A Variable Step-Size Pre-Filter-Bank Adaptive Algorithm

To improve the convergence speed and reduce the mean-square error (MSE) of the gradient based adaptive algorithms in colored environments, such as acoustic echo cancellation, a pre-filter-bank (PFB) adaptive algorithm is proposed by minimizing a weighted criterion of squared errors in subbands. The optimal solution obtained by minimizing this criterion is the Wiener filter, independent of the weights. However, these weights have a strong impact on the behavior of the algorithm and have relations with the subband step-sizes. In particular, the optimal weights, which are derived for a random walk time-varying plant in this paper, depend on the spectra of the input signal and the additive noise. Without a priori knowledge of the spectra, for faster initial convergence and better tracking performance in nonstationary environments, a simple variable step-size (VS) algorithm is introduced to the PFB algorithm in each subband for adjusting the subband step-sizes. This new multistep-size algorithm, which is called the variable step-size pre-filter-bank (VSP) algorithm, improves significantly over the traditional full-band VS algorithms in colored environments. The more colored the noise and the input signal, the more significant the improvement.The drawback of this algorithm is the increase of the computational complexity. As the filters in the filter bank are commonly narrow-band; the nondecimated outputs of these filters are highly correlated. This correlation permits us to approximate the subband autocorrelation matrices by single rank matrices to reduce the computational complexity of the algorithm. The simplified version has almost the same performance as the original VSP algorithm. Simulations show that the proposed algorithms are more efficient than LMS in terms of tracking capabilities for colored environments.