# Low-Complexity Hybrid Optical OFDM with High Spectrum Efficiency for Dimming Compatible VLC System
## 3 Proposed Dimming Compatible Hybrid O-OFDM
### Dcho-Ofdm  
In order to implement dimming control, the PWM signal needs to be designated for incorporating the O-OFDM transmission. Specifically, the period of the PWM is set to be as many as the \(K\) times of a single O-OFDM symbol duration \(T_{s}\), which can be represented as \(T=KT_{s}\), where \(K\) is an integer. Accordingly, the duration of ON state of PWM is set to \(T_{ON}=K^{\prime}T_{s}\), where \(K^{\prime}\) denotes the number of O-OFDM symbols transmitted at ON state. It can be observed that the PWM signal remains constant in a single O-OFDM symbol duration \(T_{s}\), which implies that the introduced interference is imposed only on the 0-th subcarrier, as depicted in Figure 1d. Since the transmitted signal in VLC has to be constrained by the limited linear transmission range of LEDs, the O-OFDM components needs to be carefully designed, in order to incorporate PWM for the purpose of dimming control. Taking the characteristic of the PWM signal into consideration, a signal with negative polarity is desired during the ON state, while a positive-valued signal is required for the OFF state. Therefore, instead of combining the unipolar signal of ACO-OFDM and of PAM-DMT as seen in the conventional HACO-OFDM scheme, we invoke the unclipped double-side ACO-OFDM signal in our proposed DCHO-OFDM to amalgamated with either the upper-clipped PAM-DMT signal \(\lceil y_{PAM,n}\rceil_{c}\) or the down-clipped PAM-DMT signal \(\lfloor y_{PAM,n}\rceil_{c}\) as:\[\left\{ \begin{array}{ll}s_{n}^{\text{on}}=x_{ACO,n}+\lceil y_{PAM,n}\rceil_{c},& \text{ON state}\\ s_{n}^{\text{off}}=x_{ACO,n}+\lfloor y_{PAM,n}\rfloor_{c},&\text{OFF state}\end{array} \right., \tag{7}\]  
depending on the state of PWM signal. Note that the upper-clipped PAM-DMT signal is given by:  
\[\lceil y_{PAM,n}\rceil_{c}=\left\{ \begin{array}{ll}0,&y_{PAM,n}\geq 0\\ y_{PAM,n},&y_{PAM,n}<0\end{array} \right.. \tag{8}\]  
Similar to the HACO-OFDM scheme, the ACO-OFDM symbols in our DCHO-OFDM are allocated to the odd-indexed subcarriers, where the PAM-DMT symbols are carried by the imaginary proportion of the even-indexed subcarriers, as shown in (1) and (3). On the contrary, the ACO-OFDM branch in the proposed DCHO-OFDM scheme is designed to remain unclipped, yielding even-indexed subcarriers that are free of clipping noise contamination. According to [27], the clipping distortion generated by the down-clipped PAM-DMT is imposed only on the real-part of the even-indexed subcarriers. Furthermore, upon the analysis provided in Appendix A, the clipping distortion caused by the upper-clipped PAM-DMT is also encountered only by the real-portion of the even-indexed subcarriers. Therefore, it implies that the overall generated clipping distortion in DCHO-OFDM of either the combined signal \(s_{n}^{\text{on}}\) or \(s_{n}^{\text{off}}\) is orthogonal to the information-carrying subcarriers, which is demonstrated in Figure 1b. As a benefit, the bipolar signal of \(s_{n}^{\text{on}}\) and \(s_{n}^{\text{off}}\) can be obtained in an interference-orthogonal way. Furthermore, in HACO-OFDM scheme, the clipped ACO-OFDM and PAM-DMT branch are superposed directly, which leads to a higher amplitude since the both components are non-negative. In contrast, by superposing the bipolar ACO-OFDM and the unipolar PAM-DMT signal, a lower peak-to-average-power-ratio (PAPR) can be expected, compared to that of the conventional HACO-OFDM. The hybrid signal in Equation (7) has double-sided polarity, as seen in Figure 2a,b. In order to incorporate the PWM signal, it has to be converted to the unipolar signal. To tackle this issue, we introduce a time-varying biasing scheme based on the Proposition 1, which converts the the bipolar signal of \(s_{n}^{\text{on}}\) and \(s_{n}^{\text{off}}\) to negative-valued and positive-valued signals for the ON and OFF states, respectively. Moreover, the time-varying bias does not induce any additional interference imposed on the legitimate transmitted symbols. To be specific, the Proposition 1 is exhibited as follows. **Proposition 1**.