# Localization of Radio Sources Using High Altitude Platform Station (HAPS)
## 3 Results
### Multiple Radio Source Localization  
As shown in Figure 12, multiple transmission sources were simulated within a 100 km \(\times\) 100 km area. However, since the area is extensive, building obstructions were not considered, and only terrain effects were included in the simulation. For propagation modeling, only the direct wave and ground reflection were taken into account. The antenna used was the same as the one shown in Figure 5, tilted 45\({}^{\circ}\) downward. The HAPS was positioned at the center of the area, and localization was performed. The evaluation results for different numbers of transmission sources are presented in Table 6 and Figure 13. For each case, 1000 simulation patterns were analyzed. Figure 11: Cumulative distribution of localization error for a single source with edge diffraction. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **5 km** & **20 km** \\ \hline Mean Error [m] & 52.9 & 368.2 \\ CDF 90\% [m] & 95.5 & 251.1 \\ Detection Percentage [\%] & 99.5 & 97.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Localization of a single source considering edge diffraction. The MUSIC spectrum for localization corresponding to each number of transmission sources is presented in Figure 14. These spectra illustrate the estimated DOA peaks, indicating the detected directions of incoming signals for different source configurations. Next, the evaluation results for the case where 10 transmission sources were present are presented. The element spacing was varied from 1 to 4 times the reference spacing, and the impact on localization accuracy was analyzed. The obtained results are summarized in Table 7 and Figure 15. \begin{table}
\begin{tabular}{c c c c c} \hline  & **10 Tx** & **20 Tx** & **30 Tx** & **40 Tx** \\ \hline Mean Error [m] & 1717.9 & 3645.9 & 8142.2 & 11579 \\ CDF 50\% [m] & 337.7 & 493.7 & 767.2 & 1093.8 \\ CDF 90\% [m] & 2017.5 & 3932.7 & 7384.9 & 1328.9 \\ Detection Percentage [\%] & 99.85 & 99.62 & 99.50 & 99.09 \\ \hline \end{tabular}
\end{table} 
Table 6: Localization of multiple sources. Figure 12: Transmission source generation area. Figure 13: Cumulative distribution of localization error for multiple sources. Figure 14: MUSIC spectrum for multiple sources. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \(\mathbf{\times 1}\) & \(\mathbf{\times 2}\) & \(\mathbf{\times 3}\) & \(\mathbf{\times 4}\) \\ \hline Mean Error [m] & 1717.9 & 516.4 & 411.8 & 360.8 \\ CDF 50\% [m] & 337.7 & 277.6 & 256.5 & 248.1 \\ CDF 90\% [m] & 2017.5 & 918.0 & 788.7 & 754.5 \\ Detection Percentage [\%] & 99.85 & 99.94 & 99.97 & 99.98 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Localization of multiple sources with varying element spacing. Figure 15: Cumulative distribution of localization error for multiple sources with varying element spacing. Additionally, simulations were performed in a scenario with 40 transmission sources, where the element spacing was varied. The evaluation results are presented in Table 8 and Figure 17.  
Figure 16: MUSIC spectrum for multiple sources with varying element spacing. Figure 17: Cumulative distribution of localization error with varying element spacing (40 transmission sources). Next, localization simulation was performed by incorporating the directional elements of each antenna element into the steering vector of the MUSIC spectrum. The number of signal sources was set to 10, and the antenna element spacing was set to the standard interval. The evaluation results are shown in Table 9 and Figure 18. For comparison, we also present the results obtained using a standard antenna without considering element directivity, as well as the results when the element spacing was doubled without considering element directivity.