# LDPC-Coded CAP with Spatial Diversity for UVLC Systems over Generalized-Gamma Fading Channel
## 4 Results and Discussion  
In this section, the BER performance of the proposed LDPC-coded CAP with spatial-diversity UVLC system was evaluated using a Monte Carlo simulation under different turbulence conditions and diversity orders. Meanwhile, the analytical BER of uncoded CAP with spatial-diversity UVLC system (given by Equation (20)) was verified by comparing analytical and simulation results. The simulation parameters for this study are given in Table 2.  
First, the theoretical and simulated PDFs of the GG distribution are presented in Figure 2, showing good agreement, hence ensuring accurate GG turbulence channels for BER estimation. Figure 3 shows the BER performance of uncoded CAP with spatial diversity over GG turbulence channels, where we assumed subchannels were independent of each other. For comparison, results for the system without diversity (i.e., \(N=1\)) are also presented. Figure 3 shows that spatial diversity was effective in mitigating the adverse turbulence effect. Furthermore, analytical BERs approximately matched simulated BERs, validating the analysis. Obviously, BERs increase with increasing constellation size and turbulence strength. A larger diversity order or power penalty is required for 16-CAP to obtain the same BER performance as that of 4-CAP. For example, in weak turbulence channel with \(\delta_{1}^{2}=0.2\), 16-CAP with \(N=2\) needed an additional SNR of 6.5 dB to obtain a BER of \(10^{-3}\) compared to 4-CAP. Additionally, to achieve a BER of \(10^{-4}\) at the SNR of \(\sim\)25 dB, diversity orders were 2 and 4 for 4-CAP and 16-CAP,  
respectively. Thus, a trade-off between spectral efficiency and reliability should be carefully considered in practical implementation. To obtain further performance improvement, we studied the effect of LDPC to mitigate fading on the basis of MC simulations. The BER performance of LDPC-coded 4- and 16-CAP without diversity in a GG turbulence UVLC channel is shown in Figure 4. LDPC codes were effective in mitigating the adverse effect of turbulence for the 4- and 16-CAP systems over a weak turbulence channel with \(\delta_{\rm I}^{2}=0.2\). For example, using LDPC codes, a waterfall of BER of 4-CAP was achieved at the SNR of \(\sim\)24 dB and the BER of 16-CAP fall by an order of magnitude at the SNR of 30 dB. However, LDPC codes did not provide significant improvement over a strong turbulence channel with \(\sigma_{\rm I}^{2}=1.4\). That is because the performance of LDPC-coded schemes depends on the input of the LDPC decoder, i.e., soft-demapping information. Hence, the performance of a coded CAP scheme with spatial diversity was studied to mitigate the turbulence effect. Figure 5 shows the BER performance of the coded CAP with spatial diversity under turbulent UVLC channels. In weak turbulence with \(\delta_{\rm I}^{2}=0.2\), the coded spatial-diversity scheme with \(N=2\) had better performance than that of the spatial-diversity-only scheme with \(N=4\), resulting in BER waterfalls at SNRs of \(\sim\)15 and \(\sim\)19 dB for 4- and 16-CAP, respectively. In strong turbulence with \(\sigma_{I}^{2}=1.4\), the coded spatial-diversity scheme with \(N=4\) could obtain high coding gain and achieve a BER of \(10^{-4}\) at SNRs \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline \(M\) & 4, 16 \\ Pseudorandom bits length (PRBS) & \(>\)217 \\ Symbol duration & \(4\times 10^{-8}\) s \\ Roll factor, \(\beta\) & 0.15 \\ Upsampling factor & 20 \\ Carrier frequency: symbol rate \(\times\) (\(1+\beta\))/2 & 14.375 MHz \\ Normalised DC bias & 3 \\ GG-distributed parameters (\(m\), \(\
u\)) & (1.5,1), (0.5,0.6) \\ Scintillation index & 0.2,1.4 \\ LDPC code length and rate & 2304, 1/2 \\ Diversity order & 1, 2, 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation parameters. Note: GG, generalized-gamma; LDPC, low-density parity check. Figure 2: Probability-density function (PDF) of GG distribution. Figure 4: BERs of LDPC-coded 4- and 16-CAP single-branch UVLC over turbulent channels.