GNN-Aided Over-the-Air Reciprocity Calibration for Cell-Free Massive MIMO Systems

Over-the-air (OTA) reciprocity calibration (RC) is essential in cell-free massive multiple-input multiple-output (CF-mMIMO) systems to enable the downlink coherent beamforming from uplink channel estimates. Conventional least-squares (LS) calibration typically treats all pilot links equally and relies on a singular value decomposition-based solution, which can be sensitive to low signal-to-noise ratio (SNR) observations and incurs high computational cost. This letter proposes a graph neural network (GNN)-aided OTA RC framework, where the distributed access-point network is modeled as a directed graph and calibration coefficients are learned from bidirectional pilot measurements. In particular, the proposed dual-head attention mechanism effectively captures link importance, thereby mitigating the adverse impact of low-SNR links. Moreover, the forward inference only involves simple matrix multiplications, yielding low computational complexity. Simulation results demonstrate that the proposed GNN consistently outperforms LS across all considered system configurations. Moreover, it generalizes well across different data distributions, network scales, and topologies, highlighting its robustness and practical applicability in dynamic CF-mMIMO systems.