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.>

The detection of a vanishingly small, known signal in multi-variate noise is considered. Efficacy is used as a criterion of detector performance, and the locally optimal detector (LOD) for multivariate noise is derived. It is shown that this is a generalization of the well-known LOD for independent, identically distributed (i.i.d.) noise. Several characterizations of multivariate noise are used as examples; these include specific examples and some general methods of density generation. In particular, the class of multivariate densities generated by a zero-memory nonlinear transformation of a correlated Gaussian source is discussed in some detail. The detector structure is derived and practical aspects of obtaining detector subsystems are considered. Through the use of Monte Carlo simulations, the performance of this system if compared to that of the matched filter and of the i.i.d. LOD. Finally, the class of multivariate densities generated by a linear transformation of an i.i.d, noise source is described, and its LOD is shown to be a form frequently suggested to deal with multivariate, non-Gaussian noise: a linear filter followed by a memoryless nonlinearity and a correlator.