^Resultsjonjhe Detection of Signals in Spherically Invariant Random Noise

A relationship between well-known estimator-correlator results from detection theory and the detection of signals in spherically invariant random noise is described. This relationship gives a general result concerning the structure of the likelihood ratio for this detection problem. Furthermore, an alternate formulation of both the likelihood ratio and the optimal estimator that arises in the estimator-correlator structure is given. This alternate formulation is important because it yields a closed-form solution for this optimal estimator without requiring explicit knowledge of a prior distribution for the unknown quantity being estimated. Since interest in modeling actual noise processes as spherically invariant random processes has recently appeared, the results here should help not only to give insight into the optimal detection structure in such noise but also to give guidance in formulating suboptimal detectors for problems of practical interest.