Extended Joint EVD Algorithm for Widely Linear ARMA Source Separation

In this article, a new approximate joint diagonalization problem is formulated for the blind separation of possibly dependent sources, modelled as widely linear autoregressive moving average (WL-ARMA) signals. The latter modelling gives rise to two sets of matrix parameters, sharing each a specific diagonal structure transform. A new method is proposed to achieve the desired source separation using a novel extended joint eigen value decomposition (JEVD) of both sets of matrices. The separation method proceeds in two steps, the first one identifies the WL-ARMA parameters, while the second step identifies the separation matrix through the extended JEVD of two particular matrix sets. We have developed a new Jacobi-like JEVD algorithm based on Shear and Givens rotations. This algorithm, referred to as Extended Optimal Phase Joint Eigen Value Decomposition, realizes the simultaneous diagonalization of two sets of matrices with different structures and outperforms the existing algorithms in difficult scenarios. Simulation results are provided to illustrate the effectiveness of the proposed algorithm.