Optimal QAM Constellation for Over-the-Air Computation in the Presence of Heavy-Tailed Channel Noise

2026-02-24

AI Summary

This work addresses the severe degradation of aggregation accuracy in over-the-air computation (OAC) caused by heavy-tailed channel noise—such as Cauchy-distributed interference—which lacks finite second-order moments and thus undermines conventional QAM-based constellation designs. The authors formulate a mean squared error (MSE) minimization problem under an average power constraint and, for the first time, derive closed-form conditions for optimal QAM-like constellations in such heavy-tailed noise environments. Their constellation design, grounded in constrained optimization and tailored to Cauchy noise modeling with rigorous MSE analysis, naturally extends to nomographic functions, broader constellation families, and other noise models. Numerical experiments demonstrate that the proposed constellations significantly reduce aggregation MSE, thereby enhancing both robustness and accuracy of OAC systems operating under heavy-tailed interference.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments

Abstract

Over-the-air computation (OAC) enables low-latency aggregation over multiple-access channels (MACs) by exploiting the superposition property of the wireless medium to compute functions efficiently in distributed networks. A critical but often overlooked challenge is that electromagnetic interference in practical radio channels frequently exhibits heavy-tailed behavior, causing strong impulsive noise that severely degrades computation performance. This work studies digital OAC with QAM-based signaling under heavy-tailed interference modeled by a Cauchy distribution (lacking a finite second moment). We seek QAM-like constellations that minimize the mean-squared error (MSE) of sum aggregation subject to an average-power constraint. The problem is formulated as a constrained optimization, whose solution yields unique optimality conditions. Numerical results confirm the effectiveness of the proposed design. Notably, the framework extends naturally to nomographic functions, broader constellation families, and alternative noise models.

Problem

• Over-the-air computation
• QAM constellation
• heavy-tailed noise
• mean-squared error
• Cauchy distribution

Innovation

• Over-the-air computation
• Heavy-tailed noise
• Optimal QAM constellation
• Cauchy distribution
• Mean-squared error minimization