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On the Performance of Tri-Hybrid Beamforming Using Pinching Antennas

Zhenqiao Cheng, Chongjun Ouyang, Nicola Marchetti

TL;DR

This work addresses the challenge of high-frequency path loss and blockage by integrating a Pinching-Antenna System (PASS) as an outer-layer beamformer into tri-hybrid digital-analog beamforming. It derives the optimal tri-hybrid precoders and PA placements, and establishes tight upper/lower bounds on channel capacity, along with a power-scaling law that characterizes how capacity grows with the number of pinching antennas. The analysis covers both single- and multi-RF scenarios, supported by numerical results showing substantial gains over conventional hybrid beamforming and identifying the existence of an optimal number of PAs. The findings suggest PASS-enabled tri-hybrid beamforming as a promising, scalable architecture for 6G-like systems, particularly in LoS-dominated regimes, with practical PM/PS operating modes for multiuser deployments.

Abstract

The Pinching-Antenna System (PASS) reconfigures wireless channels through \emph{pinching beamforming}, in which the active positions of pinching antennas (PAs) along dielectric waveguides are optimized to shape the radiation pattern. This article investigates the performance of PASS-enabled tri-hybrid beamforming, where pinched waveguides are integrated with a hybrid digital-analog beamformer to mitigate path loss and enhance spectral efficiency. The channel capacity of the proposed system is characterized by deriving the optimal tri-hybrid beamformer at both the digital and analog domains, as well as the optimal placement of PAs. Closed-form upper and lower bounds of the channel capacity are obtained, leading to a capacity scaling law with respect to the number of PAs. Numerical results verify the tightness of the derived bounds and demonstrate that applying PASS to tri-hybrid beamforming yields a significant performance gain over conventional hybrid beamforming under the same number of radio-frequency chains.

On the Performance of Tri-Hybrid Beamforming Using Pinching Antennas

TL;DR

This work addresses the challenge of high-frequency path loss and blockage by integrating a Pinching-Antenna System (PASS) as an outer-layer beamformer into tri-hybrid digital-analog beamforming. It derives the optimal tri-hybrid precoders and PA placements, and establishes tight upper/lower bounds on channel capacity, along with a power-scaling law that characterizes how capacity grows with the number of pinching antennas. The analysis covers both single- and multi-RF scenarios, supported by numerical results showing substantial gains over conventional hybrid beamforming and identifying the existence of an optimal number of PAs. The findings suggest PASS-enabled tri-hybrid beamforming as a promising, scalable architecture for 6G-like systems, particularly in LoS-dominated regimes, with practical PM/PS operating modes for multiuser deployments.

Abstract

The Pinching-Antenna System (PASS) reconfigures wireless channels through \emph{pinching beamforming}, in which the active positions of pinching antennas (PAs) along dielectric waveguides are optimized to shape the radiation pattern. This article investigates the performance of PASS-enabled tri-hybrid beamforming, where pinched waveguides are integrated with a hybrid digital-analog beamformer to mitigate path loss and enhance spectral efficiency. The channel capacity of the proposed system is characterized by deriving the optimal tri-hybrid beamformer at both the digital and analog domains, as well as the optimal placement of PAs. Closed-form upper and lower bounds of the channel capacity are obtained, leading to a capacity scaling law with respect to the number of PAs. Numerical results verify the tightness of the derived bounds and demonstrate that applying PASS to tri-hybrid beamforming yields a significant performance gain over conventional hybrid beamforming under the same number of radio-frequency chains.

Paper Structure

This paper contains 14 sections, 2 theorems, 39 equations, 6 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. Signal Model
  4. Channel Model
  5. Problem Formulation
  6. Tri-Hybrid Beamforming Design
  7. Single-RF Scenario
  8. Antenna Position Refinement
  9. Performance Upper and Lower Bounds
  10. Power Scaling Law
  11. Multiple-RF Scenario
  12. Extension
  13. Numerical Results
  14. Conclusion

Key Result

Lemma 1

Given that $\Delta_{\min}\ll H_m$, the maximum array gain for the $m$th waveguide can be approximated as follows: where $f_{\rm{ub}}(x)\triangleq\ln(\sqrt{1+x^2}+x)$.

Figures (6)

  • Figure 1: Illustration of the tri-hybrid beamforming architecture.
  • Figure 2: Illustration of the system model.
  • Figure 3: Single-RF received SNR vs the number of PAs $N$. $x_{\rm{u}}=y_{\rm{u}}=0$ m.
  • Figure 4: Multiple-RF capacity vs the number of PAs $N$. $x_{\rm{u}}=y_{\rm{u}}=0$ m.
  • Figure 5: Average channel capacity.
  • ...and 1 more figures

Theorems & Definitions (5)

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