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Equalization of Time-Varying Channels using a Recurrent Neural Network Trained with Kalman Filters

칼만필터로 훈련되는 순환신경망을 이용한 시변채널 등화


Abstract

Recurrent neural networks have been successfully applied to communications channel equalization. Major disadvantages of gradient-based learning algorithms commonly employed to train recurrent neural networks are slow convergence rates and long training sequences required for satisfactory performance. In a high-speed communications system, fast convergence speed and short training symbols are essential. We propose decision feedback equalizers using a recurrent neural network trained with Kalman filtering algorithms. The main features of the proposed recurrent neural equalizers, utilizing extended Kalman filter (EKF) and unscented Kalman filter (UKF), are fast convergence rates and good performance using relatively short training symbols. Experimental results for two time-varying channels are presented to evaluate the performance of the proposed approaches over a conventional recurrent neural equalizer.

Keywords

References

  1. S. Qureshi, 'Adaptive equalization,' Proceedings of the IEEE, vol. 73, no. 9, pp. 1349-1387, 1985 https://doi.org/10.1109/PROC.1985.13298
  2. S. Chen, B. Mulgrew, and S. McLaughlin, 'Adaptive Bayesian equalizer with decision feedback,' IEEE Transactions on Signal Processing, vol. 41, pp. 2918-2927, September 1993 https://doi.org/10.1109/78.236513
  3. S. Siu, G. J. Gibson, and C. F. N. Cowan, 'Decision feedback equalization using neural network structures and performance comparison with standard architecture,' IEEE Proceedings: Part I, vol. 137, no. 4, pp. 221-225,1990 https://doi.org/10.1049/ip-i-2.1990.0031
  4. A. Zerguine, A. Shafi, and M. Bettayeb, 'Multilayer perception-based DFE with lattice structure,' IEEE Transactions on Neural Networks, vol. 12, pp. 532-545, May 2001 https://doi.org/10.1109/72.925556
  5. B. Mulgrew, 'Applying radial basis function networks,' IEEE Signal Processing Magazine, pp. 50-65, March 1996
  6. S. Haykin, Neural Networks: a Comprehensive Foundation, 2nd Ed. Upper Saddle River, NJ: Prentice Hall, 1999
  7. G. Kechriotis, E. Zervas, and E. S. Manolakos, 'Using recurrent neural networks for adaptive communication channel equalizations,' IEEE Transactions on Neural Networks, vol. 5, pp. 267-278, March 1994 https://doi.org/10.1109/72.279190
  8. S. Ong, C. You, S. Choi, and D. Hong, 'A decision response filter,' IEEE Transactions on Signal Processing, vol. 45, pp. 2851-2858, November 1997 https://doi.org/10.1109/78.650112
  9. R. Parisi, E. D. D. Claudio, G. Orlandi, and B. D. Rao, 'Fast adaptive digital equalization by recurrent neural networks,' IEEE Transactions on Signal Processing, vol. 45, pp. 2731-2739, November 1997 https://doi.org/10.1109/78.650099
  10. K. Hacioglu, 'An improved recurrent neural network for M-PAM symbol detection,'IEEE Transactions on Neural Networks, vol. 8, pp. 779-783, May 1997 https://doi.org/10.1109/72.572113
  11. R. J. Williams and D. Zipser, 'A learning algorithm for continually running fully recurrent neural networks,' Neural Computation, vol. 1, pp. 270-280,1989 https://doi.org/10.1162/neco.1989.1.2.270
  12. J. D. Ortiz-Fuentes and M. L. Forcada, 'A comparison Conference on Acoustics, Speech, and Signal Processing, pp. 3281-3284,1997
  13. F. Ling and J. G. Proakis, 'Adaptive lattice decision feedback equalizers-Their performance and application to time-variant multipath channels,' IEEE Transactions on Communications, vol. 33, pp. 348-356, April 1985
  14. Q. Liang and J. M. Mendel, 'Equalization of nonlinear time-varying channels using type-2 fuzzy adaptive filters,'IEEE Transactions on Fuzzy Systems, vol. 8, pp. 551-563, October 2000 https://doi.org/10.1109/91.873578
  15. C. Cowan and S. Semnani, 'Time-variant equalization using a novel non-linear adaptive structure,' International Journal of Adaptive Control and Signal Processing, vol. 12, no. 2, pp. 195-206,1998 https://doi.org/10.1002/(SICI)1099-1115(199803)12:2<195::AID-ACS487>3.0.CO;2-K
  16. M. Solazzi, A. Uncini, E. D. D. Claudio, and R. Parisi, 'Complex discriminative learning Bayesian neural equalizer,'in Proceedings of the 1999 IEEE International Symposium on Circuits and Systems (ISCAS '99), pp. 343-346,1999 https://doi.org/10.1109/ISCAS.1999.777579
  17. J. Elman, 'Finding structure in time,' Congnitive Science, vol. 14, pp. 179-211, 1990 https://doi.org/10.1016/0364-0213(90)90002-E
  18. P. J. Werbos, 'Back-propagation through time: What it does and how to do it,' Proceedings of the IEEE, vol. 78, pp. 1550-1560, October 1990 https://doi.org/10.1109/5.58337
  19. S. Haykin, Adaptive Filter Theory, 4th Ed. Upper Saddle River, NJ: Prentice Hall, 2002
  20. L. A. Feldkamp and G. V. Puskorius, 'A signal processing framework based on dynamic neural networks with application to problems in adaptation, filtering and classification,' Proceedings of the IEEE, vol. 86, pp. 2259-2277, 1998 https://doi.org/10.1109/5.726790
  21. S. J. Julier and J. K. Uhlmann, 'A new extension of the Kalman filter to nonlinear systems,' in Proceedings of AeroSence: The 11th International Symposium on Aerospace/Defence Sensing, Simulation and Controls, 1997
  22. E. A. Wan and R. van der Merwe, 'The unscented Kalman filter,' in Kalman Filtering and Neural Networks, Edited by S. Haykin. John Wiley and Sons, Inc., 2001
  23. E. A. Wan and R. van der Merwe, 'The unscented Kalman filter for nonlinear estimation,' in Proceedings of the IEEE 2000 Adaptive Systems for Signal Processing, Communications and Control Symposium (AS-SPCC), pp. 153-158,2000 https://doi.org/10.1109/ASSPCC.2000.882463
  24. S. Chen, B. Mulgrew, and S. McLaughlin, 'Adaptive equalization of finite nonlilear channels using multilayer perceptions,' Signal Processing, vol. 20, 1990