Coverage Analysis of Dynamic Coordinated Beamforming for LEO Satellite Downlink Networks

In this paper, we investigate the coverage performance of downlink satellite networks employing dynamic coordinated beamforming. Our approach involves modeling the spatial arrangement of satellites and users using Poisson point processes situated on concentric spheres. We derive an analytical expression for the coverage probability which is formulated in terms of various parameters, including the number of antennas per satellite, satellite density, fading characteristics, and path-loss exponent. This coverage probability validates the advantages of coordinated beamforming from a spatial average perspective. Our primary finding is that dynamic coordinated beamforming significantly improves coverage compared to the absence of satellite coordination, in proportion to the number of antennas on each satellite. Moreover, we observe that the optimal cluster size, which maximizes the ergodic spectral efficiency, increases with higher satellite density, provided that the number of antennas on the satellites is sufficiently large. To offer a more intuitive understanding, we also develop an approximation for the coverage probability. Furthermore, by considering the in-cluster geometry of the coordinated satellite set, we derive an approximate coverage probability conditioned on in-cluster geometry. Our findings are corroborated by simulation results, confirming the accuracy of the derived expressions.