# Optical-OFDM VLC System: Peak-to-Average Power Ratio Enhancement and Performance Evaluation
## 3 Assessment Criteria Employed to Judge the Effectiveness of MCM Approaches
### Data Arrangement and Spectral Efficiency  
The data arrangement preceding the H.S operation, necessary to yield a real bipolar signal after the IFFT process, varies from one MCM scheme to another, as shown in Figure 7. As a result, multiple MCM schemes, including those mentioned earlier, lead to differing output spectral efficiencies [35; 40]. DCO-OFDM employs a single IFFT in the transmitter and a single FFT in the receiver, utilizing a DC bias to transmit signals in a unipolar and real form via an LED. Notably, DCO-OFDM exhibited superior SE compared to other O-OFDM methods employed in VLC. The SE of this scheme is expressed in Table 1[41]. Here, M represents the modulation order, and N denotes the IFFT/FFT size utilized in the analysis. This heightened efficiency can be attributed to the symbol structure before its application to the IFFT, as indicated in the Figure 7. Furthermore, considering the symbol structure, it is evident that the data rate of DCO-OFDM was 50% compared to conventional OFDM used in RF communication systems. The ADO-OFDM symbol structure reveals that the data rate of this method matched that of the DCO-OFDM approach, indicating it as 50% of the data rate employed in conventional OFDM for RF communication systems, as mentioned in Figure 7 and Table 1. Here, \(M_{add}\) represents the modulation order used for the  
Figure 7: The modulated symbol distribution to the different O-OFDM schemes (for example, 32-IFFT size). odd subcarriers, and \(M_{even}\) represents the modulation order used for the even subcarriers in the ADO-OFDM system. ACO-OFDM and FLIP-OFDM had identical SEs. Furthermore, ACO-OFDM's data rate was 25% of that used in conventional OFDM for RF communication systems and was 50% lower than the data rate of DCO-OFDM, as shown in the Figure 6. Based on the earlier explanation of the symbol arrangement shown in Figure 7, the ASCO-OFDM spectral efficiency evidenced that the data rate of this method was 37.5% in comparison to conventional OFDM used in RF communication systems [42]. The ASCO-OFDM's SE formula is shown in Table 1. \(M_{odd,i}\) denotes the modulation order applied to the odd subcarriers in the first IFFT process, \(M_{odd,j}\) represents the M for the odd subcarriers in the second IFFT process, and \(M_{even}\) signifies the M for the even subcarriers in the third IFFT process [9]. The data rate of a single-layer LACO-OFDM matched that of ACO-OFDM. However, when we introduced an additional layer to create a two-layer LACO-OFDM, the data rate increased to match that of ASCO-OFDM, as illustrated in Table 1. Within this context, \(M_{1}\) represents the modulation order assigned to the odd subcarriers in the first IFFT process, \(M_{2}\) designates the modulation order for the specific even subcarriers in the second IFFT process, and N denotes the IFFT size employed in the analysis. With each subsequent increment in the number of layers, the data rate consistently met an increase. Generally, varying signal constellation sizes are employed across different layers, denoted as \(M_{l}-QAM\) in the \(l^{th}\) layer to adjust the overall SE, the SE of LACO-OFDM can be articulated as follows [19]:  
\[\gamma_{LACO,l}=\frac{\sum_{l=1}^{L}\frac{1}{2^{l}}log_{2}\left(M_{l}\right)} {1+\frac{2}{N}}\qquad\qquad\mathrm{bits}/\mathrm{s}/\mathrm{Hz}, \tag{29}\]  
As a conclusion, Table 1 and Figure 8 display the variations in SE as the M changes, with the FFT/IFFT size fixed at 1024 for the previously mentioned schemes. In this study, the authors observed that as the M increased, the SE also increased. Notably, the SE of DCO-OFDM and ADO-OFDM at 4-QAM matched the SE of ACO-OFDM and FLIP-OFDM at 16-QAM. Furthermore, the SE of ACO-OFDM and FLIP-OFDM at 64-QAM equalled the SE of ASCO-OFDM and two-layer LACO-OFDM at 16-QAM.