We consider the problem of comparing two complex multivariate random signal realizations, possibly contaminated with additive outliers, to ascertain whether they have identical power spectral densities. For clean data (i.e., known to be outlier free), a binary hypothesis testing formulation in frequency-domain, utilizing estimated power spectral density (PSD) matrices, has been proposed in the literature, and it results in a generalized likelihood ratio test (GLRT). In this paper we exploit an existing robust estimator of multivariate scatter to detect the outliers, and subsequently to clean the data. The existing GLRT is then applied to the cleaned signal realizations. The approach is illustrated via simulations. The considered problem has applications in diverse areas including user authentication in wireless networks with multiantenna receivers.
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