VecComp: Vector Computing via MIMO Digital Over-the-Air Computation

2025-11-04

AI Summary

ChannelComp supports only scalar functions and exhibits insufficient robustness against channel fading, limiting its applicability to high-dimensional data tasks. To address this, we propose VecComp—the first digital over-the-air computation (AirComp) framework tailored for MIMO systems, enabling efficient and robust vector-valued function computation. VecComp jointly designs multi-antenna transmission, non-orthogonal waveforms, and signal alignment mechanisms to achieve reliable vector aggregation over multi-access fading channels. We derive a non-asymptotic upper bound on the mean-square error (MSE) and show that computational complexity scales linearly with vector dimension. Experiments demonstrate that VecComp significantly improves computation accuracy under noise and channel fading, while offering superior scalability and stability compared to scalar AirComp schemes. Its design makes it particularly suitable for edge intelligence and other localized information processing scenarios requiring distributed vector aggregation.

Technology Category

• Multiagent Systems: Agent Communication
• Machine Learning: Hardware-aware ML
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements

Abstract

Recently, the ChannelComp framework has proposed digital over-the-air computation by designing digital modulations that enable the computation of arbitrary functions. Unlike traditional analog over-the-air computation, which is restricted to nomographic functions, ChannelComp enables a broader range of computational tasks while maintaining compatibility with digital communication systems. This framework is intended for applications that favor local information processing over the mere acquisition of data. However, ChannelComp is currently designed for scalar function computation, while numerous data-centric applications necessitate vector-based computations, and it is susceptible to channel fading. In this work, we introduce a generalization of the ChannelComp framework, called VecComp, by integrating ChannelComp with multiple-antenna technology. This generalization not only enables vector function computation but also ensures scalability in the computational complexity, which increases only linearly with the vector dimension. As such, VecComp remains computationally efficient and robust against channel impairments, making it suitable for high-dimensional, data-centric applications. We establish a non-asymptotic upper bound on the mean squared error of VecComp, affirming its computation efficiency under fading channel conditions. Numerical experiments show the effectiveness of VecComp in improving the computation of vector functions and fading compensation over noisy and fading multiple-access channels.

Problem

• Extends digital over-air computation to vector functions
• Addresses channel fading susceptibility in wireless computation
• Enables scalable vector processing for data-centric applications

Innovation

• VecComp integrates ChannelComp with multiple-antenna technology
• It enables scalable vector function computation via MIMO
• It ensures robustness against channel fading impairments