## 3 PL Prediction and DWN-ANN Design
### Network Structure
Taking the classic three-layer NN structure, including an input layer, a single hidden layer comprising \(N\) neurons, and an output layer as an illustration, the final prediction results of the DWN-ANN-based PL prediction algorithm can be formulated as  
\[\begin{split}& PL_{\text{DWN-ANN}}^{\text{LoS/NLoS}}=\text{F}_{ \text{DWN-ANN}}\Big{(}d_{\text{Train}}^{\text{LoS/NLoS}},h_{\text{Train}}^{ \text{LoS/NLoS}},f_{\text{Train}}^{\text{LoS/NLoS}}\Big{|}\text{$\mathbf{\text{$ {\mathbf{w}}$}}^{\text{Total}}$},\text{$\mathbf{\text{${\mathbf{w}}$}}^{\text{Total}}$}, \sigma(\cdot)\Big{)}\\ &=\sigma_{\text{O}}\Bigg{(}\sum_{n=1}^{N}\Bigg{(}w_{n1}^{\text{ PTM(2)}}w_{n1}^{\text{OTM(2)}}\sigma_{\text{H}}\Bigg{(}w_{1n}^{\text{ PTM(1)}}w_{1n}^{\text{OTM(1)}}\Bigg{)}d_{\text{Train}}^{\text{LoS/NLoS}}+w_{2n}^{\text{ PTM(1)}}w_{2n}^{\text{OTM(1)}}h_{\text{Train}}^{\text{LoS/NLoS}}+\Bigg{)} \Bigg{)}+b_{1}^{\text{PTM(2)}}b_{1}^{\text{OTM(2)}}\Bigg{)}\\ &\text{where $w_{pq}^{\text{PTM(1/2)}}\in\text{$\mathbf{\text{${\mathbf{w}}$}}^{ \text{PTM}}$}$ and $b_{q}^{\text{PTM(1/2)}}\in\text{$\mathbf{\text{${\mathbf{w}}$}}^{\text{PTM}}$}$} \text{represent the connection weights and biases of the hidden/output layer neurons in the PTM, respectively. $w_{pq}^{\text{OTM(1/2)}}\in\text{$\mathbf{\text{${\mathbf{w}}$}}^{\text{OTM}}$}$}\text{ and $b_{q}^{\text{OTM(1/2)}}\in\text{$\mathbf{\text{${\mathbf{w}}$}}^{\text{OTM}}$}$}\text{ represent the connection weights and biases of the hidden/output layer neurons in the OTM, respectively. $\sigma_{\text{H/O}}(\cdot)\in\sigma(\cdot)$ represents the activation functions of the hidden/output layer. $\mathbf{\text{${\mathbf{w}}$}}^{\text{Total}}$ and $\mathbf{\text{${\mathbf{w}}$}}^{\text{Total}}$}\) can be calculated as the product of the corresponding elements in $\mathbf{\text{${\mathbf{w}}$}}^{\text{PTM}}$ and $\mathbf{\text{${\mathbf{w}}$}}^{\text{OTM}}$, as well as the product of the corresponding elements in $\mathbf{\text{${\mathbf{w}}$}}^{\text{PTM}}$ and $\mathbf{\text{${\mathbf{w}}$}}^{\text{OTM}}$, respectively.  
Figure 2: Network structure of proposed DWN-ANN.  
\(N\), which represents the neuron quantity of the hidden layer, significantly impacts the prediction performance and can be calculated as  
\[N=\sqrt{N_{\text{I}}+N_{\text{O}}}+a_{\text{Neuron}} \tag{12}\]  
where \(N_{\text{I}}\) and \(N_{\text{O}}\) are the neuron quantity of the input and output layer, respectively. \(a_{\text{Neuron}}\) is typically a constant with a value within the range of \([1,10]\). The introduction of activation functions enables the NN to exhibit non-linearity. The hidden layer applies the leaky rectified linear unit (LeakyReLU) function [32], which can solve the \"neuron death\" problem in the traditional rectified linear unit (ReLU) function and has a faster convergence rate, as shown in (13). The output layer applies the Purelin function, as illustrated in (14). \[\sigma_{\text{LeakyReLU}}(x)=\max(x,0)+a_{\text{LeakyReLU}}\min(x,0) \tag{13}\]  
\[PI_{\text{PTM}}^{\text{LoS/NLoS}}=\text{F}_{\text{DWN-ANN}}\left(d_{\text{RT- Train}}^{\text{LoS/NLoS}},h_{\text{RT-Train}}^{\text{LoS/NLoS}},f_{\text{RT- Train}}^{\text{LoS/NLoS}}\Big{|}\mathbf{w}^{\text{PTM}},\mathbf{b}^{\text{ PTM}},\sigma(\cdot)\,\right) \tag{9}\]0  
where \(a_{\text{LeakyReLU}}\) is a non-zero slope, typically set to 0.01. The essence of network training is to minimize the loss function value as much as possible by continuously iterating and adjusting the network parameters. Therefore, the design of the loss function directly impacts the training performance. The introduction of L2 regularization in loss functions makes the network more inclined to use smaller and more dispersed weight vectors, ensuring that all input features are considered during training, which can enhance the model's generalization ability and reduce the risk of overfitting.