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Performance Analysis of Pinching-Antenna Systems

T0 review · 2 major / 6 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read This paper derives exact closed-form formulas for the outage probability and average rate of pinching-antenna systems, waveguide losses included, and shows they beat conventional antennas.

desk verdict Solid closed-form analysis for lossy pinching-antenna systems, but the optimal-placement proposition has a wrong branch and the benchmark is generous to the PAS. read the letter →

arxiv 2502.06701 v2 pith:QBXF37MY submitted 2025-02-10 cs.NI

Dimitrios Tyrovolas , Sotiris A. Tegos , Panagiotis D. Diamantoulakis , Sotiris Ioannidis , Christos K. Liaskos , George K. Karagiannidis This is my paper · ORCID
classification cs.NI
keywords pinchingantennasdielectricwaveguidesoutageprobabilityaveragerateclosed-formexpressionswaveguideattenuationflexible-antennasystems
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper aims to give pinching-antenna systems a quantitative performance theory. A pinching antenna radiates from a movable point along a dielectric waveguide, so the system can cut path loss by placing the antenna near the user. The paper models a single user at a random location in a rectangle, with the channel described only by free-space path loss and exponential attenuation along the waveguide, and derives closed-form expressions for outage probability and average rate. It also solves where on the waveguide to put the pinching antenna to maximize the received signal-to-noise ratio. The practical payoff is that an engineer can compare a pinching-antenna system with a fixed antenna and see how waveguide length and loss change reliability and rate, without running simulations.

What carries the argument

The load-bearing mechanism is the received SNR formula $\gamma_r = \eta P_t e^{-\alpha x_p}/(\sigma^2((x_m-x_p)^2+y_m^2+h^2))$, where $\eta = \lambda^2/(16\pi^2)$ is the reference path loss at 1 m, $\alpha$ is the waveguide absorption coefficient, $(x_p,0,h)$ is the pinching-antenna position, and $(x_m,y_m,0)$ is the user position. The exponential factor is the waveguide attenuation and the denominator is the squared Euclidean distance from antenna to user; every performance metric is an expectation of a function of this ratio over the uniform user rectangle. The optimal-placement result comes from maximizing $f(x_p)=e^{-\alpha x_p}/((x_m-x_p)^2+y_m^2+h^2)$, whose derivative roots form a quadratic whose discriminant selects the maximizer in Eq. (25).

What would settle it

In a nearly anechoic room at 28 GHz with a dielectric waveguide of known absorption coefficient, place the pinching antenna at the user's $x$-coordinate and record the SNR for a large uniform sample of user positions; the measured fraction of SNR values below threshold should match Table I within Monte Carlo noise. A systematic mismatch would show the closed forms depend on the no-fading assumption in a way that fails in practice.

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Extended reading notes

Core claim

On its own terms, the central discovery is that a single-user downlink pinching-antenna system (PAS) with a uniformly random user position has exact closed-form performance metrics. The outage probability is the piecewise expression in Table I, built from $C = \eta P_t/(\gamma_{\mathrm{thr}}\sigma^2)$; the average rate is Eq. (16), expressed through the dilogarithm; and in the lossless-waveguide limit the outage probability reduces to Eq. (13), a simple square-root piecewise form. The paper also shows that the received SNR as a function of antenna position has at most one interior local maximum, giving the explicit optimal $x$-coordinate in Eq. (25). For multiple pinching antennas used for beamforming, the single-antenna closed forms remain a tight approximation with $C$ or $A$ multiplied by the number of antennas $N$. The paper validates all closed forms against Monte Carlo simulation.

Load-bearing premise

The derivations assume the channel has no small-scale fading or shadowing, only deterministic line-of-sight path loss plus waveguide attenuation, so the only randomness is the uniform user location.

Editorial extensions

If this is right

  • If the closed forms are correct, outage probability and average rate for a PAS can be evaluated instantly for any rectangle size, waveguide height, length, and absorption coefficient, without Monte Carlo simulation.
  • The formulas imply that a PAS with one pinching antenna outperforms a fixed antenna at the waveguide feedpoint, and the advantage grows as the deployment area grows.
  • For multiple pinching antennas used for beamforming, the single-antenna expressions remain a tight approximation with $C$ or $A$ scaled by the number of antennas, so array gain needs no new distributional analysis.
  • Placing the antenna at the user's $x$-coordinate is nearly optimal for typical small $\alpha$, while Eq. (25) gives the exact correction when waveguide loss is large.
  • The average rate of the PAS stays nearly flat as the deployment length $D_x$ grows, whereas a conventional fixed antenna degrades sharply, so PASs decouple data rate from coverage-area size.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • One extension the paper leaves open is to use the closed forms as fast objective functions for transmit-power control or user scheduling in multi-user PAS deployments, replacing expensive Monte Carlo evaluation in system optimization.
  • The same exponential-loss over distance-squared ratio appears in any flexible antenna fed by a lossy transmission line, so the quadratic maximization in Eq. (25) would carry over with $\alpha$ reinterpreted as the per-meter feed loss.
  • Because the model has no small-scale fading, the reported outage and rate values are optimistic in rich-scattering environments; at 28 GHz with a strong line-of-sight component the gap should be small, but a fading-aware extension would require distributional averaging beyond these closed forms.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 6 minor

Summary. The paper considers a downlink pinching-antenna system (PAS) in which a dielectric waveguide of length Dx at height h carries a signal from a feed point to a user randomly and uniformly located in a Dx × Dy rectangle. The channel model combines free-space path loss, a phase term from the guided wavelength, and exponential attenuation e^{−αx} along the waveguide. The authors derive closed-form outage probability (Table I and Proposition 1), a lossless-waveguide special case (Proposition 2), average rate (Proposition 3, Eq. (16)), and an optimal antenna placement rule (Proposition 4, Eq. (25)) that maximizes received SNR. Numerical results validate the expressions via Monte Carlo simulation and compare the PAS against a conventional antenna fixed at (0,0,0), as well as against colocated multi-antenna baselines.

Significance. If the results hold, the paper provides a useful analytical framework for PAS performance evaluation that explicitly accounts for waveguide attenuation, a topic of current interest given the rapid growth of the PAS literature. Propositions 1 and 3 are nontrivial closed forms and are validated by independent Monte Carlo simulation, which gives confidence in the algebra; the derivations are self-contained and use no fitted parameters. The optimal-placement characterization in Proposition 4, once corrected, would provide practical design insight. The paper is also honest in presenting the lossless-waveguide special case as a sanity check. These strengths make the manuscript a potentially valuable contribution to the analysis of pinching-antenna systems.

major comments (2)
  1. [Section III-C, Proposition 4, Eq. (25)] The Δ=0 branch of Eq. (25) is incorrect. When Δ=0, we have α^2(y_m^2+h^2)=1, and the numerator of f'(x_p) in Eq. (27) becomes −α e^{−α x_p} (x_m − x_p − 1/α)^2 divided by a positive denominator. Hence f'(x_p) ≤ 0 for every x_p in [0, D_x], with a single zero at x_p = x_m − 1/α = x_{o2}; there is no sign change from positive to negative. The function f(x_p) is therefore nonincreasing on the feasible interval, and the global maximizer is the left endpoint x_p = 0, not x_{o2}. For a concrete instance, take α = 0.1, y_m^2+h^2 = 100, and x_m = 50 (so Δ=0): f(0) = 1/2600 ≈ 3.85×10^{−4}, while f(x_{o2}) = f(40) = e^{−4}/200 ≈ 9.16×10^{−5}, so x_{o2} is strictly worse than 0. This error is load-bearing because Proposition 4 is explicitly advertised as characterizing the optimal placement under waveguide losses. The Δ>0 branch and the closed-form outage and rate expressions are unaffected, but the stated Δ=0 branch must be corrected or replaced by an explicit discussion of the boundary case.
  2. [Abstract and Section V] The abstract and conclusion state without qualification that PASs 'consistently outperform conventional systems' in reliability and data rate. The numerical support (Figs. 2, 4, 5, 6) is obtained only for a conventional antenna fixed at (0,0,0) or at the waveguide feedpoint; a conventional system with a more favorable fixed placement, such as at the center of the served area, is not considered. The claim is therefore too broad. Please qualify the statement as being relative to the specific fixed baseline used in the figures, or extend the comparison to a more favorably placed conventional antenna.
minor comments (6)
  1. [Section IV, Fig. 3] The legend entry 'Simulation Results (25)' is ambiguous because Eq. (25) gives the optimal antenna position, not the outage probability. Please rephrase, for example, 'Simulation with optimal placement from (25)'.
  2. [Section II, channel model] The analysis assumes a deterministic line-of-sight channel with no small-scale fading or shadowing, so the phrase 'under realistic conditions' in the abstract overstates the scope. Please add an explicit statement that fading and shadowing are left for future work.
  3. [Remark 1 and Section IV, Fig. 4] For N pinching antennas, the substitution C = η N P_t / (γ_thr σ^2) assumes a coherent-combining SNR gain of N. If the total transmit power is split among the N antennas rather than scaled with N, the scaling would be different. Please clarify the power normalization used.
  4. [Appendix B and Eq. (17)] The dilogarithm is denoted inconsistently as 'Li,2' in the appendix and 'Li2' in Eq. (17); please unify the notation throughout.
  5. [Section IV, parameters] The absorption coefficient α is given values 0.01, 0.05, and 0.1 with reference [19], but its units (per meter) are never stated explicitly. Please specify the units and justify the chosen range in the context of dielectric waveguides at 28 GHz.
  6. [Table I] There are minor typographical issues in Table I, including a missing closing parenthesis in the third-row expression involving h tan^{−1}(·). Please proofread the table for consistent notation.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: outage, rate, and optimal-placement results are derived from the stated SNR model and validated by independent Monte Carlo simulation.

full rationale

The derivation chain is self-contained. The SNR model in Eq. (5) follows from the stated physical assumptions in Eqs. (1)-(3) (free-space path loss, waveguide phase shift, and exponential attenuation), with no fitted parameters. Proposition 1 computes the outage probability by integrating the stated uniform user-location density over the event y_m^2 >= C e^{-alpha x_m} - h^2; Proposition 2 is the alpha=0 limit of that same derivation; Proposition 3 evaluates E[log2(1+SNR)] via substitutions and dilogarithm identities; Proposition 4 maximizes f(x_p) by solving f'(x_p)=0 and checking domain constraints. Each step is derived from the model rather than assumed from a target result. Numerical validation uses independent Monte Carlo simulation with 10^6 realizations, and the analytical curves in the figures are not fitted to the simulations. Citations to prior work are contextual or reuse the known lossless rate expression [22, (6)]; they are not load-bearing for the new closed forms. The reader's noted defect in the Delta=0 branch of Proposition 4 is a mathematical correctness issue (the derivative does not change sign at x_o2), not a circularity: the claimed optimum is still derived from the model rather than being equivalent to an input. No fitted-input-as-prediction, self-definitional, or self-citation-forcing pattern is present.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The central claim rests on a simplified LoS channel model, a uniform user location model, and a set of standard mathematical identities. No free parameters are fitted to data; the absorption coefficient alpha and other system constants are taken from prior literature. No new physical entities are introduced.

assumptions (5)
  • domain assumption The user position xm is uniformly distributed over [0,Dx] and ym uniformly over [-Dy/2,Dy/2], independent of xm.
    Used in Propositions 1-3 to average over user locations; the closed forms depend on this rectangular-uniform model.
  • domain assumption The channel is deterministic LoS path loss with no small-scale fading or shadowing; received SNR is given by Eq. (5) as eta Pt exp(-alpha xp)/(sigma^2 ||psi_m - psi_p||^2).
    This is the core channel model. It excludes multipath fading, which would change the outage probability. Stated in Section II, Eq. (1)-(5).
  • domain assumption Waveguide attenuation is exponential with absorption coefficient alpha, and the guided phase shift uses effective refractive index neff; these are taken from prior literature [19], [20].
    The exponential decay exp(-alpha xp) and phase exp(-j 2*pi/lambda_g xp) are assumed in Eq. (2)-(3).
  • domain assumption For the outage/rate analysis, the pinching antenna is placed at xp=xm (the user's x-coordinate), which assumes perfect knowledge of user position and instantaneous reconfiguration.
    Set at the start of Section III; this is the 'minimal distance' placement strategy.
  • standard math Standard integral identities including dilogarithm relations from Gradshteyn and Ryzhik [26] are used in Appendices A and B.
    Used to evaluate IA, IB, Ii, Ij integrals.

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Pith. "Pith review of Performance Analysis of Pinching-Antenna Systems." pith.science (2026). https://pith.science/paper/QBXF37MY

@misc{pith2026250206701,
  author       = {Pith},
  title        = {Pith review of: Performance Analysis of Pinching-Antenna Systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QBXF37MY}},
  note         = {Machine review of arXiv:2502.06701}
}
read the original abstract

The sixth generation of wireless networks envisions intelligent and adaptive environments capable of meeting the demands of emerging applications such as immersive extended reality, advanced healthcare, and the metaverse. However, this vision requires overcoming critical challenges, including the limitations of conventional wireless technologies in mitigating path loss and dynamically adapting to diverse user needs. Among the proposed reconfigurable technologies, pinching antenna systems (PASs) offer a novel way to turn path loss into a programmable parameter by using dielectric waveguides to minimize propagation losses at high frequencies. In this paper, we develop a comprehensive analytical framework that derives closed-form expressions for the outage probability and average rate of PASs while incorporating both free-space path loss and waveguide attenuation under realistic conditions. In addition, we characterize the optimal placement of pinching antennas to maximize performance under waveguide losses. Numerical results show the significant impact of waveguide losses on system performance, especially for longer waveguides, emphasizing the importance of accurate loss modeling. Despite these challenges, PASs consistently outperform conventional systems in terms of reliability and data rate, underscoring their potential to enable high-performance programmable wireless environments.

Figures

Figures reproduced from arXiv: 2502.06701 by the authors.

Figure 1
Figure 1. Overview of pinching antenna system. allows the position of the antenna to be dynamically adjusted along the waveguide to optimize link quality. Specifically, unlike traditional wireless systems, a PAS enables efficient transmission of high-frequency signals within the waveguide with minimal loss, while allowing the signal to radiate from any point along the waveguide using a controlled ”pinching” mechanism. In addi… view at source ↗
Figure 2
Figure 2. Outage probability versus γt for a PAS with one pinching antenna. antennas to adjust their position along the dielectric waveguide to be closer to the user, effectively mitigating path loss and maintaining strong LoS communication links. In contrast, the fixed placement of the conventional antenna introduces significant large-scale path loss, particularly in larger areas, where the outage probability deteriorates si… view at source ↗
Figure 3
Figure 3. a and Fig. 3b show the outage probability of a PAS with a single pinching antenna for various absorption coefficients α, including the ideal case of a lossless waveguide. Fig. 3a corresponds to the range of Dx = 10 m, while Fig. 3b represents the case of Dx = 30 m. The α values studied range from α = 0.01, representing low-loss materials, to 90 95 100 105 110 10−5 10−4 10−3 10−2 10−1 100 γt (dB) Pout Lossless Wavegu… view at source ↗
Figures from the paper (2 more)
Figure 5
Figure 5. Figure 5: Average rate versus γt for a PAS with one pinching antenna. cation with fewer antennas compared to conventional systems [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: Average rate versus γt for a PAS with N pinching antennas. V. CONCLUSION In this work, we provided a comprehensive analytical frame￾work for evaluating the performance of PASs by deriving closed-form expressions for critical metrics, including outage probability and av…

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Forward citations

Cited by 3 Pith papers

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    A theoretical formula for successful transmission probability in multi-waveguide pinching-antenna indoor systems is derived and supported by Monte Carlo simulation.

  2. Analytical Optimization for Antenna Placement in Pinching-Antenna Systems

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    For fairness-based OMA, the optimal pinching-antenna location is the mean of users' x-coordinates and does not depend on their distance from the waveguide; for NOMA it moves exponentially toward the user nearest the w...

  3. On the Performance of Pinching-Antenna Systems (PASS) with Orthogonal and Non-Orthogonal Multiple Access

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    For a two-room pinching-antenna setup, the line-of-sight user's outage probability drops sharply compared to a fixed antenna, while the non-line-of-sight user keeps diversity order one and changes little.

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