Over-the-Air Federated Learning in Cell-Free MIMO With Long-Term Power Constraint

Wireless networks supporting artificial intelligence have gained significant attention, with Over-the-Air Federated Learning (OTA-FL) emerging as a key application due to its unique transmission and distributed computing characteristics. This letter derives error bounds for OTA-FL in a cell-free MIMO system and formulates an optimization problem to minimize the optimality gap via the joint optimization of transmit and receive beamforming. We introduce the MOP-LOFPC algorithm, which employs Lyapunov optimization to decouple long-term constraints across rounds while requiring only causal channel state information. Experimental results demonstrate that MOP-LOFPC achieves a better and more flexible trade-off between the model’s training loss and adherence to long-term power constraints compared to existing baselines.