Digital Communication over Fading Channels (Wiley Series in Telecommunications and Signal Processing) [ハードカバー]

Dealing with fading effects is always a challenge from a modeling standpoint, and anyone who has dealt with it knows that there are basically three techniques used. One of them is to model the fading effects using empirical models, which is the least expensive computationally but has the disadvantage of having a substantial geographic dependence. Another is to calculate the effects using path tracing, which is very expensive computationally but seems to be the most accurate. The third is to use statistical modeling, which is the least accurate but is tractable computationally. If one is performing a simulation of a wireless network and wants to incorporate fading effects, then the third technique can be used effectively by performing the calculations offline (not during the actual simulation). This book is extremely helpful in this goal in that it offers for the most part explicit closed-form expressions for such quantities as the average signal to noise ratio, outage probability, and the average bit error probability. Using any of the symbolic and numerical software tools that are available, these expressions, which typically involve well-known special functions, can easily be calculated and the results integrated into a real simulation.

The authors consider the average SNR, outage probability, average bit error probability, amount of fading, and average outage duration to be system performance measures and are defined rigorously in the introduction to the book. For those readers charged with modeling fading effects in adaptive wireless networks, satellite networks, or cognitive networks, the last two of these performance measures will be the most important, for they allow the modeler to quantify how slot scheduling, power transmission, dynamic bandwidth assignment, and quality of service (QoS) will be affected by the statistics of fading.

The mathematical physics behind fading channels is discussed in detail in chapter 2, and at a level of rigor appropriate for this type of book. This material may be familiar to the more experienced reader, but readers who have not confronted the different statistical models of fading will find a particularly lucid discussion. The discussion on multipath fading brings out the difference between a purely random situation (Rayleigh fading) and a situation where there is a line-of-sight (LOS) component. In actual practice, it is much easier from a modeling perspective to deal with total randomness than when an LOS component is in place. This is born out in this chapter by the difference between the expression for the moment generating function for Rayleigh fading (just an exponential distribution), and that of Rice-Nakagami-n fading, the latter of which involves a Kummer confluent hypergeometric function. Also interesting is the use of the log-normal distribution, a distrubution used quite heavily in financial modeling, and used in this book to quantify the effects of shadowing on link quality.

Chapter 3 is more of a review of standard terminology in digital communications, and could be skipped by those readers familiar with the covered material. The chapter does serve as a good reference for the different digital modulation techniques.

Chapter 4 would be just a standard overview of special functions if it weren't for the discussion on an alternative representation of the Marcum Q-function, which is due to the authors and can be easily expressed in symbolic programming languages such as Mathematica. This representation is used in the next chapter to write down explicit expressions for the average error probability for different types of modulation schemes.

The discussions in Chapter 7 are interesting not only because they deal with how signals are received when they pass through fading channels but also the compromises one must make when doing a model implementation. Such compromises are a daily occurrence for modelers who are faced with quantifying highly complex, heterogeneous wireless networks that can become intractable from a mathematical standpoint. The optimization problem at hand is that of finding the largest a posteriori conditional probability of extracting the original signal given a set of replicas of the original signal that have passed through the fading channel. Bayesian reasoning and the maximum likelihood principle, coupled with the channel state information give an expression for these conditional probabilities in terms of averages over the parameters (amplitudes, phases, and delays). The authors first deal with the case where all of these parameters are known, giving what has been called the 'RAKE' receiver, and serving as a baseline or ideal standard of comparison. The authors then proceed to derive expressions for the conditional probabilities for the different cases where one set out of three of these parameters is unknown, and for different types of fading (Rayleigh, Nakagami-m, etc). They also treat the case where all three sets of parameters are unknown.

The main interest of this reviewer was in chapter 8, which deals with the mathematical modeling of single-channel receivers. As expected the authors utilize the idiosyncratic expressions that they derived earlier in the book. The clarity of the exposition and the compactness and practicality of these expressions justifies their inclusion in the book, and this reviewer found them of enormous help in the understanding and modeling of multipath fading in cognitive wireless networks.

Chapter 10, which deals with outage probabilities in communications systems with multiple users, should be of interest to those readers who are modeling cellular networks or military communication networks. The authors restrict their analysis to multipath fading (no shadowing), and give several useful mathematical expressions for the outage probability when this type of fading is present and when interference between users cannot be ignored.

In Chapter 13, the authors depart from their assumption that the transmissions were uncoded in order to analyze the situation where error correction is deployed when fading effects are present. The goal is to estimate the upper bounds of the average bit error probability and the authors do this by taking two possible transmitted symbol sequences and then calculating the probability of choosing one of these over another. This is called the 'pairwise error probability' and the bounds are the familiar Chernoff bounds from information theory. The true upper bound is obtained by first summing the pairwise error probability over all sequence pairs that correspond to a given transmitted sequence. Each term of this sum is then weighted by the number of bit errors associated with the error event, and this is then statistically averaged over the possible transmitted sequences. The resulting expression is then divided by the number of input bits per transmission. The authors calculate this weighted sum by using the 'transfer function bound' method for the cases of perfect channel state information and unknown channel state information for specific types of coding. The technique of transfer function bound goes back four decades, having been originally proposed by A. J. Viterbi for convolution codes subjected to white noise. The authors treatment is rather curt but very lucid, and they give an example dealing with QPSK coding.

The other chapters of this book were not studied, and so their review will be omitted.