Scalable Hybrid Beamforming for Multi-User MISO Systems: A Graph Neural Network Approach

Hybrid beamforming is a promising technology for enhancing the energy- and spectral-efficiency of wireless networks with large-scale antenna arrays, yet the current designs fall short of concurrently achieving low computational complexity and high communication scalability. In this paper, we propose a scalable and effective hybrid beamforming framework for multi-user systems, where the bipartite graph neural network (BGNN) is leveraged to exploit the graph topological structure for sum-rate maximization. To capture permutation properties of the sum-rate maximization problem, we model the wireless network as a bipartite graph, where two disjoint sets of vertices respectively model users and radio frequency (RF) chains, and the edges connecting adjacent vertices characterize interactions between users and RF chains. Based on the bipartite graph, we partition the hybrid beamforming optimization into the updates of feature vectors at user and RF chain vertices, which are realized by alternately activating four kinds of vertex operators that constitute the proposed BGNN. The inputs and outputs of each vertex operator are specifically designed to be independent of the user number and RF chain number in terms of dimension. Numerical results validate the superiority of the proposed BGNN framework from the perspectives of achievable sum rate, computation complexity, and scalability.