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Convex Combination of Nonlinear Filters using Improved Proportionate Least Mean Square/Fourth Algorithm for Sparse System Identification

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Abstract

Purpose

Real-time systems are affected by nonlinearities which might be due to the use of passive devices. To model these nonlinearities, a combined split adaptive exponential functional link network (cSAEFLN) architecture is proposed which uses the AEFLN-based modeling that enhances the architecture's capability for nonlinear system identification.

Method

The cSAEFLN architecture consists of one linear adaptive filter and a convex combination of two nonlinear adaptive filters. To address the sparsity issue and deal with the nonlinearities resulting from the functional expansion of the input signal, a novel improved proportionate least mean square/fourth (IPLMS/F) algorithm is introduced for updating the nonlinear adaptive filter coefficients.

Results

Different experiments related to the system identification problem are examined to analyze the robustness of the proposed architecture. The testified outcome indicates the efficiency of the cSAEFLN architecture in terms of mean square error and convergence rate for different systems.

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Data availability statement

Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

References

  1. Patnaik A, Nanda S (2020) The variable step-size LMS/F algorithm using nonparametric method for adaptive system identification. Int J Adapt Control Signal Process 34(12):1799–1811

    Article  MathSciNet  Google Scholar 

  2. Patnaik A, Nanda S (2018 October) A modified variable step-size continuous mixed p-norm algorithm for system identification. In: 2018 International Conference on Applied Electromagnetics, Signal Processing and Communication (AESPC). Vol. 1. IEEE. pp. 1–3

  3. Pogula R, Kumar TK, Albu F (2019) Robust sparse normalized LMAT algorithms for adaptive system identification under impulsive noise environments. Circuits Syst Signal Process 38(11):5103–5134

    Article  Google Scholar 

  4. Patnaik A, Nanda S (2021 April) Reweighted Zero-Attracting Modified Variable Step-Size Continuous Mixed p-Norm Algorithm for Identification of Sparse System Against Impulsive Noise. In: Proceedings of International Conference on Communication, Circuits, and Systems: IC3S 2020. Vol. 728. Springer Nature. p. 509

  5. Benesty J et al (2001) Advances in network and acoustic echo cancellation. Springer Berlin, Heidelberg

    Book  Google Scholar 

  6. Li Y, Wang Y, Jiang T (2016) Sparse-aware set-membership NLMS algorithms and their application for sparse channel estimation and echo cancelation. AEU-Int J Electron Commun 70(7):895–902

    Article  Google Scholar 

  7. Sahoo S, Barapatre YK, Sahoo HK, Nanda S (2021) FPGA implementation of fuzzy sparse adaptive equalizer for indoor wireless communication systems. Appl Soft Comput 111:107616

    Article  Google Scholar 

  8. Haykin SS (2008) Adaptive filter theory. Pearson Education India, Upper Saddle River, NJ

    Google Scholar 

  9. Spelta MJM, Martins WA (2020) Normalized LMS algorithm and data-selective strategies for adaptive graph signal estimation. Signal Process 167:107326

    Article  Google Scholar 

  10. Gui G, Peng W, Adachi F (2014) Adaptive system identification using robust LMS/F algorithm. Int J Commun Syst 27(11):2956–2963

    Article  Google Scholar 

  11. Papoulis EV, Stathaki T (2004) A normalized robust mixed-norm adaptive algorithm for system identification. IEEE Signal Process Lett 11(1):56–59

    Article  ADS  Google Scholar 

  12. Yang F, Yang J (2018) A comparative survey of fast affine projection algorithms. Dig Signal Process 83:297–322

    Article  Google Scholar 

  13. Guo Y, Wang H, Li L, (2022 August) Improved Zero-Attracting LMS Algorithm for the Adaptive Identification of Sparse System. In: 2022 IEEE 5th International Conference on Electronic Information and Communication Technology (ICEICT). IEEE. pp. 196–201

  14. Gui G, Mehbodniya A, Adachi F (2013 September) Least mean square/fourth algorithm for adaptive sparse channel estimation. In: 2013 IEEE 24th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC). IEEE. pp. 296–300

  15. Li Y, Wang Y, Albu F (2016 August) Sparse channel estimation based on a reweighted least-mean mixed-norm adaptive filter algorithm. In: 2016 24th European Signal Processing Conference (EUSIPCO). IEEE. pp. 2380–2384

  16. Albu F, Li Y, Wang Y (2017) Low-complexity non-uniform penalized affine projection algorithms for active noise control. In: 2017 25th European Signal Processing Conference (EUSIPCO). IEEE. pp. 1275–1279

  17. Duttweiler DL (2000) Proportionate normalized least-mean-squares adaptation in echo cancelers. IEEE Trans Speech Audio Process 8(5):508–518

    Article  Google Scholar 

  18. Benesty J, Gay SL (2002 May) An improved PNLMS algorithm. In: 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing. Vol. 2. IEEE. pp. II-1881

  19. Jin Z, Ding X, Jiang Z, Li Y (2019 January) An Improved μ-law Proportionate NLMS Algorithm for Estimating Block-Sparse Systems. In: 2019 IEEE 2nd International Conference on Electronic Information and Communication Technology (ICEICT). IEEE. pp. 205–209

  20. Albu F, Caciula I, Li Y, Wang Y (2017 October) The ℓ p-norm proportionate normalized least mean square algorithm for active noise control. In: 2017 21st International Conference on System Theory, Control and Computing (ICSTCC). IEEE. pp. 396–400

  21. Ma W, Duan J, Cao J, Li Y, Chen B (2018) Proportionate adaptive filtering algorithms based on mixed square/fourth error criterion with unbiasedness criterion for sparse system identification. Int J Adapt Control Signal Process 32(11):1644–1654

    Article  MathSciNet  Google Scholar 

  22. Yang Z, Zheng YR, Grant SL (2011 May) Proportionate affine projection sign algorithms for sparse system identification in impulsive interference. In: 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE. pp. 4068–4071

  23. Gogineni VC, Mula S (2018) Improved proportionate-type sparse adaptive filtering under maximum correntropy criterion in impulsive noise environments. Dig Signal Process 79:190–198

    Article  MathSciNet  Google Scholar 

  24. Radhika S, Albu F, Chandrasekar A (2021) Proportionate maximum versoria criterion-based adaptive algorithm for sparse system identification. IEEE Trans Circuits Syst II Express Briefs 69(3):1902–1906

    Google Scholar 

  25. Rosalin NKR, Das DP (2019) Filter proportionate normalized least mean square algorithm for a sparse system. Int J Adapt Control Signal Process 33:1695–1705

    Article  MathSciNet  Google Scholar 

  26. Kuech F, Kellermann W (2003 September) Proportionate NLMS algorithm for second-order Volterra filters and its application to nonlinear echo cancellation. In: Proc. Int. Workshop on Acoustic Echo and Noise Control (IWAENC), Kyoto (Vol. 188)

  27. Zhao H, Zeng X, Zhang J (2010) Adaptive reduced feedback FLNN filter for active control of nonlinear noise processes. Signal Process 90(3):834–847

    Article  Google Scholar 

  28. Raghuwanshi J, Mishra A, Singh N (2020) Combined functional link adaptive filter for nonlinear acoustic echo cancellation. Analog Integr Circ Signal Process 105(2):249–262

    Article  Google Scholar 

  29. Comminiello D, Scarpiniti M, Azpicueta-Ruiz LA, Arenas-García J, Uncini A (2014) Nonlinear acoustic echo cancellation based on sparse functional link representations. IEEE/ACM Trans Audio Speech Lang Process 22(7):1172–1183

    Article  Google Scholar 

  30. Comminiello D, Scarpiniti M, Azpicueta-Ruiz LA, Arenas-García J, Uncini A (2017) Combined nonlinear filtering architectures involving sparse functional link adaptive filters. Signal Process 135:168–178

    Article  Google Scholar 

  31. Comminiello D, Scarpiniti M, Azpicueta-Ruiz LA, Arenas-García J, Uncini A (2015 September) A nonlinear architecture involving a combination of proportionate functional link adaptive filters. In: 2015 23rd European Signal Processing Conference (EUSIPCO). IEEE. pp. 2869–2873

  32. Patel V, Gandhi V, Heda S, George NV (2016) Design of adaptive exponential functional link network-based nonlinear filters. IEEE Trans Circuits Syst I Regul Pap 63(9):1434–1442

    Article  MathSciNet  Google Scholar 

  33. Azpicueta-Ruiz LA, Arenas-García J, Silva MT, Candido R (2018) Combined Filtering Architectures for Complex Nonlinear Systems. Adaptive learning methods for nonlinear system modeling. Butterworth-Heinemann, Oxford, pp 243–264

    Chapter  Google Scholar 

  34. Digital Network Echo Cancellers (2002), ITU-T Recommendations G.168

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Authors and Affiliations

  1. School of Electronics Engineering, KIIT Deemed to Be University, Bhubaneswar, India

    Ansuman Patnaik & Sarita Nanda

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  1. Ansuman Patnaik
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  2. Sarita Nanda
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Correspondence to Sarita Nanda.

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Patnaik, A., Nanda, S. Convex Combination of Nonlinear Filters using Improved Proportionate Least Mean Square/Fourth Algorithm for Sparse System Identification. J. Vib. Eng. Technol. 12, 941–951 (2024). https://doi.org/10.1007/s42417-023-00885-w

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  • DOI: https://doi.org/10.1007/s42417-023-00885-w

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