# Performance Analysis of a Vertical FSO Link with Energy Harvesting Strategy
## 3 System Performance
### EH Performance  
An EH module is added to the receiver to collect the energy from the received signal. This module extracts the DC component, \(I_{\text{DC}}\), of the electrical signal that is obtained by the PD, \(i\). The DC current is then either stored or directly used to feed other modules such as the information detection module and the UAV's motor, which translates into extending the UAV's battery lifetime. Figure 2 illustrates a block diagram of the receiver where the EH and information detection modules are shown. As it can be observed, the EH module is formed by a Schottky diode and a low-pass filter (LPF), which are passive devices, and thus, its associated power consumption is limited and could be included in the conversionefficiency, \(\zeta\)[46]. Furthermore, this approach does not require either any control logic or any additional module to obtain the DC current.  
As described in [29; 31; 47], the harvested energy per second in the optical receiver is given by  
\[EH=fV_{t}I_{DC}\ln\left(1+\frac{I_{DC}}{I_{o}}\right), \tag{14}\]  
where \(f\), \(V_{t}\) and \(I_{o}\) stand for the photo-detector's fill factor, thermal voltage, and dark saturation current, respectively. The DC component of the output current, \(I_{DC}\), is written as [47]:  
\[I_{DC}=RhP_{av}. \tag{15}\]  
Here, \(R\) denotes the PD responsivity in A/W, with \(h\) being the composite channel attenuation coefficient, whereas \(P_{av}\) represents the average transmitted power.  
As can be noticed, the harvested energy is random due to the influence of the channel attenuation coefficient \(h\). Therefore, to obtain the collected energy over a long period of time, the average EH (AEH) is derived as:  
\[\text{AEH}=\int_{h>0}f_{h}(h)fV_{t}RhP_{av}\ln\left(1+\frac{RhP_{av}}{I_{o}} \right)dh, \tag{16}\]  
where \(f_{h}(h)\) is the pdf of the composite channel attenuation according to (12). Employing the expressions [48] (Eqs. (07.34.21.0011.01) and (07.34.21.0085.01)), the solution of this integral can be written in a closed-form as  
\[\text{AEH}=\frac{\gamma^{2}fV_{t}R_{av}A_{o}h_{l}}{\alpha\beta\Gamma(\alpha) \Gamma(\beta)}G_{5,3}^{1.5}\bigg{(}\frac{A_{o}h_{l}RP_{av}}{I_{o}\alpha\beta} \bigg{|}\begin{array}{c}1,1,-\gamma^{2},-\alpha,-\beta\\ 1,-1-\gamma^{2},0\end{array}\bigg{)}. \tag{17}\]  
Moreover, when only the effect of turbulent fading is considered, and \(f_{h}(h)\) is given by (5), the above equation reduces to  
\[\text{AEH}=\frac{fV_{t}RP_{av}(A_{o}h_{l})^{2}}{(\alpha\beta)^{2}\Gamma(\alpha )\Gamma(\beta)}G_{5,3}^{1.5}\bigg{(}\frac{A_{o}h_{l}RP_{av}}{I_{o}\alpha\beta} \bigg{|}\begin{array}{c}1,1,-1,-1-\alpha,-1-\beta\\ 1,-2,0\end{array}\bigg{)}. \tag{18}\]  
where the term \(P_{av}\), which is present in Equations (16)-(18), is expressed as \(P_{av}=P_{m}(1+\zeta)/2\) in case of OOK-EH. From Equations (17) and (18), the amount of harvested energy is not depending on the modulation scheme itself but on the average transmitted power. Of  
Figure 2: Block diagram of the proposed receiver structure with EH. An optical circular converging lens would be placed in front of the PD.  
course, the particular channel conditions and the type of PD and rest of modules shown in Figure 2 will influence on the amount of energy any UAV can extract.