Theoretical Derivation of Minimum Mean Square Error of RBF based Equalizer

  • Lee Jung-Sik (School of Electronics & Information Eng., Kunsan National University)
  • 발행 : 2006.08.01

초록

In this paper, the minimum mean square error(MSE) convergence of the RBF equalizer is evaluated and compared with the linear equalizer based on the theoretical minimum MSE. The basic idea of comparing these two equalizers comes from the fact that the relationship between the hidden and output layers in the RBF equalizer is also linear. As extensive studies of this research, various channel models are selected, which include linearly separable channel, slightly distorted channel, and severely distorted channel models. In this work, the theoretical minimum MSE for both RBF and linear equalizers were computed, compared and the sensitivity of minimum MSE due to RBF center spreads was analyzed. It was found that RBF based equalizer always produced lower minimum MSE than linear equalizer, and that the minimum MSE value of RBF equalizer was obtained with the center spread which is relatively higher(approximately 2 to 10 times more) than variance of AWGN. This work provides an analytical framework for the practical training of RBF equalizer system.

키워드

참고문헌

  1. G.J. Gibson, S.Siu, and C.F.N. Cowan, 'Application of Multilayer Perceptrons as Adaptive Channel Equalizers,' IEEE Int. Conf. Acoust. Speech, Signal Processing, Glasgow, Scotland, pp. 1183-1186, 1989
  2. P. R Chang and B. C. Wang 'Adaptive Decision Feedback Equalization for Digital Channels using Multilayer Neural Networks,' IEEE J. Selected Areas Commun., Vol. 13, pp.316-324, Feb. 1995 https://doi.org/10.1109/49.345876
  3. K. A. Al-Mashouq, I. S. Reed, ''The Use of Neural Nets to Combine Equalization with Decoding for Severe Intesymbol Interference Channels,' IEEE Trans. Neural Networks, Vol.5, pp..982-988, Nov. 1994 https://doi.org/10.1109/72.329696
  4. S. Chen, B. Mulgrew, and P. M Grant, 'A Clustering Technique for Digital Communication Channel Equalization using Radial Basis Function Networks,' IEEE Trans. Neural Networks, Vol.4, pp.570-579, Jill. 1993 https://doi.org/10.1109/72.238312
  5. B. Mulgrew, 'Applying Radial Basis Functions,' IEEE Sig. Proc. Mag., pp.50-65, Mar. 1996
  6. S. K. Patra and B. Mulgrew, 'Computational Aspects of Adaptive Radial Basis Function Equalizer Design,' IEEE Int. Symposium on Circuits and Systems, Hong Kong. pp.521-524, Jun. 1997
  7. J. Lee, A Radial Basis Function Equalizer with Reduced Number of Centers, Ph.D. dissertation, Florida Institute of Technology, 1996
  8. J. Lee, C.B. Beach, and N. Tepedelenlioglu, 'A Practical Radial Basis Function Equalizer,' IEEE Trans. Neural Networks, Vol.10, pp.450-455, Mar. 1991 https://doi.org/10.1109/72.750577
  9. M Ibnkahla, 'Applications of Neural Networks to Digital Communications- a Survey,' Signal Processing, pp. 1185-1215, Mar. 1999
  10. E. Lee and D. Messerschmitt, Digital Communication, second edition, Springer, 1993
  11. S. Haykin, Adpative Filter Theory, third edition, Prentice Hall, 1996
  12. J. G. Proakis, Digital Communications, third edition, McGraw Hill, 1995