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Optimal Movable Antenna Placement for Near-Field Wireless Sensing

Jinjian Liu, Xianxin Song, Xianghao Yu

Abstract

Movable antennas (MAs) have emerged as a promising technology for wireless sensing by reconfiguring antenna positions to exploit additional spatial degrees of freedom (DoFs). This paper investigates a robust movable antenna placement strategy for near-field wireless sensing to minimize the worst-case squared position error bound (SPEB). By temporarily relaxing the minimum inter-element spacing constraint, we first establish the optimality of centro-symmetric antenna position distribution, which simplifies the identification of the worst-case source, locating it at the array broadside on the Rayleigh boundary. Moreover, by leveraging moment-based analysis with the Richter-Tchakaloff theorem, we derive a closed-form optimal solution with three points supported on the center and two edges of the array. Guided by this structural insight, we finally develop an efficient three-point discrete deployment strategy to ensure the minimum inter-element spacing. Simulations demonstrate that the proposed design consistently outperforms conventional fixed antenna arrays and matches the exhaustive search benchmark at negligible computational complexity.

Optimal Movable Antenna Placement for Near-Field Wireless Sensing

Abstract

Movable antennas (MAs) have emerged as a promising technology for wireless sensing by reconfiguring antenna positions to exploit additional spatial degrees of freedom (DoFs). This paper investigates a robust movable antenna placement strategy for near-field wireless sensing to minimize the worst-case squared position error bound (SPEB). By temporarily relaxing the minimum inter-element spacing constraint, we first establish the optimality of centro-symmetric antenna position distribution, which simplifies the identification of the worst-case source, locating it at the array broadside on the Rayleigh boundary. Moreover, by leveraging moment-based analysis with the Richter-Tchakaloff theorem, we derive a closed-form optimal solution with three points supported on the center and two edges of the array. Guided by this structural insight, we finally develop an efficient three-point discrete deployment strategy to ensure the minimum inter-element spacing. Simulations demonstrate that the proposed design consistently outperforms conventional fixed antenna arrays and matches the exhaustive search benchmark at negligible computational complexity.
Paper Structure (13 sections, 6 theorems, 29 equations, 4 figures)

This paper contains 13 sections, 6 theorems, 29 equations, 4 figures.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. Problem Reformulation and Analysis
  4. Optimal MA Geometry Analysis via Moment Methods
  5. Moment-Based Structural Analysis for Symmetric Distribution
  6. Closed-Form Optimal Array Design
  7. Numerical Results
  8. Conclusion
  9. Proof of Lemma 1
  10. Proof of Proposition 1
  11. Proof of Proposition 2
  12. Proof of Lemma 2
  13. Proof of Lemma 3

Key Result

Lemma 1

The source SPEB is given by

Figures (4)

  • Figure 1: The 1D MA array geometry for single-source sensing in the near field.
  • Figure 2: Optimal $q^\star$ versus $a/\lambda$.
  • Figure 3: The heatmap for near field region.
  • Figure 4: Worst-case $\text{SPEB}$ performance comparison versus (a) Received SNR; (b) Number of antennas $N$.

Theorems & Definitions (7)

  • Remark 1
  • Lemma 1
  • Proposition 1
  • Proposition 2
  • Lemma 2
  • Lemma 3
  • Theorem 1