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

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Abstract

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.

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Authors and Affiliations

  1. State Key Laboratory on Microwave and Digital Communications, Department of Electronics Engineering, Tsinghua University, 100084, Beijing, China

    Gu Yuantao, Tang Kun, Cui Huijuan & Du Wen

Authors
  1. Gu Yuantao
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  2. Tang Kun
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  3. Cui Huijuan
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  4. Du Wen
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Correspondence to Gu Yuantao.

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Gu, Y., Tang, K., Cui, H. et al. Optimal variable step-size LMS model and algorithm with independence assumption. Sci China Ser F 46, 409–419 (2003). https://doi.org/10.1360/01yf0621

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  • DOI: https://doi.org/10.1360/01yf0621

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