This paper addresses the behaviour of a classical multi-antenna GLR test that allows to detect the presence of a known signal corrupted by a multipath propagation channel when the number of sensors M , the sample size N , and the number of paths L are large and of the same order of magnitude. In the asymptotic regime where M, N and L converge towards ∞ at the same rate, the test statistics is shown to be asymptotically Gaussian under each hypothesis. The results of this paper extend previous contributions of the authors that addressed the case where the number of paths L is much smaller than M and N , and used these results in order to propose a pragmatic Gaussian approximation of the test statistics when L is large. Simulation results indicate that the proposed Gaussian approximation of the test statistics is more reliable than the above mentioned pragmatic approximation .