Abstract
We propose a new method for blind source separation of cyclostationary sources, whose cyclic frequencies are unknown and may share one or more common cyclic frequencies. The suggested method exploits the second-order cyclostationarity statistics of observation signals to build a set of matrices which has a particular algebraic structure. We also introduce an automatic point selection procedure for the determination of these matrices to be joint diagonalized in order to identify the mixing matrix and recover the source signals as a result. The non-unitary joint diagonalization is ensured by Broyden-Fletcher-Goldfarb-Shanno (BFGS) method which is the most commonly used update strategy for implementing a quasi-newton technique. Numerical simulations are provided to demonstrate the usefulness of the proposed method in the context of digital communications and to compare it with another method based upon an unitary joint diagonalization algorithm.
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References
Abed-Meraim, K., Xiang, Y., Manton, J.H., Hua, Y.: Blind source separation using second-order cyclostationary statistics. IEEE Trans. Sig. Process. 49(4), 694–701 (2001)
Belouchrani, A., Abed-Meraim, K., Cardoso, J.F., Moulines, E.: A blind source separation technique using second-order statistics. IEEE Trans. Sig. Process. 45(2), 434–444 (1997)
Cardoso, J.F., Souloumiac, A., Paris, T., Ura, C., Tdsi, G.: Blind beamforming for non Gaussian signals, vol. 140, pp. 1–17. IEEE, September 1993
Chabriel, G., Kleinsteuber, M., Moreau, E., Shen, H., Tichavsky, P., Yeredor, A.: Joint matrices decompositions and blind source separation: a survey of methods, identification, and applications. IEEE Sig. Process. Mag. 31(3), 34–43 (2014)
Pham, D.T.: Blind separation of cyclostationary sources using joint block approximate diagonalization. In: Davies, M.E., James, C.J., Abdallah, S.A., Plumbley, M.D. (eds.) ICA 2007. LNCS, vol. 4666, pp. 244–251. Springer, Heidelberg (2007). doi:10.1007/978-3-540-74494-8_31
Ferreol, A.: On the behavior of current second and higher order blind source separation methods for cyclostationary sources. IEEE Trans. Sig. Process. 48(6), 1712–1725 (2000)
Gardner, W.A., Napolitano, A., Paura, L.: Cyclostationarity: half a century of research. Sign. Process. 86(4), 639–697 (2006)
Ghaderi, F., Makkiabadi, B., McWhirter, J.G., Sanei, S.: Blind source extraction of cyclostationary sources with common cyclic frequencies. In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP, pp. 4146–4149. IEEE (2010)
Ghennioui, H., Thirion-Moreau, N., Moreau, E., Aboutajdine, D., Adib, A.: A novel approach based on non-unitary joint block-diagonalization for the blind MIMO equalization of cyclo-stationary signals. In: European Signal Processing Conference (2008)
Ghennioui, H., Thirion-Moreau, N., Moreau, E., Aboutajdine, D.: Gradient-based joint block diagonalization algorithms: application to blind separation of FIR convolutive mixtures. Sig. Process. 90(6), 1836–1849 (2010)
Giulieri, L., Ghennioui, H., Thirion-Moreau, N., Moreau, E.: Nonorthogonal joint diagonalization of spatial quadratic time-frequency matrices for source separation. IEEE Sig. Process. Lett. 12(5), 415–418 (2005)
Hjørungnes, A., Gesbert, D.: Hessians of scalar functions of complex-valued matrices: FLA systematic computational approach. In: Proceedings of the 2007 9th International Symposium on Signal Processing and Its Appllications, ISSPA 2007 (2007)
Jallon, P., Chevreuil, A.: Separation of instantaneous mixtures of cyclo-stationary sources. Sig. Process. 87(11), 2718–2732 (2007)
Moreau, E., Macchi, O.: New self-adaptative algorithms for source separation based on contrast functions. In: IEEE Signal Processing Workshop on Higher-Order Statistics, pp. 215–219. IEEE (1993)
Walker, H.F.: Quasi-Newton methods. SIAM J. Optim. 141(10), 135–163 (1978)
Acknowledgment
The work was funded by the Erasmus Mundus Programme of the European Union. We appreciatively acknowledge their financial support.
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Brahmi, A., Ghennioui, H., Corbier, C., Lahbabi, M., Guillet, F. (2017). Blind Separation of Cyclostationary Sources with Common Cyclic Frequencies. In: Tichavský, P., Babaie-Zadeh, M., Michel, O., Thirion-Moreau, N. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2017. Lecture Notes in Computer Science(), vol 10169. Springer, Cham. https://doi.org/10.1007/978-3-319-53547-0_42
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DOI: https://doi.org/10.1007/978-3-319-53547-0_42
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