Multi-source Signal Detection With Arbitrary Noise Covariance

Detecting the presence of signals in noise from multiple sources is a fundamental problem in statistical signal processing. In this paper, we consider multi-antenna signal detection when the noise covariance matrix is assumed to be arbitrary and unknown. We address this problem in the context of cognitive radio, where a multiple-primary-user detector is analyzed. This detector is known as Wilks' detector in statistics literature, which was derived under the generalized likelihood ratio criterion. We calculate the moments of Wilks' detector, which lead to simple and accurate approximate analytical formulae for the false alarm probability, the detection probability and the receiver operating characteristic. From the considered simulation settings, performance gain over existing detection algorithms is observed in scenarios with arbitrary and unknown noise correlation and multiple primary users.