Assessment of adaptive optics-corrected optical links statistics from integrated turbulence parameters through a Gaussian process metamodel

With the development of free space optical links (FSO) for space-ground communications comes the need to mitigate the effects of the atmospheric turbulence to guarantee a lossless connection. By having a network of addressable ground stations, we want to guarantee to always target a point where the link is available. Assuming atmospheric transmission is managed thanks to site diversity, we focus only on the influence of atmospheric turbulence on the signal injected into a single mode fiber on the downlink. The use of adaptive optics (AO) is assumed to avoid turbulence-induced signal disruptions and enable a sufficiently high level of received signal for data transmission. Up to now, AO performance adequate assessment required the knowledge of high-resolution $C_n^2$ and wind profiles. With the advent of integrated atmospheric parameters measurement instruments, we investigate here the possibility to estimate AO-corrected performance from a limited number of integrated parameters. In this paper, we propose to use a Gaussian process metamodel to assess the statistics of the received optical power after an AO correction. Taking as input only four integrated parameters of the turbulence profile and associated wind profile, which can be measured with simple instruments, the estimation error on the value of the 1% quantile of the received optical power is inferior to $0.7\text{dB}$. We also demonstrate the possibility to estimate the half correlation time of the received optical power using the same integrated parameters.