam intelligence

to spectrum management problems, where each CR embedded with this algorithm

can evolve to show a collective intelligence. However, there is still much work to do

in order to critically derive analytical results. Unless the advantages can still hold in

a scalable CRAHN, we can hardly apply the existing schemes directly. For example,

the authors of [81]indicate that the additional information is not always advantageous

by using a consensus protocol.

3.12 Conclusive Remarks

We discussed the essential models and approaches regarding CRAHNs in this chapter.

In the next chapter, we will discuss in more detail about the proposed local control

approach for spectrum sharing.

39

Chapter 4

Local Control Schemes for Spectrum Sharing

In this chapter, we first introduce the concept of local control schemes, by which a

CR can locally perform a spectrum sharing process with sensing inputs and decision

outputs. Then we define the spectrum sharing fairness issue and investigate the con-

vergence condition when applying a consensus-based protocol to spectrum sharing to

address the defined fairness issue. Based on the local observation and local control

scheme using spectrum-related information, an individual cognitive node can effec-

tively perform the spectrum sharing. Supported with computer simulation results,

we show the effectiveness of using the proposed consensus-based protocol to solve

spectrum sharing problems in CRAHNs.

4.1 Applicability of A Local Control Scheme to CRAHNs, CRSNs, And

Sensor Networks for CRAHNs

We discuss how to apply a local control scheme in these types of networks due to the

characteristics of the CRAHNs, CRSNs, and sensor networks for CRAHNs.

Compared to the classical ad hoc network, a CRAHN is able to deal with the

4.1. APPLICABILITY OF A LOCAL CONTROL SCHEME TOCRAHNS, CRSNS, AND SENSOR NETWORKS FOR CRAHNS 40

problems caused by changing radio environment and to protect licensed users trans-

missions. Compared to classical CRNs. CRAHNs inherit some important features

from ad hoc networks, such as node mobility, hop-by-hop spectrum availability, and

unidirectional links. Other features in CRAHNs include spectrum-dependent links,

topology control, multi-channel transmission, and spectrum mobility, implying more

challenges than those in either classical CRNs or ad hoc networks. Due to the lack of

central network entities in CRAHNs [8], each CR node necessitates that all spectrum-

related CR capabilities and distributed operations must be based mostly on local

observations.

In CRSNs, each cognitive sensor node has cognitive capability and the network is

usually intensively deployed with co-located PUs. Therefore, this type of networks

inherits the similar cognitive modules as those in CRAHNs. A CRSN can use similar

local control schemes in the spectrum sharing module. A CRSN, which has limited

coverage and power supply, can be considered as the extension of a CRAHN, so the

local control schemes can be applied to CRSNs.

Moreover, a local control scheme is suitable for another network paradigm called

sensor networks for CRAHNs, where sensor nodes are aided for cognitive actuation.

With local observation and local knowledge, sensor nodes perform the collective be-

havior for spectrum sharing, monitoring, and decision. The enabling technology for

this network, called sensor network-aided cognitive radio, is discussed in [82]. As the

local control scheme on sensor nodes in this network is very similar to the CRs in a

CRAHN, we will not give detailed discussion for this network in this study.

Based on the aforementioned discussion, we see that CRAHN is a more general

network prototype than the sensor network for CRAHNs or CRSN, and a local control

4.2. REVISIT OF SPECTRUM SHARING IN THE PERSPECTIVEOF LOCAL CONTROL SCHEMES 41

scheme for CRAHNs is also applicable to CRSNs. Therefore, we will focus on how

the local control scheme can be applied to CRAHNs.

4.2 Revisit of Spectrum Sharing in the Perspective of Local Control

Schemes

The radio environment in CRAHNs is subject to change from time to time, which is

the major problem for the spectrum sharing function. Typically, a change of radio

environment can be caused by:

1. PU activities;

2. Interference during communications;

3. Spatial-temporal characteristics of radio signals.

In this work, we only consider the first two factors.

CR

CRCR CR

CR

CR

CR

CR

CR

CR CR

CR

CR

CR

CR

CRCR

CRCR

CR

Radio Environment

PU

PU

PU

PU

PU

PU

Figure 4.1: A CRAHN deployed in a radio environment

As an example, Fig. 4.1 shows that CRs are deployed in an area with a changing

radio environment. Each CR senses and observes the local radio environment. When

4.3. FRAMEWORK OF LOCAL CONTROL SCHEMES 42

CRs request the spectrum bands occupied by PUs, they need to invoke local control

to share spectrum resources. A natural question one may raise is how the local control

for spectrum sharing can be performed by using local observation? In order to answer

the question, we introduce a block diagram to present a local control scheme, which

each CR will run for a spectrum sharing process.

4.3 Framework of Local Control Schemes

Process for spectrum

sharing

Feedback

[·]Sensing Input Output

Radio environment

Figure 4.2: Framework of a local control scheme

In Fig. 4.2, a local control scheme framework can be represented in a block dia-

gram. In this block diagram, when a CR receives a sensing input from sensors (e.g.,

a spectrum sensor or a global positioning system device, etc.), together with feed-

back information, a CRs will process the information and make a spectrum sharing

decision. At the sensing input, due to the different sensing capabilities, a CR may

have comprehensive, partial, or strictly limited sensing information. At the junction

of sensing input and feedback, we can adopt arbitrary types of combinations, where

we use the symbol “·” to represent any combination. In Fig. 4.2, the feedback block

is important for a decision-making process, which may contain a consensus feedback

(i.e., feedback from consensus process of nodes in a CRAHN), or a partial consensus

feedback (i.e., feedback partially from consensus), or no feedback. In the spectrum

sharing process block, a dynamic or a static process may be involved. A dynamic

process occurs at an individual CR when the position or spectrum availability of PUs

4.4. FAIRNESS IN SPECTRUM SHARING 43

and CRs in CRAHNs changes. A static process occurs when the position or spectrum

availability of PUs and CRs does not change. At the decision output, we can have

different kinds of solutions, such as optimal solution, sub-optimal solution, or inter-

mediate solution. If an optimal solution, such as Pareto optimum, is not achievable,

it is feasible to find a sub-optimal solution. The intermediate solution may neither be

optimal or sub-optimal; however, this solution can achieve the optimal or sub-optimal

solution by iterations.

To give an example for the aforementioned framework, we can consider a local con-

trol scheme in each CR in a CRAHN where each CR only takes the local information

as sensing inputs, such as the network-related information and spectrum information

from neighbors. After running a process for spectrum sharing functions in the local

control scheme, a CR will make a decision of what spectrum bands to use based on

the available spectrum resources.

4.4 Fairness in Spectrum Sharing

Definition 2. (fairness) The spectrum resource allocation is fair to each CR at time

t if the available spectrum resources at time t are evenly distributed among CRs.

We mainly consider the available spectrum bands as a spectrum resource requiring

fairness. The fairness of spectrum sharing is important as: (1) it can help ensure equal

communication opportunity for each CR; (2) it best responds to the changing radio

environment in terms of available spectrum bands.

In order to achieve fairness by local observation, each CR tries to achieve fairness

by considering the number of available spectrum bands of surrounding neighbors. In

order to achieve this goal, we propose to use a consensus feedback in the local control


scheme, which can be mathematically formulated in the following.

Suppose the CRAHN can be represented by a graph G = (V (t), E(t)), where V (t)

is the set of vertices at time t and E(t) is the set of communication edges at time t.

We can analyze the system performance using a local control scheme executed by each

CR node. In an ideal condition (without any time delay), the consensus feedback is

defined in the form of variation as follows:

xi(t) =∑j∈Ni

aij(xj(t)− xi(t)) (4.1)

where the dot operator in xi(t) is used to show the variation of the values of x(t)

between CR i and neighboring nodes, xi(t) indicates the number of spectrum bands

available to a node i at time t, Ni(t) is the set of neighbors of node i at time t,

and aij is the 0 − 1 element in adjacency matrix of the network G. Equation (4.1)

shows that the spectrum allocation decision is made based on the feedback informa-

tion xi(t)calculated from neighbors spectrum information xj(t) and xi(t). With the

aforementioned notations, in order to measure fairness, we use the following expres-

sion:

σF =

√√√√√ M∑i=1

(xi(t)−m)2

M, (4.2)

where m is the fairness goal (e.g., m equals to the desired number of spectrum bands

of a CR) and M is the total number of CR nodes.

From (4.1), the fairness can be ensured if we can make sure that the number of


spectrum bands are evenly distributed among CRs. However, since the CRAHN per-

forms hop-by-hop communication, a one-hop time delay t is inevitable when receiving

the information of spectrum availability from immediate neighbors. Then, (4.1) can

be transformed as

xi(t− τ) =∑j∈Ni

aij(xj(t− τ)− xi(t− τ)) (4.3)

Note that (4.1) and (4.3) are inherited from the Vicsek model [83].

In fact, the challenge of using the consensus protocol is to to make sure the domain

of xi(t) is applicable to the domain of spectrum bands. Therefore, we must prove that

the consensus feedback can be used in this spectrum sharing problem.

Proposition 1. Suppose ωi(t) is the number of available spectrum bands at the i-th n-

ode in a CRAHN at time t, where ωi(t) ∈ K and C is a constant, K= k < C|k ∈ Z+.

Given a discrete-time consensus feedback ωi(t) =∑

j∈Ni aij (ωj(t)− ωi(t)), ωj(t) ∈

R+, there exists a mapping γ : R+ → K, with which this consensus feedback can

ensure the fairness of spectrum sharing over the CRAHN.

Proof. The discrete consensus protocol can reach the average ωl = 1n

∑ωi when

ωi(t) ∈ R+. Therefore, when ω ∈ Z+, Z+ ⊂ R+, the discrete-time consensus

protocol holds. Now we have to prove that the consensus still holds in a mapping

function γ, which is:

f(γ) = dωi(t) mod |K|e (4.4)

where |K| is the length of K, i.e., the maximum number of spectrum bands available

to a CR.

From the mapping function f(γ), we can see that ωi(t) is essentially a periodic


function with period |K| and we can see ωi(t) ∈ xi(t), where both xi(t) and t

are continuous. To see the stability of this transformed consensus protocol, first we

take the Laplace transformation of 4.3 by assuming x(t) is not a periodic function,

and thus we get

sXi(s)− xi(0−) =∑j∈Ni

aije−sτij (Xj(s)−Xi(s)) (4.5)

Then, considering the n periods n|K| in 4.5, we can get the Laplace transform of

xi(t) as+∞∑n=0

xi (t− n|K|) = Xi(s)+∞∑n=0

e−ns|K| =Xi(s)

1− e−s|K|(4.6)

Combining (4.5) and (4.6), we get the transfer function of 4.5 shown as follows

G(s) =[(In − e−s|K|L

) (sIn + e−sτL

)]−1(4.7)

where In is the identity matrix and L is the graph Laplacian defined by

lij =

∑n

k=1 aik, j = i

−aij, j 6= i(4.8)

Now we have to prove the stable conditions of (4.7). From Gershgorin’s theorem,

as L is strictly diagonally dominant and symmetric, the eigenvalues of L can be ranked

in a descending order as

0 = λ1 ≤ λ2 ≤ · · · ≤ λn ≤ 2 max d(i) (4.9)

where d(i) is the degree of node i. Suppose βm is the mth normalized eigenvector of


L associated with the eigenvalues λm in an ascending order. Thus, when s = 0 in

the direction β1, G(s)−1 = Lβ1 = 0. When s 6= 0, then G(s)−1βm = (1− e−s|K|)(s +

e−τijsλm)βm = 0, (m > 1).

Since βm > β1 = 0 and 1 − e−s|K| ∈ (0, 1) when s > 0, s + e−τijsλm = 0. If we

suppose the one-hop time delay is identical to all the CRs, i.e., τij = τ , we get

s+ e−τsλm = 0 (4.10)

Note that the convergence condition of G(s) with a upper bound of τ has been

proven in [84], which is τ ∈ (0, τ ∗) with τ ∗ = π2λn

, λn = λmax(L). As such, we know

max(τ) = π4 max d(i)

.

For some cases that not all the CRs have the same need of spectrum resources,

i.e., different groups of nodes have different degrees of fairness, the degree of fairness

needs to be defined.

Definition 3. (degree of fairness) We refer the value of consensus feedback as a

degree of fairness for a node, which is defined as:

DF(i) = minE[Xi,j −Xi,j+1], j ∈ N

where Xij is the number of spectrum bands of the jth node in the ith group of nodes.

We denote by DFj(i) the degree of fairness for a node j in the ith group of nodes.

Definition 4. (fairness group) A set of CRs with the same degree of fairness is

called a fairness group (FG), i.e., group i and group j are in the same fairness group,

if DF(i) = DF(j) = p, where p is a constant. The notation FG can be used to denote

the number of fairness groups in CRAHNs.


The concept of fairness group is useful when describing the heterogeneous nodes

that require different spectrum bands. Moreover, the concept can be used to virtually

divide a large-scale network into different groups with different degrees of fairness.

In order to show the stability shown in Proposition 1, we can see in Fig. 4.3, by

using Nyquist criterion, the two Nyquist plots on the top show the fairness solution

for spectrum sharing is stable, as we can see that the point (−1, j0) is not encircled.

However, the Nyquist plot at the bottom of Fig. 4.3 shows the spectrum fairness

solution for spectrum sharing is unstable. If the time delay of the links is beyond the

maximum value, the system is unstable. In other words, if the hop-by-hop time delay

in a CRAHN is over the maximum value, the fairness cannot be guaranteed.

-30 -20 -10 0 10 20 30 40

0

20

40

Ima

gin

ary

Nyquist Plot (max(di) = 3, t=0.0105, l=6)

Real

-30 -20 -10 0 10 20 30

0

20

40

Ima

gin

ary

Nyquist Plot (max(di) = 3, t=0.0524, l=6)

Real

-40 -20 0 20 40

0

20

40

60

Ima

gin

ary

Real

iNyquist Plot (max(d ) = 3, t=1.0472, l=6)

Figure 4.3: Analytical results for stability when using the consensus-based feedback.Nyquist plots with different time delays τ and with maximum degree ofthree in the CRAHN

4.5. PROTOCOL DESIGN AND EXPERIMENTAL RESULTS 49

4.5 Protocol Design And Experimental Results

4.5.1 System Model

In this section, we will mainly perform computer simulations to show the convergence

performance of the local control scheme without a consensus feedback and with a

consensus feedback for spectrum sharing in CRAHNs. The general system model

for computer simulations is based on Fig. 4.1 and 4.2, where each CR runs a local

control scheme in a CRAHN. CRs will use a common control channel to communicate

with each other for the information of spectrum availability. Moreover, we will focus

on the spectrum allocation performance and convergence performance of the local

control scheme.

In order to evaluate an open-loop local control scheme (i.e., the local control

scheme without a consensus feedback), we use a grid topology in the CRAHN with

the number of CR nodes, M , where each CR is denoted by the row number and

column number in a grid network, i.e., (i, j). We describe the proposed open-loop

local control scheme for evaluation in the following. The sensing input is the spectrum

bands chosen by the neighboring CRs. The initial spectrum bands are randomly

allocated to each CR. The local information used here is the spectrum bands selected

by a CRs immediate neighbors. The proposed process in this local control scheme is

to randomly select the available bands of neighboring CRs, i.e., the local information

is the available spectrum bands chosen by eight immediate neighboring nodes (where

in this case the average number of |Ni| equals to 8). To make the local control scheme

configurable, we set a control parameter λ in the process to represent the frequency

parameter with which a CR randomly selects a portion of spectrum bands from a

neighbor. This parameter can be considered as the feedback information shown in


Fig. 4.2.

Fig. 4.4 shows the results of the aforementioned open-loop local control scheme

(which can also be considered as a zero-player game) in different scenarios, where the

spectrum utilization results can reflect the convergence performance of the scheme

and the results are smoothed every 20 iterations. The spectrum utilization is defined

as the ratio of already allocated spectrum bands to a CR and the total available

spectrum bands to a CR. From Fig. 4.4, we can see that, although the spectrum

bands are randomly selected based on the neighbors spectrum availability and the

parameter λ, the spectrum utilization can show a certain pattern. By changing the

value of λ from 1.0 to 1+ε, where ε is a small positive number, a phase transition

occurs. When λ > 1.0, the spectrum utilizations are fluctuating among the available

spectrum bands; however, when λ = 1.0, the spectrum utilization over the network

is bifurcated into two groups—one is increasing and the other is declining. To show

whether the phase transition is applicable to the case with more spectrum bands

(i.e., |K| > 3), we plot the Fig. 4.4(d), where the phase transition still happens when

|K| = 8. We also found when |K| > 1 the results are similar. In fact, we found the

number of nodes and we find the phase transition is only dependent on the control

parameter λ.

From this example, we can conclude that the overall performance in terms of spec-

trum utilization is to some extent controllable by using the limited local information.

However, as the convergence cannot be achieved, this controllability may not be suf-

ficient to some applications as more variables should be considered. Furthermore, we

can see the possible structure of a local control scheme with local information, where

the local control scheme described above is an open-loop local control scheme without


0 100 200 300 400 500 600 700 800 900 10000.32

0.325

0.33

0.335

0.34

0.345

0.35

Iterations

Spe

ctru

m U

tiliz

atio

n

Spectrum band #1Spectrum band #2Spectrum band #3

(a)

0 100 200 300 400 500 600 700 800 900 10000.32

0.325

0.33

0.335

0.34

0.345

0.35

Iterations

Spe

ctru

m U

tiliz

atio

n


(b)

0 100 200 300 400 500 600 700 800 900 10000.1

0.2

0.3

0.4

0.5

0.6

0.7

Iterations

Spe

ctru

m U

tiliz

atio

n


(c)

0 100 200 300 400 500 600 700 800 900 10000

0.1

0.2

0.3

0.4

0.5

0.6

Iterations

Spe

ctru

m U

tiliz

atio

n

Spectrum band #1Spectrum band #2Spectrum band #3Spectrum band #4Spectrum band #5Spectrum band #6Spectrum band #7Spectrum band #8

(d)

Figure 4.4: Results of the proposed open-loop local control scheme for spectrum al-location in a CRAHN


any feedback. Therefore, the local information may be helpful to spectrum sharing if

we employ it in a closed-loop local control scheme with a feedback.

We will use the spectrum information to calculate the consensus feedback in the

closed-loop local control scheme in the following simulations.

4.5.2 Protocol Design

Before doing a further simulation using the consensus feedback, we propose a commu-

nication protocol based on the theory in Section IV. The protocol is expected to show

the applicability of using a consensus feedback to solve the fairness problem for spec-

trum sharing fairness. The protocol is briefly described in Fig. 4.5, where Step (1)

aims to process the proposed consensus-based feedback from neighboring nodes, while

Step (2) performs standard data communications in the RTS/CTS MAC protocol.

For example, after a CR receives the handshaking frames with spectrum information

from neighboring CRs, it will update its local cache with available spectrum band

indexes, and the fairness group it belongs to from the value p. Then, a CR can know

the available spectrum bands from the neighbors feedbacks and then inform the other

CRs in the similar way.


FOR EACH CR node i at time slot t

IF a spectrum change is detected

do spectrum sensing

do overhear incoming RTS/CTS frames from neighboring CRs

(1) IF the frame piggybacked spectrum information

do parse the information from frames, xi(t)= k, DFi(j) = p

do perform the local control scheme based on the consensus feedback of the

spectrum information in the same FG

ELSE

(2) do normal communication with other CRs

END IF

ELSE

do normal communication with other CRs

END IF

END FOR

Figure 4.5: Pseudo code of consensus-based spectrum allocation protocol

In addition, in order to determine which spectrum bands the neighboring CRs

are using, we assume that a CR node can acquire this information by overhearing

the neighboring CRs communications. A feasible and economic way of overhearing

that information is by encapsulating a data field containing that information and

piggybacking it in a frame sent by a neighboring CR. For example, the consensus

feedback is derived from the spectrum information piggybacked in protocol-specific

frames or packets, such as request-to-send (RTS) or clear-to-send (CTS) frames in an


IEEE 802.11-based MAC protocol. The slotted time characteristic in the 802.11-like

MAC protocol can also meet the requirements of the proposed protocol. Therefore,

the proposed protocol can be readily integrated in the IEEE 802.11 based CRAHN.

More importantly, the proposed consensus-based protocol will not result in extra

communication efforts or cause delays affecting throughput.

Now we analyze the complexity of the proposed protocol. We denote by M the

number of CRs, and denote by d the average degree of a CR. The spectrum sensing

takes s1 time units; Step (1) and Step (2) take s2 and s3 time units, respectively.

Step (1) will repeat at maximum dM times, so the average time spent on each CR

is dM(cs2 + (1 − c)s3) + s1, where c is a constant denoting the fraction of times

that the protocol will go to Step (1). As CRs in different FGs can individually

perform the protocol, and in each group we have approximately MFG

nodes, the total

number of times is therefore MFG

(dM(s2 + s3) + s1). Therefore, we can obtain the time

complexity as O((

MFG

)2)

, and we can see that more FGs result in less complexity.

Then we analyze the power consumption of the propose protocol based on RT-

S/CTS handshaking procedure. We take the typical value of the RTS frame length

and CTS frame length as 20 bytes and 14 bytes, respectively, and we consider

the power consumption model for 802.11 transmissions with 2Mbps speed in [85].

The power consumption of sending an RTS frame and receiving a CTS, EA, is

1.9 × 20 + 454 + 0.5 × 14 + 356 = 855µW ; similarly, the power consumption of

receiving an RTS and sending a CTS frame, EB, is 846.6µW ; the power consumption

of only receiving an RTS, EC , is 0.5 × 20 + 356 = 366µW ; and the power of only

receiving a CTS, ED, is 0.5×14+356 = 363µW . With this profile, if we have one fair-

ness group (FG=1), considering the 4-way RTS and CTS handshaking procedure, the


energy consumption of the protocol, E, has the form as E = M(EA+EB+d·EC+d·ED

2d·c

),

where 2d · c is the total number of the surrounding CRs of the two CRs who involve

in the RTS/CTS procedure, and c is the ratio parameter (≤ 1) because the two CRs

may share some neighbors.

4.5.3 Computer Simulation Results

In this section, we are going to show the results based on the proposed consensus-based

communication protocol, implemented by using the simulator NetLogo 4.1 (available

at http://ccl.northwestern.edu/netlogo). We will compare the proposed protocol with

a classical scheme on CRs, called device centric Rule-A [9], where a so-called prop-

erty line measure calculated from the available spectrum bands of neighboring CRs

is used for spectrum sharing. The reason we make comparison with Rule-A is that

Rule-A is the most similar scheme to our proposed protocol with basic local informa-

tion (i.e., connectivity and spectrum availability of neighboring CRs) without extra

communication efforts, while some other schemes like the local bargaining scheme or

graph coloring scheme are centralized and require extra information through extra

communication efforts. Moreover, the max-min fairness based schemes, which have

a different spectrum sharing objective from the proposed Definition 2, will not be

considered in the thesis.

Suppose the number of spectrum bands at a CR at the beginning is randomly

allocated. Each CR performs the proposed consensus-based protocol to ensure the

number of spectrum bands is decided by the consensus feedback from immediate

neighbors. The consensus-based communication protocol will be executed once in

an iteration; and therefore a successful run needs several iterations. Considering


PU activities, the spectrum band availability varies at the beginning of each run.

Moreover, we keep the total number of available spectrum bands in the network as

1900 for the following simulations.

Next, we describe the simulation settings for this computer simulation. In Fig.

4.6, we can see a dense CRAHN with 350 CR nodes (i.e., M = 350) and each link

has a negligible data transmission delay. The darkness of the node color indicates a

higher number of available spectrum bands. The darker the node color, the more the

number of available spectrums for CR nodes.

4.5.4 Convergence Performance And Feedback Quality

We compare the convergence performance using the metric of unallocated spectrum

bands after running the proposed consensus-based protocol and device centric Rule-A.

The results are shown in Fig. 4.7 and Fig. 4.8.


Figure 4.6: A randomly distributed CRAHN with 350 CRs and initially allocatedspectrum bands

1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 60

5

10

15

20

25

30

Una

lloca

ted

Spe

ctru

m B

ands

(%

)

Consensus-based protocolDevice centric Rule-ADevice centric Rule-A (P)

+ +

+ +

+ +

Figure 4.7: Convergence performance of the proposed consensus-based protocol,Rule-A, and Rule-A (P)


5 10 15 20 25 300

5

10

15

20

25

30

Iterations

Una

lloca

ted

spec

trum

ban

ds (

%)

Consensus-based protocolDevice centric Rule-A

Figure 4.8: Convergence performance of the consensus-based protocol and Rule-A inmultiple iterations

The convergence performance of Rule-A and the proposed consensus-based pro-

tocol is shown in Fig. 4.7, where we can see that the proposed consensus protocol

converges very quickly, whereas Rule-A and Rule-A (P) has stable convergence per-

formance in one iteration. Rule-A (P) in Fig. 4.7 is the improved version of Rule-A,

where we increase the accuracy of the poverty line as the feedback; it has better

performance than the original Rule-A. At the end of the iteration, all the CRs are

allocated with spectrum bands. The reason that the consensus protocol is better

is the consensus spectrum availability information is accurate during the spectrum

sharing process, while the device centric Rule-A and Rule-A (P) use the feedback

based on poverty line, which does not accurately estimate the spectrum availability

of CR nodes.

In Fig. 4.8 we can see how the consensus-based protocol converges over multiple

iterations, where at the end of each iteration (i.e., each run of the protocol) all the

nodes can be successfully assigned with desired spectrum bands. We use a randomly


i+1

i

i-1

i-2

1

L(1)

(a)

i+1

i

i-1

i-2

1

L(1)

L(2)

(b)

Figure 4.9: An example of the ZigZag network. In (a), there is only one shadedregion of PU activity L, while in (b), there are two shaded regions of PUactivities, denoted by L(1) and L(2), respectively. We will show that thefeedback adopted in Rule-A is overestimated in both cases.

generated topology for the CRAHN in each iteration epoch, during which the con-

sensus protocol will converge as expected, i.e., it can make all the spectrum bands

be shared among all the CRs. Moreover, the convergence time is quite stable even

if we change the network topology before each iteration. In addition, the spectrum

information mentioned in Step (1) of Fig. 4.5 in this simulation is the spectrum

bands.

The proposed scheme outperforms Rule-A because the inaccurate so-called poverty

line is used as a feedback in Rule-A. This inaccurate feedback is considered as a low-

quality feedback in the view of local control framework. We give an example to show

why the poverty line feedback is not sufficient to provide accurate feedback. In the

network shown in Fig. 4.9, where each CR node (except for the start node i+ 1 and

end node 1) has a degree of two.


Ω(i+ 1) = L(i+ 1)− Ω(i)

Ω(i) = L(i)− Ω(i+ 1)− Ω(i− 1)

Ω(i− 1) = L(i− 1)− Ω(i)− Ω(i− 2)

...

Ω(2) = L(2)− Ω(3)− Ω(1)

Ω(1) = L(1)− Ω(2) (4.11)

where Ω(i) is the number of spectrum bands chosen by a CR node i, and L(i) is the

number of available spectrum bands left by the PU activities.

We can further derive ((4.11)) as

L =3∑i+1

j=1 Ω(j)− Ω(1)− Ω(i+ 1)

i+ 1(4.12)

The value of L fluctuates with Ω if Ω(i + 1) = Ω(i), i ∈ Z+. From the results

shown in Fig. 4.10, we can see that the value of L overestimates the number of

maximum spectrum bands no matter what the value of M is. In other words, the

estimation using the poverty line is not accurate, and it gives low quality feedback

for the spectrum sharing problem.

4.5.5 Fairness Performance in Various Network Sizes

In order to see the fairness performance in different network sizes, we plot Fig. 4.11,

where the fairness measure is calculated by (2). From Fig. 4.11, we can see that the


0 20 40 60 80 1000

20

40

60

80

100

120

140

160

Max. number of spectrum bands

Val

ue

of

L

M=40

M=100M=1000

Figure 4.10: The value of L versus the maximum number of spectrum bands with thedifferent number of CR nodes M

fairness measure of Rule-A is larger than the fairness measure of proposed consensus-

based protocol when network size varies, which means the proposed consensus pro-

tocol has better fairness performance than Rule-A. Furthermore, we can see how the

spectrum sharing goal is achieved by these two algorithms, where we count the num-

ber of CRs with distributed spectrum bands in Fig. 4.11. Fig. 4.11(a)-(d) show

the proposed consensus-based protocol can fairly distribute and meet the spectrum

sharing goal better than Rule-A.

Now we are going to discuss the fairness group in the spectrum sharing process.

First, we show the intermediate results of using the consensus protocol for spectrum

allocation in Fig. 4.12, where the nodes pointed by arrows indicate different leading

nodes in FGs, and, in the initial stage, only the leading nodes have been allocated

with spectrum bands. From Fig. 4.12(a), we can see the CRs running the consensus

protocol can adjust the spectrum availability based on a leading node, which gives

response to the changing spectrum bands and thus causes the spectrum reallocation


0 2 4 6 8 10 12 14 16 18 200

20

40

60

80

100

Spectrum band index per CR

Dis

trib

utio

n of

the

num

ber

of C

Rs

(%)

Device centric Rule-A (F=6.33)

Consensus-based protocol (F=0.00)

(a)

1 2 3 4 5 6 7 8 9 10 11 12 130

20

40

60

80

100


Dis

trib

utio

n of

the

num

ber

of C

Rs

(%)



(b)

1 2 3 4 5 6 7 8 9 100

20

40

60

80

100


Dis

trib

utio

n of

the

num

ber

of C

Rs

(%)



(c)

1 2 3 4 5 60

20

40

60

80

100


Dis

trib

utio

n of

the

num

ber

of C

Rs

(%)



(d)

Figure 4.11: Fairness performance versus different network sizes when (a) M=100,(b) M=150, (c) M=200, and (d) M=350

to neighboring CRs. The neighboring CRs will run the proposed consensus-based

protocol to spontaneously change their spectrum bands. In other words, the leading

node can share the spectrum bands to the rest of CRs in this case. Similarly, in

Fig. 4.12(b) and (c), the leading nodes can share the spectrum bands to the other

CRs. Therefore, we can see that the nodes following the spectrum information of the

leading node belong to the same FG. Furthermore, if the leading nodes are considered

as cluster heads reflecting the accurate changing radio environment, all the CRs in a

cluster can instantly be informed of the spectrum change accordingly. If we consider

the extreme case that the number of FGs equals to the number of CRs, we can actually


(a) (b)

(c)

Figure 4.12: Intermediate spectrum sharing results in CRAHN when (a) FG=1, (b)FG=2, and (c) FG=3


convert this case to the CRAHN similar to Fig. 4.6.

5 10 15 20 25 30 350

20

40

60

80

100

Iterations

Una

lloca

ted

spec

trum

ban

ds (

%)

FG=1FG=2FG=3

Figure 4.13: Convergence performance with different number of FGs

In order to see the convergence performance of the proposed consensus-based

protocol versus different FGs, we compare the convergence performance in three net-

works with one FG, two FGs, and three FGs, respectively. The experimental results

are shown in Fig. 4.13, where all the nodes can be shared with spectrum bands at

the end of each run. Moreover, we can see that the convergence time per iteration

when FG=1 is in general longer than the convergence time when FG=2 or FG=3.

This makes sense because the more FGs in a network, the fewer nodes in each FG,

and therefore the quicker decision can be made by a consensus protocol. This phe-

nomenon can also be explained by the aforementioned complexity expression. If we

experiment with a larger number of FGs, similar results can be obtained.

Additionally, as we have evaluate the fairness performance when FG=1 (as shown

in Fig. 4.11), here we evaluate the fairness performance when FG=2 and FG=3 in

Fig. 4.14. In Fig. 4.14(a), we evenly divide the network into two fairness group with

two separate spectrum sharing goals, where one group wants to get three spectrum


1 2 3 4 5 60

10

20

30

40

50


Dis

trib

utio

n of

the

num

ber

of C

Rs

(%)

Device centric Rule-A (FG1

=0.46, FG2

=2.03)

Consensus-based protocol (FG1

=0, FG2

=0.07)

(a)

1 2 3 4 5 60

5

10

15

20

25

30

35


Dis

trib

utio

n of

the

num

ber

of C

Rs

(%)

Device centric Rule-A (FG1

=0.34, FG2

=0.56, FG3

=1.57)

Consensus-based protocol (FG1

=0, FG2

=0, FG3

=0.16)

(b)

Figure 4.14: Fairness performance in a network when (a) FG=2 (b) FG=3


bands (m=3) and the other group wants to get six spectrum bands (m=6). From

the results shown in Fig. 4.14(a), we can see that after running the two schemes,

the proposed consensus-based protocol can fairly distribute the spectrum bands and

meet the desired spectrum goal. Similarly, in Fig. 4.14(b), we evenly divide the

network into three fairness groups and the spectrum goals are m=2, m=4, and m=6,

respectively. From Fig. 4.14(b), the proposed consensus-based protocol can meet the

spectrum sharing goal while obtaining much better fairness performance than Rule-A.

In conclusion, the proposed consensus-based protocol can meet the spectrum sharing

goals in different FGs compared to Rule-A.


In this chapter, we have explored the effectiveness of using a consensus-based proto-

col to solve the fairness problem in spectrum sharing. Consensus-based protocols can

provide light-weight and efficient solutions for CRAHNs but the theoretical ground

needs to be investigated for spectrum sharing fairness. In order to analyze the con-

vergence condition using a consensus protocol, we introduce the local control scheme

as we can consider the consensus procedure as the consensus feedback in the system

block diagram of the local control scheme. In this way, the convergence condition is

identical to the system stability of the local control scheme. Furthermore, we have

proven and shown the applicability of using a proposed consensus-based protocol for

spectrum sharing problems in CRAHNs. We show the effectiveness of applying the

proposed consensus-based protocol to a randomly deployed network, by which the

desired convergence and fairness can be achieved. When we show the cases of apply-

ing the concept of FG in the spectrum sharing for CRAHNs, the CR nodes that lead


to spectrum changes are subject to being affected by PU activities, which result in

spectrum availability. In addition, although in a small-scale network, a centralized

spectrum sharing scheme may be more efficient than the proposed consensus-based

protocol, the proposed consensus-based protocol is economic, robust, and efficient for

keeping spectrum sharing fairness in a large-scale network. Besides, the related work

presented in this chapter has been published in [86, 87, 88].

68

Chapter 5

Local Control Driven Medium Access Control

Protocol

In this chapter, we propose a cognitive MAC protocol called CM-MAC which address-

es CR mobility and PER issues in CRAHNs. We adopt the local control concept in

the MAC design considering the local information. Then, we analyze the throughput

and spectrum utilization of CM-MAC protocol assuming that the PU traffic follows

a Poisson process. In the end, we show that the throughput and spectrum utilization

are improved by CM-MAC compared to classical MAC protocols.

5.1 System Model

Before further discussion, we detail the system model used in this section. The

CRAHN is deployed in a plane containing Np PUs and NCR CR nodes. In a certain

time interval, a set of channels, denoted by Ki(t), is available to a CR node i and thus

the total number of channels available to CR node i is |Ki(t)|. The set of channels

on the transmission link between ith CR and (i + 1)th CR is Ki,i+1(t). There are

5.1. SYSTEM MODEL 69

K spectrum bands available in total to CRs and PUs, while the (K + 1)th out-

of-band common control channel (CCC) is used for control information exchange.

When the jth PU is active for transmission, its traffic flow takes one channel Ck, i.e.,

Kj(t) = Ck. For simplicity, we will use the following notation:Kj(t) = k. When

multiple PUs are active, Kj(t) = k|k > 1 and k ≤ K. In this chapter, the PU

traffic flow is assumed to follow a Poisson process with parameter λ [89]. Besides, a

PU that occupies multiple channels is equivalent to multiple PUs that occupy different

channels.

PU CR

ε

SPER

Figure 5.1: A CRAHN with a PER and multiple CRs

We consider a CRAHN with PER regions as shown in Fig. 5.1. A PER area

operating on channel k is denoted by SPER(k). SPER(k) (i.e., the shaded area shown in

Fig. 5.1) has a radius of R0, and the interference region (i.e., the area circled by dotted

line in Fig. 5.1) has a radius ofR, whereR0 < R. In the SPER(k), CR communications

will not only severely affect the PU, but also cause interference to CRs; while within

the interference region, a CR has less effect on the PU communications.

In [11], the combination of two models (a cooperation model and a coexistence

5.2. PRIMARY EXCLUSIVE REGIONS 70

model) with two types of spectrum-sharing arrangements (i.e., sharing among equal-

s and primary-secondary sharing) is introduced. In this chapter, we will use the

model with primary-secondary sharing arrangement and coexistence-based model for

CRAHNs. The coexistence-based model means that devices try to avoid interference

without explicit signaling [11]; and the primary-secondary sharing arrangement re-

sults in the primary system having exclusive rights to access the spectrum through

licensing.

5.2 Primary Exclusive Regions

A MAC protocol needs to decide the available spectrum bands for current and future

transmissions. These spectrum bands will facilitate the upper-layer protocol (e.g.,

routing protocol) to obtain an optimized path for packet transmissions. Moreover, in

order to keep a desirable throughput, a MAC protocol needs to perform local obser-

vation without inducing extra communication efforts. As such, the communication

procedures on top of CSMA/CA MAC protocol are not favored by CRAHNs.

Traditionally, the MAC sub-layer is at the link layer, where the link layer is in

charge of the communication between adjacent nodes. Therefore, if we follow the

layered perspective for the CRAHN protocol stack, the challenge becomes maintaining

the communications with adjacent nodes while keeping the spectrum resources shared

among nodes.

To see why a CRAHN MAC is important, we consider a typical packet transmis-

sion in CRAHNs shown in Fig. 5.2, where a source S tries to transmit data packets

to destination D through the path from CR node 1 to CR node 4. Suppose that

in the previous time slots the data transmission occurs on channel 3. However, PU


Figure 5.2: An example of the necessity of a CRAHN MAC protocol in a CRAHN.The available spectrum bands for the nodes covered by a PU are shown inbrackets. The links are broken (shown in dashed arrows) when the datatransmission from S to D is operated on channel 3.

2 is now active and channel 3 is taken and the links from node 3 to node 4 and

node 4 to node D are broken. Therefore, the rest of nodes (i.e., S and node 1 to 3)

need to be informed of the spectrum change of nodes 4 and D. Besides, perform-

ing updates of spectrum change is efficient before each transmission, as a result of

the opportunistic and unpredictable PU activity, which can take a spectrum band.

Furthermore, the CRAHN MAC protocol needs to consider PER regions, which can

affect the throughput performance.

To see how PER region can affect CR and PU throughput, we consider the network

of Fig. 5.1, where CRs are distributed out of PER of a PU when CRs and PUs are

operating on the same channel k.

In the case of one PU transmitter and multiple CRs covered by the PU transmit


range, Vu et al. [50] derive the worst-case interference power that the PU transmitter

experienced from all CR nodes (where a PU transmitter communicates with another

PU receiver at a distance R0) as:

E[I0]α=4 = θπP

[R2

(R2 −R20)

2 +(R + ε)2

ε2(2R0 + ε)2

](5.1)

where αis the path loss exponent, R0 is the radius of SPER(k) and R is the coverage

radius of the PU; θ is the density of the CR nodes; ε is the guard band radius, which

ensures the interference caused by CRs will not affect the PU communications.

As a CSMA/CA MAC protocol is based on time frames, we consider a time interval

[0, T ]. If the PU transmitter/receiver pair is active for v time units, while CR nodes

are active for the entire time span, CRs can interfere with PU communications in the

v time units. Based on the data rate equation in [50], and, in this case, the data rate

of PU, DPU , and data rate of CR, DCR, can be expressed as:

DPU ≤ν

Tlog

(1 +

PPUR2

0(N0 + E [I0])

)(5.2)

DCR ≤ν

Tlog

(1 +

PCR

(R0 + ε)2(N0 + PPU)

)+ (1− ν

T)log(1 +

PCR

(R0 + ε)2N0

) (5.3)

where N0 is the noise power spectral density, and PPU and PCR are the transmit

power of a PU and a CR, respectively.

In reality, PU activities may not be continuous and v is not a constant, but

a random variable. If we assume the PU activity follows a Poisson process with


parameter λ, the mean of the probability of inter-arrival time is 1/λ. In this sense,

on average, CR nodes can be considered to have v = T (1− x/λ) time units without

interfering with PUs during [0, T ], where x is the number of PU flows. Additionally,

we can adjust the value of v to reflect the spectrum sharing technique in (5.2) and

(5.3). For example, if we let v be T in (5.3), then (5.2) and (5.3) can represent a

spectrum sharing model where PUs and CRs can access the spectrum resources at

the same time and avoid interference without explicit signaling.

Based on (5.2) and (5.3), Fig. 5.3 shows two cases in which adjusting the CR

transmit power PCR or the radius of PER can change the data rates for both CRs

and PUs, when CR nodes are distributed with a density θ. These two cases exemplify

the effect of PER region and throughput. Furthermore, we can see that in order to get

an optimal DPU we should choose a proper R/R0, which is 1.33 in the example shown

in Fig. 5.3(a). In Fig. 5.3(a), as PCR increases, DCR increases more quickly than the

declining DPU , which is the reason that throughput always rises when PCR increases.

In Fig. 5.3(b), DCR increases more slowly than the declining DPU . In fact, in order

to choose a proper value of PCR, we have to consider a feasible range of PCR. We

can select a reasonable value of PCR by considering the maximum transmit power for

PPU and PCR regulated in current wireless network standards, such as Global System

for Mobile Communications (GSM) (where PPU is about 1˜2W), IEEE 802.22 (where

PPU is less than 4W [90]), IEEE 802.11 (where PCR is less than 100mW), IEEE

802.15.4 (where PCR is less than 100mW).

With the aforementioned discussion, we can see that the PER region has significant

impact on the throughput of both PUs and CRs. Furthermore, given a certain data

rate C0 for a PU, and a certain CR output power, PCR, based on a standard regulation,


(a)

(b)

Figure 5.3: The normalized throughput of a PU and CRs versus PCR and R/R0,when (a) v = 0.3 and (b) v = 0.7

5.3. PROPOSED CM-MAC PROTOCOL 75

we can choose an optimal value of R/R0.

5.3 Proposed CM-MAC Protocol

5.3.1 Overview

In order to meet the requirements of a CRAHN MAC protocol, we have to improve the

traditional CSMA/CA based MAC protocol shown in Fig. 5.4(a). In Fig. 5.4(b), we

use an out-of-band common control channel (CCC) in order to exchange the control

packets such as RTS packets, CTS packets, and acknowledgement (ACK) packets.

After the MAC protocol data unit (MPDU) transmission, a node will wait for a short

inter-frame space (SIFS) period and then transmit the ACK packet. Before sending

an RTS packet, the spectrum sensing process will be initiated by a CR to make sure

there is a data transmission link on a certain channel k.

ACKCW MPDU

RT

S

CT

S

SIF

S

SIF

S

SIF

S

(a)

CWCommon Control Channel

MPDU

MPDU

Channel 1

Channel 2

Channel k

… …

TS

S

MPDU

RS

S

RT

S

CT

S

SIF

S

SIF

S

ACK

ACK

ACK

SIF

S

AC

TS

SIF

S

(b)

CWCommon Control Channel

MPDU

MPDU

Channel 1

Channel 2

Channel k

… …

TS

S

MPDU

RS

S

RT

S

CT

S

SIF

S

SIF

S

ACK

ACK

ACK

SIF

S

AC

TS

SIF

S

RSS: Receiver Spectrum Sensing CW: Contention WindowTSS: Transmitter Spectrum Sensing RTS: Request to SendSIFS: Short Inter Frame Space CTS: Clear to SendMPDU: MAC Protocol Data Unit ACK: AcknowledgmentACTS: Acknowledgement CTS

Figure 5.4: Frame structures of (a) the traditional CSMA/CA-based MAC protocoland (b) the proposed CM-MAC protocol

There are two advantages of using a CCC in CRAHNs. First, possible collisions


of control packets and data packets can be avoided. Second, assigning a CCC can

alleviate the communication efforts required to consult other CRs in a new spectrum

band for exchanging control messages when spectrum availability changes.

The transmitter spectrum sensing (TSS)/receiver spectrum sensing (RSS) proce-

dure is employed, which is dedicated to ensuring spectrum availability of links for

upcoming packet transmissions. Checking the spectrum availability before transmis-

sion on links can avoid transmission failures. The TSS is done by a CR transmitter

and the transmitter will combine the spectrum information into the immediate RTS

packet field meanwhile RSS is completed by a receiver and the spectrum information

into the CTS packet. After the broadcasting stage of RTS/CTS packets with piggy-

backed spectrum information, the neighboring CRs of the transmitter and receiver

have the local knowledge of the one-hop spectrum availability. We should note that

as we integrate the spectrum information into the RTS/CTS routine, the update fre-

quency of spectrum information on neighboring CRs is dependent on the RTS/CTS

request frequency (i.e., the data transmission load). It is expected that in the satu-

rated mode of a CRAHN (i.e., a CR always has data payload to send), the spectrum

information can be frequently updated. For CRAHNs with less data load, the spec-

trum information may be updated less frequently, subject to the possible failures of

data transmissions caused by inaccurate spectrum information on the links.

Another solution to the problem of notifying CRs of the spectrum availability is

to use a periodic updating mechanism that maintains broadcast packets containing

the spectrum information. This solution may cause collisions with the routine con-

trol packets and may result in significant delays; therefore, we will not consider this

solution in the study.


5.3.2 Channel Aggregation Technique

The separation of CCC and data channel cannot significantly improve the through-

put. This is because the data transmission channel cannot be utilized at all before a

successful RTS/CTS process.

A feasible way to further improve the throughput is to decrease the transmission

time of a data packet. We will employ the channel aggregation, in a similar manner

to the method mentioned in [37, 40]. An example of channel aggregation is shown in

Fig. 5.5(a), where compared with Fig. 5.4, the transmission time for a data payload

in a MPDU is reduced as the MPDU is split into three segments and transmitted on

three channels simultaneously. In each segment, we will add a sequence number to

each split data payload.

We should note that the channels used for this technique are dependent on the

available channels assigned by the spectrum sharing scheme. In Fig. 5.5(b), we can

see that the actual channels for transmission are obtained after a negotiation stage,

which can be a RSS/TSS procedure or the SPEC CHANGE notification procedure

from MSA algorithm, which we will discuss later. Because the channel aggregation is

used, the sender is expected to receive three ACKs for the three split data payloads.

SIF

SMPDU#1-1

ACK

SIF

SMPDU#1-2

ACK

SIF

SMPDU#2-1

ACK

SIF

SMPDU#2-2

ACK

Channel k

Channel k+1

SIF

SMPDU#1-3

ACK S

IFSMPDU

#2-3

ACK Channel k+2

(a)

ith CR (i+1)th CR

ACK(1)

Transmission Stage:Transmit data on the

channels

Negotiation Stage: Get agreement on the

transmission channels

ACK(2)

ACK(3)

TSS/RSS

SPEC_CHANGE

(b)

Figure 5.5: An example of channel aggregation in the view of (a) the MAC frame and(b) the sequence diagram


5.3.3 Spectrum Access and Sharing

In the proposed CM-MAC, a simplified spectrum access scheme is considered where a

CR will access the minimum available channels that can meet a certain rate DCR on

the link between ith CR and (i+ 1)th CR. Therefore, the set of channels accessed by

the CR on this link is Ki,i+1(t) = Ki(t)∪Ki+1(t) and RCR =|Ki,i+1(t)|∑

k=1

r(k), where r(k)

is the rate supported on channel k. Besides, if we consider the case that a CR uses

all available channels to meet the rate DCR, the link will have |Ki,i+1(t)| available

channels for data transmissions.

For spectrum sharing, instead of using the central coordination in IEEE 802.22

standard [91], we will employ the distributed spectrum information exchange. An

important goal in the proposed CM-MAC is to ensure a successful next one-hop trans-

mission. Therefore, it is necessary to show the convergence of spectrum information

exchange of the TSS/RSS procedure.

1

2

4

5

3

67RTS

(a)

1

2

4

5

3

67CTS

(b)

1

2

4

5

3

67ACTS

(c)

Figure 5.6: An example of intermediate results of the spectrum sharing procedureafter (a) a RTS transmission, (b) a CTS transmission, and (c) an ACTStransmission. The dotted lines are transmission ranges of CR node 1 andCR node 6.

For example, Fig. 5.6 shows that after TSS procedure, CR nodes 2, 4, and 6 have

the updated spectrum information of CR node 1; after RSS procedure, CR nodes 1,

3, 5, 7 can get spectrum information updates from node 6. Although CR nodes 2


and 4 cannot get the updated spectrum information of CR node 6, we can see it is

not a problem as CR nodes 2 and 4 will not be on the next transmission link. The

candidate CR nodes for the next transmission are CR nodes 1, 3, 5, and 7. As such,

we can see that the TSS/RSS procedure integrated in RTS/CTS/ACTS handshaking

is sufficient enough and no significant communication overhead will occur. All neigh-

boring CRs can receive the spectrum information which assures the successful next

one-hop transmission.

The time for spectrum sensing is not negligible in the proposed CM-MAC protocol

because a spectrum sensing can take around 6ms [92] in a 100ms frame duration,

which is comparable to a typical short inter-frame space (SIFS) duration. Although

it is better to reduce the number of times running spectrum sensing when PUs are

inactive, the TSS/RSS procedure with RTS/CTS is the most general way as PU

activity may not be known in advance.

5.3.4 Mobility Support Algorithm

As CRs in a CRAHN are able to move and cause significant interference to PU traffic,

we have to consider the case that CRs may move in a PER. The negative effects when

a CR moves into a PER include: (1) PU communications will experience interference

and (2) CRs communications will experience interference. Both of these situations

result from the case that PUs are not aware of the spectrum band the CRs are using.

As such, we need an algorithm to deal with these problems.

A challenge here is how a CR can know its vicinity to the PER region with low

cost. We propose to use the radio signal strength indicator (RSSI) at the PHY layer

to solve this problem. As the radio signal strength (RSS) received by a ith CR,


RSS(i, j), is inversely proportional to the distance (d) between the ith CR and the

jth PU , the RSS value can readily indicate the vicinity to a PU if RSS(i, j) is close to a

constant threshold RSSthres. If we assume all the PUs have the same transmit power,

the RSSthres value is sufficient at the network level. If we assume the (i + 1)th CR

node is communicating with the ith CR node, we can describe the proposed mobility

support algorithm (MSA) as follows:

In Fig. 5.7, State(i) records the current CM-MAC state on a CR. If the ith CR

is in a PER region then State(i) = MAC PER; if the CR is out of a PER then

State(i) = MAC OPER; if the CR is in a CTS/ACTS procedure with a transmit-

ter, then State(i) = MAC CTS/ACTS; if a CR is transmitting data packets then

State(i) = MAC TRANSMIT ; State(i) = MAC IN TRANSMIT means some

packet segments have been transmitted through the channel aggregation technique.

func SS(j) is the spectrum sensing routine to sense which channel is occupied by the

jth PU. The STOP packet contains short control information on the current channel,

while the SPEC CHANGE packet contains the available channels for transmission.

When the (i+ 1)th CR receives SPEC CHANGE packet, it will then use the avail-

able channels to send the data packets. If a CR is in the process of sending CTS/ACTS

packets, then an updated CTS/ACTS will be resent to the transmitter/receiver with

the updated channel information in the packets.

From the MSA algorithm, we can see that once the CR is in the PER region, the

data transmission should immediately stop and may cause retransmissions of packets.

When the state is MAC IN TANSMIT , meaning the packets or packet segments

have been in the process of transmission, the CR in a PER region should notify the

transmitter immediately in order to resume the transmission of remaining packets or


Input: RSSI(i, j), State(i), Ki,i+1(t), Kj(t)FOR EACH CRIF RSSI(i, j) > RSSIthres AND State(i) == MAC OPERKj(t)← func SS(j)

IF Kj(t) ∈ Ki,i+1(t)IF State(i) == MAC TRANSMITIF |Ki,i+1(t)| == 1

send a STOP frame over CCC to the (i+ 1)th node on channelthe (i+ 1)th node will stop the data transmission

ELSE IF |Ki,i+1(t)| > 1Ki,i+1(t)← k|k ∈ Ki,i+1(t), k /∈ Kj(t)send the SPEC CHANGE frame with Ki,i+1(t) to the (i+ 1)th node

END IFEND IFIF State(i) == MAC IN TRANSMIT

send a STOP frame over CCC to the (i+ 1)th nodethe (i+ 1)th node will record the data frames/segments already transmittedthe (i+ 1)th node will reinitiate the transmission for the remaining frames

END IFIF State(i) == MAC CTS/ACTS

Ki,i+1(t)← k|k ∈ Ki,i+1(t), k /∈ Kj(t)send a CTS or ACTS frame piggybacking Ki,i+1(t) to the transmitter over

CCCEND IFIF RSSI(i, j) ≤ RSSIthres AND State(i) == MAC PER

State(i)←MAC OPEREND IFEND FOR

Figure 5.7: Description of the mobility support algorithm (MSA)

5.4. THROUGHPUT ANALYSIS 82

segments on the other CR.

5.4 Throughput Analysis

This section provides the throughput analysis of the proposed CM-MAC. The theo-

retical spectrum utilization for the two scenarios will also be discussed. First we will

discuss the scenario of one pair of transmitter and receiver CRs. Then we will analyze

the link throughput.

PU CR

Figure 5.8: An example of a CRAHN with PUs and CRs

As the PU topology can affect the performance in terms of throughput and spec-

trum utilization, we assume that the center of each PU network will be at a distance

of at least 2R. An example of this CRAHN is shown in Fig. 5.8.


5.4.1 Average Time Spent on Mobility

The mobility should be considered in the throughput analysis as it affects the time

spent on spectrum sensing and MSA algorithm. We let the coverage of a CR be SCR,

where ‖SPER‖ > ‖SCR‖, and we assume all the CRs have identical coverage disk in

the CRAHN. CR nodes are deployed in the disk area SPER (with radius R), following

a homogeneous Poisson process with density θ per unit area.

When a CR node moving into the PER, it will run the MSA algorithm. We are

interested in the number of moving nodes in an annulus area with radius [R0−r0, R0+

e+ r0] shown in Fig. 5.8. We can get the average degree [93] between the CRs inside

the PER and the CRs outside the PER at a distance r0, i.e.,

E[Deg] = 2πθ

∫ R0+ε+r0

R0−r0P (Λ(i, i+ 1)|s(i, i+ 1))sds (5.4)

where Λ(i, i+ 1) means the event that ith CR and (i+ 1)th CR has a radio link while

s(i, i+ 1) is the distance between them. From [93], if we assume s(i, i+ 1) = r0

P (Λ(i, i+ 1)|s(i, i+ 1)) =1

2− 1

2erf

(10α√

2ϑlog

r0

10βth

α10dB

)(5.5)

where βth is the threshold value of the received power to maintain the radio link; ϑ

is the shadow fading variance; a is the path loss exponent.

When there is mobility, there is still connectivity to a CR node outside the PER,

and we know that P (Deg > 0) = 1 − e−E[Deg]. By algebraically manipulating (5.4)

and (5.5), we can determine the value of r0.

Next, we assume all CRs are moving and we consider the case that at time t, a

CR in the area with radius [R0− r0, R0 + e+ r0] just moved in the PER, the average


time spent regarding MSA is

E[TMSA] = P0 (TSS + (P11T STOP + P12TS CHANGE)P1 + TSTOPP2 + TCTSP3) (5.6)

where P1 = P (state = MAC TRANSMIT ), P2 = P (state = MAC IN TRANSMIT ),

P3 = P (state = MAC CTS/ACTS). P11 is the probability of sending a STOP pack-

et

P12 is the probability of sending a S CHANGE packet. The average time spent

on one shot of spectrum sensing is TSS; TSTOP and TS CHAGE are the time spent on

transmitting the STOP and SPEC CHANGE packets, respectively. P0 is the prob-

ability that the ith CR just moves in a PER region, we can obtain P0 = P (state(t) =

MAC PER|state(t− 1) = MAC OPER). As it is difficult to give an exact value of

P1, P2, or P3 due to the fact that they are application-specific, we use an estimated

value for each of them. For P1, we can take TdataTdata+TCTS+ω

as its value, where ω is the

delay and empty slot time to consider.

For P3, we can take TCTSTdata+TCTS+ω

as its value. P2 is difficult to know because when

there is a bulk of data to send, P2 is large; when there is a small bulk of data to send,

P2 is small. However, we can know the maximum probability to P2, i.e., ωTdata+TCTS+ω

.

Furthermore, as P0 is usually dependent on the mobility pattern of the CRs, if we

assume the CRs are moving following 1-dimensional (i.e., 1-D) correlated random

walks with bounds [0, 2R] with equal probability moving in two opposite directions,

the steady-state probability at any location is 1/4R [94] if the speed is one-unit length

per time, which can be used as the estimate value for P0.


5.4.2 Link Throughput Performance

The link throughput performance for a CR is considered, and we use the normalized

throughput defined in [95] as:

η =E[Payload transmitted in a slot time]

E[length of a slot time](5.7)

If a CR has a successful transmission, it should be noted that the spectrum avail-

ability may change because of the PU activity. As such, we let the time spent on

during the TSS procedure and data transmission be Tct, and the time spent during

the RSS procedure and data transmission be Tcr. We can obtain:

Tct = TCTS+RTS + SIFS +D + SIFS + TRSS (5.8)

Tcr = TCTS + SIFS +D (5.9)

where D is the propagation delay.

Moreover, for the PU activity following a Poisson process (N(t), t ≥ 0 with

rate parameter λ) during the time interval [0, Ts]. Thus, we denote by Pre(k) the

probability that an available channel will be taken by a PU activity on data channel

k during Ts. If the number of PU flow in a time frame is larger than zero, the data

channel k will be taken by PUs and in this case we have

Pre(k) = P (N(t+ Ts)−N(t) > 0) = 1− e−λTs (5.10)

Apart from Pre(k), probabilities that affect the length of a time slot include: (a) the


probability of no CR transmitting 1 − Ptr where Ptr is the probability that there

is at least one transmission in the considered slot time; (b) the probability of a

packet successfully transmitted PtrPs, where Ps is the probability of a transmission

occurring on the channel is successful; (c) the probability of a packet not successfully

transmitted because of a collision Ptr(1−Ps). Based on the aforementioned discussion,

we can determine from (5.7) that

TS

S

RS

S

RT

S

CT

S

SIF

S

D D

Common Control Channel

SIF

S

MPDU Channel kACK

D

DIF

S

AC

TS

SIF

S

SIF

S

D

D: propagation delay

Figure 5.9: Description of a successful data transmission

η =PsPtrE[P ]

(1− P0)(

(1− Ptr)σ + PtrPsTs + Ptr(1− Ps)Tc + Pre(k)Ts1−Pre(k)

)+ P0TMSA

(5.11)

where Ts is the slot time length of a successful transmission; Tc is the time length that

a channel is busy because of a collision; s is the empty slot time; P0 is the probability

of CRs moving into PER regions (P0 < 1); TMSA is the average time length spent

on MSA algorithm when mobility occurs and the data transmission time after MSA

process; and P is the data packet length (i.e., the length of MPDU). Moreover, from

Fig. 5.9, although we have a CCC and the other channel for data transmission, we


can combine the factors on these two channels together so that

Ts = DIFS + TRTS+CTS+ACTS + 4D + 4SIFS + TRRS

+ TTRS + Tdata + TACK

(5.12)

where TRTS+CTS+ACTS = TRTS +TCTS +TACTS, while Tc is related to the RTS packet

collision on CCC as

Tc = SIFS +D +DIFS (5.13)

At this point, from the assumption that the packets have the same length (i.e.,

E[P ] = P ), and the expressions of functions Ptrand Ps of p, where p is the stationary

probability of a packet transmission by a CR, as well as equations (5.8)-(5.13), we

can get the average throughput result as

η =Pζ

(1− P0)(σ + (Tc − σ)ζ ′ + (Ts − Tc)ζ + CTs1−C ) + P0TMSA

(5.14)

where ζ = np(1− p)n−1, ζ ′ = (1− p)n, C = 1−e−λTse−λTs

, and n is the number of CRs for

transmission. If we suppose the payload in MPDU will be transmitted on the available

channels on the link between the ith CR and (i + 1)th CR, the time spent on each

available channel can be |Ki,i+1(t)| times less at most (when each available channel

has the same bandwidth). However, in order to assemble the split data packets on the

receiver side, we keep the same MPDU header for each available channel. Therefore,

the average time length on a data packet transmission is

T ′data = Tdata

(ϕ+ 1−ϕ

|Ki,i+1(t)|

)(5.15)


where ϕis the ratio of header length to payload length in MPDU, which is usually

less than 1.

The new throughput will be readily derived if we substitute the Tdatawith T ′data

in (5.12). We can express η as η (n, p, λ, |Ki,i+1(t)| , P0).

5.4.3 Upper Bound of Spectrum Utilization

First we discuss the spectrum utilization of CM-MAC. For the general case that the

spectrum band of the link from the ith CR to the (i + 1)th CR affected by the PU

traffic, we can derive the average spectrum utilization of a CR as

UCR =|Ki,i+1(t)|

K, (5.16)

where |Ki,i+1(t)| is the available channels for data transmissions on a link. Then

we consider the case when a PU operates on Kp channels (Kp < K) in a PER

region. In a time interval [0, T ], the inter-arrival time τ = (τ1, τ2, ..., τq) follows an

exponential distribution with mean 1λ. The inter-arrival time of PU traffic is therefore

P (τ < T ) = 1− e−λτ . If we consider the PU activity factor m = TONTOFF

, i.e., the ratio

of PU traffic activity and PU traffic inactivity, the channels not occupied by PUs are

Kp(1+m)K

. In this sense, we can further derive UCR as:

UCR =Kp

(1 +m)K+ S (5.17)

where 0 ≤ S ≤ K−Kp

K. S = K−Kp

Konly if the rest of channels are fully utilized. When

CR Poisson traffic is considered with parameter λ′, S = (1− e−λ′T )K−Kp

K. Note that

as limλ→∞

11+m

= 0, which means that when PU traffic is heavy a CR has no chance to


operate on the Kp channels occupied by PU. Moreover, if we want to obtain a more

accurate value of UCR over the entire CRAHN, we need to get the mean value of UCR.

By assuming that the rest of the channels that are not occupied by PUs can be fully

used by a CR, we can get an upper bound of the link throughput.

5.4.4 A Special Case of the Proposed CM-MAC Protocol

If CR’s traffic model also follows a Poisson process N ′(t), t ≥ 0 with parameter

λ′, we can conduct the similar analysis in order to estimate the CR link throughput

in this case. Compared to the aforementioned analysis in the saturated-mode case

(i.e., a CR always has a packet to send), the special case we are discussing now is

the non-saturated mode (i.e., a CR does not always have a packet to transmit). The

introduction of Poisson traffic model will impose two changes to the aforementioned

analytical model. One is the stationary transmission probability p of a packet; the

other is retransmission times of a packet.

We denote by p′ the new stationary transmission probability of a packet. From

[96], by assuming each CR has a packet buffer and the probability of a packet arrival

is q, the non-saturated mode of CRs will finally affect the value of transmission

probability. Moreover, for the Poisson traffic model, q = PN ′(t) = 1 = 1 − e−λ′T .

The value of p′ can be calculated by the collision probability pc and the total number

of stages ρ, as well as q.

We can obtain the retransmission probability on a channel k, P ′re(k), as follows

P ′re(k) = PN(t) > 0|N ′(t) > 0 = 1− e−λTs (5.18)

As such, we can derive the estimated link throughput results when we consider

5.5. NUMERICAL RESULTS 90

Poisson traffic model for both PUs and CRs.

However, if there is no MSA algorithm and TSS/RSS procedure, the retransmis-

sion probability,Pre(k), can be calculated by the channel availability and spectrum

hole sufficiency [37]. If we take the channel aggregation factor as one, we can obtain

[37]:

Pre(k) = 1−(

1− UCR · n(1− UCR+PU)r

)1

m+ 1(5.19)

where r is the dynamic operating range (i.e., the number of channels a PU is operating

on). Therefore, we can substitute the variable C in (5.14) with (5.19). In this sense,

we can compare the proposed CM-MAC protocol with SCA-MAC protocol.

5.5 Numerical Results

This section shows some numerical results based on the aforementioned analysis.

The parameters are shown in Table 5.1. Besides, all the switching intervals from

transmitting to receiving are set to zero. We assume that the number of CRs N , is

identical to n in (5.14), and these CRs are transmitters in a CRAHN and can interfere

with each other. Moreover, the channel aggregation is not considered in SCA-MAC

and CM-MAC. The essential parameters represented in Table 5.1, for example, are

ϕ = 0.03,P = 8584bits, TRTS+CTS+ACTS = 768µs, Tc = 141µs, and TACK = 240µs.

With the parameter values, we can get Ts = 1151.03 + 7938.48|Ki,i+1(t)| . Then, we can

derive (5.14) as

η =8584(

91ζ′

ζ+

257.6P0+50+(1151.03+7938.481

K−KP)C/(1−C)

ζ

)+ (1010.03 + 7938.48

K−KP)

(5.20)


Table 5.1: Parameters

Parameter ValueMAC data payload 8184bitsMAC header 272bitsPHY header 128bitsRTS payload 160bits + PHY headerCTS payload 112bits + PHY headerACTS payload 112bits + PHY headerSIFS 20µsDIFS 120µsSlot Time 50µsChannel bit rate 1MbpsACK length 112 bits + PHY headerPropagation delay (D) 1µsNo. of spectrum bands (K) 6PHY max transmit power 100mWPHY sensitivity −100dBmRx spectrum sensing time (TRSS) 20µsTx spectrum sensing time (TTSS) 20µsEmpty slot time (σ) 50µsReceiving threshold power (βth) 50dBPath loss exponent (α) 4Dynamic operating range (r) 1000Stationary probability of a CR (p)(saturated mode) 0.02

where Kp = K−E [|Ki,i+1(t)|], i.e., the average number of available channels on a CR.

For the non-saturated mode throughput, note that the variable C and p will change.

Moreover, it is expected that the larger the value of λ, the more frequent the PU

traffic occupies the available spectrum bands. Note that the throughput η is defined

as the probability of successful transmitted frames per frame time. Furthermore, we

will compare CM-MAC protocol with the aforementioned special case of CM-MAC

protocol.


0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Number of CRs

Thr

ough

put

CM-MACCSMA/CA RTS/CTS MACSCA-MAC

=0.001 =0.002 =0.003 =0.004(Kp=1; P0=0.5)

PU Poisson traffic (parameter λ)Saturated mode for CR traffic

(a)

0 20 40 60 80 1000

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

=0.002, =0.0001

Number of CRs

Thr

ough

put

=0.002, =0.0015

CM-MACCSMA/CA RTS/CTS MACSCA-MAC

(pc = 0.3; ρ = 3; Kp=1; P0=0.5)

PU Poisson traffic (parameter λ)CR Poisson traffic (parameter λ)

(b)

Figure 5.10: Description of a successful data transmission


Fig. 5.10(a) shows the throughput performance versus the number of CRs (as-

sumed to be in the saturated mode) when we take the value Kp = 1 for all links.

The CR throughput decreases when the value of λ increases. This is because the

PU traffic with increasing λ has a high possibility of affecting TSS/RSS procedures.

In this case, the PU becomes more active which reduces CR access. Moreover, as

shown in Fig. 5.10(a), with any given value of λ and N , the throughput performance

of CM-MAC outperforms that of SCA-MAC. The reason for this result is that the

delay caused by MSA algorithm and TSS/RSS procedures in CM-MAC is smaller

than that of SCA-MAC. Furthermore, when the PU traffic is heavy, CM-MAC can

successfully reduce the effect of the existence of PER regions. Besides, if we consider

the non-saturated mode for CR traffic (Fig. 5.10(b)), we can see that the CM-MAC

still outperforms CSMA/CA MAC and SCA-MAC protocols.

Fig. 5.11 shows how the CR throughput changes versus N and λ′. We can see

that, when the CR traffic intensity increases, the throughput curves rise, reach a

maximum, and then decline. Moreover, in Fig. 5.11(a) and (b), when N increases

from 10 to 20, the CR throughput increases as well. However, in Fig. 5.11(c), when

N = 50, the throughput sharply increases when λ′ is small and decreases faster than

the throughput curves shown in Fig. 5.11(a) and (b). The reason of this phenomenon

is that having more CRs will increase the traffic which increases the chances of more

packet transmission conflicts. This results in decreased CR throughput.

Fig. 5.12 shows how the CR throughput changes versus N and PU Poisson traffic

parameter, λ. It can be seen that the throughput curves decline with the increasing

intensity of PU traffic. Furthermore, in Fig. 5.12(a) and (b), when N increases

from 10 to 20, the CR throughput increases correspondingly; however, when N = 50,


0 0.5 1 1.5

x 10-3

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Thr

ough

put

N=10λ=0.0015

(a)

0 0.5 1 1.5

x 10-3

0

0.05

0.1

0.15

0.2

0.25

0.3

Thr

ough

put

N=20λ=0.0015

(b)

0 0.5 1 1.5

x 10-3

0

0.05

0.1

0.15

0.2

0.25

0.3

Thr

ough

put

N=50λ=0.0015

(c)

Figure 5.11: CR link throughput versus N and λ′


0 0.5 1 1.5

x 10-3

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

Thr

ough

put

N=10λ′=0.0015

(a)

0 0.5 1 1.5

x 10-3

0.05

0.1

0.15

0.2

0.25

0.3

Thr

ough

put

N=20λ′=0.0015

(b)

0 0.5 1 1.5

x 10-3

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

Thr

ough

put

N=50λ′=0.0015

(c)

Figure 5.12: CR link throughput versus N and λ


the overall throughput is slightly less than the throughput when N = 20. This is

expected because the increasing number of CR nodes results in increasing conflicts in

the packet transmission, which affects the throughput performance.

Fig. 5.13 shows how the throughput performance can be affected by the different

values of Kp (i.e., the number of exclusive channels occupied by PUs). Fig. 5.13(a)

shows the analytical results when CR Poisson traffic is in saturated mode. The results

for Poisson CR traffic (i.e., non-saturated mode) are presented in Fig. 5.13(b) and (c).

We can see that when we consider different intensities of CR Poisson traffic (reflected

by λ′), the throughput performance will change accordingly. Furthermore, we can

see from Fig. 5.13(a)-(c) that when the number of available spectrum bands to CRs

increases (i.e., Kp decreases), the throughput performance improves correspondingly.

These results meet our expectations because with more channels available to CRs,

the overall throughput will increase.

Fig. 5.14 displays how the CR mobility factor, P0, affects the CM-MAC through-

put performance. Fig. 5.14(a) mainly shows the MSA algorithm when the CR traffic

is in the saturated mode; Fig. 5.14(b) and (c) show the throughput performance re-

sults for CR Poisson traffic. It is clear that P0 only slightly decreases the throughput

performance. Therefore, we can conclude the proposed CM-MAC is robust in the CR

mobility case.

The simulation results are shown in Fig. 5.15, where a CRAHN is randomly de-

ployed in a square area and the average speed of CR nodes is about 5m/s. The other

parameters are used as listed in Table 5.1. Fig. 5.15(a) shows that our proposed

protocol has a slightly longer average response time than the CSMA/CA RTS/CTS


0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Number of CRs

Thr

ough

put

KP=0KP=1KP=2KP=3KP=4KP=5

PU Poisson traffic: λ=0.002Mobility probability: P0=0.5

(a)

0 20 40 60 80 1000

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Number of CRs

Th

rou

ghpu

t KP=0

KP=1KP=2KP=3KP=4KP=5

PU Poisson traffic: λ=0.002CR Poisson traffic: λ'= 0.0001Mobility probability: P0=0.5

(b)

0 20 40 60 80 1000

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Number of CRs

Thr

oug

hpu

t

KP=0KP=1KP=2KP=3KP=4KP=5

PU Poisson traffic: λ=0.002CR Poisson traffic: λ'= 0.0015Mobility probability: P0=0.5

(c)

Figure 5.13: CR link throughput performance with different values of Kp in the (a)saturated mode, and (b)-(c) non-saturated mode


0 20 40 60 80 1000

0.05

0.1

0.15

0.2

0.25

0.3

Number of CRs

Thr

ough

put

P0= 0.0

P0= 0.1

P0= 0.3

P0= 0.5

P0= 0.7

PU Poisson traffic: λ=0.0015

(a)

0 20 40 60 80 1000

0.05

0.1

0.15

0.2

0.25

0.3

Number of CRs

Thr

ough

put

P0= 0.0

P0= 0.1

P0= 0.3

P0= 0.5

P0= 0.7

PU Poisson traffic: λ=0.0015CR Poisson traffic: λ'= 0.0001

(b)

0 20 40 60 80 1000

0.05

0.1

0.15

0.2

0.25

0.3

Number of CRs

Thr

ough

put

P0= 0.0

P0= 0.1

P0= 0.3

P0= 0.5

P0= 0.7

PU Poisson traffic: λ=0.0015CR Poisson traffic: λ'= 0.0015

(c)

Figure 5.14: CR link throughput performance versus P0, where CR traffic is in the(a) saturated mode and (b)-(c) non-saturated mode with PU traffic


CM-MACCSMA/CA RTS/CTS MAC

0 10 20 30 40 50 600

0.02

0.04

0.06

0.08

0.1

0.12

Network size

Res

pons

e tim

e (s

)

(a)

0 10 20 30 40 50 600

10

20

30

40

50

60

Network size

Thro

ughp

ut (s

ucce

ss ra

te%

)

CM-MAC (Simulation)CM-MAC (Simulation w/ mobility)CM-MACCSMA/CA RTS/CTS MAC (Simulation)CSMA/CA RTS/CTS MAC (Simulation w/ mobility)CSMA/CA RTS/CTS MAC

(b)

Figure 5.15: Simulation results. (a) Response time and (b) throughout performance

MAC. This is because we employed the ACTS and some spectrum management fea-

tures in the protocol. In Fig. 5.15(b), as the essential features have been captured

by the analysis, the simulation throughput results have the same tendency as the

analytical results. Moreover, the mobility of the CR nodes in CM-MAC has slighter

effect than that of the CSMA/CA RTS/CTS MAC.

In the simulation, we used a speed that can address the P0 in the analysis. How-

ever, we have to make sure the nodes are moving within the deployed area in order

to model the case in the analytical discussion where CR nodes can switch a spectrum

band to maintain the data transmissions. Furthermore, If a different channel bit rate


(e.g., 54Mb/s) is used, the simulation results are expected in the same tendency as

the link throughput is not mainly dependent on the channel bit rate. Besides, we can

expect the performance of other CSMA/CA based protocols like the IEEE 802.15.4

MAC protocol, which may have a better response time when RTS/CTS mechanism

is reduced.


In this chapter, we have introduced the CM-MAC protocol, a MAC protocol for

CRAHNs, by mainly considering CR mobility of CRs and PUs PER regions. We

included the spectrum sensing in the handshaking procedure, and thus the spectrum

information updates on CRs are highly dependent on the PU traffic and the CR

data traffic. Moreover, we demonstrated the effectiveness of CM-MAC by showing

the analytical link throughput, which is mainly related to the following parameters:

number of CRs, stationary probability of a packet transmission by a CR, probability of

CR mobility, PU and CR traffic (Poisson factors), and the set of available channels.

These parameters can be considered for a local control scheme and the feedback

information and the inaccurate or changing value of the parameters can result in

different throughput performance. The analytical results showed that the CM-MAC

protocol outperforms the IEEE 802.11 MAC and SCA-MAC protocols in terms of

throughput performance. The results also showed the proposed protocol is effective

and robust with respect to CR movements. The work related to this chapter has been

published in [97]. In the next chapter, we will discuss the system-level throughput of

CRAHNs.

101

Chapter 6

Scaling Law of CRAHNs Based on Local Control

This chapter discusses the theoretical throughput performance of a CRAHN based

on local control. We discuss the scaling law of throughput for CRAHNs using the

resultant channel model in multi-hop transmission scenarios. Our work extends the

current scaling law analysis in single-hop cognitive radio networks to CRAHNs. We

show the derived throughput results based on the stochastic geometry framework in

the system level.

6.1 PU Interference Region

Definition 5. (PU interference region) The region being interfered by PU transmis-

sions using a specific spectrum band is called a PU interference region (PUIR).

In a CRAHN, as PUs may use different spectrum bands, a PUIR has spatial-

temporal characteristics.

Proposition 2. If we denote by Si a PUIR having one or more PU interferers,

and the CRs are deployed following a Poisson point process Φ, the shot-noise [98]

6.2. NETWORK MODEL 102

experienced by a CR in Si is as follows

I0i =

∑Xj∈Φ,j 6=i

F ij/l(|Xj −Xi|)

where Xi and Xj are the locations of CRs and the PU, respectively, F ij is the fading

from the interfering PU j to a CR i, and l(·)is the omni-directional path-loss model.

If we denote by I0i the so-called shot-noise experienced by CRs in a j-th PUIR

Sj from PUs, we can get the SINR of a CR transmitter in (6.1). For the Rayleigh

fading, the shot-noise is∑

i f(|Xi −Xj|α′), where α′ is the path loss exponent.

SINR(i, j) =F ii /l(|Xi − yi|)W + I1

i + I0j

(6.1)

where W is the shot-noise of Gaussian noise, I0j is the shot-noise between CRs and

the interfering PU in PUIRs, while I1i is the shot-noise only between CRs.

Now we can get the throughput of the CRAHN. The average transmission rate of

a CR transmitter can be expressed as

τ(r, λS) = E [log(1 + SINR(0, j)|e0 = 1] (6.2)

where e0 is the retaining indicator and e0 = 1 means a transmission event occurs.

Because different PUIRs may cause different interferences to CRs, we need a

specific network model in order to derive the network-level throughput.


Figure 6.1: Network layout of a CRAHN

6.2 Network Model

We consider a basic CRAHN network, where a PU coexists with multiple CRs. In

general, this network in a broad area includes two types of networks, i.e., the PU

network and the CR network. However, in reality, as the TV stations are sparsely

deployed in different regions, we can consider the network as a basic cell with one

PU transmitter and multiple CR transmitters, as shown in Fig. 6.1. This model

can be extended to a network with multiple PU transmitters, where the multiple PU

activities can be modelled as the activities from one virtual PU transmitter.

In this basic network, the CR network is deployed following a Poisson point process

with the intensity parameter λS. There are K spectrum bands available per PU. The

nodes in the CR network are assumed to follow a bipolar model in single-hop data

transmission scenario, where nodes are exactly split into transmitter-receiver pairs.


The PU’s activity on a channel follows a Poisson traffic model. This Poisson traffic

model over K channels allows us to estimate the probability of the availability of m

channels during a time period T .

In summary, we can list the following assumptions made to this network model.

1. The PU transmitter-receiver pair is stationary with known locations.

2. CRs are deployed following a Poisson point process with the intensity parameter

λS;

3. Each CR pair has a transmission radius r;

4. PUs and CRs experience the Rayleigh fading.

For a large CRAHN composed by multiple basic networks as shown in Fig. 6.1,

we assume the communication among CRs will not suffer from interference in the

overlap region between basic networks. This assumption also implies that the PUs

cannot communicate with each other.

For the CR communication with Aloha protocol in the MAC layer, similar to the

Kendall-like notation used in [98], the model mentioned above is GIW+M/M+D/M

type,

where GI means in the nominator a general distribution for the virtual power F, M/M

means the shot-noise interference is generated by a Poisson pattern of interferers (M)

with a Rayleigh distribution (M) for the virtual powers, and the D/M means the

deterministic distribution of PU interferers with a Rayleigh distribution of virtual

powers.

We can obtain the results of the coverage of a CR node (or probability of a


successful transmission) in two areas S1 and S2 as [57]:

E0

[es(I

1+W )]

= LI1(s)LW (s)

E1

[es(I

1+I01+W )]

= LI1(s)LI01 (s)LW (s)

E2

[es(I

1+I02+W )]

= LI1(s)LI02 (s)LW (s) (6.3)

where L(·) is the Laplace transform and s = µρl(r), and ρ is the reception threshold

seen by CR receiver from CR transmitter and µ is the mean of the Rayleigh fading

random variables. Therefore, the total throughput of CRs in this case is

τtotal(r, λS, S) = λS |S| τ(r, λS) (6.4)

τ(r, λS) = p0E0 + p1E1 + p2E2 (6.5)

where pi is the probability of area Si.

Because the values of r1 and r2 are dependent on the CRs in areas S1 and S2, it is

useful to calculate the average length of r1 and r2. As the distribution of CRs follows

a Poisson point process, we know the number of CRs in S1 is λS|S1|.

Because r1 and r2 are highly related to pi, we can substitute pi with r1 and r2 in

(6.4).

6.2.1 Virtual PU in the Resultant Spectrum Band

With PUIR, we are able to consider multiple PUs into a single virtual PU. We are

able to consider a PU operating in multiple spectrum bands in a PUIR as a virtual PU

operating in a single resultant spectrum band by using the resultant channel model


[69] introduced in Chapter 3. With the resultant channel model, for the ith PU, the

time in “busy” state or “idle” state is exponentially distributed with mean αi and βi,

respectively.

We know that, with resultant channel model, the expected length of the resultant

busy and idle periods E[Ton] and E[Toff ] are

E[Ton] =1∑K

i=1 βi−1

(6.6)

E[Toff ] = E[Ton]1−

∏Ki=1 ω1,i∏K

i=1 ω1,i

(6.7)

In order to simplify our discussion, we represent E[Ton] by Ton and E[Toff ] by

Toff .

The steady state probability of idle and busy states on channel i are

ω0,i =αi

αi + βi, ω1,i =

βiαi + βi

(6.8)

The aforementioned model can be extended to a network with multiple PU trans-

mitters, where the multiple PU activities can be virtually modelled as the activities

from one virtual PU transmitter. In this way, the network model with one (virtual)

PU and multiple CRs shown in Fig. 6.1 is sufficient for our discussion.

Suppose there are K spectrum bands which can be used by PUs. We can plot

the results of Toff and Ton shown in Fig. 6.2, where we can see when K > 3, Toff

increases.


1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Available spectrum bands (K)

Exp

ecte

d le

ngth

of t

he r

esul

tant

per

iod

α = 0.4, β=0.6

Ton

Toff

Figure 6.2: Toff and Ton based on resultant channel model

6.2.2 Medium Access Probability

The term medium access probability (MAP) [99, 100] is the probability of a node

trying to access the wireless medium. Thus, MAP determines the probability of data

transmission and the throughput performance of the PU and CR networks.

In order to simplify our discussion, we consider the time-slotted MAC protocol.

In [91], Stevenson et al. analyzed the throughput order of CRs with multiple PU

pairs and employed a 25-TDMA transmission pattern for PU activities. However, we

consider a general case that the PU pairs and CRs coexist, and PU activities are not

limited in specified TDMA slots. In order to simplify our analysis, we assume that

the PU activities are conceptually separated into time frames, each with a length T .

The time frame T can be considered as a time slotted MAC protocol.

Based on the resultant channel model, we can transform a K-channel case into


a single-channel case. Therefore, as we are interested in finding out the throughput

of the PU network and the CR network, we can focus on evaluating the number

of packets sent during the T = Toff + Ton period. Without loss of generality, we

can assume a PU does not transmit packets during [0, Toff ] but it transmits packets

during (Toff , T ] in the busy state at time ti following the so-called retaining indicator:

UPj = 1Toff<ti<T (6.9)

In (6.9), CR i can transmit packets at time ti with the following retaining indicator:

USi = 1ti<Toff + 1Toff<ti<T1FS−P0,i /|TSi,0−RP0 |α

′<ρ (6.10)

In fact, (6.10) depends on a spectrum sharing model. If we just allow a PU to

exclusively occupy a channel when it is in the busy state, then we can simplify (6.10)

to

USi = 1ti<Toff (6.11)

The retaining indicator in (6.10) can be referred as the underlay spectrum sharing,

where the CRs try to perform the data transmissions with or without PU activities.

The retaining indicator in (6.11) can be referred as the overlay spectrum sharing,

where CRs only transmit without PU activities.

Then the MAP or transmission probability of a CR is:

P (USi = 1) = P (ti ≤ Toff ) + P (Toff < t < T )P (F S−P

i,0 /|T Si,0 −RP0 | < ρ) (6.12)

6.3. NETWORK DIVISIONS 109

For the given parameters µ = 10, ρ = 15, α′ = 3, R0 = (0.2, 0.2) in a unit circular

area, we can plot the MAP results in Fig. 6.3.

Based on [101], given a CR transmitter at location y and a CR receiver at location

z in the CRAHN shown in Fig. 6.1, the coverage probability (COP) can then be

obtained as:

PCOPS = Py,z(SINR

Si > Pth)

= Py,zFS−S1,1 > Pthr

α′(W (z) + F P−S0,1 /|z|α′ + ΓS(z))

= Ey,z[e−µPthrα

′W (z)]Ey,z[e

−µPthrα′FP−S0,1 /|z|α′ ]Ey,z[e

−µPthrα′ΓS(z)]

= LW (µPthrα′)LFP−S0,1

(µPthr

α′

|z|α′)(1− E[US

i ] + E[USi ]

|T Si − z|α′

|T Si − z|α′ + Pthrα

′ )

(6.13)

where E[USi ] = P (US

i = 1).

Usually, in a CRAHN, the parameters α′, µ, Pth, z, and λS are known a priori. In

this way, although the multi-integral in 6.13 can hardly be derived into a simple form

but it can be solved by the Monte Carlo method. We can even make the CRAHN

more general if one or more parameters are not known.

Furthermore, if we assume that CR transmitters are in the saturated mode, each

CR transmitter will immediately transmit packets once a spectrum band is not oc-

cupied and a transmission back-off timer expires.

6.3 Network Divisions

It is not unusual that a network needs to be divided into different areas of CRs.

Suppose we divide the CRAHN with area S into two areas S1 and S2, we can obtain

the throughput of CRs as

6.3. NETWORK DIVISIONS 110

0 0.5 1 1.5 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Mean of idle state holding time

Med

ium

acc

ess

prob

abili

ty

K=3

Underlay spectrum sharingOverlay spectrum sharing

(a)

0 0.5 1 1.5 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Mean of idle state holding time

Med

ium

acc

ess

prob

abili

ty

K=5

Underlay spectrum sharingOverlay spectrum sharing

(b)

Figure 6.3: MAP results based on the resultant channel model

6.4. MULTI-HOP DATA TRANSMISSION SCENARIO 111

CR 1 CR 2 CR n...

PUIR

Figure 6.4: Multi-hop data transmission from CR 1 to CR n.

P SCOP = λS

∫S1

P SCOP (y)(1− e−µρ|y−RP0 |α

′

)dy + λS

∫S2

P SCOP (y)(1− e−µρ|y−RP0 |α

′

)dy

(6.14)

If a PER region is considered in the CRAHN with the area SPER = S1 and

therefore S2 = S ∪ \S1, then the throughput can be readily derived accordingly by

(6.14).

6.4 Multi-Hop Data Transmission Scenario

An important feature in CRAHNs is the multi-hop data transmission. We are now

extending the aforementioned analysis from a single-hop data transmission scenario

to a multi-hop data transmission scenario. Fig. 6.4 is an example of the multi-hop

transmission scenario, where each CR tries to transmit the packets over multiple hops.

In Fig. 6.4, we can see that as all CRs are covered by the same PUIR, we can assume

the data transmission over each link is independent. In this way, if we have n CRs in

a data transmission scenario over n− 1 hops, the retaining indicator in this case is:


The retaining indicator in the multi-hop fashion can be represented as

U(n)S =n−1∏i=1

USi (6.15)

Because there are n− 1 CR transmitters in the unidirectional multi-hop scenario,

from (6.12), we can derive the multi-hop transmission probability and COP as

P (U(n)Si = 1) =n−1∏i=1

P (USi ) (6.16)

PCOPS (n)(U(n)Si = 1) =

n−1∏i=1

P (USi )PCOP

i,S (6.17)

Here we discuss how the local control and information can affect PCOPS (n). In

(6.17), PCOPi,S is the COP in a hop i. Due to the inaccurate feedback or local infor-

mation regarding radio environment, the parameters (e.g., α′, µ, etc.) are subject to

change from link to link and therefore PCOPi,S is different from link to link. Given a

local control scheme which can result in the identical value of PCOPi,S for all links, we

can simplify PCOPi,S to PCOP

Si. If we divide the CRAHN with c identical subareas, then

Si = S/c.

In the model shown in Fig. 6.4 we need to know the average number of hops

from the source CR to the destination CR directly from the average distance of CR

transmitter-receiver pairs. However, with our model, CR transmitters are distributed

following a Poisson point process, so we are able to estimate the probability for a

certain number of hops along a transmission path.


6.4.1 Probability of A Transmission over Multiple Hops

In a Poisson point process, the connectivity of a CRAHN can be expressed as a

function of distance distributions between nodes [102]. If the CRs in a Borel set S is

distributed in a Poisson process with parameter λS, the probability of having n CRs

along a path is

P (n, S) =(λSL(S))n

n!e−λSL(S). (6.18)

where L(S) = πr2 and r is the radius of the circular area S. In an area S, the

probability that it contains exactly n CRs (or n− 1 hops) is (6.18).

The probability of the origin to the nth nearest point in an area S can be expressed

as

P (n, S) =

∫S

2(πλS)n

(n− 1)!r2n−1e−πλSr

2

dr (6.19)

Eq. (6.18) can be used to calculate the probability of an exact number of hops,

but this probability is suited to the case that a circular area contains exactly n CR

nodes (or n−1 hops). The limitation of (6.18) is that a CRAHN needs to be carefully

divided into small circular areas without overlaps. For a network in a small circular

area and a low density of CRs, (6.18) is appropriate. For a network with a large

number of hops with CRs beyond the PU coverage, using (6.18) is not accurate.

Eq. (6.19) is suited to the case when we want to guarantee a data transmission

involves n− 1 hops in a given area S. Therefore, we should not use (6.19) to the case

of traditional networks with a constant link length per hop.

From the aforementioned two equations, we know the route selection is important


to determine the probability of having an exact number of CRs in the multi-hop fash-

ion. There are two generic route selection schemes corresponding to (6.18) and (6.19)

if we have specified the hop count: (1) the route selection for a CR link transmitter is

randomly chosen in a given area S; (2) the route selection for a CR link transmission

is determined by the subareas Si ⊂ S where each subarea Si should guarantee the

single-hop transmission.

6.4.2 Packet Reception Probability

There are several transmission scenarios when we consider the multi-hop transmission

on routers. We introduce the packet reception possibility, Prx, which indicates the

possibility when a router receives a packet from a node. With Prx, we are able to

discuss the different transmission cases on a router. For example, if a router uses

a flooding routing algorithm where the transmission progresses in the broadcasting

fashion, we can take Prx = 1. If a router employs an opportunistic routing algorithm

where the next hop is randomly chosen, we can take Prx = c, 0 < c < 1.

In the multi-hop transmission model we discussed above, if we take Prx into con-

sideration, we can derive the throughput over n− 1 hops as P n−1rw PCOP

S , where PCOPS

depends on (6.13) and the route selection schemes in (6.18) or (6.19).

6.5 Scaling Law of CRAHNs

We discuss the throughput results using the aforementioned analysis. The throughput

performance is measured based on the derived COP as in the Poisson point process

the probability of having CRs in an area is important. For the multi-hop data com-

munication we shown above, COP can be translated as the successfully transmitted


packets per second per unit area. We take the values of the key parameters as: K = 5,

α′ = 3, αi = 1.5, βi = 1, r = 0.3, R0 = (0.2, 0.2), µ = 10, ρ = 15, and Pth = 15.

First, the results of the single-hop data transmission are shown in Fig. 6.5. From

the aforementioned discussion, we employ the underlay spectrum sharing in the CR

network as it can reflect the interference induced by PUs. From Fig. 6.5, the curve

of the CR throughput linearly grows with the increasing value of λS, because, in the

single-hop scenario, growing CR density directly increases MAP and the concurrent

transmission sessions. However, because the PU suffers from the interference of the

increasing CR transmission, the curve of PU throughput declines with the increasing

value of λS. Compared to Fig. 6.5(a), Fig. 6.5(b) show the results when we consider

a subarea of a network in an area S. The throughput performance for CRs drops in

Fig. 6.5(b) mainly because the number of CR transmitters becomes less in this case.

In Fig. 6.6, we show the throughput result using the route selection scheme in

(6.18) and the throughput result using an opportunistic routing scheme (Prw = 0.98)

in the multi-hop data transmission scenario. When λS is less than 1.45, the 2-hop

transmission case has better throughput than the 3-hop and 4-hop transmission cases.

However, when λS is greater than 1.85, a throughput curve with a greater hop count

has better performance than a curve with a smaller hop count. The reason of this

phenomenon is that with more number of CRs per area, a greater number of hops

can help relay the data; a smaller number of hops can result in the longer average

link length and therefore reduce the probability of delivering a packet. We note

that all curves in Fig. 6.6 become zero as λS increases. This is because we adopt

the probability of an exact number of hops in (6.18), and it is readily to see that

when the density of CRs increases, the probability of having exact 2, 3 or 4 hops


0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.5

1

1.5

2

2.5

3

Thro

ughp

ut (P

acke

ts/s

/m2 )

PUCR

S

(a)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.2

0.4

0.6

0.8

1

1.2

1.4

Thro

ughp

ut (P

acke

ts/s

/m2 )

PUCR

S

(b)

Figure 6.5: Throughput results of a single-hop scenario. (a) The whole network with-in an area S is considered; (b) the throughput performance in a subareaof S is considered.


0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.05

0.1

0.15

0.2

0.25

0.3

0.35

λS

Suc

cess

fully

tran

smitt

ed p

acke

ts

Hop count=2Hop count=3Hop count=4Hop count=2 (Opportunistic)Hop count=3 (Opportunistic)Hop count=4 (Opportunistic)

Figure 6.6: Normalized throughput results when hop counts are 2, 3, and 4 in abounded circular area.

in an area becomes less. Moreover, as the packet reception probability can affect

the probability of successfully transmitted packets, the throughput result with the

opportunistic routing scheme has a bit lower performance than the result without a

opportunistic routing scheme.

Keeping the same condition, we show the throughput results with the second route

selection scheme based on (6.19) and the the throughput results with an opportunistic

routing scheme (Prw = 0.98) in Fig. 6.7, where the throughput increases with the

increasing number of hops involved in the data transmissions. Fig. 6.7 also shows

that when λS < 2.45 a curve a the smaller hop count has greater throughput than

the one with a larger hop count, where this phenomenon is consistent with the results

shown in Fig. 6.6. When λS > 2.45, the curve with a smaller hop count has less

throughput than the one with a larger hop count. This tendency results from two


factors. First, as we make the guaranteed number of hops in a given area, which is

a part of the entire network, with the density of CRs increases, the probability of

ensuring the small number of hops (e.g. 2, 3, or 4) increases. Second, as the area for

a one-hop transmission is reduced, the throughput is actually decreased. Similarly,

the throughput results with opportunistic routing scheme have the same tendency

and theoretical ground as the results without the opportunistic routing scheme.

In summary, from the results in Fig. 6.6 and 6.7, we know that the route selection

is important when the density of CRs is increased.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

λS

Suc

cess

fully

tran

smitt

ed p

acke

ts

Hop count=2Hop count=3Hop count=4Hop count=2 (Opportunistic)Hop count=3 (Opportunistic)Hop count=4 (Opportunistic)

Figure 6.7: Normalized throughput results of a multi-hop scenario with different hopcounts.

The applications of the two generic route selection schemes can be applied in

several different areas. Specifically, the first route selection scheme is suitable for a

randomly deployed CRAHN where the hop distance between CRs is not known a

priori but the maximum number of hops is expected. For example, a CRAHN with

a bunch of cognitive sensor nodes by random deployment without an infrastructure

6.6. DISCUSSION ON IEEE 802.22 BASED CRAHNS & IEEE 802.11BASED CRAHNS 119

Table 6.1: Common parameters

Parametersµ Rayleigh fading parameter

SPER Area of primary exclusive regionλS Poisson point process parameter of CRsK Number of spectrum bands

can be seen as the first route selection scheme. The second route selection scheme

is for the CRAHN with a constant hop-distance. For example, a CRAHN used in

the micro grids of a Smart Grid where CRs in the micro grids are almost static with

known distance between each other can be considered in this case.

6.6 Discussion on IEEE 802.22 Based CRAHNs & IEEE 802.11 Based

CRAHNs

From the above discussion, we have derived the theoretical results based on a time-

slotted abstracted MAC model. However, it is possible to extend the analysis to the

real-world networks compatible with existing standards.

The aforementioned throughput performance can be applied to the IEEE 802.22

[103] based CRAHNs and the IEEE 802.11-based CRAHNs, because the network can

be formed in the similar way and the key parameters used in the proposed network

model can be used in these networks.

The key parameters of PHY and MAC layers shared in both IEEE 802.22 or IEEE

802.11 based CRAHNs are shown in Table 6.1. These parameters capture the global

radio environment in the two networks. With additional parameters given in the IEEE

802.22 or IEEE 802.11 based CRAHNs, we can extend the results in a fine granularity.

In IEEE 802.22 based networks, the TV stations can be statistically modelled by the


Voronoi diagrams [104], which means that the network can be divided into cells with

one PU per cell. Furthermore, we know the minimum channel for data transmission

can be included in the throughput expression. In this way, the IEEE 802.11 based

CRAHN has similar throughput results to IEEE 802.22 based CRAHN, because the

support of multiple channels is a must in the IEEE 802.11 based CRAHN.


In this chapter, we have discussed the scaling law of the CR throughput in single-hop

and multi-hop transmission scenarios when CR transmitters can communicate with

each other in the network. The model proposed in this chapter can estimate the

throughput of PUs and CRs for the underlay spectrum sharing and overlay spectrum

sharing. In this sense, the key parameters of a cross-layer protocol of CRAHNs can

be analyzed. Moreover, although we studied the basic network topology of CRAHNs

which contains a PU and multiple CRs, we can derive more complicated topologies

based on this topology. Furthermore, the route selection scheme was considered as

a key factor for throughput performance because of the characteristics of a Poisson

point process. We showed the effectiveness of the proposed models by the presented

results. Moreover, for some real-world CRAHNs with fixed number of nodes in a

given area [105], the binomial point process can be employed as the CRs following

Poisson point process have no definite locations in a given area.

121

Chapter 7

Conclusion

7.1 Summary of Contributions

The increasing demand for wireless services and the spectrum sharing policies has led

to spectrum scarcity in wireless communications. As a precious resource, the under-

utilized spectrum is required to be put to use in CRAHNs with spectrum management.

Research on CRAHNs can provide solutions to this problem and to a broad spectrum

of wireless network paradigms.

In this preliminary study, we focused on the local control approach in order to

address the spectrum sharing fairness, cognitive MAC protocol design, and system-

level throughput performance in CRAHNs.

In Chapter 4, we proposed the framework of local control approach. This approach

allows us to model and analyze the stability of consensus-based protocols for spectrum

sharing. Then we discussed two local control schemes with feedback and without

feedback and compared their performance in terms of convergence and fairness. With

the local information brought by local observations from spectrum sensing and MAC-

layer functions, the proposed local control scheme can effectively achieve the goal of

7.2. FUTURE WORK 122

the spectrum sharing fairness.

In Chapter 5, we proposed the cognitive MAC protocol with mobility support,

which is called CM-MAC. In the design of CM-MAC we employed the local control

concept to devise the mobility support algorithm, which can take advantage of the

local information from the neighboring CRs and address the negative effects induced

by the existence of the PER area in a CRAHN.

In Chapter 6, we discussed the throughput in single-hop and multi-hop scenarios.

We discussed the local control concept in the analysis with the inaccurate local infor-

mation from observations. In this way, we can comprehensive investigate the scaling

law based on the network model with abstract PHY and MAC functions. Although

the network modelling is not in a fine granularity, the theoretical results give hints

on the scaling law and fundamental limits of a CRAHN.

7.2 Future Work

A few open topics and questions are discussed in the following.

Local Control Schemes

• A local control scheme in spectrum sharing was proposed in the thesis. More

schemes can be investigated for possible applications. We assumed each CR

has the same capability but the heterogeneity of CRAHNs is not unusual in

many applications. It is worthwhile to investigate local control schemes for the

heterogenous CRs. Moreover, it is worthwhile to explore a local control scheme

with a learning algorithm.

• The applicability of using local control approach to analyze other CR enabled


networks worth being investigated. For example, if we consider a CRSN as

a CRAHN with new PHY features. A CRSN brings more topological and

hardware constrains compared to CRAHNs. However, with several essential

common characteristics between the two networks, the system-level analysis in

CRAHNs can be extended to and local control approach for protocol design can

be applied.

Models in the MAC Layer

• In this thesis, the 1-D mobility was addressed in the mobility analysis; how-

ever, more sophisticated mobility models in higher dimensions and in different

topologies need to be investigated in the future work. For example, the CR de-

vices can move following 2-D or 3-D random walks in a bounded area or space,

and the performance may vary because of the possible transmission handoffs

and unpredictable interference caused by primary exclusive regions.

• Different PU activity models need to be considered in different scenarios. Al-

though it is popular to model the PU activity as a Poisson process, it is possible

in some applications that a PU activity pattern can be modelled as a more com-

plex model. Moreover, real-world data for PU activities can be employed in the

evaluation in order to see the stability and applicability of the protocol.

System-Level Modelling and Analysis

• The PHY and MAC layers were abstracted in the system-level analysis. A

further detailed modelling for either PHY or MAC layers is expected to result

in new theoretical bounds.


• The multi-hop data transmission can involve quite a few CRs, where the CRs

along the path can be formed in different ways. We assumed the path was

formed by two route selection schemes but other route selection schemes need

to be considered. Moreover, a path can be formed in many ways if we involve

different NWK features. Therefore, the formation of a path and throughput

performance needs to be investigated further because it may hinder data trans-

missions along the path. Besides, a closed-form approximated expression of the

throughput with the routing schemes with local control schemes needs to be

investigated.

BIBLIOGRAPHY 125

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