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

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

Une nouvelle solution pour l’identification aveugle de mélanges de sources cyclostationnaires appliquée aux signaux de télécommunication

International audienceIn this communication, we introduce a semi-analytical solution for the blind identification of the mixing matrix in the case of linearly mixed signals from cyclostationnary sources whose cyclic frequencies are unknown and different. The identification combines the eigenvalue decomposition of a set of cyclic autocorrelation matrices of the observation signals constituted by a detector of rank-one matrices with a hierarchical classification method. The proposed approach is applied to telecommunications signals and the theoretical results are supported by numerical simulations in different noise contexts.Dans cette communication, nous introduisons une solution semi-analytique pour l’identification aveugle de la matrice de mélange dans le cas d’un mélange linéaire de sources cyclostationnaires dont les fréquences cycliques sont inconnues et différentes. L’identification combine la décomposition en valeurs propres d’un ensemble de matrices d’autocorrélations cycliques des signaux d’observations constitué grâce à un détecteur de matrices de rang un avec une méthode de classification hiérarchique. L’approche proposée est appliquée aux signaux de télécommunication et les résultats théoriques sont appuyés par des simulations numériques dans différents contextes de bruit