Detector design using a density fit to non-Gaussian noise

Suboptimal nonlinear detectors for known small signals in non-Gaussian noise are investigated. It is assumed that either the locally optimal nonlinearity is too complex to use or that the noise density is not known precisely. A memoryless suboptimal nonlinearity (ZNL) can be chosen, and the family of densities for which it is optimal is found. A member of this family is then fitted to the observed noise, and the corresponding detector is used. When a rational function is chosen for the nonlinearity, the Pearson family is the set of solution densities. This is not only a general family which contains many common univariate densities, but for nearly Gaussian noise the method of moments can be used efficiently to fit a member density to the noise. The coefficients of a ZNL are estimated for several (non-Pearson) densities using the first four noise moments