Exploiting the Underdetermined System in Multichannel Active Noise Control for Open Windows

Active noise control (ANC) is a re-emerging technique to mitigate noise pollution. To reduce the noise power in large spaces, multiple channels are usually required, which complicates the implementation of ANC systems. In this paper, we separate the multichannel ANC problem into two subproblems, where the subproblem of computing the control filter is usually an underdetermined problem. Therefore, we could leverage the underdetermined system to simplify the ANC system without degrading the noise reduction performance. For a single incidence, we compare the conventional fully-coupled (pseudoinverse) multichannel control with the colocated (diagonal) control method and find that they can achieve equivalent performance, but the colocated control method is less computationally intensive. Furthermore, the underdetermined system presents an opportunity to control noise from multiple incidences with one common fixed filter. Both the full-rank and the overdetermined optimal control filters are realized. The performance of these control methods was analyzed numerically with the Finite Element Method (FEM) and the results validate the feasibility of the full-rank and overdetermined optimal control methods, where the latter could even offer more robust performance in more complex noise scenarios.