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The complex fast independent component analysis (c-FastICA) algorithm is one of the most ubiquitous methods for solving the ICA problems with complex-valued data. In this study, we extend the work of Bingham and Hyvarinen to the more general case of noncircular sources by deriving a new fixed-point algorithm that uses the information in the pseudo-covariance matrix. This modification provides significant improvement in performance when confronted with noncircular sources, specifically with sub-Gaussian noncircular signals such as binary phase-shift keying (BPSK) signals, where c-FastICA fails to achieve separation. We also present a rigorous local stability analysis that we use to quantify the effects of noncircularity on performance. Simulations are presented to demonstrate the effectiveness of our method.
Novey et al. (Wed,) studied this question.