Comparing multivariate complex random signals: Performance analysis and application

We consider a recently proposed generalized likelihood ratio test (GLRT) for comparing two complex multivariate random signal realizations to ascertain whether they have identical power spectral densities. In this paper we analyze the performance of this GLRT by deriving an approximate asymptotic distribution of the test statistic under the alternative hypothesis. We also provide robustification of this approach by adding artificial white noise to the received noisy signals. The results are illustrated via computer simulations which include application to user authentication in wireless networks with multiantenna receivers.