# Optical-OFDM VLC System: Peak-to-Average Power Ratio Enhancement and Performance Evaluation
## 2 Multicarrier Modulation Schemes Based on the VLC System  
### Dco-Ofdm  
In this depicted framework, located in Figure 1, the initial step at the transmitter involves the mapping of input serial data bits into complex modulated symbols utilizing either M-PSK or M-QAM mapper formats, denoted as \(S(W)\), where \(W\) ranges from 1 to \(\frac{N}{2}-1\). They subsequently convert from a serial to a parallel configuration of length (\(N\)/2-1) before being applied to the data organization block [22]. The organization block aims to arrange the input complex symbols into the Hermitian symmetry (H.S) format known as \(X(k)\), as detailed in (1). The formatted \(X(k)\) is then applied to the IFFT stage, where \({}^{\prime}k^{\prime}\) represents the subcarrier indices.  
\[X(k)=X^{*}(N-k),\ \ \ 1\leq k\leq N/2-1,\ \text{where}\ X(0)=X(N/2)=0, \tag{1}\]  
In this context, \({}^{\prime}k^{\prime}\) signifies the size of IFFT, and \((.)^{*}\) denotes the complex conjugate operator. Two different domains for notation exist in the context of the O-OFDM technique: the frequency domain (represented by capital indicators such as \(X(k)\)) and the time domain (represented by lowercase indicators such as \(x(n)\)). Subsequently, the output samples x(n) undergo serialization. In this framework, \(x(n)\) is first elevated using a DC-biasing shift, and then the real bipolar data samples are clipped to create unipolar samples, which are designated as \(x_{DC}(n)\). The related signal's root mean square value and the DC shift, \(F_{DC}\), are exactly proportional, as described in Equation (2) [9; 23].  
\[F_{DC}=A\sqrt{E(x^{2}(n))}, \tag{2}\]  
Here, A represents a proportionality constant, and the expectation or mean value of the signal is indicated by the symbol \(E(.)\). The proportionality constant (\(A\)) is calculated as shown in the equation \(\gamma_{DC}=10*\log_{10}\bigl{(}A^{2}+1\bigr{)}\mathrm{dB}\), where \(\gamma_{DC}\) is an arbitrary constant. Following the addition of the DC level, denoted as \(F_{DC}\), the final represented DC signal is denoted as \(x_{DC}(n)\)[24].  
\[x_{DC}(n)=x(n)+F_{DC}, \tag{3}\]  
Subsequently, a clipping operation can occur, leading to the introduction of a clipping noise component denoted as \(cnt_{DC}\), so  
\[x_{c}(n)=x_{DC}(n)+cn_{DC}, \tag{4}\]  
\[x_{c}(n)=x(n)+F_{DC}+cn_{DC}, \tag{5}\]  
Once the signal is clipped to obtain \(x_{c}(n)\), a CP can be appended before the broadcast through the channel. On the receiving side, an inverse operation is performed. Various biasing levels, such as 7, 10, and 13 dB, can be utilized in the DCO-OFDM system prior to the clipping process. The assessment of the DCO-OFDM system hinges on three key variables: the DC-biasing level utilized for the bipolar signal, the impact of clipping noise on the transmitted signal, and the optical power of the transmitted signal relative to the applied DC shift. A trade-off exists among these factors: when the DC shift is raised, clipped noise diminishes, while it results in an energy-inefficient communication system with excessive power dissipation [25].  
When employing high modulation orders, such as 512-QAM, and using low DC-biasing levels, such as 7 and 10 dB, the system's performance is notably subpar, with a high bit error rate of \(10^{-3}\) even for high SNR levels. However, the system performs better when employing the same high modulation order but with a higher DC shift of 13 dB. This improvement is attributable to the reduced impact of clipping noise, resulting in a lower BER of \(10^{-4}\) even for lower levels of SNR compared to the scenarios at 7 and 10 dB [13].