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

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.Index Terms-Acoustic echo cancellation, adaptive filtering, beamforming, generalized sidelobe canceller, statistical analysis

On the mean-square performance of the constrained LMS algorithm

“…Then, we derive theoretical expressions for the transient as well as steady-state values of the MSD of the CLMS algorithm. Following the same line of analysis, we also derive a theoretical expression for the steady-state On the Mean-Square Performance of the Constrained LMS Algorithm Reza Arablouei, Kutluyıl Doğançay, and Stefan Werner C misadjustment of the CLMS algorithm and show that it is in agreement with the one given in [6] and [7]. Our simulation results exhibit a good agreement between the theoretically predicted and experimentally found values of the MSD.…”

“…Note that although (28) is seemingly different from the expression derived in [6] and [7] for the steady-state misadjustment, i.e.,…”

“…Note that the meansquare stability upper-bound for in (13) is the same as the one given in [4] and [7] although our analytical approach is different from those of [4] and [7].…”

“…These bounds are derived under the assumption that the input vectors are temporally independent and have multivariate Gaussian distribution. In [6] and [7], the mean-square performance of the CLMS algorithm is analyzed and its theoretical steady-state mean output-power and misadjustment are computed. The former studies the behavior of the weight covariance matrix and the latter considers the weight-error covariance matrix.…”

“…The former studies the behavior of the weight covariance matrix and the latter considers the weight-error covariance matrix. However, the analyses in [6] and [7] are carried out for the particular application of adaptive beamforming where the objective is to minimize the filter output energy and there is no observed reference or training signal. Moreover, the analytical methods employed in these works are not suitable for studying the dynamics of the algorithm's mean-square deviation (MSD).…”