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Achieving high data rates in GEO Feeder optical uplinks faces challenges due to the fading nature of the channel induced by atmospheric turbulence. Adaptive optics pre-compensation using downlink measurements is a solution to mitigate the impact of the turbulence. However, the point-ahead angle anisoplanatism, inherent to the bidirectional link geometry, limits the uplink correction efficiency, leading to persistent signal fades and loss of information onboard the satellite. We recently proposed a new minimum mean square error method that improves the phase estimation at the PAA based on the downlink phase and log amplitude measurements, reducing the anisoplanatism impact on the coupled flux. Alternatively, a laser guide star can be used to measure the phase at the PAA. However, it is currently challenging to retrieve the tip, tilt, and focus modes, whose correction is essential to improve the link quality. In this article, we propose to combine both techniques to estimate the tip, tilt, and focus at the PAA by incorporating the LGS high-order measurements in the MMSE formalism. We develop the associated analytical reconstructor and evaluate the performance of the phase estimation and the gain on the coupled flux statistics aboard the GEO satellite, considering an idealized LGS system. The new estimator is shown to reduce the tip, tilt, and focus error variances by up to 70% of their initial value.

We present a method to estimate the pre-compensation phase of ground-to-geostationary orbit (GEO) optical links based on downlink phase and log-amplitude measurements from two ground apertures. This method allows us to reduce the point-ahead anisoplanatism that currently limits the telecom performance of GEO-feeder links. It is shown to reduce the anisoplanatic phase variance by 50%, hence improving the statistics of the coupled flux aboard the satellite. It also outperforms the one-aperture estimation method for very severe atmospheric conditions. Besides, only low-resolution amplitude measurements are required on the second aperture to reach the performance of the novel estimator.