In a hands-free communication device acoustic echo cancellation (AEC) is required to achieve full-duplex communication. Echo cancellation signficantly improves the overall quality of the communication. Due to the time-varying nature of the echo path and the possible non-linear distortions, the adaptive filter cannot attenuate the echo below a perceptual level. Thus, a post-filter is required after an echo canceller. In this paper, we will introduce how based on the statistical properties of the adaptive filter of the echo canceller, the step-size and the post-filter can be controlled jointly.
In Variable Stepsize and Regularization Parameters for NLMS, it was described that the optimal stepsize is based on an estimate of the residual echo. The optimal stepsize is
where the expectation value of the residual error at frequency ω at time n is
In Post Filtering for Residual Echo Control, it is shown that the post-filter should also be controlled by the residual echo
where D̂(ω,n) is the estimate of the residual echo at frequency ω. Equations (1) and (2) show that μopt(ω,n) and H(ω,n) are both dependent on an estimate of the residual echo.
In a joint adaptation of the optimum step-size and the optimum post-filter, it can be shown that they are complementary: μopt(ω,n) + H(ω,n) = 1. Therefore, for initial convergence or re-adaptation, the step-size should be close to one because the residual echo is large, and the post-filter should be close to zero in order to sufficiently attenuate the residual echo. Thus, when the residual echo is low, it is no longer required for the post-filter to be low and should approach one. To further improve the steady-state convergence of the echo canceller the step-size should approach zero. In order to control both filters, an estimate of the residual echo is required, which can be obtained from eres(ω,n) = β(ω,n) * X(ω,n), where X(ω,n) is the excitation signal and β(ω,n) is the convergence state of the echo canceller. In Estimating The Convergence State of An Echo Canceller, it is described how an estimate of the convergence state can be obtained.