# A Relay Optimization Method for NOMA-Based Power Line Communication Systems
## 3 Optimization Process and Performance Analysis
### Uplink from Relay Node to Other Users
The gray area in the figure represents the initial power allocation, and the blue area represents the optimized power allocation. The optimized allocation significantly favors distant users, with their power levels considerably higher than the initial allocation, while the power for nearby users is drastically reduced. This optimization strategy adheres to the fairness principle in wireless communications by allocating more power to distant users to compensate for their poorer channel conditions. The optimization algorithm successfully enhances system capacity under power constraints, while meeting fairness requirements among users. \[\text{MAE}=\frac{1}{M}\sum_{i=1}^{M}\left|\text{CSI}_{i}-\text{CSI}_{i}\right| \tag{37}\]0 Power Allocation Comparison. To verify the effectiveness of the algorithm, a comparative experiment was conducted using a distance-based power allocation scheme without optimization. In this approach, users farther from the signal source are allocated more power, with a proportional increase. The resulting experimental comparison with our method is shown in the figure. The results indicate that the optimized power allocation significantly exceeds the distance-based method, especially for distant users. The distance-based approach distributes power more evenly and increases linearly. Communication performance improves by 5.6% compared to the distance-based power allocation method. In order to further verify the effectiveness and advancement of the improved simulated annealing algorithm and verify the previous conclusions, other optimization algorithms are now further compared. The compared algorithms include improved simulated annealing algorithm, PSO, GA, and distance-based power distribution algorithm (DB). The result is shown in \[\text{MAE}=\frac{1}{M}\sum_{i=1}^{M}\left|\text{CSI}_{i}-\text{CSI}_{i}\right| \tag{37}\]1  
\[\text{MAE}=\frac{1}{M}\sum_{i=1}^{M}\left|\text{CSI}_{i}-\text{CSI}_{i}\right| \tag{37}\]2 SNR values for each user. \[\text{MAE}=\frac{1}{M}\sum_{i=1}^{M}\left|\text{CSI}_{i}-\text{CSI}_{i}\right| \tag{37}\]3 Power allocation optimization. Under the same experimental conditions, the results show that the power distribution of SA and DB is more balanced, avoiding the overload of individual users, which conforms to the principle of fairness. However, DB is only allocated according to distance, and cannot consider whether it satisfies many constraints. In this experiment, because the PLC system is sensitive to distance, DB as a benchmark method is stable but lacks optimization flexibility, but in other communication environments, the performance of this algorithm will be greatly reduced. The power allocation of some users in GA and PSO is significantly higher, which may lead to resource waste or interference. GA focuses on capacity maximization due to fitness function at the expense of power efficiency. The swarm intelligence characteristic of PSO may lead to local centralized allocation. By comparison, the improved simulated annealing algorithm shows better performance and adaptability. In the PLC system, under certain conditions, the increase in system capacity will bring about an increase in system power consumption. Therefore, in this experiment, the relationship diagram between power consumption and system capacity of different  
\[\text{MAE}=\frac{1}{M}\sum_{i=1}^{M}\left|\text{CSI}_{i}-\text{CSI}_{i}\right| \tag{37}\]4 Power allocation comparison. (**a**) Comparison of user power distribution between the two methods; (**b**) comparison of system capacity between the two methods. \[\text{MAE}=\frac{1}{M}\sum_{i=1}^{M}\left|\text{CSI}_{i}-\text{CSI}_{i}\right| \tag{37}\]5 Comparison of user power allocation by optimization method. optimization methods is also verified when other constraints are met, as shown in \[\text{MAE}=\frac{1}{M}\sum_{i=1}^{M}\left|\text{CSI}_{i}-\text{CSI}_{i}\right| \tag{37}\]6 The experimental results show that the optimized system capacity of GA is higher than that of other algorithms, but the power loss is much higher than that of other algorithms.