Two-channel forward NLMS algorithm combined with simple variable step-sizes for speech quality enhancement

  • Redha BendoumiaEmail author


This paper addresses the problem of speech quality enhancement by adaptive two-channel filtering algorithms. Recently, the forward blind source separation structure has been proposed and combined with normalized least-mean-square algorithm (FNLMS). The main drawback of two-channel FNLMS algorithm is its poor performance in steady state regime when the fixed step-sizes values are selected large. However, the slow convergence rate is observed with the small fixed step-size values. In this paper, we propose three new combinations of the basic FNLMS algorithm with simple variable step-sizes approaches, for improving both the steady state values and convergence rate (noted TVSF for Two-channel Variable Step-size Forward). In these modifications, we propose new configuration of two-channel forward structure by three simple and efficient variable step-sizes estimations. To confirm the good performance of three proposed TVSF algorithms compared with the classical fixed-step-size version, we have carried out several simulations in very noisy situations using several criteria.


Variable step-size Speech quality Output SNR Adaptive filtering algorithm Two-channel forward structure 


  1. 1.
    Buchner, H., et al. (2005). A generalization of blind source separation algorithms for convolutive mixtures based on second order statistics. IEEE Transactions on Speech and Audio Processing, 13(1), 120–134.CrossRefGoogle Scholar
  2. 2.
    Gabrea, M. (2003). Double affine projection algorithm-based speech enhancement algorithm. In Proc. ICASSP Montréal, Canada: IEEE, vol. 2 (pp. 904–907).Google Scholar
  3. 3.
    Djendi, M., & Bendoumia, R. (2013). A new adaptive filtering subband algorithm for two-channel acoustic noise reduction and speech enhancement. Computers & Electrical Engineering, 39(8), 2531–2550.CrossRefGoogle Scholar
  4. 4.
    Djendi, M., & Bendoumia, R. (2014). A new efficient two-channel backward algorithm for speech intelligibility enhancement: A subband approach. Applied Acoustics, 76, 209–222.CrossRefGoogle Scholar
  5. 5.
    Djendi, M., Scalart, P., & Gilloire, A. (2013). Analysis of two-sensors forward BSS structure with post-filters in the presence of coherent and incoherent noise. Speech Communication, 55, 975–987.CrossRefGoogle Scholar
  6. 6.
    Bendoumia, R., & Djendi, M. (2015). Two-channel variable-step-size forward-and-backward adaptive algorithms for acoustic noise reduction and speech enhancement. Signal Processing, 108, 226–244.CrossRefGoogle Scholar
  7. 7.
    Bendoumia, R., & Djendi, M. (2014). Variable step-sizes new efficient two-channel backward algorithm for speech intelligibility enhancement: a subband approach. Applied Acoustics, 76, 209–222.CrossRefGoogle Scholar
  8. 8.
    Darazirar, I., & Djendi, M. (2015). A two-sensor Gauss-Seidel fast affine projection algorithm for speech enhancement and acoustic noise reduction. Applied Acoustics, 96, 39–52.CrossRefGoogle Scholar
  9. 9.
    Gerven, S. V., & Compernolle, D. V. (1995). Signal separation by symmetric adaptive decorrelation: stability, convergence, and uniqueness. IEEE Transactions on Signal Processing, 43(7), 1602–1612.CrossRefGoogle Scholar
  10. 10.
    Djendi, M., & Zoulikha, M. (2014). New automatic forward and backward blind sources separation algorithms for noise reduction and speech enhancement. Computers & Electrical Engineering, 40, 2072–2088.CrossRefGoogle Scholar
  11. 11.
    Kwong, R. H., & Johnston, E. W. (1992). A variable step size LMS algorithm. IEEE Transactions on Signal Processing, 40(7), 1633–1642.CrossRefzbMATHGoogle Scholar
  12. 12.
    Aboulnasr, T., & Mayyas, K. (1997). A robust variable step-size LMS-type algorithm: Analysis and simulations. IEEE Transactions on Signal Processing, 45(3), 631–639.CrossRefGoogle Scholar
  13. 13.
    Zipf, J. G. F., et al. (2008). A VSSLMS algorithm based on error autocorrelation. In 16th European signal processing conference (EUSIPCO), Lausanne, Switzerland, August 25–29, 2008.Google Scholar
  14. 14.
    Herault, J., et al. (1985). Détection de grandeurs primitives dans un message composite par une architecture de calcul neuromimétique en apprentissage non supervisé. In Proc. GRETSI 85, Dixième colloque sur le Traitement du Signal et des Images, Nice, France (pp. 1017–1022).Google Scholar
  15. 15.
    Djendi, M. (2016). An efficient frequency-domain adaptive forward BSS algorithm for acoustic noise reduction and speech quality enhancement. Computers & Electrical Engineering, 52, 12–27.CrossRefGoogle Scholar
  16. 16.
    Vallauri, A. (1992). L’étude et le développement de méthodes de reconnais-sance de la parole et de réduction du bruit, et application. Ph.D. Thesis, Univ. Nice, France.Google Scholar
  17. 17.
    Zoulikha, Meriem, & Djendi, Mohamed. (2016). A new regularized forward blind source separation algorithm for automatic speech quality enhancement. Applied Acoustics, 112, 192–200.CrossRefGoogle Scholar
  18. 18.
    Bendoumia, Rédha, & Djendi, Mohamed. (2018). Acoustic noise reduction by new two-channel proportionate forward symmetric adaptive decorrelating algorithms in sparse systems. Applied Acoustics, 137, 69–81.CrossRefGoogle Scholar
  19. 19.
    Araki, S., Makino, S., Aichner, R., Nishikawa, T., Saruwatari, H. (2003). Subband based blind source separation with appropriate processing for each frequency band. In IEEE. ICA 2003, Nara, Japan (pp. 499–504).Google Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Department of Electronic, Signal Processing and Image Laboratory (LATSI)University of Blida 1BlidaAlgeria

Personalised recommendations