Model-Based GNN Enabled Energy-Efficient Beamforming for Ultra-Dense Wireless Networks

This paper proposes a novel deep learning enabled beamforming design for ultra-dense wireless networks by integrating prior knowledge and graph neural network (GNN), termed model-based GNN. An energy efficiency (EE) maximization problem is first subject to the power budget and quality of service (QoS) requirements, and then reformulated based on the minimum mean square error scheme and the hybrid zero-forcing and maximum ratio transmission scheme. The model-based GNN is designed to realize the mapping from channel state information to beamforming vectors to address the reformulated problems. Particularly, the multi-head attention mechanism and the residual connection are adopted to enhance the feature extracting, and a scheme selection module is designed to improve the adaptability to channel conditions. The unsupervised learning is adopted, and a various-input training strategy is proposed to enhance the stability of the model-based GNN. Numerical results demonstrate that the proposed model-based GNN can realize a millisecond-level inference with limited performance loss, the scalability to different numbers of users and the adaptability to various channel conditions and QoS requirements in ultra-dense wireless networks.