Bigraph GNN-Aided Energy Efficiency Maximization for Cell-Free Massive MIMO

Cell-free massive MIMO (CFmMIMO) networks offer significant potential for improving coverage and capacity in future networks but optimizing their energy efficiency (EE) in real-time remains a challenge. Although the accelerated projected gradient (APG) method is currently the fastest solution for maximizing EE, it still becomes cumbersome for real-time implementations as the network size increases. To address this issue, we propose a graph neural network (GNN) designed to rapidly maximize EE in CFmMIMO networks. Our approach represents M access points and K user equipments of a network as nodes in a complete bipartite graph, with channels between them as edges. By formulating the EE maximization problem as a supervised edge-level prediction task, our GNN leverages an attention mechanism to update node features and incorporates channel information in edge features. Compared to the APG method, our GNN offers a substantial reduction in computational complexity, from ${\mathcal{O}}\left({M{K^2}}\right)$ to ${\mathcal{O}}(MK)$. Simulations across various network sizes demonstrate that our proposed GNN method achieves near-optimal EE with up to 100 times fewer floating-point operations compared to the APG method, making it a promising solution for real-time CFmMIMO deployments.