  Federated Learning (FL) is a collaborative learning framework that enables
edge devices to collaboratively learn a global model while keeping raw data
locally. Although FL avoids leaking direct information from local datasets,
sensitive information can still be inferred from the shared models. To address
the privacy issue in FL, differential privacy (DP) mechanisms are leveraged to
provide formal privacy guarantee. However, when deploying FL at the wireless
edge with over-the-air computation, ensuring client-level DP faces significant
challenges. In this paper, we propose a novel wireless FL scheme called private
federated edge learning with sparsification (PFELS) to provide client-level DP
guarantee with intrinsic channel noise while reducing communication and energy
overhead and improving model accuracy. The key idea of PFELS is for each device
to first compress its model update and then adaptively design the transmit
power of the compressed model update according to the wireless channel status
without any artificial noise addition. We provide a privacy analysis for PFELS
and prove the convergence of PFELS under general non-convex and non-IID
settings. Experimental results show that compared with prior work, PFELS can
improve the accuracy with the same DP guarantee and save communication and
energy costs simultaneously.
