The character of multipath-induced propagational fading is reviewed, along with the interpretations underlying use of the Rayleigh fading model to describe the process statistics. The relationship between this model and contemporary laboratory fading simulators is also outlined. The effects of the fading upon data communications are described, along with the techniques of modulation, diversity, coding, and adaptive equalization used in modern modem designs for operation over such channels. Finally, the system engineering problems are discussed of attempting to provide quantitative estimates of long-term link or network performance that takes into account the longer term channel variabilities.

A concise formula is derived for the probability distribution of the instantaneous frequency of an arbitrary bandpass signal plus Gaussian noise. The results are presented in terms of Marcum'sQ-functions, with well-known properties. The results are applicable in the performance analysis ofn-ary FM and PM data transmission systems. Illustrative examples of the application of the formula are worked out for binary FSK.

A general result is presented for the error-rate performance of common binary signaling-detection techniques for reception in additive Gaussian noise, including {\em all} possible conditions of nonorthogonality of signal, and correlations in the noise processes. These forms include frequency-shift keying with non-coherent detection, generalized to {\em all} noncoherent detection systems utilizing two basic waveforms, and phase-shift keying with a noisy reference signal, generalized to {\em all} coherent detection systems utilizing a single basic waveform. The unified result is achieved by exploiting a fundamental relationship between noncoherent and coherent operation. Also, some useful and not widely-known mathematical techniques involving the Q function are presented and utilized in the derivations.

The general theoretical difficulties in analyzing the effect of a random input signal on a known system are pointed out. Basically, if certain output statistics are computed directly, each statistic represents a complete, separate problem. An alternative analytical computational procedure is suggested, using a Monte Carlo type technique in which the output is obtained by numerical integration from sequences of values which represent members of the statistical ensemble of the input process. For such applications, or for other possible uses such as in testing, it is necessary to generate statistical sequences, analogous to tables of random numbers. Techniques are discussed for analytically generating such sequences, to correspond to gaussian probability distributions which are further characterized by arbitrarily specified power spectra or autocorrelation functions. The procedure makes use of the standard tables of random numbers, these numbers being distributed uniformly and without correlation. The exact statistical generation ofNvalues of a sequence is shown to require, in general, the diagonalization (or solution for the eigenvalues and eigenvectors) of anNth order matrix; two simpler approximate procedures are also described.