# Optical-OFDM VLC System: Peak-to-Average Power Ratio Enhancement and Performance Evaluation
## 4 PAPR Reduction Methodology and Proposed Model
### PAPR Reduction Methodology  
In this study, we introduced and explained VLM methodology as a precoding technique (PCT) [50]. This technique is employed to tackle the challenge of high PAPR in communication schemes, focusing on VLC systems using LED transmitters. The primary objective of VLM is to reconfigure the power distribution of the transmitted signal across both the frequency and time domains, aiming to minimise signal peaks and achieve a more uniform power distribution [3].  
The VLM methodology achieves this power redistribution by utilizing signal processing algorithms, including precoding matrices of dimensions \(N\times N\). This matrix is applied before the IFFT stage to alter the transmitted signal before sending it through the LED. These techniques carefully manipulate the signal characteristics to reduce PAPR and optimize power distribution [49].  
\[pc=\begin{bmatrix}p_{00}&p_{01}\dots\dots\dots\dots&p_{0(n-1)}\\ p_{10}&p_{11}\dots\dots\dots\dots&p_{1(n-1)}\\ \vdots&\vdots&\vdots\\ p_{(n-1)0}&p_{(n-1)1}\dots\dots\dots&p_{(n-1)(n-1)}\end{bmatrix}, \tag{35}\]  
Here, '\(pc\)' represents a precoding matrix with dimensions \(N\times N\). By redistributing power, the transmitted signal is guaranteed to stay within the LEDs' linear functioning range via the VLM methodology, avoiding the nonlinear region where distortion is more likely to occur. This approach enhances the overall signal quality and efficiently utilises the LED's power characteristics.  
The VLM technique plays a crucial role in preventing distortion and inefficiency in LED transmission by mitigating the presence of large signal peaks. This is of paramount importance because LEDs possess a limited dynamic range and may exhibit nonlinear behavior when operated near their maximum power levels. The reduction of significant signal peaks helps prevent nonlinear distortion and safeguards system performance [20].  
Through the adoption of the VLM method, VLC systems can effectively alleviate the negative consequences of high PAPR, including nonlinear distortion and inefficient LEDtransmission. This, in turn, leads to enhanced system performance, increased reliability, and improved spectral efficiency in VLC communication [51; 52].  
The VLM precoding technique is a newly utilized method in O-OFDM systems. It is employed to reduce the PAPR of the transmitted signal. By reducing the autocorrelation between the data, the VLM precoding technique helps mitigate the occurrence of high-power peaks in the transmitted signal. This contributes to a more efficient utilization of the power amplifiers and reduces the likelihood of distortion and nonlinear effects.  
Within the present study, the specific VLM matrix utilized is described in Equation (36). The structure and composition of this VLM matrix are specifically designed to achieve effective PAPR reduction in the mentioned O-OFDM systems [50].  
\[PC_{mn}=\sqrt{\frac{2}{N+1}}cos\bigg{(}\frac{2}{N+1}(m-1)(n-1)\bigg{)}\, \tag{36}\]  
where \(0\leq m,n\leq N-1\), the m\({}^{\text{th}}\) row index, \(n^{th}\) column index, and \(N\) represents the matrix size.  
The VLM precoding matrix is invertible. This means that using the inverse operation of this transformation, the original signal may be precisely recovered at the receiver side. The invertibility of this transform is a crucial property that allows for reliable signal reconstruction and decoding. It ensures that the information contained in the transformed domain may be reliably decoded and reconstructed in its original form.