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This paper addresses the problem of blind separation of convolutive mixturesof BPSK and circular linearly modulated signals with unknown (and possiblydifferent) baud rates and carrier frequencies. In previous works, weestablished that the Constant Modulus Algorithm (CMA) is able to extract asource from a convolutive mixture of circular linearly modulated signals. Weextend the analysis of the extraction capabilities of the CMA when the mixingalso contains BPSK signals. We prove that if the various source signals do notshare any non zero cyclic frequency nor any non conjugate cyclic frequencies,the local minima of the constant modulus cost function are separating filters.Unfortunately, the minimization of the Godard cost function generally failswhen considering BPSK signals that have the same rates and the same carrierfrequencies. This failure is due to the existence of non-separating localminima of the Godard cost function. In order to achieve the separation, wepropose a simple modification of the Godard cost function which only requiresknowledge of the BPSK sources frequency offsets at the receiver side. Weprovide various simulations of realistic digital communications scenarios thatsupport our theoretical statements.

Blind source separation of convolutive mixtures of non circular linearly modulated signals with unknown baud rates