The symbol error probability of Gaussian MSK using differential detection in a Rician fast fading channel is investigated. In the analysis, the effect of the infinite sequence of intersymbol interference inherent in this modulation is included exactly, and the performance can be evaluated at narrow shaping bandwidths where the intersymbol interference is extensive. Numerical results are presented for parameters typically encountered in the satellite-to-mobile channel.>

Sums of infinite sequences of weighted binary random variables arise in communications problems involving signal-dependent interferences. In many cases of practical importance, the distribution functions of these sums are singular and often of Cantor type; they are continuous but do not have a density function. For this reason, special methods of calculating expectations are needed. Results of this type are derived. The method is used to compute error probabilities for differential detection of minimum shift keying, and for noncoherent detection of frequency shift keying. In each case the model assumed is a Rician fading channel.>

The sum of an infinite series of weighted binary random variables arises in communications problems involving intersymbol and adjacent-channel interference. If the weighting decays asymptotically at least exponentially and if the decay is not too slow, the sum has an unusual distribution which has neither a density nor a discrete mass function, and therefore cannot be manipulated with usual techniques. The distribution of the sum is given, and the calculus for dealing with the distribution is presented. It is shown that these Cantor-type random variables arise in a range of digital communications models, and exact explicit expressions for performance measures, such as the probability of error, may be obtained. Several examples are given.>