Advertisement

Circuits, Systems, and Signal Processing

, Volume 36, Issue 3, pp 1322–1339 | Cite as

Nonparametric Variable Step-Size LMAT Algorithm

  • Sihai Guan
  • Zhi LiEmail author
Short Paper

Abstract

This paper proposes a nonparametric variable step-size least mean absolute third (NVSLMAT) algorithm to improve the capability of the adaptive filtering algorithm against the impulsive noise and other types of noise. The step-size of the NVSLMAT is obtained using the instantaneous value of a current error estimate and a posterior error estimate. This approach is different from the traditional method of nonparametric variance estimate. In the NVSLMAT algorithm, fewer parameters need to be set, thereby reducing the complexity considerably. Additionally, the mean of the additive noise does not necessarily equal zero in the proposed algorithm. In addition, the mean convergence and steady-state mean-square deviation of the NVSLMAT algorithm are derived and the computational complexity of NVSLMAT is analyzed theoretically. Furthermore, the experimental results in system identification applications presented illustrate the principle and efficiency of the NVSLMAT algorithm.

Keywords

LMAT Variable step-size Impulsive noise Nonparametric Most of the noise densities System identification 

Notes

Acknowledgments

This work was partially supported by the National Natural Science Foundation of China (Grant: 61074120) and the Ph.D. Programs Foundation of the Ministry of Education of China (Grant: 20110203110004).

References

  1. 1.
    W.P. Ang, B. Farhang-Boroujeny, A new class of gradient adaptive step-size LMS algorithms. IEEE Trans. Signal Process. 49(4), 805–810 (2001)CrossRefGoogle Scholar
  2. 2.
    J. Benesty, H. Rey, L. Rey, Vega, S. Tressens, A nonparametric VSS NLMS algorithm. IEEE Signal Process. Lett. 13(10), 581–584 (2006)CrossRefGoogle Scholar
  3. 3.
    D. Bismor, LMS algorithm step-size adjustment for fast convergence. Arch. Acoust. 37(1), 31–40 (2012)CrossRefGoogle Scholar
  4. 4.
    S.H. Cho, S.D. Kim, H.P. Moom, J.Y. NA, The least mean absolute third (LMAT) adaptive algorithm: mean and mean-squared convergence properties. In Proceedings of Sixth Western Pacific Reg. Acoust. Conf., Hong Kong, 22(10), 2303–2309 (1997)Google Scholar
  5. 5.
    P.S.R. Diniz, Adaptive Filtering, vol. Fourth (Springer, Boston, 2013)CrossRefzbMATHGoogle Scholar
  6. 6.
    E. Eweda, Dependence of the stability of the least mean fourth algorithm on target weights nonstationarity. IEEE Trans. Signal Process. 62(7), 1634–1643 (2014)MathSciNetCrossRefGoogle Scholar
  7. 7.
    E. Eweda, N. Bershad, Stochastic analysis of a stable normalized least mean fourth algorithm for adaptive noise canceling with a white gaussian reference. IEEE Trans. Signal Process. 60(12), 6235–6244 (2012)MathSciNetCrossRefGoogle Scholar
  8. 8.
    X.Z. FU, Z. Liu, C.X. LI, Anti-interference performance improvement for sigmoid function variable step-size LMS adaptive algorithm. J. Beijing Univ. Posts Telecommun. 34(6), 112–120 (2011)Google Scholar
  9. 9.
    K. Hirano, Rayleigh Distribution (Wiley, London, 2014)CrossRefGoogle Scholar
  10. 10.
    S.D. Kim, S.S. Kim, S.H. Cho, Least mean absolute third (LMAT) adaptive algorithm: part II. Perform. Eval. Algorithm 22(10), 2310–2316 (1997)Google Scholar
  11. 11.
    R.H. Kwong, E.W. Johnston, A variable step-size LMS algorithm. IEEE Trans. Signal Process. 40(7), 1633–1642 (1992)CrossRefzbMATHGoogle Scholar
  12. 12.
    Y.H. Lee, D.M. Jin, D.K. Sang, S.H. Cho, Performance of least mean absolute third (LMAT) adaptive algorithm in various noise environments. Electron. Lett. 34(3), 241–243 (1998)CrossRefGoogle Scholar
  13. 13.
    J.C. Liu, X. Yu, H.R. Li, A nonparametric variable step-size NLMS algorithm for transversal filters. Appl. Math. Comput. 217(17), 7365–7371 (2011)MathSciNetzbMATHGoogle Scholar
  14. 14.
    K. Mayyas, A variable step-size selective partial update LMS algorithm. Digit. Signal Process. 23, 75–85 (2013)MathSciNetCrossRefGoogle Scholar
  15. 15.
    A.H. Sayed, Adaptive Filters (Wiley, Hoboken, 2008)CrossRefGoogle Scholar
  16. 16.
    H.C. Shin, A.H. Sayed, W.J. Song, Variable step-size NLMS and affine projection algorithms. IEEE Signal Process. Lett. 11(2), 132–135 (2004)CrossRefGoogle Scholar
  17. 17.
    M.R. Spiegel, Mathematical Handbook of Formulas and Tables (McGraw-Hill, New York, 2012)Google Scholar
  18. 18.
    P. Wang, P.Y. Kam, An automatic step-size adjustment algorithm for LMS adaptive filters and an application to channel estimation. Phys. Commun. 5, 280–286 (2012)CrossRefGoogle Scholar
  19. 19.
    H.X. Wen, X.H. Lai, L. Chen, Z. Cai, Nonparametric VSS-APA based on precise background noise power estimate. J. Cent. South Univ. 22, 251–260 (2015)CrossRefGoogle Scholar
  20. 20.
    J.W. Yoo, J.W. Shin, P.G. Park, An improved NLMS algorithm in sparse systems against noisy input signals. IEEE Trans. Circuits Syst. II Expr. Br. 62(3), 271–275 (2015)CrossRefGoogle Scholar
  21. 21.
    X. Yu, J.C. Liu, H.R. Li, An adaptive inertia weight particle swarm optimization algorithm for IIR digital filter. In Proceedings of the 2009 International Conference on Artificial Intelligence and Computational Intelligence (AICI2009), pp. 114–118 (2009)Google Scholar
  22. 22.
    A. Zerguine, Convergence and steady-state analysis of the normalized least mean fourth algorithm. Digit. Signal Process. 17(1), 17–31 (2007)CrossRefGoogle Scholar
  23. 23.
    H. Zhao, Y. Yu, S. Gao, Z. He, A new normalized LMAT algorithm and its performance analysis. Signal Process. 105(12), 399–409 (2014)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.School of Electro-Mechanical Engineering Xidian UniversityXi’anChina

Personalised recommendations