Skip to main content

Equalization of Sparse Intersymbol-Interference Channels Revisited

Abstract

Sparse intersymbol-interference (ISI) channels are encountered in a variety of communication systems, especially in high-data-rate systems. These channels have a large memory length, but only a small number of significant channel coefficients. In this paper, equalization of sparse ISI channels is revisited with focus on trellis-based techniques. Due to the large channel memory length, the complexity of maximum-likelihood sequence estimation by means of the Viterbi algorithm is normally prohibitive. In the first part of the paper, a unified framework based on factor graphs is presented for complexity reduction without loss of optimality. In this new context, two known reduced-complexity trellis-based techniques are recapitulated. In the second part of the paper a simple alternative approach is investigated to tackle general sparse ISI channels. It is shown that the use of a linear filter at the receiver renders the application of standard reduced-state trellis-based equalization techniques feasible without significant loss of optimality.

[1234567891011121314151617181920212223242526272829]

References

  1. 1.

    Rappaport TS: Wireless Communications—Principles and Practice. Prentice-Hall, Upper Saddle River, NJ, USA; 1996.

    Google Scholar 

  2. 2.

    Lee FKH, McLane PJ: Design of nonuniformly spaced tapped-delay-line equalizers for sparse multipath channels. IEEE Transactions on Communications 2004,52(4):530–535. 10.1109/TCOMM.2004.826351

    Article  Google Scholar 

  3. 3.

    Fevrier IJ, Gelfand SB, Fitz MP: Reduced complexity decision feedback equalization for multipath channels with large delay spreads. IEEE Transactions on Communications 1999,47(6):927–937. 10.1109/26.771349

    Article  Google Scholar 

  4. 4.

    Cotter SF, Rao BD: The adaptive matching pursuit algorithm for estimation and equalization of sparse time-varying channels. Proceedings of the 34th Asilomar Conference on Signals, Systems and Computers, November 2000, Pacific Grove, Calif, USA 2: 1772–1776.

  5. 5.

    Haratsch EF, Blanksby AJ, Azadet K: Reduced-state sequence estimation with tap-selectable decision-feedback. Proceedings of IEEE International Conference on Communications (ICC '00), June 2000, New Orleans, La, USA 1: 372–376.

  6. 6.

    Rontogiannis AA, Berberidis K: Efficient decision feedback equalization for sparse wireless channels. IEEE Transactions on Wireless Communications 2003,2(3):570–581. 10.1109/TWC.2003.811189

    Article  Google Scholar 

  7. 7.

    Benvenuto N, Marchesani R: The Viterbi algorithm for sparse channels. IEEE Transactions on Communications 1996,44(3):287–289. 10.1109/26.486320

    Article  MATH  Google Scholar 

  8. 8.

    McGinty NC, Kennedy RA, Hoeher PA: Parallel trellis Viterbi algorithm for sparse channels. IEEE Communications Letters 1998,2(5):143–145. see also: N. C. McGinty, R. A. Kennedy, and P. A. Hoeher, "Equalization of sparse ISI channels using parallel trellises," in Proceedings of 7th Communication Theory Mini-Conference in conjunction with IEEE Globecom '98, pp. 65–70, 1998 10.1109/4234.673661

    Article  Google Scholar 

  9. 9.

    McGinty NC: Reduced complexity equalization for data communication, Ph.D. dissertation. , Canberra, Australia; 1997.

    Google Scholar 

  10. 10.

    Lee FKH, McLane PJ: Iterative parallel-trellis MAP equalizers with nonuniformly-spaced prefilters for sparse multipath channels. Proceedings of 56th IEEE Vehicular Technology Conference (VTC '02), September 2002, Vancouver, BC, Canada 4: 2201–2205.

  11. 11.

    Forney GD Jr.: Maximum-likelihood sequence estimation of digital sequences in the presence of intersymbol interference. IEEE Transactions on Information Theory 1972,18(3):363–378. 10.1109/TIT.1972.1054829

    MathSciNet  Article  MATH  Google Scholar 

  12. 12.

    Bahl LR, Cocke J, Jelinek F, Raviv J: Optimal decoding of linear codes for minimizing symbol error rate. IEEE Transactions on Information Theory 1974,20(2):284–287.

    MathSciNet  Article  MATH  Google Scholar 

  13. 13.

    Badri-Hoeher S: Digitale Empfängeralgorithmen für TDMA-Mobilfunksysteme mit besonderer Berücksichtigung des EDGE-Systems, Ph.D. dissertation. , Erlangen, Germany; 2001.

    Google Scholar 

  14. 14.

    Gerstacker WH, Obernosterer F, Meyer R, Huber JB: On prefilter computation for reduced-state equalization. IEEE Transactions on Wireless Communications 2002,1(4):793–800. 10.1109/TWC.2002.804159

    Article  Google Scholar 

  15. 15.

    Badri-Hoeher S, Hoeher PA: Fast computation of a discrete-time whitened matched filter based on Kalman filtering. IEEE Transactions on Wireless Communications 2004,3(6):2417–2424. 10.1109/TWC.2004.833442

    Article  Google Scholar 

  16. 16.

    Hagenauer J: A soft-in/soft-out list sequential (LISS) decoder for turbo schemes. Proceedings of IEEE International Symposium on Information Theory (ISIT '03), June-July 2003, Kanagawa, Japan 382.

  17. 17.

    Kuhn C: A bidirectional list-sequential (BI-LISS) equalizer for turbo schemes. Proceedings of the 14th IST Mobile & Wireless Communications Summit, June 2005, Dresden, Germany paper no. 306

  18. 18.

    Liu L, Leung WK, Ping L: Simple iterative chip-by-chip multiuser detection for CDMA systems. Proceedings of 57th IEEE Vehicular Technology Conference (VTC '03), October 2003, Orlando, Fla, USA 3: 2157–2161.

  19. 19.

    Loeliger H-A: An introduction to factor graphs. IEEE Signal Processing Magazine 2004,21(1):28–41. 10.1109/MSP.2004.1267047

    Article  Google Scholar 

  20. 20.

    Colavolpe G, Germi G: On the application of factor graphs and the sum-product algorithm to ISI channels. IEEE Transactions on Communications 2005,53(5):818–825. 10.1109/TCOMM.2005.847129

    Article  Google Scholar 

  21. 21.

    Douillard C, Jezequel M, Berrou C, Picart A, Didier P, Glavieux A: Iterative correction of intersymbol interference: turbo-equalization. European Transactions on Telecommunications and Related Technologies 1995,6(5):507–511. 10.1002/ett.4460060506

    Article  Google Scholar 

  22. 22.

    Park J, Gelfand SB: Turbo equalizations for sparse channels. Proceedings of IEEE Wireless Communications and Networking Conference (WCNC '04), March 2004, Atlanta, Ga, USA 4: 2301–2306.

  23. 23.

    Cusani R, Mattila J: Equalization of digital radio channels with large multipath delay for cellular land mobile applications. IEEE Transactions on Communications 1999,47(3):348–351. 10.1109/26.752812

    Article  Google Scholar 

  24. 24.

    Eyuboǧlu MV, Qureshi SUH: Reduced-state sequence estimation with set partitioning and decision feedback. IEEE Transactions on Communications 1988,36(1):13–20. 10.1109/26.2724

    Article  Google Scholar 

  25. 25.

    Duel-Hallen A, Heegard C: Delayed decision-feedback sequence estimation. IEEE Transactions on Communications 1989,37(5):428–436. 10.1109/26.24594

    Article  Google Scholar 

  26. 26.

    Kammeyer K-D: Time truncation of channel impulse responses by linear filtering: a method to reduce the complexity of Viterbi equalization. AEÜ International Journal of Electronics and Communications 1994,48(5):237–243.

    Google Scholar 

  27. 27.

    Haykin S: Adaptive Filter Theory. 4th edition. Prentice Hall, Upper Saddle River, NJ, USA; 2002.

    Google Scholar 

  28. 28.

    Al-Dhahir N, Cioffi JM: Efficiently computed reduced-parameter input-aided MMSE equalizers for ML detection: a unified approach. IEEE Transactions on Information Theory 1996,42(3):903–915. 10.1109/18.490553

    Article  MATH  Google Scholar 

  29. 29.

    Proakis JG: Digital Communications. 4th edition. McGraw-Hill, New York, NY, USA; 2001.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Jan Mietzner.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Mietzner, J., Badri-Hoeher, S., Land, I. et al. Equalization of Sparse Intersymbol-Interference Channels Revisited. J Wireless Com Network 2006, 029075 (2006). https://doi.org/10.1155/WCN/2006/29075

Download citation

Keywords

  • Communication System
  • Significant Loss
  • Unify Framework
  • Complexity Reduction
  • Equalization Technique