# Optical-OFDM VLC System: Peak-to-Average Power Ratio Enhancement and Performance Evaluation
## 4 PAPR Reduction Methodology and Proposed Model
### Proposed PAPR Reduction System
\(x_{avg}=\) mean\(\Big{(}\big{|}x_{cp}\big{|}^{2}\Big{)}\), Average power calculation
38. \(PAPR=\) 10 * \(log_{10}\Big{(}x_{peak}/x_{avg}\Big{)}\), PAPR calculation
39. \(TX=\) [ \(TX\ x_{cp}\)] ; \(\rightarrow\) Transmitted signal
40. \(PAPR_{TOTAL}=\) [ \(PAPR_{TOTAL}\ PAPR\)]; \(\rightarrow\) PAPR for the transmitted signal
41. endfor
42. [cdf, \(\text{papr}\)] = **ecdf**(\(PAPR_{TOTAL}\)); \(\rightarrow\) Calculate the complementary cumulative distribution function

## 5 Simulation Results and Discussion

In this part, we delve into the numerical simulations and outcomes concerning the multiple O-OFDM approaches designed for VLC communication systems, incorporating the novel precoding technique known as VLM. The received time-domain signal after using one of the previously mentioned approaches can described as follows [8]:

\[y=gx_{OOFDM}+n, \tag{37}\]

where \(y\) is the received time-domain signal, \(x_{OOFDM}\) is the transmitted time-domain signal, and \(g\) is the total channel gain, which can be described as \(g=\eta Rh\); \(\eta\) is the electrical-to-optical efficiency of the LED. \(R\) is the responsivity of the photodetector (PD), and h is the optical channel gain, which is expressed as follows [53]:

\[h=\frac{(m+1)A\ T(\psi)\ g(\psi)}{2\pi d^{2}}\ cos^{m}(\varphi)cos(\psi), \tag{38}\]

where \(m\) is the Lambertian emission order, and \(A\) is the photodetector area. \(T(\psi)\) is the optical filter gain, and \(g(\psi)=r^{2}/sin^{2}(\psi)\) is the gain of the optical concentrator with a refractive index \(r\). \(\psi\) and \(\phi\) denote the incident and emission angles, respectively. d is the distance between the transmitter and the receiver. The Lambertian order m can be calculated by

\[m=\frac{-1}{log_{2}(cos\phi_{1/2})}\, \tag{39}\]where \(\phi_{1/2}\) is the half power angle of LED. The noise \(n\) follows the following Gaussian probability distribution function [15]:

\[p(n)=\frac{1}{\sqrt{2\pi\sigma^{2}}}exp\left(\frac{-(n-\mu)^{2}}{2\sigma^{2}} \right), \tag{40}\]

where \(\mu\) and \(\sigma^{2}\) are the mean and the variance, respectively. Here, we assume \(\mu=0\) and \(\sigma^{2}=N_{0}/2\), and we assume that \(g\) is known at the receiver. Hence, the received symbol after equalization is:

\[\widetilde{y}=x_{OOFDM}+\widetilde{n}, \tag{41}\]

where \(\widetilde{n}=n/g\) is the additive Gaussian noise scaled by the total channel gain. To simplify the notation, we let \(\widetilde{y}\) denote the equalized received symbol in the simulation results. Therefore, the simulation results are obtained by assuming the communication channel is the AWGN channel as [2; 3; 9; 16; 18; 20; 22; 24; 41; 42; 48; 49; 51]. We have employed the O-OFDM approaches mentioned earlier using Matlab R2016b (9.1) software. Our simulations adhere to the parameters outlined in Table 5, with the AWGN channel serving as the communication medium between the sender and recipient. To evaluate the influence of modulation on system performance, we analyzed the simulation results for several constellation orders. For DCO and ADO-OFDM systems, DC-biasing levels of 7, 10, and 13 dB were utilized in the simulation to assess the impact of DC biasing on system performance. We began by examining the BER and PAPR performance of these O-OFDM schemes, comparing them under identical constellation orders. Subsequently, we extended our analysis to compare their performance at the same SE. ### Exploring BER and PAPR for DCO-OFDM

The BER of the DCO-OFDM system is evaluated and depicted in Figure 11a. When examining constellation sizes of 4-QAM and 16-QAM, it becomes clear that the 10 dB and 13 dB DC bias levels consistently demonstrated poorer BER performance than the 7 dB DC bias level. However, for higher constellation sizes, it is worth noting that the 10 dB and 13 dB DC bias levels delivered improved BER performance compared to the 7 dB DC bias level. Upon comprehensive analysis of the results, it is evident that the 10 dB DC bias level consistently outperformed the 13 dB level across the 16, 64, and 256 modulation orders.