A Statistical Analysis of the Detection Performance of a Broadband Splitbeam Passive Sonar

An operational passive sonar is required to detect signals from sources, which are subject to spatial and temporal coherence losses via modifications by the ocean environment. Furthermore, these signals are to be detected in the presence of frequency-dependent correlated noise fields. For a system which employs splitbeam cross-correlation processing, the spatial and spectral properties of the signal and noise are of significant import. Therefore, the exact probability density and cumulative distribution functions of the N-sampled correlator outputs of a splitbeam broadband passive sonar are derived for the case of Gaussian inputs which are described by arbitrary cross-spectral density matrices. The validity of approximating the exact probability density function (pdf) as a Gaussian distribution is investigated. The effect of signal coherence loss and noise correlation on the detection performance is considered and the associated processing loss is expressed as a degradation factor within the detection threshold equation