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On Testing for Impropriety of Multivariate Complex-Valued Random Sequences

We consider the problem of testing whether a complex-valued vector random sequence is proper, i.e., if the sequence is uncorrelated with its complex conjugate. Previous nonparametric approaches to impropriety testing are limited to a sequence of independent random vectors, typically assumed to be Gaussian. In this paper, we extend the results to stationary vector sequences that can be non Gaussian. A binary hypothesis testing approach is formulated and a generalized likelihood ratio test (GLRT) is derived using the power spectral density estimator of an augmented sequence. An asymptotic analytical solution for calculating the test threshold is provided. The performance of the GLRT is analyzed by deriving an approximate asymptotic distribution of the GLRT statistic under the alternative hypothesis. The results are illustrated via simulations.