# Flickering-Free Distance-Independent Modulation Scheme for OCC
## 3 Theoretical Description of the Proposed Modulation
### Wake up Process
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**State** & \(\mu_{ROI(a)}\) & \(\sigma_{ROI(a)}\) & \(\mu_{ROI(b)}\) & \(\sigma_{ROI(b)}\) & \(\mu_{ROI(c)}\) & \(\sigma_{ROI(c)}\) \\ \hline Waiting & 223.87 & 4.22 & 252.52 & 4.26 & 168.95 & 4.66 \\ Transmitting & 208.39 & 18.76 & 231.43 & 27.28 & 120.74 & 55.93 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Waking up examples from transmissions shown in Figure 6. The case (a) corresponds to gray-scale images of \(640\times 480\) taken in a room with the light turned on. For the case (b), the camera acquired color images of \(1280\times 720\) with default characteristics in a room where the light was turned off. In the last case (c), the camera’s settings were high contrast, low brightness, and low exposure time for \(1280\times 720\) color images taken in a room with the light turned off. For this particular explanation, illustrated in Figure 8, the number of consecutive frames used to represent each symbol was set to three (\(m=3\)), therefore \(t_{symbol}=3T_{\text{CAM}}\). In the same way, the first transmitted symbol corresponds to the perfectly correlated frequency (\(f_{\text{SW}}=\alpha f_{\text{CAM}}\)). In the first case (Figure 8a), the emission began previous to the emitter's signal acquisition by the receiver, therefore the 2D standard deviation of the ROI in the first frame, \(F_{1}\), is bigger than the defined threshold (\(\sigma_{F_{1}}>3\%\)) and the transmission is detected on that frame. The ROIs extracted from \(F_{1}\), \(F_{2}\), and \(F_{3}\) are stored for demodulation. The data can be obtained without problem from those images, the calculated average PCC of the three stored ROI is equal to one (\(PCC(F_{1},F_{2})=PCC(F_{2},F_{3})=1\implies\overline{PCC}=1\)), so the symbol is perfectly identified. In the second case (Figure 8b), the emission started after the emitter's acquisition, therefore the 2D standard deviation of the ROI from frame \(F_{1}\) is lower than the defined threshold (\(\sigma_{F_{1}}<3\%\)) and the transmission is not detected on that frame. However, the calculated 2D standard deviation of frame \(F_{2}\) is bigger than the threshold (\(\sigma_{F_{2}}>3\%\)) and the transmission is detected on the second frame. Since each symbol is emitted for three times the frames' acquisition period (\(3T_{\text{CAM}}\)), the ROIs extracted from \(F_{2}\), \(F_{3}\) and \(F_{4}\) are stored for demodulation. The data can be obtained without problem from those images. The calculated average PCC of those three stored ROIs is equal to one (\(PCC(F_{2},F_{3})=PCC(F_{3},F_{4})=1\implies\overline{PCC}=1\)), so the symbol is perfectly identified. In these two scenarios, the information is successfully extracted from all the stored frames. Nevertheless, the third case (Figure 8c) is different. Since the transmission starts during the acquisition process, one part of the ROI from frame F1 has a wide bright strip. This band corresponds to the time previous to the data transmission, when the emitter is continuously turned on. Depending on the remaining acquisition time, there are two possibilities: the ROI has dark strips; or the ROI has only bright rows. In the first scenario, due to the presence of darker strips, the 2D standard deviation of the ROI is bigger than the threshold (\(\sigma_{F_{1}}>3\%\)) and the transmission is detected on this frame. The ROI extracted from \(F_{1}\), \(F_{2}\) and \(F_{3}\) should be stored for demodulation. Nevertheless, the data can not be appropriately obtained from those images. As seen in Figure 8c, the calculated PCC of the two first stored ROIs is positive and less than one (\(0<PCC(F_{1},F_{2})<1\)), so the symbol is wrongly identified, while the PCC of the remaining stored ROI is equal to one (\(PCC(F_{2},F_{3})=1\)) and the symbol is identified. The second scenario is similar to the case where the emission started after the emitter's acquisition.