An iterative algorithm using second order moments applied to blind separation of sources with same spectral densities

In this paper, we are interested in the separation of N independent sources recorded simultaneously by N receivers. The mixture is realized instantaneously through an unknown constant matrix M. When the spectral densities of the sources are different, several methods using second order moments have been proposed whose results are convincing. Nevertheless, these methods are no more efficient when their spectral densities are the same. Our talk is interested in this special case where sources may even be white. The method we propose is based on the evaluation of second order moments estimated from extracted series of the observations. We will talk of conditional second order moments. An iterative algorithm is proposed which calculates, at each step, a matrix K-i so that KnKn-1...K1M tends, when n increases, to DIT, product of a diagonal matrix and a permutation matrix. We show that restrictive conditions on the probability distributions of the sources must be verified to assure the separation. In the two-dimensional case, we prove that the algorithm separates uniformly distributed sources, and that it doesn't separate gaussian sources. The algorithm proposed is robust towards the number of sources; simulations with more than 20 uniformly distributed sources were successful.