We develop 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 downlink user data rate for a Cell-Free Massive
MIMO system - a key 6G wireless technology. The state-of-the-art method is a
bisection search on second order cone programming feasibility test (B-SOCP)
which is a magnitude too slow for practical systems. Our approach relies on
representing OLP as a node-level prediction task on a graph. We construct a
graph that accurately captures the interdependence relation between access
points (APs) and user equipments (UEs), and the permutation equivariance of the
Max-Min problem. Our neural network, named OLP-GNN, is trained on data obtained
by B-SOCP. We tailor the OLP-GNN size, together with several artful data
preprocessing and postprocessing methods to meet the runtime requirement. We
show by extensive simulations that it achieves near optimal spectral efficiency
in a range of scenarios with different number of APs and UEs, and for both
line-of-sight and non-line-of-sight radio propagation environments.

我们开发了一种名为 OLP-GNN 的图神经网络，通过在 1 到 2 毫秒的时间预算内计算最优线性前编码器以实现最小下行用户数据速率的最大化，该方法在不同 AP 和 UE 数量以及不同的可见光和非可见光射频传播环境下实现了接近最优的频谱效率。