The quaternion LMS algorithm for adaptive filtering of hypercomplex processes
IEEE Transactions on Signal Processing
Adaptive IIR filtering of noncircular complex signals
IEEE Transactions on Signal Processing
Complex-valued neural networks: the merits and their origins
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
IEEE Transactions on Neural Networks
Complex independent component analysis by entropy bound minimization
IEEE Transactions on Circuits and Systems Part I: Regular Papers
Recent progress in applications of complex-valued neural networks
ICAISC'10 Proceedings of the 10th international conference on Artifical intelligence and soft computing: Part II
Constrained complex-valued ICA without permutation ambiguity based on negentropy maximization
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
Journal of Signal Processing Systems
A two-stage Independent Component Analysis-based method for blind detection in CDMA systems
Digital Signal Processing
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In this paper, we use complex analytic functions to achieve independent component analysis (ICA) by maximization of non-Gaussianity and introduce the complex maximization of non-Gaussianity (CMN) algorithm. We derive both a gradient-descent and a quasi-Newton algorithm that use the full second-order statistics providing superior performance with circular and noncircular sources as compared to existing methods. We show the connection among ICA methods through maximization of non-Gaussianity, mutual information, and maximum likelihood (ML) for the complex case, and emphasize the importance of density matching for all three cases. Local stability conditions are derived for the CMN cost function that explicitly show the effects of noncircularity on convergence and demonstrated through simulation examples.