## 2 Path Loss Simulation for Optimal Relay Position
Simultaneously, we use the receiving antenna with an ideal isotropic pattern, which helps to observe the effect by the surrounding environment without the influence of the antenna pattern itself. Figure 1: Configuration of the S-band telemetry system with main and relay stations. Figure 4 illustrates the path loss distributions in the analysis area at rocket altitudes of 0 m and 1000 m. To obtain the simulated result, up to 25 rays are calculated between the transmitting antenna and the receiving antenna. In addition, we arranged receivers at 10 m intervals in the analysis area, and the altitude is limited to less than 1000 m, because the communication link is more significantly influenced by the surrounding terrain surface and buildings, especially when the rocket is at a low altitude. When the rocket's altitude is 0 m, the path loss at \(p_{1}\) is the lowest among all the candidate \begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbols** & **Coordinates** & **Distance (Tx. to Rx.)** \\ \hline \(p_{1}\) & (\(x\),\(y\)) = (689 m,237 m) & 50 m \\ \(p_{2}\) & (\(x\),\(y\)) = (521 m,292 m) & 198 m \\ \(p_{3}\) & (\(x\),\(y\)) = (671 m,767 m) & 581 m \\ \(p_{4}\) & (\(x\),\(y\)) = (707 m,1290 m) & 1104 m \\ \(p_{5}\) (main station) & (\(x\),\(y\)) = (711 m,2097 m) & 1952 m \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Coordinates of the main station and candidate positions of the relay stations. Figure 3: Simulation model for analysis area. Figure 2: Location of the Naro Space Center and the analysis area. positions, as shown in Figure 4a. As can be seen, some areas around the basin and buildings have a higher path loss due to the lack of LoS between the rocket and observation points. On the other hand, at a rocket altitude of 1000 m, those areas can have a better LoS, resulting in lower path loss, as shown in Figure 4b. Figure 5 presents the path loss at the main station and the candidate positions along the altitude of the rocket. To obtain this result, we simulated the path loss between the rocket and the relay station by varying the rocket's altitude from 0 m to 1000 m with an increment of 1 m. The black line shows the path loss of the main station, and other color lines indicate the path loss of the candidate positions \(p_{1}\), \(p_{2}\), \(p_{3}\), and \(p_{4}\), respectively. The path loss at the four candidate positions have different rate increase of along the rocket altitude, and thus the path losses of four candidate positions intersect with the path loss of the main station at different rocket height. The altitude of the rocket where the path loss intersects between the candidate site and the main station is very important. Below the crossing altitude the reception is dominantly handled by the relay station, above which the main station is responsible for reception. Therefore, once the rocket altitude that the relay station will receive is determined, the optimal position of the relay station can also be decided. However, since there are fast fluctuations in the path loss, it is difficult to obtain the rate of increase and the interaction altitude. Therefore, the running average was applied to the path loss result to facilitate the acquisition of the rate of increase and intersection altitude. Figure 6 represents the running averaged path losses at the main station and the candidate positions along the rocket altitude using the running average as shown in the following equation [21]:  
\[x_{i}(K)=\frac{1}{K}\sum_{k=l_{0}+1}^{l_{0}+K}x_{i}(k) \tag{1}\]  
where \(x_{i}\) is original data, and \(K\) is the window size in which the sample values are averaged. In this work, \(K\) is selected as 100. As shown in Figure 6, the running averaged data \(x_{i}(K)\) becomes smoother, and the crossing altitude is also more clearly observed.