# Optical-OFDM VLC System: Peak-to-Average Power Ratio Enhancement and Performance Evaluation
## 2 Multicarrier Modulation Schemes Based on the VLC System
### Laco-Ofdm  
LACO-OFDM's three-layer structure is depicted in Figure 6. The input signal \(S(W)\) was divided into the necessary number of layers after undergoing the H.S operation to achieve a predetermined output data rate. The overall composite signal was created by merging frames, each consisting of a defined number of symbols, each with a size of N. The signalling strategy in the first layer (\(L=1\)) closely emulated that of ACO-OFDM, as  
Figure 5: ASCO-OFDM block diagram based on a VLC system.  
elucidated in references [19; 34; 35]. This layer included N/4 CS, with their CC allocated in the odd subcarriers and integrated with zero in the even subcarriers, as represented in Equation (26).  
\[X_{ACO}\left(K\right)=\left[0,\,S_{1},\,0,\,S_{2},\,\,\ldots,\,0,\,S_{N/4},\,0, \,S_{N/4}^{*},\,0,\,\ldots\,\ldots,\,S_{2}^{*},\,0,\,S_{1}^{*}\right], \tag{26}\]  
In \(L=2,\,\,\,N/8\) CS with their CC are allocated to the even subcarriers and integrated with zero in the other subcarriers, as depicted in Equation (27).  
\[X_{SE,1}\left(K\right)=\left[0,0,\,S_{\frac{N}{4}+1},\,0,0,0,\,S_{\frac{N}{4}+ 2^{\prime}},\,\ldots\ldots,\,0,\,S_{\frac{N}{8}},\,0,0,0,\,S_{\frac{N}{8}}^{*},\,0,\ldots\ldots,\,S_{\frac{N}{8}+2^{\prime}},\,0,0,0,\,S_{\frac{N}{8}+1}^{*},0,0,0\right]\!. \tag{27}\]  
In \(L=3,\,N/16\) CS with their CC are assigned to the even subcarriers and zeros integrated into the residual subcarriers, as depicted in Equation (28).  
\[X_{SE,2}\left(K\right)=\left[0,0,0,0,\,S_{\frac{N}{4}+1},\,0,0,0,0,0,0,\,S_{ \frac{N}{8}+2^{\prime}},\,\ldots\ldots,\,0,\,S_{\frac{N}{8}},\,0,0,0,0,0,0,\,S_{ \frac{N}{8}+2^{\prime}}^{*},\,0,0,0,0,0,0,\,S_{\frac{N}{8}+1}^{*},0,0,0,0\right]\!. \tag{28}\]  
Generally, for \(L>1,\,\left(N/2^{L+1}\right)\) CC and their CS are transmitted on subcarriers \(2^{L-1}(2m+1)\), where \(m\) ranges from \(0\) to \(N/2^{L+1}-1\). Subsequently, the residual subcarriers are set to zero. \(X_{ACO}(K)\), \(X_{SE,1}(K)\), and \(X_{SE,2}(K)\) are transformed into the time domain using three IFFT stages, and the resulting signals are denoted as \(x_{ACO}(n)\), \(x_{SE,1}(n)\), and \(x_{SE,2}(n)\), respectively. The signals \(x_{ACO}(n)\), \(x_{SE,1}(n)\), and \(x_{SE,2}(n)\), after zero clipping, are combined for single-segment transmission before the addition of the CP, as depicted in Figure 6. In this scenario, applying clipping to the IFFT resulting signal of one layer can introduce distortion in the frequency domain for the subsequent layer [35].  
Therefore, in the data recovery at the receiver, a successive detection approach was employed, as outlined in [35], where symbols were reconstructed layer by layer from the received signal \(y(n)\), as illustrated in Figure 6. It is worth noting that for \(L=1\), the modulated symbols remained unaffected by distortion. The associated symbols, \(Y_{ACO}(k)\), can be directly identified, like in ACO-OFDM, as described in Section 2.2. These symbols were subsequently utilized in the second layer to eliminate the corresponding distortion before proceeding with signal detection for the \(L^{th}\) layer, following the procedure depicted in Figure 6. As previously explained, LACO, in contrast to ACO, simultaneously transmits  
Figure 6: Three-layered LACO-OFDM block diagram based on a VLC system.  
different layers, enabling the utilization of varying constellation sizes within each layer to attain a specified data rate. Consequently, it can achieve its target BER with a lower required SNR. In essence, LACO offers improved spectral efficiency and the added benefit of reducing PAPR [19].