Distributed Average Consensus via Noisy and Non-Coherent Over-the-Air Aggregation
Huiwen Yang, Xiaomeng Chen, Lingying Huang, Subhrakanti Dey, Ling Shi
TL;DR
This paper addresses distributed average consensus in wireless multi-agent networks employing over-the-air aggregation with noisy, non-coherent transmissions and half-duplex nodes. It proposes a joint communication and consensus protocol where each node updates according to $x_i(k+1) = (1 - \alpha(k) \sum_j a_{ij}) x_i(k) + \alpha(k)(|y_i(k)|^2 - \sigma_i^2)$ using amplitude-encoded transmissions, and proves mean-square average consensus and almost-sure consensus under decreasing $\alpha(k)$. The convergence analysis accounts for state-dependent noise from non-coherent aggregation and leverages a mean Laplacian $\bar{\mathcal{L}}$ to drive consensus, with extensions to time-varying topologies under joint connectivity. Simulations on networks up to 50 nodes confirm robustness to noise and fading and demonstrate significant resources savings compared to coherent, full-CSI alternatives, highlighting practical impact for decentralized wireless systems.
Abstract
Over-the-air aggregation has attracted widespread attention for its potential advantages in task-oriented applications, such as distributed sensing, learning, and consensus. In this paper, we develop a communication-efficient distributed average consensus protocol by utilizing over-the-air aggregation, which exploits the superposition property of wireless channels rather than combat it. Noisy channels and non-coherent transmission are taken into account, and only half-duplex transceivers are required. We prove that the system can achieve average consensus in mean square and even almost surely under the proposed protocol. Furthermore, we extend the analysis to the scenarios with time-varying topology. Numerical simulation shows the effectiveness of the proposed protocol.