Probability of false alarm estimation in oversampled active sonar systems

The probability of false alarm (P_fa) in active sonar systems is an important system performance measure. This measure is typically estimated by the proportion of alarms to opportunities over some finite window, essentially forming the sample exceedance distribution function (EDF). It is common for sonar systems to be `over-sampled´; that is, to have a sampling rate higher than the minimum required for representing the bandwidth of the received signal, resulting in reverberation data that are correlated from sample to sample. The performance of the sample EDF in P_fa estimation under such conditions is of interest. It is easily shown that the estimator remains unbiased with correlated data. However, it is shown in this paper that the variance of the estimator may be reduced from that for independent data by oversampling. Further, the variance is seen to fall between the Cramer-Rao lower bound based on independent thresholded (binary) data and that based on the complex matched filter output data