  In this paper, we study the problem of federated learning (FL) over a
wireless channel, modeled by a Gaussian multiple access channel (MAC), subject
to local differential privacy (LDP) constraints. We show that the superposition
nature of the wireless channel provides a dual benefit of bandwidth efficient
gradient aggregation, in conjunction with strong LDP guarantees for the users.
We propose a private wireless gradient aggregation scheme, which shows that
when aggregating gradients from $K$ users, the privacy leakage per user scales
as $\mathcal{O}\big(\frac{1}{\sqrt{K}} \big)$ compared to orthogonal
transmission in which the privacy leakage scales as a constant. We also present
analysis for the convergence rate of the proposed private FL aggregation
algorithm and study the tradeoffs between wireless resources, convergence, and
privacy.
