Fundamentals of Wireless Communication
`
`The past decade has seen many advances in physical-layer wireless communi-
`cation theory and their implementation in wireless systems. This textbook takes
`a unified view of the fundamentals of wireless communication and explains
`the web of concepts underpinning these advances at a level accessible to an
`audience with a basic background in probability and digital communication.
`Topics covered include MIMO (multiple input multiple output) communication,
`space-time coding, opportunistic communication, OFDM and CDMA. The
`concepts are illustrated using many examples from wireless systems such as
`GSM, IS-95 (CDMA), IS-856 (1× EV-DO), Flash OFDM and ArrayComm
`SDMA systems. Particular emphasis is placed on the interplay between
`concepts and their implementation in systems. An abundant supply of exercises
`and figures reinforce the material in the text. This book is intended for use on
`graduate courses in electrical and computer engineering and will also be of great
`interest to practicing engineers.
`
`David Tse is a professor at the Department of Electrical Engineering and
`Computer Sciences, University of California at Berkeley.
`
`Pramod Viswanath is an assistant professor at the Department of Electrical
`and Computer Engineering, University of Illinois at Urbana-Champaign.
`
`INTEL-1024
`10,079,707
`
`

`

`

`

`Fundamentals of
`Wireless Communication
`
`David Tse
`University of California, Berkeley
`
`and
`
`Pramod Viswanath
`University of Illinois, Urbana-Champaign
`
`

`

`c a m b r i d g e u n i v e r s i t y p r e s s
`Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo
`
`c a m b r i d g e u n i v e r s i t y p r e s s
`The Edinburgh Building, Cambridge CB2 2RU, UK
`
`Published in the United States of America by Cambridge University Press, New York
`
`www.cambridge.org
`Information on this title: www.cambridge.org/9780521845274
`
`© Cambridge University Press 2005
`
`This book is in copyright. Subject to statutory exception
`and to the provisions of relevant collective licensing agreements,
`no reproduction of any part may take place without
`the written permission of Cambridge University Press.
`
`First published 2005
`
`Printed in the United Kingdom at the University Press, Cambridge
`
`A catalog record for this book is available from the British Library
`
`ISBN-13 978-0-521-84527-4 hardback
`ISBN-10 0-521-84527-0 hardback
`
`Cambridge University Press has no responsibility for the persistence or accuracy of URLs for
`external or third-party internet websites referred to in this book, and does not guarantee that any
`content on such websites is, or will remain, accurate or appropriate.
`
`

`

`To my family
`DT
`
`To my parents and to Suma
`PV
`
`

`

`

`

`Contents
`
`Preface
`Acknowledgements
`List of notation
`
`1 Introduction
`1.1 Book objective
`1.2 Wireless systems
`1.3 Book outline
`
`2 The wireless channel
`2.1 Physical modeling for wireless channels
`2.1.1 Free space, fixed transmit and receive antennas
`2.1.2 Free space, moving antenna
`2.1.3 Reflecting wall, fixed antenna
`2.1.4 Reflecting wall, moving antenna
`2.1.5 Reflection from a ground plane
`2.1.6 Power decay with distance and shadowing
`2.1.7 Moving antenna, multiple reflectors
`2.2 Input /output model of the wireless channel
`2.2.1 The wireless channel as a linear time-varying system
`2.2.2 Baseband equivalent model
`2.2.3 A discrete-time baseband model
`Discussion 2.1 Degrees of freedom
`2.2.4 Additive white noise
`2.3 Time and frequency coherence
`2.3.1 Doppler spread and coherence time
`2.3.2 Delay spread and coherence bandwidth
`2.4 Statistical channel models
`2.4.1 Modeling philosophy
`2.4.2 Rayleigh and Rician fading
`
`vii
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`page xv
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`viii
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`Contents
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`2.4.3 Tap gain auto-correlation function
`Example 2.2 Clarke’s model
`Chapter 2 The main plot
`2.5 Bibliographical notes
`2.6 Exercises
`
`3 Point-to-point communication: detection, diversity
`and channel uncertainity
`3.1 Detection in a Rayleigh fading channel
`3.1.1 Non-coherent detection
`3.1.2 Coherent detection
`3.1.3 From BPSK to QPSK: exploiting the degrees
`of freedom
`3.1.4 Diversity
`3.2 Time diversity
`3.2.1 Repetition coding
`3.2.2 Beyond repetition coding
`Summary 3.1 Time diversity code design criterion
`Example 3.1 Time diversity in GSM
`3.3 Antenna diversity
`3.3.1 Receive diversity
`3.3.2 Transmit diversity: space-time codes
`3.3.3 MIMO: a 2× 2 example
`Summary 3.2 2× 2 MIMO schemes
`3.4 Frequency diversity
`3.4.1 Basic concept
`3.4.2 Single-carrier with ISI equalization
`3.4.3 Direct-sequence spread-spectrum
`3.4.4 Orthogonal frequency division multiplexing
`Summary 3.3 Communication over frequency-selective channels
`3.5 Impact of channel uncertainty
`3.5.1 Non-coherent detection for DS spread-spectrum
`3.5.2 Channel estimation
`3.5.3 Other diversity scenarios
`Chapter 3 The main plot
`3.6 Bibliographical notes
`3.7 Exercises
`
`4 Cellular systems: multiple access and interference management
`4.1 Introduction
`4.2 Narrowband cellular systems
`4.2.1 Narrowband allocations: GSM system
`4.2.2 Impact on network and system design
`
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`

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`ix
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`Contents
`
`4.2.3 Impact on frequency reuse
`Summary 4.1 Narrowband systems
`4.3 Wideband systems: CDMA
`4.3.1 CDMA uplink
`4.3.2 CDMA downlink
`4.3.3 System issues
`Summary 4.2 CDMA
`4.4 Wideband systems: OFDM
`4.4.1 Allocation design principles
`4.4.2 Hopping pattern
`4.4.3 Signal characteristics and receiver design
`4.4.4 Sectorization
`Example 4.1 Flash-OFDM
`Chapter 4 The main plot
`4.5 Bibliographical notes
`4.6 Exercises
`
`5 Capacity of wireless channels
`5.1 AWGN channel capacity
`5.1.1 Repetition coding
`5.1.2 Packing spheres
`Discussion 5.1 Capacity-achieving AWGN
`channel codes
`Summary 5.1 Reliable rate of communication
`and capacity
`5.2 Resources of the AWGN channel
`5.2.1 Continuous-time AWGN channel
`5.2.2 Power and bandwidth
`Example 5.2 Bandwidth reuse in cellular systems
`5.3 Linear time-invariant Gaussian channels
`5.3.1 Single input multiple output (SIMO) channel
`5.3.2 Multiple input single output (MISO) channel
`5.3.3 Frequency-selective channel
`5.4 Capacity of fading channels
`5.4.1 Slow fading channel
`5.4.2 Receive diversity
`5.4.3 Transmit diversity
`Summary 5.2 Transmit and recieve diversity
`5.4.4 Time and frequency diversity
`Summary 5.3 Outage for parallel channels
`5.4.5 Fast fading channel
`5.4.6 Transmitter side information
`Example 5.3 Rate adaptation in IS-856
`5.4.7 Frequency-selective fading channels
`
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`x
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`Contents
`
`5.4.8 Summary: a shift in point of view
`Chapter 5 The main plot
`5.5 Bibliographical notes
`5.6 Exercises
`
`6 Multiuser capacity and opportunistic communication
`6.1 Uplink AWGN channel
`6.1.1 Capacity via successive interference cancellation
`6.1.2 Comparison with conventional CDMA
`6.1.3 Comparison with orthogonal multiple access
`6.1.4 General K-user uplink capacity
`6.2 Downlink AWGN channel
`6.2.1 Symmetric case: two capacity-achieving schemes
`6.2.2 General case: superposition coding achieves capacity
`Summary 6.1 Uplink and downlink AWGN capacity
`Discussion 6.1 SIC: implementation issues
`6.3 Uplink fading channel
`6.3.1 Slow fading channel
`6.3.2 Fast fading channel
`6.3.3 Full channel side information
`Summary 6.2 Uplink fading channel
`6.4 Downlink fading channel
`6.4.1 Channel side information at receiver only
`6.4.2 Full channel side information
`6.5 Frequency-selective fading channels
`6.6 Multiuser diversity
`6.6.1 Multiuser diversity gain
`6.6.2 Multiuser versus classical diversity
`6.7 Multiuser diversity: system aspects
`6.7.1 Fair scheduling and multiuser diversity
`6.7.2 Channel prediction and feedback
`6.7.3 Opportunistic beamforming using dumb antennas
`6.7.4 Multiuser diversity in multicell systems
`6.7.5 A system view
`Chapter 6 The main plot
`6.8 Bibliographical notes
`6.9 Exercises
`
`7 MIMO I: spatial multiplexing and channel modeling
`7.1 Multiplexing capability of deterministic MIMO channels
`7.1.1 Capacity via singular value decomposition
`7.1.2 Rank and condition number
`
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`

`

`xi
`
`Contents
`
`7.2 Physical modeling of MIMO channels
`7.2.1 Line-of-sight SIMO channel
`7.2.2 Line-of-sight MISO channel
`7.2.3 Antenna arrays with only a line-of-sight path
`7.2.4 Geographically separated antennas
`7.2.5 Line-of-sight plus one reflected path
`Summary 7.1 Multiplexing capability of MIMO channels
`7.3 Modeling of MIMO fading channels
`7.3.1 Basic approach
`7.3.2 MIMO multipath channel
`7.3.3 Angular domain representation of signals
`7.3.4 Angular domain representation of MIMO channels
`7.3.5 Statistical modeling in the angular domain
`7.3.6 Degrees of freedom and diversity
`Example 7.1 Degrees of freedom in clustered
`response models
`7.3.7 Dependency on antenna spacing
`7.3.8 I.i.d. Rayleigh fading model
`Chapter 7 The main plot
`7.4 Bibliographical notes
`7.5 Exercises
`
`8 MIMO II: capacity and multiplexing architectures
`8.1 The V-BLAST architecture
`8.2 Fast fading MIMO channel
`8.2.1 Capacity with CSI at receiver
`8.2.2 Performance gains
`8.2.3 Full CSI
`Summary 8.1 Performance gains in a MIMO channel
`8.3 Receiver architectures
`8.3.1 Linear decorrelator
`8.3.2 Successive cancellation
`8.3.3 Linear MMSE receiver
`8.3.4 Information theoretic optimality
`Discussion 8.1 Connections with CDMA multiuser detection
`and ISI equalization
`8.4 Slow fading MIMO channel
`8.5 D-BLAST: an outage-optimal architecture
`8.5.1 Suboptimality of V-BLAST
`8.5.2 Coding across transmit antennas: D-BLAST
`8.5.3 Discussion
`Chapter 8 The main plot
`8.6 Bibliographical notes
`8.7 Exercises
`
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`

`

`xii
`
`Contents
`
`9 MIMO III: diversity–multiplexing tradeoff and universal
`space-time codes
`9.1 Diversity–multiplexing tradeoff
`9.1.1 Formulation
`9.1.2 Scalar Rayleigh channel
`9.1.3 Parallel Rayleigh channel
`9.1.4 MISO Rayleigh channel
`9.1.5 2× 2 MIMO Rayleigh channel
`× nr MIMO i.i.d. Rayleigh channel
`9.1.6 nt
`9.2 Universal code design for optimal diversity–multiplexing
`tradeoff
`9.2.1 QAM is approximately universal for scalar channels
`Summary 9.1 Approximate universality
`9.2.2 Universal code design for parallel channels
`Summary 9.2 Universal codes for the parallel channel
`9.2.3 Universal code design for MISO channels
`Summary 9.3 Universal codes for the MISO channel
`9.2.4 Universal code design for MIMO channels
`Discussion 9.1 Universal codes in the downlink
`Chapter 9 The main plot
`9.3 Bibliographical notes
`9.4 Exercises
`
`10 MIMO IV: multiuser communication
`10.1 Uplink with multiple receive antennas
`10.1.1 Space-division multiple access
`10.1.2 SDMA capacity region
`10.1.3 System implications
`Summary 10.1 SDMA and orthogonal multiple access
`10.1.4 Slow fading
`10.1.5 Fast fading
`10.1.6 Multiuser diversity revisited
`Summary 10.2 Opportunistic communication and multiple
`receive antennas
`10.2 MIMO uplink
`10.2.1 SDMA with multiple transmit antennas
`10.2.2 System implications
`10.2.3 Fast fading
`10.3 Downlink with multiple transmit antennas
`10.3.1 Degrees of freedom in the downlink
`10.3.2 Uplink–downlink duality and transmit beamforming
`10.3.3 Precoding for interference known at transmitter
`10.3.4 Precoding for the downlink
`10.3.5 Fast fading
`
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`
`

`

`xiii
`
`Contents
`
`10.4 MIMO downlink
`10.5 Multiple antennas in cellular networks: a system view
`Summary 10.3 System implications of multiple antennas on
`multiple access
`10.5.1 Inter-cell interference management
`10.5.2 Uplink with multiple receive antennas
`10.5.3 MIMO uplink
`10.5.4 Downlink with multiple receive antennas
`10.5.5 Downlink with multiple transmit antennas
`Example 10.1 SDMA in ArrayComm systems
`Chapter 10 The main plot
`10.6 Bibliographical notes
`10.7 Exercises
`
`Appendix A Detection and estimation in additive Gaussian noise
`A.1 Gaussian random variables
`A.1.1 Scalar real Gaussian random variables
`A.1.2 Real Gaussian random vectors
`A.1.3 Complex Gaussian random vectors
`Summary A.1 Complex Gaussian random vectors
`A.2 Detection in Gaussian noise
`A.2.1 Scalar detection
`A.2.2 Detection in a vector space
`A.2.3 Detection in a complex vector space
`Summary A.2 Vector detection in complex Gaussian noise
`A.3 Estimation in Gaussian noise
`A.3.1 Scalar estimation
`A.3.2 Estimation in a vector space
`A.3.3 Estimation in a complex vector space
`Summary A.3 Mean square estimation in a complex vector space
`A.4 Exercises
`
`Appendix B Information theory from first principles
`B.1 Discrete memoryless channels
`Example B.1 Binary symmetric channel
`Example B.2 Binary erasure channel
`B.2 Entropy, conditional entropy and mutual information
`Example B.3 Binary entropy
`B.3 Noisy channel coding theorem
`B.3.1 Reliable communication and conditional entropy
`B.3.2 A simple upper bound
`B.3.3 Achieving the upper bound
`Example B.4 Binary symmetric channel
`Example B.5 Binary erasure channel
`B.3.4 Operational interpretation
`
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`

`

`xiv
`
`Contents
`
`B.4 Formal derivation of AWGN capacity
`B.4.1 Analog memoryless channels
`B.4.2 Derivation of AWGN capacity
`B.5 Sphere-packing interpretation
`B.5.1 Upper bound
`B.5.2 Achievability
`B.6 Time-invariant parallel channel
`B.7 Capacity of the fast fading channel
`B.7.1 Scalar fast fading channnel
`B.7.2 Fast fading MIMO channel
`B.8 Outage formulation
`B.9 Multiple access channel
`B.9.1 Capacity region
`B.9.2 Corner points of the capacity region
`B.9.3 Fast fading uplink
`B.10 Exercises
`
`References
`Index
`
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`554
`
`

`

`Preface
`
`Why we wrote this book
`
`The writing of this book was prompted by two main developments in wireless
`communication in the past decade. First is the huge surge of research activities
`in physical-layer wireless communication theory. While this has been a subject
`of study since the sixties, recent developments such as opportunistic and mul-
`tiple input multiple output (MIMO) communication techniques have brought
`completely new perspectives on how to communicate over wireless channels.
`Second is the rapid evolution of wireless systems, particularly cellular net-
`works, which embody communication concepts of increasing sophistication.
`This evolution started with second-generation digital standards, particularly
`the IS-95 Code Division Multiple Access standard, continuing to more recent
`third-generation systems focusing on data applications. This book aims to
`present modern wireless communication concepts in a coherent and unified
`manner and to illustrate the concepts in the broader context of the wireless
`systems on which they have been applied.
`
`Structure of the book
`
`This book is a web of interlocking concepts. The concepts can be structured
`roughly into three levels:
`
`1. channel characteristics and modeling;
`2. communication concepts and techniques;
`3. application of these concepts in a system context.
`
`A wireless communication engineer should have an understanding of the
`concepts at all three levels as well as the tight interplay between the levels.
`We emphasize this interplay in the book by interlacing the chapters across
`these levels rather than presenting the topics sequentially from one level to
`the next.
`
`xv
`
`

`

`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 Joviˇci´c, 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
`
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`

`xix
`
`Acknowledgements
`
`Rajiv Laroia have significantly influenced our view of the system aspects of
`wireless communication. Several of his ideas have found their way into the
`“system view” discussions in the book.
`Finally we would like to thank the National Science Foundation, whose
`continual support of our research led to this book.
`
`

`

`Notation
`
`Some specific sets
`(cid:1) Real numbers
`(cid:2) Complex numbers
`(cid:3) A subset of the users in the uplink of a cell
`
`Scalars
`Non-negative integer representing discrete-time
`m
`Number of diversity branches
`L
`Scalar, indexing the diversity branches
`(cid:1)
`Number of users
`K
`Block length
`N
`Number of tones in an OFDM system
`Nc
`Coherence time
`Tc
`Delay spread
`Td
`Bandwidth
`W
`Number of transmit antennas
`nt
`Number of receive antennas
`nr
`Minimum of number of transmit and receive antennas
`nmin
`Scalar channel, complex valued, at time m
`h(cid:2)m(cid:3)
`∗
`Complex conjugate of the complex valued scalar h
`h
`Channel input, complex valued, at time m
`x(cid:2)m(cid:3)
`Channel output, complex valued, at time m
`y(cid:2)m(cid:3)
`(cid:4) (cid:4)(cid:5)(cid:6) (cid:7) 2(cid:8) Real Gaussian random variable with mean (cid:5) and variance (cid:7) 2
`(cid:2)(cid:4) (cid:4)0(cid:6) (cid:7) 2(cid:8) Circularly symmetric complex Gaussian random variable: the
`real and imaginary parts are i.i.d. (cid:4) (cid:4)0(cid:6) (cid:7) 2/2(cid:8)
`Power spectral density of white Gaussian noise
`Additive Gaussian noise process, i.i.d. (cid:2)(cid:4) (cid:4)0(cid:6) N0(cid:8) with time m
`Additive colored Gaussian noise, at time m
`Average power constraint measured in joules/symbol
`Average power constraint measured in watts
`Signal-to-noise ratio
`Signal-to-interference-plus-noise ratio
`
`N0
`(cid:9)w(cid:2)m(cid:3)(cid:10)
`z(cid:2)m(cid:3)
`P
`
`¯P
`SNR
`SINR
`
`xx
`
`

`

`xxi
`
`List of notation
`
`(cid:5)
`b Energy per received bit
`Pe Error probability
`Capacities
`Capacity of the additive white Gaussian noise channel
`Cawgn
`(cid:11)-Outage capacity of the slow fading channel
`C(cid:11)
`Sum capacity of the uplink or the downlink
`Csum
`Symmetric capacity of the uplink or the downlink
`Csym
`Csym
`(cid:11)-Outage symmetric capacity of the slow fading uplink channel
`(cid:11)
`Outage probability of a scalar fading channel
`pout
`pAla
`Outage probability when employing the Alamouti scheme
`out
`prep
`Outage probability with the repetition scheme
`out
`pul
`Outage probability of the uplink
`out
`pmimo
`Outage probability of the MIMO fading channel
`out
`pul—mimo
`Outage probability of the uplink with multiple antennas at the
`out
`base-station
`
`Vectors and matrices
`h
`Vector, complex valued, channel
`x
`Vector channel input
`y
`Vector channel output
`(cid:2)(cid:4) (cid:4)0(cid:6) K(cid:8)
`Circularly symmetric Gaussian random vector with
`mean zero and covariance matrix K
`Additive Gaussian noise vector (cid:2)(cid:4) (cid:4)0(cid:6) N0I(cid:8)
`w
`h∗
`Complex conjugate-transpose of h
`d
`Data vector
`˜d
`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
`Identity n× n matrix
`In
`Diagonal matrices
`(cid:12)(cid:6) (cid:13)
`diag(cid:9)p1(cid:6) (cid:14) (cid:14) (cid:14) (cid:6) pn(cid:10) Diagonal matrix with the diagonal entries equal
`to p1(cid:6) (cid:14) (cid:14) (cid:14) (cid:6) pn
`Circulant matrix
`Normalized codeword difference matrix
`
`C
`D
`
`Operations
`(cid:6)(cid:2)x(cid:3) Mean of the random variable x
`(cid:7)(cid:9)A(cid:10)
`Probability of an event A
`Tr(cid:2)K(cid:3) Trace of the square matrix K
`√
`sinc(cid:4)t(cid:8) Defined to be the ratio of sin(cid:4)(cid:15)t(cid:8) to (cid:15)t
`(cid:1) 
`−x2/2 dx
`2(cid:15)(cid:8) exp
`a (cid:4)1/
`Q(cid:4)a(cid:8)
`(cid:8)(cid:4)·(cid:6)·(cid:8) 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
`
`

`

`2
`
`Introduction
`
`systems and will be the central theme of this book. Although this book takes
`a physical-layer perspective, it will be seen that in fact the management of
`fading and interference has ramifications across multiple layers.
`Traditionally the design of wireless systems has focused on increasing the
`reliability of the air interface; in this context, fading and interference are
`viewed as nuisances that are to be countered. Recent focus has shifted more
`towards increasing the spectral efficiency; associated with this shift is a new
`point of view that fading can be viewed as an opportunity to be exploited.
`The main objective of the book is to provide a unified treatment of wireless
`communication from both these points of view. In addition to traditional
`topics such as diversity and interference averaging, a substantial portion of
`the book will be devoted to more modern topics such as opportunistic and
`multiple input multiple output (MIMO) communication.
`An important component of this book is the system view emphasis: the
`successful implementation of a theoretical concept or a technique requires an
`understanding of how it interacts with the wireless system as a whole. Unlike
`the derivation of a concept or a technique, this system view is less malleable
`to mathematical formulations and is primarily acquired through experience
`with designing actual wireless systems. We try to help the reader develop
`some of this intuition by giving numerous examples of how the concepts are
`applied in actual wireless systems. Five examples of wireless systems are
`used. The next section gives some sense of the scope of the wireless systems
`considered in this book.
`
`1.2 Wireless systems
`
`Wireless communication, despite the hype of the popular press, is a field
`that has been around for over a hundred years, starting around 1897 with
`Marconi’s successful demonstrations of wireless telegraphy. By 1901, radio
`reception across the Atlantic Ocean had been established; thus, rapid progress
`in technology has also been around for quite a while. In the intervening
`hundred years, many types of wireless systems have flourished, and often
`later disappeared. For example, television transmission, in its early days, was
`broadcast by wireless radio transmitters, which are increasingly being replaced
`by cable transmission. Similarly, the point-to-point microwave circuits that
`formed the backbone of the telephone network are being replaced by optical
`fiber. In the first example, wireless technology became outdated when a wired
`distribution network was installed; in the second, a new wired technology
`(optical fiber) replaced the older technology. The opposite type of example is
`occurring today in telephony, where wireless (cellular) technology is partially
`replacing the use of the wired telephone network (particularly in parts of
`the world where the wired network is not well developed). The point of
`these examples is that there are many situations in which there is a choice
`
`

`

`3
`
`1.2 Wireless systems
`
`between wireless and wire technologies, and the choice often changes when
`new technologies become available.
`In this book, we will concentrate on cellular networks, both because they are
`of great current interest and also because the features of many other wireless
`systems can be easily understood as special cases or simple generalizations
`of the features of cellular networks. A cellular network consists of a large
`number of wireless subscribers who have cellular telephones (users), that can
`be used in cars, in buildings, on the street, or almost anywhere. There are
`also a number of fixed base-stations, arranged to provide coverage of the
`subscribers.
`The area covered by a base-station, i.e., the area from which incoming
`calls reach that base-station, is called a cell. One often pictures a cell as
`a hexagonal region with the base-station in the middle. One then pictures
`a city or region as being broken up into a hexagonal lattice of cells (see
`Figure 1.1a). In reality, the base-stations are placed somewhat irregularly,
`depending on the location of places such as building tops or hill tops that
`have good communication coverage and that can be leased or bought (see
`Figure 1.1b). Similarly, mobile users connected to a base-station are chosen
`by good communication paths rather than geographic distance.
`When a user makes a call, it is connected to the base-station to which it
`appears to have the best path (often but not always the closest base-station).
`The base-stations in a given area are then connected to a mobile telephone
`switching office (MTSO, also called a mobile switching center MSC) by high-
`speed wire connections or microwave links. The MTSO is connected to the
`public wired telephone network. Thus an incoming call from a mobile user
`is first connected to a base-station and from there to the MTSO and then to
`the wired network. From there the call goes to its destination, which might
`be an ordinary wire line telephone, or might be another mobile subscriber.
`Thus, we see that a cellular network is not an independent network, but rather
`an appendage to the wired network. The MTSO also plays a major role in
`coordinating which base-station will handle a call to or from a user and when
`to handoff a user from one base-station to another.
`When another user (either wired or wireless) places a call to a given user, the
`reverse