Cramér–Rao-Induced Bound for Blind Separation of Stationary Parametric Gaussian Sources

The performance of blind source separation algorithms is commonly measured by the output interference-to-signal ratio (ISR). In this paper, we derive an asymptotic bound on the attainable ISR for the case of Gaussian parametric auto-regressive (AR), moving-average (MA), or auto-regressive moving-average (ARMA) processes. Our bound is induced by the Crameacuter-Rao bound on estimation of the mixing matrix. We point out the relation to some previously obtained results, and provide a concise expression with some associated important insights. Using simulation, we demonstrate that the bound is attained asymptotically by some asymptotically efficient algorithms

[1]  Serge Dégerine,et al.  Separation of an instantaneous mixture of Gaussian autoregressive sources by the exact maximum likelihood approach , 2004, IEEE Transactions on Signal Processing.

[2]  Dinh Tuan Pham,et al.  Blind separation of instantaneous mixture of sources via the Gaussian mutual information criterion , 2000, 2000 10th European Signal Processing Conference.

[3]  Arie Yeredor,et al.  A computationally affordable implementation of an asymptotically optimal BSS algorithm for ar sources , 2006, 2006 14th European Signal Processing Conference.

[4]  A. Yeredor.  Blind separation of Gaussian sources via second-order statistics with asymptotically optimal weighting , 2000, IEEE Signal Processing Letters.

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

[6]  Erkki Oja,et al.  Performance analysis of the FastICA algorithm and Crame/spl acute/r-rao bounds for linear independent component analysis , 2006, IEEE Transactions on Signal Processing.

[7]  E. Oja,et al.  Corrections to "Performance Analysis of the FastICA Algorithm and Cram´ er-Rao Bounds for Linear Independent Component Analysis", TSP 04/06 , 2007 .

[8]  Andreas Ziehe,et al.  TDSEP { an e(cid:14)cient algorithm for blind separation using time structure , 1998 .

[9]  Arie Yeredor,et al.  Asymptotically Optimal Blind Separation of Parametric Gaussian Sources , 2004, ICA.

[10]  Joe Brewer,et al.  Kronecker products and matrix calculus in system theory , 1978 .

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

[12]  Philippe Garat,et al.  Blind separation of mixture of independent sources through a quasi-maximum likelihood approach , 1997, IEEE Trans. Signal Process..

[13]  Monson H. Hayes,et al.  Statistical Digital Signal Processing and Modeling , 1996 .