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Movable Antenna Enhanced Wireless Sensing Via Antenna Position Optimization

Wenyan Ma, Lipeng Zhu, Rui Zhang

TL;DR

This work addresses AoA sensing performance in wireless systems by enabling movable-antenna (MA) arrays that adjust antenna positions within a region. It develops CRB-based analyses for 1D and 2D MA geometries and proposes optimization strategies: a closed-form, globally optimal APV for 1D lines, and an alternating optimization framework for 2D regions (with a special solution for circular movement regions) to minimize the min-max AoA estimation CRBs. The proposed method yields substantial reductions in both the CRB and the actual MUSIC AoA MSE compared with fixed-position arrays, by shaping steering-vector orthogonality and expanding array aperture. These results highlight the practical potential of MA-aided sensing to enhance angular resolution and adaptability in ISAC systems, while keeping antenna counts fixed.

Abstract

In this paper, we propose a new wireless sensing system equipped with the movable-antenna (MA) array, which can flexibly adjust the positions of antenna elements for improving the sensing performance over conventional antenna arrays with fixed-position antennas (FPAs). First, we show that the angle estimation performance in wireless sensing is fundamentally determined by the array geometry, where the Cramer-Rao bound (CRB) of the mean square error (MSE) for angle of arrival (AoA) estimation is derived as a function of the antennas' positions for both one-dimensional (1D) and two-dimensional (2D) MA arrays. Then, for the case of 1D MA array, we obtain a globally optimal solution for the MAs' positions in closed form to minimize the CRB of AoA estimation MSE. While in the case of 2D MA array, we aim to achieve the minimum of maximum (min-max) CRBs of estimation MSE for the two AoAs with respect to the horizontal and vertical axes, respectively. In particular, for the special case of circular antenna movement region, an optimal solution for the MAs' positions is derived under certain numbers of MAs and circle radii. Thereby, both the lower- and upper-bounds of the min-max CRB are obtained for the antenna movement region with arbitrary shapes. Moreover, we develop an efficient alternating optimization algorithm to obtain a locally optimal solution for MAs' positions by iteratively optimizing one between their horizontal and vertical coordinates with the other being fixed. Numerical results demonstrate that our proposed 1D/2D MA arrays can significantly decrease the CRB of AoA estimation MSE as well as the actual MSE compared to conventional uniform linear arrays (ULAs)/uniform planar arrays (UPAs) with different values of uniform inter-antenna spacing.

Movable Antenna Enhanced Wireless Sensing Via Antenna Position Optimization

TL;DR

This work addresses AoA sensing performance in wireless systems by enabling movable-antenna (MA) arrays that adjust antenna positions within a region. It develops CRB-based analyses for 1D and 2D MA geometries and proposes optimization strategies: a closed-form, globally optimal APV for 1D lines, and an alternating optimization framework for 2D regions (with a special solution for circular movement regions) to minimize the min-max AoA estimation CRBs. The proposed method yields substantial reductions in both the CRB and the actual MUSIC AoA MSE compared with fixed-position arrays, by shaping steering-vector orthogonality and expanding array aperture. These results highlight the practical potential of MA-aided sensing to enhance angular resolution and adaptability in ISAC systems, while keeping antenna counts fixed.

Abstract

In this paper, we propose a new wireless sensing system equipped with the movable-antenna (MA) array, which can flexibly adjust the positions of antenna elements for improving the sensing performance over conventional antenna arrays with fixed-position antennas (FPAs). First, we show that the angle estimation performance in wireless sensing is fundamentally determined by the array geometry, where the Cramer-Rao bound (CRB) of the mean square error (MSE) for angle of arrival (AoA) estimation is derived as a function of the antennas' positions for both one-dimensional (1D) and two-dimensional (2D) MA arrays. Then, for the case of 1D MA array, we obtain a globally optimal solution for the MAs' positions in closed form to minimize the CRB of AoA estimation MSE. While in the case of 2D MA array, we aim to achieve the minimum of maximum (min-max) CRBs of estimation MSE for the two AoAs with respect to the horizontal and vertical axes, respectively. In particular, for the special case of circular antenna movement region, an optimal solution for the MAs' positions is derived under certain numbers of MAs and circle radii. Thereby, both the lower- and upper-bounds of the min-max CRB are obtained for the antenna movement region with arbitrary shapes. Moreover, we develop an efficient alternating optimization algorithm to obtain a locally optimal solution for MAs' positions by iteratively optimizing one between their horizontal and vertical coordinates with the other being fixed. Numerical results demonstrate that our proposed 1D/2D MA arrays can significantly decrease the CRB of AoA estimation MSE as well as the actual MSE compared to conventional uniform linear arrays (ULAs)/uniform planar arrays (UPAs) with different values of uniform inter-antenna spacing.
Paper Structure (20 sections, 2 theorems, 58 equations, 13 figures, 1 table, 1 algorithm)

This paper contains 20 sections, 2 theorems, 58 equations, 13 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. CRB Characterization for 1D MA Array
  3. System Model
  4. AoA Estimation
  5. CRB Minimization
  6. CRB Characterization for 2D MA Array
  7. System Model
  8. AoA Estimation and CRB Minimization
  9. Optimal Solution for Problem (P2) for Circular Region $\mathcal{C}^\textrm{cir}$
  10. Performance Analysis for General 2D Region $\mathcal{C}$
  11. APV Optimization for 2D MA Array
  12. Optimization of $\bm{x}$ with Given $\bm{y}$
  13. Optimization of $\bm{y}$ with Given $\bm{x}$
  14. Overall Algorithm
  15. Numerical Results
  16. ...and 5 more sections

Key Result

Theorem 1

The optimal APV for minimizing the CRB of AoA estimation MSE in the 1D line segment is given by The corresponding minimum CRB, given by PAND and 50, decreases with $A$ in the order of $\mathcal{O}(A^{-2})$.

Figures (13)

  • Figure 1: The 1D MA array for target angle estimation.
  • Figure 2: Illustration of the optimal MAs' positions for the 1D MA array.
  • Figure 3: The 2D MA array for target angle estimation.
  • Figure 4: Illustration of the AoAs and geometrical parameters for the 2D MA array.
  • Figure 5: Illustration of the optimal MAs' positions in circular region $\mathcal{C}^\textrm{cir}$.
  • ...and 8 more figures

Theorems & Definitions (4)

  • Theorem 1
  • proof
  • Theorem 2
  • proof