## 4 Performance Analysis
### Transmission Performance  
The required transmission power to achieve the desired outage performance is shown in Figure 3. The transmission performances are compared for the systems designed by the proposed misalignment model and the pointing jitter as the only source of pointing error. The increase in pointing error for stronger turbulence requires more power to establish the communication links. Furthermore, more transmitted beams and fewer positioning sensors for misalignment detection make performance degradation severe as the pointing error increases. To analyze the transmission performance for MIMO based FSO systems, the system configuration for bi-directional communication should be considered. For data reception at the ground terminal, the increased number of transceivers at the ground causes an increase in the incident beams in the positioning sensors at the UAV, which increases the detected misalignment. Furthermore, the number of transceivers at the ground makes the arrangement of transceivers larger. In contrast, the increased number of transceivers at the UAV causes the averaging effect in the detected misalignment to decrease the pointing error. However, the number of transceivers is still maintained, so the divergence loss does not change. These system configurations show better performance for the large number of transceivers at the UAV and the small number at the ground. Figure 2: Variance of misalignment for different numbers of channels in MIMO transmissions. However, the system characteristics described above are reversed for data reception at the UAV terminal. The equivalent system configurations with the large number of transceivers at the UAV and the small number at the ground show poor performance due to increased divergence loss and pointing error. Therefore, the overall transmission performance of the bi-directional MIMO based FSO system is down-leveled to the worse performance. The outage performance for data reception at the ground terminal with two fixed transceivers at the UAV is shown in Figure 4. The 1 \(\times\) 2 system has a single transmitted beam to detect misalignment, so the pointing error remains equivalent to the pointing jitter. The range of \(M\) receivers and the pointing error by the \(M\) transmitted beams to the UAV increase as the number of transceivers increases at the ground. Thus, the improvement of diversity gain becomes smaller as the pointing error increases by the total number of diversity channels. Compared to the outage performance in Figure 4, the outage performance for data reception at the UAV is shown in Figure 5. The system characteristics are reversed due to the increasing number of \(M\) transceivers at the ground. The outage performance of \(1\times 2\) systems is worse than that of the ground due to the larger number of receivers at the UAV. However, the pointing error due to multiple beam transmissions decreases as the \(M\) positioning sensors at the ground increase. In contrast, the range of \(N\) receivers at the UAV is maintained. Thus, the improvement of diversity gain becomes larger with the number of channels. These results show an inversely proportional performance between the number of transceivers at the UAV and the ground. Therefore, the system configuration for bi-directional MIMO based FSO systems is significant. Figure 3: Required transmit power for the different number of channels. The overall outage performance with the same total number of four and nine diversity channels is shown in Figure 6. It is difficult for the single-input single-output (SISO) based FSO system to achieve the desired performance due to limited transmission power in severe atmospheric turbulence. Thus, the spatial diversity technique is required to mitigate atmospheric fading by diversity gain. When the number of transceivers at the ground and UAV is different, the transmission performance of the system is down-leveled towards the worse.