Abstract

The optimal detection of signals requires detailed knowledge of the noise statistics. In many applications, the assumption of Gaussian noise allows the use of the linear correlator (LC), which is known to be optimal in these circumstances. However, the performance of the LC is poor in warm shallow waters where snapping shrimp noise dominates in the range 2-300 kHz. Since snapping shrimp noise consists of a large number of individual transients, its statistics are highly non-Gaussian. We show that the noise statistics can be described accurately by the symmetric-alpha-stable family of probability distributions. Maximum-likelihood (ML) and locally optimal detectors based on the detailed knowledge of the noise probability distribution are shown to demonstrate enhanced performance. We also establish that the sign correlator, which is a nonparametric detector, performs better than the LC in snapping shrimp noise. Although the performance of the sign correlator is slightly inferior to that of the ML detector, it is very simple to implement and does not require detailed knowledge of the noise statistics. This makes it an attractive compromise between the simple LC and the complex ML detector.