# Performance Analysis of Cooperative Non-Orthogonal Multiple Access in Visible Light Communication
## 4 Numerical Results and Discussion  
In this section, we evaluate the performance of the proposed cooperative PD-NOMA-VLC downlink system. We provide Monte Carlo simulations to substantiate the accuracy of the derived BER analytical expressions. We investigate the BER and achievable rate performance based on the system model proposed in Section 2. A realistic indoor environment of a \(4\)\(\text{m}\times 4\)\(\text{m}\times 3\)\(\text{m}\) room is considered with the main LED source placed at the center of the ceiling with total optical power of \(1\)\(\text{W}\). We consider the same system parameter as in [21] where three users are assumed to be served via PD-NOMA simultaneously. We use a fixed power allocation (FPA) strategy where the power allocated to the \(k\)-th user is \(a_{k}^{2}=\Delta a_{k-1}^{2}\) under the constraint \(\sum_{l=1}^{M}a_{l}^{2}=1\), where \(\Delta\) is the power allocation factor (\(0<\Delta<1\)) and the best BER performance achieved at \(\Delta=0.3\) as in [8]. We summarize the simulation parameters of the proposed scenario in Table 2, and show all fixed user locations, FOV and channel gains in Table 3.  
Figure 7 demonstrates cooperative and non-cooperative PD-NOMA-VLC BER performance of the two users under perfect CSI. Although the far user (i.e., \(U_{1}\)) has the worst channel condition, it achieves better BER due to the high power allocated to its signal. Therefore, as the decoding order decreases the BER performance increases, which allows \(U_{1}\) to have the best BER performance by decoding its own signal directly and treating others as noise. Since \(U_{2}\) is the nearest to the main LED source it only has one PD to receive the transmitted signal during direct transmission phase. It decodes and subtracts the message intended for \(U_{1}\) using SIC before decoding its own signal. Then in the cooperative phase, \(U_{2}\) acts as a relay to retransmit the \(U_{1}\) message. Therefore, there is no change in the BER performance of \(U_{2}\) in non-cooperative and cooperative PD-NOMA. Moreover, \(U_{1}\) receives \(y_{1}\) from the LED transmitter and the ML decoded signal \(y_{2,1}\) from \(U_{2}\). MRC is used to combine the received signals from both direct transmission and cooperative phases. It can be seen that cooperative PD-NOMA improved \(U_{1}\) BER performance by about 8.2 dB at \(10^{-6}\) compared to non-cooperative. Figure 8 shows the BER of cooperative and non-cooperative PD-NOMA in a three-user scenario where \(U_{2}\) and \(U_{3}\) act as relays. In this scenario, \(U_{3}\) is the nearest to the main LED source. It decodes and subtracts the messages intended for \(U_{1}\) and \(U_{2}\) using SIC before decoding its own signal. Therefore, in the direct transmission phase, \(U_{2}\) receives \(y_{2}\) from the main LED. While in the cooperative phase, it receives the ML decoded signal \(y_{2,2}\) from \(U_{3}\) in the first time slot. Similarly, \(U_{1}\) receives signals from the LED transmitter, from \(U_{3}\) during the first time slot, and from \(U_{2}\) during the second time slot. MRC is used at \(U_{2}\) and \(U_{1}\) receivers to combine the signals from both phases. It is noted that the BER performance of \(U_{3}\) is the same in both phases while the BERs of \(U_{2}\) and \(U_{1}\) improved by about 2 dB and 9 dB at \(10^{-6}\), respectively.