## 2 Path Loss Simulation for Optimal Relay Position  
Figure 1 presents the configuration of the S-band telemetry system for rocket launching, where the main station and the relay station are used simultaneously to receive status information from the rocket. Immediately after launching the rocket, detailed status information of the rocket is broadcasted, and the main station should consistently receive the information to monitor the rocket status without interruption. However, since the rocket, when at lower altitudes, is significantly influenced by the terrain and nearby buildings, the communication link between the rocket at lower altitude and the main station can be seriously affected. In order to maintain a stable communication link, it is necessary to place an additional relay station at a location where the path loss is lower than at the main station. The altitude of the rocket is denoted by \(h\), and the distance from the rocket to the relay station and the main station is indicated by \(d_{R}\) and \(d_{M}\), respectively. As \(h\) increases, the radio wave shading region is widened due to the weak radiation pattern of the transmitting antenna in the tail direction of the rocket. On the other hand, as \(d_{R}\) decreases, the path loss between the rocket and relay station becomes lower. The receiver closer to the rocket can have less path loss, but it may quickly enter the radio shaded area as the rocket altitude rises. Thus, the optimal additional receiver position should be determined considering the radio wave shaded area and distance between the rocket and the relay station. Considering these issues, we investigated the optimal location of the relay station at the Naro Space Center in Korea. Figure 2 shows detailed location information for the Naro Space Center on the eastern side of Oenaro-island. The analysis area is limited to a \(1.2\times 2.4\) km range, including the Naro Space Center. Since this area is surrounded by various outdoor features such as the sea, terrain, and buildings, they are included as accurately as possible in our simulation, as shown in Figure 3.  
Figure 3 shows the model for the EM analysis, which approximates the analysis area with triangular meshes, including the main station and the relay station. The four candidate locations of the relay stations that are determined considering the ease of placement are denoted by \(p_{1}\), \(p_{2}\), \(p_{3}\), and \(p_{4}\), and the main station is denoted by \(p_{5}\). In this rocket launch scenario, the position of the main station is given previously. However, in this work, the position of the relay station can be changed. The relay station just plays the role that supports the main station when it is difficult for the main station to receive signals. The relay station can maintain a communication link with the rocket when a received power of more than \(-100\) dBm is obtained by the receiving antenna. Thus, it is very important to select the advantageous position of the relay station for a better overall communication link. Of the candidate locations, the position \(p_{1}\) is closest to the rocket and the position \(p_{4}\) is closest to the main station. The detailed coordinate parameters for the candidate positions and the main station are listed in Table 1. To calculate the path losses from the rocket to the candidate relay station, a ray tracing-based EM simulation software (Wireless InSite [20]) is utilized along with the model shown in Figure 3. The transmitting and receiving antenna patterns are also included in the simulation. The transmitting antenna is assumed to be a half-wavelength dipole antenna with vertical polarization, and it is also assumed that there is no pattern distortion caused by the rocket. Therefore, maximum gain is 2.15 dBi, and radiation pattern is omni-directional pattern in the azimuth direction with a half-power beam width of \(90^{\circ}\) in the elevation direction.