  We propose a novel uplink communication method, coined 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 model aggregation 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, while significantly reducing the channel estimation overhead at
the receiver. Theoretical analyses with respect to both communication and
machine learning performances are carried out. In particular, an explicit
relationship among the convergence rate, the number of clients and the number
of antennas is established. Experimental results validate the effectiveness and
efficiency of random orthogonalization for FL in massive MIMO.
