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TTD Configurations for Near-Field Beamforming: Parallel, Serial, or Hybrid?

Zhaolin Wang, Xidong Mu, Yuanwei Liu, Robert Schober

TL;DR

This work tackles near-field wideband hybrid beamforming with true-time delayers (TTDs) by comparing parallel, serial, and hybrid configurations in XL-MIMO. It develops an insertion-loss equalization approach and derives beamforming solutions that enable reduced per-TTD delays, delivering a closed-form solution for single-user cases and a penalty-based, multi-user optimization framework with a hybrid-forward-and-backward (HFB) variant. The proposed methods demonstrate that serial and hybrid configurations can significantly lower the required delay per TTD, while the hybrid configuration excels in single-user scenarios and HFB boosts multi-user performance. These results provide practical guidelines for hardware-constrained near-field systems and highlight the trade-offs between hardware complexity, insertion losses, and spectral efficiency in wideband XL-MIMO networks.

Abstract

True-time delayers (TTDs) are popular components for hybrid beamforming architectures to combat the spatial-wideband effect in wideband near-field communications. In this paper, a serial and a hybrid serial-parallel TTD configuration are investigated for hybrid beamforming architectures. Compared to the conventional parallel configuration, the serial configuration exhibits a cumulative time delay caused by multiple TTDs, which potentially alleviates the maximum delay requirements on the individual TTDs. However, independent control of individual TTDs becomes impossible in the serial configuration. Therefore, a hybrid TTD configuration is proposed as a compromise solution. Furthermore, a power equalization approach is proposed to address the cumulative insertion loss of the serial and hybrid TTD configurations. The wideband near-field beamforming design for different configurations is studied to maximize the spectral efficiency in both single-user and multiple-user systems. 1) For single-user systems, a closed-form solution for the beamforming design is derived. The preferred user locations and the required maximum time delay of each TTD configuration are characterized. 2) For multi-user systems, a penalty-based iterative algorithm is developed to obtain a stationary point of the spectral efficiency maximization problem for the considered TTD configurations. In addition, a hybrid-forward-and-backward (HFB) implementation is proposed to enhance the performance of the serial configuration. Our numerical results confirm the effectiveness of the proposed designs and unveil that i) compared to the conventional parallel configuration, both the serial and hybrid configurations can significantly reduce the maximum time delays required for the individual TTDs and ii) the hybrid configuration excels in single-user systems, while the HFB serial configuration is preferred in multi-user systems.

TTD Configurations for Near-Field Beamforming: Parallel, Serial, or Hybrid?

TL;DR

This work tackles near-field wideband hybrid beamforming with true-time delayers (TTDs) by comparing parallel, serial, and hybrid configurations in XL-MIMO. It develops an insertion-loss equalization approach and derives beamforming solutions that enable reduced per-TTD delays, delivering a closed-form solution for single-user cases and a penalty-based, multi-user optimization framework with a hybrid-forward-and-backward (HFB) variant. The proposed methods demonstrate that serial and hybrid configurations can significantly lower the required delay per TTD, while the hybrid configuration excels in single-user scenarios and HFB boosts multi-user performance. These results provide practical guidelines for hardware-constrained near-field systems and highlight the trade-offs between hardware complexity, insertion losses, and spectral efficiency in wideband XL-MIMO networks.

Abstract

True-time delayers (TTDs) are popular components for hybrid beamforming architectures to combat the spatial-wideband effect in wideband near-field communications. In this paper, a serial and a hybrid serial-parallel TTD configuration are investigated for hybrid beamforming architectures. Compared to the conventional parallel configuration, the serial configuration exhibits a cumulative time delay caused by multiple TTDs, which potentially alleviates the maximum delay requirements on the individual TTDs. However, independent control of individual TTDs becomes impossible in the serial configuration. Therefore, a hybrid TTD configuration is proposed as a compromise solution. Furthermore, a power equalization approach is proposed to address the cumulative insertion loss of the serial and hybrid TTD configurations. The wideband near-field beamforming design for different configurations is studied to maximize the spectral efficiency in both single-user and multiple-user systems. 1) For single-user systems, a closed-form solution for the beamforming design is derived. The preferred user locations and the required maximum time delay of each TTD configuration are characterized. 2) For multi-user systems, a penalty-based iterative algorithm is developed to obtain a stationary point of the spectral efficiency maximization problem for the considered TTD configurations. In addition, a hybrid-forward-and-backward (HFB) implementation is proposed to enhance the performance of the serial configuration. Our numerical results confirm the effectiveness of the proposed designs and unveil that i) compared to the conventional parallel configuration, both the serial and hybrid configurations can significantly reduce the maximum time delays required for the individual TTDs and ii) the hybrid configuration excels in single-user systems, while the HFB serial configuration is preferred in multi-user systems.
Paper Structure (34 sections, 1 theorem, 82 equations, 10 figures, 2 tables, 1 algorithm)

This paper contains 34 sections, 1 theorem, 82 equations, 10 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Prior Works
  3. Motivation and Contributions
  4. Organization and Notations
  5. System Model and Problem Formulation
  6. Signal Model
  7. TTD Configurations
  8. Parallel Configuration
  9. Serial Configuration
  10. Hybrid Configuration
  11. Insertion Loss and Power Equalization
  12. Problem Formulation
  13. Single-User System
  14. Infinite-Range TTDs
  15. Finite-Range TTDs
  16. ...and 19 more sections

Key Result

Lemma 1

Define $J(r, \theta) \triangleq 2 r \cos \theta / \sin^2 \theta$. Time delay $t^{\infty}_q$ monotonically increases with respect to $q$ if and it monotonically decreases with respect to $q$ if $t_q^\infty$ first increases and then decreases with respect to $q$ if where the monotonicity changes at the point $q = q_c \triangleq Q/2 + 1 + \lfloor J(r, \theta)/(2N_{\mathrm{\text{sub}}} d)\rfloor$.

Figures (10)

  • Figure 1: Illustration of the considered parallel, serial, and hybrid configurations of TTD-based hybrid beamforming architectures. In the depicted example, each RF chain is connected to $Q = 4$ TTDs.
  • Figure 2: Illustration of the power splitter coefficients for the serial configuration.
  • Figure 3: Illustration of the time delay introduced by infinite-range TTDs for mitigating the beam split effect.
  • Figure 4: Illustration of the monotonicity regions given in Lemma \ref{['lemma_1']}. Here, the BS is positioned at $(0,0)$, equipped with $N = 512$ antennas with half-wavelength spacing and operating at $0.1$ THz.
  • Figure 5: Spectral efficiency versus the direction of a user located at a distance of $10$ m from the BS.
  • ...and 5 more figures

Theorems & Definitions (4)

  • Remark 1
  • Remark 2
  • Lemma 1
  • Remark 3