# Visible Light Communication: An Investigation of LED Non-Linearity Effects on VLC Utilising C-OFDM
## 3 Simulation Results and Discussion
### BER Performance  
Figure 4 demonstrates the BER performance of the conventional 4-QAM OFDM under the operation condition of the 200 AC level and different bias points. The solid black curve represents the theoretical curve BER performance in all coming figures. From Figure 4, it could be observed that the BER managed to meet the designated BER target \(10^{-4}\) at \(\rm E_{b}/N_{o}\)\(\sim\)20 dB when the bias point was 100 mA. Moreover, Figure 5 illustrates the BER performance of 2-PAM F-OFDM. It showed a slight improvement and met the BER target at \(\rm E_{b}/N_{o}<10\) dB. However, Figure 5 infers that the BER performance when the DC bias point was more the 500 mA failed to meet the BER target \(10^{-4}\). On the other hand, Figure 6 illustrates the BER performance of 2-PAM C-OFDM under the same operating condition of the DC bias point. An improvement in the BER was shown in Figure 6 using C-OFDM. An improvement in the BER could be observed in contrast to OFDM, F-OFDM and C-OFDM in Figures 4-6, respectively. The 16-QAM OFDM BER performance was depicted in Figure 7. It showed that the BER target had not been achieved at the low \(\rm E_{b}/N_{o}\). Figure 8 illustrates the BER performance as a function of \(\rm E_{b}/N_{o}\) for 4-PAM F-OFDM. In Figure 8, it can be noted that for most of the different bias point values, the BER target was not achieved. The BER performance of 4-PAM C-OFDM was presented in Figure 9. It showed a significant improvement in the BER performance, where all the BER  
Figure 5: BER performance as a function of \(\rm E_{b}/N_{o}\) for F-OFDM with 2-PAM and 200 AC.  
Figure 6: BER performance as a function of \(\rm E_{b}/N_{o}\) for C-OFDM with 2-PAM and 200 AC.  
Figure 7: BER performance as a function of \(\rm E_{b}/N_{o}\) for OFDM with 16-QAM and 200 AC.  
Moreover, for all the bias points, the C-OFDM's BER's performance was better than the conventional OFDM and F-OFDM. Furthermore, Figures 6 and 9 show the BER performance of the proposed systems with 2-PAM and 4-PAM, respectively, where both showed an improved BER performance in contrast to the typical OFDM and F-OFDM. Finally, we changed the AC level to 600 mA, as seen in Figures 10-12, for OFDM, F-OFDM and C-OFDM, respectively. It can be seen from Figures 10 and 12 that an \(\sim\)10 dB improvement was achieved at the first bias point compared to conventional OFDM and C-OFDM. At DC bias 300 and 500, an improvement of \(\sim\)4 dB and 9 dB was achieved when compared between C-OFDM and F-OFDM, respectively, in Figures 11 and 12. However, the BER did not reach the target using F-OFDM with the 600 DC level and an ac bias point greater than 500 mA.  
Figure 8: BER performance as a function of \(\rm{E_{b}/N_{o}}\) for F-OFDM with 4-PAM and 200 AC.  
Figure 9: BER performance as a function of \(\rm{E_{b}/N_{o}}\) for C-OFDM with 4-PAM and 200 AC.  
Figure 11: BER performance as a function of \(\rm E_{b}/N_{o}\) for F-OFDM with 2-PAM and 600 AC.  
Figure 10: BER performance as a function of \(\rm E_{b}/N_{o}\) for OFDM with 4-QAM and 600 AC.  
In general, in this section, we explained the change in the performance of the BER as a function of E\({}_{\text{b}}\)/N\({}_{\text{o}}\) when several bias points changed, along with the DC level. As can be observed in Figures 6, 9 and 12 that the BER target was achieved with the lowest power penalty for E\({}_{\text{b}}\)/N\({}_{\text{o}}\) in comparison with Figures 4, 5, 7, 8, 10 and 11. Moreover, a remarkable improvement was achieved by comparing this power penalty between the conventional OFDM, F-OFDM and C-OFDM under the same bias point conditions and DC level displays. All the previous comparisons showed the advantages of C-OFDM over the normal OFDM and F-OFDM.