Globally convergent blind source separation based on a multiuser kurtosis maximization criterion

We consider the problem of recovering blindly (i.e., without the use of tra ining sequences) a number of independent and identically distributed source (user) signals that are transmitted simultaneously through a linear instan taneous mixing channel. The received signals are, hence, corrupted by inter user interference (IUI), and we can model them as the outputs of a linear m ultiple-input-multiple-output (MIMO) memoryless system. Assuming the transm itted signals to be mutually independent, i.i.d., and to share the same non -Gaussian distribution, a set of necessary and sufficient conditions for th e perfect blind recovery (up to scalar phase ambiguities) of all the signal s exists and involves the kurtosis as well as the covariance of the output signals. We focus on a straightforward blind constrained criterion stemming from these conditions. From this criterion, we derive an adaptive algorith m for blind source separation, which we call the multiuser kurtosis (MUK) a lgorithm. At each iteration, the algorithm combines a stochastic gradient u pdate and a Gram-Schmidt orthogonalization procedure in order to satisfy th e criterion's whiteness constraints. A performance analysis of its stationa ry points reveals that the MUK algorithm is free of any stable undesired lo cal stationary points for any number of sources; hence, it is globally conv ergent to a setting that recovers them all.