# Highly Sensitive SPAD-Based Receiver for Dimming Control in LiFi Networks +
## 2 System Model  
The system model in this study is depicted in Figure 1. Assuming an indoor setting, an array of LEDs is used as a transmitter to generate the modulated, dimmed optical signal, with ambient light also being received from natural and/or unnatural light sources after optical filtering. The signal modulator block denotes one of the various modulation techniques used in this study, which include OOK, VOOK, DCO-OFDM, and ACO-OFDM. In the considered indoor VLC system, the received optical signal consists of a line of sight (LOS) and/or non-line of sight (NLOS) components and both contribute to the channel pathloss, \(\zeta\). Denoting the dimming factor as \(\gamma\) and the maximum average transmitted optical power as \(\overline{P}_{\text{TX,max}}\), the relationship between \(\gamma\) and the average transmitted optical power \(\overline{P}_{\text{TX}}\), can be defined as follows  
\[\gamma(\%)=\frac{\overline{P}_{\text{TX}}}{\overline{P}_{\text{TX,max}}}\times 1 00\%. \tag{1}\]  
To achieve a specific illumination level for dimming purpose, the simplest, most intuitive, and a cost-effective solution is using analogue dimming or continuous current reduction  
Figure 1: Block diagram of the considered VLC system with the proposed SPAD receiver. (CCR) [33]. In such a scheme, the dimming control is realized by adjusting the average transmitted light power so that \(\overline{P}_{\text{TX}}=\gamma\overline{P}_{\text{TX,max}}\) holds. It is worth noting that for OFDM modulation the AC power of the signal will be adjusted accordingly with the change in the dimming level to avoid excessive waveform distortion. Digital dimming, on the other hand, occurs when the signal is digitally altered such as changing its duty cycle, as explained in the next section. With dimming control, the average received optical power, \(P_{R}\), can be expressed as  
\[P_{R}=\zeta\gamma\overline{P}_{\text{TX,max}}. \tag{2}\]  
Note that in this work it is assumed that the signaling bandwidth is smaller than the light source's bandwidth, hence the channel-frequency response is relatively flat across the signaling spectrum and the effect of channel-induced ISI is negligible [34; 35]. The SPAD array detector is employed at the receiver of the considered system. After a photon detection, a SPAD has to be quenched for a brief period of time after each avalanche, during which it becomes blind to any incident photon arrivals. This period is referred to as the _\"dead time\"_. Because of the nonlinearity caused by the dead time, the throughput of OWC systems with SPAD receivers is severely constrained. Typical SPAD receivers use active-quenched (AQ) or passive-quenched (PQ) circuits. PQ SPAD is identified as a paralyzable detector where any counts occurring during the dead time (including signal, dark count, and afterpulse) are not counted but they extend the dead time. Compared with PQ SPAD, the configuration of AQ SPAD is more complex and requires more area and power, but when any photon arrives during the dead time, it is not registered and does not prolong the dead time. In contrast to AQ SPAD, our receiver uses a PQ SPAD array with a large number of micro-cells, which is more sensitive, economical, and has a simpler circuit architecture [36]. The photon transfer function of PQ SPAD is given by [37]  
\[\lambda_{\text{D}}=\lambda\text{exp}(-\lambda\tau_{\text{d}}), \tag{3}\]  
where \(\lambda\) is the received photon rate, \(\tau_{\text{d}}\) is the dead time, and \(\lambda_{\text{D}}\) is the detected photon rate. From (3), we can deduce that the detected photon count first increases and subsequently declines with an increase in the incident photon rate. This suggests that the PQ SPAD's paralysis property results in a nonlinear distortion of the incoming signal.