Cooperative Communication and Cognitive Radio

Thesis

presented at The Higher School of Communication of Tunis

To obtain the degree of

DOCTOR

In

Information and Communication Technologies

By

Hela HAKIM

Cooperative Communication and Cognitive Radio

Supervised by

Hatem Boujemaa

Defended on February 5th , 2014.

Thesis Committee :

President: Mr. Ammar Bouallegue, Professor, ENIT, Tunisia.

Reporters: Mr. Mohamed Slim Alouini, Professor, KAUST, Saudi Arabia.

Mr. Nouredine Hamdi, Professor, INSAT, Tunisia.

Examiner : Mr. Sofiane Cherif, Professor, Sup’Com, Tunisia.

Thesis supervisor: Mr. Hatem Boujemaa, Professor, Sup’Com, Tunisia.

Cooperative Communication and Cognitive Radio

by

Hela HAKIM

A thesis submitted to

The Graduate Studies School at

The Higher School of Communication of Tunis

in partial fulfillment for the degree of

Doctor

in

Information and Communication Technologies

Thesis Supervisor

Prof. Hatem Bouejmaa

January, 2014

c⃝Hela HAKIM

i

Abstract

This thesis focuses on two major issues. First, the design and investigation of novel relay-

ing protocols that induce end-to-end cooperative diversity for broadcast networks, cooperative

Direct-Sequence and Multi-Carrier Code Division Multiple Access networks. Second, the study

and investigation of spectrum sharing schemes in cognitive radio networks.

Concerning the first issue, several single relay selection schemes in broadcast wireless net-

works using either selective digital relaying or selective analog relaying have been investigated.

The key idea is to classify the nodes in the considered broadcast network into two sets. A set

of “reliable” nodes, whose source-node signal-to-noise ratio exceeds a threshold value and a set

of “unreliable” nodes gathering the remaining ones. Then, one node among “reliable” nodes is

activated as a relay. We derive closed form expressions of the end-to-end bit error probabilities

of some proposed single relay selection schemes for selective digital relaying. The data rate loss

due to the cooperation is also studied. Analytical results along with simulations prove that

compared to the direct transmission, the single relay selection schemes improve signicantly the

bit error probability performance of the broadcast network. In the other hand, the performance

of cooperative Multi-Carrier and Direct-Sequence Code Division Multiple Access systems have

been studied. First, we have derived the end-to-end Bit Error Probability for cooperative Multi-

Carrier Code Division Multiple Access systems using selective threshold digital relaying. Second,

we have derived the end-to-end Bit Error Probability for cooperative Direct-Sequence Code Di-

vision Multiple Access systems using incremental selective relaying which combines selective

relaying with incremental relaying protocols in the presence of multipath propagation.

Concerning the second issue, first we have studied the influence of the use of fixed transmit

power in underlay spectrum sharing. In fact, the use of fixed transmit power nodes alleviates the

signaling requirements of underlay cognitive radio networks compared to the adaptive transmit

power nodes. Nevertheless, it influences its performances. Our comparison study shows that

ii

fixed transmit power has a positive impact on the data rate and power consumption performance

while it deteriorates the symbol error probability performance.

Second, we have investigated several broadcast transmission schemes to enable spectrum

sharing in broadcast cognitive radio networks. We have also proposed dynamic spectrum sharing

schemes where a pair of secondary users and a pair of primary users bidirectionally communicate.

A secondary relay is deployed to assist the secondary transmissions and improve the secondary

access to the spectrum. We have dealt with both cases where the relay has a single antenna and

where it has multiple antennas.

iii

To the memory of my grand mother

To my parents and my brothers

To my uncle and his wife

To my aunt and her husband

To my friends and every person who has helped me throughout my studies

Hela HAKIM

iv

Acknowledgement

I would like to express my deep gratitude to my supervisor Prof. Hatem Boujemaa for his

guidance during this thesis. He did not save any effort to scarify his skills and expertise for the

benefit of my thesis. His valuable comments and ideas have helped in enriching my thesis work

and ameliorating its quality. Also, his enthusiasm for research and continuous encouragement

and felicitations have made my doctoral study a very enjoyable experience.

I would also like to express my deep gratitude to Prof. Wessam Ajib who significantly

helped me ameliorate the quality of my thesis work and benefit me with valuable and insightful

comments. His contribution in this thesis work is significant. Also, I’am very grateful to him

for hosting me in his research laboratory “Telecommunication, Reseaux, Informatique Mobile

et Embarquee” at the Universite de Quebec A Montreal for three scientific stays of averagely

four months per year and providing me with an excellent research environment.

The thesis Scholarship that I have received under the research project entitled “QoS Opti-

mization In Broadband Wireless Networks and Development of new value-added Mobile Systems

and Services for e-advertising and e-Tourism” at Sup’Com and awarded by the Qatar National

Research Fund under Grant NPRP 08 - 577 - 2 - 24, was curial to start my graduate studies and

made this journey possible. In this occasion, I would also like to thank all the senior researchers

who have participated in this project for their great work and their continuous helpfulness.

Special thanks to all the members of my thesis defence committee for accepting to evaluate

my work and make this journey possible.

v

Table of Contents

Abstract ii

Acknowledgement v

Table of Contents vi

List of Figures xi

List of Tables xiv

List of Acronyms xv

1 Introduction 1

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2.1 Relay selection schemes in wireless networks . . . . . . . . . . . . . . . . . 2

1.2.2 Spectrum access schemes in cognitive radio networks . . . . . . . . . . . . 3

1.3 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Background on Cooperative Communication and Cognitive Radio 6

2.1 Cooperative Communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1.1 Cooperative Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1.2 Preliminaries of Multihop Relaying . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Cognitive Radio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2.1 Software-defined Radio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2.2 Cognitive Radio network paradigms . . . . . . . . . . . . . . . . . . . . . 10

2.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

vi

3 Single relay selection in Broadcast Wireless Networks 12

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.2 System Model and Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . 15

3.2.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.2.2 Relaying scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.3 Relay Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.3.1 Average SNR Threshold based relay selection (AST based RS) . . . . . . 17

3.3.2 SNR Threshold based Relay Selection (ST based RS) . . . . . . . . . . . 17

3.3.3 Max-Min Relay Selection (MM RS) . . . . . . . . . . . . . . . . . . . . . 19

3.3.4 Min Max Error Relay Selection (MME RS) . . . . . . . . . . . . . . . . . 19

3.4 E2E BEP Derivation of the AST based RS using STDR . . . . . . . . . . . . . . 21

3.4.1 Case 1: k is the selected relay . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.4.2 Case 2: k is not the selected relay . . . . . . . . . . . . . . . . . . . . . . 22

3.5 E2E BEP Derivation of the ST based RS using STDR . . . . . . . . . . . . . . . 22

3.5.1 case 1: k is a “reliable” node . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.5.2 Case 2: k is an “unreliable” node . . . . . . . . . . . . . . . . . . . . . . . 23

3.6 Numerical and Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4 Performance Analysis of Cooperative MC CDMA and DS CDMA Systems 31

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.2 Performance Analysis of Cooperative MC CDMA Systems using Selective Relaying 33

4.2.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.2.2 E2E BEP Analysis of the System . . . . . . . . . . . . . . . . . . . . . . . 36

4.2.3 Numerical and Simulation Results . . . . . . . . . . . . . . . . . . . . . . 39

4.3 Performance Analysis of Cooperative DS CDMA Systems using combined Selec-

tive and Incremental Relaying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.3.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.3.2 E2E BEP Analysis of the System . . . . . . . . . . . . . . . . . . . . . . . 42

4.3.3 Throughput Analysis of the System . . . . . . . . . . . . . . . . . . . . . 46


4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

vii

5 Performance Comparison between Adaptive and Fixed Transmit Power in

Underlay Cognitive Radio Networks 50

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

5.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

5.3 Relaying schemes in underlay cognitive radio network . . . . . . . . . . . . . . . 55

5.3.1 Opportunistic DF Relaying with FTP (O-DF with FTP) . . . . . . . . . 55

5.3.2 Opportunistic AF Relaying with FTP (O-AF with FTP) . . . . . . . . . 55

5.3.3 Partial relay selection with FTP (PR with FTP) . . . . . . . . . . . . . . 56

5.3.4 Opportunistic DF relaying with adjustable transmit power (O-DF with

ATP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

5.3.5 Opportunistic AF relaying with adjustable transmit power (O-AF with

ATP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

5.3.6 Partial relay selection with adjustable transmit power (PR with ATP) . . 56

5.3.7 Signaling requirements comparison . . . . . . . . . . . . . . . . . . . . . . 57

5.4 SEP Analysis of the relaying protocols . . . . . . . . . . . . . . . . . . . . . . . . 58

5.4.1 SEP analysis of the O-DF with FTP . . . . . . . . . . . . . . . . . . . . . 59

5.4.2 SEP Analysis of the O-AF with FTP . . . . . . . . . . . . . . . . . . . . . 60

5.4.3 SEP Analysis of the PR with FTP . . . . . . . . . . . . . . . . . . . . . . 62

5.5 Data rate and power consumption Analysis . . . . . . . . . . . . . . . . . . . . . 62

5.5.1 Data rate Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.5.2 Power Consumption Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 63


5.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

6 Spectrum Sharing Techniques for Broadcast Cognitive Radio Networks 72

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

6.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

6.3 Proposed transmission schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

6.3.1 Underlay with OBF transmission scheme (UO) . . . . . . . . . . . . . . . 75

6.3.2 Overlay with OBF and Interference Cancelation transmission scheme (OOIC) 77

6.3.3 Overlay with OBF and Cooperation transmission scheme (OOC) . . . . . 78

6.4 Outage probability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

6.4.1 Outage probability of PR . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

viii

6.4.2 Outage probability of SRs . . . . . . . . . . . . . . . . . . . . . . . . . . . 82


6.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

7 Spectrum Sharing Techniques for Bidirectional Communication 88

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

7.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

7.3 Spectrum Sharing Exploiting a Single-antenna Relay . . . . . . . . . . . . . . . . 91

7.3.1 The proposed Spectrum Sharing Scheme exploiting a single-antenna relay

(PSC-SAR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

7.3.2 Underlay Spectrum Sharing Scheme with single-antenna relay (U-SAR) . 94


7.4 Spectrum Sharing Exploiting Multi-antenna Relay . . . . . . . . . . . . . . . . . 97

7.4.1 The first proposed Spectrum Sharing Scheme using Beamforming (PSC-

OB1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

7.4.2 First underlay Spectrum Sharing Scheme using Beamforming (U-OB1) . . 102

7.4.3 The second proposed Spectrum Sharing Scheme using Beamforming (PSC-

OB2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

7.4.4 Second Underlay Spectrum Sharing Scheme using Beamforming (U-OB2) 105

7.4.5 Outage Probability and BEP Performance Analysis of PSC-OB1 . . . . . 106

7.4.6 Outage Probability Performance Analysis of PSC-OB2 . . . . . . . . . . . 108


7.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

8 Conclusion and Future Work Directions 117

Bibliography 120

A Derivation for Chapter III 129

A.1 Expression of ξi in (3.14) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

A.2 Derivation of double integrals given in the paper . . . . . . . . . . . . . . . . . . 129

A.3 Derivation of P(E ikcoop) in (3.17) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

A.3.1 Case 1: k is a “reliable” node . . . . . . . . . . . . . . . . . . . . . . . . 131

A.3.2 Case 2: k is an “unreliable” node . . . . . . . . . . . . . . . . . . . . . . . 131

ix

A.4 Derivation of P(RSel = i|R = Θ) . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

A.5 Distribution of A2(SDR)i defined in (3.3) . . . . . . . . . . . . . . . . . . . . . . . 132

A.6 Derivation of P(E ikcoop) in (3.21) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

A.6.1 Case 1: k ∈ ∆ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

A.6.2 Case 2: k ∈ ∆ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

B Derivations for Chapter V 135

B.1 Expression of MΓS,D(s) and MΓ

RO-DFs D

(s) in the presence of primary interference 135

B.2 Expression of MΓRO-DFs D

(s) in the absence of primary interference . . . . . . . . . 136

B.3 Expression of MγSRPR with FTP

s D(s) . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

C Derivation for chapter VI 138

C.1 Derivation of the PDF of γST,SRkgiven in (6.25) . . . . . . . . . . . . . . . . . . 138

C.2 Expression of Pr(γ2SRk

< 22Rths − 1) in (6.32) . . . . . . . . . . . . . . . . . . . . . 140

D List of Publications 141

x

List of Figures

2.1 Relaying communication with half-duplex nodes. (a) No cooperation. (b) Coop-

eration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.1 The selected relay forwards data to other nodes. . . . . . . . . . . . . . . . . . . 15

3.2 (a) Signaling overhead structure type I. (b) Signaling overhead structure type II. 16

3.3 Average BEP Comparison, STDR, γt = 2dB. . . . . . . . . . . . . . . . . . . . . 25

3.4 Average BEP Comparison, STDR, γt = 8dB. . . . . . . . . . . . . . . . . . . . . 25

3.5 Average BEP Comparison, STDR, γt = γ∗t . . . . . . . . . . . . . . . . . . . . . . 27

3.6 Average BEP Comparison, STAR, γt = γ∗t . . . . . . . . . . . . . . . . . . . . . . 27

3.7 Aggregate data rate Comparison: (a) STDR, (b) STAR for γt = γ∗t . . . . . . . . 29

4.1 Phase 1: S transmits a signal to D while the remaining N − 1 users listen. . . . . 34

4.2 Phase 2: A selected relay among “reliable” relays retransmits the source signal

to D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.3 BEP of cooperative MC CDMA systems using STDR for ITU Pedestrian B chan-

nels, N=3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.4 Effect of users numbers on BEP of cooperative MC CDMA systems using STDR

for ITU Pedestrian B channels, γt = 2dB. . . . . . . . . . . . . . . . . . . . . . . 40

4.5 Phase 1: S broadcasts a signal to D while relays listen . . . . . . . . . . . . . . . 41

4.6 Effect of time delay spacing on BER, L=2, M=2, γt = 6 dB . . . . . . . . . . . . 48

4.7 Throughput comparison for η = Tc, L=2, M=2 and γt = 6 dB . . . . . . . . . . 48

4.8 BER comparison for η = Tc, L=2, M=2 and γt = 6 dB . . . . . . . . . . . . . . . 49

5.1 System model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

5.2 Signaling overhead structure used by fixed transmit power relays. . . . . . . . . . 57

xi

5.3 Signaling overhead structure used by adaptive transmit power relays. . . . . . . . 58

5.4 SEP comparison of O-DF with FTP and O-DF with ATP (a) Mr=4 relays, (b)

Mr=2 relays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.5 Data rate comparison of O-DF with FTP and O-DF with ATP for Mr=4 relays

and Mr=2 relays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

5.6 Power consumption comparison of O-DF with FTP and O-DF with ATP for

Mr=4 relays and Mr=2 relays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

5.7 SEP comparison of O-AF with FTP and O-AF with ATP for Mr=4 relays . . . . 67

5.8 Data rate comparison of O-AF with FTP and O-AF with ATP for Mr=4 relays . 68

5.9 Power consumption comparison of O-AF with FTP and O-AF with ATP for

Mr=4 relays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

5.10 SEP comparison of PR with FTP and PR with ATP for Mr ==4 relays . . . . . 69

5.11 Data rate comparison of PR with FTP and PR with ATP for Mr =4 relays . . . 69

5.12 Power consumption comparison of PR with FTP and PR with ATP for Mr =4

relays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

6.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

6.2 The UO transmission signals process . . . . . . . . . . . . . . . . . . . . . . . . . 76

6.3 The OOIC transmission signals process . . . . . . . . . . . . . . . . . . . . . . . 77

6.4 The OOC transmission signals process during the nth sub-slot . . . . . . . . . . . 79

6.5 Primary average outage probability versus PT transmit power . . . . . . . . . . . 84

6.6 The rate of served SRs versus PT transmit power . . . . . . . . . . . . . . . . . . 85

6.7 The rate of served SRs versus ST transmit power . . . . . . . . . . . . . . . . . . 86

6.8 The rate of served SRs versus the secondary required data rate . . . . . . . . . . 87

7.1 System Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

7.2 (a) Time division access in the absence of SUs. (b) Time division access in the

presence of SUs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

7.3 Time division access if PUs are not in outage. . . . . . . . . . . . . . . . . . . . . 93

7.4 Time division access for SUs when Rabs < Rp. (a) Cooperation is needed (b)

Cooperation is not needed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

7.5 Underlay spectrum sharing scheme time division access. . . . . . . . . . . . . . . 94

7.6 Underlay spectrum sharing scheme time division access when PUs are silent. . . 95

xii

7.7 Average outage probability versus primary transmit SNR, Rp = 1 and Rs = 0.5

bits/s/Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

7.8 Average outage probability versus secondary maximum SNR, Rp = 1 and Rs =

0.5 bits/s/Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97


0.5 bits/s/Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

7.10 (a) Time division access for primary users in the absence of secondary users when

Rabs ≤ Rp (b) Proposed time division access for spectrum sharing . . . . . . . . . 103

7.11 (a) Primary transmission in the absence of secondary users (b) Underlay Spectrum

Sharing scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

7.12 Average outage probability versus γPT , Rp = 1 and Rs = 0.5 bits/s/Hz. . . . . . 112

7.13 Average outage probability versus γPT , Rp = 2 and Rs = 1 bits/s/Hz. . . . . . . 113

7.14 Average BEP versus Pmaxs , for γPT=10 dB. . . . . . . . . . . . . . . . . . . . . . 114

7.15 Average outage probability versus primary transmit SNR, Rp = 1 and Rs = 0.2

bits/s/Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115


0.2 bits/s/Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

xiii

List of Tables

3.1 Required CSI for the different RS schemes . . . . . . . . . . . . . . . . . . . . . . 20

5.1 Required CSI for the different RS schemes. . . . . . . . . . . . . . . . . . . . . . 58

7.1 Values of Pmaxr (watt) for Rp = 1, Rs = 0.5 ( bits/s/Hz) . . . . . . . . . . . . . 112

7.2 Values of Pmaxr (watt) for Rp = 2, Rs = 1 ( bits/s/Hz) . . . . . . . . . . . . . . 112

xiv

List of Acronyms

AF Amplify and Forward

AST based RS Average SNR Threshold based relay selection

ATP Adaptive Transmit Power

AWGN Additive White Gaussian Noise

BEP Bit Error Probability

BPSK Binary Phase Shift Keying

CDF Cumulative Distribution Function

CSI Channel State Information

D Destination

DS-CDMA Direct-Sequence Code Division Multiple Access

E2E End-to-End

FTP Fixed Transmit Power

MC-CDMA Multi-Carrier Code Division Multiple Access

MM RS Max-Min Relay Selection

MME RS Min Max Error Relay Selection

MGF Moment Generating Function

MRC Maximal Ratio Combining

xv

MIMO Multiple Input Multiple Output

M-QAM M-Quadrature Amplitude Modulation

OBF Orthogonal Beamforming

OC Optimum Combining

OOC Overlay with OBF with Cooperation

OOIC Overlay with OBF with post-Interference Cancelation

O-AF Opportunistic Amplify-and-Forward

O-DF Opportunistic Decode-and-Forward

PD Primary Destination

PDF Probability Distribution Function

PR Partial Relaying

PT Primary Transmitter

PU Primary User

QoS Quality of Service

R Relay

SEP Symbol Error Probability

SNR Signal-to-Noise Ratio

ST based RS SNR Threshold based relay selection

STAR Selective Threshold Analog Relaying

STDR Selective Threshold Digital Relaying

SINR Signal-to-Interference plus Noise Ratio

SR Secondary Receiver

SU Secondary User

xvi

UO Underlay with OBF

xvii

Chapter 1

Introduction

1.1 Motivation

The exploitation of the new information and communication technologies in all fields of life

has created an explosive demand in terms of high quality services. Future wireless systems

are provisioned to ensure services with high data rate, ubiquitous coverage and uninterrupted

connectivity. However, the wireless channels is highly vulnerable to several channels variations

effects such as path loss, shadowing, fading, etc. This makes the maintenance of a robust

and reliable wireless channels a difficult issue. In the other hand, the radio frequency spectrum

remains a limited and non-stretching natural resource. In addition, the majority of this spectrum

is allocated or auctioned to specific users with a license for a long period of time in a very wide

geographical area. In general, these licensed users are reluctant to share their spectrum resources

with intruder users, even competitors. Thus, the ever increasing demand for wireless services

burdens the available spectrum resources which become unable to satisfy this demand and suffer

from severe scarcity. In consequence, the world of wireless communications meets two major

difficulties: the unreliability of the wireless channels and the scarcity of the spectral resources.

Due to these blockades, the achievement of the required qualities of services (QoS) is not

a trivial issue. To mitigate the unreliability of the wireless channels, the diversity is proved to

be a powerful technique to increase the robustness of the wireless channels. There are several

types of diversity: spatial, temporal, frequency and polarization diversity. Recently, an efficient

spatial diversity techniques has been proposed by Sendoranis et al. relying on the cooperation

between mobile users called cooperative diversity [1],[2]. Its main idea is to exploit the broadcast

nature of the wireless medium to form a virtual antennas array by creating independent paths

1

between transmitter and receiver via the introduction of a relay. Cooperative diversity is a pow-

erful alternative of other spatial diversity techniques when the deployment of multiple antenna

is troublesome. In the other hand, to mitigate the scarcity of spectral resources, a promising

technology has recently emerged called cognitive radio [3]. It optimizes the spectrum resources

exploitation by using the licensed spectrum in an opportunistic fashion [4]. In this technology,

any cognitive secondary user may share the spectrum with a licensed primary user as long as the

former fulfills its QoS requirement. In this thesis, the application of cooperative communication

to improve the end-to-end (e2e) decoding performances in several wireless networks in investi-

gated. In the other hand, cooperative communication is exploited to enable spectrum access in

several cognitive radio networks. The main contributions are summarized below.

1.2 Contributions

1.2.1 Relay selection schemes in wireless networks

Single relaying schemes in Broadcast networks

Achieving the goal of reliably delivering data to all nodes in broadcast wireless networks is

very challenging since wireless channels may experience severe variations in signal strength and

channel impairments. To mitigate this problem, one or several relays can be used as collaborators

to forward the broadcasted signal to other nodes. In this work, we propose and investigate several

single relay selection schemes in broadcast wireless networks using either STDR or selective

threshold analog relaying (STAR). The nodes are classified into two sets. A set of “reliable”

nodes, whose source-node signal-to-noise ratio (SNR) exceeds a threshold value and a set of

“unreliable” nodes gathering the remaining ones. Then, one node among “reliable” nodes is

activated as a relay. We derive closed form expressions of the e2e Bit Error Probability (BEP) of

some proposed single relay selection schemes for STDR. The data rate loss due to the cooperation

is also studied. Analytical results along with simulations prove that compared to the direct

transmission, the single relay selection schemes improve signicantly the e2e BEP performance

of the broadcast network.

Selective and incremental relaying schemes in DS CDMA and MC CDMA networks

Besides the broadcast network, we have also been interested in the cooperative Direct-Sequence

Code Division Multiple Access (DS-CDMA) and Multi-Carrier Code Division Multiple Access

2

(MC-CDMA) networks. This interest is motivated by the fact that, in spite of their wide use,

no earlier work have addressed the relay selection in these kind of cooperative networks. In this

part, we derive the e2e BEP of cooperative MC-CDMA networks using selective threshold digital

relaying (STDR). We use the best relay selection where the activated relay is the relay with the

largest SNR in relay-destination link. The derived BEP results are valid for any multipath

intensity profile of the channel. In addition, we derive exact form expressions for the e2e and

throughput of DS-CDMA networks using incremental selective relaying which combines STDR

with incremental relaying protocols in the presence of multipath propagation. In STDR, a set

of potential relays whose received SNR exceeds a threshold value γt, called “reliable” relays, is

formed. Then, only the best relay among “reliable” relays is allowed to retransmit the received

signal. In incremental relaying, the cooperation is performed only when the destination requires

it. The derived results are valid for any multipath intensity profile of the channel and any path

delays. They also consider the correlation of the multipath gains. Simulation results along with

analytical studies of BEP and throughput prove that the combination of incremental relaying

with STDR in cooperative DS-CDMA systems improve significantly the throughput performance

and can achieve the maximum possible spatial diversity when it is required by destination.

1.2.2 Spectrum access schemes in cognitive radio networks

In the second part, we investigate the use of fixed transmit power by secondary transmitters

to access the spectrum without causing harmful interference to primary users. In addition,

we exploit relaying techniques to enable secondary users in cognitive radio networks access the

primary spectrum and transmit their data.

Performance comparison between fixed and adaptive transmit power in underlay

networks

This contribution consists in comparing the performance in terms of symbol error probability,

data rate and power consumption of the use of fixed transmit power (FTP) and adaptive trans-

mit power (ATP) in underlay cognitive radio networks. The use of FTP alleviates the signaling

requirements of underlay cognitive radio networks compared to the ATP. Nevertheless, the use

of FTP influences the performances of the underlay cognitive radio networks. To study this in-

fluence, we consider three relay selection schemes using FTP: opportunistic decode-and-forward

(O-DF), opportunistic amplify and forward (O-AF) and partial relay selection (PR). We com-

3

pare the performances of these schemes in terms of symbol error probability, data rate and power

consumption with three relay selection schemes using ATP: opportunistic decode and forward

with ATP (O-DF with ATP), opportunistic amplify-and-forward with ATP (O-AF with ATP)

and partial relay selection with ATP (PR with ATP). We provide exact and/or lower bound

expressions of the symbol error probabilities of O-DF, O-AF and PR with FTP. The analytical

study for the data rate and the power consumption is also provided. Our comparison study

shows that FTP has a positive impact on the data rate and power consumption performance

while it deteriorates the symbol error probability performance.

Spectrum Sharing Techniques for Broadcast Cognitive Radio Networks

This contribution consists in developing and investigating three broadcast transmission schemes.

The first one is simple and operates in underlay mode where the ST broadcasts its data simul-

taneously as the primary transmission. The second scheme operates in overlay mode where ST

helps the primary transmission by means of cooperative diversity transmission. Secondary re-

ceivers exploit a post-transmission interference cancellation technique to cancel the interference

caused by the primary transmission. The third scheme operates also in overlay mode and the

secondary network exploits also the cooperative diversity technique. The metric used to evalu-

ate the performance of secondary broadcast network is the rate of served SRs. We compare the

performances of the three schemes by simulations. Also, analytical expressions of the outage

probability for the first and second schemes are provided. Simulations along with analytical

results proved that our two overlay proposed schemes ensure low secondary outage probability

Spectrum access schemes for secondary bidirectional communications

In this work, we propose dynamic spectrum sharing protocols where a pair of secondary users

and a pair of primary users bidirectionally communicate. A secondary relay is deployed to assist

the secondary transmissions and improve the secondary access to the spectrum. We employ

a new time division access so that no interference may exist between primary and secondary

users. We investigate the cases where the relay has one antenna and multiple antennas. The

proposed scheme is then compared to the axiomatic and simple schemes where the secondary

users communicate with each other with the assistance of the relay in underlay mode. We study

and compare the performances of the two schemes in terms of outage probability. An upper

bound for the secondary outage probability of the proposed scheme is derived. Our simulation

4

results prove that the proposed schemes significantly outperform the underlay spectrum sharing

schemes while the primary outage probability is kept identical to the case where secondary users

were absent.

1.3 Organization

The reminder of this thesis is divided into seven chapters and is organized as follows. In chapter

II, we give a brief overview about cooperative communication and cognitive radio. Chapter III

investigates single relay selection techniques in cooperative broadcast networks. In chapter IV,

we present our work on analytical studies of cooperative relaying protocols on cooperative DS-

CDMA and MC-CDMA networks. Chapter V is dedicated to the presentation of our works on

the performance analysis of relaying schemes using fixed transmit power and adaptive transmit

power nodes in underlay cognitive radio networks. Chapter VI is dedicated to the presentation of

spectrum sharing techniques for broadcast networks. In chapter VII, we propose spectrum char-

ing techniques for bidirectional communications. Finally, chapter VIII draws some concluding

remarks and a summary of our findings.

In the beginning of each chapter, the literature which is particularly relevant to that chapter is

reviewed. Wherever necessary, the references that are relevant to multiple chapters are reviewed

more than once, from each chapters viewpoint. A list of the papers published are also given as

an appendix.

5

Chapter 2

Background on Cooperative

Communication and Cognitive Radio

In wireless communications, the transmitted signal encounters reflectors, scattering objects and

attenuators during propagation. Thus, the receiver detects multiple copies of the signal each

has travelled through different paths. The superposition of these different copies of signals is

not always constructive leading to a mutipath induced fading. To mitigate fading in wireless

communication, some kinds of diversity must be implemented. One of the most promising

and effective diversity techniques is the cooperative diversity. In this chapter, we will give an

overview about the different aspects of the cooperative diversity. In section 2.1, we present the

cooperative diversity and the preliminaries of multihop relaying. In section 2.2, we give a brief

overview about the software defined radio and the cognitive radio network paradigms. In section

2.3, we give some concluding remarks.

2.1 Cooperative Communication

2.1.1 Cooperative Diversity

In wireless networks, the transmitted signal can be heard by all the users situated around the

source. The broadcast nature of the wireless communication can be exploited to induce a spatial

diversity at the destination user (DU) by making one or multiple user, among the users which

have heard the transmitted signal destined to DU, re-forward this signal. Given the independent

channels statistics between the different users and the DU, then DU can combine the different

6

copies of the signal. The induced spatial diversity is called cooperative diversity. One of the first

studies that introduced the concept of cooperative diversity was realised by Sendonaris et al. [1].

In this paper, an uplink scenario is considered, in which two users cooperate by relaying data for

each other. After showing the potential of cooperation in enlarging the achievable rate region of

the two users, the authors demonstrated that cooperation can improve other measures such as

outage capacity, error probability and coverage. The first practical cooperative relaying protocols

have been proposed by Laneman et al. in [5]. In this paper, the authors identified different classes

of cooperative diversity protocols such as fixed protocols, in which the relay always retransmits,

selective protocols, in which the relay retransmits only when it decodes reliably, and incremental

protocols, in which the relay retransmits only when the direct transmission fails.

2.1.2 Preliminaries of Multihop Relaying

Relaying protocols can be classified into two categories according to the processing performed

at the relay: Analog Relaying (AR) and Digital Relaying (DR) [6]. AR can be implemented in a

very primitive way in which the relay has just to retransmit the received signal. In DR, the relay

performs detection and has to generate a noise-free version of the original signal based on his

own detection. The decoded version of the signal has then to be modulated and retransmitted.

AR and DR incur different limitations in practice. In DR the decoding and the remodulating

of the signal consumes the relay energy and causes more latency than AR. In the other hand,

if error correction must be performed, the relay has to be computationally efficient. All these

operations make the DR more complicated and costly than the AR. However, the AR can cause

constant interference to the rest of the network. Moreover the retransmitted signal by the relay

is affected by the noise.

The relay nodes can operate in half-duplex or full-duplex mode. In full duplex mode, the

relay can transmit and receive at the same time and in the same frequency band. To imple-

ment full-duplex communication, the self-interference must be efficiently cancelled or reduced.

Nevertheless, in practice the mitigation of self-interference in full-duplex communication is not

a straightforward issue and constitutes today the most active research area. The half-duplex

nodes are simpler for implementation, However half-duplex communication requires the use of

orthogonal channels for the transmission and the reception which deteriorates significantly the

spectral efficiency. We consider a basic cooperative network composed of three nodes. a source

S, a relay R and a destination D. We assume that all the nodes are half-duplex. In Fig. 2.1, we

7

present a relaying communication.

BER performance of AR deteriorates at low Signal-to-noise ratio (SNR) since analog relays

amplify both the noise and the information bearing parts of the received signal. In the presence

of distance dependent attenuation only, DR performs significantly better than AR [7]. In Fig.2.1

S

R

D

S → D

TS

S→D R→D

1/2 TS

(a)

(b)

Figure 2.1: Relaying communication with half-duplex nodes. (a) No cooperation. (b) Coopera-

tion.

(a), the source sends its data to D during the whole time slot. If cooperative communication

is used, the time slot is divided into two orthogonal sub-slots. This is shown in Fig.2.1 (b). In

the first sub-slot, the source sends the data to D while R listens. In the second sub-slot, the

relay will retransmits the received signal according to AR or DR processing. With this protocol,

relaying can be easily integrated to wireless networks using time-division multiple access. As

the number of hops increases, the number of time slots allocated for delivering data from the

source to the destination increases.

8

2.2 Cognitive Radio

Data communication networks are an essential component of any modern society. They are

extensively used in several services and applications, including financial transactions, social

interactions, education, national security, commerce, tourism, etc. In particular, both wired

and wireless devices are capable of realizing a plethora of advanced functions that support

a wide range of services, such as web browsing, voice telephony and streaming multimedia,

and data transfer. With the rapid growth of demand in terms of communication services,

the electromagnetic spectrum become very crowded. The electromagnetic spectrum, and in

particular the so-called radio frequency portion of this spectrum, is rapidly becoming one of

our Global most valuable and precious natural resources. It has no inherent functionality, yet

it is viewed as a sufficiently scarce and valuable resource that relatively small portions of this

commodity, as measured in spectral and geographic dimensions, command prices measured in

billions of American dollars. To mitigate the scarcity of spectrum resources, Cognitive Radio

has emerged as an efficient and powerful technique promising radical changes [4]. With the rapid

evolution of microelectronics, wireless transceivers are becoming more versatile, powerful, and

portable. This has enabled the development of software-defined radio technology, where the radio

transceivers perform the baseband processing entirely in software: modulation/demodulation,

error correction coding, and compression. Next, we give a brief overview about the software-

defined Radio and the different Cognitive Radio network paradigms.

2.2.1 Software-defined Radio

Software-defined radio refers to technologies wherein the functionalities of a wireless node are

performed by software modules running on digital signal processors, field programmable gate

arrays , general-purpose processors, or a combination thereof. This enables programmability of

both Digital Down Converter/Digital Uplink Converter and base-band processing blocks. Hence,

operation characteristics of the radio, such as coding, modulation type, and frequency band,

can be modified simply by loading a new software. Also multiple radio devices using different

modulations can be replaced by a single radio device that can perform the same operations. If

the Analog Digital/Digital Analog conversion can be pushed further into the Radio Frequency

block, the programmability can be extended to the Radio Frequency front end and an ideal

software radio can be implemented. However, there are a number of challenges in the transition

9

from hardware radio to software (-defined) radio. First, transition from hardware to software

processing results in a substantial increase in computation, which in turn results in increased

power consumption. However, this reduces significantly the battery life. The software-defined

radio are exploited to form cognitive radio networks. Each software-defined radio represents a

cognitive user.

2.2.2 Cognitive Radio network paradigms

Upon the network side information and environment awareness that cognitive users have, there

are three different Cognitive Radio approaches or paradigms; Underlay, Overlay and Interweave

[3].

Underlay paradigm: Underlay paradigm allows cognitive users simultaneously transmit with

non-cognitive users, owners of the license of the considered portion of spectrum, assuming that

they can control the interference they cause to non-cognitive users and that they can keep the

level of this interference below a predefined threshold [3]. Particulary, cognitive users need Chan-

nel Side Information to estimate how will their transmission affect or interfere to non-cognitive

users. To measure the level of interference at non-cognitive users, Federal Communications

Commission introduced a concept called Interference Temperature. The so-called interference

Temperature measures the Radio Frequency power available at the receiving antenna to be deliv-

ered to a receiver, reflecting the power generated by other emitters and noise sources [8], limiting

the amount of the interference that the non-cognitive user could authorize. This interference

constraint at the receiver can be modelled as a power constraint at the cognitive transmitter,

where optimal power adaptation is similar to the water filling case. Capacity is achieved by

Gaussian code book when the cognitive transmitter has complete Channel Side Information [3].

Overlay paradigm: In Overlay paradigm, cognitive users require Code book Side Informa-

tion as well as the messages that non-cognitive users send. This knowledge is used to mitigate

interference or sometimes even completely cancel it. In this way, cognitive users can transmit si-

multaneously with non-cognitive users by assigning part of their transmit power to assist or relay

non-cognitive users. Since cognitive users know the message and the code book used to code this

message, they can use different coding schemes so that both their data rate and non-cognitive

users data rate is improved. The cognitive transmitter can use several coding schemes such as

Superposition Coding and Dirty Paper Coding. However, the best coding scheme known at the

10

moment is Rate-splitting. In some cases, e.g. strong interference (Superposition Coding achieves

capacity without requiring Rate-splitting), Gaussian channel in weak interference (which is sum

capacity optimal after Dirty Paper Coding) or Common Information (Rate-splitting and Super-

position Coding achieve capacity), capacity can be determined. Nevertheless, in most of the

cases the reachable capacity is still unknown. In fact, one of the main research focus of Overlay

paradigm is to characterize the capacity region for a general case [3].

Interweave paradigm: Interweave paradigm consists on identifying available spectrum por-

tions for a specific temporary location and time and exploiting these spectrum holes for cognitive

unlicensed transmissions. It is based on Dynamic Opportunistic Access and pretends to benefit

from under used spectrum. In this case, instead of the Channel State Information (CSI) or

the Code book, some Activity Side Information is required. To get the occupancy information

necessary to determine spectrum holes, accurate sensing has to be implemented [3].

2.3 Conclusion

In this chapter, we gave a brief overview about the cooperative communication namely the

preliminaries of relaying and the cooperative diversity approach. We have particulary indi-

cated that relaying can be classified into two categories namely Digital Relaying and Analog

Relaying. Then, we have introduced the Cognitive Radio Technologies. We have described the

specificities of the Software Defined Radio and its adaptability in implementing Cognitive Radio

technology. Then we gave an overview about the different paradigms of cognitive radio networks

namely, Underlay, Overlay and Interweave paradigms. In the next chapters, we will present our

contributions in the fields of cooperative communication and Cognitive Radio.

11

Chapter 3

Single relay selection in Broadcast

Wireless Networks

3.1 Introduction

Broadcasting is a widely used technique in wireless networks that allows simultaneous transmis-

sion of a signal to multiple destinations. Examples of broadcasting can be found in traditional

cellular networks where a base station delivers messages to mobile users, or in a sensor network

where a data fusion center sends command information to multiple sensors. The main goal in a

broadcast network is to reliably deliver the broadcasted signal to the whole destinations. How-

ever, the achievement of this goal is not a straightforward issue since wireless channels between

the source and destinations may experience severe and independent fading conditions.

To mitigate this problem, cooperative diversity can be exploited to create a virtual array of

antennas and induce spatial diversity [1]-[5]. The idea is to generate independent paths between

the source and a destination by introducing relay node(s) whose mission is to re-forward the

broadcasted signal.

Cooperative diversity in broadcast networks have been exploited and investigated in earlier

works [9]-[17]. The authors of [9] and [10] exploit cooperative diversity with relays using space-

time block codes for broadcasting. Orthogonal transmissions have been assumed in [12]-[15]. In

[12] nodes in a broadcast network can accumulate received power from successive transmissions.

In [13], Hong et al. analyse the energy savings provided by a form of cooperative broadcast

transmission, called the Opportunistic Large Arrays (OLA). Two energy efficient schemes have

been proposed in [14]: OLA-threshold for general OLA transmission and OLA Concentric Rout-

12

ing Algorithm for upstream routing in the topology of wireless sensor networks. A centralized

and distributed cooperative broadcast algorithms have been proposed in [15]. In [16], inactive

nodes are used as relays and exploited as an extra dimension for performance improvement in

broadcast networks. In [17], Sirkeci et al. assume non orthogonal transmissions and a source

node initiates the broadcast by transmitting a packet. Every node having a signal-to-noise ratio

(SNR) higher than a predetermined threshold forwards the same packet till data reaches all

nodes. However, this is inefficient for broadcast networks not authorizing simultaneous trans-

missions since to transmit one block, we need as many time slots as the number of forwarding

nodes. Thereby, the investigation of efficient single relay selection (RS) schemes in broadcast

networks is interesting. Comparing to the use of multiple relays, the main advantage that can

be availed by the use of single RS schemes is the enhancement of the reliability of signals in

broadcast networks with half-duplex nodes without dramatically deteriorating the performance

in terms of data rate.

There are many studies investigating single RS in unicast networks, [18]-[27]. But, these

techniques can not be applied in the broadcast networks. This is because of the particularity

of broadcasting where the data has to reach N destinations. In unicast transmissions, only

one destination is considered and hence a candidate relay has one source-relay channel and

one relay-destination channel contrarily to broadcast networks where a candidate relay has

one source-relay channel and multiple relay-destination channels. Thereby, single RS schemes

proposed in literature for non broadcast networks can take into account the quality of only

one relay-destination channels and thus can not be applied in broadcast networks. The only

technique found in literature that can be used in our case is partial RS scheme. Partial RS

scheme was firstly proposed for analog relaying (amplify-and-forward) in [28] and extended to

digital relaying (decode-and-forward) in [29]. As described in [28], partial RS scheme selects

the relay with the largest SNR in source-relay channel. It was motivated by the requirement of

partial (channel state information) CSI (CSI of source-relay channels only) instead of full CSI

knowledge, i.e., CSI of source-relay, and relay-destination channels. By definition, partial RS

scheme, ignores relay-destination channels qualities and thus it is indifferent if the candidate

relay has one relay-destination channel or multiple relay-destination channels. Thereby, partial

RS scheme can be used in non broadcast networks as well as in broadcast networks. But, as

this RS scheme rely on partial CSI knowledge, it suffers from a lack of efficiency.

In this chapter, we propose and investigate efficient single relay selection schemes for broad-

13

cast networks. The destination nodes whose received source-node SNR are above a predeter-

mined threshold value are called “reliable” nodes and one relay of them is selected to cooperate

and help the source node. This approach avoids the need to involve auxiliary nodes to act as

candidate relays as in [16]. The considered broadcast network uses STDR or STAR. In STDR,

only a single relay among “reliable” relays, cooperates by decoding the signal and forwarding

it. In STAR, only a single relay among “reliable” nodes cooperates by amplifying the signal

and forwarding it. BEP expressions of some of the proposed single relay selection schemes are

derived for STDR. The data rate loss caused by cooperative transmissions is also studied. Both

analytical and simulation results show that compared to the direct transmission, cooperative

transmission using our RS schemes improves significantly the performance in terms of BEP of

the broadcast network at the price of a loss in data rate. Hence, it is very interesting for ap-

plications requiring low BEP performance. Moreover, our simplest and least efficient scheme

requires no CSI at all and has better performance than partial RS scheme existing in literature

The remainder of this chapter is organized as follows. In section 3.2, we describe the system

model. In section 3.3, we present our proposed single RS schemes for broadcast networks.

Section 3.4 is dedicated to the end-to-end (e2e) BEP analysis of the first proposed RS scheme

called Average SNR threshold based RS (AST based RS) while section 3.5 is dedicated to the

e2e BEP analysis of the second proposed RS scheme called SNR threshold based RS (ST based

RS). Numerical results are shown and discussed in section 3.6, followed by a summary of our

main findings and contributions in section 3.7.

Notation: The instantaneous received SNR, the channel coefficient and the noise term of a

channel (kl) are denoted by γkl, hkl and nkl, respectively. The bit error event that occurs when

a node j combines the incorrectly regenerated relay signal forwarded by a “reliable” node i and

the source signal is referred as error propagation and denoted by E ijprop. The term cooperative

error is used to refer to the event that a bit error occurs when a node j combines the correctly

regenerated relay signal and the source signal. It is denoted by E ijcoop. The bit error event at

a channel (k l) between two nodes k and l is denoted by Ekl. The e2e bit error event at

a node k is denoted by Ek. P(E) denotes the probability of the event E and fX denotes the

probability density function (PDF) of the random variable X. For a given set ζ, ζ and |ζ| denote

its complement and cardinality, respectively.

14

3.2 System Model and Problem Statement

3.2.1 Assumptions

U1

Uj

UNd

R1

Ri

RNr

Source (S)

Unreliable node (γSUj< γt)Reliable node (γSRi

≥ γt)

Selected relay

Figure 3.1: The selected relay forwards data to other nodes.

We consider a cooperative network as shown in Fig. 3.1, where a single source noted S

broadcasts data towards N destinations. All nodes are equipped with a single antenna. More-

over, they are half-duplex and thus cannot transmit and receive simultaneously. Without loss

of generality, we assume that all transmissions use binary phase shift keying (BPSK) modula-

tion. The extension to other modulation schemes is straightforward. All channels experience

independent Rayleigh fading and path loss attenuation. The received signal at node l from the

node k is denoted by ykl =√Pkhklxk + nkl, where Pk and xk are the transmit power and the

transmitted symbol by node k, respectively. The channel between two nodes k and l is assumed

to consist of path loss and independent fading effect as hkl = Xkld−α

2kl , where dkl is the distance

between k and l and α is the path loss exponent. Xkl is the fading coefficient modeled as a

circular symmetric complex Gaussian random variable with variance 1. A time slot is used as

a time unit. Channels coefficients may vary independently each two time slots. The noise, nkl,

is modeled as an Additive White Gaussian Noise (AWGN) with two sided spectral density N0.

The instantaneous received SNR, γkl, is an exponential random variable with mean σ2kl.

15

3.2.2 Relaying scenario

Communication time is equal to two time slots. We use two-phase communication scenario,

except in some particular cases detailed at the end of this subsection. In the first phase, during

the first time slot, the source broadcasts a symbol x. The received signal at a destination

l, l = 1 . . . N is denoted by ySl =√PShSlx + nSl. As shown in Fig. 3.1, we can classify the

destinations into two sets. The first one is named the set of “reliable” nodes and is denoted by

R = R1, . . . Ri, . . . RNr, where Nr is the number of “reliable” nodes. It gathers nodes whose

source-node SNRs exceed a given threshold γt. The second set of “unreliable” nodes is denoted

by U = U1, . . . Uj , . . . UNU, where NU is the number of “unreliable” nodes.

Following the building of the two sets, a suitable relay selection scheme is needed to select

one “reliable” node belonging to R .

Node Id CSIT

(a)

CSIR IdNode Id CSIR IdT . . .

(b)

Figure 3.2: (a) Signaling overhead structure type I. (b) Signaling overhead structure type II.

In the second phase, we distinguish between two cases: STAR and STDR. When STAR is

used, a selected “reliable” node i amplifies and forwards the received signal using an amplification

factor given by Gi =√

PiPS |hSi|2+N0

, where Pi and PS are the transmit power used by the relay

and the source, respectively. In the second case, when STDR is used, a selected “reliable” node

first decodes the signal, re-encodes it, and then retransmits it.

The forwarded signal will be decoded by the other destinations nodes as shown in Fig. 3.2.

These nodes use a maximum ratio combiner (MRC) to combine the signals received from both

the relay and the source. Hence, to get the data to all N nodes, two transmission cycle have to

be performed. Meanwhile, if R is an empty set (R = ∅) or if all the N nodes are classified as

“reliable” (R = 1, . . . N) , only one transmission cycle is performed since in these particular

cases, cooperation is not performed and the source transmits the next data during the second

time slot to avoid that the system remains idle.

16

3.3 Relay Selection

In this section, we present the proposed strategies for the single relay selection in the broadcast

network. Our single relay selection schemes are based on centralized approaches. The source

acts also as a central schedular that collects CSI and selects the suitable relay. Methods to

obtain a global knowledge about CSI in some efficient way will be subsequently detailed.

3.3.1 Average SNR Threshold based relay selection (AST based RS)

In this RS scheme, for each relay, we take into account the average combined SNR of direct and

relaying channels (i.e., average SNR at the output of the MRC combiner). The selected relay is

chosen to be the one providing an average combined SNR larger than γt for the largest possible

number of “unreliable” nodes. Mathematically, this can be expressed as follows.

If STDR is used, let A1(STDR)i denote the number of nodes j for which the “reliable” node

i, (i.e., i is a node belonging to R ), can verify γSj + γij > γt. A1(STDR)i is given by

A1(STDR)i =

∑j∈U

H(γSj + γij − γt). (3.1)

The selected relay R1(STDR)Sel , is chosen as R

1(STDR)Sel = argmax

i∈RA1(STDR)

i .

If STAR is used, let A1(STAR)i denote the number of nodes j for which the “reliable” node i,

can verify γSj + γeqSij > γt. A1(STAR)i is given by

A1(STAR)i =

∑j∈U

H(γSj + γeqSij − γt), (3.2)

where X denotes the average of X, H(z) is the Heaviside step function, which is equal to 0 if

z is negative and 1 otherwise, γeqSij =γSiγij

γSi+γij+1 is the equivalent SNR of the relaying channel

(S − i− j). The selected relay R1(STAR)Sel , is chosen as R

1(STAR)Sel = argmax

i∈RA1(STAR)

i .

If more than one candidate relay has the largest metric, this RS scheme selects randomly one

of them. Since this scheme consider average SNRs, the final decision is based on the location of

the nodes. This scheme doesn’t require instantaneous CSI feedback since the central schedular

(source) is assumed to know in advance the locations of the different nodes.

3.3.2 SNR Threshold based Relay Selection (ST based RS)

The ST based RS decisions are based on the instantaneous SNR of direct and relaying channels.

It selects the relay that offers a combined SNR larger than the predetermined threshold γt for

17

the largest possible number of “unreliable” nodes. Thus, they will likely decode the broadcasted

signal with no errors. Mathematically, this can be expressed as follows.

If STDR is used, let A2(STDR)i denote the number of nodes j for which the “reliable” node

i, i is a node belonging to R , can verify γSj + γij > γt. A2(STDR)i is given by

A2(STDR)i =

∑j∈U

H(γSj + γij − γt). (3.3)

The selected relay is chosen based on the following criterion

R2(STDR)Sel = argmax

i∈RA2(STDR)

i . (3.4)

If STAR is used, let A2(STAR)i denote the number of nodes j for which a “reliable” node i,

can verify γSj + γeqSij > γt. A2(STAR)i is given by

A2(STAR)i =

∑j∈U

H(γSj + γeqSij − γt). (3.5)

The selected relay is chosen based on the following criterion

R2(STAR)Sel = argmax

i∈RA2(STAR)

i . (3.6)

If more than one candidate relays has the largest metric, the ST based RS selects randomly

one of them.

The ST based RS requires a perfect knowledge about the CSI of several channels in the

network. As mentioned in section 3.2, the CSI are assumed to be invariant during two time

slots and may change independently each two time slots. In the following, we describe a way to

acquire enough CSI knowledge.

After the first transmission, each node should compare the SNR of its direct channel to the

used threshold and know if it is classified as a “reliable” or “unreliable” node. At the beginning

of the second time slot, only “unreliable” nodes inform the source about the CSI of their direct

channels and the CSI of their channels towards “reliable” nodes which are often measured with

the assistance of explicit training sequences (i.e. pilot signals), e.g. [30], using explicit feedback

messages. Clearly, “reliable” nodes do not need to feedback any information since we assume

channel reciprocity. Knowing the identities of “unreliable” nodes, the source easily recognizes

that the rest of nodes are “reliable”. Consequently, the source will have enough CSI knowledge

to calculate metrics and select the suitable relay.

18

3.3.3 Max-Min Relay Selection (MM RS)

This scheme selects the “reliable” node that offers the best possible combined SNR at each

“unreliable” node. The first step is to determine the lowest SNR that could be offered by each

“reliable” node. Then, the node which offers the largest value of the lowest combined SNRs is

selected. According to the used relaying protocol (STAR or STDR), MM RS can be formulated

as follows.

If STDR is used, MM RS can be formulated as

R3(STDR)Sel = argmax

i∈Rminj∈U

γSj + γij. (3.7)

If STAR is used, MM RS can be formulated as

R3(STAR)Sel = argmax

i∈Rminj∈U

γSj + γeqij , (3.8)

where R3(STDR)Sel and R

3(STAR)Sel are the selected relay by the MM RS when using STDR and

STAR, respectively.

This RS scheme requires the CSI of direct channel and potential relaying channels. The same

method described in the previous subsection can be used to know the CSI of these channels.

3.3.4 Min Max Error Relay Selection (MME RS)

In this scheme, the selected relay is the one that minimizes the maximum of e2e instantaneous

BEPs through the N nodes.

If STDR is used, for a given “reliable” relay i, the maximum of e2e instantaneous BEPs

through the N nodes is given by

A4(STDR)i = max

j∈1...N\i

1

2Q(√

2γSi) + (1−Q(√

2γSi))Q

(√2(γSj + γij)

), Q(√

2γSi

),

(3.9)

where 12 is the worst case value of the instantaneous probability of error propagation, Q(

√2γSi)

is the instantaneous probability of bit error at relay i and Q(√

2(γSj + γij))is the instantaneous

probability of cooperative error at destination j. The selected relay R4(STDR)Sel is given by

R4(STDR)Sel = argmin

i∈RA4(STDR)

i . (3.10)

If STAR is used, for a given “reliable” relay i, the maximum of e2e instantaneous BEPs

through the N nodes is given by

A4(STAR)i = max

j∈1...N\i

Q(√

2(γSj + γeqSij)), Q(√

2γSi

). (3.11)

19

AST based RS• No CSI

Partial relay selection• CSI of S-Ri, Ri ∈ 1, . . . , N

ST based RS

• CSI of S-Ri, Ri ∈ R

• CSI of Ri-Uj , i ∈ R, Uj ∈ U

MM RS


• CSI of Ri-Uj , Ri ∈ R, Uj ∈ U

MME RS

• CSI of S-Ri, Ri ∈ 1, . . . , N


• CSI of Ri-Uj , Ri ∈ R, Uj ∈ U

Table 3.1: Required CSI for the different RS schemes

where Q(x) =∫∞x

1√2π

exp(−z2/2)dz.

This RS scheme is very complicated for practical implementation since it requires full CSI

knowledge of all the channels in the network and high computational capacities. It is considered

in this work for performance comparison purposes only.

The CSI required by the different proposed RS schemes along with the partial RS scheme

are summarized in Table 3.1. The “unreliable” nodes must indicate to the source the CSI of its

direct channels as well as the CSIs of its different channels towards “reliable” nodes. Hence, we

distinguish between two types of signaling overhead structures. In Fig. 3.2 (a), we present the

first type used by “unreliable” nodes to deliver the CSIs of their direct channels to the central

scheduler (source). It has three fields. To help the source recognize the overhead structure, a

bit indicating the type (T) of the signaling overhead is appended in the first field. Then, the

“unreliable” node indicates its identity (Node id) in the second field. The latest field contains

20

the CSI of the source-node channel in consideration. In Fig. 3.2 (b), we present the signaling

overhead structure of type II used by “unreliable” nodes to provide the CSI of their channels

towards all the “reliable” nodes. Type II structure has 2(Nr + 1) fields. The two first fields are

identical to the type I structure. The third field contains the identity of a given “reliable” node

(R Id) and the next field contains the CSI of the channel toward the considered “reliable” node.

The “unreliable” node continues to append the R Id and the corresponding CSI in this manner

till the CSI towards all the “reliable” nodes are indicated.

3.4 E2E BEP Derivation of the AST based RS using STDR

In this section, we derive the e2e BEP of the AST based RS in the considered broadcast network

using STDR with an SNR threshold γt. The average e2e BEP at a given node k (among the N

destinations) is denoted by BEP 1k (γt) and is given by

BEP 1k (γt) =

∑Θ⊂1,...,N

P(R = Θ)P(Ek|R = Θ), (3.12)

where Θ denotes a possible subset of “reliable” nodes. Next, we derive each terms in (3.12) as

a function of the average values of SNRs. Since γXY is an exponential random variable with

mean σ2XY , the probability that only nodes in Θ are “reliable”, i.e., their SNRs are higher than

γt, is given by

P(R = Θ) =∏i∈Θ

e−γt/σ2Si

∏j∈Θ

(1− e−γt/σ2Sj ), (3.13)

where Θ = 1, . . . , N\Θ. According to our system setup, cooperation is not performed when

the set of “reliable” relays is empty (|R | = 0) and when all the N nodes are “reliable” (|R | = N).

Thus, the second term of (3.12) will be firstly derived for 1 ≤ |R | < N , and then we discuss the

particular cases where |R | = 0 and |R | = N .

If 1 ≤ |R | < N , then the second term of equation (3.12) can be written as

P(Ek|R = Θ) =∑i∈Θ

ξiP(Ek|R = Θ, RSel = i), (3.14)

where RSel denotes the selected relay and the expression of ξi is given in appendix B.1.

When k is the selected relay, it forwards the received signal to other nodes and thus will not

benefit from cooperation. Hence, to calculate the conditional probability P(Ek|R = Θ, RSel = i),

we distinguish between two cases: k is the selected relay and k is not the selected relay.

21

3.4.1 Case 1: k is the selected relay

In this case, the conditional probability P(Ek|R = Θ, RSel = k) is given by

P(Ek|R = Θ, RSel = k) =

∫ ∞

γt

Q(√

2γ)fγSk|γSk>γt(γ)dγ. (3.15)

The expression of this integral is given by [31]

P(Ek|R = Θ, RSel = k) = Q(√2γt)− exp(

γtσ2Sk

)

√σ2Sk

1 + σ2Sk

Q

(√2γt(1 +

1

σ2Sk

)

). (3.16)

3.4.2 Case 2: k is not the selected relay

In this case, the node k will benefit from cooperation and the conditional probability P(Ek|R =

Θ, RSel = i) is given by

P(Ek|R = Θ, RSel = i) = P(ESi|γSi > γt)P(E ikprop) + (1− P(ESi|γSi > γt))P(E ik

coop), (3.17)

where the probability of error propagation can be approximated by the worst case value i.e.,

P(E ikprop) ≈ 1

2 [32] and [33]. The expression of P(ESi|γSi > γt) can be obtained by replacing σ2Sk

by σ2Si in (3.16) and the expression of P(E ik

coop) is derived in appendix A.3. Using appendix A.3

and (3.17), we obtain the expression of P(Ek|R = Θ, RSel = i) when k is not the selected relay.

For each case, we substitute in (3.14) the corresponding expression of P(Ek|R = Θ, RSel = i)

and the expression of ξi given in appendix B.1 to obtain the expression of P(Ek|R = Θ). By using

the obtained result, (3.12) and (3.13), we obtain the expression of BEP 1k (γt) when 1 ≤ |R | < N .

When |R | = N and |R | = 0, the e2e BEP can be straightforwardly developed using similar

derivations to the ones presented in this section.

3.5 E2E BEP Derivation of the ST based RS using STDR

In this section, we derive the e2e BEP of the ST based RS using STDR with an SNR threshold

γt. Considering a destination node k, k = 1 . . . N , the average e2e BEP at k is denoted by

BEP 2k (γt) =

∑Θ⊂1...N

P(R = Θ)P(Ek|R = Θ), where P(R = Θ) is given by (3.13) and P(Ek|R =

Θ) will be derived through this section.

We first consider the case of 1 ≤ |R | < N , and then we discuss the particular cases where

|R | = 0 and |R | = N .

22

For 1 ≤ |R | < N , if k is a “reliable” node, then its direct SNR γSk is higher than γt.

Otherwise, if k is an “unreliable” node, then γSk is below γt. Thus, to derive P(Ek|R = Θ), two

cases arise: k is a “reliable” node and k is an “unreliable” node.

3.5.1 case 1: k is a “reliable” node

In this case, the conditional probability P(Ek|R = Θ), can be written as


P(RSel = i|R = Θ)P(Ek|R = Θ, RSel = i), (3.18)

where P(RSel = i|R = Θ) is derived in appendix C.1 and P(Ek|R = Θ, RSel = k) is given by

(3.16) if k is the selected relay and by (A.4) otherwise. Using appendix C.1, (3.16), (A.4) and

(3.18), we obtain the expression of P(Ek|R = Θ) when k is a “reliable” node.

3.5.2 Case 2: k is an “unreliable” node

In this case, for the derivation of P(Ek|R = Θ), let Vij = γSj + γij |γSj < γt, where i denotes a

“reliable” node and j denotes an “unreliable” node. Note that Vik may be higher or less than

γt. Let Ω denote the set of nodes j belonging to U with an SNR Vij higher than γt. Hence, the

conditional probability P(Ek|R = Θ) can be written as follows


∑∆⊂U

P(Ω = ∆, RSel = i|R = Θ)P(Ek|R = Θ,Ω = ∆, RSel = i),(3.19)

where ∆ is a possible subset of U. Next, we derive each term of (3.19).

Similar to the derivation of P(RSel = i|R = Θ) in appendix C.1, the first term of (3.19) is

obtained as

P(Ω = ∆, RSel = i|R = Θ) = P(ATi = |∆|)

∏j∈∆

ϕij(γt)∏j′∈∆

(1− ϕij′(γt))

∏i1∈Θ\i

|∆|−1∑q=0

P(ATi1 = q)

+∑

Θ′⊂Θ\i

∏i2∈Θ′

P(ATi2 = |∆|)

∏i3∈Θ′

|∆|−1∑q=0

P(ATi3 = q)

1

|Θ′|+ 1

, (3.20)

where ∆ = U\∆.

The second term of (3.19) can be written as

P(Ek|R = Θ,Ω = ∆, RSel = i) = P(ESi|γSi > γt)P(E ikprop) + (1− P(ESi|γSi > γt))P(E ik

coop),

(3.21)

23

where E ikprop ≈ 1

2 , P(ESi|γSi > γt) is obtained by replacing σ2Sk by σ2

Si in (3.16) and P(E ikcoop) is

derived in appendix A.6.

Using appendix A.6, (3.16) and (3.21), we obtain the expression of P(Ek|R = Θ,Ω =

∆, RSel = i). By replacing the expression of P(Ek|R = Θ,Ω = ∆, RSel = i) and (3.20) in

(3.19), we obtain the expression of P(Ek|R = Θ) when k is an “unreliable” node.

For each case, we substitute the final expression of P(Ek|R = Θ) and (3.13) in (3.12), to

obtain the expression of BEP 2k (γt) when 1 ≤ |R | < N .

The cases where |R | = N and |R | = 0 can be straightforwardly investigated using similar

derivations to the ones presented in this section.

3.6 Numerical and Simulation Results

In this section, we present the simulation results carried out in order to evaluate and compare

the BEP performance of the proposed RS schemes. As we have mentioned in subsection 3.3.4,

the BEP curve of MME RS is used as a benchmark. The presented RS schemes sometimes

require two TS to achieve a transmission while direct transmission always requires only one

TS. Thus, a data rate loss may be caused when applying the RS schemes. To highlight this

issue, besides studying how far the proposed RS scheme ameliorate the BEP performance of a

broadcast network, we study also the data rate loss caused when applying them. For that, we

define the aggregate data rate of the system as the amount of data correctly received by all the

destination nodes per one time slot and we present a comparison of the data rate performances of

the proposed RS schemes. For the direct transmission, since the communication time is always

one time slot, then the data rate is given by

T d =∏

k∈1...N

1−BEP dk , (3.22)

whereBEP dk is the BEP for the direct transmission at a node k. From [7], BEP d

k = 12

(1−

√1

1+ 1

σ2Sk

).

The data rate depends on the used γt. For a given γt, the data rate of the AST and ST based

RS can be written as follows

T x =∏

k∈1...N

1−BEP xk (γt)

E(Tx), x ∈ 1, 2, (3.23)

where x = 1 stands for AST based RS and x = 2 stands for ST based RS. The expected

number of TS for both AST and ST based RS is given by E(Tx) = 1 × (P(Θ = ∅) + P(Θ =

24

1, . . . , N)) + 2× (1− (P(Θ = ∅) + P(Θ = 1, . . . , N)).

In our numerical results, We set N = 5 nodes and the path loss exponent to α = 3. Simula-

tions were averaged over many random topologies of the broadcast network.

0 5 10 15 2010

−4

10−3

10−2

10−1

100

Eb/N

0 (dB)

BE

R

Simu: Direct TransmissionSimu: AST based RSSimu: ST based RSSimu: MM RSSimu: Optimal RSTheo: AST based RSTheo: ST based RS

Figure 3.3: Average BEP Comparison, STDR, γt = 2dB.

0 5 10 15 2010

−4

10−3

10−2

10−1

100

Eb/N

0 (dB)

Ave

rag

e B

EP

Simu: Direct TransmissionSimu: AST based RSSimu: ST based RSSimu: MM RSSimu: MME RSTheo: AST based RSTheo: ST based RS

Figure 3.4: Average BEP Comparison, STDR, γt = 8dB.

Fig. 3.3 and Fig. 3.4 show the average BEP over the whole nodes for γt = 2 dB and

γt = 8 dB, respectively. We notice that the AST based RS has the worst performance over other

relay selection schemes. This is expected since the AST based RS rely on the average SNR which

makes its decision not adaptive to channels instantaneous conditions. From Fig. 3.3, we observe

25

that the BEP performance of the different schemes tend to be superposed at high SNR. This is

due to the use of a low-value threshold which blocks relay selection and cooperative transmission

at high SNR: with the use of a low-value threshold, at high SNR, the direct SNR at all the N

nodes can easily exceed the threshold value. Consequently, all the N nodes will be classified as

“reliable” and cooperation will not be performed. Also, the BEP curves of different RS schemes

tend to be “parallel” to the BEP curve of the direct transmission. This is due to the virtual

array gain1, which depends on the value of γt [34]. From Fig. 3.4, we observe that the BEP

performance of the different RS schemes are superposed at low SNR. This is due to the use of

a high-value threshold which blocks relay selection and cooperative transmission at low SNR:

when the value of threshold is high, at low SNR, the set of “reliable” nodes will be often empty

and hence cooperation will not be performed. We notice that with the use of high threshold

value, the BEP performance of the MM RS is superposed to MME RS: when the threshold

value is high, the instantaneous BEP at a relay i, Q(√2γSi) will tend to 0 and hence the MME

RS criterion in (3.24) falls back to R4(STDR)Sel = argmax

i∈Rmin

j∈1...N\iQ(

√2(γSj + γij)) which is

equivalent to the MM RS criterion in (3.8).

At a given Eb/N0, the optimal threshold γ∗t , is computed numerically as follows

γ∗t = argminγt

maxk∈1...N

BEP 2k (γt). (3.24)

where BEP 2k (γt), is the average e2e BEP of the ST based RS at the node k with the use of

a threshold value γt. We use the same values for AST based RS. This optimal threshold is

calculated only one time at the source. Then, the source informs all the nodes about the values

of the optimal threshold that must be used.

In Fig. 3.5, we compare the average BEP performances of the different proposed schemes

along with the partial RS scheme existing in literature. We use the optimal threshold values

computed in (3.24). Fig. 3.5 demonstrates that our proposed RS schemes outperform partial

RS. In the other hand, partial RS requires more signaling than our proposed AST based RS

scheme which relies only on nodes locations knowledge. We observe that the MM RS has the

best suboptimal BEP performance. Besides, its performance is very close to MME RS. With the

use of optimal threshold values, we observe a significant amelioration of the BEP performance of

each RS scheme. The MM RS outperforms the ST based RS by about 0.5 dB at Eb/N0 = 20 dB

while the MME RS outperforms it by about 1 dB at the same Eb/N0. From table I, we observe

1If the error rate is plotted versus the SNR on a log-log scale the diversity order can be interpreted as the

slope of the so-obtained curve while the virtual array gain corresponds to the horizontal position of the curve.

26

0 2 4 6 8 10 12 14 16 18 2010

−4

10−3

10−2

10−1

100

Eb/N

0 (dB)

Ave

rage

BE

P

Simu: Direct TransmissionSimu: Partial RSSimu: AST based RSSimu: ST based RSSimu: MM RSSimu: MME RSTheo: Direct TransmissionTheo: AST based RSTheo: ST based RS

Figure 3.5: Average BEP Comparison, STDR, γt = γ∗t .

that ST based RS and MM RS require the same amount of CSI, but our simulation results show

that MM RS has better performance than ST based RS. From that, we can conclude that it

is more efficient to exploit this CSI knowledge in applying MM RS rather than ST based RS.

Theoretical and numerical curves are in perfect accordance which proves that our derivations

are correct.

0 5 10 15 2010

−4

10−3

10−2

10−1

100

Eb/N

0 (dB)

Ave

rag

e B

EP

Direct TransmissionPartial relayingAST based RSST based RsMM RSMME RS

Figure 3.6: Average BEP Comparison, STAR, γt = γ∗t .

For STAR, the optimal threshold values are determined by simulations using the same crite-

rion used for the STDR and presented in (3.24). Fig. 3.6 shows the average BEP performances

27

of the proposed RS schemes when the broadcast network uses STAR and optimal threshold

values. We compare our RS schemes with partial relaying. Fig. 3.6 demonstrates that with

the use of STAR, our proposed RS schemes outperform also partial RS scheme. This finding

is very relevant mainly if we compare partial RS scheme with the AST based RS since this

former requires more signaling and has worse BEP performance than our proposed AST based

RS scheme. We observe that the ST based RS outperforms the AST based RS by about 2 dB at

Eb/N0 = 18 dB. The ST based RS provides BEP performance close to MME RS while that of

MM RS is conformed to MME RS. This is excepted when using analog relaying: if the threshold

value is optimal, the instantaneous BEP at the relays will tend to 0. Hence, MM RS in analog

relaying falls back to minimize the maximum of instantaneous BEP at each destination except

the relay. This is equivalent to choose the max min of combined SNR at each node. Hence,

for broadcast networks using STAR, using an optimal threshold makes the MM RS the best

solution.

As proved by our analytical and simulations results, our cooperative schemes ameliorate

significantly the BEP performance compared to the direct transmission and thus they are very

interesting for applications requiring low BEP. It is widely known that all cooperative schemes

employing the same time division as [5] are efficient to induce a spatial diversity gain but

they cause a data rate loss comparing to the direct transmissions. This is because cooperative

transmission consumes an additional time slot over the direct transmission to transmit the

same amount of data [5]. Next, we evaluate how much cooperative transmissions in our work

deteriorate the data rate performance compared to the direct transmission using STDR and

STAR, respectively.

In Fig. 3.7, we present the aggregate data rate as defined earlier to be the amount of data

correctly received by all the nodes per one time slot. Since we have the analytical expressions

of the BEP of AST and ST based RS, we plot the theoretical and simulation curves of data

rate. For the other schemes only simulation is used. Fig. 3.7 (a) shows that in low SNR region,

the data rate of our RS schemes is close to that of the direct transmission. This is because,

in low SNR region, nodes suffer from high BEP when relying only on the direct transmission

and hence often cooperation is not performed because all nodes are “unreliable”. The difference

between the data rate performances of our proposed RS and that of the direct transmission is

getting larger as the average SNR increases. For γt = γ∗t , comparing to the direct transmission,

we notice a deterioration in data rate by about 0.3 bits/s/Hz but an amelioration of the BEP

28

0 5 10 15 200.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Eb/N

0 (dB)

Aggre

gate

data

rate

Theoretical curvesSimu: Direct TransmissionSimu: AST based RSSimu: ST based RSSimu: MM RSSimu: MME RSSimu: Partial RS γ

t=2 dB γ

t=γ

t*

γt=8 dB

(a)

0 5 10 15 200.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Eb/N

0 (dB)

Aggre

gate

data

rate

Direct TransmissionAST based RSST based RSMM RSMME RSPartial RS

(b)

Figure 3.7: Aggregate data rate Comparison: (a) STDR, (b) STAR for γt = γ∗t .

performance by about 10−2 is realized thanks to the MM RS. In high SNR, for γt = 2 dB,

the data rate of our RS schemes are higher than those when γt = γ∗t . Nevertheless, the BEP

performances are deteriorated when not using the optimal value γ∗t . When using γt = 8 dB, the

data rate performances are deteriorated and the BEP remains the same comparing to the use

of γ∗t . When using a high threshold value, the cooperation deteriorates the data rate without

significantly ameliorates the BEP performance. Finally, observe that theoretical and simulations

curves are in perfect accordance. From Fig. 3.7 (b), we observe that for STAR, at high SNR the

data rate is deteriorated by about 0.4 bits/s/Hz while the BEP is ameliorated by about 3×10−2

29

comparing to direct transmission. Note that some works have focused on the use of network

coding to mitigate data rate loss in multi-source cooperative systems (e.g, [35] and references

therein). But this does not fit to our system model since we have a single source. As motioned

earlier, in our work, cooperative transmissions are not performed when all nodes are “reliable”

(no need to cooperative transmission) or when all nodes are “unreliable” (absence of a “reliable”

relay). This helps mitigate data rate loss. If cooperative transmissions are always performed,

the data rate will have 0.5 as a ceiling value at high SNR [36]. In Fig. 3.7, we observe that

the data rates of our protocols at high SNR exceeds the value 0.5 thanks to performing the

cooperation only when it is needed and efficient in ameliorating the BEP. Finally, our proposed

protocols are interesting for applications requiring low BEP and having relaxed constraints on

data rate.

3.7 Conclusion

In this chapter, we have proposed and investigated three single RS schemes for broadcast net-

works using STDR or STAR: AST based RS, ST based RS and MM RS. A fourth RS scheme

called MME RS that selects the relay minimizing the maximum e2e BEP through destinations

is used to compare the performance of the first three schemes. Several analytical studies and

simulations are performed to evaluate and compare the performances in terms of BEP and data

rate of the proposed RS schemes. We have included a comparison with partial relay selection

scheme which is the only existing technique applicable in broadcast networks. For STDR, we

prove that when the optimal threshold value is used, the MM RS has the best performance and

achieve a BEP performance close to MME RS. The ST based RS requires the same amount

of signaling but has worst performance than MM RS. For STAR, when the optimal threshold

value is used, the MM RS achieves a BEP performance conformed to MME RS. Moreover, we

have found that our simplest and least efficient RS scheme outperforms partial RS scheme. The

cooperative transmissions using our RS schemes improves significantly the BEP performance

at the price of a data rate loss. Hence, our approaches are very interesting for applications

requiring low BEP performance.

30

Chapter 4

Performance Analysis of Cooperative

MC CDMA and DS CDMA Systems

4.1 Introduction

Cooperative Communication is an innovative technique to create spatial diversity without any

reliance on multiple antennas. It consists in introducing relay node(s) to increase diversity order

by relaying the transmitter signal to the receiver [1]–[5]. This chapter focuses on digital relaying

mode where the relay decodes the received message from the source and then forwards the

decoded message to the destination.

If the relay correctly detects the received signal, the symbol error probability at the desti-

nation is significantly decreased by combining signal copies coming from two branches: source-

destination and relay-destination. However, if the relay forwards an erroneous detected signal, a

symbol error at the destination is strongly probable. This event is called error propagation, and

can significantly deteriorate the performance of the relaying protocol. To mitigate this problem,

a threshold digital relaying approach has been proposed [31]–[38]. Namely in [38], Onat et. al

have proposed a threshold digital relaying cooperation protocol where only relays whose received

SNR are above a threshold value, which we call “reliable” relays, are authorized to retransmit.

If only one relay among “reliable” relays cooperates, we call this kind of protocol STDR.

Performance of Selective Decode-and-Forward in terms of capacity outage probability and

BEP have been analyzed in [39]–[41]. In selective decode-and-forward, the activated relay is

which has the largest SNR in relay-destination link. In incremental relaying (IR), the process of

relay selection and cooperative transmission is done only if the SNR in source-destination link is

31

below a predetermined threshold γt. Otherwise, no cooperative transmission will be performed

and the source transmits the next data [42]. In case where the SNR in source-destination link is

below γt, the system uses the selective threshold digital relaying protocol (STDR) which consists

in building a set of “reliable” relays, defined as the relays having an SNR in source-relay link

beyond γt. Only one “reliable” relay is selected to cooperate. We consider the selection of the

relay having the largest SNR in the relay-destination link. The motivation behind the use of

STDR is to prevent relays which receive the source signal with an SNR below γt to partici-

pate in cooperation process since they are likely not able to correctly decode the source signal

and thus they can not forward a correct information to destination. The selection of one relay

among “reliable” relays avoid that the system squanders many time slots (a time slot for each

“reliable” relay) to transmit one symbol. The combination of incremental relaying and several

relaying schemes has been studied in earlier works and their performances have been analyzed

over Rayleigh fading environments in the presence of a single path propagation [42]-[45]. In [42],

the performance of the incremental-relay-selection decode-and-forward technique over indepen-

dent non-identical Rayleigh fading channels is derived in terms of average bit error probability

(BEP), outage probability and average channel capacity. [43] proposes a new incremental re-

laying transmission technique in conjunction with selective digital relaying, and provides its

performance in terms of outage probability and bit error probability. In [44], the authors have

derived a closed-form expression for the end-to-end (e2e) bit-error rate (BER) of incremental

opportunistic relaying scheme which combines incremental relaying scheme and opportunistic

relaying scheme. In [45], Chen et. all have derived closed-form expressions for error probability

of incremental-selective digital relaying scheme which combines the incremental digital relaying

and the selective digital relaying. In [46], the author derived the BEP for selective digital re-

laying assuming multipath propagation. However, the combination with incremental relaying is

not considered and throughput performance is not studied. Besides, the relay selection in [46]

is different from the one considered in our work.

All previous works dealing with the STDR protocol or the combination of incremental relay-

ing with other relaying schemes consider Rayleigh fading environments and single path channels.

In this chapter, we consider first a cooperative wireless network using MC-CDMA where N users

communicate with a single destination D, that can be a Base-Station (BS) or an Access Point

(AP). For a source user which communicates with D, the remaining N-1 users serve as potential

relays. The system use the STDR and the activated relay is which has the largest SNR in the

32

relay-destination link. We derive the exact e2e BEP of the considered cooperative MC CDMA

systems using STDR protocol in the presence of multipath propagation. Then, we consider

cooperative DS-CDMA systems and multipath propagation channels. We analyze e2e BEP and

throughput performances of incremental selective relaying (ISR). The considered cooperative

system uses incremental relaying protocol in conjunction with selective relaying. We assume

that the destination knows the SNR of RΘ − D links through training sequences, where Θ is

the set of “reliable” relays and RΘ denotes the relays in the set Θ. Based on the collected SNR

information, the destination selects one relay among Θ. The derived results are valid for any

multipath intensity profile of the channel, any path delays and take into account the correlation

between path gains.

This chapter is devised into three sections: (i) section 4.2 where we present the performance

analysis of cooperative MC CDMA systems. (ii) Section 4.3 where we present the performance

analysis of DS-CDMA systems. (iii) Section 4.4 where we give some concluding remarks and a

summary of our findings. Section 4.2 is organized as follows: in subsection 4.2.1, we present the

system model. In subsections 4.2.2 and 4.3.3, we derive e2e BEP and throughput expressions of

DS-CDMA cooperative system using ISR in the presence of multipath propagation. In section

4.2.3, we present simulation and theoretical results. Section 4.3 is organized as follows. In

subsection 4.3.1, we present the system model. In subsections 4.3.2 and 4.3.3, we derive e2e

BEP and throughput expressions of DS-CDMA cooperative system using ISR in the presence of

multipath propagation. Finally, in section 4.3.4, we present simulation and theoretical results.

4.2 Performance Analysis of Cooperative MC CDMA Systems

using Selective Relaying

4.2.1 System Model

Relaying protocol

We consider a wireless network with a circular cell. We assume that N uniformly distributed

users within the cell communicate with a destination (D), that can be a BS/AP, located at

the center of the cell. Each user transmits a signal to D while the remaining N-1 users serve

as potential relays. Nodes are assumed to communicate in half-duplex mode, i.e., they can

not transmit and receive simultaneously. A two-phase relaying protocol is considered. In the

33

first phase, during the first time slot, a source user (S) transmits a signal to D while the N-1

remaining users listen, as shown in Fig. 4.1. Users which receive the source signal with an SNR

above the threshold value γt, send training symbols so that D can determine the SNR of the

relay-destination link. Based on the collected SNR information, D activates the relay which has

the largest SNR relay-destination link. In the second phase of the considered relaying protocol,

during the second time slot, the activated relay re-transmits source signal to D, as shown in Fig.

4.2.

Figure 4.1: Phase 1: S transmits a signal to D while the remaining N − 1 users listen.

Models of transmitted and received signals

An MC-CDMA transmitter spreads the original signal using a spreading code in the frequency

domain [47]-[48]. Without loss of generality, the number of subcarriers, L, is assumed to be

equal to the spreading factor. The equivalent base-band transmitted signal can be written as

e(t) =

√EX

L

∑k

skg(t− kTs)

L−1∑m=0

cX,kL+mej2πfmt, (4.1)

where sk is the k-th transmitted symbol, EX is the transmitted energy per symbol by X, Ts is

the symbol period, cX,kL+mL−1m=0 is a unit modulus spreading sequence used by X, g(t) is a

rectangular pulse response with the unit useful energy and duration Ts = T us + η, where T u

s is

the useful symbol period and η is the guard interval, fm = f0 + m∆f is the m-th subcarrier

frequency, f0 is the frequency of the first subcarrier and ∆f = 1/T us is the subcarrier separation.

If the channel delay spread is lower than the guard interval η, then the restriction of the received

34

Figure 4.2: Phase 2: A selected relay among “reliable” relays retransmits the source signal to

D.

signal to the interval [kTs + η, (k + 1)Ts] can be written as

r(t) =

√EX

L

sk√Ts − η

L−1∑m=0

cX,kL+mej2πfmtFXY (fm; t) + nXY (t), (4.2)

where

FXY (fm; t) =

∫fXY (τ ; t)e

−j2πfmτdτ, (4.3)

where fXY (τ ; t) is the impulse response of the Rayleigh multipath fading channel of the X-Y

link at the time instant t, and nXY (t) is an AWGN with two-sided power spectral density N0.

An MC-CDMA receiver uses a Discrete Fourier Transformation (DFT) to recover the trans-

mitted signal over the different subcarriers [47]-[48]. In the following, a perfect synchronization

on the different subcarrier frequencies is assumed. After removing the received signal during

the guard interval and compensating the modulation due to the spreading sequence, the DFT

outputs for symbol sk can be written as

zkXY = (zkXY , . . . , zkXY,L−1)

T

=

√EX

LskFXY + nXY , (4.4)

where FXY = (FXY (f0; kTs), . . . , FXY (fL−1; kTs))T and nXY = (nk

XY,0, . . . , nkXY,L−1)

T is a vec-

tor of AWGNs with covariance matrix N0IL, where IL is the identity matrix with size L×L, and

35

(.)T is the transpose operator.

Assuming perfect channel estimation, the optimal soft output of the MC-CDMA receiver is

given by

ΛkXY =

√EX

L

F†XY z

kXY

N0, (4.5)

where (.)† denotes the Hermitian operator. Hence the instantaneous SNR at the output of the

receiver is given by

γXY =EX

L

F†XY FXY

N0. (4.6)

4.2.2 E2E BEP Analysis of the System

In this section, we derive the e2e BEP at D for BPSK modulation. The e2e BEP at D can be

written as

Pe,D =N−1∑m=0

P (|Θ| = m)P (e||Θ| = m), (4.7)

where Θ denotes the set of users which receive the source user signal with an SNR above γt and

|Θ| denotes the cardinality of Θ. Following the same methodology presented in [46] to obtain

the PDF of the SNR at the output of a Rake Receiver, we deduce the PDF of the SNR in (4.6)

pγXY (x) =

L∑j=1

π(j)XY

β(j)XY

exp(− x

β(j)XY

), if x ≥ 0, (4.8)

where

β(j)XY = λ

(j)XY

EX

LN0(4.9)

π(j)XY =

∏1≤k≤Lk =j

λ(j)XY

λ(j)XY − λ

(k)XY

, (4.10)

where λ(j)XY is the j-th eigenvalue of the FXY correlation matrix QXY=E(FXY F

†XY ).

The probability that γXY < γt is given by

P (γXY < γt) =

L∑j=1

π(j)XY [1− exp(− γt

β(j)XY

)]. (4.11)

The probability that γXY ≥ γt is given by

P (γXY ≥ γt) =L∑

j=1

π(j)XY exp(−

γt

β(j)XY

). (4.12)

36

Hence, for m > 1, we have

P (|Θ| = m) =

CmN−1∑n=1

∏i∈U(n)

L∑j=1

π(j)SRi

exp(− γt

β(j)SRi

)∏

k∈U(n)

L∑j=1

π(j)SRk

(1− exp(− γt

β(j)SRk

)

) , (4.13)

where U(n) is the n-th possible combination of m “reliable” relay users among the set of N − 1

relay users and CmN−1 =

(N−1)!m!(N−1−m)! , where (.)! denotes factorial operator.

P (e||Θ| = m) =

CmN−1∑n=1

P (e||Θ| = m,Θ = U(n))P (Θ = U(n)||Θ| = m). (4.14)

The last term of the above equation is given by

P (Θ = U(n)||Θ| = m) =

∏i∈U(n)

L∑j=1

π(j)SRi

exp(− γt

β(j)SRi

)∏

k∈U(n)

L∑j=1

π(j)SRk

[1− exp(− γt

β(j)SRk

)]

P (|Θ| = m).

(4.15)

Let I1 = |Θ| = m,Θ = U(n). Hence, the conditional bit error probability P (e|I1) can be

written as

P (e|I1)=∑q∈Θ

P (e|I1, RSelΘ = q)P (RSelΘ = q), (4.16)

where RSelΘ is the activated relay in Θ.

We have γRSelΘD = maxRi∈Θ

γRiD. Hence, the probability P (RSelΘ = q) is given by

P (RSelΘ = q) =∏k∈Θk =q

P (γRqD > γRkD). (4.17)

The obtained expression of P (RSelΘ = q) is given by


L∑j=1

π(j)RqD

L∑l=1

π(l)RkD

β(l)RkD

β(l)RkD

−β(j)RqD

β(l)RkD

β(j)RqD

+ β(l)RkD

. (4.18)

If RSelΘ decodes incorrectly the received signal, it retransmits an erroneous signal to D

leading to error propagation event. The bit error probability at D due to error propagation

is denoted by Peprop,D. The bit error probability at D given that RSelΘ has retransmitted a

correctly decoded signal is denoted by Pecoop,D. Hence, the probability P (e|I1, RSelΘ = q) can

be written as

P (e|I1, RSelΘ = q) = Pe,RSelΘPeprop,D + (1− Pe,RSelΘ

)Pecoop,D, (4.19)

37

where Pe,RSelΘis the bit error probability at RSelΘ. The bit error probability at D due to error

propagation Peprop,D can be bounded by the worst case value i.e., Peprop,D ≈ 12 [32]. The bit

error probability Pe,RSelΘcan be written as

Pe,RSelΘ=

∫ ∞

γt

Q(√2x)pγSRSelΘ

|γSRSelΘ≥γtdx, (4.20)

where Q(x) = 1√2π

∫ +∞x e−t2/2. The conditional PDF pγSRSelΘ

|γSRSelΘ≥γt is given by

pγSRSelΘ|γSRSelΘ

≥γt =

pγSRSelΘ

(x)

ΥSRSelΘ(γt)

if x ≥ γt

0 o.w,

(4.21)

where ΥXY (γt) = P (γXY ≥ γt). Using integration by parts and an adequate variable substitu-

tion we obtain

Pe,RSelΘ=

L∑j=1

π(j)SRSelΘ

ΥSRSelΘ(γt)

Q(√

2γt)e− γt

β(j)SRSelΘ −

√√√√ β(j)SRSelΘ

1 + β(j)SRSelΘ

Q

√2γt(1 +1

β(j)SRSelΘ

)

.

(4.22)

The bit error probability Pecoop,D is given by

Pecoop,D=

∫ ∞

0

∫ ∞

0Q(√

2(x+ u))pγSD(x)pγRSelΘD(u)dxdu. (4.23)

To determine the PDF of γRSelΘD, we use the following result [49]

pγRselΘD(γ) =

∑i∈Θ

pγRiD(γ)∏l∈Θl =i

PγRlD(γ), (4.24)

where PX(γ) is the cumulative Distribution Function (CDF) of X

PγXY (γ) =L∑

k=1

π(k)XY

[1− exp(− γ

β(k)XY

)

]. (4.25)

Let l(Θ, i, p)|Θ|−1p=1 be the set of relays indices which belong to Θ and different from i. The

obtained expression of the PDF of γRSelΘD is given by

pγRSelΘD(x) =

∑i∈Θ

L∑k=1

π(k)RiD

β(k)RiD

L∑m1=1

π(m1)Rl(Θ,i,1)D

. . .L∑

m|Θ|−1=1

π(m|Θ|−1)

Rl(Θ,i,|Θ|−1)D

2|Θ|−1−1∑n=0

(−1)ξ(n)exp(− x

αnikm1...m|Θ|−1

),

(4.26)

where ϵn,|Θ| = (ϵn,|Θ|(1), . . . ϵn,|Θ|(|Θ| − 1)) is the binary representation of 0 ≤ n ≤ 2|Θ|−1 − 1,

ξ(n) =

|Θ|−1∑p=1

ϵn,|Θ|(p), (4.27)

38

and

1

αnikm1...m|Θ|−1

=1

β(k)RiD

+

|Θ|−1∑p=1

ϵn,|Θ|(p)

β(mp)Rl(Θ,i,p)D

. (4.28)

To determine the expression of Pecoop,D in (B.4), we use the following result which can be

obtained using integration by parts∫ ∞

0

∫ ∞

0Q(√

2(x+ u))exp(−x

a )

a

exp(−ub )

bdxdu = Ψ(a)

a

a− b+Ψ(b)

b

b− a, (4.29)

where

Ψ(x) =1

2

[1−

√x

x+ 1

]. (4.30)

Using the PDF of γRSelΘD in (4.26) and the equations above, we obtain the expression of Pecoop,D

given by

Pecoop,D=L∑

j=1

π(j)SD

∑i∈Θ

L∑k=1

π(k)RiD

β(k)RiD

L∑m1=1

π(m1)Rl(Θ,i,1)D

. . .L∑

m|Θ|−1=1

π(m|Θ|−1)

Rl(Θ,i,|Θ|−1)D

2|Θ|−1−1∑n=0

(−1)ξ(n)

×

Ψ(β(j)SD)

β(j)SDαnikm1...m|Θ|−1

β(j)SD − αnikm1...m|Θ|−1

+Ψ(αnikm1...m|Θ|−1)

α2nikm1...m|Θ|−1

αnikm1...m|Θ|−1− β

(j)SD

.

(4.31)

4.2.3 Numerical and Simulation Results

This section provides some numerical and simulations results of the considered cooperative MC-

CDMA system. Subcarriers separation was set to ∆f = 50 kHz corresponding to Ts = 25µs

and η = 5µs. The number of subcarriers was set to L = 16. Simulations results were performed

for ITU Pedestrian B channels. The Multipath Intensity Profile (MIP) of the ITU channels is

as follows

ΦXY (τ) =

PXY∑i=1

E(|f iXY |2)δ(τ − τ iXY ), (4.32)

where PXY , f iXY and τ iXY are respectively, the number of paths, the complex gain and the

i-th path of the X-Y link, δ(.) is the Dirac function and E(.) is the expectation operator. The

average power of the i-th path depends of the distance deffXY between X and Y as follows

E(|f iXY |2) =

piς

dϱXY

, (4.33)

where dXY = deffXY /d0 is the normalized distance between X and Y , d0 is the arbitrary reference

distance, ς is the path loss at the reference distance, 0 < pi ≤ 1 is the relative average power of

39

the i-th path so that∑PXY

i=1 pi = 1 and ϱ is the path loss exponent. ς and ϱ was set to 1 and

3, respectively. The reference distance d0 is chosen to be dSD. The cell radius was set to 10 m

and simulations were carried out for different random topologies. We have allocated the same

power to source and relay i.e., EX = Eb/2.

0 2 4 6 8 1010

−3

10−2

10−1

Eb/N

0 (dB)

BE

P

Simu: Direct TransmissionSimu: STDR=6 dB

Simu: STDR, γt=2 dB

Theo: Direct Transmission

Theo: γt= 6 dB

Theo: STDR, γt=2 dB

Figure 4.3: BEP of cooperative MC CDMA systems using STDR for ITU Pedestrian B channels,

N=3.

0 2 4 6 8 1010

−3

10−2

10−1

Eb/N

0 (dB)

BE

P

Simu: Direct TransmissionSimu: STDR, N=3Simu: STDR, N=6Theo: Direct TransmissionTheo: STDR, N=3Theo: STDR, N=6

Figure 4.4: Effect of users numbers on BEP of cooperative MC CDMA systems using STDR for

ITU Pedestrian B channels, γt = 2dB.

40

Fig. 4.3 shows the BEP of the considered cooperative MC CDMA system using STDR for

ITU pedestrian B channel and number of users equal 3. We used two different SNR threshold

values. Observe that the use of a high SNR threshold deteriorates the BEP performance at

low SNR. This is because at low SNR, received SNRs at relays will rarely exceed the threshold

value and hence no cooperation will be performed. We observe that there is a match between

theoretical and simulations curves which validates our derived BEP expressions.

Fig. 4.4 shows the BEP for different number of users in the cell. We observe that the BEP

performance improves as the number of relays increases. This is because the destination will

be more lucky to select better suitable relay. Theoretical and simulations results are in perfect

match.

4.3 Performance Analysis of Cooperative DS CDMA Systems

using combined Selective and Incremental Relaying

4.3.1 System Model

Scenario of the combined digital relaying protocol

We consider a source S, a destination D and M potential relays Ri. We assume that the

destination knows the SNR of RΘ − D links, where Θ is the set of RΘ, the “reliable” relays.

Based on the collected SNR information, the destination selects one relay belonging to Θ. The

derived results are valid for any multipath intensity profile of the channel, any path delays and

take into account the correlation between path gains.

Figure 4.5: Phase 1: S broadcasts a signal to D while relays listen

41

A two-phase digital relaying protocol is considered. In the first phase (1st time slot) the

source broadcasts its signal as shown in Fig. 4.5. If the destination has a received SNR above a

threshold value γt, it feeds back this information informing the potential relays that cooperation

is not required and then the source transmits the next data during the 2nd time slot. Otherwise,

the destination selects the relay belonging to Θ having the largest SNR in RΘ − D links. In

the second phase (2nd time slot), the selected relay forwards data to the destination. Then, the

destination uses a Rake receiver to estimate the transmitted symbol from the source and the

selected relay. Finally, it combines these estimates using maximum ratio combining (MRC).

Let LXY , flXY and τ lXY the number of paths, the complex gain and the delay of the path l

of the X-Y link. The noise at Y is an additive white gaussian noise with variance NXY .

The mth correlation of the Rake receiver at Y during the kth symbol period can be written

as [46]

zmXY (k) = sk

LXY∑l=1

f lXY (kTs)q(τ

mXY − τ lXY ) + nm(k), (4.34)

where sk is the k-th transmitted symbol, nm(k) is a term due to noise, q(τ) = (g g)(τ), denotes the convolution operation and g(t) is the shaping filter.

4.3.2 E2E BEP Analysis of the System

In this section, we derive the e2e BEP at D for Binary Phase Shift Keying (BPSK) modulation

and Rayleigh fading channels. The e2e BEP at D can be written as

Pe,D = P (γSD < γt)Pndiv(e|γSD < γt) + P (γSD ≥ γt)Pdirect(e|γSD ≥ γt), (4.35)

where Pndiv(e|γSD ≥ γt) is the average conditional BEP at the destination given that γSD ≥ γt,

i.e., the destination needs a cooperative diversity and Pdirect(e|γSD < γt) is the average BEP at

the destination given that γSD < γt, i.e., the destination relies only on the direct transmission.

Next, we derive each term of (4.35). The probability density function (PDF) of γXY is [46]:

pγXY (x)=

LXY∑j=1

π(j)XY

β(j)XY

exp(− x

β(j)XY

), if x ≥ 0, (4.36)

where

β(j)XY = λ

(j)XY

EX

NXY, (4.37)

42

and

π(j)XY=

∏1≤k≤LXY

k =j

λ(j)XY

λ(j)XY − λ

(k)XY

, (4.38)

where λ(j)XY is the jth eigenvalue of the matrix

√QXY E(fXY f

†XY )

√QXY . The probability that

γXY < γt is given by

P (γXY < γt)=

LXY∑j=1

π(j)XY [1− exp(− γt

β(j)XY

)]. (4.39)

The conditional probability Pdirect(e|γSD ≥ γt) can be written as

Pdirect(e|γSD ≥ γt)=

∫ ∞

γt

Q(√2x)pγSD|γSD≥γtdx, (4.40)

where Q(x) = 1√2π

∫ +∞x e−t2/2dt and

pγSD|γSD≥γt =

pγSD

(x)

ΛSD(γt), if x ≥ γt

0, o.w.

(4.41)

where ΛXY (γt) = P (γXY ≥ γt). Using integration by parts and an adequate variable substitu-

tion we obtain

Pdirect(e|γSD ≥ γt) =

LSD∑j=1

π(j)SD

ΛSD(γt)

Q(√2γt)e

− γt

β(j)SD −

√√√√ β(j)SD

1 + β(j)SD

Q

(√2γt(1 +

1

β(j)SD

)

) .

(4.42)

On the other hand, Pndiv(e|γSD < γt) can be written as

Pndiv(e|γSD < γt) =∑Θ

P (Θ)Pndiv(e|γSD < γt,Θ), (4.43)

where

P (Θ) =∏i∈Θ

LSRi∑j=1

π(j)SRi

exp(− γt

β(j)SRi

)∏k∈Θ

LSRk∑j=1

π(j)SRk

[1− exp(− γt

β(j)SRk

)]. (4.44)

If Θ contains more than two relays, we have

Pndiv(e|γSD < γt,Θ) =∑q∈Θ

Pndiv(e|I)P (RSelΘ = q), (4.45)

where I = γSD < γt,Θ, RSelΘ = q and RSelΘ is the activated relay in Θ. The probability

P (RSelΘ = q) is given by


P (γRqD > γRkD). (4.46)

43

The obtained expression of P (RSelΘ = q) is given by


LRqD∑j=1

π(j)RqD

LRkD∑l=1

π(l)RkD

β(l)RkD

β(l)RkD

−β(j)RqD

β(l)RkD

β(j)RqD

+ β(l)RkD

. (4.47)

If the selected relay belonging to Θ (RSelΘ) decodes incorrectly the received signal, it forwards

an erroneous signal leading to error propagation event. The BEP at the destination due to

error propagation is denoted Pprop,D(e|I) whereas the BEP at the destination given that RSelΘ

forwarded a correctly decoded signal is Pcoop,D(e|I).

Pndiv(e|I) = PRSelΘ(e|I)Pprop,D(e|I) + (1− PRSelΘ

(e|I))Pcoop,D(e|I), (4.48)

where PRSelΘ(e|I) is the BEP at RSelΘ. Pprop,D(e|I) can be bounded by the worst case value i.e.,

Pprop,D(e|I) ≈ 12 as in [33] and [32]. Following the same methodology to obtain the conditional

probability Pdirect(e|γSD < γt) in (7.42), we obtain the BEP at RSelΘ,

PRSelΘ(e|I) =

LSRSelΘ∑j=1

π(j)SRSelΘ

ΛSRSelΘ(γt)

Q(√

2γt)e− γt

β(j)SRSelΘ −

√√√√ β(j)SRSelΘ

1 + β(j)SRSelΘ

Q

√2γt(1 +1

β(j)SRSelΘ

)

.

(4.49)

The conditional probability Pcoop,D(e|I) is given by

Pcoop,D(e|I) =

∫ ∞

0

∫ γt

0Q(√

2(x+ u))pγSD|γSD<γt(x)pγRSelΘD(u)dxdu. (4.50)

The conditional PDF pγSD|γSD<γt is given by

pγSD|γSD<γt(x) =

pγSD

(x)

ΥSD(γt), if 0 ≤ x < γt

0, o.w.

(4.51)

where ΥSD(γt) = P (γSD < γt). Let F denotes the integral

F =

∫ γt

0Q(√

2(x+ u))pγSD|γSD<γt(x)dx. (4.52)

Using integration by parts, after some manipulation we obtain the expression of F given by

F =

LSD∑j=1

π(j)SD

1− ΛSD(γt)

Q(√2u)−Q(

√2(γt + u))e

−γt

β(j)SD −

exp( u

β(j)SD

)√1 + 1

β(j)SD

(Q

(√2(1 +

1

β(j)SD

)u

)

−Q

(√2(1 +

1

β(j)SD

)(γt + u)

))].

(4.53)

44

The SNR of RSelΘ −D is given by

γRSelΘD = maxi∈Θ

γRiD. (4.54)

Let l(Θ, i, p)|Θ|−1p=1 be the set of relays indices which belong to Θ and different from i. The

PDF of γRSelΘDis given in [[46], eq. (36)] where ϵn,|Θ| = (ϵn,|Θ|(1), . . . ϵn,|Θ|(|Θ| − 1)) is the

binary representation of 0 ≤ n ≤ 2|Θ|−1 − 1, ξ(n) =∑|Θ|−1

p=1 ϵn,|Θ|(p) and 1αnikm1...m|Θ|−1

=

1

β(k)RiD

+∑|Θ|−1

p=1ϵn,|Θ|(p)

β(mp)

Rl(Θ,i,p)D

. To determine the expression of Pcoop,D(e|I) in (B.4), we use the

following result which can be proved using integration by parts

Ψ(a, b, α) =

∫ ∞

0Q(

√au+ b)

1

αexp(−u

α)du

= Q(√b)−

√1

1 + 2aα

exp(b

aα)Q

(√b(1 +

2

aα)

). (4.55)

Using (4.53) and (4.55), we find the expression of Pcoop,D(e|I) given by

Pcoop,D(e|I) =∑i∈Θ

LRiD∑k=1

π(k)RiD

β(k)RiD

LRl(Θ,i,1)D∑m1=1

π(m1)Rl(Θ,i,1)D

. . .

LRl(Θ,i,|Θ|−1)D∑m|Θ|−1=1

π(m|Θ|−1)

Rl(Θ,i,|Θ|−1)D

2|Θ|−1−1∑n=0

(−1)ξ(n)αnikm1...m|Θ|−1

×LSD∑j=1

π(j)SD

1− ΛSD(γt)

[Ψ(2, 0, αnikm1...m|Θ|−1

)− e

−γt

β(j)SD Ψ(2, 2γt, αnikm1...m|Θ|−1

)

−α′nijkm1...m|Θ|−1

αnikm1...m|Θ|−1

√β(j)SD+1

β(j)SD

[Ψ

(2(1 +

1

β(j)SD

), 0, α′nijkm1...m|Θ|−1

)

−Ψ

(2(1 +

1

β(j)SD

), 2(1 +1

β(j)SD

)γt, α′nijkm1...m|Θ|−1

)]], (4.56)

where 1α′nijkm1...m|Θ|−1

= 1αnikm1...m|Θ|−1

− 1

β(j)SD

. By substituting equations (4.56) and (4.49) in

(4.48), we obtain the expression of Pndiv(e|I). By substituting the result equation and (4.47)

in (4.45), we obtain the expression of Pndiv(e|γSD<γt,Θ). Finally, by substituting the result

equation and (4.44) in (4.43), we obtain the expression of Pndiv(e|γSD<γt). The expressions of

the conditional probability Pndiv(e|γSD<γt,Θ) for the cases where Θ contains a single relay and

Θ is an empty set can be straightforwardly obtained using similar derivations.

By substituting the obtained expressions of Pndiv(e|γSD<γt) and Pdirect(e|γSD ≥ γt) in (4.35),

we obtain the expression of Pe,D.

45

4.3.3 Throughput Analysis of the System

Throughput is the amount of data successfully delivered per time unit. The throughput of the

three protocols is given by

Thx =R(1− P x

e,D)

E(Tx), (4.57)

where R (bits/s/Hz) is the target transmission rate and E(Tx), x ∈ IR, SR, ISR is the

expected number of time slots and P xe,D, x ∈ IR, SR, ISR is the average e2e BEP at D for

IR, SR and ISR, respectively.

Throughput Analysis of IR: For IR, the average e2e BEP P IRe,D is given by

P IRe,D =P (γSD ≥ γt) (1− Pdirect(e|γSD ≥ γt)) + P (γSD < γt)(1− Pcoop,D(e|γSD < γt)), (4.58)

where Pdirect(e|γSD ≥ γt) is given in (7.42), P (γSD ≥ γt) = 1 − P (γSD < γt), P (γSD < γt) is

given by (4.39) and Pcoop,D(e|γSD < γt) is given by (4.56).

The expected number of time slots is given by

E(TIR)=P (γSD < γt)× 2 + P (γSD ≥ γt)× 1. (4.59)

Throughput Analysis of SR: For SR, the average e2e BEP PSRe,D is given by

PSRe,D = Γ(γt)(1− Pdirect(e)) + (1− Γ(γt))(1− Pcoop,D(e)), (4.60)

where Γ(γt) =M∏i=1

P (γSRi < γt) and is given by

Γ(γt) =

M∏i=1

LSRi∑j=1

π(j)SRi

[1− exp(− γt

β(j)SRi

)]

. (4.61)

Pdirect(e) is given by [46, eq. (18)]. Pcoop,D(e) can be written as

Pcoop,D(e) =∑Θ

P (Θ)Pcoop,D(e|Θ), (4.62)

where P (Θ) is given in equation (4.44). If Θ contains more than two relays, we have

Pcoop,D(e|Θ, RSelΘ)=

∫ ∞

0

∫ ∞

0Q(√

2(γ + β))pγSD(γ)pγRSelΘD(β)dγdβ. (4.63)

The expression of Pcoop,D(e|Θ) is given in [46, eq. (30)],

46

Pcoop,D(e|Θ) =

LSD∑j=1

π(j)SD

∑i∈Θ

LRiD∑k=1

π(k)RiD

β(k)RiD

LRl(Θ,i,1)D∑m1=1

π(m1)Rl(Θ,i,1)D

. . .

LRl(Θ,i,|Θ|−1)D∑m|Θ|−1=1

π(m|Θ|−1)

Rl(Θ,i,|Θ|−1)D

2|Θ|−1−1∑n=0

(−1)ξ(n)

×∆nijkm1...m|Θ|−1, (4.64)

where

∆nijkm1...m|Θ|−1= Ω(β

(j)SD)

β(j)SDαnikm1...m|Θ|−1

β(j)SD − αnikm1...m|Θ|−1

+Ω(αnikm1...m|Θ|−1)

α2nikm1...m|Θ|−1

αnikm1...m|Θ|−1− β

(j)SD

,

(4.65)

where Ω(x) = 12

[1−

√x

x+1

].


E(TSR) = Γ(γt)× 1 + (1− Γ(γt))× 2. (4.66)

Throughput Analysis of ISR: For ISR, the average e2e BEP P ISRe,D is given by

P ISRe,D = P (γSD ≥ γt) (1− Pdirect(e|γSD ≥ γt)) + P (γSD < γt)Γ(γt) (1− Pdirect(e|γSD < γt))

+(1− Γ(γt)) (1− Pcoop,D(e|γSD < γt))P (γSD < γt). (4.67)


E(TISR) =[P (γSD ≥ γt) + P (γSD < γt)Γ(γt)]× 1 + P (γSD < γt)(1− Γ(γt))× 2. (4.68)


In this subsection, we provide numerical and simulation results in terms of BER and throughput

performances for BPSK modulation. We allocate the same power to the source and the activated

relay, i.e. EX = Eb/2, where Eb is the transmitted energy per bit. All the paths of a given link

have equal average power and i.i.d gains.

For a link X-Y, let LXY and τ lXY be the number of paths and the delay of the path l,

respectively. Fig.4.6 studies the effect of time delay spacing η = τ2XY − τ1XY on the BEP for

LXY = L = 2, M = 2 and γt = 6 dB. We observe that the diversity decreases as path delays

decrease. At high SNR, the BER performance tends to have a diversity order of 1. This is

because at high SNR, the destination will rarely need any retransmission from the relay, thus no

cooperative transmission will be performed and hence the system will have a diversity order equal

47

0 2 4 6 8 10 12 14 16 18 2010

−5

10−4

10−3

10−2

10−1

100

Eb/N

0 (dB)

BE

R

Theo: Direct transmission, η=Tc/4

Theo: Direct Transmission, η=Tc

Theo: Incremental relaying+STDR, η=Tc/4

Theo: Incemental relaying+STDR, η=Tc

Sim: Direct Transmission, η=Tc/4

Sim: Direct transmission, η=Tc

Sim: Incremental relaying+STDR, η=Tc/4

Sim: Incremental relaying+STDR, η=Tc

Figure 4.6: Effect of time delay spacing on BER, L=2, M=2, γt = 6 dB

0 2 4 6 8 10 12 14 16 18 200.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

Eb/N

0 (dB)

Thr

ough

put

Theo: STDRTheo: Incremental RelayingTheo: STDR+Incremental RelayingSim: STDRSim: Incremental RelayingSim: STDR+Incremental Relaying

Figure 4.7: Throughput comparison for η = Tc, L=2, M=2 and γt = 6 dB

to 1. Finally, we observe a perfect agreement between analytical BEP results and simulations

curves.

Fig.4.7 and Fig.4.8 compare throughput and BER performances of IR, SR and the combined

ISR protocol, respectively, for R = 1 bit/s/Hz. We observe that ISR provides significantly

higher throughput compared to SR or IR exclusively without deteriorating the BER performance

mainly at medium SNR. At low SNR, performances of the combined protocol in terms of BER

is confused with those of SR, while at high SNR they tend to those of IR. This is because at low

SNR, the SNR of S-D link is often below γt so relaying process is controlled by the SR protocol

only. At high SNR, the SNR of the links between S and relays are often beyond γt, hence, only

48

0 5 10 15 2010

−6

10−5

10−4

10−3

10−2

10−1

100

Eb/N

0

BE

R

Direct transmissionIncremental RelayingIncremental relaying+STDRSTDR

Figure 4.8: BER comparison for η = Tc, L=2, M=2 and γt = 6 dB

IR protocol controls the system.

4.4 Conclusion

In this chapter, we have derived exact e2e BEP at D of the considered cooperative MC-CDMA

systems using Selective Threshold Digital Relaying (STDR) with best relay selection, relay with

largest SNR in relay-destination link, in the presence of multipath propagation. The derived

results are valid for any multipath intensity profile. In the other hand, we have studied BEP

and throughput performances of cooperative DS-CDMA systems using incremental relaying in

conjunction with best relay selection in the presence of multipath propagation. The derived

results are valid for any multipath intensity profile, any path delays, and take into account the

correlation between path gains. Throughput performance analysis shows that the combination

between selective and incremental relaying significantly improves the system throughput without

deteriorating BER performance.

49

Chapter 5

Performance Comparison between

Adaptive and Fixed Transmit Power

in Underlay Cognitive Radio

Networks

5.1 Introduction

Ever increasing demand for high data rate wireless services burdens the available spectrum

resources which become unable to satisfy this demand and suffer from severe scarcity. Cognitive

radio has emerged as a promising technology to optimize spectrum resources exploitation by

using the licensed spectrum in an opportunistic fashion [4]. In this technology, any cognitive

secondary user may share the spectrum with a licensed primary user as long as the latter fulfills

its Quality of Service (QoS) requirement. The protocols settling the coexistence of primary

and secondary users are classified into three approaches [3]: (i) interweave approach where the

secondary user can operate as long as the primary user is idle and must switch off whenever

this latter becomes active; (ii) overlay approach where the secondary and primary users share

simultaneously the spectrum whereas the secondary nodes must implement and perform some

techniques in order to assist the primary communications; (iii) finally, an underlay approach

where secondary users share the spectrum with the primary one but have to adjust their transmit

power to keep the induced interference always below a given allowable threshold. To fulfill the

50

interference constraint, the secondary transmitter uses generally low transmit power which limits

largely the performances of the cognitive radio network and hence this network may suffer from

low data rate and high symbol error probability (SEP). A way to ameliorate the performances

of the secondary network is the use of relaying. Recently, several works have focused on relaying

techniques in cognitive radio network [50]-[56]. In [50], Zou et al. have proposed to select the

relay with the largest SNR in relay-destination link under the constraint of satisfying a required

primary outage probability. In [51], Chen et al. have proposed a distributed relay selection

scheme while considering adaptive modulation and coding and energy states of relay nodes.

The same authors have proposed in [52] a relay selection scheme that maximizes the secondary

data rate whilst ensuring a minimum required primary data rate. In [53], a distributed relay

selection concurrently considering the channel states of all related links and residual energy

state of the relay nodes have been proposed. In [54], krishna et al. have proposed that relays

use beam steering capability to impose a target Signal-to-Interference plus Noise Ratio (SINR)

whilst fulfilling the primary requirement. In [55], Lin et al. have used the pricing function in

game theory to propose a novel low-interference relay selection derived from the conventional

max-min relay selection. In [56], amplify-and-forward relay selection scheme is investigated in

the presence of interference from primary transmitter.

All previous works assume that secondary transmitters can adjust their transmit power. Re-

cently, some efforts have focused on the use of secondary transmitter nodes using fixed transmit

power (FTP) [57]-[60]. In these works, several relaying schemes are investigated where sec-

ondary transmitters (source and relay) use their maximum available power when the primary

interference constraint is verified and remain silent otherwise. This approach is solely proposed

in [57]-[60] and is different from the approach where the relay remains silent when the direct

link is of high quality [20].

In this chapter, we consider a secondary network composed by simple nodes transmitting with

FTP. The secondary network consists of a source, a destination and several available relays. We

investigate the use of FTP which requires less signaling than the use of ATP. We investigate and

compare the performances of three relay selection schemes: opportunistic DF relaying with FTP

(O-DF with FTP), Opportunistic AF relaying with FTP (O-AF with FTP) and partial relay

selection with FTP (PR with FTP). We study analytically and by simulations the performances

of the considered relay selection schemes in terms of SEP, data rate and power consumption.

Using FTP in underlay cognitive radio network alleviates the signaling requirements compared

51

to the ATP nodes. But, it influences the performance of the cognitive radio system. The target

of our work is to study this by comparing the performances of FTP and ATP in terms of symbol

error probability, data rate and power consumption. This gives insights to cognitive network

architectures if using ATP or FTP is worthy. The relaying schemes when ATP is used are called:

O-DF with ATP, O-AF with ATP and PR with ATP. Our comparison study shows that FTP

has a positive impact on the data rate and power consumption performance while it deteriorates

the symbol error probability performance.

In [57]-[60], authors have considered only the FTP and have not provided a performance

comparison between FTP and ATP. Also they have considered only amplify and forward (AF)

relaying and have omitted the interference caused by the primary transmitter to the secondary

receivers. Moreover, they have analysed only the SEP and the outage probability performances.

In addition, in these works, all relays are assumed to be equidistant from primary receiver. The

contribution of our work compared to [57]-[60] consists in providing performance comparison

between the FTP and ATP in terms of SEP, data rate and power consumption. Moreover, we

have considered both decode and forward (DF) and AF relaying modes. In addition, we have

provided analytical study and simulation results of SEP, data rate and power consumption of

the secondary network in the presence and absence of interference from the primary transmitter.

The relays positions in our work are uniformly generated in a square 3x3 and simulation and

numerical results are averaged over many topologies.

The remainder of this chapter is organized as follows. In section 5.2, we describe our system

model. In section 5.3, we present the new relaying schemes. Section 5.4 is dedicated to present

the SEP analysis of each relaying scheme using FTP. Section 5.5 is dedicated for the data rate

and power consumption analysis. Section 5.6 shows and discusses theoretical and simulation

results. Finally section 5.7 draws some concluding remarks.

5.2 System Model

We consider an underlay cognitive radio network operating near a primary network. The primary

network consists of a primary transmitter (PT) communicating with a primary destination

(PD). The cognitive radio network consists of a source S communicating with a destination D

simultaneously with the primary communication. We assume that Mr relays are available to

assist S. The system model is depicted in Fig.5.1. We denote the set of the Mr available relays by

52

D

R1

Ri

RM

S

Direct transmission

Cooperative transmission

Primary transmitter (PT) Primary destination (PD)

Interference caused to PD

Figure 5.1: System model.

R. We assume that each transmission is subject to an additive white Gaussian noise (AWGN)

with zero mean and variance N0. The channel coefficient of the link X-Y is denoted by hX,Y

and is assumed to consist of path loss and independent fading effect as hX,Y = XX,Y d−α

2X,Y , where

dX,Y is the distance between X and Y and α is the path loss exponent. XX,Y is the fading

coefficient modeled as a circular symmetric complex Gaussian random variable with variance 1.

We assume that the channels coefficients are invariant during two time slots and may change

independently each two time slots. Nodes are assumed to be half duplex.

The communication time is divided into two time slots. In the first time slot, S sends its

signal while the M relays listen as shown by bold arrows in Fig.5.1. The transmitted signal is

also perceived by PD and hence causes some interference. In underlay cognitive radio network,

the interference level at PD caused by the secondary transmitters (source and relays) must be

below an interference threshold noted Ith. The interference caused by a transmitter X, noted

IX using a fixed transmit power PFX is as follows

IX = PFX | hX,PD |2≤ Ith, (5.1)

where PFX denotes the FTP used by the transmitter X. If the secondary transmitter X (S or

Ri) finds that the constraint (5.1) is satisfied, then it transmits with PFX . Hence, the SINR of

the link X-Y is given by

ΓX,Y =PFX |hX,Y |2

Pp|hPT,Y |2 +N0. (5.2)

If the secondary transmitter is unable to satisfy the primary interference constraint, then it

53

remains silent. This implies that the transmission process starts only if S satisfies the interference

constraint in (5.1). S transmits with a fixed power noted PFS and each relay Ri ∈ R, transmits

with a fixed power noted PFRi. The values of PF

S and PFRi

are set at the activation of the cognitive

radio network and remains fixed during all the transmissions.

The relays and D receive useful data from S and interference from PT as shown in Fig.5.1.

Thereby, the received signal at D during the first time slot can be written as follows.

yD =√

PFS hS,Dxs +

√PPhPT,Dx

1p + n1

D, (5.3)

where xs is the secondary symbol, x1p and n1D are the primary transmitted symbol and the noise

at D during the first time slot. Some relays, with the use of their FTP, will fall short of the

interference constraint and thus they can not be selected to forward the secondary signal. The

set of relays satisfying the interference constraint is denoted by U .

In the second time slot, one relay belonging to U is selected to forward the received signal.

Two relaying modes can be used: DF and AF.

If DF relaying is used, a subset from U , denoted by C gathering decoding relays is formed,

i.e., the relays that have correctly decoded the received signal. The selected relay from C,

denoted by RO-DFs , decodes the received signal then regenerates and forwards it. The received

signal at D during the second time slot is given by

yO-DF,2D =

√PFRO-DF

shRO-DF

s ,Dxs +√

PPhPT,Dx2p + n2

D. (5.4)

where x2p and n2D are the primary transmitted symbol and the noise at D during the second time

slot.

If AF relaying is used, the selected relay from U , denoted by RO-AFs , amplifies the received

signal using an amplification factor G =

√PF

RO-AFs

PFS |h

S,RO-AFs

|2+Pp|hPT,RO-AFs

|2+N0. Then, the selected

relay forwards the amplified signal to D. The received signal at D during the first and second

time slots are respectively given by

yO-AF,2D = GhRO-AF

S ,Dy1RO-AF

s+√

PPhPT,Dx2p + n22

D ,

where y1RO-AF

s=

√PShS,RO-AF

sxs+

√PPhPT,RO-AF

sx1p+nRO-AF

s, is the signal received by the selected

relay during the first time slot.

The transmission during the second time slot is shown by a dashed arrow in Fig.5.1.

54

5.3 Relaying schemes in underlay cognitive radio network

The relay selection process must respect the end-to-end SINR as well as the interference con-

straint imposed by the primary system. In the following, we present the three relaying schemes

using FTP: namely the O-DF with FTP, O-AF with FTP and PR with FTP. Then, we present

the corresponding relaying schemes using ATP: namely O-DF with ATP, O-AF with ATP and

PR with ATP.

5.3.1 Opportunistic DF Relaying with FTP (O-DF with FTP)

In underlay cognitive radio network operating in DF mode, the selected relay must respect the

three following constraints

• Interference constraint: the level of the interference caused by the selected relay should be

below the threshold allowed by the primary receiver.

• Decoding constraint: the selected relay should correctly decode the secondary signal.

• Finally, the selected relay should maximize the SINR of the relay-destination link.

To select a relay, we first determine the set U , then, the subset C (C ⊂ U). Finally, the selected

relay is the one in C maximizing the SINR of the relay-destination link. Hence RO-DFs =

argmaxRi∈C

ΓRiD, where ΓRiD is defined in (5.2).

5.3.2 Opportunistic AF Relaying with FTP (O-AF with FTP)

When the network operates in AF mode, the selected relay must respect two constraints

• Interference constraint: the interference perceived by the primary receiver is lower than

Ith.

• The selected relay maximizes the SINR of the source-relay-destination link.

The SINR of the relaying link source-relay-destination is given by

ΓSRiD =ΓSRiΓRiD

ΓSRi + ΓRiD + 1. (5.5)

For the relay selection, we first determine the set U . Then, the selected relay for O-AF with

FTP, denoted by RO-AFs , is chosen as RO-AF

s = argmaxRi∈U

ΓSRiD.

55

5.3.3 Partial relay selection with FTP (PR with FTP)

The proposed O-AF scheme requires knowing the state of source-relay and relay-destination

channels. When the number of available relays increases, the amount of required signaling

becomes important. This increases the complexity and may constitute an implementation bot-

tleneck. An alternative solution is to rely only on the SINR of source-relay link to moderate

signaling requirement. This idea was first proposed for non-cognitive radio network in [28]. The

new scheme is called partial relay selection. Consequently, the selected relay should

• Satisfy the interference constraint imposed by the primary user.

• Maximize the SINR of the source-relay link.

Hence, the selected relay for PR with FTP, denoted by RPRs , is chosen as RPR

s = argmaxRi∈U

ΓSRi .

5.3.4 Opportunistic DF relaying with adjustable transmit power (O-DF with

ATP)

In this scheme, in order to maximize the system performance while respecting the interference

constraint, each transmitter adjusts its power before each transmission as follows

PAX = min(

Ith|hX,PD|2

, PmaxX ), (5.6)

where PAX denotes the ATP used by the transmitter X, Pmax

X is the maximum available power

for the transmitter X. To select a relay, the decoding set of relays C is first formed. Then, each

relay Ri in C adjusts its power as in (5.6). The selected relay, denoted by RO-DF, ATPs , is the

one that maximizes the SINR of the relay-destination link such as: RO-DF, ATPs = argmax

Ri∈CΓRiD.

5.3.5 Opportunistic AF relaying with adjustable transmit power (O-AF with

ATP)

In this scheme, each relay Ri ∈ R, adjusts its power as in (5.6). Then, the relay maximizing the

SINR of the relaying link source-relay-destination denoted by RO-AF, ATPs is selected as follows

RO-AF, ATPs = argmax

Ri∈UΓSRiD, where ΓSRiD is defined in (5.5).

5.3.6 Partial relay selection with adjustable transmit power (PR with ATP)

In this scheme, each relay Ri ∈ R, adjusts its power as in (5.6). Then, the relay which maximizes

the SINR of the relaying link source-relay is selected. The selected relay is denoted by RPR, ATPs

56

Relay node Id CSI of Ri-D link

Figure 5.2: Signaling overhead structure used by fixed transmit power relays.

and is given by RPR, ATPs = argmax

Ri∈RΓSRi .

5.3.7 Signaling requirements comparison

We compare the signaling requirements of FTP and ATP and we show that FTP requires less

signaling than ATP.When the signaling requirements increases, extra resources must be provided

to carry more signaling information. This increases the practical implementation complexity of

the designed wireless system. We assume that S is the central scheduler that collects information

and selects the relay.

Fixed Transmit Power

If FTP nodes are used, each relay Ri compares the amount PFRi|hRi,PD|2 to the interference

threshold Ith. If Ri finds that PFRi|hRi,PD|2 < Ith, then it sends its identity and the value of

hRi,D to S. The signaling overhead structure used by FTP relays is shown in Fig.5.2. S then

collects the identities of the relays verifying the interference constraint and since it is assumed

to have a prior knowledge about the values of PFRi, ∀ Ri ∈ R, it can selects the best relay.

Adaptive transmit Power

If ATP nodes are used, to select the best relays, each relay Ri verifying PARi|hRi,PR|2 < Ith, has

to send its identity, the value of hRi,D and the value of its transmit power PARi

to S. The signaling

overhead structure of ATP is shown in Fig.5.4.

In Table.5.1, we compare the signaling requirements of the use of FTP and ATP. We can

easily see that comparing to FTP, in ATP, relays have to further send the values of their adapted

transmit powers to S. Obviously, when the number of relays increases. The signaling amount

required to transmit this information becomes huge.

57

Relay node Id CSI of Ri-D link value of PARi

Figure 5.3: Signaling overhead structure used by adaptive transmit power relays.

Fixed transmit Power nodes Adaptive Transmit Power nodes

• Identity of Ri

• The CSI of Ri-SR link

• Identity of Ri

• The CSI of Ri-D link

• The transmit power PARi

Table 5.1: Required CSI for the different RS schemes.

5.4 SEP Analysis of the relaying protocols

In this section, we derive the exact form expression of the SEP of O-DF with FTP and exact

and lower bound form of the SEP of O-AF and PR with FTP in the absence of interference

from PT. The exact SEP expression of the O-DF with FTP in the presence of interference from

PT is also derived while for O-AF and PR with FTP, only lower bound expressions are given,

due to the intractability of the exact form expressions.

To derive the SEP at a node X, we use the moment generating function (MGF) of the SINR

at X, ΓX , defined as follows

MΓX(s) = E(e−sΓX ), (5.7)

where E(.) is the expectation operator. For M-PSK modulation, the SEP at X can be deduced

from the MGF of ΓX as follows [61]

Ps,X =1

π

∫ πM−1M

0MΓX

(gpsk

sin2(θ)

)dθ, (5.8)

where gpsk = sin2( πM ). Similar expressions can be obtained for M-Quadrature Amplitude

Modulation (M-QAM) modulations.

58

5.4.1 SEP analysis of the O-DF with FTP

For the O-DF, the SEP at D can be written as

PO-DFs,D =

∑Θ⊂R

PO-DFs,D|U=ΘP(U = Θ). (5.9)

The probability P(U = Θ) is given by

P(U = Θ) =∏Ri∈Θ

P(IRi,PD ≤ Ith)∏

Rj∈Θ

P(IRj ,PD > Ith), (5.10)

where Θ = R\Θ and

P(IRi,PD ≤ Ith) = 1− exp(− Ith

IRi,PD

), (5.11)

where IRi,PD = PRiE(|hRi,PD|2). To derive PO-DFs,D|U=Θ, two cases arise.

Case 1: if U = ∅, then the conditional probability PO-DFs,D|U=Θ is given by

PO-DFs,D|U=Θ =

1

π

∫ πM−1M

0MΓS,D

(gpsk

sin2(θ)

)dθ, (5.12)

where MΓS,D(s) can be obtained by using the probability density function (PDF) of the SINR

ΓS,D given in (B.2) in Appendix B.1 and equation (5.7). In the absence of interference (i.e., the

interference from PT is negligible and could be approximated by 0, MΓS,D(s), can simply be

written as MΓS,D(s) = 1

1+λ2S,Ds

, where λ2XY =

PFX

dαxyN0.

Case 2: if U = ∅, then given that in O-DF with FTP, only relays belonging to U and having

correctly decoded the signal are retained as candidate relays, PO-DFs,D|U=Θ can be written as

PO-DFs,D|U=Θ =

∑J⊂U

PO-DFs,D|U=Θ,C=JP(C = J |U = Θ). (5.13)

Next, we derive each term of (5.13).

PO-DFs,D|U=Θ,C=J , is given by (5.12), if C = ∅. Otherwise, it is given by

PO-DFs,D|U=Θ,C=J =

1

π

∫ πM−1M

0MΓS,D

(gpsk

sin2(θ)

)MΓ

RO-DFs D

(gpsk

sin2(θ)

)dθ, (5.14)

where the expression of MΓRO-DFs D

(s) is derived in Appendix B.1. In the absence of interference,

MΓRO-DFs D

(s) is derived in Appendix B.2.

P(C = J |U = Θ), is given by

P(C = J |U = Θ) =∏Ri∈J

(1− Ps,Ri)∏Rj∈J

(Ps,Rj ), (5.15)

where J = U\J and Ps,X is the SEP at X given by (5.12) by replacing D by node X.

59

5.4.2 SEP Analysis of the O-AF with FTP

In this subsection, we provide an exact form and a lower bound expression of the SEP for the

O-AF with FTP in the absence of primary interference. The lower bound expression is derived

to provide which is simpler than the exact one since this latter is given in the form of double

integral. Due to the intractability of the exact form expression of the SEP in the presence of

interference from PT, only the lower bound expression is derived.

Exact form expression

The SEP at D can be written as

PO-AFs,D =

∑θ⊂R

PO-AFs,D|U=θP(U = θ), (5.16)

where P(U = θ) is given by (5.10). Next, we derive the exact form expression of the first term

of (6.18). To derive PO-AFs,D|U=θ, two cases arise.

Case 1: if U = ∅, then PO-AFs,D|U=θ is given by (5.12), where MΓS,D

(s) = 11+λ2

S,Ds.

Case 2: if U = ∅, then we have

PO-AFs,D|U=θ =

1

π

∫ πM−1M

0MΓS,D

(gpsk

sin2(θ)

)MΓ

SRO-AFs D

(gpsk

sin2(θ)

)dθ, (5.17)

where MΓSRO-AF

s D(s) can be computed as in (5.7) using the PDF of ΓSRO-AF

s D which can be

written as [62]

fΓSRO-AF

s D(γ) =

∑Ri∈U

fΓSRiD(γ)

∏Rj∈URj =Ri

FΓSRjD(γ), (5.18)

where fΓSRiD(γ) and FΓSRiD

(γ) are the PDF and the cumulative distribution function (CDF)

of ΓSRiD.

fΓSRiD(γ) and FΓSRiD

(γ) are given respectively by [63]

fΓSRiD(γ) = 2e−(νRi

+µRi)γ

[νRiµRi(2γ + 1)K0

(2√

νRiµRiγ(γ + 1)

)+(νRi + µRi)

√νRiµRiγ(γ + 1)K1

(2√

νRiµRiγ(γ + 1)

)], (5.19)

FΓSRiD(γ) = 1− 2e−(νRi

+µRi)γ√νRiµRiγ(γ + 1)K1

(2√

νRiµRiγ(γ + 1)

), (5.20)

where νRi =1

λ2SRi

, µRi =1

λ2RiD

and Kv(.) is the v-th order modified Bessel function of the second

kind.

60

Lower Bound expression

ΓSRiD can be upper-bounded as follows

ΓSRiD < min(ΓSRi ,ΓRiD)= ΓRi

up. (5.21)

Next, we derive the lower bound expression in the absence and in the presence of interference

from PT.

Absence of interference from PT: When the interference from PT is not considered, we

have ΓSRi and ΓRiD are two exponential random variables with mean λ2SRi

and λ2RiD

, respec-

tively. Thus, ΓRiup is an exponential random variable with mean

λ2SRi

λ2RiD

λ2SRi

+λ2RiD

.

Let ΓSelup denotes the maximum of ΓRi

up, Ri ∈ U . Hence, the MGF of ΓSelup can be deduced

from (B.5) as follows

MΓSelup

(s) =∑i∈U

2|U|−1−1∑p=0

(−1)ξ(p)

ωRis+ 1 +|U |−1∑k=1

ωRiξp(k)

ωRlRi,k

, (5.22)

where ωRi =λ2SRi

λ2RiD

λ2SRi

+λ2RiD

and lRi,k|U |−1k=1 is the set of relays indices in U\Ri.

Presence of interference from PT: In the presence of interference from PT, the CDF of

ΓRiup can be written as

FΓRiup(γ) = 1−

(σ2S,Ri

σ2S,Ri

+ σ2PT,Ri

γexp(− N0γ

σ2S,Ri

)

)(σ2Ri.D

σ2Ri,D

+ σ2PT,Dγ

exp(− N0γ

σ2Ri,D

)

), (5.23)

where σ2X,Y = PF

Xd−αX,Y . The PDF of ΓRi

up denoted by fΓRiup

can be found by deriving the CDF of

ΓRiup given above. Finally, the PDF of ΓSel

up can be computed as

fΓSelup

(γ) =∑Ri∈U

fΓRiup(γ)

∏Rj∈URj =Ri

FΓRiup(γ), (5.24)

and the MΓSelup

(s) can be deduced from (5.24) as in (5.7).

Using these results, a lower bound of PO-AFs,D|U=Θ is given by

BO-AFlow =

1

π

∫ πM−1M

0MΓS,D

(gpsk

sin2(θ)

)MγSel

up

(gpsk

sin2(θ)

)dθ. (5.25)

Substituting the lower bound of PO-AFs,D|U=Θ given in (5.25) and (5.10) in (5.16), we obtain a lower

bound for the SEP of O-AF with FTP.

61

5.4.3 SEP Analysis of the PR with FTP

We first give the exact form expression of the SEP of PR with FTP in the absence of interference

from PT. Lower bound expressions are derived in the presence and in the absence of interference

from PT.

Exact form expression

Considering the PR with FTP scheme, the SEP at D can be written as

PPRs,D =

∑Θ⊂R

PPRs,D|U=ΘP(U = Θ), (5.26)

where P(U = Θ) is given by (5.10). To derive PPRs,D|U=Θ, two cases arise.

If U = ∅, then PPRs,D|J=U is given by (5.12). Otherwise, if U = ∅, then, PPR

s,D|J=U is given by

PPRs,D|J=U =

1

π

∫ πM−1M

0MΓS,D

(gpsk

sin2(θ)

)MΓ

SRPRs D

(gpsk

sin2(θ)

)dθ, (5.27)

where MΓSRPR

s D(s) is derived in appendix B.3.

Lower Bound expression

ΓSRiD can be upper-bounded as (5.21). Let the upper bound of ΓSRiD be denoted by ΓSelup . The

MGF of ΓSelup , can be expressed as follows

MΓSelup

(s) =∑Ri∈U

MΓRiup(s)P(RPR

s = Ri), (5.28)

where P (RPRs = Ri) is given by (B.7) and M

ΓRiup(s) is the MGF of ΓRi

up. In the presence of

interference from PT, the expression of ΓRiup is computed similar to the previous section while in

the absence of interference it is given by MΓRiup(s) = 1

1+ωRis . Hence, a lower bound of PPR

s,D|J=U

is given by

BPRlow =

∑Ri∈U

P(RPRs = Ri)

1

π

∫ πM−1M

0

1

1 + ωRi

(gpsk

sin2(θ)

)dθ. (5.29)

Substituting the lower bound of PPRs,D|J=U given in (5.29) and (5.10) in (5.26), we obtain a lower

bound for the SEP of PR with FTP.

5.5 Data rate and power consumption Analysis

We derive the data rate and power consumption expressions for the three relaying protocols,

O-DF with FTP, O-AF with FTP and PR with FTP.

62

5.5.1 Data rate Analysis

The data rate is defined to be the amount of data successfully delivered per time unit. For the

direct transmission, the data rate can be written as

thx =ρ(1− Px

s,D)

E(T ), (5.30)

where ρ (bits/s/Hz) is the target transmission rate, x ∈ ’O-DF’,’O-AF’,’PR’, ’d’, where x = ’d’

stands for the direct transmission, Pxs,D is the SEP of the relaying scheme ′x′. The exact form

expression of PO-DFs,D is derived in subsection 5.4.1, in the presence and absence of primary inter-

ference. The exact form expressions of PO-AFs,D and PO-PR

s,D in the absence of primary interference

are derived in subsections 5.4.2 and 5.4.3, respectively. The upper bounds of the data rate ex-

pressions of O-AF and PR with FTP in the presence of interference are also given in subsections

5.4.2 and 5.4.3, respectively. Pds,D is given in (5.12).

E(T ) is the expected number of time slots to transmit one symbol. According to our system

setup, E(T ) for O-DF with FTP can be computed as follows

E(T ) = P(IS,PD > Ith)+P(IS,PD ≤ Ith) [(1− P(C = ∅)) (P(U = ∅) + 2(1− P(U = ∅))) + P(C = ∅)] .

(5.31)

For O-AF and PR with FTP, E(T ) can be computed as follows

E(T ) = P(IS,PD > Ith) + P(IS,PD ≤ Ith) [P(U = ∅) + 2(1− P(U = ∅))] . (5.32)

5.5.2 Power Consumption Analysis

The power consumption is the power consumed by the source and the selected relay to transmit

one symbol. For O-DF with FTP, the power consumption can be computed as follows

PO-DFConsumed = P(IS,PD ≤ Ith)×

Ps +∑Θ⊂RΘ =∅

P(U = Θ)

∑J⊂UJ =∅

P(C = J |U = Θ)

×

∑Ri∈C

P(Ri = Rxs |U = Θ, C = J)PRi

, (5.33)

63

where

P(Ri = RO-DFs |U = Θ, C = J) =

∏Rk∈CRk =Ri

∫ ∞

0

σ2RO-DF

s ,D

σ2RO-DF

s ,D+ σ2

PT,Dγexp(− N0γ

σ2RO-DF

s ,D

)

×

[N0

σ2Rk,D

+ σ2PT,Dγ

exp(− N0γ

σ2Rk,D

) +σ2Rk,D

σ2PT,D

(σ2Rk,D

+ σ2PT,Dγ)

2exp(− N0γ

σ2Rk,D

)

]dγ.

(5.34)

For O-AF and PR with FTP, the power consumption can be computed as follows

PxConsumed = P(IS,PD ≤ Ith)×

Ps +∑Θ⊂RΘ =∅

P(U = Θ)

∑Ri∈U

P(Ri = Rxs |U = Θ)× PRi

,(5.35)

where x ∈ ’O-AF’, ’PR’; P(RPRs = Ri) is given in (B.7) in appendix B.3 and the expression

of P(Ri = RO-AFs |U = Θ) is given by

P(Ri = RO-AFs |U = Θ) =

∏Rk∈CRk =Ri

∫ ∞

0(1− FΓSRiD

(γ))fΓSRkD(γ)dγ. (5.36)


In this section, we present theoretical and simulation results carried out in order to compare

the performance of relaying schemes using FTP nodes with those using ATP nodes. Simulation

results are averaged over many random topologies generated in a square 3 × 3. The path loss

exponent is set to 3. Without loss of generality, we have considered a simple binary phase

shift keying (BPSK) modulation. The maximum transmit power of the secondary source is

PmaxS = 0.5 watt. The same value is used for relays, Pmax

Ri= 0.5 watt, ∀Ri ∈ R. We assume

that all relays use the same fixed transmit power denoted PF . For each given primary transmit

power, we choose the fixed transmit powers PS and PF at the beginning of simulations. To do

so, we may find numerically the FTP values that minimize the secondary SEP or the ones that

maximize the secondary data rate. Without loss of generality, we choose the ones that minimize

the secondary SEP assuming that applications require low error rates. The primary transmit

power Pp is set to 0.5 watt. Our simulations are carried out to compare the SEP , the data rate

and the power consumption of the investigated relaying scheme using FTP nodes over relaying

schemes using ATP nodes. For the direct transmission, the source transmits only when it is able

to respect the interference constraint. The value of Ith is set to 0.05 watt. In the Figures, we

denote by Ip the interference caused by PT.

64

10 15 20 25 3010

−5

10−4

10−3

10−2

10−1

100

SNR (dB)

SE

P

Theoretical curves

Direct Transmission

O−DF with FTP (IP>0)

O−DF with ATP (IP>0)

O−DF with FTP (IP ≈ 0)

O−DF with ATP (IP ≈ 0)

(a)

10 12 14 16 18 20 22 24 26 2810

−5

10−4

10−3

10−2

10−1

100

SNR (dB)

SE

P

Direct Transmission

O−DF with FTP (Ip>0)

O−DF with ATP (Ip>0)

O−DF with FTP (Ip ≈ 0)

O−DF with ATP. (Ip ≈ 0)

(b)

Figure 5.4: SEP comparison of O-DF with FTP and O-DF with ATP (a) Mr=4 relays, (b)

Mr=2 relays

In Fig. 5.4, Fig. 5.5 and Fig. 5.6, we compare the SEP, the data rate and the power consumed

to transmit one symbol of the O-DF with FTP and O-DF with ATP, respectively for a number

of relays Mr = 2 and Mr = 4. In the presence of primary interference, the deterioration of SEP

performance due to the use of FTP nodes is by about 0.4× 10−1 at 30 dB. Moreover, Fig. 5.6

shows that O-DF with ATP consumes more power than O-DF with FTP. This is because, in

O-DF with FTP the cooperation is not always performed and hence the power that may be used

by the selected relay is saved.

65

10 15 20 25 30

0.4

0.5

0.6

0.7

0.8

0.9

1

SNR (dB)

Da

ta R

ate

Theoretical curves

Direct Transmissiom

O−DF with FTP (Ip ≈ 0)

O−DF with ATP (Ip ≈ 0)

O−DF with FTP (Ip >0)

O−DF with ATP (Ip >0)

Mr=2 relays

Mr= 4 relays

Mr=4 relays

Mr=2 relays

Figure 5.5: Data rate comparison of O-DF with FTP and O-DF with ATP for Mr=4 relays and

Mr=2 relays

10 15 20 25 300.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

SNR (dB)

Po

we

r co

nsu

mp

tion

Direct Transmission

O−DF with FTP

O−DF with ATP

Theoretical curves

Mr= 2 relays

Mr= 4 relays

Figure 5.6: Power consumption comparison of O-DF with FTP and O-DF with ATP for Mr=4

relays and Mr=2 relays

In the absence of interference, the difference between the SEP of O-DF with FTP and O-DF

with ATP becomes more important. In high SNR, O-DF with ATP significantly outperforms

the SEP of O-DF with FTP. This is mainly because at high SNR, transmitting with low power

is more efficient mainly in the absence of primary interference. Besides, in O-DF with FTP,

cooperation is not performed when relays disrespect the primary interference constraint while

in O-DF with ATP, the cooperation is always performed. Hence, the SEP of O-DF with ATP

66

is significantly better than that of O-DF with FTP. We observe that the presence of primary

interference largely deteriorates the SEP performances of the secondary network. For the same

consumed power, the performance of O-DF with FTP are deteriorated by about 0.5 × 10−1 at

20 dB.

In terms of data rate, Fig. 5.5 shows that O-DF with FTP slightly outperforms O-DF with

ATP. This is due to the fact that in O-DF with FTP, the cooperation is not always performed.

We observe that when the number of relays increases the SEP performances of the secondary

systems improve. This is because, when the number of relays increases, the central schedular S

may have better choices to select the best relay. Moreover, when the number of relays increases

the probability that all the relay do not respect the interference constraint decrease and hence

cooperation will often be performed. In terms of data rate, the performances decreases when

the number of relay increases. This is because, as explained earlier when the number of relay

increases, the cooperation is often performed which deteriorates the data rate. Obviously, when

the cooperation is always performed, the secondary system will dispense more power (power

allocated for the relay). Finally, we observe that analytical and simulation curves are in perfect

accordance which validates the presented performances analysis.

10 15 20 25 3010

−4

10−3

10−2

10−1

100

SNR (dB)

SE

P

Direct Transmission

O−AF with FTP (Ip >0)

O−AF with ATP (Ip >0)

O−AF with FTP (Ip ≈ 0)

O−AF with ATP (Ip ≈ 0)

Theoretical exact curve

Theoretical lower bound curve

Figure 5.7: SEP comparison of O-AF with FTP and O-AF with ATP for Mr=4 relays

In Fig. 5.7, Fig. 5.8 and Fig. 5.9, we compare the SEP, the data rate and the power

consumed to transmit one symbol of the O-AF with FTP and O-AF with ATP, respectively

for a number of relays Mr = 4. In the presence of primary interference, we observe that the

deterioration in SEP of O-AF with FTP compared to O-AF with ATP is not significant. Fig.

67

10 15 20 25 30

0.4

0.5

0.6

0.7

0.8

0.9

1

SNR (dB)

Dat

a R

ate

Direct Transmission

O−AF with FTP (Ip>0)

O−AF with ATP (Ip>0)

O−AF with FTP (Ip ≈ 0)

O−AF with ATP (Ip ≈ 0)


Theoretical upper bound curve (Ip>0)

Figure 5.8: Data rate comparison of O-AF with FTP and O-AF with ATP for Mr=4 relays

10 15 20 25 300.4

0.5

0.6

0.7

0.8

0.9

1

SNR (dB)

Po

we

r C

on

sum

ptio

n

Direct Transmission

O−AF with FTP

O−AF with ATP

Theoretical curves

Figure 5.9: Power consumption comparison of O-AF with FTP and O-AF with ATP for Mr=4

relays

5.9 indicates that O-AF with ATP requires more power than O-AF with FTP. In the absence of

interference, the deterioration in performance becomes a little important that in the presence of

primary interference. This is expected since the primary interference has a great impact on the

SEP performances of the secondary network. For data rate performance, Fig. 5.8 shows that

O-AF with FTP slightly outperforms O-AF with ATP. This is because in O-AF with FTP, the

cooperation is not always performed contrarily to O-AF with ATP where cooperation is always

performed. Form Fig. 5.7-Fig. 5.9, we conclude that O-AF with FTP requires less power than

68

O-AF with ATP while preserving close SEP performance to this latter and so, in this case it is

more interesting for practical implementation than O-AF with ATP. The theoretical curves in

Fig. 5.7-Fig. 5.9 match well with the simulation curves. Moreover, the lower bound curves are

very close to the exact curves.

10 12 14 16 18 20 22 24 26 2810

−4

10−3

10−2

10−1

SNR (dB)

SE

P

Direct transmission

PR with FTP (Ip>0)

PR with ATP (Ip>0)

PR with FTP (Ip ≈ 0)

PR with ATP (Ip ≈ 0)


Theoretical lower bound curve

Figure 5.10: SEP comparison of PR with FTP and PR with ATP for Mr ==4 relays

10 15 20 25 30

0.4

0.5

0.6

0.7

0.8

0.9

1

SNR (dB)

Dat

a R

ate

Direct Transmission

PR with FTP (Ip>0)

PR with ATP (Ip>0)

PR with FTP (Ip ≈ 0)

PR with ATP (Ip ≈ 0)


Figure 5.11: Data rate comparison of PR with FTP and PR with ATP for Mr =4 relays

In Fig .5.10, Fig. 5.11 and Fig. 5.12, we compare the SEP, data rate and the average power

consumed to transmit one symbol of the PR with FTP and the PR with ATP, respectively for

a number of relays Mr = 4. Like other schemes, we note that the SEP performances of both

69

10 15 20 25 300.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

Eb/N

0 (dB)

Pow

er

Consu

mptio

n

Direct Transmission

PR with FTP

PR with ATP

Theoretical curve

Figure 5.12: Power consumption comparison of PR with FTP and PR with ATP for Mr =4

relays

PR with FTP and PR with ATP are close. Meanwhile, a difference in power consumption is

observed in Fig. 5.12. In the absence of interference, the deterioration in SEP performance of

PR with FTP compared to PR with ATP is more important due to the improvement of the

channels qualities. In terms of data rate, Fig. 5.11 shows that the data rate of PR with FTP

is a little higher than that of PR with ATP. The data rate of both schemes remain close in the

absence of interference. We observe that the exact curves matches well with the simulation ones.

Moreover, the provided lower bound curves are close to the exact ones.

We conclude that in the presence of interference, which is a practical case, the deterioration

in performances due to the use of FTP nodes is slight. These results can be exploited to have

insights in designing simple and efficient cognitive radio networks. Also, for O-DF relaying,

figures show that the deterioration of SEP performance compared to O-DF with ATP is more

important than O-AF with FTP and PR with FTP relaying. This is due to the efficiency of

cooperation in DF relaying compared to AF relaying. Since in FTP the cooperation is not

always performed, this influences the SEP performance when using DF relaying more that AF

relaying.

70

5.7 Conclusion

In this chapter, we have showed that FTP needs less signaling than the ATP and we have

evaluated the performance degradation incurred by the FTP nodes compared to the ATP. We

have investigated three relaying schemes using FTP for an underlay radio cognitive network

operating near a primary receiver: O-DF with FTP, O-AF with FTP and PR with FTP. Our

proposed relaying schemes work by selecting a relay that is able to satisfy the interference

constraint imposed by primary receiver. The corresponding relaying schemes with ATP are

also presented in order to compare the performances of relaying schemes with FTP: O-DF with

ATP, O-AF with ATP and PR with ATP. In these schemes, relays adjust their transmit power

in order to respect the primary interference constraint. Exact form expressions in the absence

and presence of primary interference of the SEP, the data rate and power consumption of O-

DF are presented in order to validate simulation results. For simplification reasons, exact form

expressions for the SEP, the data rate and the power consumption of O-AF with FTP and PR

with FTP are provided in the absence of primary interference. Bounds of the performances of

O-AF with FTP and PR with FTP are given in both the absence and the presence of primary

interference. We proved that the use of O-AF with FTP and PR with FTP consumes less power

than O-AF with ATP and PR with ATP, respectively. But, O-AF with FTP and PR with

FTP incurs a slight deterioration in SEP performances compared to O-AF with FTP and PR

with ATP. For O-DF with FTP relaying, we found that the deterioration of SEP performance

compared to O-DF with ATP is more important than O-AF with FTP and PR with FTP

relaying.

71

Chapter 6

Spectrum Sharing Techniques for

Broadcast Cognitive Radio Networks

6.1 Introduction

As mentioned in chapter II, broadcasting is widely used in several applications such as control

and alarm message diffusion, satellite communications, TV-broadcasting, news-broadcasting,

etc. In this chapter, we address the problem of spectrum access in cognitive radio networks

to enable secondary broadcast communications. The main performance metric of broadcast

transmission is the number of receivers able to correctly decode the desired signal. Increasing

this number in a cognitive radio environment is very challenging due to the coexistence of

primary and secondary transmissions.

The use of Multi-Input Multi-Output (MIMO) technology in cognitive radio nodes may

enhance greatly the performances of secondary and primary networks [64]-[66]. Precoding for

secondary unicast transmissions have been previously investigated [67]-[72]. In [67], precoding

have been exploited to avoid co-channel interference for multi-user MIMO systems. In [68],

authors have proposed an orthogonal beamforming method to support several secondary users

with no interference to PRs. In [69], Zhang et. al. exploit the multiple antennas at the ST to

efficiently balance between spatial multiplexing for the secondary transmission and interference

avoidance at PRs. A beamforming scheme for a spectrum-sharing environment where multiple

antennas are used for both primary and secondary users is proposed in [70]. Gharavol et. al.

The contribution in this chapter was the fruit of the co-supervision of an internship student. I have contributed

in the design of the spectrum sharing schemes and in the redaction of the work

72

[71] design a beamforming matrix for downlink multi-user MIMO cognitive radio network which

allows to minimize the secondary transmit power. [72] considers one secondary transmission

coexisting with multiple primary transmissions and proposes an optimized beamforming at the

ST to maximize the secondary service probability while controlling the interference perceived at

PRs.

The previous works dealing with unicast or point-to-multipoint transmissions are not suit-

able for a broadcast network. Indeed, when the same data has to be delivered to multiple

destinations, unlike point-to-multipoint system, we do not need a multiplexing technique. In

this chapter, we consider a broadcast secondary network having one multi-antenna ST and large

number of SRs in the presence of a primary communication. We consider the orthogonal beam-

forming [73]-[74] (OBF) technique which requires limited channels feedback and provides low

computational complexity. Also OBF makes an efficient use of the transmit power and handles

SRs fairly and independently of their locations. We propose two secondary broadcast trans-

mission schemes using multi-antenna capability at the ST. Assuming that the primary allowed

interference threshold is set to zero. The two schemes use OBF to avoid interference received by

PR and they are based-on overlay approach. In the first scheme, SRs cancel out the interference

received from PT. It is named Overlay with OBF with post-Interference Cancelation (OOIC).

In the second scheme, we exploit decode and forward cooperative relaying technique [75] to re-

transmit the secondary signal. The second scheme is named Overlay with OBF and Cooperation

(OOC). A simple scheme based-on underlay approach (named underlay with OBF (UO)) is used

as a benchmark for comparison purpose. Overlay transmissions cannot always guarantee that

the primary system achieves the same data rate as if the secondary system is absent. Hence,

we assume that UO scheme is always implemented with OOIC or with OOC scheme and can be

used when overlay transmission scheme is harmful to the primary system. Anyhow, we do not

investigate an adaptive scheme that could switch between OOIC and OOC schemes, since it is

not practical and it is not efficient as will be seen in subsection 6.3.3. We study and compare the

performances of the proposed schemes in terms of primary outage probability and the rate of

correctly served SRs. In spite of the several applications of broadcast network, to the best of our

knowledge, it has not been previously investigated in cognitive radio environment. Therefore,

the performance comparison of OOIC and OOC schemes with other works is not provided. An-

alytical expressions of the outage probabilities for UO and OOIC are derived, given that OOC

is analytically intractable. The analytical performance of OBF technique for MIMO system is

73

not provided in earlier works. In this chapter, we derive the analytical expression of the PDF of

SNR for OBF technique, where the system is made of a single two-antenna transmitter and two

single-antenna receivers. Analytical and simulation results show that the two overlay schemes

improve significantly the secondary performances compared to the underlay scheme.

The rest of this chapter is organized as follows. In Section 6.2, the system model is detailed.

The proposed schemes are described in Section 6.3 and in section 6.4, the analytical studies are

presented and discussed. In section 6.5, the simulation results are given. Finally, conclusions

are drawn in section 6.6.

Throughout this chapter, ∥ . ∥ denotes the 2-norm. E(.) denotes the expectation operator.

[.]* denotes the conjugate operator. | . | denotes the modulo operator and .† denotes the

conjugate transpose operator. CN×M denotes all the complex N × M matrices. A complex

Gaussian random variable Z with mean µ and variance σ2 is denoted as Z ∼ CN (µ, σ2). The

SINR on the link X-Y is denoted by γX,Y and IN denotes the N ×N identity matrix.

6.2 System Model

We consider a secondary cognitive radio network consisting of one multi-antenna ST that broad-

casts data toward K single-antenna SRs and a primary communication between two single-

antenna nodes (PT to PR). The system model is shown in Fig. 6.1. Without loss of generality,

we assume that ST is equipped with two antennas. If ST has more than two antennas, we also

use the OBF technique to avoid the interference at PR and to transmit the secondary signal to

many orthogonal directions with equal transmit powers. PR and SRs use Optimum Combining

(OC) technique [76]-[77] when multiple copies of the same signal are received. In the presence of

interference, OC provides optimal SINR values and hence it is better than the Maximum Ratio

Combiner (MRC) [76]. Besides, when the transmissions are interference-free, the OC provides

the same performances as MRC [77].

All receivers generate additive white Gaussian noise (AWGN) with zero mean and variance

N0. The channel coefficient on the link X-Y, is denoted by hX,Y ∼ CN (0, d−αX,Y ), where α is the

path loss component and dX,Y is the normalized distance between X and Y . Hence, the Signal

to Noise Ratio (SNR) is modelled as an exponential random variable with mean λX,Y =PXd−α

X,Y

N0.

The energy of transmitted signals is equal to unity. The time is divided into time slots (TS) and

each TS is divided into two sub-slots. We assume that the channels state is invariant during

74

Figure 6.1: System Model

a TS, but it may change independently from a TS to another. Besides, we assume that ST

has a perfect knowledge of the ST-PR channel state. This knowledge is crucial to build the

beamforming matrix and to have zero interference at PR. We assume that PR (respectively

SR) correctly decodes the primary signal only if the achievable data rate on the link PT-PR

(respectively PT-SR) is higher than the required primary data rate denoted by Rthp . Also, SR

correctly decodes the secondary signal only if the achievable data rate is higher than the required

secondary data rate denoted by Rths .

6.3 Proposed transmission schemes

In this section, we describe the three schemes that we propose for the secondary broadcast

transmission.

6.3.1 Underlay with OBF transmission scheme (UO)

In this scheme, PT and ST transmit simultaneously and ST uses the OBF technique to avoid

the interference at PR as illustrated in Fig. 6.2.

The primary and the secondary weight vectors (denoted wp and ws respectively) are formed

using Gram-Schmidt algorithm [74] as follows:

wp =hST,PR

†

||hST,PR||,

ws =x−wp(wp

†x)

||x−wp(wp†x)||

, (6.1)

75

Figure 6.2: The UO transmission signals process

where x =

0

1

. The OBF matrix is written as: B = (wp ws). It is important to note that

||wp|| = 1 , ||ws|| = 1 and hST,PRws = 0. Hence, thanks to the OBF, PR receives the primary

signal with no interference. The received signal by PR is then given by:

yPR =√

PPThPT,PRxP + nPR, (6.2)

where PPT is the primary transmit power, xp is the primary transmitted symbol and nPR is the

AWGN at PR. Consequently, the achievable primary data rate is given by

RPR = log2

(1 +

PPT |hPT,PR|2

N0

). (6.3)

Each SR receives the useful secondary signal and the unwanted primary signal and hence

suffers from interference. The signal received by SRk, k ∈ 1 . . .K is given by

ySRk=√

PSThST,SRkwsxs +

√PPThPT,SRk

xP + nSRk, (6.4)

where PST is the secondary transmit power, xs is the secondary transmitted symbol and nSRk

is the AWGN at SRk. The achievable rate on the link ST-SRk is given by

RSRk= log2

(1 +

PST |hST,SRkws|2

N0 + PPT |hPT,SRk|2

). (6.5)

In the rest of this chapter, we assume that UO scheme is always implemented since it is

simple and requires no additional effort for its implementation. For the transmission schemes

OOIC and OOC, at the beginning of each time slot, ST estimates the achievable data rate on

the link PT-ST and the required transmit power to relay the primary signal. When the ST is

not able to correctly decode the primary signal during the first sub-slot or when it is not able

76

Figure 6.3: The OOIC transmission signals process

to provide to the primary network the same data rate as if the secondary network is absent,

then UO scheme is used. We do not consider any adaptive selection between OOIC and OOC

schemes.

6.3.2 Overlay with OBF and Interference Cancelation transmission scheme

(OOIC)

At the beginning of each TS, ST estimates the achievable data rate on the link PT-ST. When

ST is able to correctly decode the primary signal during the first sub-slot, the OOIC scheme

is applied. Otherwise, UO scheme is applied. In this scheme, the primary and secondary

transmissions are performed in two phases. Through the first sub-slot, xp is sent from PT and

received by PR, ST and SRs. During the second sub-slot, ST decodes the primary signal, and

transmits it simultaneously with the secondary signal. ST uses the OBF technique to avoid the

interference at PR. The transmission process of the OOIC scheme is depicted in Fig. 6.3. ST

devotes a fraction of its transmit power (denoted by β1PST ) to forward the primary signal. β1

should allow the primary system to achieve the same data rate as if the secondary network is

absent.

Using (6.1), the vector of the signals received by PR throughout the TS is written as

yPR =

√PPThPT,PR

√β1PST ||hST,PR||

xp + nPR, (6.6)

77

where nPR is the noise vector at PR. Hence, the achievable primary data rate can be written as

RPR =1

2log2

(1 +

PPT |hPT,PR|2

N0+

β1PST ||hST,PR||2

N0

). (6.7)

The secondary transmit power fraction β1 devoted to relay the primary signal is calculated

by solving the following optimization problem:

minimize β1

subject toPPT |hPT,PR|2

N0+

β1PST ||hST,PR||2N0

≥ γth,

where γth = (1 +12PPT |hPT,PR|2

N0)2 − 1 is a primary SNR threshold calculated as if secondary

network is absent.

The vector of signals received by SRk throughout the TS is given by

ySRk=

√PPThPT,SRk

0√β1PSThST,SRk

wp

√(1− β1)PSThST,SRk

ws

xp

xs

+ nSRk. (6.8)

To cancel out the interference at SRk, two cases arise:

• Case 1: If SRk correctly decode the primary signal during the first sub-slot, then SRk

subtracts the primary signal from the received signal. In this case the achievable data rate

on the link ST-SRk is given by

R(1)SRk

=1

2log2

(1 +

(1− β1)PST |hST,SRkws|2

N0

). (6.9)

• Case 2: If SRk is unable to correctly decode the primary signal during the first sub-slot,

then it multiplies the received vector of signals by the following orthogonal vector to cancel

out the interference

VSRk=(

−√

β1PSTPPT

hST,SRkwp

hPT,SRk∗

|hPT,SRk|2 1

). (6.10)

In this case, the achievable data rate on the link ST-SRk is given by

R(2)SRk

=1

2log2

1 +(1− β1)PST |hST,SRk

ws|2

N0

(1 +

β1PST |hST,SRkwp|2

PPT |hPT,SRk|2

) . (6.11)

6.3.3 Overlay with OBF and Cooperation transmission scheme (OOC)

Without loss of generality, we detail the transmission process during the n-th time slot (denoted

TSn) and we denote the primary and secondary signals to be transmitted during this TS by xnp

78

Figure 6.4: The OOC transmission signals process during the nth sub-slot

and xns respectively. At the beginning of TSn, ST estimates the data rate on PT-ST link. If

the estimated data rate is higher than Rthp , then the transmissions are done according to the

OOC scheme. Otherwise, UO scheme is applied and no cooperation is performed. In OOC

scheme, the transmissions of primary and secondary signals are done in two phases. At the

first sub-slot, PT transmits xnp , while ST stays silent. Simultaneously, a previously selected SR

(SRn−1Sel ) rebroadcasts x

n−1s as shown in Fig. 6.4. The SRn−1

Sel is selected at the beginning of TSn.

ST decodes xnp and after that it precodes xnp and xns , then transmits them during the second

sub-slot. Let define Gn1 as the set of SRs which have correctly decoded xns at the first sub-slot.

Let Ani denotes the metric representing the number of SRs that will be served if a candidate

relay SRi is selected at the TSn. Ani can be expressed as follows

Ani =

∑j∈1...K

j =i

H(Rn+1SRi,SRj

−Rths ), i ∈ Gn

1 , (6.12)

where H is the heaviside step function defined as H(z)=0 if z < 0 and H(z)=1 otherwise,

and Rn+1SRi,SRj

is the average data rate on the link SRi-SRj during TSn+1 given by

Rn+1SRi,SRj

=1

2log2(1 +

d−αSRi,SRj

PSRi

N0). (6.13)

At the beginning of the first sub-slot of the TSn, ST builds the set Gn2 including the candidate

relays having the largest metric Ani . Then, ST chooses, among the set Gn

2 , the SR that has the

worst channel coefficient with the PR in order to minimize. The rationality behind this selection

criteria is to minimize the interference received by PR from secondary transmission. Then, the

79

ySRk=

√β2PSThST,SRk

wpxnp +


wsxns

√PPThPT,SRk

xn+1p +

√PSRSel

hSRSel,SRkxns

+ nSRk. (6.18)

selected SR (SRnSel) is given by

SRnSel = arg min

i∈Gn2

|hSRi,PR|2. (6.14)

If no SR has decoded xns (i.e., Gn1 = ∅) during the second sub-slot of the TSn, then no

SR can be selected to relay xns in TSn+1. In this particular case, there will be no cooperation

transmission for the secondary signal xns .

At the second sub-slot, the ST uses the OBF matrix B defined in (6.1) to relay xnp with a

transmit power β2PST and broadcasts xns toward the K SRs with a transmit power (1−β2)PST .

An optimal choice of the coefficient β2 can be done as follows

minimize β2

subject toPPT |hPT,PR|2

PSRSel|hSRSel,PR|2+N0

+β2PST ||hST,PR||2

N0≥ γth, (6.15)

where γth is the primary SNR threshold defined in the optimization problem in subsection 6.3.2.

The vector of signals received by PR during TSn can be written as

yPR =

√PPThPT,PRx

np +

√PSRSel

hSRSel,PRxn−1s

√β2PST ||hST,PR||xnp

+ nPR. (6.16)

Consequently, the primary data rate is given by

RPR =1

2log2

(1 +

PPT |hPT,PR|2

PSRSel|hSRSel,PR|2 +N0

+β2PST ||hST,PR||2

N0

). (6.17)

The received signal by SRk is given by (6.18) in the next page.

The SRk uses OC to combine the two copies of the received secondary signals. So, the

achievable data rate on the link ST-SRk is given by

RSRk=

1

2log2(1 + c†dJ

−1cd), (6.19)

where J and cd are given by (6.20) in the top of the next page.

cd =


ws√PSRSel

hSRSel,SRk

. (6.21)

80

J =

β2PST |hST,PRkwp|2 +N0

√β2PSTPPThST,SRk

wphPT,SRk

∗

√β2PSTPPThST,SRk

∗w∗phPT,SRk

PPT |hPT,SRk|2 +N0

. (6.20)

It is important to note that it may appear interesting to investigate the idea of implementing

both OOIC and OOC schemes and use an adaptive technique to select one of the two schemes.

After investigation, we can easily see that implementing both schemes is not practical because

selecting the best scheme requires too much information. Moreover, OOC scheme proposes a

shifting of one sub-slot between primary and secondary transmissions (each transmissions lasts

two sub-slots), whereas there is no such shifting in OOIC scheme. Hence the adaptive scheme

should leave one sub-slot unused sometimes which degrades the achievable data rate. For these

reasons, we do not consider any possible switching between OOIC and OOC schemes.

6.4 Outage probability Analysis

In this section, we derive the outage probability expressions at PR and SRs considering the pro-

posed broadcast transmission schemes. The analytical study of the secondary outage probability

Poutk using OOC scheme is intractable and hence it will not be provided.

6.4.1 Outage probability of PR

An outage event occurs at PR when the data rate falls below the required value Rthp . Since all

the proposed transmission scheme do not affect the primary performance, the primary outage

probability at a given location of PR can be written as

Poutp(Rthp ) = Pr

(log2(1 +

PPT |hPT,PR|2

N0) < Rth

p

). (6.22)

Given that hPT,PR ∼ CN (0, d−αPT,PR), consequently the primary outage probability is written as

Poutp(Rthp ) = 1− exp

(−2R

thp − 1

λPT,PR

). (6.23)

81

6.4.2 Outage probability of SRs

An outage event is declared at SRk when its data rate is below Rths . Hence, the outage probability

of SRk at a given PR and SRk positions can be written as

Poutk

(Rth

s

)= Pr

(log2(1 + γST,SRk

) < Rths

). (6.24)

Next, we derive the outage probability Poutk through the UO and OOIC schemes.

UO scheme

To derive the expression of Poutk

(Rth

s

)through the UO scheme, we need the PDF of γSRk

for

UO.

Lemma 1 The PDF of γSRkfor UO is given by

fγST,SRk(x) =

exp(− xa1)(a1 + a1a2 + a2x)

(a1 + a2x)2, (6.25)

where a1 =PSTN0

d−αST−SRk

and a2 =PPTN0

d−αPT−SRk

. Proof is in Appendix C.1.

Consequently, the outage probability of SRk is given by

Poutk

(Rth

s

)= 1−

a1 exp(−2Rths −1a1

)

a1 + a2(2Rths − 1)

. (6.26)

OOIC scheme

According to (6.9) and (6.11), the SINR at SRk depends on the achievable data rate on the link

PT-SRk in the first sub-slot

γST,SRk=

γ1ST,SRk=

(1−β1)PST |hST,SRkws|2

N0, if γPT,SRk

≥ 22Rthp − 1

γ2ST,SRk=

(1−β1)PST |hST,SRkws|2

N0

(1+

β1PST |hST,SRkwp|2

PPT |hPT,SRk|2

) , if γPT,SRk< 22R

thp − 1.

(6.27)

Hence, the outage probability at SRk is given by

Poutk

(Rth

s , Rthp

)= Pr(γPT,SRk

≥ 22Rthp − 1)Pr(γ

1ST,SRk

< 22Rths − 1) + Pr(γPT,SRk

< 22Rthp − 1)

×Pr(γ2ST,SRk

< 22Rths − 1). (6.28)

82

Next, we derive the terms of (6.28). Given that γPT,SRkfollows an exponential distribution

of parameter λPT,SRk, then we have:

Pr(γPT,SRk≥ 22R

thp − 1) = exp

(− 22R

thp −1

λPT,SRk

). (6.29)

In order to simplify the derivation of the other terms of (6.28), we assume that β1 depends

only on the SRk position, so β1 is given by:

β1 =(1 + 1

2PPTd−αPT,PR

N0)2 − 1− PPT d−α

PT,PR

N0

PST d−αST,PR

N0

. (6.30)

Consequently, the second term of (6.28) can be written as

Pr(γ1ST,SRk

< 22Rths − 1) = 1− exp

(−(22R

ths − 1)

b1

), (6.31)

where b1 = (1− β1)λST,SRk.

The fourth term of (6.28) can be written as

Pr(γ2ST,SRk

< 22Rths − 1) = 1− exp

(−22R

ths − 1

(1− β1)

)+

β1(22Rth

s − 1)

(1− β1)λPT,SRk

exp

(β1(2

2Rths − 1)

(1− β1)λPT,SRk

)

×Ei

(− β1(2

2Rths − 1)

(1− β1)λPT,SRk

), (6.32)

where Ei denotes the exponential integral. The proof is given in Appendix C.2.

OOC scheme

From (6.19), the achievable data rate on the link ST-SRk for OOC scheme is written as:

RSRk=

1

2log2(1 + c†dJ

−1cd),

where

cd =


ws√PSRSel

hSRSel,SRk

. (6.33)

To derive the expression of the outage probability through OOC scheme, we need to know

the PDF of c†dJ−1cd and hence the PDF of |hSRSel,SRk

|. However, the selected SR (SRSel)

should (as explained in subsection 6.3.3), correctly decode the secondary signal, maximize the

number of served SRs and minimize the interference caused to PR. For this reason, the analytical

expression of the PDF of |hSRSel,SRk| is intractable and hence the analytical expression of the

outage probability considering OOC can not be provided.

83

0 5 10 15 20 25 3010

−3

10−2

10−1

100

PT transmit power (dB)

Prim

ary

outa

ge p

roba

bilit

y

OOIC: simulation UO: simulationOOC: simulationUO, OOIC, OOC: analytical

Figure 6.5: Primary average outage probability versus PT transmit power


In this section, we compare the performances of OOIC and OOC transmission schemes to UO

performances. We provide the simulation results to confirm the validity of our analytical re-

sults. We consider a rectangular area with a normalized size 1.5 × 1.5. PT and ST are placed

respectively at points (0, 0.75) and (1.5, 0). PR and SRs positions are generated randomly with

a uniform distribution. The presented results are averaged over a large number of random lo-

cations of PR and SRs. PR requires a data rate of 1 bit/s/Hz to decode correctly the primary

signal. We assume that Rths = 0.5 bit/s/Hz unless otherwise mentioned. The pathloss coeffi-

cient α is equal to 4. The noise variance is set to N0 = 1. We consider 20 SRs and one PR.

Simulation results are independent of the number of SRs when this number is larger than the

number of ST antennas, since all the SRs have the same average outage probability. Through

the comparison between schemes performances, the energy used by the primary network and

also by the secondary network, to transmit signals during a TS, are the same for all schemes.

Indeed, if we consider that the transmit powers of PT and ST are PPT and PST respectively in

UO scheme, then the transmit powers of PT and ST are 2PPT and 2PST respectively in OOIC

scheme. Likewise, in OOC scheme, the transmit powers of PT, ST and SRSel are set to 2PPT ,

PST and PST respectively.

Fig. 6.5 shows the primary average outage probability versus the PT transmit power for

different techniques UO, OOIC and OOC. The ST transmit power is set to 10 dB. UO technique

84

0 5 10 15 20 25 300.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

PT transmit power (dB)

Ra

te o

f se

rve

d S

Rs

OOIC: simulationUO: simulationOOC: simulationOOIC: analyticalUO: analytical

Figure 6.6: The rate of served SRs versus PT transmit power

provides to the primary network the same performance as if the secondary network is absent

as explained in subsection 6.3.1. This figure shows that primary outage probabilities through

OOIC, OOC and UO techniques are the same. Hence, we prove that OOIC and OOC do not

affect the primary performances. It can be also seen that the analytical results for primary

outage probability matches well with the simulation results.

Fig. 6.6 exhibits the rate of served SRs versus the primary transmit power when the sec-

ondary transmit power is set to PST = 10 dB. It is to be noted that the rate of served SRs

equal to 1− Poutk . It is shown that both OOIC and OOC schemes outperform the UO scheme.

Moreover, we find that OOC scheme is more efficient than OOIC scheme for low PPT , since

the primary interference perceived at SRs is limited. So, the interference cancelation has less

positive impact on the performance. However, when the primary transmit power increases, the

interference at SRs becomes more harmful. Hence, the OOC performance decreases and OOIC

becomes more efficient. This figure shows also the exactitude of the analytical secondary outage

probability expression. In fact, the analytical results matches well with the simulation results.

Fig. 6.7 shows the rate of served SRs versus the secondary transmit power. The transmit

power of PT is set to 10 dB. For low PST , we observe that OOIC slightly outperforms the OOC.

Indeed, through the OOC technique, when the interfered primary signal power level at SRs is

higher than the secondary signal power level, the SINR becomes low and SRs are not able to

correctly decode the secondary signal. However, through OOIC technique, the interference is

canceled out which provide better performance. This figure confirms also the statement that

85

0 5 10 15 20 25 300.4

0.5

0.6

0.7

0.8

0.9

1

ST transmit power (dB)

Ra

te o

f se

rve

d S

Rs

OOIC: simulationUO: simulationOOC: simulationOOIC: analyticUO: analytic

Figure 6.7: The rate of served SRs versus ST transmit power

OOIC and OOC outperforms UO.

Fig. 6.8 shows the rate of served SRs as a function of the required secondary data rate Rths .

The transmit power of PT and ST are set to PPT = 10 dB and PST = 10 dB respectively. We

observe that the rate of served SRs for the three schemes decreases when the secondary required

data rate increases. We observe also that OOIC and OOC maintains close performances. We

can also see the conformity between the analytical results for secondary outage probability and

the simulation results.

6.6 Conclusion

In this chapter, we have considered a secondary broadcast network composed of one multi-

antenna secondary transmitter which broadcasts data to single-antenna secondary receivers in

the presence of a primary communication. We have proposed two secondary broadcast trans-

mission schemes using orthogonal beamforming: OOIC and OOC schemes. The performances of

proposed schemes is compared to UO scheme performances. The proposed transmission schemes

allow the secondary network to access the spectrum without affecting the outage probability of

the primary receiver. Moreover, we have presented the performance analysis of the secondary

transmissions for UO and OOIC schemes. Transmission techniques operating in overlay mode

offer better secondary average outage probability compared to the first transmission schemes

operating in underlay mode. We have found that OOIC and OOC schemes have close perfor-

86

0.5 0.6 0.7 0.8 0.9 10.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

Secondary required data rate ((bits/s)/Hz)

Ra

te o

f se

rve

d S

Rs

OOIC: simulationUO: simulationOOC: simulationOOIC: analyticUO: analytic

Figure 6.8: The rate of served SRs versus the secondary required data rate

mances. We also notice that, for OOIC scheme, SRs require additional information to cancel out

the interference. Indeed, in OOIC scheme, each SR seeks to decode the primary signal at each

transmission and hence SRs must have knowledge about the transmission techniques of primary

system. For this reason, depending on the secondary nodes capability and available information,

the system adopts OOIC scheme or OOC scheme. Otherwise, if SRs do not have any knowl-

edge about the transmission techniques of primary system, the OOC scheme is recommended.

We conclude that the technique with interference cancelation provides high performance while

avoiding the implementation complexity.

87

Chapter 7

Spectrum Sharing Techniques for

Bidirectional Communication

7.1 Introduction

Several spectrum sharing protocols have been proposed to provide SUs a better access to the

spectrum. Exploiting multiple antennas has been proposed in [69] to allow secondary transmis-

sions in the presence of multiple primary receivers. Devoting a fraction of the transmit power of

an SU to relay primary signal is used in [75] to allow spectrum access where the SU transmits its

data using the rest of its transmit power. In [78], an opportunistic spectrum sharing approach

is proposed to maximize the downlink throughput of the cognitive radio system and limit the

interference perceived by the PU where communications exist between a cognitive base station

and multiple SUs. In [79], cooperative Orthogonal Frequency Division Multiplexing (OFDM)

relays are exploited to relay the primary signal on a fraction of the subcarriers and use the rest

of subcarriers to transmit secondary data. By overhearing and exploiting limited channel state

information (CSI) from PUs, SUs can gain spectrum access in [80]. Recently, spectrum sharing

with two way relaying have attracted considerable attention [81]-[83]. In [81], the authors con-

sidered a cognitive radio network where two secondary users can communicate with each other

via the help of a PU. In addition, applying network coding to a spectrum sharing system with

two-way relaying by using a decode-and-forward (DF) protocol was considered in [82]. In [83],

a pair of PUs bidirectionally communicate and the SU obtains spectrum access by devoting a

part of its power to perform two way relaying for PUs and use the rest of its power to transmit

secondary data. In [84], primary and secondary bidirectional communications between a pair of

88

secondary users and a pair of primary users is conducted with the help of a single-antenna relay.

The transmissions are done in two phases: a relay receiving phase and a relay transmitting

phase. The communications are always performed only via the relay.

In this chapter, we propose efficient and simple spectrum sharing techniques to conduct one

secondary and one primary bidirectional communications with the assistance of a relay. We

consider first a relay equipped with one antenna. Then, we deal with the case where the relay

is equipped with multiple antennas. Unlike [84], the relay intervenes only if the data rate of

the primary and/or secondary users are below the required values. For the proposed schemes,

we employ a time division access so that each user transmits in a fraction of time with no

interference. Then, the relay helps either primary or secondary users or both whenever their

data rates are below the required values. We compare the proposed schemes with the axiomatic

scheme where secondary users transmit and the relay cooperates with them in an underlay

mode. We provide analytical study for the performance of the secondary network in terms of

outage probability and BEP. Both analytical and simulation results prove that our proposed

schemes largely outperforms the simple underlay spectrum sharing scheme while the primary

outage probability remains the same as if the secondary users were absent.

This chapter is devised into four sections: (i) In section 7.2 we present the system model.

(ii) In section 7.3 we present our proposed spectrum sharing scheme when the relay has a single

antenna. (iii) In Section 7.4, we present two proposed spectrum sharing schemes when the relay

has multiple-antennas: in the first proposed spectrum sharing scheme no Beamforming tech-

niques will be exploited. In the second proposed spectrum sharing scheme some Beamforming

techniques will be exploited. (iv) In section 7.5 some concluding remarks and a summary of our

findings will be given. Section 7.3 is organized as follows. In subsection 7.3.1 we describe the

proposed spectrum sharing scheme. For comparison purposes, we present the underlay scheme

in subsection 7.3.2. Numerical and simulation results are presented in subsection 7.3.3. Section

7.4 is organized as follows. In subsection 7.4.1, we present the proposed spectrum sharing scheme

when no Beamforming techniques are used. For comparison reasons, we present the axiomatic

underlay spectrum sharing scheme in subsection 7.4.2. Subsections 7.4.3 and 7.4.4 are devoted

to present the proposed spectrum sharing scheme and the axiomatic underlay scheme when us-

ing Beamforming techniques, respectively. Performance analysis in terms of outage probability

and eventually BEP performance of the two proposed schemes are given in subsection 7.4.5 and

7.4.6. Numerical results can be found in subsection 7.4.7

89

Notations:

Let y ∈ 1, 2, y = 1, 2 \ y, x ∈ 1, 2 and x = 1, 2 \ x. The channel gain between

PUy and PUy, SUx and SUx, SUx and PUy, the j-th antenna of the relay R and a SUx and

the j-th antenna of R and PUy are denoted by hppyy, hssxx, h

spxy, hsx,j and hpy,j , respectively; ∥.∥

denotes the 2-norm; [.]H denotes the transpose conjugate operator; [.]t denotes the transpose

operator; [.]−1 denotes the inverse of the matrix; CN×M denotes all the N × M matrices; |.|

denotes the modulo operator; E(.) is the expectation operator;, IM denotes the identity matrix

of size M .pectru

7.2 System Model

We consider a cognitive radio network composed of two SUs (SU1 and SU2), two PUs (PU1

and PU2) and a secondary relay denoted by R as depicted in Fig. 7.1. All nodes are assumed

to be half duplex. The relay is equipped with M antennas while other nodes have single an-

PU1

PU2

SU1 SU2

R

Figure 7.1: System Model.

tenna, where M ≥ 1. The channel between two nodes k and l is assumed to have (i) a pathloss

component (a = d−α

2kl ), where dkl is the distance between k and l and α is the path loss expo-

nent and (ii) an independent fading effect component modeled as a circular symmetric complex

Gaussian random variable with variance 1. The noise is modeled as additive white gaussian

noise (AWGN) with zero mean and N0 variance. We assume that the state of the channels

are invariant during one time slot and may change independently each time slot. We assume

a bidirectional communication between SUs. Also, a bidirectional communication between PUs

exists where PUy starts the transmission with a probability 12 . The entire communication time

is one time slot (TS). We assume a bidirectional communication between SUs. Also, a bidirec-

90

tional communication between PUs exists where PUy starts the transmission with a probability

12 . The entire communication time is one time slot. The received signals at SUx and PUy can

be written respectively as

rsxx =√

Ps,xhssxxq

sx +

√Pp,yh

psyxq

py + ns

x, (7.1)

rpyy =√

Pp,yhppyyq

py +

√Ps,xh

spxyq

sx + np

y, (7.2)

where qsx, qpy (E(|qsx|2) = E(|qpy |2) = 1) are the transmitted symbols by SUx and PUy , respec-

tively; Ps,x and Pp,y are the transmit powers and nsx and np

y are the noise terms at SUx and

PUy, respectively.

The received vector of signals by the relay during the TSn is given by

rxy = M

qsx

qpy

+

n1

n2

, (7.3)

where nj , j ∈ 1, 2 are the received signal and the noise at the j-th antenna of R and

M =

√Ps,xhsx,1

√Pp,yh

py,1√

Ps,xhsx,2

√Pp,yh

py,2

.

We assume that the relay uses the optimum maximum likelihood (ML) detection technique to

decode the primary signal [85].

In TSn+1, SUx and PUy transmit their data simultaneously and R attempts to decode qpy .

To maximize the signal-to-interference and noise ratio (SINR), we assume that receivers use

OC to combine multiple copies of signals [86]. In the presence of interference, OC is proved to

provide higher SINR than the MRC [86].

7.3 Spectrum Sharing Exploiting a Single-antenna Relay

7.3.1 The proposed Spectrum Sharing Scheme exploiting a single-antenna

relay (PSC-SAR)

In this subsection, we assume that M , the number of antennas at the relay, is 1. Without loss

of generality, we suppose that PUy starts to transmit. In the absence of secondary network, the

time slot is divided into two sub-slots (12 time slot). During the first sub-slot, PUy transmits

data to PUy. Then, in the second sub-slot, PUy transmits data to PUy. This is depicted in Fig.

7.2 (a). Let Rp and Rs, denotes the primary and secondary required data rate, respectively.

91

At the beginning of each time slot, the data rate of PUs as if SUs are absent, denoted by

Rabs is computed as follows Rabs = 12 log2(1 +

Pp|hssyy |

2

N0), where PP denotes the transmit power

of PUs. We suppose that PUs transmit only if Rabs is below Rp. This helps PUs save energy

since their transmissions are in outage even if SUs are silent. If Rabs is higher than Rp, then to

allow SUs access the spectrum and perform their transmissions, we propose the following time

division access. In the first eighth of time slot, PUy transmits data to PUy. If the data rate at

PUy is below Rp, then during the second eighth of time slot, R forwards the received signal to

PUy to reach out the required value Rp. In the third eighth of time slot, SUx transmits data to

SUx with a power P xs , so that the data rate at SUx be equal to the required value Rs. As SUx

has a maximum available power Pmaxs , the transmit power P x

s can be given by

P xs = min(Pmax

s , P xreq), (7.4)

where P xreq is the power required to have Rs at SUx, given by P x

req =(28Rs−1)N0

|hssx,x|2

. If P xreq > Pmax

s ,

then the data rate at SUx is below Rs and hence R will forward the received signal from SUx

to help SUx reach the required data rate Rs. The proposed time division access is depicted in

Fig. 7.2 below.

PUy→PUy

TS

1/2 TS

SUx→SUx PUy→PUySUx→SUx SR→SUxSR→SUx

1/8 TS

PUy→PUy

SR→PUy

PUy→PUy

SR→PUy

(a)

(b)

Figure 7.2: (a) Time division access in the absence of SUs. (b) Time division access in the

presence of SUs.

In this case, the data rate at SUx can be written as

Rpropsec,x =

1

8log2(1 +

P xs |hssxx|2

N0+

Pr|hsx,1|2

N0), (7.5)

where Pr = min(Pmaxr , N0

|hsx,1|2

(28Rs − 1 − Pxs |hss

xx|2

N0)) and Pmax

r is the maximum available power

for R.

If the data rate at PUy is higher than Rp, then SUx transmits data to SUx during 716 of time

92

slot. If the data rate at SUx is below Rs, then during the next 716 of time slot, R forwards the

received signal from SUx to help SUx reach the required data rate Rs. Otherwise, if the data

rate at SUx is higher than Rs, SUx continues to transmit data during the next 716 of time slot.

Fig. 7.3 illustrates the described time division access.

PUy→PUy SUx→SUx PUy→PUy SUx→SUx SR→SUxSR→SUx

1/8 TS 7/16 TS

Figure 7.3: Time division access if PUs are not in outage.

If Rabs is below Rp, as mentioned earlier PUs remain silent. Hence SUs are free to use the

spectrum. The proposed time division access in this case is as follows. SUx transmits data to

SUx during the first quarter of time slot. If the data rate at SUx is below Rs, then during the

second quarter of time slot, R forwards the received signal to SUx in order to help it reach the

required data rate Rs. If the data rate at SUx is higher than Rs, then SUx continues to transmit

data to SUx during the second quarter of time slot. In the second half of time slot, SUx and

SUx substitutes rules and R helps SUx only if it is needed. This is also depicted in Fig. 7.4.

SUx→SUxSUx→SUx SR→SUxSR→SUx

1/4 TS

SUx→SUxSUx→SUx

1/2 TS

(a)

(b)

Figure 7.4: Time division access for SUs when Rabs < Rp. (a) Cooperation is needed (b)

Cooperation is not needed.

Note that when the data rate at PUy is below Rp, R must forward the signal received from

PUy with the following transmit power

P primr =

N0

|hpy,1|2(28Rp − 1−

Pp|hppyy|2

N0). (7.6)

If P primr is higher than Pmax

r , R can not help PUy and the spectrum sharing becomes impossible.

Hence, at the beginning of each time slot, the R verifies if P primr is within its power budget and

93

informs PUs and SUs that spectrum sharing is possible. Otherwise, SUs remain silent.

7.3.2 Underlay Spectrum Sharing Scheme with single-antenna relay (U-SAR)

In this scheme, each time slot is divided into two half time slots. Each half time slot is further

divided into four sub-slots. In the first sub-slot, SUx transmits data to SUx and PUy transmits

data to PUy, simultaneously. In the second sub-slot, if the data rate at SUx is below Rs , then R

forwards the signal received during the first sub-slot to SUx in order to reach out the data rate to

Rs. Otherwise, if the data rate at SUx is higher than Rs, SUx continues to transmit data to SUx

during the second sub-slot. In the third sub-slot, SUx and SUx substitutes roles and the same

process described above is executed in the fourth sub-slot. The same transmissions are repeated

in the second half of time slot. The proposed time division access for the underlay spectrum

sharing scheme is depicted in Fig. 7.5. As explained earlier, PUs transmit only if they estimate

that Rabs is higher than Rp. If Rabs ≥ Rp, SUs may access the spectrum simultaneously with

PUs by adapting their power so that the data rate at the primary receiver be Rp. For example,

if SUx wants to transmit, it is authorized to use the following power to not cause a harmful

interference to PUs

Pauth =1

|hssxx|2

(Pp|hppyy|2

22Rp − 1−N0

). (7.7)

Given that SUx has a maximum available power Pmaxs and the data rate at SUx must be equal

to Rs, then the used power by SUx can be written as

P′xs = min(Pmax

s , Pauth, P′xreq), (7.8)

where P xreq = (24Rs−1)N0

|gxx|2 , is the required power to have a data rate equal to Rs at SUx. If

Rabs < Rp, PUs will not transmit and SUs use the power as in (7.31).

PUy→PUy

TS

1/2 TS

SUx→SUx

PUy→PUy

SUx→SUxSR→SUx SR→SUx

1/4 TS

Figure 7.5: Underlay spectrum sharing scheme time division access.

94

PUy→PUy

TS

1/2 TS

SUx→SUx

PUy→PUy

SUx→SUx

1/2 TS

(a)

(b)

Figure 7.6: Underlay spectrum sharing scheme time division access when PUs are silent.

The data rate at SUx using the underlay spectrum sharing scheme is as follows

Runderlaysec,x =

1

4log2(1 +

P′xs |hssxx|2

N0 + Pp|hpsyx|2+

P ′r|hsx,1|2

N0 + Pp|hpsyx|2), (7.9)

where P ′r is given by

P ′r = min(Pmax

r ,N0

|hsx,1|2(24Rs − 1− |hssxx|2

N0),

1

|hpy,1|2(Pp|hppyy|2

22Rp − 1−N0)). (7.10)


In this subsection, some simulation results are presented to study the performance of our pro-

posed spectrum sharing scheme. We assume BPSK modulation. We consider a system topology

in a 2-D X-Y plane, where SU1, SU2, PU1 and PU2 are located at points (0, 0) and (1, 0), (0,

3) and (1, 3), respectively. Relay position is randomly distributed in a square 1× 1. Numerical

results are averaged over many random relay positions and path loss exponent is set to 3.5.

In Fig. 7.7, we present the secondary and primary average outage probabilities versus pri-

mary transmit SNR for Rp = 1 and Rs = 0.5 bits/s/Hz. The secondary transmit SNR is fixed

to 20 dB. The maximum available power for R, Pmaxr is fixed to 30 dB. We observe that the pro-

posed spectrum sharing scheme outperforms significantly the underlay spectrum sharing scheme.

This proves the robustness of our proposed spectrum sharing scheme. Moreover, we observe that

the outage probability performance of the proposed scheme is almost constant versus the pri-

mary transmit SNR. This is because our proposed spectrum sharing scheme is designed so that

the interference from the PUs is avoided. So whatever is the power used by the PUs, the perfor-

mance of our secondary network will not be affected. We observe that for low primary transmit

SNR, the outage probability of the secondary network is slightly better than the medium range

of the primary transmit SNR. This is because when the primary transmit SNR is low, Rabs is

95

10 12 14 16 18 2010

−3

10−2

10−1

100

Primary Transmit SNR (dB)

Out

age

prob

abili

ty

Primary usersPrimary users in absence of secondary usersU−SARPSC−SAR

Figure 7.7: Average outage probability versus primary transmit SNR, Rp = 1 and Rs = 0.5

bits/s/Hz.

often lower than Rp. Hence, PUs will not transmit and will leave the spectrum for the SUs. This

ameliorates the performance of the secondary network. As far as for the high transmit primary

SNR, the PUs will not need the help of R and hence SUs find larger time to transmit. Observe

that the primary outage probability in the absence of SUs and when our proposed spectrum

sharing scheme is applied are identical. This proves that our proposed spectrum sharing scheme

allows SUs to access spectrum and perform their transmission without affecting the performance

of the primary network and offers a secondary outage probability performance much better than

that of the underlay spectrum sharing scheme.

In Fig. 7.8, we present the outage probability of the proposed scheme and the underlay

spectrum sharing scheme versus the secondary transmit SNR. The primary transmit SNR and

Pmaxr are fixed to 20 and 30 dB, respectively. We observe that the outage probability performance

of the underlay spectrum sharing scheme decreases as the secondary transmit SNR increases.

This is because when the secondary transmit SNR increases, the maximum power available for

SUs increases and hence SUs can use higher power to satisfy their required data rate as long

as this do not harm the PUs. We observe that the performance of the outage probability of

the proposed spectrum sharing scheme is almost invariant versus the secondary transmit SNR.

This is because the relay R is designed to hide the power insufficiency of SUs. In other words,

if the available power of SUs is insufficient to reach the required value Rs, then R will dispense

its power to cooperate with the transmitting SU to make the data rate at the receiving SU

96

10 12 14 16 18 2010

−3

10−2

10−1

100

Secondary Transmit SNR (dB)

Out

age

prob

abili

ty

Primary usersPrimary users in absence of secondary usersU−SARPSC−SAR

Figure 7.8: Average outage probability versus secondary maximum SNR, Rp = 1 and Rs = 0.5

bits/s/Hz.

be equal to the required value. Moreover R is free to use the sufficient power as long as this

is within its power budget because R do not have any interference constraint toward PUs. In

Fig. 7.9, we present the outage probability performances of the underlay and the proposed

spectrum sharing scheme versus the maximum available power of R, Pmaxr . We set the primary

and secondary transmit SNR to 20 dB. We observe that the outage probability performance

of the underlay spectrum sharing scheme is invariant versus Pmaxr . This is because R has an

interference constraint toward the PUs and even if it has an extra power range, it can not use

it since its transmit power is controlled by the interference constraint imposed by PUs. For the

proposed spectrum sharing scheme, as we have designed a time division access so that SUs and

R transmit with no interference constraints, we observe that when Pmaxr increases, the outage

probability decreases. This is because, in the proposed scheme, R is free to use the power

sufficient to satisfy the data rate constraint of SUs as long as this power is within its power

budget. To conclude, the available power of the R is a key parameter that influences the outage

probability performance of the secondary network.

7.4 Spectrum Sharing Exploiting Multi-antenna Relay

In this section, without loss of generality, we assume that M , the number of antennas at the

relay, is 2. If M > 2, a selection of the two best antennas can be performed. In the following,

97

20 22 24 26 28 3010

−3

10−2

10−1

Maximum power of SR Prmax (dB)

Out

age

prob

abili

ty

U−SARPSC−SAR


bits/s/Hz.

we propose two efficient spectrum sharing techniques when we do not exploit Beamforming and

when we exploit Beamforming.

7.4.1 The first proposed Spectrum Sharing Scheme using Beamforming (PSC-

OB1)

Let Rs and Rp denote the required data rate by the secondary and primary users, respectively.

Without loss of generality, we consider the data rate at SUx. To attain Rs, SUx must transmit

with the following power

P reqx =

(23Rs − 1)(N0 + Pp,y|hpsyx|2)|hssxx|2

. (7.11)

Meanwhile, the maximum transmit power available for each SU is Pmaxs . Consequently, the

transmit power used by SUx is given by

Ps,x = min (Pmaxs , P req

x ) . (7.12)

Obviously, if P reqx > Pmax

s , then an outage occurs at SUx. Hence, if a given average outage

probability is required by the secondary network, then Pmaxs must be accordingly chosen using

empirical or numerical methods. At the end of TSn+1, the data rates at PUy and PUy are given

respectively by

Rn+1y =

1

2log2(1 +

Pp,y|hppyy|2

N0 + Ps,x|hspxy|2), (7.13)

98

Rn+1y =

1

2log2(1 +

Pp,y|hppyy|2

N0 + Ps,x|hspxy|2). (7.14)

These data rates are compared to Rp and three possible cases arise.

The two PUs reach Rp: This implies that the secondary transmission did not prevent PUs

from reaching its required data rate. Hence, cooperation is not needed. In the TSn+2, both

primary and secondary users transmit their next data.

The two PUs do not reach Rp: To help PUs reaching Rp, the relay performs two way

relaying for both PU1 and PU2 as follows. The relay uses cyclic redundancy check (CRC) to

verify if it has correctly decoded the primary received signal. Hence, the behaviour of R differs

according to the two cases: successful decoding and unsuccessful decoding.

Successful decoding: If the primary signal is correctly decoded then R uses the ZF precoding

to relay data to PUs during TSn+1.

The ZF precoding matrix , B ∈ C2×2, is defined as follows

B = HH(HiHH)−1 = (Wy Wy), (7.15)

where Wy,Wy ∈ C2×1 are the weight vectors used by R for PUy and PUy, respectively, and

H =

hpy,1 hpy,1

hpy,2 hpy,2

.

Let the power devoted to retransmit qpy be denoted by βy and the power devoted to retransmit

qy be denoted by βy. Using the ZF precoding matrix B, the received signal at y during TSn+2

is given by

rpy =

√βy

∥Wy∥2qpy + np,2

y . (7.16)

Since noises and interfering signals are uncorrelated , using OC the data rates at PUy and PUy

can be written respectively as [86]

Rn+2y =

1

3log2(1 + UH

yyC−1xy Uyy), (7.17)

where the coefficient 13 is due to the three-phase transmissions;

Uyy =

√Pp,yhppyy√

βy

∥Wy∥2

, Cxy = N0IM +

Ps,x | hspxy |2 0

0 0

.

99

To maintain Rp at both PUs, βy and βy must be as follows

βy = N0∥Wy∥2(23Rp − 1−Pp,y|hppyy|2

N0 + Ps,x | hspxy |2). (7.18)

The total power of R required to have Rp at both PUs is denoted by P reqr and is given by

P reqr = βy + βy. Given that Pmax

r is the maximum available power for the relay R, its transmit

power, Pr, is as follows

Pr = min(Pmaxr , P req

r ), (7.19)

Clearly, if P reqr > Pmax

r , PUs fall in outage. We assume that PUs impose an average outage

probability equal to or below a tolerable value ε. To make relay spend the minimum sufficient

power in favor of PUs, Pmaxr can be empirically or numerically set so that the average outage

probability is equal to ε. The average outage probability is computed over all the possible cases

(three cases) at given primary transmit signal to noise ratios (SNR), γyPT =Pp,y

N0, y ∈ 1, 2,

and a maximum secondary transmit SNR, γmaxST = Pmax

sN0

. To alleviate writing, we note simply

γST instead of γmaxST . For high values of γST , P

maxr will not depend from γST since the average

secondary transmit powers will be constant for high values of γST .

Note that βy and βy are always positive because both primary users do not reach the required

data rate Rp.

Unsuccessful decoding: The R failed to correctly decoded the primary signal using ML

detection and hence it will cooperates with PUs using amplify-and-forward relaying. Thanks to

its two antennas, R recovers two copies of each primary signal as shown in (7.3). To combine

them, it uses OC. Without loss of generality, considering that SUx and PUy transmit. Let the

desired propagation vector and the interfering propagation vector be denoted by Udp,y and U i

s,x,

respectively. We have

Udp,y =

√Pp,yhpy,1√

Pp,yhpy,2

, U is,x =

√Ps,xhsx,1√

Ps,xhsx,2

. (7.20)

The weights vector used to combine the signals of rxy is given by [87] Wxy = C′−1xy Ud

p,y, where

C′xy = N0IM + Us,xU

Hs,x.

The combined signal is then amplified using the following amplification factor Gxy =

√β′y

∥Wy∥2√|Wt

xyrxy|2,

where β′y is the power devoted to transmit data for PUy. Finally, the relay SR uses the ZF

100

precoding matrix in (7.15) to transmit the following signals vector

e =

GxyWtxyrxy

GxyWtxyrxy

, (7.21)

The data rates at PUy can be written as

R′n+2y =

1

3log2(1 +

γyγy′

γy + γy′ + 1

), (7.22)

where γy = UHyyC

−1xy Uyy and γ

′y =

β′y

N0∥Wy∥2 . To maintain Rp, β′y must be as follows

β′y =

N0

∥W iy∥2

(23Rp − 1− γy)(γy + 1)

γy − (23Rp − 1− γy). (7.23)

The power required by R is P′reqr = β

′y + β

′y. Due to power constraint, the transmit power of R

is P′r = min(Pmax

r , P′reqr ).

Only one PU reaches Rp: Suppose that PUy reaches Rp without resorting to cooperation

while PUy requires cooperation to reachRp. A second test must be done. It consists in comparing

the data rate of PUy supposing that it will not benefit from cooperation in TSn+2. The expression

of this data rate is given by

R′′n+2y =

1

3log2(1 +

Pp,y|hppyy|2

N0 + Ps,x|hspxy|2). (7.24)

If the data rate at PUy given in (7.24) is higher or equal to Rp, then the antenna of R offering

the highest channel quality is selected to transmit the data to PUy only. Otherwise, the system

will proceed like the case described in subsection 7.4.1.

If R succeeds to correctly decode qsy, then it transmits the decoded and remodulated signal

to PUy. The data rate at PUy is given by

R′′n+2y =1

3log2

(1 +

Pp,y|hppyy|2

N0 + Ps,x|hspxy|2+

P′′req|hpy,sel|

2

N0

),

(7.25)

where the subscript sel stands for the selected antenna of R and P′′req is the transmit power

required to maintain Rp at PUy given by

P′′req =

N0(23Rp − 1− Pp,y |hpp

yy |2

N0+Ps,x|hspxy |2

)

|hpy,sel|2. (7.26)

101

Due to power constraint, the used power by R is P′′r = min(Pmax

r , P′′reqr ).

If R does not succeed to correctly decode qsy, then it transmits the amplified signal given by√P

′′′req

|Wtxyrxy |2

Wtxyrxy, where P

′′′req must be as follows

P′′′req =

N0(23Rp − 1− γy)(γy + 1)

γy − (23Rp − 1− γy). (7.27)

Note that the secondary required power in (7.11) is defined supposing that the communica-

tion time lasts 3 TS. If the communication time lasts 2 TS (case 1), Rs remains within the reach

of SUs. The case where N available relays are deployed do not have any impact on the primary

outage probability performance but affects the power consumed by the activated relay. Since

relays always provide the sufficient transmit power to ensure for PUs the required performance.

As power consumption is not studied here, this general case may be dealt with in further works.

7.4.2 First underlay Spectrum Sharing Scheme using Beamforming (U-OB1)

Without loss of generality, supposing that during TSn. SUx transmits data to SUx and PUy

transmits data to PUy, simultaneously. During TSn+1, SUs substitute roles and so PUs do. The

deployed relay R will be exploited to perform two-way relaying for SUs. In underlay scheme, to

access spectrum, SUx must use a power denoted by P tx so that

P(Rn+1y < Rp) = ε, (7.28)

where Rn+1y is the data rate at y at the end of TSn+1, given by (7.13).

The expression of P tx is given by [50]

P tx =

Λyy

λxy(22Rp − 1)[

1

1− εexp(−(22Rs − 1)

Λyy)− 1], (7.29)

where λxy = 1dαxy

and Λyy =Pp,y

dαyy. Note that P t

x may be negative. Hence, the transmit power of

SUx is P t+x = max(0, P t

x). During TSn+2, if R succeeds to correctly decode secondary signals

then it uses ZF precoding matrix to transmit data to SUs. If R does not succeed to correctly

decode secondary signal then it combines the multiple copies of the secondary signals using OC.

The combined signals are then amplified and sent using ZF precoding matrix as follows

es =

√β′x

∥Wx∥2√|Ut

xxC−1yx

tryx|2

(UtxxC

−1yx

tryx)√

β′x

∥Wx∥2√|Ut

xxC−1yx

tryx|2

(UtxxC

−1yx

tryx)

. (7.30)

102

7.4.3 The second proposed Spectrum Sharing Scheme using Beamforming

(PSC-OB2)

Without loss of generality, we suppose that PUy starts to transmit. In the absence of secondary

network, the time slot is divided into two sub-slots (12 time slot). During the first sub-slot,

PUy transmits data to PUy. Then, in the second sub-slot, PUy transmits data to PUy. This is

depicted in Fig. 7.10 (a). In the presence of SUs, each half time slot is further divided into three

sub-slots (16 time slot), see Fig. 7.10 (b). At the beginning of each TS, the data rate of PUs as

if SUs were absent, denoted by Rabs is computed as follows Rabs = 12 log2(1 +

Pp|hppyy |

2

N0). If Rabs

is below Rp, then PUs will not transmit to save energy since their transmissions are in outage

even if SUs are silent. In this case, SUx transmits during the first sub-slot, SUx transmits during

the second sub-slot and a third sub-slot is devoted to R to assist the secondary transmissions.

This transmission is repeated at the second half of the time slot. If Rabs is higher than Rp, then

to allow SUs access the spectrum and perform their transmissions, we propose the following

time division access. In the first sub-slot, PUy transmits to PUy. In the second sub-slot SUx

transmits to SUx with a power P xs , so that the data rate at SUx be equal to the required value

Rs. As SUx has a maximum available power Pmaxs , the transmit power P x

s can be given by

P xs = min(Pmax

s , P xreq), (7.31)

where P xreq is the power required to have Rs at SUx, given by P x

req =(26Rs−1)N0

|hssx,x|2

.

PUy→PUy

TS

1/2 TS (a)

(b)

PUy→PUy SUx→SUx

PUy→PUy

PUy→PUy SUx→SUx

1/6 TS

SR→PUy

orSR→SUx

SR→PUy

SR→SUx

or

Figure 7.10: (a) Time division access for primary users in the absence of secondary users when

Rabs ≤ Rp (b) Proposed time division access for spectrum sharing

In the third sub-slot, the relay helps the user(s) in outage to reach the required data rate.

The functioning of R differs according to two cases as explained in the following.

103

Case 1: Both primary and secondary users are in outage: The data rate of primary

and secondary users are below Rp and Rs, respectively. If R receives the data from primary

and secondary users with an SNR higher than a threshold γt, then it decodes and forwards

the correspondent signals to both users in order to help them reach their required data rates.

Otherwise, if it receives the data from only the primary user with an SNR higher than γt, then it

proceeds as explained in subsection 7.4.3. Otherwise, it remains silent. To cooperate with both

users, R employs zero forcing beamforming (ZF-BF) thanks to its ability to null the interference

by transforming the channels into orthogonal and independent sub-channels [88]. The vector of

signals transmitted by R is given by

x = Bs (7.32)

where s ∈ C2×1 is the vector of primary and secondary signals and B ∈ C2×2, is the ZF-BF

precoding matrix. B is defined as follows

B = HH(HHH)−1 = (Wx Wy), (7.33)

where Wx,Wy ∈ C2×1 are the weight vectors used by R for SUx and PUy, respectively, and

H =

hsx,1 hpy,1

hsx,2 hpy,2

.

Let P xr and P y

r , be the power fractions used by R to relay the secondary and primary signals,

respectively. After cooperation, the data rate at PUy can be written as

Ry =1

6log2(1 +

Pp|hy,y|2

N0+

P yr

N0∥Wy∥2). (7.34)

The data rate of SUx can be written similarly to (7.34). To reach the required performances,

P xr and P y

r must be as follows

P xr = ∥Wx∥2N0(2

6Rs − 1−Pmaxs |hssx,x|2

N0), (7.35)

P yr = ∥Wy∥2N0(2

6Rp − 1−Pp|hppy,y|2

N0), (7.36)

We suppose that R has a maximum available power noted by Pmaxr . Hence, R could transmit

using ZF-BF only if the following power constraint is verified: P xr +P y

r ≤ Pmaxr . At the beginning

of each time slot, if the R estimates that the power constraint is not verified, it informs SUs to

transmit in underlay mode using the scheme described in 7.3.2.

104

Case 2: Only the primary or the secondary user is in outage: If only the primary or

the secondary user has the data rate below the required value, then if R receives the data (to

be forwarded) with an SNR higher than γt, it decodes and forwards it. Otherwise, it remains

silent. Exploiting the full channels knowledge at R, the optimal beamforming method that

maximizes the data rate at the user in outage is the singular value decomposition beamforming

(SVD-BF) [85]. Without loss of generality, we suppose that R has to re-forward data to PUy.

Similar expressions could be easily given when the relay has to forward a secondary signal. Let

G =(hpy,1 hpy,2

). We can decompose G in SVD form as follows G = UΣVH , where U = −1,

V ∈ C2×2 is an unitary matrix and Σ =(√

|hpy,1|2 + |hpy,2|2 0). Then, the SVD beamforming

matrix used by R is V and the vector transmitted is V.

qpy

0

. By multiplying the received

signal at PUy by U , it will have the following form

r =

√P y′r (|hpy,1|2 + |hpy,2|2)q

py + n′, (7.37)

where P y′r is the power used by R to forward the data to PUy, n

′ = U.n and n is the AWGN

noise at PUy. Note that the distribution of n is invariant under unitary transformation. To

keep the primary outage probability identical to the case where SUs are absent, P y′r must be set

as follows

P y′r =

N0

|hsy,1|2 + |hsy,2|2(26Rp − 1− Pp|hyy|2

N0). (7.38)

At the beginning of each time slot, if the R estimates that P y′r > Pmax

r , it informs SUs to

transmit in underlay mode using the scheme described in section 7.3.2. In the second half time

slot, the same division is used and primary and secondary users substitute roles as shown in Fig.

7.10 (b).

7.4.4 Second Underlay Spectrum Sharing Scheme using Beamforming (U-

OB2)

In this scheme, each time slot is divided into two half time slots. Each half time slot is further

divided into three sub-slots. In the first sub-slot, SUx transmits data to SUx and PUy transmits

data to PUy, simultaneously. In the second sub-slot, SUx transmits data to SUx and PUy

transmits data to PUy, simultaneously. This is depicted in Fig. 7.11.

In the third sub-slot, if the relay receives the data from both SUs with an SNR higher than

γt, then it cooperates with both SUs using ZF-BF. Otherwise, if the relay receives the data from

105

PUy→PUy

TS

1/2 TS

SUx→SUx

PUy→PUy

SUx→SUxSR→SUx SR→SUx

1/4 TS

Figure 7.11: (a) Primary transmission in the absence of secondary users (b) Underlay Spectrum

Sharing scheme

only one SU with an SNR higher than γt, then it cooperates only with this SU using SVD-BF.

If the relay receives the data from both SUs with an SNR below than γt, then it remains silent

to avoid error propagation. As explained earlier, PUs transmit only if they estimate that Rabs

is higher than Rp. If Rabs ≥ Rp, SUs may access the spectrum jointly with PUs by adapting

their power so that the data rate at the primary receiver be Rp. For example, if SUx want to

transmit, then it adapts its transmit power Px as follows

Px =1

|hssxx|2

(Pp|hppyy|2

22Rp − 1−N0

)(7.39)

If Rabs < Rp, PUs will not transmit and SUs use the power as in (7.31).

7.4.5 Outage Probability and BEP Performance Analysis of PSC-OB1

In this section, we analyse the performance of the secondary network in terms of average outage

probability and average BEP. Without loss of generality, we consider that the node SUx is

receiving data from SUx and interference from PUy.

Average outage probability Analysis: The average outage probability at SUx is given by

Pout,SUx = P((23Rs − 1)(N0 + Pp,y|hpsyx|2)

|hssxx|2> Pmax

s ). (7.40)

This can be yet formulated as

Pout,SUx =

∫ ∞

Θ

∫ z

0

1

ρyxexp(−z − (23Rs − 1)N0

ρyx)1

σxxexp(− t

σxx)dzdt, (7.41)

106

where Θ = (23Rs − 1)N0, ρyx =(23Rs−1)Pp,y

dαyxand σxx = Pmax

sdαxx

. Solving this double integral yields

to the following expression

Pout,SUx = 1− σxxσxx + ρyx

exp(− Θ

σxx). (7.42)

Average BEP Analysis: According to our setup, the SINR at SUx is given by

γx,y =

Pmaxs |hss

xx|2

N0+Pp,y |hpsyx|2

, If outage

23Rs − 1, o.w.

(7.43)

Consequently, the average BEP at SUx can be written as

Pe,SUx = Pe,SUx|outPout,SUx + Pe,SUx|no−out(1− Pout,SUx), (7.44)

where Pe,SUx|out and Pe,SUx|no−out are the conditional average BEPs given that SUx is in outage

and SUx is not in outage, respectively. If there is an outage at SUx (i.e., γx,y < 23Rs − 1), the

conditional PDF of γx,y|out is given by

fγx,y |out(γ) =1

1− σxxσxx+βyx

exp(− Θσxx

)

[N0

σxx + Λyxγexp(−N0γ

σxx) +

σxxΛyx

(σxx + Λyxγ)2exp(−N0γ

σxx)

],

for 0 ≤ γ ≤ 23Rs − 1.

(7.45)

where σxx = Pmaxsdαxx

and Λyx =Pp,y

dαyx.

Using the conditional PDF of γx,y|out, the expression of Pe,SUx|out can be written as

Pe,SUx|out =

∫ 23Rs−1

0AQ(

√Bγ)fγx,y |out(γ)dγ, (7.46)

where A and B depend on the considered modulation (e.g., A=1 and B=2, for binary phase

shift keying (BPSK) modulation). In case of no outage, the conditional probability Pe,SUx|no−out

is simply given by

Pe,SUx|no−out = AQ(√

B(23Rs − 1)). (7.47)

Substituting (7.42), (7.61) and (7.47) in (7.63), we obtain the expression of the average BEP at

SUx.

107

7.4.6 Outage Probability Performance Analysis of PSC-OB2

In this subsection, we analyse the performance of the SUs in terms of average outage probability.

Without loss of generality, we consider the outage probability at the node SUx. The outage

probability at the node SUx can be similarly derived. For Rabs ≥ RP , let E1 denote the event

that R receives the data from the primary users with an SNR lower than γt and the secondary

interference makes the primary data rate below Rp. E2 denotes the event that the maximum

available power at R is insufficient to help PUs. To simplify the analysis, we suppose that if E1

or E2 comes true, then an outage occurs at SUx (Normally, in our proposed scheme, if E1 or

E2 come trues, then SUs operates in underlay mode and may not suffer from outage). This will

give an upper bound expression of the outage probability of SUx. If E1 and E2 do not come

true, then an outage occurs at SUx if one of the following events comes true:

• E3 :Pmaxs (|hs

x,1|2+|hs

x,2|2)

N0< γt and P x

req > Pmaxs ;

• E4 : R helps both PUy and SUx using ZF-BF and P xr > (Pmax

r − P yr ) and P x

req > Pmaxs ;

• E5 : R helps only SUx using SVD-BF and P x′r > Pmax

r and P xreq > Pmax

s .

For Rabs < RP , an outage occurs at SUx if one of the following events comes true

• E6 : SUx is in outage andPmaxs (|hs

x,1|2+|hs

x,2|2)

N0< γt;

• E7 : Both SUx and SUx are in outage and the maximum power available for R is insufficient

to help them using ZF-BF;

• E8 : Only SUx is in outage and the maximum power available for R is insufficient to help

it using SVD-BF.

Thus, the outage probability at SUx can be expressed as

Pxout = P(Rabs ≥ Rp)(PE1 + PE2 + ((1− PE1)(1− PE2))

×(PE3 + PE4 + PE6) + P(Rabs < Rp)(PE6 + PE7 + PE8).

(7.48)

Next, we derive the terms of (7.48). According to the definition of E1, we have

PE1 = P

(Pp(|hpy,1|2 + |hpy,2|2)

N0< γt

)

×P(|hyy|2 <

N0

Pp(26Rp − 1)

). (7.49)

108

Let X =Pp(|hp

y,1|2+|hp

y,2|2)

N0. As X is the sum of two exponential random variables, then its PDF

is given by

fX(γ) =exp(− γ

σpy,1

)− exp(− γσpy,2

)

σpy,1 − σp

y,2

, (7.50)

where σpy,1 =

Ppdp−α

y,1

N0, dpy,1 denotes the distance between Puy and the first antenna of R . Hence,

P

(Pp(|hpy,1|2 + |hpy,1|2)

N0< γt

)=

exp(− γtσpy,2

)− exp(− γtσpy,1

)

σpy,2 − σp

y,1

. (7.51)

As |hyy|2 follows an exponential distribution with parameter 1d−αyy

, we have

P(|hyy|2 <

N0

Pp(26Rp − 1)

)= 1− exp(−

N0Pp

(26Rp − 1)

d−αyy

), (7.52)

and

P(Rabs ≥ Rp) = exp(−N0Pp

(22Rp − 1)

d−αyy

). (7.53)

To determine PE2 , we have to determine the probability density function (PDF) of P yr in (7.36).

For that, let Wy =

w1y

w2y

. We have

hsx,1w

1y + hpy,1w

2y = 1

hsx,2w1y + hpy,2w

2y = 0.

(7.54)

By resolving this system to determine w1y and w2

y, we obtainw1y =

hpy,2

hsx,1h

py,2−hs

x,2hpy,1

w2y =

−hsx,1

hsx,1h

py,2−hs

x,2hpy,1

.

(7.55)

Hence, ∥Wy∥2 =|hp

y,2|2+|hs

x,1|2

|hsx,1h

py,2−hs

x,2hpy,1|2

. This can be yet approximated as

∥Wy∥2 ≈|hpy,2|2 + |hsx,1|2

|hsx,1hpy,2|2 + |hsx,2h

py,1|2

. (7.56)

LetXy denote the random variable given as approximation of ∥Wy∥2. The PDF of the numerator

|hpy,2|2+ |hsx,1|2 can be deduced from (7.50). Let Z = |hsx,2hpy,1|2 and Y = |hsx,1h

py,2|2. As Z is the

product of two independent exponential random variables, hence its PDF is given by

fZ(β) =

∫ ∞

0

1

γdsx,2−α exp(− γ

dsx,2−α )

1

dpy,1−α exp(− β

γdpy,1−α )dγ. (7.57)

109

The PDF of Y can be computed similarly to Z. Using fZ and fY , the PDF of Z + Y can be

determined as fZ+Y (γ) = fZ(γ) ∗ fY (γ), where ∗ denotes the convolution operation. Finally,

the PDF of Xy can be computed as follows

fXy(γ) =

∫ ∞

0βfZ+Y (β)

exp(− γσpy,2

)− exp(− γβσsx,1

)

σpy,2 − σs

x,1

dβ. (7.58)

The PDF of Y ′ = N026Rp − N0 − Pp|hppy,y|2 can be easily deduced from the PDF of |hppy,y|2 as

follows

fY ′(γ) =1

Ppd−αyy

exp(β −N0(1− 26Rp)

Ppd−αyy

), for 0 ≤ β ≤ N0(26Rp − 1). (7.59)

Hence, the PDF of the random variable P yr in (7.36) can be deduced as follows

fP yr(γ) =

∫ ∞

0

1

βfZ+Y (β)fY ′(

γ

β)dβ. (7.60)

Using these results, PE2 can be computed as follows PE2 =∫∞Pmaxr

fP yr(γ)dγ.

From the definition of E3, we have

PE3 = P(P xreq > Pmax

s )P(P xs (|hsx,1|2 + |hsx,2|2)

N0< γt). (7.61)

It is easy to show that:

fPxreq

(γ) =1

(2RS − 1)N0d−αxx γ

2exp(− 1

(2RS − 1)N0d−αxx γ

). (7.62)

and hence P(P xreq > Pmax

s ) = 1−exp(− 1(2RS−1)N0d

−αxx Pmax

s). Moreover, using the PDF of the sum

of two exponentials, we have P(Pmaxs (|hs

x,1|2+|hs

x,2|2)

N0< γt) =

exp(− γtσsx,2

)−exp(− γtσsx,1

)

σsx,1−σs

x,2. Substituting

these expressions in (7.61), we obtain the expression of PE3 .

The probability that E4 comes true is given by

PE4 = PE14P(P x

req > Pmaxs )P(P x

r > Pmaxr − P y

r ), (7.63)

where E14 denotes the event that R helps both PUy and SUx using ZF-BF. The expression of

PE14is given in (C.7) in the top of the next page

PE14= (1− exp(−26Rp − 1

σ2yy

))(1− exp(−26Rs − 1

σ2xx

))P(Pmaxs (|hsx,1|2 + |hsx,2|2)

N0≥ γt)

×P(Pp(|hpy,1|2 + |hpy,2|2)

N0≥ γt), (7.64)

110

and

P(P xr > Pmax

r − P yr ) =

∫ ∞

0

∫ Pmaxr −β

0fPx

r(γ)f

P yr(β)dγdβ. (7.65)

The probability that E5 comes true can be written as

PE5 = PE15P(P x

req > Pmaxs )P(P x′

r > Pmaxr ), (7.66)

where E15 denotes the event that R helps only SUx using SVD-BF. This can be computed as

P(E15) = exp(−26Rp − 1

σ2yy

)(1− exp(−26Rs − 1

σ2xx

))P(Pmaxs (|hsx,1|2 + |hsx,2|2)

N0≥ γt)). (7.67)

To determine P(P x′r > Pmax

r ), let Z ′ = N0

|hpy,1|2+|hp

y,2|2. It is easy to show that:

fZ′(γ) =

1N0γ2 (

1dpy,2

exp(− 1N0d

py,2γ

)− 1dpx,2

exp(− 1N0d

px,2γ

))

N0(dpy,2 − dpx,2)

. (7.68)

Hence, the PDF of P x′r is given by

fPx′r(γ) =

∫ ∞

0

1

βfZ′(γ)

1

Pmaxs dyy

exp(

γβ −N0(1− 26Rs)

Pmaxs dxx

)dβ. (7.69)

Finally P(P x′r > Pmax

r ) =∫∞Pmaxr

fPx′r(γ)dγ. PE6 to PE8 can be deduced from the derivations

above.


In this subsection, some numerical results are presented to study the performance of our proposed

spectrum sharing scheme. We assume BPSK modulation. We consider a system topology in a

2-D X-Y plane, where SU1, SU2, PU1 and PU2 are located at points (0, 0) and (1, 0), (0, 3)

and (1, 3), respectively. Relay position is randomly distributed in a square 1 × 1. Numerical

results are averaged over many random relay positions and path loss exponent is set to 3.5. The

average outage probability tolerated by PUs is ε = 10−2. We have empirically determined the

values of Pmaxr yielding to a primary average outage probability equal to 10−2. According to

the later specified scenarios, the found values of Pmaxr are presented in Table 7.1 and Table 7.2.

In Fig. 7.12, we present the secondary and primary average outage probabilities versus γPT

for Rp = 1 and Rs = 0.5 bits/s/Hz. Using the values of Pmaxr in table I, the primary average

outage probability is maintained to 10−2. If γPT ≥ 22 dB, the secondary transmission doesn’t

disturb the primary performance and hence no cooperation is performed (Pmaxr = 0 watt in table

111

PPPPPPPPPPPPPγST (dB)

γPT (dB)10 12 14 16 18 20 22 24 26 28 30

20 2.1 1.35 0.85 0.55 0.36 0.2 0 0 0 0 0

30 2.4 1.6 1 0.8 0.6 0.4 0 0 0 0 0

Table 7.1: Values of Pmaxr (watt) for Rp = 1, Rs = 0.5 ( bits/s/Hz)

PPPPPPPPPPPPPγST (dB)

γPT (dB)10 12 14 16 18 20 22 24 26 28 30

20 95 75 55 38 25 14.5 10 6 4 3 1.2

30 95 85 65 48 35 31.5 18 11 10 8 6

Table 7.2: Values of Pmaxr (watt) for Rp = 2, Rs = 1 ( bits/s/Hz)

10 12 14 16 18 20 22 24 26 28 3010

−3

10−2

10−1

100

γPT

(dB)

Ave

rage

out

age

prob

abili

ty

Theoretical curves

PSC−OB1: SUs, γST

=20 dB


=30 dB

PSC−OB1: PUs,γST

=20 dB

PSC−OB1: Pus, γST

=30 dB

U−OB1:SUs, γST

=20 dB

U−OB1: SUs,γST

=30 dB

Figure 7.12: Average outage probability versus γPT , Rp = 1 and Rs = 0.5 bits/s/Hz.

112

10 12 14 16 18 20 22 24 26 28 3010

−3

10−2

10−1

100

γPT

(dB)

Ave

rage

out

age

prob

abili

ty

Theoretical curves


=20 dB


=30 dB

PSC−OB1: PUs, γST

=20 dB

PSC−OB1: PUs, γST

=30 dB

U−OB1, SUs, γST

=20 dB

U−OB1 , SUs, γST

=30 dB

Figure 7.13: Average outage probability versus γPT , Rp = 2 and Rs = 1 bits/s/Hz.

I). The secondary average outage probability increases in function of γPT . This is due to the

interference caused by PUs to SUs which becomes more harmful as γPT increases. We observe

that with γST = 30 dB, the secondary average outage probability is significantly decreased

comparing to γST = 20 dB while Pmaxr slightly increases. This is expected, since when γST

increases, SUs can use more power and hence the interference caused to PUs increases. So, the

relay has to use more power to compensate the interference induced by SUs.

We compare our spectrum sharing scheme with the underlay scheme described in section

7.3.2. Note that, in underlay scheme, the primary average outage probability is always 10−2

according to (7.28). From Fig. 7.12, we observe that our proposed spectrum sharing scheme

significantly outperforms the underlay scheme while respecting the primary requirement. For

γST = 30 dB, our scheme is always better than the underlay scheme because γST is high enough

to always satisfy the secondary data rate requirement. For γPT ≥ 22 dB, we observe that the

outage probability increases. This is because for γPT ≥ 22 dB, cooperation is not performed

since Pmaxr is fixed to 0. For γST = 20 dB, the performance of our proposed scheme and the

underlay scheme tend to be converged. This is because at high γPT , PUs can tolerate high

interference from SUs and thus the secondary transmit power required to reach Rs is often

constrained only by Pmaxs . Thus, our proposed scheme and the underlay scheme converge. For

γST = 30 dB, we observe that the amelioration of the secondary outage probability performance

compared to the underlay scheme is quite interesting. This is because the maximum power

available for SUs, Pmaxs is interesting.

113

1 1.5 2.5 3.9 6.3 10 15.8 25.1 39.8 63 10010

−2

10−1

100

Psmax (watt)

Ave

rag

e B

EP

TheorySimulation

Rs=0.2 bits/s/Hz

Rs=0.5 bits/s/Hz

Rs=1 bits/s/Hz

Figure 7.14: Average BEP versus Pmaxs , for γPT=10 dB.

In Fig. 7.13, for Rp = 2 and Rs = 1 bits/s/Hz, we use the values of Pmaxr in table II. We

observe that these values are getting so much higher than the first scenario (values in table I).

The reason is that when Rs increases, SUs cause more interference to PUs and the relay has

to spend more power to compensate this interference, this comes along with the increase in Rp

which demands more power from the relay. The secondary average outage probability increases

also as the same value of γST is used in the two cases. We observe that our proposed scheme

significantly outperforms the underlay scheme. Moreover, with the use of our spectrum sharing

scheme and the values of Pmaxr in table II, the primary average outage probability is maintained

to the allowable value ε. In Fig. 7.12 and Fig. 7.13, the theoretical and simulation curves are

in perfect accordance which validates our outage probability analysis.

In Fig. 7.14. we present the average BEP performance of SUs versus Pmaxs . We observe that

the average BEP is almost constant versus Pmaxs . This is because often the SINR at secondary

users is equal to 23Rs −1 and hence the average BEP keeps a floor mainly for high Pmaxs because

in high region the SINR is always 23Rs − 1. Simulation and theoretical curves are in perfect

accordance which validates our BEP analysis.

Next, for evaluating the performances of the proposed spectrum sharing scheme using the

Beamforming techniques, we have fixed γt = 2 dB and Pmaxr = 10 dB.

In Fig. 7.15, we present the secondary and primary average outage probabilities versus

primary transmit SNR for Rp = 1 and Rs = 0.2 bits/s/Hz. The secondary transmit SNR is

fixed to 20 dB. We observe that the secondary average outage probability decreases in function

114

10 11 12 13 14 15 16 17 18 19 2010

−3

10−2

10−1

100

Primary Transmit SNR (dB)

Out

age

prob

abili

ty

Primary outage probabilityPrimay Outtage probability in absence of SUsSecondary outage probability: U−OB2Secondary outage probability: PSC−OB2 Derived upper Bound

Figure 7.15: Average outage probability versus primary transmit SNR, Rp = 1 and Rs = 0.2

bits/s/Hz.

of the primary transmit SNR. This is because when the primary transmit SNR increases, the

probability that PUs fall in outage decreases and hence the R can benefit to help SUs only. We

observe that our scheme significantly outperforms the underlay scheme. This proves that our

proposed technique is efficient. Moreover, the outage probability of the primary user remains

the same as if SUs were absent. Observe that the derived upper bound for the outage probability

of SUs is close to the simulation curve.

We define the secondary maximum SNR as the ratio of the maximum available power for

SUs (Pmaxs ) to the noise power N0. In Fig. 7.16, we present the secondary and primary average

outage probabilities versus secondary maximum SNR for Rp = 1 and Rs = 0.2 bits/s/Hz.

The primary transmit SNR is fixed to 20 dB. We observe that the secondary average outage

probability of the proposed scheme decreases in function of the secondary maximum SNR. This

is because when the secondary maximum SNR increases, the value of Pmaxs increases and hence

the probability that the power required to have Rs at SUs be higher than Pmaxs decreases. The

outage probability of the primary user remains the same as if SUs were absent. We observe that

the outage probability for the the underlay scheme remains constant even if the value of PmaxS

increases. This is because the transmit power of SUs is always constrained by the interference

level allowable by PUs (the power used by SUs must be controlled so that the primary outage

probability be equal Rp). Hence, increasing the Pmaxs has no effect on the outage probability

performance of the underlay scheme since increasing Pmaxs will give SUs an extra power range

115

10 11 12 13 14 15 16 17 18 19 2010

−3

10−2

10−1

Secondary Maximum SNR (dB)

Out

age

prob

abili

ty

Primary outage probabiltyPrimary outage probabilty in absence of SUsSecondary outage probabilty: U−OB2Secondary outage probability: PSC−OB2


bits/s/Hz.

but this could not be exploited by SUs. Finally, our results prove that the proposed scheme

is very efficient and largely outperforms the axiomatic scheme where SUs operate in underlay

mode. Using the proposed approach, we enhance significantly the outage probability of the SUs

over the underlay scheme while the primary outage probability remains the same as if SUs were

absent.

7.5 Conclusion

In this chapter, we have considered a bidirectional communications between a pair of secondary

users and a pair of primary users. We have investigated new spectrum sharing schemes that

provide the secondary users a better access to the spectrum with the help of a secondary relay.

We have dealt with the both cases where the relay is a single-antenna node and a multi-antenna

node. We have proposed a time division access policy so that the primary and secondary

transmissions are performed with no interference. When the relay has multiple antennas, we have

proposed two spectrum sharing schemes with and without the use of Beamforming techniques.

The proposed schemes are then compared to the axiomatic schemes where the SUs operate

in underlay mode. Our results show that the proposed schemes significantly outperform the

underlay scheme while the primary outage probability is kept the same as if secondary users

were absent.

116

Chapter 8

Conclusion and Future Work

Directions

In the first part of this thesis, we have proposed and study the performance of several relay

selection schemes in conventional wireless networks (non cognitive radio). In the second part,

we have studied and compared the performance of the use of fixed transmit power and adaptive

transmit power in cognitive radio networks. In addition, we have exploited cooperative diversity

for enabling spectrum sharing in cognitive radio networks. Chapters I and II were dedicated

for an introduction for this thesis and a brief overview about cooperative communication and

Cognitive Radio, respectively.

In chapter III, we have proposed and investigated single relay selection schemes for broadcast

networks using STDR or STAR: AST based RS, ST based RS and MM RS. Several analytical

studies and simulations are performed to study the performances in terms of BEP and data

rate. For STDR, we have showed that when the optimal threshold value is used, the MM RS

has the best performance and achieve a BEP performance close to optimal. The ST based

RS has also good performance and its BEP performance is very close to MM RS. For STAR,

when the optimal threshold value is used, the MM RS achieves a BEP performance conformed

to optimal. Future works on this topic my focus on the use of full-duplex communication to

mitigate the data rate loss caused by the orthogonal transmissions.

In chapter IV, we have considered a cooperative wireless network using MC-CDMA where

N users communicate with a single destination D that can be a BS/AP. we have derived ex-

act e2e BEP at D of the considered cooperative MC-CDMA systems using STDR with best

117

relay selection, relay with largest SNR in relay-destination link, in the presence of multipath

propagation. The derived results are valid for any multipath intensity profile. In the second

time, we have derived BEP and throughput performances of cooperative DS-CDMA systems

using incremental relaying in conjunction with best relay selection in the presence of multipath

propagation. The derived results are valid for any multipath intensity profile, any path delays,

and take into account the correlation between path gains. Throughput performance analysis

shows that the combination between selective and incremental relaying significantly improves

the system throughput without deteriorating BER performance. Future works on this topic may

focus on the performance analysis of other relay selection schemes in cooperative DS-CDMA and

MC-CDMA networks. Cooperative DS-CDMA and MC-CDMA brodcast networks can be in-

vestigated.

In chapter V, we have proposed and investigated the influence of the use of fixed transmit

power on the performances of underlay cognitive radio networks. We have considered three

relaying schemes using fixed transmit power for an underlay cognitive network operating near

a primary receiver: O-DF, O-AF and PR. Our proposed relaying schemes work by eliminating

those relays which do not satisfy the interference constraint. Three relaying schemes using ad-

justable transmit powers have also been presented in order to compare the SEP and throughput

performances of relaying schemes using ATPs: O-DF using ATP, O-AF using ATP and PR using

ATP. In these schemes ,relays adjusts their transmit power in order to respect the interference

constraint imposed by primary user. A closed form expressions of the SEP of relaying schemes

with FTPs are presented in order to confirm simulations results. Lower bounds for the SEP of

O-AF and PR with simple form expression are also provided. We proved that the use of O-AF

and PR consumes much less power while keeping the same SEP and throughput performances

over O-AF using ATP and PR using ATP. Moreover, relaying schemes using FTPs are very

attractive for practical implementation because they use simple and cheap nodes comparing to

nodes able to perform transmit power adaptation. For O-DF, we find that the deterioration of

its performance over O-DF using ATP is important. In this case it is worthy to deploy complex

ATP nodes to have much better performance. Other types of underlay transmissions can be

considered in future works such as broadcast, bidirectional and multicast transmissions.

In chapter VI, we have considered a secondary broadcast network composed of one multi-

antenna secondary transmitter which broadcasts data to single-antenna secondary receivers in

the presence of a primary communication. We have proposed two secondary broadcast trans-

118

mission schemes using orthogonal beamforming: OOIC and OOC schemes. The performances of

proposed schemes is compared to UO scheme performances. The proposed transmission schemes

allow the secondary network to access the spectrum without affecting the outage probability of

the primary receiver. Moreover, we have presented the performance analysis of the secondary

transmissions for UO and OOIC schemes. Transmission techniques operating in overlay mode

offer better secondary average outage probability compared to the first transmission schemes

operating in underlay mode. We have found that OOIC and OOC schemes have close perfor-

mances. We also notice that, for OOIC scheme, SRs require additional information to cancel out

the interference. Indeed, in OOIC scheme, each SR seeks to decode the primary signal at each

transmission and hence SRs must have knowledge about the transmission techniques of primary

system. For this reason, depending on the secondary nodes capability and available information,

the system uses OOIC scheme or OOC scheme. Otherwise, if SRs do not have any knowledge

about the transmission techniques of primary system, the OOC scheme is recommended. We

conclude that the technique with interference cancelation provides higher performance while

avoiding the implementation complexity. Futur works on this topic may focus on the inves-

tigation of muti-source systems, where multiple sources have to broadcast data with different

priorities.

In chapter VII, we have considered a bidirectional communications between a pair of sec-

ondary users and a pair of primary users. We have proposed new spectrum sharing schemes that

provides the secondary users a better access to the spectrum with the help of a secondary relay.

For that, we have proposed a time division access policy so that the primary and secondary

transmissions are performed in orthogonal channels. We have considered the two cases where

the relay has a single antenna and where it has multiple antenna. If the relay has multiple

antennas, we have designed two spectrum sharing schemes. The first scheme do not employ

Beamforming techniques while the second one employs zero forcing and singular value decom-

position Beamforming techniques. We have compared the proposed schemes to the axiomatic

schemes where the secondary nodes access the spectrum in an underlay mode. Future works

in this topic may focus on the use of full-duplex secondary nodes to enhance the performance

of the secondary networks and the comparison of the performance of spectrum sharing schemes

with Beamforming and without Beamforming.

119

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128

Appendix A

Derivation for Chapter III

A.1 Expression of ξi in (3.14)

If Θ contains one node, then the coefficient ξi is equal to 1. Otherwise, if Θ contains more than

one node, then ξi is given by

ξi =

1, if ∀ i′ ∈ Θ\i, A

1(SDR)i > A

1(SDR)i′

1|Γ|+1 , if ∀ i′ ∈ Γ ⊂ Θ\i, A

1(SDR)i = A

1(SDR)i′ = max

j∈RA1(SDR)

j

0, o.w.

(A.1)

A.2 Derivation of double integrals given in the paper

In this appendix, we derive the general double integral given by

I(a, b, c, d, λ, ω) =

∫ b

a

∫ d

cQ(√

λx+ ωy))fγSk|a<γSk<b(x)fγik|c<γik<d(y)dxdy,

where a, b, c, d, λ and ω are real constants. To derive this double integral, we first derive the

following integral

J(a, b, y, λ, ω) =

∫ b

aQ(√

λx+ ωy))1

exp(− aσ2Sk)− exp(− b

σ2Sk)

1

σ2Sk

exp(− x

σ2Sk

)dx.

From the definition of the Q function, we have:

dQ(√λx+ωy)dx = − 1√

2πλ2

1√λx+ωy

exp (−(λx+ ωy)/2). Hence, using integration by parts, J(a, b, y, λ, ω)

129

can be expressed as

J(a, b, y, λ, ω) =1


σ2Sk)

(−Q

(√λx+ ωy

)exp(−x/σ2

Sk)|ba

−∫ b

a

1√2π

λ

2√λx+ ωy

exp

(−x(

λ

2+

1

σ2Sk

)− ω

2y

)dx

).

Using the new integration variable u =√

(λx+ ωy)(1 + 2λσ2

Sk), we obtain

J(a, b, y, λ, ω) =1


σ2Sk)

[Q(√

(λa+ ωy))exp(− a

σ2Sk

)−Q(√

(λb+ ωy))

× exp(− b

σ2Sk

)−exp( ωy

λσ2Sk)√

1 + 2λσ2

Sk

(Q

(√(λa+ ωy)(1 +

2

λσ2Sk

)

)−Q

(√(λb+ ωy)(1 +

2

λσ2Sk

)

)) .

Note that for a particular case where (a = 0, λ = 2, ω = 0),

limb→+∞

J(0, b, y, 2, 0) =∫∞0 Q(

√2y) 1

σ2Sk

exp(− yσ2Sk)dy = 1

2

(1−

√1

1+ 1

σ2Sk

)which is conform to the

expression provided by [7].

Let the integral K(c, d, α, β, δ) be as follows

K(c, d, α, β, δ) =

∫ d

cQ(√

αy + β)1

exp(− cδ )− exp(−d

δ )

1

δexp(−y

δ)dy. (A.2)

Following similar development, the integral K(c, d, α, β, δ) is given by

K(c, d, α, β, δ) =1

exp(− cδ )− exp(−d

δ )

[Q(√

αc+ β)exp(− c

δ)−Q

(√αd+ β

)exp(−d

δ)

−exp( β

αδ )√1 + 2

αδ

(Q

(√(1 +

2

αδ)(αc+ β)

)−Q

(√(1 +

2

αδ)(αd+ β)

)) .

Finally, we can deduce the expression of the double integral I(a, b, c, d) which is equal to

I(a, b, c, d, λ, ω) =1


σ2Sk)

[K(c, d, ω, λa, σ2

ik

)exp(− a

σ2Sk

)−K(c, d, ω, λb, σ2

ik

)× exp(− b

σ2Sk

)−σ

′2ik

σ2ik

√1 + 2

λσ2Sk

(K

(c, d, ω(1 +

2

λσ2Sk

), λ(1 +2

λσ2Sk

)a, σ′2ik

)

−K

(c, d, ω(1 +

2

λσ2Sk

), λ(1 +2

λσ2Sk

)b, σ′2ik

))],

where 1

σ′2ik

= 1σ2ik− ω

λσ2Sk.

Note that simple integrals can also be computed using the same method.

130

A.3 Derivation of P(E ikcoop) in (3.17)

When k is a “reliable” node, we have γSk ≥ γt. Otherwise, when k is an “unreliable” node, we

have γSk < γt . Hence, for the derivation of the probability P(E ikcoop), we have to distinguish

between the two cases: k is a “reliable” node and k is an “unreliable” node.

A.3.1 Case 1: k is a “reliable” node

In this case, we have

P(E ikcoop|γSk > γt) =

∫ ∞

γt

∫ ∞

0Q(√2(γ + β))fγSk|γSk>γt

(γ)fγik(β)dγdβ. (A.3)

Using appendix B.2, this double integral can be expressed as

P(E ikcoop|γSk > γt) = Ψ(2, 2γt, σ

2ik)−

σ′2ik

σ2ik

√σ2Sk

σ2Sk + 1

eγt

σ2Sk Ψ

(2(1 +

1

σ2Sk

), 2(1 +1

σ2Sk

)γt, σ′2ik

),

(A.4)

where 1

σ′2ik

= 1σ2ik− 1

σ2Sk

and Ψ(a, b, α) is given by

Ψ(a, b, α) = Q(√b)−

√1

1 + 2aα

exp(b

aα)Q

(√b(1 +

2

aα)

). (A.5)

Note that when γt tends to 0, the double integral in (C.7) corresponds to the BEP at k without

threshold constraint.

By making γt tends to 0 in (A.4), we obtain P(E ikcoop) =

12

(1− σ2

Sk

σ2Sk−σ2

ikSSk −

σ2ik

σ2ik−σ2

SkSik

), where

SXY =

√σ2XY

σ2XY +1

. This expression is conform to that in [38, eq. (7)] which proves the exactitude

of the generalized form expression provided.

A.3.2 Case 2: k is an “unreliable” node

In this case we have

P(E ikcoop|γSk < γt) =

∫ γt

0

∫ ∞

0Q(√

2(γ + β))fγSk|γSk<γt

(γ)fγik(β)dγdβ. (A.6)

Using the development of the double integral in appendix B.2, we obtain

P(E ikcoop|γSk < γt) =

1

1− exp(−γt/σ2Sk)

[Ψ(2, 0, σ2

ik)− e−γtσ2Sk Ψ(2, 2γt, σ

2ik)−

σ′2ik

σ2ik

√σ2Sk

σ2Sk + 1

×[Ψ

(2(1 +

1

σ2Sk

), 0, σ′2ik

)−Ψ

(2(1 +

1

σ2Sk

), 2(1 +1

σ2Sk

)γt, σ′2i,k

)]].

(A.7)

131

Note that when γt tends to +∞, the double integral in (A.6) corresponds to the BEP at k without

threshold constraint. By making γt tends to +∞ in (A.7), we obtain the same expression as in

[38, eq. (7)].

A.4 Derivation of P(RSel = i|R = Θ)

A given “reliable” node i can be selected by the ST based RS only if i has the largest A2(SDR)i

and all the other “reliable” nodes i′ have A2(SDR)i′ less than A

2(SDR)i , or all of them have the

same A2(SDR)i′ as i or only a subset of “reliable” nodes have the same A

2(SDR)i′ as i. Hence, the

conditional probability P(RSel = i|R = Θ) is given by

P(RSel = i|R = Θ) =

Nu∑l=1

∏i′∈Θ\i

l−1∑l′=0

P(A2(SDR)

i′= l

′)

P(A2(SDR)i = l) +

Nu∑l=0

∏i′∈Θ

P(A2(SDR)

i′ = l)

Nr

+∑

Θ′⊂Θ\i

Nu∑l=1

∏i′∈Θ′

l−1∑l′=0

P(A2(SDR)

i′= l′)

∏i′′∈Θ′

P(A2(SDR)

i′′= l)

P(A2(SDR)i = l)

|Θ′|+ 1,

(A.8)

where Θ′ = Θ\i, \Θ′ and the probability P(A2(SDR)i = l) can be determined using the

distribution of A2(SDR)i in appendix B.3.

A.5 Distribution of A2(SDR)i defined in (3.3)

To determine the distribution of A2(SDR)i defined in (3.3), we define a discrete random variable

Xij as follows Xij = H(Vij − γt), where Vij is a conditional random variable given by Vij =

γSj + γij |γSj < γt. The distribution of Xij can be expressed as

P(Xij = q) =

P(Vij ≥ γt), if q = 1

P(Vij < γt), if q = 0

0, o.w.

(A.9)

To determine this distribution, we need the pdf of Vij which can be computed as follows

fVij (x) = fγSj |γSj<γt(x) ⋆ fγij (x),

132

where ⋆ denotes the convolution operator. The obtained expression of fVij is given by

fVij (x) =

exp(− x

σ2ij

)−exp(− x

σ2Sj

)

(σ2ij−σ2

Sj)(1−exp(− γtσ2Sj

)), if 0 < x < γt

[1−exp(γt(1

σ2ij

− 1

σ2Sj

))] exp(− x

σ2ij

)

(σ2ij−σ2

Sj)(1−exp(− γtσ2Sj

)), if x ≥ γt

0, o.w.

(A.10)

Using (A.10), the probability that Vij is beyond γt is given by

P(Vij ≥ γt) =σ2ij

(σ2ij − σ2

Sj)(1− exp(− γtσ2Sj))

(exp(− γt

σ2ij

)− exp(− γtσ2Sj

)

)︸︷︷︸

ϕij(γt)

. (A.11)

From the definition of A2(SDR)i in (3.3) and (A.11), we deduce the distribution of A

2(SDR)i

P(A2(SDR)i = q) =

∑L

∏j∈L

ϕij(γt)∏j′∈L

(1− ϕij′(γt)

), if 0 ≤ q ≤ |U|

0, o.w.

(A.12)

where L is the set of the possible combinations of q nodes from U and L = U \ L.

A.6 Derivation of P(E ikcoop) in (3.21)

For an “unreliable” node k, the Vik could be higher than γt (k ∈ ∆) or below γt (k ∈ ∆). Thus,

to derive P(E ikcoop) we will deal with each of these two cases separately.

A.6.1 Case 1: k ∈ ∆


P(E ikcoop) =

∫ ∞

γt

Q(√2x)fVij |Vij>γt(x)dx. (A.13)

Using integration by parts similar to the one presented in appendix B.2, we obtain

P(E ikcoop) =

σ2ik

[1− exp

(γt(

1σ2ik− 1

σ2Sk))]

ϕik

(1− exp(− γt

σ2Sk)) (

σ2ik − σ2

Sk

)[Q(√

2γt) exp(−γtσ2ik

)−

√σ2ik

1 + σ2ik

Q

(√2γt(1 +

1

σ2ik

)

)].

(A.14)

133

A.6.2 Case 2: k ∈ ∆


P(E ikcoop) =

∫ γt

0Q(

√2x)fVij |Vij<γt(x)dx. (A.15)

Using integration by parts similar to the one presented in appendix B.2, we obtain the

following

P(E ikcoop) =

1

(1− ϕik(γt)) (σ2ik − σ2

Sk)(1− exp(− γt

σ2Sk)) [σ2

ikΛ(σ2ik, γt)− σ2

SkΛ(σ2Sk, γt)

],

(A.16)

where

Λ(x, y) =1

2−Q(

√2y) exp(−y

x)− 1√

1 + 1x

(1

2−Q

(√2y(1 +

1

x)

)). (A.17)

134

Appendix B

Derivations for Chapter V

B.1 Expression of MΓS,D(s) and MΓ

RO-DFs D

(s) in the presence of

primary interference

To derive the expression of MΓSD(s), we need to derive the PDF and CDF of ΓSD.

We have ΓSD =PS |hS,D|2

Pp|hPT,Y |2+N0. Let Z = PS |hS,D|2 and Y = N0 + Pp|hPT,D|2. |hS,D|2 and

|hPT,D|2 are two exponential random variable with means 1dαS,D

and 1dαPT,D

, respectively. The

CDF of ΓSD = ZY is given by

FΓSD(γ) =

∫ ∞

N0

(1− exp(− z

σ2S,D

)1

σ2PT,Dγ

)exp(− t−N0

σ2PT,Dγ

)dt, for γ ≥ 0, (B.1)

where σ2X,Y = PX

dαX,Yand σ2

PT,Y =Pp

dαPT,Y. Solving this integral yields to the following expression

FΓS,D(γ) = 1−

σ2S,D

σ2S,D + σ2

PT,Dγexp(−N0γ

σ2S,D

).

The PDF of ΓS,D can be obtained by making the derivative of this expression with respect to

γ. The obtained expression is given by

fΓS,D(γ) =

N0

σ2S,D + σ2

PT,Dγexp(−N0γ

σ2S,D

) +σ2S,Dσ

2PT,D

(σ2S,D + σ2

PT,Dγ)2exp(−N0γ

σ2S,D

), for γ ≥ 0

The expression of MΓS,D(s) can be obtained by using the expression of fΓS,D

(γ) as in (5.7). For

the derivation of MΓRO-DFs D

(s), we need the PDF of ΓRO-DFs D. This is can be determined as

follows

fΓRO-DFs D

(γ) =∑i∈U

fΓi,D(γ)

∏k∈U,k =i

FΓi,D(γ).

135

This can be yet expressed as follows [46]

fΓRO-DFs D

(γ) =∑Ri∈C

2∑n=1

Λn(γ)

2|C|−1−1∑p=0

(−1)ξ(p)|C|−1∏k=1

σ2RlRi,k

σ2RlRi,k

+σ2PT,Dγ

ξp(k)

× exp

−γ(N0

σ2RiD

+

|C|−1∑k=1

N0ξp(k)

σ2RlRi,k

,D

)

, (B.2)

where lRi,k|C|−1k=1 is the set of relays indices in C\Ri, [ξp(1), . . . , ξp(|C| − 1)] is the binary

representation of 0 ≤ p ≤ 2|C|−1 − 1, ξ(p) =|C|−1∑k=1

ξp(k) and

Λ1(γ) =N0

σ2Ri,D

+ σ2PT,Dγ

and Λ2(γ) =σ2Ri,D

σ2PT,D

(σ2Ri,D

+ σ2PT,Dγ)

2. (B.3)

Finally, the expression ofMΓRO-DFs D

(s) can be obtained by using the expression of fΓRO-DFs D

(γ)

as in (5.7).

B.2 Expression of MΓRO-DFs D

(s) in the absence of primary inter-

ference

If we ignore the interference from PT, then the PDF of ΓRO-DFs D when C = ∅ is given by [46]

pΓRO-DFs D

(γ) =∑Ri∈C

2|C|−1−1∑p=0

(−1)ξ(p)

λ2RiD

exp

−γ

1

λ2RiD

+

|C|−1∑k=1

ξp(k)

λ2RlRi,k

D

, (B.4)

where lRi,k|C|−1k=1 is the set of relays indices in C\Ri, [ξp(1), . . . , ξp(|C| − 1)] is the binary

representation of 0 ≤ p ≤ 2|C|−1 − 1 and ξ(p) =|C|−1∑n=1

ξp(n).

Using the PDF of ΓRO-DFs D in (B.4), we can deduce its MGF,

MΓRO-DFs D

(s) =∑Ri∈C

2|C|−1−1∑p=0

(−1)ξ(p)

λ2RiD

s+ 1 +|C|−1∑k=1

λ2RiD

ξp(k)

λ2RlRi,k

D

. (B.5)

B.3 Expression of MγSRPR with FTP

s D(s)

The expression of MΓSRPR with FTP

s D(s) can be written as

MΓSRPR with FTP

s D(s) =

∑Ri∈U

MΓSRPR with FTP

s D|RPR with FTP

s =Ri(s)P(RPR with FTP

s = Ri). (B.6)

136

The probability P(RPR with FTPs = Ri) is given by [89]

P(RPR with FTPs = Ri) =

∑Rk∈URk =Ri

2|U|−2−1∑p=0

(−1)ξ(p)

1 +λ2SRk

λ2SRi

+ λ2SRk

|U |−2∑n=1

ξp(n)

λ2SRlRi,Rk,n

, (B.7)

where lRi,Rk,n|U |−2n=1 = U\Ri, Rk is the set of relays indices except Ri and Rk.

The conditional MGF MD|RPR with FTPs =Ri

= MΓS,D(s)MΓSRiD

(s), where, the expression of

MΓSRiD(s) is given by [63]

MΓSRiD(s) =

νRi + µRi

φ+νRi

,µRi(s)− φ−

νRi,µRi

(s)[Ψ(1, 0;φ−

νRi,µRi

(s))−Ψ(1, 0;φ+νRi

,µRi(s))]

×

(1 +

φ+νRi

,µRi(s) + φ−

νRi,µRi

(s)

[φ+νRi

,µRi(s)− φ−

νRi,µRi

(s)]2

)+

νRiµRi

φ+νRi

,µRi(s)− φ−

νRi,µRi

(s)

[Ψ(1, 1;φ−

νRi,µRi

(s))

− Ψ(1, 1;φ+νRi

,µRi(s))

](1 +

φ+νRi

,µRi(s) + φ−

νRi,µRi

(s)

12 [φ

+νRi

,µRi(s)− φ−

νRi,µRi

(s)]2

)− νRi + µRi

[φ+νRi

,µRi(s)− φ−

νRi,µRi

(s)]2

×[φ−νRi

,µRi(s)Ψ(2, 1;φ−

νRi,µRi

(s)) + φ+νRi

,µRi(s)Ψ(2, 1;φ+

νRi,µRi

(s))]− 2νRiµRi

[φ+νRi

,µRi(s)− φ−

νRi,µRi

(s)]2

×[φ−νRi

,µRi(s)Ψ(2, 2;φ−

νRi,µRi

(s)) + φ+νRi

,µRi(s)Ψ(2, 2;φ+

νRi,µRi

(s))], (B.8)

where Ψ(a, b; z) is the Tricomi’s confluent hypergeometric function [90] and

φ±ν,µ(s) ,

1

2[s+ ν + µ±

√(s+ ν + µ)2 − 4νµ].

Using (B.6) and (B.7), we obtain the MGF of MγSRPR with FTP

s D(s) when U = ∅.

137

Appendix C

Derivation for chapter VI

C.1 Derivation of the PDF of γST,SRkgiven in (6.25)

In UO scheme, the SINR at SRk is given by

γST,SRk=

PST |hST,SRkws|2

N0 + PPT |hPT,SRk|2. (C.1)

Let Z =PST |hST,SRk

ws|2N0

and Y = 1 +PPT |hPT,SRk

|2N0

.

To derive the PDF of γST,SRk, we need first to determine the PDF of Y and Z. We have

hPT,SRk∼ CN (0, d−α

PT−SRk), so

PY (y) =1

λPT,SRk

exp(− y − 1

λPT,SRk

), y ∈ [1,+∞[. (C.2)

To derive the PDF of Z, we decompose the channel vector hST,SRkinto a parallel component

and a perpendicular component to w†s as follow:

hST,SRk= h

∥ST,SRk

w†s + h⊥ST,SRk

w†p, (C.3)

where h∥ST,SRk

and h⊥ST,SRkare the orthogonal projection of hST,SRk

on ws and on wp respec-

tively. Consequently,

|hST,SRkws|2 = |h∥ST,SRk

|2,

|hST,SRkwp|2 = |h⊥ST,SRk

|2. (C.4)

According to equation (7.61), the secondary weight vector is written as:

ws =

w1s

w2s

=

x−wp(wp†x)

||x−wp(wp†x)||

. (C.5)

138

On the other hand, x−wp(wp†x) can be simplified as follows:

x−wp(wp†x) =

0

1

−

−h1ST,PR

h2ST,PR

h2ST,PR∗

|h1ST,PR|2 + |h2ST,PR|2

=

−h1ST,PRh2ST,PR

∗

|h2ST,PR|2

|h1ST,PR|2 + |h2ST,PR|2

. (C.6)

Consequently, we deduce that

||x−wp(wp†x)|| =

√√√√ |h2ST,PR|2

|h1ST,PR|2 + |h2ST,PR|2(C.7)

Using (C.5)-(C.7), we obtain the following results:

|w1s | =

|h1ST,PR|√|h1ST,PR|2 + |h2ST,PR|2

,

|w2s | =

|h2ST,PR|√|h1ST,PR|2 + |h2ST,PR|2

. (C.8)

Hence, we can conclude that ws has the same distribution as wp. Consequently, according

to [[91], Appendix I], we conclude that:

|hST,SRkws|2 ∼ Γ(d−α

ST,SRk, 1),

|hST,SRkwp|2 ∼ Γ(d−α

ST,SRk, 1), (C.9)

where X ∼ Γ(p, λ) means that X is distributed according to the gamma distribution with

parameter (p, λ). Consequently, we deduce that Z ∼ Γ(a1, 1). Hence, the PDF of γST,SRkcan

be computed as follows

pγST,SRk(x) =

∫ +∞

1

1

a1a2x exp(−zx

a1) exp(−z − 1

a2)dz. (C.10)

Solving this integral yields to the expression of the PDF of γST,SRkgiven in (6.25).

139

C.2 Expression of Pr(γ2SRk

< 22Rths − 1) in (6.32)

According to the OOIC, if γPT,SRk< 22R

thp − 1, then

γSRk=

(1− β)PST |hST,SRkws|2

N0

(1 +

βPST |hST,SRkwp|2

PPT |hPT,SRk|2

) . (C.11)

Let Q1 =(1−β)PST |hST,SRk

ws|2N0

, Q2 =βPST |hST,SRk

wp|2

PPT |hPT,SRk|2 , b1 = (1 − β)λST,SRk

, b2 = βλST,SRk.

Hence γSRkcan be written as γSRk

= Q11+Q2 . We have Q1 ∼ CN (0, b1).

Next, we determine the PDF of 1+Q2. Using the PDF of |hST,SRkwp|2 in (C.9) in appendix

C.1, we have

PQ2(z) =1

b2b3

+∞∫0

x

z2exp

(− x

b2

)exp

(− x

zb3

)dx

=1

b2b3

(zb2

+ 1a3

)2 , z ∈]0,+∞[ (C.12)

Using (C.12), we can deduce the PDF of 1 +Q2 as follows

Pr (1 +Q2 = z) =1

b2b3

(z−1b2

+ 1a3

)2 , z ∈]1,+∞[ (C.13)

Using the PDF of Q1 and 1 +Q2, the PDF of SINRSRkcan be written as:

PγSRk(x) =

∞∫x

x+ z

b1b2b3

exp(− z+x

b1

)(

zb2

+ xa3

)2 dz (C.14)

Solving this integral yields to the following expression

PγSRk(x)

=λPT,SRk

− b2b1λPT,SRk

exp

(− x

b1

)− b2

b21λ2PT,SRk

Ei

(−b2x

b1λPT,SRk

)× exp

(−b2 − λPT,SRk

b1λPT,SRk

x

)(b1λPT,SRk

+ (b2 − λPT,SRk)x)

(C.15)

Using (C.15), we obtain the expression of Pr(γ2SRk

< 22Rths − 1) in (6.32).

140

Appendix D

List of Publications

Chapter III

1. H. Hakim, H. Boujemaa, W. Ajib, “Single Relay Selection Schemes for Broadcast Net-

works”, IEEE Trans. on Wireless Commun. Vol. 12, No. 6, pp. 2646-2657, June 2013.

Chapter IV

1. H. Hakim, H. Boujemaa, W. Ajib, “BEP and Throughput Analysis of Incremental Selec-

tive Relaying in DS-CDMA Systems”, in Proc. IEEE Veh. Tech. Conf. (IEEE VTC-fall

2012), Quebec City, QC, Canada, 3-6 Sept. 2012.

2. H. Hakim, H. Boujemaa, W. Ajib, “Exact BEP of Cooperative MC-CDMA Systems using

Selective Threshold Digital Relaying”, in Proc. IEEE Int. Symp. on Personal, Indoor and

Mobile Radio Communications (IEEE PIMRC 2011), Toronto, ON, Canada, 11-14 Sept.

2011.

Chapter V

1. H. Hakim, H. Boujemaa, W. Ajib, “Performance comparison between fixed and adapative

transmit power in underlay cognitive radio networks”, in IEEE Trans. on Commun. Vol

61, No 12, pp 4836 - 4846, Dec. 2013.

141

Chapter VI

1. M. chraiti, H. Hakim, W. Ajib, H. Boujemaa, “Spectrum Sharing Techniques for Broad-

cast Cognitive Radio Networks”, in IEEE Trans. on Wireless Commun, Vol 12, No 11, pp

5880-5888, Nov. 2013.

Chapter VII

1. H. Hakim, W. Ajib, H. Boujemaa, “Spectrum Sharing for Bidirectional Communication

exploiting Zero-Forcing and Singular Value Decomposition Beamforming” in Proc. IEEE

Global Commun. Conf. (IEEE Globecom 2013), Atlanta, GA, USA, 9-13 Dec. 2013.

2. H. Hakim, W. Ajib, H. Boujemaa, “Spectrum Sharing for Bi-directional Communication

in Cognitive Radio Networks”, in Proc. IEEE Int. Conference on Wireless and Mobile

Computing, Networking and Communications (IEEE WiMob 2013), Lyon, France, 7-9

Oct. 2013.

3. H. Hakim, W. Ajib, H. Boujemaa, “A New Relay-Assisted Spectrum Sharing Scheme

for Bidirectional Communication”, in Proc. IEEE International Symposium on Wireless

Communication Systems (IEEE ISWCS 2013), Ilmenau, Germany, 27-30 Aug. 2013.

142

Cooperative Communication and Cognitive Radio

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