## 10 Comparative Analysis of Propagation Models
### Computational Time Comparison  
One of the key advantages of empirical and hybrid wave propagation models over deterministic approaches lies in their significantly lower computational complexity. As a result, simulations and evaluations based on these models require considerably less processing time, which greatly facilitates and accelerates various spectrum management and interference analysis tasks. In the case of Parabolic Equation Modeling (PEM), it is necessary to discretize the two-dimensional computational domain, which is strongly dependent on the wavelength under investigation. As frequency increases, the wavelength decreases, requiring a finer computational grid to maintain numerical accuracy. This leads to a higher number of unknowns in the system of equations, resulting in longer computation times. Another limiting factor of PEM is that the simulation must be carried out over the entire two-dimensional domain (distance vs. terrain elevation), in order to properly enforce boundary conditions and close the problem space--even when results are required only at discrete points or along specific paths, such as 10 m above ground level in the direction away from the base station. In environments with minimal terrain elevation variation (e.g., flat landscapes), this requirement has limited impact. However, in hilly or mountainous areas, where elevation ranges can span several thousand meters, the number of unknowns--and consequently, the computation time--increases substantially. Similarly, the maximum propagation distance considered from the base station also has a major influence on the overall runtime. It is important to note that computation time is not determined solely by the theoretical complexity of the models, but also depends significantly on the software and hardware environment in which the simulations are executed. Therefore, absolute values are of limited informativeness, and it is more appropriate to consider the relative computational \begin{table}
\begin{tabular}{l l c c c} \hline \hline  & \multicolumn{4}{c}{**6 GHz**} \\ \hline
**Model** & **Base Station** & \(\sigma_{\text{ terrain}}\) & \(\sigma_{\text{ FST}}\) & **Pearson \(r\)** \\ \hline \multirow{4}{*}{PEM} & TestBS.1—Test points & 71.54 & 44.56 & \multirow{4}{*}{**0.8229**} \\  & TestBS.2—Test points & 7.99 & 11.68 & \\  & TestBS.3—Test points & 139.91 & 42.37 & \\  & TestBS.1—Line-based & 101.10 & 52.63 & \\  & TestBS.2—Line-based & 5.48 & 11.84 & **0.7782** \\  & TestBS.3—Line-based & 213.65 & 47.81 & \\ \hline \multirow{4}{*}{SUI} & TestBS.1—Test points & 71.54 & 7.76 & \multirow{4}{*}{**0.3855**} \\  & TestBS.2—Test points & 7.99 & 9.38 & \\ \cline{1-1}  & TestBS.3—Test points & 139.91 & 10.34 & \\ \cline{1-1}  & TestBS.1—Line-based & 101.10 & 21.07 & \\ \cline{1-1}  & TestBS.2—Line-based & 5.48 & 19.92 & **0.2716** \\ \cline{1-1}  & TestBS.3—Line-based & 213.65 & 20.29 & \\ \hline \multirow{4}{*}{ITU-R P.452-17} & TestBS.1—Test points & 71.54 & 22.12 & \multirow{4}{*}{**0.9134**} \\  & TestBS.2—Test points & 7.99 & 7.73 & \\ \cline{1-1}  & TestBS.3—Test points & 139.91 & 24.39 & \\ \cline{1-1}  & TestBS.1—Line-based & 101.10 & 31.02 & \\ \cline{1-1}  & TestBS.2—Line-based & 5.48 & 10.13 & **0.6829** \\ \cline{1-1}  & TestBS.3—Line-based & 213.65 & 25.68 & \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Standard deviation of terrain height and received field strength for the models at 6 GHz, grouped by propagation model and simulation type. demands of the models.