Acoustic Feedback and Echo Cancellation Strategies for Multiple-Microphone and Single-Loudspeaker Systems

Acoustic feedback/echo cancellation in a multiple-microphone and single-loudspeaker system is often carried out using a cancellation filter for each microphone channel, and the filters are adaptively estimated, independently of each other. In this work, we consider another strategy by estimating all the cancellation filters jointly and in this way exploit information from all microphone channels. We determine the statistical system behavior for the joint estimation strategy in terms of the convergence rate and steady-state behavior across time and frequency. We assess if an improved cancellation performance is achievable compared to the independent estimation strategy. Furthermore, we relate the joint estimation strategy to a stereophonic echo cancellation system and provide analytic expressions for its system behavior.