## 4 Analysis of Simulation Results  
A software package, SignalPro(r), by EDX Wireless, Inc., was used to conduct the simulations. It provides a set of simulation tools for wireless communication systems. To facilitate simulations with site-specific geographic information, SignalPro(r) supports the \begin{table}
\begin{tabular}{c c} \hline \hline
**Category** & **Value** \\ \hline Input length & 502 \\ Output length & 1 \\ Number of hidden layers & 3 \\ Number of hidden neurons & 502, 128, 8 \\ Dropout rate & 0.18 \\ Batch size & 128 \\ Optimizer & Adam \\ Loss function & MSE \\ Activation function for feature extraction (\(\varphi_{i}\)) & ReLU \\ Activation function for path loss regression (\(\phi\)) & Sigmoid \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Hyper-parameters of the deep neural network in the proposed path loss modeling. import of digital maps. In this study, a 3D map of urban Taipei City was imported to the software package. Figure 4 shows the top view of the simulation environment, which covered an area of 900 \(\times\) 900 m\({}^{2}\). The polygons in the figure represent buildings with different heights. The means and standard deviations of building heights were 15.7 m and 8.7 m, respectively. The maximum and minimum building heights were 46 m and 4 m, respectively. Seven base stations with omnidirectional antennae were deployed and are designated by encircled crosses (\(\oplus\)) in Figure 4. The center of the simulation environment was latitude 25.057457\({}^{\circ}\) N and longitude 121.534808\({}^{\circ}\) E. Readers can use Google Maps or OpenStreetMap to see more details about the regional information. In the simulations, the effective isotropic radiated power and the height of the base stations were set to 50 dBm and 30 m, respectively. Receivers with a height of 1.5 m were placed on the roads. Distances between the Tx and Rx pairs ranged from 10 m to 500 m. The ray-tracing model was applied for the path loss calculations at the 3.5 GHz frequency band. As a result, the received power levels at all the Rx locations were recorded. At the cost of high computational complexity, the performance of the ray-tracing model was satisfactory when compared to the field measurements [21,22]. In this work, the simulation results using the ray-tracing model were taken as the ground truth for the path loss predictions. In the simulations, 22,198 records were collected, where each record contained the receiving power and the path profile of the specific Tx-Rx pair. All the records were partitioned into training and test datasets, with an 80/20 split. Using the test dataset, Figure 5 shows the prediction performance of the proposed path loss model and the conventional models, i.e., the ABG model and the CI model. Note that the Walfisch-Ikegami model is excluded here because the operation frequency of 3.5 GHz is out of its frequency range. In the figure, black dots are the ground-truth values, whereas red dots are the predicted values by using the proposed model. The conventional models exhibited good matches with the mean values of path loss, while the variations between the predictions and the ground-truth values are large. Figure 4: Top view of the simulation environment which covers an area of 900 m \(\times\) 900 m. Buildings are represented by colored polygons. The base stations with omnidirectional antennae are designated by the encircled crosses (\(\oplus\)). Defining prediction error as the difference between the predicted value and the ground-truth value, i.e., \(e_{i}=\hat{y}_{i}-y_{i},\ 1\leq i\leq M\), Table 2 shows the statistics of the prediction errors. In terms of mean error, all the models showed good performance with only slight variances. In terms of the standard deviation, however, the proposed model outperformed the ABG and the CI models by reductions of about 4.71 dB and 4.84 dB, respectively. Furthermore, Figure 6 shows the cumulative distribution of the absolute error of path loss prediction, \(|e_{i}|\). The proposed model outperformed the conventional models.