Blind Separation of Independent Sources from Convolutive Mixtures

The problem of separating blindly independent sources from a convolutive mixture cannot be addressed in its widest generality without resorting to statistics of order higher than two. The core of the problem is in fact to identify the para-unitary part of the mixture, which is addressed in this paper. With this goal, a family of statistical contrast is first defined. Then it is shown that the problem reduces to a Partial Approximate Joint Diagonalization (PAJOD) of several cumulant matrices. Then, a numerical algorithm is devised, which works block-wise, and sweeps all the output pairs. Computer simulations show the good behavior of the algorithm in terms of Symbol Error Rates, even on very short data blocks.

[1]  Comon.  5 - Analyse en composantes indépendantes et identification aveugle , 1990 .

[2]  Pierre Comon,et al.  Analytical blind channel identification , 2002, IEEE Trans. Signal Process..

[3]  P. McCullagh.  Tensor Methods in Statistics , 1987 .

[4]  E. Moreau,et al.  New criteria for blind signal separation , 2000, Proceedings of the Tenth IEEE Workshop on Statistical Signal and Array Processing (Cat. No.00TH8496).

[5]  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..

[6]  Pierre Comon,et al.  BLIND SEPARATION OF CONVOLUTIVE MIXTURES A CONTRAST-BASED JOINT DIAGONALIZATION APPROACH , 2001 .

[7]  Ananthram Swami,et al.  Multichannel ARMA processes , 1994, IEEE Trans. Signal Process..

[8]  Pierre Comon,et al.  From source separation to blind equalization, contrast-based approaches , 2001 .

[9]  Antoine Souloumiac,et al.  Jacobi Angles for Simultaneous Diagonalization , 1996, SIAM J. Matrix Anal. Appl..

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

[11]  Pierre Comon,et al.  Blind MIMO equalization and joint-diagonalization criteria , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[12]  P. Vaidyanathan.  Multirate Systems And Filter Banks , 1992 .

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

[14]  Ehud Weinstein,et al.  New criteria for blind deconvolution of nonminimum phase systems (channels) , 1990, IEEE Trans. Inf. Theory.

[15]  Eric Moulines,et al.  A blind source separation technique using second-order statistics , 1997, IEEE Trans. Signal Process..

[16]  Gene H. Golub,et al.  Matrix computations , 1983 .