Blind MIMO-AR System Identification and Source Separation With Finite-Alphabet

In this paper, a new method for system identification and blind source separation in a multiple-input multiple-output (MIMO) system is proposed. The MIMO channel is modeled by a multi-dimensional autoregressive (AR) system. The transmitted signals are assumed to take values from a finite alphabet, modeled by the Gaussian mixture model (GMM) with infinitesimal variances. The expectation-maximization (EM) algorithm for estimation of the MIMO-AR model parameters is derived. The performance of the proposed algorithm in terms of probability of error in signal detection and root mean squared error (RMSE) of the system parameters and system transfer function estimates is evaluated via simulations. It is shown that the obtained probability of error is very close to the probability of error of the optimal algorithm which assumes known channel state information.

[1]  Alan V. Oppenheim,et al.  Parameter estimation for autoregressive Gaussian-mixture processes: the EMAX algorithm , 1997, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[2]  Joseph Tabrikian,et al.  MIMO-AR System Identification and Blind Source Separation for GMM-Distributed Sources , 2009, IEEE Transactions on Signal Processing.

[3]  Richard Todd Causey,et al.  Blind multiuser detection based on second-order statistics , 1999 .

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

[5]  Richard D. Wesel,et al.  Multi-input multi-output fading channel tracking and equalization using Kalman estimation , 2002, IEEE Trans. Signal Process..

[6]  Arnon D. Cohen,et al.  Detection of One-Lung Intubation Incidents , 2008, Annals of Biomedical Engineering.

[7]  J. Magnus,et al.  Matrix Differential Calculus with Applications in Statistics and Econometrics (Revised Edition) , 1999 .

[8]  Jeff A. Bilmes,et al.  A gentle tutorial of the em algorithm and its application to parameter estimation for Gaussian mixture and hidden Markov models , 1998 .

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

[10]  Philippe Loubaton,et al.  Prediction error method for second-order blind identification , 1997, IEEE Trans. Signal Process..

[11]  Yuan-Chieh Cheng,et al.  Blind estimation of finite alphabet digital signals using eigenspace-based beamforming techniques , 2004, Signal Process..

[12]  Joseph Tabrikian,et al.  MIMO-AR System Identification and Blind Source Separation using GMM , 2007, 2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07.

[13]  Zhi Ding,et al.  Blind source separation of signals with known alphabets using ε-approximation algorithms , 2003, IEEE Trans. Signal Process..

[14]  A. Yeredor,et al.  Separation of polynomial post non-linear mixtures of discrete sources , 2005, IEEE/SP 13th Workshop on Statistical Signal Processing, 2005.

[15]  Steven Kay,et al.  Modern Spectral Estimation: Theory and Application , 1988 .

[16]  Dinh-Tuan Pham,et al.  Blind separation of instantaneous mixtures of nonstationary sources , 2001, IEEE Trans. Signal Process..

[17]  S. Kay.  Fundamentals of statistical signal processing: estimation theory , 1993 .

[18]  P. Comon,et al.  Blind separation of discrete sources , 1998, IEEE Signal Processing Letters.

[19]  New York Dover,et al.  ON THE CONVERGENCE PROPERTIES OF THE EM ALGORITHM , 1983 .

[20]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[21]  Zhi Ding,et al.  Multiuser Channel Estimation from Higher-Order Statistical Matrix Pencil , 2002, EURASIP J. Adv. Signal Process..

[22]  J.E. Mazo,et al.  Digital communications , 1985, Proceedings of the IEEE.

[23]  H. Akaike.  A new look at the statistical model identification , 1974 .

[24]  Pierre Comon,et al.  Analytical blind discrete source separation , 2000, 2000 10th European Signal Processing Conference.

[25]  Byoung Soo Kim,et al.  Utilization of finite-alphabet (FA) signals for the underdetermined blind source separation in a weakly nonlinear channel , 2004, Proceedings of 2004 International Symposium on Intelligent Signal Processing and Communication Systems, 2004. ISPACS 2004..

[26]  J. Magnus,et al.  Matrix Differential Calculus with Applications in Statistics and Econometrics , 1991 .

[27]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[28]  Ronald A. Iltis,et al.  Joint detection and channel estimation algorithms for QS-CDMA signals over time-varying channels , 2002, IEEE Trans. Commun..

[29]  Philippe Loubaton,et al.  Second order blind equalization in multiple input multiple output FIR systems: a weighted least squares approach , 1996, 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings.

[30]  Adel Belouchrani Jean-Fran,et al.  Maximum likelihood source separation for discrete sources , 2007 .

[31]  Jorma Rissanen,et al.  The Minimum Description Length Principle in Coding and Modeling , 1998, IEEE Trans. Inf. Theory.

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