## 2 VLC System Model
### Receptor  
To differentiate the sources (transmitters) of light beams entering the receiver, it is made up of three PDs, each of them equipped with a wavelength light beam filter corresponding to the wavelengths used by the transmitters. This dynamic is illustrated in Figure 2. It should be noted that for illustrative purposes, in Figure 2, the colors are used only to distinguish the light that a PD receives about a specific LED. Here, \(\psi_{i}\) represents the angle of light irradiation by the LED with respect to the location of the PD, \(\phi_{i}\) denotes the angle of incidence of light on the PD, and \(d_{i}\) corresponds to the Euclidean distance between the PD and the LED \(i\) at position \((x_{i},y_{i},z_{i})\). For simplicity, it should be noted that the three PDs used are treated as if they were located together. In the context of the orientation of LEDs and PDs, it is assumed that the receiver PDs are oriented vertically upward. In addition, it is assumed that the transmitters are aligned in the same direction and pointing downward. Under this assumption, it can be inferred that \(\phi_{i}=\psi_{i}\). Furthermore, it is necessary to take into account the gain of the optical concentrator, which is represented by [35]  
\[g_{i}(\psi_{i})= \begin{cases}\frac{n_{i}^{2}}{\sin^{2}\Psi_{ci}},&0\leq\psi_{i} \leq\Psi_{ci}\\ 0,&\psi_{i}>\Psi_{ci},\end{cases}  \tag{4}\]  
where \(n_{i}\) represents the refractive index of the optical concentrator and \(\Psi_{ci}<\pi/2\) denotes the Field of View (FoV) of the PD. It is also important to include and consider the impact of the optical filter gain (\(T_{s}(\psi_{i})\)) on signal reception. Continuing with the process of receiving and processing the optical signal received, the power received from each PD is measured and transmitted to a processing system via WiFi by using the IEEE 802.11 standard [36]. This process is carried out to determine the distance between the receiver and each LED, enabling an estimation of the target's location. In addition, the use of WiFi as an uplink provides the advantage of using existing infrastructure within the hospital. The decision to use Wi-Fi only as a communication technology for uplink without adopting existing Wi-Fi-based localization algorithms is the result of the nuanced requirements of hospital equipment localization and certain technical reasons that are detailed below:  
* **Accuracy and precision:** WiFi-based location algorithms may not offer the same level of precision and precision needed to locate hospital equipment. VLC-based schemes, which use three LEDs with different wavelengths and incorporate a trilateration algorithm enhanced by PSO, are designed specifically to address the stringent accuracy demands of medical equipment localization [37]. * **Interferences and environmental factors:** Hospital environments can be dynamic and subject to various interferences. WiFi signals can be affected by environmental factors, causing fluctuations in accuracy. VLC, which operates in the visible light spectrum, is less prone to interference and provides a more stable and reliable means of localization [38]. * **Customization for hospital requirements:** The proposed method is designed taking into account the unique characteristics of hospital environments. The choice of VLC  
Figure 2: Transmission and reception dynamics. and the specific modifications made, such as the use of different wavelengths for LEDs, are designed to overcome the specific challenges of healthcare settings. In the described localization system, the receivers are also equipped with WiFi modules/interfaces, allowing wireless data transmission over the existing WiFi infrastructure of the hospital, a standard feature in modern healthcare facilities [39, 40]. This design leverages the hospital-wide WiFi network to ensure the efficient delivery of location information from optical receivers to the Central Processing Unit (CPU).