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arxiv: 2510.25192 · v2 · submitted 2025-10-29 · 📡 eess.SP

Spectral and Energy Efficiency Tradeoff for Pinching-Antenna Systems

Zihao Zhou , Zhaolin Wang , Yuanwei Liu This is my paper

Pith reviewed 2026-05-18 03:43 UTC · model grok-4.3

classification 📡 eess.SP
keywords pinching-antenna systemsspectral efficiencyenergy efficiencybeamforming designsingle-user optimizationmulti-user scenarioalternating optimization
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The pith

Optimal pinching antenna positions are independent of transmit beamforming in single-user scenarios.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a joint transmit and pinching beamforming design to balance spectral efficiency and energy efficiency in pinching-antenna systems under practical channel and energy models. It proves that in the single-user case the best pinching antenna positions can be selected without reference to the transmit beamformer. This separation supports a two-stage procedure that first finds a general placement across multiple waveguides and then computes the optimal beamformer in closed form. For multiple users an alternating optimization routine iteratively tunes both elements while respecting quality-of-service constraints and is shown to converge when placement limits are observed. Numerical tests confirm improved SE-EE performance and robustness to shifts in the service area along the waveguide.

Core claim

In pinching-antenna systems the joint transmit and pinching beamforming design is proposed for the spectral-efficiency and energy-efficiency tradeoff. In the single-user scenario it is proved that the optimal pinching antenna positions are independent of the transmit beamforming. This insight yields a two-stage design: a general placement framework for multi-waveguide systems followed by a closed-form beamformer solution. In the multi-user scenario an alternating-optimization algorithm balances the tradeoff subject to quality-of-service requirements and is guaranteed to converge when no pinching-antenna placement constraints are violated.

What carries the argument

The independence of optimal pinching-antenna positions from transmit beamforming, which decouples the single-user optimization into a general placement stage and a closed-form beamformer stage.

If this is right

  • A two-stage procedure suffices for the optimal joint design in single-user cases.
  • The alternating-optimization algorithm converges for multi-user cases when placement constraints remain satisfied.
  • The system exhibits strong robustness to changes in service area along the waveguide direction.
  • Numerical evaluation confirms effective improvement in the joint spectral-energy efficiency performance.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Fixed geometric placement rules derived from the independence result could reduce the need for real-time repositioning hardware.
  • The same separation may simplify control algorithms when pinching antennas are deployed in larger arrays or along curved waveguides.
  • The demonstrated robustness suggests the approach remains useful when user locations vary over time within the service region.

Load-bearing premise

The practical channel and energy consumption models used to formulate the spectral-energy tradeoff objective and constraints accurately describe real pinching-antenna systems.

What would settle it

A single-user simulation or measurement in which the best pinching-antenna positions change when the transmit beamformer is altered would falsify the independence result.

Figures

Figures reproduced from arXiv: 2510.25192 by Yuanwei Liu, Zhaolin Wang, Zihao Zhou.

Figure 1
Figure 1. Figure 1: System model for PASS-enabled single-user communications. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: System model for PASS-enabled multi-user communications. [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: SE and EE performance in single-user case under different [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Convergence of (a) the objective function in ( [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The SE-EE trade-off under different (a) PT , (b) N, and (c) Dx [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: Achieved SE versus PT for various β. it achieves significantly faster convergence speed on (P2-8) compared to the using second-order Taylor expansion, while both approaches converge to the same optimal value [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
read the original abstract

The joint transmit and pinching beamforming design for spectral efficiency (SE) and energy efficiency (EE) tradeoff in pinching-antenna systems (PASS) is proposed, under practical channel and energy consumption models. In the single-user scenario, it is proved that the optimal pinching antenna (PA) positions are independent of the transmit beamforming. Based on this insight, a two-stage joint beamforming design is proposed. Specifically, in the first stage, a general PA placement framework is proposed for multi-waveguide systems. In the second stage, the closed-form solution for the optimal transmit beamformer is derived given the optimized PA positions. In the multi-user scenario, an alternating optimization (AO)-based joint beamforming design is proposed to balance the SE-EE performance while taking the quality-of-service (QoS) requirements into account. It is proved that the proposed AO-based algorithm is guaranteed to converge when no constraints are violated in PA placement subproblem. Numerical results demonstrate that: 1) the proposed algorithms effectively improve joint SE-EE performance; 2) PASS exhibits strong robustness against variations in the service area along the waveguide direction.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript proposes joint transmit and pinching beamforming design to optimize the spectral efficiency (SE) and energy efficiency (EE) tradeoff in pinching-antenna systems (PASS) under practical channel and energy consumption models. In the single-user case, it proves that the optimal pinching antenna (PA) positions are independent of the transmit beamforming vector, enabling a two-stage optimization: a general PA placement framework for multi-waveguide systems followed by a closed-form transmit beamformer solution. For the multi-user case, an alternating optimization (AO) algorithm is developed that incorporates QoS constraints, with a proof of convergence when PA placement subproblem constraints are satisfied. Numerical results show improved joint SE-EE performance and robustness to variations in the service area along the waveguide direction.

Significance. If the independence result holds, the two-stage design substantially reduces computational complexity for PASS systems by decoupling PA placement from beamforming, which is a notable practical advantage. The convergence guarantee for the AO algorithm and the reported numerical gains in SE-EE tradeoff represent clear strengths, particularly the robustness findings. These elements could support more efficient implementations if the underlying channel and power models are validated.

major comments (1)
  1. [Single-user scenario analysis] Single-user scenario: the central claim that optimal PA positions are independent of transmit beamforming (enabling the two-stage design) requires explicit verification that the SE-EE objective separates cleanly. The manuscript should detail in the relevant derivation how the effective gain after waveguide propagation factors from the transmit covariance without position-dependent cross terms, and confirm that the energy consumption model (circuit plus transmit power) introduces no coupling that would invalidate the separation.
minor comments (2)
  1. [Abstract and Section on single-user design] The abstract states proofs of independence and convergence but the main text would benefit from a brief outline of the key steps in the independence proof to improve readability for readers focused on the two-stage approach.
  2. [Numerical results] Numerical results section: clarify the specific parameter values used for the practical channel and energy models to allow reproducibility of the reported SE-EE gains.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the thorough and constructive review of our manuscript on spectral and energy efficiency tradeoff for pinching-antenna systems. The comment on the single-user scenario analysis is appreciated, as it helps strengthen the clarity of our derivations. We address the point in detail below and have revised the manuscript to provide additional explicit verification of the objective separation.

read point-by-point responses

  1. Referee: Single-user scenario: the central claim that optimal PA positions are independent of transmit beamforming (enabling the two-stage design) requires explicit verification that the SE-EE objective separates cleanly. The manuscript should detail in the relevant derivation how the effective gain after waveguide propagation factors from the transmit covariance without position-dependent cross terms, and confirm that the energy consumption model (circuit plus transmit power) introduces no coupling that would invalidate the separation.

    Authors: We thank the referee for this observation. In the single-user formulation, the SE-EE objective is expressed in terms of the effective channel gain after waveguide propagation to the chosen PA positions and the transmit covariance matrix. The waveguide propagation model yields a position-dependent scalar gain factor that multiplies the beamformed transmit signal; this factor appears outside the covariance term in the SNR expression, producing no position-dependent cross terms that couple the PA locations directly to the beamforming vector. Consequently, the optimization separates: the positions are chosen first to maximize the scalar gain (via the general placement framework), after which the optimal transmit beamformer admits a closed-form solution for the given positions. The energy consumption model consists of a constant circuit power term plus a transmit power term that depends only on the beamformer norm; because neither term depends on the PA positions, no additional coupling arises that would invalidate the separation. We have expanded the derivation in the revised Section III-A with intermediate algebraic steps to make this factorization explicit and to confirm the absence of cross terms. revision: yes

Circularity Check

0 steps flagged

No circularity: independence proof and two-stage design follow directly from separability in the stated channel and power models

full rationale

The paper derives the claimed independence of optimal PA positions from transmit beamforming by inspecting the structure of the SE-EE objective under the given practical channel model (waveguide propagation factors) and energy consumption model (circuit plus transmit power). This separability is shown via the paper's own equations rather than by fitting parameters to the target metric or by self-citation chains. The two-stage algorithm and AO convergence proof are likewise constructed from the same model without reducing to tautological inputs. No load-bearing step matches any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work rests on standard wireless channel models and energy consumption expressions for pinching antennas; no new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Practical channel and energy consumption models for pinching-antenna systems
    Invoked to define the SE-EE objective and constraints in both single-user and multi-user formulations.

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Energy Efficiency Maximization for Discrete Activation based NOMA-assisted Pinching-Antenna Systems

    eess.SP 2026-04 unverdicted novelty 4.0

    A matching-based outer layer and closed-form inner power allocation solve the mixed-integer EE maximization problem for NOMA-assisted pinching-antenna systems, yielding gains over fixed-antenna baselines while approac...

  2. Pinching Antenna Systems (PASS): Enabling Reconfigurable and Controllable Wireless Channels -- A Comprehensive Survey

    cs.IT 2026-04 unverdicted novelty 2.0

    The paper provides a comprehensive review and categorization of pinching antenna systems (PASS) for objectives including network coverage, data rate, secure transmission, sensing, integrated sensing and communication,...

Reference graph

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