Receiver Design and Performance Study for Amplify-and-Forward Cooperative Diversity Networks ...

231 Pages·2014·1.92 MB·English

Receiver Design and Performance Study for
Amplify-and-Forward Cooperative Diversity
Networks with Reduced CSI Requirement
by
Peng Liu
A thesis submitted to the
Department of Electrical and Computer Engineering
in conformity with the requirements for
the degree of Doctor of Philosophy
Queen’s University
Kingston, Ontario, Canada
June 2014
Copyright (cid:13)c Peng Liu, 2014
Abstract
This thesis aims to tackle the theoretical challenges of characterizing the fundamental
performance limits of amplify-and-forward (AF) cooperative networks and to resolve
the practical challenges in the receiver design for AF systems.
First of all, we study the Shannon-theoretic channel capacity which serves as a
benchmark for practical wireless communications systems. Specifically, we derive
exact expressions of the ergodic capacity in a single-integral form for general multi-
branch AF relay networks with/without the direct link (DL). Moreover, we derive
closed-form and tight upper bounds on the ergodic capacity, which facilitate the
evaluation of the ergodic capacity. These expressions provide useful theoretical tools
for the design of practical wireless AF relaying systems.
We then tackle the practical challenges involved in the design of AF receivers,
aiming to substantially reduce the channel state information (CSI) signaling overhead
yet achieving satisfactory error performance.
Wetakethemaximum-likelihood(ML)andgeneralizedlikelihoodratiotest(GLRT)
approaches to develop detectors under four typical wireless communications scenarios
with little/no knowledge of the CSI. Firstly, for a semi-coherent scenario where only
the product of channel coefficients of each relay branch is known, we develop the
i
ML symbol-by-symbol (SBS) detector, which reduces the instantaneous CSI signal-
ing overhead by 50% while achieving comparable performance to the ideal coherent
receiver. Secondly, for the noncoherent scenario with only the (second-order) channel
statistics and noise variances, we develop a noncoherent ML SBS detector for AF
networks employing differential modulations. Thirdly, for AF networks with only the
knowledge of the noise variance, we develop a sequence detector using GLRT. Lastly,
for a completely blind scenario where the instantaneous CSI, channel statistics, and
noise variances are all unknown, we develop a GLRT-based sequence detector. The
proposed detectors achieve significant performance improvements over the state-of-
the-art counterparts.
The conducted theoretical analysis and practical design will facilitate the design
of reliable communications over wireless AF networks with reduced CSI requirement.
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Acknowledgments
I would like to express my sincere gratitude to my supervisors, Dr. Il-Min Kim and
Dr. Saeed Gazor. The work presented in this thesis would not have been completed
without their continuous guidance and support. Their enthusiasms for high quality
research and dedications to my work have helped me reach many academic milestones
and prepared me to reach more.
I am also grateful to my thesis committee members, Dr. Greg Smith, Dr. Ahmad
Afsahi, Dr. Aboelmagd Noureldin, Dr. Glen Takahara, and Dr. Ali Ghrayeb for
helpful suggestions with respect to the thesis. In particular, I would like to thank
Dr. Takahara for his expert review of the thesis and constructive comments. I also
enjoyed his graduate course in mathematical statistics very much.
I would like to thank my lab colleagues (past and present): MinChul Ju, Zhihang
Yi, Mamoun Malkawi, Ali Ramezani-Kebrya, Tian Lu, Saeed Akhavan Astaneh, Ali
Gobadzadeh, Mohammad Hassan Shariat, and Ishrat Kabir for their generous help.
Last but not the least, I am deeply thankful to my parents, my wife, my lovely
daughter, and my sisters for their support, understanding, and love.
iii
Contents
Abstract i
Acknowledgments iii
Contents vii
List of Tables viii
List of Figures ix
List of Abbreviations xiv
Chapter 1: Introduction 1
1.1 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1.1 Coherent AF Systems . . . . . . . . . . . . . . . . . . . . . . 5
1.1.2 Semi-Coherent AF Systems . . . . . . . . . . . . . . . . . . . 8
1.1.3 Noncoherent/Differential AF Systems . . . . . . . . . . . . . . 9
1.1.4 Shannon-Theoretic Limit . . . . . . . . . . . . . . . . . . . . . 10
1.2 Motivation and Objective of Thesis . . . . . . . . . . . . . . . . . . . 11
1.3 Contribution of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.4 Overview of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Chapter 2: Fundamental Limits of AF Cooperative Networks: Er-
godic Capacity Analysis 19
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3 Exact Analysis of Ergodic Capacity for Single-Relay Networks . . . . 25
2.3.1 Useful Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.3.2 Exact Expression of the Ergodic Capacity . . . . . . . . . . . 29
2.4 Closed-Form Upper Bound on the Ergodic Capacity . . . . . . . . . . 32
2.4.1 Novel Upper Bound on the End-to-End SNR . . . . . . . . . . 32
2.4.2 Upper Bound on the Ergodic Capacity . . . . . . . . . . . . . 40
iv
2.5 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.5.1 Single-Relay Case . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.5.2 Multi-Relay Case . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Chapter 3: LimitedInstantaneousCSI:Optimum/Sub-optimumSymbol-
by-Symbol Detection 53
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.2 System Model and CSI Signalling Strategies . . . . . . . . . . . . . . 55
3.2.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.2.2 CSI Signalling Strategies . . . . . . . . . . . . . . . . . . . . . 57
3.3 Optimum ML Detection . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.4 Sub-optimum detection rules . . . . . . . . . . . . . . . . . . . . . . . 62
3.4.1 Enhanced Gaussian approximation-based detection . . . . . . 62
3.4.2 Unconditional PDF-based detection . . . . . . . . . . . . . . . 65
3.4.3 Hybrid sub-optimum detection . . . . . . . . . . . . . . . . . . 69
3.5 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.5.1 Convergence Speed Test of (3.17) . . . . . . . . . . . . . . . . 70
3.5.2 Average BER Performance Analysis . . . . . . . . . . . . . . . 71
3.5.3 Computational Time Consuming . . . . . . . . . . . . . . . . 75
3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Chapter 4: Statistical CSI and Noise Variance: Noncoherent ML
Symbol-by-Symbol Detection 78
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.3 Exact NC-ML-SBS detector for M-DPSK . . . . . . . . . . . . . . . 82
4.3.1 Exact NC-ML-SBS detector . . . . . . . . . . . . . . . . . . . 83
4.3.2 Reduction of the ML Candidate Set . . . . . . . . . . . . . . . 85
4.4 Approximate ML detector for M-DPSK . . . . . . . . . . . . . . . . 86
4.4.1 Closed-Form Approximation for the Likelihood Function . . . 87
4.4.2 Closed-Form Approximate ML Detector for M-DPSK . . . . . 89
4.4.3 Complexity Comparison . . . . . . . . . . . . . . . . . . . . . 89
4.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Chapter 5: Noise Variance Only: Generalized Likelihood Sequence
Detection 97
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.3 Generalized Likelihood Sequence Detector with σ2 . . . . . . . . . . . 101
d
v
5.4 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
Chapter 6: Completely Blind Scenario: Generalized Likelihood Se-
quence Detection 108
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
6.2.1 M-DPSK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.2.2 Noncoherent M-FSK . . . . . . . . . . . . . . . . . . . . . . . 114
6.2.3 Amplifying Coefficient G . . . . . . . . . . . . . . . . . . . . 115
r
6.3 Proposed Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.4 Performance Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.4.1 Exact PEP Analysis . . . . . . . . . . . . . . . . . . . . . . . 123
6.4.2 Exact BER Analysis . . . . . . . . . . . . . . . . . . . . . . . 124
6.4.3 Asymptotic Diversity Performance Analysis . . . . . . . . . . 127
6.5 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.5.1 Simulation Settings . . . . . . . . . . . . . . . . . . . . . . . . 128
6.5.2 State-of-the-Art Noncoherent Detectors . . . . . . . . . . . . . 131
6.5.3 Comparison of the Symbol-by-Symbol Detectors in Rayleigh
Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
6.5.4 Comparison of the Symbol-by-Symbol Detectors in Rician and
Nakagami-m Fading . . . . . . . . . . . . . . . . . . . . . . . 139
6.5.5 Performance of the Sequence Detectors . . . . . . . . . . . . . 144
6.5.6 Analytical versus Simulation Results . . . . . . . . . . . . . . 144
6.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Chapter 7: Conclusions and Future Work 147
7.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
7.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
Bibliography 153
Appendix A: Proofs for Chapter 2 172
A.1 Proof of Lemma 2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
A.2 Proof of Lemma 2.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
A.3 Proof of Lemma 2.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
A.4 Proof of Lemma 2.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
A.5 Proof of Theorem 2.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
Appendix B: Proofs for Chapter 3 183
B.1 Proof of Lemma 3.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
vi
Appendix C: Proofs for Chapter 4 186
C.1 Proof of Lemma 4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
C.2 Proof of Theorem 4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
C.3 Proof of Corollary 4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
Appendix D: Proofs for Chapter 5 195
D.1 Proof of Theorem 5.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
Appendix E: Proofs for Chapter 6 198
E.1 Proof of Theorem 6.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
E.2 Proof of Theorem 6.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
E.3 Proof of Theorem 6.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
E.4 Proof of Theorem 6.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
Appendix F: List of Publications/Submissions 213
vii
List of Tables
1.1 Summary of the exact analysis of ergodic capacity for AF networks. . 16
1.2 Summary of the bounds/approximations on the ergodic capacity of AF
networks; the proposed upper bound in Chapter 2 is the only result
that is not only tight but also given in closed-form. . . . . . . . . . . 17
1.3 Summary of the receivers for AF networks with different levels of in-
stantaneous CSI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.4 SummaryofthereceiversforAFnetworkswithdifferentlevelsofstatis-
tical channel/noise information, where × represents the scenario that
is not addressed and may be studied as a future work. . . . . . . . . . 17
√
6.1 Summary of noncoherent detectors, where means “parameter re-
quired” and × means “parameter not required”. . . . . . . . . . . . . 129
viii
List of Figures
1.1 A cooperative diversity network where the source transmits informa-
tion to the destination, with the help of adjacent relays. . . . . . . . . 3
1.2 A K-hop relay network. . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 A multi-branch relay network with K relays and the direct link. . . . 6
2.1 Two-hop parallel relay network consisting of a source T , a destination
0
T , and K relays {T }K . . . . . . . . . . . . . . . . . . . . . . . . . 23
d k k=1
2.2 Comparison of the complementary CDFs for i.i.d. case where a =
1
a = 5 dB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2
2.3 Comparison of the complementary CDFs for i.n.d. case where a = 10
1
dB and a = 15 dB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2
2.4 Ergodic capacity at medium to high SNRs of single-relay AF network
with the direct link under asymmetric channel setting where η = 0.4. 42
r
2.5 Ergodic capacity at medium to high SNRs of single-relay AF network
with the direct link under symmetric channel setting where η = 0.5. . 43
r
2.6 Ergodic capacity at low SNRs of single-relay AF network with the
direct link under asymmetric channel setting where η = 0.6. . . . . . 44
r
2.7 Ergodic capacity of single-relay AF network without the direct link
under asymmetric channel setting where η = 0.6. . . . . . . . . . . . 45
r
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