  In this paper, we consider decentralized federated learning (FL) over
wireless networks, where over-the-air computation (AirComp) is adopted to
facilitate the local model consensus in a device-to-device (D2D) communication
manner. However, the AirComp-based consensus phase brings the additive noise in
each algorithm iterate and the consensus needs to be robust to wireless network
topology changes, which introduce a coupled and novel challenge of establishing
the convergence for wireless decentralized FL algorithm. To facilitate
consensus phase, we propose an AirComp-based DSGD with gradient tracking and
variance reduction (DSGT-VR) algorithm, where both precoding and decoding
strategies are developed for D2D communication. Furthermore, we prove that the
proposed algorithm converges linearly and establish the optimality gap for
strongly convex and smooth loss functions, taking into account the channel
fading and noise. The theoretical result shows that the additional error bound
in the optimality gap depends on the number of devices. Extensive simulations
verify the theoretical results and show that the proposed algorithm outperforms
other benchmark decentralized FL algorithms over wireless networks.
