ADAPTIVE OPTIMUM DETECTION - SYNCHRONOUS-RECURRENT TRANSIENTS

Adaptive optimum†detection theory is applied to the problem of detecting a recurrence phenomenon in noise. This phenomenon consists of one of a finite number of possible transient waveforms whose temporal uncertainty is synchronous Poisson. The optimum (likelihood ratio) receiver is designed from the viewpoint of obtaining a receiver implementation with a practical memory size while at the same time maintaining optimum†detection performance. The optimum detector for the synchronous†Poisson case recirculates and averages a nonlinear function of the input data in contrast to the optimum detector for the periodic case that recirculates and averages the input data itself. The detection performance is evaluated, and the receiver operating characteristics (ROC) are presented as a function of average duty factor Ȋ½, number of synchronous intervals k, transient waveform energy Ec, and the noise power per unit bandwidth N 0. At low transient signal†to†noise ratios and low average duty factors, the detectability d is given approximately by Ȋ½2 k (2Ec /N0). The effect of transient uncertainty on detectability is also presented on the ROC. © 1968, Acoustical Society of America. All rights reserved.