  Over-the-air federated learning (AirFL) allows devices to train a learning
model in parallel and synchronize their local models using over-the-air
computation. The integrity of AirFL is vulnerable due to the obscurity of the
local models aggregated over-the-air. This paper presents a novel framework to
balance the accuracy and integrity of AirFL, where multi-antenna devices and
base station (BS) are jointly optimized with a reconfigurable intelligent
surface (RIS). The key contributions include a new and non-trivial problem
jointly considering the model accuracy and integrity of AirFL, and a new
framework that transforms the problem into tractable subproblems. Under perfect
channel state information (CSI), the new framework minimizes the aggregated
model's distortion and retains the local models' recoverability by optimizing
the transmit beamformers of the devices, the receive beamformers of the BS, and
the RIS configuration in an alternating manner. Under imperfect CSI, the new
framework delivers a robust design of the beamformers and RIS configuration to
combat non-negligible channel estimation errors. As corroborated
experimentally, the novel framework can achieve comparable accuracy to the
ideal FL while preserving local model recoverability under perfect CSI, and
improve the accuracy when the number of receive antennas is small or moderate
under imperfect CSI.
