Superior step-size theorem and its application

Parallel variable step-size LMS filters algorithm


With independence assumption, this paper proposes and proves the superior step-size theorem on least mean square (LMS) algorithm, from the view of minimizing mean squared error (MSE). Following the theorem we construct a parallel variable step-size LMS filters algorithm. The theoretical model of the proposed algorithm is analyzed in detail. Simulations show the proposed theoretical model is quite close to the optimal variable step-size LMS (OVS-LMS) model. The experimental learning curves of the proposed algorithm also show the fastest convergence and fine tracking performance. The proposed algorithm is therefore a good realization of the OVS-LMS model.

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  1. 1.

    Haykin, S., Adaptive Filter Theory (3rd ed.), Beijing: Publishing House of Electronics Industry, 1998.

    Google Scholar 

  2. 2.

    Gu, Y. T., Tang, K., Cui, H. J. et al., Novel variable step-size NLMS algorithm, Journal of Tsinghua Univ. (in Chinese), 2002, 42(1): 15–18.

    Google Scholar 

  3. 3.

    Park, M. S., Song, W., Jin, A., Complementary pair LMS algorithm for adaptive filtering, IEICE Trans. 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 Signal Processing, 1992, 40(7): 1633–1642.

    MATH  Article  Google Scholar 

  5. 5.

    Harris, R. W., Chabries, D. M., Bishop, F. A., A variable step (VS) adaptive filter algorithm, IEEE Trans. Acous., Speech, and Signal Processing, 1986, ASSP-34(2):309–313.

    Article  Google Scholar 

  6. 6.

    Gu, Y. T., Tang, K., Cui, H. J. et al., Optimal variable step-size LMS model and algorithm with independence assumption, Science in China, Ser. F., 2003, 46(6): 409–419.

    MATH  Article  Google Scholar 

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Correspondence to Yuantao Gu.

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Gu, Y., Tang, K. & Cui, H. Superior step-size theorem and its application. Sci China Ser F 47, 151–160 (2004).

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  • adaptive filtering
  • LMS
  • superior step-size theorem
  • parallel variable step-size LMS filters algorithm