Distribution-Level AirComp for Wireless Federated Learning Under Data Scarcity and Heterogeneity

Federated Learning (FL) has gained considerable attention as a privacy-preserving and localized approach to implementing edge artificial intelligence (AI). However, conventional FL methods face critical challenges in realistic wireless edge networks, where training data is both limited and heterogeneous, often leading to unstable training and poor generalization. To address these challenges, we propose a Bayesian wireless FL framework that captures model uncertainty via posterior distributions and performs distribution-level aggregation, mitigating local overfitting and client drift. However, this formulation increases communication overhead and prevents the direct use of conventional Over-the-Air Computation (AirComp), which is widely used to improve communication efficiency in standard FL. To overcome this, we develop a transmission-compatible reformulation of posterior aggregation that enables distribution-level Bayesian updates to be computed over the air, along with a closed-form distributed transmit power control strategy derived from convergence analysis under practical wireless impairments. Extensive simulations demonstrate that the proposed framework significantly improves test accuracy and calibration performance compared to conventional FL methods, particularly in data-scarce and heterogeneous environments.