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A Study on Characterization of Near-Field Sub-Regions For Phased-Array Antennas

Mehdi Monemi, Sirous Bahrami, Mehdi Rasti, Matti Latva-aho

Abstract

We characterize three near-field sub-regions for phased array antennas by elaborating on the boundaries {\it Fraunhofer}, {\it radial-focal}, and {\it non-radiating} distances. The {\it Fraunhofer distance} which is the boundary between near and far field has been well studied in the literature on the principal axis (PA) of single-element center-fed antennas, where PA denotes the axis perpendicular to the antenna surface passing from the antenna center. The results are also valid for phased arrays if the PA coincides with the boresight, which is not commonly the case in practice. In this work, we completely characterize the Fraunhofer distance by considering various angles between the PA and the boresight. For the {\it radial-focal distance}, below which beamfocusing is feasible in the radial domain, a formal characterization of the corresponding region based on the general model of near-field channels (GNC) is missing in the literature. We investigate this and elaborate that the maximum-ratio-transmission (MRT) beamforming based on the simple uniform spherical wave (USW) channel model results in a radial gap between the achieved and the desired focal points. While the gap vanishes when the array size $N$ becomes sufficiently large, we propose a practical algorithm to remove this gap in the non-asymptotic case when $N$ is not very large. Finally, the {\it non-radiating} distance, below which the reactive power dominates active power, has been studied in the literature for single-element antennas. We analytically explore this for phased arrays and show how different excitation phases of the antenna array impact it. We also clarify some misconceptions about the non-radiating and Fresnel distances prevailing in the literature.

A Study on Characterization of Near-Field Sub-Regions For Phased-Array Antennas

Abstract

We characterize three near-field sub-regions for phased array antennas by elaborating on the boundaries {\it Fraunhofer}, {\it radial-focal}, and {\it non-radiating} distances. The {\it Fraunhofer distance} which is the boundary between near and far field has been well studied in the literature on the principal axis (PA) of single-element center-fed antennas, where PA denotes the axis perpendicular to the antenna surface passing from the antenna center. The results are also valid for phased arrays if the PA coincides with the boresight, which is not commonly the case in practice. In this work, we completely characterize the Fraunhofer distance by considering various angles between the PA and the boresight. For the {\it radial-focal distance}, below which beamfocusing is feasible in the radial domain, a formal characterization of the corresponding region based on the general model of near-field channels (GNC) is missing in the literature. We investigate this and elaborate that the maximum-ratio-transmission (MRT) beamforming based on the simple uniform spherical wave (USW) channel model results in a radial gap between the achieved and the desired focal points. While the gap vanishes when the array size becomes sufficiently large, we propose a practical algorithm to remove this gap in the non-asymptotic case when is not very large. Finally, the {\it non-radiating} distance, below which the reactive power dominates active power, has been studied in the literature for single-element antennas. We analytically explore this for phased arrays and show how different excitation phases of the antenna array impact it. We also clarify some misconceptions about the non-radiating and Fresnel distances prevailing in the literature.

Paper Structure

This paper contains 16 sections, 6 theorems, 58 equations, 14 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background and Contributions
  3. Organization
  4. Notations
  5. System Model
  6. Characterization of Fraunhofer Region for Off-boresight Scenarios
  7. On-boresight Fraunhofer distance
  8. Characterizing the off-boresight Fraunhofer region for phased array antennas
  9. Characterization of Radial Beamfocusing Region
  10. Characterization and properties of beamfocusing in the radial domain
  11. Radial Focal Gap and Spot Beamfocusing in the asymptotic scenario
  12. Beamformer design to realize radial focal point in the non-asymptotic scenario
  13. Characterization of Non-Radiating Region
  14. Conclusions
  15. Proof of Theorem \ref{['th:ULA_asymptotic_ratio']}
  16. ...and 1 more sections

Key Result

Theorem 1

For phased array antennas, the Fraunhofer distance $d^{\mathrm{F}}$ is obtained as where $F(\theta)=8|\cos(\theta)|\sin^2(\theta)$, and $\theta^{\mathrm{F}}=\pi/2-F^{-1}(\frac{\lambda}{2D})$ in which $F^{-1}(\frac{\lambda}{2D})$ is the value of $\theta$ corresponding to the solution of $F(\theta)=\frac{\lambda}{2D}$ closet to $\pi/2$.

Figures (14)

  • Figure 1: Various characterized near-field sub-regions for a phased array antenna (dashed lines), versus a center-fed single-element antenna having the same dimension (dotted lines).
  • Figure 2: The system model for UPA and ULA antennas.
  • Figure 3: Antenna with diameter $D$. (a): UE located at an arbitrary distance. (b): UE located at Fraunhofer distance on the boresight.
  • Figure 4: $N$-element ULA antenna with diameter $D$ for two scenarios regarding the position of the transmitter.
  • Figure 5: The exact and approximated value of $\theta^{\mathrm{F}}$ for various number of array elements $N$ for a ULA antenna with half-wavelength inter-element spacing.
  • ...and 9 more figures

Theorems & Definitions (17)

  • Remark 1
  • Theorem 1
  • proof
  • Definition 1
  • Corollary 1
  • proof
  • Definition 2
  • Definition 3
  • Definition 4
  • proof
  • ...and 7 more