GLRT-Based Direction Detectors in Homogeneous Noise and Subspace Interference

Abstract—In this paper, we derive and assess decision schemes to discriminate, resorting to an array of sensors, between the 0 hypothesis that data under test contain disturbance only (i.e., noise plus interference) and the 1 hypothesis that they also contain signal components along a direction which is a priori unknown but constrained to belong to a given subspace of the observables. The disturbance is modeled in terms of complex normal random vectors plus deterministic interference assumed to belong to a known subspace. We assume that a set of noise-only (secondary) data is available, which possess the same statistical characteriza-tion of noise in the cells under test. At the design stage, we resort to either the plain generalized-likelihood ratio test (GLRT) or the two-step GLRT-based design procedure. The performance analysis, conducted resorting to simulated data, shows that the one-step GLRT performs better than the detector relying on the two-step design procedure when the number of secondary data is comparable to the number of sensors; moreover, it outperforms a one-step GLRT-based subspace detector when the dimension of the signal subspace is sufficiently high. Index Terms—Adaptive detection, direction detection, dis-tributed targets, generalized likelihood ratio test, interference rejection. I