## 3 Results and Discussions
### Experimental Results  
Based on the above simulation parameters, the corresponding hardware experiments were further performed. The experimental setup of a point-to-point VLC system using a blue mini-LED is illustrated in Figure 4, where the inset shows the photo of the overall experimental testbed. Firstly, the transmitted signal which was digitally generated offline by MATLAB was fed into an arbitrary waveform generator (AWG, Tektronix AFG31102) with a sampling rate of 250 MSa/s, where the signal bandwidth was set to 96 MHz. The AWG output signal was further combined with a 120 mA DC bias current via a bias-tee (MiniCircuits, ZFBT-6 GW+) and the resultant signal was used to drive a blue mini-LED (HCCLS2021 CHI03). Subsequently, a pair of biconvex lenses each with a diameter of 12.7 mm and a focal length of 20 mm were employed to ensure that most of the light emitted by the LED was focused on the active area of a photodetector (PD, Thorlabs PDA10A2). The PD had a bandwidth of 150 MHz and an active area of 0.8 mm\({}^{2}\). After that, the detected signal was recorded by a digital storage oscilloscope (DSO, LeCroy WaveSurfer432) with a sampling rate of 1 GSa/s, which was further processed offline by MATLAB. The detailed experimental parameters are given in Table 3.  
Figure 5a,b illustrate the measured nonlinear voltage-current curve and the low-pass frequency response of the system, respectively. It can be clearly observed that the system exhibits notable nonlinearity which is mainly caused by the blue mini-LED. We can also see  
Figure 3: Simulation BER vs. SNR for 4 CAP-IM and 4 CAP-DM achieving the same SE of 2.5 bits/s/Hz over the AWGN channel. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline AWG sampling rate & 250 MSa/s \\ Signal bandwidth & 96 MHz \\ DC bias current & 120 mA \\ Diameter of biconvex lenses & 12.7 mm \\ Focal length of biconvex lenses & 20 mm \\ Bandwidth of PD & 150 MHz \\ Active area of PD & 0.8 mm\({}^{2}\) \\ DSO sampling rate & 1 GSa/s \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimental Parameters. that the system reflects a typical low-pass characteristic which can result in an unbalanced SNR between the high-frequency subbands and the low-frequency subbands in the 4 CAP signal. Figure 6 shows the measured BER versus the peak-to-peak voltage (Vpp) of the AWG output signal for different cases, where the transmission distance is fixed at 80 cm. It can be clearly seen that 4 CAP-DM greatly outperforms both 4 CAP-IM and 4 CAP-IM with PWC, achieving the lowest BER of \(1.3\times 10^{-3}\) at Vpp = 2 V. Compared with 4 CAP-DM, 4 CAP-DM with PWC can achieve further significant BER improvement, obtaining the lowest BER of \(4.45\times 10^{-4}\) at Vpp = 2 V. Moreover, nearly the same BER performance can be achieved for PWC-based 4 CAP-DM with and without 2D chaotic encryption, suggesting that the application of 2D chaotic encryption does not affect the BER performance of PWC-based 4 CAP-DM. It can also be observed that, for PWC-based 4 CAP-DM with 2D chaotic encryption, the BER with no key and the BER with only the key for CMS are always about 0.38, and the BER with only the key for CCS is always about 0.21, which indicates that the application of 2D chaotic encryption can efficiently ensure the security of the transmitted 4 CAP-DM signal. The insets (a)-(d) in Figure 6 depict the corresponding received constellation diagrams at Vpp = 2 V.  
Figure 7 shows the measured BER versus the transmission distance for different cases with Vpp = 2 V. We can see that the BER of 4 CAP-IM cannot reach the 7% FEC coding limit of BER = \(3.8\times 10^{-3}\) when the distance is in the range from 80 to 110 cm. The maximum distances that can be transmitted by 4 CAP-IM with PWC, 4 CAP-DM, and 4 CAP-DM with PWC at BER = \(3.8\times 10^{-3}\) are 83.0, 87.0, and 98.8 cm, respectively. Hence, a 4.82% improvement of transmission distance can be achieved by 4 CAP-DM in comparison to 4 CAP-DM with PWC.