通过设备年龄优化选择与功率调控，提升无线联邦学习的公平性与效率

Recently, over-the-air federated learning (FL) has attracted significant attention for its ability to enhance communication efficiency. However, the performance of over-the-air FL is often constrained by device selection strategies and signal aggregation errors. In particular, neglecting straggler devices in FL can lead to a decline in the fairness of model updates and amplify the global model's bias toward certain devices' data, ultimately impacting the overall system performance. To address this issue, we propose a joint device selection and transmit power optimization framework that ensures the appropriate participation of straggler devices, maintains efficient training performance, and guarantees timely updates. First, we conduct a theoretical analysis to quantify the convergence upper bound of over-the-air FL under age-of-information (AoI)-based device selection. Our analysis further reveals that both the number of selected devices and the signal aggregation errors significantly influence the convergence upper bound. To minimize the expected weighted sum peak age of information, we calculate device priorities for each communication round using Lyapunov optimization and select the highest-priority devices via a greedy algorithm. Then, we formulate and solve a transmit power and normalizing factor optimization problem for selected devices to minimize the time-average mean squared error (MSE). Experimental results demonstrate that our proposed method offers two significant advantages: (1) it reduces MSE and improves model performance compared to baseline methods, and (2) it strikes a balance between fairness and training efficiency while maintaining satisfactory timeliness, ensuring stable model performance.