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Fluid Antenna Array Enhanced Over-the-Air Computation

Deyou Zhang, Sicong Ye, Ming Xiao, Kezhi Wang, Marco Di Renzo, Mikael Skoglund

TL;DR

This work tackles mean squared error minimization in over-the-air computation (AirComp) by leveraging fluid antenna (FA) arrays to gain movement-based degrees of freedom. It proposes an alternating-optimization framework that jointly optimizes user transmit coefficients, AP decoding, and the antenna-position vector (APV), with convex QCQP subproblems for $\bm b$, a convex least-squares subproblem for $\bm m$, and a primal-dual interior-point method for the non-convex APV $\bm x$. The approach yields a locally optimal solution that significantly improves $MSE$ performance over fixed-position antenna arrays, as demonstrated by numerical results across varying SNR, FA count, and user load. The findings suggest FA-enabled AirComp can substantially enhance fast data aggregation in dense wireless networks and may benefit applications such as wireless federated learning, motivating future work on broader system settings.

Abstract

Over-the-air computation (AirComp) has emerged as a promising technology for fast wireless data aggregation by harnessing the superposition property of wireless multiple-access channels. This paper investigates a fluid antenna (FA) array-enhanced AirComp system, employing the new degrees of freedom achieved by antenna movements. Specifically, we jointly optimize the transceiver design and antenna position vector (APV) to minimize the mean squared error (MSE) between target and estimated function values. To tackle the resulting highly non-convex problem, we adopt an alternating optimization technique to decompose it into three subproblems. These subproblems are then iteratively solved until convergence, leading to a locally optimal solution. Numerical results show that FA arrays with the proposed transceiver and APV design significantly outperform the traditional fixed-position antenna arrays in terms of MSE.

Fluid Antenna Array Enhanced Over-the-Air Computation

TL;DR

This work tackles mean squared error minimization in over-the-air computation (AirComp) by leveraging fluid antenna (FA) arrays to gain movement-based degrees of freedom. It proposes an alternating-optimization framework that jointly optimizes user transmit coefficients, AP decoding, and the antenna-position vector (APV), with convex QCQP subproblems for , a convex least-squares subproblem for , and a primal-dual interior-point method for the non-convex APV . The approach yields a locally optimal solution that significantly improves performance over fixed-position antenna arrays, as demonstrated by numerical results across varying SNR, FA count, and user load. The findings suggest FA-enabled AirComp can substantially enhance fast data aggregation in dense wireless networks and may benefit applications such as wireless federated learning, motivating future work on broader system settings.

Abstract

Over-the-air computation (AirComp) has emerged as a promising technology for fast wireless data aggregation by harnessing the superposition property of wireless multiple-access channels. This paper investigates a fluid antenna (FA) array-enhanced AirComp system, employing the new degrees of freedom achieved by antenna movements. Specifically, we jointly optimize the transceiver design and antenna position vector (APV) to minimize the mean squared error (MSE) between target and estimated function values. To tackle the resulting highly non-convex problem, we adopt an alternating optimization technique to decompose it into three subproblems. These subproblems are then iteratively solved until convergence, leading to a locally optimal solution. Numerical results show that FA arrays with the proposed transceiver and APV design significantly outperform the traditional fixed-position antenna arrays in terms of MSE.
Paper Structure (7 sections, 1 theorem, 33 equations, 2 figures, 2 algorithms)

This paper contains 7 sections, 1 theorem, 33 equations, 2 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. System Model
  4. Problem Formulation
  5. Transceiver and APV Design
  6. Numerical Results
  7. Conclusions

Key Result

Theorem 1

Algorithm Alg-AO converges to a locally optimal point of problem OP0 after several iterations.

Figures (2)

  • Figure 1: Illustration of the considered system model.
  • Figure 2: MSE performance versus the number of iterations, SNR, the number of FAs, and the number of users

Theorems & Definitions (1)

  • Theorem 1