Analytical minimization of cross cumulant for stationary and non-stationary sources recovery

Abstract

This paper solves the problem of blind separation of the instantaneous linear mixture of statistically independent sources for the noisy and noiseless cases. The proposed solution is performed by an analytical determination of a set of adequate rotating angles which transform the uncorrelated signals into statistically independent signals. In the case of (2 × 2), the proposed solution is based on a single fourth-order cross cumulant by which we determine the parameters that constitute a sinusoidal objective function that leads to the appropriate rotating angle. For the case of (n × n) we can easily reach the global separation by a simple generalization of the case (2 × 2) and the obtained results from several simulations prove the efficiency and the reliability of the proposed algorithm to achieve the statistical independence whatever the type of signals (stationary or non-stationary).