Beam-Hopping Pattern Design for Grant-Free Random Access in LEO Satellite Communications

Increasing demand for massive device connectivity in underserved regions drives the development of advanced low Earth orbit (LEO) satellite communication systems. Beam-hopping LEO systems without connection establishment provide a promising solution for achieving both demand-aware resource allocation and low access latency. This paper investigates beam-hopping pattern design for the grant-free random access systems to dynamically allocate satellite resources according to traffic demands across serving cells. We formulate a binary optimization problem that aims to maximize the minimum successful transmission probability across cells, given limited satellite beam generation capacity. To solve this problem, we propose novel beam-hopping design algorithms that alternately enhance the collision avoidance rate and decoding success probability within an alternating optimization framework. Specifically, the algorithms employ a bisection method to optimize illumination allocation for each cell based on demand, while using the alternating direction method of multipliers (ADMM) to optimize beam-hopping patterns for maximizing decoding success probability. Furthermore, we enhance the ADMM by replacing the strict binary constraint with two equivalent continuous-valued constraints. Simulation results demonstrate the superiority of the proposed algorithms compared to other beam-hopping methods and verify robustness in managing traffic demand imbalance.