  Cooperative beamforming design has been recognized as an effective approach
in modern wireless networks to meet the dramatically increasing demand of
various wireless data traffics. It is formulated as an optimization problem in
conventional approaches and solved iteratively in an instance-by-instance
manner. Recently, learning-based methods have emerged with real-time
implementation by approximating the mapping function from the problem instances
to the corresponding solutions. Among various neural network architectures,
graph neural networks (GNNs) can effectively utilize the graph topology in
wireless networks to achieve better generalization ability on unseen problem
sizes. However, the current GNNs are only equipped with the node-update
mechanism, which restricts it from modeling more complicated problems such as
the cooperative beamforming design, where the beamformers are on the graph
edges of wireless networks. To fill this gap, we propose an
edge-graph-neural-network (Edge-GNN) by incorporating an edge-update mechanism
into the GNN, which learns the cooperative beamforming on the graph edges.
Simulation results show that the proposed Edge-GNN achieves higher sum rate
with much shorter computation time than state-of-the-art approaches, and
generalizes well to different numbers of base stations and user equipments.
