Fachgebiet Methoden der Signalverarbeitung Technische Universität München Linear Precoding and Analysis of Performance Criteria in MIMO Interference Channels Samer Bazzi Vollständiger Abdruck der von der Fakultät für Elektrotechnik und Infor- mationstechnik der Technischen Universität München zur Erlangung des akademischen Grades eines Doktor-Ingenieurs genehmigten Dissertation. Vorsitzender: Prof. Dr. -Ing. Wolfgang Kellerer Prüfer der Dissertation: 1. Prof. Dr. -Ing. Wolfgang Utschick 2. Prof. David Gesbert, Ph. D. Die Dissertation wurde am 28.09.2015 bei der Technischen Universität München eingereicht und durch die Fakultät für Elektrotechnik und In- formationstechnik am 04.03.2016 angenommen. Contents Acknowledgments v Abstract vii 1. Introduction 1 1.1. Thesis Context ............................ 1 1.2. Thesis Overview and Contributions ................. 2 1.3. Notations ............................... 5 2. MIMO Systems: An Overview 7 2.1. MIMO Communications in Noise Limited Networks . 7 2.1.1. Channel Capacity and Fundamental Limits of Communi- cations ............................. 7 2.1.2. Advantages of MIMO Systems ............... 8 2.2. MIMO Communications in Interference Limited Networks . 14 2.3. Massive MIMO Systems ....................... 16 2.4. Duplex Modes and CSI Acquisition Mechanisms . 18 2.5. Figures of Merit ........................... 20 2.6. Summary ............................... 20 3. Linear Precoding Methods in MIMO Interference Channels 23 3.1. System Model ............................. 23 3.1.1. The K-User MIMO Interference Channel . 23 3.1.2. Number of Antennas and Precoding . 25 3.1.3. Degrees of Freedom ..................... 26 3.2. Interference Alignment Methods . 26 3.2.1. Concept and Conditions of Interference Alignment . 26 3.2.2. Closed-Form Solutions .................... 28 3.2.3. Iterative Solutions ...................... 30 3.2.4. Feasibility of Interference Alignment . 37 3.3. Other Approaches for MIMO Interference Channels . 38 3.4. Other Channel Configurations .................... 43 3.4.1. Configurations Where Interference Cannot be Overcome . 43 3.4.2. Configurations With Full-Spatial Multiplexing . 43 3.5. Classification From a Game Theory Point of View . 46 3.6. Common Drawbacks of Cooperative Methods . 46 i Contents 3.7. Relation to LTE Cooperative Transmission Schemes . 47 3.8. Summary ............................... 48 4. Large System Performance of Interference Alignment 51 4.1. Preliminaries ............................. 52 4.1.1. The Mar˘cenko-Pastur Distribution . 52 4.1.2. The Shannon Transform ................... 52 4.1.3. The Quarter Circle Distribution . 53 4.2. Equivalent Modified Channel and Transmit Power Models . 53 4.3. Large System Rate Analysis ..................... 54 4.3.1. Direct Channels’ Asymptotic Eigenvalue Distribution . 55 4.3.2. Large System Analysis and The Law of Large Numbers . 56 4.3.3. Achievable Rates Under Equal Power Allocation . 56 4.3.4. Achievable Rates Under Water-Filling . 58 4.4. Simulation Results and Discussion . 64 4.5. Summary ............................... 66 5. Performance of Non-Cooperative Methods 71 5.1. Large System Performance of Eigenmode Precoding . 71 5.1.1. Achievable Lower Bounds . 72 5.1.2. Large System Analysis .................... 74 5.1.3. Comparison To Interference Alignment Large System Properties ........................... 76 5.2. Performance of Maximum Ratio Transmission . 77 5.2.1. Limited CSIR Model ..................... 78 5.2.2. Ergodic Lower Bounds .................... 79 5.3. Simulation Results and Discussion . 81 5.4. Summary ............................... 83 6. How Much Antennas is "Massive"? 87 6.1. Coherence Interval Structures .................... 88 6.1.1. Maximum Ratio Transmission . 89 6.1.2. Eigenmode Based Precoding . 89 6.1.3. Interference Alignment .................... 89 6.2. Spectral Efficiency Analysis ..................... 91 6.2.1. Eigenmode Precoding vs. Interference Alignment . 91 6.2.2. Maximum Ratio Transmission vs. Interference Alignment 92 6.2.3. Closing Remarks ....................... 93 6.3. Numerical Examples ......................... 93 6.4. Summary ............................... 97 7. Conclusions 99 ii Contents A. Mathematical Basics 103 A.1. Linear Transformations . 103 A.2. The Eigenvalue Decomposition . 103 A.3. The Central Limit Theorem . 103 A.4. The Law of Large Numbers . 104 B. Capacity of Point-to-Point MIMO Links 105 B.1. Capacity-Achieving Precoders . 105 B.2. Water-Filling Power Allocation . 106 C. Derivations and Proofs 109 C.1. Distributions of Inner Vector Products . 109 C.2. Moments of Matrix Products . 110 C.3. Convergence Proof of A(σ) . 112 D. Abbreviations and Acronyms 113 E. List of Author’s Publications 115 List of Figures 117 Bibliography 119 iii Acknowledgments First of all, I would like to express my gratitude to DOCOMO Euro-Labs for giving me the chance to complete my thesis and perform research on various interesting and challenging subjects. Special thanks go to my DOCOMO super- visor Prof. Guido Dietl for his valuable help, advice, and comments on different aspects of my thesis. He gave me his trust, was very supportive through my the- sis and was always available for discussions and idea exchange. Special thanks go to Prof. Wolfgang Utschick as well for agreeing to be my thesis supervisor and treating me like an internal member of his group. He provided critical valuable comments, carefully judged my research output, and pointed out to new direc- tions whenever necessary. Both supervisors’ excitement to explore new wireless communications topics was a constant motivation for me and their knowledge in different theoretical and practical aspects shaped my work. I thank Hauke, Serkan, and later Emmanuel for being such easygoing and friendly office mates, with which I could have numerous discussions on work and non-work related topics. I thank my remaining colleagues in the wireless team Jamal, Petra, Patrick, Toshi, Iwamura-san, Marwa, and Gerhard for being friendly and for providing a relaxed working atmosphere in the office in general. During my six years in Munich, I have met new friends or reunited with old friends. These include but are not limited to David, Abdallah, Layal, Mo- hammed, Ronnie, Jelena, Noemi, Mari, and Nabil. I greatly cherish them and thank them for the great times we had together and for making life in Munich a pleasant one so far. Finally, my deepest gratitude goes to my parents and siblings for their un- conditional support, care, and love in addition to their trust in me. I am lucky to have them and I dedicate this work to them. v Abstract A lot of interest has been directed towards wireless multiple-input multiple- output (MIMO) interference channels in the past years. This interest was trig- gered by interference alignment (IA), a technique which creates noise-limited channels out of interference-limited channels through transmitter cooperation. The existing literature on MIMO interference channels now covers a variety of linear precoding techniques, whose advantages and disadvantages are well understood by now. On the other hand, much less results exist on the analytical performance characterization of those techniques in terms of achievable rates. Such a char- acterization is important for different reasons. For instance, closed-form rate expressions reveal how different system parameters affect the resulting perfor- mance, an aspect that is not revealed by simulations. Furthermore, closed-form expressions are useful for benchmarking purposes, and save simulations time and cost. Additionally, they can be used in a variety of optimization problems. Random matrix theory tools alleviate the task of obtaining closed-form ex- pressions substantially. Even though such tools result in expressions that are only exact asymptotically, these expressions usually provide accurate estimates for finite system parameters as well. In this thesis, we use random matrix theory tools to derive closed-form rate expressions of IA techniques, and closed-form rate lower bounds of eigenmode precoding in MIMO interference channels. Ad- ditionally, rate lower bounds of the maximum ratio transmission technique are derived. Due to the special nature of the latter, this can be performed without the need for random matrix theory. The performance characterization of the lat- ter two precoding types is especially important in scenarios where transmitters are equipped with large antenna arrays (massive MIMO), in which case these non- cooperative and relatively simple techniques exhibit a good performance. The ultimate measure to characterize performance is the spectral efficiency, which takes into account any signaling overheads not related to data transmis- sion. The most important overheads to consider are the channel state informa- tion acquisition training overheads, taking place over the air link. We calculate the training overheads of the different considered precoding techniques in time- division-duplex mode, which, in addition to the derived rate expressions, allow characterizing the spectral efficiencies of these different techniques. The spectral efficiency analysis allows investigating how many transmit an- tennas do the considered non-cooperative techniques require to emulate the per- vii Contents formance of a noise-limited system, i.e., to perform similarly to a system where transmitters have a fixed number of antennas and employ IA. The reason for such an investigation is that the considered non-cooperative techniques might be more feasible than IA in practical