arxiv: 2604.14736 · v1 · submitted 2026-04-16 · 📡 eess.SP

Optimization for Pinching Antennas System With Multiple Carriers and Rate Splitting Multiple Access

Peiyu Wang , Hong Wang , Yaru Fu , Rongfang Song This is my paper

Pith reviewed 2026-05-10 10:51 UTC · model grok-4.3

classification 📡 eess.SP

keywords pinching antennasrate splitting multiple accessposition optimizationsum rate maximizationmultiple carriershigh-frequency communicationsbeamforming6G wireless systems

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The pith

A two-stage optimization of pinching antenna positions maximizes sum rate in multi-carrier RSMA systems while adding robustness to inaccuracies.

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

The paper develops an optimization framework for a rate splitting multiple access system assisted by pinching antennas on multiple waveguides and carriers to maximize the overall sum rate in high-frequency scenarios. It introduces a two-stage approach where positions are first coarsely adjusted to minimize path loss and then finely tuned through a one-dimensional search that minimizes composite phase shift errors, drawing on a closed-form derivation for the ideal phase shift in simpler cases. After fixing the positions, beamforming vectors are obtained in closed form via the Lagrange dual method to meet quality of service requirements. Simulations demonstrate higher sum rates and greater tolerance to position inaccuracies than alternative multiple-access techniques.

Core claim

The central claim is that a two-stage PA position optimization method, consisting of coarse large-scale path loss minimization followed by fine-grained adjustment via one-dimensional search to minimize the composite phase shift error across all users and carriers, enables significant sum rate gains in overloaded high-frequency RSMA systems, with RSMA proving more robust to inaccurate PA positions from discrete channel estimation and hardware limitations than other access schemes, and with fine adjustment being especially important at high frequencies.

What carries the argument

The two-stage pinching antenna position optimization method that first minimizes path loss for coarse adjustment and then applies a one-dimensional line search to reduce composite phase shift error, using a closed-form ideal phase shift derived for the single-user single-carrier case.

If this is right

The proposed scheme achieves significant improvement in sum rate.
RSMA exhibits stronger robustness to inaccurate PA positions caused by discrete position channel estimation and physical hardware compared to other multiple-access techniques in PA-assisted systems.
Fine-grained PA position adjustment is particularly crucial in high-frequency bands.
Beamforming vectors admit closed-form solutions via the Lagrange dual method once PA positions are determined.

Where Pith is reading between the lines

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

The two-stage method may extend naturally to other high-frequency antenna systems where phase coherence depends on precise positioning.
Greater robustness to position errors could reduce hardware precision requirements in practical pinching antenna deployments.
Similar staged optimization of positions might improve performance in other overloaded multi-carrier scenarios beyond the RSMA framework studied here.

Load-bearing premise

The assumption that a phase shift error minimization derived from single-user single-carrier closed-form solutions will translate effectively to optimize the full multi-user multi-carrier RSMA system without introducing substantial errors or suboptimal positions.

What would settle it

A simulation or hardware test in which applying the fine-grained one-dimensional phase shift error minimization step produces no measurable increase in sum rate over coarse path loss adjustment alone, especially in high-frequency bands, or where RSMA loses its robustness advantage over other multiple-access techniques when PA positions are inaccurate.

Figures

Figures reproduced from arXiv: 2604.14736 by Hong Wang, Peiyu Wang, Rongfang Song, Yaru Fu.

**Figure 2.** Figure 2: The sum rate versus the number of iterations with [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗

**Figure 3.** Figure 3: The sum rate versus the transmit power budget with [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

**Figure 5.** Figure 5: The sum rate versus the number of PAs on each [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗

**Figure 6.** Figure 6: The sum rate versus the deployment region size with [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗

**Figure 7.** Figure 7: The sum rate versus the length of search step with [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗

read the original abstract

To meet the urgent demands for spectral efficiency and multi-user access in high-frequency application scenario for the sixth-generation wireless communication, this paper investigates a rate splitting multiple access (RSMA) system assisted by pinching antennas (PAs) with multiple waveguides and multiple carriers, aiming to maximize the overall system sum rate. To address the high sensitivity of high-frequency signals to PA movement in the overloaded scenarios, a two-stage PA position optimization method based on both path loss and phase shift error minimization is proposed under RSMA framework. Specifically, the first step is to perform coarse adjustment by minimizing large-scale path loss. Then, based on the derivation of a closed-form solution for the ideal phase shift in a single-user single-carrier case, the fine-grained positions of PAs are optimized via a one-dimensional line search to minimize the composite phase shift error across all users and carriers. In order to meet the quality of service requirements, the Lagrange dual method is employed to obtain the closed form of beamforming vectors after the PA positions are determined. Simulation results demonstrate that the proposed scheme achieves significant improvement in sum rate and confirm that RSMA exhibits stronger robustness to inaccurate PA positions caused by both discrete position channel estimation and physical hardware compared to other multiple-access techniques in PA-assisted systems. Furthermore, the results validate that fine-grained PA position adjustment is particularly crucial in high-frequency bands.

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.

Desk Editor's Note private letter to a colleague

The two-stage PA optimization extends prior work to RSMA and multi-carrier cases but the fine-grained phase-error search is a loose proxy that may not reliably improve the actual sum-rate objective.

read the letter

The main takeaway is that this paper applies a two-stage position adjustment to pinching antennas in a multi-waveguide, multi-carrier RSMA setup and reports sum-rate gains plus better robustness for RSMA. The first stage does coarse placement by minimizing path loss. The second stage takes a closed-form ideal phase shift from the single-user single-carrier case and runs a one-dimensional search to cut a composite phase error across users and carriers. After positions are set, they solve beamforming in closed form with the Lagrange dual method. Simulations then show the scheme beats baselines and that RSMA handles position errors from estimation or hardware better than other multiple-access options, with the fine adjustment mattering more at high frequencies. That robustness result is the part worth noting for high-frequency work. The soft spot is the second stage. Minimizing the aggregated phase error is an engineering shortcut, but the sum rate in the full RSMA system depends on how positions shape the effective channels, the common and private rates, and the subsequent beamforming. Nothing in the construction shows the error metric is equivalent to or even monotonically improves the rate objective, so the claimed high-frequency gains rest on an unverified proxy. The simulations support the overall story but would be more convincing with explicit checks on whether the phase search actually moves the rate in the right direction. This is for researchers working on pinching antennas or RSMA in 6G high-frequency settings. A reader who needs concrete optimization steps and robustness comparisons in that niche would get something usable from it. The paper deserves a serious referee because the method is a legitimate extension with supporting simulations. I would send it to review and ask the authors to tighten or validate the link between the phase minimization and the sum-rate objective.

Referee Report

1 major / 2 minor

Summary. The manuscript proposes a two-stage optimization framework for pinching antenna (PA) positions in a multi-carrier, multi-waveguide RSMA system aimed at maximizing the sum rate. The first stage performs coarse PA positioning by minimizing large-scale path loss. The second stage derives a closed-form ideal phase shift for the single-user single-carrier case and optimizes fine-grained positions through a one-dimensional search minimizing the aggregate phase shift error across all users and carriers. Beamforming is solved via the Lagrange dual method to satisfy QoS constraints. Simulation results are presented to show sum-rate gains and RSMA's superior robustness to PA position errors compared to other MA schemes, emphasizing the importance of fine-grained adjustment in high-frequency bands.

Significance. If the two-stage method is shown to be effective, this work would provide a computationally tractable approach for PA deployment in 6G high-frequency RSMA systems, with closed-form solutions for phase shifts and beamforming offering practical value. The simulation evidence for RSMA robustness could inform multiple-access choices in PA-assisted networks. The paper credits the use of derived closed-forms and search methods as strengths for efficiency.

major comments (1)

[§IV-B] §IV-B (fine-grained PA position optimization): The one-dimensional line search minimizes the composite phase-shift error aggregated from the single-user single-carrier closed-form ideal phase shifts. No analysis or proof is given that this minimization is equivalent to (or monotonically improves) the multi-user multi-carrier sum-rate objective under RSMA, which depends on the joint effect of positions on effective channels for common/private streams and the subsequent Lagrange-dual beamforming solution. This equivalence is load-bearing for the central claims of sum-rate improvement and robustness to inaccurate PA positions.

minor comments (2)

[§V] Simulation section (§V): Include the number of Monte Carlo trials, error bars on sum-rate curves, and explicit parameter values (e.g., carrier frequencies, waveguide counts) in figure captions or tables to support reproducibility and statistical assessment of the reported gains.
[§II] Notation: Ensure consistent definition of phase-shift variables (e.g., ideal vs. actual) upon first appearance in the system model and optimization sections.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed and constructive review of our manuscript. We address the major comment on the fine-grained PA position optimization below.

read point-by-point responses

Referee: [§IV-B] §IV-B (fine-grained PA position optimization): The one-dimensional line search minimizes the composite phase-shift error aggregated from the single-user single-carrier closed-form ideal phase shifts. No analysis or proof is given that this minimization is equivalent to (or monotonically improves) the multi-user multi-carrier sum-rate objective under RSMA, which depends on the joint effect of positions on effective channels for common/private streams and the subsequent Lagrange-dual beamforming solution. This equivalence is load-bearing for the central claims of sum-rate improvement and robustness to inaccurate PA positions.

Authors: We acknowledge that the manuscript does not provide a rigorous proof or analysis establishing equivalence or monotonic improvement between the composite phase-shift error minimization and the multi-user multi-carrier sum-rate objective. The fine-grained stage is a heuristic motivated by the dominant role of phase alignment in high-frequency regimes, where the derived closed-form ideal phase shift for the single-user single-carrier case identifies the phase that maximizes effective channel gain in that setting. Minimizing the aggregated error across users and carriers serves as a tractable proxy intended to enhance the effective channels used by both common and private streams in RSMA. Beamforming is then optimized exactly via the Lagrange dual method for the resulting positions and channels. While this does not guarantee optimality with respect to the joint sum-rate objective, the simulation results in the paper consistently show sum-rate gains and superior robustness to position errors relative to other multiple-access schemes. In the revised manuscript, we will expand §IV-B with additional discussion of the heuristic rationale, its limitations, and further empirical validation to better support the claims. revision: partial

Circularity Check

0 steps flagged

No circularity: two-stage heuristic optimization and standard dual method remain independent of target sum-rate by construction

full rationale

The derivation proceeds by first minimizing large-scale path loss for coarse PA placement, then deriving a single-user single-carrier closed-form ideal phase shift and extending it heuristically via 1D search on a composite phase-error metric across users/carriers; beamforming vectors are obtained afterward via the standard Lagrange dual method. None of these steps defines the final sum-rate objective in terms of itself, renames a fitted quantity as a prediction, or relies on a load-bearing self-citation whose content reduces to the present result. The phase-error surrogate is an explicit approximation whose relation to RSMA sum rate is not claimed to be exact, so the reported simulation gains are not forced by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The approach relies on standard assumptions in wireless channel modeling and optimization techniques common in the field, with the key domain assumption being the applicability of the single-user phase shift solution to the multi-user multi-carrier setting.

axioms (2)

domain assumption Closed-form solution exists for ideal phase shift in single-user single-carrier case.
Invoked to derive the fine-grained optimization step.
standard math Lagrange dual method can obtain closed-form beamforming vectors after positions are fixed.
Used to solve for beamforming under QoS constraints.

pith-pipeline@v0.9.0 · 5547 in / 1527 out tokens · 60528 ms · 2026-05-10T10:51:07.661228+00:00 · methodology

discussion (0)

Reference graph

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