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

TL;DR

This paper provides a comprehensive statistical analysis of a jointly optimized beamformer-assisted acoustic echo canceler using GSC and LMS, offering models for performance prediction, stability bounds, and design guidelines, validated by simulations.

Contribution

It introduces a new analytical model for the joint optimization of beamformer and AEC, enabling accurate performance prediction and stability analysis.

Findings

Analytical models accurately predict transient and steady-state residual echo power.

Derived stability bounds for step-size matrix ensure convergence.

Simulation results validate the models and design guidelines.

Abstract

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.