Abstract

Detection of a known signal in presence of noise is a common requirement in many applications including sonar, ranging, environmental sensing and communications. The optimal detection of signals in noise requires detailed knowledge of the noise statistics. The linear correlator, commonly used in the form of a matched filter, is known to be optimal in the presence of Gaussian noise. However, the performance of the linear correlator is poor in warm shallow waters where snapping shrimp dominate acoustic noise in the range 2-300 kHz. Since snapping shrimp noise consists of a large number of individual transients, its statistics are highly non-Gaussian. In this paper, we show that the ambient noise statistics can be described accurately by the symmetric alpha-stable family of probability distributions. The knowledge of the probability distribution allows us to design maximum-likelihood and locally optimal detectors, which perform well in such noise. Surprisingly, we found that a simple non-parametric sign correlation detector also performs well in presence of snapping shrimp noise. Although the performance of the sign correlator is slightly inferior to that of the maximum-likelihood detector, it is very simple to implement and does not require detailed knowledge of the noise statistics. This makes it an attractive detector for use in warm shallow waters.