Noise control and cancellation over a spatial region is a fundamental problem in acoustic signal processing. In this paper, we utilize wave-domain adaptive algorithms to iteratively calculate the secondary source driving signals and to cancel the primary noise field over the control region. We propose wave-domain active noise control algorithms based on two minimization problems: first, minimizing the wave-domain residual signal coefficients, and second, minimizing the acoustic potential energy over the region, and derive the update equations with respect to two variables, the loudspeaker weights and wave-domain secondary source coefficients. Simulation results demonstrate the effectiveness of the proposed algorithms, more specifically the convergence speed and the noise cancellation performance in terms of the noise reduction level and acoustic potential energy reduction level over the entire spatial region.

Conducting the spatial active noise control (ANC) in wave-domain has been shown advantageous over conventional point-based methods. In the existing schemes, signals at all error microphones are collected and processed in a centralized manner to update the secondary source driving signals. The high computational complexity of this centralized strategy represents one of the major challenges for applying multi-channel ANC systems in large-scale applications. In order to address this issue, this work presents a distributed wave-domain ANC scheme by resorting to distributed optimization techniques. The global ANC problem is formulated as a sum of local costs, and the diffusion adaptation strategies are subsequently utilized to provide a distributed solution that only requires local information exchanges. Simulation results show that the proposed algorithms achieve sufficiently good performance compared to its centralized counterpart.

Personal sound zone (PSZ) refers to the technique that uses an array of loudspeakers and digital signal processing tools to achieve spatial soundfield control. To generate the target sound zones, this technique generally requires to know the acoustic transfer functions (ATFs) between the loudspeakers and the spots where soundfields are to be controlled. In practical applications, however, the true ATFs are never accessible and they have to be measured or estimated. Due to many sophisticated reasons, the measured ATFs generally deviate from the true ones, which may lead to significant degradation in performance of sound zone reproduction. In this work, a robust pressure matching (RPM) algorithm is presented for sound zone generation. It exploits a complex Gaussian mixture model (CGMM) to model the ATFs and their perturbations. The CGMM parameters are estimated using the expectation-maximization (EM) algorithm. To improve the robustness of the pressure matching method, an uncertainty constraint is applied to the ATF estimates and the pressure matching problem is then formulated as one of biconvex optimization. The coordinate descent algorithm is subsequently used to solve the optimization problem, thereby obtaining the optimal control filter. In comparison with the existing pressure matching methods without considering the effect of ATF perturbations, the presented algorithm is able to achieve lower normalized signal distortion energy and higher signal to interference ratio. Numerical simulations justify the effectiveness of the presented algorithm as well as its advantages over the traditional methods.

All spatial active noise control (ANC) systems, when deployed in typical room environments, have time-varying acoustic channels between the secondary sources and the error microphones. The conventional online secondary path modeling techniques, which introduce additive auxiliary random noise to estimate the secondary paths, become challenging especially in a multichannel setup. In this work, we propose to use higher-order variable-directivity sound sources as secondary sources for spatial ANC, in which both the interior residual noise field within the control region and exterior sound field due to secondary source radiation are jointly controlled. The aim of controlling the exterior sound field is to minimize room reverberation generated by the secondary sources so that the secondary paths in the proposed algorithm can be approximated as free-field propagation and thus can be pre-calibrated. The system is implemented in an adaptive manner to track noise variations. The results show that the proposed method can effectively cancel spatial noise field and control exterior sound field at an acceptable low level in time-varying room environments.