## 4 Experiment  
Figure 9 shows the experimental setup in the anechoic chamber in Nanjing University, and the system configuration is the same as that adopted in Figure 4. Nine microphones are evenly placed in the error plane, and 11 microphones are arranged in a line to measure the SPL distribution in the evaluation plane \(x=0\), with an interval of 0.3 m, which is approximately 1/6 wavelength of 200 Hz. The type of all the microphones is Anty M1212 [22], and all the microphones were calibrated using a calibrator (Bruel & Kjaer, type 4231). Figure 8: The distribution of SPL and NR when the target direction is \(\theta=\pi/6\) and \(\varphi=\pi/2\). (**a**) SPL without control, (**b**) SPL with control and (**c**) NR with the secondary source located at \(\mathbf{r}_{\text{s1}}\), (**d**) SPL without control, and (**e**) SPL with control and (**f**) NR with the secondary source located at \(\mathbf{r}_{\text{s2}}\). Figure 7: (**a**) The angular spectrum estimation error when the source is at different locations. (**b**) The NR at the receiver when the secondary source is located at different positions in the \(z=-0.6\) m plane, and the target direction is \(\theta=\pi/6\) and \(\varphi=\pi/2\). In the experiment, the sound pressures at the error microphones generated by the primary and secondary sources were measured using a multi-channel analyzer PULSE 3560D, and the transfer functions from the loudspeakers to all the microphones are obtained by recording the sound pressures at the microphones excited by the primary and secondary loudspeakers. The optimal input fed to the secondary loudspeaker is then calculated with Equation (10) and the weighting vector **W** is calculated with Equation (9). Therefore, the secondary sound field at evaluation microphones can be obtained. The total sound pressure level after control is then obtained by superimposing the primary and secondary sound fields, and the noise reduction is the difference between the primary sound pressure level and that after control. Finally, the voltage was fed to the secondary loudspeaker for active directivity noise control, and the noise reduction was obtained by measuring the sound pressure level in the evaluation plane before and after control. Figure 10 shows the distribution of sound pressure levels and the corresponding NR in the evaluation plane when the target direction is chosen as \(\theta=0\). The average SPL at 11 orange points spaced 0.3 m apart in Figure 10c,f is reduced by 15.7 dB and 2.0 dB, respectively, when the secondary loudspeaker is located at \(\mathbf{r}_{\mathrm{s1}}\) and \(\mathbf{r}_{\mathrm{s2}}\). Table 2 shows the NR of the average SPL at the 11 orange points when the target direction is \(\theta=0\). The difference between the noise reduction in the point source model simulation and in the offline simulation is within 2.3 dB. The noise reduction with the  
Figure 10: The distribution of measured SPL and NR when the target direction is \(\theta=0\). **(a)** Primary SPL, **(b)** the SPL with control, **(c)** NR with the secondary loudspeaker at \(\mathbf{r}_{\mathrm{s1}}\), **(d)** primary SPL, **(e)** the SPL with control, and **(f)** NR with the secondary loudspeaker at \(\mathbf{r}_{\mathrm{s2}}\). Figure 9: The experimental setup in the anechoic chamber. Yellow solid circles represent the 9 error microphones. secondary source at \(\mathbf{r}_{\text{s1}}\) is significantly larger than that with the secondary source at \(\mathbf{r}_{\text{s2}}\), because the estimation error of the angular spectrum is smaller when the secondary source is placed at \(\mathbf{r}_{\text{s1}}\). Figure 11 compares the measured noise reduction when the target direction is chosen as \(\theta=\pi/6\) and \(\varphi=\pi/2\). As predicted in Figure 7b, more effective noise reduction in the target direction is achieved by placing the secondary loudspeaker at \(\mathbf{r}_{\text{s2}}\) because of the smaller angular spectrum estimation error of the secondary source.