Annals of Telecommunications

, Volume 73, Issue 11–12, pp 711–717 | Cite as

An analytical derivation for second-order blind separation of two signals

  • Abdelfettah Meziane Bentahar Meziane
  • Thierry Chonavel
  • Abdeldjalil Aïssa-El-BeyEmail author
  • Adel Belouchrani


In this paper, we propose analytical formulas that involve second-order statistics for separating two signals. The method utilizes source decorrelation and correlation function diversity. In particular, the proposed SOBAS (second-order blind analytical separation) algorithm differs from the ASOBI (analytical second-order blind identification) algorithm in that it does not require prior knowledge or estimation of the noise variance. Computer simulations demonstrate the effectiveness of the proposed method.


Blind source separation Second-order statistics TITO systems 


  1. 1.
    Abed-Meraim K, Attallah S, Lim T, Damen M (2000) A blind interference canceller in DS-CDMA. In: IEEE International Symposium on Spread Spectrum Techniques and Applications. Parsippany, pp 358–362Google Scholar
  2. 2.
    Aïssa-El-Bey A, Abed-Meraim K, Grenier Y (2007) Underdetermined blind audio source separation using modal decomposition. EURASIP J Audio Speech Music Process 2007(85438):1–15CrossRefGoogle Scholar
  3. 3.
    Aziz-Sbaï SM, Aïssa-El-Bey A, Pastor D (2012) Contribution of statistical tests to sparseness-based blind source separation. EURASIP J Appl Signal Process 2012:169CrossRefGoogle Scholar
  4. 4.
    Belouchrani A, Abed-Meraim K, Cardoso JF, Moulines E (1997) A blind source separation technique using second-order statistics. IEEE Trans Signal Process 45(2):434–444. CrossRefGoogle Scholar
  5. 5.
    Belouchrani A, Bourennane E, Abed-Meraim K (2006) A closed form solution for the blind separation of two sources from two sensors using second order statistics. In: European Signal processing conferenc (EUSIPCO). FlorenceGoogle Scholar
  6. 6.
    Comon P, Jutten C (2010) Handbook of blind source separation: independent component analysis and applications, 1st edn. Academic PressGoogle Scholar
  7. 7.
    Durán-Díaz I, Cruces-Alvarez SA (2007) A joint optimization criterion for blind DS-CDMA detection. EURASIP J Adv Signal Process 2007(79248):1–11zbMATHGoogle Scholar
  8. 8.
    Hypvarinen A, Karhunen J, Oja E (2001) Independent component analysis. WileyGoogle Scholar
  9. 9.
    Itakura F, Saito S (1968) Analysis synthesis telephony based on the maximum likelihood method. In: 6th International Congress on Acoustics, vol C. Tokyo, pp 17–20Google Scholar
  10. 10.
    Rouxel A, Guennec D L, Macchi O (2000) Unsupervised adaptive separation of impulse signals applied to EEG analysis. In: IEEE International Conference on Acoustics, Speech, Signal Processing (ICASSP), vol 1. Istanbul, pp 420-423Google Scholar
  11. 11.
    Varajarajan V, Krolik J (2001) Multichannel system identification methods for sensor array calibration in uncertain multipath environments. In: IEEE Signal processing workshop on statistical signal processing (SSP). Singapore, pp 297–300Google Scholar
  12. 12.
    Wang Z, Zhang X, Cao T (2006) Intelligent control and automation: International Conference on Intelligent Computing, ICIC 2006 Kunming, China, August 16–19, 2006, chap. A new blind source separation algorithm based on second-order statistics for TITO. Springer, Berlin, pp 29–34. CrossRefGoogle Scholar

Copyright information

© Institut Mines-Télécom and Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Abdelfettah Meziane Bentahar Meziane
    • 1
  • Thierry Chonavel
    • 2
  • Abdeldjalil Aïssa-El-Bey
    • 2
    Email author
  • Adel Belouchrani
    • 1
  1. 1.Ecole Nationale PolytechniqueAlgiersAlgeria
  2. 2.IMT Atlantique, UMR CNRS 6285 Lab-STICC, UBLBrest CedexFrance

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