Enabling Scalable Distributed Beamforming via Networked LEO Satellites Toward 6G

In this paper, we propose scalable distributed beamforming schemes over networked low Earth orbit (LEO) satellite systems that rely solely on statistical channel state information (CSI). We begin by introducing the LEO satellite network system model and presenting pragmatic yet effective analog beamformer and user-scheduling designs. We then derive a closed-form lower bound on the ergodic sum rate, based on the hardening bound, using which we formulate a per-satellite power-constrained sum rate maximization problem for the digital beamformer design. Next, we provide a centralized solution, obtained via the weighted minimum mean squared error (WMMSE) framework, establishes performance limits and motivates decentralized strategies. We subsequently introduce two decentralized optimization schemes, based on approximating the hardening bound and decentralizing the WMMSE framework, for two representative inter-satellite link (ISL) topologies, i.e., Ring and Star topologies. In the Ring topology-based beamforming scheme, satellites update beamformers locally and exchange intermediate parameters sequentially. On the other hand, in the Star topology-based beamforming scheme, edge satellites update beamformers locally and in parallel, achieving consensus on intermediate parameters at a central satellite using a penalty-dual decomposition (PDD) framework. Extensive simulations demonstrate that the proposed distributed beamforming schemes achieve similar performance with the centralized beamforming scheme while improving scalability significantly. Additionally, we reveal the delay–overhead trade-off between the two topologies.