Blind identification of under-determined complex mixtures of independent sources

This paper is devoted to under-determined linear mixtures of independent random variables (i.e. with more inputs than outputs). Blind identifiability of general under-determined mixtures is first discussed, and the maximum number of sources is given, depending on the hypotheses assumed. Then an algorithm proposed by Taleb, essentially usable for 2-dimensional mixtures, is extended to the complex field. A procedure is proposed in order to avoid the enormous increase in complexity. Computer simulations demonstrate the ability of the algorithm to identify mixtures of N QPSK sources received on 1 or 2 sensors.