The authors present a different view of the discrete-time detection problem in impulsive noise. The approach used is 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 can be used as a theoretical justification of preprocessing the data to eliminate impulsive samples prior to detection.
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