# Performance Analysis of a Vertical FSO Link with Energy Harvesting Strategy
### Contributions  
Despite their relevance, none of the aforementioned studies, e.g., [6; 29; 30; 31; 32; 33], consider two important aspects: (i) the random nature of the EH, which is inherited from the variability of the optical channel; and (ii) the trade-off between bit error rate (BER) and EH. In this paper, we investigate the influence of this random behavior on the design of EH-optimized links, while fulfilling a target BER. This will be achieved by transmitting a certain fraction, \(\zeta\), of the peak transmission power, \(P_{m}\), with the logical symbol '0'. As shown in this paper, a proper design of the \(\zeta\) maximizes the harvested energy while fulfilling a desirable reliability in terms of the BER.  
More specifically, we aim to respond to the following inquiries: (i) the optimum \(\zeta\) value to maximize the harvested energy while fulfilling a target BER; and (ii) the maximum average harvested energy that can be achieved under realistic link conditions. To address those two issues we derive some closed-form expressions for the two main metrics here considered: the average BER and the average harvested energy. Therefore, the paper's contributions can be summarized as follows:  
1. We propose an accurate mathematical model for the UAV-based approach to provide backhaul connectivity for 5G+ networks [6]. To this end, ground stations and UAVs establish FSO links with EH to recharge the UAVs batteries and extend the service time. Furthermore, the UAVs will have another FSO link with the BSs to provide backhaul connectivity. The mathematical model considers realistic channel impairments such as turbulence fading (scintillation), atmospheric loss, pointing errors, and additive white Gaussian noise (AWGN).
2. We derive analytical closed-form expressions of the average harvested energy as a function of the FSO link parameters. These expressions can be used to improve energy harvesting efficiency of the FSO links.
3. Closed-form expressions for the BER have been obtained for links using a variant of the on-off Keying (OOK) scheme that has been properly modified to maximize the EH. With this scheme, which is referred to as OOK-EH, a certain fraction, \(\zeta\), of the peak optical power, \(P_{m}\), is also transmitted with the symbol '0' to recharge the batteries of the UAV.
4. We obtain the optimal \(\zeta\) value that maximizes the average harvested energy while maintaining its associated BER smaller than a _target_ BER. Such a target BER is defined in practical communication standards to guarantee a reliable transmission.
5. The performance associated with the proposed scheme is corroborated with extensive Monte Carlo (MC) simulations in diverse and realistic atmospheric conditions. An excellent agreement between theoretical and simulation results is observed. Results reveal that the combination of FSO, EH, and UAVs provide reliable backhaul links while capturing energy to extend the UAVs service time. Let us recall that short lifetime of the batteries mounted on drones is seen as the main limitation of the proposed approach. For this reason, one of the main targets of our work is to obtain the optimal amount of energy that can be collected to charge the batteries of the UAVs involved in the system, as discussed in [30; 31], while maintaining its performance in terms of BER.  
The rest of the paper is structured as follows. In Section 2 the system model is mathematically described, including the signal as the channel model. Then, the main metrics are presented and derived in Section 3, namely, the expressions for the amount of harvested energy by the system and its BER. In Section 4 numerical results are obtained to assess the benefits of the proposed scheme, which allows to identify both trends and limiting factors. Finally, relevant conclusions are discussed in Section 5.