## 3 Dynamic Area Optimization Based on an NN Considering Intercell Relationships  
### Dynamic Area Optimization through the Application of NN  
This study introduces an area optimization approach based on a supervised learning model that is pretrained on the solutions obtained by GA to address the problem mentioned in Section 2. Due to a complicated relationship between user distribution and beam parameters in area optimization, linear regression or rule-based models cannot precisely represent the relationships. Therefore, we choose an NN model that can learn nonlinear relationships and is easy to implement.  
Employing the supervised learning model enables us to utilize previous solutions as the training data. After the training process, the model no longer needs to explore solutions, which is a necessary step in the case of GA. Additionally, the computational process for prediction is simplified to matrix multiplication, greatly lowering the computational cost and enabling prompt adjustment to sudden distribution shifts.  
The NN learns GA optimization results, as illustrated in Figure 4. The inputs and outputs consist of the user distribution information and the optimal horizontal beam directions generated by GA, respectively. To obtain the statistical information on user distribution within the service area, the area is partitioned uniformly into fan-shaped segments, and the user densities in the segments are utilized as the inputs for NN. The \(k\)-th input for the \(m\)-th NN model (\(x_{m,k}^{\text{NN}}\)) and the inputs for the \(m\)-th model (\(x_{m}^{\text{NN}}\)) are expressed as follows:  
\[x_{m,k}^{\text{NN}}=\frac{N_{k}}{N_{all}}, \tag{15}\]  
\[x_{m}^{\text{NN}}=[x_{m,1}^{\text{NN}},x_{m,2}^{\text{NN}},...,x_{m,k}^{ \text{NN}}]. \tag{16}\]  
Here, \(N_{k}\) and \(N_{all}\) represent the number of users in the \(k\)-th sector and across all sectors, respectively. We have adopted fan-shaped segments to avoid overfitting caused by overly detailed inputs, enable the acquisition of necessary horizontal information for learning the horizontal beam directions, and simplify the mapping between inputs and outputs. The model employs the categorical cross-entropy loss function, which is commonly used in multiclass classification. The function can be expressed as follows:  
\[L=\frac{1}{N_{D}}\sum_{n=1}^{N_{D}}\sum_{k=1}^{K}t_{n,k}\log p_{n,k}. \tag{17}\]  
Herein, \(n\), \(N_{D}\), \(k\), and \(K\) represent the data index, the total amount of data, the class index, and the number of classes, respectively. \(t_{n,k}\) and \(p_{n,k}\) indicate the true class for the \(n\)-th data, that is, whether it belongs to class \(k\) or not (indicated by 1 or 0), and the probability of the \(n\)-th data belonging to the \(k\)-th class. The \(k\)-th class is considered the \(k\)-th fan-shaped segment in this study. To estimate the horizontal beam direction, we utilize the angle bisector of this \(k\)-th segment. This configuration is used as the basis for training the model that estimates the horizontal beam direction.  
Nevertheless, as depicted in Figure 5, interferences or uncovered areas among beams (or cells) can arise due to an incorrect cell interval when antenna parameters for the multicell configuration are output either all at once or separately for each cell. Consequently, communication capacity cannot be fully improved. The problem stems from the fact that each cell learns independently, optimizing its own beams without accounting for those of neighboring cells. This implies a need to consider the interactions among neighboring cells during the learning process to effectively improve communication capacity.