Skip to main content
SpringerLink
Log in

Kernel Filtered-x LMS Algorithm for Active Noise Control System with Nonlinear Primary Path

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

In active noise control (ANC) systems, the primary path may exhibit nonlinear impulse responses. Conventional linear ANC controllers based on a filtered-x least mean square (FxLMS) algorithm exhibit performance degradation when compensating for nonlinear distortions of the primary path. Several nonlinear active noise control algorithms, including Volterra filtered-x least mean square (VFxLMS) and filtered-s least mean square (FsLMS), have been utilized to overcome this nonlinear effect. However, the performance still needs to be improved when the reference noise is mixed with multiple narrowband signals and additional Gaussian white noise. Over the last several years, kernel adaptive filters have exhibited powerful capabilities in multiple signal processing domains. When kernel adaptive filters are introduced into the ANC system, a great challenge is to compensate for the inherent delay caused by the secondary path. Due to the implicit mapping of the kernel method, it is difficult to filter the reference signal in the high-dimensional feature space. In this paper, an approximate method is proposed in which the filtered reference signal is mapped to the high-dimensional feature space. In addition, a kernel filtered-x least mean square (KFxLMS) algorithm is developed for an ANC system with a nonlinear primary path. Simulation experiments demonstrate that the performance of the proposed KFxLMS algorithm is better than that of the FxLMS, VFxLMS, and FsLMS algorithms.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. N. Aronszajn, Theory of reproducing kernels. Trans. Am. Math. Soc. 68(3), 337–404 (1950)

    Article  MathSciNet  Google Scholar 

  2. M. Aslam, M. Raja, A new adaptive strategy to improve online secondary path modeling in active noise control systems using fractional signal processing approach. Signal Process. 107((C)), 433–443 (2015). https://doi.org/10.1016/j.sigpro.2014.04.012

    Article  Google Scholar 

  3. H. Bao, I. Panahi, Active noise control based on kernel least-mean-square algorithm, in 2009 Conference Record of the Forty-Third Asilomar Conference on Signals, Systems and Computers, pp. 642–644 (2009)

  4. S. Behera, D. Das, B. Subudhi, Adaptive nonlinear active noise control algorithm for active headrest with moving error microphones. Appl. Acoust. 123, 9–19 (2017). https://doi.org/10.1016/j.apacoust.2017.03.002

    Article  Google Scholar 

  5. J. Chen, W. Gao, C. Richard, J. Bermudez, Convergence analysis of kernel LMS algorithm with pre-tuned dictionary, in 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 7243–7247 (2014)

  6. I. Constantin, R. Lengelle, Performance analysis of kernel adaptive filters based on LMS algorithm. Procedia Comput. Sci. 20(2), 39–45 (2013). https://doi.org/10.1016/j.procs.2013.09.236

    Article  Google Scholar 

  7. H. Dai, Y. Huang, J. Wang, L. Yang, Resource optimization in heterogeneous cloud radio access networks. IEEE Commun. Lett. 22(3), 494–497 (2017). https://doi.org/10.1109/LCOMM.2017.2787676

    Article  Google Scholar 

  8. D. Das, S. Mohapatra, A. Routray, T. Basu, Filtered-s LMS algorithm for multichannel active control of nonlinear noise processes. IEEE Trans. Audio Speech Lang. Process. 14(5), 1875–1880 (2006). https://doi.org/10.1109/TSA.2005.858543

    Article  Google Scholar 

  9. D. Das, D. Moreau, B. Cazzolato, Nonlinear active noise control for headrest using virtual microphone control. Control Eng. Pract. 21(4), 544–555 (2013). https://doi.org/10.1016/j.conengprac.2012.11.007

    Article  Google Scholar 

  10. D. Das, G. Panda, Active mitigation of nonlinear noise processes using a novel filtered-s LMS algorithm. IEEE Trans. Speech Audio Process. 12(3), 313–322 (2004). https://doi.org/10.1109/TSA.2003.822741

    Article  Google Scholar 

  11. W. Gao, J. Chen, C. Richard, J. Huang, Online dictionary learning for kernel LMS analysis and forward-backward splitting algorithm. Statistics 62(11), 2765–2777 (2013)

    MATH  Google Scholar 

  12. N. George, G. Panda, A robust filtered-s LMS algorithm for nonlinear active noise control. Appl. Acoust. 73(8), 836–841 (2012). https://doi.org/10.1016/j.apacoust.2012.02.005

    Article  Google Scholar 

  13. J. Gil-Cacho, M. Signoretto, T. Waterschoot, M. Moonen, Nonlinear acoustic echo cancellation based on a sliding-window leaky kernel affine projection algorithm. IEEE Trans. Audio Speech Lang. Process. 21(9), 1867–1878 (2013). https://doi.org/10.1109/TASL.2013.2260742

    Article  Google Scholar 

  14. P. Kumar, K. Prabhu, D. Das, Block filtered-s least mean square algorithm for active control of non-linear noise systems. IET Signal Proc. 4(2), 168–180 (2010). https://doi.org/10.1049/iet-spr.2008.0157

    Article  Google Scholar 

  15. S. Kuo, D. Morgan, Active Noise Control Systems: Algorithms and DSP Implementations, 1st edn. (Wiley, New York, 1995)

    Google Scholar 

  16. S. Kuo, H. Wu, Nonlinear adaptive bilinear filters for active noise control systems. IEEE Trans. Circuits Syst. 52(3), 617–624 (2005). https://doi.org/10.1109/TCSI.2004.842429

    Article  MathSciNet  Google Scholar 

  17. C. Li, Y. Li, K. Song, L. Yang, Energy efficient design for multiuser downlink energy and uplink information transfer in 5g. Sci. China Inf. Sci. 59(2), 1–8 (2016). https://doi.org/10.1007/s11432-015-5510-8

    Article  Google Scholar 

  18. C. Li, K. Song, D. Wang, F. Zheng, L. Yang, Optimal remote radio head selection for cloud radio access networks. Sci. China Inf. Sci. 59(10), 102315 (2016). https://doi.org/10.1007/s11432-016-0060-y

    Article  Google Scholar 

  19. C. Li, X. Wang, L. Yang, W. Zhu, A joint source and relay power allocation scheme for a class of mimo relay systems. IEEE Trans. Signal Process. 57(12), 4852–4860 (2009). https://doi.org/10.1109/TSP.2009.2027409

    Article  MathSciNet  MATH  Google Scholar 

  20. T. Li, J. Jiang, Filtered-x second-order Volterra adaptive algorithms. Electron. Lett. 33(8), 671–672 (1997). https://doi.org/10.1049/el:19970477

    Article  Google Scholar 

  21. T. Li, J. Jiang, Adaptive Volterra filters for active control of nonlinear noise processes. IEEE Trans. Signal Process. 49(8), 1667–1676 (2001). https://doi.org/10.1109/78.934136

    Article  Google Scholar 

  22. S.H.W. Liu, J.C. Principe, Kernel Adaptive Filtering: A Comprehensive Introduction (Wiley, Hoboken, 2010)

    Book  Google Scholar 

  23. W. Liu, P. Pokharel, J. Principe, The kernel least-mean-square algorithm. IEEE Trans. Signal Process. 56(2), 543–554 (2008). https://doi.org/10.1109/TSP.2007.907881

    Article  MathSciNet  MATH  Google Scholar 

  24. L. Lu, H. Zhao, Improved filtered-x least mean kurtosis algorithm for active noise control. Circuits Syst. Signal Process. 36(4), 1586–1603 (2017). https://doi.org/10.1007/s00034-016-0379-3

    Article  MathSciNet  Google Scholar 

  25. L. Luo, J. Sun, B. Huang, D. Quoc, Efficient combination of feedforward and feedback structures for nonlinear narrowband active noise control. Signal Process. 128, 494–503 (2016). https://doi.org/10.1016/j.sigpro.2016.05.014

    Article  Google Scholar 

  26. Y. Nakajima, M. Yukawa, Nonlinear channel equalization by multi-kernel adaptive filter, in 2012 IEEE 13th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), pp. 384–388 (2012)

  27. W. Parreira, J. Bermudez, C. Richard, J. Tourneret, Stochastic behavior analysis of the gaussian kernel least-mean-square algorithm. IEEE Trans. Signal Process. 60(5), 2208–2222 (2012). https://doi.org/10.1109/TSP.2012.2186132

    Article  MathSciNet  MATH  Google Scholar 

  28. V. Patel, V. Gandhi, S. Heda, N. George, Design of adaptive exponential functional link network-based nonlinear filters. IEEE Trans. Circuits Syst. 63(9), 1434–1442 (2016). https://doi.org/10.1109/TCSI.2016.2572091

    Article  MathSciNet  Google Scholar 

  29. A. Rahimi, B. Recht, Random features for large-scale kernel machines, in International Conference on Neural Information Processing Systems, pp. 1177–1184 (2007)

  30. G. Sicuranza, A. Carini, A generalized FLANN filter for nonlinear active noise control. IEEE Trans. Audio Speech Lang. Process. 19(8), 2412–2417 (2011). https://doi.org/10.1109/TASL.2011.2136336

    Article  Google Scholar 

  31. W. Tan, M. Matthaiou, S. Jin, X. Li, Spectral efficiency of dft-based processing hybrid architectures in massive mimo. IEEE Wirel. Commun. Lett. 6(5), 586–589 (2017). https://doi.org/10.1109/LWC.2017.2719036

    Article  Google Scholar 

  32. N. Thai, X. Wu, J. Na, Y. Guo, N. Tin, P. Le, Adaptive variable step-size neural controller for nonlinear feedback active noise control systems. Appl. Acoust. 116, 337–347 (2017). https://doi.org/10.1016/j.apacoust.2016.09.022

    Article  Google Scholar 

  33. S. Zhao, B. Chen, P. Zhu, J. Ncipe, Adaptive RSOV filter using the FELMS algorithm for nonlinear active noise control systems. Mech. Syst. Signal Process. 34(1), 378–392 (2013). https://doi.org/10.1016/j.ymssp.2012.06.020

    Article  Google Scholar 

  34. H. Zhao, X. Zeng, Z. He, S. Yu, B. Chen, Improved functional link artificial neural network via convex combination for nonlinear active noise control. Appl. Soft Comput. 42((C)), 351–359 (2016). https://doi.org/10.1016/j.asoc.2016.01.051

    Article  Google Scholar 

  35. H. Zhao, X. Zeng, Z. He, S. Yu, B. Chen, Improved functional link artificial neural network via convex combination for nonlinear active noise control. Appl. Soft Comput. 42((C)), 351–359 (2016). https://doi.org/10.1016/j.asoc.2016.01.051

    Article  Google Scholar 

  36. S. Zhao, B. Chen, P. Zhu, J. Ncipe, Fixed budget quantized kernel least-mean-square algorithm. Signal Process. 93(9), 2759–2770 (2013). https://doi.org/10.1016/j.sigpro.2013.02.012

    Article  Google Scholar 

  37. D. Zhou, V. DeBrunner, Efficient adaptive nonlinear filters for nonlinear active noise control. IEEE Trans. Circuits Syst. 54(3), 669–681 (2007). https://doi.org/10.1109/TCSI.2006.887636

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Automatic Testing and Control, Harbin Institute of Technology, No. 2 Yi-Kuang Street, Nangang District, Harbin, 150080, China

    Yuqi Liu, Chao Sun & Shouda Jiang

Authors
  1. Yuqi Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chao Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shouda Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chao Sun.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, Y., Sun, C. & Jiang, S. Kernel Filtered-x LMS Algorithm for Active Noise Control System with Nonlinear Primary Path. Circuits Syst Signal Process 37, 5576–5594 (2018). https://doi.org/10.1007/s00034-018-0832-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-018-0832-6

Keywords

Search

Navigation