A Model-Based GNN for Learning Precoding

Learning precoding policies with neural networks enables low complexity implementation, robustness to channel impairments, and joint optimization with channel acquisition. However, pure data-driven methods for learning precoding suffer from high complexity of training and poor generalizability to problem scales, while existing model-driven learning methods are either algorithm-specific or problem-specific. In this paper, we propose a model-based graph neural network (GNN) to learn precoding policies by harnessing their properties and relevant mathematical model. We first show that a vanilla GNN cannot learn zero-forcing precoding when the numbers of antennas and users are large, and is not generalizable to the numbers of users. Then, we conceive a new GNN structure by resorting to the iterative Taylor's expansion of matrix pseudo-inverse, which can adapt to the interference strength among users. Simulation results show that the proposed GNN can well-learn different precoding policies (say spectral efficient and energy efficient precoding policies as well as coordinated beamforming) with low training complexity. Moreover, it can be generalized to the number of users, which is highly desirable in practice since the number of scheduled users may change in milliseconds.