Robust Spectrum-Based Comparison of Multivariate Complex Random Signals

Abstract

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 the estimated power spectral density matrices, has been proposed in the literature, and it results in a generalized likelihood ratio test (GLRT). In this paper, we first present an alternative, principled derivation of the existing GLRT using the asymptotic distribution of a frequency-domain sufficient statistic, based on the discrete Fourier transform of the two signal realizations. In order to robustify this GLRT in the presence of additive outliers, we first 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 through simulations. The considered problem has applications in diverse areas, including user authentication in wireless networks with multi-antenna receivers.