## 2 System Description
To efficiently utilise that dynamic range, the structure-specific signal pre-clipping has to be performed within the range [\(k_{\rm b}\), \(k_{\rm t}\)], which denotes the predefined bottom and top clipping levels, respectively, as shown in Figure 2. Then, the pre-clipped PA DCO-OFDM signal is biased to fit the linear dynamic range of the LED by a bias current, \(i_{\rm bias}\). The biasing process is employed to facilitate the minimal bottom and top levels signal clipping by placing the signal mean in the middle of the LED's linear dynamic region [8]. The pre-clipping levels can be defined as follows  
\[k_{\rm b}=i_{\rm min}-i_{\rm bias},\hskip 28.452756 ptk_{\rm t}=i_{\rm max}-i_{ \rm bias} \tag{4}\]  
In the zero signal clipping scenario, the signal clipping is defined as: \(k_{\rm b}=-\infty\), and \(k_{\rm t}=+\infty\). The clipping levels of the PA DCO-OFDM waveform can be negative and/or positive, as long as the two clipping levels are not equal, \(k_{\rm b}<k_{\rm t}\). In insufficient biasing scenarios, the signal is pre-clipped at the bottom level, \(k_{\rm b}\). Furthermore, the signal is pre-clipped at the top level, \(k_{\rm t}\). Therefore, the clipped signal \(x_{\rm clip}[n]\) can be expressed as follows:  
\[x_{\rm clip}[n]= \begin{cases}k_{\rm t}&\text{if}~{}~{}x_{\rm scaled}[n]\geq k _{\rm t},\\ x_{\rm scaled}[n]&\text{if}~{}~{}k_{\rm b}<x_{\rm scaled}[n]<k_{\rm t},\\ k_{\rm b}&\text{if}~{}~{}x_{\rm scaled}[n]\leq k_{\rm b}.\end{cases}  \tag{5}\]  
When an OFDM time-domain signal is clipped, it changes its mean, and as a result, its average optical power. To convert the electrical signal into an optical one and achieve maximum signal power, the linear dynamic range \(P_{\rm min}\) and \(P_{\rm max}\) should be mapped by the clipping levels, \(k_{\rm b}\) and \(k_{\rm t}\), as depicted in Figure 2. Hence, to form such a mapping, an input biasing power \(P_{\rm bias}=\beta\times i_{\rm bias}\), is required and can be expressed as  
\[P_{\rm min}=\beta(k_{\rm b}+i_{\rm bias}),\hskip 28.452756 ptP_{\rm max}=\beta(k_{ \rm t}+i_{\rm bias}) \tag{6}\]  
where \(\beta\) is the electrical-to-optical conversion coefficient. The clipped continuous time-domain waveform, \(x(t)\), is obtained from \(x_{\rm clip}[n]\) following the digital-to-analogue conversion (DAC) process to modulate the intensity of the optical source. In general, the entire forward voltage range across the LED is  
Figure 2: An illustration of the VLC optical source electrical signal to optical signal conversion. constant bias source which converts the bipolar time-domain baseband waveform to a unipolar signal. The bias current is combined with the data waveform current, producing the total forward current through the LED. Since the radiated optical power by the LED is proportional to the forward current, the data waveform, the bias current \(i_{\text{bias}}\), and the system constraints imposed by the front-end devices are described in terms of optical power [8]. Therefore, the average transmitted optical power from the LED is given as  
\[P_{\text{opt}}=\beta\times\text{E}[\text{x}(\text{t})]+\text{P}_{\text{bias}} \tag{7}\]  
The PA DCO-OFDM frame is assumed to be transmitted within the 3 dB bandwidth of the LED; hence, the optical channel is assumed flat over the entire transmitted OFDM frame. The signal is unlikely to be clipped at the receiver side. For example, the photodetector (PD) has a linear dynamic range much higher than that of the transmitter, which needs a very high amount of radiated power in order to drive the PD to its saturation region. At the receiver, a PD converts the received optical radiation into a current signal prior to the trans-impedance amplifier (TIA) which converts the current signal into the corresponding voltage. The voltage signal is then amplified to an appropriate level to obtain \(y(t)\) prior to the analogue to digital conversion (ADC) process.