## 4 Evaluation Experiment  
We conducted a number of experiments to evaluate the effectiveness of the proposed method. In the following experiments, we recorded the outputs of the 22.2 multichannel audio using the signal generated by VBAP and the proposed SH expansion-based method. From hereafter, we use the notation \"conventional method\" for VBAP and \"proposed method\" for the proposed SH expansion-based method. The experimental environment and equipment are shown in Table 2. The loudspeakers were placed at the positions shown in Table 3.  
Here, the listening point was the center of the surrounded area by the loudspeakers, 1.2 m in height from the floor. In addition, each loudspeaker was 1.9 m away from the listening point.In these experiments, we used band-limited white noise with a duration of 3.0 s as the sound source for the conventional and proposed methods. The frequency band of the band-limited white noise was set to 0-800 Hz. This is because the signal with high frequency components should be represented with the higher-order spherical harmonic expansion, however, it is difficult to obtain the coefficients for SH expansion. Furthermore, in accordance with the highest frequency of the sound source, the maximum order of the SH expansion \(N\) in Equation (18) was set to 5 for all experiments. The positions of each target sound image are shown in Table 4. Here, (a) and (b), (c) and (d), (e) and (f), and (g) and (h) are, respectively, the same direction and different distance of each target sound image. The emitted sound was recorded by the dummy head microphone placed at the position shown in Table 5. \begin{table}
\begin{tabular}{c c} \hline Environment & Experiment room (\(T_{60}=300\) ms) \\ Ambient noise level & 37.0 dB \\ Sound pressure level & 70.0 dB at the listening point \\ \hline Dummy head & 3 Dio, Free Space Pro II \\ Loudspeaker & YAMAHA, VXS5 \\ Loudspeaker (LFE) & YAMAHA, VXS10S \\ Loudspeaker amplifier & YAMAHA, XMV8280 \\ Analog-to-digital converter & RME, Fireface UFX \\ Digital-to-analog converter & RME, M-32 DA \\ \hline \end{tabular}
\end{table} 
Table 2: Experimental environment and equipment. Figure 8: Example of directivity pattern \(D^{\text{tar}}(\theta,\phi)\) obtained by multiple signal classification (MUSIC). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Layer**} & \multirow{2}{*}{**Channel No.**} & \multirow{2}{*}{**Channel Name**} & \multicolumn{2}{c}{**Setting Position**} \\ \cline{4-5}  & & & **Azimuth** & **Elevation** \\  & & & **(\% [deggs.])** & **(\% [deggs.])** \\ \hline \multirow{3}{*}{Middle} & 1 & Front left (FL) & 150 & 90 \\ \cline{2-5}  & 2 & Front right (FR) & 30 & 90 \\ \cline{2-5}  & 3 & Front center (FC) & 90 & 90 \\ \hline \multirow{3}{*}{Lower} & 4 & Low frequency effects-1 & 150 & 118.3 \\ \hline \multirow{3}{*}{Middle} & 5 & Back left (BL) & 210 & 90 \\ \cline{2-5}  & 6 & Back right (BR) & 330 & 90 \\ \cline{2-5}  & 7 & Front left center (FLc) & 120 & 90 \\ \cline{2-5}  & 8 & Front right center (FRc) & 120 & 90 \\ \cline{2-5}  & 9 & Back center (BC) & 270 & 90 \\ \hline \multirow{3}{*}{Lower} & 10 & Low frequency effects-2 & 30 & 118.3 \\ \hline \multirow{3}{*}{Middle} & 11 & Side left (SiL) & 180 & 90 \\ \cline{2-5}  & 12 & Side right (SiR) & 0 & 90 \\ \hline \multirow{3}{*}{Upper} & 13 & Top front left (TpFL) & 150 & 52 \\ \cline{2-5}  & 14 & Top front right (TpFR) & 30 & 52 \\ \cline{2-5}  & 15 & Top front center (TpFC) & 90 & 52 \\ \cline{2-5}  & 16 & Top center (TpC) & - & 0 \\ \cline{2-5}  & 17 & Top back left (TpBL) & 210 & 52 \\ \cline{2-5}  & 18 & Top back right (TpBR) & 330 & 52 \\ \cline{2-5}  & 19 & Top side left (TpSiL) & 180 & 52 \\ \cline{2-5}  & 20 & Top side right (TpSiR) & 0 & 52 \\ \cline{2-5}  & 21 & Top back center (TpBC) & 270 & 52 \\ \hline \multirow{3}{*}{Lower} & 22 & Bottom front center (BtFC) & 90 & 118.3 \\ \cline{2-5}  & 23 & Bottom front left (BtFL) & 150 & 118.3 \\ \cline{2-5}  & 24 & Bottom front right (BtFR) & 30 & 118.3 \\ \hline \hline \end{tabular}
\end{table}