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This paper presents the analytical derivation of joint probability density functions (pdfs) of the maximum likelihood (ML) estimates of a real and complex persymmetric correlation matrices (PCM) of multivariate Gaussian processes. It is oriented at the modifications of the classical Wishart’s–Goodman’s pdfs adapted to the ML estimates of the data CMs in a wide class of signal processing (SP) problems in systems with centrally symmetric (CS) receive channels. The importance of the derived modified pdfs for such CS systems could be as great as that of the classical Wishart’s–Goodman’s pdfs for systems with arbitrary receive channels. Some properties of the new obtained joint pdfs are featured.

To the theory of adaptive signal processing in systems with centrally symmetric receive channels