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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 JD problem and takes advantage from combining Givens and Shear rotations to attempt the approximate joint diagonalization (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. Also, since several methods exist already in the literature, we propose herein a brief overview of existing NOJD algorithms then we provide an extensive comparative study to illustrate the effectiveness and stability of the CJDi w.r.t. various system parameters and application contexts.Index Terms-Non orthogonal joint diagonalization, Performance comparison of NOJD algorithm, Givens and Shear rotations.

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This letter proposes a novel technique for the blind separation of autoregressive (AR) sources. The latter relies on the joint diagonalization (JD) of appropriate AR matrix coefficients of the observed signals and can be applied to the separation of statistically dependent sources. The developed algorithm is referred to as 'DARSS-JD' (for Dependent AR Source Separation using JD). Through the simulation experiments, DARSS-JD is shown to overcome existing second order separation methods with a relatively moderate computational cost.