Conditional GLRT detection of a wideband source in the presence of a directional interference

In this paper we present results concerning passive detection of a source in the presence of a directional interference as well as a spatially white ambient noise. Under the assumption that the power spectral density of the signal and/or interference is unknown, different likelihood ratio test (LRT) or generalized LRT (GLRT) detectors result from different statistical models of the interference and/or desired source signals. We derive the conditional GLRT processor (which uses the probability density function of the received signal, conditioned on the signal(s) of unknown spectrum, in the LRT) and we show that for all cases of known/unknown source and/or interference power spectrum, it is basically a null steering system. The depth and the shape of the null as well as the post-beamforming temporal filter are affected by the assumed model. We present expressions for performance indices of the different detectors and we exploit their dependency on the array beam pattern, as well as on the source and interference signal-to-noise ratio.