  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. Experimental results validate the
effectiveness and efficiency of random orthogonalization for FL in massive
MIMO.
