## 3 Simulation Results and Discussion
### Improvement Using Spatial Diversity  
The spatial diversity reception technology is adopted to further improve the receiver sensitivity. Figure 7 depicts the BER curve as a function of the SNR with different aperture numbers of receivers. Figure 7a-c show the weak, moderate, and strong turbulences, respectively. Here, 1R, 2R, 4R, and 6R represent the aperture number 1, 2, 4, and 6, respectively. In the case of weak turbulence shown in Figure 7a, the system performance cannot be further improved by increasing the aperture number since the sensitivity of a single receiver is sufficient. In the moderate turbulence (see Figure 7b), the performance of two-aperture spatial diversity is much better than the single receiver. At the SNR of 6 dB, the required BER drops from \(2.45\times 10^{-3}\) to \(6.10\times 10^{-4}\) if the two-aperture receiver array is used instead of the single receiver. By further increasing the aperture number to four, the  
Figure 4: BER curves of the OFDM-QPSK signal and the SC-QPSK signal.  
Figure 5: Constellation diagrams of **(a)** OFDM-QPSK and **(b)** and SC-QPSK at the SNR of 6 dB.  
Figure 6: BER curves of the OFDM signal under different turbulence conditions.  
BER is further reduced to 3.89 \(\times\) 10\({}^{-4}\) by using four-aperture receivers. Under the strong turbulence, the BER cannot be reduced below 0.01 using a single receiver, even when the SNR is increased to as high as 20 dB. Using two-aperture spatial diversity reception, the BER can reach approximately 1 \(\times\) 10\({}^{-3}\). While four-aperture receivers are adopted, the BER is reduced to 1 \(\times\) 10\({}^{-4}\) when the SNR is about 10 dB. At the SNR of 6 dB, the BERs are 2.14 \(\times\) 10\({}^{-2}\), 6.23 \(\times\) 10\({}^{-3}\), 1.16 \(\times\) 10\({}^{-3}\), and 6.87 \(\times\) 10\({}^{-4}\) for the single receiver, two-aperture receivers, four-aperture receivers, and six-aperture receivers, respectively. It can be seen that the FSO link performance of the OFDM-QPSK signal is effectively improved using the spatial diversity reception.  
Figure 7: BER curves of the spatial diversity reception under different turbulence conditions: (**a**) weak turbulence, (**b**) moderate turbulence, and (**c**) strong turbulence.  
The above analysis shows that the OFDM-QPSK link performance can be effectively improved by using spatial diversity, but the improvement becomes limited as the receiver aperture number increases. Therefore, it is reasonable to consider an optimal aperture number of receivers under the requirement of a certain BER. Here, a requirement for the number of apertures is proposed, where the maximum BER of 1 \(\times\) 10\({}^{-3}\) is permitted when the signal SNR is 6 dB. In this way, Figure 8 shows the required aperture number of receivers under different turbulent conditions. As turbulence strength increases, the required aperture number of receivers increases accordingly. When the turbulence is weak, a single receiver is sufficient. For the moderate turbulences (such as \(C_{n}^{2}\) is 5 \(\times\) 10\({}^{-14}\) m\({}^{-2/3}\) and 1 \(\times\) 10\({}^{-13}\) m\({}^{-2/3}\), corresponding to the Rytov coefficients of 0.99 and 1.99, respectively), 2-4 aperture receivers are needed to satisfy the BER requirement. Moreover, at least 6 aperture receivers are required to keep the BER below 1 \(\times\) 10\({}^{-3}\) under strong turbulence with \(C_{n}^{2}\) of 5 \(\times\) 10\({}^{-13}\) m\({}^{-2/3}\) (the Rytov coefficient is 9.95). In practical applications, the appropriate aperture number of receivers should be selected according to the channel conditions.