ADAPTIVE REALIZATIONS OF OPTIMUM DETECTORS FOR SYNCHRONOUS AND SPORADIC RECURRENT SIGNALS IN NOISE

Abstract
The extension of the theory of signal detectability to include optimum signal processing of a recurrence phenomenon in noise is presented. This phenomenon is a fixed waveform, initially uncertain but learnable, that recurs randomly in time. The fixed waveform is uncertain in the sense that it is selected from a finite class of possible waveforms. Three basic types of recurrence time uncertainties are considered: (1) Sporadic-Poisson, (2) synchronous-Poisson, and (3) Periodic. The SporadicPoisson is the most uncertain and the Periodic the least uncertain time structure. Several realizations of the optimum receiver are presented for each of the three basic recurrence time uncertainties. In order to obtain a receiver design with a practical memory size, a basic technique is presented in which the signal ensemble is described indirectly in terms of the fixed waveform and the time structure. The receiver design is obtained by realizing the likelihood ratio in a sequential manner rather than by postulating a sequential learning model per se. The effect on detectability of the uncertainty in arrival times of the fixed waveform is investigated by evaluating the detection performance in terms of the receiver operating characteristic. The performance results show the substantial effects that uncertain arrival times can have on detectability.

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