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Mathematical Problems in Engineering
Volume 2017, Article ID 2546838, 9 pages
Research Article

Blind Separation of Cyclostationary Sources Sharing Common Cyclic Frequencies Using Joint Diagonalization Algorithm

1Université de Lyon, UJM-Saint-Etienne, LASPI, IUT de Roanne, 42334 Roanne, France
2Université Sidi Mohamed Ben Abdellah, FSTF, LSSC, BP 2202, Route d’Immouzzer, Fès, Morocco

Correspondence should be addressed to Amine Brahmi; rf.enneite-ts-vinu@imharb.enima

Received 9 October 2016; Accepted 31 January 2017; Published 22 February 2017

Academic Editor: Thomas Schuster

Copyright © 2017 Amine Brahmi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 cyclic correlation function of observation signals to compose a set of matrices which has a particular algebraic structure. The aforesaid matrices are automatically selected by proposing two new criteria. Then, they are jointly diagonalized so as to estimate the mixing matrix and retrieve the source signals as a consequence. The nonunitary joint diagonalization (NU-JD) is ensured by Broyden-Fletcher-Goldfarb-Shanno (BFGS) method which is the most commonly used update strategy for implementing a quasi-Newton technique. The efficiency of the method is illustrated by numerical simulations in digital communications context, which show good performances comparing to other state-of-the-art methods.