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Movable Antenna Assisted Dual-Polarized Multi-Cell Cooperative AirComp: An Alternating Optimization Approach

Mingyu Hu, Nan Liu, Wei Kang

TL;DR

This work tackles over-the-air computation in a multi-cell network by introducing movable dual-polarized antennas (D-PMA) at the base stations and jointly optimizing beamforming, user transmit coefficients, polarization, and antenna positions. An alternating optimization framework combines closed-form updates for W and a, with SCA-SDR techniques for polarization and gradient-based methods for antenna placement, further extended to a two-time-scale approach under statistical CSI. The proposed scheme consistently outperforms movable single-polarized and fixed-antenna baselines in terms of sum MSE across instantaneous and statistical channels, demonstrating the value of integrating polarization diversity and movable geometry. The results highlight practical gains in AirComp accuracy and scalability for distributed optimization in next-generation multi-cell networks.

Abstract

Over-the-air computation (AirComp) is a key enabler for distributed optimization, since it leverages analog waveform superposition to perform aggregation and thereby mitigates the communication bottleneck caused by iterative information exchange. However, AirComp is sensitive to wireless environment and conventional systems with fixed single-polarized base-station arrays cannot fully exploit spatial degrees of freedom while also suffering from polarization mismatch. To overcome these limitations, this paper proposes a multi-cell cooperative air-computation framework assisted by dual-polarized movable antennas (D-PMA), and formulates a mean squared error (MSE) minimization problem by jointly optimizing the combining matrix, polarization vectors, antenna positions, and user transmit coefficients. The resulting problem is highly nonconvex, so an alternating algorithm is developed in which closed-form updates are obtained for the combining matrix and transmit coefficients. Then a method based on successive convex approximation (SCA) and semidefinite relaxation (SDR) is proposed to refine polarization vectors, and the antenna positions are updated using a gradient-based method. In addition, we develop a statistical-channel-based scheme for optimizing the antenna locations, and we further present the corresponding algorithm to efficiently obtain the solution. Numerical results show that the proposed movable dual-polarized scheme consistently outperforms movable single-polarized and fixed-antenna baselines under both instantaneous and statistical channels.

Movable Antenna Assisted Dual-Polarized Multi-Cell Cooperative AirComp: An Alternating Optimization Approach

TL;DR

This work tackles over-the-air computation in a multi-cell network by introducing movable dual-polarized antennas (D-PMA) at the base stations and jointly optimizing beamforming, user transmit coefficients, polarization, and antenna positions. An alternating optimization framework combines closed-form updates for W and a, with SCA-SDR techniques for polarization and gradient-based methods for antenna placement, further extended to a two-time-scale approach under statistical CSI. The proposed scheme consistently outperforms movable single-polarized and fixed-antenna baselines in terms of sum MSE across instantaneous and statistical channels, demonstrating the value of integrating polarization diversity and movable geometry. The results highlight practical gains in AirComp accuracy and scalability for distributed optimization in next-generation multi-cell networks.

Abstract

Over-the-air computation (AirComp) is a key enabler for distributed optimization, since it leverages analog waveform superposition to perform aggregation and thereby mitigates the communication bottleneck caused by iterative information exchange. However, AirComp is sensitive to wireless environment and conventional systems with fixed single-polarized base-station arrays cannot fully exploit spatial degrees of freedom while also suffering from polarization mismatch. To overcome these limitations, this paper proposes a multi-cell cooperative air-computation framework assisted by dual-polarized movable antennas (D-PMA), and formulates a mean squared error (MSE) minimization problem by jointly optimizing the combining matrix, polarization vectors, antenna positions, and user transmit coefficients. The resulting problem is highly nonconvex, so an alternating algorithm is developed in which closed-form updates are obtained for the combining matrix and transmit coefficients. Then a method based on successive convex approximation (SCA) and semidefinite relaxation (SDR) is proposed to refine polarization vectors, and the antenna positions are updated using a gradient-based method. In addition, we develop a statistical-channel-based scheme for optimizing the antenna locations, and we further present the corresponding algorithm to efficiently obtain the solution. Numerical results show that the proposed movable dual-polarized scheme consistently outperforms movable single-polarized and fixed-antenna baselines under both instantaneous and statistical channels.
Paper Structure (35 sections, 73 equations, 11 figures, 5 algorithms)

This paper contains 35 sections, 73 equations, 11 figures, 5 algorithms.

Table of Contents

  1. Introduction
  2. System Model
  3. Channel Model
  4. Responsive Channel Model
  5. Polarized Channel Model
  6. Signal Model
  7. Distributed Optimization
  8. Local Cumputing and Uplink Transmission
  9. Sharing and Updating
  10. Downlink Transmission
  11. Problem Formulation
  12. Power Budget
  13. Polarized Constraint
  14. Antenna Position
  15. Mean Squared Error
  16. ...and 20 more sections

Figures (11)

  • Figure 1: System model of D-PMA-aided AirComp system.
  • Figure 2: Description of signal propagation angles and scattering environment
  • Figure 3: Iteration number versus MSE
  • Figure 4: Number of antennas per BS versus MSE
  • Figure 5: Number of cells versus MSE
  • ...and 6 more figures