Robust and Efficient Average Consensus with Non-Coherent Over-the-Air Aggregation

TL;DR

This work tackles robust distributed average consensus under non-coherent over-the-air (OTA) aggregation. It reformulates consensus as a distributed optimization and implements a decentralized projected gradient descent (D-PGD) method, augmented with energy-based non-coherent aggregation and a transmit power control/receive scaling (PCSS) module. The key contributions are (i) a D-PGD-based consensus that achieves mean-square convergence to the true average $x^*=rac{1}{N}\sum x_n[0]$ despite non-coherent interference, and (ii) an SDP-based alternating-minimization approach to optimize $\alpha$ and $\gamma$ to accelerate convergence. Simulations show significant speedups and unbiased accuracy compared to prior non-coherent OTA methods, highlighting practical potential for scalable wireless multi-agent systems.

Abstract

Non-coherent over-the-air (OTA) computation has garnered increasing attention for its advantages in facilitating information aggregation among distributed agents in resource-constrained networks without requiring precise channel estimation. A promising application scenario of this method is distributed average consensus in wireless multi-agent systems. However, in such scenario, non-coherent interference from concurrent OTA transmissions can introduce bias in the consensus value. To address this issue, we develop a robust distributed average consensus algorithm by formulating the consensus problem as a distributed optimization problem. Using decentralized projected gradient descent (D-PGD), our proposed algorithm can achieve unbiased mean square average consensus even in the presence of non-coherent interference and noise. Additionally, we implement transmit power control and receive scaling mechanisms to further accelerate convergence. Simulation results demonstrate that our method can significantly enhance the convergence speed of the D-PGD algorithm for OTA average consensus without compromising accuracy.

Figures (3)

• Figure 1: Computation process for distributed average consensus with non-coherent OTA aggregation over wireless fading channels.
• Figure 2: The evolution of $x_{n}[t]$ for 9 nodes in 10000 iterations.
• Figure 3: Convergence performance comparison. (a) Root mean square error (RMSE). (b) Consensus error (CE).