Abstract
A mathematical model that leads to singular detection (i.e., detection with arbitrarily low probability of error) is usually a poor model of the physical problem. However, in general, it has been difficult to establish the possibility of singular detection without a detailed evaluation of the probability of error. Such an evaluation is difficult because it requires the solution of various integral equations, the computation of eigenvalues, etc. In this paper some simple methods are given for predicting the possibility of singular detection of known signals in additive gaussian noise. Such methods are useful in the formulation of suitable mathematical models.
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