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Optimal step size of least mean absolute third algorithm

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Abstract

This paper proposes an optimized least mean absolute third (OPLMAT) algorithm to improve the capability of the adaptive filtering algorithm against Gaussian and non-Gaussian noises when the unknown system is a time-varying parameter system under low signal–noise rate. The optimal step size of the OPLMAT is obtained based on minimizing the mean-square deviation at the current time. In addition, the mean convergence and steady-state error of the OPLMAT algorithm are derived theoretically, and the computational complexity of OPLMAT is analyzed. Furthermore, the simulation experimental results of system identification presented illustrate the principle and efficiency of the OPLMAT algorithm. Simulation results demonstrate that the proposed algorithm performs much better than the LMAT and NLMAT algorithms.

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References

  1. Sayed, A.H.: Adaptive Filters. Wiley, Hoboken (2008)

    Book  Google Scholar 

  2. Shin, H.C., Sayed, A.H., Song, W.J.: Variable step size NLMS and affine projection algorithms. IEEE Signal Process. Lett. 11(2), 132–135 (2004)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  4. Ang, W.P., Farhang-Boroujeny, B.: A new class of gradient adaptive step size LMS algorithms. IEEE Trans. Signal Process. 49(4), 805–810 (2001)

    Article  Google Scholar 

  5. Wang, P., Kam, P.-Y.: An automatic step size adjustment algorithm for LMS adaptive filters and an application to channel estimation. Phys. Commun. 5, 280–286 (2012)

    Article  Google Scholar 

  6. Liu, J.C., Yu, X., Li, H.R.: A nonparametric variable step size NLMS algorithm for transversal filters. Appl. Math. Comput. 217(17), 7365–7371 (2011)

  7. Benesty, J., Rey, H., Vega, L.R., et al.: A nonparametric VSSNLMS algorithm. IEEE Signal Process. Lett. 13(10), 581–584 (2006)

    Article  Google Scholar 

  8. Huang, H.-C., Lee, J.: A new variable step size NLMS algorithm and its performance analysis. IEEE Trans. Signal Process. 60(4), 2055–2060 (2012)

    Article  MathSciNet  Google Scholar 

  9. Zhao, S., Jones, D.L., Khoo, S., et al.: New variable step sizes minimizing mean-square deviation for the LMS-type algorithms. Circuits Syst. Signal Process. 33(7), 2251–2265 (2014)

    Article  Google Scholar 

  10. Lee, C.H., Park, P.G.: Optimal step size affine projection algorithm. IEEE Signal Process. Lett. 19(7), 431–434 (2012)

    Article  Google Scholar 

  11. Zhi, Y.F., Shang, F.F., Zhang, J., et al.: Optimal step size of pseudo affine projection algorithm. Appl. Math. Comput. 273, 82–88 (2016)

    MathSciNet  Google Scholar 

  12. Ciochină, S., Paleologu, C., Benesty, J.: An optimized NLMS algorithm for system identification. Signal Process. 118, 115–121 (2016)

    Article  Google Scholar 

  13. Lee, Y.H., Mok, J.D., Kim, S.D., Cho, S.H.: Performance of least mean absolute third (LMAT) adaptive algorithm in various noise environments. IET Electron. Lett. 34(2), 241–243 (1998)

    Article  Google Scholar 

  14. Walach, E., Widrow, B.: The least mean fourth (LMF) adaptive algorithm and its family. IEEE Trans. Inf. Theory 30(2), 275–283 (1984)

    Article  Google Scholar 

  15. Eweda, E., Bershad, N.J.: 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)

    Article  MathSciNet  Google Scholar 

  16. Zhao, H., Yu, Y., Gao, S., et al.: A new normalized LMAT algorithm and its performance analysis. Signal Process. 105(12), 399–409 (2014)

    Article  Google Scholar 

  17. Arikan, O., Cetin, A.E., Erzin, E.: Adaptive filtering for non-Gaussian stable processes. IEEE Signal Process. Lett. 2(11), 1400–1403 (1995)

    Google Scholar 

  18. Aydin, G., Arikan, O., Cetin, A.E.: Robust adaptive filtering algorithms for \(\alpha \)-stable random processes. IEEE Trans. Circuits Syst. II Analog Digit. Signal Process. 46(2), 198–202 (1999)

    Article  MATH  Google Scholar 

  19. Price, R.: A useful theorem for nonlinear devices having Gaussian inputs. IRE Trans. Inf. Theory 4(2), 69–72 (1958)

    Article  MathSciNet  MATH  Google Scholar 

  20. Spiegel, M.R.: Mathematical Handbook of Formulas and Tables. McGraw-Hill, New York (2012)

    Google Scholar 

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Acknowledgements

This work was supported by National Natural Science Foundation of China (61074120, 61673310) and the State Key Laboratory of Intelligent Control and Decision of Complex Systems of Beijing Institute of Technology.

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  1. School of Electro-Mechanical Engineering Xidian University, No. 2 South Taibai Road, Xi’an, 710071, Shaanxi, China

    Sihai Guan & Zhi Li

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  1. Sihai Guan
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  2. Zhi Li
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Correspondence to Zhi Li.

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Guan, S., Li, Z. Optimal step size of least mean absolute third algorithm. SIViP 11, 1105–1113 (2017). https://doi.org/10.1007/s11760-017-1064-0

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  • DOI: https://doi.org/10.1007/s11760-017-1064-0

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