The use of spectral information in optimal detection of a source in the presence of a directional interference

The detection of a passive sonar target in the presence of ambient noise and a plane wave interference is discussed. Intuitively, such a detector consists of a spatial filter which nulls the interference, followed by a temporal filter. In this paper we study the role of the a priori knowledge of the spectrum of the interference and/or signal in improving detector performance. We develop three different generalized likelihood ratio test (GLRT) detectors, resulting from different cases of prior spectral information. We show that, for all cases of known/unknown source and/or interference power spectrum, the GLRT detectors are, as expected, null steering systems. The depth and shape of the null, as well as the postbeamforming temporal filter, are different and are functions of the a priori known spectrum. Under the assumption that all signals and noise are zero-mean Gaussian processes, we analyze the performance of the different detectors and we exploit their dependency on the array beampattern, as well as on the source and interference signal-to-noise ratio. This analysis serves to identify scenarios where the use of prior spectral information leads to significant performance improvement