Robust matched filters

Two general aspects of the problem of designing robust matched filters for situations in which there is uncertainty in the signal structure or noise statistics are examined. First, maximum robust designs are evaluated for a general Hilbert-space formulation of the matched filtering problem and explicit solutions are obtained for two intuitively appealing models for uncertainty. Second, the theoretical maximum results are applied to the particular problem of designing filters to combat uncertain nonlinear channel distortion, which is modeled by considering an unknown received signal differing in L2-norm from the transmitted or nominal signal by no more than a fixed amount. The effect of the channel distortion is determined to be equivalent to that of adding a white noise to the channel whose spectral height depends on the degree of distortion. General expressions are presented for the determination of the robust filter and its performance, and numerical results are obtained for the case of baseband detection in Gauss-Markov noise.