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

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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.

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Notes

  1. With QPSK input, the adaptation of a(n) of NSA-NSA is given as \(a(n+1)\hbox { }=a(n)+\rho _a \mathrm{conj}\{\mathrm{sign}\{e(n)\}\}[y_1 (n)-y_2 (n)]\lambda (n)[1-\lambda (n)]\), where \(\mathrm{conj}\{\cdot \}\) denotes conjugate operation.

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    Impulsive noise in ISI channel

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  2. The derivation of VSS-NSA, VSS-APSA, and NRMN is different from the original literatures, when input signal is the complex number. For paper length optimization, and in order to focus on the simplicity of the proposed approach, we have decided to only compare to NLMS-NSA algorithm.

References

  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

    Article  Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  Google Scholar 

  5. S.C. Douglas, A family of normalized LMS algorithms. IEEE Signal Process. Lett. 1(3), 49–51 (1994). doi:10.1109/97.295321

    Article  Google Scholar 

  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)

  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

    Article  Google Scholar 

  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

    Article  Google Scholar 

  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)

  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)

    MathSciNet  Google Scholar 

  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

    Article  MathSciNet  Google Scholar 

  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. 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

    Article  MATH  Google Scholar 

  14. C.P. Kwong, Dual sign algorithm for adaptive filtering. IEEE Trans. Commun. 34(12), 1272–1275 (1986). doi:10.1109/TCOM.1986.1096490

    Article  Google Scholar 

  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)

  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

    Article  MATH  Google Scholar 

  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)

  18. D.P. Mandic, NNGD algorithm for neural adaptive filters. Electronics Lett. 36(9), 845–846 (2000). doi:10.1049/el:20000631

    Article  Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  MATH  Google Scholar 

  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)

  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

    Article  Google Scholar 

  24. D.I. Pazaitis, A.G. Constantinides, LMS+F algorithm. Electronics Lett. 31(17), 1423–1424 (1995). doi:10.1049/el:19951026

    Article  Google Scholar 

  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

    Article  MathSciNet  MATH  Google Scholar 

  26. A.H. Sayed, Fundamentals of Adaptive Filtering (Wiley IEEE Press, New York, 2003)

    Google Scholar 

  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)

  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

    Article  Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

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Acknowledgments

The authors want to express their deep thanks to the anonymous reviewers for many valuable comments which greatly helped to improve the quality of this work. This work was supported in part by National Natural Science Foundation of China (Grants: 61271340, 61571374, 61134002, 61433011, U1234203), the Sichuan Provincial Youth Science and Technology Fund (Grant: 2012JQ0046), and the Fundamental Research Funds for the Central Universities (Grant: SWJTU12CX026).

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Authors and Affiliations

  1. Key Laboratory of Magnetic Suspension Technology and Maglev Vehicle, Ministry of Education, and School of Electrical Engineering, Southwest Jiaotong University, Chengdu, China

    Lu Lu & Haiquan Zhao

  2. Computational Neuro-Engineering Laboratory, University of Florida, Gainesville, FL, 32611, USA

    Kan Li

  3. School of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an, China

    Badong Chen

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  1. Lu Lu
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Correspondence to Haiquan Zhao.

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Lu, L., Zhao, H., Li, K. et al. A Novel Normalized Sign Algorithm for System Identification Under Impulsive Noise Interference. Circuits Syst Signal Process 35, 3244–3265 (2016). https://doi.org/10.1007/s00034-015-0195-1

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