Beam Footprint Design, Scheduling, and Spectrum Assignment in Low Earth Orbit Mega-Constellations

Owing to the advantages of ubiquitous connectivity and high capacity, low earth orbit mega-constellations have drawn much attention. However, it is challenging to maximize network throughput under much available beam resource, complex inter-beam interference, and spatially uneven traffic demand with low computation complexity. In this paper, we formulate a novel beam management problem including beam footprint design, beam scheduling, and spectrum assignment. Considering the tight coupling among them, we first develop a fast beam footprint design method for earth-fixed cells, which adapts to dynamic satellite attitudes. Then, with the reformulation of objective and constraints, the primal problem is transformed into a beam scheduling and spectrum assignment problem with much smaller solution space, and an optimum algorithm is designed by combining branch-and-bound and interior point methods. Towards practical application, a more scalable graph-based heuristic algorithm is proposed. Simulation results show that the developed beam footprint design method can significantly reduce inter-beam interference and improve network throughput, and the proposed heuristic algorithm achieves comparable throughput but reduces execution time by two orders of magnitude compared with the optimum one. Moreover, in scenarios with 120 cells, our proposal increases network throughput by over 60$\%$ compared to the baseline based on integer recovery.