## 4 Evaluation Experiments  
### Experimental Conditions  
To demonstrate the effectiveness of the proposed method, we carried out evaluation experiments in which we compared the results of numerical simulations and practical measurements. The experimental environment and conditions are summarized in Table 1, and the equipment used in the experiments is listed in Table 2. The PAL used in the experiments is shown in Figure 6; it consists of 8 columns of 10 ultrasonic transducers. Figure 6: Photograph of the parametric array loudspeaker used in experiments. As shown in Figure 7, we prepared two experimental setups for the evaluation: one without reflection and the other with reflection. In Figure 7a, the PAL is placed at \(\left[0,0,0\right]^{\text{T}}\) in the \(xyz\)-coordinate system, and the propagation axis of the PAL overlaps the \(z\)-axis. In Figure 7b, the PAL is rotated around the \(y\)-axis by \(45\) deg, and a reflector parallel to the \(z\)-axis is set to reflect the sound emitted from the PAL. The propagation axis collides with the reflector at \(\left[0.5,0,0.5\right]^{\text{T}}\). The reflector is made of acrylic plastic, and the reflection attenuation coefficient is measured in advance with the same procedure as [37]. Beyond the area shown in Figure 7, the environment is regarded as an open space, and all of the acoustic rays beyond those areas are absorbed. Therefore, the simulations for evaluation are terminated after all acoustic rays reach the boundary of the area where \(-0.5\leq x\leq 0.5\), \(-0.5\leq y\leq 0.5\), and \(0\leq z\leq 2.0\). \begin{table}
\begin{tabular}{l l} \hline Environment & Soundproof room \\  & (Width: 2.3 m/Depth: 3.2 m/Height: 2.2 m ) \\ \hline Ambient noise level & \(L_{\text{A}}=22.8\) dB \\ \hline Reverberation time & \(T_{60}=150\) ms \\ \hline Frame interval & \(\Delta t=0.15\) ms \\ \hline Carrier frequency & \(f_{\text{c}}=40\) kHz \\ \hline Sideband frequency & \(f_{\text{s}}=33,34,\cdots,\)39 kHz \\ \hline Demodulated frequency & \(f_{\text{d}}=1,2,\cdots,7\) kHz \\ \hline Applied voltage & 15 V \\ \hline \end{tabular}
\end{table} 
Table 1: Experimental environment and conditions. \begin{table}
\begin{tabular}{l l} \hline Ultrasonic sound pressure meter & RION, UN-14 \\ \hline Microphone & Sennheiser, MKH 8020 \\ \hline A/D, D/A converter & RME, Fireface UFX \\ \hline Power amplifier & JVC, PS-A2002 \\ \hline Ultrasonic transducer & SPL Limited, UT1007-Z325R \\ \hline \end{tabular}
\end{table} 
Table 2: Experimental equipment. Figure 7: Setups of evaluation experiments: (**a**) experimental setup without reflection; (**b**) experimental setup with reflection. We set multiple points for the determination of the parameters to approximate the real environment, as described in Section 3. As shown in Figure 7a, we used the measurement results on the propagation axis to calibrate the parameters, including the generation efficiency of virtual source \(\zeta\) and the distance attenuation ratio \(\chi\). A simple recursion based on Equation (31) is utilized to calculated these parameters in a backward manner. A practical PAL generally has a frequency-dependent response [28]; therefore, we set calibration coefficients in the simulation according to the sideband frequency \(f_{\mathrm{s}}\) (\(f_{\mathrm{s}}=f_{\mathrm{c}}-f_{\mathrm{d}}\) for lower sideband modulation). The coefficients were calculated based on the measurement results at the points for parameter determination and are given in Table 3. A practical PAL also has directivity in the ultrasonic range [26; 27]; therefore, we measured the frequency-dependent directivity in advance. The PAL was set on a pan-rotation unit to measure the directivity characteristics, which is same as the experiments in [27]. We also defined multiple evaluation points to evaluate whether the simulation results matched those of the practical measurement in Figure 7a. Here, some points were set for both parameter determination and evaluation, while other points were set for evaluation only.