Energy and Spectrum Efficient Federated Learning via High-Precision Over-the-Air Computation

Federated learning (FL) enables mobile devices to collaboratively learn a shared prediction model while keeping data locally. However, there are two major research challenges to practically deploy FL over mobile devices: (i) frequent wireless updates of huge size gradients v.s. limited spectrum resources, and (ii) energy-hungry FL communication and local computing during training v.s. battery-constrained mobile devices. To address those challenges, in this paper, we propose a novel multi-bit over-the-air computation (M-AirComp) approach for spectrum-efficient aggregation of local model updates in FL and further present an energy-efficient FL design for mobile devices. Specifically, a high-precision digital modulation scheme is designed and incorporated in the M-AirComp, allowing mobile devices to upload model updates at the selected positions simultaneously in the multi-access channel. Moreover, we theoretically analyze the convergence property of our FL algorithm. Guided by FL convergence analysis, we formulate a joint transmission probability and local computing control optimization, aiming to minimize the overall energy consumption (i.e., iterative local computing + multi-round communications) of mobile devices in FL. Extensive simulation results show that our proposed scheme outperforms existing ones in terms of spectrum utilization, energy efficiency, and learning accuracy.