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This work presents a statistical analysis of a class of jointly optimizedbeamformer-assisted acoustic echo cancelers (AEC) with the beamformer (BF)implemented in the Generalized Sidelobe Canceler (GSC) form and using theleast-mean square (LMS) algorithm. The analysis considers the possibility ofindependent convergence control for the BF and the AEC. The resulting modelspermit the study of system performance under typical handling of double-talkand channel changes. We show that the joint optimization of the BF-AEC isequivalent to a linearly-constrained minimum variance problem. Hence, thederived analytical model can be used to predict the transient performance ofgeneral adaptive wideband beamformers. We study the transient and steady-statebehaviors of the residual mean echo power for stationary Gaussian inputs. Aconvergence analysis leads to stability bounds for the step-size matrix anddesign guidelines are derived from the analytical models. Monte Carlosimulations illustrate the accuracy of the theoretical models and theapplicability of the proposed design guidelines. Examples include operationunder mild degrees of nonstationarity. Finally, we show how a high convergencerate can be achieved using a quasi-Newton adaptation scheme in which thestep-size matrix is designed to whiten the combined input vector.

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