  Wireless federated learning (WFL) undergoes a communication bottleneck in
uplink, limiting the number of users that can upload their local models in each
global aggregation round. This paper presents a new multi-carrier
non-orthogonal multiple-access (MC-NOMA)-empowered WFL system under an adaptive
learning setting of Flexible Aggregation. Since a WFL round accommodates both
local model training and uploading for each user, the use of Flexible
Aggregation allows the users to train different numbers of iterations per
round, adapting to their channel conditions and computing resources. The key
idea is to use MC-NOMA to concurrently upload the local models of the users,
thereby extending the local model training times of the users and increasing
participating users. A new metric, namely, Weighted Global Proportion of
Trained Mini-batches (WGPTM), is analytically established to measure the
convergence of the new system. Another important aspect is that we maximize the
WGPTM to harness the convergence of the new system by jointly optimizing the
transmit powers and subchannel bandwidths. This nonconvex problem is converted
equivalently to a tractable convex problem and solved efficiently using
variable substitution and Cauchy's inequality. As corroborated experimentally
using a convolutional neural network and an 18-layer residential network, the
proposed MC-NOMA WFL can efficiently reduce communication delay, increase local
model training times, and accelerate the convergence by over 40%, compared to
its existing alternative.
