## 2 Theoretical Fundaments  
Based on trigonometric relations and camera parameters, Equations (1) and (2) have been obtained. These equations estimate the 2D pixel projection (\(x\), \(y\)) in a picture of a real distance (\(d_{x}\), \(d_{y}\), \(D\)) in function of the separation between the object and the camera, the relative angle of the object (vertical or horizontal), and the camera's specific characteristics. \[x=\frac{1}{\varphi_{x}}\cdot\left[\left(tan^{-1}\frac{d_{x}sin\gamma}{2D-d_{x} cos\gamma}\right)+\left(tan^{-1}\frac{d_{x}sin\gamma}{2D+d_{x}cos\gamma} \right)\right] \tag{1}\]  
\[y=\left\{ \begin{array}{l}\frac{2}{\varphi_{y}}\cdot\left[tan^{-1}\frac{d_{y }}{2D+d_{x}cos\gamma}\right]\\ \frac{2}{\varphi_{y}}\cdot\left[tan^{-1}\frac{d_{y}}{2D-d_{x}cos\gamma}\right] \end{array} \right.\text{;Farthest elements} \tag{2}\]  
As shown in Figure 2, \(D\) is the distance between transmitter and receiver, \(d_{x}\) and \(d_{y}\) are the horizontal and vertical distances between the sources respectively, \(\gamma\) is the angle of the emitter-receiver vertical plane intersecting the emitter's normal plane, and \(\beta\) is the angle of the emitter-receiver horizontal plane intersecting the transmitter's normal plane. Finally, \(\varphi\) depends only on the receiver characteristics and relates the Field of View (FOV) and the resolution in pixels (\(N_{x,y}\)) of the selected camera. Figure 1: Wireless Sensor Network implementation using Optical Camera Communication (OCC) in an office (\(3\times 3\times 3\) m\({}^{3}\)). The receiver is a dome camera installed in the ceiling (height 3.00 m) with 90\({}^{\circ}\) Field of View (FOV). The sensor’s emitters are LED matrices (\(60\times 60\) mm\({}^{2}\)). Two sensors are located on the desk (height 0.80 m) and one sensor is over an autonomous robotic vacuum cleaner (height 0.10 m). For determining the optical interference, the relation between the pixels from the link transmission source and the pixels from one close emitter within the corresponding channel (related with the selected wavelength) was deduced. The communication system has two main blocks: the channel and the camera process, as can be observed in Figure 3, where \(P(\lambda)\) is the transmitted optical power spectrum; \(H(\lambda,0)\) is the channel gain; \(\alpha\) is a geometric correction factor for each light ray depending on how it fell on the lenses; \(R(\lambda)\) is the photodiode Silicon Responsivity; \(F_{\mathrm{S}}(\lambda)\) is the camera's Bayer Filter response over the channel of the source S; \(\tau\) is a nonlinear transformation due to the possible saturation from the analog/digital converter; and the image is the formed frame including all the sources. The light from any source X that arrives at the camera can be expressed as \(\int P_{X}(\lambda)H(\lambda,0)d\lambda\). First, the lenses will focus the light into the image sensor where each device has a Silicon Responsivity \(R(\lambda)\). Depending on the selected channel (Red, Green or Blue), the camera will use a Bayer Filter with response \(F_{\mathrm{S}}(\lambda)\) over the signal. Finally, the analog-to-digital converter (ADC) transforms the signal using the function \(\tau\{\cdot\}\). Therefore, in the obtained image the amount of pixels from a source X can be expressed by \(\alpha_{X}\cdot\tau\big{\{}\int P_{X}(\lambda)H(\lambda,0)R(\lambda)F_{ \mathrm{S}}(\lambda)d\lambda\big{\}}\). This Signal to Interference and Noise Ratio (SINR) depends only on the amount of pixels in the frame with information from multiple sources simultaneously. For this work, the worst case scenario is assumed, both light sources are transmitting simultaneously all the time. Obviously, since the camera's shutter speed defines the integration time of the image, and the two LEDs are turned on synchronously, the SINR is not affected by the camera's shutter speed.