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Analyzing URA Geometry for Enhanced Near-Field Beamfocusing and Spatial Degrees of Freedom

Ahmed Hussain, Asmaa Abdallah, Abdulkadir Celik, Emil Björnson, Ahmed M. Eltawil

Abstract

With the deployment of large antenna arrays at high-frequency bands, future wireless communication systems are likely to operate in the radiative near-field. Unlike far-field beam steering, near-field beams can be focused on a spatial region with a finite depth, enabling spatial multiplexing in the range dimension. Moreover, in the line-of-sight MIMO near-field, multiple spatial degrees of freedom (DoF) are accessible, akin to a scattering- rich environment. In this paper, we derive the beamdepth for a generalized uniform rectangular array (URA) and investigate how the array geometry influences near-field beamdepth and its limits. We define the effective beamfocusing Rayleigh distance (EBRD), to present a near-field boundary with respect to beamfocusing and spatial multiplexing gains for the generalized URA. Our results demonstrate that under a fixed element count constraint, the array geometry has a strong impact on beamdepth, whereas this effect diminishes under a fixed aperture length constraint. Moreover, compared to uniform square arrays, elongated configurations such as uniform linear arrays (ULAs) yield narrower beamdepth and extend the effective near-field region defined by the EBRD. Building on these insights, we design a polar codebook for compressed-sensing-based channel estimation that leverages our findings. Simulation results show that the proposed polar codebook achieves a 2 dB NMSE improvement over state-of-the-art methods. Additionally, we present an analytical expression to quantify the effective spatial DoF in the near-field, revealing that they are also constrained by the EBRD. Notably, the maximum spatial DoF is achieved with a ULA configuration, outperforming a square URA in this regard.

Analyzing URA Geometry for Enhanced Near-Field Beamfocusing and Spatial Degrees of Freedom

Abstract

With the deployment of large antenna arrays at high-frequency bands, future wireless communication systems are likely to operate in the radiative near-field. Unlike far-field beam steering, near-field beams can be focused on a spatial region with a finite depth, enabling spatial multiplexing in the range dimension. Moreover, in the line-of-sight MIMO near-field, multiple spatial degrees of freedom (DoF) are accessible, akin to a scattering- rich environment. In this paper, we derive the beamdepth for a generalized uniform rectangular array (URA) and investigate how the array geometry influences near-field beamdepth and its limits. We define the effective beamfocusing Rayleigh distance (EBRD), to present a near-field boundary with respect to beamfocusing and spatial multiplexing gains for the generalized URA. Our results demonstrate that under a fixed element count constraint, the array geometry has a strong impact on beamdepth, whereas this effect diminishes under a fixed aperture length constraint. Moreover, compared to uniform square arrays, elongated configurations such as uniform linear arrays (ULAs) yield narrower beamdepth and extend the effective near-field region defined by the EBRD. Building on these insights, we design a polar codebook for compressed-sensing-based channel estimation that leverages our findings. Simulation results show that the proposed polar codebook achieves a 2 dB NMSE improvement over state-of-the-art methods. Additionally, we present an analytical expression to quantify the effective spatial DoF in the near-field, revealing that they are also constrained by the EBRD. Notably, the maximum spatial DoF is achieved with a ULA configuration, outperforming a square URA in this regard.
Paper Structure (41 sections, 6 theorems, 46 equations, 19 figures, 2 tables, 1 algorithm)

This paper contains 41 sections, 6 theorems, 46 equations, 19 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Contribution
  4. Notations and Organization of the Paper
  5. System Model
  6. Analysis of Near-field Beamforming
  7. Finite Beamdepth and EBRD
  8. Impact of Spatial Focus Region and Array Geometry
  9. Spatial Focus Region
  10. Array Geometry
  11. Limits of Beamfocusing
  12. Multiuser Capacity Analysis
  13. SE vs. EBRD
  14. SE vs. Array Geometry
  15. Axial vs. Lateral Beam Pattern Analysis
  16. ...and 26 more sections

Key Result

Theorem 1

For a generalized URA, the $\unit[3]{dB}$ beamdepth $r_{\mathrm{\hbox{BD} }}$ obtained by focusing a beam at a distance $r_{\mathrm{\hbox{F}}}$ from the BS is given by

Figures (19)

  • Figure 1: URA setup and a single prospective user.
  • Figure 2: Near-field beam with finite beamdepth and beamwidth in the axial and lateral dimensions, respectively.
  • Figure 3: Numerical and analytical beamdepth for a $(256 \times 16)$URA operating at $\unit[30]{GHz}$. The zoom inset highlights the beamdepth for focus distances less than $2D = 5$.
  • Figure 4: Near-field boundary in terms of ERD and EBRD for a ULA. Here $f_c = \unit[28]{GHz}$, $N_{\mathrm{\hbox{BS} }}=256$, $r_{\mathrm{\hbox{RD} }}=\unit[348]{m}$.
  • Figure 5: Beamdepth with respect to azimuth angle $\varphi$ for different array configuration $\eta$ and elevation angle $\theta$.
  • ...and 14 more figures

Theorems & Definitions (10)

  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Corollary 1
  • Corollary 2
  • Theorem 3
  • proof
  • Theorem 4
  • proof