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Receiver operating characteristics (ROC's) for the classic problem of detecting the presence or absence of one of M orthogonal signals is presented. Previous results were valid for low detectability, for which the ROC is approximately normal (i.e., appears as a straight line with unit slope on normal normal probability paper) and the detectability depends on the logarithm of the number of possible signals M. For high detectability, however, the ROC departs from normality. In addition, the rate at which detectability decreases as M increases is more rapid than that predicted by the classical approximation.
Nolte et al. (Wed,) studied this question.