Blind identification of underdetermined mixtures of complex sources based on the characteristic function

In this work we consider the problem of blind identification of underdetermined mixtures using the generating function of the observations. This approach has been successfully applied on real sources but had not been extended to the more attractive case of complex mixtures of complex sources. This is the main goal of the present study. By developing the core equation in the complex case, we arrive at a particular tensor stowage which involves an original tensor decomposition. Exploiting this decomposition, an algorithm is proposed to blindly estimate the mixing matrix. Three versions of this algorithm based on 2nd, 3rd and 4th-order derivatives of the generating function are evaluated on complex mixtures of 4-QAM and 8-PSK sources and compared to the 6-BIOME algorithm by means of simulation results.