## 2 MISO VLC System Model
Total received power (dBm) for (**d**) the 4 arrays model, (**e**) the 9 arrays model, and (**f**) the 16 arrays model. \begin{table}
\begin{tabular}{c c c c c} \hline
**Receiver FOV** & **Received Power (dBm)** & **4 Arrays** & **9 Arrays** & **16 Arrays** \\ \hline \multirow{2}{*}{70\({}^{\circ}\)} & First Reflection & \(-\)4.64 & \(-\)5.42 & \(-\)4.28 \\  & Total Power & 2.57 & 3.75 & 2.53 \\ \hline \multirow{2}{*}{60\({}^{\circ}\)} & First Reflection & \(-\)4.95 & \(-\)5.19 & \(-\)4.54 \\  & Total Power & 3.13 & 4.35 & 3.06 \\ \hline \multirow{2}{*}{50\({}^{\circ}\)} & First Reflection & \(-\)4.78 & \(-\)5.21 & \(-\)4.49 \\  & Total Power & 3.97 & 5.34 & 3.74 \\ \hline \end{tabular}
\end{table} 
Table 3: Maximum power received after changing the FOV. The received power, \(P_{r}\), increases significantly when compared to the case of \(\varnothing_{1/2}=70^{\circ}\), and so does \(P_{r}\) STD. The case of 16 arrays outperforms the other two configurations under the fixed system parameters defined, having the highest average \(P_{r}\) and the least \(P_{r}\) STD. Still, the system needs to be tested for practicality, as these LEDs are placed with the main purpose of illumination, the level of illuminance for the case of \(\varnothing_{1/2}=10^{\circ}\) has to be within the typical office illuminance requirements (i.e., 200 to 1000 lux) [3]. Using Equation (2), the illuminance of the three transmitter configurations at \(\varnothing_{1/2}=10^{\circ}\) is plotted in Figure 5. The plots show poor performance in all three cases. Table 5 shows the maximum and average illuminance (lux) for each case. The average illuminance in all cases is not within the required range for illumination, which is due to the fact that, from Equation (1), the radiation intensity and illuminance depend heavily on the value of  
However, the presence of commercial LEDs with small \(\varnothing_{1/2}\) encouraged further investigation on utilizing the advantage of using LEDs with small half power angles. This increase in received power can be very useful in applications that require a high SNR. The proposed model performance is further evaluated by obtaining its BER, employing on-off keying with \(\varnothing_{1/2}=30^{\circ}\). The BER and SNR are, respectively, given by [3]:  
\[\text{BER}=\text{Q}\Big{(}\sqrt{\text{SNR}}\Big{)} \tag{6}\]  
where the Q-function is defined as  
\[\text{Q}(x)=1-\Phi(x) \tag{7}\]  
given \(\Phi(x)\) as the cumulative distribution function of the normal Gaussian distribution and  
\[SNR=\frac{(RP_{r})^{2}}{\sigma_{T}^{2}} \tag{8}\]  
where the photodiode responsivity is represented by \(R\). As presented in References [21; 22; 23], the total noise variance \(\sigma^{2}_{T}\) is  
\[\sigma_{T}^{2}=2 qRP_{r}I_{2}B+\frac{8\pi kT}{G}\eta AI_{2}B^{2}+\frac{16\pi^{2 }kT\Gamma}{g_{m}}\eta^{2}A^{2}I_{3}B^{3} \tag{9}\]  
where \(q\) is the charge of electron and \(k\) is Boltzmann constant. The BER parameters are shown below in Table 6, and the BER for each transmitter configuration at \(\varnothing_{1/2}=30^{\circ}\) is presented in Figure 6. It is observed that the BER in almost the entire room, excluding the corners, has a constant value. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Photodiode Responsivity, \(R\) & 0.54 \\ Photodetector Surface Area, \(A\) & 1 cm\({}^{2}\) \\ Bandwidth Factor, \(I_{2}\) & 0.562 \\ Bandwidth Factor, \(I_{3}\) & 0.0868 \\ Data Rate, \(B\) & 30 Mb/s \\ Temperature, \(T\) & 298 K \\ Capacitance per unit Area, \(\eta\) & 112 pF/cm\({}^{2}\) \\ FET Transconductance, \(g_{m}\) & 30 mS \\ FET Channel Noise Factor, \(\Gamma\) & 1.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: BER parameters [24]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Illuminance (lux)** & **4 Arrays** & **9 Arrays** & **16 Arrays** \\ \hline Average & 55 & 54 & 53 \\ Maximum & 584 & 261 & 147 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Illuminance at \(\varnothing_{1/2}=10^{\circ}\).