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Low-Complexity Near-Field Localization with XL-MIMO Sectored Uniform Circular Arrays

Shicong Liu, Xianghao Yu

TL;DR

This work addresses near-field localization for XL-MIMO by leveraging a sectored uniform circular array and a backprojection framework in the polar domain. It introduces an ambiguity function $F_k(r, \varphi)$ that backpropagates received signals to reveal target locations, and provides analytical resolutions for angular and distance estimates along with minimum antenna requirements. An FFT-based implementation substantially lowers computational complexity while maintaining accuracy, enabling large-scale deployments to outperform traditional MUSIC approaches in both speed and precision. The results demonstrate that angular resolution scales with $\lambda$, $R$, and $\sin\alpha$, while distance resolution scales with the bandwidth $f_{BW}$, making the method practical for wideband XL-MIMO sensing in the near-field.

Abstract

Rapid advancement of antenna technology catalyses the popularization of extremely large-scale multiple-input multiple-output (XL-MIMO) antenna arrays, which pose unique challenges for localization with the inescapable near-field effect. In this paper, we propose an efficient near-field localization algorithm by leveraging a sectored uniform circular array (sUCA). In particular, we first customize a backprojection algorithm in the polar coordinate for sUCA-enabled near-field localization, which facilitates the target detection procedure. We then analyze the resolutions in both angular and distance domains via deriving the interval of zero-crossing points, and further unravel the minimum required number of antennas to eliminate grating lobes. The proposed localization method is finally implemented using fast Fourier transform (FFT) to reduce computational complexity. Simulation results verify the resolution analysis and demonstrate that the proposed method remarkably outperforms conventional localization algorithms in terms of localization accuracy. Moreover, the low-complexity FFT implementation achieves an average runtime that is hundreds of times faster when large numbers of antenna elements are employed.

Low-Complexity Near-Field Localization with XL-MIMO Sectored Uniform Circular Arrays

TL;DR

This work addresses near-field localization for XL-MIMO by leveraging a sectored uniform circular array and a backprojection framework in the polar domain. It introduces an ambiguity function that backpropagates received signals to reveal target locations, and provides analytical resolutions for angular and distance estimates along with minimum antenna requirements. An FFT-based implementation substantially lowers computational complexity while maintaining accuracy, enabling large-scale deployments to outperform traditional MUSIC approaches in both speed and precision. The results demonstrate that angular resolution scales with , , and , while distance resolution scales with the bandwidth , making the method practical for wideband XL-MIMO sensing in the near-field.

Abstract

Rapid advancement of antenna technology catalyses the popularization of extremely large-scale multiple-input multiple-output (XL-MIMO) antenna arrays, which pose unique challenges for localization with the inescapable near-field effect. In this paper, we propose an efficient near-field localization algorithm by leveraging a sectored uniform circular array (sUCA). In particular, we first customize a backprojection algorithm in the polar coordinate for sUCA-enabled near-field localization, which facilitates the target detection procedure. We then analyze the resolutions in both angular and distance domains via deriving the interval of zero-crossing points, and further unravel the minimum required number of antennas to eliminate grating lobes. The proposed localization method is finally implemented using fast Fourier transform (FFT) to reduce computational complexity. Simulation results verify the resolution analysis and demonstrate that the proposed method remarkably outperforms conventional localization algorithms in terms of localization accuracy. Moreover, the low-complexity FFT implementation achieves an average runtime that is hundreds of times faster when large numbers of antenna elements are employed.
Paper Structure (12 sections, 1 theorem, 19 equations, 6 figures, 1 table, 1 algorithm)

This paper contains 12 sections, 1 theorem, 19 equations, 6 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Proposed Near-Field Localization Method
  4. Resolution Analysis of the Proposed Method
  5. Angular Resolution
  6. Distance Resolution
  7. Minimum Number of Antennas
  8. Low-Complexity Implementation
  9. Simulation Results
  10. Simulation Setup
  11. Numerical Results
  12. Conclusions

Key Result

Proposition 1

There exists only one unique location coordinate $(r,\varphi)$ that maximizes the power of $F_k^{(\ell)}(r,\varphi)$ at $(r,\varphi) = (r_\ell,\varphi_\ell)$.

Figures (6)

  • Figure 1: The considered near-field communication scenario.
  • Figure 2: The ambiguity functions of (a) ULA and (b) sUCA with two targets in the near-field region, the (c) $x$-axis projection, and (d) $\varphi$-axis projection of the ambiguity functions.
  • Figure 3: Minimum number of antennas according to \ref{['eq:minantenna']} for $\pi/4\leq \alpha < \pi/2$ and \ref{['eq:minantenna2']} for $0< \alpha < \pi/2$.
  • Figure 4: The reconstruction pattern of the proposed algorithm in the (a) angular and (b) distance domains, and the corresponding lobe widths estimated according to \ref{['eq:lobewidth']} and \ref{['eq:lobedis']}, respectively.
  • Figure 5: The empirical CDF of the localization error of the proposed method and MUSIC algorithm.
  • ...and 1 more figures

Theorems & Definitions (2)

  • Proposition 1
  • proof