Multi-Layer Airborne FSO Systems: Performance Analysis and Optimization

With its ultra-high-capacity, free space optical (FSO) communication stands out as a powerful connectivity solution for airborne backhauling. In this paper, we consider typical backhauling scenarios for single-layer and multi-layer airborne networks and characterize the underlying multi-hop FSO transmission. In the first scenario, we consider a single-layer airborne backhaul system where a fleet of high-altitude platform stations (HAPSs) continuously rotates on a circular track at a specific altitude. It is assumed that the communication links are always established with the closest HAPS. In such a scenario, a dual-hop FSO transmission is required where the first hop is from the gateway node to HAPS and the second hop is from the HAPS to the base station. In the second scenario, we consider a two-layer system where HAPSs are assisted by rotary-wing unmanned aerial vehicles (UAVs) at lower operation altitudes to ease line of sight (LoS) requirement, which might be especially critical in urban scenarios. This mainly corresponds to a three-hop configuration where the first hop is from the gateway to HAPS, the second hop is from HAPS to UAV and the final hop is from UAV to the base station. For both scenarios under consideration, we first develop a channel model for the airborne link to describe atmospheric attenuation, geometrical loss, and pointing error. The transmission distance of the HAPS-based link is subject to continuous change due to movement and leads to a time-varying atmospheric attenuation loss and geometric loss. These mobility-induced variations in the average received power effectively introduce a fading effect. We develop a probability density function (PDF) to capture this effect. While pointing error can be ignored for HAPS-based links under certain conditions, rotary-wing UAVs introduce displacements in both <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {X}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {Y}$ </tex-math></inline-formula> directions. We further characterize this phenomenon and quantify the resulting variance of displacements. Based on the developed PDFs, we derive the end-to-end bit error rate (BER) for two-hop and three-hop airborne systems under consideration. We further propose a power allocation scheme to optimize the BER performance, ensuring that the overall performance is not dominated by a single hop.