## 3 Dynamic Area Optimization Based on an NN Considering Intercell Relationships
### Communication Performance
This is because the ensemble approach has many solution candidates and can select superior solutions for the constraints from them. It should be noted that the constraint violation ratios are greater for the six-cell condition than for the three-cell condition in both NN and NN+CC scenarios, which is caused by the learning difficulty due to more complex beam relationships in a six-cell configuration. Figure 12 depicts the cumulative distribution functions (CDFs) of the total throughput in the three-cell and six-cell configurations when each method is applied to all the user distributions. The total throughput \(T\) is based on [PERSON]'s theory and defined as follows:  
\[T=\sum_{u=1}^{N_{u}}\frac{B}{N_{\mathrm{C}_{u}}}\log_{2}\Big{(}1+10^{\frac{72 \mathrm{SNR}_{u}}{10}}\Big{)}. \tag{22}\]  
In both three- and six-cell conditions, the total throughput improves gradually by incorporating the CC and ensemble approach when compared with the default state. We evaluate this based on the degradation ratio, which measures how much the total throughput median of each method is degraded compared to that of GA. In the three-cell condition, the degradation ratio is 10.5% for the default state, while it reduces to 5.6%, 2.9%, and 1.1% for NN, NN+CC, and NN+CC+Ensemble, respectively. In the six-cell condition, it is 13% for the default state, whereas it reduces to 11%, 7.5%, and 0.67% for NN, NN+CC, and  
Figure 10: SINR heatmaps based on the estimated beams for three-cell configuration (NN, NN+CC, and GA). NN+CC+Ensemble, respectively. The CDFs achieved by NN+CC+Ensemble align well with those of GA, suggesting that accounting for neighboring cell relationships with the aid of CC refines beam intervals, thereby improving throughput. Furthermore, the incorporation of the ensemble approach helps to select the best prediction from all CC predictions with different performances for various user distributions. Incidentally, in the six-cell condition, the improvements by NN and NN+CC are smaller than those of the three-cell condition. The main reason for this observation is the high complexity of learning neighboring beam relationships by changing the configuration from three-cell to six-cell. This is almost the same as the discussion on the constraint violation ratio mentioned earlier. Figure 13 presents the CDFs of the errors between the predicted and learned beam directions, averaged for each cell. The error \(E\) is expressed as follows:  
\[E=\underset{i=-1,0,1}{\text{min}}\Bigg{(}\frac{1}{\mathcal{C}}\sum_{c=1}^{C} \text{diff}(pred_{C},true_{mod(c+i,C)})\Bigg{)}, \tag{23}\]  
where \(C\) is the number of cells, and \(pred_{c}\) and \(true_{c}\) are the predicted and learned beam direction of the \(c\)-th cell, respectively. The function \(\text{diff}(x,y)\) is expressed as follows:  
\[\text{diff}(x,y)=\min(\text{abs}(x-y,360-\text{abs}(x-y))). \tag{24}\]  
The error \(E\) considers the possibility of the prediction being offset by one cell. For instance, in the case of a three-cell configuration, the degrees of (0, 120, 240) could be predicted as (120,  
Figure 11: Constraint violation ratios for three- and six-cell configurations (NN, NN+CC, NN+CC+Ensemble). Figure 12: Cumulative distribution curves of the total throughput for the (**a**) three- and (**b**) six-cell configurations. 240, 360). It should be noted that \(pred_{0}\) and \(true_{0}\) mean \(pred_{C}\) and \(true_{C}\), respectively, for simplicity. The CDFs of the errors in the three-cell and six-cell configurations are depicted in Figure 12(a) and Figure 12(b), respectively. There is an improvement in the errors for both configurations. Nevertheless, despite the similarity in the total throughput between our proposed method and GA, as shown in Figure 12, our method still predicts some beams incorrectly. For the three-cell condition (Figure 12(a)), the majority of errors, accounting for around 80%, are less than 10\({}^{\circ}\), whereas the leftover errors range from 10\({}^{\circ}\) to 60\({}^{\circ}\).