A comprehensive theory for Nth-order space diversity reception combined with various equalization techniques in digital data transmission over frequency-selective fading channels is developed. The channels are characterized by N arbitrary impulse responses possessing random parameters as well as N additive Gaussian noise sources. Various combiner-equalizers that minimize the mean-squared error are determined. Formulas are presented for the attainable least-mean-squared errors and upper bounds on average probabilities of error. The theory is applied to optimize system parameters and to predict performance for QAM data transmission operating over a model for the mobile radio channel. For this model, estimates of average attainable error rates and outage probabilities are provided as functions of system parameters. In the channel models the uncoded data rates as well as Shannon capacity are regarded as random variables.>

For Pt.I, see ibid., vol.40, no.5, p.885-94 (1992). The probability distributions of the data rates that can be supported by optimum receiver structures as well as the distribution of the Shannon capacity are studied. The dependences among the important system parameters are exhibited graphically for several illustrative examples including QPSK. At outage probabilities>

Digital communication systems are frequently operated over nonlinear channels with memory. The analysis of the performance of these systems is difficult and no complete analytical treatment of the problem has been obtained before. Several recent efforts have been directed toward the computation of error probabilities via Monte-Carlo simulation using a complete system model. These simulations require excessively large sample sizes and are not practical for estimating very low values of error probabilities. This paper presents a modified Monte-Carlo simulation technique for estimating error probabilities in digital communication systems operating over nonlinear channels. An importance-sampling technique is used to modify the probability density function of the noise process in a way to make simulation possible. Theoretical results as well as realistic examples are presented, showing that the number of samples needed for simulation is reduced considerably.

In this paper four approaches to the calculation of error rates for optical fiber system repeaters are compared ("Exact" calculation, Monte Carlo simulation, Chernoff bounds and the Gaussian approximation). We conclude that the "Exact" and Monte Carlo calculations are in complete agreement. This allows the Monte Carlo results to be used to calibrate other methods. The relatively simple Chernoff bound is in very good agreement with the above, and should be used whenever computational facilities allow. For simpler calculations, or analytical expressions for the effects of parameter variations, the Guassian approximation gives a reasonable good estimate of the receiver sensitivity. However, it tends to underestimate the threshold setting and overestimate the optimal avalanche gain.