Canonical correlations for target detection in a passive radar network

Abstract

In this work, we consider a two-channel multiple-input multiple-output (MIMO) passive detection problem, in which there is a surveillance array and a reference array. The reference array is known to carry a linear combination of broadband noise and a subspace signal of known dimension but unknown basis. The question is whether the surveillance channel carries a linear combination of broadband noise and a subspace signal of unknown basis, which is correlated with the subspace signal in the reference channel. We consider a second-order detection problem where these subspace signals are structured by an unknown, but common, p-dimensional random vector of symbols transmitted from sources of opportunity, and then received through unknown M × p matrices at each of the M-element arrays. The noises in each channel have arbitrary spatial correlation. We derive the generalized likelihood ratio test (GLRT) statistic and show it is a monotone function of canonical correlations between the reference and surveillance channels.