Non-Gaussian and Multivariate Noise Models for Signal Detection.

This report deals with the problems of detecting a known signal in non-Gaussian or dependent noise. Although likelihood ration LR detectors are discussed, primary attention is paid to asymptotic detector performance, and therefore to maximum efficacy or locally optimal LO detectors. The detectors considered consist of a nonlinearity followed by a filter and a threshold comparator. The asymptotic performance of three common suboptimal detectors is considered for several families of noise densities as the input signal-to-noise ratio SNR varies. Contours of equal detector performance are plotted allowing the relative utility of the detectors to be assessed. A method of designing suboptimal detector nonlinearities is presented. A suboptimal nonlinearity is chosen, and the family of densities for which it is locally optimal is found. A member of this family is then fitted to the observed noise, and the corresponding detector is used. When the nonlinearity is a rational function, the Pearson family of densities results.