# Linear Precoding Designs for MIMO VLC Using Multi-Color LEDs under Multiple Lighting Constraints
## 5 Simulation Results  
In this section, we carry out some simulations in the practical indoor MIMO VLC scenario. Simulation parameters of the MIMO VLC system are shown in Table 1. Note that the angle of irradiance \(\phi\) and the angle of incidence \(\psi\) are calculated according to the position arrangements of devices. The two-level PAM signal formed in the range of \([-1,1]\) is transmitted. RAGBLEDs chosen from the LUXEON C Color product line (LUMILEDS) are employed as the transmitters [31]. In the iterative algorithm, we set the iteration time \(n_{ite}=150\) and the loop time \(n_{loop}=50\) to obtain a trade-off between the complexity and precision. To extend the limited modulation bandwidth of commercial multi-color LEDs, the pre-equalization technology is utilized in our MIMO VLC system [32]. As shown in Figure 3, based on a single and cascaded bridged-T amplitude equalizer, the bandwidth of multiple color chips is extended to about 260 MHz from 100 MHz after the equalization. After introducing the roll-off factor \(\alpha=0.3\), the total data rate \(R\) can be calculated as:  
\[R=\frac{1}{1+\alpha}2B\log_{2}\left(M\right)\cdot NN_{t}, \tag{27}\]  
\(B\) is the bandwidth of the multi-color LED. Thus, the throughput of our proposed system can be derived by:  
\[T=R\cdot\left(1-P_{e}\right). \tag{28}\]  
where \(P_{e}\) is the data transmission error property. We first present the convergence performance of our proposed iterative algorithm. Figure 4 demonstrates the convergence performance versus luminous flux with different interference ratio \(\eta\) when CCT = 5000 K. It can be seen that the values of MSE converge to the optimal solutions after about \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline The size of MIMO & \(4\times 4\) \\ Type of multi-color LED & RAGBLED \\ Maximum forward current for each chip \(I_{Dm}\) & 700 mA \\ Half power angle of LED \(\Phi_{1/2}\) & \(10^{\circ}\) \\ Room height & 3 m \\ Table height & 0.75 m \\ LED distance \(D_{t}\) & 0.5 m \\ PD distance \(D_{r}\) & 0.1 m \\ FOV of the receiver & 90\({}^{\circ}\) \\ PD physical area \(A_{R}\) & 1 cm\({}^{2}\) \\ Receiver responsibility \(\delta\) & 0.4 A/W \\ Noise variance \(\sigma^{2}\) & 0.06 mW\({}^{2}\) \\  & R 664 nm \\ Peak wavelength of each color & A 594 nm \\  & G 538 nm \\  & B 465 nm \\  & R (0.6941, 0.3026) \\ Chromaticity coordinate of each chip & A (0.5979, 0.3995) \\  & G (0.2297, 0.7099) \\  & B (0.1230, 0.0925) \\  & R 0.021 A/lm \\ Luminance - Current conversion coefficient for each chip & A 0.014 A/lm \\  & G 0.005 A/lm \\  & B 0.015 A/lm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters used in the MIMO VLC system. 100 iterations, so the iteration time \(n_{ite}=150\) we set is reasonable. Besides, the convergence value of MSE when \(\eta=0\) is always smaller than \(\eta=0.1\) obviously due to the lower crosstalk interference. The throughput performance of our system for different order of PAM modulation when CCT = 5000 K is brought forward in Figure 5. The data transmission error property is approximated by the bit error rate (BER). It could be seen that the throughput of this system achieves over 10 Gbit/s, which is higher than traditional white light MIMO VLC systems [32]. Besides, we could also draw out  
Figure 4: Convergence performance of the iterative algorithm with different luminous fluxes and interference ratios \(\eta\) when CCT = 5000 K.  
Figure 3: The amplitude-frequency response characteristics of multiple colors after pre-equalization. the conclusion that the higher-order modulation would suffer more severe performance loss caused by the clipping distortion. Next, we compare the BER performance of our proposed method with some conventional precoding methods. The BER is calculated by the Monte Carlo method, and the length of transmitted data is set to be \(10^{8}\) in the simulations. In [21], a precoding design is proposed for fixed chromaticity (denoted as the chromaticity-fixed method).