Abstract
In this work we consider a two-channel passive detection problem, in which there is a surveillance array where the presence/absence of a target signal is to be detected, and a reference array that provides a noise-contaminated version of the target signal. We assume that the transmitted signal is an unknown rank-one signal, and that the noises are uncorrelated between the two channels, but each one having an unknown and arbitrary spatial covariance matrix. We show that the generalized likelihood ratio test (GLRT) for this problem rejects the null hypothesis when the largest canonical correlation of the sample coherence matrix between the surveillance and the reference channels exceeds a threshold. Further, based on recent results from random matrix theory, we provide an approximation for the null distribution of the test statistic.
Highlights
In this work we consider a passive detection problem in which there is a surveillance channel where the presence/absence of a target signal is to be detected, and a reference channel that provides a noise-contaminated version of the target signal, and assists the surveillance channel in the detection process
We address the passive detection problem in a multivariate normal model when the surveillance and reference channels are equipped with M antennas, the transmitted signal is an unknown rank-one signal, and the noises at surveillance and reference channels are uncorrelated between them, but each having an unknown and arbitrary spatial covariance matrix
We show that the generalized likelihood ratio test (GLRT) for our problem rejects the null hypothesis when the largest canonical correlation of the sample coherence matrix between the surveillance and the reference channels exceeds a threshold
Summary
In this work we consider a passive detection problem in which there is a surveillance channel where the presence/absence of a target signal is to be detected, and a reference channel that provides a noise-contaminated version of the target signal, and assists the surveillance channel in the detection process. We address the passive detection problem in a multivariate normal model when the surveillance and reference channels are equipped with M antennas, the transmitted signal is an unknown rank-one signal, and the noises at surveillance and reference channels are uncorrelated between them, but each having an unknown and arbitrary spatial covariance matrix. This a problem of testing the covariance structure in a two-channel multivariate normal model. We provide an approximation for the null distribution that allows us to set the threshold for a given probability of false alarm
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