Statistical Distribution of Beamforming Gains in Satellite Swarms Under Imperfect Phase Synchronization

In this paper, we analytically study the distribution of the main-lobe gain in a low-Earth orbit (LEO) satellite swarm scenario under imperfect phase synchronization, based on an open-loop process. The provided analytical framework determines the maximum tolerable error in phase estimation under which the desired beamforming gain can still be achieved. Consequently, we are able to determine the highest value of accuracy (worst-case scenario) in position estimation between satellites (inter-node ranging) required for phase synchronization. Notably, the analytical framework reveals that in millimeter-wave bands, the required maximum precision in inter-node ranging to guarantee just a small performance deterioration is in the order of millimetres. Finally, numerical results based on Monte Carlo simulations validate the analytical framework.