Combating Interference for Over-the-Air Federated Learning: A Statistical Approach via RIS

TL;DR

The paper tackles robustness challenges in over-the-air federated learning by leveraging reconfigurable intelligent surfaces to induce phase-manipulated favorable propagation and channel hardening, enabling unbiased gradient estimation under interference. It introduces two RIS-based robust aggregation schemes that jointly design power control, RIS phase shifts, and a denoising factor to suppress interference, with closed-form MSE expressions and convergence guarantees. The analysis shows that computation and interference errors scale as $igO(1/N)$ and noise as $igO(1/N^2)$ with the number of RIS elements $N$, and that asymptotically optimal convergence can be achieved by increasing $N$. Numerical results on MNIST and CIFAR-10 confirm the theoretical findings, demonstrating superior performance of the RIS schemes over baselines and highlighting cost-efficiency advantages over large antenna arrays. The work provides practical guidelines for implementing RIS-enabled AirFL in interference-rich wireless environments and points to future extensions like FedProx and active RIS variants.

Abstract

Over-the-air computation (AirComp) integrates analog communication with task-oriented computation, serving as a key enabling technique for communication-efficient federated learning (FL) over wireless networks. However, owing to its analog characteristics, AirComp-enabled FL (AirFL) is vulnerable to both unintentional and intentional interference. In this paper, we aim to attain robustness in AirComp aggregation against interference via reconfigurable intelligent surface (RIS) technology to artificially reconstruct wireless environments. Concretely, we establish performance objectives tailored for interference suppression in wireless FL systems, aiming to achieve unbiased gradient estimation and reduce its mean square error (MSE). Oriented at these objectives, we introduce the concept of phase-manipulated favorable propagation and channel hardening for AirFL, which relies on the adjustment of RIS phase shifts to realize statistical interference elimination and reduce the error variance of gradient estimation. Building upon this concept, we propose two robust aggregation schemes of power control and RIS phase shifts design, both ensuring unbiased gradient estimation in the presence of interference. Theoretical analysis of the MSE and FL convergence affirms the anti-interference capability of the proposed schemes. It is observed that computation and interference errors diminish by an order of $\mathcal{O}\left(\frac{1}{N}\right)$ where $N$ is the number of RIS elements, and the ideal convergence rate without interference can be asymptotically achieved by increasing $N$. Numerical results confirm the analytical results and validate the superior performance of the proposed schemes over existing baselines.

Figures (9)

• Figure 1: The framework of an RIS-enhanced AirFL system with interference.
• Figure 2: The effects of long-term bias and instantaneous random fluctuation on the convergence performance and rate.
• Figure 3: The MSE versus $N$ with $K=20$ and $M=10$.
• Figure 4: The MSE versus $P$ with $K=20$ and $M=10$.
• Figure 5: The MSE versus $K$ with $N=256$ and $P=0~{\rm dBm}$.