On the optimality of detectors defined over the ambiguity plane

We study the detectors based on the ambiguity function. These detectors have been shown to be useful for the detection of linear frequency modulated (LFM) signals in the literature. We show that the detectors based on the projection of the cross-ambiguity surface are optimal for the detection of non-fluctuating targets in the Bayesian sense. The given optimality property strengthens the earlier results in the literature and enables us to compare different classes of detectors.