# The Utilization of Artificial Neural Network Equalizer in Optical Camera Communications +
## 2 Constant Power-PAM in RS-Based OCC System  
The OCC system is mainly composed of a light source-based Tx with normalized length (diameter) represented in \(L\), and a camera-based Rx, which is modeled using a single convex lens with a focal length \(f\). The transmission speed in the RS-based OCC system is defined by the amount of the information that can be captured by an image at the distance \(d\), which depends on the acquired number of samples (i.e., pixel rows) and is given by [32]:  
\[N_{\text{row}}=2\;f\times tan\left(\frac{\text{FoV}}{2}\right)=2\;f\times\frac {L}{2d}\;, \tag{1}\]  
where FoV is the angular field of view. Note that the acquired \(N_{\text{row}}\) is incorporated with the sampling frequency of the IS, known as the rolling rate of IS, \(F_{s}\) (i.e., the frequency at which the row pixels are sampled at the image plane). Therefore, the maximum frequency of the transmitted signal is limited \(\frac{F_{s}}{2}\) according to [PERSON]'s theorem. The \(F_{s}\) value depends on the pixel clock and \(T_{\text{exp}}\) (i.e., the time that every sample (pixel) of the IS is exposed to the light). Note, \(T_{\text{exp}}\) acts as a moving-average filter [10; 33] with the frequency resolution given by:  
\[\Delta f=\frac{1}{T_{\text{exp}}}=\frac{F_{s}}{N_{\text{row}}(d)}\;, \tag{2}\]  
\(F_{s}\) is defined in terms of the bandwidth of the transmitted signal \(f_{\text{Tx}}\) and the number of received pixels per symbol, \(N_{\text{pps}}\), which is given by:  
\[F_{s}=N_{\text{pps}}\;.\;\;f_{\text{Tx}}\;, \tag{3}\]  
Note, (_i_) \(N_{\text{pps}}\) varies with the payload \(P_{\text{bit}}\); and (_ii_) the maximum transmission distance is proportional to both \(\Delta f\) and the size (diameter) of the light source. Higher \(T_{\text{exp}}\) resultsin increased signal intensity levels, and, therefore, higher signal-to-noise-ratio (SNR) at the cost of reduced Rx bandwidth. With reference to Equations (1)-(3), a communications link can be established at low \(R_{g}\) but with flickering, which is due to the variation in the mean value of light intensity during a time period larger than the optical bandwidth of the human eye. This may occur provided there are many consecutive symbols with the same logical state. The flicker index is a relative measure of the cyclic variation in the output of various sources at given frequencies [34; 35]. It considers the waveform of the light output and its amplitude, which can be determined by dividing the area above the line of average light output by the total area under the light output curve for a single curve, see Figure 1, and is given by:  
\[\text{Flicker index}=\frac{\text{area 1}}{\text{area 1}+\text{area 2}}\,, \tag{4}\]  
The flicker index has a range of 0 to 1.0, with 0 representing the steady light output level. Area 2 may be close to zero provided the light output varies as periodic spikes, thus leading to a flickering index close to 1. Higher values indicate an increased possibility of noticeable flickering. To mitigate flickering, CP-PAM can be adopted to equalize the mean intensity value of all symbols, i.e., \(I_{\text{ave}}\)[18]. In CP-PAM, each PAM symbol is temporally divided into two equal chips, (_i_) the 1 st chip for the intensity of the PAM symbol \(I_{S}\); and (_ii_) the 2 nd chip for the stabilization level, i.e., \(2I_{\text{ave}}-I_{S}\), see Figure 2. For example, a symbol with a level of \"2\" will be stabilized in the following chip with another symbol with a level of \"1\" to ensure performance equality, as clarified in Table 1. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Input Data**} & \multirow{2}{*}{**Conventional PAM Level**} & \multicolumn{3}{c}{**Constant Power 4-PAM**} \\ \cline{3-4}  & & **First Level** & **Stabilization Level** \\  & & **(\(I_{S}\))** & **(\(2I_{\text{ave}}-I_{S}\))** \\ \hline
11 & 3 & 3 & 0 \\
10 & 2 & 2 & 1 \\
01 & 1 & 1 & 2 \\
00 & 0 & 0 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Proposed CP 4-PAM levels. Figure 1: Defining Flicker Index [34; 35].