Quantized Analog Beamforming Enabled Multi-task Federated Learning Over-the-air

TL;DR

The paper tackles inter-task interference in multi-task over-the-air federated learning (AirFL) by introducing a quantized analog beamforming design at the parameter server. It leverages favorable propagation in large-array regimes to statically suppress interference without CSIT, showing that interference power scales as $O(1/N_r)$ regardless of phase-quantization precision. The main contributions include a closed-form continuous-phase analog beamforming scheme, extension to discrete (quantized) phases, and demonstration that the performance can approach the ideal, error-free benchmark with sufficiently many low-precision phase shifters. The results indicate a cost-effective alternative to fully-digital, RO-based approaches, enabling scalable multi-task FL in resource-constrained wireless networks.

Abstract

Over-the-air computation (AirComp) has recently emerged as a pivotal technique for communication-efficient federated learning (FL) in resource-constrained wireless networks. Though AirComp leverages the superposition property of multiple access channels for computation, it inherently limits its ability to manage inter-task interference in multi-task computing. In this paper, we propose a quantized analog beamforming scheme at the receiver to enable simultaneous multi-task FL. Specifically, inspiring by the favorable propagation and channel hardening properties of large-scale antenna arrays, a targeted analog beamforming method in closed form is proposed for statistical interference elimination. Analytical results reveal that the interference power vanishes by an order of $\mathcal{O}\left(1/N_r\right)$ with the number of analog phase shifters, $N_r$, irrespective of their quantization precision. Numerical results demonstrate the effectiveness of the proposed analog beamforming method and show that the performance upper bound of ideal learning without errors can be achieved by increasing the number of low-precision analog phase shifters.

Figures (3)

• Figure 1: Element-wise power of the interference versus $N_r$ ($K=100, N=4$).
• Figure 2: Element-wise power of the interference versus $N$ ($K=100, N_r=200$).
• Figure 3: Test accuracy versus communication rounds ($K=20$, $N=2$, $\text{SNR}=0$ dB).