Nearly optimal detection of signals in non-Gaussian noise

This dissertation addresses the problem of finding nearly optimal detector structures for non-Gaussian noise environments. It is assumed that the noise statistics are unknown except for a very loose characterization. Under this condition, the goal is to study adaptive detector structures that are simple, yet capable of high levels of performance. Attention is focused on the discrete-time locally optimal detector for a constant signal in independent, identically distributed noise. A definition for non-Gaussian noise is given, several common univariate density models are exhibited, and some physical non-Gaussian noise data is discussed. Two approaches in designing adaptive detector nonlinearities are presented, where it is assumed that the noise statistics are approximately stationary. Both proposals utilized simple measurements of the noise behavior to adapt the detector, and in several examples the adaptive detectors are shown capable of attaining nearly optimal performance levels. A simulation is presented demonstrating their successful application.