## 6 Results
### Comparison with Propagation Loss Models from the Literature  
The results presented by the proposed RNA-based models for densely forested environments for IoT networks in the 915 MHz frequency range were compared with empirical models CI and FI, as well as with models adapted for vegetated environments, namely Weissberger, Early ITU-R, Cost235, and FITU-R.  
Figure 14 shows the comparison of the proposed RNA-based models and vegetation-adapted models to the measured data for a height of 6 m VV. As seen in Figure 13, the  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**ANNs** & **RMSE** & \(\sigma\) & **Training Time (s)** \\ \hline GRNN & 3.8600 & 3.8558 & 0.3634 \\ MLPNN & 3.8614 & 3.8564 & 2.0839 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Evaluation metrics for the ANNs.  
Figure 13: Measured data and prediction of MLPNN and GRNN.  
MLPNN and GRNN models better represented the average behavior of the measured data, obtaining RMSE and standard deviation values that were similar and lower than the other analyzed models. This is due to RNA-based propagation models being able to estimate the variability in propagation loss more accurately at a single point, as well as representing the signal behavior in the studied environment.  
The other empirical propagation models obtained higher RMSE and standard deviation values than the proposed models. In particular, the FI and CI models, which were adjusted according to the measured data using the linear least squares technique, showed higher RMSE values. However, the FI model performed slightly better than the CI model, as it considers the measured initial point as its own reference, while the CI model considers the value of FSPL as the initial reference point.  
For the propagation loss models in vegetated environments, the one that best represented the measured data was COST235, followed by ITU-R, Weissberger, and finally the FITU-R model. The FITU-R model performs better than the ITU-R and Weissberger models up to the first 50 m. The comparisons of propagation models, through the RMSE and \(\sigma\) metrics, for the other heights and polarizations, are presented in Table 7.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Type**} & **Metrics** & **GRNN** & **MLPNN** & **CI** & **FI** & **WEISSB.** & **ITU-R** & **COST** & **FITU-R** \\ \hline \multirow{2}{*}{SF12-6 m-HH} & RMSE & 3.46 & 3.39 & 7.83 & 7.69 & 22.12 & 16.90 & 9.91 & 25.70 \\  & \(\sigma\) & 4.21 & 4.14 & 7.86 & 7.73 & 6.51 & 6.17 & 17.23 & 9.30 \\ \hline \multirow{2}{*}{SF12-6 m-VV} & RMSE & 4.12 & 4.11 & 8.05 & 7.85 & 22.42 & 17.40 & 9.76 & 25.62 \\  & \(\sigma\) & 4.97 & 4.96 & 8.08 & 7.88 & 6.95 & 6.46 & 18.73 & 9.95 \\ \hline \multirow{2}{*}{SF12-12 m-HH} & RMSE & 4.11 & 4.19 & 8.11 & 7.84 & 26.70 & 21.30 & 7.83 & 30.40 \\  & \(\sigma\) & 5.71 & 5.80 & 8.15 & 7.89 & 7.35 & 6.73 & 17.77 & 10.21 \\ \hline \multirow{2}{*}{SF12-12 m-VV} & RMSE & 3.66 & 3.61 & 7.44 & 7.42 & 19.59 & 14.50 & 11.75 & 23.32 \\  & \(\sigma\) & 4.29 & 4.24 & 7.45 & 7.45 & 6.09 & 6.35 & 16.00 & 8.16 \\ \hline \multirow{2}{*}{SF12-18 m-HH} & RMSE & 4.01 & 4.04 & 9.38 & 8.53 & 23.99 & 18.43 & 10.01 & 28.26 \\  & \(\sigma\) & 5.30 & 5.31 & 9.41 & 8.58 & 8.20 & 7.30 & 19.13 & 11.48 \\ \hline \multirow{2}{*}{SF12-18 m-VV} & RMSE & 3.82 & 3.86 & 7.24 & 7.10 & 21.42 & 16.21 & 10.10 & 25.10 \\  & \(\sigma\) & 5.11 & 5.16 & 7.27 & 7.13 & 6.22 & 6.12 & 16.72 & 8.77 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Results of the propagation models’ comparison.  
Figure 14: Propagation loss models and applied and proposed MLPNN and GRNN models.