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 $M \rightarrow +\infty$ , $N \rightarrow +\infty$ in such a way that $M/N \rightarrow c$ for $c in (0,+\infty )$ . 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.