Abstract
Some improved normalized subband adaptive filter algorithms derived from nonlinear cost functions, such as the logarithmic function and the arctangent function, have shown splendid robustness against the impulsive noises. However, due to the usage of the constant control parameter in their cost functions, these algorithms need to make a balance between the steady-state error and the convergence rate, especially when the unknown impulse response changes suddenly. For settling this trade-off issue, a way of obtaining the variable control parameter (VCP) recursively is constructed by an exponential function in this paper. In the contexts of system identification and acoustic echo cancellation, simulation results testified the improved performance of these proposed VCP algorithms in terms of the convergence rate, steady-state error, and tracking capability.
Similar content being viewed by others
References
S. Haykin, Adaptive Filter Theory, 4th edn. (Prentice-Hall, Upper Saddle River, 2002)
F. Huang, J. Zhang, S. Zhang, NLMS algorithm based on variable parameter cost function robust against impulsive interferences. IEEE Trans. Circuits Syst. II Exp. Briefs 64(5), 600–604 (2017)
J. Kim, J. Chang, S. Nam, Sign subband adaptive filter with L1-norm minimization-based variable step-size. Electron. Lett. 49(21), 1325–1326 (2013)
K.A. Lee, W.S. Gan, Improving convergence of the NLMS algorithm using constrained subband updates. IEEE Signal Process. Lett. 11(9), 736–739 (2004)
K.A. Lee, W.S. Gan, Inherent decorrelating and least perturbation properties of the normalised subband adaptive filter. IEEE Trans. Signal Process. 54(11), 4475–4480 (2006)
K.A. Lee, W.S. Gan, S.M. Kuo, Subband Adaptive Filtering: Theory and Implementation (Wiley, Hoboken, 2009)
L. Lu, H. Zhao, W. Wang, Y. Yu, Performance analysis of the robust diffusion normalized least mean p-power algorithm. IEEE Trans. Circuits Syst. II Express Briefs 65(12), 2047–2051 (2018)
L. Lu, W. Wang, X. Yang, W. Wu, G. Zhu, Recursive Geman–McClure estimator for implementing second-order Volterra filter. IEEE Trans. Circuits Syst. II Express Briefs 66, 1–5 (2019)
L. Lu, Y. Yu, X. Yang, W. Wu, Time delay Chebyshev functional link artificial neural network. Neurocomputing 329, 153–164 (2019)
J. Ni, F. Li, Variable regularisation parameter sign subband adaptive filter. Electron. Lett. 46(24), 1605–1607 (2010)
J. Ni, X. Chen, J. Yang, Two variants of the sign subband adaptive filter with improved convergence rate. Signal Process. 96, 325–331 (2014)
P.J. Rousseeuw, A.M. Leroy, Robust Regression and Outlier Detection (Wiley, New York, 1987)
A.H. Sayed, Adaptive Filters (Wiley, New York, 2008)
M. Sayin, N. Vanli, S. Kozat, A novel family of adaptive filtering algorithms based on the logarithmic cost. IEEE Trans. Signal Process. 62(17), 4411–4424 (2014)
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)
Z. Shen, Y. Yu, T. Huang, Two novel arctangent normalized subband adaptive filter algorithms against impulsive interferences. Circuits Syst. Signal Process. 37(2), 883–900 (2017)
Z. Shen, T. Huang, K. Zhou, L0-norm constraint normalized logarithmic subband adaptive filter algorithm. Signal Image Video Process. 12(5), 861–868 (2018)
J.W. Shin, J.W. Yoo, P.G. Park, Variable step-size sign subband adaptive filter. IEEE Signal Process. Lett. 20(2), 173–176 (2013)
M.M. Sondhi, The history of echo cancellation. IEEE Signal Process. 23(5), 95–98 (2006)
P. Wen, S. Zhang, J. Zhang, A novel subband adaptive filter algorithm against impulsive noise and it’s performance analysis. Signal Process. 127, 282–287 (2016)
J.W. Yoo, J.W. Shin, P.G. Park, A band-dependent variable step-size sign subband adaptive filter. Signal Process. 104, 407–411 (2014)
Y. Yu, H. Zhao, B. Chen, Steady-state mean-square-deviation analysis of the sign subband adaptive filter algorithm. Signal Process. 120, 36–42 (2016)
Y. Yu, H. Zhao, B. Chen, Z. He, Two improved normalized subband adaptive filter algorithms with good robustness against impulsive interferences. Circuits Syst. Signal Process. 35(12), 4607–4619 (2016)
Y. Yu, H. Zhao, R.C. de Lamare, Y. Zakharov, L. Lu, Robust distributed diffusion recursive least squares algorithms with side information for adaptive networks. IEEE Trans. Signal Process. 67(6), 1566–1581 (2019)
Y. Yu, H. Zhao, R.C. de Lamare, L. Lu, Sparsity-aware subband adaptive algorithms with adjustable penalties. Digit. Signal Proc. 84, 93–106 (2019)
J. Zeng, Y. Lin, L. Shi, A normalized least mean square algorithm based on the arctangent cost function robust against impulsive interference. Circuits Syst. Signal Process. 35(8), 3040–3047 (2016)
Y. Zou, S.C. Chan, T.S. Ng, A recursive least M-estimate (RLM) adaptive filter for robust filtering in impulse noise. IEEE Signal Process. Lett. 7(11), 324–326 (2000)
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant No. 61473239).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Shen, Z., Huang, T., Yang, L. et al. Improved NSAF Algorithms with Variable Control Parameter Against Impulsive Noises. Circuits Syst Signal Process 39, 2207–2222 (2020). https://doi.org/10.1007/s00034-019-01245-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00034-019-01245-4