## 5 Results and Discussion  
Although the efficacy of the PA technique is proven in [5], the aim here is to show that the presented analysis is valid for predicting the DCO-OFDM-based VLC performance in the presence of clipping noise and PAPR reduction with the PA technique. The performance of PA DCO-OFDM and conventional DCO-OFDM systems are compared in the presence of double-sided signal clipping under AWGN channel in terms of BER and as a function of electrical SNR. The analytical study is verified by simulation for both systems. The two systems are simulated using 4-QAM modulation format and IFFT/FFT size of 2048 with total number of active subcarriers, \(N_{\mathrm{subs}}=1023\). The optical path gain coefficient, the system bandwidth and the electrical-to-optical conversion coefficient, \(\beta\), are constrained to unity in order to prevent any possible noise addition to the system. The optical source is assumed to be an LED with a linear dynamic range between \(i_{\mathrm{min}}=5\) mA and \(i_{\mathrm{max}}=50\) mA, which is assumed to be the source of clipping noise [8]. No clipping at the receiver is assumed. The two systems are compared at an ideal case with no clipping introduced in addition to three clipping cases for analytical and simulation BER performance. In the three clipping cases, the clipping levels are calculated according to the amount of the added bias current, \(i_{\mathrm{bias}}\), to the transmitted signal and the LED's linear dynamic range where, \(i_{\mathrm{bias}}=9.8\) mA is selected as in [8]. Hence, the bipolar signal is pre-clipped prior to biasing process at bottom level, \(k_{\mathrm{b}}=i_{\mathrm{min}}-i_{\mathrm{bias}}\), and at the top level, \(k_{\mathrm{t}}=i_{\mathrm{max}}-i_{\mathrm{bias}}\). In the first case (case 1), both signals are clipped at the bottom level, \(k_{\mathrm{b}}=-4.8\) and at the top level, \(k_{\mathrm{t}}=40.2\). In the second case (case 2), the signals are clipped at \(k_{\mathrm{b}}=-3.8\) and \(k_{\mathrm{t}}=41.2\), whereas it is clipped at \(k_{\mathrm{b}}=-3\) and \(k_{\mathrm{t}}=42\) in the third case (case 3). These clipping levels are obtained by reducing the \(i_{\mathrm{bias}}\) which increases the lower clipping level. The data signal is generated, scaled, clipped, and biased in MATLAB as detailed in Section 2 to form the DCO-OFDM signal. In addition, the same data symbols with the same process and parameters are generated with the PAPR reduction algorithm using \(R=10\) iterations to generate the PA DCO-OFDM signal. This process is implemented to investigate the effect of reducing the high PAPR peaks of the signal on the system BER performance. Furthermore, the two signals are compared in terms of BER at the same scaling factor and biasing point for every clipping level. In addition, as a benchmark for comparison with existing results, the ideal case and case 1 for DCO-OFDM in [8] is selected, and signal scaling, biasing, and clipping levels are included. Hence, the average transmitted optical power \(P_{\mathrm{opt}}=10\) mW. In the ideal case where no clipping is introduced to the transmitted signals, the two systems have achieved identical BER performance, as illustrated in Figure 4a. In clipping case 1, the \(i_{\mathrm{bias}}\) is found to be 9.8 mA, and \(\sigma_{x_{\mathrm{scaled}}}=4.9\) mA for DCO-OFDM as obtained in [8]. Whereas, for PA DCO-OFDM, \(\sigma_{x_{\mathrm{scaled}}}=4.69\) mA at the same scaling factor \(\alpha\) and \(i_{\mathrm{bias}}\). This scaling and biasing setup yield the following normalised clipping levels. In DCO-OFDM, the normalised bottom clipping level \(k_{\mathrm{b}_{\mathrm{norm}}}=-0.98\), and the normalised top clipping level \(k_{\text{norm}}=8.2\). In PA DCO-OFDM, \(k_{\text{hom}}=-1.02\), and \(k_{\text{t}_{\text{norm}}}=8.57\). The analytical simulations of this case for the two systems are illustrated in Figure 4b. In the second case (case 2), the bias current is reduced to \(i_{\text{bias}}=8.8\) mA, which increases the lower clipping level, and hence, increases the clipping noise.