Detection performance of Roy´s largest root test when the noise covariance matrix is arbitrary

Detecting the presence of a signal embedded in noise from a multi-sensor system is a fundamental problem in signal and array processing. In this paper we consider the case where the noise covariance matrix is arbitrary and unknown but we are given both signal bearing and noise-only samples. Using a matrix perturbation approach, combined with known results on the eigenvalues of inverse Wishart matrices, we study the behavior of the largest eigenvalue of the relevant covariance matrix, and derive an approximate expression for the detection probability of Roy´s largest root test. The accuracy of our expressions is confirmed by simulations.