Testing for Impropriety of Multivariate Complex Random Processes

Abstract

We consider the problem of testing whether a complex-valued vector random sequence is proper. Past work on this problem is limited to a sequence of independent Gaussian random vectors whereas we allow an arbitrary stationary vector sequence 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 results are illustrated via simulations.