Fast LMS/Newton algorithms based on autoregressive modeling and their application to acoustic echo cancellation

We propose two new implementations of the LMS/Newton algorithm for efficient realization of long adaptive filters. We assume that the input sequence to the adaptive filter can be modeled as an autoregressive (AR) process whose order may be kept much lower than the adaptive filter length. The two algorithms differ in their structural complexity. The first algorithm, which will be an exact implementation of the LMS/Newton algorithm if the AR modeling assumption is accurate, is structurally complicated and fits best into a digital signal processing (DSP)-based implementation. On the other hand, the second algorithm is structurally simple and is tailored more toward very large-scale integrated (VLSI) custom chip design. Analyses of the proposed algorithms are given. It is found that for long filters, both algorithms perform about the same. However for short filters, a noticeable difference between the two may be observed. Simulation results that confirm our theoretical findings are given. Moreover, experiments with speech signals for modeling the acoustics of an office room show the superior convergence of the proposed algorithms when compared with the normalized LMS algorithm.