Second-Order Blind Source Separation: A New Expression of Instantaneous Separating Matrix for Mixtures of Delayed Sources

In this paper, we study the blind separation of mixtures of propagating waves (delayed sources) encountered for example in underwater telephone (UWT) systems. We suggest a new second-order statistics method using as many observations as sources. First, we show that each of the N delayed sources can be developed as a particular linear combination of the different temporal-derivatives of the N observations. Under some assumptions, an instantaneous rectangular separating matrix is then identified by the joint diagonalization of a set of covariance matrices estimated from the observations and its derivatives. The algorithm used takes into account the particular structure of the spectral mixing matrix encountered. A numerical simulation is provided in a 3-sources/3- observations case for propagating audio signals