## 3 Sound Field Simulation and Its Analysis Using Acoustic Parameters
### Simulation Test for the Reverberant Environment
#### 3.1.2 Simulation Results and Analysis
EDT includes the direct sound and early reflections, and RT20 has the smallest energy decay time  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**A**} & \multicolumn{2}{c}{**B**} & \multicolumn{2}{c}{**C**} & \multicolumn{2}{c}{**D**} \\ \hline  & **135\({}^{\circ}\)** & **1 m** & **90\({}^{\circ}\)** & **1.5 m** & **90\({}^{\circ}\)** & **2 m** & **75\({}^{\circ}\)** & **2.5 m** \\ \hline \multirow{2}{*}{PML} & 135 & 1.06 & 90 & 1.56 & 90 & 2.06 & 75 & 2.55 \\  & (\(\Delta\theta=0^{\circ}\)) & (\(r_{\rm e}=6\%\)) & (\(\Delta\theta=0^{\circ}\)) & (\(r_{\rm e}=4\%\)) & (\(\Delta\theta=0^{\circ}\)) & (\(r_{\rm e}=3\%\)) & (\(\Delta\theta=0^{\circ}\)) & (\(r_{\rm e}=2\%\)) \\ \hline \multirow{2}{*}{\(\alpha=0.9\)} & 135 & 1.07 & 90 & 1.48 & 90 & 1.98 & 75 & 2.47 \\  & (\(\Delta\theta=0^{\circ}\)) & (\(r_{\rm e}=7\%\)) & (\(\Delta\theta=0^{\circ}\)) & (\(r_{\rm e}=1.3\%\)) & (\(\Delta\theta=0^{\circ}\)) & (\(r_{\rm e}=1\%\)) & (\(\Delta\theta=0^{\circ}\)) & (\(r_{considered for the reverberation time indices. EDT and RT20 are expressed in the same equation as follows [43]:  
\[\mathrm{L(t)}=10\log\frac{\int_{t}^{\infty}\mathrm{p}^{2}\mathrm{dt}}{\int_{0}^{ \infty}\mathrm{p}^{2}\mathrm{dt}} \tag{20}\]  
Equation (20) normalizes the signal power, and we can calculate the time when power decreases from 0 to \(-10\) dB and from \(-5\) to \(-25\) dB through the time variable in the denominator. The time difference of the former is defined as EDT, and the latter is defined as RT20. When considering the two indices as the early reflection perspective in the RIR, the EDT can physically determine if a large amount of early reflection occurs at the measured location after the direct sound is played. This is because the EDT is the time from the measurement of the direct sound until the signal with an early reflection decrease of \(-10\) dB. RT20 strictly refers to the time when the reverberation energy decreases gradually except for the direct sound and strong early reflection. To analyze the relationship between the absorption coefficient and EDT/RT20, the microphone was placed at the representative intrusion position shown in Figure 7, and the microphone array signals were compared with the signals of the microphones distributed in the space. Figure 10a shows the arrangement of the microphones to confirm the operation of the active localization method proposed here. The first to seventh microphones were the array of microphones used in the proposed system, and the eighth to eleventh microphones were placed in the representative positions A, B, C, and D, respectively. Figure 10b shows the energy decay curve for the impulse response of the ninth microphone. The energy decay curve of the ninth microphone did not decrease linearly but in a staircase form. This was because the space represented in this simulation was not diffuse. In other words, no diffuse-field reverberation occurred owing to the small space of the simulation and the proximity of the loudspeaker and microphone. As a result, the energy decay curve had an approximate exponential shape of a decay curve, but not the diffuse decay curve (Figure 10b). However, the equation was considered to be suitable for analyzing the space from a physical perspective to confirm the operating conditions of the proposed method. This was because the proposed method was analyzed based on a short time, and the changes in the early reflections were presented by the variation of the EDT and RT20 parameters. Figure 11 shows the results of EDT and RT20 for each microphone as the sound absorption coefficient decreased. The main point is whether the numerical values measured at the boundaries of  
Figure 10: Configuration of (**a**) acoustic parameter tests to verify the active localization method according to the change in absorption coefficient \(\alpha\). (**b**) Energy decay curve of the ninth microphone. the control spaces from microphones 1 to 7 and those measured in the control space from microphones 8 to 11 exhibited a specific trend.