## 5 Explainability of the Proposed Model  
To obtain insight into the internal mechanism of the proposed deep-learning-based path loss model, particular inputs were selected to explore the behavior of the deep neural network. Specifically, eight relevant features were considered, as follows:  
1. Mean value of building height: the obstruction of buildings results in propagation loss; therefore, this feature is the arithmetic mean of building heights along the profile. Figure 7 shows three selected path profiles with low, medium, and high values of this feature. These profiles were inputted into the network and their corresponding outputs were reordered. The subfigure in the bottom right of Figure 7 shows the relationship between the path losses and the path profiles. The \(x\)-axis in the subfigure is the index of the path profile, and the \(y\)-axis is the output of the proposed deep learning model, which is a normalized path loss. This subfigure can be interpreted as the mean value of building height being relevant to outcomes of the proposed path loss model. Note that although the three classes, namely, low, medium and high, may not be sufficient to derive the exact relationship, e.g., linear, cubic, quadratic, etc., they are sufficient to verify the relevance between the feature and the path loss. 2. Standard deviation of building height: this feature refers to the standard deviation of building heights along the profile. Figure 8 shows three selected path profiles with zero, medium, and high values of this feature. These three profiles were inputted into the network and their corresponding outputs were reordered. The subfigure in the bottom right of Figure 8 suggests a positive linear correlation between this feature and the predicted path loss. 3. Normalized mean value of building distance: analogously to the two aforementioned features which take the statistics in the vertical axis, this feature and the subsequent one take the statistics in the horizontal axis. This feature is the arithmetic mean of the distances from the Tx to the buildings along the profile. The mean value is normalized by the Tx-Rx separation distance. Figure 9 shows three selected path profiles with buildings that are near the Tx, far from the Tx, and in between the Tx-Rx pair. These profiles were inputted into the network and their corresponding outputs were reordered. The subfigure in the bottom right of Figure 9 indicates a non-linear relationship between this feature and the predicted path loss. 4. Normalized standard deviation of building distance: this feature refers to the standard deviation of the distances from the Tx to the buildings along the profile. The standard deviation is normalized by the Tx-Rx separation distance. Figure 10 shows three selected path profiles with concentrated buildings, scattered buildings, and moderate buildings. These profiles were inputted into the network and their corresponding outputs were reordered. The subfigure in the bottom right of Figure 10 indicates a non-linear relationship between this feature and the predicted path loss. 5. Building density: in addition to the above two statistics in the horizontal axis, this feature describes the percentage of buildings along the profile. Figure 11 shows three selected path profiles with low, medium, and high values of this feature. These profiles were inputted into the network and their corresponding outputs were reordered. The subfigure in the bottom right of Figure 11 shows that this feature and the predicted path loss have a positive relationship that can be approximated in a linear form. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Mean Error (dB)** & **Standard Deviation (dB)** \\ \hline ABG model & 0.05 & 13.84 \\ CI model & 0.15 & 13.97 \\ Proposed model & 0.04 & 9.13 \\ Improvement over the ABG model & - & 4.71 (34\%) \\ Improvement over the CI model & - & 4.84 (34\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Path loss prediction error in simulations.