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

Abstract : 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.
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Gilles Chabriel-, Jean Barrère. Second-Order Blind Source Separation: A New Expression of Instantaneous Separating Matrix for Mixtures of Delayed Sources. 2006 IEEE 7th Workshop on Signal Processing Advances in Wireless Communications , Jul 2006, Cannes, France. pp.1 - 5, ⟨10.1109/SPAWC.2006.346397⟩. ⟨hal-01427439⟩

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