A learning algorithm with adaptive exponential stepsize for blind source separation of convolutive mixtures with reverberations

First, convergence properties in blind source separation (BSS) of convolutive mixtures are analyzed. A fully recurrent network is taken into account. Convergence is highly dependent on relation among signal source power, transmission gain and delay in a mixing process. Especially, reverberation degrade separation performance. Second, a learning algorithm is proposed for this situation. In an unmixing block, feedback paths have an FIR filter. The filter coefficients are updated through the gradient algorithm starting from zero initial guess. The correction is exponentially scaled along the tap number. In other words, stepsize is exponentially weighted. Since the filter coefficients with a long delay are easily affected by the reverberations, their correction is suppressed. Exponential weighting is automatically adjusted by approximating an envelop of the filter coefficients in a learning process. Through simulation, good separation of performance, which is the same as in no reverberations condition, can be achieved by the proposed method.