Reconfigurable Intelligent Surfaces-Aided Federated Learning in Over-the-Air Computation

In this letter, we investigate a joint design scheme of phase shifts and a beamforming vector in over-the-air federated learning (FL) with a reconfigurable intelligent surface (RIS). It is well known that the more edge devices participate in FL the better the learning performance over error-free wireless channels. However, the FL performance can be degraded when devices with poor channel conditions participate in the learning within the over-the-air computation (AirComp) system. Therefore, we present a beamforming vector and RIS phase-shift design algorithm that maximizes the number of participating devices under the aggregation error constraint. We first reformulate the conventional problem to a sparse optimization problem and apply the alternating optimization (AO) approach. Then, we propose a low-complexity algorithm using the majorization minimization (MM) approach and the projected subgradient method. Simulation results demonstrate that RIS helps to accommodate more devices in AirComp FL and the proposed algorithms achieve performance close to that of an ideal FL system.