Analysis of the Stereophonic LMS/Newton Algorithm and Impact of Signal Nonlinearity on Its Convergence Behavior

The strong cross-correlation that exists between the two input audio channels makes the problem of stereophonic acoustic echo cancellation (AEC) complex and challenging to solve. Recently, two new implementations of the LMS/Newton algorithm that uses a linear decorrelation technique were proposed. This method helps to mitigate the effect of the ill-conditioned problem on the convergence rate of the LMS/Newton adaptive algorithm. The complexity of these algorithms is significantly lower than the recursive least-squares (RLS) algorithm, which is known to provide excellent echo cancellation. Furthermore, unlike the various versions of the RLS algorithm, the LMS/Newton algorithm is more robust to numerical errors. It has also been suggested that applying nonlinearities to signals at the two audio channels will help to alleviate the misalignment problem of stereophonic AEC systems. Simulation studies reveal that application of certain classes of nonlinearities to the two-channel LMS/Newton algorithms helps to further reduce the misalignment but it also leads to an unexpected and significant reduction in the rate of convergence of the mean-square error. The contributions of this paper are twofold. First, we provide an analysis of the two-channel LMS/Newton algorithm that was proposed in our earlier work. Second, we provide a theoretical understanding for the appearance of the slow modes of convergence in the presence of nonlinearities and show that they can be resolved through a preprocessing step.