RIS-Assisted Over-the-Air Federated Learning in Millimeter Wave MIMO Networks

In this paper, we propose a reconfigurable intelligent surface (RIS) assisted over-the-air federated learning (FL), where multiple antennas are deployed at each edge device to enable simultaneous multidimensional model transmission over a millimeter wave (mmWave) network. We conduct rigorous convergence analysis for the proposed FL system, taking into account dynamic channel fading and analog transmissions. Inspired by the convergence analysis, we propose to jointly optimize the receive digital and analog beamforming matrices at the access point, the RIS phase-shift matrix, as well as the transmit beamforming matrices at transmitting devices to minimize the transmission distortion. The optimization variable coupling and non-convex constraints make the formulated problem challenging to be solved. To this end, we develop a low-complexity Riemannian conjugate gradient (RCG)-based algorithm to solve the unit modulus constraints and decouple the optimization variables. Simulations show that the proposed RCG algorithm outperforms the successive convex approximation algorithm in terms of the learning performance.