Wireless consensus methods speed up network cooperation without exact channels
Non-Coherent Over-the-Air Distributed Consensus: Algorithm Design and Power Control Optimization
Information Theory
Summary
Getting many wireless devices to agree on a shared number is tricky because signals can get messy and out of sync. The paper introduces a way to help devices reach exact agreement without needing to know the detailed conditions of the wireless connection. It also proposes a new technique to adjust how strongly devices send signals to make this process faster and more reliable. Tests showed this method works better than earlier approaches and helps networks agree quicker.
What this means in practice
- •For wireless network engineers: Improve synchronization of distributed devices by applying power control to reach consensus faster without precise channel knowledge.
- •For sensor network designers: Design sensor systems that efficiently compute average values over noisy wireless links without needing exact signal alignment.
Authors
Yuhang Deng, Zheng Chen, Erik G. Larsson
Abstract
Non-coherent over-the-air (NCOTA) aggregation offers a scalable and communication-efficient approach to distributed average consensus in wireless networks, without requiring instantaneous channel state information (CSI) or phase alignment. However, persistent aggregation errors pose fundamental challenges in achieving exact average consensus under nominal distributed averaging protocols. In this paper, we develop an NCOTA consensus framework that accommodates row-stochastic mixing, without requiring the conventional average-preservation property of doubly stochastic mixing matrices. Building on a distributed optimization formulation of average consensus, we propose a decentralized projected gradient descent with row-stochastic mixing (DPGD-RS) algorithm and establish its mean-square convergence to the exact average of the agents' initial states. We further derive a closed-form upper bound on the mean-square consensus error, characterizing the effects of aggregation uncertainty, network connectivity, and mixing imbalance. Guided by this analysis, we propose a spectral-reshaping power control (SR-PC) scheme that jointly optimizes transmit powers and receive-scaling factors to accelerate convergence by balancing aggregation accuracy and network mixing. Numerical results validate the theoretical convergence guarantees and demonstrate that the proposed power control scheme significantly accelerates convergence compared with full-power transmission and spectral-radius-minimization benchmarks.