Complex blind source separation: optimal nonlinearity and approximation

Abstract

This paper discusses the performance of complex blind source separation via the EASI algorithm. In particular, we show that the optimum amplitude nonlinearity used in the algorithm can be derived from the sources' distribution. In addition, this nonlinearity can be further approximated by a piecewise constant quantizer to reduce the complexity of the system. These results are obtained with an approach based on the magnitude-phase representation of complex signals and a circularly symmetric source PDF assumption. However, in the QAM signal separation case where this assumption is not true, the optimum nonlinearity and its approximation derived will still deliver good performances if a good amplitude PDF model is matched to the QAM source distribution.