On-line Convolutive Blind Source Separation of Non-Stationary Signals
Journal of VLSI Signal Processing Systems
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This paper addresses the blind separation of convolutive mixtures of independent sources where at most one is Gaussian. The mixing filters are considered to have a finite impulse response and they are allowed to be non-causal. We present a block-based Gauss-Newton algorithm which is able to obtain the separation solution using only a specific set of output cross-cumulants and the hypothesis of soft mixtures. The order of the cross-cumulants involved is chosen to obtain a particular form of the Jacobian matrix that ensures convergence and reduces computational burden. The soft mixture hypothesis is valid when each observed signal receives a dominant contribution from one of the sources, situation which arises when each sensor is closer to a different source and the sources have similar power. The proposed algorithm can be seen as an extension and improvement of the Gerven-Compernolle's Symmetric Adaptive Decorrelation method with the use of higher order statistics. Moreover, the convergence analysis presented in the paper give a theoretical background to derive an asymptotically stable version of the Nguyen-Jutten algorithm based in fourth order cross-cumulants.