## 6 The Objective Evaluation Experiment
### The Experimental Conditions with Objective Evaluation  
Tables 1-3 show the experimental equipment, the experimental conditions, and the specific experimental conditions for the PAL, respectively.  
\begin{table}
\begin{tabular}{l l} \hline PAL & MITSUBISHI ELECTRIC ENGINEERING in Tokyo, Japan, \\  & MSP-50E \\ \hline Conventional loudspeaker & ELAC in Kiel, Germany, BS302 \\ \hline Power amplifier & YAMAHA in Shizuoka, Japan, XM4180 \\ \hline Microphone & SENNHEISER in Wedemark, Germany, MKH8020 \\ \hline A/D, D/A converter & RME in Haimhausen, Germany, Fireface UFX II \\ \hline Living room & 15,808, Building 15, Osaka Sangyo University in Osaka, Japan \\ \hline Live studio & 17,104, Building 17, Osaka Sangyo University in Osaka, Japan \\ \hline \end{tabular}
\end{table}
Table 1: Experimental equipment.  
\begin{table}
\begin{tabular}{l l} \hline Reverberation time & Living room: \(T_{60}=380\) ms \\  & Live studio: \(T_{60}=765\) ms \\ \hline Sampling frequency & 96 kHz \\ \hline Quantization & 16 bits \\ \hline \end{tabular}
\end{table}
Table 2: Experimental conditions.  
\begin{table}
\begin{tabular}{l l} \hline Carrier frequency & 40 kHz \\ \hline Modulation method & AM-DSB \\ \hline \end{tabular}
\end{table}
Table 3: Experimental conditions for the PAL.  
In this experiment, we measured the impulse responses using the time-stretched pulse (TSP) method [46; 47].  
Parametric and conventional loudspeakers were calibrated by adjusting the power amplifier so that \(L_{A}\) = 80 dB at the position of the listener's ears. The proposed method has a sweet spot, similar to conventional surround sound techniques. The extent of the sweet spot depends on the distance between the parametric loudspeaker and the listener, as well as the radiation characteristics of the parametric loudspeaker. The parametric loudspeaker used in this experiment has a directivity angle of 25\({}^{\circ}\), forming a sweet spot approximately 0.9 m in diameter at a distance of 2 m. Within this sweet spot, the VSS can be constructed using the proposed method even if the listeners move.  
To evaluate the performance in different environments, we conducted experiments in two settings--a living room and a live studio--with different reverberation times, as shown in Table 2. The impulse responses were measured at 0.1 m intervals, from 0 to 2 m in the living room environment and from 0 to 1.5 m in the live studio environment.  
The sound source was a TSP signal (signal length: 219 samples; bandwidth: 0 to 8 kHz). The weighting function \(\xi_{r}\) for DRR correction was calculated using the RIRs measured at 0.1 m, 0.2 m, and 0.3 m. The DRR of the VSS synthesized using the proposed method is considered more accurate when it is closer to the DRR calculated from the RIR measured for the loudspeaker. The DRRs were calculated using Equations (11) and (12).  
We evaluated the following four conditions:  
* **Real** : The real sound source using a loudspeaker;
* **Conventional**: The conventional method [45];
* **Proposed w/o DRR correction**: The proposed method without DRR correction;
* **Proposed**: The proposed method.  
Figure 5 illustrates the weighting functions in the proposed method, and Table 4 presents the parameters for the correction function. We calculated the alpha and beta parameters using linear approximation with the least squares method [48].  
As shown in Figure 5 and Table 4, we confirmed that the weighting function was appropriately designed in both environments.  
\begin{table}
\begin{tabular}{l c c} \hline \hline  & **Living Room** & **Live Studio** \\ \hline \(\alpha\) & 2.70 & 2.75 \\ \hline \(\beta\) & 0.12 & 0.17 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Parameters for correction function.  
Figure 5: Weighting functions in the proposed method. (a) Living room (\(d=2.0\) m, \(T_{60}=380\) ms). (b) Live studio (\(d=1.5\) m, \(T_{60}=765\) ms).