The robustness of suboptimal nonlinear detectors for known discrete-time signals in non-Gaussian noise is investigated. The measure of robustness used is the degradation of asymptotic relative efficiency (compared to a linear detector) from that achieved by an optimal nonlinear detector. The first order density of non-Gaussian noise is modeled as a mixture of a small variance Gaussian background noise pdf and a large variance impulsive pdf.

A first-order mixture noise density is considered as a model for impulsive noise channels. It consists of a mixture of a small variance, probably Gaussian, background noise pdf and a large variance impulsive pdf. Optimal nonlinear detector structures for known discretetime signals in such noise are derived. Their large-sample performance compared to that of a linear detector is studied using asymptotic relative efficiency.

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.

A tutorial paper on an adaptive receiver that is suitable for high-speed digital signaling over slowly time-varying, band-limited channels which have impulse responses that are unknown at the receiver is presented. The receiver utilizes a steepest-descent technique for adjusting its parameters to existing channel conditions. A treatment of the speed of adaptation of the receiver is included.