OPTIMAL RESOURCE ALLOCATION AND CROSS-LAYER CONTROL IN COGNITIVE AND ...

211 Pages·2011·2.48 MB·English

OPTIMAL RESOURCE ALLOCATION AND CROSS-LAYER CONTROL IN
COGNITIVE AND COOPERATIVE WIRELESS NETWORKS
by
Rahul Urgaonkar
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)
May 2011
Copyright 2011 Rahul Urgaonkar
Dedication
To Aai-Baba, BB, and Paulami
ii
Acknowledgments
This work would not have been possible without the encouragement, help, and guidance
that I received over the years from many individuals. First and foremost is my advisor,
Prof. Michael J. Neely. I remember attending a seminar talk that he gave at USC as
a new faculty member sometime in early 2004. At that time, I was a Master’s student,
barely contemplating the idea of pursuing a Ph.D. I still remember the sense of awe that
I felt listening to him talk about his doctoral work. I thought that if I were to ever
pursue a Ph.D., this is the kind of research I would want to do. I am forever grateful
to Prof. Neely for taking me as his student and patiently helping me through thick and
thin, from being a role model and a guide to sharing his candid assessments of my work
and providing valuable feedback. I hope I have been able to achieve at least some of what
I set out to do in my work.
I would like to express my sincere thanks to Prof. Bhaskar Krishnamachari who was
my research advisor during my Master’s studies and who served on my committee. It
was with Bhaskar that I got the first opportunity to do research in the area of Wireless
Networks. Hisenthusiasmforresearch,learning,andmentoringstudentsistrulyinspiring
and I feel lucky to have benefitted from that. I am also thankful to my other committee
iii
members: Prof. Giuseppe Caire, Prof. Leana Golubchik, Prof. Keith M. Chugg, and
Prof. C.-C. Jay Kuo for their time.
WorkingintheCommunicationSciencesInstitutewasmadememorablebymyfriends
and colleagues Ozgun, Chih-ping, and Longbo as well as Gerrie, Anita, Mayumi, and
Milly. I also thank Apoorva, my room-mate for several years, and Sumit and Anant, for
their friendship. I wish everyone the best in all future endeavors of their lives.
My family has been the constant force supporting me religiously in my darkest hours.
I could count on them to discuss with me at any hour what now seem the most trivial of
all “problems”. My parents, Narendra and Dr. Charu Urgaonkar, have been my greatest
fans and this work is dedicated to them. My brother, Prof. Bhuvan Urgaonkar has been
a role model and a friend whose advice has helped me in innumerable ways. I am also
thankful to my Uncle and Aunt, Dr. Mohan and Shachi Gawande and my grandfather,
Dr. Trimbak Gawande for providing me a home away from home.
Last, but not the least of all who helped me jump “The Fence” is my best friend,
my dear wife Paulami whose love for me knows no bounds. The best thing that ever
happened to me was meeting with her. Thank you Paulami, for making every day with
you an adventure!
Rahul Urgaonkar
March 2011
iv
Table of Contents
Dedication ii
Acknowledgments iii
List of Figures viii
Abstract x
Chapter 1: Introduction 1
1.1 Models for Cognitive Radio Networks . . . . . . . . . . . . . . . . . . . . 3
1.2 Summary of Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Outline of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Chapter 2: Reliable Scheduling in Cognitive Radio Networks 9
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Network Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.1 Mobility Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.2 Interference Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.3 Primary User Traffic Model . . . . . . . . . . . . . . . . . . . . . . 16
2.2.4 Channel State Information Model . . . . . . . . . . . . . . . . . . 17
2.2.5 Queueing Dynamics and Control Decisions . . . . . . . . . . . . . 20
2.2.6 Discussion of Network Model . . . . . . . . . . . . . . . . . . . . . 21
2.3 Maximum Throughput Objective . . . . . . . . . . . . . . . . . . . . . . . 22
2.4 Optimal Control Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4.1 Cognitive Network Control Algorithm (CNC) . . . . . . . . . . . . 25
2.4.2 Comparison with a Counter Based Algorithm . . . . . . . . . . . . 28
2.4.3 Performance Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.5 Stochastic Lyapunov Optimization . . . . . . . . . . . . . . . . . . . . . . 35
2.5.1 Lyapunov Drift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.5.2 Optimal Stationary, Randomized Policy . . . . . . . . . . . . . . . 39
2.6 Distributed Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.7 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.8 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
v
Chapter 3: Delay-Limited Cooperative Communication 49
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.2 Basic Network Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.2.1 Example of Channel State Information Models . . . . . . . . . . . 57
3.2.2 Control Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.2.3 Discussion of Basic Model . . . . . . . . . . . . . . . . . . . . . . . 61
3.3 Control Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.4 Optimal Control Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.5 Known Channels, Unknown Statistics . . . . . . . . . . . . . . . . . . . . 70
3.5.1 Regenerative DF, Orthogonal Channels . . . . . . . . . . . . . . . 72
3.5.2 Non-Regenerative DF, Orthogonal Channels . . . . . . . . . . . . . 75
3.5.3 AF, Orthogonal Channels . . . . . . . . . . . . . . . . . . . . . . . 76
3.5.4 DF with DSTC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.5.5 AF with DSTC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.6 Unknown Channels, Known Statistics . . . . . . . . . . . . . . . . . . . . 81
3.6.1 Simulation Based Method . . . . . . . . . . . . . . . . . . . . . . . 82
3.7 Multi-Source Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.8 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.9 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Chapter 4: Opportunistic Cooperation in Cognitive Networks 91
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.2 Basic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.2.1 Control Decisions and Queueing Dynamics . . . . . . . . . . . . . 99
4.2.2 Control Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.3 Solution Using The “Drift-plus-Penalty” Ratio Method . . . . . . . . . . . 104
4.4 The Maximizing Policy of (4.16) . . . . . . . . . . . . . . . . . . . . . . . 107
4.4.1 Proof Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.5 Performance Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
4.6 Extensions to Basic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
4.6.1 Multiple Secondary Users . . . . . . . . . . . . . . . . . . . . . . . 120
4.6.2 Fading Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
4.7 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
4.8 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
Chapter 5: Optimal Routing with Mutual Information Accumulation 134
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
5.2 Network Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
5.3 Minimum Delay Routing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
5.3.1 Timeslot and Transmission Structure . . . . . . . . . . . . . . . . . 141
5.3.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . 143
5.3.3 Characterizing the Optimal Solution of (5.1) . . . . . . . . . . . . 145
5.3.4 Proof of Theorem 6 . . . . . . . . . . . . . . . . . . . . . . . . . . 147
5.3.5 Exact Solution for a Line Network . . . . . . . . . . . . . . . . . . 154
5.4 Minimum Energy Routing with Delay Constraint . . . . . . . . . . . . . . 156
vi
5.4.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . 157
5.4.2 Characterizing the Optimal Solution of (5.9) . . . . . . . . . . . . 158
5.4.3 A Greedy Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 161
5.5 Minimum Delay Broadcast . . . . . . . . . . . . . . . . . . . . . . . . . . 162
5.5.1 Timeslot and Transmission Structure . . . . . . . . . . . . . . . . . 162
5.5.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . 163
5.5.3 Characterizing the Optimal Solution of (5.10) . . . . . . . . . . . . 164
5.5.4 Proof of Theorem 9 . . . . . . . . . . . . . . . . . . . . . . . . . . 165
5.5.5 A Greedy Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 168
5.6 Distributed Heuristics and Simulations . . . . . . . . . . . . . . . . . . . . 169
5.6.1 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
5.7 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
Chapter 6: Conclusions 175
Bibliography 178
Appendix A
Appendices for Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
A.1 Lyapunov Drift under policy STAT . . . . . . . . . . . . . . . . . . . . . . 186
A.2 Convergence of Markov Chains . . . . . . . . . . . . . . . . . . . . . . . . 188
A.3 On Greedy Maximal Weight Matchings . . . . . . . . . . . . . . . . . . . 188
Appendix B
Appendices for Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
B.1 Proof of Theorem 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
B.2 Solution to (3.17) using KKT conditions . . . . . . . . . . . . . . . . . . . 191
B.3 Solution to (3.21) using KKT conditions . . . . . . . . . . . . . . . . . . . 192
Appendix C
Appendices for Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
C.1 Proof of Lemma 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
C.2 Proof of Theorem 5, parts (2) and (3) . . . . . . . . . . . . . . . . . . . . 195
C.3 Computing D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
Appendix D
Appendices for Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
D.1 Proof of Lemma 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
D.2 Proof of Lemma 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
D.3 A Simple Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
vii
List of Figures
2.1 Example cognitive network showing primary and secondary users . . . . . 13
2.2 Two state Markov Chain example for primary user channel occupancy
process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 Total average congestion vs. input rate under the Counter Based Algo-
rithm and CNC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.4 Example cell-partitioned network used in simulation . . . . . . . . . . . . 45
2.5 Total average congestion vs. input rate for different values of V . . . . . . 48
2.6 Achieved throughput vs. input rate for different values of V . . . . . . . . 48
3.1 Example 2-hop network with source, destination and relays. The time slot
structures for different transmission strategies are also shown. Due to the
half-duplex constraint, cooperative protocols need to operate in two phases. 51
3.2 A snapshot of the example network used in simulation. . . . . . . . . . . . 87
3.3 Average Sum Power vs. V. . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.4 Average Reliability Queue Occupancy vs. V. . . . . . . . . . . . . . . . . 89
4.1 Example femtocell network with primary and secondary users. . . . . . . 96
4.2 Frame-based structure of the problem under consideration. Each frame
consists of two periods: PU Idle and PU Busy. . . . . . . . . . . . . . . . 97
4.3 Birth-Death Markov Chain over the system state where the system state
represents the primary user queue backlog. . . . . . . . . . . . . . . . . . 110
4.4 Average Secondary User Throughput vs. V. . . . . . . . . . . . . . . . . . 130
viii
4.5 Average Secondary User Queue Occupancy vs. V. . . . . . . . . . . . . . 131
4.6 Moving Average of Secondary User Throughput over Frames. . . . . . . . 133
4.7 Moving Average of Power used by the Secondary User for Cooperative
Transmissions over Frames. . . . . . . . . . . . . . . . . . . . . . . . . . . 133
5.1 Example network with source, destination and 4 relay nodes. When a
node transmits, every other node that has not yet decoded the packet
accumulates mutual information at a rate given by the capacity of the link
between the transmitter and that node. . . . . . . . . . . . . . . . . . . . 140
5.2 Example timeslot and transmission structure. In each stage, nodes that
have already decoded the full packet transmit on orthogonal channels in
time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
5.3 Optimal timeslot and transmission structure. In each stage, only the node
that decodes the packet at the beginning of that stage transmits. . . . . . 145
5.4 A line network. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
5.5 Optimaltimeslotandtransmissionstructureforminimumdelaybroadcast.
In each stage, at most one node from the set of nodes that have the full
packet transmits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
5.6 A25nodenetworkwheretheroutesfortraditionalminimumdelay,Heuris-
tics 1 and 2, and optimal mutual information accumulation are shown. . . 171
5.7 The CDF of the ratio of the minimum delay under the two heuristics and
the traditional shortest path to the minimum delay under the optimal
mutual information accumulation solution. . . . . . . . . . . . . . . . . . . 172
D.1 The 4 node example network used in Appendix D.3. . . . . . . . . . . . . 200
ix
Abstract
We investigate four problems on optimal resource allocation and cross-layer control in
cognitive and cooperative wireless networks with time-varying channels. The first three
problems consider different models and capabilities associated with cognition and coop-
eration in such networks. Specifically, the first problem focuses on the dynamic spectrum
access model for cognitive radio networks and assumes no cooperation between the li-
censed (or “primary”) and unlicensed (or “secondary”) users. Here, the secondary users
try to avoid interfering with the primary users while seeking transmission opportunities
on vacant primary channels in frequency, time, or space. The second problem considers
a relay-based fully cooperative wireless network. Here, cooperative communication tech-
niques at the physical layer are used to improve the reliability and energy cost of data
transmissions. The third problem considers a cooperative cognitive radio network where
the secondary users can cooperatively transmit with the primary users to improve the
latter’s effective transmission rate. In return, the secondary users get more opportunities
for transmitting their own data when the primary users are idle.
Inallofthesescenarios,ourgoalistodesignoptimalcontrolalgorithmsthatmaximize
time-average network utilities (such as throughput) subject to time-average constraints
(such as power, reliability, etc.). To this end, we make use of the technique of Lyapunov
x