## 3 Sound Field Simulation and Its Analysis Using Acoustic Parameters
### Simulation Test for the Reverberant Environment
#### 3.1.2 Simulation Results and Analysis
Figure 11b indicates that the result of the fourth microphone, which was located at the same position as the loudspeaker, was very small compared with the results of other microphones. This was because the loudspeaker and microphone arrangements were very similar such that the characteristics of the room were not sufficiently reflected. Therefore, when analyzing the results of RT20, a criterion for the minimum value to be used for the analysis was necessary. This criterion was selected as the maximum time for the sound from the loudspeaker to reach the person and back to the microphone again. This is because we can determine that the direct sound and strong early reflection are dominant in a microphone signal if the measured time of RT20 is shorter than the propagation time of the sound source generated by the loudspeaker. The farthest distance in the configuration of this study was 2.62 m, which was the distance from microphone 4 to the upper corner (2.92 m) minus the distance of 0.3 m at which a person can stand. The criterion time can be selected as follows:  
\[\mathrm{t_{c}}=\frac{2\mathrm{d_{max}}}{\mathrm{c}}\times 100= \frac{2\times 2.62}{342}\times 100=15.3\,\mathrm{ms} \tag{21}\]  
where \(\mathrm{t_{c}}\) is the criterion time, \(\mathrm{d_{max}}\) is the maximum distance of a sound source in the control domain, and \(\mathrm{c}\) is the speed of sound. Therefore, when analyzing RT20, values less than \(\mathrm{t_{c}}\) were excluded from the analysis. Figure 12 is a graph showing the minimum, maximum, and median values of EDT and RT20 in the microphone array and control space according to \(\alpha\). In this scenario, the microphone signal that did not satisfy \(\mathrm{t_{c}}\) was excluded from the RT20 analysis. The results of the microphones in the array and control space are represented by the red dashed and blue solid lines, respectively. The marker on each graph is the median value, the top line of the deviation is the maximum value, and the bottom line is the minimum value. The EDT results shown in Figure 12a indicate that the median value of the microphones in the control space was higher than that in the array. However, the deviation confirmed that the EDT results in the array were large depending on the absorption coefficient. The RT20 results depicted in Figure 12b indicate that until \(\alpha=0.7\), the median value of the control space was larger than that of the array, but from 0.6, the opposite result was observed. The deviation tended to increase and decrease as \(\alpha\) decreased. Figure 11: (**a**) Early decay time and (**b**) reverberation time according to change in \(\alpha\) based on the finite-difference time-domain (FDTD) simulation. Analyzing the values in Figure 12 according to the conclusion in Section 3.1.2 that the proposed approach operated in an environment with \(\alpha>0.7\), the following features were obtained. From the EDT results in Figure 12a, we observed that the maximum values of the array became smaller than the maximum values of the control space when \(\alpha\) was greater than 0.7. When the results of RT20 in Figure 12b were analyzed as a median value, when alpha is greater than 0.7, the median values of the array were smaller than those of the control space. The results are summarized in Table 2.  
As the results in Tables 1 and 2 show, the active localization method proposed in this paper can detect the position of a person and an object under the following conditions:  
\[\max.\left[\mathrm{EDT}_{\mathrm{m}}^{\mathrm{array}}\right]<\max.\left[ \mathrm{EDT}_{\mathrm{m}}^{\mathrm{spatial}}\right] \tag{22}\]  
\[\mathrm{median}\left[\mathrm{RT20}_{\mathrm{m}}^{\mathrm{array}}\right]< \mathrm{median}\left[\mathrm{RT20}_{\mathrm{m}}^{\mathrm{spatial}}\right] \tag{23}\]  
\[\left( \begin{array}{c}\mathrm{RT20}_{\mathrm{m}}^{\mathrm{array}}>t_{ \mathrm{c}}\\ \mathrm{RT20}_{\mathrm{m}}^{\mathrm{spatial}}>t_{\mathrm{c}}\end{array} \right. \tag{24}\]  
where m is the microphone index and \(t_{\mathrm{c}}\) is the criterion time.