Abstract
Adaptive digital filtering has traditionally been developed based on the minimum mean square error (MMSE) criterion and has found ever-increasing applications in communications. This paper presents an alternative adaptive filtering design based on the minimum symbol error rate (MSER) criterion for communication applications. It is shown that the MSER filtering is smarter, as it exploits the non-Gaussian distribution of filter output effectively. Consequently, it provides significant performance gain in terms of smaller symbol error over the MMSE approach. Adopting Parzen window or kernel density estimation for a probability density function, a block-data gradient adaptive MSER algorithm is derived. A stochastic gradient adaptive MSER algorithm, referred to as the least symbol error rate, is further developed for sample-by-sample adaptive implementation of the MSER filtering. Two applications, involving single-user channel equalization and beamforming assisted receiver, are included to demonstrate the effectiveness and generality of the proposed adaptive MSER filtering approach.
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References
B. Widrow, S. D. Stearns. Adaptive Signal Processing. Prentice-Hall, Englewood Cliffs, NJ, 1985.
S. Haykin. Adaptive Filter Theory. 3rd edition, Prentice-Hall, Upper Saddle River, NJ, 1996.
E. Shamash, K. Yao. On the Structure and Performance of a Linear Decision Feedback Equalizer Based on the Minimum Error Probability Criterion. In Proceedings of International Communications Conference, pp. 25F1–25F5, 1974.
S. Chen, E. S. Chng, B. Mulgrew, G. Gibson. Minimum-BER Linear-combiner DFE. In Proceedings of International Communications Conference, Dallas, Texas, vol. 2, pp. 1173–1177, 1996.
C. C. Yeh, J. R. Barry. Approximate Minimum Bit-Error Rate Equalization for Binary Signaling. In Proceedings of International Communications Conference, Montreal, Canada, vol. 2, pp. 1095–1099, 1997.
S. Chen, B. Mulgrew, E. S. Chng, G. Gibson. Space Translation Properties and the Minimum-BER Linear-combiner DFE. IEE Proceedings of Communications, vol. 145, no. 5, pp. 316–322. 1998.
B. Mulgrew, S. Chen. Stochastic Gradient Minimum-BER Decision Feedback Equalisers. In Proceedings of IEEE Symposium on Adaptive Systems for Signal Processing, Communication and Control, Lake Louise, Alberta, Canada, Oct. 1–4, pp. 93–98, 2000.
C. C. Yeh, J. R. Barry. Adaptive Minimum Bit-Error Rate Equalization for Binary Signaling. IEEE Transactions Communications, vol. 48, no. 7, pp. 1226–1235, 2000.
B. Mulgrew, S. Chen. Adaptive Minimum-BER Decision Feedback Equalisers for Binary Signaling. Signal Processing, vol. 81, no. 7, pp. 1479–1489, 2001.
N. B. Mandayam, B. Aazhang. Gradient Estimation for Sensitivity Analysis and Adaptive Multiuser Interference Rejection in Code-division Multi-access Systems. IEEE Transactions on Communications, vol. 45, no. 7, pp. 848–858, 1997.
C. C. Yeh, R. R. Lopes, J. R. Barry. Approximate Minimum Bit-Error Rate Multiuser Detection. In Proceedings of Globecom’ 98, Sydney, Australia, pp. 3590–3595, 1998.
X. F. Wang, W. S. Lu, A. Antoniou. Constrained Minimum-BER Multiuser Detection. In Proceedings of International Conference on Acoustics Speech and Signal Processing, Phoenix, USA, vol. 5, pp. 2603–2606, May 14–18, 1999.
I. N. Psaromiligkos, S. N. Batalama, D. A. Pados. On Adaptive Minimum Probability of Error Linear Filter Receivers for DS-CDMA Channels. IEEE Transactions Communications, vol. 47, no. 7, pp. 1092–1102, 1999.
S. Chen, A. K. Samingan, B. Mulgrew, L. Hanzo. Adaptive Minimum-BER Linear Multiuser Detection. In Proceedings of International Conference on Acoustics Speech and Signal Processing. Salt Lake City, Utah, USA, vol.4, pp. 2253–2256, May 7–11, 2001.
S. Chen, A. K. Samingan, B. Mulgrew, L. Hanzo. Adaptive Minimum-BER Linear Multiuser Detection for DS-CDMA Signals in Multipath Channels. IEEE Transactions on Signal Processing, vol. 49, no. 6, 1240–1247, 2001.
R. C. de Lamare, R. Sampaio-Neto. Adaptive MBER Decision Feedback Multiuser Receivers in Frequency Selective Fading Channels. IEEE Communications Letters, vol. 7, no. 2, pp. 73–75, 2003.
S. Chen, N. N. Ahmad, L. Hanzo. Smart Beamforming for Wireless Communications: A Novel Minimum Bit-error Rate Approach. In Proceedings of 2nd IMA International Conference Mathematics in Communications, Lancaster, U.K., Dec. 16–18, 2002.
S. Chen, L. Hanzo, N. N. Ahmad. Adaptive Minimum Biterror Rate Beamforming Assisted Receiver for Wireless Communications. In Proceedings of International Conference on Acoustics Speech and Signal Processing 2003, Hong Kong, China, vol. IV, pp. 640–643, April 6–10, 2003.
S. Chen, N. N. Ahmad, L. Hanzo. Adaptive Minimum Bit-Error Rate Beamforming. IEEE Transactions on Wireless Communications, vol. 4, no. 2, pp. 341–348, 2005.
J. G. Proakis. Digital Communications. 3rd ed., McGraw-Hill, New York, 1995.
E. Parzen. On Estimation of a Probability Density Function and Mode. The Annals of Mathematical Statistics, vol. 33, pp. 1066–1076, 1962.
B. W. Silverman. Density Estimation. Chapman Hall, London, 1996.
A. W. Bowman, A. Azzalini. Applied Smoothing Techniques for Data Analysis. Oxford University Press, Oxford, UK, 1997.
R. Johnson, Jr. P. Schniter, T. J. Endres, J. D. Behm, D. R. Brown, R. A. Casas. Blind Equalization Using the Constant Modulus Criterion: A Review. Proceedings of IEEE, vol. 86, no. 10, pp. 1927–1950, 1998.
S. Chen, B. Mulgrew, P. M. Grant. A Clustering Technique for Digital Communications Channel Equalisation Using Radial Basis Function Networks. IEEE Transactions on Neural Networks, vol. 4, no. 4, pp. 570–579, 1993.
S. Chen, B. Mulgrew, S. McLaughlin. Adaptive Bayesian Equaliser with Decision Feedback. IEEE Transactions on Signal Processing, vol. 41, no. 9, pp. 2918–2927, 1993.
S. Chen, S. McLaughlin, B. Mulgrew, P. M. Grant. Bayesian Decision Feedback Equaliser for Overcoming Co-Channel Interference. IEE Proceedings of Communications, vol. 143, no. 4, pp. 219–225, 1996.
S. Chen, A. K. Samingan, L. Hanzo. Support Vector Machine Multiuser Receiver for DS-CDMA Signals in Multipath Channels. IEEE Transactions on Neural Networks, vol. 12, no. 3, pp. 604–611, 2001.
S. Chen, B. Mulgrew, L. Hanzo. Adaptive Least Error Rate Algorithm for Neural Network Classifier. In Proceedings of 2001 IEEE Workshop Neural Networks for Signal Processing, Falmouth, MA, USA, pp. 223–232, Sept. 10–12, 2001.
S. Chen, B. Mulgrew, L. Hanzo. Least Bit-Error Rate Adaptive Nonlinear Equalizers for Binary Signalling. IEEE Proceedings of Communications, vol. 150, no. 1, pp. 29–36, 2003.
S. Chen, L. Hanzo, A. Wolfgang. Nonlinear Multi-Antenna Detection Methods. EURASIP Journal of Applied Signal Processing, vol. 2004, no. 9, pp. 1225–1237, 2004.
M. S. Bazaraa, H. D. Sherali, C. M. Shetty. Nonlinear Programming: Theory and Algorithms. John Wiley, New York, 1993.
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Sheng Chen obtained a B.Eng degree in control engineering from the East China Petroleum Institute, Dongying, China, in 1982, and a Ph.D. degree in control engineering from the City University at London in 1986. He joined the School of Electronics and Computer Science at the University of Southampton in September 1999. He previously held research and academic appointments at the Universities of Sheffield, Edinburgh and Portsmouth.
He has published over 240 research papers. His recent research interests include adaptive nonlinear signal processing, wireless communications, modeling and identification of nonlinear systems, neural networks and machine learning, finite-precision digital controller design, evolutionary computation methods and optimization.
Dr Chen is a Senior Member of IEEE.
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Chen, S. Adaptive linear filtering design with minimum symbol error probability criterion. Int J Automat Comput 3, 291–303 (2006). https://doi.org/10.1007/s11633-006-0291-6
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DOI: https://doi.org/10.1007/s11633-006-0291-6