## 5 Numerical Results  
In this paper, the satellite height is 3.6 \(\times\) 10\({}^{3}\) km and the altitude of receiver is 0. According to simulation, \(C_{n}^{2}(h)\) changes little with satellite height increasing, when the height is over 20 km. The satellite slew rate is related to the height, which influences the rms wind speed. The laser wavelength is 1550 nm.  
It is assumed that the aperture area is variable, the power of the signal received by the aperture increases and the scintillation index of irradiance decreases with the aperture diameter increasing. The BER against aperture area are shown in Figure 1. Each curve has its certain satellite zenith angle, atmospheric parameter, and \(\rho_{0}\) in (17).  
To investigate the improvement of aperture averaging in further, Figure 2 shows BER of the receiver with different apertures against the average SNR \(\gamma_{0}\). When the zenith angle is larger and the atmosphere turbulence is stronger, the effect of aperture averaging is more obvious. According Figure 2b with weak turbulence and small zenith angle, the improvement of aperture averaging is limited, when \(d\geq 50\) cm. In Figure 2c, when BER = 10\({}^{-8}\), the noise endurance differences between d = 10 cm and d = 20 cm is nearly 2 dB, the same as the noise endurance difference between d = 20 cm and d = 50 cm.  
Figure 1: Performance of bit error rate (BER) when the aperture area is variable.  
Similar to the analyzing of BER, the outage probability is analyzed in two ways. In Figure 3, the outage probability decreases rapidly with aperture diameter increasing, once the average SNR is over the threshold. Here the average SNR in unit aperture area \(\rho_{0}\) is set to be 20 dB, and the threshold value of the SNR \(\gamma_{th}\) is 10 dB. When the diameter is smaller than 0.36 m, the outage probability values are all nearly 1 as a result of lower SNR and higher scintillation index.  
The effect made by different aperture diameters, different zenith angles and atmospheric conditions on the outage probability is shown in Figure 4. The SNR threshold \(\gamma_{th}\) is set to be 10 dB. When the SNR exceeds the threshold, the curves of point receiver model (\(d=0\)) drop more slowly than others. When the outage probability is \(10^{-4}\) in Figure 4c, the aperture with d = 20 cm needs more than 1 dB higher SNR than d = 50 cm.  
Figure 3: Performance of outage probability when the aperture area is variable.  
The average capacity against the aperture diameter when \(\rho_{0}=25\) dB and \(\rho_{0}=35\) dB is shown in Figure 5. Each curve with the same average SNR overlaps with each other nearly in spite of the different atmospheric conditions and satellite zenith angles. To some extent, enough average SNR play more important role in average capacity than the atmospheric condition.  
The average capacity against the average SNR is shown in Figure 6. When the zenith angle is larger and the turbulence is stronger, the differences of the average capacity with different aperture diameters are more obvious. According to the curves, the aperture averaging effect of average capacity is less obvious than the effect of BER. The curves overlap with each other nearly when d = 10 cm, 20 cm, 30 cm, 40 cm, 50 cm, especially in Figure 6b.  
Figure 5: Performance of average capacity when the aperture area is variable.