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

This paper is devoted to the blind separation of convolutive mixtures of possibly non circular linearly modulated signals with unknown (and possibly different) baud rates and carrier frequencies. In this context, the received signal is sampled at any rate satisfying the Shannon sampling theorem. The corresponding discrete-time signal is cyclostationary with unknown cyclic frequencies. It is shown that if the various source signals do not share any cyclic frequency, the local minima of the constant modulus cost function are separating filters. In contrast with the circular sources case, the minimization of the Godard cost function in general fails if non circular sources have the same rates and the same carrier frequencies. It is shown that this is due to the existence of non separating local minima of the Godard cost function. If the frequency offsets of the sources are available at the receiver side, a simple modification of the Godard criterion is proposed. It achieves the separation of any non circular linearly modulated signals sources. The results of this paper show that the separation of unknown non circular linearly modulated signals is possible only if their frequency offsets can be blindly estimated prior to the separation scheme.