## 2 MISO VLC System Model  
The VLC system parameters that are used in References [12; 13; 14; 15] are initially adopted (see Table 1) in this paper to compare the system performances of the different LED arrangements. The transmitters consist of 2-D rectangular white LED [16] arrays of low intensities. These array patterns are distributed as shown in Figure 1 along the ceiling. Phosphorescent white LEDs used in this paper are assumed to generate a Lambertian radiation pattern. At the receiving plane, the radiation intensity is given by Reference [3]. \[I(\varnothing)=I(0)cos^{m_{l}}(\varnothing) \tag{1}\]  
where \(\varnothing\) is the irradiance angle with respect to the axis perpendicular to the transmitter surface. \(I(0)\) is the center luminous intensity, and \(m_{l}\) is the Lambertian emission order which is defined by:  
\[m_{l}=\frac{ln(2)}{ln(\cos\varnothing_{1/2})} \tag{2}\]  
where \(\varnothing_{1/2}\) is the LED semi-angle at half illuminance. On the other hand, the received power is given by Reference [3]:  
\[P_{r}=(H_{LOS}(0)+H_{nLOS}(0))P_{t}=\left(H_{LOS}(0)+\sum_{refl}H_{refl}(0) \right)P_{t} \tag{3}\]  
where the transmitted power is \(P_{t}\), \(H_{LOS}(0)\) is the LOS link DC gain, \(H_{nLOS}(0)\) is the non-LOS link DC gain, and \(H_{refl}(0)\) represents the reflected path DC gain. The DC gain for a LOS link receiver with a Lambertian source can be approximated as [3]:  
\[H_{LOS}(0)= \begin{cases}\frac{A_{r}(m_{l}+1)}{2\pi d^{2}}cos^{m_{l}}(\varnothing )T_{s}(\varphi)g(\varphi)\cos(\varphi)&0\leq\varphi\leq\varphi_{con}\\ 0&\text{elsewhere}\end{cases}  \tag{4}\]  
where \(\varphi\) is the incident angle to the axis perpendicular to the receiver surface. The incident angle is given that \(0\leq\varphi\leq\varphi_{con}\), where \(\varphi_{con}\) is the field-of-view (FOV) receiver angle. The receiver area is \(A_{r}\), while \(T_{s}(\varphi)\) and \(g(\varphi)\) are the filter transmission coefficient and the concentrator gain, respectively. The distance between the LED source and the photodetector surface is \(d\). \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Parameter** & **Value** \\ \hline \multirow{2}{*}{Room} & Dimensions & \(5\times 5\times 3\) m\({}^{3}\) \\  & Reflection Coefficient from Walls & 0.8 \\ \hline \multirow{3}{*}{Source} & Number of LEDs & 14,400 \\  & LED Transmitted power & 20 mW \\  & Half power angle & 70\({}^{\circ}\) \\ \hline \multirow{3}{*}{Receiver} & Receiver plane above ground & 0.85 m \\  & Active surface area & 1 cm\({}^{2}\) \\  & Half -angle FOV & 70\({}^{\circ}\) \\ \cline{1-1}  & Refractive index of lens & 1.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Visible light communication (VLC) System Parameters. Figure 1: LEDs arrangements for (**a**) the 4 arrays model, (**b**) the 9 arrays model, and (**c**) the 16 arrays model. The reflected path DC gain is given by [14]:  
\[H_{refl}(0)= \begin{cases}\frac{(m_{l}+1)}{2\pi d_{1}^{2}d_{2}^{2}}\mathit{odA}_{ wall}cos^{m_{l}}(\varnothing)\cos(\alpha)\cos(\beta)T_{s}(\varphi)g(\varphi)\cos( \varphi)&0\leq\varphi\leq\varphi_{c}\\ 0&\text{elsewhere}\end{cases}  \tag{5}\]  
where the distance between the LED source and a reflection point is \(d_{1}\), the distance between a reflection point and the receiver surface is \(d_{2}\), and \(\rho\) is the reflectance coefficient. The reflective area of a small region is \(dA_{wall}\), \(\alpha\) is the incident angle to a reflection point, and \(\beta\) is the irradiance angle to the receiver. The power radiated among the room from the three different array patterns is plotted in Figure 2 by applying Equations (3)-(5). The total number of LEDs in all models is fixed. The performance of the models is summarized in Table 2, which shows the average, minimum, maximum, and standard deviation (STD) of the received power for each model. It is observed that the 9 arrays model has the highest average \(P_{r}\). However, it also has the highest deviation between the minimum and maximum \(P_{r}\).