Learning Power Allocation for Cell-free Massive MIMO System with Graph Neural Networks

Optimizing power allocation among access points (APs) is an effective way to improve the spectral efficiency of user-centric cell-free multi-antenna systems, where each user equipment (UE) associates with adjacent APs, leading to dynamic association relationship. The serving APs can adopt different beamforming strategies, say distributed beamforming (D-BF) and centralized beamforming (C-BF). Although D-BF requires lower fronthaul capacity than C-BF, it is unable to eliminate inter-AP interference. To reduce the high computational complexity of numerical algorithms for solving optimization problems, deep neural networks (DNNs) have been designed to learn the power allocation policies with D-BF, which however disregard the impact of dynamic association and are with high training complexity. Besides, there are no existing works to learn the power allocation policies with C-BF, where the power constraint of each AP needs to be satisfied. In this paper, we design graph neural networks (GNNs), including D-GNN and C-GNN, to learn the power allocation policies under D-BF and C-BF, respectively. For achieving high learning efficiency, these GNNs exploit the permutation properties of the optimal policies. The D-GNN is adaptive to dynamic association and the C-GNN can satisfy the per-AP power constraint. Simulation results show that the designed GNNs outperform the existing DNNs with low training complexity and short inference time, and are generalizable to the numbers of APs, antennas, and UEs.