Optimum nonlinearity and approximation in complex FastICA

This paper discusses the performance of complex blind source separation via the FastICA algorithm. In particular, we show that the optimum nonlinearity for the algorithm can be derived from the common source 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. For QAM signal separation where this assumption is not true, the optimum nonlinearity and its approximation derived will still perform well if a good amplitude PDF model is matched to the QAM source distribution.