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Performance Bounds for Near-Field Localization with Widely-Spaced Multi-Subarray mmWave/THz MIMO

Songjie Yang, Xinyi Chen, Yue Xiu, Wanting Lyu, Zhongpei Zhang, Chau Yuen

TL;DR

This work analyzes near-field localization with widely-spaced multi-subarrays (WSMS) in mmWave/THz MIMO and derives closed-form Cramér-Rao bounds (CRBs) for angle and range. It introduces SW-WSMS and HSPW-WSMS models, derives CRBs using a Riemann-sum-based approach, and reveals that CRBs are governed by the angular span to the target, with identical normalized CRBs for WSMSs sharing the same span. The study demonstrates that WSMS can outperform uniform arrays under certain conditions, and that HSPW-WSMS offers a tractable, decomposable CRB form with SW and PW components. Simulations validate the closed-form expressions and provide insights into system design, suggesting promising directions for integrated sensing and communications (ISAC) with WSMS architectures.

Abstract

This paper investigates the potential of near-field localization using widely-spaced multi-subarrays (WSMSs) and analyzing the corresponding angle and range Cramér-Rao bounds (CRBs). By employing the Riemann sum, closed-form CRB expressions are derived for the spherical wavefront-based WSMS (SW-WSMS). We find that the CRBs can be characterized by the angular span formed by the line connecting the array's two ends to the target, and the different WSMSs with same angular spans but different number of subarrays have identical normalized CRBs. We provide a theoretical proof that, in certain scenarios, the CRB of WSMSs is smaller than that of uniform arrays. We further yield the closed-form CRBs for the hybrid spherical and planar wavefront-based WSMS (HSPW-WSMS), and its components can be seen as decompositions of the parameters from the CRBs for the SW-WSMS. Simulations are conducted to validate the accuracy of the derived closed-form CRBs and provide further insights into various system characteristics. Basically, this paper underscores the high resolution of utilizing WSMS for localization, reinforces the validity of adopting the HSPW assumption, and, considering its applications in communications, indicates a promising outlook for integrated sensing and communications based on HSPW-WSMSs.

Performance Bounds for Near-Field Localization with Widely-Spaced Multi-Subarray mmWave/THz MIMO

TL;DR

This work analyzes near-field localization with widely-spaced multi-subarrays (WSMS) in mmWave/THz MIMO and derives closed-form Cramér-Rao bounds (CRBs) for angle and range. It introduces SW-WSMS and HSPW-WSMS models, derives CRBs using a Riemann-sum-based approach, and reveals that CRBs are governed by the angular span to the target, with identical normalized CRBs for WSMSs sharing the same span. The study demonstrates that WSMS can outperform uniform arrays under certain conditions, and that HSPW-WSMS offers a tractable, decomposable CRB form with SW and PW components. Simulations validate the closed-form expressions and provide insights into system design, suggesting promising directions for integrated sensing and communications (ISAC) with WSMS architectures.

Abstract

This paper investigates the potential of near-field localization using widely-spaced multi-subarrays (WSMSs) and analyzing the corresponding angle and range Cramér-Rao bounds (CRBs). By employing the Riemann sum, closed-form CRB expressions are derived for the spherical wavefront-based WSMS (SW-WSMS). We find that the CRBs can be characterized by the angular span formed by the line connecting the array's two ends to the target, and the different WSMSs with same angular spans but different number of subarrays have identical normalized CRBs. We provide a theoretical proof that, in certain scenarios, the CRB of WSMSs is smaller than that of uniform arrays. We further yield the closed-form CRBs for the hybrid spherical and planar wavefront-based WSMS (HSPW-WSMS), and its components can be seen as decompositions of the parameters from the CRBs for the SW-WSMS. Simulations are conducted to validate the accuracy of the derived closed-form CRBs and provide further insights into various system characteristics. Basically, this paper underscores the high resolution of utilizing WSMS for localization, reinforces the validity of adopting the HSPW assumption, and, considering its applications in communications, indicates a promising outlook for integrated sensing and communications based on HSPW-WSMSs.
Paper Structure (21 sections, 10 theorems, 83 equations, 8 figures)

This paper contains 21 sections, 10 theorems, 83 equations, 8 figures.

Table of Contents

  1. Introduction
  2. System Model and CRB
  3. Signal Model
  4. General CRB Expressions
  5. CRBs for SW-WSMS
  6. Array Layout and Manifolds
  7. CRB Derivation
  8. Array Manifold Functions
  9. Calculation of sum formulas
  10. Closed-Form CRB
  11. CRBs for HSPW-WSMS
  12. Array Manifolds
  13. CRB Derivation
  14. Array Manifold Functions
  15. Calculation of sum formulas
  16. ...and 6 more sections

Key Result

Corollary 3.4

When $\theta=0$, two important conclusions can be drawn: 1) $G_{\theta}(\psi,\theta=0)$ and $G_{\theta r}(\psi,\theta=0)$ are odd functions of $\psi$, hence it can be inferred that $\mathcal{S}_{\theta}=0$ and $\mathcal{S}_{\theta r}=0$ at $\theta=0$, and 2) $G_{\theta^2}(\psi,\theta=0)$ and $G_{ r}

Figures (8)

  • Figure 1: The bi-static sensing system.
  • Figure 2: The three different array layouts
  • Figure 3: The root CRBs of SW-WSMS and SW-WSMS Approx. with different $K$ and $r$.
  • Figure 4: The root CRBs of SW-/HSPW-/PW-WSMW with different $\{K,I,r\}$.
  • Figure 5: The root CRBs of SW-/HSPW-/PW-WSMS with different $\{K,I,\theta\}$.
  • ...and 3 more figures

Theorems & Definitions (13)

  • Remark 3.3
  • Corollary 3.4
  • Corollary 3.5
  • Corollary 3.7
  • Corollary 3.8
  • Remark 3.9
  • Corollary 4.2
  • Corollary 4.3
  • Remark 4.5
  • Corollary 4.6
  • ...and 3 more