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Near-field Boundary Distance in mmWave and THz Communications with Misaligned Antenna Arrays

Peng Zhang, Vitaly Petrov, Emil Björnson

Abstract

Wireless communications in the millimeter wave (mmWave) and terahertz (THz) spectrum allow harnessing large frequency bands, thus achieving ultra-high data rates. However, the inherently short wavelengths of mmWave and THz signals lead to an extended radiative near-field region, where certain canonical far-field assumptions fail. Most prior works aimed to characterize this radiative near-field region either do not consider antenna arrays on both communicating nodes or, if they do, assume perfect alignment between the arrays. However, such assumptions break down in many realistic deployments, where both sides must employ large-scale mmWave/THz antenna arrays to maintain the desired communication range, while perfect antenna alignment cannot be guaranteed particularly under nodes mobility. In this work, a generalized mathematical framework is presented to characterize the radiative near-field distance in directional mmWave and THz communication systems under various realistic array rotations and misalignments. With the use of the developed framework, compact closed-form expressions are derived for the near-field boundary distance in a wide range of antenna configurations, including array-to-array and array-to-point setups, considering both linear and planar arrays. Our numerical study reveals that the presence of antenna misalignment may significantly adjust the boundaries of the near-field region in mmWave and THz communication systems.

Near-field Boundary Distance in mmWave and THz Communications with Misaligned Antenna Arrays

Abstract

Wireless communications in the millimeter wave (mmWave) and terahertz (THz) spectrum allow harnessing large frequency bands, thus achieving ultra-high data rates. However, the inherently short wavelengths of mmWave and THz signals lead to an extended radiative near-field region, where certain canonical far-field assumptions fail. Most prior works aimed to characterize this radiative near-field region either do not consider antenna arrays on both communicating nodes or, if they do, assume perfect alignment between the arrays. However, such assumptions break down in many realistic deployments, where both sides must employ large-scale mmWave/THz antenna arrays to maintain the desired communication range, while perfect antenna alignment cannot be guaranteed particularly under nodes mobility. In this work, a generalized mathematical framework is presented to characterize the radiative near-field distance in directional mmWave and THz communication systems under various realistic array rotations and misalignments. With the use of the developed framework, compact closed-form expressions are derived for the near-field boundary distance in a wide range of antenna configurations, including array-to-array and array-to-point setups, considering both linear and planar arrays. Our numerical study reveals that the presence of antenna misalignment may significantly adjust the boundaries of the near-field region in mmWave and THz communication systems.
Paper Structure (26 sections, 1 theorem, 82 equations, 16 figures, 2 tables)

This paper contains 26 sections, 1 theorem, 82 equations, 16 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Prior Work on Near-field Distance Characterization
  3. Near-field Distance with Misaligned Antennas
  4. Our Novelty and Contribution
  5. System Model
  6. ULA-to-ULA Case
  7. UPA-to-UPA Case
  8. ULA Near-Field Distance Calculation
  9. General Approach
  10. ULA-to-ULA case (on-boresight)
  11. ULA-to-ULA case (off-boresight)
  12. ULA-to-point case (off-boresight)
  13. UPA Near-Field Distance Calculation
  14. UPA-to-UPA case (on-boresight)
  15. UPA-to-UPA case (off-boresight) with single-angle rotation
  16. ...and 11 more sections

Key Result

Proposition 1

The off-boresight near-field distance is dominated by case (a), i.e., $r_{\mathrm{F,off}}^{\mathrm{L2L}}(\theta,\alpha)=r_{(\mathrm{a})}^{\mathrm{L2L}}(\theta,\alpha)$, provided that the angles $\theta'$ and $\alpha$ satisfy $|\theta'|,\, |\alpha| < \vartheta_{\mathrm{th}},$ where $\theta'\triangleq with $\kappa = {\pi\max \left( D_1, D_2 \right) }/{(\lambda \varphi)}$.

Figures (16)

  • Figure 1: Considered ULA-to-ULA scenario (analyzed in Sec. \ref{['sec:ULA']}). Section \ref{['sec:ULA-to-ULA(on-boresight)']} covers the on-boresight case ($\alpha = 0$), while Sec. \ref{['sec:ULA-to-ULA(off-boresight)']} -- the off-boresight case ($\alpha \neq 0$); Sec. \ref{['sec:ULA-to-point']} explores a special ULA-to-point setup ($N_{1} = 1$).
  • Figure 2: Considered UPA-to-UPA scenario (analyzed in Sec. \ref{['sec:UPA']}). Section \ref{['sec:UPA-to-UPA(on-boresight)']} covers the on-boresight case ($\alpha = 0$), Sec. \ref{['sec:UPA-to-UPA(off-boresight,1)']} discusses the off-boresight case ($\alpha \neq 0$) with the Tx rotation in only one plane ($\phi = 0$, $\theta \neq 0$), while Sec. \ref{['sec:UPA-to-UPA(off-boresight,2)']} -- the off-boresight case ($\alpha \neq 0$) with the Tx rotation in two planes ($\phi \neq 0$, $\theta \neq 0$); Sec. \ref{['sec:UPA-to-point']} explores a special UPA-to-point setup ($N_{1} = 1$).
  • Figure 3: On-boresight ULA scenario ($\alpha = 0$, $\theta \neq 0$, analyzed in Sec. \ref{['sec:ULA-to-ULA(on-boresight)']}).
  • Figure 4: Selection region of expressions \ref{['equ:U2U_off_a']} and \ref{['equ:U2U_off_b']} under different angle pairs $(\theta', \alpha)$, along with the threshold region boundary $\mathcal{Q}_{\mathrm{th}}$ by Proposition \ref{['prop:dominant_a']}.
  • Figure 5: Off-boresight ULA-to-point system model (Sec. \ref{['sec:ULA-to-point']}).
  • ...and 11 more figures

Theorems & Definitions (1)

  • Proposition 1