Selective collaboration in distributed FxLMS active noise control systems

This paper addresses the selection of the collaboration configuration on distributed active noise control (ANC) systems. ANC systems aim to cancel out acoustic noise within a listening area. In distributed systems, the control task is delegated among multiple acoustic control nodes that generate the control signals by filtering a noise reference signal. The coefficients of each node filter are iteratively calculated using the filtered-X LMS algorithm. The stability is achieved when the adaptive filters computed in each node converge to finite values. However, acoustic coupling among nodes could lead to instability (i.e., divergence). Collaboration among selected nodes may avoid this phenomenon, although not just any collaboration configuration guarantees network stability. On the other hand, a collaborative distributed system presents two drawbacks: the stability assessment is computationally expensive, and communication requirements increase with the number of collaborations among nodes. In this paper, we propose and discuss several methods to establish a collaboration configuration that ensures system stability. The optimal configuration, which is characterized by the minimal number of necessary collaborations between nodes, can be identified through exhaustive search. However, this approach incurs a high computational cost, particularly in networks with many nodes. To address this challenge, we introduce several heuristic methods aimed at efficiently obtaining stable configurations.