Hardware-Impaired Over-the-Air Computation with Fluid Antenna Array

Abstract: This paper investigates a fluid antenna (FA) array-enhanced over-the-air computation (AirComp) system in the presence of hardware impairments (HWIs), exploiting the new degrees of freedom offered by reconfigurable antenna positioning. To minimize the mean squared error (MSE) of the aggregated signal, we jointly optimize transmit power control, receive beamforming, and the antenna position vector (APV), subject to practical constraints such as HWI-induced distortion noise, FA movement energy consumption, and total power budgets. The resulting optimization problem is non-convex and highly coupled. To address it efficiently, we adopt a block coordinate descent (BCD) framework, decomposing it into three manageable subproblems. For each subproblem, closed-form solutions or efficient numerical algorithms are derived. Simulation results demonstrate that the proposed joint transceiver and APV design significantly reduces the MSE compared to conventional fixed-position antenna (FPA) arrays and exhibits enhanced robustness against hardware impairments. The effectiveness and convergence of the proposed algorithm are further validated under various system configurations.