On the probability density of signal-to-noise ratio in an improved adaptive detector

The main advantage of our previously presented [10] principal-component method of adaptive detection, in comparison with the method based on the inverse of the estimated covariance matrix, is that much less data is required to produce a given, needed level of SNR with high probability. In this paper we present an outline of the derivation of the approximate probability density of the SNR for this adaptive detector. To simplify the derivation we assume that the noise consists of a strong gaussian rank-one-covariance interference component plus a component of white gaussian background noise. The approximations and the final probability density are tested through simulation.