THE IMPACT OF IMPERFECT FEEDBACK ON THE CAPACITY OF WIRELESS NETWORKS A Dissertation Presented to the Faculty of the Graduate School of Cornell University in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy by Alireza Vahid January 2015 c 2015 Alireza Vahid ALL RIGHTS RESERVED THE IMPACT OF IMPERFECT FEEDBACK ON THE CAPACITY OF WIRELESS NETWORKS Alireza Vahid, Ph.D. Cornell University 2015 The defining metric for any wireless communication network is the maximum reliable data rate, also known as capacity. Before any data bit can be commu- nicated over a wireless channel, information about the network state such as connectivity, channel statistics, or channel gains, is required. Receiver nodes feed such information back to other wireless nodes using feedback channels and feedback mechanisms. Considering the role of feedback makes the char- acterization of the network capacity a daunting theoretical task. As a result, researchers have overwhelmingly simplified the feedback channels to come up with tractable models. Specifically, it has commonly been assumed that feed- back channel has infinite capacity and has no delay. While these assumptions could be justified for small, static, or slow-fading networks, they are not viable in the context of large-scale, mobile, or fast-fading wireless networks. In fact, feedback channel is low-rate, unreliable, scarce, and is subject to delay. The recent dramatic increase in wireless data traffic, caused by the success of on- line media streaming and the proliferation of smart phones and tablets, obliges researchers to understand the capacity of large-scale mobile networks. Thus, given the limited, scarce nature of feedback channels, future progress in wire- less data communications crucially depends on a deeper understanding of the impact of feedback on the capacity of wireless networks. In this work, we aim to adjust the assumptions on feedback channels in a way to open doors to better understanding of real world, large-scale wire- less networks. In particular, wireless networks are considered with rate-limited feedback links, with outdated channel state information, and with local views of the network state. BIOGRAPHICAL SKETCH Alireza Vahid received the B.Sc. degree in Electrical Engineering from Sharif University of Technology, Tehran, Iran, in 2009, and the M.Sc. degree in Elec- trical and Computer Engineering from Cornell University, Ithaca, NY, in 2012. As of September 2014, he is a postdoctoral scholar at Information Initiative at Duke University (iiD), Durham, NC. His research interests include information theory and wireless communications, statistics and machine learning. He has received the Director’s Ph.D. Teaching Assistant Award in 2010 from the school of electrical and computer engineering, Cornell University, and Ja- cobs Scholar Fellowship in 2009. He has also received Qualcomm Innovation Fellowship in 2013 for his research on “Collaborative Interference Manage- ment.” He was ranked second among more than 450000 participant in Iranian National Entrance Exam 2004. iii To my beloved family, Mohammad Bagher, Simin, Sara, and Sina. iv ACKNOWLEDGEMENTS I would like to express my most sincere gratitude to my advisor, Professor Salman Avestimehr for his unconditional support of my research. Not only did he teach me how to conduct research, he also helped me pick problems of sig- nificant importance. I have truly learned from his unique style of research and presentation. His dedication to his work and his students has always been a source of inspiration to me, and his immense enthusiasm even after so many achievements has always surprised me. I would like to thank my PhD committee members, Professor Lang Tong and Professor Stephen Wicker for their valuable comments and their guidance. I have gained valuable insights from them. As a student, I have also learned significant amount of knowledge in the courses they presented. I would also like to thank Dr. Mohammad Ali Maddah-Ali for sharing his knowledge and experience with me. I had an amazing experience working with him. It was through him that I learned the meaning of “thinking outside the box!” He truly does his best to provide his colleagues with the best support he can. He has exceptional knowledge of the field that has helped me a lot during the last two years of my PhD studies. I would also like to express my gratitude to Professor Ashutosh Sabharwal for his thoughtful comments and discussions throughout the joint projects. He is a great mentor and I have gathered priceless training from his style of writing and his thought process. I would like to thank Dr. Vaneet Aggarwal for his help and support during our collaboration. Not only is he a colleague to me, he is also a close friend. I am confident that our collaboration and friendship will go on. v Finally, I would like to extend my deepest gratitude, love and affection to my beloved family for always being there for, supporting me unconditionally, believing in me and wishing me the best. I owe every single one of my achieve- ments to them. vi TABLE OF CONTENTS Biographical Sketch . iii Dedication . iv Acknowledgements . .v Table of Contents . vii List of Tables . ix List of Figures . .x 1 Introduction 1 1.1 Motivation . .1 1.2 Prior Work . .4 1.3 Contributions . .6 2 Communication with Delayed Channel State Information 17 2.1 Introduction . 17 2.2 Problem Setting . 18 2.3 Statement of Main Results . 21 2.4 Overview of Key Ideas . 31 2.5 Achievability Proof of Theorem 2.2 [Delayed-CSIT] . 44 2.6 Converse Proof of Theorem 2.2 [Delayed-CSIT] . 60 2.7 Achievability Proof of Theorem 2.3 [Delayed-CSIT and OFB] . 63 2.8 Converse Proof of Theorem 2.3 [Delayed-CSIT and OFB] . 68 2.9 Achievability Proof of Theorem 2.4 [Instantaneous-CSIT and OFB] 71 2.10 Converse Proof of Theorem 2.4 [Instantaneous-CSIT and OFB] . 77 2.11 Extension to the Non-Homogeneous Setting . 79 2.12 Conclusion and Future Directions . 85 3 Capacity results for Gaussian Networks with Delayed Channel State Information 89 3.1 Introduction . 89 3.2 Problem Setting . 92 3.3 Statement of Main Result . 94 3.4 Achievability Proof of Theorem 3.1 . 98 3.5 Converse Proof of Theorem 3.1 . 105 3.6 Gap Analysis . 108 3.7 Extension to K-user MISO BC . 111 3.8 Conclusion and Future Directions . 119 4 Communication with Local Network Views 121 4.1 Introduction . 121 4.2 Problem Formulation . 124 4.3 Motivating Example . 130 4.4 An Algebraic Framework for Inter-Session Coding with Local View . 133 vii 4.5 Optimality of the Strategies . 142 4.6 Concluding Remarks . 164 5 Communication with Rate-Limited Feedback Links 166 5.1 Introduction . 166 5.2 Problem Formulation and Network Model . 168 5.3 Motivating Example . 173 5.4 Deterministic Interference Channel . 176 5.5 Linear Deterministic Interference Channel . 188 5.6 Gaussian Interference Channel . 193 5.7 Concluding Remarks . 214 A Chapter 1 of appendix 216 A.1 Achievability Proof of Theorem 2.1 [Instantaneous-CSIT] . 216 A.2 Converse Proof of Theorem 2.1 [Instantaneous-CSIT] . 229 A.3 Achievability Proof of Theorem 2.2: Sum-rate for 0 ≤ p < 0:5 ... 230 A.4 Achievability Proof of Theorem 2.2: Corner Point C ........ 236 A.5 Proof of Lemma 2.2 . 247 A.6 Achievability Proof of Theorem 2.3: Corner Point 1 − q2; 0 .... 249 B Chapter 2 of appendix 257 B.1 Lattice Quantizer . 257 B.2 Determining D such that RQ(D)=C2×1 ≤ 1 ............... 258 C Chapter 3 of appendix 260 C.1 Converse Proof for Case (2) of Theorem 4.2 . 260 C.2 Proof of Lemma 4.1 . 261 C.3 Proof of Lemma 4.2 . 263 D Chapter 4 of appendix 265 D.1 Proof of Theorem 5.2 . 265 D.2 Achievability Proof of Theorem 5.3 . 269 D.3 Proof of Theorem 5.4 . 273 D.4 Gap Analysis of Theorem 5.6 . 280 viii LIST OF TABLES 2.1 Illustration of our main results through an example in which p = 0:5..................................... 28 2.2 All possible channel realizations and transitions from the initial queue to other queues; solid arrow from tranmsitter Txi to re- ceiver Rx j indicates that Gi j[t] = 1, i; j 2 f1; 2g, t = 1; 2;:::; n. Bit “a” represents a bit in Q1!1 while bit “b” represents a bit in Q2!2. 88 A.1 Summary of Phase 1 for the Achievability Scheme of Corner Point B. Bit “a” represents a bit in Q1!1 while bit “b” represents a bit in Q2!2................................ 253 A.2 Summary of Phase 2 for the Achievability Scheme of Corner Point B. Bit “a” represents a bit in Q1;INT while bit “b” represents a bit in Q2;INT ............................... 254 A.3 Summary of Phase 1 for the Achievability Scheme of Corner Point C. Bit “a” represents a bit in Q1!1 while bit “b” represents a bit in Q2!2................................ 255 A.4 Summary of Phase 2 for the Achievability Scheme of Corner Point B. Bit “a” represents a bit in Q1;INT while bit “b” represents a bit in Q2;INT ............................... 256 ix LIST OF FIGURES 1.1 (a) The two-user binary fading interference channel, and (b) the capac- ity region for three architectures. ....................7 1.2 Two-user Multiple-Input Single-Output (MISO) Complex Gaus- sian Broadcast Channel. 10 1.3 Depiction of a typical scenario, where Nodes A and B have to rely on different partial views about the network to make their transmission decisions. ................................ 11 1.4 Illustration of two different model for network state at node N.