## 10 Comparative Analysis of Propagation Models
### Comparison of Propagation Models on 3.6 GHz--ITU-R P.1546-6, PEM, ITU-R P.452-17  
For the 3.6 GHz frequency band, three models were examined: the Parabolic Equation Modeling (PEM) method used as a reference, the empirical ITU-R P.1546-6 model, and the hybrid ITU-R P.452-17 model. The comparative error metrics are presented in Table 11.  
In the case of TestBS_1, located in an urban and slightly hilly environment, the results reveal significant error percentages for both the ITU-R P.1546-6 and ITU-R P.452-17 models when compared to the PEM reference. The ITU-R P.1546-6 model tends to overestimate the deterministic results when the sample size is small, but underestimates them when the sample size is larger. In contrast, the ITU-R P.452-17 model consistently overestimates the deterministic field strength values. Due to these substantial discrepancies, it can be concluded that neither the empirical nor the hybrid model provides reliable or accurate results in this environment, limiting their applicability in comparison to the PEM. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline  & & & \multicolumn{3}{c}{**3.6 GHz**} & & \\ \hline \multirow{2}{*}{**Base Station**} & \multirow{2}{*}{**Model**} & \multirow{2}{*}{**Type**} & \multirow{2}{*}{\(n\)} & **RMSE** & **MAE** & **Bias** & **RelErr** \\  & & & & **(dB\({}_{\text{W}}\)/m)** & **(dB\({}_{\text{W}}\)/m)** & **(dB\({}_{\text{W}}\)/m)** & **(\%)** \\ \hline \multirow{2}{*}{TestBS\_1} & \multirow{2}{*}{ITU-R P.1546-6} & Test points & 30 & 32.45 & 25.30 & 12.03 & 159.26 \\  & & Line-based & 12,766 & 31.60 & 24.25 & \(-\)13.48 & 170.99 \\ \cline{2-7} \multirow{2}{*}{TestBS\_1} & \multirow{2}{*}{ITU-R P.452-17} & Test points & 30 & 27.80 & 20.22 & 13.02 & 148.24 \\  & & Line-based & 12,766 & 31.86 & 20.24 & 9.37 & 265.98 \\ \hline \multirow{2}{*}{TestBS\_2} & \multirow{2}{*}{ITU-R P.1546-6} & Test points & 30 & 28.51 & 27.71 & \(-\)27.71 & 41.28 \\  & & Line-based & 11,047 & 36.69 & 33.39 & \(-\)33.02 & 43.86 \\ \hline \multirow{2}{*}{TestBS\_2} & \multirow{2}{*}{ITU-R P.452-17} & Test points & 30 & 6.49 & 5.57 & \(-\)4.53 & 8.27 \\  & & Line-based & 11,047 & 9.83 & 6.51 & \(-\)4.26 & 8.11 \\ \hline \multirow{2}{*}{TestBS\_3} & \multirow{2}{*}{ITU-R P.1546-6} & Test points & 30 & 51.30 & 38.35 & 38.35 & 488.13 \\  & & Line-based & 11,065 & 39.12 & 29.86 & 8.24 & 629.04 \\ \hline \multirow{2}{*}{TestBS\_3} & \multirow{2}{*}{ITU-R P.452-17} & Test points & 30 & 20.50 & 11.15 & 4.59 & 112.82 \\  & & Line-based & 11,065 & 36.62 & 25.41 & 7.07 & 467.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Error metrics of models ITU-R P.1546-6 and ITU-R P.452-17 relative to the PEM model at 3.6 GHz, based on both test point and path-based simulations. Figure 31: An example of the lines along which the line-based calculations were performed. In flat rural conditions (TestBS_2), notable differences emerge between the ITU-R P.1546-6 and ITU-R P.452-17 models: while both tend to underestimate the field strength relative to the deterministic reference, the hybrid model approximates the deterministic results with reasonable accuracy (the relative error is around 8%), thus offering a reliable and computationally efficient alternative. In the mountainous terrain analyzed for TestBS_3, the ITU-R P.1546-6 model exhibits extreme errors, significantly overestimating the field strength levels. The same tendency is observed for the hybrid model, although with a lower relative error, indicating comparatively better accuracy. Overall, the hybrid model outperforms the empirical model across all three terrain types at 3.6 GHz. Between the two, it may offer a viable, though compromised, alternative to the deterministic parabolic equation modeling. The empirical model tends to underestimate, while the hybrid model generally overestimates the deterministic values. Consequently, the ITU-R P.452-17 model is more suitable for interference analysis, whereas the ITU-R P.1546-6 model may be better suited for conservative (pessimistic) network planning.