# Enhanced Gain Difference Power Allocation for NOMA-Based Visible Light Communications
## 3 Proposed Power Allocation Scheme
### Allocation Principle Formulation
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Sum Rate (Mbit/s)**} & \multicolumn{6}{c}{**Energy Efficiency \({}^{*}\)**} \\ \cline{2-9}  & **K = 3** & **K = 10** & **K = 15** & **K = 20** & **K = 25** & **K = 30** & **K = 2** & **K = 3** \\ \hline GRPA & 102.85 & 88.42 & 86.61 & 84.72 & 84.17 & 83.27 & 52.5 & 48.2 \\ NGDPA & 108.74 & 94.73 & 93.40 & 91.77 & 91.44 & 90.7 & 58.5 & 56.3 \\ MFPA & 109.27 & 112.96 & 112.77 & 111.07 & 107.49 & 102.08 & 58.3 & 58.5 \\ Proposed scheme & 109.29 & 113.2 & 113.43 & 113.73 & 113.71 & 113.94 & 59.2 & 59.5 \\ \hline The performance gain of the proposed scheme over GRPA & 5.62\% & 26.33\% & 30.97\% & 33.39\% & 35.11\% & 36.26\% & 12.76\% & 23.44\% \\ \hline The performance gain of the proposed scheme over NGDPA & 0.54\% & 18.03\% & 21.45\% & 23.33\% & 24.36\% & 25.09\% & 1.20\% & 5.68\% \\ \hline The performance gain of the proposed scheme over MFPA & 0.004\% & 0.12\% & 0.59\% & 2.11\% & 5.79\% & 10.87\% & 1.54\% & 1.71\% \\ \hline \hline \end{tabular}

* The values (Mbit/s/W) were measured when the transmission power was 15 W.

\end{table} 
Table 2: Comprehensive comparison of different schemes. Figure 10: Error probability of the proposed scheme with increasing optical power between two users. **Author Contributions**: Conceptualization, P.M.; methodology, P.M.; formal analysis, X.Z. ; data curation, X.Z. ; writing--original draft preparation, X.Z. ; writing--review and editing, X.Z., P.M. and X.W. ; validation, X.Z. and X.W. ; supervision, P.M.; project administration, P.M.; funding acquisition, P.M. All authors have read and agreed to the published version of the manuscript. **Funding**: This research was partially funded by the Shandong Provincial Natural Science Foundation under grant ZR2023 MF096, and by the National Natural Science Foundation of China under grant 61801257. **Data Availability Statement**: The data presented in this study are available upon request from the corresponding authors. **Conflicts of Interest**: The authors declare no conflicts of interest. ## References

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