# A Novel Ranging Technique Based on Optical Camera Communications and Time Difference of Arrival
## 4 System Performance and Constraints
However, in both cases (RS and GS), the transmitted information is contained within the projection of the light source on the image sensor. The lamp's spot size in the captured image depends on the actual lamp's size and the distance between lamp and camera. Figure 6 depicts the geometric diagram. \(d\) is the distance between lamp and camera, \(H\) and \(A\) are the actual lamp's dimensions and \(D_{y}\) and \(D_{x}\) are the vertical and horizontal lamp's dimensions in the camera's image (in pixels). \(N_{y}\) and \(N_{x}\) are the total image's size in pixels. \(\Theta_{LY}\) and \(\Theta_{LX}\) are the angles from the camera position corresponding \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Format**} & \multirow{2}{*}{**Resolution**} & \multirow{2}{*}{**Lines**} & **Frame Rate (fps)** & **Sampling Frequency (kHz)** & **Time Resolution (μs)** & \(d_{min}\) & \(d_{max}\) \\ \cline{3-8}  & & & 480 & 25 & 12 & 83.33 & 28.58 & 13.72 \\ \cline{3-8} VGA & \multirow{2}{*}{640 \(\times\) 480} & \multirow{2}{*}{480} & \multirow{2}{*}{50} & \multirow{2}{*}{24} & \multirow{2}{*}{41.67} & \multirow{2}{*}{14.29} & \multirow{2}{*}{6.86} \\ \cline{3-8}  & & & 480 & 50 & 24 & 41.67 & 14.29 & 6.86 \\ \hline Standard & \multirow{2}{*}{768 \(\times\) 576} & \multirow{2}{*}{576} & \multirow{2}{*}{25} & \multirow{2}{*}{14.4} & \multirow{2}{*}{69.44} & \multirow{2}{*}{23.82} & \multirow{2}{*}{13.76} \\ Definition (SD) & & & & & & & \\ \hline \multirow{2}{*}{High Definition(HD)} & \multirow{2}{*}{1280 \(\times\) 720} & \multirow{2}{*}{720} & \multirow{2}{*}{50} & \multirow{2}{*}{36} & \multirow{2}{*}{27.78} & \multirow{2}{*}{9.53} & \multirow{2}{*}{6.86} \\ \cline{3-8}  & & & & & & & \\ \hline Full HD & 1920 \(\times\) 1080 p & 1080 & 25 & 27 & 37.04 & 12.70 & 13.72 \\ \hline Ultra HD & 3840 \(\times\) 2160 & 2160 & 25 & 54 & 18.52 & 6.35 & 13.72 \\ \hline Full Dome & 4096 \(\times\) 4096 & 4096 & 30 & 122.88 & 8.14 & 2.79 & 11.48 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Resolution and range for different video formats. Figure 5: Different illuminated areas corresponding to different distances. (a) short distance; (b) medium distance; (c) long distance. to the vertical and horizontal edges of the lamp, and \(FOV_{v}\) and \(FOV_{h}\) are the camera's vertical and horizontal Fields of View, which determine the limits of the area scanned by the camera. Therefore, in the case of RS, the amount of data that can be transmitted within each frame time depends on the source's height in the image. Concretely, to make the data retrievable by the OCC receiver, the maximum number of rows the transmitted packet can occupy on the picture must satisfy the restriction of Equation (3). \[f_{frame}\cdot N_{y}\cdot T_{packet}\leq\frac{D_{y}}{2} \tag{3}\]  
where \(T_{packet}\) is the packet duration. Furthermore, since there is no synchronization between the image sensor and the light source, the receiver must capture at least two frames per packet and, hence, the emitter must repeat its transmission at least once during that two frames. In the case of the proposed ranging system, the latter restriction can be reformulated since the \"packet\" is symmetrical and only comprises the pulse duration and a guard time \(T_{guard}\), which separates the transmitted pulses. Since the objective of the measurement system is to estimate the pulse duration (which is directly related to distance), the lamp's image size must allocate at least two pulses and one guard time for error-free measurement, yielding to Equation (4). The value of \(T_{guard}\) must ensure that the packet is entirely allocated within the lamp's projection. Furthermore, this guard time must be long enough to allow correct pulse duration estimation. High \(T_{guard}\) values allow easy pulse discrimination but reduce the error-free measurement range since the packet would not fit into the source's image for longer distances.