## 5 Comparison of Experimental and Numerical Results and Discussions
### Ground Reflection Experiment  
Measured and simulated ground-reflected waves are compared in Figure 23. In the numerical evaluations, a two-ray model is employed to account for ground reflection [66]. Since the ground where the demonstration experiment was conducted was grassy, the parameters were set assuming a wet ground [66]. The distribution of measured and simulated values is slightly different, but the distribution is the same: throughput increases up to a certain altitude and then decreases again due to larger distance attenuation. The difference between the measured and simulated values can be attributed to the different values of conductivity and dielectric constant due to differences in the ground environment, and the fact that the ground geometry is not ideal in the actual experiment. Furthermore, numerical evaluations were conducted with an antenna gain of 25.4 dBi and different ground materials to confirm the effect [66; 69]. The results are shown in Figure 24. The ground parameters utilized in the numerical evaluation are in Table 6. The trend of the measured values did not exactly follow the specific material, even the conductor, metal. One of the main reasons for this discrepancy could be due to the influence of the ground  
Figure 21: Comparison of direct experiments considering positioning error. Figure 22: Comparison of coverage measurements considering positioning error. geometry, which was not perfectly flat as assumed in the numerical analysis. The next section will investigate this issue via the introduction of scattering waves. Consider ground reflection where the ground is rough and multiple waves arrive due to scattering, the received power in dB can be calculated with the following equation. \[P_{r}=10\text{log}\left(P_{t} \begin{vmatrix}\sqrt{G_{t0}G_{r0}}\times\frac{ \lambda}{4\pi r_{d}}+\sqrt{G_{t1}G_{r1}}\times\frac{\lambda}{4\pi r_{d_{r}}} \times\Gamma_{1}\times e^{-j\frac{2\pi}{\lambda}(r_{d}-r_{d})}\\ +\sum\sqrt{G_{ti}G_{ri}}\times\frac{\lambda}{4\pi r_{d_{ri}}}\times\Gamma_{i} \times e^{-j\frac{2\pi}{\lambda}(r_{d}-d_{ri})}\end{vmatrix} ^{2}\right)-L_{ox} \tag{13}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Type** & **Dielectric Constant** & **Conductivity (S/m)** \\ \hline Poor Soil (Dry) & \(\epsilon_{r}=7\) & \(\sigma=1\times 10^{-3}\) \\ Good Soil (Wet) & \(\epsilon_{r}=30\) & \(\sigma=2\times 10^{-2}\) \\ Sea & \(\epsilon_{r}=81\) & \(\sigma=5\) \\ Conductor (Iron) & \(\epsilon_{r}=\infty\) & \(\sigma=10^{7}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Ground parameters for each material used in the numerical evaluation. Figure 23: Comparative results of ground reflection experiment. Figure 24: Comparative results of ground reflection experiment for various ground materials. \[\Gamma=\Gamma_{0}e^{-\left(\frac{4\pi\omega}{\lambda}\right)^{2}} \tag{14}\]  
where \(\sigma\) is the surface roughness (root mean square (RMS) square value), \(r_{d}\) is the linear distance between drones, \(r_{d}\) is the minimum distance of ground reflected wave, \(d_{ri}\) is the distance of scattering waves, \(\Gamma\) is the value of the reflection coefficient, and \(\Gamma_{0}\) is the specular reflection at that point [70]. An image of the scattered wave arrival model for ground reflection is shown in Figure 25. We assume that the scattering waves fall to the ground and arrive randomly with a normal distribution against the center located at 2.5 m in between the two drones. Figure 26 summarizes numerical data taken from 100,000 ground reflection positions of the scattering waves derived numerically using our Monte Carlo simulation. The red line is a normal distribution approximation of 100,000 data. Empirically, this approximated normal distribution has a mean value of 2.5007 m, a maximum value of 4.8346 m, a minimum value of 0.397 m, and a standard deviation of 0.5003 m.  
Figure 25: Image of scattering wave arrival.