Detection of stochastic signals in non-Gaussian noise^a)

A new technique for the detection of Gaussian signals in the presence of non-Gaussian noise is developed. This technique involves an approximation to the likelihood-ratio statistic for such situations, which in turn is based on the Masreliez approximation of nonlinear filtering. This approximation allows calculation of the likelihood-ratio statistic using a pair of sufficient statistics satisfying nonlinear recursive filtering equations. The performance of the proposed detector in impulsive noise is compared with that of the quadratic detector, and considerable performance gain is seen to result from the proposed technique in this case. A locally optimum (small signal-to-noise ratio) detection statistic for this situation is also presented.