Distributed Cooperative Beamforming for Spectrum Sharing in GEO-LEO Heterogeneous Multi-Satellite System

Abstract

Due to their resilience and global coverage, satellite networks are poised to become a key component for non-terrestrial networks in the future. However, given the scarcity of spectrum resources, the dense deployment of low Earth orbit (LEO) satellites introduces significant interference challenges. Meanwhile, the limited computing power and backhaul capacity of satellites have become bottlenecks hindering the development of advanced interference mitigation techniques. This paper studies beamforming in GEO-LEO heterogeneous multi-satellite systems. For the GEO system, we develop a multicast beamforming approach based on a nonlinear eigenvalue problem (NEPv) for beam direction design and Lagrange dual decomposition (LDD) for power allocation. For the LEO system, we propose a general distributed beamforming framework and two distributed beamforming methods. Specifically, we first leverage equivalent multi-dimensional fractional programming (FP) to decompose the objective function. The resulting subproblems are then optimized in a distributed manner across multiple satellites via the parallel block coordinate descent (PBCD) method. For the distributed optimization subproblems, we derive semi-closed-form solutions using Lagrangian dual ascent (LDA) and alternating direction method of multipliers (ADMM) for scenarios without and with GEO-LEO interference avoidance, respectively. Simulation results show that the proposed NEPv-LDD method strictly satisfies the QoS constraints of users and achieves near-optimal performance with low complexity. For the LEO beamforming, the developed distributed FP (DiFP) framework exhibits strong scalability in large-scale constellations. Built upon the DiFP framework, the proposed DiFP-NoSIA incurs almost no performance loss, while DiFP-ADMM shows only an 8.58% performance degradation compared to the centralized benchmark.