Optimum detection of signals in non-Gaussian noise

Abstract

The purpose of this paper is to derive optimum processing structures for use in the detection of signals in additive non-Gaussian noise. The cases chosen for analysis are of particular interest in sonar detection problems since it has been reported that ambient ocean noise may, under sone conditions, deviate from the Gaussian model. The processing structures are considered to be models of the likelihood ratio which is an optimum test no matter what the signal and noise statistics, and optimum single channel and array processors are derived for the small signal-to-noise ratio cases where (1) the signal is completely known, and (2) the signal is a noiselike, not necessarily Gaussian, zero-mean process. Expressions are derived which compare the performance of processors optimized for non-Gaussian noise with those optimized for Gaussian noise for each of the two cases, with transfer functions for the required optimum nonlinear filters and the expected improvements in performance determined using some ’’typical’’ non-Gaussian probability density functions. Justification of these particular density functions is beyond the scope of this paper except to note that very good agreement is obtained with some published experimental data. New results include the derivation of optimum array processors for the detection of plane wave signals when the array is steered at the signal arrival angle, in a non-Gaussian noise field and the development of expressions to predict their performance for the case where the signal is a zero-mean, noiselike process.