# Low-Complexity Hybrid Optical OFDM with High Spectrum Efficiency for Dimming Compatible VLC System
## 4 Numerical Results  
This section provides our simulations for quantifying the proposed DCHO-OFDM, where we employ \(N=256\) for the O-OFDM VLC system. The lower bound and the upper bound of LED are referred to as \(I_{l}=0\) and \(I_{h}=1\), respectively. In order to evaluate the non-linear distortion, a pair of scaling factors \(\beta_{ACO}\) and \(\beta_{PAM}\) are defined as \(\beta_{ACO}=(I_{h}-I_{l})/\sigma_{ACO}\) and \(\beta_{PAM}=(I_{h}-I_{l})/\sigma_{PAM}\), where \(\sigma_{ACO}\) and \(\sigma_{PAM}\) denote the standard variance of the unclipped ACO-OFDM and PAM-DMT, respectively. To begin with, we investigate the PAPR performance of the proposed DCHO-OFDM scheme, compared to that of the HACO-OFDM, where the associated complimentary cumulative distribution function (CCDF) can be seen in Figure 4[26]. It is observed that the proposed DCHO-OFDM achievesa much lower PAPR than that of the conventional HACO-OFDM. This observation is as expected for the reason that the unclipped ACO-OFDM is invoked in DCHO-OFDM, which is capable of avoiding relatively high amplitudes. Note that a lower PAPR results in a better ability to resist the non-linearity [26]. Therefore, unlike the HACO-OFDM, the proposed OFDM scheme is capable of alleviating the undesired non-linear distortion in the presence of the non-linear transfer characteristic of LED. In this case, a better BER performance can be achieved by the proposed DCHO-OFDM, leading to an improved achievable spectrum efficiency compared to HACO-OFDM, as shown in the following figures. Figure 5 quantifies the dimming level for the various values of duty cycle \(\rho\). Upon observing, the dimming level is linearly changed upon adjusting the duty cycle of PWM signal, which is consistent with our theoretical analysis in Section 3.2. Additionally, a wide range of dimming level is achieved in DCHO-OFDM. To expound, the proposed scheme is capable of achieving a fairly low or high dimming level, upon further increasing the value of the scaling factors, albeit at a cost to power inefficiency. In Figure 6, we demonstrate the BER performance of DCHO-OFDM vs the variance of signal under different values of duty cycle, where a standard OFDM receiver is directly employed. Upon observing Figure 6, the attained BER of the proposed scheme first becomes better upon increasing the variance of signal, while it deteriorates afterwards due to the clipping noise generated by the limited dynamic range of LEDs. Additionally, we observe that the same BER performance is obtained with various values of duty cycle \(\rho\), which indicates that the BER performance of DCHO-OFDM is invulnerable to the various duty cycles of PWM. This can be explained by noting that the dimming control in the proposed DCHO-OFDM scheme does not affect the information transmission, so that both the functionality of illuminations and communications in VLC can be achieved without disturbing each other. Hence, the symbols transmitted by the proposed DCHO-OFDM can be directly detected through a standard OFDM receiver without requiring additional operation of PWM signal detection. Figure 4: CCDF curves of PAPR for the proposed DCHO-OFDM scheme, compared to that of the HACO-OFDM scheme. For a target BER of \(2\times 10^{-3}\), we further explore the spectrum efficiency of the proposed scheme, as depicted in Figures 7 and 8, in a scenario of high (\(-2\) dBm) and of low (\(-8\) dBm) noise power, respectively. For comparison, the spectrum efficiency of DCO-OFDM and the dimmable HACO-OFDM proposed in [22] are also provided. Upon observing, the achievable spectrum efficiency of DCHO-OFDM is superior to that of the conventional DCO-OFDM and HACO-OFDM in a wide range of dimming levels, where the transmission in DCO-OFDM is easily affected by dimming control due to the non-linear distortion.