Weighted Improved Multiband-Structured Sub-Band Adaptive Filter Algorithms

An improved multiband-structured sub-band adaptive filter (IMSAF) applies the input regressors at each sub-band to increase the convergence speed of multiband-structured sub-band adaptive filter. In the conventional IMSAF algorithm, the effect of all regressors and sub-bands in updating the filter coefficients is the same. In this brief, we present three weighted IMSAF (WIMSAF) algorithms so that the regressors or sub-bands are weighted through the adaptation. In the weighted sub-band IMSAF algorithm, the sub-bands can be weighted at each iteration. In weighted regressor IMSAF, the input regressors at each sub-band are weighted. In weighted sub-band and regressor IMSAF, the sub-bands and the regressors are jointly weighted at each adaptation. Weights in all versions of WIMSAF algorithms are selected in order to decrease the mean-square deviation during the iterations. At each adaptation, the weights are set between zero and one. When the weight in the sub-band/regressor is set to one, it means the maximum effect of that sub-band/regressor in updating the filter coefficients. The coefficients update is not performed in sub-bands/regressors with zero weights. Assigning appropriate weights leads to the fast convergence speed and low misadjustment error. Furthermore, the elimination of zero-weight sub-bands/regressors achieves lower computational complexity than conventional IMSAF algorithm. The mean-square performance analysis of the proposed algorithms is studied and theoretical expressions for learning curve is derived. The simulation results justify the good performance of the proposed algorithms.