{"title":"A Novel Convergence Accelerator for the LMS Adaptive Algorithm","authors":"Jeng-Shin Sheu, Jenn-Kaie Lain, Tai-Kuo Woo, Jyh-Horng Wen","volume":41,"journal":"International Journal of Information and Communication Engineering","pagesStart":922,"pagesEnd":927,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/121","abstract":"The least mean square (LMS) algorithmis one of the\r\nmost well-known algorithms for mobile communication systems\r\ndue to its implementation simplicity. However, the main limitation\r\nis its relatively slow convergence rate. In this paper, a booster\r\nusing the concept of Markov chains is proposed to speed up the\r\nconvergence rate of LMS algorithms. The nature of Markov\r\nchains makes it possible to exploit the past information in the\r\nupdating process. Moreover, since the transition matrix has a\r\nsmaller variance than that of the weight itself by the central limit\r\ntheorem, the weight transition matrix converges faster than the\r\nweight itself. Accordingly, the proposed Markov-chain based\r\nbooster thus has the ability to track variations in signal\r\ncharacteristics, and meanwhile, it can accelerate the rate of\r\nconvergence for LMS algorithms. Simulation results show that the\r\nLMS algorithm can effectively increase the convergence rate and\r\nmeantime further approach the Wiener solution, if the\r\nMarkov-chain based booster is applied. The mean square error is\r\nalso remarkably reduced, while the convergence rate is improved.","references":"[1] S. Gazor, \"Predictions in LMS-type adaptive algorithms for smoothly\r\ntime-varying environments,\" IEEE Trans. Signal Process., vol. 47, no. 7,\r\npp. 1735-1739, Jun. 1999.\r\n[2] D. G. Manolakis, V. K. Ingle, and S. M.Kogan, Statistical and Adaptive\r\nSignal Processing. New York: McGraw-Hill Int. Editions, 2000.\r\n[3] Haykin, S.: \u00d4\u00c7\u00ffAdaptive Filter Theory- (Prentice Hall, 1995.)\r\n[4] V. Solo and X. Kong, Adaptive Signal Processing Algorithms: Stability\r\nand Performance. Englewood Cliffs, NJ: Prentice-Hall, 1995.\r\n[5] Evans, J. B., Xue, P. and Liu, B.: \u00d4\u00c7\u00ffAnalysis and implementation of\r\nvariable step size adaptive algorithm-, IEEE Trans. Signal Processing,\r\n1993, vol. 41, pp. 2517-2535.\r\n[6] Aboulnasr, T. and Mayyas, K.: \u00d4\u00c7\u00ffA robust variable step-size LMS-type\r\nalgorithm: Analysis and simulations-, IEEE Trans. Signal Processing,\r\n1997, vol. 45, pp. 631-639.\r\n[7] Hosur, S. and Tewfik, A. H., \"Wavelet transform domain LMS\r\nalgorithm,\" Proc. ICASSP, April 1993, Minneapolis, Minnesota, USA,\r\npp. 508-510.\r\n[8] Erdol, N. and Basbug, F., \"Performance of wavelet transform based\r\nadaptive filters-. Proc.ICASSP, April 1993, Minneapolis, Minnesota,\r\nUSA, pp. 500-503.\r\n[9] Narayan, S. S., Peterson, A. M. and Narashima, M. J., \"Transform\r\ndomain LMS algorithm\", IEEE Trans. Acoust., Speech, Signal\r\nProcessing, June. 1983, vol. 31, pp. 4609-615.\r\n[10] Widrow, B., \"Fundamental relations between the LMS algorithm and the\r\nDFT,\" IEEE Trans. Circuits Syst., vol. CAS-34, pp. 814-819.\r\n[11] Von Neumann, J., Kent, R. H., Bellinson, H. R. and Habt, B. I., \"The\r\nmean square successive difference,\"Ann.Math. Statist. Vol. 12, 1941, pp.\r\n153-162.\r\n[12] Ghosh, M. and Meeden, G.: \u00d4\u00c7\u00ffOn the non-attainability of Chebychev\r\nbounds-, American Statistician, 1977, 31, pp. 35-36.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 41, 2010"}