Learning Precoding Policy: CNN or GNN?

Optimizing precoding with deep learning enables its real-time implementation. In addition to the learning perfor-mance such as sum rate, training complexity is also important since neural networks (NNs) have to be re-trained in time-varying channels. By leveraging the prior-known property for a policy to be learned, inductive biases can be introduced to the structure of NNs to balance the learning performance and training com-plexity. Most existing works use convolutional neural networks for learning precoding policy, without considering whether their inductive biases match the precoding task. In this paper, we first show that full-digital precoding policy exhibits permutation equivariance property and introduce graph NN (GNN) to learn the policy. We then analyze and show the connections between the structures and inductive biases of several NNs. Simulation results show that the inductive bias of the GNN is well-matched to the precoding policy, and hence achieves higher sum-rate with given number of training samples and needs lower training complexity to achieve the same sum-rate than other NNs.