# Some Practical Acoustic Design and Typical Control Strategies for Multichannel Active Noise Control
## 2 Practical Acoustic Design  
### Effect of Reflecting Surface on ANC  
Compared to the free-field control, the noise control in an enclosure is somewhat more difficult due to the reflecting surfaces that may cause complicated acoustic mode distribution [10]. A lot of research has been carried out to understand the effects of reflecting surfaces physically [11; 12]. In a recent study [13], it was found that introducing a reflecting surface could increase sound pressure generated by the secondary sources such that the noise reduction performance is improved. It also found that the beneficial frequency range extends with the number of channels of the control system. In addition, the upper limit frequency range is determined by the distance between the secondary sources and the location of the secondary sources around the primary source. It indicated that the multichannel system may have a better performance than the single channel one in terms of both the controllable area and the frequency range.  
Table 1 shows the simulation results in [PERSON]'s 2017 paper [13]. The cross frequency and the optimal noise reduction (NR) at a frequency of 800 Hz are listed. The NR results in both the free space and a half space with a reflecting surface are compared. The cross frequency is defined as the minimal frequency that the optimal noise reduction of the system with a reflecting surface equals to that in free field. The higher the cross frequency is, the wider the controllable frequency range becomes. It can be seen that the improvement of the optimal noise reduction by introducing a reflecting surface increases with the number of channels of ANC systems.  
In [13], experiments were also conducted in an anechoic chamber as shown in Figure 1. A wooden plate is used as the reflecting surface. ANC systems with different numbers of loudspeakers and error microphones were tested. The primary source was placed in the center of the half-circle frames. In Figure 1a, the wooden plate was mounted and five error microphones in total were placed on the half-circle frames. In Figure 1b, the free field was considered and five more error microphones were used. The loudspeakers that work as the secondary sources of the multichannel ANC system were mounted on a small adjustable frame as shown in Figure 1c,d. The experimental and simulated optimal NR results are compared in Figure 2. The results verify that the noise reduction can be improved by  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Channel Number** & **2-Channel** & **3-Channel** & **4-Channel** \\ \hline Cross frequency (Hz) & 970 & 1180 & 1280 \\ Optimal NR in free space (dB) & 4.7 & 8.5 & 10 \\ Optimal NR with a reflecting surface (dB) & 6.4 & 17.0 & 28 \\ Improvement of the optimal NR (dB) & 1.7 & 8.5 & 18 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulation results for the cross frequency and the optimal noise reduction at 800 Hz using 2-channel, 3-channel, and 4-channel ANC systems in [PERSON]’s 2017 paper [13].  
introducing the reflecting surface and the improvement is more significant if more channels are used.