Adaptive filtering with decorrelation for coloured AR environments

The aim of this paper is to improve the convergence speed and steady state error of LMS-type adaptive algorithms for coloured and nonstationary signals such as in acoustic echo cancellation. The performance of these algorithms is limited by the eigenvalue spread of the correlation matrix of the input signal and also by the power of the additive noise. In this paper, the decorrelating adaptive algorithms are classified into four types: input-decorrelating, error-decorrelating, joint-prefiltering and a combination of joint-prefiltering and input-decorrelating. The last two types of algorithms are studied and guidelines are given to choose the proper algorithms based on the power spectral densities of the input signal and noise. For a prefiltering structure, it is proven that if the adaptive filter operates on any prefiltered pair of input and desired signal the optimal solution will remain unchanged. It is suggested that a new adaptive decorrelation prefilter be included that is designed to achieve two objectives simultaneously: to increase the speed of convergence by reducing the correlation between the prefiltered samples of the input; and to improve the tracking and the steady state performance by reducing the noise power in the prefiltered domain. Simulations and theoretical results confirm that the introduced auxiliary whitening processes improve the performance of the adaptive algorithms by jointly whitening the input and the error signal.