## 2 Pseudo-Flicker Weight Functionalized Derivative Equalization in Li-Fi Transmission  
Figure 1 shows the concept of reducing 120 Hz flicker noise using the proposed technique. When the NRZ-OOK signal is injected into the LED driving circuit, the light from the white LED is simultaneously modulated by the flicker noise generated in the driving circuit and the NRZ-OOK signal. After the modulated LED light is transmitted wirelessly, the output signal, which is mixed 120 Hz flicker noise with NRZ-OOK signal, is produced at the photodetector. Here, since the frequency of the flicker noise is smaller than the maximum frequency of the NRZ-OOK signal, the flicker noise acts as an envelope and the NRZ-OOK signal is loaded on it. Therefore, as shown in the upper right of Figure 1, the intensity of the NRZ-OOK signal changes according to the change in the intensity of the flicker noise. In this case, the signal-to-noise ratio (SNR) of the NRZ-OOK signal may be reduced. We propose a pseudo-flicker weight functionalized derivative equalization technique to reduce the intensity of the flicker noise. The proposed technique reduces flicker noise through the following process. In the waveform of the NRZ-OOK signal mixed with flicker noise (flicker noised NRZ-OOK signal), the waveform of NRZ-OOK pulse corresponding to 0 (low) and 1 (high) is distorted according to the waveform of the flicker noise as shown in the bottom of Figure 1 (see the blue pulse). Here, if the waveform of the tilted NRZ-OOK pulse is recovered close to the input NRZ-OOK signal, the flicker noise can be reduced. At first, the absolute value of the derivative values between sampling points corresponding to the period of NRZ-OOK signal pulse (T\({}_{\text{p}}\)) is calculated to recover close to the input NRZ-OOK signal waveform. If the absolute difference between the calculated derivative values is greater than the preset threshold, the intensity of the corresponding sampling point is suppressed. This process is repeated until the absolute difference between derivative values becomes smaller than the preset threshold. The flicker noise reduction can be summarized as follows using mathematical equations. The NRZ-OOK symbol can be described as in Equation (1). \[s(i)=\sum_{k=1}^{N}B(k,i)g\Big{(}\frac{(t(i)-kT)}{T}\Big{)},g(\alpha)= \begin{cases} 1,&\text{\emph{for} }0\leq\alpha<1\\ 0,&\text{\emph{otherwise}}\end{cases}  \tag{1}\]  
where \(B(k,i)\) is a pseudo-random bit sequence (PRBS), \(g(\alpha)\) is an NRZ-OOK pulse. \(N\) is the total number of NRZ-OOK symbols. The flicker noise corresponding to the NRZ-OOK symbol can be expressed in the form of a sinusoidal function as in Equation (2). \[e(i)=C(i)exp(j2\pi f_{0}t(i)+\phi(i)) \tag{2}\]  
Figure 1: The 120 Hz flicker noise reduction using pseudo-flicker weight functionalized derivative equalization. where \(C(i)\) is an intensity of flicker noise at the sampling point of \(i\). \(M\) is the total number of sampling points for one symbol. \(N\) is the total number of NRZ-OOK symbols. \(f_{0}\) is the frequency of flicker noise. \(\phi(i)\) is a random phase uncorrelated for each \(i\), which is generated due to the use of the LED driving circuit. Next, the light from white LED, which is directly modulated by NRZ-OOK symbol and flicker noise, can be written as Equation (3). \[A_{s}(i)=(s(i)+e(i))\sum\
olimits_{m=-\prod_{0}}^{\prod_{0}}exp\{j(2\pi(\
u_{0} +m\delta\
u_{0})t(i)+\Phi(m)\} \tag{3}\]  
where \(\
u_{0}\) is the center optical frequency in the spectral region of white LED light. \(\delta\
u_{0}\) is the elemental frequency spacing of the white LED light. \(\Phi\) is random optical phase uncorrelated for each \(m\). When \(B_{0}\) is the total spectral width of white LED light, \(\prod_{0}\) is \(\frac{B_{0}}{2\pi\
u_{0}}\). When the modulated light is received at the photodetector, four different kinds of signals (NRZ-OOK signal, flicker noise, and two different shot noises) are generated.