INSIGHT INTO DETECTION OF DETERMINISTIC AND GAUSSIAN SIGNALS IN CORRELATED PLUS IMPULSIVE NOISE ENVIRONMENTS

It has long been known that many important noise environments for the signal detection problem are distinctly non-Gaussian; some of these environments are termed impulsive due to the fact that the non-Gaussian disturbances tend to be of high amplitude and short duration. The purpose of this paper is to present a different view of the discrete-time detection problem in impulsive noise. The approach used will be to examine the geometry (from a subspace viewpoint) of two detectors: the clairvoyant matched filter and the clairvoyant power detector. They are clairvoyant in that the locations of the impulses in the received data sample are assumed known. In the presence of impulses, both detectors use this knowledge for properly weighting these samples to reduce the effects of the impulses. Unfortunately, since it is never reasonable to assume that the impulse locations are known, these are unrealizable detectors; however, these clairvoyant detectors provide insight into the problem of detection in an impulsive environment when the nominal component is correlated and suggest detectors which are realizable. The results of this paper can be used as a theoretical justification of preprocessing the data to eliminate impulsive samples prior to detection.