Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Mixed Near-field and Far-field Localization in Extremely Large-scale MIMO Systems

Cong Zhou, Changsheng You, Chao Zhou, Hongqiang Cheng, Shuo Shi

TL;DR

The paper tackles mixed near-field and far-field target localization in extremely large MIMO systems with hybrid UPAs. It develops a three-step decoupled-subspace framework: signal reconstruction to recover full-dimension signals from a reduced hybrid array, a virtual sparse-UltraPA MUSIC-based angle–range decoupling with a decoupled 2D angle search, and a range-domain pattern–driven classification to resolve angular ambiguity and estimate near-field ranges, complemented by a closed-form CRB for mixed-field localization. The approach yields near-3D-MUSIC performance with substantially lower computational complexity and demonstrates improved target-classification accuracy and RMSE over benchmarks, particularly benefiting from the larger XL-MIMO aperture when using half-wavelength spacing. The work provides a practical sensing solution for 6G/ISAC scenarios, enabling accurate, low-complexity localization in hybrid-array XL-MIMO deployments. Future directions include low-complexity extensions, active sensing scenarios, and handling higher target densities or correlated channels.

Abstract

In this paper, we study efficient \emph{mixed near-field and far-field} target localization methods in extremely large-scale multiple-input multiple-output (XL-MIMO) systems Compared with existing works, we address two new challenges in target localization of MIMO communication systems via using decoupled subspace methods, arising from the half-wavelength antenna spacing constraint and \emph{hybrid uniform planar array} (UPA) architectures.To this end, we propose a new three-step mixed-field localization method. First, we reconstruct the equivalent signals received at UPA antennas by judiciously designing analog combining matrices over time with minimum recovery errors.Second, based on recovered signals, we extend the modified multiple signal classification (MUSIC) algorithm to the UPA architectures by constructing a new covariance matrix of a virtual sparse UPA (S-UPA) to decouple the 2D angles and range estimation.Due to the structure of the S-UPA, there exist ambiguous angles when estimating true angles of targets.In the third step, we design an effective classification method to distinguish mixed-field targets, determine true angles of all targets, as well as estimate the ranges of near-field targets.In particular, angular ambiguity is resolved by showing an important fact that the three types of estimated angles (i.e., far-field, near-field, and ambiguous angles) exhibit significantly different patterns in the range-domain MUSIC spectrum.Furthermore, to characterize the estimation error lower-bound, we obtain a matrix closed-form Cramér-Rao bounds for mixed-field target localization.Finally, numerical results demonstrate the effectiveness of our proposed mixed-field localization method, which improves target-classification accuracy and achieves a lower root mean square error than various benchmark schemes.

Mixed Near-field and Far-field Localization in Extremely Large-scale MIMO Systems

TL;DR

The paper tackles mixed near-field and far-field target localization in extremely large MIMO systems with hybrid UPAs. It develops a three-step decoupled-subspace framework: signal reconstruction to recover full-dimension signals from a reduced hybrid array, a virtual sparse-UltraPA MUSIC-based angle–range decoupling with a decoupled 2D angle search, and a range-domain pattern–driven classification to resolve angular ambiguity and estimate near-field ranges, complemented by a closed-form CRB for mixed-field localization. The approach yields near-3D-MUSIC performance with substantially lower computational complexity and demonstrates improved target-classification accuracy and RMSE over benchmarks, particularly benefiting from the larger XL-MIMO aperture when using half-wavelength spacing. The work provides a practical sensing solution for 6G/ISAC scenarios, enabling accurate, low-complexity localization in hybrid-array XL-MIMO deployments. Future directions include low-complexity extensions, active sensing scenarios, and handling higher target densities or correlated channels.

Abstract

In this paper, we study efficient \emph{mixed near-field and far-field} target localization methods in extremely large-scale multiple-input multiple-output (XL-MIMO) systems Compared with existing works, we address two new challenges in target localization of MIMO communication systems via using decoupled subspace methods, arising from the half-wavelength antenna spacing constraint and \emph{hybrid uniform planar array} (UPA) architectures.To this end, we propose a new three-step mixed-field localization method. First, we reconstruct the equivalent signals received at UPA antennas by judiciously designing analog combining matrices over time with minimum recovery errors.Second, based on recovered signals, we extend the modified multiple signal classification (MUSIC) algorithm to the UPA architectures by constructing a new covariance matrix of a virtual sparse UPA (S-UPA) to decouple the 2D angles and range estimation.Due to the structure of the S-UPA, there exist ambiguous angles when estimating true angles of targets.In the third step, we design an effective classification method to distinguish mixed-field targets, determine true angles of all targets, as well as estimate the ranges of near-field targets.In particular, angular ambiguity is resolved by showing an important fact that the three types of estimated angles (i.e., far-field, near-field, and ambiguous angles) exhibit significantly different patterns in the range-domain MUSIC spectrum.Furthermore, to characterize the estimation error lower-bound, we obtain a matrix closed-form Cramér-Rao bounds for mixed-field target localization.Finally, numerical results demonstrate the effectiveness of our proposed mixed-field localization method, which improves target-classification accuracy and achieves a lower root mean square error than various benchmark schemes.

Paper Structure

This paper contains 18 sections, 4 theorems, 71 equations, 11 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Works
  3. Contribution and Organization
  4. System Model
  5. Channel Models
  6. Signal Model
  7. Proposed Mixed-field Localization Method
  8. Signal Reconstruction
  9. Angle Estimation
  10. Estimation of angle parameter $\beta$
  11. Estimation for angle parameter $\alpha$
  12. Target Classification, Near-field Target Range Estimation and Ambiguity Elimination
  13. Extensions and Discussions
  14. Cramér-Rao bound derivation
  15. Numerical Results
  16. ...and 3 more sections

Key Result

Lemma 1

The optimal solution to Problem ( P1), denoted by $\mathbf{W}_0^{\ast}$, should satisfy the following two conditions: 1) ${\rm Rank}(\mathbf{W}_0^{\ast}) = N$, 2) $\sum\limits_{u=1}^U \mathbf{W}^{\ast}(u)^H\mathbf{W}^{\ast}(u)$ is a diagonal matrix.

Figures (11)

  • Figure 1: Considered mixed-field target localization system, where the BS is equipped with a (sub-connected) hybrid UPA.
  • Figure 2: The framework of proposed mixed-field localization algorithm and relation between signals.
  • Figure 3: Illustration of angle estimation. System parameters are set as $f = 10$ GHz and $N_x = N_y = 61$. The elevation and azimuth angles for far-field targets are ($\frac{\pi}{3}$, $-\frac{\pi}{4}$, $1000$ m) and ($\frac{\pi}{8}$, $\frac{2\pi}{3}$, $1500$ m), while the locations for near-field targets are set as ($\frac{5\pi}{13}$, ${0.23\pi}$, $50$ m) and ($\frac{\pi}{4}$, $\frac{5\pi}{21}$, $60$ m).
  • Figure 4: Spectrum of far-field estimator in \ref{['eq:2D MUSIC for far-field']} proposed in he2011efficient. System parameters are set as $f = 10$ GHz and $N_x = N_y = 61$. The elevation and azimuth angles for far-field targets are ($\frac{\pi}{3}$, $-\frac{\pi}{4}$, $1000$ m) and ($\frac{\pi}{8}$, $\frac{2\pi}{3}$, $1500$ m), while the locations for near-field targets are set as ($\frac{5\pi}{13}$, ${0.23\pi}$, $30$ m) and ($\frac{\pi}{4}$, $\frac{5\pi}{21}$, $40$ m).
  • Figure 5: Illustration of proposed classification method. System parameters are set as $f = 10$ GHz and $N_x = N_y = 61$. The ranges of the two near-field targets are $50$ and $60$ m.
  • ...and 6 more figures

Theorems & Definitions (6)

  • Lemma 1
  • Lemma 2
  • proof
  • Lemma 3
  • Lemma 4
  • proof