Statistical analysis of jointly-optimized GSC implementations of beamformer-assisted acoustic echo cancelers

Beamformer-assisted acoustic echo cancelers have raised a lot of interest lately. The same performance can be obtained with a reduced length acoustic echo canceler (AEC) as the beamformer (BF) performs spatial cancellation. Structures that jointly optimize the BF and the AEC coefficients are preferred in order to exploit synergies. Analytical models have been already derived for the behavior of the direct form implementation of such systems adapted using the constrained least-mean square (CLMS) algorithm. This work extends the analysis to the popular generalized sidelobe canceler (GSC) structure, while allowing for a positive definite step-size matrix. Analytical models are derived for the mean and mean-square behaviors of the adaptive coefficients. Simulation results are shown to be in excellent agreement with the performance predicted by the theory.