Joint Beamforming and Integer User Association using a GNN with Gumbel-Softmax Reparameterizations

Machine learning (ML) models can effectively optimize a multi-cell wireless network by designing the beamforming vectors and association decisions. Existing ML designs, however, often needs to approximate the integer association variables with a probability distribution output. We propose a novel graph neural network (GNN) structure that jointly optimize beamforming vectors and user association while guaranteeing association output as integers. The integer association constraints are satisfied using the Gumbel-Softmax (GS) reparameterization, without increasing computational complexity. Simulation results demonstrate that our proposed GS-based GNN consistently achieves integer association decisions and yields a higher sum-rate, especially when generalized to larger networks, compared to all other fractional association methods.