On Differential Privacy for Wireless Federated Learning with Non-coherent Aggregation

In this paper, we study distributed training by majority vote with the sign stochastic gradient descent (signSGD) along with over-the-air computation (OAC) under local differential privacy constraints. In our approach, the users first clip the local stochastic gradients and inject a certain amount of noise as a privacy enhancement strategy. Subsequently, they activate the indices of OFDM subcarriers based on the signs of the perturbed local stochastic gradients to realize a frequency-shift-keying-based majority vote computation at the parameter server. We evaluate the privacy benefits of the proposed approach and characterize the per-user privacy leakage theoretically. Our results show that the proposed technique improves the privacy guarantees and limits the leakage to a scaling factor of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{O}(1/\sqrt{K})$</tex>, where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$K$</tex> is the number of users, thanks to the superposition property of the wireless channel. With numerical experiments, we show that the proposed non-coherent aggregation is superior to quadrature-phase-shift-keying-based coherent aggregation, namely, one-bit digital aggregation (OBDA), in learning accuracy under time synchronization errors when the same privacy enhancement strategy is introduced to both methods.