# Performance of UAV-to-Ground FSO Communications with APD and Pointing Errors
## 4 Performance Results
For example, with the weak atmospheric turbulence condition \(C_{n}^{2}=10^{-17}\) m\({}^{-2/3}\) using \(G=18\), the system SER-performance can be approximately achieved at \(10^{-9}\). However, \begin{table}
\begin{tabular}{c c c} \hline \hline
**Description** & **Parameter** & **Value setting** \\ \hline Variance of orientation deviation & \(\sigma_{to}^{2}\) & 6 cm \\ \hline _FSO link parameters_ & & \\ \hline Link length & \(L\) & 800 m \(\div\) 900 m \\ \hline Attenuation coefficient & \(\chi\) & 3.436 \\ \hline Strength of weak turbulence & \(C_{n}^{2}\) & \(10^{-17}\) m\({}^{-2/3}\) \\ \hline Strength of moderate turbulence & \(C_{n}^{2}\) & \(5\times 10^{-15}\) m\({}^{-2/3}\) \\ \hline Strength of strong turbulence & \(C_{n}^{2}\) & \(10^{-14}\) m\({}^{-2/3}\) \\ \hline _FSO Rx parameters_ & & \\ \hline Lens radius & \(r\) & 0.04 m \\ \hline Average APD gain & \(G\) & 18 \(\div\) 30 \\ \hline Excess noise factor of APD & \(F\) & 2.75 \\ \hline Electrical bandwidth of APD & \(B_{e}\) & \(10^{9}\) Hz \\ \hline Optical filter bandwidth & \(B_{0}\) & \(10^{-9}\) m \\ \hline The Planck constant & \(h_{Planck}\) & \(6.626\times 10^{-34}\) m\({}^{2}\). Kg/s \\ \hline APD’s load resistance & \(R_{L}\) & 1000 \(\Omega\) \\ \hline Receiver noise temperature & \(T\) & 300\({}^{0}\) K \\ \hline Ionization factor & \(k_{A}\) & 0.7 \\ \hline Boltzmann’s constant & \(k_{B}\) & \(1.38\times 10^{-23}\) J/K \\ \hline Amplifier noise figure & \(F_{n}\) & 2 \\ \hline Receiver aperture diameter & \(D\) & 0.08 m \\ \hline Rx’s FOV angle & \(\theta_{FOV}\) & 20 mrad \\ \hline Variance of position deviation & \(\sigma_{rp}^{2}\) & 30 cm \\ \hline Variance of orientation deviation & \(\sigma_{ro}^{2}\) & 6 cm \\ \hline Spectral radiance of the background radiations & \(N_{b}(\lambda)\) & \(10^{-3}\) Watts/cm\({}^{2}\)-\(\mu\)m-srad \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._with the strong atmospheric turbulence condition \(C_{n}^{2}=10^{-14}\) m\({}^{-2/3}\) increasing \(G\) to 25, the system SER-performance will be approximately achieved at \(10^{-5}\). Then, Figure 6 provides the impact of the beam waist radius \(\omega_{0}\) on the Tx to SER-performance for different values of turbulence strength and pointing error displacement standard deviations of \(\sigma_{\rm s}\) = 0.05, 0.07, 0.1, with a transmission link length of 800 m and an APD's gain \(D\) = 20. We found that the system performance strongly depends on this. It is highlighted in the results that by increasing the beam waist radius at the Tx to a proper value, the SER-performance of the specific APD receiver for all the pointing error displacement standard deviations decrease significantly. Then, the system-performance converge to the minimum of SER at the optimal value of \(\omega_{0}\). Consequently, \(\omega_{0}\) would be selected for the best performance from 2 cm \(\div\) 2.2 cm operating under various system parameters. In addition, when increasing the value of \(\sigma_{\rm s}\) from the optimal gain, the SER-performance steadily increases and progresses to saturation levels. For example, SER \(\approx 10^{-1}\) when \(\omega_{0}\geq 0.05\) m for the system operating under moderate atmospheric turbulence conditions. This is reasonable because the higher the level of instability of the UAV is at the Tx, the wider the optical beam to reduce the influence of fluctuations on the Rx is. Then, we investigate in Figure 7 the performance of a UAV-based FSO system versus the link distance \(L\) for, again, different values of turbulence strength and pointing error displacement standard deviations of \(\sigma_{\rm s}\) = 0.05, 0.07, 0.1, using the optimal beam waist radius. As we can observe, the results from Figure 7 show that a decreasing \(L\) can compensate for the effects of UAV's fluctuation on the system performance. Finally, we show in Figure 8 the performance of the UAV-based FSO system versus the average electrical SNR for different QAM modulation schemes, e.g., 8-PSK and 16-QAM, with/without pointing error.