Multichannel system identification and deconvolution: performance bounds

We consider the problem of estimating the parameters of an unknown multi-input multi-output (MIMO) linear system and the related problem of deconvolving and recovering its inputs. Only the system outputs are assumed to be observable. The system inputs are assumed to be non-Gaussian. We derive simple closed-form asymptotic expressions for the Cramer-Rao lower bound (CRLB) for the system parameters, as well as lower bounds on the signal reconstruction performance. These show that the identification/deconvolution performance depend on the accuracy with which the location (mean) and the scale (standard deviation) parameters of the input probability density functions can be identified from observation of the input signals.

[1]  B. Friedlander,et al.  Blind multi-channel system identification and deconvolution: performance bounds , 1996, Proceedings of 8th Workshop on Statistical Signal and Array Processing.

[2]  Ehud Weinstein,et al.  Multichannel signal separation: methods and analysis , 1996, IEEE Trans. Signal Process..

[3]  Ehud Weinstein,et al.  Maximum likelihood and lower bounds in system identification with non-Gaussian inputs , 1994, IEEE Trans. Inf. Theory.

[4]  Dinh-Tuan Pham,et al.  Blind separation of instantaneous mixture of sources via an independent component analysis , 1996, IEEE Trans. Signal Process..

[5]  Meir Feder,et al.  Multi-channel signal separation by decorrelation , 1993, IEEE Trans. Speech Audio Process..

[6]  Eric Moreau,et al.  High order contrasts for self-adaptive source separation criteria for complex source separation , 1996 .

[7]  Jean-Louis Lacoume,et al.  Separation of independent sources from correlated inputs , 1992, IEEE Trans. Signal Process..

[8]  D. Brillinger.  Time series - data analysis and theory , 1981, Classics in applied mathematics.

[9]  Pierre Comon,et al.  Blind separation of sources, part II: Problems statement , 1991, Signal Process..

[10]  Debasis Sengupta,et al.  Efficient estimation of parameters for non-Gaussian autoregressive processes , 1989, IEEE Trans. Acoust. Speech Signal Process..

[11]  A. Gorokhov,et al.  Equivariant blind deconvolution of MIMO-FIR channels , 1997, First IEEE Signal Processing Workshop on Signal Processing Advances in Wireless Communications.

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

[13]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

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

[15]  Eric Ross Weinstein.  Estimation of trajectory parameters from passive array measurements , 1978 .

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

[17]  S. Bellini,et al.  Asymptotically efficient blind deconvolution , 1990 .