# Localization of Radio Sources Using High Altitude Platform Station (HAPS)
## 4 Discussion
### Localization of Multiple Sources  
Localization simulations were performed to investigate the differences in estimation accuracy depending on the number of sources, changes in estimation accuracy when the element spacing was varied, and mobile terminal estimation assuming a cell deployment by base stations. As the number of sources increased, the accuracy worsened. In the MUSIC method, the direction of arrival is estimated using eigenvectors derived from the signal correlation matrix. Since an antenna array with 196 elements was used in this simulation, the number of eigenvectors available for direction estimation was reduced by the number of sources. As the number of sources increases, the number of available eigenvectors decreases, leading to a reduction in estimation accuracy. However, although the evaluation results appear to show a significant difference based on the number of sources, the cumulative distribution results do not reveal a substantial difference. This is likely due to the angle resolution. As shown in Figure 14, as the number of sources increases, the sharpness of the peaks decreases. As a result, when sources are closely spaced, the peaks overlap, and only a single peak may appear where two sources actually exist. Consequently, a small peak elsewhere may be incorrectly selected, leading to large errors, particularly when there are many sources. To address this, we attempted to improve the angle resolution by increasing the element spacing. The evaluation results confirmed an improvement in the estimation accuracy. The cumulative distribution results also showed a reduction in poor accuracy cases. Increasing the element spacing increases the aperture length of the antenna, improving the angle resolution. As shown in Figure 15, increasing the element spacing improves the angle resolution. It was also confirmed that increasing the element spacing enables high estimation accuracy even when the number of sources is large. However, increasing the element spacing causes grating lobes (aliasing of peaks), as observed in Figure 15. Although no significant degradation in accuracy was observed in this simulation, it is possible that differences in source power could have an impact. Furthermore, changing the element spacing is not as easy as tilting the element plate. Therefore, we performed similar simulations by incorporating the directivity of each element into the steering vector. The estimation accuracy was improved similarly to when the element spacing was increased. Although the mean error worsened, this is likely because, in cases where estimation failed, the error was larger than in other scenarios. Additionally, two differences from the spectrum without directivity consideration were observed. First, the peak values corresponding to each source were nearly equal. Since the MUSIC method generates the spectrum using eigenvectors from the noise subspace, peak values are not affected by the source power. This suggests that incorporating directivity enables the pure noise components to be effectively used for direction estimation. Second, the peaks were sharper. In the spectrum without directivity consideration, the peaks were rounded. This is also likely due to the pure utilization of noise components. These results suggest that directivity should be considered. However, incorporating directivity requires real-time calculation of steering vectors that reflect the frequently changing element directivity. Although differences were observed in the spectrum, the evaluation results did not show a significant difference compared to varying element spacing. Therefore, it is necessary to verify the superiority of each method through experiments.