Random Orthogonalization for Federated Learning in Massive MIMO Systems

We propose a novel communication design, termed random orthogonalization, for federated learning (FL) in a massive multiple-input and multiple-output (MIMO) wireless system. The key novelty of random orthogonalization comes from the tight coupling of FL and two unique characteristics of massive MIMO - channel hardening and favorable propagation. As a result, random orthogonalization can achieve natural over-the-air model aggregation without requiring transmitter side channel state information (CSI) for the uplink phase of FL, while significantly reducing the channel estimation overhead at the receiver. We extend this principle to the downlink communication phase and develop a simple but highly effective model broadcast method for FL. We also relax the massive MIMO assumption by proposing an enhanced random orthogonalization design for both uplink and downlink FL communications, that does not rely on channel hardening or favorable propagation. Theoretical analyses with respect to both communication and machine learning performance are carried out. In particular, an explicit relationship among the convergence rate, the number of clients, and the number of antennas is established. A preliminary version of this work has been presented at the 2022 IEEE International Conference on Communications [1]. Xizixiang Wei and Cong Shen are with the Charles L. Brown Department of Electrical and Computer Engineering, University of Virginia, USA. Jing Yang is with the Department of Electrical Engineering, The Pennsylvania State University, USA. H. Vincent Poor is with the Department of Electrical and Computer Engineering, Princeton University, USA.