Non-Coherent Over-the-Air Distributed Consensus: Algorithm Design and Power Control Optimization

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.