# Multiuser Transmit Precoding Design for Dimming Compatible Visible Light Communications
## 4 Numerical Results and Discussion  
In this section, our numerical results are presented for evaluating the performance of the proposed TPC combined with dimming control. The multiuser VLC system as shown in Figure 3 was comprised of nine LED arrays distributed uniformly on the ceiling to offer sufficient illumination [16]. We considered the scenarios of \(N_{r}=6\) (Scenario 1) and \(N_{r}=8\) (Scenario 2) users decentralized on the receiver plane, whose locations w.r.t. the LED arrays are presented in Figure 3. Two kinds of typical modulations in VLC were adopted in the simulation, namely bipolar PAM with zero mean and PPM with positive mean. The linear dynamic range of a single LED was set to \(1\sim 20\) mW. Other major parameters are listed in Table 1.  
Figure 4 illustrates the bit error rate (BER) of the proposed TPC scheme using PAM at different dimming levels, in which the BER of the traditional pseudo-inverse based ZF TPC from RF is also provided for comparison [24]. Observe in Figure 4 that for both scenarios, the proposed TPC achieved a significant BER performance gain compared to the ZF TPC. The BER performance became better when the dimming level tended towards 50%, since the linear dynamic range of LED can be fully exploited in this case. Additionally, the BER performance for Scenario 1 with six users was better than Scenario 2 with eight users, implying that the BER performance of the dimming compatible VLC system degraded when supporting more users. From Figure 4, we also observe that the performance of the multiuser VLC system degraded with the increasing PAM modulation order.  
In Figure 5, we portray the BER of the multiuser VLC system employing 2-PPM and 4-PPM, which both have the non-zero mean. It can be observed from Figure 5 that our TPC scheme still achieved much better performance than the ZF TPC for PPM, which verifies the applicability of the proposed scheme to modulations with the non-zero mean. In contrast to PAM, a better performance was achieved when employing the higher-order PPM. This is because as the modulation order increased, the power efficiency of PPM was improved at the cost of its bandwidth efficiency deterioration [25]. Moreover, under relatively low or high dimming levels, the multiuser VLC system employing PAM exhibited a  
\begin{table}
\begin{tabular}{l c} \hline
**Parameter** & **Value** \\ \hline Number of LED arrays & 9 \\ Number of LEDs per array & 3600 (60 \(\times\) 60) \\ LED pitch & 0.01 m \\ Size of LED array & 0.59 m \(\times\) 0.59 m \\ Transmitter semi-angle & 70 deg. \\ Receiver FOV & 60 deg. \\ Detector responsivity & 0.53 A /W \\ Physical area of the detector & 1 cm\({}^{2}\) \\ Gain of optical filter & 1.0 \\ Refractive index & 1.5 \\ Bandwidth & 100 MHz \\ \hline \end{tabular}
\end{table}
Table 1: Parameters of the MU-MISOindoor VLC system.  
Figure 3: The room model. The room size was 7.5 m \(\times\) 7.5 m \(\times\) 3 m. The height of the receiver was 0.7 m from the floor. The height of LED arrays was 3 m from the floor [16].  
performance loss, while the TPC employing PPM performed well. PPM appeared to be a beneficial design choice to provide a stable communication link at relatively low or high dimming levels despite its low spectrum efficiency compared to PAM.