A Multi-User Kurtosis Algorithm for Blind Source Separation

In earlier work we had presented a set of necessary and sufficient conditions for the blind separation of a number of independent identically distributed (i.i.d.) source signals that share the same distribution and are mutually independent. In this paper we present an algorithm for implementing the Multi-User Kurtosis (MUK) constrained optimization criterion suggested by these conditions. The algorithm is derived directly from the MUK cost function via a stochastic-gradient update at each iteration, followed by a Gram-Schmidt orthogonalization to project onto the criterion's constraint. A convergence analysis of the derived algorithm reveals that it is globally convergent (in the absence of noise) to a desired setting that recovers all the input sources, up to an arbitrary phase rotation each.