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  • Research Article
  • Open Access

Fast Adaptive Blind MMSE Equalizer for Multichannel FIR Systems

EURASIP Journal on Advances in Signal Processing20062006:014827

  • Received: 30 December 2005
  • Accepted: 22 June 2006
  • Published:


We propose a new blind minimum mean square error (MMSE) equalization algorithm of noisy multichannel finite impulse response (FIR) systems, that relies only on second-order statistics. The proposed algorithm offers two important advantages: a low computational complexity and a relative robustness against channel order overestimation errors. Exploiting the fact that the columns of the equalizer matrix filter belong both to the signal subspace and to the kernel of truncated data covariance matrix, the proposed algorithm achieves blindly a direct estimation of the zero-delay MMSE equalizer parameters. We develop a two-step procedure to further improve the performance gain and control the equalization delay. An efficient fast adaptive implementation of our equalizer, based on the projection approximation and the shift invariance property of temporal data covariance matrix, is proposed for reducing the computational complexity from to , where is the number of emitted signals, the data vector length, and the dimension of the signal subspace. We then derive a statistical performance analysis to compare the equalization performance with that of the optimal MMSE equalizer. Finally, simulation results are provided to illustrate the effectiveness of the proposed blind equalization algorithm.


  • Minimum Mean Square Error
  • Finite Impulse Response
  • Signal Subspace
  • Equalization Algorithm
  • Shift Invariance

Authors’ Affiliations

Département d'Électronique, École Nationale Polytechnique (ENP), 10 avenue Hassen Badi El-Harrach, Algiers, 16200, Algeria
Département Traitement du Signal et de l'Image, École Nationale Supérieure des Télécommunications (ENST), 37–39 rue Dareau, Paris, 75014, France


  1. Abed-Meraim K, Chkeif A, Hua Y: Fast orthogonal PAST algorithm. IEEE Signal Processing Letters 2000, 7(3):60–62. 10.1109/97.823526View ArticleGoogle Scholar
  2. Abed-Meraim K, Loubaton P, Moulines E: A subspace algorithm for certain blind identification problems. IEEE Transactions on Information Theory 1997, 43(2):499–511. 10.1109/18.556108View ArticleGoogle Scholar
  3. Abed-Meraim K, Qiu W, Hua Y: Blind system identification. Proceedings of the IEEE 1997, 85(8):1310–1322. 10.1109/5.622507View ArticleGoogle Scholar
  4. Badeau R, David B, Richard G: Yet another subspace tracker. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '05), March 2005, Philadelphia, Pa, USA 4: 329–332.Google Scholar
  5. Belouchrani A, Abed-Meraim K: Constant modulus blind source separation technique: a new approach. Proceedings of the International Symposium on Signal Processing and Its Applications (ISSPA '96), August 1996, Gold Coast, Australia 1: 232–235.Google Scholar
  6. Brewer JW: Kronecker products and matrix calculus in system theory. IEEE Transactions on Circuits and Systems 1978, 25(9):772–781. 10.1109/TCS.1978.1084534MathSciNetView ArticleGoogle Scholar
  7. Cardoso J-F, Moulines E: Asymptotic performance analysis of direction-finding algorithms based on fourth-order cumulants. IEEE Transactions on Signal Processing 1995, 43(1):214–224. 10.1109/78.365301View ArticleGoogle Scholar
  8. Chkeif A, Abed-Meraim K, Kawas-Kaleh G, Hua Y: Spatio-temporal blind adaptive multiuser detection. IEEE Transactions on Communications 2000, 48(5):729–732. 10.1109/26.843180View ArticleGoogle Scholar
  9. Davila CE: Efficient, high performance, subspace tracking for time-domain data. IEEE Transactions on Signal Processing 2000, 48(12):3307–3315. 10.1109/78.886994MathSciNetView ArticleGoogle Scholar
  10. Gazzah H, Regalia PA, Delmas J-P, Abed-Meraim K: A blind multichannel identification algorithm robust to order overestimation. IEEE Transactions on Signal Processing 2002, 50(6):1449–1458. 10.1109/TSP.2002.1003068View ArticleGoogle Scholar
  11. Gerstacker WH, Taylor DP: Blind channel order estimation based on second-order statistics. IEEE Signal Processing Letters 2003, 10(2):39–42. 10.1109/LSP.2002.807866View ArticleGoogle Scholar
  12. Godard DN: Self-recovering equalization and carrier tracking in two-dimensional data communication systems. IEEE Transactions on Communications 1980, 28(11):1867–1875. 10.1109/TCOM.1980.1094608View ArticleGoogle Scholar
  13. Haykin S: Adaptive Filter Theory. 3rd edition. Prentice Hall, Englwood Cliffs, NJ, USA; 1996.MATHGoogle Scholar
  14. Kacha I, Abed-Meraim K, Belouchrani A: A fast adaptive blind equalization algorithm robust to channel order over-estimation errors. Proceedings of the 3rd IEEE Sensor Array and Multichannel Signal Processing Workshop, July 2004, Barcelona, Spain 148–152.Google Scholar
  15. Kacha I, Abed-Meraim K, Belouchrani A: A new blind adaptive MMSE equalizer for MIMO systems. Proceedings of the 16th Annual IEEE International Symposium on Personal Indoor and Mobile Radio Communications, September 2005, Berlin, GermanyGoogle Scholar
  16. Li X, Fan H: Direct estimation of blind zero-forcing equalizers based on second-order statistics. IEEE Transactions on Signal Processing 2000, 48(8):2211–2218. 10.1109/78.852002View ArticleGoogle Scholar
  17. Liavas AP, Regalia PA, Delmas J-P: Blind channel approximation: effective channel order determination. IEEE Transactions on Signal Processing 1999, 47(12):3336–3344. 10.1109/78.806077View ArticleGoogle Scholar
  18. Moulines E, Duhamel P, Cardoso J-F, Mayrargue S: Subspace methods for the blind identification of multichannel FIR filters. IEEE Transactions on Signal Processing 1995, 43(2):516–525. 10.1109/78.348133View ArticleGoogle Scholar
  19. Neeser FD, Massey JL: Proper complex random processes with applications to information theory. IEEE Transactions on Information Theory 1993, 39(4):1293–1303. 10.1109/18.243446MathSciNetView ArticleGoogle Scholar
  20. Sato Y: A method of self-recovering equalization for multilevel amplitude-modulation. IEEE Transactions on Communications 1975, 23(6):679–682. 10.1109/TCOM.1975.1092854View ArticleGoogle Scholar
  21. Shen J, Ding Z: Direct blind MMSE channel equalization based on second-order statistics. IEEE Transactions on Signal Processing 2000, 48(4):1015–1022. 10.1109/78.827535View ArticleGoogle Scholar
  22. Sheng M, Fan H: Blind MMSE equalization: a new direct method. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '00), June 2000, Istanbul, Turkey 5: 2457–2460.Google Scholar
  23. Tong L, Xu G, Kailath T: A new approach to blind identification and equalization of multipaths channels. Proceedings of 25th Asilomar Conference on Circuits, Systems and Computers, November 1991, Pacific Grove, Calif, USA 856–860.Google Scholar
  24. Tsatsanis MK, Giannakis GB: Modelling and equalization of rapidly fading channels. International Journal of Adaptive Control and Signal Processing 1996, 10(2–3):159–176. 10.1002/(SICI)1099-1115(199603)10:2/3<159::AID-ACS346>3.0.CO;2-MView ArticleGoogle Scholar
  25. van der Veen A-J, Paulraj A: An analytical constant modulus algorithm. IEEE Transactions on Signal Processing 1996, 44(5):1136–1155. 10.1109/78.502327View ArticleGoogle Scholar
  26. Xavier J, Barroso V: A channel order independent method for blind equalization of MIMO systems. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '99), March 1999, Phoenix, Ariz, USA 5: 2897–2900.Google Scholar
  27. Yang B: Projection approximation subspace tracking. IEEE Transactions on Signal Processing 1995, 43(1):95–107. 10.1109/78.365290View ArticleGoogle Scholar


© Ibrahim Kacha et al. 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.