Abstract : The low Earth orbit (LEO) satellite communication systems have drawn much attention as a promising solution for providing global wireless connectivity. This paper studies the downlink performances of LEO satellite communication systems performing a directional beamforming with a stochastic geometry. As the beamwidth of the satellite increases, the beam coverage increases but the interference from other satellites also increases. This is vice versa for the smaller beamwidth. Accordingly, the optimal beamwidth control is necessary to balance the beam coverage and the network interference. To address such issue, we first derive the conditional distance distribution to serving line-of-sight (LoS) and non-line-of-sight (NLoS) satellites, conditioned on that there exists at least one satellite in the satellite-visible region and the user is located within the beam coverage of the satellite. Then, we derive the exact and approximated formulas for the coverage probability and the ergodic rate as a function of the beamdwidth. With some numerical examples, we investigate how various system parameters such as altitude and satellite density affect on the optimal beamwidth and demonstrate that the optimal control of the beamwidth of the satellites can maximize the performances by efficiently controlling the amount of interference and beam coverage.
Index terms : Coverage probability, ergodic rate, satellites, stochastic geometry.