Adaptive Detector Performance Given Clutter Covariance Matrix in Subspace Orthogonal to Signal

In this article, analytical results are derived for the probability of a false alarm and the probability of detection when information about the clutter-plus-noise covariance matrix in the subspace orthogonal to the signal space is given. Such information enables the prewhitening of multiple clutter-plus-noise random variables in the orthogonal channels. For multivariate complex Gaussian clutter models, the prewhitening makes these random variables statistically independent, and as such, it is only the cross-correlation information between each of the orthogonal clutter-plus-noise channels and the clutter-plus-noise in the signal channel that needs to be estimated from appropriately transformed training data for purposes of clutter suppression. Because of the finite amount of clutter-plus-noise training data, a loss in signal-to-clutter-plus-noise ratio (SCNR) is involved. An approach for estimating the probability density function of the SCNR loss factor is derived. This is used to derive analytical expressions for the probability of a false alarm and the probability of detection for a detector that has knowledge of the clutter-plus-noise covariance submatrix. Performance results are compared with those of the clairvoyant detector. Analytical expressions for the two cases are shown to be similar in form except that one has to take into account the effect of the SCNR loss factor in the detector that has partial clutter-plus-noise covariance matrix information.