# A Novel OFDM Format and a Machine Learning Based Dimming Control for LiFi
## 4 Analysis of DC Bias for DPO  
In this section, we analyze the DC bias termed as \(I_{Bias}\) for DPO. This is an extension of the concepts that are described in [5; 15]. Here, \(I_{Bias}\) is defined as the bias to make unipolar signals from the composite signals. Now, if the root mean square (RMS) of the unclipped  
Figure 2: DC-biased pulse amplitude modulated orthogonal frequency division multiplexing (DPO-OFDM) receiver transforms the optical signal into electrical and then separates the dc-biased optical OFDM (DCO-OFDM) and pulse amplitude modulated discrete multitone (PAM-DMT) components. Note that Rcv stands for received, while A/D, CP, S/P and IFFT stand for analog-to-digital, cyclic prefix, serial-to-parallel, and inverse fast Fourier transform.  
DCO and PAM-DMT are labeled as \(\sigma_{DCO}\) and \(\sigma_{PAM}\), respectively, then we can write the average amplitude of the DPO signal as  
\[I_{D}=\frac{\sigma_{DCO}}{\sqrt{2\pi}}+\frac{\sigma_{PAM}}{\sqrt{2\pi}}+I_{Bias} \tag{9}\]  
The scaling factor of DCO is expressed as \(\beta_{DCO}=\frac{I_{H}-I_{Bias}}{\sigma_{DCO}}\). Similarly, the scaling factor of PAM-DMT is \(\beta_{PAM}=\frac{I_{H}-I_{Bias}}{\sigma_{DCO}}\). In both cases, \(I_{H}\) and \(I_{L}\) are the maximum value and the minimum value of the signal constrained by LED. Furthermore, the dimming level, \(\eta\), is defined by,  
\[\eta=\frac{I_{D}-I_{Bias}}{I_{H}-I_{L}} \tag{10}\]  
The optical intensity or brightness will be higher depending on the higher dimming level. The expression (10) can be written as  
\[I_{D}=I_{L}(1-\eta)+\eta I_{H} \tag{11}\]  
By rearranging (9), we obtain the following expressions:  
\[I_{Bias}=I_{D}-\frac{\sigma_{DCO}}{\sqrt{2\pi}}-\frac{\sigma_{PAM}}{\sqrt{2\pi}} \tag{12}\]  
\[I_{Bias}=I_{D}-\frac{I_{H}-I_{Bias}}{\sqrt{2\pi}\beta_{DCO}}-\frac{I_{H}-I_{Bias} }{\sqrt{2\pi}\beta_{PAM}} \tag{13}\]  
Using the value of root mean square as \(\sigma_{DCO}\) and \(\sigma_{PAM}\), we can finally express \(I_{Bias}\) as,  
\[I_{Bias}=\frac{\{I_{L}-\pi(I_{L}-I_{Bias})\sqrt{2\pi}\beta_{DCO}\beta_{PAM}-I_ {H}\beta_{DCO}-I_{H}\beta_{PAM}}}{\sqrt{2\pi}\beta_{DCO}\beta_{PAM}-\beta_{ DCO}-\beta_{PAM}} \tag{14}\]  
Therefore, \(I_{Bias}\) depends on the scaling factor of the individual components of the technique and \(I_{L}\) and \(I_{H}\). It is a complex function, and by varying the value of \(I_{Bias}\), different dimming levels are obtained.  
The dimming levels versus bias values are plotted in Figure 3 using (14) with \(I_{H}=1\) and \(I_{L}=0\), following the concept of [5,15]. It illustrates the plots of \(I_{Bias}\) versus \(\eta\) for different scaling factors. It is observed that with the increase in the scaling factor, a wider dimming range can be obtained. It can be shown that a wide dimming range can be obtained for the case of larger values of a scaling factor. Since the level of the average amplitude of the combined signal is higher than the DC bias, with the increment of DC bias, the dimming level increases. The combined signal suffers slightly at low and high dimming levels due to DCO element clipping.  
Figure 3: Dimming level, \(\eta\), versus bias, \(I_{Bias}\), values in dc-biased pulse amplitude modulated orthogonal frequency division multiplexing (DPO-OFDM), where \(\beta\) terms represent scaling factors.