  This paper addresses the behaviour of a classical multi-antenna GLRT test
that allows to detect the presence of a known signal corrupted by a multi-path
propagation channel and by an additive 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 goes to
infinity, N goes to infinity in such a way that M/N goes to c for c in (0,
infinity). The purpose of this paper is to study the behaviour of a GLRT test
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.
