In this paper we review the most peculiar and interesting information-theoretic and communications features of fading channels. We first describe the statistical models of fading channels which are frequently used in the analysis and design of communication systems. Next, we focus on the information theory of fading channels, by emphasizing capacity as the most important performance measure. Both single-user and multiuser transmission are examined. Further, we describe how the structure of fading channels impacts code design, and finally overview equalization of fading multipath channels.

/pdf/fading-channels-information-theoretic-and-communications-2ipqbail97.pdf

Fading channels: information-theoretic and communications aspects

Cyclostationarity: half a century of research

It has been well established that the appropriate criterion for optimum trellis-coded modulation design on the additive white Gaussian noise channel is maximization of the free Euclidean distance. It is shown that when the trellis-coded modulation is used on a Rician fading channel with interleaving/deinterleaving, the design of the code of optimum performance is guided by other factors, in particular, the length of the shortest error-event path, and the product of branch distances (possibly normalized by the Euclidean distance of the path) along the path. Although maximum free distance (d/sub free/) is still an important consideration, it plays a less significant role the more severe the fading is on the channel. These considerations lead to the definition of a new distance measure of optimization of trellis codes transmitted over Rician fading channels. If no interleaving/deinterleaving is used, then once again the design of the trellis code is guided by maximizing d/sub free/. >

The design of trellis coded MPSK for fading channels: performance criteria

For pt. I see ibid., vol. 35, no. 7, p. 90, 1997. In Part I of this tutorial, the major elements that contribute to fading and their effects in a communication channel were characterized. In Part II, these phenomena are briefly summarized, and emphasis is then placed on methods to cope with these degradation effects. Two particular mitigation techniques are examined: the Viterbi equalizer implemented in the Global System for Mobile Communication (GSM), and the RAKE receiver used in CDMA systems built to meet Interim Standard 95 (IS-95).

/pdf/rayleigh-fading-channels-in-mobile-digital-communication-3i3posp320.pdf

Rayleigh Fading Channels in Mobile Digital Communication Systems Part II: Mitigation

M inimum Shift Keying (MSK) [ 11 or Fast Frequency Shift Keying (FFSK) is a digital modulation technique with constant amplitude which has been studied extensively during recent years. The properties of MSK are now understood [2-51. In this article, we report on methods to improve on MSK while maintaining a constant amplitude. By improvement we mean a narrower power spectrum, lower spectral sidelobes, better error probability, or all of the above. The cost of signal processing and the speed and complexity with which it can be performed has steadily been improved over recent years. Further improvements are to be expected. Therefore, it is reasonable to study what can be accomplished with methods that might be too complex for cost effective realization today, but perhaps may be easily achievable tomorrow. In this paper, we consider a number of methods for constructing constant amplitude signals which significantly outperform MSK [5-1031. We also discuss at what level of complexity these improvements are obtained and realized.

Continuous phase modulation

The performance of 8-PSK and 8-DPSK trellis codes is presented for a class of fast fading, land mobile satellite communication channels. The fading model is Rician but, in addition, the line-of-sight path is subjected to a fast lognormal attenuation that represents tree shadowing. The fading parameters used in this study represent the degree of shadowing and are based on measured data. The primary application considered is for digital speech transmission and thus, bit error probabilities in the order of 10/sup -3/ are emphasized. Sensitivity of the bit error probability to amplitude fading, amplitude and phase fading, and decoding delay is presented. Performance is determined via digital computer simulation. Optimal four- and eight-state codes are determined and optimality is found to be dependent on the presence of lognormal shadowing. >

PSK and DPSK trellis codes for fast fading, shadowed mobile satellite communication channels

The problem of designing and evaluating the performance of a maximum likelihood sequence receiver for binary PSK transmission over bandlimited nonlinear channels is considered in this paper. The effects of intersymbol interference followed by AM/AM and AM/PM conversions are taken into account while optimizing the performance in the presence of white Gaussian noise. A new representation for the output of a bandpass nonlinearity is given when the input consists of a carrier signal modulated by a sum of binary overlapping pulses. The structure of a maximum likelihood sequence receiver for a bandlimited nonlinear channel is derived using this representation. The receiver uses a modified Viterbi algorithm to determine the most likely sequence of data symbols transmitted. An upperbound on the probability of symbol error for this receiver is obtained. Numerical results illustrating the applicability of the present work to optimizing the performance of a digital satellite communications link are also presented.

Maximum Likelihood Sequence Estimation of Binary Sequences Transmitted Over Bandlimited Nonlinear Channels

In automatic detection in radar systems an estimate of background clutter power is used to set the detection threshold. Usually detection cells surrounding the cell under test for the presence of a target are used to estimate the clutter power. In the research reported herein, the target location is taken to be uncertain and thus returns from a target could corrupt this clutter power estimate. It is shown how the threshold should be varied to compensate for the resulting degradation in detection performance. The threshold control procedure is based on a priori information about target location that could be supplied by the radar's tracking system. In addition, a simple procedure for calculating detection and false alarm probabilities for Swerling II target models is presented.

Threshold Control for Automatic Detection in Radar Systems

It has previously been shown that MSK modulation with correlative encoded symbols, using first- and second-order encoding polynomials, can give rise to signals with excellent bandwidth efficiency. In this paper we specify and analyze the Viterbi receiver for such signals. The receivers are not very complex as they either require four or eight states to be stored and processed during each symbol interval. Our analysis concerns the bit error rate and the transfer function bound technique is utilized. Perfect coherent operation of the receiver is assumed in the error analysis.

The Viterbi Receiver for Correlative Encoded MSK Signals

In this paper we specify an optimal receiver filter for 2phase PSK transmission over a channel consisting of the tandem connection of a linear filter and a bandpass nonlinearity, with thermal noise added at the channel output. This filter minimizes the bit estimation error subject to the constraint that it be a linear filter. Our main aim is to consider satellite communication channels and as such the system nonlinearity is taken to have both AM/AM and AM/PM conversions. In these systems we assume the up-link signal-to-noise ratio is large and thus our work relates to large transmit terminal applications. In an example the probability of error performance of the optimal received filter is found to be 2 dB better in terms of the effective output SNR as compared with that of a standard choice for the receiver filter.

P.J. McLane

Papers

PSK and DPSK trellis codes for fast fading, shadowed mobile satellite communication channels

Maximum Likelihood Sequence Estimation of Binary Sequences Transmitted Over Bandlimited Nonlinear Channels

Threshold Control for Automatic Detection in Radar Systems

The Viterbi Receiver for Correlative Encoded MSK Signals

Optimal Receiver Filters for BPSK Transmission over a Bandlimited Nonlinear Channel