# Channel and Bit Adaptive Power Control Strategy for Uplink NOMA VLC Systems
## 4 Simulations  
In this section, we will carry out simulations to examine the performance of our proposed adaptive power control (APC) strategy for an equivalent uplink NOMA VLC system by comparing with GRPA, FPA, and TDMA schemes.  
In this paper, we carry out the simulations in a \(4.0\text{ m}\times 4.0\text{ m}\times 3.0\text{ m}\) room model for indoor environment, which is a typical simulation model in VLC systems [33; 34; 35]. As illustrated by Figure 1(a),the PD receiver is located at the ceiling and the LED transmitters are located at a plane with a height of 0.85 m, which is denoted by Receiver Plane. The other key system parameter settings according to [33; 34; 35] are illustrated by Table 1. The channel coefficients between the LED transmitters and the PD receiver can be computed based on (2) and without loss of generality, they are normalized by being divided by the maximum channel coefficient in our simulation. In addition, the SNR is defined by \(\frac{1}{\sigma^{2}}\) with the peak optical power being normalized. All the schemes to be compared are given as follows:  
1. **Gain Ratio Power Allocation (GRPA)**[17]: The signal transmitted by the \(i\)-th LED is denoted by \(x_{GRPA_{i}}=P_{i}s_{i}\), where \(P_{i}=(\frac{h_{1}}{h_{i}})^{2}P_{i-1}\) and \(s_{i}\in\{k\}_{k=0}^{k=2^{K_{i}}-1}\), \(1\leq i\leq N\). In this simulation, we set \(P_{1}=1\).
2. **Fixed Power Allocation (FPA)**[17; 19]: The transmitted signal of LED \(i\) is denoted by \(x_{FPA_{i}}=F_{i}s_{i}\), where \(F_{i}=\alpha F_{i-1}\) and \(s_{i}\in\{k\}_{k=0}^{k=2^{K_{i}}-1}\), \(1\leq i\leq N\). In this simulation, we set \(\alpha=0.1\) and \(F_{1}=1\).
3. **Time Division Multiple Access (TDMA)**[3]: With the successive \(N\) time slots, the transmitted signal of the \(N\) LEDs is given by \(\mathbf{x_{TDMA}}=[s_{1},s_{2},\cdots,s_{N}]\), where \(s_{i}\in\{k\}_{k=0}^{k=2^{N_{i}}-1}\), \(1\leq i\leq N\).
4. **Adaptive Power Control (APC)**: Our proposed APC strategy is given in Algorithm 1.  
In this paper, we simulate the users' average BER performance of the above schemes for two LEDs, three LEDs, and four LEDs scenarios. For two LEDs scenario, the coordinates of the two LEDs are \((1.0\) m, \(2.0\) m, \(0.85\) m) and \((3.0\) m, \(2.0\) m, \(0.85\) m). For three LEDs scenario, the coordinates of the three LEDs are \((1.0\) m, \(1.5\) m, \(0.85\) m), \((2.0\) m, \(3.0\) m, \(0.85\) m), and \((3.0\) m, \(1.5\) m, \(0.85\) m). For four LEDs scenario, the coordinates of the four LEDs are \((1.0\) m, \(1.0\) m, \(0.85\) m), \((1.0\) m, \(3.0\) m, \(0.85\) m), \((3.0\) m, \(3.0\) m, \(0.85\) m), and \((3.0\) m, \(1.0\) m, \(0.85\) m). Since the obtained gains of our proposed design over other schemes at the error rate of \(10^{-4}\) have reached our expectations, the BER in all simulation figures are plotted up  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Room size & \(4.0\) m \(\times\) 4.0 m \(\times\) 3.0 m \\ PD detector area & \(A=1\) cm\({}^{2}\) \\ Field-of-view angle & \(60^{\circ}\) \\ Gain of optical concentrator & \(1.0\) \\ Half-power angle & \(60^{\circ}\) \\ Gain of optical filter & \(1.0\) \\ Height of user plane & \(0.85\) m \\ \hline \hline \end{tabular}
\end{table}
Table 1: Key System Parameters  
Figure 2: **(a)** Multiple access room model for simulation; **(b)** Two users’ BER performance comparisons of our proposed adaptive power control (APC) and time division multiple access (TDMA) for different \((K_{1},K_{2})\).  
to \(10^{-4}\) in this paper. In addition, the ML demodulator is adopted by all schemes to make all the comparisons fair and the simulations are detailed as follows.