Learned Digital Over-the-Air Computing for Federated Edge Learning

Over-the-air (OTA) aggregation enables federated edge learning (FEEL) by exploiting the superposition property of the wireless channel to merge communication with computation, eliminating the need to schedule and decode devices individually. Analog OTA schemes transmit uncoded updates but are sensitive to noise, fading, and power misalignment, motivating more robust digital alternatives. However, state-of-the-art (SoTA) digital OTA designs that combine unsourced random access (URA) with compressed sensing struggle in the low signal-to-noise ratio (SNR) regimes common in Internet of Things (IoT) deployments, where symbol recovery and active-device estimation become unreliable. We propose a learned digital OTA framework that jointly trains a URA codebook with an unrolled approximate message passing (AMP)-based decoder. The learned decoder incorporates per-layer damping, residual scaling, temperature-controlled Bayesian denoising, and a lightweight convolutional neural network (CNN) refinement, while the codebook is optimised end-to-end through a factorised parameterisation. At near-perfect-aggregation accuracy, the proposed design extends the viable SNR range by approximately 7,dB over the SoTA baseline at the same uplink overhead, and generalises across models, activity levels, and heterogeneous data.