Blind adaptive separation of wide-band sources

Conventional antenna array processing techniques are based on the use of second order statistics but rest on restrictive assumptions. Thus, when a priori information about the propagation or the geometry of the array is hardly available, the model is close to a blind source separation model. It supposes the statistical independence of the sources and their non-Gaussianity. We focus in this paper on the generalization of the source separation problem to convolutive mixtures of wide-band sources with no assumption on their probability densities. We propose a blind cost function, using a specific decomposition and parametrization of the complex gains of the convolutive filters. An adaptive gradient algorithm can be associated to the function and we prove that no local minima exist. Consequently, it assumes that the proposed algorithm converges towards the good solutions