Non-unitary joint zero-block diagonalization of matrices using a conjugate gradient algorithm

This communication addresses a new problem which is the Non-Unitary Joint Zero-Block Diagonalization of a given set of complex matrices. This problem can occur in fields of applications such as blind separation of convolutive mixtures of sources and generalizes the non unitary Joint Zero-Diagonalization problem. We present a new method based on the Conjugate Gradient algorithm. Our algorithm uses a numerical diagram of opti mization which requires the calculation of the complex gradient matrix. The main advantages of the proposed method stem from the conjugate gradient properties: it is fast, stable and robust. Computer simulations are provided in order to illustrate the good behavior of the proposed method in dif ferent contexts. Two cases are studied: in the first scenario, a set of exactly zero-block-diagonal matrices are considered, then these matrices are progressively perturbed by an additive Gaussian noise.