Multichannel blind deconvolution and equalization using the natural gradient

Multichannel deconvolution and equalization is an important task for numerous applications in communications, signal processing, and control. We extend the efficient natural gradient search method of Amari, Cichocki and Yang (see Advances in Neural Information Processing Systems, p.752-63, 1995) to derive a set of on-line algorithms for combined multichannel blind source separation and time-domain deconvolution/equalization of additive, convolved signal mixtures. We prove that the doubly-infinite multichannel equalizer based on the maximum entropy cost function with natural gradient possesses the so-called "equivariance property" such that its asymptotic performance depends on the normalized stochastic distribution of the source signals and not on the characteristics of the unknown channel. Simulations indicate the ability of the algorithm to perform efficient simultaneous multichannel signal deconvolution and source separation.

[1]  P. Kumar,et al.  Theory and practice of recursive identification , 1985, IEEE Transactions on Automatic Control.

[2]  Chrysostomos L. Nikias,et al.  A new eigenvector-based algorithm for multichannel blind deconvolution of input colored signals , 1993, 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[3]  Zhi Ding,et al.  Local convergence of the Sato blind equalizer and generalizations under practical constraints , 1993, IEEE Trans. Inf. Theory.

[4]  Lang Tong,et al.  Blind identification and equalization based on second-order statistics: a time domain approach , 1994, IEEE Trans. Inf. Theory.

[5]  T. Kailath,et al.  A least-squares approach to blind channel identification , 1995, IEEE Trans. Signal Process..

[6]  Terrence J. Sejnowski,et al.  An Information-Maximization Approach to Blind Separation and Blind Deconvolution , 1995, Neural Computation.

[7]  Shun-ichi Amari,et al.  Recurrent Neural Networks For Blind Separation of Sources , 1995 .

[8]  Chrysostomos L. Nikias,et al.  EVAM: an eigenvector-based algorithm for multichannel blind deconvolution of input colored signals , 1995, IEEE Trans. Signal Process..

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

[10]  Philippe Loubaton,et al.  Second order blind equalization in multiple input multiple output FIR systems: a weighted least squares approach , 1996, 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings.

[11]  Jitendra K. Tugnait,et al.  Blind equalization and channel estimation for multiple-input multiple-output communications systems , 1996, 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings.

[12]  Yingbo Hua,et al.  Fast maximum likelihood for blind identification of multiple FIR channels , 1996, IEEE Trans. Signal Process..

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

[14]  Jean-François Cardoso,et al.  Equivariant adaptive source separation , 1996, IEEE Trans. Signal Process..

[15]  Te-Won Lee,et al.  Blind Separation of Delayed and Convolved Sources , 1996, NIPS.

[16]  Eric A. Wan,et al.  Adjoint LMS: an efficient alternative to the filtered-x LMS and multiple error LMS algorithms , 1996, 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings.

[17]  Shun-ichi Amari,et al.  Stability Analysis Of Adaptive Blind Source Separation , 1997 .

[18]  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.

[19]  S. Amari,et al.  Multichannel blind separation and deconvolution of sources with arbitrary distributions , 1997, Neural Networks for Signal Processing VII. Proceedings of the 1997 IEEE Signal Processing Society Workshop.

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