Analytical blind channel identification

A novel analytical blind single-input single-output (SISO) identification algorithm is presented, based on the noncircular second-order statistics of the output. It is shown that statistics of order higher than two are not mandatory to restore identifiability. Our approach is valid, for instance, when the channel is excited by phase shift keying (PSK) inputs. It is shown that the channel taps need to satisfy a polynomial system of degree 2 and that identification amounts to solving the system. We describe the algorithm that is able to solve this particular system entirely analytically, thus avoiding local minima. Computer results eventually show the robustness with respect to noise and to channel length overdetermination. Identifiability issues are also addressed.

[1]  Georgios B. Giannakis,et al.  A simple proof of a known blind channel identifiability result , 1999, IEEE Trans. Signal Process..

[2]  William A. Gardner,et al.  A new method of channel identification , 1991, IEEE Trans. Commun..

[3]  Sergio Benedetto,et al.  Digital Transmission Theory , 1987 .

[4]  S. Barbarossa,et al.  Blind equalization using cost function matched to the signal constellation , 1997, Conference Record of the Thirty-First Asilomar Conference on Signals, Systems and Computers (Cat. No.97CB36136).

[5]  Bernard C. Picinbono,et al.  On circularity , 1994, IEEE Trans. Signal Process..

[6]  Joe W. Harris,et al.  Algebraic Geometry: A First Course , 1995 .

[7]  Pierre Comon.  Circularité et signaux aléatoires à temps discret , 1994 .

[8]  Lang Tong,et al.  Blind identification and equalization based on second-order statistics: a time domain approach , 1994, IEEE Trans. Inf. Theory.

[9]  Jean-Louis Lacoume,et al.  Statistics for complex variables and signals - Part I: Variables , 1996, Signal Process..

[10]  B. Mourrain,et al.  Algorithms for residues and Lojasiewicz exponents , 2000 .

[11]  Jitendra K. Tugnait,et al.  Comments on 'New criteria for blind deconvolution of nonminimum phase systems (channels)' , 1992, IEEE Trans. Inf. Theory.

[12]  Philippe Loubaton,et al.  Subspace methods for blind identification of SIMO-FIR systems , 1996, 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings.

[13]  Bernard Mourrain,et al.  Solving projective complete intersection faster , 2000, ISSAC.

[14]  Ioannis Z. Emiris,et al.  Monomial bases and polynomial system solving (extended abstract) , 1994, ISSAC '94.

[15]  Victor Y. Pan,et al.  Multivariate Polynomials, Duality, and Structured Matrices , 2000, J. Complex..

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

[17]  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.

[18]  T. Kailath,et al.  A least-squares approach to blind channel identification , 1995, IEEE Trans. Signal Process..

[19]  J. Lacoume,et al.  Statistiques d'ordre supérieur pour le traitement du signal , 1997 .

[20]  Daniel Yellin,et al.  Blind identification of FIR systems excited by discrete-alphabet inputs , 1993, IEEE Trans. Signal Process..

[21]  F. S. Macaulay.  Some Formulæ in Elimination , 1902 .

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

[23]  N. R. Goodman.  Statistical analysis based on a certain multivariate complex Gaussian distribution , 1963 .

[24]  R. Wooding.  The multivariate distribution of complex normal variables , 1956 .

[25]  Ioannis Z. Emiris,et al.  Monomial bases and polynomial system solving , 1994, ISSAC 1994.

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

[27]  Philippe Loubaton,et al.  On subspace methods for blind identification of single-input multiple-output FIR systems , 1997, IEEE Trans. Signal Process..

[28]  Donal O'Shea,et al.  Ideals, varieties, and algorithms - an introduction to computational algebraic geometry and commutative algebra (2. ed.) , 1997, Undergraduate texts in mathematics.

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

[30]  Ta-Hsin Li,et al.  Blind identification and deconvolution of linear systems driven by binary random sequences , 1992, IEEE Trans. Inf. Theory.

[31]  O. Grellier,et al.  Closed-form blind channel identification with MSK inputs , 1998, Conference Record of Thirty-Second Asilomar Conference on Signals, Systems and Computers (Cat. No.98CH36284).

[32]  Ye Li,et al.  ARMA system identification based on second-order cyclostationarity , 1994, IEEE Trans. Signal Process..