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Near-field Beam-focusing Pattern under Discrete Phase Shifters

Haodong Zhang, Changsheng You, Cong Zhou

TL;DR

The paper addresses near-field beam focusing for XL-arrays using low-resolution discrete PSs and introduces a Fourier series expansion (FSE) to analytically characterize the beam patterns under phase quantization. It reveals that discretization induces additional grating lobes while preserving a main lobe with beam-focusing that improves with PS resolution; two grating-lobe types are identified and explained via an array-of-subarrays view. The proposed FSE framework enables precise insights into main and grating-lobe behavior in both near-field and far-field regimes, and results show that 3-bit PSs can match continuous PS performance in rate while delivering substantially higher energy efficiency, especially when combined with digital precoding. The work highlights trade-offs between rate performance and energy efficiency in practical XL-array deployments and guides design choices for hybrid beamforming with discrete PSs in multi-user near-field systems.

Abstract

Extremely large-scale arrays (XL-arrays) have emerged as a promising technology for enabling near-field communications in future wireless systems. However, the huge number of antennas deployed pose demanding challenges on the hardware cost and power consumption, especially when the antennas employ high-resolution phase shifters (PSs). To address this issue, in this paper, we consider low-resolution discrete PSs at the XL-array which are practically more energy efficient, and investigate the impact of PS resolution on the near-field beam-focusing effect. To this end, we propose a new Fourier series expansion method to efficiently tackle the difficulty in characterizing the beam pattern properties under phase quantization. Interestingly, we analytically show, for the first time, that 1) discrete PSs introduce additional grating lobes; 2) the main lobe still exhibits the beam-focusing property with its beam power increasing with PS resolution; and 3) there are two types of grating lobes, featured by the beam-focusing and beam-steering properties, respectively. In addition, we provide intuitive understanding for the appearance of grating lobes under discrete PSs from an array-of-subarrays perspective. Finally, numerical results demonstrate that the grating lobes generally degrade communication rate performance. However, a low-resolution of 3-bit PSs can achieve similar beam pattern and rate performance with the continuous PS counterpart, while it attains much higher energy efficiency.

Near-field Beam-focusing Pattern under Discrete Phase Shifters

TL;DR

The paper addresses near-field beam focusing for XL-arrays using low-resolution discrete PSs and introduces a Fourier series expansion (FSE) to analytically characterize the beam patterns under phase quantization. It reveals that discretization induces additional grating lobes while preserving a main lobe with beam-focusing that improves with PS resolution; two grating-lobe types are identified and explained via an array-of-subarrays view. The proposed FSE framework enables precise insights into main and grating-lobe behavior in both near-field and far-field regimes, and results show that 3-bit PSs can match continuous PS performance in rate while delivering substantially higher energy efficiency, especially when combined with digital precoding. The work highlights trade-offs between rate performance and energy efficiency in practical XL-array deployments and guides design choices for hybrid beamforming with discrete PSs in multi-user near-field systems.

Abstract

Extremely large-scale arrays (XL-arrays) have emerged as a promising technology for enabling near-field communications in future wireless systems. However, the huge number of antennas deployed pose demanding challenges on the hardware cost and power consumption, especially when the antennas employ high-resolution phase shifters (PSs). To address this issue, in this paper, we consider low-resolution discrete PSs at the XL-array which are practically more energy efficient, and investigate the impact of PS resolution on the near-field beam-focusing effect. To this end, we propose a new Fourier series expansion method to efficiently tackle the difficulty in characterizing the beam pattern properties under phase quantization. Interestingly, we analytically show, for the first time, that 1) discrete PSs introduce additional grating lobes; 2) the main lobe still exhibits the beam-focusing property with its beam power increasing with PS resolution; and 3) there are two types of grating lobes, featured by the beam-focusing and beam-steering properties, respectively. In addition, we provide intuitive understanding for the appearance of grating lobes under discrete PSs from an array-of-subarrays perspective. Finally, numerical results demonstrate that the grating lobes generally degrade communication rate performance. However, a low-resolution of 3-bit PSs can achieve similar beam pattern and rate performance with the continuous PS counterpart, while it attains much higher energy efficiency.
Paper Structure (21 sections, 10 theorems, 45 equations, 12 figures)

This paper contains 21 sections, 10 theorems, 45 equations, 12 figures.

Table of Contents

  1. Introduction
  2. Contributions, Organization, and Notations
  3. System Model
  4. Channel Model
  5. Signal Model
  6. Beam-Focusing Pattern Representation under Discrete Phase Shifters
  7. Near-Field Beam Pattern under Phase Quantization
  8. Beam Pattern Analysis Based on Fourier Series Expansion
  9. Beam Pattern Characterization under Discrete Phase Shifters: General Case
  10. Properties of Principle Components
  11. Properties of Main/Grating Lobes
  12. Main lobe
  13. Grating lobes
  14. Far-field Beam Pattern under Discrete PSs
  15. Beam Pattern Characterization under Discrete Phase Shifters: Special Cases and Discussions
  16. ...and 6 more sections

Key Result

Lemma 1

The near-field beam pattern of $\mathbf{f}(\theta_{\rm u},r_{\rm u})$ under $B$-bit PSs, given in neq6, can be equivalently expressed as where $\Delta_k\triangleq k\sin\theta_{\rm u}-\sin\theta$ is defined as the spatial angle difference and $\Phi_k\triangleq-k\frac{\cos^2\theta_{\rm u}}{r_{\rm u}}+\frac{\cos^2\theta}{r}$ is named as the ring differencecui2022channel. $f_k^{(B)}(\theta,r;\theta_{

Figures (12)

  • Figure 1: An XL-array multi-user communication system under discrete PSs.
  • Figure 2: The near-field beam pattern with $N=513$, $\theta_{\rm u}=\pi/5$, $r_{\rm u}=25$ m in different scenarios.
  • Figure 3: The value of $\eta({B})$ versus the PS resolution $B$.
  • Figure 4: The far-field beam pattern with $N=65$, $\theta_{\rm u}=\pi/5$, $r_{\rm u}=25$ m under 1-bit PSs.
  • Figure 5: The overlap case in the near-field with $N=513$, $\theta_{\rm u}=0$, $r_{\rm u}=25$ m under 1-bit PSs.
  • ...and 7 more figures

Theorems & Definitions (24)

  • Definition 1: Beam pattern
  • Definition 2: Beam-width
  • Definition 3: Beam-depth
  • Definition 4: Beam-height
  • Lemma 1
  • Lemma 2: NN-based phase quantization
  • Lemma 3
  • proof
  • proof
  • Proposition 1
  • ...and 14 more