Theoretical Foundations of Second-Order-Statistics-Based Blind Source Separation for Non-Stationary Sources

The aim of "blind source separation" is to recover mutually independent unknown source signals from observations obtained through an unknown linear mixture system. Simultaneous diagonalization of correlation matrices (second-order statistics) of observations is one of the resolutions, when the unknown source signals are non-stationary. Although it is trivial that the true separation matrix simultaneously diagonalizes all the correlation matrices, it is not well investigated whether a simultaneous diagonalizer of the correlation matrices is always a separation matrix. In this paper, we give explicit solutions of simultaneous diagonalizers of the correlation matrices and we also clarify the condition that the solutions always achieve the blind source separation