## 4 New Propagation Model
### Shadowing Loss
\begin{table}
\begin{tabular}{l l l l l} \hline \hline \multirow{2}{*}{**Environment**} & \multicolumn{2}{c}{**Vertical**} & \multicolumn{2}{c}{**Horizontal**} \\ \cline{2-5}  & **Mean(dB)** & \multicolumn{2}{c}{**Standard**} & \multicolumn{1}{c}{**Mean(dB)**} & \multicolumn{1}{c}{**Standard**} \\  & **Deviation (dB)** & \multicolumn{1}{c}{**Mean(dB)**} & \multicolumn{1}{c}{**Deviation (dB)**} \\ \hline Suburban & 16.8603 & 5.0019 & 23.9999 & 5.0019 \\ \hline Urban & 19.5104 & 5.0119 & 26.1119 & 5.0119 \\ \hline Dense Urban & 21.3564 & 5.0124 & 26.6517 & 5.0124 \\ \hline High-Rise urban & 16.5303 & 5.0136 & 21.0535 & 5.0136 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mean and variance of normal distribution at 70 degrees and frequency 2.1 GHz. Figure 4: (**a–d**) Normalized histogram of shadowing loss at 2.1 GHz for elevation angle 70\({}^{\circ}\). vertical polarization, whereas this is not the case for horizontal polarization. Here, altitudes range from 100 to 500 m.  
These revealed a significant increase in shadowing loss at these higher frequencies and altitudes. Figures 6 and 7 show the parameters of a normal distribution mean and standard deviation for three different carrier frequencies and elevation angles ranging from 1 to 89 degrees across all four environmental scenarios, considering a UAV altitude of 200 m. A rational function was developed to effectively model the mean of a normal distribution, while a linear function was used to represent the standard deviation based on the simulation results depicted in Figures 4 and 5. Equation (7) approximates the normal distribution's mean value, and Equation (8) approximates the standard deviation. \[\mu=\frac{p_{1}\theta+p_{2}}{\theta+p_{3}} \tag{7}\]  
\[\sigma=s_{1}\theta+s_{2} \tag{8}\]  
where \(\theta\) is the elevation angle in degrees; \(p_{1}\), \(p_{2}\), and \(p_{3}\) are empirical parameters for the mean; and \(s_{1}\), \(s_{2}\) are for standard deviation. An extensive series of experiments was conducted to analyze communication dynamics at various altitudes, ranging from 100 m to 500 m, reflecting the height of base stations in an Indian city. The frequencies examined during this research are 1.8 GHz, 2.1 GHz, and 5.8 GHz, frequencies used by many operators in India. The objective was to accurately model the mean and standard deviation of a normal distribution associated with these parameters. This study focused on both vertical and horizontal polarizations, and it was carried out under a wide range of environmental conditions, ensuring that the findings would be robust and applicable in real-world scenarios. The results of our extensive experimentation provide valuable insights into the empirical parameters of the means and standard deviations of the normal distribution as per Equations (7) and (8), which are systematically presented in Tables 3-5. Within Tables 3 and 4, we identify empirical parameters labeled \(p_{1}\), \(p_{2}\), and \(p_{3}\). These parameters reflect the mean values obtained from our rigorous experimental processes, showcasing the central tendencies across different conditions. Figure 5: CDF of shadowing loss for horizontal and vertical polarization at 2.1 GHz for dense urban environment. Figure 6: (a–d) mean of normal distribution for horizontal and vertical polarization at 1.8 GHz, 2.1 GHz, and 5.8 GHz for different environments for a range of elevation angles. Figure 7: (a–d) Standard deviation of normal distribution for horizontal and vertical polarization at 1.8 GHz, 2.1 GHz, and 5.8 GHz for different environments for a range of elevation angles.