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Variable Step Size Norm-Constrained Adaptive Filtering Algorithms

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Abstract

Variable step size norm-constrained adaptive filtering algorithms are proposed in the paper. A variable step size is derived by minimizing the variance of the noise-free a posterior error. Thus, the update equation can obtain a reasonable step size at each iteration. Due to the introduction of variable step size, the proposed algorithms based on the constrained conditions of \(L_{1}\) and \(L_{0}\) norm have a significant advantage that the convergence rate is faster than some well-known algorithms in the sparse system. The simulation results illustrate the good performance of the proposed algorithms.

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References

  1. M.S.E. Abadi, Proportionate normalized subband adaptive filter algorithms for sparse system identification. Signal Process. 89(7), 1467–1474 (2009)

    Article  MATH  Google Scholar 

  2. T. Aboulnasr, K. Mayyas, A robust variable step-size LMS-type algorithm: analysis and simulations. IEEE Trans. Signal Process. 45(3), 631–639 (1997)

    Article  Google Scholar 

  3. E. Beck, E.L.O. Batista, R. Seara, Norm-constrained adaptive algorithms for sparse system identification based on projections onto intersections of hyperplanes. Signal Process. 118, 259–271 (2016)

    Article  Google Scholar 

  4. J. Benesty, S. L. Gay, An improved PNLMS algorithm, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, Orlando, FL (May 2002), pp. 1881–1884

  5. M.Z.A. Bhotto, A. Antoniou, A family of shrinkage adaptive filtering algorithms. IEEE Trans. Signal Process. 61(7), 1689–1697 (2013)

    Article  MathSciNet  Google Scholar 

  6. Y.S. Choi, Subband adaptive filtering with l1-norm constraint for sparse system identification. Math. Probl. Eng. (2013). doi:10.1155/2013/601623

    MATH  Google Scholar 

  7. D.L. Dunweiler, Proportionate normalized least mean square adaptation in echo cancellers. IEEE Trans. Speech Audio Process. 8(5), 508–518 (2000)

    Article  Google Scholar 

  8. H. Deng, M. Doroslovacki, Improving convergence of the PNLMS algorithm for sparse impluse response identification. IEEE Signal Process. Lett. 12(3), 181–184 (2005)

    Article  Google Scholar 

  9. H. Deng, M. Doroslovacki, Proportionate adaptive algorithms for network echo cancellation. IEEE Trans. Signal Process. 54(5), 1794–1803 (2006)

    Article  Google Scholar 

  10. Y. Dong, H. Zhao, Y. Yu, Adaptive combination of proportionate NSAF with individual activation factors. Circuits Syst. Signal Process. (2016). doi:10.1007/s00034-016-0386-4

    Google Scholar 

  11. Y. Gu, J. Jin, S. Mei, \(l_{0}\)-Norm constraint LMS algorithm for sparse system identification. IEEE Signal Process. Lett. 16(9), 774–777 (2009)

    Article  Google Scholar 

  12. R.H. Kwong, E.W. Johnston, A variable step size LMS algorithm. IEEE Trans. Signal Process. 40(7), 1633–1642 (1992)

    Article  MATH  Google Scholar 

  13. Y. Kopsinis, K. Slavakis, S. Theodoridis, Online sparse system identification and signal reconstruction using projections onto weighted \(\ell \)1 balls. IEEE Trans. Signal Process. 59(3), 936–952 (2011)

    Article  MathSciNet  Google Scholar 

  14. L. Lu, H. Zhao, Z. He, B. Chen, A novel sign adaptation scheme for convex combination of two adaptive filters. AEU-Int. J. Electron. Commun. 69(11), 1590–1598 (2015)

    Article  Google Scholar 

  15. L. Lu, H. Zhao, Adaptive Volterra filter with continuous \(l_{p}\)-norm using a logarithmic cost for nonlinear active noise control. J. Sound Vib. 364, 14–29 (2016)

    Article  Google Scholar 

  16. L. Lu, H. Zhao, Adaptive combination of affine projection sign subband adaptive filters for modeling of acoustic paths in impulsive noise environments. Int. J. Speech Technol. (2016). doi:10.1007/s10772-016-9382-0

    Google Scholar 

  17. L. Lu, H. Zhao, C. Chen, A normalized subband adaptive filter under minimum error entropy criterion. Signal Image Video Process. 10(6), 1097–1103 (2016)

    Article  Google Scholar 

  18. P. Loganathan, A.W.H. Khong, P.A. Naylor, A class of sparseness-controlled algorithms for echo cancellation. IEEE Trans. Audio Speech Lang. Process. 17(8), 1591–1601 (2009)

    Article  Google Scholar 

  19. A.H. Sayed, Fundamentals of Adaptive Filtering (Wiley, New York, 2003)

    Google Scholar 

  20. X.Y. See, K.A. Lee, W.S. Gan, Proportionate subband adaptive filtering, in Proceedings of ICALIP (2008), pp. 128–132

  21. C. Wang, Y. Zhang, A new \(l_{0}\)-LMS algorithm with adaptive zero attractor. IEEE Commun. Lett. 19(12), 2150–2153 (2015)

    Article  Google Scholar 

  22. Y. Yu, H. Zhao, Memory proportionate APSA with individual activation factors for highly sparse system identification in impulsive noise environment, in IEEE International Conference on Wireless Communications and Signal Processing (WCSP) (China, 2014), pp. 1–6

  23. Y. Yu, H. Zhao, B. Chen, Sparseness-controlled proportionate affine projection sign algorithms for acoustic echo cancellation. Circuits Syst. Signal Process. 34(12), 3933–3948 (2015)

    Article  MathSciNet  Google Scholar 

  24. Y. Yu, H. Zhao, B. Chen, A new normalized subband adaptive filter algorithm with individual variable step sizes. Circuits Syst. Signal Process. 35(4), 1407–1418 (2015)

    Article  MathSciNet  Google Scholar 

  25. Y. Yu, H. Zhao, A band-independent variable step size proportionate normalized subband adaptive filter algorithm. AEÜ Int. J. Electron. Commun. 70(9), 1179–1186 (2016). doi:10.1016/j.aeue.2016.05.016

    Article  Google Scholar 

  26. Y. Yu, H. Zhao, B. Chen, Sparse normalized subband adaptive filter algorithm with l0-norm constraint. J. Franklin Inst. (2016). doi:10.1016/j.jfranklin.2016.09.022

    MATH  Google Scholar 

  27. H. Zhao, Y. Yu, S. Gao, X. Zeng, Z. He, Memory proportionate APA with individual activation factors for acoustic echo cancellation. IEEE/ACM Trans. Audio Speech Lang. Process. 22(6), 1047–1055 (2014)

    Article  Google Scholar 

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Acknowledgements

This work was partially supported by National Science Foundation of People’s Republic of China (Grants: 61571374, 61271340, and 61433011).

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Authors and Affiliations

  1. Key Laboratory of Magnetic Suspension Technology and Maglev Vehicle, Ministry of Education, Chengdu, China

    Long Shi & Haiquan Zhao

  2. School of Electrical Engineering, Southwest Jiaotong University, Chengdu, China

    Long Shi & Haiquan Zhao

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  1. Long Shi
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  2. Haiquan Zhao
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Correspondence to Haiquan Zhao.

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Shi, L., Zhao, H. Variable Step Size Norm-Constrained Adaptive Filtering Algorithms. Circuits Syst Signal Process 36, 4278–4291 (2017). https://doi.org/10.1007/s00034-017-0506-9

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  • DOI: https://doi.org/10.1007/s00034-017-0506-9

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