## 4 Simulation Results  
In this section, simulations are carried out for the practical multi-color based VLC system to testify the performance of our proposed energy-efficient power allocation scheme, where RAGB-LED was employed as the transmitter. The simulation parameters are listed in Table 2. Without loss of generality, the two-level PAM signal with \(M=2\) was utilized for transmission. We first compare the error performance of our proposed system model and the conventional WDM-VLC model ignoring crosstalk under different crosstalk coefficients \(\epsilon\) at CCT = 5000 K. As shown \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Type of multi-color LED & RAGB LED \\ Room size & 5 m \(\times\) 5 m \(\times\) 3 m \\ LED height & 2.5 m \\ Table height & 0.85 m \\ FOV \(\mathbb{V}_{C}\) & 60\({}^{\circ}\) \\ Half power angle of LED \(\Phi_{1/2}\) & 60\({}^{\circ}\) \\ Irradiance angle \(\phi\) & 30\({}^{\circ}\) \\ Incidence angle \(\psi\) & 30\({}^{\circ}\) \\ Effective detector area of PD & 1 cm\({}^{2}\) \\ O/E conversion efficiency \(\rho\) & 0.5 A/W \\ P/F conversion efficiency \(K_{m}\) & 20 lm/W \\ minimum transmission power \(p_{i}^{min}\) & 1 W \\ maximum transmission power \(p_{i}^{max}\) & 10 W \\ SINR requirement \(\chi_{i}\) & 10 dB \\ Noise variance \(\sigma^{2}\) & 10\({}^{-14}\) W\({}^{2}\) \\ R 664 nm \\ A 594 nm \\ Peak wavelength of each color & G 538 nm \\ B 465 nm \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation parameters utilized in the RAGB LED VLC system. O/E, optical/electric; P/F, power to luminous flux. in Figure 5, compared with the WDM-VLC model, our proposed scheme can improve the error performance and achieve a 0.58-dB SNR gain with crosstalk coefficients \(\epsilon=0.05\) at a targeted bit error rate (BER) of \(10^{-3}\), while the SNR gain was 0.98 dB with \(\epsilon=0.1\). Thus, we can conclude that the proposed scheme considering crosstalk can achieve better error performance for the practical VLC system. As for the influence of the data rate, based on a single and cascaded bridged-T amplitude equalizer, the bandwidth of the multi color chips was about 260 MHz after equalization [10]. After introducing the roll-off factor \(\alpha=0.3\), the total data rate R can be calculated as:  
\[R=\frac{1}{1+\alpha}2B\log_{2}(M\times N), \tag{29}\]  
where \(B\) is the bandwidth of the multi-color LED and \(M\) is the modulation order of the PAM signal. Therefore, we can conclude that higher-order modulation can achieve high data rate, while it may suffer performance loss caused by the clipping distortion. Since Ref. [15] has been established to modify the chromaticity tolerances in the quadrangle range to replace a fixed point in the CIE 1931 chromaticity diagram, more degrees of freedom can be achieved to improve the performance of the system. Figure 6 indicates the transmitted optical power of different colors versus the luminance requirement ranging from 10-150 lm. Compared with the fixed chromaticity coordinate constraint, which is regarded as the center point of the target color, the proposed scheme with the quadrangle range chromaticity constraint behaved more energy efficiently, reducing about 20% of the power consumption at most. We can see that the proportion of the optical power distribution for four colors kept relatively constant because of the quadrangle range constraint at low luminous flux. As the luminous flux became larger than 60 lm, the total transmission power increased with the luminance requirement, which implies that the luminance requirement became the main constraint at high luminous flux. Since the parameters of the quadrangle range changed with the CCT values, the total transmission power under the chromaticity constraint of the quadrangle range is discussed for the different CCT values. As illustrated in Figure 7, the curves had a consistent variation tendency for different CCT values.