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`Fundamentals of Digital Communication
`
`This textbook presents the fundamental concepts underlying the design of
`modern digital communication systems, which include the wireline, wire-
`less, and storage systems that pervade our everyday lives. Using a highly
`accessible, lecture style exposition, this rigorous textbookfirst establishes a
`firm grounding in classical concepts of modulation and demodulation, and
`then builds on these to introduce advanced concepts in synchronization, non-
`coherent communication, channel equalization, information theory, channel
`coding, and wireless communication. This up-to-date textbook covers turbo
`and LDPC codesin sufficient detail and clarity to enable hands-on imple-
`mentationand performance evaluation, as well as “just enough” information
`theory to enable computation of performance benchmarks to compare them
`against. Other unique features include the.use of complex baseband represen-
`. tation as a unifying framework for transceiver design and implementation;
`wireless link design for a number of modulation formats, including space—
`time communication; geometric insights into noncoherent communication;
`- and equalization. Thepresentationis self-contained, and the topics are selected
`so as to bring the readerto the cutting edge of digital communications research
`and development.
`Numerous examplesare usedto illustrate the key principles, with a view to
`allowing the reader to perform detailed computations and simulations based
`on the ideas presented in the text.
`With homework problems and numerous examples for each chapter, this
`textbook is suitable for advanced undergraduate and graduate students of
`electrical and computer engineering, and can be used as the basis for a one
`or two semester course in digital communication. It will also be a valuable
`resource for practitioners in the communications industry.
`Additional resources for this title, including instructor-only solutions, are
`available online at www.cambridge.org/9780521874144.
`
`Upamanyu Madhowis Professor of Electrical and Computer Engineering at the
`University of California, Santa Barbara. He received his Ph.D. in Electrical
`Engineering from the University of Ilinois, Urbana-Champaign, in 1990,
`where he later served on the faculty. A Fellow of the IEEE, he worked for
`several years at Telcordia before moving to academia.
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`Fundamentals of
`Digital Communication
`
`| Upamanyu Madhow |
`
`University of California, Santa Barbara
`
` wee UNIVERSITY PRESS
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`CAMBRIDGE
`UNIVERSITY PRESS
`
`University Printing House, Cambridge CB2 8BS, United Kingdom
`
`Published In the United States ofAmerica by Cambridge University Press, New York
`
`Cambridge University Press is part of the University ofCambridge.
`It furthers the University’s mission by disseminating knowledgein the pursuit of
`education, leaming and researchat the highest Intemationallevels of excellence.
`
`www.cambridge.org
`Information on thistitle: www.cambridge.org/9780521874144
`
`© Cambridge University Press 2008
`This publication is in copyright. Subject to statutory exception
`andto the provisionsofrelevantcollective licensing agreements,
`no reproductionof any part may take place withoutthe written
`permission of Cambridge University Press.
`
`First published 2008
`Acatalogue recordforthis publication Is available from the British Library
`ISBN 978-0-521-87414-4 Hardback
`Cambridge University Press has no responsibility for the persistence or accuracy of
`URLsfor external or third-party Internet websites referred to in this publication,
`and does not guarantee that any content on such websitesIs, or will remain, accurate
`or appropriate.
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`Contents
`
`Preface
`Acknowledgements
`
`page xiii
`Xvi
`
`A
`11
`1.2
`
`13
`
`Introduction
`Components of a digital communication system
`Text outline
`Further reading
`
`Modulation
`Preliminaries
`Complex baseband representation
`Spectral description of random processes
`Complex envelope for passband random processes
`Modulation degrees of freedom
`Linear modulation
`Examples of linear modulation
`Spectral occupancyof linearly modulated signals
`The Nyquistcriterion: relating bandwidth to symbolrate
`Linear modulation as a building block
`Orthogonal and biorthogonal modulation
`Differential modulation
`Further reading
`Problems
`Signals and systems
`Complex baseband representation
`Random processes
`Modulation
`
`21
`2.2
`2.3
`2.3.1
`2.4
`
`2.5
`2.5.1
`2.9.2
`2.5.3
`2.5.4
`
`2.6
`2.7
`2.8
`2.9
`2.9.1
`2.9.2
`2.9.3
`2.9.4
`
`w
`3.1
`3.2
`
`Demodulation
`Gaussian basics
`Hypothesis testing basics
`
`vii
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`AWW=
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`viii
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`Contents
`
`3.3 Signal space concepts
`3.4 Optimal reception in AWGN
`3.4.1 Geometry of the ML decision rule
`3.4.2 Soft decisions
`3.5 Performance analysis of ML reception
`3.5.1 Performance with binary signaling
`3.5.2 Performance with M-ary signaling
`3.6 Bit-level demodulation
`3.6.1 Bit-level soft decisions
`3.7 Elements of link budget analysis
`3.8 Further reading
`3.9 Problems
`3.9.1 Gaussian basics
`3.9.2 Hypothesis testing basics
`3.9.3 Receiver design and performance analysis for the AWGN channel
`3.9.4 Link budget analysis
`3.9.5 Some mathematical derivations
`
`4 Synchronization and noncoherent communication
`4.1 Receiver design requirements
`4.2 Parameter estimation basics
`4.2.1 Likelihood function of a signal in AWGN
`4.3 Parameter estimation for synchronization
`4.4 Noncoherent communication
`4.4.1 Composite hypothesis testing
`4.4.2 Optimal noncoherent demodulation
`4.4.3 Differential modulation and demodulation
`4.5 Performance of noncoherent communication
`4.5.1 Proper complex Gaussianity
`4.5.2 Performance of binary noncoherent communication
`4.5.3 Performance of M-ary noncoherent orthogonalsignaling
`4.5.4 Performance of DPSK
`4.5.5 Block noncoherent demodulation
`4.6 Further reading
`4.7 Problems
`
`5 Channel equalization
`5.1 The channel model
`5.2, Receiver front end
`5.3 Eye diagrams
`5.4 Maximum likelihood sequence estimation
`5.4.1 Alternative MLSE formulation
`5.5 Geometric model for suboptimal equalizer design
`5.6 Linear equalization
`
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`102
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`Contents
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`5.6.1 Adaptive implementations
`5.6.2 Performance analysis
`5.7 Decision feedback equalization
`5.7.1 Performance analysis
`5.8 Performance analysis of MLSE
`5.8.1 Union bound
`
`5.8.2 Transfer function bound
`5.9 Numerical comparison of equalization techniques
`5.10 Further reading
`5.11 Problems
`5.11.1 MLSE
`
`a Information-theoretic limits and their computation
`6. =
`Capacity of AWGNchannel: modeling and
`geometry
`6.1.1 From continuous to discrete time
`6.1.2 Capacity of the discrete-time AWGN channel
`6.1.3 From discrete to continuous time
`6.1.4 Summarizing the discrete-time AWGN model
`6.2. Shannon theory basics
`6.2.1 Entropy, mutual information, and divergence
`6.2.2 The channel coding theorem
`6.3 Some capacity computations
`6.3.1 Capacity for standard constellations
`6.3.2 Parallel Gaussian channels and waterfilling
`6.4 Optimizing the input distribution
`6.4.1 Convex optimization
`6.4.2 Characterizing optimal inputdistributions
`6.4.3 Computing optimal input distributions
`6.5 Further reading
`6.6 Problems
`
`7 Channel coding
`7.1 Binary convolutional codes
`7.1.1 Nonrecursive nonsystematic encoding
`7.1.2 Recursive systematic encoding
`7.1.3 Maximum likelihood decoding
`7.1.4 Performance analysis of ML decoding
`7.1.5 Performance analysis for quantized observations
`7.2 Turbo codes and iterative decoding
`7.2.1 The BCJR algorithm: soft-in, soft-out decoding
`7.2.2 Logarithmic BCJR algorithm
`7.2.3 Turbo constructions from convolutional codes
`7.2.4 The BER performance of turbo codes
`
`223
`226
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`Contents
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`7.2.5 Extrinsic information transfer charts
`7.2.6 Turbo weight enumeration
`7.3 Low density parity check codes
`7.3.1 Some terminology from coding theory
`7.3.2 Regular LDPC codes
`7.3.3 Irregular LDPC codes
`7.3.4 Message passing and density evolution
`7.3.5 Belief propagation
`7.3.6 Gaussian approximation
`7.4 Bandwidth-efficient coded modulation
`7.4.1 Bit interleaved coded modulation
`7.4.2 Trellis coded modulation
`7.5 Algebraic codes
`7.6 Further reading
`7.7 Problems
`
`8 Wireless communication
`8.1 Channel modeling
`8.2, Fading and diversity
`8.2.1 The problem with Rayleigh fading
`8.2.2 Diversity through coding and interleaving
`8.2.3 Receive diversity
`8.3 Orthogonal frequency division multiplexing
`8.4 Direct sequence spread spectrum
`8.4.1 The rake receiver
`8.4.2 Choice of spreading sequences
`8.4.3 Performance of conventional reception in CDMA systems
`8.4.4 Multiuser detection for DS-CDMA systems
`8.5 Frequency hop spread spectrum
`8.6 Continuous phase modulation
`8.6.1 Gaussian MSK
`8.6.2 Receiver design and Laurent’s expansion
`8.7 Space-time communication
`8.7.1 Space-time channel modeling
`8.7.2 Information-theoretic limits
`8.7.3 Spatial multiplexing
`8.7.4 Space-time coding
`8.7.5 Transmit beamforming
`8.8 Further reading
`8.9 Problems
`
`,
`
`Appendix A Probability, random variables, and random processes
`A.1 Basic probability
`A.2 Random variables
`
`329
`336
`342
`343
`345
`347
`349
`352
`354
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`358
`360
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`367
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`409
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`xi
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`Contents
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`A.3 Random processes
`A.3.1 Wide sense stationary random processes through LTI systems
`A.3.2 Discrete-time random processes
`A.4 Further reading
`
`Appendix B The Chernoff bound
`
`Appendix C Jensen’‘s inequality
`
`References
`Index
`
`478
`478
`479
`481
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`482
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`485
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`Preface
`
`The field of digital communication has evolved rapidly in the past few
`decades, with commercial applications proliferating in wireline communi-
`cation networks (e.g., digital subscriber loop, cable, fiber optics), wireless
`communication (e.g., cell phones and wireless local area networks), and stor-
`age media(e.g., compact discs, hard drives). The typical undergraduate and
`graduate student is drawn to the field because of these applications, but is
`often intimidated by the mathematical background necessary to understand
`communication theory. A good lecturer in digital communication alleviates
`this fear by means of examples, and covers only the concepts that directly
`impactthe applications being studied. The purposeof this text is to provide
`such a lecture style exposition to provide an accessible, yet rigorous, intro-
`duction to the subject of digital communication. This bookis also suitable for
`self-study by practitioners who wish to brush up on fundamental concepts.
`The book can be used as a basis for one course, or a two course sequence,in
`digital communication. The following topics are covered: complex baseband
`representation of signals and noise (and its relation to modern transceiver
`implementation); modulation (emphasizing linear modulation); demodulation
`(starting from detection theory basics); communication over dispersive chan-
`nels, including equalization and multicarrier modulation, computation of per-
`formance benchmarks using information theory; basics of modern coding
`strategies (including convolutional codes and turbo-like codes); and introduc-
`tion to wireless communication. The choice of material reflects my personal
`bias, but the concepts covered represent a large subset of the tricks of the
`trade. A student who masters the material here, therefore, should be well
`equipped for research or cutting edge development in communication sys-
`tems, and should have the fundamental grounding and sophistication needed
`to explore topics in further detail using the resources that any researcher or
`designer uses, such as research papers and standards documents.
`
`Chapter 1 provides a quick perspective on digital communication. Chapters 2
`and 3 introduce modulation and demodulation, respectively, and contain
`
`Organization
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`xiv
`
`Preface
`
`material that I view as basic to an understanding of modern digital communi-
`cation systems. In addition, a review of “just enough” backgroundin signals
`and systems is woven into Chapter 2, with a special focus on the complex
`baseband representation of passband signals and systems. The emphasis is
`placed on complex baseband becauseit is key to algorithm design and imple-
`mentation in modern digital transceivers. In a graduate course, many students
`will have had a first exposure to digital communication, hence the instructor
`may choose to discuss only a few key concepts in class, and ask students to
`read the chapter as a review. Chapter 3 focuses on the application of detection
`and estimation theory to the derivation of optimal receivers for the additive
`white Gaussian noise (AWGN) channel, and the evaluation of performance
`as a function of £,/No for various modulation strategies. It also includes a
`glimpse of soft decisions and link budget analysis.
`Once students are firmly grounded in the material of Chapters 2 and 3,
`the remaining chapters more or less stand on their own. Chapter 4 contains
`a framework for estimation of parameters such as delay and phase, starting
`from the derivation of the likelihood ratio of a signal in AWGN. Optimal non-
`coherent receivers are derived based on this framework. Chapter 5 describes
`the key ideas used in channel equalization, including maximum likelihood
`sequence estimation (MLSE) using the Viterbi algorithm,
`linear equaliza-
`tion, and decision feedback equalization. Chapter 6 containsa brief treatment
`of information theory, focused on the computation of performance bench-
`marks. This is increasingly important for the communication system designer,
`now that turbo-like codes provide a framework for approaching information-
`theoretic limits for virtually any channel model. Chapter 7 introduces channel
`coding, focusing on the shortest route to conveying a working understanding
`of basic turbo-like constructions and iterative decoding. It includes convolu-
`tional codes,serial and parallel concatenated turbo codes, and low density
`parity check (LDPC) codes. Finally, Chapter 8 contains an introduction to
`wireless communication, and includes discussion of channel models, fading,
`diversity, common modulation formats used in wireless systems, such as
`orthogonal frequency division multiplexing, spread spectrum, and continuous
`phase modulation, as well as multiple antenna, or space-time, communica-
`tion, Wireless communication is a richly diverse field to which entire books
`are devoted, hence my goal in this chapter is limited to conveying a subset
`of the concepts underlying link design for existing and emerging wireless
`systems. I hopethat this exposition stimulates the reader to explore further.
`
`How to use this book
`
`My view of the dependencies among the material covered in the different
`chapters is illustrated in Figure 1, as a rough guideline for course design
`or self-study based on this text. Of course, an instructor using this text
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`xv
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`Preface
`
`
`Chapter 2 (modulation)
`Chapter 3 (demodulation)
`
`
`
`Chapter 4 (synchronization and
`noncoherent communication)
`
`Chapter6 (information-theoretic
`limits and their computation)
`
`
`
`
`Chapter7 (channe! coding)
`
`
`
`
`
`
`Chapter 8 (wireless communication)
`
`Figure 1 Dependencies among may be able to short-circuit some of these dependencies, especially the
`various chapters. Dashed lines=weak ones indicated by dashed lines. For example, much of the material
`denote weak dependencies.
`in Chapter 7 (coding) and Chapter 8 (wireless communication) is accessible
`without detailed coverage of Chapter 6 (information theory).
`In terms of my personal experience with teaching the material at the Uni-
`versity of California, Santa Barbara (UCSB),
`in the introductory graduate
`course on digital communication, I cover the material in Chapters 2, 3, 4,
`and 5 in one quarter, typically spendinglittle time on the material in Chapter 2
`in class, since most students have seen some version of this material. Some-
`times, depending on the pace of the class, I am also able to provide a glimpse
`of Chapters 6 and 7. In a follow-up graduate course, I cover the material in
`Chapters 6, 7, and 8. The pace is usually quite rapid in a quarter system, and
`the same material could easily take up two semesters when taught in more
`depth, and at a more measured pace.
`An alternative course structure that is quite appealing, especially in terms
`of systematic coverage of fundamentals, is to cover Chapters 2, 3, 6, and part
`of 7 in an introductory graduate course, and to cover the remaining topics in
`a follow-up course.
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`Acknowledgements
`
`This book is an outgrowth of graduate and seniorlevel digital communication
`courses that I have taught at the University of California, Santa Barbara
`(UCSB)and the University of Illinois at Urbana~Champaign (UIUC), I would,
`therefore, like to thank students over the past decade who have been guinea
`pigs for my various attempts at course design at both of these institutions.
`This book is influenced heavily by my research in communication systems,
`and I would like to thank the funding agencies who have supported this work.
`These include the National Science Foundation, the Office of Naval Research,
`the Army Research Office, Motorola, Inc., and the University of California
`Industry-University Cooperative Research Program.
`A number of graduate students have contributed to this book by gener-
`ating numerical results and plots, providing constructive feedback on draft
`chapters, and helping write solutions to problems. Specifically, I would like
`to thank the following members and alumni of my research group: Bharath
`Ananthasubramaniam, Noah Jacobsen, Raghu Mudumbai, Sandeep Ponnuru,
`Jaspreet Singh, Sumit Singh, Eric Torkildson, and Sriram Venkateswaran.I
`would also like to thank Ibrahim El-Khalil, Jim Kleban, Michael Sander, and
`Sheng-Luen Wei for pointing out typos. I would also like to acknowledge
`(in order of graduation) some former students, whose doctoral research influ-
`enced portions of this textbook: Dilip Warrier, Eugene Visotsky, Rong-Rong
`Chen, Gwen Barriac, and Noah Jacobsen.
`I would alsolike to take this opportunity to acknowledge the supportive and
`stimulating environment at the University of Illinois at Urbana-Champaign
`(UIUC), which I experienced both as a graduate student and as a tenure-track
`faculty. Faculty at UIUC who greatly enhanced my graduate student experi-
`ence include my thesis advisor, Professor Mike Pursley (now at Clemson
`University), Professor Bruce Hajek, Professor Vince Poor (now at Princeton
`University), and Professor Dilip Sarwate. Moreover, as a faculty at UIUC,
`J benefited from technical interactions with a number of other faculty in
`the communications area, including Professor Dick Blahut, Professor Ralf
`Koetter, Professor Muriel Medard, and Professor Andy Singer. Among my
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`Acknowledgements
`
`UCSBcolleagues, I would like to thank Professor Ken Rose for his helpful
`feedback on Chapter 6, and I would like to acknowledge my collaboration
`with Professor Mark Rodwell in the electronics area, which has educated me
`on a number of implementation considerations in communication systems.
`Past research collaborators who have influenced this book indirectly include
`Professor Mike Honig and Professor Sergio Verdu.
`I would like to thank Dr. Phil Meyler at Cambridge University Press
`for pushing me to commit to writing this textbook. I also thank Professor
`Venu Veeravalli at UIUC and Professor Prakash Narayan at the University
`of Maryland, College Park, for their support and helpful feedback regarding
`the book proposal that I originally sent to Cambridge University Press.
`Finally, I would like to thank my family for always making life unpre-
`dictable and enjoyable at home, regardless of the number of professional
`commitments I pile on myself.
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`
`
`Introduction
`
`We define communication as information transfer between different points
`in space or time, where the term information is loosely employed to cover
`standard formats that we are all familiar with, such as voice, audio, video,
`data files, web pages, etc. Examples of communication between two points
`in space include a telephone conversation, accessing an Internet website from
`our homeor office computer, or tuning in to a TV orradio station. Examples
`of communication between two points in time include accessing a storage
`device, such as a record, CD, DVD, or hard drive. In the preceding exam-
`ples, the information transferred is directly available for human consumption.
`However, there are many other communication systems, which we do not
`directly experience, but which form a crucial part of the infrastructure that
`_ we rely upon in our daily lives. Examples include high-speed packet trans-
`fer between routers on the Internet, inter- and intra-chip communication in
`integrated circuits, the connections between computers and computer periph-
`erals (such as keyboards and printers), and control signals in communication
`networks.
`.
`In digital communication, the information being transferred is represented
`in digital form, most commonly as binary digits, or bits. This is in contrast to
`analog information, which takes on a continuum of values, Most communica-
`tion systems used for transferring information today are either digital, or are
`being converted from analog to digital. Examples of some recent conversions
`that directly impact consumers include cellular telephony (from analog FM
`to several competing digital standards), music storage (from vinyl records to
`CDs), and video storage (from VHS orbeta tapes to DVDs). However, we
`typically consume information in analog form; for example, reading a book
`or a computer screen, listening to a conversation or to music. Why, then,
`is the world going digital? We considerthis issue after first discussing the
`components of a typical digital communication system.
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`2
`
`Introduction
`
`1.1 Components of a digital communication system
`
`Consider the block diagram of a digital communication link depicted in
`Figure 1.1. Let us now briefly discuss the roles of the blocks shown in the
`figure.
`
`Informationtheory tells us that any information can beeffi-
`Sourceencoder
`ciently represented in digital form up to arbitrary precision, with the number
`of bits required for the representation depending on the required fidelity. The
`task of the source encoderis to accomplish this in a practical setting, reducing
`the redundancyin the original information in a mannerthat takes into account
`the end user’s requirements. For example, voice can beintelligibly encoded
`into a 4 kbit/s bitstream for severely bandwidth constrained settings, or sent at
`64 kbit/s for conventional wireline telephony. Similarly, audio encoding rates
`have a wide range - MP3 players for consumer applications may employ
`typical bit rates of 128 kbit/s, while high-end digital audio studio equipment
`may require around ten times higherbit rates. While the preceding examples
`refer to lossy source coding (in which a controlled amount of information
`is discarded), lossless compression of data files can also lead to substantial
`reductions in the amountof data to be transmitted.
`
`Channel encoder and modulator While the source encoder eliminates
`unwanted redundancy in the information to be sent, the channel encoder
`introduces redundancy in a controlled fashion in order to combat errors that
`may arise from channel imperfections and noise. The output of the channel
`encoder is a codeword from a channel code, which is designed specifically
`for the anticipated channel characteristics and the requirements dictated by
`higher network layers. For example, for applicationsthat are delay insensitive,
`the channel code may be optimized for error detection, followed by a request
`for retransmission. On the other hand, for real-time applications for which
`retransmissions are not possible, the channel code may be optimized for
`error correction. Often, a combination of error correction and detection may
`be employed. The modulator translates the discrete symbols output by the
`channel code into an analog waveform that can be transmitted over the
`
`1
`
`Figure 1.1 Block diagram of a
`digital communication link.
`
`I
`''
`
`Channel||'
`information
`Source
`'
`
`From
`information
`generator
`
`consumer
`
`
`
`
`Source
`encoder
`
`_| decoder
`
`1
`
`11
`
`
`
`
`
`
`.
`
`Scopeofthis textbook
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`1.1 Components of a digital communication system
`
`physical channel. The physical channel for an 802.11b based wireless local
`area network link is, for example, a band of 20 MHz width at a frequency of
`approximately 2.4 GHz.For this example, the modulatortranslates a bitstream
`of rate 1, 2, 5.5, or 11 Mbit/s (the rate varies, depending on the channel
`conditions) into a waveform that fits within the specified 20 MHz frequency
`band.
`.
`
`Thephysical characteristics of communication channels can vary
`Channel
`widely, and good channel modelsare critical to the design of efficient commu-
`nication systems. While receiver thermal noise is an impairment common to
`most communication systems, the channel distorts the transmitted waveform
`in a manner that may differ significantly in different settings. For wireline
`communication, the channel is well modeled as a linear time-invariant sys-
`tem, and the transfer function in the band used by the modulator can often
`be assumed to be known at the transmitter, based on feedback obtained
`from the receiver at the link set-up phase. For example, in high-speed digital
`subscriber line (DSL) systems over twisted pairs, such channel feedback is
`exploited to send more information at frequencies at which the channel gain
`is larger. On the other hand, for wireless mobile communication, the channel
`may vary because of relative mobility between the transmitter and receiver,
`which affects both transmitter design (accurate channel feedbackis typically
`not available) and receiver design (the channel musteither be estimated, or
`methods that do not require accurate channel estimates must be used). Fur-
`ther, since wireless is a broadcast medium, multiple-access interference due
`to simultaneous transmissions must be avoided either by appropriate resource
`sharing mechanisms, or by designing signaling waveforms and receivers to
`provide robust performancein the presence ofinterference.
`
`Demodulator and channel decoder The demodulator processes the analog
`received waveform, which is a distorted and noisy version of the transmitted
`waveform. One of its key tasks is synchronization: the demodulator must.
`account for the fact that the channel can produce phase, frequency, and
`time shifts, and that the clocks and oscillators at the transmitter and receiver
`are not synchronized a priori. Another task may be channel equalization, or
`compensation of the intersymbol interference induced by a dispersive channel.
`Theultimate goal of the demodulator is to produce tentative decisions on the
`transmitted symbols to be fed to the channel decoder. These decisions may be
`“hard”(e.g., the demodulator guessesthata particular bit is 0 or 1), or “soft”
`(e.g., the demodulator estimatesthe likelihood of a particular bit being 0 or 1).
`The channel decoder then exploits the redundancy in the channel to code to
`improve upon the estimates from the demodulator, with its final goal being
`to produce an estimate of the sequence of information symbols that were the
`input to the channel encoder. While the demodulator and decoder operate
`independently in traditional receiver designs, recent advances in coding and
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`Constellation Exhibit 2003
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`Introduction
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`communication theory show thatiterative information exchange between the
`demodulator and the decoder can dramatically improve performance.
`
`Source decoder The source decoder converts the estimated information
`bits produced by the channel decoder into a format that can be used by the
`end user. This may or may not be the sameas the original format that was
`the input to the source encoder. For example, the original source encoder
`could have translated speech into text, and then encodedit into bits, and the
`source decoder may then display the text to the end user, rather than trying
`to reproduce the original speech.
`Weare now ready to consider why the world is going digital. The two key
`advantages of the digital communication approach to the design of transmis-
`sion and storage media are as follows:
`
`Source-independent design. Once information is transformed into bits by
`the source encoder, it can be stored or transmitted without interpretation: as
`long as the bits are recovered, the information they represent can be recon-
`structed with the same degree of precision as originally encoded. This means
`that the storage or communication medium can be independentof the source
`characteristics, so that a variety of information sources can share the same
`communication medium. This leads to significant economies of scale in the
`design of individual communication links as well as communication networks
`comprising manylinks, such as the Internet. Indeed, when information has to
`traverse multiple communication links in a network, the source encoding and
`decoding in Figure 1.1 would typically be done at the end points alone, with
`the network transporting the information bits put out by the source encoder .
`without interpretation.
`
`the channel
`Channel-optimized design For each communication link,
`encoder or decoder and modulator or demodulator can be optimized for the
`specific channel characteristics. Since the bits being transported are regener-
`ated at each link, there is no “noise accumulation.”
`The preceding framework is based on a separation of source coding and
`channel coding. Not only does this separation principleyield practical advan-
`tages as mentioned above, but weare also reassured by the source—channel
`separation theorem of information theory thatit is theoretically optimal for
`point-to-point links (under mild conditions), While the separation approach
`is critical to obtaining the economies of scale driving the growth ofdigital
`communication systems, we note in passing that joint source and channel
`coding can yield superior performance, both in theory and practice, in certain
`settings (e.g., multiple-access and broadcast channels, or applications with
`delay or complexity constraints).
`The scope ofthis textbook is indicated in Figure 1.1: we consider modula-
`tion and demodulation, channel encoding and decoding, and channel modeling.
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`5
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`1.2 Text outline
`
`Source encoding and decoding are not covered. Thus, we implicitly restrict
`attention to communication systems based on the separation principle.
`
`1.2 Text outline
`
`The objective of this text is to convey an understanding of the principles
`underlying the design of a modern digital communication link. An introduc-
`tion to modulation techniques (i-e., how to convert bits into a form that can
`be sent over a channel) is provided in Chapter 2, We emphasize the impor-
`tant role played by the complex baseband representation for passband signals
`in both transmitter and receiver design, descr