## 4 New Propagation Model
### Shadowing Loss  
The analysis of additional path loss resulting from the shadowing effect of buildings using the uniform theory of diffraction (UTD) [37; 38; 39] and the method outlined in ITU-R P.526-14 for diffraction-based propagation using UTD [40]. This methodology applies to both vertical and horizontal polarizations to predict diffraction loss induced by a finitely conducting wedge. It is pertinent in diffraction scenarios around building corners, across terrain featuring a wedge-shaped hill, or over roof ridges. The method requires the conductivity and relative dielectric constant of the obstructing wedge and assumes that no transmission occurs through the wedge material. Furthermore, the method accounts for diffraction in both shadow and line-of-sight regions, facilitating a smooth transition between these zones. Figure 3 visualizes the geometry associated with wedge diffraction as delineated by UTD. Figure 2: Geometry of LoS and NLoS scenario. The UTD formulation for the electric field at the field point:  
\[E_{UTD}=E_{0}\frac{e^{-jk(s_{1}+s_{2})}}{s_{1}}D\ \sqrt{\frac{s_{1}}{s_{2}(s_{1}+s_{2})}} \tag{3}\]  
where \(E_{UTD}\) is the electric field at the field point; \(E_{0}\) is relative source amplitude, \(s_{1}\) and \(s_{2}\) are distanced from the source point to the diffracting edge and the diffracting edge to the field point, respectively; \(k\) is the wave number; \(D\) is the diffraction coefficient depending on the polarization (parallel or perpendicular to the plane of incidence) of the incident field on edge; (refer to [39] for formulas of \(D\) for vertical and horizontal polarization); and s is the distance between transmitter and receiver with obstruction. The relative field strength at the field point to the field in the absence of the obstruction is  
\[E_{UTD}(dB)=20\text{log}\left(\left|\frac{sE_{UTD}}{e^{-jks}}\right|\right) \tag{4}\]  
The relative diffraction loss based on UTD model is  
\[L_{UTD}\ =20\text{log}\Bigg{(}\frac{\sqrt{s_{1}s_{2}(s_{1}+s_{2})}}{s|D|}\Bigg{)} \tag{5}\]  
This simulation study explores the diffraction loss experienced in various environmental contexts by examining vertical and horizontal polarization. The calculations are conducted at an elevation angle of 70 degrees, a frequency of 2.1 GHz, and an altitude of 200 m across four distinct environments: suburban, urban, dense urban, and high-rise. The normalized histogram of the diffraction loss is presented in Figure 4a-d. The histogram indicates that the distribution of loss values closely resembles a normal distribution. It was observed that the histogram aligns well with this pattern. To further support this finding, the probability density function (pdf) of the normal distribution is fitted to the simulated data, as shown in Figure 4. This fitting highlights the consistency of the diffraction loss across different environments, thereby enhancing the credibility of the simulation results. The pdf of the normal distribution is given by  
\[p(z)=\frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{(z-y)^{2}}{2\sigma^{2}}} \tag{6}\]  
Figure 3: Geometry of wedge diffraction. where \(p\) is the normalized probability, \(\mu\) is the mean value in dB, and \(\sigma\) is the standard deviation. Table 2 gives the normal distribution's mean and standard deviation. Further, the cumulative distribution function (CDF) of vertical and horizontal polarization across all environments is simulated for elevation angles ranging from 10 to 80 degrees, as illustrated in Figure 5. The dashed curve in the figure denotes the CDF of the normal distribution of the simulated data. The close correspondence between the simulated data and the normally distributed data is evident from the figure. The graph demonstrates that the CDF for elevation angles between 10\({}^{\circ}\) and 40\({}^{\circ}\) is nearly identical for elevation angles between 10\({}^{\circ}\) and 40\({}^{\circ}\).