# Some Practical Acoustic Design and Typical Control Strategies for Multichannel Active Noise Control
## 3 Three Active Control Strategies
### Distributed Control  
The distributed noise control is a technique that was developed in the recent 5 years [35]. Several different linking networks have been adopted in ANC algorithms. An incrementally collaborative structure [46] was first used in ANC systems. As shown in Figure 10, each node represents an ANC controller for a channel and the distributed structure allows communication between different controllers (see Figure 6c). It was found that the distributed structure is more robust than the decentralized ANC algorithm [35]. The incremental control shown in Figure 10a, however, suffers from several drawbacks for real-time adaptation over networks, such as the sensitivity to the failure of a single node, the limited data communication between nodes, and the fixed simple cyclic path for incremental steps. To overcome these problems, the diffusion strategy [47], as shown in Figure 10b, has been developed. New diffusion MEfx-like ANC algorithms have been proposed recently [36; 48]. In [48], the convergence behavior of the diffusion ExLMS (Diff-ExLMS) algorithm was investigated. The mean and mean squares difference equations for the adaptive process were derived, based on which the convergence curves and conditions, and the steady-state solutions were obtained. In the mean performance analysis, it was found that the combining strategy brings in an estimation bias to the Wiener solution of the controller. The estimation bias is caused by the difference in the primary and secondary paths at different channels (the primary path represents the acoustic response from the noise source to the error microphone while the secondary path represents the response from the anti-sound loudspeaker to the error microphone). Specifically, since the primary and secondary paths are different, the  
Figure 10: Distributed network of node \(k\): (**a**) an incremental structure where nodes update along a cyclic loop, and (**b**) a diffusion structure where nodes communicate within a neighborhood \(N_{k}\). Node \(k\) collects the residue and reference data set \([c_{k}(n),x_{k}(n)]\) at time index \(n\). Figure 9: The kinetic energy of the plate with the excitation of the loudspeaker in the cavity between 1 and 1 kHz without control (dashed line), and when the two control loops (**a**), nine control loops (**b**) are implemented (solid line). Figures are cited from [PERSON]’s 2015 paper [43]. optimal solutions to controllers at each channel are also different. When the diffusion strategy is applied and combines the local estimates at each channel, the spatial averaging brings in an estimation bias. To quantify such an estimation bias, both theoretical analysis and simulations are carried out. It is assumed that the primary paths \(p_{i}\) are randomly distributed on a circle of radius \(r\) centered at \(p_{0}\), i.e., \(p_{i}=p_{0}+r_{S_{i}}\), for \(i=1,2,\,\ldots\), and \(g_{i}\) is a Gaussian sequence of unit norm. Figure 11 examines whether the controllers converge to the Wiener solution or the theoretical steady-state solution derived in [48]. The curves show that the deviation of the estimate to the Wiener solution (denoted as \(\mathrm{v}^{0}\) in the Figure) is larger than that to the theoretical steady-state solution (denoted as \(\mathrm{v}^{\mathrm{inf}}\) in the Figure). Therefore, an increased bias will be observed in diffusion ANC systems. The theoretical analysis of the mean squares performance of the Diff-FxLMS is further verified in Figure 12. Generally, the theoretical and simulated global excess mean square error (EMSE) curves agree well with each other under different settings of step-sizes \(\mu\) and radius \(r\). It also shows that as the value of \(r\) increases, i.e., the optimal solution to each node becomes more different from each other, the steady-state EMSE becomes larger. Finally, three different multichannel strategies are compared in Figure 13. To have a reasonable comparison, the step-sizes are set to be identical.