## 3 Simulation Results and Discussion  
### Improvement Based on OFDM  
In the simulation, the initial values of the used parameters are shown in Table 1. The optical carrier output from the transmitter was supposed to satisfy the Gaussian distribution. The transmission length was divided into 10 segments with the equal spacing, and one phase screen was placed at the end of each segment. In total, 1000 samples were collected to investigate the atmospheric turbulence effect on laser transmission. Figure 3a-c show the normalized optical intensity variations under weak, moderate, and strong turbulence conditions. With the turbulence strengthened, the fluctuations of the optical intensity are enhanced. The variance of the optical intensities is 0.0088, 0.2104, and 0.4898 for weak, moderate, and strong turbulences, respectively.  
The performance of the OFDM-FSO transmission link was evaluated in an atmospheric turbulence channel. A 20 Gbit/s pseudo-random bit sequence (PRBS) was mapped to the QPSK modulation format, and then loaded onto 64 sub-carriers. Another 8 sub-carriers were used as the CP to eliminate the inter-symbol interference (ISI). Finally, the IFFT with a size of 128 was used to convert the data into an OFDM signal. Figure 4 shows the BER curve of this OFDM-QPSK signal in the turbulence channel with the refractive-index structure parameters \(C_{n}^{2}\) of 5.0 \(\times\) 10\({}^{-15}\) m\({}^{-2/3}\), where the BER of the single carrier QPSK (SC-QPSK) signal was also simulated for comparison. The BER of the OFDM-QPSK signal is much lower than that of the SC-OFDM signal without sub-carriers. At the SNR of 6 dB, the achieved BERs of the SC-QPSK and the OFDM-QPSK signals are 2.87 \(\times\) 10\({}^{-3}\) and 2.98 \(\times\) 10\({}^{-4}\), which are efficiently reduced. Figure 5a,b show the constellation diagrams of the OFDM-QPSK and the SC-QPSK signal at the same SNR of 6 dB. Their error vector magnitudes are 0.3481 and 0.4903, which means that the OFDM-QPSK signal has a better quality than the SC-QPSK signal.  
Figure 6 shows the BER of the OFDM-QPSK signal as a function of the SNR under different turbulence conditions, as shown in Table 1. At the SNR of 6 dB, the BER of the OFDM signal under weak, moderate, and strong turbulences is 2.98 \(\times\) 10\({}^{-4}\), 2.45 \(\times\) 10\({}^{-3}\), and 2.14 \(\times\) 10\({}^{-2}\), respectively. The transmission quality degrades as the turbulence strengthens. In Figure 6, the BER curves become flat under moderate and strong turbulence. The reason may be that the degradation caused by the turbulence is too heavy to be fully compensated by the DSP. The signal quality cannot be further improved even though the SNR increases.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Symbol** & **Value** \\ \hline Wavelength, \(\lambda\) & 1550 nm \\ Link distance, \(L\) & 1000 m \\ Phase screen size & 0.5 m \(\times\) 0.5 m \\ Inner scale, \(l_{0}\) & 0 \\ Outer scale, \(L_{0}\) & 100 m \\  & \(5\times 10^{-15}\) m\({}^{-2/3}\) (weak turbulence) \\ Refractive-index structure parameters, \(C_{n}^{2}\) & \(5\times 10^{-14}\) m\({}^{-2/3}\) (moderate turbulence) \\  & \(5\times 10^{-13}\) m\({}^{-2/3}\) (strong turbulence) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulation parameter values.  
Figure 3: Normalized optical intensity variations under (**a**) weak turbulence, (**b**) moderate turbulence and (**c**) strong turbulence.