Performance Analysis of Adaptive Detectors for Point Targets in Subspace Interference and Gaussian Noise

Abstract

This paper investigates the statistical performance of three adaptive detectors in the presence of subspace interference and Gaussian noise. The interference is deterministic and lies in a known subspace but with unknown coordinates, while the noise is Gaussian distributed with unknown covariance matrix. For performance evaluation, we consider a more general case, namely, the case of subspace signal mismatch, where the actual signal does not completely lie in the presumed signal subspace. We derive the exact statistical distributions of the detectors, and then obtain analytical expressions for probabilities of detection and false alarm. The theoretical study reveals that the interference and signal mismatch affects the detection performance through two angles, which are the angle between the interference subspace and actual signal, and the angle between the actual signal and presumed signal subspace after they are both projected onto the interference-orthogonalized subspace. Numerical examples are provided to verify the theoretical results.