Guard
`inten·als
`
`Symbols
`
`INTEL-1023
`10,079,707
`
`

`

`Multi-Carrier Digital
`Communications
`Theory and Applications of OFDM
`Second Edition
`
`

`

`

`

`Multi-Carrier Digital
`Communications
`Theory and Applications of OFDM
`Second Edition
`
`Ahmad R. S. Bahai
`National Semiconductor
`Stanford University
`University of California Berkeley
`
`Burton R. Saltzberg
`Consultant on Digital Communications
`Formerly Bell Laboratories
`
`Mustafa Ergen
`University of California Berkeley
`
`~ Springer
`
`

`

`Library of Congress Control Number: 2004052575
`
`Bahai, Ahmad R. S.,
`Multi-Carrier Digital Communications: Theory and Applications of OFDM/
`Ahmad R. S. Bahai, Burton R. Saltzberg, Mustafa Ergen - 2nd ed.
`
`p. cm. (Information Technology: Transmission, Processing and Storage)
`1. Digital Communications. 2. Multiplexing. 3. Spread spectrum communications.
`4. Orthogonalization methods. I. Saltzberg, Burton R. II. Ergen, Mustafa.
`III. Title. IV. Series.
`
`ISBN: 978-0-387-22575-3 (13)
`
`ISBN: 0-387-22575-7 (10) E- ISBN: 978-0-387-22576-0
`
`Printed on acid-free paper
`
`Copyright © 2004 by Springer Science +Business Media, LLC
`All rights reserved. This work may not be translated or copied in whole or in part without the written
`permission of the publisher (Springer Science +Business Media, LLC, 233 Spring Street, New York, NY
`10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in
`connection with any form of information storage and retrieval, electronic adaptation, computer software,
`or by similar or dissimilar methodology now known or hereafter developed is forbidden.
`The use in this publication of trade names, trademarks, service marks and similar terms, even if they are
`not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject
`to proprietary rights.
`
`9 8 7 6 5 4 3
`
`springer.com
`
`

`

`Contents
`
`Preface
`
`Acknowledgements
`
`1 Introduction to Digital Communications
`
`1.1 Background . . . . .
`
`1.2 Evolution of OFDM .
`
`2 System Architecture
`
`2.1 Wireless Channel Fundamentals
`
`2.1.1
`
`Path Loss .
`
`2.1.2 Shadowing
`
`2.1.3 Fading Parameters
`2.1.4 Flat Fading ....
`
`XVII
`
`XXI
`
`1
`
`1
`
`5
`
`15
`
`15
`
`16
`
`17
`
`18
`
`21
`
`

`

`vi
`
`2.1.5 Frequency Selective Fading
`
`2.1.6 Fast Fading .
`
`2.1.7 Slow Fading
`
`2.1.8 Rayleigh Fading
`
`2.1.9 Ricean Fading
`
`2.1.10 Distortions for Wireless Systems .
`
`22
`
`23
`
`23
`
`23
`
`25
`
`26
`
`2.1.11 Diversity Techniques in a Fading Environment 26
`
`2.2 Digital Communication System Fundamentals .
`
`2.2.1 Coding ..
`
`2.2.2 Modulation
`
`2.3 Multi-Carrier System Fundamentals
`
`2.4 DFT . . . .
`
`2.5 Partial FFT
`
`2.6 Cyclic Extension
`
`2.7 Channel Estimation
`
`2.8 Modelling of OFDM for Time-Varying Random Chan-
`nel . . . . . . . . . . . . . . . . . . . . . . . . .
`
`2.8.1 Randomly Time-Varying Channels . . . . . .
`
`2.8.2 OFDM in Randomly Time-Varying Channels
`
`3 Performance over Time-Invariant Channels
`
`3.1 Time-Invariant Non-Flat Channel with Colored Noise
`
`3.2 Error Probability
`
`3.3 Bit Allocation . .
`
`27
`
`28
`
`29
`
`33
`
`35
`
`41
`
`42
`
`45
`
`48
`
`48
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`51
`
`55
`
`55
`
`56
`
`59
`
`

`

`3.4 Bit and Power Allocation Algorithms for Fixed Bit Rate 66
`
`vii
`
`4 Clipping in Multi-Carrier Systems
`4.1
`
`Introduction . . . . . . . . . .
`
`4.2 Power Amplifier Non-Linearity .
`
`4.3 Error Probability Analysis
`System Model ..
`4.3.1
`4.3.2 BER Due to Clipping .
`
`4.4 Performance in AWGN and Fadihg.
`4.5 Bandwidth Regrowth .........
`
`5 Synchronization
`
`5.1 Timing and Frequency Offset in OFDM
`5.2 Synchronization & System Architecture
`
`5.3 Timing and Frame Synchronization
`
`5.4 Frequency Offset Estimation
`5.5 Phase Noise . . . . . . . . .
`
`6 Channel Estimation and Equalization
`
`In.troduction . . . .
`
`6.1
`6.2 Channel Estimation
`
`6.2.1 Coherent Detection .
`
`6.2.2 Block-Type Pilot AtTangement .
`6.2.3 Comb-Type Pilot Arrangement .
`
`6.2.4
`
`Interpolation Techniques . . . .
`
`69
`
`69
`71
`
`73
`
`77
`78
`
`86
`94
`
`99
`
`99
`104
`
`105
`
`107
`108
`
`117
`
`117
`
`117
`
`119
`122
`
`126
`
`127
`
`

`

`viii
`
`6.2.5 Non-coherent Detection
`
`6.2.6 Performance
`
`. . . . . .
`
`6.2.7 Channel Estimation for MIMO-OFDM
`
`6.3 Equalization . . . . . . . . . . . . .
`
`6.3.1 Time Domain Equalization .
`
`6.3.2 Equalization in DMT .
`
`6.3.3 Delay Parameter
`
`. . .
`
`6.3.4 AR Approximation of ARMA Model
`
`6.3.5 Frequency Domain Equalization
`
`6.3.6 Echo Cancellation
`
`. . . . . . .
`
`130
`
`130
`
`134
`
`137
`
`138
`
`142
`
`145
`
`146
`
`149
`
`152
`
`6.3.7 Appendix - Joint Innovation Representation
`of ARMA Models
`. . . . . . . . . . . . . . 160
`
`7
`
`Channel Coding
`
`7.1 Need for Coding
`
`7.2 Block Coding in OFDM
`
`7.3 Convolutional Encoding
`
`7.4 Concatenated Coding . .
`
`7.5 Trellis Coding in OFDM
`
`7.6 Turbo Coding in OFDM
`
`8 ADSL
`
`8.1 Wired Access to High Rate Digital Services
`
`8.2 Properties of the Wire-Pair Channel . . . .
`
`167
`
`167
`
`168
`
`173
`
`179
`
`180
`
`185
`
`189
`
`189
`
`190
`
`

`

`8.3 ADSL Systems
`
`. . . . ................ 200
`
`ix
`
`9 Wireless LAN Applications
`
`9.1
`
`Introduction . . . . .
`
`9.1.1 Background .
`
`9.1.2 Pros and Cons
`9.2 Topology ........
`
`9.2.1
`
`Independent BSS
`
`9.2.2
`
`Infrastructure BSS
`
`9.2.3 Services .
`
`9.3 Architecture ...
`
`9.4 Medium Access Control
`9.4.1 DCF Access ..
`9.4.2 Markov Model of DCF .
`
`9.4.3 PCF.
`
`9.5 Management
`
`Synchronization
`9.5.1
`9.5.2 Scanning ....
`9.5.3 Power Management
`
`9.5.4 Security . . . . . . .
`
`9.6
`
`IEEE 802.11 and 802.11 b Physical Layer
`
`9.6.l
`
`Spread Spectrum . . .
`
`9.6.2 FHSS Physical Layer .
`
`9.6.3 DSSS Physical Layer .
`
`203
`
`203
`
`203
`
`204
`
`206
`
`206
`
`208
`
`211
`
`213
`
`217
`
`221
`
`227
`
`233
`
`239
`
`239
`
`240
`
`241
`
`242
`
`244
`
`245
`
`247
`
`249
`
`

`

`X
`
`9.6.4
`
`IR Physical Layer . . . . .
`
`9.6.5 HR/DSSS Physical Layer
`
`9.6.6 RF Interference . . . .
`
`9.7
`
`IEEE 802.1 la Physical Layer .
`
`9.7.1 OFDM Architecture
`
`9.7.2 Transmitter
`
`9.7.3 Receiver
`
`9.7.4 Degradation Factors
`
`9.8 Performance of 802.1 la Transceivers .
`
`9.8.1 Data Rate ..
`
`9.8.2 Phase Noise .
`
`9.8.3 Channel Estimation .
`
`9.8.4 Frequency Offset
`
`9.8.5
`
`IQ Imbalance . .
`
`9.8.6 Quantization and Clipping Error
`
`9.8.7 Power Amplifier Nonlinearity
`
`9.8.8 Hard or Soft Decision Decoding
`
`9.8.9 Co-channel Interference
`
`9.8.10 Narrow band Interference .
`9.8.11 UWB Interference ...
`9.8.12 Performance of 64QAM
`
`9.9 Rate Adaptation . . .
`
`9.10 Zero IF Technology
`
`252
`
`252
`
`253
`
`254
`
`255
`
`256
`
`269
`
`274
`
`275
`
`276
`
`278
`
`279
`
`280
`
`281
`
`283
`
`285
`
`286
`
`286
`
`288
`
`288
`
`289
`
`291
`
`292
`
`

`

`9.11 IEEE 802.lle MAC Protocol . . . . .
`
`9.11.1 IEEE 802.1 le MAC Services.
`
`9.11.2 IEEE 802.1 le MAC Architecture
`
`9.11.3 Hybrid Coordination Function (HCF)
`
`9.11.4 HCF Controlled Channel Access .
`9.11.5 Admission Control ....
`
`9.11.6 Block Acknowledgement.
`
`9.11.7 Multi-rate Support
`
`9.11.8 Direct Link Protocol
`
`9.12 HIPERLAN/2 . . . . . . . .
`
`9.121 Protocol Architecture
`
`9.12.2 Data Link Control
`
`9.12.3 Convergence Layer .
`
`9.12.4 HIPERLAN/2 vs 802.11 a
`
`9.13 MMAC-HiSWAN . . . . . . . . .
`9.14 Overview of IEEE 802. 11 Standards
`
`xi
`
`293
`
`294
`
`295
`
`295
`
`299
`
`300
`
`301
`
`301
`
`301
`
`302
`
`304
`
`304
`
`310
`
`310
`
`312
`
`312
`
`9.14.1 IEEE 802.1 lc - Bridge Operation Procedures 312
`
`9.14.2 IEEE 802.11 d - Global Harmonization . . .
`
`9.14.3 IEEE 802.1 lf - Inter Access Point Protocol
`
`313
`
`313
`
`9.14.4 IEEE 802.1 lg - Higher Rate Extensions in the
`2.4GHz Band . . . . . . . . . . . . . . . . . 313
`
`9.14.5 IEEE 802.11 h - Spectrum Managed 802 .11 a . 314
`
`9J4.6 £EBE 802.1 li - MAC Enhancements for En-
`hanced Security . . . . . . . . . . . . . . . . 315
`
`

`

`xii
`
`9.14.7 IEEE 802.lx - Port Based Network Access
`Control
`. . . . . . . . . . . . . . . . .
`
`9.14.8 IEEE 802.lp - QoS on the MAC Level.
`
`10 Digital Broadcasting
`
`IO.I Broadcasting of Digital Audio Signals
`
`10.2 Signal Format . . . . . . . . . . . .
`
`10.3 Other Digital Broadcasting Systems
`
`10.3.1 DAB in the U.S.A
`
`10.4 Digital Video Broadcasting
`
`11 OFDM based Multiple Access Techniques
`
`1 I .1 Introduction . .
`
`11.2 OFDM-FDMA
`
`11.3 OFDM-TDMA
`
`11.4 Multi Carrier CDMA (OFDM-CDMA) .
`
`11.5 OFDMA . . . . . . . . . . . .
`
`11.5.1 OFDMA Architecture
`
`11.5 .2 Resource Allocation Regarding QoS .
`
`11.5 .3 Resource Allocation Regarding Capacity
`
`11.6 Flash-OFDM
`
`.
`
`11.7 OFDM-SDMA
`
`12 Ultra WideBand Technologies
`
`12. I Impulse Radio . . . . . . .
`
`316
`
`316
`
`317
`
`317
`
`320
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`323
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`323
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`324
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`327
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`327
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`329
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`330
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`331
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`336
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`337
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`341
`
`342
`
`343
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`346
`
`349
`
`350
`
`

`

`12.2 Multiband Approach
`
`12.3 Multiband OFDM . .
`
`13 IEEE 802.16 and WiMAX
`
`13.l Introduction
`
`13.2 WiMAX ..
`
`13.3 WirelessMAN OFDM.
`
`13.4 802.16 MAC
`
`13.5 Conclusion
`
`14 Future Trends
`
`14.1 Comparison with Single Carrier Modulation
`
`14.2 Mitigation of Clipping Effects
`
`14.3 Overlapped Transforms ...
`
`14.4 Advances in Implementation
`
`Bibliography
`
`List of Figures
`
`List of Tables
`
`Index
`
`xiii
`
`352
`
`352
`
`357
`
`357
`
`358
`
`359
`
`361
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`362
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`363
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`363
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`365
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`366
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`370
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`373
`
`393
`
`405
`
`407
`
`

`

`

`

`We dedicate this book
`to our families ...
`
`

`

`

`

`Preface
`
`M ulti-carrier modulation, Orthogonal Frequency Division Multi(cid:173)
`
`plexing (OFDM) particularly, has been successfully applied to
`a wide variety of digital communications applications over the past
`several years. Although OFDM has been chosen as the physical layer
`standard for a diversity of important systems, the theory, algorithms,
`and implementation techniques remain subjects of current interest.
`This is clear from the high volume of papers appearing in technical
`journals and conferences.
`
`Multi-carrier modulation continues to evolve rapidly. It is hoped
`that this book will remain a valuable summary of the technology, pro(cid:173)
`viding an understanding of new advances as well as the present core
`technology.
`
`The Intended Audience
`
`This book is intended to be a concise summary of the present state of
`the art of the theory and practice of OFDM technology. The authors
`believe that the time is ripe for such a treatment. Particularly based
`on one of the author's long experience in development of wireless
`systems (AB) and the other's in wireline systems (BS), we have at(cid:173)
`tempted to present a unified presentation of OFDM performance and
`
`

`

`xviii
`
`implementation over a wide variety of channels.
`
`It is hoped that this will prove valuable both to developers of such
`systems and to researchers and graduate students involved in analysis
`of digital communications.
`
`In the interest of brevity, we have minimized treatment of more
`general communication issues. There exist many excellent texts on .
`communication theory and technology. Only brief summaries of top(cid:173)
`ics not specific to multi-carrier modulation are presented in this book
`where essential. As a background, we presume that the reader has a
`clear knowledge of basic fundamentals of digital communications.
`
`Highlights of the Second Edition
`
`During the past few years since the publication of the first edition
`of this text, the technology and application of OFDM has continued
`their rapid pace of advancement. As a result, it became clear to us that
`a new edition of the text would be highly desirable. The new edition
`provides an opportunity to make those corrections and clarifications
`whose need became apparent from continued discussions with many
`readers. However, the main purpose is to introduce new topics that
`have come to the forefront during the past few years, and to amplify
`the treatment of other subject matter.
`
`Because of the particularly rapid development of wireless systems
`employing OFDM, we have introduced a section early in the text on
`wireless channel fundamentals. We have extended and modified our
`analysis of the effects of clipping, including simulation results that
`have been reported in a recent publication. These new results are re(cid:173)
`stated here. A section on channel estimation has been added to the
`chapter on equalization. The chapter on local area networks has been
`greatly expanded to include the latest technology and applications.
`Three totally new chapters are added, on OFDM multiple access tech-
`
`

`

`xix
`
`nology, on ultra wideband technology and on WiMAX (IEEE 802.16).
`
`Organization of This Book
`
`We begin with a historical overview of multi-carrier communications,
`wherein its advantages for transmission over highly dispersive chan(cid:173)
`nels have long been recognized, particularly before the development
`of equalization techniques. We then focus on the bandwidth efficient
`technology of OFDM, in particular the digital signal processing tech(cid:173)
`niques that have made the modulation format practical. Several chap(cid:173)
`ters describe and analyze the sub-systems of an OFDM implementa(cid:173)
`tion, such as clipping, synchronization, channel estimation, equaliza(cid:173)
`tion, and coding. Analysis of performance over channels with various
`impairments is presented.
`
`The book continues with descriptions of three very important and
`diverse applications of OFDM that have been standardized and are
`now being deployed. ADSL provides access to digital services at sev(cid:173)
`eral Mbps over the ordinary wire-pair connection between customers
`and the local telephone company central office. Digital Broadcasting
`enables the radio reception of high quality digitized sound and video.
`A unique configuration that is enabled by OFDM is the simultaneous
`transmission of identical signals by geographically dispersed trans(cid:173)
`mitters. And, the new development of wireless LANs for multi-Mbps
`communications is presented in detail. Each of these successful appli(cid:173)
`cations required the development of new fundamental technology.
`
`Finally, the book concludes with describing the OFDM based mul(cid:173)
`tiple access techniques, ultra wideband technology and WiMAX.
`
`

`

`

`

`Acknowledgements
`
`The two authors of the first edition of this text are very pleased to
`include our colleague as an additional author, and gratefully acknowl(cid:173)
`edge his extensive contributions in making this second edition possi(cid:173)
`ble.
`
`The first edition of this text has been used for classes in University
`of California Berkeley, Stanford University, University of Cambridge,
`CBI-Europe and in other institutions. We are grateful to colleagues in
`the institutions where this book has been used. For the first edition,
`we acknowledge the extensive review and many valuable suggestions
`of Professor Kenji Kohiyama, our former colleagues at AT&T Bell
`Laboratories and colleagues at Algorex. Gail Bryson performed the
`very difficult task of editing and assembling this text. The continuing
`support of Kambiz Homayounfar was essential to its completion.
`
`In preparing the second edition, we acknowledge Professor Pravin
`Varaiya for his valuable help, Dr. Haiyun Tangh for providing some
`graphs, National Semiconductor and IMEC for providing the MAT(cid:173)
`LAB simulation tool, Sinem Coleri for proof-reading. We wish to ex(cid:173)
`press our appreciation to Fran Wilkinson for editing.
`
`Last, but by no means least, we are thankful to our families for
`their support and patience.
`
`Despite all our efforts to keep the text error free, for any that re(cid:173)
`main, any comments, corrections and suggestions received will be
`much appreciated for the future printings. We can be reached via
`e-mail at bahai@stanford.edu, bsaltzberg@worldnet.att.net, and er(cid:173)
`gen@eecs.berkeley.edu. We will post any corrections and comments
`at the Web site http://ofdm.eecs.berkeley.edu/ in addition to the sup(cid:173)
`port materials that may be necessary to prepare a lecture or paper.
`
`

`

`

`

`Introduction to Digital
`Communications
`
`1.1 Background
`T he physical layer of digital communications includes mapping of
`
`digital input information into a waveform for transmission over
`a communication channel and mapping of the received waveform into
`digital information that hopefully agrees with the original input since
`the communication channel may introduce various forms of distortion
`as well as noise [3].
`
`The simplest form of such communication, as least conceptually,
`is Pulse Amplitude Modulation (PAM), shown in Figure 1.1. Here the
`transmitted waveform is of the form
`
`n
`
`(1.1)
`
`where the information to be transmitted is given by the sequence of
`ans, 1/T is the symbol rate, and g(t) is the impulse response of the
`
`

`

`2
`
`Chapter 1. Introduction to Digital Communications
`
`Input Bit
`Stream
`
`---,..i Serial/Parallel
`
`Noise
`
`Channel
`
`Clock
`
`Parallel/Serial
`
`Data Out
`
`Figure 1.1: A basic PAM system
`
`transmit filter, usually low-pass. The ans are chosen from an alphabet
`of size L, so the bit rate is tzog2 L. It is desirable that the alphabet be
`both zero mean and equally spaced. The values of an can be written
`as
`
`{-A(L-1), ... ,-A,A, ... ,A(L-1)}.
`
`(1.2)
`
`Assuming the ans are equiprobable, the transmitted power is
`
`L2 - 1 Joo
`T
`3
`
`g2(t)dt.
`-oo
`
`A2
`
`(1.3)
`
`At the receiver, the signal is filtered by r(t.) , which may include
`an adaptive equalizer (sampled), and the nearest permitted member of
`the alphabet is output. In order to avoid inter-symbol interference, it
`is desirable that x(t) = g(t) * h(t) * r(t) = 0 for all t = kT, k an
`integer =J 0, where h(t) is the channel impulse response. This is the
`Nyquist criterion, which is given in the frequency domain by:
`
`

`

`1.1. Background
`
`I::xu +;)=canst
`
`3
`
`(1.4)
`
`m
`The minimum bandwidth required is 1/2T . This is met by a fre(cid:173)
`quency response that is constant for -1/2T < f < l/2T, whose
`corresponding time response is
`
`x(t) = sin(1rt/T)
`(1rt/T)
`
`(1.5)
`
`Some excess bandwidth, denoted by the roll-off factor, is desirable in
`order for the time response to decay more quickly. Note that r( t) is not
`a matched filter, because it must satisfy the inter-symbol interference
`constraint.
`
`If r ( t) has gain such that the alphabet levels of x ( 0) are also spaced
`by 2A, then errors will occur when the noise at the sampler satisfies
`[nl > A for interior levels, or n > A or n < -A for the outer levels. If
`the noise is Gaussian with power spectral density N (f) at the receiver
`input, then the noise variance is:
`
`and the error probability per symbol is
`
`p = 2(L- l)Q(A)
`L
`a-
`'
`
`e
`
`where
`
`(1.6)
`
`(1.7)
`
`(1.8)
`
`is the n01mal error integral.
`
`PAM is only suitable over channels that exist down to, but might
`not necessarily include, zero frequency. If zero frequency is absent, a
`modulation scheme that puts the signal spectrum in the desired fre(cid:173)
`quency band is required. Of particular interest, both in its own right
`
`

`

`4
`
`Chapter 1. Introduction to Digital Communications
`
`Data
`In
`
`cos
`
`sin
`
`sin
`
`clock
`
`Figure 1.2: A basic QAM system
`
`and as a component of OFDM, is Quadrature Amplitude Modulation
`(QAM). The simplest form of QAM, shown in Figure 1.2, may be
`thought of as two PAM signals, modulated by carriers at the same fre(cid:173)
`quency but 90 degrees out of phase. At the receiver, demodulation by
`the same carriers separates the signal components. Unlike some other
`modulation schemes, such as FM, QAM is bandwidth efficient in that
`it requires the same bandwidth as a PAM signal of the same bit rate.
`Furthermore, the performance of QAM in noise is comparable to that
`of PAM. The QAM line signal is of the form
`
`L ang(t - nT)coswt - L bng(t -· nT)sinwt.
`
`(1.9)
`
`n
`
`n
`
`This line signal may also be written in the form of:
`
`n
`
`(1.10)
`
`

`

`1.2. Evolution of OFDM
`
`5
`
`X X
`
`X X
`
`X X
`
`X X
`
`X X
`
`X X
`
`X X
`
`X X
`
`Figure 1.3: A QAM constellation
`
`where the pair of real symbols an and bn are treated as a complex
`symbol en = a,t + jbn. The required bandwidth for transmitting such
`complex symbols is 1/T. The complex symbol values are shown as a
`"constellation" in the complex plane. Figure 1.3 shows the constella(cid:173)
`tion of a 16-point QAM signal, which is formed from 4-point PAM.
`
`It is not necessary that the constellation be square. Figure 1.4
`shows how input information can be mapped arbitrarily into constel(cid:173)
`lation points. A constellation with a more circular boundary provides
`better noise performance. By grouping n successive complex symbols
`as a unit, we can treat such units as symbols in 2n-dimensional space.
`In this case, Figure 1.4 can be extended to include a large enough
`serial-to-parallel converter that accommodates the total number of bits
`in n symbols, and a look-up table with 2n outputs.
`
`1.2 Evo]ution of OFDM
`
`The use of Freyuency Division Multiplexing (FDM) goes back over a
`century, where more than one low rate signal, such as telegraph, was
`carried over a relatively wide bandwidth channel using a separate car-
`
`

`

`6
`
`Chapter 1. Introduction to Digital Communications
`
`Input Bit Stream - -~ Serial/Parallel
`
`Address
`
`Lookup
`Table
`
`Figure 1.4: General form of QAM generation
`
`rier frequency for each signal. To facilitate separation of the signals at
`the receiver, the carrier frequencies were spaced sufficiently far apart
`so that the signal spectra did not overlap. Empty spectral regions be(cid:173)
`tween the signals assured that they could be separated with readily
`realizable filters. The resulting spectral efficiency was therefore quite
`low.
`
`Instead of carrying separate messages, the different frequency car(cid:173)
`riers can carry different bits of a single higher rate message. The
`source may be in such a parallel format, or a serial source can be
`presented to a serial-to-parallel converter whose output is fed to the
`multiple carriers.
`
`Such a parallel transmission scheme can be compared with a sin(cid:173)
`gle higher rate serial scheme using the same channel. The parallel
`system, if built straightforwardly as several transmitters and receivers,
`will certainly be more costly to implement. Each of the parallel sub(cid:173)
`channels can carry a low signalling rate, proportional to its bandwidth.
`The sum of these signalling rates is less than can be carried by a sin(cid:173)
`gle serial channel of that combined bandwidth because of the unused
`guard space between the parallel sub-carriers. On the other hand, the
`
`

`

`1.2. Evolution of OFDM
`
`7
`
`single channel will be far more susceptible to inter-symbol interfer(cid:173)
`ence. This is because of the short duration of its signal elements and
`the higher distortion produced by its wider frequency band, as com(cid:173)
`pared with the long duration signal elements and narrow bandwidth
`in sub-channels in the parallel system.
`
`Before the development of equalization, the parallel technique was
`the preferred means of achieving high rates over a dispersive chan(cid:173)
`nel, in spite of its high cost and relative bandwidth inefficiency. An
`added benefit of the parallel technique is reduced susceptibility to
`most forms of impulse noise.
`
`The first solution of the bandwidth efficiency problem of multi(cid:173)
`tone transmission (not the complexity problem) was probably the Kine(cid:173)
`plex system. The Kineplex system was developed by Collins Radio
`Co. [ 4] for data transmission over an H.F. radio channel subject to se(cid:173)
`vere multi-path fading. In that system, each of 20 tones is modulated
`by differential 4-PSK without filtering. The spectra are therefore of
`the sin(kf)/ f shape and strongly overlap. However, similar to mod(cid:173)
`em OFDM, the tones are spaced at frequency intervals almost equal
`to the signalling rate and are capable of separation at the receiver.
`
`The reception technique is shown in Figure 1.5. Each tone is de(cid:173)
`tected by a pair of tuned circuits. Alternate symbols are gated to one
`of the tuned circuits, whose signal is held for the duration of the next
`symbol. The signals in the two tuned circuits are then processed to
`determine their phase difference, and therefore the transmitted infor(cid:173)
`mation. The older of the two signals is then quenched to allow input
`of the next symbol. The key to the success of the technique is that the
`time response of each tuned circuit to all tones, other than the one to
`which it is tuned, goes through zero at the end of the gating interval,
`at which point that interval is equal to the reciprocal of the frequency
`separation between tones. The gating time is made somewhat shorter
`than the symbol period to reduce inter-symbol interference, but ef(cid:173)
`ficiency of 70% of the Nyquist rate is achieved. High performance
`over actual long H.F. channels was obtained, although at a high im-
`
`

`

`8
`
`Chapter 1. Introduction to Digital Communications
`
`In
`
`Gate
`
`Tuned Circuit
`
`Tuned Circuit
`
`Tuned Circuit
`
`Tuned Circuit
`
`Gate
`
`Phase Detector
`
`Phase Detector
`
`Out
`
`Figure 1.5: The Collins Kineplex receiver
`
`plementation cost. Although fully transistorized, the system required
`two large bays of equipment.
`
`A subsequent multi-tone system [5] was proposed using 9-point
`QAM constellations on each carrier, with correlation detection em(cid:173)
`ployed in the receiver. Carrier spacing equal to the symbol rate pro(cid:173)
`vides optimum spectral efficiency. Simple coding in the frequency do(cid:173)
`main is another feature of this scheme. The above techniques do pro(cid:173)
`vide the orthogonality needed to separate multi-tone signals spaced by
`the symbol rate. However the sin( kf) / f spectrum of each component
`has some undesirable properties. Mutual overlap of a large number of
`sub-channel spectra is pronounced. Also, spectrum for the entire sys(cid:173)
`tem must allow space above and below the extreme tone frequencies
`to accommodate the slow decay of the sub-channel spectra. For these
`reasons, it is desirable for each of the signal components to be ban(cid:173)
`dlimited so as to overlap only the immediately adjacent sub-carriers,
`while remaining orthogonal to them. Criteria for meeting this objec-
`
`

`

`1.2. Evolution of OFDM
`
`9
`
`Add
`
`Clock
`
`Figure 1.6: An early version of OFDM
`
`tive is given in References [ 6] and [7].
`
`In Reference [8] it was shown how bandlimited QAM can be em(cid:173)
`ployed in a multi-tone system with orthogonality and minimum car(cid:173)
`rier spacing (illustrated in Figure 1.6). Unlike the non-bandlimited
`OFDM, each carrier must carry Staggered (or Offset) QAM, that is,
`the input to the I and Q modulators must be offset by half a symbol
`period. Furthermore, adjacent carriers must be offset oppositely. It is
`interesting to note that Staggered QAM is identical to Vestigial Side(cid:173)
`band (VSB) modulation. The low-pass filters g(t) are such that G2(J),
`the combination of transmit and receive filters, is Nyquist, with the
`roll-off factor assumed to be less than I.
`
`

`

`10
`
`Chapter 1. Introduction to Digital Communications
`
`Real component of an OFDM signal
`
`Imaginary component of an OFDM
`signal
`
`J}
`
`V\;V\J
`
`/
`/
`
`j
`
`Figure 1.7: OFDM modulation concept: Real and Imaginary compo(cid:173)
`nents of an OFDM symbol is the superposition of several harmonics
`modulated by data symbols
`
`

`

`1.2. Evolution of OFDM
`
`11
`
`f
`
`Figure 1.8: Spectrum overlap in OFDM
`
`The major contribution to the OFDM complexity problem was the
`application of the Fast Fourier Transform (FFf) to the modulation
`and demodulation processes [9]. Fortunately, this occurred at the same
`time digital signal processing techniques were being introduced into
`the design of modems. The technique involved assembling the input
`information into blocks of N complex numbers, one for each sub(cid:173)
`channel. An inverse FFf is performed on each block, and the resultant
`transmitted serially. At the receiver, the information is recovered by
`performing an FFf on the received block of signal samples. This form
`of OFDM is often referred to as Discrete Multi-Tone (DMT). The
`spectrum of the signal on the line is identical to that of N separate
`QAM signals, at N frequencies separated by the signalling rate. Each
`such QAM signal carries one of the original input complex numbers.
`The spectrum of each QAM signal is of the form sin(kf)/ f, with
`nulls at the center of the other sub-carriers, as in the earlier OFDM
`systems, and as shown in Figure 1.8 and Figure I .9.
`
`

`

`12
`
`Chapter 1. Introduction to Digital Communications
`
`f
`
`Figure 1.9: Spectrum of OFDM signal
`
`A block diagram of a very basic DMT system is shown Figure 1.10.
`Several critical blocks are not shown. As described more thoroughly
`in Chapter 2, care must be taken to avoid overlap of consecutive trans(cid:173)
`mitted blocks, a problem that is solved by the use of a cyclic prefix.
`Another issue is how to transmit the sequence of complex numbers
`from the output of the inverse FFf over the channel. The process is
`straightforward if the signal is to be further modulated by a modulator
`with I and Q inputs.
`
`Otherwise, it is necessary to transmit real quantities. This can be
`accomplished by first appending the complex conjugate to the original
`input block. A 2N-point inverse FFf now yields 2N real numbers to
`be transmitted per block, which is equivalent to N complex numbers.
`
`The most significant advantage of this DMT approach is the ef(cid:173)
`ficiency of the FFf algorithm. An N-point FFf requires only on the
`order of NlogN multiplications, rather than N 2 as in a straightfor(cid:173)
`ward computation. The efficiency is particularly good when N is a
`power of 2, although that is not generally necessary. Because of the
`use of the FFf, a DMT system typically requires fewer computations
`per unit time than an equivalent single channel system with equaliza(cid:173)
`tion. An overall cost comparison between the two systems is not as
`clear, but the costs should be approximately equal in most cases. It
`should be noted that the bandlimited system of Figure 1.6 can also
`
`

`

`1.2. Evolution of OFDM
`
`13
`
`Data In
`
`Block into N complex numbers
`
`Channel
`
`Channel
`
`Equalize
`
`~ - -~ Data Out
`Unblock
`
`Figure 1.10: Very basic OFDM system
`
`be implemented with FFT techniques [10], although the complexity
`and delay will be greater than DMT. Over the last 20 years or so,
`OFDM techniques and, in particular, the DMT implementation, has
`been used in a wide variety of applications [64]. Several OFDM voice(cid:173)
`band modems have been introduced, but did not succeed commer(cid:173)
`cially because they were not adopted by standards bodies. DMT has
`been adopted as the standard for the Asymmetric Digital Subscriber
`Line (ADSL), which provides digital communication at several Mbps
`from a telephone company central office to a subscriber, and a lower
`rate in the reverse direction, over a normal twisted pair of wires in
`the loop plant. OFDM has been particularly successful in numerous
`wireless applications, where its superior 'performance in multi-path
`environments is desirable. Wireless receivers detect signals distorted
`by time and frequency selective fading. OFDM in conjunction with
`proper coding and interleaving is a powerful technique for combating
`the wireless channel impairments that a typical OFDM wireless sys(cid:173)
`tem might face, as is shown in Figure 1.11. A particularly interesting
`configuration, discussed in Chapter 10, is the Single Frequency Net(cid:173)
`work (SFN) used for broadcasting of digital audio or video signals.
`Here many geographically separated transmitters broadcast identical
`and synchronized signals to cover a large region. The reception of
`such signals by a receiver is equivalent to an extreme form of multi-
`
`

`

`14
`
`Chapter 1. Introduction to Digital Communications
`
`Information
`source
`
`Symbol
`level Freq.
`Interleaver
`
`Inner
`coding
`
`Bit
`Leve[
`Interleaver
`
`Modulation
`
`Cyclic Ext./
`Pulse
`Shaping
`Zero padding
`
`Frequency/Time Selective fading
`Channel, AWGN
`
`Channel
`Estimation
`
`AGC/Coarse
`Synchronization
`
`De(cid:173)
`modulation
`
`Bit Level
`De•
`interleaver
`
`Sott
`Decision
`Inner
`Decoding
`
`Symbol
`level Freq.
`De•
`Interleaver
`
`Information
`Sink
`
`coding
`
`Figure Ll 1: A typical wireless OFDM architecture
`
`path. OFDM is the technology that makes this configuration viable.
`
`Another wireless application of OFDM is in high speed local area
`networks (LANs). Although the absolute delay spread in this environ(cid:173)
`ment is low, if very high data rates, in the order of many tens of Mbps,
`is desired, then the delay spread may be large compared to a symbol
`interval. OFDM is preferable to the use of long equalizers in this ap(cid:173)
`plication. It is expected that OFDM will be applied to many more new
`communications systems over the next several years.
`
`

`

`12·
`
`Chapter
`
`_____________ ____.
`
`System A