Circuits, Systems, and Signal Processing

, Volume 38, Issue 7, pp 3107–3132 | Cite as

Underdetermined Independent Component Analysis Based on First- and Second-Order Statistics

  • Qiao SuEmail author
  • Yimin Wei
  • Yuehong Shen
  • Changliang Deng


This paper proposes a class of new algorithms based on first- and second-order statistics for independent source extraction of circular signals in underdetermined complex-valued mixture. The complex-valued mixing matrix is estimated by two extremely cost-effective novel methods based on the conditional mean of the mixtures which require some prior knowledge of the positive support of the real and/or imaginary parts of the sources. And the sources are recovered by combining the conventional minimum mean-squared error-based beamforming approach with the acquired prior knowledge. Based on how much prior knowledge is got, we propose several new algorithms. The complexity analysis about the proposed algorithms suggests that the algorithms which employ more prior knowledge have higher complexity, but their computational cost is significantly low. Two examples are provided for showing the possible applications of these proposed algorithms. Simulation results validate the effectiveness and reliability of all presented methods.


Independent component analysis First-order statistics Minimum mean-squared error-based (MMSE) beamforming Underdetermined complex-valued mixture 



This work was supported by the National Natural Science Foundation of China under Grant Nos. 61172061 and 61201242 and the Natural Science Foundation of Jiang Su Province in China under Grant No. BK2012057.


  1. 1.
    L. Albera, A. Ferreol, P. Comon et al., Blind identification of overcomplete mixtures of sources (BIOME). Linear Algebra Appl. 391, 1–30 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    P. Bofill, M. Zibulevsky, Underdetermined blind source separation using sparse representations. Signal Process. 81(11), 2353–2362 (2001)CrossRefzbMATHGoogle Scholar
  3. 3.
    R.M. Clemente, S.H. Mellado, J.L.C. Olivares, Fast independent component analysis using a new property, in International Work Conference on Artificial Neural Networks (IWANN) (2011), pp. 477–483Google Scholar
  4. 4.
    P. Comon, C. Jutten et al., Handbook of Blind Source Separation: Independent Component Analysis and Applications (Academic Press, New York, 2010)Google Scholar
  5. 5.
    S.H. Hsu, T.R. Mullen, T.P. Jung et al., Real-time adaptive EEG source separation using online recursive independent component analysis. IEEE Trans. Neural Syst. Rehabil. Eng. 24(3), 309–319 (2016)CrossRefGoogle Scholar
  6. 6.
    A. Karfoul, L. Albera, D.L. Lathauwer, Iterative methods for the canonical decomposition of multi-way arrays: application to blind underdetermined mixture identification. Signal Process. 91(8), 1789–1802 (2011)CrossRefzbMATHGoogle Scholar
  7. 7.
    S. Kim, C.D. Yoo, Underdetermined blind source separation based on subspace representation. IEEE Trans. Signal Process. 57(7), 2604–2614 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Z. Koldovský, P. Tichavský, A.H. Phan et al., A two-stage MMSE beamformer for underdetermined signal separation. IEEE Signal Process. Lett. 20(12), 1227–1230 (2013)CrossRefGoogle Scholar
  9. 9.
    D. Kumar, C.S. Rai, S. Kumar, Analysis of unsupervised learning techniques for face recognition. Int. J. Imaging Syst. Technol. 20(3), 261–267 (2010)CrossRefGoogle Scholar
  10. 10.
    D.L. Lathauwer, J. Castaing, J.F. Cardoso, Fourth-order cumulant based blind identification of underdetermined mixtures. IEEE Trans. Signal Process. 55(6), 2965–2973 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    D.L. Lathauwer, J. Castaing, Blind identification of underdetermined mixtures by simultaneous matrix diagonalization. IEEE Trans. Signal Process. 56(3), 1096–1105 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    H. Lin, T. Thaiupathump, S.A. Kassam, Blind separation of complex I/Q independent sources with phase recovery. IEEE Signal Process. Lett. 12(5), 419–422 (2005)CrossRefGoogle Scholar
  13. 13.
    F. Petre, M. Engels, A. Bourdoux et al., Extended MMSE receiver for multiuser interference rejection in multipath DS-CDMA channels, in Vehicular Technology Conference, vol. 3 (1999), pp. 1840–1844Google Scholar
  14. 14.
    R. Phlypo, V. Zarzoso, I. Lemahieu, Source extraction by maximizing the variance in the conditional distribution tails. IEEE Trans. Signal Process. 58(1), 305–316 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    G.K. Sang, D.Y. Chang, Underdetermined independent component analysis by data generation, in Independent Component Analysis and Blind Source Separation (ICA) (2004), pp. 445–452Google Scholar
  16. 16.
    P.F. Stenumgaard, On radiated emission limits for pulsed interference to protect modern digital wireless communication systems. IEEE Trans. Electromagn. Compat. 49(4), 931–936 (2007)CrossRefGoogle Scholar
  17. 17.
    Q. Su, Y. Shen, Y. Wei et al., SSP-based UBI algorithms for uniform linear array. Circuits Syst. Signal Process. 36(10), 4077–4096 (2017)CrossRefzbMATHGoogle Scholar
  18. 18.
    Q. Su, Y. Wei, C. Deng et al., Fast extraction for skewed source signals using conditional expectation. J. Sens. 2018, 1–6 (2018)Google Scholar
  19. 19.
    P. Tichavský, Z. Koldovský, Weight adjusted tensor method for blind separation of underdetermined mixtures of nonstationary sources. IEEE Trans. Signal Process. 59(3), 1037–1047 (2011)CrossRefGoogle Scholar
  20. 20.
    B. Xerri, B. Borloz, An iterative method using conditional second-order statistics applied to the blind source separation problem. IEEE Trans. Signal Process. 52(2), 313–328 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    P.C. Xu, Y.H. Shen, H. Li et al., Independent component analysis of complex valued signals based on first-order statistics. Radioengineering 22(4), 1194–1201 (2013)Google Scholar
  22. 22.
    L. Yang, H. Zhang, Y. Cai, A low-complexity PARAFAC decomposition for underdetermined blind system identification with complex mixtures. Circuits Syst. Signal Process. 37, 4842–4860 (2018)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Z. Yang, Y. Xiang, Y. Rong et al., A convex geometry-based blind source separation method for separating nonnegative sources. IEEE Trans. Neural Netw. 26(8), 1635–1644 (2015)MathSciNetCrossRefGoogle Scholar
  24. 24.
    W. Yu, R. Lui, Dual methods for nonconvex spectrum optimization of multicarrier systems. IEEE Trans. Commun. 54(7), 1310–1322 (2006)CrossRefGoogle Scholar
  25. 25.
    V. Zarzoso, R.M. Clemente, S.H. Mellado, Independent component analysis based on first-order statistics. Signal Process. 92(8), 1779–1784 (2012)CrossRefGoogle Scholar
  26. 26.
    H. Zhu, S. Zhang, H. Zhao, Single-channel source separation of multi-component radar signal with the same generalized period using ICA. Circuits Syst. Signal Process. 35(1), 353–363 (2016)MathSciNetCrossRefzbMATHGoogle Scholar

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

Authors and Affiliations

  1. 1.Graduate SchoolArmy Engineering University of PLANanjingChina
  2. 2.College of Communications EngineeringArmy Engineering University of PLANanjingChina

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