Digital Over-the-Air Federated Learning in Multi-Antenna Systems

TL;DR

This paper tackles federated learning over realistic wireless MIMO channels using digital modulation and AirComp. It introduces a joint transmit/receive beamforming design guided by an ANN that predicts local FL updates, enabling effective model aggregation despite the nonlinearity of high-order modulations. A convergence-based analysis links beamforming and demodulation errors to FL performance, and a closed-form beamforming solution is derived from predicted updates. Extensive experiments on Fashion-MNIST and CIFAR-10 show up to 10–30% gains in accuracy and faster convergence compared to analog or BPSK AirComp baselines, validating practical benefits for bandwidth-limited wireless networks.

Abstract

In this paper, the performance optimization of federated learning (FL), when deployed over a realistic wireless multiple-input multiple-output (MIMO) communication system with digital modulation and over-the-air computation (AirComp) is studied. In particular, a MIMO system is considered in which edge devices transmit their local FL models (trained using their locally collected data) to a parameter server (PS) using beamforming to maximize the number of devices scheduled for transmission. The PS, acting as a central controller, generates a global FL model using the received local FL models and broadcasts it back to all devices. Due to the limited bandwidth in a wireless network, AirComp is adopted to enable efficient wireless data aggregation. However, fading of wireless channels can produce aggregate distortions in an AirComp-based FL scheme. To tackle this challenge, we propose a modified federated averaging (FedAvg) algorithm that combines digital modulation with AirComp to mitigate wireless fading while ensuring the communication efficiency. This is achieved by a joint transmit and receive beamforming design, which is formulated as an optimization problem to dynamically adjust the beamforming matrices based on current FL model parameters so as to minimize the transmitting error and ensure the FL performance. To achieve this goal, we first analytically characterize how the beamforming matrices affect the performance of the FedAvg in different iterations. Based on this relationship, an artificial neural network (ANN) is used to estimate the local FL models of all devices and adjust the beamforming matrices at the PS for future model transmission. The algorithmic advantages and improved performance of the proposed methodologies are demonstrated through extensive numerical experiments.

Figures (13)

• Figure 1: Illustration of our methodology and system model. An FL algorithm is deployed over multiple devices and one PS in a MIMO communication system. We design the transmit and receive beamforming matrices to optimize the FL training process.
• Figure 2: An example of 16-QAM constellation at the PS with 4 devices.
• Figure 4: Testing accuracy of the proposed AirComp-based FL system over communication rounds, for an IID data allocation on the Fashion-MNIST task. We see that our proposed method provides substantial improvements over the baselines, approaching the noiseless channel case.
• Figure 5: Test accuracy of the proposed AirComp-based FL system over time on the Fashion-MNIST task, for an non-IID data allocation. The overall trends are similar to those observed in Fig. \ref{['SNRCNN1']}.
• Figure 6: Test accuracy of the proposed AirComp-based FL system across communication rounds, for an IID data allocation on the CIFAR-10 dataset. Compared to Fig. \ref{['SNRCNN1']}, we observe significant improvements over the baselines. The larger gap from the noiseless channel case shows the impact of noise on more complex learning tasks (CIFAR-10 vs. Fashion-MNIST).