## 3 The Proposed Method
### CNN Architecture  
A CNN typically consists of multiple convolutional layers that automatically extract features by using filters (or kernels). The filters are adjustable parameters that can be determined by training based on loss functions. A CNN usually includes pooling and fully connected (FC) layers in addition to the convolution layers. Pooling layers can reduce the size of an activation map. The activation maps are the output of the convolutional layer and are expected to contain the features extracted by the convolutional layer. Based on the features extracted by the upper convolutional layers, the FC layers can be trained to generate final output with the supervision of the label(s). The proposed CNN model takes a LAMS image as its input and produces a predicted Reference Signal Received Power (RSRP) value as the output [12]. The 3D-LAMS algorithm extracts the topographical data between a Tx and a Rx from the 3D map data and generates a 3D image sampled at uniform intervals proportional to the distance. Since the image generated through this algorithm contains only the important topographical data that affect the predicted path loss value, the CNN model can learn the features of the path loss environment more easily. As the image passes through the convolution layers, useful latent features of path loss are expected to be extracted. Pooling layers are not included in the proposed model. In general, the pooling layers can speed up learning by reducing the number of parameters and preventing overfitting, but they can also cause the loss of information included in the feature maps. In this work, we consider that it is advantageous to keep the size of the feature map unchanged, since the 3D-LAMS image contains only simplified information about the shape of buildings. The Rectified Linear Unit (ReLU) function is used as the activation function in the proposed model. The CNN model includes three convolution layers, as illustrated in Figure 2. The FC layer consists of two scalar input values, i.e., the relative angle and the distance between a Tx and a Rx, taken as additional inputs of the flattened layer of two hidden layers of 10 and 5 neurons, respectively, with ReLU activation functions. Relative angle is the difference of the angle between the direction from Tx to Rx and that of the main lobe of each antenna (azimuth or downtilt of Tx). The detailed model parameters are summarized in Table 2. The architecture is chosen to have the CNN model to approximate the highly nonlinear underlying path loss functions as closely as possible. Figure 1: 3D-LAMS Pseudo Image. As shown in Figure 3, additional nodes receiving the relative angle and distance are concatenated and become the input of the FC Network. Based on the assumption that path loss can be regarded as a function of variables representing a large number of environmental factors that affect signal propagation, we can take advantage of the universal approximation capability of neural networks [26]. Path loss modeling in dense urban scenarios, where the heights and construction materials of buildings have a large amount of influence, requires 3D morphological information between a Tx and a Rx. The 3D CNN takes this information as its input data, as generated by the 3D LAMS algorithm, and learns important latent features in order to update its parameters (weights) trying to best approximate the underlying path loss function. Unfortunately, it is extremely difficult to explain how a trained neural network approximate an underlying \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Convolution Layer** & **1 st** & **2 nd** & **3 rd** \\ \hline Input size & 20, 20, 20 & 9, 9, 9 & 5, 5, 5 \\ Input channel & 1 & 80 & 20 \\ Output size & 9, 9, 9 & 5, 5, 5 & 4, 4, 4 \\ Output channel & 80 & 20 & 5 \\ Kernel size & 4, 4, 4 & 2, 2, 2 & 2, 2, 2 \\ Stride size & 2 & 2 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: 3D CNN Path Loss Model Parameters. Figure 2: 3D CNN Path Loss Model Structure.