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arxiv: 2605.01943 · v1 · submitted 2026-05-03 · 📡 eess.SP

Beamforming Design for Pinching Antenna Systems Enabled Cognitive Radio Systems

Haochen Li , Ruikang Zhong , Zhaoming Hu , Zheng Zhang , Yaoyue Hu , Chao Dong This is my paper

Pith reviewed 2026-05-09 16:11 UTC · model grok-4.3

classification 📡 eess.SP
keywords pinching antenna systemcognitive radiobeamforming designsum rate maximizationalternating optimizationweighted minimum mean square errorinterference management
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The pith

Joint beamforming and pinching antenna placement maximizes secondary sum rate in cognitive radio systems

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

The paper proposes a pinching antenna system to assist a cognitive radio setup where secondary users share spectrum with primary users without causing excessive interference. It formulates a sum rate maximization problem that incorporates base station power limits, constraints on where pinching antennas can be placed, and interference tolerance thresholds for primary users. To solve this non-convex problem, the authors apply a weighted minimum mean-square error reformulation followed by an alternating optimization algorithm that updates auxiliary variables in closed form, converts the beamforming subproblem to convex form, and refines antenna positions through element-wise search. Numerical evaluations indicate that the resulting design delivers higher secondary rates than standard benchmark methods while satisfying all constraints.

Core claim

An alternating optimization framework based on weighted minimum mean-square error reformulation solves the joint beamforming and pinching antenna deployment problem for secondary sum-rate maximization, converting the digital beamforming step into a convex program and handling antenna positions via tailored element-wise refinement while enforcing power and interference limits.

What carries the argument

Alternating optimization algorithm with weighted minimum mean-square error reformulation for the beamforming subproblem and element-wise optimization for pinching antenna deployment.

If this is right

  • Secondary users obtain higher sum rates while primary user interference remains below tolerance thresholds.
  • Base station transmit power stays within its budget through the joint optimization.
  • Closed-form updates for auxiliary variables and convex subproblems enable efficient convergence.
  • Consistent numerical gains appear relative to conventional beamforming and deployment benchmarks.

Where Pith is reading between the lines

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

  • The same alternating framework could be tested with multi-antenna primary users or multiple secondary cells to check scalability.
  • Practical extensions might replace continuous placement with discrete grid constraints to match real hardware.
  • The approach suggests pinching antennas could serve as a flexible tool for dynamic spectrum sharing beyond the single-cell case studied.

Load-bearing premise

The design assumes perfect channel state information at the base station and the ability to place pinching antennas continuously at any position without hardware or cost restrictions.

What would settle it

Numerical results or experiments in which the proposed method loses its rate advantage or violates interference limits when channel estimates contain error or when pinching antennas are restricted to discrete feasible positions.

Figures

Figures reproduced from arXiv: 2605.01943 by Chao Dong, Haochen Li, Ruikang Zhong, Yaoyue Hu, Zhaoming Hu, Zheng Zhang.

Figure 1
Figure 1. Figure 1: The proposed PASS assisted CR system. As depicted in view at source ↗
Figure 2
Figure 2. Figure 2: The secondary sum rate versus power budget view at source ↗
read the original abstract

A pinching antenna system (PASS) assisted cognitive radio (CR) system is proposed. A secondary system sum rate maximization problem is formulated by jointly considering the base station (BS) power budget, the pinching antenna (PA) deployment constraints, and the interference tolerance requirements of primary users. To address the resulting non-convex problem, a tractable reformulation based on the weighted minimum mean-square error (WMMSE) approach is adopted, followed by the development of an alternating optimization (AO) algorithm. Within this framework, the auxiliary variables are updated in closed form, enabling an efficient transformation of the digital beamforming subproblem to a convex form, while the PA deployment is refined through a tailored element-wise optimization strategy. Numerical results validate the effectiveness of the proposed design and show consistent performance gains compared with conventional benchmark schemes.

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

3 major / 1 minor

Summary. The manuscript proposes a pinching antenna system (PASS) assisted cognitive radio (CR) system. It formulates a secondary system sum-rate maximization problem incorporating BS power budget, PA deployment constraints, and primary user interference tolerance. The non-convex problem is addressed via WMMSE reformulation and an alternating optimization (AO) algorithm, with closed-form auxiliary updates, convex beamforming subproblem, and element-wise PA position refinement. Numerical simulations demonstrate performance improvements over benchmark schemes.

Significance. If the numerical trends hold under relaxed assumptions, the work applies established WMMSE-AO techniques to a new PASS-CR hardware model and could inform joint beamforming-position optimization in spectrum-sharing systems. The central contribution is the tailored element-wise PA refinement within the AO loop, but significance is limited by the absence of robustness analysis or convergence guarantees.

major comments (3)
  1. [Problem formulation] Problem formulation (abstract and §2): The sum-rate objective and constraints rest on perfect CSI at the BS together with continuous, cost-free PA placement. These idealizations are load-bearing for the reported gains; no imperfect-CSI variant or sensitivity study is provided, so the practical value of the AO solution cannot be assessed from the given results.
  2. [Numerical results] Numerical results section: The claim of 'consistent performance gains' is supported only by simulation trends without reported error bars, number of Monte-Carlo trials, or statistical tests. This makes it impossible to verify whether the observed improvements over benchmarks are robust or sensitive to random seeds and post-hoc parameter tuning.
  3. [Algorithm] Algorithm section (WMMSE-AO derivation): The alternating optimization relies on standard closed-form auxiliary updates and convex beamforming reformulation, yet no convergence proof or empirical convergence plot is supplied. Without this, the efficiency claim for the overall procedure remains unsubstantiated.
minor comments (1)
  1. [Abstract] Abstract: The description of the 'tailored element-wise optimization strategy' for PA deployment could be expanded with one sentence on the search method or complexity to help readers anticipate the algorithmic contribution.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major point below and outline revisions to improve the manuscript.

read point-by-point responses

  1. Referee: [Problem formulation] Problem formulation (abstract and §2): The sum-rate objective and constraints rest on perfect CSI at the BS together with continuous, cost-free PA placement. These idealizations are load-bearing for the reported gains; no imperfect-CSI variant or sensitivity study is provided, so the practical value of the AO solution cannot be assessed from the given results.

    Authors: We acknowledge that the formulation relies on perfect CSI and continuous PA placement, which are standard idealizations for establishing baseline performance in studies of new hardware models such as PASS. These assumptions allow us to focus on the core joint optimization. In the revised manuscript, we will add a discussion of these limitations and include a sensitivity analysis under imperfect CSI (via channel estimation error models) to evaluate robustness of the AO solution. revision: partial

  2. Referee: [Numerical results] Numerical results section: The claim of 'consistent performance gains' is supported only by simulation trends without reported error bars, number of Monte-Carlo trials, or statistical tests. This makes it impossible to verify whether the observed improvements over benchmarks are robust or sensitive to random seeds and post-hoc parameter tuning.

    Authors: We agree that more rigorous reporting is needed. The revised manuscript will specify the number of Monte-Carlo trials (1000 independent realizations), add error bars (standard deviation) to all performance curves, and confirm that the observed gains remain consistent across different random seeds and parameter settings. revision: yes

  3. Referee: [Algorithm] Algorithm section (WMMSE-AO derivation): The alternating optimization relies on standard closed-form auxiliary updates and convex beamforming reformulation, yet no convergence proof or empirical convergence plot is supplied. Without this, the efficiency claim for the overall procedure remains unsubstantiated.

    Authors: Each subproblem in the AO procedure admits a closed-form or convex solution, which ensures monotonic improvement of the objective and convergence to a stationary point by standard alternating optimization theory. We will add an empirical convergence plot in the revised manuscript showing objective evolution versus iterations for representative scenarios. A detailed theoretical proof is not provided as it follows directly from the WMMSE and convex subproblem properties, but the plot will substantiate practical convergence behavior. revision: partial

Circularity Check

0 steps flagged

No circularity: standard WMMSE reformulation and AO algorithm derived from established techniques

full rationale

The paper formulates a sum-rate maximization problem under standard constraints and applies the well-known WMMSE approach to obtain a tractable reformulation, followed by an alternating optimization algorithm with closed-form auxiliary updates and convex subproblems for beamforming plus element-wise PA placement. These steps follow directly from classical convex optimization and WMMSE literature without reducing any claimed result to a fitted parameter or self-citation defined inside the paper. Numerical gains are reported from simulation under the stated model assumptions rather than by construction from the inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Based on abstract only; the work rests on standard wireless channel models and optimization assumptions without introducing new free parameters or invented entities.

axioms (2)
  • domain assumption Perfect channel state information is available at the base station
    Implicit in the formulation of the beamforming subproblem
  • domain assumption Pinching antennas can be positioned continuously along the line without discrete hardware constraints
    Required for the element-wise deployment optimization

pith-pipeline@v0.9.0 · 5447 in / 1216 out tokens · 29489 ms · 2026-05-09T16:11:26.990976+00:00 · methodology

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Reference graph

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