Multi-Carrier Digital
`Communications
`Theory and Applications of OFDM
`Second Edition
`
`Ford Motor Co.
`Exhibit 1024
`Page 001
`
`

`

`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
`
`Ford Motor Co.
`Exhibit 1024
`Page 002
`
`

`

`eBook ISBN:
`Print ISBN:
`
`0-387-22576-5
`0-387-22575-7
`
`©2004 Springer Science + Business Media, Inc.
`
`Print ©2004 Springer Science + Business Media, Inc.
`Boston
`
`All rights reserved
`
`No part of this eBook may be reproduced or transmitted in any form or by any means, electronic,
`mechanical, recording, or otherwise, without written consent from the Publisher
`
`Created in the United States of America
`
`Visit Springer's eBookstore at:
`and the Springer Global Website Online at:
`
`http://www.ebooks.kluweronline.com
`http://www.springeronline.com
`
`Ford Motor Co.
`Exhibit 1024
`Page 003
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`

`

`Contents
`
`Preface
`Acknowledgements
`
`1 Introduction to Digital Communications
`
`1.1
`
`1.2
`
`Background
`
`Evolution of OFDM
`
`2 System Architecture
`
`2.1 Wireless Channel Fundamentals
`
`2.1.1
`
`2.1.2
`
`2.1.3
`
`2.1.4
`
`Path Loss
`
`Shadowing
`
`Fading Parameters
`
`Flat Fading
`
`XVII
`
`XXI
`
`1
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`1
`
`5
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`15
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`15
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`16
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`21
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`vi
`
`2.1.5
`
`2.1.6
`
`2.1.7
`
`2.1.8
`
`2.1.9
`
`Frequency Selective Fading
`
`Fast Fading
`
`Slow Fading
`
`Rayleigh Fading
`
`Ricean Fading
`
`2.1.10
`
`Distortions for Wireless Systems
`
`Diversity Techniques in a Fading Environment
`
`2.1.11
`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
`
`22
`
`23
`
`23
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`23
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`25
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`26
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`26
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`27
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`28
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`29
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`33
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`35
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`41
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`51
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`55
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`55
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`56
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`59
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`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
`
`4.3.1
`
`4.3.2
`
`System Model
`
`BER Due to Clipping
`
`4.4 Performance in AWGN and Fading
`
`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
`
`6.1 Introduction
`
`6.2 Channel Estimation
`
`6.2.1
`
`6.2.2
`
`6.2.3
`
`6.2.4
`
`Coherent Detection
`
`Block-Type Pilot Arrangement
`
`Comb-Type Pilot Arrangement
`
`Interpolation Techniques
`
`69
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`69
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`71
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`73
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`77
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`78
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`86
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`127
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`viii
`
`6.2.5 Non-coherent Detection
`
`6.2.6
`
`6.2.7
`
`Performance
`
`Channel Estimation for MIMO-OFDM
`
`6.3 Equalization
`
`6.3.1
`
`6.3.2
`
`6.3.3
`
`6.3.4
`
`6.3.5
`
`6.3.6
`
`6.3.7
`
`Time Domain Equalization
`
`Equalization in DMT
`
`Delay Parameter
`
`AR Approximation of ARMA Model
`
`Frequency Domain Equalization
`
`Echo Cancellation
`
`Appendix - Joint Innovation Representation
`of ARMA Models
`
`7 Channel Coding
`
`7.1
`
`7.2
`
`7.3
`
`7.4
`
`7.5
`
`7.6
`
`Need for Coding
`
`Block Coding in OFDM
`
`Convolutional Encoding
`
`Concatenated Coding
`
`Trellis Coding in OFDM
`
`Turbo Coding in OFDM
`
`8 ADSL
`
`8.1
`
`8.2
`
`Wired Access to High Rate Digital Services
`
`Properties of the Wire-Pair Channel
`
`130
`
`130
`
`134
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`137
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`138
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`142
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`145
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`146
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`149
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`152
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`160
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`167
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`8.3 ADSL Systems
`
`9 Wireless LAN Applications
`
`9.1
`
`Introduction
`
`9.1.1 Background
`
`9.1.2
`
`Pros and Cons
`
`9.2 Topology
`
`9.2.1
`
`9.2.2
`
`9.2.3
`
`Independent BSS
`
`Infrastructure BSS
`
`Services
`
`9.3 Architecture
`
`9.4 Medium Access Control
`
`9.4.1
`
`9.4.2
`
`9.4.3
`
`DCF Access
`
`Markov Model of DCF
`
`PCF
`
`9.5 Management
`
`9.5.1
`
`9.5.2
`
`9.5.3
`
`9.5.4
`
`Synchronization
`
`Scanning
`Power Management
`
`Security
`
`9.6 IEEE 802.11 and 802.11b Physical Layer
`
`9.6.1
`
`9.6.2
`
`9.6.3
`
`Spread Spectrum
`
`FHSS Physical Layer
`
`DSSS Physical Layer
`
`ix
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`200
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`203
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`203
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`203
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`204
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`206
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`249
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`x
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`9.6.4
`
`9.6.5
`
`9.6.6
`
`IR Physical Layer
`
`HR/DSSS Physical Layer
`
`RF Interference
`
`9.7
`
`IEEE 802.11a Physical Layer
`
`9.7.1
`
`9.7.2
`
`9.7.3
`
`9.7.4
`
`OFDM Architecture
`
`Transmitter
`
`Receiver
`
`Degradation Factors
`
`9.8
`
`Performance of 802.11a Transceivers
`
`9.8.1
`
`9.8.2
`
`9.8.3
`
`9.8.4
`
`9.8.5
`
`9.8.6
`
`9.8.7
`
`9.8.8
`
`9.8.9
`
`Data Rate
`
`Phase Noise
`
`Channel Estimation
`
`Frequency Offset
`
`IQ Imbalance
`
`Quantization and Clipping Error
`
`Power Amplifier Nonlinearity
`
`Hard or Soft Decision Decoding
`
`Co-channel Interference
`
`9.8.10
`
`Narrowband 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
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`256
`
`269
`
`274
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`275
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`276
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`278
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`279
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`280
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`281
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`283
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`285
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`286
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`286
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`288
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`291
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`292
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`Exhibit 1024
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`

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`9.11 IEEE 802. 11e MAC Protocol
`
`9.11.1
`
`IEEE 802.11e MAC Services
`
`9.11.2
`
`IEEE 802.11e 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
`
`9.12.1
`
`Protocol Architecture
`
`9.12.2
`
`Data Link Control
`
`9.12.3
`
`Convergence Layer
`
`9.12.4
`
`HIPERLAN/2 vs 802.11a
`
`9.13 MMAC-HiSWAN
`
`9.14 Overview of IEEE 802.11 Standards
`
`9.14.1
`
`IEEE 802.11c - Bridge Operation Procedures
`
`9.14.2
`
`IEEE 802.11d - Global Harmonization
`
`9.14.3
`
`IEEE 802.11f - Inter Access Point Protocol
`
`9.14.4
`
`IEEE 802.11g - Higher Rate Extensions in the
`2.4GHz Band
`
`9.14.5
`
`IEEE 802.11h - Spectrum Managed 802.11a
`
`9.14.6
`
`IEEE 802.11i - MAC Enhancements for En-
`hanced Security
`
`xi
`
`293
`
`294
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`295
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`295
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`299
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`300
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`301
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`301
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`301
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`304
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`304
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`310
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`315
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`xii
`
`9.14.7 IEEE 802.1x - Port Based Network Access
`Control
`
`9.14.8 IEEE 802.1p - QoS on the MAC Level
`
`10 Digital Broadcasting
`
`10.1
`
`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
`
`11.1
`
`Introduction
`
`11.2
`
`11.3
`
`11.4
`
`OFDM-FDMA
`
`OFDM-TDMA
`
`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
`
`12.1 Impulse Radio
`
`316
`
`316
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`317
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`317
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`320
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`323
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`323
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`

`12.2
`
`Multiband Approach
`
`12.3
`
`Multiband OFDM
`
`13 IEEE 802.16 and WiMAX
`
`13.1
`
`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
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`359
`
`361
`
`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
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`393
`
`405
`
`407
`
`Ford Motor Co.
`Exhibit 1024
`Page 012
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`

`

`We dedicate this book
`to our families...
`
`Ford Motor Co.
`Exhibit 1024
`Page 013
`
`

`

`Preface
`
`Multi-carrier modulation‚ Orthogonal Frequency Division Multi-
`
`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-
`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-
`tempted to present a unified presentation of OFDM performance and
`
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`

`

`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-
`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-
`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-
`
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`

`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-
`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-
`niques that have made the modulation format practical. Several chap-
`ters describe and analyze the sub-systems of an OFDM implementa-
`tion‚ such as clipping‚ synchronization‚ channel estimation‚ equaliza-
`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-
`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-
`mitters. And‚ the new development of wireless LANs for multi-Mbps
`communications is presented in detail. Each of these successful appli-
`cations required the development of new fundamental technology.
`
`Finally‚ the book concludes with describing the OFDM based mul-
`tiple access techniques‚ ultra wideband technology and WiMAX.
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`Exhibit 1024
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`

`

`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-
`edge his extensive contributions in making this second edition possi-
`ble.
`
`The first edition of this text has been used for classes in University
`of California Berkeley‚ Stanford University‚ University of Cambridge‚
`CEI-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-
`LAB simulation tool‚ Sinem Coleri for proof-reading. We wish to ex-
`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-
`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-
`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-
`port materials that may be necessary to prepare a lecture or paper.
`
`Ford Motor Co.
`Exhibit 1024
`Page 017
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`

`

`Chapter 1
`
`Introduction to Digital
`Communications
`
`1.1 Background
`
`The 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
`
`where the information to be transmitted is given by the sequence of
`1/T is the symbol rate, and
`is the impulse response of the
`
`Ford Motor Co.
`Exhibit 1024
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`
`

`

`2
`
`Chapter 1. Introduction to Digital Communications
`
`Figure 1.1: A basic PAM system
`
`are chosen from an alphabet
`transmit filter, usually low-pass. The
`of size L, so the bit rate is
`It is desirable that the alphabet be
`both zero mean and equally spaced. The values of
`can be written
`as
`
`Assuming the
`
`are equiprobable, the transmitted power is
`
`which may include
`At the receiver, the signal is filtered by
`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
`for all
`an
`integer
`where
`is the channel impulse response. This is the
`Nyquist criterion, which is given in the frequency domain by:
`
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`Exhibit 1024
`Page 019
`
`

`

`1.1. Background
`
`3
`
`The minimum bandwidth required is 1/2T . This is met by a fre-
`quency response that is constant for
`whose
`corresponding time response is
`
`Some excess bandwidth, denoted by the roll-off factor, is desirable in
`order for the time response to decay more quickly. Note that
`is not
`a matched filter, because it must satisfy the inter-symbol interference
`constraint.
`
`are also spaced
`has gain such that the alphabet levels of
`If
`by 2A, then errors will occur when the noise at the sampler satisfies
`for interior levels, or
`or
`for the outer levels. If
`the noise is Gaussian with power spectral density
`at the receiver
`input, then the noise variance is:
`
`and the error probability per symbol is
`
`where
`
`is the normal 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-
`quency band is required. Of particular interest, both in its own right
`
`Ford Motor Co.
`Exhibit 1024
`Page 020
`
`

`

`4
`
`Chapter 1. Introduction to Digital Communications
`
`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-
`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
`
`This line signal may also be written in the form of:
`
`Ford Motor Co.
`Exhibit 1024
`Page 021
`
`

`

`1.2. Evolution of OFDM
`
`5
`
`Figure 1.3: A QAM constellation
`
`are treated as a complex
`and
`where the pair of real symbols
`symbol
`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-
`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-
`lation points. A constellation with a more circular boundary provides
`better noise performance. By grouping
`successive complex symbols
`as a unit, we can treat such units as symbols in
`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
`symbols, and a look-up table with
`outputs.
`
`1.2 Evolution of OFDM
`
`The use of Frequency 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-
`
`Ford Motor Co.
`Exhibit 1024
`Page 022
`
`

`

`6
`
`Chapter 1. Introduction to Digital Communications
`
`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-
`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-
`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-
`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-
`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-
`gle serial channel of that combined bandwidth because of the unused
`guard space between the parallel sub-carriers. On the other hand, the
`
`Ford Motor Co.
`Exhibit 1024
`Page 023
`
`

`

`1.2. Evolution of OFDM
`
`7
`
`single channel will be far more susceptible to inter-symbol interfer-
`ence. This is because of the short duration of its signal elements and
`the higher distortion produced by its wider frequency band, as com-
`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-
`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-
`tone transmission (not the complexity problem) was probably the Kine-
`plex system. The Kineplex system was developed by Collins Radio
`Co. [4] for data transmission over an H.F. radio channel subject to se-
`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
`shape and strongly overlap. However, similar to mod-
`ern 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-
`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-
`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-
`ficiency of 70% of the Nyquist rate is achieved. High performance
`over actual long H.F. channels was obtained, although at a high im-
`
`Ford Motor Co.
`Exhibit 1024
`Page 024
`
`

`

`8
`
`Chapter 1. Introduction to Digital Communications
`
`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-
`ployed in the receiver. Carrier spacing equal to the symbol rate pro-
`vides optimum spectral efficiency. Simple coding in the frequency do-
`main is another feature of this scheme. The above techniques do pro-
`vide the orthogonality needed to separate multi-tone signals spaced by
`the symbol rate. However the
`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-
`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-
`dlimited so as to overlap only the immediately adjacent sub-carriers,
`while remaining orthogonal to them. Criteria for meeting this objec-
`
`Ford Motor Co.
`Exhibit 1024
`Page 025
`
`

`

`1.2. Evolution of OFDM
`
`9
`
`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-
`ployed in a multi-tone system with orthogonality and minimum car-
`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-
`band (VSB) modulation. The low-pass filters
`are such that
`the combination of transmit and receive filters, is Nyquist, with the
`roll-off factor assumed to be less than 1.
`
`Ford Motor Co.
`Exhibit 1024
`Page 026
`
`

`

`10
`
`Chapter 1. Introduction to Digital Communications
`
`Figure 1.7: OFDM modulation concept: Real and Imaginary compo-
`nents of an OFDM symbol is the superposition of several harmonics
`modulated by data symbols
`
`Ford Motor Co.
`Exhibit 1024
`Page 027
`
`

`

`1.2. Evolution of OFDM
`
`11
`
`Figure 1.8: Spectrum overlap in OFDM
`
`The major contribution to the OFDM complexity problem was the
`application of the Fast Fourier Transform (FFT) 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-
`channel. An inverse FFT is performed on each block, and the resultant
`transmitted serially. At the receiver, the information is recovered by
`performing an FFT 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
`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 1.9.
`
`Ford Motor Co.
`Exhibit 1024
`Page 028
`
`

`

`12
`
`Chapter 1. Introduction to Digital Communications
`
`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-
`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 FFT 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 FFT 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-
`ficiency of the FFT algorithm. An N -point FFT requires only on the
`order of NlogN multiplications, rather than
`as in a straightfor-
`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 FFT, a DMT system typically requires fewer computations
`per unit time than an equivalent single channel system with equaliza-
`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
`
`Ford Motor Co.
`Exhibit 1024
`Page 029
`
`

`

`1.2. Evolution of OFDM
`
`13
`
`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-
`band modems have been introduced, but did not succeed commer-
`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-
`tem might face, as is shown in Figure 1.11. A particularly interesting
`configuration, discussed in Chapter 10, is the Single Frequency Net-
`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-
`
`Ford Motor Co.
`Exhibit 1024
`Page 030
`
`

`

`14
`
`Chapter 1. Introduction to Digital Communications
`
`Figure 1.11: 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-
`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-
`plication. It is expected that OFDM will be applied to many more new
`communications systems over the next several years.
`
`Ford Motor Co.
`Exhibit 1024
`Page 031
`
`

`

`Chapter 2
`
`System Architecture
`
`This chapter presents a general overview of system design for multi-
`
`carrier modulation. First, a review of wireless channels are dis-
`cussed. Second, fundamentals of digital communication is cited and
`finally, the major system blocks of OFDM is analyzed.
`
`2.1 Wireless Channel Fundamentals
`
`Wireless transmission uses air or space for its transmission medium.
`The radio propagation is not as smooth as in wire transmission since
`the received signal is not only coming directly from the transmitter,
`but the combination of reflected, diffracted, and scattered copies of
`the transmitted signal. It is interesting and rewarding to examine the
`effects of propagation to a radio signal since consequences determine
`data rate, range, and reliability of the wireless system.
`
`Reflection occurs when the signal hits a surface where partial en-
`ergy is reflected and the remaining is transmitted into the surface. Re-
`flection coefficient, the coefficient that determines the ratio of reflec-
`
`Ford Motor Co.
`Exhibit 1024
`Page 032
`
`

`

`16
`
`Chapter 2. System Architecture
`
`Figure 2.1: Wireless propagation
`
`tion and transmission, depends on the material properties. Diffrac-
`tion occurs when the signal is obstructed by a sharp object which de-
`rives secondary waves. Scattering occurs when the signal impinges
`upon rough surfaces, or small objects. Received signal is sometimes
`stronger than the reflected and diffracted signal since scattering spreads
`out the energy in all directions and consequently provides additional
`energy for the receiver which can receive more than one copies of the
`signal in multiple paths with different phases and powers. Figure 2.1
`illustrates the propagation mechanisms [2].
`
`Models play an important role in the designs of wireless com-
`munication systems. There are key modelling parameters that help
`to characterize a wireless channel: path loss, delay spread, coherence
`bandwidth, doppler spread, and coherence time.
`
`2.1.1 Path Loss
`
`The average received power diminishes with the distance. In free space
`when there is a direct path between transmitter and receiver and when
`
`Ford Motor Co.
`Exhibit 1024
`Page 033
`
`

`

`2.1. Wireless Channel Fundamentals
`
`17
`
`there are no secondary waves from the medium objects, the received
`power is inversely proportional to square of the carrier frequency and
`square of the distance. If
`and
`are the received and transmitted
`powers respectively, the following relation describes free space prop-
`agation [1],
`
`is the distance between transmit-
`is the carrier frequency,
`where
`ter and receiver, G is the power gain from the transmit and receive
`antennas,
` is the path loss component and path loss is defined
`as
`One can infer from the equation that the larger the carrier
`frequency the smaller the operating range.
`
`When there is clutter in the medium, it is not easy to determine
`the received signal since now the direct path component is added with
`the multipath components at the receiver. Adopted method is to use a
`model that is deri