Detectors for discrete-time signals in non-Gaussian noise

The structure and performance of a class of nonlinear detectors for discrete-time signals in additive white noise are investigated. The detectors considered consist of a zero-memory nonlinearity (ZNL) followed by a linear filter whose output is compared with a threshold. That this class of detectors is a reasonable one to study is apparent from the fact that both the Neyman-Pearson optimum and the locally optimum (i.e., weak-signal optimum) detectors for statistically independent noise samples can be put into this form. The measure of detector performance used is the asymptotic relative efficiency (ARE) of the nonlinear detector under study with respect to a linear detector appropriate for the same detection problem. A general expression for this ARE is given along with the result that the non-linearity maximizing this expression is any linear function of the nonlinearity in the appropriate constant-signal locally optimum detector. To illustrate the structure and performance of these nonlinear detectors for a wide range of non-Gaussian noise distributions, three general classes of symmetric, unimodal, univariate probability density functions are introduced that are generalizations of the Gaussian, Cauchy, and beta distributions.