Journal of Communications and Networks

The Korean Institute of Commucations and Information Sciences (한국통신학회)
권호 표지

Iterative LBG Clustering for SIMO Channel Identification

  • Published : 2003.06.01
Download PDF
⟨ Previous Next ⟩

Abstract

This paper deals with the problem of channel identification for Single Input Multiple Output (SIMO) slow fading channels using clustering algorithms. Due to the intrinsic memory of the discrete-time model of the channel, over short observation periods, the received data vectors of the SIMO model are spread in clusters because of the AWGN noise. Each cluster is practically centered around the ideal channel output labels without noise and the noisy received vectors are distributed according to a multivariate Gaussian distribution. Starting from the Markov SIMO channel model, simultaneous maximum ikelihood estimation of the input vector and the channel coefficients reduce to one of obtaining the values of this pair that minimizes the sum of the Euclidean norms between the received and the estimated output vectors. Viterbi algorithm can be used for this purpose provided the trellis diagram of the Markov model can be labeled with the noiseless channel outputs. The problem of identification of the ideal channel outputs, which is the focus of this paper, is then equivalent to designing a Vector Quantizer (VQ) from a training set corresponding to the observed noisy channel outputs. The Linde-Buzo-Gray (LBG)-type clustering algorithms [1] could be used to obtain the noiseless channel output labels from the noisy received vectors. One problem with the use of such algorithms for blind time-varying channel identification is the codebook initialization. This paper looks at two critical issues with regards to the use of VQ for channel identification. The first has to deal with the applicability of this technique in general; we present theoretical results for the conditions under which the technique may be applicable. The second aims at overcoming the codebook initialization problem by proposing a novel approach which attempts to make the first phase of the channel estimation faster than the classical codebook initialization methods. Sample simulation results are provided confirming the effectiveness of the proposed initialization technique.

Keywords

References

  1. Y. Linde, A. Buzo,and R. M. Gray,'An algorithm for vector quantizer de-sign', IEEE Trans. Commun.. Vol. C0M-28, No. 1, pp. 84-95, Jan. 1980
  2. J. G. Proakis,'Digital communications', Mc Graw-Hill Publishers, 3-rd edition, 1995
  3. G. L. Stuber,'Principles of mobile communication', Kluwer Academic Publisher, first edition, Jun. 1996
  4. Y. Sato,'A blind sequence detection and its application to digital mobile communication', IEEE J. on Select. Areas Commun., Vol. 13, No. 1, pp.49-58,Jan. 1995 https://doi.org/10.1109/49.363146
  5. H. Kong, E. Shwedyk,'Sequence detection and channel state estimation over finite state markov channels', IEEE Trans. Veh. Technol., Vol. 48, pp. 833-839, May 1999 https://doi.org/10.1109/25.765000
  6. G. K. Kaleh, R. Vallet.'Joint parameter estimation and symbol detection for linear or nonlinear unknown channels', IEEE Trans. Commun., Vol. 42, pp. 2406-2413, Jul. 1994 https://doi.org/10.1109/26.297849
  7. L. R. Rabiner,'A tutorial on hidden markov models and selected appli-cations in speech recognition',in Proc., Vol. 77, No. 2, Feb. 1989, pp.257-286
  8. L. Tong,'Blind sequence estimation', IEEE Trans. Commun., Vol. 43, No. 12, pp. 2986-2994, Dec. 1995 https://doi.org/10.1109/26.477501
  9. C. Anton-Haro et al.,'On the inclusion of channel's time dependence in a hidden markov model for blind channel estimation', IEEE Trans. Veh. Technol., Vol. 50, No. 3, pp. 867-873, May 2001 https://doi.org/10.1109/25.933319
  10. W. Turin,'MAP decoding in channels with memory, IEEE trans.' Commun., Vol. 48, No. 5, pp. 757-763, May 2000 https://doi.org/10.1109/26.843188
  11. G. Xu et al.,'A least-squares approach to blind channel identification', IEEE Trans. Signal Processing, Vol. 43, No. 12, pp. 2982-2993, Dec. 1995 https://doi.org/10.1109/78.476442
  12. L. Tong, G. Xu.and T. Kailath,'Blind identification and equalization based on second-order statistics: A time-domain approach', IEEE Trans. Inform. Theory, Vol. 40, No. 2, pp. 340-349, Mar. 1994 https://doi.org/10.1109/18.312157
  13. L. Tong et al.,'Blind channel identification based on second-order statis-tics: A frequency-domain approach', IEEE Trans. Inform. Theory, Vol 41, No. 1, pp. 329-334, Jan. 1995 https://doi.org/10.1109/18.370088
  14. Kimura et al.,'Blind channel identification using RLS method based on second order statistics,' in Proc. IEEE Workshop on Signal Processing Advances in Wireless Communications. 1999. pp. 78-81
  15. M. C. Vanderveen. A. Paulraj,'Improved blind channel identification us-ing a parametric approach', IEEE Commun. Lett., Vol. 2, No. 8, pp. 226-228. Aug.1998 https://doi.org/10.1109/4234.709439
  16. Radionov, V., Mayrargue, S., 'Semi-blind approach to second order iden-tification of SIMO-FIR channel driven by finite-alphabet sequence', in Proc., DSP 97., Vol. 1, Jul. 1997, pp. 115-118
  17. L. Tong, S. Perreau, 'Multichannel blind identification: From subspace to maximum likelihood methods', in Proc., Vol. 86, No. 10, Oct. 1998, pp. 1951-1968 https://doi.org/10.1109/5.720247
  18. P. Ciblat, E. Serpedin.and Y. Wang, 'On a blind fractionally sampling-based carrier frequency offset estimator for noncircular transmissions', IEEE Signal Processing Lett., Vol. 10, No. 4, pp. 89-92, Apr. 2003 https://doi.org/10.1109/LSP.2003.809031
  19. Ghogho, M., Swami,and A., Durrani, T., 'On blind carrier recovery in time-selective fading channels, conference record of the thirty-third asilo-mar conference on signals', Systems and Computers, Vol. 1, pp. 243-247,1999
  20. N. Seshardi, 'Joint data and channel estimation using trellis search tech-niques', IEEE Trans. Commun., Vol. C0M-42, No. 2/3/4, pp. 1000-1011,Feb./Mar./Apr. 1994
  21. G. D. Fomey, 'Maximum likelihood sequence estimation of digital se-quence in the presence of intersymbol interference', IEEE Trans. Inform. Theory, Vol. IT-18, pp. 363-378, May 1972
  22. M. Abramowitz and I. A. Stegun, 'Handbook of mathematical functions with fonnulas, graphs, and mathematical tables', 1964
  23. A. Gersho, R. M. Gray, 'Vector quantization and signal compression', Kluwer Academic Publisher, 1992
  24. S. Haykin, 'Adapdve Blter theory', Prentice-Hall International, 2-nd edi-tion,1993