## 3 Proposed Convolutional Neural Network Structure and Learning Process  
To enhance the SE performance, we apply BN process into the structure of the CNN. The BN scheme is the process of normalizing each node in the CNN structure, which is adjusting the input or output values of the activation function of each layer to the proper range. By using BN, techniques, such as dropout, to prevent overfitting can be replaced, and the learning rate can be set higher. Thus, the BN scheme can improve the learning speed and solve the problem of weight initial value and weight loss [16]. Figure 2 shows our proposed CNN structure with BN process. Figure 1: System model for transmit power control. As seen in Figure 2, the first thing to learn in the proposed scheme is to obtain the normalized channels after changing to dB scale. The normalized channel powers, \(\hat{h}_{i,j}\), are then obtained as  
\[\hat{h}_{i,j}=\frac{\log_{10}(h_{i,j})-\mathbb{E}[\log_{10}(h_{i,j})]}{\sqrt{ \mathbb{E}[(\log_{10}(h_{i,j})-\mathbb{E}[\log_{10}(h_{i,j})])^{2}]}}. \tag{6}\]  
After that, we perform the BN process, as in Figure 2, which normalizes the structure of neural network through the mean and standard deviation of each batch data. Figure 3 shows the convolutional operations without BN and with BN. In the figure, it is described that the output can be normalized by adding two additional processes for BN in a fundamental convolutional operation. Subsequently, using \(\hat{h}_{i,j}\) in Equation (6), we obtain the output of the BN process for transmitter \(i\) and receiver \(j\), \(Y_{i,j}^{BN}\), as follows:  
\[F_{\mu,\sigma}=\frac{\hat{h}_{i,j}-\mu}{\sqrt{\sigma^{2}+\epsilon}}, \tag{7}\]  
and  
\[F_{\gamma_{L_{k}},\eta_{L_{k}}}=\gamma_{L_{k}}F_{\mu,\sigma}+\eta_{L_{k}} \triangleq Y_{i,j}^{BN}, \tag{8}\]  
where \(\mu\), \(\sigma\), and \(\epsilon\) are mini-batch mean, mini-batch standard deviation, and the value that prevents the denominator from becoming zero, respectively. In particular, \(\gamma_{L_{k}}\) and \(\eta_{L_{k}}\), which can be trainable, determine the scale and shift of normalized values, respectively, where \(L_{k}\) is the layer index of \(k=\{1,2,\cdots,8\}\). The output of BN process is used as the input of the rectified linear unit (ReLU) layer in Figure 2, and then the output of the ReLU layer is expressed, as follows:  
\[Y_{i,j}^{ReLU}=\max{(Y_{i,j}^{BN},0)}, \tag{9}\]  
where it is noted that the ReLU layer prevents a negative value and provides nonlinearity to CNN [19] by performing \(\max(\cdot,0)\) operation. The output of the ReLU layer goes into the convolution layer, where the \(3\times 3\) weight matrix of convolution layer, \(\mathbf{W}^{C}\), is used [19]. In this paper, it is assumed that the depth of the convolution layer is eight as in [13]. The output of the convolution layer is then obtained, as follows:  
\[Y_{i,j}^{conv}=\sum_{m=0}^{2}\sum_{n=0}^{2}Y_{m+i-1,n+j-1}^{ReLU}W_{m,n}^{C}, \tag{10}\]  
where \(W_{m,n}^{C}\) is the \((m,n)\)-th element of \(\mathbf{W}^{C}\). The convolution layer is operated with the step size of 1 in the convolution filter and zero padding, by which the size of the output is equal to that of the input. The CNN model is more advantageous than the general neural network when two-dimensional input data are given by the form of the two-dimensional product rather than the one-dimensional product of the convolution layer. It is noted that each of Equations (8)-(10) is performed for all of the normalized  
Figure 2: Proposed CNN model. channel powers, i.e., \(\hat{h}_{i,j}\) for \(i=1,2,\cdots,N\) and \(j=1,2,\cdots,N\). Subsequently, letting the output matrix of the convolutional layer be denoted as \(\mathbf{Y}^{\mathbf{conv}}\), the size of \(\mathbf{Y}^{\mathbf{conv}}\) is \(N\times N\times 8\). Because the convolution part consists of eight layers, as shown in Figure 2, the process in Equations (8)-(10) is performed eight times in series. After carrying out the convolution part with eight layers, its output goes into the BN process again.