On the CFAR Property of GLRT-Based Direction Detectors

Direction detection is aimed at discriminating, over multiple “snapshots,” between a disturbance-only hypothesis and a useful-signal plus disturbance alternative with useful signals modeled in terms of a common (i.e., over different snapshots) direction of the signal subspace. We will show that generalized-likelihood ratio test (GLRT)-based direction detectors, designed assuming Gaussian noise with unknown covariance matrix plus deterministic interference, belonging to a preassigned subspace of the observables, possess the constant false alarm rate property with respect to the unknown covariance matrix of the noise.