Circuits, Systems, and Signal Processing

, Volume 37, Issue 8, pp 3206–3226 | Cite as

A Complex-Valued Mixing Matrix Estimation Algorithm for Underdetermined Blind Source Separation

  • Qiang Guo
  • Guoqing RuanEmail author
  • Liangang Qi


This paper considers complex-valued mixing matrix estimation in underdetermined blind source separation. An effective estimation algorithm based on both single-source-point (SSP) detection and modified dynamic data field clustering is proposed. First, array-processing-based time–frequency SSP detection is applied to improve signal sparsity, therein utilizing the real and imaginary components of the observed signals in the time–frequency domain. The algorithm can be applied to the estimation of complex-valued mixing matrix based on L-shaped arrays and uniform circular arrays. Then, to overcome the limitation that the clustering performance of traditional algorithms is affected by noise, data cleansing detection is introduced to reselect the SSPs with high potential energy as representative objects to achieve preliminary data classification. Finally, a dynamic data field clustering algorithm is adopted to move and merge the representative objects until all column vectors of the mixing matrix are estimated. Simulation results show that the proposed method can effectively estimate complex-valued mixing matrices with high accuracy, especially in real-world noncooperative cases without prior knowledge.


Underdetermined blind source separation Complex-valued mixing matrix estimation Data cleansing detection Modified dynamic data field clustering 



This work is supported by the National Natural Science Foundation of China (No. 61371172), the International S&T Cooperation Program of China (ISTCP) (No. 2015DFR10220), the National Key Research and Development Program of China (No. 2016YFC0101700), the Fundamental Research Funds for the Central Universities (No. HEUCF1508), and the Natural Science Foundation of Heilongjiang Province (No. F201337).


  1. 1.
    F. Abrard, Y. Deville, A time-frequency blind signal separation method applicable to underdetermined mixtures of dependent sources. Signal Process. 85(7), 1389–1403 (2005)CrossRefzbMATHGoogle Scholar
  2. 2.
    M. Aharon, M. Elad, A. Bruckstein, K-SVD an algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans. Signal Process. 54(11), 4311–4322 (2006)CrossRefzbMATHGoogle Scholar
  3. 3.
    P. Bofill, M. Zibulevsky, Underdetermined blind source separation using sparse representations. Signal Process. 81(11), 2353–2362 (2001)CrossRefzbMATHGoogle Scholar
  4. 4.
    T.B. Dong, Y. Lei, J. Yang, An algorithm for underdetermined mixing matrix estimation. Neurocomputing 104(15), 26–34 (2013)CrossRefGoogle Scholar
  5. 5.
    B. Eunhyon, L. Kyunkyung, Closed-form 3-D localization for single source in uniform circular array with a center sensor. IEICE Trans. Communication. 92(3), 1053–1056 (2009)Google Scholar
  6. 6.
    G. Giachetta, Advanced classical field theory (World Scientific, Singapore, 2009)CrossRefzbMATHGoogle Scholar
  7. 7.
    Q. Guo, P. Nan, J. Wan, Signal classification method based on data mining for multi-mode radar. J. Syst. Eng. Electron. 27(5), 1010–1017 (2016)CrossRefGoogle Scholar
  8. 8.
    Y.B. Hua, T.K. Sarkar, D.D. Weiner, An L-shaped array for estimating 2-D directions of wave arrival. IEEE Trans. Antennas Propag. 39(2), 143–146 (1991)CrossRefGoogle Scholar
  9. 9.
    A. Jourjine, S. Rickard, Blind separation of disjoint orthogonal signals: demixing N sources from 2 mixtures. Acoust. Speech Signal Process. ICASSP 5, 2985–2988 (2000)Google Scholar
  10. 10.
    S.G. Kim, C.D. Yoo, Underdetermined blind source separation based on subspace representation. IEEE Trans. Signal Processing. 57(7), 2604–2614 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Y. Li, S.I. Amari, A. Cichocki et al., Underdetermined blind source separation based on sparse representation. IEEE Trans. Signal Process. 54(2), 423–437 (2006)CrossRefzbMATHGoogle Scholar
  12. 12.
    Y. Li, A. Cichocki, S.I. Amari, Analysis of sparse representation and blind source separation. Neural Comput. 16(6), 1193–1234 (2004)CrossRefzbMATHGoogle Scholar
  13. 13.
    Y. Li, W. Nie, F. Ye, A complex mixing matrix estimation algorithm based on single source points. Circuits Syst. Signal Process. 34(11), 3709–3723 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    H. Li, Y.H. Shen, J.G. Wang, X.S. Ren, Estimation of the complex-valued mixing matrix by single-source-points detection with less sensors than sources. Trans. Emerg. Tel. Tech. 23(2), 137–147 (2012)CrossRefGoogle Scholar
  15. 15.
    B. Liu, Orthogonal discrete frequency-coding waveform set design with minimized autocorrelation sidelobes. IEEE Trans. Aerosp. Electron. Syst. 45(4), 1650–1657 (2009)Google Scholar
  16. 16.
    M. Puigt, Y. Deville, Time-frequency ratio-based blind separation methods for attenuated and time-delayed sources. Mech. Syst. Signal Process. 19(6), 1348–1379 (2005)CrossRefGoogle Scholar
  17. 17.
    V.G. Reju, S.N. Koh, I.Y. Soon, An algorithm for mixing matrix estimation in instantaneous blind source separation. Signal Process. 89(9), 1762–1773 (2009)CrossRefzbMATHGoogle Scholar
  18. 18.
    J. Sun, Y. Li, J. Wen, S. Yan, Novel mixing matrix estimation approach in underdetermined blind source separation. Neurocomputing 173, 623–632 (2016)CrossRefGoogle Scholar
  19. 19.
    G. Tang, G.G. Luo, W.H. Zhang, Underdetermined blind source separation with variational mode decomposition for compound roller bearing fault signals. Sensors 16(6), 897–913 (2016)CrossRefGoogle Scholar
  20. 20.
    J.J. Thiagarajan, K.N. Ramamurthy, A. Spanias, Mixing matrix estimation using discriminative clustering for blind source separation. Digital Signal Process 23(1), 9–18 (2013)MathSciNetCrossRefGoogle Scholar
  21. 21.
    S. Wang, W. Gan, D.Y. Li, D.R. Li, Data field for hierarchical clustering. Int. J. Data Warehous. Min. 7(4), 43–63 (2011)CrossRefGoogle Scholar
  22. 22.
    S.J. Wu, J.Z. Zhang, S. Zhang, Array geometry based on fixed elements. J Harbin Eng. Univ. 24(2), 221–225 (2003)Google Scholar
  23. 23.
    O. Yilmaz, S. Rickard, Blind separation of speech mixture via time-frequency masking. IEEE Trans. Signal Process. 52(7), 1830–1847 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    H. Zhang, G. Wang, P. Cai et al., A fast blind source separation algorithm based on the temporal structure of signals. Neurocomputing 139(9), 261–271 (2014)CrossRefGoogle Scholar

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

Authors and Affiliations

  1. 1.College of Information and Communication EngineeringHarbin Engineering UniversityHarbinChina

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