# Enhanced Gain Difference Power Allocation for NOMA-Based Visible Light Communications
## 3 Proposed Power Allocation Scheme
### Allocation Principle Formulation
Regarding the PDs, the detection area and the optical-electrical responsivity are 1 cm\({}^{2}\) and 0.53 A/W, respectively. For brevity, the main simulation parameters are listed in Table 1. We assume that the users are uniformly distributed with stationary positions. Additionally, the OMA strategy with equal power allocation is evaluated here for performance comparison. ### Comparisons of Achievable Rates with Different User Numbers

For \(K=2\), Figure 3 demonstrates the achievable data rate provided by each LED at different relative distances. It can be seen that the data rates of the two methods exhibit minimal difference when the relative distance is below 1.6 m. As the relative distance ranges from 1.6 m to 2.4 m, the data rates of each LED are rapidly diminished. Nonetheless, we find that the reduction in data rates is relatively moderate when using the proposed EGDPA. For instance, as the distance grows from 2 m to 2.4 m, the rate for \(L_{2}\) using the proposed EGDPA reduces from 56.9 Mbits/s to 54.9 Mbits/s, while that of NGDPA drops more visually from 55.6 Mbits/s to 53.1 Mbits/s. When the relative distance exceeds 2.8 m, the rate of \(L_{2}\) rebounds and stabilizes at about 57.7 Mbit/s while that of \(L_{1}\) declines greatly due to its poor channel conditions. The proposed scheme achieves better results relative to the NGDPA method, albeit by a small margin. Figure 4 compares the achievable sum rate with different power allocation schemes. The results demonstrate that as the relative distance rises, the sum rate for OMA and GRPA is dramatically decreased. Only a slight performance degradation is introduced in the proposed scheme. When the relative distance is less than 1.6 m, NGDPA, MFPA [25], and the proposed scheme completely overlap. However, after the relative distance exceeds 1.6 m, the rates of NGDPA and MFPA fluctuate below that of the proposed scheme. For instance, for \(K=2\), at a relative distance of 2.4 m, the minimum sum rate is attained by NGDPA, MFPA, and the proposed scheme. However, by utilizing the proposed scheme, a greater sum rate of 106.9 Mbit/s is attained, which still surpasses the 102.7 Mbit/s and 104.4 Mbit/s accomplished by MFPA and NGDPA. For \(K=3\), at relative distances of 2 m and 4 m, the sum rate of NGDPA remains relatively low, achieving approximately 105 Mbit/s and 104.9 Mbit/s, respectively. Nonetheless, the proposed scheme achieves better rates of 111.7 Mbit/s and 109.7 Mbit/s, respectively, at these distances. Compared with alternative methods, the proposed scheme displays notable resistance to interference, indicating the robustness of the system. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Cell radius (\(R\)) & 4 m \\ Height of room (L1) & 3 m \\ Height of receiving panel (L2) & 0.85 m \\ LED spacing & 1 m \\ PD spacing & 4 cm \\ Semi-angle of the LED (\(\phi_{1/2}\)) & 50\({}^{\circ}\) \\ Optical filter gain (\(T_{\mathrm{s}}\)) & 1 \\ Refractive index (\(n\)) & 1.5 \\ Modulation index (\(\zeta\)) & 0.5 \\ Optical-electrical responsivity (\(\gamma_{\mathrm{ee}}\)) & 0.53 A/W \\ FOV (\(\psi_{\mathrm{C}}\)) & 72\({}^{\circ}\) \\ Active area (\(A_{PD}\)) & 1 cm\({}^{2}\) \\ Modulation bandwidth (\(B\)) & 10 MHz \\ Transmitted optical power (\(P_{o}\)) & 10 W \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. The gain in sum rate obtained by the proposed ECDPA when compared to the traditional NGDPA is demonstrated in Figure 5. The results clearly show that the sum rate gain of the proposed EGDPA over the traditional NGDPA increases substantially when the number of users increases from 2 to 3. As compared with NGDPA at \(r=2\) m, the proposed scheme achieves improvements in data rate by 2.12% and 6.25% for \(K=2\) and 3, respectively. Furthermore, when the relative distance is set as 4 m, the proposed scheme achieves a gain of 4.58% for \(K=3\) since the furthest user is at the edge of the cell. The aforementioned analysis substantiates the effectiveness of the proposed scheme.