# A Relay Optimization Method for NOMA-Based Power Line Communication Systems
## 3 Optimization Process and Performance Analysis
### Uplink from Relay Node to Other Users
However, as the distance increases, the signal energy rapidly decays, resulting in poor channel conditions for distant users. This highlights the key role of distance in determining channel quality in power line communication and underscores the importance of optimized power allocation for distant users, as demonstrated by the subsequent results. In the experiment, an AR model was used to simulate background noise, as shown in Figure 6.  
The background noise is distributed in a random fashion but exhibits some smoothness. While there are significant local fluctuations, the overall noise values are concentrated around 0. The smoothness and autocorrelation of the noise suggest that the AR model effectively captures the characteristics of background noise in power line communication. The high peak noise interference observed in the fluctuations between positions 40 and 60 in the figure could cause transient performance degradation, especially under low SNR conditions. At the same time, impulse noise in the experiment was modeled using a Markov chain, as shown in \[\text{BER}_{i}=0.5\cdot\text{erfc}\Big{(}\sqrt{\text{SINR}_{i}}\Big{)} \tag{36}\]0  
\[\text{BER}_{i}=0.5\cdot\text{erfc}\Big{(}\sqrt{\text{SINR}_{i}}\Big{)} \tag{36}\]1 Channel gains vs. distance. \[\text{BER}_{i}=0.5\cdot\text{erfc}\Big{(}\sqrt{\text{SINR}_{i}}\Big{)} \tag{36}\]2 Background noise. The impulse noise appears as intermittent spikes, with amplitudes significantly higher than the background noise. These spikes are randomly distributed, such as near positions 10, 60, and 80. The impulse noise, generated based on the Markov chain, simulates burst-like interference in communication systems. Its characteristics--high amplitude and intermittent nature--demand higher system robustness. In training the LIST model, the specific performance is shown in Figures 8 and 9. Figure 8 compares the real CSI values with the predicted CSI values. The blue line represents the actual values, and the red dashed line represents the predicted values. It is evident from the figure that the predicted and actual values follow the same general trend, though some fluctuations and errors exist. Figure 9 shows the prediction errors, i.e., the differences between the actual and predicted values. The errors fluctuate between 0  
\[\text{BER}_{i}=0.5\cdot\text{erfc}\Big{(}\sqrt{\text{SINR}_{i}}\Big{)} \tag{36}\]3 True value vs. predicted value. \[\text{BER}_{i}=0.5\cdot\text{erfc}\Big{(}\sqrt{\text{SINR}_{i}}\Big{)} \tag{36}\]4 Impulse noise. \[\text{BER}_{i}=0.5\cdot\text{erfc}\Big{(}\sqrt{\text{SINR}_{i}}\Big{)} \tag{36}\]5 Error value. and \(-0.1\), indicating larger errors at certain points, but overall, the errors remain relatively stable. This suggests that the LSTM model is capable of effectively learning the time series characteristics of the CSI and predicting short-term variations. The high prediction accuracy indicates that the LSTM model is well suited for handling complex nonlinear channel dynamics. Such predictions can support power allocation tasks, thereby improving the communication system's efficiency. The computed performance metrics are as follows: MAE = 0.0835, MSE = 0.0110, RMSE = 0.1050. These metrics indicate that there is some discrepancy between the predicted and actual values. The data generation process incorporated log-normal fading channels and background noise, which increased the data complexity. Nevertheless, the errors are not overly large, and normalization of the data helped improve the LSTM model's training effectiveness, demonstrating its predictive capability. The LSTM model was employed to capture the temporal dependencies within the sequence data, a common approach for predicting time series data. Dropout layers were used during training to prevent overfitting, and the Adam optimizer was employed for optimization. The prediction errors may stem from several factors, such as the random noise in the data, which affects prediction accuracy. Additionally, further optimization of the model parameters may be needed.