Age-Based Device Selection and Transmit Power Optimization in Over-the-Air Federated Learning

Recently, over-the-air federated learning (OTA-FL) has attracted significant attention for its ability to enhance communication efficiency. However, the performance of OTA-FL is constrained by the complex interplay among straggler effects, data heterogeneity, and signal aggregation errors. To address these coupled challenges, we propose a joint device selection and transmit power optimization framework. First, we conduct a theoretical analysis to quantify the convergence upper bound of OTA-FL under partial device participation. Our analysis theoretically proves that both the selected device set and the signal aggregation errors significantly determine the convergence upper bound. Crucially, we identify a critical trade-off in system optimization: Simply prioritizing strong channels to minimize aggregation errors leads to model bias due to data heterogeneity; conversely, indiscriminately including stragglers forces the system to wait for the slowest device, significantly delaying model updates and reducing training efficiency. To resolve this dilemma, we introduce the age of information (AoI) as a regulation metric. Accordingly, we propose minimizing the expected weighted sum peak age of information (EWS-PAoI) to theoretically bound model deviation while maintaining training efficiency. To achieve this, we calculate device priorities for each communication round using Lyapunov optimization and select the highest-priority devices via a greedy algorithm. Subsequently, to minimize the aggregation error identified in our theoretical analysis, we formulate a transmit power and normalizing factor optimization problem. By leveraging Karush-Kuhn-Tucker (KKT) conditions, we derive a closed-form “clip-or-scale” solution for efficient power control. Experimental results on CIFAR-10 and CIFAR-100 datasets demonstrate that our method significantly outperforms various baselines by effectively reducing both the mean squared error (MSE) and training latency while maintaining high test accuracy. Overall, the proposed framework achieves a superior balance among training efficiency, model accuracy, and user fairness.