## 4 Proposed Methodologies
### System Reliability  
The reliability of a healthcare data transmission is tremendously significant. Any error in reception can lead to serious issues with patient health. To assess the reliability of the transmission system, several parameters are evaluated in this section, such as outage probability, BER, and quality of service (QoS).  
Interference from neighboring RF cells is a main cause of outage in BLE. Current indoor/outdoor infrastructures are installed with abundant RF devices using the 2.4 GHz band, generating a considerable amount of interference. Path loss is another significant contributor to the overall outage probability. BLE outage can be considered to occur below a certain SINR threshold, denoted by \(\chi\). The BLE outage probability is calculated as [65]:  
\[\text{O}_{\text{P\_BLE}}=1-\exp\left[-\frac{\chi}{\text{P}_{\text{P}_{\text{b}}} }\sum_{\text{k}=1}^{\text{N}_{\text{b}}}\text{I}_{\text{T}}(\text{k})\right] \tag{15}\]  
where \(\text{N}_{\text{b}}\) denotes the total number of interfering sources with the BLE spectrum, k signifies a specific source, and \(\text{I}_{\text{T}}(\text{k})\) represents the total power received by the BLE for the specific interfering source.  
The interference of neighboring optical sources in OCC is also non-negligible. The interfering elements can be spatially separated from the image pixels, as each pixel acts as a photo detector. However, outage occurs when the LED array is beyond the AOV of the camera. In the scenario of Section 4, the outage probability can be expressed as \[\mathrm{O}_{\mathrm{P,OCC}}=\frac{n(d_{\alpha,\beta}^{\mathrm{max}})\left[a_{ \mathrm{room}}h_{\mathrm{room}}-\varepsilon p_{\mathrm{im}}q_{\mathrm{im}}\left( \frac{\mathrm{d}_{\mathrm{d}}}{f_{\mathrm{o}}}\right)^{2}+\frac{2\mathrm{d}_{ \mathrm{d}}p_{\mathrm{im}}(k-1)(q_{\mathrm{im}}d_{\mathrm{d}}-\theta f_{ \mathrm{o}})}{4\epsilon_{\mathrm{room}}^{2}}+\varepsilon kv\right]+a_{\mathrm{ room}}h_{\mathrm{room}}n(d_{\alpha,\beta}^{\mathrm{max}}-d_{\alpha,\beta}^{\mathrm{crit}})}{a_{ \mathrm{room}}h_{\mathrm{room}}n(d_{\alpha,\beta}^{\mathrm{max}})} \tag{16}\]  
where \(d_{\alpha,\beta}^{\mathrm{max}}\) and \(d_{\alpha,\beta}^{\mathrm{crit}}\) denote the maximum possible distance between the LED and a camera and the maximum communication range when using that camera, respectively.  
The QoS of the healthcare data transmission system significantly depends on how much error-free data is received. Achieving an excellent SINR is indispensable in this regard. Although the data rate is not a highly considerable parameter, a minimum data rate must be ensured in the communication system. We theoretically defined the QoS for the hybrid system as follows:  
\[\delta=\left\{\begin{array}{ll}\frac{(2-3\kappa)\phi_{\mathrm{ ins}}\eta_{\mathrm{ins}}}{2\phi_{\mathrm{tar}}\eta_{\mathrm{tar}}},&\{\phi_{ \mathrm{ins}}<\phi_{\mathrm{tar}}\}\&\{\eta_{\mathrm{ins}}<\eta_{\mathrm{tar}} \}\\ \frac{(2-3\kappa)\eta_{\mathrm{ins}}}{2\eta_{\mathrm{tar}}},&\{\phi_{ \mathrm{ins}}\geq\phi_{\mathrm{tar}}\}\&\{\eta_{\mathrm{ins}}<\eta_{\mathrm{tar}} \}\\ \frac{(2-3\kappa)\phi_{\mathrm{ins}}}{2\phi_{\mathrm{tar}}},&\{\phi_{ \mathrm{ins}}<\phi_{\mathrm{tar}}\}\&\{\eta_{\mathrm{ins}}\geq\eta_{\mathrm{tar}} \}\end{array}\right. \tag{17}\]  
where \(\phi_{\mathrm{ins}}\) and \(\phi_{\mathrm{tar}}\) denote the instantaneous and target data rate, \(\eta_{\mathrm{ins}}\) and \(\eta_{\mathrm{tar}}\) are the instantaneous and target SINR, and \(\kappa\) represents the BER achieved in reconstructing after reception.