  Non-geostationary (Non-GSO) satellite constellations have emerged as a
promising solution to enable ubiquitous high-speed low-latency broadband
services by generating multiple spot-beams placed on the ground according to
the user locations. However, there is an inherent trade-off between the number
of active beams and the complexity of generating a large number of beams. This
paper formulates and solves a joint beam placement and load balancing problem
to carefully optimize the satellite beam and enhance the link budgets with a
minimal number of active beams. We propose a two-stage algorithm design to
overcome the combinatorial structure of the considered optimization problem
providing a solution in polynomial time. The first stage minimizes the number
of active beams, while the second stage performs a load balancing to distribute
users in the coverage area of the active beams. Numerical results confirm the
benefits of the proposed methodology both in carrier-to-noise ratio and
multiplexed users per beam over other benchmarks.
