Circuits, Systems, and Signal Processing

, Volume 35, Issue 9, pp 3244–3265 | Cite as

A Novel Normalized Sign Algorithm for System Identification Under Impulsive Noise Interference

Article

Abstract

To overcome the performance degradation of adaptive filtering algorithms in the presence of impulsive noise, a novel normalized sign algorithm (NSA) based on a convex combination strategy, called NSA-NSA, is proposed in this paper. The proposed algorithm is capable of solving the conflicting requirement of fast convergence rate and low steady-state error for an individual NSA filter. To further improve the robustness to impulsive noises, a mixing parameter updating formula based on a sign cost function is derived. Moreover, a tracking weight transfer scheme of coefficients from a fast NSA filter to a slow NSA filter is proposed to speed up the convergence rate. The convergence behavior and performance of the new algorithm are verified by theoretical analysis and simulation studies.

Keywords

Adaptive filtering Convex combination Normalized sign algorithm System identification Impulsive noise 

References

  1. 1.
    J. Arenas-García, A.R. Figueiras-Vidal, A.H. Sayed, Mean-square performance of a convex combination of two adaptive filters. IEEE Trans. Signal Process. 54(3), 1078–1090 (2006). doi:10.1109/TSP.2005.863126 CrossRefGoogle Scholar
  2. 2.
    J. Arenas-Garcia, A.R. Figueiras-Vidal, Adaptive combination of normalised filters for robust system identification. Electron. Lett. 41(15), 874–875 (2005). doi:10.1049/el:20051936 CrossRefGoogle Scholar
  3. 3.
    J.A. Chambers, O. Tanrikulu, A.G. Constantinides, Least mean mixed-norm adaptive filtering. Electron. Lett. 30(19), 1574–1575 (1994). doi:10.1049/el:19941060 CrossRefGoogle Scholar
  4. 4.
    J. Chambers, A. Avlonitis, A robust mixed-norm adaptive filter algorithm. IEEE Signal Process. Lett. 4(2), 46–48 (1997). doi:10.1109/97.554469 CrossRefGoogle Scholar
  5. 5.
    S.C. Douglas, A family of normalized LMS algorithms. IEEE Signal Process. Lett. 1(3), 49–51 (1994). doi:10.1109/97.295321 CrossRefGoogle Scholar
  6. 6.
    S. C. Douglas, Analysis and implementation of the max-NLMS adaptive filter, in Proceedings on 29th Asilomar Conference on Signals, Systems, and Computers, pp. 659–663 (1995)Google Scholar
  7. 7.
    E. Eweda, Analysis and design of signed regressor LMS algorithm for stationary and nonstationary adaptive filtering with correlated Gaussian data. IEEE Trans. Circuits Syst. 37(11), 1367–1374 (1990). doi:10.1109/31.62411 CrossRefGoogle Scholar
  8. 8.
    S.B. Jebara, H. Besbes, Variable step size filtered sign algorithm for acoustic echo cancellation. Electronics Lett. 39(12), 936–938 (2003). doi:10.1049/el:20030583 CrossRefGoogle Scholar
  9. 9.
    B. E. Jun, D. J. Park, Y. W. Kim, Convergence analysis of sign-sign LMS algorithm for adaptive filters with correlated Gaussian data, in IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 1380–1383 (1995)Google Scholar
  10. 10.
    S. Koike, Variable step size normalized sign algorithm for fast convergent adaptive filters with robustness against impulsive noise. NEC Res. Dev. 41(3), 278–288 (2000)MathSciNetGoogle Scholar
  11. 11.
    S. Koike, Analysis of adaptive filters using normalized sign regressor LMS algorithm. IEEE Trans. Signal Process. 47(10), 2710–2723 (1999). doi:10.1109/78.790653 MathSciNetCrossRefGoogle Scholar
  12. 12.
    S. Koike, Convergence analysis of adaptive filters using normalized sign-sign algorithm. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. E88–A(11), 3218–3224 (2006)Google Scholar
  13. 13.
    R.H. Kwong, E.W. Johnston, A variable step size LMS algorithm. IEEE Trans. Signal Process. 40(7), 1633–1642 (1992). doi:10.1109/78.143435 CrossRefMATHGoogle Scholar
  14. 14.
    C.P. Kwong, Dual sign algorithm for adaptive filtering. IEEE Trans. Commun. 34(12), 1272–1275 (1986). doi:10.1109/TCOM.1986.1096490 CrossRefGoogle Scholar
  15. 15.
    L. Lu, H. Zhao, A novel convex combination of LMS adaptive filter for system identification, in 2014 12th International Conference on Signal Processing (ICSP), Hangzhou, pp. 225–229 (2014)Google Scholar
  16. 16.
    V.J. Mathews, Z. Xie, A stochastic gradient adaptive filter with gradient adaptive step size. IEEE Trans. Signal Process. 41(6), 2075–2087 (1993). doi:10.1109/78.218137 CrossRefMATHGoogle Scholar
  17. 17.
    D. P. Mandic, E. V. Papoulis, C. G. Boukis, A normalized mixed-norm adaptive filtering algorithm robust under impulsive noise interference, in IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 333–336 (2003)Google Scholar
  18. 18.
    D.P. Mandic, NNGD algorithm for neural adaptive filters. Electronics Lett. 36(9), 845–846 (2000). doi:10.1049/el:20000631 CrossRefGoogle Scholar
  19. 19.
    D.P. Mandic, J.A. Chambers, Toward the optimal learning rate for backpropagation. Neural Process. Lett. 11(1), 1–5 (2000). doi:10.1023/A:1009686825582 CrossRefGoogle Scholar
  20. 20.
    D.P. Mandic, A.I. Hanna, M. Razaz, A normalized gradient descent algorithm for nonlinear adaptive filters using a gradient adaptive step size. IEEE Signal Process. Lett. 8(11), 295–297 (2001). doi:10.1109/97.969448 CrossRefGoogle Scholar
  21. 21.
    V.J. Mathews, S.H. Cho, Improved convergence analysis of stochastic gradient adaptive filters using the sign algorithm. IEEE Trans. Acoust. Speech Signal Process. 35(4), 450–454 (1987). doi:10.1109/TASSP.1987.1165167 CrossRefMATHGoogle Scholar
  22. 22.
    V. H. Nascimento, R. C. de Lamare, A low-complexity strategy for speeding up the convergence of convex combinations of adaptive filters, in IEEE International Conference on Acoustics, Speech and Signal Processing, pp 3553–3556 (2012)Google Scholar
  23. 23.
    E.V. Papoulis, T. Stathaki, A normalized robust mixed-norm adaptive algorithm for system identification. IEEE Signal Process. Lett. 11(1), 56–59 (2004). doi:10.1109/LSP.2003.819353 CrossRefGoogle Scholar
  24. 24.
    D.I. Pazaitis, A.G. Constantinides, LMS+F algorithm. Electronics Lett. 31(17), 1423–1424 (1995). doi:10.1049/el:19951026 CrossRefGoogle Scholar
  25. 25.
    R. Price, A useful theorem for nonlinear devices having Gaussian inputs. IRE Trans. Inform. Theory 4(2), 69–72 (1958). doi:10.1109/TIT.1958.1057444 MathSciNetCrossRefMATHGoogle Scholar
  26. 26.
    A.H. Sayed, Fundamentals of Adaptive Filtering (Wiley IEEE Press, New York, 2003)Google Scholar
  27. 27.
    T. Shao, Y. R. Zheng, J. Benesty, A variable step-size normalized sign algorithm for acoustic echo cancelation, in IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 333–336 (2010)Google Scholar
  28. 28.
    T. Shao, Y.R. Zheng, J. Benesty, An affine projection sign algorithm robust against impulsive interferences. IEEE Signal Process. Lett. 17(4), 327–330 (2010). doi:10.1109/LSP.2010.2040203 CrossRefGoogle Scholar
  29. 29.
    J. Shin, J. Yoo, P. Park, Variable step-size affine projection sign algorithm. Electronics Lett. 48(9), 483–485 (2012). doi:10.1049/el.2012.0751 CrossRefGoogle Scholar
  30. 30.
    J. Soo, K.K. Pang, A multi step size (MSS) frequency domain adaptive filter. IEEE Trans. Signal Process. 39(1), 115–121 (1991). doi:10.1109/78.80770 CrossRefGoogle Scholar
  31. 31.
    O. Tanrikulu, J.A. Chambers, Convergence and steady-state properties of the least-mean mixed-norm (LMMN) adaptive algorithm. IEE Proc. Vis. Image Signal Process. 143, 137–142 (1996)CrossRefGoogle Scholar
  32. 32.
    P. Yuvapoositanon, J. Chambers, An adaptive step-size code-constrained minimum output energy receiver for nonstationary CDMA channels, in IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 465–468 (2003)Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Key Laboratory of Magnetic Suspension Technology and Maglev Vehicle, Ministry of Education, and School of Electrical EngineeringSouthwest Jiaotong UniversityChengduChina
  2. 2.Computational Neuro-Engineering LaboratoryUniversity of FloridaGainesvilleUSA
  3. 3.School of Electronic and Information EngineeringXi’an Jiaotong UniversityXi’anChina

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