A Novel Convergence Accelerator for the LMS Adaptive Algorithm
The least mean square (LMS) algorithmis one of the
most well-known algorithms for mobile communication systems
due to its implementation simplicity. However, the main limitation
is its relatively slow convergence rate. In this paper, a booster
using the concept of Markov chains is proposed to speed up the
convergence rate of LMS algorithms. The nature of Markov
chains makes it possible to exploit the past information in the
updating process. Moreover, since the transition matrix has a
smaller variance than that of the weight itself by the central limit
theorem, the weight transition matrix converges faster than the
weight itself. Accordingly, the proposed Markov-chain based
booster thus has the ability to track variations in signal
characteristics, and meanwhile, it can accelerate the rate of
convergence for LMS algorithms. Simulation results show that the
LMS algorithm can effectively increase the convergence rate and
meantime further approach the Wiener solution, if the
Markov-chain based booster is applied. The mean square error is
also remarkably reduced, while the convergence rate is improved.
[1] S. Gazor, "Predictions in LMS-type adaptive algorithms for smoothly
time-varying environments," IEEE Trans. Signal Process., vol. 47, no. 7,
pp. 1735-1739, Jun. 1999.
[2] D. G. Manolakis, V. K. Ingle, and S. M.Kogan, Statistical and Adaptive
Signal Processing. New York: McGraw-Hill Int. Editions, 2000.
[3] Haykin, S.: ÔÇÿAdaptive Filter Theory- (Prentice Hall, 1995.)
[4] V. Solo and X. Kong, Adaptive Signal Processing Algorithms: Stability
and Performance. Englewood Cliffs, NJ: Prentice-Hall, 1995.
[5] Evans, J. B., Xue, P. and Liu, B.: ÔÇÿAnalysis and implementation of
variable step size adaptive algorithm-, IEEE Trans. Signal Processing,
1993, vol. 41, pp. 2517-2535.
[6] Aboulnasr, T. and Mayyas, K.: ÔÇÿA robust variable step-size LMS-type
algorithm: Analysis and simulations-, IEEE Trans. Signal Processing,
1997, vol. 45, pp. 631-639.
[7] Hosur, S. and Tewfik, A. H., "Wavelet transform domain LMS
algorithm," Proc. ICASSP, April 1993, Minneapolis, Minnesota, USA,
pp. 508-510.
[8] Erdol, N. and Basbug, F., "Performance of wavelet transform based
adaptive filters-. Proc.ICASSP, April 1993, Minneapolis, Minnesota,
USA, pp. 500-503.
[9] Narayan, S. S., Peterson, A. M. and Narashima, M. J., "Transform
domain LMS algorithm", IEEE Trans. Acoust., Speech, Signal
Processing, June. 1983, vol. 31, pp. 4609-615.
[10] Widrow, B., "Fundamental relations between the LMS algorithm and the
DFT," IEEE Trans. Circuits Syst., vol. CAS-34, pp. 814-819.
[11] Von Neumann, J., Kent, R. H., Bellinson, H. R. and Habt, B. I., "The
mean square successive difference,"Ann.Math. Statist. Vol. 12, 1941, pp.
153-162.
[12] Ghosh, M. and Meeden, G.: ÔÇÿOn the non-attainability of Chebychev
bounds-, American Statistician, 1977, 31, pp. 35-36.
[1] S. Gazor, "Predictions in LMS-type adaptive algorithms for smoothly
time-varying environments," IEEE Trans. Signal Process., vol. 47, no. 7,
pp. 1735-1739, Jun. 1999.
[2] D. G. Manolakis, V. K. Ingle, and S. M.Kogan, Statistical and Adaptive
Signal Processing. New York: McGraw-Hill Int. Editions, 2000.
[3] Haykin, S.: ÔÇÿAdaptive Filter Theory- (Prentice Hall, 1995.)
[4] V. Solo and X. Kong, Adaptive Signal Processing Algorithms: Stability
and Performance. Englewood Cliffs, NJ: Prentice-Hall, 1995.
[5] Evans, J. B., Xue, P. and Liu, B.: ÔÇÿAnalysis and implementation of
variable step size adaptive algorithm-, IEEE Trans. Signal Processing,
1993, vol. 41, pp. 2517-2535.
[6] Aboulnasr, T. and Mayyas, K.: ÔÇÿA robust variable step-size LMS-type
algorithm: Analysis and simulations-, IEEE Trans. Signal Processing,
1997, vol. 45, pp. 631-639.
[7] Hosur, S. and Tewfik, A. H., "Wavelet transform domain LMS
algorithm," Proc. ICASSP, April 1993, Minneapolis, Minnesota, USA,
pp. 508-510.
[8] Erdol, N. and Basbug, F., "Performance of wavelet transform based
adaptive filters-. Proc.ICASSP, April 1993, Minneapolis, Minnesota,
USA, pp. 500-503.
[9] Narayan, S. S., Peterson, A. M. and Narashima, M. J., "Transform
domain LMS algorithm", IEEE Trans. Acoust., Speech, Signal
Processing, June. 1983, vol. 31, pp. 4609-615.
[10] Widrow, B., "Fundamental relations between the LMS algorithm and the
DFT," IEEE Trans. Circuits Syst., vol. CAS-34, pp. 814-819.
[11] Von Neumann, J., Kent, R. H., Bellinson, H. R. and Habt, B. I., "The
mean square successive difference,"Ann.Math. Statist. Vol. 12, 1941, pp.
153-162.
[12] Ghosh, M. and Meeden, G.: ÔÇÿOn the non-attainability of Chebychev
bounds-, American Statistician, 1977, 31, pp. 35-36.
@article{"International Journal of Information, Control and Computer Sciences:49267", author = "Jeng-Shin Sheu and Jenn-Kaie Lain and Tai-Kuo Woo and Jyh-Horng Wen", title = "A Novel Convergence Accelerator for the LMS Adaptive Algorithm", abstract = "The least mean square (LMS) algorithmis one of the
most well-known algorithms for mobile communication systems
due to its implementation simplicity. However, the main limitation
is its relatively slow convergence rate. In this paper, a booster
using the concept of Markov chains is proposed to speed up the
convergence rate of LMS algorithms. The nature of Markov
chains makes it possible to exploit the past information in the
updating process. Moreover, since the transition matrix has a
smaller variance than that of the weight itself by the central limit
theorem, the weight transition matrix converges faster than the
weight itself. Accordingly, the proposed Markov-chain based
booster thus has the ability to track variations in signal
characteristics, and meanwhile, it can accelerate the rate of
convergence for LMS algorithms. Simulation results show that the
LMS algorithm can effectively increase the convergence rate and
meantime further approach the Wiener solution, if the
Markov-chain based booster is applied. The mean square error is
also remarkably reduced, while the convergence rate is improved.", keywords = "LMS, Markov chain, convergence rate, accelerator.", volume = "4", number = "5", pages = "857-5", }