Over-the-Air Decentralized Federated Learning Under MIMO Noisy Channel

Decentralized federated learning (DFL) is an emerging paradigm for leveraging the rapidly growing data from wireless devices in a fully distributed manner. However, the deployment of DFL is facing some pivotal challenges, including communication bottlenecks due to extensive inter-device message exchanges and the difficulty for edge devices to achieve consensus. To address these challenges, this paper proposes to employ the over-the-air computation (Aircomp) technique to improve communication efficiency and introduces a mixing matrix mechanism to guarantee consensus. Specifically, we present a novel multiple-input multiple-output over-the-air DFL (MIMO OA-DFL) framework for addressing the DFL design problem in general ad hoc networks. A rigorous convergence bound is derived to quantitatively capture the impact of mixing matrix and communication error on the system performance. The results show that the communication errors, the spectral gap of the mixing matrix, and the mixing matrix itself have a significant impact on the learning performance. Building on this result, we formulate a joint communication-learning optimization problem to optimize transceiver beamformers and mixing matrix. Numerical experiments demonstrate the substantial performance enhancement achieved by our proposed scheme.