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

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