Combating Interference for Over-the-Air Federated Learning: A Statistical Approach via RIS
Wei Shi, Jiacheng Yao, Wei Xu, Jindan Xu, Xiaohu You, Yonina C. Eldar, Chunming Zhao
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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf{\mathcal{O}}\left(\frac{\textbf{1}}{\boldsymbol{N}}\right)$</tex-math></inline-formula> where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> is the number of RIS elements, and the ideal convergence rate without interference can be asymptotically achieved by increasing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula>. Numerical results confirm the analytical results and validate the superior performance of the proposed schemes over existing baselines.