Learning-based Multiuser Beamforming for Holographic MIMO~Systems

Abstract

Holographic multiple-input multiple-output (HMIMO) can improve spectral efficiency (SE) with low hardware cost, but conventional alternating optimization (AO) methods for jointly optimizing digital and holographic beamformers are computationally expensive. Learning-based beamforming offers a low-complexity alternative, and graph neural networks (GNNs) are particularly attractive because they can exploit permutation equivariance (PE). The optimal HMIMO beamforming policy exhibits PE properties across multiple dimensions. Existing methods either use high-dimensional GNNs, increasing model size and training complexity, or exploit only partial PE properties, leading to performance degradation. To address this issue, we reformulate the problem by learning an equivalent beamformer that removes the RF-chain dimension from the network output while preserving the PE property of the original problem. The reformulation introduces a nontrivial column-space constraint because the equivalent beamformer must be representable by the phase-pattern matrix. We then develop a cascaded architecture consisting of a gradient-based graph neural network (GGNN) and two projection modules. The GGNN jointly learns the holographic and equivalent beamformers using update equations motivated by their coupled gradient structures, while the projection modules recover the digital beamformer and enforce the column-space and transmit-power constraints. Simulation results show that the proposed method achieves higher SE with lower inference latency than the AO baseline and exhibits better generalization than existing learning-based baselines.