# 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 optimization result of PSO is the worst for the test system. The final power consumption difference between the improved simulated annealing algorithm and the DB is not large, which is also reflected in \[\text{MAE}=\frac{1}{M}\sum_{i=1}^{M}\left|\text{CSI}_{i}-\text{CSI}_{i}\right| \tag{37}\]7 However, the system capacity of SA is larger than that of DB. Now in order to further explore the comparison of system capacity and power in several algorithms, we use the index of power efficiency to complete. Power efficiency is a measure of how much power a system uses per unit of system capacity. It is given by _system capacity_/_total power_. As can be seen from Figure 19, the high system capacity of GA algorithm also brings high power consumption, that is, extremely low power efficiency. The power efficiency of PSO is very high because its denominator is small, that is, the total power is too low, and its system capacity is too low to meet the communication needs. The improved SA algorithm obtains a better power efficiency index by means of power consumption and high system capacity. According to Figures 18 and 19, the improved simulated annealing algorithm can indeed meet the total power reduction under the system capacity requirements. The effectiveness of SA-LSTM is also verified. \[\text{MAE}=\frac{1}{M}\sum_{i=1}^{M}\left|\text{CSI}_{i}-\text{CSI}_{i}\right| \tag{37}\]8 Power efficiency and system capacity. \[\text{MAE}=\frac{1}{M}\sum_{i=1}^{M}\left|\text{CSI}_{i}-\text{CSI}_{i}\right| \tag{37}\]9 Power consumption and system capacity. In the optimization process, the computational complexity of each algorithm is calculated, and the real-time performance analysis is carried out. This is beneficial for actual deployment. The results of quantization of the calculation cost of each module are shown in \[\text{MSE}=\frac{1}{M}\sum_{i=1}^{M}(\text{CSI}_{i}-\text{CSI}_{i})^{2} \tag{38}\]0  
To evaluate the robustness of the proposed framework in large-scale networks, we extended simulations to three scenarios with different user densities. The experiment included three user densities: low density of 5 users, medium density of 30 users, and high density of 50 users. Users uniformly distributed in a 10 m \(\times\) 10 m area. As a result, the probability of interruption increases from 2% at low density to 12% at medium density, and finally to 25% at high density. As shown in the result, the interruption probability of users increases due to the increased user density in the area. While the framework performs well in small-scale networks (\(\leq\)30 users), ultra-dense deployments (\(\geq\)50 users) reveal two critical challenges: exponential complexity growth and channel prediction accuracy drop, and LSTM's CSI prediction MAE increases from 0.0835 (5 users) to 0.21 (50 users) due to overlapping channel signatures in dense clusters. In order to solve the problem of poor performance in high-density users, a sub-cluster optimization algorithm can be adopted. For example, if 10 users are divided into a cluster, first optimize the power distribution and repeater position between the clusters, and then optimize the two times between the users within the cluster, which can effectively avoid the problem of poor effect of the algorithm in the face of high-density user situations. To further validate the proposed method, we conducted experiments using a hardware testbed in a real-world low-voltage power line environment. The testbed consists of the following: PLC modems: ST7540 transceivers with OFDM/NOMA capability; a signal generator: Rigol DG4162 for injecting controlled interference; data acquisition: National Instruments PXIe-5171 oscilloscope; relay nodes: Raspberry Pi 4B with custom PLC interface boards. The test environment includes a 220 V/50 Hz residential power line network spanning 50 m, with five user nodes deployed at distances of 10 m, 20 m, 30 m, 40 m, and 50 m from the source. The final results of the measured experiment are shown in Tables 5 and 6.