Statistical Analysis of a Jointly Optimized Beamformer-Assisted Acoustic Echo Canceler

This work presents a statistical analysis of a jointly optimized beamformer-assisted acoustic echo canceler (AEC). It is shown that the constrained joint optimization problem can be formulated so that it becomes equivalent to the linearly-constrained minimum variance problem. The new formulation leads to analytical models that can be used to predict the transient performance of adaptive wideband beamformers. A stochastic model is derived for the transient and steady-state behaviors of the residual echo power. A convergence analysis provides a stability bound for the adaptation step-size. Monte Carlo simulations illustrate the accuracy of the model, which is then used to provide design guidelines. Application of the new model confirms previous experimental findings that the same cancellation performance of a single-microphone AEC can be achieved with a shorter AEC when the possibility of spatial filtering is available.