Learning the Optimal Linear Precoding for Cell-Free Massive MIMO with a GNN

We construct a graph neural network (GNN) to compute, within a time budget of 1 to 2 milliseconds required by practical systems, the optimal linear precoder (OLP) maximizing the minimal (Max-Min) downlink user data rate for a Cell-Free Massive MIMO (CFmMIMO), a key 6G wireless technology. The state-of-the-art method is based on bisection search combined with second order cone programming (SOCP) feasibility test (B-SOCP) which is at least a magnitude too slow for practical systems. Our approach relies on a novel node-edge structure that accurately captures the interdependence relation between access points (APs) and user equipments (UEs), and the permutation equivariance of the Max-Min problem. Our model, named OLP-GNN, is trained on data obtained by B-SOCP to approximate the ideal OLP. With some artful designs of node and edge features, and pre and post processing techniques, OLP-GNN is able to achieve near optimal performance in terms of user throughput.