# Post-Flood UAV-Based Free Space Optics Recovery Communications with Spatial Mode Diversity
## 5 Results and Discussion
Overall, a significant improvement in the SINR and outage performance was observed due to spatial mode diversity. At the receiver, the received optical beam for each channel is demultiplexed to separate spatial modes. It is well-established that refractive index fluctuations in clouds from pressure and temperature fluctuations cause rain [64]. This leads to aberration of the beam wavefront from random power and phase perturbations [65]. This results in the signal initially launched in a particular mode to spread to other modes [66]. The amount of spreading is influenced by the strength of the atmospheric turbulence. On a clear day, \(C_{n}^{2}\) values were found to be between \(7\times 10^{-16}\) m\({}^{-2/3}\) and \(4\times 10^{-15}\) m\({}^{-2/3}\), peaking in the afternoon. On a clear night, the \(C_{n}^{2}\) values were found to be lower, between \(8\times 10^{-17}\) m\({}^{-2/3}\) and \(1\times 10^{-16}\) m\({}^{-2/3}\). For light rain, the \(C_{n}^{2}\) values were in the range of \(4\times 10^{-16}\) m\({}^{-2/3}\) to \(7\times 10^{-16}\) m\({}^{-2/3}\). For moderate rain, the \(C_{n}^{2}\) values were slightly higher, in the range of \(6\times 10^{-16}\) m\({}^{-2/3}\) to \(9\times 10^{-16}\) m\({}^{-2/3}\), and for heavy rain, the \(C_{n}^{2}\) values were higher, in the range of \(8\times 10^{-16}\) m\({}^{-2/3}\) to \(2\times 10^{-15}\) m\({}^{-2/3}\). The \(C_{n}^{2}\) values were found to vary more on a clear day than during rainfall. The power coupling coefficients were computed for all channels using a noninterferometric modal decomposition method [53], under various weather conditions, at the minimum and maximum \(C_{n}^{2}\) values. With knowledge of the power coupling coefficients, the modal crosstalk matrices were constructed, without and with spatial mode diversity. The power coupling coefficients were normalized to the total received optical power for the set of modes present. Samples of inter-modal crosstalk matrices before mode diversity are shown in Figures 6 and 7, at the minimum and maximum \(C_{n}^{2}\) values, respectively. Samples of inter-modal crosstalk matrices after mode diversity are shown in Figures 8 and 9. For clear weather conditions in the day and at night, the power in the dominant mode was more than 75%. Under rain, power from the transmitted mode leaked into adjacent modes. The heavier the rain, the more substantial the spreading of power into adjacent modes due to increased atmospheric turbulence. Under light rain, the power in the dominant mode was in the range of 68% to 75% before channel diversity reception and 79% to 83% after mode diversity and power were successfully maintained in the dominant modes through the switch to the backup channels during SINR dips. Under medium rain, the power in the dominant mode was in the range of 64% to 68% prior to mode diversity and improved to 75% to 78% in the presence of mode  
Figure 5: SINR versus time on a clear day. diversity. Under heavy rain, the power in the dominant mode was approximately 56% to 63% without mode diversity reception and increased to 71% to 75% with mode diversity reception. Uplink and downlink data transmissions demonstrated similar power coupling coefficient characteristics, whereas uplink and downlink data transmissions demonstrated similar power coupling coefficient characteristics. Figure 6: Variation in normalized power coupling coefficients for on _LP 01_ mode before spatial mode diversity: (**a,f**) clear night, (**b,g**) clear day, (**c,h**) light rain, (**d,i**) medium rain, (**e,j**) heavy rain. Top panel (**a–e**) shows the power coupling coefficients at low-refractive-index structure values, and bottom panel shows (**f–j**) those at high-refractive-index structure values. Color legend of normalized power coupling coefficients for all plots is on the bottom right corner. Figure 7: Variation in normalized power coupling coefficients on _LP11_ mode before spatial mode diversity: (**a,f**) clear night, (**b,g**) clear day, (**c,h**) light rain, (**d,i**) medium rain, (**e,j**) heavy rain.