  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.
