# Performance Analysis of a Vertical FSO Link with Energy Harvesting Strategy
## 4 Results and Discussions  
In this section we analyze the impact of FSO link parameters on system performance in terms of energy harvesting and quality using the AEH and BER expressions derived in the previous section. This analysis allows to identify which are the key design parameters and the trade-offs to be considered in order to properly choose such parameters. For our numerical analysis, we have assumed the values given in Table 1. In particular, we consider a vertical FSO link consisting of a ground-based optical transmitter located at a height \(z_{0}\) and a receiver mounted on a UAV hovering on the ground at a height \(Z\). Therefore, the separation between both is \(L=Z-z_{0}\). The transmitter transmits a light beam with a divergence angle \(\theta_{T}\)= 1 mrad [6] and a peak power \(P_{m}\) operating at a wavelength of 1550 nm. The receiver, as in [44], is composed of an optical circular converging lens whose effective light collection area is characterized by an aperture radius, \(r\), of 10 cm with a responsivity \(R=0.5\) A/W. Some commercial implementations following these features can be found at [55; 56] Therefore, for \(L=300\) m [57], the ratio of the beam waist to the aperture radius of the receiver is \((\omega_{z}/r)=3\) (remember that a source with a 1 mrad divergence angle was considered) while, for \(L=1000\) m, \((\omega_{z}/r)=10\). To cover a large area on the ground, a field of view FOV\(=45^{\circ}\) is assumed. Due to this large FOV, shot noise caused by ambient light is the dominant source of noise in the receiver. A spectral radiance \(S_{n}=1\) mW/(cm\({}^{2}\) nm srad), with an optical bandwidth \(B_{o}=10\) nm and a noise bandwidth \(B_{n}=1\) GHz are assumed to obtain \(\sigma_{n}^{2}\) from (2). Regarding the turbulence, we calculate the magnitudes of \(\alpha\) and \(\beta\), with the expressions (6) and (7), considering the values of \(C_{n}^{2}(z)\) provided by the Hufnagel-Valley model [39] for different link heights, assuming \(C_{n}^{2}(z_{0})=1.7\times 10^{-13}\) m\({}^{-2/3}\). Thus, \(\alpha\) and \(\beta\) vary between 25 and 30 for heights between 300 m and 1000 m, leading to \(\sigma_{R}^{2}<<1\), which corresponds to a very weak turbulence condition. In addition, we consider a jitter of \(\sigma_{s}=10\) cm [58] to model the pointing error. Finally, we use the attenuation coefficients corresponding to very clear air, clear air, and haze shown in Table 1. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **FSO Parameters** & \\ \hline
**Parameter** & **Symbol** & **Value** \\ \hline Operating Wavelength & \(\lambda\) & 1550 nm \\ \hline Transmitter divergence & \(\theta_{T}\) & 1 mrad \\ \hline Responsivity & \(R\) & 0.5 A/W \\ \hline Receiver aperture radius & \(r\) & 10 cm \\ \hline Field of view & FOV & 45\({}^{\circ}\) \\ \hline Optical Bandwidth & \(B_{o}\) & 10 nm \\ \hline Noise Bandwidth & \(B_{n}\) & 1 GHz \\ \hline Spectral radiance & \(S_{n}\) & 1 mW/cm\({}^{2}\) nm srad \\ \hline \hline
**Turbulence, pointing error and climatic parameters** & \\ \hline
**Parameter** & **Symbol** & **Value** \\ \hline Structure parameter & \(C_{n}^{2}(z_{0})\) & \(1.7\times 10^{-13}\) m\({}^{-2/3}\) \\ \hline Number of large-scale cells & \(\alpha\) & 30 \\ \hline Number of small-scale cells & \(\beta\) & 30 \\ \hline Jitter variance & \(\sigma_{s}\) & 10 cm \\ \hline Attenuation coefficient (very clear air) & \(a\) & 0.0647 dB/km \\ \hline Attenuation coefficient (clear air) & \(a\) & 0.2208 dB/km \\ \hline Attenuation coefficient (haze) & \(a\) & 0.7360 dB/km \\ \hline \hline \multicolumn{3}{c}{**EH parameters**} \\ \hline
**Parameter** & **Symbol** & **Value** \\ \hline Fill factor & \(f\) & 0.75 \\ \hline Dark saturation current & \(l_{o}\) & \(10^{-9}\) A \\ \hline Thermal voltage & \(V_{t}\) & 25 mV \\ \hline \end{tabular}
\end{table} 
Table 1: System parameters.