Performance analysis of a diffusion control method for ANC systems and the network design

Active noise control (ANC) systems have been widely used to reduce noise from indoor or outdoor sources, e.g. traffic, office/factory machines and ventilating systems. Since noise control usually needs to be executed within an extended area, the ANC network that involves a large amount of error microphones and loudspeakers is frequently employed. Distribution of the controller network saves computational burden and yields spatial diversity, which enhances the robustness of the system. This paper studies the diffusion (Diff) control for multi-channel ANC systems using filtered-x (Fx) least mean squares (LMS) algorithms. Since communication between nodes within the network makes it difficult to analyze the performance of the entire system, a comprehensive performance analysis of networked FxLMS algorithm is not available currently in literature to our best knowledge. In this paper, the convergence behavior of the Diff-FxLMS algorithm is investigated. The mean and mean squares difference equations are derived, from which the stability of the networked ANC system is analyzed and the steady-state excess mean square errors (EMSEs) for ANC controllers are obtained. Computer simulations are conducted to compare different control methods and verify the theoretical analysis. A specific 10-node network is studied in terms of the network strategy and the noise reduction performance. Moreover, using the proposed theoretical analysis, a systematic and simple design procedure for Diff-FxLMS based ANC systems is proposed. The usefulness of the theoretical analysis and design procedure is demonstrated by means of a design example.