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Learning-based precoding has been shown able to be implemented in real-time,jointly optimized with channel acquisition, and robust to imperfect channels.Yet previous works rarely explain the design choices and learning performance,and existing methods either suffer from high training complexity or depend onproblem-specific models. In this paper, we address these issues by analyzingthe properties of precoding policy and inductive biases of neural networks,noticing that the learning performance can be decomposed into approximation andestimation errors where the former is related to the smoothness of the policyand both depend on the inductive biases of neural networks. To this end, weintroduce a graph neural network (GNN) to learn precoding policy and analyzeits connection with the commonly used convolutional neural networks (CNNs). Bytaking a sum rate maximization precoding policy as an example, we explain whythe learned precoding policy performs well in the low signal-to-noise ratioregime, in spatially uncorrelated channels, and when the number of users ismuch fewer than the number of antennas, as well as why GNN is with higherlearning efficiency than CNNs. Extensive simulations validate our analyses andevaluate the generalization ability of the GNN.

Understanding the Performance of Learning Precoding Policy with GNN and CNNs