Skip to main content
SpringerLink
Log in

Fractional LMS and NLMS Algorithms for Line Echo Cancellation

  • Research Article-Electrical Engineering
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

In long haul communication environments, speech data transmission is severely affected by echoes. This phenomenon results in high bit errors as well as in degraded and annoying performance. Traditionally these problems, including hybrid and acoustic echoes, have been controlled through the use of echo suppressors. These suppressors were subsequently replaced by line echo cancellers using adaptive Finite Impulse Response filters. Fractional calculus has been applied successfully for fixed filtering with constant coefficients and in discrete time adaptive filtering that adjusts the weights according to the environment. This paper presents the Fractional Least Mean Square (FLMS) and Fractional Normalized LMS (FNLMS) algorithms for application in echo cancellation. Moreover, the performances of the FLMS and FNLMS are compared with those provided by the standard LMS, NLMS and Block Discrete Fourier Transform solutions. The mean square error criterion is used as the performance comparison criterion for two types of voice signals namely real and synthetic. The simulation results show a performance improvement of about 50% over the traditional counterparts.

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. Lillian, G.: Telecommunications essentials: the complete global source for communications fundamentals, data networking and the Internet, and next-generation networks. Addison-Wesley Professional, Boston (2002)

    Google Scholar 

  2. Fontolliet, P.-G.: ”Telecommunication system engineering:, by Roger L. Freeman, Raytheon Company, Marlborough, MA, USA. Publishers: John Wiley and Sons, Inc., Baffins Lane, Chichester, West Sussex PO19 1UD, United Kingdom, 1989, xxix+ 752 pp., ISBN 0-471-63423-9.” : 107 (1991)

  3. Riverside, H.: Recommended Standard for the UK National Transmission Plan for Public Networks, (2005)

  4. Ouyang, Y.; Yan, T.; Wang, G.: CrowdMi: scalable and diagnosable mobile voice quality assessment through wireless analytics. IEEE Int. Things J. 2(4), 287–294 (2015)

    Article  Google Scholar 

  5. Hoffmann, K.: ”Runtime-dependent switching off of the echo compensation in packet networks.” U.S. Patent Application 10/519,626, filed October 6, (2005)

  6. Gut-Mostowy, H.; Marian, K.; Piotr, B.; MichaÅ, P.; Grzegorz, S.: ”Charakterystyki i obszary zastosowaÅ telekomunikacyjnych usÅug multimedialnych.” Telekomunikacja i Techniki Informacyjne 19–40 (2002)

  7. Standard, Australian. ”Alliance Ltd.” (2015)

  8. Bjorsell, J.E.V.; Maksym S.: ”Emergency assistance calling for voice over IP communications systems.” U.S. Patent 8,537,805, issued September 17 (2013)

  9. Novoselov, S.A.; Topnikov, A.I.; Savvatin, A.I.: ”Algorithm for noise removal of speech commands by spectral tracking.” In Dokl. , pp. 224-226. (2011)

  10. Sector, Standardization, and of ITU. ”ITU-Tg. 108.2.”

  11. LeBlanc, W.: ”Interaction between echo canceller and packet voice processing.” U.S. Patent 8,472,617, issued June 25, (2013)

  12. Tenreiro Machado, J.A.; Silva, M.F.; Barbosa, R.S.; Jesus, I.S.; Reis, C.M.; Marcos, M.G.; Galhano, A.F.: Some applications of fractional calculus in engineering. Math. Prob. Eng. 2010, 34 (2009). https://doi.org/10.1155/2010/639801

    Article  MATH  Google Scholar 

  13. Zahoor, R.M.A.; Qureshi, I.M.: A modified least mean square algorithm using fractional derivative and its application to system identification. Eur. J. Sci. Res. 35(1), 14–21 (2009)

    Google Scholar 

  14. Shah, S.M.; Samar, R.; Noor, R.; han, N.M.; Raja, M.A.Z.: ”Design of fractional-order variants of complex LMS and NLMS algorithms for adaptive channel equalization”, Nonlinear Dynamics, pp. 1–20, (2017)

  15. Shah, S.M.; Samar, R.; Khan, N.M.; Raja, M.A.Z.: Fractional-order adaptive signal processing strategies for active noise control systems. Nonlinear Dyn. 85(3), 1363–1376 (2016)

    Article  MathSciNet  Google Scholar 

  16. Machado, J. T.; Lopes, A. M.: . multidimensional scaling locus of memristor and fractional order elements. J. Adv. Res. (2020)

  17. Sweilam, N.H.; Al-Mekhlafi, S.M.; Baleanu, D.: Optimal control for a fractional tuberculosis infection model including the impact of diabetes and resistant strains. J. Adv. Res. 17, 125–137 (2019)

    Article  Google Scholar 

  18. Ortigueira, M.D.; Bengochea, G.: Non-commensurate fractional linear systems: new results. Journal of Advanced Research (2020)

  19. Tufenkci, S.; Senol, B.; Alagoz, B.B.; MatuÅÅ, R.: Disturbance Rejection FOPID Controller Design in v-domain. J. Adv. Res. (2020)

  20. Tseng, C.C.: Design of variable and adaptive fractional order FIR differentiators. Sig. Process. 86, 2554–2566 (2006)

    Article  Google Scholar 

  21. Shah, S.M.: Riemann-Liouville operator-based fractional normalised least mean square algorithmwith application to decision feedback equalisation of multipath channels. IET Signal Proc. 10(6), 575–582 (2016)

    Article  Google Scholar 

  22. Adaptive filter design with RIDE-method national instruments

  23. Qureshi, S.U.H.: Adaptive equalization. Proc. IEEE 73(9), 1349–1387 (1985)

    Article  Google Scholar 

  24. Shen Q.A.: Spanias, Time and frequency domain x-block LMS algorithms for single channel active noise control. International Congress on Recent Developments in Air- and Structure-Borne Sound and Vibration, pp. 353-360. (1992)

  25. Reichard, K.M.; Swanson, D.C.: Frequency domain implementation of the filtered-x algorithm with online system identification. In Proceedings of the Recent Advances in Active Sound Vibration , pp. 562-573 (1993)

  26. Park, S.J.; Yun, J.H.; Park, Y.C.; Youn, D.H.: A delay less subband active noise control system for wideband noise control. Trans. Speech Audio Process. IEEE 9(8), 892–899 (2001)

    Article  Google Scholar 

  27. DeBrunner, V.; DeBrunner, L.; Wang, L.: Sub-band adaptive filtering with delay compensation for active control. Trans. Sig. Process. IEEE 52(10), 2932–2941 (2004)

    Article  Google Scholar 

  28. Siravara, B.; Magotra, N.; Loizou, P.: A novel approach for single microphone active noise cancellation. Circuits Syst. MWSCAS-2002, 3, III-469-III-472 (2002)

  29. Bleanu, D.; Antnio M.L.: Handbook of Fractional Calculus with Applications, (De Gruyter) (2019)

  30. Miller, K.S.; Ross, B.: An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley, New York (1993)

    MATH  Google Scholar 

  31. Oldham, K.B.; Spanier, J.: The Fractional Calculus. Mathematics in science and engineering. Vol. 111Academic Press, New York (1974)

    MATH  Google Scholar 

  32. Samko, S.G.; Kilbas, A.A.; Marichev, O.I.: Fractional Integrals and Derivatives: Theory and Applications. Reprint Taylor and Francis Books Ltd, London (2002)

    MATH  Google Scholar 

  33. Shaowei, W.; Mingyu, X.: Exact solution on unsteady Couette flow of generalized Maxwell fluid with fractional derivative. J. Acta Mech. 187(1), 103–112 (2006)

    Article  Google Scholar 

  34. Mbodje, B.; Montseny, G.: Boundary fractional derivative control of the wave equation. IEEE Trans. Autom. Contr. 40, 378–382 (1995)

    Article  MathSciNet  Google Scholar 

  35. Odibat, Z.; Momani, S.: Modified homotopy perturbation method: Application to quadratic Riccati differential equation of fractional order. Chaos Solitons Fractals 36(1), 167–174 (2008)

    Article  MathSciNet  Google Scholar 

  36. Engheta, N.: On the role of fractional calculus in electromagnetic theory. IEEE Antennas Propagat. Mag. 39, 35–46 (1997)

    Article  Google Scholar 

  37. Fenander, A.: A fractional derivative railpad model included in a railway track model. J. Sound Vib. 212(5), 889–903 (1998)

    Article  Google Scholar 

  38. Ortigueira, M.D.: Proceedings of the Institution of Electrical Engineering and proceedings of visual Image Signal Process 147, 71–78 (2000)

  39. Ortigueira, M.D.: Introduction to fractional linear systems-Part 2: Discrete-time case. Proc. Inst. Electr. Eng. Proc. Vis. Image Signal Process 147, 71–78 (2000)

    Article  Google Scholar 

  40. Machado, T. J. A.: ”Analysis and Design of Fractional-Order Digital Control Systems, Systems Analysis Modelling Simulation,” Gordon and Breach Science Publishers, 27(2-3) 107-122, (1997)

  41. Machado, T. J. A.: ”Fractional-Order Derivative Approximations in Discrete-Time Control Systems, Systems Analysis Modelling Simulation,” Gordon and Breach Science Publishers, vol. 34, pp. 419-434, ISSN: 0232-9298. (1999)

  42. Shah, S.M.; Samar, R.; Naqvi, S.M.; Chambers, J.A.: Fractional order constant modulus blind algorithms with application to channel equalisation. Electron. Lett. 50(23), 1702–1704 (2014)

    Article  Google Scholar 

  43. Shah, S.M.; Samar, R.; Raja, M.A.Z.; Chambers, J.A.: Fractional Normalized Filtered-error Least Mean Squares Algorithm for Applications in Active Noise Control Systems. Electron. Lett. 14, 973–975 (2014)

    Article  Google Scholar 

  44. Shah, S.M.; Samar, R.; Raja, M.A.Z.: Fractional-order algorithms for tracking Rayleigh fading channels. Nonlinear Dyn. 92, 1243–1259 (2018)

    Article  Google Scholar 

  45. Wang, Y.: Dynamic analysis and synchronization of conformable fractional-order chaotic systems. Eur. Phys. J. Plus 133, 481 (2018)

    Article  Google Scholar 

  46. Morales-Delgado, V.F.; Gómez-Aguilar, J.F.; Kumar, S.; Taneco-Hernndez, M.A.: Analytical solutions of the Keller-Segel chemotaxis model involving fractional operators without singular kernel. Eur. Phys. J. Plus 133, 200 (2018)

    Article  Google Scholar 

  47. Zuiga-Aguilar, C.J.; Gómez-Aguilar, J.F.; Escobar-Jimánez, R.F.; Romero-Ugalde, H.M.: Robust control for fractional variable-order chaotic systems with non-singular kernel. Eur. Phys. J. Plus 133, 103 (2018)

    Article  Google Scholar 

  48. Roohi, R.; Heydari, M.H.; Aslami, M.; Mahmoudi, M.R.: A comprehensive numerical study of space-time fractional bioheat equation using fractional-order Legendre functions. Eur. Phys. J. Plus 133(10), 412 (2018)

    Article  Google Scholar 

  49. Machado, J.T.; Kiryakova, V.; Mainardi, F.: Recent history of fractional calculus. Commun. Nonlinear Sci. Numer. Simul. 16, 1140 (2011)

    Article  MathSciNet  Google Scholar 

  50. Chaudhary, N.I.; Ahmed, M.; Khan, Z.A.; Zubair, S.; Raja, M.A.Z.; Dedovic, N.: Design of normalized fractional adaptive algorithms for parameter estimation of control autoregressive autoregressive systems. Appl. Math. Model. 55, 698 (2018)

    Article  MathSciNet  Google Scholar 

  51. Chaudhary, N.I.; Manzar, M.A.; Raja, M.A.Z.: Fractional Volterra LMS algorithm with application to Hammerstein control autoregressive model identification. Neural Comput. Appl. 31(9), 5227–5240 (2019)

    Article  Google Scholar 

  52. Sayed, Ali H.: Adaptive Filters, (Wiley Interscience), (2008)

  53. Agarwal, A.; Mammone, R.J.: Long-term memory for neural networks. In: Memmone, R.J. (ed.) Artificial Neural Networks for Speech and Vision. Chapman and Hall, London (1993)

    Google Scholar 

  54. Douglas, S.C.: Adaptive filters employing partial updates. IEEE Trans. Circuit Syst. II Analog Digit. Signal Process. 44, 209–216 (1997)

    Article  Google Scholar 

  55. Aslam, M.S.; Chaudhary, N.I.; Raja, M.A.Z.: A sliding-window approximation-based fractional adaptive strategy for Hammerstein nonlinear ARMAX systems. Nonlinear Dyn. 87(1), 519–533 (2017)

    Article  Google Scholar 

  56. Chaudhary, N.I.; Aslam, M.S.; Baleanu, D.; et al.: Design of sign fractional optimization paradigms for parameter estimation of nonlinear Hammerstein systems. Neural Comput. Appl. (2019). https://doi.org/10.1007/00521-019-04328-0

    Article  Google Scholar 

  57. Chaudhary, N.I.; Zubair, S.; Aslam, M.S.; Raja, M.A.Z.; Machado, J.T.: Design of momentum fractional LMS for Hammerstein nonlinear system identification with application to electrically stimulated muscle model. Eur. Phys. J. Plus 134(8), 407 (2019)

    Article  Google Scholar 

  58. Chaudhary, N.I.; Zubair, S.; Khan, Z.A.; Raja, M.A.Z.; Dedovic, N.: Normalized fractional adaptive methods for nonlinear control autoregressive systems. Appl. Math. Model. 66, 457–471 (2019)

    Article  MathSciNet  Google Scholar 

  59. Ortigueira, M.D.; Machado, J.T.: New discrete-time fractional derivatives based on the bilinear transformation: definitions and properties. J. Adv. Res. (2020)

  60. Boroujeny, B.F.: Adaptive filters theory and applications. John Wiley and Sons, Boston (2013)

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Comm. Technologies, Islamabad, Affiliated with Department of Electrical Engineering, University of Engineering and Technology, Peshawar, Pakistan

    Akhtar Ali Khan

  2. Department of Electrical Engineering, Capital University of Science and Technology, Islamabad, Pakistan

    Syed Muslim Shah

  3. Department of Electrical and Computer Engineering, COMSATS University Islamabad, Attock Campus, Attock, Pakistan

    Muhammad Asif Zahoor Raja

  4. Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin, Taiwan, 64002, Republic of China

    Muhammad Asif Zahoor Raja

  5. Department of Electrical Engineering, International Islamic University, Islamabad, Pakistan

    Naveed Ishtiaq Chaudhary

  6. School of Electrical Engineering and Automation, Wuhan University, Wuhan, China

    Yigang He

  7. Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, Porto, Portugal

    J. A. Tenreiro Machado

Authors
  1. Akhtar Ali Khan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Syed Muslim Shah
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Muhammad Asif Zahoor Raja
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Naveed Ishtiaq Chaudhary
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yigang He
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. J. A. Tenreiro Machado
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Muhammad Asif Zahoor Raja.

Ethics declarations

Conflicts of interest

All authors declared that there are no potential conflicts of interest.

Human and animal rights statements

All authors declared that there is no research involving human and/or animal.

Informed consent

All authors declared that there is no material that required informed consent.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary material 1 (pdf 59 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khan, A.A., Shah, S.M., Raja, M.A.Z. et al. Fractional LMS and NLMS Algorithms for Line Echo Cancellation. Arab J Sci Eng 46, 9385–9398 (2021). https://doi.org/10.1007/s13369-020-05264-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-020-05264-1

Keywords

Search

Navigation