Optimal linear processing of randomly distorted signals

This paper considers least-mean-squared-error linear estimation on signals received over a channel that can be characterized by additive noise sources and a time-invariant dispersion network whose transfer function is randomly selected. Solutions for the optimum linear receiver for the problem of continuous waveform estimation of a stationary process (Wiener filtering) and for estimating the amplitude of an isolated signal pulse (matched filtering) are presented and compared with the conventional results for a deterministic channel. The influence of the statistical properties of the channel dispersion on the optimal filter design is illustrated by examples involving particular models for the random channel. The investigation is extended to the situation where the receiver transfer function depends on a finite number of adjustable parameters, these parameters being set according to particular realizations of the channel characteristic. Conditions on the optimal form of this dependence are presented, and typical results are illustrated by an example.