Skip to main content
Log in

New Variable Step-Sizes Minimizing Mean-Square Deviation for the LMS-Type Algorithms

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

The least-mean-square-type (LMS-type) algorithms are known as simple and effective adaptation algorithms. However, the LMS-type algorithms have a trade-off between the convergence rate and steady-state performance. In this paper, we investigate a new variable step-size approach to achieve fast convergence rate and low steady-state misadjustment. By approximating the optimal step-size that minimizes the mean-square deviation, we derive variable step-sizes for both the time-domain normalized LMS (NLMS) algorithm and the transform-domain LMS (TDLMS) algorithm. The proposed variable step-sizes are simple quotient forms of the filtered versions of the quadratic error and very effective for the NLMS and TDLMS algorithms. The computer simulations are demonstrated in the framework of adaptive system modeling. Superior performance is obtained compared to the existing popular variable step-size approaches of the NLMS and TDLMS algorithms.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. T. Aboulnasr, K. Mayyas, A robust variable step-size LMS-type algorithm: Analysis and simulations. IEEE Trans. Signal Process. 45, 631–639 (Mar 1997)

    Google Scholar 

  2. W.P. Ang, B. Farhang-Boroujeny, A new class of gradient adaptive step-size LMS algorithms. IEEE Trans. Signal Process. 49(4), 805–810 (Apr 2001)

  3. F. Beaufays, Transform-domain adaptive filters: an analytical approach. IEEE Trans. Signal Process. 43, 422–431 (Feb. 1995)

    Google Scholar 

  4. R.C. Bilcu, P. Kuosmnen, K. Egiazarian, A transform domain LMS adaptive filter with variable step-size. IEEE Signal Process. Lett. 9(2), 51–53 (Feb. 2002)

    Google Scholar 

  5. T.I. Haweel, A simple variable step size LMS adaptive algorithm. Int. J. Circ. Theor. Appl. 32, 523–536 (Nov 2004)

  6. S. Haykin, Adaptive Filter Theory, 3rd edn. (Prentice-Hall, Upper Saddle River, NJ, 1996)

    Google Scholar 

  7. H.-C. Huang, J. Lee, A new variable step-size NLMS algorithm and its performance analysis. IEEE Trans. Signal Process. 60(4), 2055–2060 (Apr 2012)

  8. D.I. Kim, P. De Wilde, Performance analysis of the DCT-LMS adaptive filtering algorithm. Signal Process. 80(8), 1629–1654 (Aug. 2000)

    Google Scholar 

  9. B. Krstajić, D. Ojdanić, A. Vu\(\breve{\text{ c }}\)inić, Z. Uskoković, L. Stanković, An approach to transform domain variable step-size LMS adaptive filter. The 12th European Signal Processing Conference (EUSIPCO 2004), Sep 2004, pp. 1813–1816

  10. R.H. Kwong, E.W. Johnston, A variable step size LMS algorithm. IEEE Trans. Signal Process. 40, 1633–1642 (July 1992)

  11. J. Lee, C. Un, Performance of transform-domain LMS adaptive digital filters. IEEE Trans. Acoustic. Speech Signal Process. 34, 499–510 (1986)

    Google Scholar 

  12. A. Mader, H. Puder, G.U. Schmidt, Step-size control for acoustic echo cancellation filters: an overview. Signal Process. 80, 1697–1719 (Sep 2000)

  13. K. Mayyas, A Transform Domain LMS Algorithm with an Adaptive Step Size Equation. in The 4th IEEE International Symposium on Signal Processing and Information Technology ISSPIT’ 2004 (Rome, Italy, 2004), pp. 28–30

  14. S.S. Narayan, A.M. Peterson, M.J. Narashima, Transform domain LMS algorithm. IEEE Trans. Acoust. Speech Signal Process. 31, 609–615 (Jun 1983)

    Google Scholar 

  15. D.I. Pazaitis, A.G. Constantinides, A novel kurtosis driven variable step-size adaptive algorithm. IEEE Trans. Signal Process. 47, 864–872 (Mar 1999)

  16. A.H. Sayed, Fundamentals of Adaptive Filtering (Wiley, New York, 2003)

  17. H.C. Shin, A.H. Sayed, W.J. Song, Variable step-size NLMS and affine projection algorithms. IEEE Signal Process. Lett. 11, 132–135 (Feb 2004)

  18. A.I. Sulyman, A. Zerguine, Convergence and steady-state analysis of a variable step-size NLMS algorithm. Signal Process. 83, 1255–1273 (Jun 2003)

    Google Scholar 

  19. M. N Suma, B. Kanmani, Channel Equalization with efficient variable step-size transform domain adaptive algorithm. ELIXIR Netw. Eng. J. 38 (2011)

  20. B. Widrow, S.D. Stearns, Adaptive Signal Processing, Englewood Cliffs (Prentice-Hall, NJ, 1985)

  21. S. Zhao, Z. Man, S. Khoo, H.R. Wu, Variable step-size LMS algorithm with a quotient form. Signal Process. 89, 67–76 (2009)

    Article  MATH  Google Scholar 

  22. S. Zhao, Z. Man, S. Khoo, H.R. Wu, Stability and convergence analysis of transform-domain LMS adaptive filters with second-order autoregressive process. IEEE Trans. Signal Process. 57(1), 119–130 (Jan 2009)

    Google Scholar 

  23. Y.-G. Zhu, Y.-G. Li, S.-Y. Guan, Q.-S. Shan, A novel variable step-size NLMS algorithm and its analysis. in The 2012 International Workshop on Information and Electronics Engineer (IWIEE 2012), vol. 29, pp. 1181–1185 (2012)

Download references

Acknowledgments

This study was supported by the research grant for the Human Sixth Sense Programme at the Advanced Digital Sciences Center from Singapore’s Agency for Science, Technology and Research (A\(^*\)STAR).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Shengkui Zhao.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhao, S., Jones, D.L., Khoo, S. et al. New Variable Step-Sizes Minimizing Mean-Square Deviation for the LMS-Type Algorithms. Circuits Syst Signal Process 33, 2251–2265 (2014). https://doi.org/10.1007/s00034-014-9744-2

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-014-9744-2

Keywords

Navigation