Blind source extraction from convolutive mixtures in ill-conditioned multi-input multi-output channels

This paper presents a new approach to blind source extraction from convolutive mixtures in multi-input multi-output (MIMO) channels. Two ill-conditioned cases are considered: the number of sensors is less than the number of sources and the number of sensors is greater than or equal to the number of sources but the system is noninvertible. Although there exist several works related to ill-conditioned dynamic MIMO channels, especially on blind channel identification, how to obtain a true source only from observable convolutive mixtures is still an open problem. In this paper, beginning with introducing two blind extraction models for blind deconvolution in ill-conditioned MIMO channels, we discuss the extractability issue. Results from our extractability analysis (a necessary and sufficient condition) show that it is possible to extract individual sources from the outputs. Furthermore, all potentially separable sources (at most equal to the number of sensors) can be extracted sequentially based on these extraction models. A cost function based on cross cumulant is discussed along with the Gauss-Newton algorithm. Finally, a simulation example is presented for illustration.

[1]  Ruey-Wen Liu,et al.  A fundamental theorem for multiple-channel blind equalization , 1997 .

[2]  Jitendra K. Tugnait,et al.  Identification and deconvolution of multichannel linear non-Gaussian processes using higher order statistics and inverse filter criteria , 1997, IEEE Trans. Signal Process..

[3]  Anisse Taleb,et al.  An algorithm for the blind identification of N independent signals with 2 sensors , 2001, Proceedings of the Sixth International Symposium on Signal Processing and its Applications (Cat.No.01EX467).

[4]  Christian Jutten,et al.  Fourth-order criteria for blind sources separation , 1995, IEEE Trans. Signal Process..

[5]  S. Amari,et al.  Geometrical structures of FIR manifold and their application to multichannel blind deconvolution , 1999, Neural Networks for Signal Processing IX: Proceedings of the 1999 IEEE Signal Processing Society Workshop (Cat. No.98TH8468).

[6]  Jacek M. Zurada,et al.  Blind extraction of singularly mixed source signals , 2000, IEEE Trans. Neural Networks Learn. Syst..

[7]  Phillip A. Regalia,et al.  Properties of some blind equalization criteria in noisy multiuser environments , 2001, IEEE Trans. Signal Process..

[8]  Yujiro Inouye,et al.  Iterative algorithms based on multistage criteria for multichannel blind deconvolution , 1999, IEEE Trans. Signal Process..

[9]  Pierre Comon,et al.  Blind Separation of Independent Sources from Convolutive Mixtures , 2003, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[10]  Philippe Loubaton,et al.  On blind multiuser forward link channel estimation by the subspace method: identifiability results , 2000, IEEE Trans. Signal Process..

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

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

[13]  Yujiro Inouye,et al.  Super-exponential algorithms for multichannel blind deconvolution , 2000, IEEE Trans. Signal Process..

[14]  Pierre Comon,et al.  Blind channel identification and extraction of more sources than sensors , 1998, Optics & Photonics.

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

[16]  A. Cichocki,et al.  Blind Separation and Extraction of Binary Sources , 2003, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[17]  Tommy W. S. Chow,et al.  Neural blind deconvolution of MIMO noisy channels , 2001 .

[18]  Sze Fong Yau,et al.  A cumulant-based super-exponential algorithm for blind deconvolution of multi-input multi-output systems , 1998, Signal Process..

[19]  Zhi Ding,et al.  A two-stage algorithm for MIMO blind deconvolution of nonstationary colored signals , 2000, IEEE Trans. Signal Process..

[20]  Andrzej Cichocki,et al.  Adaptive Blind Signal and Image Processing - Learning Algorithms and Applications , 2002 .

[21]  Noboru Ohnishi,et al.  Multichannel blind separation of sources algorithm based on cross-cumulant and the Levenberg-Marquardt method , 1999, IEEE Trans. Signal Process..

[22]  Seungjin Choi,et al.  Cascade neural networks for multichannel blind deconvolution , 1998 .

[23]  Liqing Zhang,et al.  Semiparametric model and superefficiency in blind deconvolution , 2001, Signal Process..

[24]  Jitendra K. Tugnait,et al.  Blind spatio-temporal equalization and impulse response estimation for MIMO channels using a Godard cost function , 1997, IEEE Trans. Signal Process..

[25]  Lang Tong,et al.  Identification of multichannel MA parameters using higher-order statistics , 1996, Signal Process..

[26]  Y. Inouye,et al.  A system-theoretic foundation for blind equalization of an FIR MIMO channel system , 2002 .

[27]  Shun-ichi Amari,et al.  Adaptive blind signal processing-neural network approaches , 1998, Proc. IEEE.

[28]  Andrzej Cichocki,et al.  Geometrical Structures of FIR Manifold and Multichannel Blind Deconvolution , 2002 .

[29]  Shoji Makino,et al.  Blind source separation of convolutive mixtures , 2006, SPIE Defense + Commercial Sensing.

[30]  Hui Luo,et al.  Direct blind separation of independent non-Gaussian signals with dynamic channels , 1998, 1998 Fifth IEEE International Workshop on Cellular Neural Networks and their Applications. Proceedings (Cat. No.98TH8359).

[31]  Scott C. Douglas,et al.  Blind Signal Separation and Blind Deconvolution , 2018, Handbook of Neural Network Signal Processing.