This lecture will be mainly focused on broadband communication networks based Low Earth Orbit satellite constellations.
It will first describe the structure of these constellations, their overall functionalities, as well as the economic and strategic context of their current deployment.
It will then survey recent and ongoing results on the mathematical analysis of such networks.
It will first show that the stochastic geometry framework for planar cellular networks can be extended to this new spherical geometry setting. This leads to a system level analysis of coverage and spectral efficiency of this new
class of networks.
In addition, it will show that a dynamical system analysis of this class of networks leads to new results on their ergodic or periodic behavior. The consequences on the dynamics of association, handover, and routing algorithms used in these networks will also be discussed.