The quaternion LMS algorithm for adaptive filtering of hypercomplex processes
IEEE Transactions on Signal Processing
IEEE Transactions on Neural Networks
Complex blind source extraction from noisy mixtures using second-order statistics
IEEE Transactions on Circuits and Systems Part I: Regular Papers
Complex independent component analysis by entropy bound minimization
IEEE Transactions on Circuits and Systems Part I: Regular Papers
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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.