## 4 Rician K-Factor Characteristics  
### Rician K-Factor in Simple Propagation Environment  
Figure 11 shows the difference in the main paths with high path power calculated using the ray-tracing method according to the UAV altitude in the S environment. Figure 11a,b show the results at \(H\) = 10 m and \(H\) = 30 m, respectively. The black line is the direct wave, the red line is the ground reflection wave, the blue line is the building reflection wave, the purple line is the building-ground reflection wave, and the light blue line is the building diffraction wave. Comparing Figure 11a,b, the result for \(H\) = 10 m shows that the scattered waves include the reflected waves from the building and the ground, while the results for \(H\) = 30 m show that there are no reflected waves from the building, and the scattered waves have turned into the diffracted waves from the building. Figure 12 shows the characteristics of the Rician K-factor in the S environment as a function of the UAV altitude. Figure 12a,b show the estimated Rician K-factors using the moment method with the measured data and the dummy fading data, depicted as box-and-whisker plots, for \(D\) = 5 m and 10 m, respectively. The orange or green colors are the measured data, the black color is the analytical outcomes, and the gray line is the static Rician K-factor using the ray-tracing method. Figure 10: Estimated Rician K-factor and cumulative distribution function for the horizontal installation at \(H\) = 10 m in a complex propagation environment. Figure 11: Main paths in a simple propagation environment: (**a**) \(H\) = 10 m and (**b**) \(H\) = 30 m.  
Figure 12: Radio propagation characteristics in a simple propagation environment: (**a**) estimated Rician K-factor at \(D\) = 5 m; (**b**) estimated Rician K-factor at \(D\) = 10 m and (**c**) proportion of each type of scattered wave. The static Rician K-factor is calculated by adding up the power of each path obtained by the ray-tracing method, and it can be expressed based on the following equation:  
\[K=\frac{P_{dir}}{\sum\limits_{i=1}^{N}P_{sca,i}}=\frac{P_{dir}}{\sum\limits_{i=1 }^{N}|r_{i}|^{2}} \tag{6}\]  
where \(P_{dir}\) is the direct wave power, and \(P_{sca,i}\) is the power of each scattered wave at the point where the distance between the UAV and the receiving antenna is the shortest along the moving path. Figure 12c shows the contribution rate of maximum path power among the paths of each scattering type as seen in Figure 11 based on the ray-tracing results as a function of the UAV altitude. The red line shows the contribution rate of the ground reflection wave. The blue line shows the contribution rate of the building reflection wave. The purple line shows the contribution rate of the building and ground reflection wave. The light blue line shows the contribution rate of the scattered wave with building diffraction. The solid and dashed lines are the results at \(D\) = 10 m and 5 m, respectively. In the figure, there are no reflected waves from the building at the UAV altitudes shown in yellow (\(H\) > 22.8 m). First, looking at the static Rician K-factor using the ray-tracing method, those are generally smaller than the median of the Rician K-factor estimated from the analytical results. This is because the denominator in Equation (6) represents the maximum power that can be calculated with the scattered waves, and since this power is reduced by considering the phase of each path, the Rician K-factor necessarily increases as the denominator becomes smaller. Therefore, the static Rician K-factor obtained using the ray-tracing method tends to be an underestimate. Comparing Figure 12a,b, the Rician K-factor increases with increasing the distance between the antenna and the building. The path length of the ground-reflected wave is the same regardless of the distance \(D\), but the contribution rate of the ground-reflected wave at \(D\) = 10 m is higher than that at \(D\) = 5 m, as shown in Figure 12c.