Doppler characterization for LEO satellites

Mobile ground-based terminals observe significant Doppler on the forward channel when communicating through low Earth orbit (LEO) satellites. This paper deals with the analytic derivation of the Doppler shift measured by a user on the surface of Earth on a signal transmitted by a circular orbit LEO satellite. Two simplifications are performed to obtain the analytical expression of the Doppler shift as a function of time. First, during the visibility duration of the satellite at a terminal, the trajectory of the satellite with respect to the Earth is approximated by a great circle arc. Second, the angular velocity of the satellite with respect to the user is assumed to be constant. Numerical results validate the approximations. Another result of our analysis is an expression for the visibility window duration of a satellite at a terminal as a function of the maximum elevation angle. An algorithm for estimating the parameters of the Doppler curve based on a couple of Doppler and Doppler-rate measurements is also presented.