Gradient Adaptive Paraunitary Filter Banks for Spatio-Temporal Subspace Analysis and Multichannel Blind Deconvolution

Paraunitary filter banks are important for several signal processing tasks, including coding, multichannel deconvolution and equalization, adaptive beamforming, and subspace processing. In this paper, we consider the task of adapting the impulse response of a multichannel paraunitary filter bank via gradient ascent or descent on a chosen cost function. Our methods are spatio-temporal generalizations of gradient techniques on the Grassmann and Stiefel manifolds, and we prove that they inherently maintain the paraunitariness of the multichannel adaptive system over time. We then discuss the necessary practical approximations, modifications, and simplifications of the methods for solving two relevant signal processing tasks: (i) spatio-temporal subspace analysis and (ii) multichannel blind deconvolution. Simulations indicate that our methods can provide simple, useful solutions to these important problems.

[1]  Andrzej Cichocki,et al.  Relationships between instantaneous blind source separation and multichannel blind deconvolution , 1998, 1998 IEEE International Joint Conference on Neural Networks Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36227).

[2]  J. G. Kenney,et al.  Allpass forward equalizer for decision feedback equalization , 1995 .

[3]  R. Lambert.  Multichannel blind deconvolution: FIR matrix algebra and separation of multipath mixtures , 1996 .

[4]  S. Amari,et al.  A self-stabilized minor subspace rule , 1998, IEEE Signal Processing Letters.

[5]  S.C. Douglas,et al.  Multichannel blind deconvolution and equalization using the natural gradient , 1997, First IEEE Signal Processing Workshop on Signal Processing Advances in Wireless Communications.

[6]  Benjamin Friedlander,et al.  Estimation of spatial and spectral parameters of multiple sources , 1983, IEEE Trans. Inf. Theory.

[7]  Jr. Earl E. Swartzlander,et al.  VLSI Signal Processing Systems , 1985 .

[8]  Sun-Yuan Kung,et al.  Principal Component Neural Networks: Theory and Applications , 1996 .

[9]  Kari Torkkola,et al.  Blind separation of convolved sources based on information maximization , 1996, Neural Networks for Signal Processing VI. Proceedings of the 1996 IEEE Signal Processing Society Workshop.

[10]  Phillip A. Regalia,et al.  Attainable error bounds in multirate adaptive lossless FIR filters , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[11]  Pierre Comon,et al.  Independent component analysis, A new concept? , 1994, Signal Process..

[12]  Nathalie Delfosse,et al.  Adaptive blind separation of independent sources: A deflation approach , 1995, Signal Process..

[13]  S.C. Douglas,et al.  On the relationship between blind deconvolution and blind source separation , 1997, Conference Record of the Thirty-First Asilomar Conference on Signals, Systems and Computers (Cat. No.97CB36136).

[14]  A. Gorokhov,et al.  Equivariant blind deconvolution of MIMO-FIR channels , 1997, First IEEE Signal Processing Workshop on Signal Processing Advances in Wireless Communications.

[15]  D. Fuhrmann.  A geometric approach to subspace tracking , 1997, Conference Record of the Thirty-First Asilomar Conference on Signals, Systems and Computers (Cat. No.97CB36136).

[16]  B. Widrow,et al.  Adaptive inverse control , 1987, Proceedings of 8th IEEE International Symposium on Intelligent Control.

[17]  Björn E. Ottersten,et al.  Direction-of-arrival estimation for wide-band signals using the ESPRIT algorithm , 1990, IEEE Trans. Acoust. Speech Signal Process..

[18]  Qin Lin,et al.  A unified algorithm for principal and minor components extraction , 1998, Neural Networks.

[19]  P. Comon,et al.  Contrasts for multichannel blind deconvolution , 1996, IEEE Signal Processing Letters.

[20]  U. Helmke,et al.  Optimization and Dynamical Systems , 1994, Proceedings of the IEEE.

[21]  Sun-Yuan Kung,et al.  On gradient adaptation with unit-norm constraints , 2000, IEEE Trans. Signal Process..

[22]  Georgios B. Giannakis,et al.  Principal component filter banks for optimal multiresolution analysis , 1995, IEEE Trans. Signal Process..

[23]  Sun-Yuan Kung,et al.  Gradient Adaptive Algorithms for Contrast-Based Blind Deconvolution , 2000, J. VLSI Signal Process..

[24]  Shun-ichi Amari,et al.  Novel On-Line Adaptive Learning Algorithms for Blind Deconvolution Using the Natural Gradient Approach , 1997 .

[25]  B. Farhang-Boroujeny,et al.  Adaptive phase equalization using all-pass filters , 1991, ICC 91 International Conference on Communications Conference Record.

[26]  A. Benveniste,et al.  Robust identification of a nonminimum phase system: Blind adjustment of a linear equalizer in data communications , 1980 .

[27]  Sun-Yuan Kung,et al.  Extraction of independent components from hybrid mixture: KuicNet learning algorithm and applications , 1998, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).

[28]  J. Pesquet,et al.  Generalized contrasts for multichannel blind deconvolution of linear systems , 1997, IEEE Signal Processing Letters.

[29]  Scott C. Douglas,et al.  Self-stabilized gradient algorithms for blind source separation with orthogonality constraints , 2000, IEEE Trans. Neural Networks Learn. Syst..

[30]  Minyue Fu,et al.  A fast O(N) algorithm for adaptive filter bank design , 1998, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).

[31]  Shun-ichi Amari,et al.  Natural Gradient Works Efficiently in Learning , 1998, Neural Computation.

[32]  Sun-Yuan Kung,et al.  Multimedia Image and Video Processing , 2000 .

[33]  E. Stiefel.  Richtungsfelder und Fernparallelismus in n-dimensionalen Mannigfaltigkeiten , 1935 .

[34]  Teng Joon Lim,et al.  Adaptive allpass filtering for nonminimum-phase system identification , 1994 .

[35]  Pierre Moulin,et al.  Theory and design of signal-adapted FIR paraunitary filter banks , 1998, IEEE Trans. Signal Process..

[36]  Philippe Loubaton,et al.  Rational subspace estimation using adaptive lossless filters , 1992, IEEE Trans. Signal Process..

[37]  Robert Bregovic,et al.  Multirate Systems and Filter Banks , 2002 .

[38]  P. P. Vaidyanathan,et al.  Theory and design of optimum FIR compaction filters , 1998, IEEE Trans. Signal Process..

[39]  Andrzej Cichocki,et al.  Self-whitening algorithms for adaptive equalization and deconvolution , 1999, IEEE Trans. Signal Process..

[40]  Alan Edelman,et al.  The Geometry of Algorithms with Orthogonality Constraints , 1998, SIAM J. Matrix Anal. Appl..

[41]  Andrzej Cichocki,et al.  Neural networks for blind decorrelation of signals , 1997, IEEE Trans. Signal Process..

[42]  Russell H. Lambert,et al.  Blind separation of multiple speakers in a multipath environment , 1997, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[43]  S. Amari,et al.  Quasi-Newton filtered-error and filtered-regressor algorithms for adaptive equalization and deconvolution , 1997, First IEEE Signal Processing Workshop on Signal Processing Advances in Wireless Communications.

[44]  E. Oja,et al.  On stochastic approximation of the eigenvectors and eigenvalues of the expectation of a random matrix , 1985 .

[45]  Dirk T. M. Slock,et al.  Blind fractionally-spaced equalization, perfect-reconstruction filter banks and multichannel linear prediction , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.

[46]  Lei Xu,et al.  Least mean square error reconstruction principle for self-organizing neural-nets , 1993, Neural Networks.

[47]  Roberto H. Bamberger,et al.  FIR principal component filter banks , 1998, IEEE Trans. Signal Process..

[48]  S. Amari,et al.  Fast-convergence filtered regressor algorithms for blind equalisation , 1996 .

[49]  Eduardo Abreu,et al.  Nonminimum phase channel equalization using noncausal filters , 1997, IEEE Trans. Signal Process..