# Performance of UAV-to-Ground FSO Communications with APD and Pointing Errors
## 4 Performance Results  
In this section, we provide numerical results in terms of SER to analyze the performance of the UAV-to-ground FSO communication system with APD and pointing errors under the influence of various operating conditions. The subcarrier intensity QAM modulation scheme was employed in the evaluation. Table 1 provides the relevant parameters of the UAV-to-ground FSO communication system. We considered using one UAV, under the assumption that the UAV hovers over a specific monitoring area to collect measured data from sensors on the ground. The UAV carries the payload of the FSO transmitter. In addition, an APD receiver-based FSO Rx station is located on the ground to collect data transmitted from the FSO transmitter mounted on the UAV. For the UAV and FSO Tx parameters, various typical system parameters are considered as follows. The optical operating wavelength \(\lambda=1.55\) um, the beam waist radius from 0.3 to 0.08 m, the average transmitted power per symbol \(P_{t}=-15\div 5\) dBm. Regarding the FSO link, the attenuation coefficient of \(\chi=3.436\), and the turbulence strengths of \(C_{n}^{2}=10^{-17}\) m\({}^{-2/3}\), \(5\times 10^{-15}\) m\({}^{-2/3}\), and \(10^{-14}\) m\({}^{-2/3}\) for weak, moderate, and strong turbulence, respectively. For the FSO Rx parameters, we considered the system parameters as follows. The receiver aperture diameter of \(D=0.08\) m, the electrical bandwidth of APD \(B_{e}=10^{9}\) Hz, the Planck constant of \(h_{Planck}=6.626\times 10^{-34}\) m\({}^{2}\) Kg/s, the APD's load resistance of \(R_{L}=1000\)\(\Omega\), the receiver noise temperature of \(T=300\) K, the ionization factor of \(k_{A}=0.7\), the Boltzmann's constant of \(k_{B}=1.38\times 10^{-23}\) J/K, and the amplifier noise figure of \(F_{n}=2\). Moreover, the variances in the orientation deviations of the Tx and Rx of \(\sigma_{to}^{2}=\sigma_{ro}^{2}=6\) cm for the low UAV's stability level, the variances of position deviations of the Tx and Rx of \(\sigma_{tp}^{2}=\sigma_{rp}^{2}=30\) cm [21]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Description** & **Parameter** & **Value Setting** \\ \hline _UAV and FSO Tx parameters_ & & \\ \hline Operational wavelength & \(\lambda\) & \(1.55\) μm \\ \hline Beam waist radius of Tx & \(\omega_{0}^{2}\) & \(0.3\)–\(0.08\) m \\ \hline The modulation index & \(m\) & \(1\) \\ \hline In-phase, quadrature distances & \(M_{I},M_{Q}\) & \(8,4\) \\ \hline Transmitted power per symbol & \(P_{t}\) & \(-15\div 5\) dBm \\ \hline Variance of position deviation & \(\sigma_{tp}^{2}\) & \(30\) cm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: UAV/FSO system parameters and constants. Figure 4 plots the distribution comparison of the combined channel model with the channel model proposed in [15] for the case of a strong atmospheric turbulence channel, and the transmitter beam waist radius \(\omega_{0}\) = 0.02 m. The combined channel distribution has higher density in the low region, resulting in a more unexpected impact on the system's performance. Figure 5 shows the SER-performance versus APD gain for various turbulence strengths of \(C_{n}^{2}\) with the transmission link length of 800 m, and the average transmitted power per symbol of \(P_{t}=-5\) dBm. It can be seen that the SER-performance strongly depends on the weather-related turbulence conditions. In addition, when increasing the APD's gain, the noise variances due to the desired received signal of \(\sigma_{s}^{2}\) and the undesired background radiation \(\sigma_{bg}^{2}\) also increase, leading to decreased system SER performance. More importantly, it can also be seen that the selection of the APD's gain, \(G\), has a significant impact on the system performance. By using the derived SER expressions, the \(G\)'s values are converged on the optimal line for the minimal SER value. Specifically, to achieve the best systems' SER-performance, the optimal gain value can be chosen in the range from 18 to 30.