## 4 SNR Analysis of a QADA Receiver
### Simulation Results and Discussion  
The parameters used in the simulations are summarized in Table 1. The transmitted optical power of the luminaire is set at 1 W and luminaires with two different Lambertian orders, \(m=1\) and \(m=4\), are considered. This is to represent both a non-directional and a directional source. The QADA receiver has a square aperture that has the same size as the PD. Two values for the aperture height are used: \(d=2.5\) mm and \(d=5\) mm. These correspond to FOV-Cs of \(63.4^{\circ}\) and \(45^{\circ}\), respectively. The parameters related to the quadrant PD are chosen to reflect the commercially available Hamamatsu S590 that is used in the experimental work, detailed in Section 6. The SNR results as a function of the location of the receiver as \(x\) and \(y\) are varied are presented in Figure 7. Here, \(m=1\), FOV-C \(=63.4^{\circ}\), and the receiver is parallel to the plane on which the luminaire is located. The SNR contour plots for each quadrant of the QADA receiver are shown in Figure 7a. For each quadrant, the SNR is relatively high in some locations. For example, for the fourth quadrant, the SNR is more than 20 dB, for values of \(x\) between \(-1.8\) m and \(3\) m and values of \(y\) between \(-3\) m and \(1.8\) m. This is because for this region the channel gain is large as shown in Figure 2. Figure 7b shows the SNR contour plots when the quadrant with the maximum power is selected. Now, as long as the luminaire is within the FOV-C of the receiver, the SNR is high in most locations. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Transmitted optical power, \(P_{\text{opt}}\) & \(1\) W \\ Transmitter height from the receiver & \(1.8\) m \\ Background spectral irradiance, & \(p_{n}=0.29\)\(\mu\)W/ \((\text{cm}^{2}\cdot\text{nm})\) \\ Noise equivalent power, NEP & \(1.4\times 10^{-14}\) W/\(\sqrt{\text{Hz}}\) \\ Lambertian order, \(m\) & \(1\), \(4\) \\ Optical bandwidth, \(\Delta\lambda\) & \(400\) nm \\ Electrical bandwidth, \(B\) & \(1\) MHz \\ Quadrant length, \(L_{\text{PD}}\) & \(2.5\) mm \\ Aperture height, \(d\) & \(2.5\) mm, \(5\) mm \\ PD total area, \(A\) & \(25\) mm\({}^{2}\) \\ PD responsivity, \(R\) & \(0.4\) A/W \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation Parameters. The SNR can be further improved if the signals from all quadrants are combined as shown in Figure 7c,d. After combining the signals from all quadrants, the SNR improves significantly. Figure 7c shows the results when the EGC is used and Figure 7d shows the SNR results when the MRC algorithm is applied. Using MRC (MRC algorithm is the combining method used for the rest of the paper) for combining gives the best SNR results because it effectively uses the diversity in the signals. The purple dashed lines represent the region in which light from the luminaire reaches all four quadrants of the QADA so that it can be used for VLP. It is smaller than the overall communication area; however, in this region, the SNR is always high, mostly above 40 dB. We will show in Section 5 that the communications properties will not be a limitation in VLP systems that use QADA. Figure 8 shows the SNR results when a transmitter with a higher Lambertian order of \(m=4\) is used. In comparison with the results in Figure 7, we can see that the area that has an SNR of less than 0 dB has been reduced and the SNR increased in the area directly below the transmitter. This is because when \(m\) is increased the radiation pattern becomes more directional. Figure 7: SNR in dB versus QADA location in an area equipped with a single transmitter with \(m=1\) and with the receiver parallel to the plane on which the luminaire is located with a FOV-C of \(63.4^{\circ}\) for (**a**) each quadrant, (**b**) the combined signal using selection combining, (**c**) the combined signal using EGC, (**d**) the combined signal using MRC. Figure 9 illustrates the results for the smaller FOV-C of \(45^{\circ}\) and \(m=1\).