“01-fm-i-iv-9780123744838” — 2011/3/8 — 17:53 — page 3 — #3

Wireless Communications

Over Rapidly Time-Varying

Channels

Edited by

Franz Hlawatsch

Gerald Matz

AMSTERDAM • BOSTON • HEIDELBERG • LONDONNEW YORK • OXFORD • PARIS • SAN DIEGO

SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO

Academic Press is an imprint of Elsevier

“01-copy-iv-9780123744838” — 2011/3/8 — 18:06 — page 4 — #2

Academic Press is an imprint of Elsevier

The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, UK

30 Corporate Drive, Suite 400, Burlington, MA 01803, USA

First edition 2011

Copyright c� 2011 Elsevier Ltd. All rights reserved.

No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any

means electronic, mechanical, photocopying, recording or otherwise without the prior written permission of the

publisher.

Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford,

UK: phone (+44) (0) 1865 843830; fax (+44) (0) 1865 853333; email: permissions@elsevier.com. Alternatively

you can submit your request online by visiting the Elsevier web site at http://elsevier.com/locate/permissions,

and selecting Obtaining permission to use Elsevier material.

NoticesNo responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of

products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or

ideas contained in the material herein. Because of rapid advances in the medical sciences, in particular, independent

verification of diagnoses and drug dosages should be made.

British Library Cataloguing in Publication DataA catalogue record for this book is available from the British Library.

Library of Congress Cataloging-in-Publication DataA catalog record for this book is available from the Library of Congress.

ISBN: 978-0-12-374483-8

For information on all Academic Press publications

visit our web site at www.books.elsevier.com

Printed and bound in USA

11 12 13 14 15 10 9 8 7 6 5 4 3 2 1

“03-pref-xiii-xiv-9780123744838” — 2011/3/8 — 17:43 — page xiii — #1

Preface

Wireless communications has become a field of enormous scientific and economic interest. Recentsuccess stories include 2G and 3G cellular voice and data services (e.g., GSM and UMTS), wirelesslocal area networks (WiFi/IEEE 802.11x), wireless broadband access (WiMAX/IEEE 802.16x), anddigital broadcast systems (DVB, DAB, DRM). On the physical layer side, traditional designs typicallyassume that the radio channel remains constant for the duration of a data block. However, researchersand system designers are increasingly shifting their attention to channels that may vary within a block.In addition to time dispersion caused by multipath propagation, these rapidly time-varying channelsfeature frequency dispersion resulting from the Doppler effect. They are, thus, often referred to asbeing “doubly dispersive.”

Historically, channels with time variation and frequency dispersion were first considered mostly inthe context of ionospheric and tropospheric communications and in radio astronomy. The theoreticalfoundations of rapidly time-varying channels were established by Bello, Gallager, Kailath, Kennedy,and others in the sixties of the twentieth century. More recently, rapidly time-varying channels havebecome important in novel application scenarios with potentially high economic relevance and societalimpact.. User mobility, a source of significant Doppler frequency shifts, is an essential factor in today’s

cellular and broadband access systems. An extreme example is given by radio access links forhigh-speed trains. Channels with rapid time variation are also encountered in car-to-car and car-to-infrastructure communications, which are becoming increasingly important.. In advanced wireless networks, nodes may cooperate to achieve spatial diversity gains in a dis-tributed manner. An example is the base station cooperation option (also known as network MIMOor cooperative multipoint transmission) in 3GPP Long Term Evolution. In such systems, the car-rier frequency offsets of different nodes accumulate and, together with mobility-induced Dopplerfrequency shifts, result in channels with rapid time variation.. In underwater acoustic communications, the relative Doppler shifts are potentially much largerthan in terrestrial radio systems because the speed of sound is much smaller than the speed of light.Furthermore, the smaller propagation speed of acoustic waves results in larger propagation delays.Underwater channels are, therefore, instances of particularly harsh doubly dispersive channels.

Rapid channel variations induced by Doppler shifts provide an extra dimension that offers addi-tional gains. At the same time, doubly dispersive channels pose tough design challenges and necessitatethe use of sophisticated methods to combat the detrimental effects of the channel and to realize theadditional gains. Thus, understanding the fundamental properties of doubly dispersive channels andthe resulting design paradigms will become essential know-how in the future wireless arena.

This book explains the system-theoretic and information-theoretic foundations of doubly disper-sive channels and describes the current state of the art in algorithm and system design. It is intended topresent a comprehensive and coherent discussion of the challenges and developments in the field,which will help researchers and engineers understand and develop future wireless communicationtechnologies. Contributed by leading experts, the individual chapters of this book address the mostimportant aspects of the theory and methodology of wireless communications over rapidly time-varying channels. Wireless transceiver design and modern techniques such as iterative turbo-style

xiii

“03-pref-xiii-xiv-9780123744838” — 2011/3/8 — 17:43 — page xiv — #2

xiv Preface

detection, multicarrier (OFDM) modulation, and multiantenna (MIMO) processing are given specialattention.

In the introductory chapter, Chapter 1, we discuss the properties and mathematical charac-terization of doubly dispersive channels. Further topics addressed include propagation effects,system-theoretic aspects, stochastic channel characterizations, parsimonious channel models, andmeasurement principles.

Chapter 2, by G. Durisi, V. Morgenshtern, H. Bolcskei, U. Schuster, and S. Shamai, discussesinformation-theoretic aspects of random time-varying channels, including MIMO channels. This chap-ter focuses on noncoherent channel capacity (i.e., channel capacity in the absence of channel stateinformation) in the large-bandwidth and high-SNR regimes.

Chapter 3, by E. Viterbo and Y. Hong, addresses the design of channel codes for fast-fading chan-nels, using methods from algebraic number theory and lattice theory. The sphere decoder is discussedas an efficient means to recover the transmitted code words.

Chapter 4, by G. Leus, Z. Tang, and P. Banelli, considers the estimation of rapidly time-varyingchannels in single-carrier and multicarrier communication systems. A block-based approach isadopted that builds on a basis expansion model for the channel and the transmission of dedicated pilot(training) symbols.

Chapter 5, by M. Dong, B. M. Sadler, and L. Tong, complements Chapter 4 by discussing train-ing designs for the estimation of time-varying channels. The optimization of the number, placement,and power of pilot symbols is studied for various system configurations (single carrier, multicarrier,multiantenna) and performance criteria.

Chapter 6, by P. Schniter, S.-J. Hwang, S. Das, and A. P. Kannu, presents equalization techniquesfor doubly dispersive channels. Both coherent and noncoherent detection are addressed, using linearand tree-search methods, iterative approaches, and joint detection-estimation schemes.

Chapter 7, by L. Rugini, P. Banelli, and G. Leus, is dedicated to orthogonal frequency division multi-plex (OFDM) transmissions over time-varying channels. This chapter discusses methods for equalizingintercarrier interference and for channel estimation and comments on the relevance of these methodsto existing standards.

Chapter 8, by C. Dumard, J. Jalden, and T. Zemen, considers a multiuser system employing multipleantennas and a multicarrier CDMA transmission format. An iterative (turbo) receiver is developed,which performs estimation of the time-varying channels, multiuser separation, and channel decoding,with complexity reductions due to Krylov subspace and sphere decoding techniques.

The final chapter, Chapter 9, by A. Papandreou-Suppappola, C. Ioana, and J. J. Zhang, discusseswideband channels that are more suitably characterized in terms of Doppler scaling than in termsof Doppler shifts. Theoretical considerations and advanced receiver designs are exemplified by anunderwater acoustic communication system.

We would like to thank all people who contributed to this book in one way or another. We are espe-cially grateful to the chapter authors for their expertise and hard work, and for accepting the constraintsof a predefined, common notation. We thank Tim Pitts of Elsevier for inviting us to edit this book. Timand his colleagues—Melanie Benson, Susan Li, Melissa Read, and Naomi Robertson—provided muchappreciated assistance during the various stages of this project. Finally, we acknowledge support by theAustrian Science Fund (FWF) under Grants S10603 (Statistical Inference) and S10606 (InformationNetworks) within the National Research Network SISE.

Franz Hlawatsch

Gerald Matz

“04-ate-xv-xvi-9780123744838” — 2011/3/8 — 17:40 — page xv — #1

About the Editors

Franz Hlawatsch received the Dipl.-Ing., Dr. techn., and Univ.-Dozent (habilitation) degrees in elec-trical engineering/signal processing from Vienna University of Technology, Vienna, Austria, in 1983,1988, and 1996, respectively. Since 1983, he has been with the Institute of Telecommunications, ViennaUniversity of Technology, as an associate professor. During 1991–1992, as a recipient of an ErwinSchrodinger Fellowship, he spent a sabbatical year with the Department of Electrical Engineering,University of Rhode Island, Kingston, RI, USA. In 1999, 2000, and 2001, he held one-month visitingprofessor positions with INP–ENSEEIHT/TeSA (Toulouse, France) and IRCCyN (Nantes, France). He(co)authored a book, a review paper that appeared in the IEEE Signal Processing Magazine, about 180refereed or invited scientific papers and book chapters, and three patents. He coedited three books. Hisresearch interests include signal processing for wireless communications, statistical signal processing,and compressive signal processing. Prof. Hlawatsch was a Technical Program Co-Chair of EUSIPCO2004 and has served on the technical committees of numerous international conferences. From 2003 to2007, he served as an associate editor for the IEEE Transactions on Signal Processing. He is currentlyserving as an associate editor for the IEEE Transactions on Information Theory. From 2004 to 2009,he was a member of the IEEE Signal Processing for Communications Technical Committee. He iscoauthor of a paper that won an IEEE Signal Processing Society Young Author Best Paper Award.

Gerald Matz received the Dipl.-Ing. and Dr. techn. degrees in electrical engineering in 1994 and2000, respectively, and the Habilitation degree for communication systems in 2004, all from ViennaUniversity of Technology,Vienna, Austria. Since 1995, he has been with the Institute of Telecommu-nications, Vienna University of Technology, where he currently holds a tenured position as associateprofessor. From March 2004 to February 2005, he was on leave as an Erwin Schrodinger Fellowwith the Laboratoire des Signaux et Systemes, Ecole Superieure d’Electricite, France. During summer2007, he was a guest researcher with the Communication Theory Lab at ETH Zurich, Switzerland. Hehas directed or actively participated in several research projects funded by the Austrian Science Fund(FWF), the Vienna Science and Technology Fund (WWTF), and the European Union. He has publishedmore than 140 papers in international journals, conference proceedings, and edited books. His researchinterests include wireless communications, statistical signal processing, and information theory. Prof.Matz serves as a member of the IEEE Signal Processing Society (SPS) Technical Committee on SignalProcessing for Communications and Networking and of the IEEE SPS Technical Committee on Sig-nal Processing Theory and Methods. He was an associate editor for the IEEE Transactions of SignalProcessing (2006–2010), for the IEEE Signal Processing Letters (2004–2008), and for the EURASIPjournal Signal Processing (2007–2010). He was a Technical Program Co-Chair of EUSIPCO 2004 andhas been on the Technical Program Committee of numerous international conferences. In 2006, hereceived the Kardinal Innitzer Most Promising Young Investigator Award.

xv

“05-con-xvii-xviii-9780123744838” — 2011/3/8 — 17:38 — page xvii — #1

Contributing Authors

Paolo Banelli, Universita di Perugia (Perugia, Italy)

Helmut Bolcskei, ETH Zurich (Zurich, Switzerland)

Sibasish Das, Qualcomm Inc. (San Diego, CA, USA)

Min Dong, University of Ontario Institute of Technology (Oshawa, Ontario, Canada)

Charlotte Dumard, FTW Forschungszentrum Telekommunikation Wien (Vienna, Austria)

Giuseppe Durisi, Chalmers University of Technology (Gothenburg, Switzerland)

Franz Hlawatsch, Vienna University of Technology (Vienna, Austria)

Yi Hong, Monash University (Clayton, Melbourne, Australia)

Sung-Jun Hwang, Qualcomm Inc. (Santa Clara, CA, USA)

Cornel Ioana, National Polytechnic Institute of Grenoble (Grenoble, France)

Joakim Jalden, Royal Institute of Technology (KTH) (Stockholm, Sweden)

Arun P. Kannu, Indian Institute of Technology (Madras, Chennai, India)

Geert Leus, Delft University of Technology (Delft, The Netherlands)

Gerald Matz, Vienna University of Technology (Vienna, Austria)

Veniamin I. Morgenshtern, ETH Zurich (Zurich, Switzerland)

Antonia Papandreou-Suppappola, Arizona State University (Tempe, AZ, USA)

Luca Rugini, Universita di Perugia (Perugia, Italy)

Brian M. Sadler, Army Research Laboratory (Adelphi, MD, USA)

Philip Schniter, Ohio State University (Columbus, OH, USA)

Ulrich G. Schuster, Robert Bosch GmbH (Stuttgart, Germany)

Shlomo Shamai (Shitz), Technion–Israel Institute of Technology (Haifa, Israel)

Zijian Tang, TNO Defence, Security and Safety (The Hague, The Netherlands)

Lang Tong, Cornell University (Ithaca, NY, USA)

Emanuele Viterbo, Monash University (Clayton, Melbourne, Australia)

Thomas Zemen, FTW Forschungszentrum Telekommunikation Wien (Vienna, Austria)

Jun Jason Zhang, Arizona State University (Tempe, AZ, USA)

xvii

“08-ch01-001-064-9780123744838” — 2011/3/9 — 14:53 — page 1 — #1

CHAPTER

1Fundamentals ofTime-Varying CommunicationChannels

Gerald Matz, Franz HlawatschVienna University of Technology, Vienna, Austria

1.1 INTRODUCTIONWireless communication systems, i.e., systems transmitting information via electromagnetic (radio)or acoustic (sound) waves, have become ubiquitous. In many of these systems, the transmitter or thereceiver is mobile. Even if both link ends are static, scatterers – i.e., objects that reflect, scatter, ordiffract the propagating waves – may move with significant velocities. These situations give rise totime variations of the wireless channel due to the Doppler effect. Nonideal local oscillators are anothersource of temporal channel variations, even in the case of wireline channels. Because of their practicalrelevance, linear time-varying (LTV) channels have attracted considerable interest in the fields of signalprocessing, communications, propagation, information theory, and mathematics. In their most generalform, LTV channels are also referred to as time-frequency (TF) dispersive or doubly dispersive, as wellas TF selective or doubly selective.

In this chapter, we discuss the fundamentals of wireless channels from a signal processing and com-munications perspective. In contrast to existing textbooks (e.g., Jakes, 1974; Molisch, 2005; Parsons,1992; Vaughan & Bach Andersen, 2003), our focus will be on LTV channels. Many of the theoreti-cal foundations of LTV channels were laid in the 1950s and 1960s. Zadeh (1950) proposed a “systemfunction” that characterizes an LTV system in a joint TF domain. Driven by increasing interest inionospheric channels, Kailath complemented Zadeh’s work by introducing a dual system function,discussing sampling models, and addressing measurement issues (Kailath, 1959, 1962). A relateddiscussion focusing on the concept of duality (an important notion in TF analysis) was provided byGersho (1963). In a seminal paper on random LTV channels. Bello (1963) introduced the assumptionof wide-sense stationary uncorrelated scattering (WSSUS), which has been used almost universallysince. The estimation of channel statistics was addressed by Gallager (1964) and a few years later byGaarder (1968). A fairly comprehensive coverage of the modeling of and communication over randomLTV channels was provided by Kennedy (1969). Information-theoretic aspects of LTV channels wereaddressed in Biglieri, Proakis and Shamai (1998) and in Gallager (1968) (see also Chapter 2).

This chapter provides a review of this early work and a discussion of several more recent results. InSection 1.2, we summarize the most important physical aspects of LTV channels. Some basic tools for adeterministic description of LTV channels are discussed in Section 1.3, while the statistical descriptionof random LTV channels is considered in Section 1.4. Section 1.5 is devoted to the important class ofunderspread channels and their properties. Parsimonious channel models are reviewed in Section 1.6.

Wireless Communications Over Rapidly Time-Varying Channels. DOI: 10.1016/B978-0-12-374483-8.00001-7Copyright c� 2011 Elsevier Ltd. All rights reserved.

1

“09-ch02-065-116-9780123744838” — 2011/3/10 — 4:42 — page 65 — #1

CHAPTER

2Information Theory ofUnderspread WSSUSChannels

Giuseppe Durisi1, Veniamin I. Morgenshtern2, Helmut Bolcskei2,Ulrich G. Schuster3, Shlomo Shamai (Shitz)4

1Chalmers University of Technology, Gothenburg, Sweden

2ETH Zurich, Switzerland

3Robert Bosch GmbH, Stuttgart, Germany

4Technion – Israel Institute of Technology, Haifa, Israel

2.1 THE ROLE OF A SYSTEM MODEL2.1.1 A Realistic ModelIn this chapter, we are interested in the ultimate limit on the rate of reliable communication throughRayleigh-fading channels that satisfy the wide-sense stationary (WSS) and uncorrelated scattering(US) assumptions and are underspread (Bello, 1963; Kennedy, 1969). Therefore, the natural settingis an information-theoretic one, and the performance metric is channel capacity (Cover & Thomas,1991; Gallager, 1968).

The family of Rayleigh-fading underspread WSSUS channels (reviewed in Chapter 1) constitutesa good model for real-world wireless channels: their stochastic properties, like amplitude and phasedistributions match channel measurement results (Schuster, 2009; Schuster & Bolcskei, 2007). TheRayleigh-fading and the WSSUS assumptions imply that the stochastic properties of the channel arefully described by a two-dimensional power spectral density (PSD) function, often referred to as scat-

tering function (Bello, 1963). The underspread assumption implies that the scattering function is highlyconcentrated in the delay-Doppler plane.

To analyze wireless channels with information-theoretic tools, a system model, not just a channel

model, needs to be specified. A system model is more comprehensive than a channel model because itdefines, among other parameters, the transmit-power constraints and the channel knowledge availableat the transmitter and the receiver. The choice of a realistic system model is crucial for the insightsand guidelines provided by information theory to be useful for the design of practical systems. Twoimportant aspects need to be accounted for by a model that aims at being realistic:

1. Neither the transmitter nor the receiver knows the realization of the channel: In most wirelesssystems, channel state information (CSI) is acquired by allocating part of the available resourcesto channel estimation. For example, pilot symbols can be embedded into the data stream, asexplained in Chapters 4 and 5, to aid the receiver in the channel-estimation process. From aninformation-theoretic perspective, pilot-based channel estimation is just a special case of coding.

Wireless Communications Over Rapidly Time-Varying Channels. DOI: 10.1016/B978-0-12-374483-8.00002-9Copyright c� 2011 Elsevier Ltd. All rights reserved.

65

“10-ch03-117-154-9780123744838” — 2011/3/9 — 12:22 — page 117 — #1

CHAPTER

3Algebraic Coding for Fast

Fading Channels

Emanuele Viterbo and Yi HongMonash University, Clayton, Australia

3.1 INTRODUCTIONElementary number theory has played a fundamental role in the development of error-correcting codes,in the early age of coding theory. Finite fields were the key tool in the design of powerful binary codesand gradually entered in the general mathematical background of communications engineers. Thanksto the technological developments and increased processing power available in digital receivers, thefocus of coding theory moved to the design of signal space codes in the framework of coded modula-tion systems. In the 1980s, the theory of Euclidean lattices became of great interest for the design ofdense signal constellations well suited for transmission over the additive white gaussian noise (AWGN)channel. More recently, the incredible boom of wireless communications forced coding theorists to dealwith fading channels. New code design criteria had to be considered in order to improve the poor per-formance of wireless transmission systems. The need of bandwidth efficient coded modulation becameeven more important due to the scarce availability of radio bands.

Algebraic number theory was shown to be a very useful mathematical tool that enables the designof good coding schemes for fading channels (Sethuraman, Sundar Rajan, & Shashidhar, 2003). Thesecodes are constructed as multidimensional lattice signal sets (or constellations) with particular geomet-ric properties. Coding gain is obtained by introducing the so-called modulation diversity in the signalset, which results in a particular type of bandwidth efficient diversity technique.

Two approaches were proposed to construct high-modulation-diversity constellations. The first wasbased on the design of intrinsic high-diversity algebraic lattices, obtained by applying the canonical

embedding of an algebraic number field into its ring of integers. Only later was it realized that highmodulation diversity could also be achieved by applying a particular rotation to a multidimensionalquadrature amplitude modulation (QAM) signal constellation in such a way that any two points achievethe maximum number of distinct components. Still, rotations giving diversity can be designed usingalgebraic number theory.

An attractive feature of modulation diversity technique is that a significant improvement in errorperformance is obtained, without requiring the use of conventional channel coding. In fact, we maythink of the rotation as a precoder or a rate one code. This can always be added later if required.

Finally, dealing with lattice constellations has the major advantage that it is possible to use anefficient decoding algorithm known as the sphere decoder.

Wireless Communications Over Rapidly Time-Varying Channels. DOI: 10.1016/B978-0-12-374483-8.00003-0

Copyright c� 2011 Elsevier Ltd. All rights reserved.117

“11-ch04-155-198-9780123744838” — 2011/3/10 — 0:41 — page 155 — #1

CHAPTER

4Estimation of Time-Varying

Channels – A Block

Approach

Geert Leus1, Zijian Tang2, Paolo Banelli31Delft University of Technology, Delft, The Netherlands

2TNO Defence, Security and Safety, The Hague, The Netherlands3University of Perugia, Perugia, Italy

4.1 INTRODUCTIONFor coherent detection in a wireless communication system, channel state information (CSI) is indis-pensable. Channel estimation has drawn tremendous attention in the literature (see Tong, Sadler, &Dong, 2004 and references therein), where the pilot-aided method is one of the most intensively stud-ied approaches. This method is especially attractive for time-varying channels because of their shortcoherence time.

In this chapter, we will address pilot-aided channel estimation for both orthogonal frequency divi-sion multiplexing (OFDM) and single-carrier systems, where pilots are inserted in the frequencydomain and time domain, respectively. We study these two systems under one framework because inthe context of channel estimation, both systems can be characterized by data models of the same form.More specifically, the received samples can be expressed as the joint effect of the information part (dueto the pilots), the interference part (due to the unknown data symbols), and the noise. Consequently, ourtask is to design a channel estimator that can combat both the interference and the noise. Such a datamodel is typical for OFDM over time-varying channels, where due to the Doppler effect, the orthogo-nality between the subcarriers is destroyed, and the channel matrix in the frequency domain becomeseffectively a diagonally dominant yet full matrix instead of a diagonal matrix. As a result, the receivedfrequency-domain samples depend on both the pilots and the unknown data symbols. For single-carriersystems, the channel matrix in the time domain is a strictly banded matrix if a finite impulse response(FIR) assumption for the channel is applied, and therefore, we can, in practice, find some receivedsamples that solely depend on the pilots. However, it is sometimes beneficial to also consider receivedsamples that depend on the unknown data symbols as well, to better suppress the interference and thenoise. In any case, the resulting data model for single-carrier systems looks very similar to the datamodel for OFDM systems, and similar channel estimation techniques can be applied. Note that theconsidered data model can also account for superimposed pilot schemes (Ghogho & Swami, 2006;He & Tugnait, 2007), where the pilots and the data symbols coexist on the same subcarriers or timeinstants.

Whether we are dealing with OFDM or single-carrier systems, estimating a time-varying channelimplies estimating a large number of unknowns, making the channel estimation problem much more

Wireless Communications Over Rapidly Time-Varying Channels. DOI: 10.1016/B978-0-12-374483-8.00004-2Copyright c� 2011 Elsevier Ltd. All rights reserved.

155

“12-ch05-199-236-9780123744838” — 2011/3/9 — 19:08 — page 199 — #1

CHAPTER

5Pilot Design and Optimization

for Transmission over

Time-Varying Channels

Min Dong1, Brian M. Sadler2, Lang Tong3

1University of Ontario Institute of Technology, Oshawa, Ontario, Canada

2Army Research Laboratory, Adelphi, MD, USA

3Cornell University, Ithaca, NY, USA

5.1 INTRODUCTIONTo facilitate data transmission over linear time-varying (LTV) channels, pilot symbols1 are typicallyinserted in the information-bearing data stream. These symbols are known at the receiver and areexploited for channel estimation, receiver adaptation, and optimal decoding. Such design structure, alsocalled pilot-assisted transmission (PAT) (Tong, Sadler, & Dong, 2004), is prevalent in modern com-munication systems, and a specific pilot design is included in almost any of the current standardizedwireless systems, e.g., Global System for Mobile Communication (GSM), Wideband Code-DivisionMultiple Access (WCDMA), CDMA-2000, IEEE802.11, IEEE802.16, DVB-T, and 3GPP Long TermEvolution (LTE). See Fig. 5.1 for examples.

Pilot symbols carry no information about the data; the resource (time, frequency, power, and so on)used on sending pilot symbols is a resource taken away from transmitting information data. Therefore,pilot design requires optimization. This includes the amount of pilot symbols, the locations of thesesymbols in the data stream, and the power allocated for them. In this chapter, we will look at thesedesign issues.

In Section 5.2, we present a general model that captures a number of pilot design schemes at thetransmitter. Specifically, we view the problem of pilot design as one of allocating power in differentdesign spaces. Receiver structures are discussed next, followed by possible design metrics.

Sections 5.3–5.5 consider the design issues in a traditional single antenna single carrier system.We first focus on the optimal pilot pattern from a channel estimation and symbol detection point ofview. For any fixed percentage of pilot symbols and their power allocation, the optimal placementof pilot symbols in the data stream is derived for channel tracking and data decoding in Section 5.3.The LTV channel is assumed flat fading and modeled by a Gauss-Markov process. Time-divisionmultiplexing (TDM) of pilot symbols and data are considered there, and a causal Kalman filter is usedfor channel tracking. The optimal pattern among all possible periodic placements is found to be singlepilot periodic placement. In Section 5.4, we look at an alternative multiplexing scheme where pilot

1Pilot symbols are also called training symbols.

Wireless Communications Over Rapidly Time-Varying Channels. DOI: 10.1016/B978-0-12-374483-8.00005-4

Copyright c� 2011 Elsevier Ltd. All rights reserved.199

“13-ch06-237-284-9780123744838” — 2011/3/9 — 19:48 — page 237 — #1

CHAPTER

6Equalization of Time-Varying

Channels

Philip Schniter1, Sung-Jun Hwang2, Sibasish Das3, Arun P. Kannu4

1The Ohio State University, Columbus, OH, USA2Qualcomm, Inc., Santa Clara, CA, USA

3Qualcomm, Inc., San Diego, CA, USA4Indian Institute of Technology, Madras, Chennai, India

6.1 INTRODUCTIONAs discussed in Chapter 1, the wireless communication channel can be modeled as a time-varying(TV) linear1 system whose output is corrupted by additive noise. To reliably recover the transmittedinformation from the channel output, the receiver must address the effects of both linear distortion andadditive noise. Although, in theory, the mitigation of linear distortion and additive noise should bedone jointly, in practice the task is often partitioned into two tasks, equalization and decoding, in orderto reduce implementation complexity.

Roughly speaking, equalization leverages knowledge of channel structure to mitigate the effects ofthe linear distortion, whereas decoding leverages knowledge of code structure to mitigate the channel’sadditive noise component. The equalizer might be well informed about the channel (e.g., knowing thecomplete channel impulse response) or relatively uninformed (e.g., knowing only the maximum chan-nel length). In some cases, knowledge of symbol structure (e.g., the symbol alphabet or, if applicable,the fact that the symbols have a constant modulus) is assumed to be in the domain of the equalizer,whereas in other cases, it is assumed to be in the domain of the decoder; because the equalizer anddecoder work together to infer the transmitted information from the channel output, the role of equali-zation versus decoding is somewhat a matter of definition. For this chapter, however, we assume thatexploitation of code structure is not in the domain of the equalizer.

Generally speaking, the output of the equalizer is a sequence of symbol (or bit) estimates whichhave been, to the best of the equalizer’s ability, freed of channel corruption. These estimates are thenpassed to the decoder for further refinement and final decision making. In so-called turbo equalizationschemes (Douillard et al., 1995; Koetter, Singer, & Tuchler, 2004), the decoder passes refined soft bitestimates back to the equalizer for further refinement, and the equalizer passes further refined soft bitestimates to the decoder. The process is then iterated until the equalizer and decoder “agree” on the softbit estimates. Note that the use of soft bit estimates implies that the equalizer treats the bits as (a priori)independent. Turbo equalization is illustrated in Fig. 6.1 and will be discussed in more detail later.

1Some channels are better modeled as nonlinear, but such channels are not the focus of this book.

Wireless Communications Over Rapidly Time-Varying Channels. DOI: 10.1016/B978-0-12-374483-8.00006-6Copyright c� 2011 Elsevier Ltd. All rights reserved.

237

“14-ch07-285-336-9780123744838” — 2011/3/9 — 22:03 — page 285 — #1

CHAPTER

7OFDM Communicationsover Time-Varying Channels

Luca Rugini1, Paolo Banelli1, Geert Leus2

1University of Perugia, Perugia, Italy2Delft University of Technology, Delft, The Netherlands

7.1 OFDM SYSTEMSOrthogonal frequency-division multiplexing (OFDM), also known as multicarrier modulation(Bingham, 1990; Cimini Jr, 1985; Keller & Hanzo, 2000; Le Floch, Alard, & Berrou, 1995; Sari,Karam, & Jeanclaude, 1995; Wang & Giannakis, 2000; Zou & Wu, 1995), relies on the concept ofparallel data transmission in the frequency domain and mainly owes its success to the easy equaliza-tion for linear time-invariant (LTI) frequency-selective channels. In OFDM systems, the data symbolstream is split into L parallel flows, which are transmitted on equispaced frequencies called subcar-riers, each one characterized by a transmission rate that is 1/L times lower than the original datarate. This is obtained by splitting the original data stream into multiple blocks, which are transmit-ted in consecutive time intervals, where each symbol of a block is associated to a specific subcarrier.This frequency-domain multiplexing can be efficiently performed by means of fast Fourier transformalgorithms.

Due to the use of orthogonal (equispaced) subcarriers, OFDM systems with LTI frequency-selectivechannels avoid the so-called intercarrier interference (ICI) among the data symbols of the same OFDMblock. Differently from conventional frequency-division multiplexing, a frequency overlapping amongthe spectra associated to different substreams is permitted, resulting in a significant reduction of thebandwidth requirements. Moreover, for LTI frequency-selective channels, the absence of ICI allowsan easy channel equalization, which can be performed on a per-subcarrier basis by means of scalardivisions. The intersymbol interference (ISI)1 among data symbols of different OFDM blocks, inducedby multipath propagation, is avoided by a suitable cyclic extension of each OFDM block, usuallyreferred to as cyclic prefix (CP) (Sari et al., 1995; Wang & Giannakis, 2000; Zou & Wu, 1995).

However, when the channel experiences a nonnegligible time variation, each subcarrier under-goes a Doppler spreading effect that destroys the subcarrier orthogonality, producing significant ICI(Robertson & Kaiser, 1999; Russell & Stuber, 1995; Stantchev & Fettweis, 2000). Dually to the ISI insingle-carrier systems, the ICI power reduces the signal-to-interference-plus-noise ratio (SINR) and,when left uncompensated, impairs the performance of OFDM systems. A simple method that reducesthe ICI is the shortening of the OFDM block duration. This way the channel becomes (almost) constant

1The ISI is also known as interblock interference, while the OFDM blocks are also known as OFDM symbols.

Wireless Communications Over Rapidly Time-Varying Channels. DOI: 10.1016/B978-0-12-374483-8.00007-8Copyright c� 2011 Elsevier Ltd. All rights reserved.

285

“15-ch08-337-374-9780123744838” — 2011/3/9 — 14:14 — page 337 — #1

CHAPTER

8Multiuser MIMO Receiver

Processing for Time-Varying

Channels

Charlotte Dumard1, Joakim Jalden2, Thomas Zemen1

1FTW Forschungszentrum Telekommunikation Wien, Vienna, Austria2Royal Institute of Technology (KTH), Stockholm, Sweden

8.1 INTRODUCTIONWireless broadband communications for mobile users at vehicular speed is the cornerstone of futurefourth-generation systems. This chapter deals with joint iterative channel estimation and multiuserdetection for the uplink of a multicarrier (MC) code division multiple access (CDMA) system. MC-CDMA is based on orthogonal frequency division multiplexing (OFDM) and employs spreadingsequences in the frequency domain (Kaiser, 1998). Both the mobile stations and the base stationemploy multiple antennas; hence, we deal with a multiuser multiple-input multiple-output (MIMO)receiver.

So far, most research on multiuser detection has dealt with block-fading frequency-selective chan-nels, where the channel state is assumed to stay constant for the duration of a single data block ofK data symbols. Even so, the optimal maximum a posteriori (MAP) detector for such a system isprohibitively complex although it can be approximated using iterative linear minimum mean-squareerror (LMMSE) multiuser detection and parallel interference cancelation (Zemen, Mecklenbrauker,Wehinger, & Muller, 2006).

This work deals with mobile users where the MIMO channels are time and frequency selective.Due to the rapid time variation of the MIMO channel, the computational complexity of conventionalmultiuser receivers, based on channel estimation, parallel interference cancelation, multiuser detection,and iterative decoding, increases drastically since the multiuser detection filters need to be recalculatedfor each data symbol individually.

In this chapter, we address this complexity issue by trading accuracy for efficiency. As a startingpoint, we adopt a joint iterative structure based on LMMSE multiuser detection and channel estimation.The decoding stage, implemented by the BCJR algorithm (Bahl, Cocke, Jelinek, & Raviv, 1974), sup-plies extrinsic probabilities (EXT) and a posteriori probabilities (APP) on the code symbols. This APPand EXT information is fed back for enhanced channel estimation and multiuser detection, respectively(Mecklenbrauker, Wehinger, Zemen, Artes, & Hlawatsch, 2006; Zemen et al., 2006).

The remainder of this chapter is organized as follows: in Section 8.2, the signal model is established,and in Section 8.3, key ideas for complexity reduction are introduced. For complexity reduction, we. approximate the MAP detector using an iterative receiver structure;. establish a low-dimensional reduced-rank model of the time-varying MIMO channel;

Wireless Communications Over Rapidly Time-Varying Channels. DOI: 10.1016/B978-0-12-374483-8.00008-X

Copyright c� 2011 Elsevier Ltd. All rights reserved.337

“16-ch09-375-416-9780123744838” — 2011/3/10 — 3:07 — page 375 — #1

CHAPTER

9Time-Scale and DispersiveProcessing for WidebandTime-Varying Channels

Antonia Papandreou-Suppappola1, Cornel Ioana2, Jun Jason Zhang1

1Arizona State University, Tempe, AZ, USA2Grenoble Institute of Technology, Grenoble, France

9.1 INTRODUCTION9.1.1 Need for Wideband Channel CharacterizationsLinear time-varying (LTV) channel characterizations have found many successes in mobile wirelesscommunications as they can be effectively used to detect, estimate, and diversify the communica-tion process. As discussed in earlier chapters, one such useful characterization of the channel outputis in terms of time shifts and Doppler (frequency) shifts on the transmitted signal; these shifts canbe due to multipath propagation and time dispersion and due to motion or carrier frequency offsets,respectively (Bello, 1963; Giannakis & Tepedelenlioglu, 1998; Molisch, 2005; Proakis, 2001; Sayeed& Aazhang, 1999). Although such a representation can be used to describe any LTV channel, it isnot well matched to all possible mobile communication channels. A very rapidly varying widebandcommunication channel can cause Doppler (scale) changes on the transmitted signal; the scale changescannot be approximated by frequency shifts (Margetts, Schniter, & Swami, 2007; Ye & Papandreou-Suppappola, 2006). For example, a shallow underwater communication channel can cause differentfrequencies to be shifted in time by different amounts (Iem, Papandreou-Suppappola, & Boudreaux-Bartels, 2002; Stojanovic, 2003; Ye & Papandreou-Suppappola, 2007). For these types of channels, amatched characterization is expected to yield more effective processing than the aforementioned chan-nel characterization that is matched to time-frequency shifts. A higher processing performance is alsoexpected when using a matched channel model instead of adopting techniques that simply compensatefor wideband or nonlinear channel transformations.

The narrowband LTV channel model represents the channel output in terms of time-frequency-shifted versions of the transmitted signal. However, when the relative motion between the transmitter,the receiver, and the scatterers in the propagation channel becomes fast, and the fractional bandwidth(ratio of bandwidth over carrier frequency) of the signal is large, then the signal is scaled (expandedor compressed) during transmission (Davies, Pointer, & Dunn, 2000; Shenoy & Parks, 1995; Weiss,1996). Under these conditions, the resulting time variation due to Doppler scaling effects, coupled withdispersive scattering due to multipath propagation, can severely limit the receiver performance. Thus,a wideband channel model needs to be considered at the receiver to improve performance.

Wireless Communications Over Rapidly Time-Varying Channels. DOI: 10.1016/B978-0-12-374483-8.00009-1Copyright c� 2011 Elsevier Ltd. All rights reserved.

375

“17-ind-417-428-9780123744838” — 2011/3/9 — 12:41 — page 417 — #1

Index

AAbelian group, 123Absorption loss, 6Acoustic channel, 2Adaptive channel estimation, 192, 322Additive white Gaussian noise channel, 66, 91, 117,

239, 251, 287, 400Adjacent-channel interference, 286Adjoint, 33Affine Fourier transform, 317Alamouti code, 318Algebraic extension, 128Algebraic integer, 129Algebraic lattice, 127, 132Algebraic number theory, 117, 127Algebraic rotation, 137Aliasing error, 52, 54Ambiguity function, 34, 55, 77, 316Ambiguity in noncoherent equalization, 262Amount of training, 223Analog-to-digital conversion, 3Angle of arrival, 4, 6, 13Angle of departure, 6, 13Angular dispersion, 14Angular domain, 13Antenna, 2Antenna array, 6, 13Antenna switching, 54AOA, 13AOD, 13Aperture, 14A posteriori log-likelihood ratio, 247, 252,

255, 265A posteriori probability, 337, 352Approximate eigenfunction, 35, 36Approximate Karhunen-Loeve expansion, 39A priori log-likelihood ratio, 247AR channel model, 45, 57, 58ARMA channel model, 44, 46, 58AR parameters, 57Array steering vector, 6, 13, 14, 22Atomic channel, 22, 38Attenuation factor, 3, 4, 6Autonomous underwater vehicle, 380Autoregressive channel model, 45, 57, 58, 193Autoregressive moving average channel model, 44,

46, 58Average local scattering function, 25, 27AWGN channel, 66, 91, 117, 239, 251, 287, 400

BBack-to-back calibration, 52Bahl, Cocke, Jelinek, Raviv, 248, 342, 350, 352Balian-Low theorem, 76, 239Banded channel matrix, 155, 248, 299Bank of matched filters, 390Baseband domain, 4Basis expansion model, 41, 47, 71, 156, 158, 213, 261, 302,

319, 343Bayesian EM algorithm, 268, 272Bayes rule, 246BCJR decoder, 248, 342, 350, 352Beamforming, 22, 94BEM coefficient, 192BEM for multiple OFDM symbols, 183BEM order, 159BEM statistics, 47–48BER, 204, 286, 293, 391Best-first tree search algorithm, 252Best linear unbiased estimator, 166, 168, 322Bhattacharyya bound, 204Binary phase-shift keying, 380, 388Biorthogonality condition, 53Biorthogonal pulses, 316Bit error rate, 204, 286, 293, 391Bit labeling, 122Block equalization, 299, 302Block fading, 20, 213, 224Block transmission, 240Block-type pilot placement, 182BLUE, 166, 168, 322Bounded distance decoding, 148BPSK modulation, 380, 388Breadth-first tree search algorithm, 252, 310Brick-shaped scattering function, 46, 88, 90Broadcasting system, 327

CCalibration, 52Canonical channel decomposition, 21Canonical embedding, 132Capacity, 29, 55, 66, 82, 84, 101, 203Carrier frequency, 2Carrier frequency offset, 5, 225, 292Car-to-car channel, 26Car-to-car communications, 26Causal observation model, 251CDMA system, 200, 227, 299Channel capacity, 29, 55, 66, 82, 84, 101, 203

417

“17-ind-417-428-9780123744838” — 2011/3/9 — 12:41 — page 418 — #2

418 Index

Channel correlation function, 24, 32, 40Channel EM(B) algorithm, 268, 272Channel equalization, 237, 238, 245, 247, 259, 261, 265,

270, 285, 299, 306, 310Channel estimation, 238, 263, 269, 318, 323, 337, 352Channel identifiability, 170, 172, 184, 189Channel impulse response, 9, 11, 13, 29, 288, 381Channel measurement, 48Channel model, 40, 44Channel sounding, 48, 49, 51, 56Channel spread, 30, 32, 36, 54, 87Channel state information, 65, 118, 155, 306Channel tracking, 216Chernoff bound, 120Chip pulse, 51Chirp pulse, 51, 317Chirp sounder, 48, 51Cholesky factorization, 145Circulant matrix, 288Circular convolution, 288Closest lattice point search, 250Clustered pilot pattern, 323Code-division multiple access, 200, 227, 299Codeword, 118Coherence bandwidth, 19, 28Coherence frequency, 30Coherence region, 19, 28, 32Coherence time, 19, 28, 30, 160, 180, 239Coherent capacity, 84Coherent equalization, 238, 245, 247, 259Coherent linear MMSE equalization, 249Coherent MMSE-DFE, 250Column permutation, 252Comb-type pilot placement, 181, 323Commutation error, 52Complex exponential BEM, 42, 159, 214, 319, 321, 343Compressed sensing, 328Compression, 4, 9Constant-modulus signal, 88Constellation, 118Constellation shaping, 122Correlation spread, 32Correlation-underspread channel, 32, 39, 40, 59Correlative channel sounding, 49, 51, 56Correlative coding, 314Cosets, 125Coupling coefficient, 22Covering radius, 148CP-OFDM, 54, 243CP-SCM, 242, 259Cramer-Rao bound, 203, 213Crest factor, 49

Critical bandwidth, 67, 86, 91Critically sampled complex exponential BEM, 214Cutoff rate, 200, 220, 221Cyclically banded matrix, 300Cyclic prefix, 53, 157, 242, 285, 339Cyclic-prefixed orthogonal frequency division multiplexing,

54, 243Cyclic-prefixed single-carrier modulation, 242, 259Cyclic-prefix reconstruction, 260Cyclostationary process, 17Cyclotomic construction, 140, 151Cyclotomic field, 140

DDAB, 290, 296Data-aided channel estimation, 323Data precoding, 156, 287, 313Decision-feedback equalization, 247, 249, 251, 307Decoding, 237Decoding failure, 148Degrees of freedom, 80Delay, 2, 7Delay diversity, 4, 17, 381Delay-domain aliasing, 328Delay-Doppler channel description, 7Delay-Doppler correlation, 24, 25, 28, 32Delay-Doppler dispersion, 25, 32Delay-Doppler diversity, 381Delay-Doppler domain, 7Delay-Doppler spreading function, 7, 13, 15, 24, 42, 69, 381Delay drift, 12, 23Delayed decision-feedback estimation, 250Delay power profile, 17, 19, 25, 31, 46Delay-scale channel description, 9Delay-scale diversity, 387Delay-scale domain, 9Delay-scale spreading function, 15, 384Delay spread, 18, 28, 30, 239Demodulation, 243Depth-first tree search algorithm, 252Deterministic channel description, 7DFE, 247, 249, 251, 307DFT, 259, 339DFT matrix, 22, 259, 287Diagonalization, 73Differential entropy, 98Diffraction, 2Digital Audio Broadcasting, 290, 296Digital Multimedia Broadcasting, 290Digital-to-analog conversion, 3Digital Video Broadcasting, 290, 296

“17-ind-417-428-9780123744838” — 2011/3/9 — 12:41 — page 419 — #3

Index 419

Dilation, 4, 9Directional resolution, 13Direct sequence spread spectrum, 395Discrete Fourier transform, 259, 339Discrete Fourier transform matrix, 22, 259, 287Discrete Karhunen-Loeve BEM, 159Discrete prolate spheroidal BEM, 44, 159, 320, 343Discretized channel, 71, 74Discriminant, 130, 131Dispersion, 2, 4, 7, 14, 30, 376, 378Dispersion spread, 30, 36, 54, 87Dispersion-underspread channel, 30, 34, 52Dispersive frequency shift, 393Dispersive spreading function, 393Distance, 6Diversity, 4, 5, 14, 17, 117, 119, 133, 381, 387Diversity order, 120, 388DMB, 290Doppler bandwidth, 340Doppler diversity, 5Doppler drift, 23Doppler effect, 4, 9, 383Doppler leakage, 43, 44Doppler power profile, 17, 19, 25, 31, 46, 292Doppler scaling, 376, 383Doppler shift, 4, 7, 383Doppler spread, 18, 28, 30, 158, 164, 214, 243, 285Double-orthogonality property, 38Doubly dispersive channel, 1Doubly selective channel, 1Duality, 77DVB, 290, 296Dyadic wavelet basis, 389

EEffective channel matrix, 240Eigen-beamforming, 94Eigenfunction, 29, 33, 72Eigenvalue, 21, 33, 72Eigenvalue decomposition, 33, 72, 288Eigenvector, 21Eisenstein integer ring, 132Electromagnetic wave, 2Ellipsoid, 145EM algorithm, 268, 272, 275Energy allocation, 221Entropy, 98Equalization, 237, 238, 245, 247, 259, 261, 265, 270,

285, 299, 306, 310Equalization based on tree search, 250, 267, 271, 310Equalization criterion, 245, 262Equivalent frequency-domain OFDM model, 295

Equivalent lattice, 126Erasure, 148Ergodic capacity, 29Error exponent, 204Error propagation, 250, 308Estimation of the local scattering function, 58Estimation of the scattering function, 17, 55, 57EXIT chart, 311Expectation-maximization algorithm, 268, 272, 275Expected ambiguity function, 16, 55, 58Exponential delay power profile, 19, 31, 46Extended Kalman filter, 270Extrinsic probability, 337, 350, 362

FFading, 6, 10, 14, 20, 117, 118, 150, 205, 213Fano algorithm, 252Fast fading, 118, 205, 213Fast Fourier transform, 285Fast joint equalization, 258Fast serial equalization, 256Field, 127Field extension, 128Filtered multitone modulation, 316Fincke-Pohst algorithm, 144Finite impulse response, 155Fisher information matrix, 204Flat fading, 20, 205Flop, 345Forward-backward algorithm, 248Fourier basis expansion model, 42, 343, 354Fourier transform, 3, 385Fractional Fourier transform, 317Frame, 39, 76Frame bound, 76Frame theory, 76Free-space propagation, 2Frequency correlation function, 17Frequency-dependent modulation function, 51Frequency dispersion, 4Frequency diversity, 4Frequency-domain channel matrix, 163, 288Frequency-domain equalization, 259Frequency-domain Kronecker delta structure, 172Frequency modulation, 394Frequency offset compensation, 18Frequency response, 11, 34, 36Frequency-selective channel, 3, 285Frequency shift, 4Fundamental parallelotope, 124Fundamental region, 124

“17-ind-417-428-9780123744838” — 2011/3/9 — 12:41 — page 420 — #4

420 Index

GGabor expansion, 39Gaussian ICI approximation, 294Gauss-Markov model, 45, 193, 199, 205, 266, 270, 324Generalized EM algorithm, 268Generalized hypergeometric function, 292Generalized likelihood ratio test, 264Generalized time shift, 393Generator matrix, 124Gibbs phenomenon, 43Global System for Mobile Communications, 199Golden number, 139Gram-Charlier series, 294Gram matrix, 124, 145Gray labeling, 122Grid matching rule, 79Grid parameter, 73Group, 122Group delay, 398Groupwise interference cancelation, 309Guard interval, 239, 242

HHard bit estimate, 247, 265Hard symbol estimate, 245, 263Hermite functions, 316Hexagonal lattice, 316High-SNR regime, 81, 106Hydrophone, 378

IIBI cancelation, 260ICI cancelation, 308ICI mitigation, 299ICI power, 292ICI shortening, 303Ideal, 134Ideal lattice, 135IEEE 802.11a standard, 289IEEE 802.11p standard, 289IEEE 802.16e standard, 289Implicit channel estimation, 263Impulse response, 9, 11, 13, 29, 288, 381Impulse-train sounding, 48Independent and identically distributed, 22Info EM(B) algorithm, 268, 272, 276Information-theoretic metric, 203Integer lattice, 124Integral basis, 130Interantenna interference, 190, 298, 317, 325Interblock interference, 157, 240, 242, 285Intercarrier interference, 54, 75, 97, 158, 226, 239, 285, 291

Interference cancelation, 260, 309, 357, 364Interleaver, 118Intersymbol interference, 54, 75, 97, 213, 285, 376Isovelocity model, 377, 396Iterative channel estimation, 269, 337Iterative equalization, 253, 272, 302, 310

JJacobi iteration, 302Jakes Doppler power profile, 19, 31, 46, 292Joint channel and symbol estimation, 238Joint channel estimation and symbol detection, 218Jointly proper Gaussian random process, 69

KKalman filter, 193, 207, 215, 228, 266, 270, 322, 324Kalman gain, 228Karhunen-Loeve expansion, 38Kernel, 11, 33KRAKEN software, 377, 400, 408Kronecker channel model, 22, 92Krylov subspace, 303, 345, 346, 355, 365

LLanczos algorithm, 345Large-bandwidth regime, 81, 82, 97Large-scale fading, 6Lattice, 117Lattice basis, 123Lattice decoding, 250Lattice determinant, 124Lattice generator matrix, 118Lattice OFDM, 316Lattice reduction, 150, 252Lattice theory, 122LDU decomposition, 250Leakage effect, 343Least-mean-square adaptive equalization, 408Least-squares channel estimation, 166, 168, 264Least-squares equalization, 301Legendre polynomials, 44Levinson algorithm, 57Likelihood function, 246Linear equalization, 246, 248, 299Linear minimum mean-square error combining, 254Linear minimum mean-square error estimation, 166, 167, 207,

343, 353Linear minimum mean-square error equalization, 249, 310,

357, 364Linear operator, 7, 12

“17-ind-417-428-9780123744838” — 2011/3/9 — 12:41 — page 421 — #5

Index 421

Linear precoding, 156, 287, 313Linear time-invariant channel, 9, 11, 29, 33, 36, 42, 73, 285Linear time-varying channel, 1, 69, 199, 287Linear zero-forcing equalization, 247, 249, 301Line-of-sight propagation, 5, 6LMMSE, see Linear minimum mean-square errorLocal observation model, 256Local scattering function, 24, 26, 40, 58Log-likelihood ratio, 247, 252, 255, 265, 310, 342, 362Log-normal distribution, 6Long term evolution, 199, 226Low-rank channel model, 41LSQR algorithm, 303LTE, 199, 226

MMA channel model, 45M-algorithm, 252MAP, see Maximum a posterioriMatched filter, 357, 401Matrix inversion lemma, 249, 254Maximum a posteriori bit detection, 245, 263Maximum a posteriori equalization, 266Maximum a posteriori sequence detection, 245, 263, 266,

341Maximum a posteriori symbol detection, 245, 263Maximum average SINR criterion, 303Maximum delay, 30, 88Maximum Doppler shift, 30, 88Maximum likelihood detection, 119, 206, 215, 246, 263,

307, 359Maximum ratio combining, 389Max-log approximation, 253, 370Maxwell’s equations, 2MC-CDMA, 327, 337Mean delay, 18, 28Mean Doppler shift, 18, 28Mean-squared error, 167, 203, 303Measurement of wireless channels, 48Mellin transform, 385Memoryless fading channel, 85, 88Message-passing algorithm, 270MIMO channel, 13, 20, 54, 92, 224, 297, 337MIMO-OFDM system, 297, 317, 325, 329MIMO system, 12, 20, 54, 92, 189, 200, 337MIMO-WSSUS channel, 20Minimal polynomial, 128Minimum band approximation error criterion, 304Minimum mean-square error channel estimation, 206, 214,

263Minimum mean-square error equalization, 246, 247, 251,

264, 301, 302

Minimum mean-square error estimation, 85Minimum product distance, 143Misinterpretation error, 52Mismatched decoder, 202Missing data, 268Mixed-type pilot placement, 182ML, see Maximum likelihoodMMSE, see Minimum mean-square errorMode extraction, 404, 409Modeling error, 160Mode separation, 398, 409Modulation diversity, 117, 120Moving average channel model, 45Multiantenna system, 12, 20, 54, 92, 189, 200, 224, 337Multicarrier code division multiple access, 327, 337Multicarrier modulation, 53, 238, 242, 256, 272, 285Multimedia system, 12Multipath component, 2, 27, 327Multipath diversity, 381Multipath-Doppler diversity, 381Multipath propagation, 2, 4, 376Multipath-scale diversity, 387Multiple-access interference, 328Multiple-input multiple-output channel, 13, 20, 54, 92, 224,

297, 337Multiple-input multiple-output system, 12, 20, 54, 92, 189,

200, 337Multiplexing gain, 4Multistage Wiener filter, 345Multitone modulation, 316Multiuser detection, 255, 337, 341, 355, 364Multiuser multiple-input multiple-output system, 337Multiuser system, 327, 337, 379Multiwindow periodogram, 58

NNarrowband Doppler approximation, 5, 383Neyman-Pearson detector, 403Nonbiorthogonal pulses, 317Noncoherent capacity, 66, 82, 84, 101Noncoherent equalization, 238, 261, 265, 270Nonlinear equalization, 306Nonredundant precoding, 314Nonstationary channel, 23Non-WSSUS channel, 23, 32, 46, 58Non-zero padding, 157Normal channel, 33Normalized MMSE, 216Nuisance parameter, 238Number field, 127Nyquist criterion, 3, 82, 101Nyquist pulse, 4

“17-ind-417-428-9780123744838” — 2011/3/9 — 12:41 — page 422 — #6

422 Index

OOFDM, 17, 53, 155, 225, 238, 243, 272, 285OFDMA, 327OFDM broadcasting system, 327OFDM symbol, 239, 285Offset QAM, 317One-tap channel equalizer, 158, 289, 293Optimal pilot placement, 209Orthogonal frequency-division multiple access, 327Orthogonal frequency division multiplexing, 17, 53, 155,

225, 238, 243, 272, 285Oscillator drift, 5, 54Oscillator phase noise, 54Outage probability, 203Overspread channel, 30

PPairwise error probability, 120Parallel interference cancelation, 309, 357, 364Parametric estimation of the scattering function, 57Parsimonious channel model, 40, 44Partial response coding, 314Path delay, 3Path loss, 6, 18, 25Path loss exponent, 6Peak power, 66Peak-to-average power ratio, 49, 83Pekeris model, 396Periodic pilot placement, 204Periodogram, 57Per-survivor processing, 267, 270Phase noise, 5, 54Phase-shift keying, 83, 207Pilot-aided channel estimation, 155Pilot-assisted transmission, 199Pilot cluster, 161Pilot placement, 181, 204, 209, 323Pilot symbol, 53, 87, 160, 199, 286, 339PN-sequence sounder, 48, 51Point scatterer, 7Polynomial BEM, 43, 159, 320Polynomial cancelation coding, 314Posterior log-likelihood ratio, 247, 252, 255, 265Posterior probability, 337, 352Power allocation, 201Power constraint, 83, 202Power control, 6Power series channel model, 293Power spectral density, 17, 65Precoding, 156, 287, 313, 318Primitive element, 128Principal ideal, 134

Probabilistic data association, 311Product distance, 119Prolate spheroidal sequences, 44, 320, 343Propagation environment, 2Propagation path, 2, 4, 7Pseudo-noise sequence sounder, 48, 51Pulse amplitude modulation, 3Pulse compression, 48, 49Pulse-compression error, 52Pulse-shaped multicarrier modulation, 68, 243, 315Pulse-shaped OFDM, 68, 243, 315Pulse-shaping filter, 50

QQR decomposition, 251, 350, 359Quadratic programming, 310Quadrature-amplitude modulation, 83Quadrature phase-shift keying, 338Quasibanded channel matrix, 241, 300Quasi-ML equalization, 309Quotient group, 125

RRadar uncertainty principle, 56Radio channel, 2Raised-cosine pulse, 77Rake receiver, 381, 389, 395Random coding bound, 204Random matrix, 345Rayleigh fading channel, 6, 14, 65, 101, 106, 118, 151, 205Ray tracing, 406Receive antenna, 2, 12Receive correlation, 96Receive correlation matrix, 92Receive pulse, 4, 315Receiver windowing, 303Receive signal, 2Receive window, 23Recursive least-squares channel estimation, 322Reduced-rank channel model, 343, 358Reduced-state sequence estimation, 250Redundant linear precoding, 313Reflection, 2Regular periodic pilot placement, 209Reliability information, 247Resource allocation, 220Rich scattering, 14Rician fading, 6Rihaczek distribution, 36Rihaczek spectrum, 16, 24Ring, 127Ring homomorphism, 130

“17-ind-417-428-9780123744838” — 2011/3/9 — 12:41 — page 423 — #7

Index 423

Ring of integers, 129Ritz-Galerkin method, 347Root-mean-square bandwidth, 35, 79Root-mean-square duration, 35, 79Rotated constellation, 150

SSampling, 37Sampling jitter, 3Scale change, 375Scattering, 2, 7, 14, 23Scattering function, 15, 24, 30, 37, 45, 46, 48, 55, 69, 86,

87, 238, 292, 383, 384, 388Scattering function matrix, 21Schnorr-Euchner sphere decoding, 252, 351Self-cancelation, 314Semiblind channel estimation, 213Semidefinite relaxation, 310Sequential decoding, 250Serial equalization, 256, 301Shadowing, 6, 23Shallow water channel, 403Shallow water environment model, 396Shaping gain, 122Short-time Fourier transform, 8, 51, 402Signal-to-interference-and-noise ratio, 215, 250, 285, 293Signal-to-interference ratio, 76Signal-to-noise ratio, 6, 120, 247, 391Signature, 130, 131Sinc function, 288Single-carrier modulation, 155, 242, 259, 270Single-frequency network, 327Singular value decomposition, 33, 42Slepian BEM, 44, 159, 320, 343, 354Slow fading, 205Small-scale fading, 6, 10Soft bit estimate, 237, 247, 265Soft equalization, 253Soft-input soft-output equalization, 238Soft-output Viterbi algorithm, 248Soft sphere decoding, 361, 363, 365Soft symbol estimate, 352Sounding of wireless channels, 48, 49, 51, 56Sounding pulse, 50SOVA, 248Space-frequency coding, 318Space-time coding, 318Space-time-frequency coding, 318Space-time-frequency correlation function matrix, 21Sparse channel, 328Spatial channel characteristic, 6Spatial correlation, 21

Spatial degrees of freedom, 92Spatial dispersion, 14Spatial diversity, 14Spatial multiplexing, 317Spatial resolution, 13Spectral efficiency, 239Spectrogram, 379, 400, 405Specular scattering, 7, 14, 23Speed of light, 4, 31Sphere decoding, 117, 119, 144, 250, 310, 349, 350, 360,

362, 365Spreading function, 7, 13, 15, 24, 42, 69, 381, 384, 393Spreading index, 243Spreading sequence, 48, 338Spread spectrum, 395Spread-spectrum-like channel sounding, 48Stack algorithm, 252Stationarity bandwidth, 28Stationarity region, 28, 32Stationarity time, 28Statistical beamforming, 94Statistical input-output relation, 16, 17, 24, 55Steady-state MMSE, 209Steering vector, 6, 13, 14, 22Stochastic channel description, 14Subcarrier, 53, 285Subcarrier orthogonality, 285Subcarrier separation, 286Subgroup, 123, 125Sublattice, 125, 126Successive interference cancelation, 308Superimposed training, 155, 201, 214, 216, 218, 329Swept time-delay cross-correlation sounder, 48, 51Symbol alphabet, 207Symbol duration, 239Symbol estimation, 245Szego’s theorem, 89, 101

TTail-biting, 248T-algorithm, 252, 310Tapped-delay line channel model, 12, 381, 386Taylor series expansion, 293TDM training, 204, 216, 218Tight frame, 76Tikhonov regularization, 303Time correlation function, 17Time delay, 7Time-delay channel description, 11Time-delay correlation function, 69Time-delay domain, 11Time-dependent delay spread, 28

“17-ind-417-428-9780123744838” — 2011/3/9 — 12:41 — page 424 — #8

424 Index

Time-dispersive channel, 2Time diversity, 5Time-division multiplexed switching, 54Time-division multiplexing, 199Time-domain channel matrix, 161Time-domain Kronecker delta structure, 172Time-domain windowing, 260Time-frequency AR model, 58Time-frequency channel description, 10Time-frequency concentrated modulation, 242, 256, 272Time-frequency correlation function, 16, 19, 25, 31, 55, 56,

69, 292Time-frequency-dependent delay power profile, 25Time-frequency-dependent Doppler power profile, 25Time-frequency-dependent path loss, 25Time-frequency dispersive channel, 1, 7, 15, 30, 376, 378Time-frequency domain, 10Time-frequency interpolation, 323Time-frequency localization, 76Time-frequency nonstationarity, 23, 25, 28Time-frequency rake receiver, 381, 395Time-frequency representation, 8, 379, 400, 402Time-frequency sampling, 37Time-frequency selective channel, 1, 10Time-frequency shift operator, 38Time-frequency transfer function, 10, 13, 16, 24, 29, 31,

34, 37, 42, 69Time-frequency transfer function matrix, 20Time-frequency Yule-Walker equations, 59Time-invariant channel, 9, 11, 29, 33, 36, 42, 73, 285Time-scale rake receiver, 389Time scaling, 9Time-selective channel, 5Time sharing, 89Time-varying channel, 1, 69, 199, 287Time-varying impulse response, 11, 239, 241, 381Time-varying transfer function, 10, 13, 16, 24, 29, 31, 34,

37, 42, 69Timing error, 4Timing recovery, 3, 18Tomlinson-Harashima precoding, 318Training-based channel estimation, 53, 155, 199, 320Training symbol, 53, 87, 160, 199, 286, 339Transfer function, 10, 29Transmission loss, 27Transmit antenna, 2, 12Transmit correlation, 96Transmit correlation matrix, 92Transmit eigenmode, 94Transmit pulse, 4, 23, 315Transmit signal, 2Transmit symbol, 4

Transmitted reference, 227Transmitter preprocessing, 313Transmitter windowing, 315Tree search algorithm, 252, 310, 351Tree-search based equalization, 250, 267, 271, 310Trellis-based equalization, 248, 265, 270Turbo equalization, 237, 247, 253, 265, 310, 324Twisted canonical embedding, 135Two-path channel model, 292

UUltra-wideband channel, 9, 69Ultra-wideband system, 227, 376, 384Unbiased LMMSE filter, 356Uncorrelated scattering, 15, 65Underspread channel, 30, 32, 34, 39, 40, 49, 52, 59, 69, 70,

106, 243Underwater acoustic channel, 377, 396Underwater acoustic communications, 376, 396, 405Underwater vehicle, 380Uniform linear array, 6, 14, 22Union bound, 119

VV-BLAST, 250Vector ARMA channel model, 46Vehicular channel, 26Vehicular communications, 26, 290Virtual carrier, 286Virtual MIMO model, 22Virtual pilot, 324Virtual sounding signal, 50Viterbi algorithm, 248, 270, 309

WWarping operator, 393, 399Wavelength, 2Wavelet basis, 389Wavelet transform, 390Wave propagation, 2Wax-Kailath algorithm, 59Weichselberger channel model, 22Weyl-Heisenberg frame, 76Weyl-Heisenberg set, 73, 76, 102Wideband channel, 9, 383Wideband channel model, 375, 392Wideband code-division multiple access, 199Wideband dispersive channel characterization, 392Wideband Doppler effect, 5, 9, 383Wideband scattering function, 15, 384, 388

“17-ind-417-428-9780123744838” — 2011/3/9 — 12:41 — page 425 — #9

Index 425

Wideband spreading function, 384Wideband wireless system, 225Wide-sense stationary, 15, 65Wide-sense stationary uncorrelated scattering channel,

1, 15, 20, 38, 44, 65, 69, 78, 293, 383Wiener filter, 323, 343Wireless channel, 2Wireless local area network, 289WSSUS channel, 1, 15, 20, 38, 44, 65, 69, 78, 293, 383WSSUS MIMO channel, 20

YYule-Walker equations, 57, 59, 193

ZZero-forcing decision-feedback equalization, 247, 249, 251,

307Zero-forcing linear equalization, 247, 249, 301Zero-padded single-carrier modulation, 242, 260Zero padding, 157