On Extending the Complex FastICA Algorithm to Noncircular Sources

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.

[1]  Terrence J. Sejnowski,et al.  COMPLEX SPECTRAL-DOMAIN INDEPENDENT COMPONENT ANALYSIS OF ELECTROENCEPHALOGRAPHIC DATA , 2003 .

[2]  Visa Koivunen,et al.  Complex random vectors and ICA models: identifiability, uniqueness, and separability , 2005, IEEE Transactions on Information Theory.

[3]  J. Cardoso,et al.  Blind beamforming for non-gaussian signals , 1993 .

[4]  Jan Larsen,et al.  Independent component analysis for clutter reduction in ground penetrating radar data , 2002, SPIE Defense + Commercial Sensing.

[5]  Moon Ho Lee,et al.  Fast Block Jacket Transform Based on Pauli Matrices , 2007, 2007 IEEE International Conference on Communications.

[6]  Bernard C. Picinbono,et al.  On circularity , 1994, IEEE Trans. Signal Process..

[7]  Andrzej Cichocki,et al.  A New Learning Algorithm for Blind Signal Separation , 1995, NIPS.

[8]  K. R. Rao,et al.  Orthogonal Transforms for Digital Signal Processing , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[9]  Aapo Hyvärinen,et al.  A Fast Fixed-Point Algorithm for Independent Component Analysis of Complex Valued Signals , 2000, Int. J. Neural Syst..

[10]  Charles R. Johnson,et al.  Topics in Matrix Analysis , 1991 .

[11]  V. Koivunen,et al.  Ieee Workshop on Machine Learning for Signal Processing Complex-valued Ica Using Second , 2022 .

[12]  T. Adali,et al.  Unmixing fMRI with independent component analysis , 2006, IEEE Engineering in Medicine and Biology Magazine.

[13]  Yi Xian Yang,et al.  Theory and Applications of Higher-Dimensional Hadamard Matrices , 2002 .

[14]  Jennifer Seberry,et al.  Orthogonal Designs: Quadratic Forms and Hadamard Matrices , 1979 .

[15]  Moon Ho Lee.  The center weighted Hadamard transform , 1989 .

[16]  A. Bos.  Complex gradient and Hessian , 1994 .

[17]  Mark E. Johnson.  C51. Computer generation of the exponential power distribution , 1979 .

[18]  Scott C. Douglas,et al.  Fixed-Point Complex ICA Algorithms for the Blind Separation of Sources Using Their Real or Imaginary Components , 2006, ICA.

[19]  Moon Ho Lee,et al.  Cocyclic Jacket Matrices and Its Application to Cryptography Systems , 2005, ICOIN.

[20]  Hualiang Li,et al.  Gradient and Fixed-Point Complex ICA Algorithms Based on Kurtosis Maximization , 2006, 2006 16th IEEE Signal Processing Society Workshop on Machine Learning for Signal Processing.

[21]  Scott C. Douglas,et al.  Fixed-Point Algorithms for the Blind Separation of Arbitrary Complex-Valued Non-Gaussian Signal Mixtures , 2007, EURASIP J. Adv. Signal Process..

[22]  B. A. D. H. Brandwood.  A complex gradient operator and its applica-tion in adaptive array theory , 1983 .

[23]  W. Wirtinger.  Zur formalen Theorie der Funktionen von mehr komplexen Veränderlichen , 1927 .

[24]  T. Adalı,et al.  ICA by Maximization of Nongaussianity using Complex Functions , 2005, 2005 IEEE Workshop on Machine Learning for Signal Processing.

[25]  Tapani Ristaniemi,et al.  Suppression of bit-pulsed jammer signals in DS-CDMA array system using independent component analysis , 2002, 2002 IEEE International Symposium on Circuits and Systems. Proceedings (Cat. No.02CH37353).

[26]  S. Wicker.  Error Control Systems for Digital Communication and Storage , 1994 .