Science in China Series F: Information Sciences

, Volume 46, Issue 6, pp 409–419 | Cite as

Optimal variable step-size LMS model and algorithm with independence assumption

  • Gu Yuantao Email author
  • Tang Kun 
  • Cui Huijuan 
  • Du Wen 


To solve the contradiction between convergence rate and steady-state error in least mean square (LMS) algorithm, basing on independence assumption, this paper proposes and proves the optimal step-size theorem from the view of minimizing mean squared error (MSE). The theorem reveals the one-to-one mapping between the optimal step-size and MSE. Following the theorem, optimal variable step-size LMS (OVS-LMS) model, describing the theoretical bound of the convergence rate of LMS algorithm, is constructed. Then we discuss the selection of initial optimal step-size and updating of optimal step-size at the time of unknown system changing. At last an optimal step-size LMS algorithm is proposed and tested in various environments. Simulation results show the proposed algorithm is very close to the theoretical bound.


LMS OVS-LMS variable step-size optimal step-size theorem 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Haykin, S., Adaptive Filter Theory (3rd ed.), Beijing: Publishing House of Electronics Industry, 1998.Google Scholar
  2. 2.
    Breining, C., Dreiseitel, P., Hansler, E. et al., Acoustic echo control, an application of very-high-order adaptive filters, IEEE Sig. Proc. Magazine, 1999, (7): 42–69.Google Scholar
  3. 3.
    Park, M. -S., Song, W. -J., A complementary pair LMS algorithm for adaptive filtering, IEICE Trans. on Fundamentals, 1998, E81-A(7):1493–1497.Google Scholar
  4. 4.
    Kwong, R. H., Johnston, E. W., A variable step size LMS algorithm, IEEE Trans. on Sig. Proc., 1992, 40(7): 1633–1642.zbMATHCrossRefGoogle Scholar
  5. 5.
    Harris, R. W., Chabries, D. M., Bishop, F. A., A variable step (VS) adaptive filter algorithm, IEEE Trans. on Acous., Speech, and Sig. Proc., 1986, ASSP-34(2):309–313.CrossRefGoogle Scholar
  6. 6.
    Mathews, V. J., Xie Zhenhua, A stochastic gradient adaptive filter with gradient adaptive step size, IEEE Trans. on Sig. Proc., 1993, 41(6): 2075–2087.CrossRefGoogle Scholar

Copyright information

© Science in China Press 2003

Authors and Affiliations

  • Gu Yuantao 
    • 1
    Email author
  • Tang Kun 
    • 1
  • Cui Huijuan 
    • 1
  • Du Wen 
    • 1
  1. 1.State Key Laboratory on Microwave and Digital Communications, Department of Electronics EngineeringTsinghua UniversityBeijingChina

Personalised recommendations