Uplink phase estimation for optical ground-to-GEO links using a Rayleigh laser guide star as a ground layer...

Ground-to-GEO optical feeder links pre-compensated by adaptive optics are fundamentally limited by phase angular anisoplanatism, which induces large residual tip-tilt errors and deep signal fades on the satellite. Recent work showed that downlink intensity provides vertical turbulence discrimination and improves tip-tilt estimation at the point ahead angle. We extend this concept by incorporating a Rayleigh laser guide star (R-LGS) as a ground-layer-dominated measurement, enabling separation of ground and upper-layer contributions within a minimum mean square error estimation framework that accounts for focal anisoplanatism and measurement noise. Using measured urban turbulence profiles, we show that uplink phase estimation based on R-LGS measurements provides strong tip-tilt improvement and reduces deep fades by up to 24 dB. The gains are especially notable under strong turbulence and high angular decorrelation, demonstrating the practical value of low-cost R-LGS for robust GEO feeder-link operation.