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Circular Holographic MIMO Beamforming for Integrated Data and Energy Multicast Systems

Qingxiao Huang, Yizhe Zhao, Jie Hu, Kun Yang, Yuguang Fang

TL;DR

This work presents a circular H-MIMO framework for Integrated Data and Energy Multicast (IDEM), deriving a closed-form near-field resolution function and proving asymptotic spatial orthogonality of circular-array channels. Leveraging this orthogonality, it develops a low-complexity, hybrid analog-digital beamforming design that maximizes the minimum data rate while satisfying energy-harvesting constraints, using three control modes (Amplitude, Binary amplitude, and Lorentzian-constrained phase) plus scaling to relax analog constraints. An asymptotically optimal fully-digital transmitter is derived, followed by an alternating optimization procedure to approximate it under hardware limits, with convergence and complexity analyzed. Numerical results validate the resolution function and orthogonality, and demonstrate that the proposed schemes achieve near-upper-bound performance with significantly lower complexity than benchmarks. The circular array extends near-field focusing in angular domains and enables multi-point energy/data focusing, offering practical benefits for large-scale IDEM deployments.

Abstract

Thanks to the application of metamaterials, holographic multiple-input multiple-output (H-MIMO) is expected to achieve a higher spatial diversity gain with lower hardware complexity. With the aid of a circular antenna arrangement of H-MIMO, integrated data and energy multicast (IDEM) can fully exploit the near-field channel to realize wider range of energy focusing and higher achievable rate. In this paper, we derive the closed-form near-field resolution function in 3D space and show the asymptotic spatial orthogonality of near-field channel for circular antenna array. We then investigate the beamforming designs for IDEM systems, where the minimum rate of data users (DUs) are maximized while guaranteeing the energy harvesting requirements for energy users (EUs). Specifically, the asymptotically optimal fully-digital beamformer is first obtained based on the spatial orthogonality. Then, the alternating optimization is adopted for the H-MIMO beamforming, where the digital beamformer is obtained in closed form and the analog beamformers of three different control modes are then obtained, respectively. Scaling schemes are also investigated to further improve the IDEM performance. Numerical results verify the correctness of the resolution function and asymptotic orthogonality. Moreover, the proposed beamforming schemes with very low complexity outperform benchmark schemes.

Circular Holographic MIMO Beamforming for Integrated Data and Energy Multicast Systems

TL;DR

This work presents a circular H-MIMO framework for Integrated Data and Energy Multicast (IDEM), deriving a closed-form near-field resolution function and proving asymptotic spatial orthogonality of circular-array channels. Leveraging this orthogonality, it develops a low-complexity, hybrid analog-digital beamforming design that maximizes the minimum data rate while satisfying energy-harvesting constraints, using three control modes (Amplitude, Binary amplitude, and Lorentzian-constrained phase) plus scaling to relax analog constraints. An asymptotically optimal fully-digital transmitter is derived, followed by an alternating optimization procedure to approximate it under hardware limits, with convergence and complexity analyzed. Numerical results validate the resolution function and orthogonality, and demonstrate that the proposed schemes achieve near-upper-bound performance with significantly lower complexity than benchmarks. The circular array extends near-field focusing in angular domains and enables multi-point energy/data focusing, offering practical benefits for large-scale IDEM deployments.

Abstract

Thanks to the application of metamaterials, holographic multiple-input multiple-output (H-MIMO) is expected to achieve a higher spatial diversity gain with lower hardware complexity. With the aid of a circular antenna arrangement of H-MIMO, integrated data and energy multicast (IDEM) can fully exploit the near-field channel to realize wider range of energy focusing and higher achievable rate. In this paper, we derive the closed-form near-field resolution function in 3D space and show the asymptotic spatial orthogonality of near-field channel for circular antenna array. We then investigate the beamforming designs for IDEM systems, where the minimum rate of data users (DUs) are maximized while guaranteeing the energy harvesting requirements for energy users (EUs). Specifically, the asymptotically optimal fully-digital beamformer is first obtained based on the spatial orthogonality. Then, the alternating optimization is adopted for the H-MIMO beamforming, where the digital beamformer is obtained in closed form and the analog beamformers of three different control modes are then obtained, respectively. Scaling schemes are also investigated to further improve the IDEM performance. Numerical results verify the correctness of the resolution function and asymptotic orthogonality. Moreover, the proposed beamforming schemes with very low complexity outperform benchmark schemes.

Paper Structure

This paper contains 25 sections, 5 theorems, 35 equations, 11 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Related Works
  4. Motivation and Contributions
  5. Circualr H-MIMO assisted Integrated Data and Energy Multicast System
  6. System Model
  7. Problem Formulation
  8. Near-field Spatial Orthogonality for Circular Antenna Array
  9. Circular Beamforming Design based on Asymptotic Spatial Orthogonality
  10. Asymptotically optimal transmitter design.
  11. Circular H-MIMO beamforming design
  12. Digital beamformer desigen
  13. Analog beamformer desigen
  14. Convergence and Complexity Analysis
  15. Convergence
  16. ...and 10 more sections

Key Result

Lemma 1

(Near-field resolution function for circular antenna array): Considering two coordinates $(r_1,\theta_1,\phi_1)$ and $(r_2,\theta_2,\phi_2)$ in the polar domain, the resolution function between them can be expressed as where $\xi_1:=\sqrt{\eta_1^2+\eta_2^2}$, $\xi_2:= \arctan\frac{\eta_1}{\eta_2}$, $\xi_3:=\sqrt{\eta_3^2+\eta_4^2}$,

Figures (11)

  • Figure 1: System model.
  • Figure 2: The geometric relationship between the circular antenna array and the user in three-dimensional space.
  • Figure 3: Validation of the resolution function in different planes: the Horizontal plane, i.e., $xoy$ (a), Vertical plane, i.e., $xoz$ (b), and angular domain (c).
  • Figure 4: Verification of asymptotic spatial orthogonality.
  • Figure 5: Near-field focusing comparison between circular and linear antenna arrays.
  • ...and 6 more figures

Theorems & Definitions (6)

  • Lemma 1
  • Lemma 2
  • Theorem 1
  • Proposition 1
  • Proposition 2
  • Proof 1