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

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.