PSO-SCG-FxRLS: an active control algorithm for improved broadband noise reduction in sparse sound fields

The performance of active noise control (ANC) systems is significantly influenced by the characteristics of the path transfer function. Consequently, the effective utilization of the sparsity inherent in the sound field transfer path response to improve the noise reduction performance of the system has become an important research topic in the current ANC field. This study proposes a sparse-aware conjugate gradient-based filtered-x recursive least squares (SCG-FxRLS) algorithm, for which the convergence is theoretically demonstrated. Additionally, the influence of sparse constraint hyperparameters on the algorithm's performance is thoroughly analyzed. Subsequently, an online particle swarm optimization (PSO) method suitable for ANC systems is introduced, which is combined with the proposed algorithm to form the PSO-SCG-FxRLS algorithm. This integration enhances the algorithm's capability to adapt effectively to the sound field characteristics within complex environments. Computational complexity analysis indicates that this algorithm exhibits lower complexity than the traditional FxRLS algorithm, thereby satisfying the computational efficiency requirements of the ANC system. Finally, simulations and experiments were used to verify the effectiveness of the proposed algorithm in various sound field environments.