Some Properties of Adaptive Neyman-Pearson Detectors.

Several upper bounds have recently been derived by the present authors, and others, for the improvement in performance achievable by an optimum adaptive receiver with respect to a receiver which, although optimum for its state of a priori information, is not adaptive to other states of prior information. This earlier work has been characterized by the general Bayesian approach to the detection problem, i.e. the criterion of optimality chosen has been to minimize the total average cost of incorrect decisions. The present paper considers the important special case of Neyman-Pearson detectors where the probability of false alarm is constrained to a pre-assigned value. Several interesting properties of these detectors are derived. In particular, it is shown that, in the presence of gaussian noise, amplitude adaptivity yields no advantage, whereas adaptivity with respect to other signal parameters generally results in a lower error probability, or conversely, in a higher probability of correct detection. As an illustrative application of the theory, the improvement in performance obtained by measuring the phase of a signal transmitted through a Rayleigh-fading channel is evaluated in detail. [ABSTRACT FROM AUTHOR]