Timing advance and Doppler shift estimation in LEO satellite networks: A recursive Bayesian study

Low earth orbit (LEO) satellite based non-terrestrial networks are a key theme of the upcoming 6G networks. These space networks are proposed to be used for high-mobility use-cases like airplanes and vehicles. The initial access process between a base station (BS) and a user equipment (UE) involves timing advance (TA) value computation at the BS, requiring precise BS location information at the UE. It becomes more challenging in LEO satellite networks due to the fast moving LEO satellites and large pathloss, in addition to the mobile UE. This paper aims to compute the TA and Doppler shift experienced at the UE by modeling the joint system dynamics in a LEO satellite-mobile UE network through an extended Kalman filter (EKF) based recursive Bayesian framework. The framework accurately models the joint system dynamics by considering the LEO satellite acceleration. It constructs the Jacobian to linearize the inherent non-linearities present in the motion. Probabilistic insights regarding the state-update and propagation are also provided. The analytical framework factors in the limited satellite visibility at the UE and the satellite-UE geometry w.r.t. the earth center. The proposed framework is also useful when the satellite and UE clocks are not in sync, with the corresponding clock drift a function of the measured time difference of arrivals. Our results showcase the efficacy and robustness of the proposed EKF framework to estimate the TA and Doppler shift, even at very high UE speeds. The work is expected to be extremely useful in realizing LEO satellite based non-terrestrial networks.