Robust Design for RIS-Assisted Over-the-Air Federated Learning With Imperfect Cascaded CSI

Abstract

Over-the-air computation (AirComp) enables spectral-efficient global model aggregation for federated learning (FL) by supporting concurrent transmission and harnessing co-channel interference. However, unfavorable channel conditions and inaccurate channel estimation are two performance-limiting factors of AirComp-assisted FL. In this paper, we leverage reconfigurable intelligent surface (RIS) to assist AirComp for gradient aggregation with imperfect cascaded channel state information (CSI), taking into account both the expectation-based and worst-case error models (i.e., stochastic and deterministic models). Guided by the convergence analysis, we minimize the gradient aggregation distortion measured by the mean-squared-error (MSE), taking into account the unit modulus constraints of RIS phase-shifts. To alleviate the performance degradation due to imperfect channel estimation, we propose two robust algorithms to optimize the receive beamforming at the edge server, RIS phase-shifts, and transmit power at the edge devices. Both algorithms are designed under an alternating optimization framework, where Schur’s complement and penalty convex–concave procedure are adopted for the worst-case error model, and Lagrange duality and difference-of-convex programming are used for the expectation-based error model. Simulations are conducted to validate the learning performance superiority of the proposed algorithms over baseline schemes, inducing the robustness against CSI errors.