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Large System Analysis of a GLRT for Detection With Large Sensor Arrays in Temporally White Noise

This paper addresses the behavior of a classical multiantenna GLRT test that allows to detect the presence of a known signal corrupted by a multipath propagation channel and by an additive temporally white Gaussian noise with unknown spatial covariance matrix. The paper is focused on the case where the number of sensors M is large, and of the same order of magnitude as the sample size N, a context which is modeled by the large system asymptotic regime M → +∞, N → +∞ in such a way that M/N → c for c ∈ (0,+∞). The purpose of this paper is to study the behaviour of a GLRT statistics in this regime, and to show that the corresponding theoretical analysis allows to accurately predict the performance of the test when M and N are of the same order of magnitude.