## 2 System Description  
The system model considered for this work is illustrated in Figure 1. First, a random bit stream is generated and encoded into complex-valued quadrature amplitude modulation (QAM) symbols \(X[m]\) for \(m=1,2,\ldots,\frac{N}{2}-1\) is the active subcarriers index in the OFDM frame, where \(N\) is the OFDM frame size. The number of bits, \(b\), that are mapped on each \(M\)-QAM symbol is given by \(b=\log_{2}(M)\). The conventional OFDM waveform is complex and bipolar. However, the transmission mechanism in the optical wireless communication system is intensity modulation with direct detection (IM/DD), which requires a real and positive waveform. This requirement is met by imposing Hermitian symmetry on the OFDM frame in the frequency domain, \(X[m]=X^{*}[N-m]\). The OFDM frame in the frequency domain is given by [16]:  
\[X[k]=\left[0,X_{1},\ldots,X_{\frac{N}{2}-1},0,X_{\frac{N}{2}-1}^{*},\ldots,X_{1 }^{*}\right] \tag{1}\]  
where \(k\) is the subcarrier index with size \(N\) and \(X[0]=X[N/2]=0\). The utilisation factor for the OFDM frame's double-sided bandwidth \(B\) is defined by \(G_{\text{B}}\) which is given as: \(G_{\text{B}}=(N-2)/N\). The total number of enabled subcarriers on the OFDM frame is \(G_{\text{B}}\times N\). The OFDM frame activates all subcarriers which can enable the different modulation format, \(M\), across the OFDM frame. The average electrical power of the \(M\)-QAM symbol, \(P_{\text{s(elec)}}=P_{\text{b(elec)}}\times\log_{2}(M)\), where \(P_{\text{b(elec)}}\) is the average electrical power per bit of the \(M\)-QAM symbol. The high PAPR peaks of the time-domain signal are reduced using PA technique by rotating the phase of \(X[k]\) prior to the inverse fast Fourier transform (IFFT) process, as detailed in Section 3. The \(X[k]\) symbols are then modulated into orthogonal subcarriers by applying an IFFT of size \(N\) to obtain a discrete time-domain signal \(x[n]\) as follows  
\[x[n]=\frac{1}{\sqrt{N}}\sum_{k=0}^{N-1}X[k]\;e^{j2\pi\frac{ln}{N}}\;;\qquad \quad 0\leq n\leq N-1 \tag{2}\]  
where \(j=\sqrt{(-1)}\). In general, a cyclic prefix (CP) is added to the OFDM-based systems to mitigate inter-carrier interference (ICI) and ISI. This is performed by copying the last few samples of the OFDM frame to the beginning of that frame. The CP length, \(N_{\text{CP}}\), must be greater than the channel delay spread to mitigate ISI, and hence, the frame length becomes (\(N+N_{\text{CP}}\)) [17]. For simplicity, the CP is omitted in this work, as it has negligible effects on the electrical SNR, spectral efficiency, and electrical PAPR values of the system [5]. The discrete time-domain signal \(x[n]\) is approximately Gaussian distributed with zero mean and a variance of \(\sigma_{x}^{2}\) according to the central limit theorem (CLT) [18]. The average electrical power of the time domain signal \(x[n]\) is proportional to its variance, \(\sigma_{x}^{2}\)[19]. Therefore, to achieve a specific SNR, \(x[n]\) should be scaled properly in relation with \(\sigma_{x}^{2}\)[8]. Hence, the signal is scaled by a factor, \(\alpha\), to produce a specific \(\sigma_{x_{\text{scaled}}}^{2}\) of the scaled signal \(x_{\text{scaled}}[n]\). The variance, \(\sigma_{x_{\text{scaled}}}^{2}\), of the scaled signal is given as follows  
Figure 1: Block diagram of the PA DCO-OFDM-based VLC system. H/S: Hermitian symmetry; P/S: Parallel-to-serial conversion; S/P: Serial-to-parallel conversion. \[\sigma_{x_{\rm scaled}}^{2}=\alpha^{2}\times\sigma_{x}^{2} \tag{3}\]  
Light sources such as LEDs have a limited dynamic range between [\(i_{\rm min},~{}i_{\rm max}\)], corresponding to minimum and maximum current points, respectively.