# Energy Efficient Transceiver Design for NOMA VLC Downlinks with Finite-Alphabet Inputs
## 4 Simulations  
In this section, we evaluate the performance of our proposed transceiver design for the NOMA VLC system by comprehensive computer simulations.  
As illustrated by Figure 2, we carry out the simulations in a \(4.0\,\mathrm{m}\times 4.0\,\mathrm{m}\times 3.0\,\mathrm{m}\) room for an indoor environment; the transmitter LED is located at \((2.0\,\mathrm{m},2.0\,\mathrm{m},3.0\,\mathrm{m})\); and all the users are located at a plane with a height of \(0.85\,\mathrm{m}\), which is denoted by user plane. Some other key system parameters are shown in Table 1. The channel coefficient of each channel realization can be computed based on (3) and normalized by being divided by the maximum channel coefficient. The SNR is defined by \(\frac{1}{\sigma^{2}}\) for the normalized peak optical power. In addition, to make all the comparisons fair, the ML demodulator is adopted by all schemes. More details of our computer simulations are given as follows.  
We first compare the average BER performance of our proposed NOMA scheme and the conventionally used TDMA. The transmitted signals of the two schemes are shown in Table 2, and we consider that all the users are randomly distributed on the user plane, as illustrated in Figure 2. We randomly select 20 user groups to simulate their average BER performance, and the simulation results for two, three or four users per user group are shown in Figures 4-6, respectively. From these  
\begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline Room size & \(4.0\,\mathrm{m}\times 4.0\,\mathrm{m}\times 3.0\,\mathrm{m}\) \\ LED coordinate & \((2.0\,\mathrm{m},2.0\,\mathrm{m},3.0\,\mathrm{m})\) \\ PD detector area & \(A=1\,\mathrm{cm}^{2}\) \\ Field-of-view angle & \(60^{\circ}\) \\ Half-power angle & \(60^{\circ}\) \\ Height of receiver plane & \(0.85\,\mathrm{m}\) \\ \hline \end{tabular}
\end{table}
Table 1: Key system parameters.  
figures, we can get that our proposed NOMA scheme significantly outperforms the conventionally used TDMA. For example, the average gain of our proposed NOMA scheme over TDMA at the error rate of \(10^{-5}\) is about 7 dB for \(M=2,K_{1}=1,K_{2}=3\). The main reason for this is that the error performance is dominated by the MED of the received constellation, and the ratio of MED of our proposed NOMA and TDMA is determined by:  
\[20\log_{10}(\frac{h_{M}}{M(2^{\sum_{j=1}^{M}K_{j}}-1)})/(\frac{h_{M}}{\sum_{i= 1}^{M}2^{MK_{i}}-M})=20\log_{10}\frac{\sum_{i=1}^{M}2^{MK_{i}}-M}{M(2^{\sum_{j =1}^{M}K_{j}}-1)} \tag{8}\]  
Then, for \(M=2,K_{1}=1,K_{2}=3\), the obtained gain of our proposed NOMA over TDMA is given by \(20\log_{10}\frac{2^{2K_{1}}+2^{2K_{2}}-2}{2(2^{K_{1}+K_{2}}-1)}=20\log_{10} \frac{2^{2\times 1}+2^{2\times 3}-2}{2(2^{1+3}-1)}\approx 6.85\) dB, which is consistent with the simulation results in Figure 4. In addition, we simulate the average BER performance of our proposed NOMA scheme with different transmitter LED position, and the simulation results are illustrated in Figure 7. From this figure, we can see that no matter where the transmitter LED is, our proposed design has a good performance over TDMA.  
Furthermore, we also compare the average BER performance of our proposed JDD algorithm and the conventional SIC algorithm. As illustrated by Figure 4, our proposed JDD algorithm outperforms the SIC algorithm. For example, the obtained gain of the JDD algorithm compared to the SIC algorithm is about 5 dB for \(M=2,K_{1}=2,K_{2}=3\).  
As illustrated in the above simulations, our proposed transceiver design for NOMA significantly outperforms SIC-based NOMA and TDMA. Using our proposed NOMA-JDD scheme, we can achieve higher rates of data transmission than using TDMA or NOMA-SIC with the same BER and SNR.  
Figure 5: Three users’ average BER comparisons of our design and TDMA.  
Figure 6: Four users’ average BER comparisons of our design and TDMA.  
Figure 7: Three users’ average BER comparisons of our design and TDMA with \(K_{1}=1,K_{2}=2,K_{3}=1\) for different transmitter positions.