Advertisement

Annales Des Télécommunications

, Volume 53, Issue 11–12, pp 449–465 | Cite as

Égalisation autodidacte et semi-autodidacte: méthodes et algorithmes

  • Vincent Buchoux
  • Lisa Perros-Meilhac
  • Olivier Cappé
  • Eric Moulines
Article

Résumé

Les techniques d’estimation, qu’elles soient autodidactes (c’est-à-dire n’utilisant pas de connaissance a priori sur l’information émise) ou semi-autodidactes (basées sur la connaissance par exemple d’une séquence d’apprentissage), constituent depuis de nombreuses années un sujet d’intérêt majeur dans le domaine des télécommunications, et plus particulièrement pour l’identification des canaux de transmission. Cet article se propose de présenter une synthèse des développements récents dans ce domaine, en présentant en particulier les techniques sous-espace exploitant les statistiques du second ordre ainsi que les méthodes de maximum de vraisemblance. L’article s’organise de manière suivante: on présente tout d’abord le principe des techniques sous-espace ainsi que les résultats théoriques essentiels concernant à la fois les contextes autodidacte et semi-autodidacte; dans un second temps, sont considérées des solutions algorithmiques, pour certaines utilisant des résultats très récents, permettant de mettre en ceuvre l’approche par maximum de vraisemblance avec un coût d’implémentation raisonnable.

Mots clés

Égalisation Apprentissage non supervisé Identification Maximum vraisemblance Espace vectoriel Fonction rationnelle Modèle Markov caché Estimation statistique Article synthèse Méthodologie Algorithme 

Blind and semi-blind equalization: methods and algorithms

Abstract

Channel identification techniques that do not require the use of a training sequence (blind methods), or that can operate with very short training sequence (semiblind methods) are a topic of major concern for modern communication applications. This paper presents a review of channel identification methods that are applicable in this context, with a strong emphasis on second-order subspace-based and maximum likelihood (Ml) estimation schemes. The main focus of the paper is on: (i) providing a clear picture of the principle and theory associated with subspace-based methods in the blind and semi-blind contexts; (ii) describing algorithmic solutions, sometimes based on novel results, that are suitable for carrying out the delicate likelihood optimization task associated withMl estimation.

Key words

Equalization Unsupervised learning Transmission channel Identification Maximum likelihood Vector space Rational function Hidden Markov model Statistical estimation Review Methodology Algorithm 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Abed-Meraim (K.), Cardoso (J. F.), Gorokhov (A.), Loubaton (P.), Moulines (E.), On subspaces methods for blind identifiction of single-input multiple-output fir systems.IEEE Transactions on Signal Processing,45 (1): 42–55, (January 1997).CrossRefGoogle Scholar
  2. [2]
    Baum (L. E.), Petrie (T. P.), Soules (G.), Weiss (N.), A maximization technique occuring in the statistical analysis of probabilistic functions of Markov chains.The Annals of Mathematical Statistics,41 (1): 164–171, (1970).MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    Brockwell (P. J.), Davis (R. A.), Times series: Theory and methods.Springer, second edition, (1991).Google Scholar
  4. [4]
    Buchoux (V.), Moulines (E.), Cappé (O.), Gorokhov (A.). Semi-blind subspace techniques for digital communication systems.IEEE Transactions on Signal Processing,98. To be submitted.Google Scholar
  5. [5]
    Buchoux (V.), Moulines (E.), Cappé (O.), Mayrargue (S.), On the feasability of the blind and semi-blind techniques in digital communications systems.Work-shop COST 254, Emerging techniques for Communication Terminals, July 1997.Enseeith-enst, Toulouse France.Google Scholar
  6. [6]
    Caines (P. E.), Linear stochastic systems.Wiley, (1988).Google Scholar
  7. [7]
    Cappé (O.), Buchoux (V.), Moulines (E.), Quasi-newton method for maximum likelihood estimation of hidden Markov models.Proc. 1CASSP, IV: 2265–2268, Seattle. (May 1998).Google Scholar
  8. [8]
    Cappé (O.), Doucet (A.), Lavielle (M.), Moulines (E.), Simulation-based methods for blind maximum-likelihood filter identification.To appear in Signal Processing,73 (1), (1999).Google Scholar
  9. [9]
    Cappé (O.) dcv: A set of matlab functions for blind deconvolution of discrete signals, http://tsi.enst.fr/~Cappe/dcvérb, (Nov. 1998).Google Scholar
  10. [10]
    Collings (I. B.), Ryden (T.), A new maximum likelihood gradient algorithm for on-line hidden Markov model identification. InProc. ICASSP, pp. 2261–2264, Seattle, (1998).Google Scholar
  11. [11]
    Dempster (A. P.), Laird (N. M.), Rubin (D. B.), Maximum likelihood from incomplete data viaEm algorithm.J. Royal Statistical Society,39 (Ser. B), (1997).Google Scholar
  12. [12]
    Ding (Z.). Multipath channel identification based on partial system information.IEEE Trans, on Sig. Proc., (Jan. 1997).Google Scholar
  13. [13]
    Slock (D.), De Carvalho (E.), Asymptotic performance of ml methods for semi-blind channel estimation.Proc. of Slst Asilomar Conf. on Signals, Systems, Computers,2: 1624–1628, (Nov. 1997).Google Scholar
  14. [14]
    Forney (G. D.), Minimal bases of rational vector spaces, with applications to multivariable linear systems.S1AM J. on Control,13 (3): 493–520, (May 1975).MATHCrossRefMathSciNetGoogle Scholar
  15. [15]
    Gorokhov (A.), Loubaton (P.), Semi-blind second order identification of convolutive channels.Proc. ICASSP, pp. 3905–3908, 1997.Google Scholar
  16. [16]
    Tsatsanis (M. K.), Cirpan (H. A.), Stochastic maximum likelihood methods for semi-blind channel equalization.IEEE Transactions on Signal Processing,5 (1): 21–24, (January 1998).CrossRefGoogle Scholar
  17. [17]
    Moore (J. B.), Collings (I. B.), Krishnamurthy (V.), On-line identification of hidden Markov models via recursive prediction error techniques.IEEE Transactions on Signal Processing, IEEE,42 (12): 3535–3539, (December 1994).CrossRefGoogle Scholar
  18. [18]
    Slock (D. T. M.), Ayadi (J.) De Carvalho (E.), Blind and semiblind maximum likelihood methods for fir multichannel identification.Proc. ICASSP,6: 3185, (1998).Google Scholar
  19. [19]
    Fonollosa (J. A. R.), Anton-Haro (C.), Fonollosa (J. R.), Blind channel estimation and data detection using hidden Markov models.IEEE Transactions on Signal Processing, IEEE,45(l):241–246, (Jan. 1997).Google Scholar
  20. [20]
    Johnson (C. R.), Schniter (P.), Endres (T. J.), Behm (J. D.), Brown (D. R.), Casas (R.), Blind equalization using the constant modulus criterion: a review.Proceedings of the IEEE,86 (10): 1927–1951, (Oct. 1998).CrossRefGoogle Scholar
  21. [21]
    Abed Meraim (K.), Loubaton (P.), Moulines (E.), A subspace algorithm for certain subspace blind identification problems.IEEE Transactions on Information Theory,43 (2): 499–511, (March 1997).MATHCrossRefGoogle Scholar
  22. [22]
    Kailath (T), Linear Systems.Prentice-Hall, Inc., (1980).Google Scholar
  23. [23]
    Kawas Kaleh (G.), Vallet (R.), Joint parameter estimation and symbol detection for linear or nonlinear unknown channels.IEEE Transactions on Communications,42 (7): 2406–2413, (July 1994).MATHCrossRefGoogle Scholar
  24. [24]
    Kay (S. M.), Fundamentals of statistical signal processing: Estimation theory.Signal processing series. Prentice-hall, (1993).Google Scholar
  25. [25]
    Koopman (S. J.), Disturbance smoother for state space models.Biometrika,80 (1): 117–126,(1993).MATHCrossRefMathSciNetGoogle Scholar
  26. [26]
    Krishnamurthy (V.), White (L. B.), Blind equalization ofFir channels with Markov inputs. InProc. IFAC Identification and system parameter estimation, (1992).Google Scholar
  27. [27]
    LeGland (R), Mevel (L.), Recursive estimation inHmms. In36th IEEE Conf. on decision and control, San Diego, (1997).Google Scholar
  28. [28]
    Paulraj (A.), Cedervall (M.), Ng (B.), Structured methods for blind multi-channel identification.Proc. 13th Int. Conf. Dig. Sig. Proc., (July 1997).Google Scholar
  29. [29]
    MacDonald (I. L.), Zucchini (W.), Hidden Markov models and other models for discrete-valued time series.Chapman & Hall, (1997).Google Scholar
  30. [30]
    Mendel (J.), Tutorial on high-order statistics (Spectra) in signal processing and system theory.Proceedings on the IEEE,79 (3): 278–305,(1991).CrossRefGoogle Scholar
  31. [31]
    Mevel (L.), Statistique asymptotique pour les modèles de Markov caché.,PhD thesis, Université de Rennes 1, (1997).Google Scholar
  32. [32]
    Loubaton (P.), Ciblat (P.), Second order blind equalization: the band limited case.Proc. ICASSP, (1998).Google Scholar
  33. [33]
    Giridhar (K.), Iltis (R.), Shynk (J.), Bayesian algorithms for blind equalization using parallel adaptive filtering.IEEE Transactions on Communications,42: 1017–1032, (1994).CrossRefGoogle Scholar
  34. [34]
    Rabiner (L.), A tutorial on hidden Markov models and selected applications in speech recognition.Proceedings of the IEEE,77 (2): 257–274, (Feb. 1989).CrossRefGoogle Scholar
  35. [35]
    Moore (J. B.), Elliot (R. J.), Aggoun (L.), Hidden Markov models: estimation and control.Springer-Verlag, New York, (1994).Google Scholar
  36. [36]
    Schell (S.), Smith (D.), Gardner (W.), Blind channel identification using cyclostationary statistics.Proc. EUSIPCO, pp. 716–719, (1994).Google Scholar
  37. [37]
    Titterington (M.), Recursive parameter estimation using incomplete data.J. Royal Statist. Soc. Ser. B,46 (2): 257–267, (1984).MATHMathSciNetGoogle Scholar
  38. [38]
    Tong (L.), Perreau (S.), Multichannel blind identification: from subspace to maximum likelihood methods.Proceedings of the IEEE,86 (10): 1951–1968, (October 1998).CrossRefGoogle Scholar
  39. [39]
    Tong (L.), Xu (G.), Kailath (T.), A new approach to blind identification and equalization of multipath channels. InProc. of the 25th Asilomar Conference, Pacific Grove, CA, pp. 856–860, (1991).Google Scholar
  40. [40]
    Paulraj (A.), Reddy (V.), Papadias (C.), Blind identifiability of certain classes of multipath channels from second order using antenna arrays.IEEE Signal Processing Letters, (May 1997).Google Scholar
  41. [41]
    Wu (C. F. J.), On the convergence properties of theEm algorithm.The Annals of Mathematical Statistics,11 (1): 95–103, (1983).MATHGoogle Scholar

Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  1. 1.ENST - TSIF-75634 Paris Cedex 13France

Personalised recommendations