## 3 Proposed Convolutional Neural Network Structure and Learning Process
Subsequently, let the output of the BN process be denoted as \(\mathbf{Y}^{\mathbf{conv}}_{0}\), and the \(N\times N\times 8\) matrix \(\mathbf{Y}^{\mathbf{conv}}_{0}\) is transformed into the \(1\times 8N^{2}\) vector \(\mathbf{x}^{\mathbf{FC}}\), which is the input of the fully connected (FC) part, as seen in Figure 2. Thus, using the input vector \(\mathbf{x}^{\mathbf{FC}}\), the output of the FC part is obtained as  
\[\mathbf{y}^{\mathbf{FC}}=\mathbf{x}^{\mathbf{FC}}\mathbf{W}^{\mathbf{FC}}+\mathbf{b}^{\mathbf{FC}}, \tag{11}\]  
where \(\mathbf{W}^{\mathbf{FC}}\) and \(\mathbf{b}^{\mathbf{FC}}\) are the weight matrix and bias vector of FC part, respectively, and the sizes of \(\mathbf{W}^{\mathbf{FC}}\) and \(\mathbf{b}^{\mathbf{FC}}\) are set to \(8N^{2}\times N\), \(1\times N\), respectively. Consequently, the size of the output vector of the FC part, \(\mathbf{y}^{\mathbf{FC}}\), is \(1\times N\). Finally, the output of the FC part enters into the sigmoid part as in Figure 2, and then the output of the sigmoid part is expressed as  
\[y^{sig}_{i}=\frac{1}{1+e^{-y^{\mathbf{FC}}_{i}}},i=1,2,\cdots,N, \tag{12}\]  
where the output \(y^{sig}_{i}\) is limited between 0 and 1. Thus, it is multiplied by \(P_{max}\) in order to set the transmit power between 0 and \(P_{max}\). Therefore, the proposed transmit power for transmitter \(i\) is expressed, as follows:  
\[\hat{h}_{i,j}=\frac{\log_{10}(h_{i,j})-\mathbb{E}[\log_{10}(h_{i,j})]}{\sqrt{ \mathbb{E}[(\log_{10}(h_{i,j})-\mathbb{E}[\log_{10}(h_{i,j})])^{2}]}}. \tag{6}\]0  
Using our CNN structure, we solve the optimization problem of Equation (5) through the off-the-shelf stochastic gradient algorithm, which is adaptive moment estimation [20]. In addition, the weight and bias values of \(\mathbf{W}^{\mathbf{FC}}\) and \(\mathbf{b}^{\mathbf{FC}}\) are initialized by a normal distribution. The deep learning optimization method learns to minimize the value of the loss function, which is defined using Equation (5), as follows:  
\[\hat{h}_{i,j}=\frac{\log_{10}(h_{i,j})-\mathbb{E}[\log_{10}(h_{i,j})]}{\sqrt{ \mathbb{E}[(\log_{10}(h_{i,j})-\mathbb{E}[\log_{10}(h_{i,j})])^{2}]}}. \tag{6}\]1  
In the loss function, \(\lambda\) is the weight to determine which of maximum SE and perfect IF is more significant in the CNN-based learning scheme, and \(0\leq\lambda\leq 1\). Especially, when \(\lambda\) is close to 1, the transmit power of the device is determined without considering the fairness, whereas, when \(\lambda\) is close to 0, the perfect fairness can be dominantly achieved while the SE maximization is rarely treated. The IF value of the proposed training model should be one in order  
\[\hat{h}_{i,j}=\frac{\log_{10}(h_{i,j})-\mathbb{E}[\log_{10}(h_{i,j})]}{\sqrt{ \mathbb{E}[(\log_{10}(h_{i,j})-\mathbb{E}[\log_{10}(h_{i,j})])^{2}]}}. \tag{6}\]2 Description of batch normalization. to maximize IF. In other words, we need to find \(\lambda^{*}\) to satisfy the maximum IF. After finding all of the possible values of \(\lambda^{*}\), we choose the maximum value of \(\lambda^{*}\) in order to maximize the sum of SE while achieving the perfect fairness. The proposed CNN-based learning scheme is trained according to the above-mentioned procedure. The trained model can derive the transmit power by receiving the channel as an input in real time. Note that, the proposed scheme can provide the appropriate transmit power, even in an untrained channel, i.e., the weight and bias values of \(\mathbf{W^{FC}}\) and \(\mathbf{b^{FC}}\) in the CNN, which are well trained, can be used for various channels.