Copula-Based Analysis of Fluid Antenna-Assisted Over-the-Air Computation

TL;DR

This paper presents a copula-based analytical framework for evaluating fluid-antenna-assisted over-the-air computation in correlated wireless channels, highlighting performance gains and limitations.

Contribution

It introduces a Gumbel copula model for channel dependence and derives closed-form MSE expressions, advancing understanding of fluid-antenna benefits in correlated environments.

Findings

FA deployment reduces MSE significantly compared to fixed antennas.

Performance gain diminishes with increasing spatial correlation.

Analytical expressions match numerical simulations accurately.

Abstract

This letter studies an uplink over-the-air computation (AirComp) framework in which multiple user equipments are equipped with fluid-antenna (FA) arrays and operate over spatially correlated fading channels. By explicitly modeling channel dependence using the Gumbel copula, closed-form analytical expressions are derived for the cumulative distribution function (CDF) of the mean-squared error (MSE) of the aggregated function. The proposed analysis provides a quantitative performance characterization of AirComp under spatial correlation and provides analytical insights into the role of FA-assisted transmission in correlated wireless environments. Numerical results validate the derived expressions and show that FA deployment can substantially reduce the MSE compared with conventional fixed-antenna systems, although the achievable gain decreases as spatial correlation becomes stronger.