# Performance Analysis of Cooperative Non-Orthogonal Multiple Access in Visible Light Communication
## 4 Numerical Results and Discussion
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Description** & **Symbol** & **Value** \\ \hline LED semi-angle & \(\phi_{1/2}\) & \(50^{\circ}\) \\ PD FOV & \(\psi_{c}\) & \(45^{\circ}\) \\ Refractive index & \(n\) & \(1.5\) \\ Optical filter gain & \(T^{\circ}(\psi_{k})\) & \(1\) \\ Responsivity & \(R_{p}\) & \(1\) A/W \\ PD detection area & \(A_{k}\) & \(1\) cm\({}^{2}\) \\ Bandwidth & \(B\) & \(10\) MHz \\ open-loop voltage gain & \(C_{ol}\) & \(10\) \\ fixed capacitance of PD & \(C_{pl}\) & \(112\) pF/cm\({}^{2}\) \\ Absolute temperature & \(T_{k}\) & \(298\) K \\ FET transconductance & \(g_{m}\) & \(30\) mS \\ Noise bandwidth factors & \(I_{3}\) & \(0.0868\) \\ FET channel noise factor & \(\Gamma\) & \(1.5\) \\ Background current & \(l_{bg}\) & \(5100\) uA \\ Noise bandwidth factors & \(I_{2}\) & \(0.562\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation parameters “Reproduced with permission from [21], IEEE, 2017”. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**User** & **Location** & **FOV** & **Channel Gain** \\ \hline \(U_{1}\) & (2.5, 2.5, 1.25) & \(60^{\circ}\) & \(0.2835\times 10^{-4}\) \\ \(U_{2}\) & (2.4, 2.4, 1.25) & \(45^{\circ}\) & \(0.4787\times 10^{-4}\) \\ \(U_{3}\) & (2.3, 2.3, 1.25) & \(45^{\circ}\) & \(0.5272\times 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Users’ setup “Reproduced with permission from [21], IEEE, 2017”. Figure 9 shows the effect of decreasing the transmitted power of the users that act as relays on the BER performance of cooperative NOMA. This demonstrates a more realistic VLC scenario where the LEDs that are used as relays have one-fourth the power of the main LED. Although the transmitted power in the direct phase is still the same, the results show that the BER performance of the cooperative NOMA highly depends on the LED power of the relays. It is noted that the BER performances of \(U_{2}\) and \(U_{1}\) in the cooperative phase are degraded when compared to Figure 8 by 1.45 dB and 6.7 dB at \(10^{-6}\), respectively. Also, another scenario can be considered without decreasing the power of the relays by adjusting the users at specific angles to exploit the non-LOS propagation of the signal. Figure 8: BER performance for cooperative PD-NOMA with three users. Figure 7: Bit error rate (BER) performance for cooperative PD-NOMA with two users. Figure 10 shows the BER performance of cooperative NOMA with different users' setup and their coordinates are depicted in Table 4; Figures 8 and 10 have the same channel gain ordering in the direct transmission phase as in Equation (8) but with different channel gain ordering in the cooperative phase. Results show degradation in the BER performance of cooperative PD-NOMA for \(U_{1}\) and \(U_{2}\) when compared to Figure 8. The BER analytical expressions are matched with the Monte Carlo simulation results and are not limited to specific physical parameters. Figure 10: BER performance for cooperative PD-NOMA with different users’ setup. Figure 9: BER performance for cooperative PD-NOMA with relay power 0.25 W.  
As shown in Figure 11, we evaluate the achievable rate in a two-user scenario. In non-cooperative PD-NOMA, \(U_{2}\) has a higher achievable rate than \(U_{1}\) owing to the ability of \(U_{2}\) to cancel \(U_{1}\) interference successfully by applying SIC. It is clear that using cooperative PD-NOMA dramatically improved \(U_{1}\) achievable rate by 14.1 bit/s/Hz at 45 dB due to increasing the SINR of \(U_{1}\). Similarly, Figure 12 presents the achievable rate in a three-user scenario where \(U_{3}\) and \(U_{2}\) act as relays. \(U_{3}\) has the highest achievable rate in non-cooperative PD-NOMA, where it is the nearest user to the LED and has the ability to successfully cancel \(U_{2}\) and \(U_{1}\) interference by applying SIC. Moreover, using cooperative PD-NOMA enhanced \(U_{2}\) and \(U_{1}\) achievable rates by 12.4 bit/s/Hz and 14.3 bit/s/Hz at 45 dB, respectively.