This work presents a statistical analysis of a class of jointly optimized beamformer-assisted acoustic echo cancelers (AEC) with the beamformer (BF) implemented in the Generalized Sidelobe Canceler (GSC) form and using the least-mean square (LMS) algorithm. The analysis considers the possibility of independent convergence control for the BF and the AEC. The resulting models permit the study of system performance under typical handling of double-talk and channel changes. We show that the joint optimization of the BF-AEC is equivalent to a linearly-constrained minimum variance problem. Hence, the derived analytical model can be used to predict the transient performance of general adaptive wideband beamformers. We study the transient and steady-state behaviors of the residual mean echo power for stationary Gaussian inputs. A convergence analysis leads to stability bounds for the step-size matrix and design guidelines are derived from the analytical models. Monte Carlo simulations illustrate the accuracy of the theoretical models and the applicability of the proposed design guidelines. Examples include operation under mild degrees of nonstationarity. Finally, we show how a high convergence rate can be achieved using a quasi-Newton adaptation scheme in which the step-size matrix is designed to whiten the combined input vector.
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