Distributed Beamforming with Incomplete Channel State Information in MISO Networks via GNNs

Beamforming is a crucial component in modern large-scale multiple-input single-output (MISO) wireless networks. However, its practical deployment is often constrained by the incomplete channel state information (CSI) and the overhead associated with centralized optimization methods, such as the weighted minimum mean-square error (WMMSE) algorithm. In this work, we propose the problem of distributed beamforming with varying degrees of CSI incompleteness and develop a graph neural network (GNN)-based approach, which enables transmitters to collaboratively optimize their beamforming strategies using only local and partial CSI. Our approach combines imitation learning with unsupervised learning for model training, where the former provides a warm start and the latter allows for superior performance beyond the "expert" strategy, while leveraging the GNN for a distributed implementation. We evaluate the proposed approach using ray tracing-based simulations in both indoor and outdoor scenarios, demonstrating that it outperforms WMMSE, particularly in environments with noisy or incomplete CSI. These results highlight the potential of our GNN-based solution for scalable, robust, and distributed beamforming strategies in future wireless networks.