Circuits, Systems, and Signal Processing

, Volume 38, Issue 5, pp 2351–2368 | Cite as

Modified Model and Algorithm of LMS Adaptive Filter for Noise Cancellation

  • Awadhesh Kumar MauryaEmail author
  • Priyanka Agrawal
  • Shubhra Dixit
Short Paper


The present research investigates the innovative concept of LMS adaptive noise cancellation by means of a modified algorithm using an LMS adaptive filter along with their detailed analysis. Three types of equations viz. output, error, and weight update are used in the LMS algorithm. The error equation of traditional LMS algorithm is modified which gives better results as compared to traditional LMS algorithm and their types. The comparison parameters used in the present analysis are signal-to-noise ratio, mean square error, maximum absolute error, and energy ratio between signals of error and output signals. The proposed modified model was found to have a higher signal-to-noise ratio with respect to the traditional model of LMS adaptive noise cancellation. The signal-to-noise ratio of the proposed model has also been compared with some other types of LMS algorithms and was found better in most of the cases.


LMS adaptive filter Noise cancellation Signal-to-noise ratio Convergence rate Mean square error 


  1. 1.
    W.M. Abd-Elhameed, E.H. Doha, Y.H. Youssri, New wavelets collocation method for solving second-order multipoint boundary value problems using Chebyshev polynomials of third and fourth kinds. Abstr. Appl. Anal. 2013, 1–9 (2013). MathSciNetzbMATHGoogle Scholar
  2. 2.
    Y. Chen, Y. Gu, A. O. Hero, Sparse LMS for system identification, in IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 3125–3128 (2009).
  3. 3.
    Y.R. Chien, W.J. Tseng, A new variable step-size method for the M-max LMS algorithms, in IEEE International Conference on Consumer Electronics, Taiwan, pp. 21–22 (2014).
  4. 4.
    R. Dallinger, M. Rupp, On robustness of coupled adaptive filters, in IEEE International Conference on Acoustics, Speech and Signal Processing, Taiwan, pp. 3085–3088 (2009).
  5. 5.
    R. Dallinger, M. Rupp, On the robustness of LMS algorithms with time-variant diagonal matrix step-size, in IEEE International Conference on Acoustics, Speech and Signal Processing, Canada, pp. 5691–5695 (2013).
  6. 6.
    M. Dhal, M. Ghosh, P. Goel, A. Kar, S. Mohapatra, M. Chandra, An unique adaptive noise canceller with advanced variable-step BLMS algorithm, in IEEE International Conference on Advances in Computing, Communications and Informatics, India, pp. 178–183 (2015).
  7. 7.
    S. Dixit, D. Nagaria, Design and analysis of cascaded LMS adaptive filters for noise cancellation. Circuits Syst. Signal Process. 36(2), 742–766 (2017). CrossRefGoogle Scholar
  8. 8.
    S. Dixit, D. Nagaria, Hardware reduction in cascaded LMS adaptive filter for noise cancellation using feedback, in Circuits Systems and Signal Processing, pp. 1–16 (2018).
  9. 9.
    S. Dixit, D. Nagaria, Neural network implementation of least-mean-square adaptive noise cancellation, in IEEE International Conference on Issues and Challenges in Intelligent Computing Techniques, pp. 134–139 (2014).
  10. 10.
    S.C. Douglas, Performance comparison of two implementations of the leaky LMS adaptive filter. IEEE Trans. Signal Process. 45(8), 2125–2129 (1997). CrossRefGoogle Scholar
  11. 11.
    F. Faccenda, L. Novarini, An amplitude constrained FxLMS algorithm for narrow-band active noise control applications, in IEEE 9th International Symposium on Image and Signal Processing and Analysis, Croatia, pp. 233–237 (2015).
  12. 12.
    D.A. Florêncio, H.S. Malvar, Multichannel filtering for optimum noise reduction in microphone arrays, in IEEE International Conference on Acoustics, Speech, and Signal Processing, USA, pp. 197–200 (2001).
  13. 13.
    J.M. Górriz, J. Ramírez, S. Cruces-Alvarez, C.G. Puntonet, E.W. Lang, D. Erdogmus, A novel LMS algorithm applied to adaptive noise cancellation. IEEE Signal Process. Lett. 16(1), 34–37 (2009). CrossRefGoogle Scholar
  14. 14.
    T. Gowri, P.R. Kumar, D.R.K. Reddy, An efficient variable step size least mean square adaptive algorithm used to enhance the quality of electrocardiogram signal, in S.M. Thampi, A. Gelbukh, J. Mukhopadhyay (eds.) Advances in Signal Processing and Intelligent Recognition Systems, pp. 463–475. Springer, Cham (2014).
  15. 15.
    J.G. Harris, J.K. Juan, J.C. Principe, Analog hardware implementation of continuous-time adaptive filter structures. Analog Integr. Circ. Sig. Process 18(2–3), 209–227 (1999). CrossRefGoogle Scholar
  16. 16.
    S. Haykin, B. Widrow, Least-mean-square adaptive filters (Wiley, New York, 2003)Google Scholar
  17. 17.
    S.S. Haykin, Adaptive filter theory (Pearson Education India, Delhi, 2008)zbMATHGoogle Scholar
  18. 18.
    J.H. Husøy, M.S.E. Abadi, Unified approach to adaptive filters and their performance. IET Signal Proc. 2(2), 97–109 (2008). MathSciNetCrossRefGoogle Scholar
  19. 19.
    S.M. Jung, J.H. Seo, P. Park, Efficient variable step-size diffusion normalised least-mean-square algorithm. Electron. Lett. 51(5), 395–397 (2015). CrossRefGoogle Scholar
  20. 20.
    M. Kalamani, S. Valarmathy, M. Krishnamoorthi, Adaptive noise reduction algorithm for speech enhancement. World Acad. Sci. Eng. Technol. Int. J. Electr. Comput. Ener. Electr. Commun. Eng. 8(6), 1007–1014 (2014)Google Scholar
  21. 21.
    N. Kalouptsidis, S. Theodoridis, Adaptive system identification and signal processing algorithms (Prentice-Hall, Inc., Upper Saddle River, 1993)Google Scholar
  22. 22.
    A. Kar, M. Chandra, Pseudo-fractional tap-length learning based applied soft computing for structure adaptation of LMS in high noise environment, in S. Patnaik, B. Zhong (eds.) Soft Computing Techniques in Engineering Applications, pp. 115–129. Springer, New York (2014).
  23. 23.
    S. Kim, C.D. Yoo, T.Q. Nguyen, Alias-free subband adaptive filtering with critical sampling. IEEE Trans. Signal Process. 56(5), 1894–1904 (2008). MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    J. Krolik, M. Joy, S. Pasupathy, M. Eizenman, A comparative study of the LMS adaptive filter versus generalized correlation method for time delay estimation. IEEE Int. Conf. Acoust. Speech Signal Process. 9, 652–655 (1984). CrossRefGoogle Scholar
  25. 25.
    H.S. Lee, S.E. Kim, J.W. Lee, W.J. Song, A variable step-size diffusion LMS algorithm for distributed estimation. IEEE Trans. Signal Process. 63(7), 1808–1820 (2015). MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    W.C. Lee, C.C.J. Kuo, Musical onset detection based on adaptive linear prediction, in IEEE International Conference on Multimedia and Expo, pp. 957–960 (2006).
  27. 27.
    F. Liu, W. Yuan, Y. Ma, Y. Zhou, H. Liu, New enhanced robust kernel least mean square adaptive filtering algorithm, in International Conference on Estimation, Detection and Information Fusion, China, pp. 282–285 (2015).
  28. 28.
    P.L. Madhuri, A.A. John, A fast convergence VSS-SDSELMS adaptive channel estimation algorithm for MIMO-OFDM system, in IEEE International Conference on Control, Instrumentation, Communication and Computational Technologies, pp. 98–103 (2015).
  29. 29.
    A.K. Maurya, Cascade-cascade least mean square (LMS) adaptive noise cancellation. Circuits Syst. Signal Process. 37(9), 3785–3826 (2018). CrossRefGoogle Scholar
  30. 30.
    K. Mayyas, T. Aboulnasr, Leaky LMS algorithm: MSE analysis for Gaussian data. IEEE Trans. Signal Process. 45(4), 927–934 (1997). CrossRefGoogle Scholar
  31. 31.
    F. Merrikh-Bayat, S. Bagheri-Shouraki, Mixed analog-digital crossbar-based hardware implementation of sign-sign LMS adaptive filter. Analog Integr. Circ. Sig. Process 66(1), 41–48 (2011). CrossRefGoogle Scholar
  32. 32.
    J. Ni, J. Chen, X. Chen, Diffusion sign-error LMS algorithm: formulation and stochastic behavior analysis. Sig. Process. 128, 142–149 (2016). CrossRefGoogle Scholar
  33. 33.
    B. Paul, P. Mythili, ECG noise removal using GA tuned sign-data least mean square algorithm, in IEEE International Conference on Advanced Communication Control and Computing Technologies, pp. 100–103 (2012).
  34. 34.
    P. Prandoni, M. Vetterli, An FIR cascade structure for adaptive linear prediction. IEEE Trans. Signal Process. 46(9), 2566–2571 (1998). CrossRefGoogle Scholar
  35. 35.
    N.G. Prelcic, F.P. González, M.E.D. Jiménez, Wavelet packet-based subband adaptive equalization. Sig. Process. 81(8), 1641–1662 (2001). CrossRefzbMATHGoogle Scholar
  36. 36.
    H. Quanzhen, G. Zhiyuan, G. Shouwei, S. Yong, Z. Xiaojin, Comparison of LMS and RLS algorithm for active vibration control of smart structures. IEEE Third Int. Conf. Meas. Technol. Mechatron. Autom. 1, 745–748 (2011). Google Scholar
  37. 37.
    L. Rugini, G. Leus, Basis expansion adaptive filters for time-varying system identification, In 2nd IEEE International Workshop in Computational Advances in Multi-Sensor Adaptive Processing, pp. 153–156 (2007)Google Scholar
  38. 38.
    A.H. Sayed, Adaptive filters (Wiley, New York, 2011)Google Scholar
  39. 39.
    M. Soflaei, P. Azmi, E. Mostajeran, Using selective partial update-selective regressor affine projection algorithms for adaptive equalization in underwater acoustic communications, in International Conference of Information and Communication Technology, pp. 372–376 (2013).
  40. 40.
    K.L. Sudha, Performance analysis of new time-varying LMS (NTVLMS) adaptive filtering algorithm in noise cancellation system, in IEEE International Conference on Communication, Information & Computing Technology, India, pp. 1–6 (2015).
  41. 41.
    B. Widrow, E. Walach, Adaptive signal processing for adaptive control, in IEEE International Conference on Acoustics, Speech, and Signal Processing, USA, pp. 191–194 (1984).
  42. 42.
    B. Widrow, J.M. McCool, M.G. Larimore, C.R. Johnson, Stationary and nonstationary learning characteristics of the LMS adaptive filter. Proc. IEEE 64(8), 1151–1162 (1976). MathSciNetCrossRefGoogle Scholar
  43. 43.
    B. Widrow, J.R. Glover, J.M. McCool, J. Kaunitz, C.S. Williams, R.H. Hearn, J.R. Zeidler, J.E. Dong, R.C. Goodlin, Adaptive noise cancelling: principles and applications. Proc. IEEE 63(12), 1692–1716 (1975). CrossRefGoogle Scholar
  44. 44.
    T. Xu, G. Jacobsen, S. Popov, J. Li, K. Wang, A.T. Friberg, Normalized LMS digital filter for chromatic dispersion equalization in 112-Gbit/s PDM-QPSK coherent optical transmission system. Opt. Commun. 283(6), 963–967 (2010). CrossRefGoogle Scholar
  45. 45.
    N.R. Yousef, A.H. Sayed, Fixed point steady-state analysis of adaptive filters. Int. J. Adapt. Control Signal Process. 17(3), 237–258 (2003). CrossRefzbMATHGoogle Scholar
  46. 46.
    C.H. Zhao, Y. Du, Blind recognition algorithm of mixed MPSK signals based on constellation diagram. J Eng 2012(4), (2012)Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Electronics and Communication Engineering, College of Engineering and TechnologyIILM Academy of Higher LearningGreater Noida, Gautam Budh NagarIndia
  2. 2.Amity UniversityNoidaIndia

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