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This paper introduces a new algorithm to approximate non-orthogonal joint diagonalization (NOJD) of a set of complex matrices. This algorithm is based on the Frobenius norm formulation of the joint diagonalization (JD) problem and takes advantage from combining Givens and Shear rotations to attempt the approximate JD. It represents a non-trivial generalization of the JDi (Joint Diagonalization) algorithm (Souloumiac 2009) to the complex case. The JDi is first slightly modified then generalized to the CJDi (i.e., Complex JDi) using complex to real matrix transformation. Several methods already exist in the literature. Consequently, we provide herein a brief overview of existing NOJD algorithms. Then we provide an extensive comparative study to illustrate the effectiveness and stability of the CJDi with respect to various system parameters and application contexts. [ABSTRACT FROM AUTHOR]

This paper considers the blind separation of nonstationary sources in the underdetermined case, when there are more sources than sensors. A general framework for this problem is to work on sources that are sparse in some signal representation do- main. Recently, two methods have been proposed with respect to the time-frequency (TF) domain. The first uses quadratic time-frequency distributions (TFDs) and a clustering approach, and the second uses a linear TFD. Both of these methods assume that the sources are disjoint in the TF domain; i.e., there is, at most, one source present at a point in the TF domain. In this paper, we relax this assumption by allowing the sources to be TF-nondisjoint to a certain extent. In particular, the number of sources present at a point is strictly less than the number of sensors. The separation can still be achieved due to subspace projection that allows us to identify the sources present and to estimate their corresponding TFD values. In particular, we propose two subspace-based algorithms for TF-nondisjoint sources: one uses quadratic TFDs and the other a linear TFD. Another contribution of this paper is a new estimation procedure for the mixing matrix. Finally, then numerical performance of the proposed methods are provided highlighting their performance gain compared to existing ones. [ABSTRACT FROM AUTHOR]

This contribution addresses the problem of estimating the parameters of multicomponent polynomial-phase signals when impinging on a multisensor array. An original approach is proposed based on a state-space modelization of the signal and the application of an extended Kalman filter for the state estimation. The use of a multisensor array allows the exploitation of a spatial information and leads to the consideration of multiple filters with different observation equations. Computer simulations are used to demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Introduces a new source separation technique exploiting the time coherence of the source signals. Formulation of problem; A second-order identification approach; Asymptotic performance analysis; Performance evaluation of the second-order blind identification (SOBI) algorithm; Conclusion of the study.