Statistical aspects concerning signal coherence applied to randomly modulated periodic signals

The signal coherence (SC) function was developed for detecting signals that exhibit an inherent nondeterminism in their genesis. To allow the use of this technique as an objective response detector, the necessary statistical apparatus is developed in this letter. It is shown that SC is, in fact, a deterministic transformation of the magnitude-squared coherence (MSC) function, whose sampling distribution has been recently derived, between a random signal and a deterministic signal. As a result, it is demonstrated that both SC and MSC exhibit virtually identical performances in the detection of randomly modulated signals.