# Hybrid Adaptive Bias OFDM-Based IM/DD Visible Light Communication System
## 4 Simulation Results  
In this section, we evaluate the performance of the proposed HABO-OFDM scheme through simulation results, and compare it with HACO-OFDM and ABO-OFDM. In the simulation, the number of subcarriers is 512 for these schemes, while the constellation sizes of QAM and PAM symbols are set to \(M\) and \(\sqrt{M}\), respectively. For HACO-OFDM, we choose 16 QAM-4 PAM, 64 QAM-8 PAM, 256 QM-16 QAM, 1024 QAM-32 PAM, and 4096 QAM-64 PAM as simulation conditions. In ABO-OFDM, 16 QAM, 64 QAM, 256 QM, 1024 QAM, and 4096 QAM are selected as simulation conditions. For HABO-OFDM, we generate signals from \(M\)-QAM and \(\sqrt{M}\)-PAM constellations, such as 16 QAM-4 PAM, 64 QAM-8 PAM, 256 QM-16 PAM, and 1024 QAM-32 PAM. Additionally, the total average electric power is normalized in different schemes. The system specifications is shown in Table 2. The bit error rate (BER) and peak-to-average-power ratio (PAPR) of the proposed HABO-OFDM \begin{table}
\begin{tabular}{c c c} \hline \hline
**Modulation** & **Transmitter** & **Receiver** \\ \hline HABO-OFDM & \(3N\log_{2}N-3N+4\) & \(3N\log_{2}N-3N+4\) \\ HACO-OFDM & \(3N\log_{2}N-3N+4\) & \(4N\log_{2}N-6N+8\) \\ PHO-OFDM & \(3N\log_{2}N-3N+4\) & \(5N\log_{2}N-3N+4\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of the complexity of the transmitter and receiver of different optical OFDM schemes. scheme are calculated and compared with HACO-OFDM and ABO-OFDM. We also present the BER performance of the three schemes in the nonlinearity limit. Moreover, calculation results in the electric power efficiency of the proposed HABO-OFDM scheme with HACO-OFDM and ABO-OFDM are also shown. Figure 3 shows the BER curves of QAM and PAM with different constellation sizes in HACO-OFDM, ABO-OFDM and the proposed HACO-OFDM scheme. It can be observed that HACO-OFDM and ABO-OFDM nearly present the same BER performance. Simultaneously, we also see that the BER performance of the proposed HABO-OFDM scheme is slightly degraded compared with the other two schemes. This is on account of the proposed HABO-OFDM scheme, where part of the power is allocated to the reserved subcarriers that are modulated at the same time, which in the ABO-OFDM scheme are not utilized. In addition, the proposed HABO-OFDM scheme can transmit more information data than HACO-OFDM under the same simulation conditions, which explains that the BER performance of HABO-OFDM is slightly worse than that of HACO-OFDM. In fact, for 256 QAM-16 PAM, the spectral efficiency of HABO-OFDM is improved to 7 bit/s/Hz, while the other two schemes are 6 bit/s/Hz. Specifically, this is about a 16.6% enhancement. Therefore, the spectral efficiency of the proposed HABO-OFDM scheme has been relatively improved compared with the other two systems. The complementary cumulative distribution function (CCDF) curves of the PAPR for different schemes are shown in Figure 4. We can clearly observe that the PAPR of HABO-OFDM has a significant reduction compared with HACO-OFDM and ABO-OFDM, which means that the influence of nonlinear distortion is greatly alleviated [22]. Specifically, there is about a 3.2 dB reduction in the PAPR compared to HACO-OFDM, and it is reduced by about 1.7 dB in comparison to ABO-OFDM. \begin{table}
\begin{tabular}{c c} \hline \hline
**Name of Parameters** & **Values** \\ \hline The number of subcarriers & 512 \\ The constellation sizes of QAM & 16, 64, 256, 1024, 4096 \\ The constellation sizes of PAM & 4, 8, 16, 32, 64 \\ The clipping ratio \(\tau\) & 9 dB \\ The BER target & \(10^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: System specifications. Figure 3: Comparison of the BER performance for HACO-OFDM, ABO-OFDM, and HABO-OFDM. Figure 5 presents the BER performance of HACO-OFDM, ABO-OFDM, and HABO-OFDM under the nonlinear constraints, where the clipping ratio \(\tau\) is set to 9 dB [23]. It is clear that the anti-nonlinearity ability of HABO-OFDM is noticeably improved compared with HACO-OFDM and ABO-OFDM.