# Enhanced Gain Difference Power Allocation for NOMA-Based Visible Light Communications
## 3 Proposed Power Allocation Scheme
### Allocation Principle Formulation
### Error Probability

The error probability achieved by the proposed scheme in the two-user scenario is illustrated in Figure 10. As the location of the users is fixed, the system's error probability reduces obviously with an increase in the LED optical power. Specifically, \(U_{1}\) (i.e., the distant user) is allocated more power, resulting in better error performance. Despite the better channel conditions of \(U_{2}\), its BER performance is slightly inferior due to receiving less power. To a certain extent, this indicates the fairness of the proposed scheme. Furthermore, as the relative distance between users rises, the error performance improves considerably when the optical power is determined. For instance, when the error probability equals \(10^{-3}\), the required optical power decreases from 2.7 W to 1.3 W as the relative distance \(r\) grows from 0.8 m to 1 m. This is due to the symmetrical geometric positioning of the two users around \(L_{2}\) when \(r\) is 1 m, resulting in power resource savings. Overall, the proposed scheme achieves a superior BER performance, indicating its reliability. ### Comprehensive Analysis

Table 2 presents a comprehensive comparison of different schemes. The proposed scheme outperforms other schemes in terms of the sum rate and energy efficiency. For example, compared to the GRPA scheme, the proposed scheme achieves a maximum sum rate gain of 36.26%, a maximum sum rate gain of 25.09% compared to the NGDPA scheme, and a gain of 10.87% compared to the MFPA scheme. Additionally, when the total transmission power of the three users is 15 W, the proposed scheme achieves an energy efficiency gain of 23.44% compared to GRPA, 5.68% compared to NGDPA, and 1.71% compared to MFPA. The proposed scheme's performance gain increases with the number of users, as its residual allocation principle effectively reduces inter-user interference caused by multiple users. Figure 5.0 Energy efficiency comparison for different power allocation schemes. ## 5 Conclusions

In this paper, an enhanced gain difference power allocation scheme has been proposed to improve the sum rate of a multi-user NOMA-based MIMO-VLC system, which adapts to user channel conditions and efficiently utilizes the gain difference. Efficient power allocation is achieved by utilizing the residual allocation principle, which emphasizes the power that remains available after allocation to the preceding users, rather than the initially assigned power. Furthermore, an assessment of performance metrics such as the achievable data rate, energy efficiency, and BER was conducted. The numerical results demonstrate that the interference in SIC can be effectively alleviated, and the proposed scheme can achieve a significant performance improvement in terms of both sum rate and energy efficiency over the traditional schemes. In addition, the proposed scheme requires more iterative operation than alternative schemes, so the consumption of hardware resources is slightly higher. In the scenario of a random geometric distribution of users, there may be users with the same channel gain. However, the sorting criterion for this case has not been taken into account. In the future, we are planning to extend our proposed EGDPA scheme into multi-cell scenarios with NLOS links. To better accommodate practice, we will consider adaptive SNR requirements and user association mode selection. The proposed EGDPA scheme will be adjusted and optimized to adapt to the various system requirements.