# Highly Sensitive SPAD-Based Receiver for Dimming Control in LiFi Networks +
## 5 Numerical Results and Discussion
### BER Performance  
The BER plots of OOK-, VOOK-, DCO-OFDM-, and ACO-OFDM-modulated signals are shown in Figure 3a-d for three dimming levels versus the received signal power, considering the higher background light power of \(P_{b}=10\) nW. The sensitivity of the SPAD detector (dash-dotted curves) is significantly higher than that of the PIN PD detector (solid curves). However, as \(P_{\text{R}}\) increases (e.g., due to the user's location/orientation towards the LED), the BER of the original SPAD array receiver initially decreases and then  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Definition** & **Value** \\ \hline \(\lambda_{\text{op}}\) & Optical wavelength & 450 nm \\ \hline \(P_{\text{B}}\) & Background light power & 1 nW and 10 nW \\ \hline \(P_{\text{max}}\) & Maximal LED power & 1 mW \\ \hline \(P_{\text{min}}\) & Minimal LED power & 0 mW \\ \hline \(B_{\text{max}}\) & LED bandwidth & 120 MHz \\ \hline \(K\) & FFT and IFFT size & 1024 \\ \hline \(\Re\) & Photo-diode responsivity & 0.25 A/W \\ \hline \(T^{\circ}\) & Load-resistor temperature & 297 K \\ \hline \(R_{\text{L}}\) & Load resistance & 50 \(\Omega\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: System parameter setting.  
Figure 2: The VOA transmittance (dimensionless), \(\xi\), versus the received signal power with background power \(P_{b}=1\) nW and a dimming level \(\gamma=20\%\).  
increases due to dead-time-induced non-linear distortion caused by SPAD's saturation. This indicates the advantage of using VOA in the proposed adaptive receiver. All the considered modulation techniques exhibit improved overall performance and effectively mitigate non-linear distortion when VOA implementation with optimal transmittance (dashed curves) is used. For instance, for \(\gamma=20\%\) and \(P_{\text{R}}=0.5\)\(\upmu\)W, the traditional OOK SPAD array achieves a BER of \(10^{-6}\), however, our VOA implementation lets the SPAD array to perform at a BER = \(10^{-7}\). The VOA receiver for VOOK in Figure 3b shows a similar trend, but compared with OOK, it achieves a BER = \(10^{-7}\) at \(P_{\text{R}}=3\)\(\upmu\)W. This also shows how VOOK is not power efficient at such dimming levels.  
A comparison between DCO-OFDM and ACO-OFDM SPAD array can be seen in Figure 3c,d. For the traditional SPAD array, DCO-OFDM outperforms the ACO-OFDM in a high-power regime. For example, when \(P_{\text{R}}=0.6\)\(\upmu\)W and \(\gamma=20\%\), SPAD receiver with DCO-OFDM can achieve a BER of \(6\times 10^{-13}\). However, in such conditions, the receiver with ACO-OFDM is already in the nonlinear saturated domain with a BER of \(7\times 10^{-3}\). In the low power regime, ACO-OFDM is in turn preferable. For instance, for \(\gamma=20\%\) and \(P_{\text{R}}=0.1\)\(\upmu\)W, ACO-OFDM gains a BER of \(10^{-9}\) whereas the corresponding BER for  
Figure 3: The BER versus the received signal power with background power. \(P_{\text{b}}=10\) nW with different dimming levels (\(\gamma\)) for considered systems; (**a**) OOK; (**b**) VOOK; (**c**) 4-QAM DCO-OFDM; (**d**) 16-QAM ACO-OFDM.  
DCO-OFDM is \(10^{-3}\). It is also demonstrated in these figures that employing the proposed adaptive receiver can avoid the increase of BER in high power regime and continue to operate optimally.  
When the background light intensity reduces to \(P_{b}=1\) nW, indicating low ambient light conditions such as during the night, the performance of the studied systems improves as expected. As shown in Figure 4a-d, the traditional SPAD array receiver does not exhibit distortion for lower received power, matching the performance of our proposed receiver, although it starts to saturate for received optical power beyond 10 \(\mu\)W. It can also be concluded that increasing the dimming level leads to a degradation in the performance of the PDs.