Blind source separation of non-stationary sources using second-order statistics

The question addressed in this paper is whether and under which conditions blind source separation is possible using only second-order statistics. It is well known that for stationary, i.i.d. sources the answer is negative due to the inherent unitary matrix ambiguity of the output second order information. It is shown however that if the sources' power is allowed to vary with time, unique identifiability is guaranteed without resorting to higher order statistics. In many applications the sources' power does change with time (e.g., speech or fading communication signals), and therefore the result has practical relevance. A novel second order source separation method is proposed based on a generalized eigenvalue decomposition of appropriate correlation matrices and the identifiability conditions are investigated. Asymptotic performance results for the output SIR are developed.