Rainfield Y. Yen This email address is being protected from spambots. You need JavaScript enabled to view it.1

1Department of Electrical Engineering, Tamkang University, Tamsui, Taiwan 251, R.O.C.


Received: April 26, 2007
Accepted: June 3, 2008
Publication Date: March 1, 2009

Download Citation: ||https://doi.org/10.6180/jase.2009.12.1.05  


We systematically analyze the biased and unbiased minimum mean square error (MMSE) equalizers of finite as well as infinite length, with and without decision feedback sections. New closed-form expressions of optimum equalizer weights, the MMSE, and symbol error probabilities (SEP), solely in terms of channel response parameters and noise power, are derived for the above receivers. These new expressions have not appeared in the literature and should be included for completeness. We also prove analytically that the biased and unbiased MMSE equalizers have the same optimum weights and that an infinitely long unbiased MMSE equalizer approaches the optimum minimum error probability equalizer. Performance curves are presented and compared for all the receivers discussed. Moreover, for all the infinite length equalizers presented, alternative error probability expressions are provided to best suit computer simulations.

Keywords: Minimum Mean Square Error (MMSE), Channel Equalization, Unbiased Estimate, Symbol Error Probability, Decision Feedback Equalizers (DFEs)


  1. [1] Proakis, J. G., Digital Communications, 4th ed. McGraw-Hill, New York (2001).
  2. [2] Gitlin, R. D., Hayes, J. F. and Weinstein, S. B., Data Communication Principles, Plenum (1992).
  3. [3] Haykin, S., Adaptive Filter Theory, 4th ed. PrenticeHall, Upper Saddle River, NJ (2002).
  4. [4] Saltzburg, B. R., “Intersymbol Interference Error Bounds with Application to Ideal Bandlimited Signaling,” IEEE Trans. Inform. Theory, Vol. IT-14, pp. 563568 (1968).
  5. [5] Lee, E. A. and Messerschmitt, D. G., Digital Communications, 2nd ed. Kluwer, Boston, MA (1994).
  6. [6] Cioffi, J. M., Dudevoir, G. P., Eyuboglu, M. V. and Forney, Jr., G. D., “MMSE Decision-Feedback Equalizera and Coding-Part I: Equalization Results,” IEEE Trans. Commun., Vol. 43, pp. 25822594 (1995).
  7. [7] Lugannani, R., “Intersymbol Interference and Probability of Error in Digital Systems,” IEEE Trans. Inform. Theory, Vol. IT-15, pp. 682688 (1969).
  8. [8] Ho, E. Y. and Yeh, Y. S., “A New for Evaluating the Error Probability in the Presence of Intersymbol Interference and Additive Gaussian Noise,” Bell Syst. Tech. J., Vol. 49, pp. 22492265 (1970).
  9. [9] Shimbo, O. and Celebiler, M., “The Probability of Error Due to Intersymbol Interference and Gaussian Noise in Digital Communication Systems,” IEEE Trans. Commun. Technol., Vol. COM-19, pp. 113119 (1971).
  10. [10] Glave, F. E., “An Upper Bound on the Probability of Error Due to Intersymbol Interference for Correlated Digital Signals,” IEEE Trans. Inform. Theory, Vol. IT-18, pp. 356363 (1972).
  11. [11] Yao, K., “On Minimum Average Probability of Error Expression for Binary Pulse-Communication System with Intersymbol Interference,” IEEE Trans. Inform. Theory, Vol. IT-18, pp. 528531 (1972).
  12. [12] Yao, K. and Tobin, R. M., “Moment Space Upper and Lower Error Bounds Digital Systems with Intersymbol Interference,” IEEE Trans. Inform. Theory, Vol. IT-22, pp. 6574 (1976).
  13. [13] Salz, J., “Optimum Mean-Square Decision-Feedback Equalization,” Bell Syst. Tech. J., Vol. 52, pp. 1341 1373 (1973).
  14. [14] Chen, S., Mulgrew, B., Chng, E. S. and Gibson, G. J., “Space Translation Properties and the Minimum-BER Linear-Combiner DFE,” IEE Proc.-Commun., Vol. 145, pp. 316322 (1998).
  15. [15] Chen, S. and Mulgrew, B., “Minimum-SER LinearCombiner Decision Feedback Equalizer,” IEE Proc. - Commun., Vol. 146, pp. 347353 (1999).
  16. [16] Chen, S., Samingan, A. K., Mulgrew, B. and Hanzo, L., “Adaptive Minimum-BER Linear Multiuser Detection for DS-CDMA Signals in Multipath Channels,” IEEE Trans. Signal Process., Vol. 49, pp. 12401247 (2001).
  17. [17] Chen, S., Hanzo, L. and Mulgrew, B., “Adaptive Minimum Symbol-Error-Rate Decision Feedback Equalization for Multilevel Pulse-Amplitude Modulation,” IEEE Trans. Signal Process., Vol. 52, pp. 20922101 (2004).
  18. [18] Yeh, C.-C. and Barry, J. R., “Adaptive Minimum BitError Rate Equalization for Binary Signaling,” IEEE Trans. Commun., Vol. 48, pp. 12261235 (2000).
  19. [19] , “Adaptive Minimum Symbol-Error Rate Equalization for Quadrature-Amplitude Modulation,” IEEE Trans. Signal Process., Vol. 51, pp. 32633269 (2003).
  20. [20] Liu, H. Y. and Yen, R. Y., “Channel Equalization Using Biased and Unbiased Minimum Error Rate Criteria,” IEICE Trans. Fundamentals, Vol. E87-A, pp. 605609 (2004).
  21. [21] Yen, R. Y., Liu, H. Y., Li, C. W. and Cheng, W. C., “The Adaptive MSINR Algorithm to Improve Error Rate for Channel Equalization,” Signal Processing, Vol. 86, pp. 19841991 (2006).
  22. [22] Yen, R. Y., “Stochstic Unbiased Minimum Mean Error Rate Algorithm for Decision Feedback Equalizers,” IEEE Trans. Signal Processing, Vol. 55, pp. 4758 4766 (2007).

Latest Articles