This paper presents a comparative performance study between the recently proposed time-varying LMS (TVLMS) algorithm and other two main adaptive approaches: the least-mean square (LMS) algorithm and the recursive least squares (RLS) algorithm. Implementational aspects of these algorithms and their computational complexity are examined. Using computer simulations, the successive trade-off between the computational complexity and system noise cancellation ability, as one proceeds from the Wiener estimate to the LMS with fixed step size, becomes apparent. Three performance criteria are utilized in this study: the algorithm execution time, the minimum mean squared error (MSE), and the required filter order. The study showed that the selection of the filter order is based on a trade-off between the MSE performance and algorithm executive time. Results also showed that the execution time of the RLS algorithm increases more rapidly with the filter order than other algorithms. Recently adaptive filtering was presented, have a nice tradeoff between complexity and the convergence speed. This paper also compares a new approach for noise cancellation in speech enhancement using the two new adaptive filtering algorithms named fast affine projection algorithm and fast Euclidean direction search algorithms for attenuating noise in speech signals. The simulation results demonstrate the good performance of the two new algorithms in attenuating the noise.

1. W. Harrison, J. Lim, E. Singer, “A new application of adaptive noise cancellation,” IEEE Trans. Acoustic Speech Signal Processing, vol.34, pp. 21-27, Jan 1986.
2. C. S. Burrus, “Block implementation of digital filters,” IEEE Trans. Circuit Theory, vol. CT-18, pp. 697-701, Nov. 1971.
3. G. A. Clark, S. K. Mitra, and S. R. Parker, “Block implementation of adaptive digital filters,” IEEE Trans. Circuits Syst., vol. CAS-28, pp. 584-592, June 1981.
4. G.A.Clark, S. R. Parker, and S. K. Mitra “A unified approach to time- and frequency-domain realization of FIR adaptive digital filters,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-31, pp. 107%1083, Oct. 1983.
5. W. B. Mikhael and F. H. Wu, “Fast gradient algorithms for block adaptive digital filters,” in Proc. IEEE Inf. Symposium on Circuits and Systems, an Jose, CA, pp. 968-971, May 1986.
6. ~- , “Fast algorithms for block FIR adaptive digital filtering,”IEEE Trans. Circuits Syst., vol.CAS-34, pp. 1152-1160, Oct.1987.
7. “A fast block FIR adaptive digital filtering algorithm with individual adaptation of parameters,” IEEE Trans. Circuits SySt., vol.CAS-36, pp. 1-10, J.+n. 1989.
8. F.H.Wu, “Time-varying gradient algorithms for block implementation of adaptive digital filter,” Ph. D. dissertation, West Virginia University, Morgantown, June 1987.
9. W. B. Mikhael, F.H.Wu, G. Kang, and L. Fransen, “Optimum adaptive algorithms with applications to noise cancellation,” IEEE Trans CircuitsSyst., vol. CAS-31, pp. 312-315, Mar. 1984.
10. W. B. Mikhael, F. H. Wu, L. G. Kazovsky, G. S. Kang, and L. L. Fransen, “Adaptive filters with individual adaption of parameters,” IEEE Tans. CircuitsSyst. Vol.CAS-33, pp. 677-686, July 1986.
11. S.Haykin, Adaptive Filter Theory, Prentice Hall, 1986.
12. M. H. Hayes, Statistical Digital Signal Processing and Modeling, John Wiley &Sons, 1996.
13. H. Leung, and J. Lam, “Design of demodulator for the chaotic modulation communication system,”
14. YS. Lau, Z. M. Hussain, and R. Harris, “A time-varying convergence parameter for the LMS algorithm in the presence of white Gaussian noise,” Submitted to the Australian Telecommunications, Networks and Applications Conference (ATNAC), Melbourne, 2003
15. B. Widrow, S. Steam, Adaptive Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1985.
16. G. Goodwin, k. Sin, Adaptive Filtering Prediction and Control. Englewood Cliffs, NJ: Prentice-Hall, 1985.
17. J. R. Treichler, C. R. Johnson, M. G. Larimore, Theory and Design of Adaptive Filters, Wiley, 1987.
18. S. I. A. Sugiyama, “An adaptive noise canceller with low signal distortion for speech codes” IEEE Trans. Signal Processing, vol. 47, pp. 665-674, Mar 1999.
19. S. Haykin, Adaptive Filter Theory, 4th ed, Prentice Hall, 2002.
20. M. Honig, D, Messerschimitt, Adaptive Filters: Structures, Algorithms and Applications. Boston Kluwer Academic Publishers, 1984.
21. F.Broujeny, Adaptive Filters: Theory and Applications, wiley, 2003.
22. A. H. Sayed, Fundamentals of Adaptive Filtering, Wiley, 2003.
23. P. S. R. Diniz, Adaptive Filtering Algorithms and Practical Implementation, 2 Editions, Kluwer, 2002.

TV-LMS LMS NLMS