Scalable Rate-Splitting Precoding via Recurrent Structure-Preserving Graph Neural Networks

Graph neural network (GNN)-based precoding has demonstrated strong potential for scalable multi-user beamforming in multi-user multiple-input single-output (MU-MISO) systems under space division multiple access (SDMA). However, direct extension to rate-splitting multiple access (RSMA) is non-trivial due to the coupled common/private-stream structure inherent to RSMA, which requires a fundamentally different graph representation and permutation equivariance structure. Motivated by this, we propose a recurrent structure-preserving graph neural network (RS-GNN) for scalable RSMA precoding. RS-GNN constructs precoder-dependent graph features at every refinement layer, enabling closed-loop interference-aware message passing, and recovers the common and private precoders through an analytically grounded structure-based reconstruction via a differentiable linear solver. This design decouples the learnable parameters from fixed system dimensions, enabling generalization to unseen system sizes without retraining. We formally prove that RS-GNN satisfies mixed permutation equivariance with respect to both user and antenna orderings, and show that RS-GNN reduces to conventional SDMA precoding as a special case by deactivating the common-stream branch. Simulation results demonstrate that RS-GNN achieves near-WMMSE sum-rate performance with significantly lower online inference time, while generalizing robustly to unseen system sizes; its SDMA special case consistently outperforms existing GNN-based precoders across unseen antenna and user configurations, SNR regimes, and channel distributions.