# Optical-OFDM VLC System: Peak-to-Average Power Ratio Enhancement and Performance Evaluation
## 2 Multicarrier Modulation Schemes Based on the VLC System
### Asco-Ofdm  
Figure 5 depicts the framework of the ASCO-OFDM scheme. It involves mapping \(S(W)\) symbols, where \(W\) is the interval from 1 to \(\frac{3N}{4}-1\). To ensure the generation of a real signal, it is necessary to establish H.S for \(S(W)\) symbols. The H.S signal is divided into \(X_{ACO,I}\) (\(K\)), \(X_{ACO,J}(K)\), and \(X_{E}(K)\) prior to the IFFT operation. \(X_{ACO,I}\) (\(K\)) and \(X_{ACOJ}(K)\) with size N consisting of \(\frac{N}{4}\) complex symbol (CS) and their complex conjugate (CC), located only in the odd subcarriers, are integrated with zero values into the even subcarriers. \(X_{E}(K)\) with size \(N\) consisting of \(\frac{N}{4}-1\) CS and their CC, located in the even subcarriers, are integrated with zero values into the odd subcarriers. \(X_{ACO,I}\) (\(K\)), \(X_{ACO,J}(K)\) and \(X_{E}(K)\) are as designated in Equations (17)-(19), respectively. They undergo processing using an IFFT process to generate real bipolar \(x_{ACO,I}(n)\), \(x_{ACO,j}(n)\), and \(x_{E}(n)\) signals, respectively [22]:  
\[X_{ACO,I}\ (K)=\big{[}0,\ S_{1},\ 0,\ S_{2},\ \ldots\ldots,\ 0,\ S_{N/4},\ 0,\ S_{N/4}^{*},\ 0,\ \ldots\ldots,\ S_{2}^{*},\ 0,\ S_{1}^{*}\big{]}, \tag{17}\]  
\[X_{ACO,J}(K)=\Big{[}0,\ S_{\frac{N}{4}+1},\ 0,\ S_{\frac{N}{4}+2},\ \ldots\ldots,\ 0,\ S_{N/2},\ 0,\ S_{N/2}^{*},\ 0,\ \ldots\ldots,\ S_{\frac{N}{4}+2}^{*},\ 0,\ S_{\frac{N}{4}+1}^{*}\big{]}, \tag{18}\]  
\[X_{E}(K)=\Big{[}0,\ 0,\ S_{\frac{N}{2}+1},\ 0,\ S_{\frac{N}{2}+2},\ \ldots\ldots,\ S_{\frac{3N}{4}-1},\ 0,\ 0,\ 0,\ S_{\frac{3N}{4}-1}^{*},\ldots\ldots,\ S_{\frac{3N}{4}+2}^{*},\ 0,\ S_{\frac{3N}{4}+1}^{*},\ 0\Big{]}, \tag{19}\]  
Figure 4: ADO-OFDM block diagram based on a VLC system.  
To fulfill the non-negative signal requirement, any negative values within \(x_{ACO,I}(n)\) and \(x_{ACO,j}(n)\) are clipped to zero, yielding \(x_{ACO,I,C}(n)\), and \(x_{ACO,J,C}(n)\) as described below [21]:  
\[x_{ACO,I,C}(n)=0.5(x_{ACO,I}(n)+|x_{ACO,I}(n)|), \tag{20}\]  
\[x_{ACO,J,C}(n)=0.5(x_{ACO,I}(n)+|x_{ACO,I}(n)|), \tag{21}\]  
When eliminating the negative samples in \(x_{E}(n)\) through clipping, half of the information originally carried in \(x_{even}(n)\) is forfeited, as there is no relationship between \(x_{E}(n)\) and \(x_{E}(n+N/2)\). Consequently, \(x_{E}(n)\) divides into \(x_{E,p}(n)\) and \(x_{E,n}(n)\). \(x_{E,p}(n)\) and \(x_{E,n}(n)\) are formed to transmit the bipolar samples of \(x_{E}(n)\). Specifically, \(x_{E,p}(n)\) represents the scenario where all the negative values within \(x_{E}(n)\) are clipped to zero. \(x_{E,n}(n)\) depicts the case where all the positive values in \(x_{E}(n)\) are clipped to zero, and the remaining negative values are transformed into positive values. They can be expressed as follows [18]:  
\[x_{E,p}(n)=0.5(x_{E}(n)+|x_{E}(n)|), \tag{22}\]  
\[x_{E,n}(n)=0.5(-x_{E}(n)+|x_{E}(n)|), \tag{23}\]  
Therefore, ASCO-OFDM uses two consecutive segments for data transmission, denoted as \(x_{ASCO,I}(n)\) and \(x_{ASCO,J}(n)\), and they can be expressed as follows:  
\[x_{ASCO,I}(n)=x_{ACO,I,C}(n)+x_{E,p}(n)=0.5(x_{ACO,I}(n)+|x_{ACO,I}(n)|+x_{E} (n)+|x_{E}(n)|), \tag{24}\]  
\[x_{ASCO,J}(n)=x_{ACO,I,C}(n)+x_{E,n}(n)=0.5\big{(}x_{ACO,J}(n)+|x_{ACO,J}(n) \big{|}-x_{E}(n)+|x_{E}(n)|\big{)}, \tag{25}\]  
The transmitted signals, \(x_{ASCO,I}(n)\) and \(x_{ASCO,J}(n)\), are concatenated as denoted \(x_{ASCO,I\&j}(n)\), equipped with cyclic prefixes, represented as \(x_{cp}(n+c)\). This signal is transmitted via LED. Upon reception, they undergo processing through an inverse procedure, mirroring the operation carried out at the transmitter [18].