On the Performance of Tri-Hybrid Beamforming Using Pinching Antennas

Technical Summary: On the Performance of Tri-Hybrid Beamforming Using Pinching Antennas

Problem Statement
While Multiple-Input Multiple-Output (MIMO) technology has transformed wireless communications, conventional hybrid digital-analog beamforming faces fundamental limitations in high-frequency 6G bands (e.g., 7–24 GHz). These limitations include severe large-scale free-space path loss and high susceptibility to blockages. Existing reconfigurable antenna solutions, such as dynamic metasurfaces and fluid antennas, are typically constrained to apertures spanning only a few to tens of wavelengths, which is insufficient to overcome these propagation challenges. Although the Pinching-Antenna System (PASS), which utilizes dielectric waveguides and movable pinching antennas (PAs), offers a solution by enabling signal radiation close to users, its integration into a tri-hybrid beamforming architecture—combining digital, analog, and pinching beamforming layers—remains unexplored. This paper addresses the gap in characterizing the performance and channel capacity of such a tri-hybrid system.

Methodology
The authors propose a novel tri-hybrid beamforming architecture where a base station (BS) equipped with $N_{rf}$ radio-frequency (RF) chains serves single-antenna users. The signal processing occurs in three stages:

1. Digital Precoding: Baseband processing using a digital precoder.
2. Analog Beamforming: Up-conversion and phase shifting via an analog precoder implemented with phase shifters.
3. Pinching Beamforming: The signal propagates through $M$ dielectric waveguides, where $N$ active PAs per waveguide radiate signals into free space. The positions of these PAs are optimized to shape the radiation pattern.

The study formulates an optimization problem to maximize channel capacity by jointly optimizing the digital precoder, analog precoder, and PA positions ($W_{pin}$). To ensure analytical tractability, the authors initially neglect in-waveguide propagation loss ($\kappa = 0$), treating this as a theoretical upper bound, before incorporating loss in numerical simulations.

The analysis proceeds in two scenarios:

• Single-RF Case ($N_{rf}=1$): The problem reduces to optimizing PA positions to maximize array gain. The authors propose an "Antenna Position Refinement" algorithm to align the phases of signals from all PAs constructively at the user.
• Multiple-RF Case ($N_{rf}>1$): The digital and analog precoders are designed to align with the effective channel vector, reducing the problem to maximizing the squared norm of the effective channel.

The authors derive closed-form upper and lower bounds for the channel capacity and analyze the power scaling laws with respect to the number of PAs ($N$). They also extend the analysis to multiuser Time-Division Multiple Access (TDMA) systems, comparing two operational modes: Pinching Switching (PS), where PA positions are reconfigured per user, and Pinching Multiplexing (PM), where PA positions remain fixed across users.

Key Contributions

1. Architectural Proposal: The paper introduces a tri-hybrid beamforming framework that integrates PASS as an outer layer to complement conventional hybrid beamforming, aiming to mitigate path loss through spatial reconfiguration.
2. Analytical Characterization: The authors derive the optimal tri-hybrid beamformer and establish tight closed-form upper and lower bounds for the channel capacity.
3. Scaling Laws: A significant contribution is the derivation of capacity scaling laws. The analysis reveals that while increasing the number of PAs initially improves performance, the Signal-to-Noise Ratio (SNR) and capacity eventually scale as $O((\ln N)^2/N)$ as $N \to \infty$. This indicates the existence of an optimal number of PAs beyond which performance degrades due to reduced power per antenna and increased path loss from distant antennas.
4. Operational Modes: The paper analyzes the trade-offs between Pinching Switching (PS) and Pinching Multiplexing (PM) in multiuser scenarios, providing an element-wise alternating optimization algorithm for the suboptimal PM case.

Results
Numerical simulations validate the analytical bounds and scaling laws:

• Bounds Tightness: The derived upper and lower bounds are shown to be tight, accurately predicting system behavior.
• Optimal PA Count: Results confirm that there is an optimal number of PAs that maximizes SNR and capacity. Increasing $N$ indefinitely leads to diminishing returns and eventual performance degradation.
• Performance Gain: Under the same number of RF chains, the proposed tri-hybrid architecture achieves significantly higher channel capacity compared to conventional hybrid beamforming. This gain is attributed to the ability of PAs to establish strong Line-of-Sight (LoS) links by positioning antennas closer to users, thereby mitigating large-scale path loss.
• Robustness to Distance: Unlike conventional hybrid systems, where capacity drops significantly as the service area expands (increasing user-to-array distance), the tri-hybrid system maintains relatively constant capacity by adaptively positioning PAs.
• PS vs. PM: In multiuser settings, PS maintains a constant sum-rate as the number of users increases because the beamformer is optimized for each specific user. In contrast, PM shows a decrease in sum-rate as the number of users grows, as a single fixed beamformer becomes suboptimal for diverse user locations.

Significance and Claims
The paper claims that integrating PASS into tri-hybrid beamforming offers a promising architecture for future 6G networks. The primary significance lies in demonstrating that reconfigurable antenna placement (pinching beamforming) can effectively address the fundamental constraints of wave propagation in high-frequency bands, specifically severe path loss and blockage. The work establishes that while adding more antennas is beneficial up to a point, system design must account for the non-linear scaling of capacity to avoid inefficiencies. The authors position this work as the first step in analyzing the performance of such systems, suggesting that future work will extend these frameworks to more complex multiuser settings. The results suggest that this architecture can yield substantial performance gains over conventional methods while maintaining low cost and energy consumption by leveraging the flexibility of dielectric waveguides.