## 6 Results
### Evaluation of the Proposed Propagation Models Based on Artificial Neural Networks (ANNs)  
The proposed models use three input variables: distance (5 to 250 m), transmitter height (6, 12, and 18 m), and the co-polarization of the transmitting and receiving antennas (HH-VV). To evaluate the accuracy and precision of the proposed models, two metrics were applied: root mean square error (RMSE) and standard deviation (\(\sigma\)). RMSE measures the square root of the squared errors' average between the values predicted by the model and the measured values. Its goal is to predict a continuous numerical value, such as propagation loss in a wireless communication system. The RMSE is calculated using Equation (12) [49]:  
\[RMSE=\sqrt{\frac{1}{n}\sum_{i=1}^{n}(y_{i}-\hat{y_{i}})^{2}} \tag{12}\]  
in which \(\sum\) indicates the sum of all elements for each sample \(i\), \(y_{i}\) represents the actual observed value in sample \(i\), \(\hat{y_{i}}\) represents the value predicted by the model for the \(i-th\) sample, and \(n\) is the total number of samples or observations in the dataset. The \(\sigma\) is a measure of dispersion or variability in the data relative to the mean. In simple terms, it tells us how far the values are from the mean. The standard deviation is calculated using the Formula (13) [50]:  
\[\sigma=\sqrt{\frac{\sum_{i=1}^{n}(x_{i}-\bar{x})^{2}}{n}} \tag{13}\]  
in which \(\sum\) indicates the sum of all elements, \(x_{i}\) is the individual value in the dataset, \(\bar{x}\) is the mean of the values, and \(n\) is the total number of examples. The importance of standard deviation in the evaluation of RNA-based propagation loss models is related to its ability to show us the variability of observed propagation loss values. The smaller the standard deviation, the more consistent and accurate the results predicted by the model. To properly evaluate an RNA-based propagation loss model, it is essential to consider both RMSE and standard deviation. RMSE provides a general idea of the model's predic \begin{table}
\begin{tabular}{c c c} \hline
**SITUATIONS** & **FI (\(d_{0}\) (m)\(\alpha\) (\beta\))** & **CI (PLE)** \\ \hline SF12-6 m-HH & 10.92 [69.02] & 4.98 & 3.93 \\ SF12-6 m-VV & 10.92 [68.29] & 4.91 & 3.85 \\ SF12-12 m-HH & 17.32 [76.56] & 5.87 & 4.15 \\ SF12-12 m-VV & 12.45 [68.34] & 4.79 & 3.73 \\ SF12-18 m-HH & 14.13 [71.43] & 5.66 & 4.08 \\ SF12-18 m-VV & 12.47 [73.30] & 4.71 & 3.86 \\ \hline \end{tabular}
\end{table} 
Table 5: Adjusted coefficient values for FI and CI. tions accuracy, while the standard deviation helps to understand the variability in the data and the prediction's reliability across different scenarios. Furthermore, it is important to emphasize that the choice of evaluation metrics also depends on the context and specific requirements of the problem at hand. For example, in critical applications such as communication systems, it is essential to have propagation loss prediction models with high accuracy and low standard deviation to ensure the proper performance of the system. The obtained results were close in terms of performance, as shown in Figure 13, and the MLP responses, represented by the red x, are close to GRNN responses, represented by the black square. Moreover, the RMSE of 3.86 for the GRNN and 3.8614 for the MLPNN suggests that both networks were able to effectively capture patterns in the data and generalize to new samples. This closeness in results may also indicate that the problem is relatively well-behaved and that both networks are providing consistent and accurate solutions. Table 6 shows the values of the evaluated metrics. It can be observed that both ANNs were very close in terms of accuracy and precision. However, regarding training time, the GRNN was approximately 82% faster than the MLPNN. Both were trained using a notebook equipped with a Core i5 12500H processor. The advantage of the GRNN in requiring lower computational cost is an important characteristic to consider, especially when addressing large volumes of data or when optimizing available resources.