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To build next-generation wireless systems, engineers must understand radio channels that fade in time, frequency, and space.

*Space-Time Wireless Channels*presents a pragmatic, first-principles approach that integrates crucial techniques from communications, electromagnetics, and random process theory. It focuses on comprehension, with many examples, illustrations, and problems. Coverage includes electromagnetic description of space-time channels; first- and second-order statistics of fading channels; angle spectrum concepts; multiple antenna and multipath techniques; array design; and more.### Details & Specs

Title:Space-Time Wireless ChannelsFormat:PaperbackPublished:October 3, 2002Publisher:Pearson EducationLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:013065647X

ISBN - 13:9780130656476

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### Customer Reviews of Space-Time Wireless Channels

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From the Author

PREFACELet me begin by saying that without my friends David A. de Wolf, Gary S. Brown,and Theodore S. Rappaport, this book would have never happened. Professor deWolf, besides being the man who introduced me to scholarly research, has proofedmuch of the mathematical content in my work and has been a great collaboratorduring my time at Virginia Tech. Professor Brown taught me most of what I knowabout electromagnetics; I borrow much of his notation from wellcrafted lectures onrough surface scattering and analytical propagation analysis. Professor Rappaportmy principle graduate advisorhas been a true friend by encouraging this projectand giving me a firstrate graduate student experience at Virginia Tech ’s Mobile &Portable Radio Research Group.Back in 1998 I was sitting through a presentation made by an elder statesman ofradio, a very accomplished and respected engineering professor. The presentationincluded many wireless channel measurements. About halfway through the talk, anintense academic discussion (i.e., argument) broke out between the professor and hiscolleagues in the audience. An endless volley ensued about the nature of the fadingobserved in the measurements. As a lowly graduate student, I just took notes quietlyin the back of the room. I observed that the argumentwhich was left unresolvedwas not a problem in understanding, but in semantics. The arguing researcherswere trying to describe a spacetime wireless channel using archaic conventions.These researchersexperts in narrowband analog communications were desperately trying and failing to describe the radio channel experienced by mobile,broadband digital radios with antenna arrays. I got the impression that the field ofchannel modeling needed to be reworked to accommodate all these new, sophisticated spacetime concepts in wireless. At the end of the presentation, I wrote downthe following analogy: "Frequency is to delay, as time is to Doppler, as space is towavenumber." I left that presentation with a great topic for a Ph.D. dissertation.I began writing my dissertation as if it were a textbook in spacetime channelmodeling, not really believing that it would actually become that one day (a goodlesson for other graduate students). Of course, that was a little too ambitious atthe time, but there was enough content after my defense to justify pursuing a bookafter my graduate work. I took a oneyear trip to the Land of the Rising Sun tocomplete what is now SpaceTime Wireless Channel.The goal of this book is the same as my Ph.D. work: to provide simple, cohesiveconcepts for understanding radio channels that fade randomly with respect to time,frequency, and space. And I wanted it to be a book that even I could read. Thismeant adding lots of pictures, gutting gratuitous mathematics, and inserting otherunderstanding aides. In the process, I found that spacetime wireless channels werenot so difficult to understand, provided a few basic principles in other disciplines(communications, random process theory, and electromagnetics) are known.My hope is that SpaceTime Wireless Channel offers a great deal to both thenovice radio engineer and the veteran wireless researcher. The text focuses on firstprinciples in radio channel modeling; it does not provide the deepest treatment ofall the signalprocessing algorithms for spacetime radios, since that type of discussion tends to multiply acronyms instead of genuine understanding. The bookcontains plenty of original material as well as new ways of looking at old problems.The seasoned researcher will notice the inclusion of many new concepts in channelmodeling and characterizationand will also notice the intentional omission of others. I have avoided the temptation of turning this book into a "cutandpaste" job,which so often constitutes engineering texts nowadays.Since it contains problem sets and a pedagogic presentation of material, thisbook may be used in graduate or even undergraduate engineering courses. Thebook is also intended to be used by graduate students or industry engineers as aresearch aid or a selfstudy course. This book is written with wireless engineers inmind. Many colleagues have pointed out that spacetime channel modeling theoryapplies to problems in optics, radar, acoustics, and imagingto name just a fewfields of study. I believe this text is useful to other engineers, physicists, or appliedmathematicians, although I apologize to them in advance for all the references towireless devices.Combining disparate fields to synthesize a theoretical foundation creates allsorts of conflicts in notation. In fact, attempts to be consistent with the multipleconventions that exist in the research literature proved to be the most difficult partof writing SpaceTime Wireless Channel. Although no desirable notation could befound, this book takes a "lesserofevils" approach to naming variables and functionsin analysis.(To underscore the notation difficulty, consider the convention of using R todescribe the autocorrelation function of random processes. This notation conflictswith the convention for signal envelopes, so instead this book uses C to denote theautocorrelation function. But to describe the probability density function (PDF) ofenvelopes, we need a lowercase value of R to be the index of the PDF. However, r iscommonly used to describe position in radial coordinate systems, so we defer to theGreek ρ for the PDF index. This move, however, conflicts with standard practiceof using ρ to denote unit autocovariance of a random process, which becomes σin this text. Without these precautions, there would have been ridiculouslookingfunctions such as RR (Δr). Do not get me started about φ.)Much of the original research contained in this book was funded by a Bradley Fellowship in Virginia Tech’s department of Electrical and Computer Engineering,ITT Defense & Electronics, and the MPRG Industrial Affiliates program. The completion of this manuscript was supported by the Japanese Society for the Promotionof Science (JSPS) in the form of a longterm fellowship for visiting researchers. AndI cannot give enough thanks to my Japanese host professors, Dr. Norihiko Morinaga and Dr. Seiichi Sampei, and all of my great friends at Morinaga Laboratoryin Osaka University.

Read from the Book

PREFACE Let me begin by saying that without my friends David A. de Wolf, Gary S. Brown,and Theodore S. Rappaport, this book would have never happened. Professor deWolf, besides being the man who introduced me to scholarly research, has proofedmuch of the mathematical content in my work and has been a great collaboratorduring my time at Virginia Tech. Professor Brown taught me most of what I knowabout electromagnetics; I borrow much of his notation from well-crafted lectures onrough surface scattering and analytical propagation analysis. Professor Rappaportmy principle graduate advisorhas been a true friend by encouraging this projectand giving me a first-rate graduate student experience at Virginia Tech 's Mobile &Portable Radio Research Group. Back in 1998 I was sitting through a presentation made by an elder statesman ofradio, a very accomplished and respected engineering professor. The presentationincluded many wireless channel measurements. About halfway through the talk, anintense academic discussion (i.e., argument) broke out between the professor and hiscolleagues in the audience. An endless volley ensued about the nature of the fadingobserved in the measurements. As a lowly graduate student, I just took notes quietlyin the back of the room. I observed that the argumentwhich was left unresolvedwas not a problem in understanding, but in semantics. The arguing researcherswere trying to describe a space-time wireless channel using archaic conventions. These researchersexperts in narrowband analog communications were desperately trying and failing to describe the radio channel experienced by mobile,broadband digital radios with antenna arrays. I got the impression that the field ofchannel modeling needed to be reworked to accommodate all these new, sophisticated space-time concepts in wireless. At the end of the presentation, I wrote downthe following analogy: "Frequency is to delay, as time is to Doppler, as space is towavenumber." I left that presentation with a great topic for a Ph.D. dissertation. I began writing my dissertation as if it were a textbook in space-time channelmodeling, not really believing that it would actually become that one day (a goodlesson for other graduate students). Of course, that was a little too ambitious atthe time, but there was enough content after my defense to justify pursuing a bookafter my graduate work. I took a one-year trip to the Land of the Rising Sun tocomplete what is now Space-Time Wireless Channel. The goal of this book is the same as my Ph.D. work: to provide simple, cohesiveconcepts for understanding radio channels that fade randomly with respect to time,frequency, and space. And I wanted it to be a book that even I could read. Thismeant adding lots of pictures, gutting gratuitous mathematics, and inserting otherunderstanding aides. In the process, I found that space-time wireless channels werenot so difficult to understand, provided a few basic principles in other disciplines(communications, random process theory, and electromagnetics) are known. My hope is that Space-Time Wireless Channel offers a great deal to both thenovice radio engineer and the veteran wireless researcher. The text focuses on firstprinciples in radio channel modeling; it does not provide the deepest treatment ofall the signal-processing algorithms for space-time radios, since that type of discussion tends to multiply acronyms instead of genuine understanding. The bookcontains plenty of original material as well as new ways of looking at old problems.The seasoned researcher will notice the inclusion of many new concepts in channelmodeling and characterizationand will also notice the intentional omission of others. I have avoided the temptation of turning this book into a "cut-and-paste" job,which so often constitutes engineering texts nowadays. Since it contains problem sets and a pedagogic presentation of material, thisbook may be used in graduate or even undergraduate engineering courses. Thebook is also intended to be used by graduate students or industry engineers as aresearch aid or a self-study course. This book is written with wireless engineers inmind. Many colleagues have pointed out that space-time channel modeling theoryapplies to problems in optics, radar, acoustics, and imagingto name just a fewfields of study. I believe this text is useful to other engineers, physicists, or appliedmathematicians, although I apologize to them in advance for all the references towireless devices. Combining disparate fields to synthesize a theoretical foundation creates allsorts of conflicts in notation. In fact, attempts to be consistent with the multipleconventions that exist in the research literature proved to be the most difficult partof writing Space-Time Wireless Channel. Although no desirable notation could befound, this book takes a "lesser-of-evils" approach to naming variables and functionsin analysis. (To underscore the notation difficulty, consider the convention of using R todescribe the autocorrelation function of random processes. This notation conflictswith the convention for signal envelopes, so instead this book uses C to denote theautocorrelation function. But to describe the probability density function (PDF) ofenvelopes, we need a lowercase value of R to be the index of the PDF. However, r iscommonly used to describe position in radial coordinate systems, so we defer to theGreek ρ for the PDF index. This move, however, conflicts with standard practiceof using ρ to denote unit autocovariance of a random process, which becomes σin this text. Without these precautions, there would have been ridiculous-lookingfunctions such as RR (Δr). Do not get me started about φ.) Much of the original research contained in this book was funded by a Bradley Fellowship in Virginia Tech's department of Electrical and Computer Engineering,ITT Defense & Electronics, and the MPRG Industrial Affiliates program. The completion of this manuscript was supported by the Japanese Society for the Promotionof Science (JSPS) in the form of a long-term fellowship for visiting researchers. AndI cannot give enough thanks to my Japanese host professors, Dr. Norihiko Morinaga and Dr. Seiichi Sampei, and all of my great friends at Morinaga Laboratoryin Osaka University.

Table of Contents

**Preface.**

**1. Introduction.**

Perspectives in Propagation. The Case for Space. Trends in Wireless Communications. About This Book.

**2. Signal Transmission.**

Baseband Representation. Channel Coherence. Using the Complete Baseband Channel. Chapter Summary.

**3 Random Fading Channels.**

Channel Correlation. Power Spectral Density (PSD). Joint Statistics. Width of the PSD. Chapter Summary.

**4. Physics Of Small-Scale Fading.**

Plane Wave Representation. The Local Area. Wave Groupings for Multipath Components. The SLAC Model. Chapter Summary.

**5. First-Order Channel Statistics.**

Mean Received Power. Envelope Probability Density Functions. Closed-Form PDF Solutions. Two-Wave with Diffuse Power PDF. Chapter Summary. Envelope Characteristic Functions.

**6. The Angle Spectrum.**

Vector and Scalar Space. Angle Spectrum Concepts. Multipath Shape Factors. Illustrative Examples. Chapter Summary.

**7. Second-Order Channel Statistics.**

The Level-Crossing Problem. Envelope Unit Autocovariance. Classical Spatial Channel Models. Properties of Wideband Channels. Chapter Summary. Approximate Spatial Autocovariance. Classical Envelope Autocovariance. Rician Mean Approximation.

**8. Diversity.**

Diversity Concept. Combining Techniques. BER and Capacity. Chapter Summary.

**9. Mimo Channels.**

Conventional Multiple Antenna Systems. Separating Channels in Multipath. Practical MIMO Signaling. Space-Time Block Coding. Chapter Summary.

**10. Array Design In Multipath.**

Rules of Spatial Decorrelation. Modeling Double Spatial Dependencies. Example System. Peer-to-Peer Space-Time Measurements. Chapter Summary. Description of Measured Parameters.

**Appendix A. Special Functions.**

Singularity Functions. Sinc Function. Gamma Function. Bessel Functions. Complete Elliptic Integral Functions. Q-function.

**Appendix B. Fourier Analysis.**

Basic Fourier Transform Definitions. Time-Doppler Transforms. Frequency-Delay Transforms. Space-Wavenumber Transforms. Trigonometric Relationships.

**Appendix C. Random Process Theory.**

Definitions. Probability Density Functions. Functions of Random Variables.

**Appendix D. Glossary.**

Mathematical Symbols and Conventions. Acronym List.

**Bibliography.**

**Index.**