Skip to main content
SpringerLink
Log in

Cascade–Cascade Least Mean Square (LMS) Adaptive Noise Cancellation

Circuits, Systems, and Signal Processing volume 37, pages 3785–3826 (2018)Cite this article

Abstract

The paper presents a new model of noise cancellation using cascading of cascaded LMS adaptive filters. The model has a combination of ‘\(2N+1\)’ LMS filters for N-stage of adaptive noise cancellation. First LMS filter works as a basic noise canceller, next two work as 1st stage of noise canceller using a cascaded form of LMS filters known as LMS Block-1, and all others have the same arrangement as LMS Block-1 known as LMS Block-2, LMS Block-3, \(\ldots \), LMS Block-N. The LMS Block has a two-stage noise reduction of the additive noise or interference. LMS Block-1 is cascaded noise canceller, determines and reduces noise again after reduction in noise from 1st LMS filter. The analysis and simulation model gives the responses of noise cancellation like error signal, output signal and signal-to-noise ratio with respect to step sizes, filter lengths and initial weight of filters. This paper also shows the simulation of cascade–cascade LMS adaptive noise cancellation for two stages (\(N = 2\)) and gives the higher signal-to-noise ratio at Nth stage with respect to previous stages. It is the next novel point of this paper that no other elements are present in the cascade–cascade LMS adaptive noise cancellation rather than LMS filters as noise canceller.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

References

  1. A.H. Abdullah, M.I. Yusof, S.R.M. Baki, Adaptive noise cancellation: a practical study of the least-mean-square (LMS) over recursive least-square (RLS) algorithm, in IEEE Student Conference on Research and Development, Malaysia, pp. 448–452 (2002)

  2. K.F. Abusalem, G. Yu, Variable step LMS algorithm using the accumulated instantaneous error concept, in Proceedings of the World Congress on Engineering, vol. 1 (2008)

  3. N. Ahmed, D. Hush, G. Elliott, R. Fogler, Detection of multiple sinusoids using an adaptive cascaded structure, in IEEE International Conference on Acoustics, Speech, and Signal Processing, USA, pp. 199–202 (1984)

  4. E.L. Batista, R. Seara, On the implementation of fully adaptive interpolated FIR filters, in IEEE 20th European Signal Processing Conference, Romania, pp. 2173–2177 (2012)

  5. E.L. Batista, O.J. Tobias, R. Seara, New insights in adaptive cascaded FIR structure: application to fully adaptive interpolated FIR structures, in IEEE 15th European Signal Processing Conference, Poland, pp. 370–374 (2007)

  6. H.J.W. Belt, H.J. Butterweck, Cascaded all-pass sections for LMS adaptive filtering, in IEEE 8th European Signal Processing Conference, Italy, pp. 1–4 (1996)

  7. 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)

  8. J.W. Choi, N.I. Cho, Suppression of narrow-band interference in DS-spread spectrum systems using adaptive IIR notch filter. Signal Process. 82(12), 2003–2013 (2002)

    Article  MATH  Google Scholar 

  9. 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)

  10. 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)

  11. 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)

  12. S. Dixit, D. Nagaria, Design and analysis of cascaded LMS adaptive filters for noise cancellation. Circuits Syst. Signal Process. 36(2), 1–25 (2017)

    Article  Google Scholar 

  13. 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, India, pp. 134–139 (2014)

  14. 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)

  15. B. Farhang-Boroujeny, An IIR adaptive line enhancer with controlled bandwidth. IEEE Trans. Signal Process. 45(2), 477–481 (1997)

    Article  Google Scholar 

  16. 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)

  17. J. Freudenberger, S. Stenzel, Suppression of engine noise harmonics using cascaded LMS filters, in 10. ITG Symposium on Speech Communication, Germany, pp. 1–4 (2012)

  18. 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)

    Article  Google Scholar 

  19. J.G. Harris, J.K. Juan, J.C. Principe, Analog hardware implementation of continuous-time adaptive filter structures. Analog Integr. Circuits Signal Process. 18(2–3), 209–227 (1999)

    Article  Google Scholar 

  20. S. Haykin, B. Widrow, Least-Mean-Square Adaptive Filters (Wiley, New York, 2003)

    Book  Google Scholar 

  21. S.S. Haykin, Adaptive Filter Theory (Pearson Education India, Delhi, 2008)

    MATH  Google Scholar 

  22. H. Huang, P. Franti, D. Huang, S. Rahardja, Cascaded RLS-LMS prediction in MPEG-4 lossless audio coding. IEEE Trans. Audio Speech Lang. Process. 16(3), 554–562 (2008)

    Article  Google Scholar 

  23. M.Z. Ilyas, A.O.A. Noor, K.A. Ishak, A. Hussain, S.A. Samad, Normalized least mean square adaptive noise cancellation filtering for speaker verification in noisy environments, in IEEE International Conference on Electronic Design, Malaysia, pp. 1–4 (2008)

  24. 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)

    Article  Google Scholar 

  25. M. Kalamani, S. Valarmathy, M. Krishnamoorthi, Adaptive noise reduction algorithm for speech enhancement. World Acad. Sci. Eng. Technol. Int. J. Electr. Comput. Energ. Electron. Commun. Eng. 8(6), 1007–1014 (2014)

    Google Scholar 

  26. H. Kim, S. Kim, N. Van Helleputte, T. Berset, D. Geng, I. Romero, R. F. Yazicioglu, Motion artifact removal using cascade adaptive filtering for ambulatory ECG monitoring system, in IEEE Biomedical Circuits and Systems Conference, Taiwan, pp. 160–163 (2012)

  27. J.G. Kim, W.G. Bae, Adaptive step control of LMS-based Interference Cancellation for WMAN ICS radio repeater, in IEEE International Conference on Information Networking, Cabodia, pp. 253–258 (2015)

  28. W.J. Kozacky, T. Ogunfunmi, A cascaded IIR-FIR adaptive ANC system with output power constraints. Signal Process. 94, 456–464 (2014)

    Article  Google Scholar 

  29. T.K. Kumar, Optimum cascaded design for speech enhancement using Kalman filter. World Acad. Sci. Eng. Technol. Int. J. Electr. Comput. Energ. Electron. Commun. Eng. 2(5), 787–791 (2008)

    Google Scholar 

  30. 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)

    Article  MathSciNet  Google Scholar 

  31. L. Li, V.J. Mathews, Efficient block-adaptive parallel-cascade quadratic filters. IEEE Trans. Circuits Syst. II: Analog Digital Signal Process. 46(4), 468–472 (1999)

    Article  Google Scholar 

  32. S. Li, S. Wu, Y. Wang, W. Guo, Y. Zhou, An improved NLMS algorithm based on speech enhancement, in IEEE Advanced Information Technology, Electronic and Automation Control Conference, China, pp. 896–899 (2015)

  33. M. Limem, M.A. Hamdi, M.A. Maaref, Denoising uterine EMG signals using LMS and RLS adaptive algorithms, in IEEE 2nd International Conference on Advanced Technologies for Signal and Image Processing, Tunisia, pp. 273–276 (2016)

  34. 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)

  35. S. Mohapatra, A. Kar, An advanced feedback Filtered-x least mean square algorithm for wideband noise removal, in IEEE 12th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology, Thailand, pp. 1–5 (2015)

  36. R. Nagal, P. Kumar, P. Bansal, Performance analysis of least mean square algorithm for different step size parameters with different filter order and iterations, in International Conference on Recent Developments in Control, Automation and Power Engineering, India, pp. 326–331 (2015)

  37. C.V. Niras, Y. Kong, LMS algorithm implementation in FPGA for noise reduction and echo cancellation, in 4th International Conference Proceedings on Advances in Recent Technology in Communication and Computing, IET India, pp. 193–195 (2012)

  38. T.M. Panicker, V.J. Mathews, G.L. Sicuranza, Adaptive parallel-cascade truncated Volterra filters. IEEE Trans. Signal Process. 46(10), 2664–2673 (1998)

    Article  Google Scholar 

  39. T.M. Panicker, V.J. Mathews, G.L. Sicuranza, Parallel-cascade adaptive volterra filters, in IEEE 8th European Signal Processing Conference, Italy, pp. 1–4 (1996)

  40. A.D. Poularikas (ed.), Handbook of Formulas and Tables for Signal Processing (CRC Press, Boca Raton, 1998)

    MATH  Google Scholar 

  41. P. Prandoni, M. Vetterli, An FIR cascade structure for adaptive linear prediction. IEEE Trans. Signal Process. 46(9), 2566–2571 (1998)

    Article  Google Scholar 

  42. N.G. Prelcic, F.P. González, M.E.D. Jiménez, Wavelet packet-based subband adaptive equalization. Signal Process. 81(8), 1641–1662 (2001)

    Article  MATH  Google Scholar 

  43. R.M. Ramli, A.O. Noor, S.A. Samad, A review of adaptive line enhancers for noise cancellation. Aust. J. Basic Appl. Sci. 6(6), 337–352 (2012)

    Google Scholar 

  44. M. Sambur, Adaptive noise canceling for speech signals. IEEE Trans. Acoust. Speech Signal Process. 26(5), 419–423 (1978)

    Article  Google Scholar 

  45. S.G. Sankaran, A.A. Beex, Acoustic echo and noise canceler improvements for hands-free telephones, in IEEE Southeastcon’97, Engineering the new Century, New York, pp. 148–150 (1997)

  46. M. Scarpiniti, D. Comminiello, R. Parisi, A. Uncini, Hammerstein uniform cubic spline adaptive filters: learning and convergence properties. Signal Process. 100, 112–123 (2014)

    Article  Google Scholar 

  47. M. Scarpiniti, D. Comminiello, R. Parisi, A. Uncini, Nonlinear system identification using IIR spline adaptive filters. Signal Process. 108, 30–35 (2015)

    Article  Google Scholar 

  48. G.D. Schuller, B. Yu, D. Huang, B. Edler, Perceptual audio coding using adaptive pre-and post-filters and lossless compression. IEEE Trans. Speech Audio Process. 10(6), 379–390 (2002)

    Article  Google Scholar 

  49. S. Shimauchi, Y. Haneda, Nonlinear acoustic echo cancellation based on piecewise linear approximation with amplitude threshold decomposition, in International Workshop on Acoustic Signal Enhancement, Germany, pp. 1–4 (2012)

  50. J.J. Shynk, Adaptive IIR filtering. IEEE ASSP Mag. 6(2), 4–21 (1989)

    Article  Google Scholar 

  51. 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)

  52. X. Sun, S.M. Kuo, Active narrowband noise control systems using cascading adaptive filters. IEEE Trans. Audio Speech Lang. Process. 15(2), 586–592 (2007)

    Article  Google Scholar 

  53. A. Ükte, A. Kızılkaya, Adaptive noise cancellation with a multirate normalized least mean squares filter, in IEEE 23nd Signal Processing and Communications Applications Conference, Malatya, pp. 1417–1420 (2015)

  54. A. Ukte, A. Kizilkaya, Comparing the performances of least mean squares based multirate adaptive filters, in IEEE 26th International Conference Radioelektronika, Slovakia, pp. 325–329 (2016)

  55. S.V. Vaseghi, Advanced Digital Signal Processing and Noise Reduction (Wiley, New York, 2008)

    Book  Google Scholar 

  56. S.H.K. Venturi, I. Panahi, Hybrid RLS-NLMS algorithm for real-time remote active noise control using directional ultrasonic loudspeaker, in 40th Annual Conference of the IEEE Industrial Electronics Society, USA, pp. 2418–2424 (2014)

  57. M. Wasimuddin, Design and implementation of least mean square adaptive filter on fetal electrocardiography, in IEEE 2014 Zone 1 Conference of the American Society for Engineering Education, USA, pp. 1–5 (2014)

  58. B. Widrow, J.R. Glover, J.M. McCool, J. Kaunitz, C.S. Williams, R.H. Hearn, R.C. Goodlin, Adaptive noise cancelling: principles and applications. Proc. IEEE 63(12), 1692–1716 (1975)

    Article  Google Scholar 

  59. 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)

    Article  MathSciNet  Google Scholar 

  60. 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)

  61. X. Wu, Z. Tan, J. Zhang, W. Li, Dual adaptive noise cancellation method based on Least Mean M-estimate of noise, in IEEE 11th World Congress on Intelligent Control and Automation, China, pp. 5741–5746 (2014)

  62. 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)

    Article  MATH  Google Scholar 

  63. R. Yu, C.C. Ko, Lossless compression of digital audio using cascaded RLS-LMS prediction. IEEE Trans. Speech Audio Process. 11(6), 532–537 (2003)

    Article  Google Scholar 

  64. J. Zhang, W. Zhang, T.D. Abhayapala, Noise cancellation over spatial regions using adaptive wave domain processing, in IEEE Workshop on Applications of Signal Processing to Audio and Acoustics, New York, pp. 1–5 (2015)

Download references

Author information

Authors and Affiliations

  1. Department of Electronics and Communication Engineering, College of Engineering and Technology, IILM Academy of Higher Learning, Greater Noida, Gautam Buddh Nagar, India

    Awadhesh Kumar Maurya

Authors
  1. Awadhesh Kumar Maurya
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Awadhesh Kumar Maurya.

Appendix

Appendix

See Tables 4, 5, 6 and Figs. 13, 14, 15.

Table 4 Combination of step sizes (\(\mu _{1}, \mu _{2}, \mu _{3})\)
Full size table
Table 5 Combination of step sizes: (\(\mu _{1}, \mu _{2})\) at constant \(\mu _{3}\), \((\mu _{2},\, \mu _{3})\) at constant \(\mu _{1}\) and (\(\mu _{1},\, \mu _{3})\) at constant \(\mu _{2}\)
Full size table
Table 6 Convergence rate of error signal for N-LMS Blocks at \(\mu \ll 1\)
Full size table
Fig. 13
figure 13

SNRs for single and new model-based cascaded LMS-ANC at \(L=L{'}=L^{\prime \prime }\). a 2, b 4, c 8, d 16, e 32, f 64 and combination of step sizes of LMS filters (\(\mu _{2}, \mu _{3})\) at constant \(\mu _{1}\)

Full size image
Fig. 14
figure 14

SNRs for single and new model-based cascaded LMS-ANC at \(L=L{'}=L^{\prime \prime }\). a 2, b 4, c 8, d 16, e 32, f 64 and combination of step sizes of LMS filters \((\mu _{1}, \mu _{3})\) at constant \(\mu _{2}\)

Full size image
Fig. 15
figure 15

SNRs for single and new model-based cascaded LMS-ANC at \(L=L{'}=L^{\prime \prime }\). a 2, b 4, c 8, d 16, e 32, f 64 and combination of step sizes of LMS filters \((\mu _{1}, \mu _{2})\) at constant \(\mu _{3}\)

Full size image

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Maurya, A.K. Cascade–Cascade Least Mean Square (LMS) Adaptive Noise Cancellation. Circuits Syst Signal Process 37, 3785–3826 (2018). https://doi.org/10.1007/s00034-017-0731-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-017-0731-2

Keywords

Search

Navigation