## Space-Time Wireless ChannelsGregory D. Durgin |

It was 15 years ago this month when Space-Time Wireless Channels was published by Pearson (Prentice-Hall). An excerpt of the preface follows:

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 de Wolf, besides being the man who introduced me to scholarly research, has proofed much of the mathematical content in my work and has been a great collaborator during my time at Virginia Tech. Professor Brown taught me most of what I know about electromagnetics; I borrow much of his notation from well-crafted lectures on rough surface scattering and analytical propagation analysis. Professor Rappaport — my principle graduate advisor — has been a true friend by encouraging this project and 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 of radio, a very accomplished and respected engineering professor. The presentation included many wireless channel measurements. About halfway through the talk, an intense academic discussion (i.e., argument) broke out between the professor and his colleagues in the audience. An endless volley ensued about the nature of the fading observed in the measurements. As a lowly graduate student, I just took notes quietly in the back of the room. I observed that the argument — which was left unresolved — was not a problem in understanding, but in semantics. The arguing researchers were trying to describe a space–time wireless channel using archaic conventions. These researchers — experts 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 of channel modeling needed to be reworked to accommodate all these new, sophisticated space–time concepts in wireless. At the end of the presentation, I wrote down the following analogy: “Frequency is to delay, as time is to Doppler, as space is to wavenumber.” 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 channel modeling, not really believing that it would actually become that one day (a good lesson for other graduate students). Of course, that was a little too ambitious at the time, but there was enough content after my defense to justify pursuing a book after my graduate work. I took a one-year trip to the Land of the Rising Sun to complete what is now {\it Space–Time Wireless Channels}. The goal of this book is the same as my Ph.D. work: to provide simple, cohesive concepts 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. This meant adding lots of pictures, gutting gratuitous mathematics, and inserting other understanding aides. In the process, I found that space–time wireless channels were not 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 Channels offers a great deal to both the novice radio engineer and the veteran wireless researcher. The text focuses on first principles in radio channel modeling; it does not provide the deepest treatment of all the signal-processing algorithms for space–time radios, since that type of discussion tends to multiply acronyms instead of genuine understanding. The book contains 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 channel modeling and characterization — and 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, this book may be used in graduate or even undergraduate engineering courses. The book is also intended to be used by graduate students or industry engineers as a research aid or a self-study course. This book is written with wireless engineers in mind. Many colleagues have pointed out that space-time channel modeling theory applies to problems in optics, radar, acoustics, and imaging — to name just a few fields of study. I believe this text is useful to other engineers, physicists, or applied mathematicians, although I apologize to them in advance for all the references to wireless devices.

Combining disparate fields to synthesize a theoretical foundation creates all sorts of conflicts in notation. In fact, attempts to be consistent with the multiple conventions that exist in the research literature proved to be the most difficult part of writing Space–Time Wireless Channels. Although no desirable notation could be found, this book takes a “lesser-of-evils” approach to naming variables and functions in analysis. (To underscore the notation difficulty, consider the convention of using R to describe the autocorrelation function of random processes. This notation conflicts with the convention for signal envelopes, so instead this book uses C to denote the autocorrelation function. But to describe the probability density function (PDF) of envelopes, we need a lowercase value of R to be the index of the PDF. However, r is commonly used to describe position in radial coordinate systems, so we defer to the Greek rho for the PDF index. This move, however, conflicts with standard practice of using rho to denote unit autocovariance of a random process, which becomes $\varrho$ in this text. Without these precautions, there would have been ridiculous-looking functions such as $R_R(\Delta r)$. Do not get me started about phi.)

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 Promotion of Science (JSPS) in the form of a long-term fellowship for visiting researchers. And I cannot give enough thanks to my Japanese host professors, Dr. Norihiko Morinaga and Dr. Seiichi Sampei, and all of my great friends at Morinaga Laboratory in Osaka University.

I am also truly indebted to my long-time friends and officemates Neal Patwari and Hao Xu and to my friends David Wenzel and Jiun Siew for proofreading parts of the manuscript. I am also grateful toward the many colleagues at MPRG who assisted this effort with encouragement, support services, and feedback: Jason Aron, Chris Anderson, Keith Blankenship, Rich Ertl, Ran Gozali, Ben Henty, Kevin and Donna Krizman, Vikas Kukshya, Bror Peterson, Bruce Puckett, Cindy Reifsnider, Hilda Reynolds, Aurelia Scharnhorst, and Christopher Steger. Additional thanks to Dr. James Isaacs of ITT Defense & Electronics and to Dr. David Auckland of Etenna Corp.