# Enhanced Gain Difference Power Allocation for NOMA-Based Visible Light Communications
## 3 Proposed Power Allocation Scheme
### Allocation Principle Formulation
Figure 6 shows the performance comparison of the achievable sum rate under different numbers of served users. Notably, the GRPA, IFS [19], and NGDPA methods employ a format dependent on the channel gain, while the MFPA method uses a modified fixed allocation format. The figure clearly shows that all schemes can achieve an excellent data rate when serving a small number of users. As \(K\) rises, the achievable data rates provided by GRPA, IFS, NGDPA, and MFPA decline sharply, while that of the proposed scheme still achieves rather stable performance. The main reason for this is that the adjacent power

Figure 4: Achievable sum rate with two and three users (\(K=2\) and 3). Figure 3: Achievable rate for each LED with two users (\(K=2\)). allocation factors of the proposed scheme are more different compared with other schemes when the number of users is increased. Additionally, the proposed EGDPA scheme has improved the sum rate by 25.2% with 30 users. ### The Impact of Residual Interference and Modulation Bandwidth

As shown in Figure 7, we investigated the impact of the residual interference factor \(\kappa\) on the sum rate when using the proposed scheme. The values of \(\kappa\) were set to 0, 0.0001, 0.001, and 0.01. As the value escalated, the rate of the proposed scheme declined. Consequently, it became apparent that the residual interference, which is not fully eliminated during the SIC process, significantly hampers the system performance. For instance, when \(\kappa\) is 0, the sum rate of 10 users in the illuminated area is approximately 113.1 Mbit/s. Nevertheless, as \(\kappa\) rises to 0.0001, 0.001, and 0.01, the sum rate decreases to 109.8 Mbit/s, 94.8 Mbit/s, and 66.1 Mbit/s, respectively. Figure 5: Sum rate gain of the proposed scheme over NGDPA. Figure 6: Comparison of the achievable sum rate under different numbers of users. Figure 8 illustrates the impact of the transmission power and modulation bandwidth on the sum rate performance for the proposed scheme. The sum rate of the proposed scheme is positively correlated with transmission power when the modulation bandwidth is fixed. As the signal power increases, the additive power also increases to a lesser extent, resulting in improved SNR and subsequently a higher rate. Furthermore, increasing the modulation bandwidth also leads to an increase in rate with a fixed transmission power. Additionally, with the increase in modulation bandwidth, the impact of transmission power on the rate of the proposed scheme becomes more prominent. For instance, for a required system sum rate of 100 Mbit/s, the power consumption is 6 W at a modulation bandwidth of 10 MHz, whereas it reduces to 1.3 W when the bandwidth is increased to 20 MHz. ### Comparisons of Energy Efficiency

The performance of energy efficiency in two-user and three-user scenarios is shown in Figure 9. The proposed scheme demonstrates superior energy efficiency in both scenarios

Figure 8: Impact of the transmission power and modulation bandwidth for the proposed scheme. Figure 7: Comparison of the achievable data rate for different numbers of users with various values of \(\kappa\). when compared to GRPA, NGDPA, and MFPA. Furthermore, the energy efficiency of the proposed scheme improves markedly as the number of users grows, while those of the GRPA and NGDPA methods exhibit a decline. As K grows from 2 to 3, the energy efficiency obtained by GRPA decreases significantly by at least 8.14%. At the same time, that of NGDPA increases initially but subsequently decreases, e.g., by 3.85% when the transmission power is 15 W. The main reason for this is that the channel differences are decreased in the three-user scenario. Nevertheless, the proposed scheme can better utilize user channel information to address power imbalances among users. Hence, the proposed scheme is suitable for energy-constrained conditions.