On comparing multivariate complex random signals

We consider the problem of comparing two complex multivariate random signal realizations to ascertain whether they have identical power spectral densities. A binary hypothesis testing approach is formulated and a generalized likelihood ratio test (GLRT) is derived. An asymptotic analytical solution for calculating the test threshold is provided. The results are illustrated via computer simulations. Past work on this problem is limited to either scalar signals or real-valued multivariate signals. The proposed test has potential applications in diverse areas including user authentication in wireless networks with multiantenna receivers and spectrum sensing in cognitive radio networks with multiantenna receivers.