Access Point Selection and Beamforming Design for Cell-Free Network: From Fractional Programming to GNN

In this paper, the cross-layer optimization problem of access point selection (APS) and beamforming (BF) in cell-free network (CFN) with local CSI is studied, where constraints of per AP power and the number of active APs are considered. Such a joint APS&BF optimization problem is modeled as a mixed-integer nonlinear programming (MINP) problem aiming at maximizing the sum rate of the whole system. Fractional programming (FP)-based and alternating optimization (AO)-based algorithms with weighted l ₁ -norm approximation are proposed to solve this MINP problem. However, the latter performs better than the former, with higher complexity. A lightweight multi-head single-body graph neural network (MHSB-GNN) algorithm is proposed, where the nodes and structures are innovatively designed. The MHSB-GNN benefits from the different node updating modules for different user equipment (UE), which introduce extra prior information into the graph and mine specific information of different UEs. Moreover, the equivalence between GNN and FP-based algorithm is proved to provide interpretability and theoretical guarantees for MHSB-GNN. The analysis of convergence and complexity validates the accuracy and effectiveness of the FP and AO-based algorithms. Leveraging the existing APS and BF solver, it is shown that the three proposed algorithms guarantee comparable performance as the exhaustive search algorithm in performance and complexity.