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 analytical expressions for
the coverage probability, which take into account the in-cluster geometry of
the coordinated satellite set. These expressions are formulated in terms of
various parameters, including the number of antennas per satellite, satellite
density, fading characteristics, and path-loss exponent. To offer a more
intuitive understanding, we also develop an approximation for the coverage
probability. Furthermore, by considering the distribution of normalized
distances, we derive the spatially averaged coverage probability, thereby
validating 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 direct 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. Our findings are
corroborated by simulation results, confirming the accuracy of the derived
expressions