# Simulation of an Indoor Visible Light Communication System Using Optisystem
## 4 VLC System Model  
Figure 7 depicts a VLC system model using a single LED mounted on the ceiling of the room and a receiver (photodetector) placed on the floor. The transmitter-radiated light's \(\phi_{r}\) property corresponds to the LED's viewing angle. After the distance \(d\) from the LED to the receiver, the light is incident with angle \(\psi_{r}\). The distances between an LED and a reflective point and between a reflective point and a photodetector are represented by the numbers \(d_{1}\) and \(d_{2}\). The angles of irradiance to a reflective point and a photodetector are represented by the quantities \(\alpha_{ir}\) and \(\beta_{ir}\). The received power is calculated when a reflection from a wall is taken into account using the channel DC gain on the directed path (\(H_{d}(0)\)) and the reflected path (\(H_{ref}(0)\)). According to references [22, 39, 40, 41] the multipath scenario's total received power is defined as follows: \begin{table}
\begin{tabular}{c c} \hline \hline
**LED1** & **LED2** \\ \hline \(l_{3}^{{}^{\prime\prime}}=13m\); & \(m_{3}^{{}^{\prime\prime}}=10.5m\); \\ \(\theta_{3}^{{}^{\prime\prime}}s=38^{\circ},\theta_{3}^{{}^{\prime\prime}}d=52^{ \circ}\) & \(\theta_{3}^{{}^{\prime\prime}}s=15^{\circ},\theta_{3}^{{}^{\prime\prime}}d=75^{ \circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._  
Figure 6: Dual LED NLOS propagation model simulation environment in Optisystem. \[P_{r}=\sum\limits^{N_{LED}}\left\{P_{t}H_{d}(0)+\int\limits_{\text{Re}flections}P_{t} dH_{ref}(0)\right\} \tag{7}\]  
where \(P_{t}\) is the transmitted optical power which is given [22] by:  
\[P_{t}=\int\limits_{\Lambda_{\min}}^{\Lambda_{\max}}\int\limits_{0}^{2\pi} \Phi_{e}d\theta d\lambda \tag{8}\]  
where \(\Lambda_{\min}\) and \(\Lambda_{\max}\) are determined by the sensitivity curve of the photodiode. The \(\Phi_{e}\) is the flux energy which is defined as:  
\[\Phi=K_{m}\int\limits_{380}^{780}V(\lambda)\Phi_{e}(\lambda)d\lambda \tag{9}\]  
where \(V(\lambda)\) is the standard luminosity curve, \(K_{m}\) is the maximum visibility defined as 683 lm/W at \(\lambda=555\) nm. The channel DC gain in the direct path is given [42, 43] as:  
\[H(0)=\left\{ \begin{array}{c}\frac{A_{r}(m_{i}+1)}{2\pi d^{2}}\text{cos}^{m_{ i}}(\phi_{r})T_{s}(\psi)g(\psi)\cos(\psi_{r}),\\ 0\leq\psi_{r}\leq\psi_{c},\\ 0,\\ \psi_{r}>\psi_{c}\end{array} \right. \tag{10}\]  
where \(T_{s}(\psi)\) is the gain of an optical filter, \(g(\psi)\) is the gain of an optical concentrator, \(A_{r}\) is the physical area of the detector in a photodiode, \(d\) is the distance between an LED and a photodiode. The size of the photodiode's field of view is determined by the constant \(\psi_{c}\). The optical concentrator \(g(\psi)\) is expressed [42] as:  
\[g(\psi)=\left\{ \begin{array}{c}\frac{n^{2}}{\text{sin}^{2}\psi_{c}},0\leq \psi_{r}\leq\psi_{c}\\ 0,0\geq\psi_{c}\end{array} \right. \tag{11}\]  
where \(n\) is the refractive index. The DC channel gain of the wall reflection is given [43] by:  
\[dH_{ref}(0)=\left\{ \begin{array}{c}\frac{(m_{i}+1)A_{r}}{2\left(\pi d_{1}d_{ 2}\right)}\rho dA_{wall}\text{cos}^{m_{i}}(\phi_{r})\cos(\alpha_{ir})\cos( \beta_{ir})T_{s}(\psi)g(\psi)\cos(\psi_{r}),\\ 0\leq\psi_{r}\leq\psi_{c},\\ 0,\\ \psi>\psi_{c}\end{array} \right. \tag{12}\]  
where \(\rho\) is the reflectance factor and \(dA_{wall}\) is a reflective area of a small region. A crucial performance requirement for the VLC system is the RMS delay spread, which is defined [39] as:  
\[D_{RMS}=\sqrt{\mu^{2}-\left(\mu\right)^{2}} \tag{13}\]  
where \(\mu\) is the mean excess delay which is defined by :  
\[\mu=\frac{\sum\limits_{i=1}^{M}P_{d,i}t_{d,i}+\sum\limits_{j=1}^{N}P_{ref,j}t _{ref,j}}{P_{rT}} \tag{14}\]  
where the received optical power from the \(i\)th direct path is \(P_{d,i}\), and the \(j\)th reflected path is \(P_{ref,j}\). The terms \(M\) and \(N\) are the numbers of direct paths from an LED source to a specific photodetector and reflection paths to the same photodetector.