## 4 Rician K-Factor Characteristics
### Rician K-Factor in Complex Propagation Environment  
Figure 13 shows the Rician K-factor characteristics in the C environment as a function of the UAV altitude. Figure 13a,b show the results for horizontal and vertical installation, respectively. The estimated Rician K-factors using the moment method with the measured data and the dummy fading data are depicted as box-and-whisker plots with 12 data points for each altitude. The red or blue 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. As shown in Figure 13a, the Rician K-factors of the measured and analytical results decrease with UAV altitude from \(H\) = 10 m to 15 m. However, above \(H\) = 20 m, the Rician K-factor of the measured data increases, while the Rician K-factor of the analytical outcome decreases. A possible reason for this is that, as the UAV altitude increases, the incidence angle of the building reflection path increases. In measurement experiments, it is assumed that reflected waves through buildings can be attenuated or lost due to unevenness in the building walls, such as balconies and windows. As a result, the contribution rate of the scattered wave power is believed to have decreased, and the Rician K-factor has increased. As shown in Figure 13b, the Rician K-factors of the measured and analytical results are the same regardless of the UAV altitude. The Rician K-factors of the measured and analytical results of the vertical installation are smaller than those of the horizontal installation, and more that of the variation of the analytical outcome is large. The reason for this will be explained in detail later using Figure 14.  
Finally, looking at the static Rician K-factor using the ray-tracing method, the results in the S environment are underestimated, just like those in the C environment. In particular, the static Rician K-factor using the ray-tracing method for vertical installations decreases significantly with increasing the UAV altitude, falling below 0 dB. In contrast, the values obtained from the simulation and measurements remain relatively constant at approximately 0 dB. This discrepancy is likely due to the limitations of the moment method used to estimate the Rician K-factor. Specifically, the moment method relies solely on the first moment, \(G_{a}\), and the RMS, \(G_{v}\), as defined in Equation (2). Consequently, it does not fully account for the power distribution between the direct wave and the scattered waves. A critical issue arises when the power of the direct path is less than the power of some scattered path, as shown in Figure 8b, so that the Rician K-factor becomes inaccurate. Figure 13: Estimated Rician K-factor in a complex propagation environment: (**a**) horizontal installation and (**b**) vertical installation. Figure 14 shows a schematic diagram of the directivity of the transmitting and receiving antennas in horizontal and vertical installations at the \(zy\)-plane in the C environment. The red directivity is the \(E_{\Earth}\) component in horizontal installation, while the blue directivity is the \(E_{\Earth}\) component in vertical installation. The black and gray lines indicate the direct wave at \(H\) = 30 m and \(H\) = 10 m, respectively. The light blue and green lines are the reflected wave from Building A at \(H\) = 30 m and \(H\) = 10 m, respectively. It can be seen from Figure 14 that when the antenna is set to horizontal installation, the directivity is omnidirectional in the \(zy\)-plane, and the direct wave and the reflected wave from Building A are transmitted and received with the same radiation gain. However, the path power of the reflected wave from Building A is less than the power of the direct wave due to spatial losses along the path and losses due to reflection.