Equivariant adaptive selective transmission

In this paper, we consider the problem of selective transmission-the dual of the blind source separation task-in which a set of independent source signals are adaptively premixed prior to a nondispersive physical mixing process so that each source can be independently monitored in the far field. Following similar procedures for information-theoretic blind source separation, we derive a stochastic gradient algorithm for iteratively estimating the premixing matrix in the selective transmission problem, and through a simple modification, we obtain a second algorithm whose performance is equivariant with respect to the channel's mixing characteristics. The local stability conditions for the algorithms about any selective transmission solution are shown to be the same as those for similar source separation algorithms. Practical implementation issues are discussed, including the estimation of the combined system matrix and the reordering and scaling of the received signals within the algorithm. Mean square error-based selective transmission algorithms are also derived for performance comparison purposes. Simulations indicate the useful behavior of the premixing algorithms for selective transmission.

[1]  Simon Haykin,et al.  Adaptive filter theory (2nd ed.) , 1991 .

[2]  Christian Jutten,et al.  Blind separation of sources, part I: An adaptive algorithm based on neuromimetic architecture , 1991, Signal Process..

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

[4]  J. Nadal,et al.  Nonlinear neurons in the low-noise limit: a factorial code maximizes information transfer Network 5 , 1994 .

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

[6]  Andrzej Cichocki,et al.  Robust learning algorithm for blind separation of signals , 1994 .

[7]  Bjorn Ottersten,et al.  The spectrum efficiency of a base station antenna array system for spatially selective transmission , 1995 .

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

[9]  Hui Liu,et al.  Multiuser blind channel estimation and spatial channel pre-equalization , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

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

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

[12]  Shun-ichi Amari,et al.  Blind source separation-semiparametric statistical approach , 1997, IEEE Trans. Signal Process..

[13]  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.

[14]  J. Cardoso.  Infomax and maximum likelihood for blind source separation , 1997, IEEE Signal Processing Letters.

[15]  Andrzej Cichocki,et al.  Stability Analysis of Learning Algorithms for Blind Source Separation , 1997, Neural Networks.

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

[17]  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.

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

[19]  Shun-ichi Amari,et al.  Why natural gradient? , 1998, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).