Separation of digital communication mixtures with the CMA: Case of unknown symbol rates

The Constant Modulus Algorithm (CMA) is very popular as far as the extraction of a source from a convolutive mixture is concerned. Though originally designed for stationary data, we have noticed in simulations the ability of the CMA to achieve the separation even in non-stationary contexts such as mixtures of linearly modulated communication signals having arbitrary symbol periods. In this paper, we address the theoretical aspect of this point. We provide sufficient conditions on the statistics of the sources under which the use of the CMA is theoretically justified. This condition is semi-analytically worked out in different scenarios of digital communications.