MIMO channel blind identification in the presence of spatially correlated noise

We address the problem of the second-order blind identification of a multiple-input multiple-output (MIMO) transfer function in the presence of additive noise. The additive noise is assumed to be (temporally) white, i.e., uncorrelated in time, but we do not make any assumption on its spatial correlation. This problem is thus equivalent to the second-order blind identification of a MIMO transfer function in the noiseless case but from a partial auto-covariance function {R/sub n/}/sub n/spl ne/0/. Our approach consists of computing the missing central covariance coefficient R/sub 0/ from this partial auto-covariance sequence. It can be described simply within the algebraic framework of rational subspaces. We propose an identifiability result that requires very mild assumptions on the transfer function to be estimated. Practical subspace-based identification algorithms are deduced and tested via simulations.

[1]  Philippe Loubaton,et al.  Blind identification of MIMO-FIR systems: A generalized linear prediction approach , 1999, Signal Process..

[2]  J. Navarro-Pedreño Numerical Methods for Least Squares Problems , 1996 .

[3]  I. Fijalkow,et al.  On the identification of noisy MA models , 1996, IEEE Trans. Autom. Control..

[4]  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..

[5]  José M. F. Moura,et al.  Closed-form blind identification of MIMO channels , 1998, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).

[6]  Philippe Loubaton,et al.  A subspace algorithm for certain blind identification problems , 1997, IEEE Trans. Inf. Theory.

[7]  Hui Liu,et al.  Recent developments in blind channel equalization: From cyclostationarity to subspaces , 1996, Signal Process..

[8]  É. Moulines,et al.  Subspace method for blind identification of multichannel FIR systems in noise field with unknown spatial covariance , 1997, IEEE Signal Processing Letters.

[9]  James E. Barger,et al.  Underwater acoustic system analysis , 1985, Proceedings of the IEEE.

[10]  Dirk T. M. Slock,et al.  Blind fractionally-spaced equalization, perfect-reconstruction filter banks and multichannel linear prediction , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.

[11]  Hui Liu,et al.  Closed-form blind symbol estimation in digital communications , 1995, IEEE Trans. Signal Process..

[12]  D. Slock Blind joint equalization of multiple synchronous mobile users using oversampling and/or multiple antennas , 1994, Proceedings of 1994 28th Asilomar Conference on Signals, Systems and Computers.

[13]  Georgios B. Giannakis,et al.  Signal Processing Advances in Wireless and Mobile Communications, Volume 2: Trends in Single- and Multi-User Systems , 2000 .

[14]  Karim Abed-Meraim,et al.  Blind identification of multi-input multi-output system using minimum noise subspace , 1997, IEEE Trans. Signal Process..

[15]  Jean-Pierre Le Cadre Parametric methods for spatial signal processing in the presence of unknown colored noise fields , 1989, IEEE Trans. Acoust. Speech Signal Process..

[16]  Thomas Kailath,et al.  Linear Systems , 1980 .

[17]  Arogyaswami Paulraj,et al.  A subspace approach to blind space-time signal processing for wireless communication systems , 1997, IEEE Trans. Signal Process..

[18]  Anthony J. Weiss,et al.  Direction finding using noise covariance modeling , 1995, IEEE Trans. Signal Process..

[19]  A. Doma Generalized Inverses of Matrices and Its Applications. , 1983 .

[20]  Marc Moonen,et al.  A stochastic subspace algorithm for blind channel identification in noise fields with unknown spatial color , 1999, 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258).

[21]  Georgios B. Giannakis,et al.  Signal processing advances in wireless and mobile communications , 2000, IEEE Signal Process. Mag..

[22]  Inbar Fijalkow,et al.  Identification of rank one rational spectral densities from noisy observations: a stochastic realization approach , 1995 .

[23]  L. Tong,et al.  Multichannel blind identification: from subspace to maximum likelihood methods , 1998, Proc. IEEE.

[24]  Lang Tong,et al.  A new approach to blind identification and equalization of multipath channels , 1991, [1991] Conference Record of the Twenty-Fifth Asilomar Conference on Signals, Systems & Computers.

[25]  Luc Deneire,et al.  A Schur method for multiuser multichannel blind identification , 1999, 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258).

[26]  Philippe Loubaton,et al.  On the identification of certain rational transfer functions from truncated autocovariance sequences , 1999, IEEE Trans. Autom. Control..

[27]  Eric Moulines,et al.  Subspace methods for the blind identification of multichannel FIR filters , 1995, IEEE Trans. Signal Process..

[28]  Jitendra K. Tugnait,et al.  Blind channel estimation and equalization of multiple-input multiple-output channels , 1999, 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258).

[29]  Jr. G. Forney,et al.  Minimal Bases of Rational Vector Spaces, with Applications to Multivariable Linear Systems , 1975 .

[30]  Marius Pesavento,et al.  Maximum-likelihood direction-of-arrival estimation in the presence of unknown nonuniform noise , 2001, IEEE Trans. Signal Process..