Skip to main content
SpringerLink
Log in

LMS-Based Variable Step-Size Algorithms: A Unified Analysis Approach

  • Research Article - Electrical Engineering
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

Several variable step-size strategies have been suggested in the literature to improve the performance of the least-mean-square (LMS) algorithm. Although they enhance performance, a major drawback is the complexity in the theoretical analysis of these algorithms. Researchers use several assumptions to find closed-form analytical solutions. This work presents a unified approach for the analysis of variable step-size LMS algorithms. The approach is then applied to several variable step-size strategies, and theoretical and simulation results are compared.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

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

    Google Scholar 

  2. Nagumo, J.; Noda, A.: A learning method for system identification. IEEE Trans. Autom. Control. 12, 282–287 (1967)

    Article  Google Scholar 

  3. Harris, R.; Chabries, D.M.; Bishop, F.: A variable step (VS) adaptive filter algorithm. IEEE Trans. Acoust. Speech Signal Process. 34, 309–316 (1986)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  5. Mathews, V.J.; Xie, Z.: A stochastic gradient adaptive filter with gradient adaptive step size. IEEE Trans. Signal Process. 41, 2075–2087 (1993)

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  7. Gollamudi, S.; Nagaraj, S.; Kapoor, S.; Huang, Y.-F.: Set-membership filtering and a set-membership normalized LMS algorithm with an adaptive step size. IEEE Signal Process. Lett. 5, 111–114 (1998)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  10. Wei, Y.; Gelfand, S.B.; Krogmeier, J.V.: Noise-constrained least mean squares algorithm. IEEE Trans. Signal Process. 49, 1961–1970 (2001)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  12. Egiazarian, K.; Kuosmanen, P.; Bilcu, R.C.: Variable step-size LMS adaptive filters for CDMA multiuser detection. In: Proceedings of TELSIKS ’03, pp. 259–264 (2003)

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

    Article  Google Scholar 

  14. Benesty, J.; Rey, H.; Vega, L.R.; Tressens, S.: A nonparametric VSS NLMS algorithm. IEEE Signal Process. Lett. 13, 581–584 (2006)

    Article  Google Scholar 

  15. Akhtar, M.T.; Abe, M.; Kawamata, M.: A new variable step size LMS algorithm-based method for improved online secondary path modeling in active noise control systems. IEEE Trans. Audio Speech Lang. Process. 14, 720–726 (2006)

    Article  Google Scholar 

  16. Zhang, Y.; Li, N.; Chambers, J.A.; Hao, Y.: New gradient-based variable step size LMS algorithms. EURASIP J. Adv. Signal Process. 2008, 1–9 (2008)

    MATH  Google Scholar 

  17. Costa, M.H.; Bermudez, J.C.M.: A noise resilient variable step-size LMS algorithm. Signal Process. 88, 733–748 (2008)

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  19. Hwang, J.-K.; Li, Y.-P.: Variable step-size LMS algorithm with a gradient-based weighted average. IEEE Signal Process. Lett. 16, 1043–1046 (2009)

    Article  Google Scholar 

  20. Filho, A.M.A.; Pinto, E.L.; Galdino, J.F.: Simple and robust analytically derived variable step-size least mean squares algorithm for channel estimation. IET Commun. 3, 1832–1842 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  21. Narasimhan, S.V.: New unbiased adaptive IIR filter: its robust and variable step-size versions and application to active noise control. Signal Image Video Process. 7, 197–207 (2013)

    Article  Google Scholar 

  22. Bin Saeed, M.O.; Zerguine, A.: A variable step-size strategy for sparse system identification. In: Proceedings of SSD ’13, pp. 1–4 (2013).

  23. Bin Saeed, M.O.; Zerguine, A.; Zummo, S.A.: A variable step-size strategy for distributed estimation over adaptive networks. EURASIP J. Adv. Signal Process. 2013, 135 (2013)

    Article  MATH  Google Scholar 

  24. Bin Saeed, M.O.; Zerguine, A.; Zummo, S.A.: A noise-constrained algorithm for estimation over distributed networks. Int. J. Adapt. Control Signal Process. 27, 827–845 (2013)

  25. Gil-Cacho, J.M.; Waterschoot, Tv; Moonen, M.; Jensen, S.H.: Wiener variable step size and gradient spectral variance smoothing for double-talk-robust acoustic echo cancellation and acoustic feedback cancellation. Signal Process. 104, 1–14 (2014)

    Article  Google Scholar 

  26. Al-Naffouri, T.Y.; Moinuddin, M.: Exact performance analysis of the \(\epsilon \)-NLMS algorithm for colored circular gaussian inputs. IEEE Trans. Signal Process. 58, 5080–5090 (2010)

    Article  MathSciNet  Google Scholar 

  27. Al-Naffouri, T.Y.; Moinuddin, M.; Sohail, M.S.: Mean weight behavior of the NLMS algorithm for correlated gaussian inputs. IEEE Signal Process. Lett. 18, 7–10 (2011)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Engineering, College of Electrical and Mechanical Engineering, National University of Sciences and Technology, Islamabad, Pakistan

    Muhammad Omer Bin Saeed

Authors
  1. Muhammad Omer Bin Saeed
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Muhammad Omer Bin Saeed.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Saeed, M.O.B. LMS-Based Variable Step-Size Algorithms: A Unified Analysis Approach. Arab J Sci Eng 42, 2809–2816 (2017). https://doi.org/10.1007/s13369-017-2453-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-017-2453-y

Keywords

Search

Navigation