Contents, Lecture notes of Computer Networks

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Contents Preface page xv Acknowledgements xviii List of notation xx 1 Introduction 1 1.1 Book objective 1 1.2 Wireless systems 2 1.3 Book outline 5 2 The wireless channel 10 2.1 Physical modeling for wireless channels 10 2.1.1 Free space, fixed transmit and receive antennas 12 2.1.2 Free space, moving antenna 13 2.1.3 Reflecting wall, fixed antenna 14 2.1.4 Reflecting wall, moving antenna 16 2.1.5 Reflection from a ground plane 17 2.1.6 Power decay with distance and shadowing 18 2.1.7 Moving antenna, multiple reflectors 19 2.2 Input /output model of the wireless channel 20 2.2.1 The wireless channel as a linear time-varying system 20 2.2.2 Baseband equivalent model 22 2.2.3 A discrete-time baseband model 25 Discussion 2.1 Degrees of freedom 28 2.2.4 Additive white noise 29 2.3 Time and frequency coherence 30 2.3.1 Doppler spread and coherence time 30 2.3.2 Delay spread and coherence bandwidth 31 2.4 Statistical channel models 34 2.4.1 Modeling philosophy 34 2.4.2 Rayleigh and Rician fading 36 vii viii Contents 2.4.3 Tap gain auto-correlation function 37 Example 2.2 Clarke’s model 38 Chapter 2 The main plot 40 2.5 Bibliographical notes 42 2.6 Exercises 42 3 Point-to-point communication: detection, diversity and channel uncertainity 49 3.1 Detection in a Rayleigh fading channel 50 3.1.1 Non-coherent detection 50 3.1.2 Coherent detection 52 3.1.3 From BPSK to QPSK: exploiting the degrees of freedom 56 3.1.4 Diversity 59 3.2 Time diversity 60 3.2.1 Repetition coding 60 3.2.2 Beyond repetition coding 64 Summary 3.1 Time diversity code design criterion 68 Example 3.1 Time diversity in GSM 69 3.3 Antenna diversity 71 3.3.1 Receive diversity 71 3.3.2 Transmit diversity: space-time codes 73 3.3.3 MIMO: a 2×2 example 77 Summary 3.2 2×2 MIMO schemes 82 3.4 Frequency diversity 83 3.4.1 Basic concept 83 3.4.2 Single-carrier with ISI equalization 84 3.4.3 Direct-sequence spread-spectrum 91 3.4.4 Orthogonal frequency division multiplexing 95 Summary 3.3 Communication over frequency-selective channels 101 3.5 Impact of channel uncertainty 102 3.5.1 Non-coherent detection for DS spread-spectrum 103 3.5.2 Channel estimation 105 3.5.3 Other diversity scenarios 107 Chapter 3 The main plot 109 3.6 Bibliographical notes 110 3.7 Exercises 111 4 Cellular systems: multiple access and interference management 120 4.1 Introduction 120 4.2 Narrowband cellular systems 123 4.2.1 Narrowband allocations: GSM system 124 4.2.2 Impact on network and system design 126 xi Contents 7.2 Physical modeling of MIMO channels 295 7.2.1 Line-of-sight SIMO channel 296 7.2.2 Line-of-sight MISO channel 298 7.2.3 Antenna arrays with only a line-of-sight path 299 7.2.4 Geographically separated antennas 300 7.2.5 Line-of-sight plus one reflected path 306 Summary 7.1 Multiplexing capability of MIMO channels 309 7.3 Modeling of MIMO fading channels 309 7.3.1 Basic approach 309 7.3.2 MIMO multipath channel 311 7.3.3 Angular domain representation of signals 311 7.3.4 Angular domain representation of MIMO channels 315 7.3.5 Statistical modeling in the angular domain 317 7.3.6 Degrees of freedom and diversity 318 Example 7.1 Degrees of freedom in clustered response models 319 7.3.7 Dependency on antenna spacing 323 7.3.8 I.i.d. Rayleigh fading model 327 Chapter 7 The main plot 328 7.4 Bibliographical notes 329 7.5 Exercises 330 8 MIMO II: capacity and multiplexing architectures 332 8.1 The V-BLAST architecture 333 8.2 Fast fading MIMO channel 335 8.2.1 Capacity with CSI at receiver 336 8.2.2 Performance gains 338 8.2.3 Full CSI 346 Summary 8.1 Performance gains in a MIMO channel 348 8.3 Receiver architectures 348 8.3.1 Linear decorrelator 349 8.3.2 Successive cancellation 355 8.3.3 Linear MMSE receiver 356 8.3.4 Information theoretic optimality 362 Discussion 8.1 Connections with CDMA multiuser detection and ISI equalization 364 8.4 Slow fading MIMO channel 366 8.5 D-BLAST: an outage-optimal architecture 368 8.5.1 Suboptimality of V-BLAST 368 8.5.2 Coding across transmit antennas: D-BLAST 371 8.5.3 Discussion 372 Chapter 8 The main plot 373 8.6 Bibliographical notes 374 8.7 Exercises 374 xii Contents 9 MIMO III: diversity–multiplexing tradeoff and universal space-time codes 383 9.1 Diversity–multiplexing tradeoff 384 9.1.1 Formulation 384 9.1.2 Scalar Rayleigh channel 386 9.1.3 Parallel Rayleigh channel 390 9.1.4 MISO Rayleigh channel 391 9.1.5 2×2 MIMO Rayleigh channel 392 9.1.6 nt ×nr MIMO i.i.d. Rayleigh channel 395 9.2 Universal code design for optimal diversity–multiplexing tradeoff 398 9.2.1 QAM is approximately universal for scalar channels 398 Summary 9.1 Approximate universality 400 9.2.2 Universal code design for parallel channels 400 Summary 9.2 Universal codes for the parallel channel 406 9.2.3 Universal code design for MISO channels 407 Summary 9.3 Universal codes for the MISO channel 410 9.2.4 Universal code design for MIMO channels 411 Discussion 9.1 Universal codes in the downlink 415 Chapter 9 The main plot 415 9.3 Bibliographical notes 416 9.4 Exercises 417 10 MIMO IV: multiuser communication 425 10.1 Uplink with multiple receive antennas 426 10.1.1 Space-division multiple access 426 10.1.2 SDMA capacity region 428 10.1.3 System implications 431 Summary 10.1 SDMA and orthogonal multiple access 432 10.1.4 Slow fading 433 10.1.5 Fast fading 436 10.1.6 Multiuser diversity revisited 439 Summary 10.2 Opportunistic communication and multiple receive antennas 442 10.2 MIMO uplink 442 10.2.1 SDMA with multiple transmit antennas 442 10.2.2 System implications 444 10.2.3 Fast fading 446 10.3 Downlink with multiple transmit antennas 448 10.3.1 Degrees of freedom in the downlink 448 10.3.2 Uplink–downlink duality and transmit beamforming 449 10.3.3 Precoding for interference known at transmitter 454 10.3.4 Precoding for the downlink 465 10.3.5 Fast fading 468 xiii Contents 10.4 MIMO downlink 471 10.5 Multiple antennas in cellular networks: a system view 473 Summary 10.3 System implications of multiple antennas on multiple access 473 10.5.1 Inter-cell interference management 474 10.5.2 Uplink with multiple receive antennas 476 10.5.3 MIMO uplink 478 10.5.4 Downlink with multiple receive antennas 479 10.5.5 Downlink with multiple transmit antennas 479 Example 10.1 SDMA in ArrayComm systems 479 Chapter 10 The main plot 481 10.6 Bibliographical notes 482 10.7 Exercises 483 Appendix A Detection and estimation in additive Gaussian noise 496 A.1 Gaussian random variables 496 A.1.1 Scalar real Gaussian random variables 496 A.1.2 Real Gaussian random vectors 497 A.1.3 Complex Gaussian random vectors 500 Summary A.1 Complex Gaussian random vectors 502 A.2 Detection in Gaussian noise 503 A.2.1 Scalar detection 503 A.2.2 Detection in a vector space 504 A.2.3 Detection in a complex vector space 507 Summary A.2 Vector detection in complex Gaussian noise 508 A.3 Estimation in Gaussian noise 509 A.3.1 Scalar estimation 509 A.3.2 Estimation in a vector space 510 A.3.3 Estimation in a complex vector space 511 Summary A.3 Mean square estimation in a complex vector space 513 A.4 Exercises 513 Appendix B Information theory from first principles 516 B.1 Discrete memoryless channels 516 Example B.1 Binary symmetric channel 517 Example B.2 Binary erasure channel 517 B.2 Entropy, conditional entropy and mutual information 518 Example B.3 Binary entropy 518 B.3 Noisy channel coding theorem 521 B.3.1 Reliable communication and conditional entropy 521 B.3.2 A simple upper bound 522 B.3.3 Achieving the upper bound 523 Example B.4 Binary symmetric channel 524 Example B.5 Binary erasure channel 525 B.3.4 Operational interpretation 525 xvi Preface • Chapter 2: basic properties of multipath wireless channels and their mod- eling (level 1). • Chapter 3: point-to-point communication techniques that increase reliability by exploiting time, frequency and spatial diversity (2). • Chapter 4: cellular system design via a case study of three systems, focusing on multiple access and interference management issues (3). • Chapter 5: point-to-point communication revisited from a more fundamental capacity point of view, culminating in the modern concept of opportunistic communication (2). • Chapter 6: multiuser capacity and opportunistic communication, and its application in a third-generation wireless data system (3). • Chapter 7: MIMO channel modeling (1). • Chapter 8: MIMO capacity and architectures (2). • Chapter 9: diversity–multiplexing tradeoff and space-time code design (2). • Chapter 10: MIMO in multiuser channels and cellular systems (3). How to use this book This book is written as a textbook for a first-year graduate course in wireless communication. The expected background is solid undergraduate/beginning graduate courses in signals and systems, probability and digital communica- tion. This background is supplemented by the two appendices in the book. Appendix A summarizes some basic facts in vector detection and estimation in Gaussian noise which are used repeatedly throughout the book. Appendix B covers the underlying information theory behind the channel capacity results used in this book. Even though information theory has played a significant role in many of the recent developments in wireless communication, in the main text we only introduce capacity results in a heuristic manner and use them mainly to motivate communication concepts and techniques. No back- ground in information theory is assumed. The appendix is intended for the reader who wants to have a more in-depth and unified understanding of the capacity results. At Berkeley and Urbana-Champaign, we have used earlier versions of this book to teach one-semester (15 weeks) wireless communication courses. We have been able to cover most of the materials in Chapters 1 through 8 and parts of 9 and 10. Depending on the background of the students and the time available, one can envision several other ways to structure a course around this book. Examples: • A senior level advanced undergraduate course in wireless communication: Chapters 2, 3, 4. • An advanced graduate course for students with background in wireless channels and systems: Chapters 3, 5, 6, 7, 8, 9, 10. xvii Preface • A short (quarter) course focusing on MIMO and space-time coding: Chap- ters 3, 5, 7, 8, 9. The more than 230 exercises form an integral part of the book. Working on at least some of them is essential in understanding the material. Most of them elaborate on concepts discussed in the main text. The exercises range from relatively straightforward derivations of results in the main text, to “back- of-envelope” calculations for actual wireless systems, to “get-your-hands- dirty” MATLAB types, and to reading exercises that point to current research literature. The small bibliographical notes at the end of each chapter provide pointers to literature that is very closely related to the material discussed in the book; we do not aim to exhaust the immense research literature related to the material covered here. Acknowledgements We would like first to thank the students in our research groups for the selfless help they provided. In particular, many thanks to: Sanket Dusad, Raúl Etkin and Lenny Grokop, who between them painstakingly produced most of the figures in the book; Aleksandar Jovičić, who drew quite a few figures and proofread some chapters; Ada Poon whose research shaped significantly the material in Chapter 7 and who drew several figures in that chapter as well as in Chapter 2; Saurabha Tavildar and Lizhong Zheng whose research led to Chapter 9; Tie Liu and Vinod Prabhakaran for their help in clarifying and improving the presentation of Costa precoding in Chapter 10. Several researchers read drafts of the book carefully and provided us with very useful comments on various chapters of the book: thanks to Stark Draper, Atilla Eryilmaz, Irem Koprulu, Dana Porrat and Pascal Vontobel. This book has also benefited immensely from critical comments from stu- dents who have taken our wireless communication courses at Berkeley and Urbana-Champaign. In particular, sincere thanks to Amir Salman Avestimehr, Alex Dimakis, Krishnan Eswaran, Jana van Greunen, Nils Hoven, Shridhar Mubaraq Mishra, Jonathan Tsao, Aaron Wagner, Hua Wang, Xinzhou Wu and Xue Yang. Earlier drafts of this book have been used in teaching courses at several universities: Cornell, ETHZ, MIT, Northwestern and University of Colorado at Boulder. We would like to thank the instructors for their feedback: Helmut Bölcskei, Anna Scaglione, Mahesh Varanasi, Gregory Wornell and Lizhong Zheng. We would like to thank Ateet Kapur, Christian Peel and Ulrich Schus- ter from Helmut’s group for their very useful feedback. Thanks are also due to Mitchell Trott for explaining to us how the ArrayComm systems work. This book contains the results of many researchers, but it owes an intellec- tual debt to two individuals in particular. Bob Gallager’s research and teaching style have greatly inspired our writing of this book. He has taught us that good theory, by providing a unified and conceptually simple understanding of a morass of results, should shrink rather than grow the knowledge tree. This book is an attempt to implement this dictum. Our many discussions with xviii xxi List of notation b Energy per received bit Pe Error probability Capacities Cawgn Capacity of the additive white Gaussian noise channel C -Outage capacity of the slow fading channel Csum Sum capacity of the uplink or the downlink Csym Symmetric capacity of the uplink or the downlink Csym -Outage symmetric capacity of the slow fading uplink channel pout Outage probability of a scalar fading channel pAla out Outage probability when employing the Alamouti scheme p rep out Outage probability with the repetition scheme pul out Outage probability of the uplink pmimo out Outage probability of the MIMO fading channel pul—mimo out Outage probability of the uplink with multiple antennas at the base-station Vectors and matrices h Vector, complex valued, channel x Vector channel input y Vector channel output  0K Circularly symmetric Gaussian random vector with mean zero and covariance matrix K w Additive Gaussian noise vector  0N0I h∗ Complex conjugate-transpose of h d Data vector d̃ Discrete Fourier transform of d H Matrix, complex valued, channel Kx Covariance matrix of the random complex vector x H∗ Complex conjugate-transpose of H Ht Transpose of matrix H Q, U, V Unitary matrices In Identity n×n matrix  Diagonal matrices diag p1     pn Diagonal matrix with the diagonal entries equal to p1     pn C Circulant matrix D Normalized codeword difference matrix Operations x Mean of the random variable x  A Probability of an event A TrK Trace of the square matrix K sinct Defined to be the ratio of sint to t Qa ∫  a 1/ √ 2 exp−x2/2 dx · · Lagrangian function C H A P T E R 1 Introduction 1.1 Book objective Wireless communication is one of the most vibrant areas in the commu- nication field today. While it has been a topic of study since the 1960s, the past decade has seen a surge of research activities in the area. This is due to a confluence of several factors. First, there has been an explosive increase in demand for tetherless connectivity, driven so far mainly by cellu- lar telephony but expected to be soon eclipsed by wireless data applications. Second, the dramatic progress in VLSI technology has enabled small-area and low-power implementation of sophisticated signal processing algorithms and coding techniques. Third, the success of second-generation (2G) digital wireless standards, in particular, the IS-95 Code Division Multiple Access (CDMA) standard, provides a concrete demonstration that good ideas from communication theory can have a significant impact in practice. The research thrust in the past decade has led to a much richer set of perspectives and tools on how to communicate over wireless channels, and the picture is still very much evolving. There are two fundamental aspects of wireless communication that make the problem challenging and interesting. These aspects are by and large not as significant in wireline communication. First is the phenomenon of fading: the time variation of the channel strengths due to the small-scale effect of multipath fading, as well as larger-scale effects such as path loss via dis- tance attenuation and shadowing by obstacles. Second, unlike in the wired world where each transmitter–receiver pair can often be thought of as an isolated point-to-point link, wireless users communicate over the air and there is significant interference between them. The interference can be between transmitters communicating with a common receiver (e.g., uplink of a cellu- lar system), between signals from a single transmitter to multiple receivers (e.g., downlink of a cellular system), or between different transmitter–receiver pairs (e.g., interference between users in different cells). How to deal with fad- ing and with interference is central to the design of wireless communication 1 4 Introduction then the closest base-station is found, and finally the call is set up through the MTSO and the base-station. The wireless link from a base-station to the mobile users is interchangeably called the downlink or the forward channel, and the link from the users to a base-station is called the uplink or a reverse channel. There are usually many users connected to a single base-station, and thus, for the downlink channel, the base-station must multiplex together the signals to the various connected users and then broadcast one waveform from which each user can extract its own signal. For the uplink channel, each user connected to a given base-station transmits its own waveform, and the base-station receives the sum of the waveforms from the various users plus noise. The base-station must then separate out the signals from each user and forward these signals to the MTSO. Older cellular systems, such as the AMPS (advanced mobile phone service) system developed in the USA in the eighties, are analog. That is, a voice waveform is modulated on a carrier and transmitted without being trans- formed into a digital stream. Different users in the same cell are assigned different modulation frequencies, and adjacent cells use different sets of fre- quencies. Cells sufficiently far away from each other can reuse the same set of frequencies with little danger of interference. Second-generation cellular systems are digital. One is the GSM (global system for mobile communication) system, which was standardized in Europe but now used worldwide, another is the TDMA (time-division multiple access) standard developed in the USA (IS-136), and a third is CDMA (code division multiple access) (IS-95). Since these cellular systems, and their standards, were originally developed for telephony, the current data rates and delays in cellular systems are essentially determined by voice requirements. Third- generation cellular systems are designed to handle data and/or voice. While some of the third-generation systems are essentially evolution of second- generation voice systems, others are designed from scratch to cater for the specific characteristics of data. In addition to a requirement for higher rates, data applications have two features that distinguish them from voice: • Many data applications are extremely bursty; users may remain inactive for long periods of time but have very high demands for short periods of time. Voice applications, in contrast, have a fixed-rate demand over long periods of time. • Voice has a relatively tight latency requirement of the order of 100ms. Data applications have a wide range of latency requirements; real-time applications, such as gaming, may have even tighter delay requirements than voice, while many others, such as http file transfers, have a much laxer requirement. In the book we will see the impact of these features on the appropriate choice of communication techniques. 5 1.3 Book outline As mentioned above, there are many kinds of wireless systems other than cellular. First there are the broadcast systems such as AM radio, FM radio, TV and paging systems. All of these are similar to the downlink part of cellular networks, although the data rates, the sizes of the areas covered by each broadcasting node and the frequency ranges are very different. Next, there are wireless LANs (local area networks). These are designed for much higher data rates than cellular systems, but otherwise are similar to a single cell of a cellular system. These are designed to connect laptops and other portable devices in the local area network within an office building or similar environment. There is little mobility expected in such systems and their major function is to allow portability. The major standards for wireless LANs are the IEEE 802.11 family. There are smaller-scale standards like Bluetooth or a more recent one based on ultra-wideband (UWB) communication whose purpose is to reduce cabling in an office and simplify transfers between office and hand-held devices. Finally, there is another type of LAN called an ad hoc network. Here, instead of a central node (base-station) through which all traffic flows, the nodes are all alike. The network organizes itself into links between various pairs of nodes and develops routing tables using these links. Here the network layer issues of routing, dissemination of control information, etc. are important concerns, although problems of relaying and distributed cooperation between nodes can be tackled from the physical-layer as well and are active areas of current research. 1.3 Book outline The central object of interest is the wireless fading channel. Chapter 2 intro- duces the multipath fading channel model that we use for the rest of the book. Starting from a continuous-time passband channel, we derive a discrete-time complex baseband model more suitable for analysis and design. Key physical parameters such as coherence time, coherence bandwidth, Doppler spread and delay spread are explained and several statistical models for multipath fading are surveyed. There have been many statistical models proposed in the literature; we will be far from exhaustive here. The goal is to have a small set of example models in our repertoire to evaluate the performance of basic communication techniques we will study. Chapter 3 introduces many of the issues of communicating over fading channels in the simplest point-to-point context. As a baseline, we start by look- ing at the problem of detection of uncoded transmission over a narrowband fading channel. We find that the performance is very poor, much worse than over the additive white Gaussian noise (AWGN) channel with the same average signal-to-noise ratio (SNR). This is due to a significant probability that the channel is in deep fade. Various diversity techniques to mitigate this adverse effect of fading are then studied. Diversity techniques increase 6 Introduction reliability by sending the same information through multiple independently faded paths so that the probability of successful transmission is higher. Some of the techniques studied include: • interleaving of coded symbols over time to obtain time diversity; • inter-symbol equalization, multipath combining in spread-spectrum systems and coding over sub-carriers in orthogonal frequency division multiplexing (OFDM) systems to obtain frequency diversity; • use of multiple transmit and/or receive antennas, via space-time coding, to obtain spatial diversity. In some scenarios, there is an interesting interplay between channel uncer- tainty and the diversity gain: as the number of diversity branches increases, the performance of the system first improves due to the diversity gain but then subsequently deteriorates as channel uncertainty makes it more difficult to combine signals from the different branches. In Chapter 4 the focus is shifted from point-to-point communication to studying cellular systems as a whole. Multiple access and inter-cell interfer- ence management are the key issues that come to the forefront. We explain how existing digital wireless systems deal with these issues. The concepts of frequency reuse and cell sectorization are discussed, and we contrast nar- rowband systems such as GSM and IS-136, where users within the same cell are kept orthogonal and frequency is reused only in cells far away, and CDMA systems, such as IS-95, where the signals of users both within the same cell and across different cells are spread across the same spectrum, i.e., frequency reuse factor of 1. Due to the full reuse, CDMA systems have to manage intra-cell and inter-cell interference more efficiently: in addition to the diversity techniques of time-interleaving, multipath combining and soft handoff, power control and interference averaging are the key interference management mechanisms. All the five techniques strive toward the same sys- tem goal: to maintain the channel quality of each user, as measured by the signal-to-interference-and-noise ratio (SINR), as constant as possible. This chapter is concluded with the discussion of a wideband OFDM system, which combines the advantages of both the CDMA and the narrowband systems. Chapter 5 studies the capacity of wireless channels. This provides a higher level view of the tradeoffs involved in the earlier chapters and also lays the foundation for understanding the more modern developments in the subse- quent chapters. The performance over the (non-faded) AWGN channel, as a baseline for comparison. We introduce the concept of channel capacity as the basic performance measure. The capacity of a channel provides the fun- damental limit of communication achievable by any scheme. For the fading channel, there are several capacity measures, relevant for different scenarios. Two distinct scenarios provide particular insight: (1) the slow fading channel, where the channel stays the same (random value) over the entire time-scale