## 5 Simulation Results with Parabolic Equation Modeling  
For the parabolic equation modeling utilized, the simulations were carried out using the MATLAB toolbox called PETOOL v 2.0 [42, 54]. During the simulations, the terrain database available in CHIRplus_BC was utilized by extracting the terrain profile between the base station and each test point as a vector from the software. These profiles were then used as input for the PEM simulations. The ground surface impedance was defined according to moderately dry ground conditions, with parameters set to \(\varepsilon_{r}=15\) and \(\sigma=0.323\,\mathrm{S/m}\). Given that PEM simulations yield a two-dimensional path loss matrix, whereas the investigations presented in the article focus on the generated field strength levels at a specific height above ground--either at a single point or along a line--a two-stage post-processing of the results provided by PETOOL was required. In the first step, we developed a script that extracts the path loss values determined by the PEM at a height of 10 m above ground level. This is achieved either directly from the path loss matrix or, where direct extraction is not feasible, via two-dimensional interpolation between neighboring values. The extracted values are then arranged into a vector as a function of their distance from the base station. Based on the path loss values obtained as a function of distance, it is then possible to determine the field strength levels simulated by the PEM at a height of 10 m above ground level across the entire investigated domain, using a straightforward calculation. It is advisable to begin with the fact that the power density \(S\), expressed in \(\mathrm{W/m^{2}}\), and the electric field strength \(E\), expressed in \(\mathrm{V/m}\), are related through the impedance of free space, \(Z_{0}\approx 377\ \Omega\). By applying the fundamental equation, converting to the logarithmic form, using the \(\mathrm{dB\mu V/m}\) unit, and determining the constants, the following expression is obtained:  
\[E_{\mathrm{V/m}}=\sqrt{SZ_{0}}\Rightarrow E_{\mathrm{dB\mu V/m}}=10\log_{10}( S)+145.76. \tag{31}\] \begin{table}
\begin{tabular}{l c c} \hline
**Feature** & **SSFM** & **CN-FDM** \\ \hline
**Smooth refractive index** & \(\surd\)Fast and efficient & \(\surd\)Works well \\
**Sharp refractive index jumps** & \(\times\) Poor handling & \(\surd\)Good performance \\
**Terrain effects** & \(\times\) Requires special treatment & \(\surd\)Naturally included \\
**Computational efficiency** & \(\surd\)Fast (FFT) & \(\times\)Slower (matrix eq. solvers) \\ \hline \end{tabular}
\end{table} 
Table 4: Comparison of Split-Step Fourier (SSFM) and Crank–Nicolson (CN-FDM) methods. The received signal power can be expressed as \(P_{r}=SA_{e}\), where \(A_{e}=\frac{\lambda^{2}G_{r}}{4\pi}\) is the effective aperture of the receiving antenna. Converting \(P_{r}\) to dBm and expressing all terms in logarithmic form yields:  
\[P_{r}=10\log_{10}(S)+20\log_{10}(\lambda)+G_{r}+19.01. \tag{32}\]  
The received signal power can be expressed in terms of the transmitted power \((P_{t})\), the gain of the transmitting antenna \((G_{t})\), the gain of the receiving antenna \((G_{r})\), and the path loss \((L)\).