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Analysis and Antenna Position Selection for Pinching-Antenna Systems in Fading Channels

Amy S. Inwood, Peter J. Smith, Hyundong Shin, Michail Matthaiou

arXiv:2610.35140v1eess.SP

TL;DR

Most PASS studies assume pure LoS, although practical channels can include scattering and spatially correlated shadowing. This paper analyzes a single-user uplink PASS under Ricean fading, deriving SNR statistics and REM-based positioning methods. Its analysis is supported by simulation, and the positioning methods achieve near-optimal performance with robustness to localization errors.

  • Problem

    Most prior PASS studies focus on pure LoS channels, while the effects of scattered components and spatially correlated fading have limited analysis.

    Source: A. Review of Related Literature · p. 2, B. Contributions · p. 2

  • Method

    The paper analyzes maximum-SNR statistics for exponential and smoothly correlated shadow fading and proposes REM-based PA positioning methods.

    Source: A. Conclusion · p. 13

  • Results

    Simulation verifies the analytical framework, and the proposed REM-based positioning methods achieve near-optimal performance with robustness to localization errors.

    Source: A. Conclusion · p. 13

  • Takeaways & Limitations

    The analysis provides a framework for PASS performance evaluation and antenna positioning beyond purely LoS channels.

    Source: A. Conclusion · p. 13

    The study uses a fixed Ricean K-factor; extending it to a position-dependent model is identified as future work.

    Source: 1) Position-Dependent K-Factor Modeling · p. 13

Abstract

from arXiv · show

Pinching-antenna systems (PASSs) are an emerging flexible antenna technology that enables the creation of line-of-sight (LoS) links by repositioning a radiating element along a dielectric waveguide (WG). Most existing studies of PASSs assume a purely LoS environment, despite the fact that many practical wireless environments exhibit scattering and spatially correlated shadow fading. In this paper, we present the first statistical analysis of PASS performance under Ricean fading with spatially correlated large-scale fading. Focusing on a fundamental single-user uplink PASS, we characterize the distribution and mean of the maximum achievable signal-to-noise ratio (SNR). For the classical exponentially correlated shadow fading scenario, we express the channel power process in terms of Brownian motion and derive highly accurate approximations for the maximum SNR distribution and mean. For a general class of smoothly correlated shadow fading processes, we derive an accurate expression for the SNR distribution by modeling the process in terms of the fade sojourn duration. To address the challenges of antenna position selection in fading environments, we propose radio environment map (REM)-based positioning strategies, including opportunistic random-look and grid-based constructions. Analytical results are validated by simulation, and the impacts of key system parameters, such as the Ricean $K$-factor, spatial correlation, WG length, and carrier frequency are investigated. The results provide insights into PASS operation beyond idealized LoS conditions and establish a general analytical framework for performance evaluation and antenna positioning in scattered environments.

I. INTRODUCTION

PASSs reposition a radiating element on a waveguide to create LoS links, but practical channels also include scattering and spatially correlated shadowing. This paper analyzes a single-user uplink PASS under Ricean fading and develops SNR analysis and REM-based position-selection methods.

I. INTRODUCTION

  • PASSs create LoS links by moving a dielectric pinching antenna along a waveguide, without adding a propagation channel.The paper describes PASSs as a flexible antenna technology that can be implemented with common industrial materials.Source: §I · p. 1
  • Scattering and shadowing make PA channels stochastic, so understanding their effect on performance and positioning is necessary beyond pure-LoS assumptions.The paper motivates this analysis against the backdrop of increasingly challenging propagation at higher carrier frequencies.Source: §I · p. 1

A. Review of Related Literature

  • Existing PASS studies largely focus on pure LoS; prior scattered-channel studies often use binary LoS/NLoS states or rely on specific environment geometry.These restrictions leave limited analysis of stochastic channels combining LoS and scattered components with correlated fading.Source: A. Review of Related Literature · p. 2, B. Contributions · p. 2

A. Channel Model

  • The analysis considers a single-user uplink PASS with Ricean fading and spatially correlated shadowing, covering exponential and smoothly correlated models.The channel includes both LoS and scattered components, and the model also accounts for waveguide attenuation.Source: B. Contributions · p. 3, A. Channel Model · pp. 3–4

B. Contributions

  • The paper derives approximate maximum-SNR distributions and mean for exponentially correlated shadow fading, plus an SNR distribution for smoothly correlated fading.The exponential model is expressed using Brownian motion; the smooth-correlation analysis uses fade sojourn duration.Source: B. Contributions · p. 3
  • Two REM construction methods—opportunistic random-look and grid-based—support nearest-neighbor and interpolation-based PA selection in scattering environments.The study also examines localization errors, benchmarks, continuous versus discrete PASSs, and key system parameters.Source: B. Contributions · p. 3

B. Statistical Characterization of the SNR

The paper approximates optimal instantaneous SNR by first choosing a position that maximizes long-term SNR, then sampling fast fading nearby. The two-stage method comes closest to the optimum when large-scale and small-scale fading decorrelate over sufficiently different distances.

B. Statistical Characterization of the SNR

  • The analysis models received signal power under Ricean fading and defines the optimal instantaneous SNR from the received signal and additive noise.The single-position channel power follows a scaled non-central chi-squared distribution with two degrees of freedom.Source: B. Statistical Characterization of the… · pp. 4–5
  • The first stage selects the position maximizing long-term SNR, and the second searches nearby for the strongest of N fast-fading samples.The search is motivated as a practical approximation to global optimization over a continuous waveguide with highly oscillatory instantaneous SNR.Source: B. Statistical Characterization of the… · pp. 4–5
  • The two-stage approach comes closest to optimal SNR when large-scale and fast-fading gains decorrelate over sufficiently different distances, dLS ≫ dSS.In that regime, the search limits large-scale loss while capturing most of the available small-scale fading diversity gain.Source: B. Statistical Characterization of the… · p. 5
  • The instantaneous SNR distribution combines the long-term optimal-SNR distribution with the distribution of the maximum fading gain across N samples.The fast-fading samples are assumed sufficiently widely spaced to be uncorrelated; the long-term SNR is treated as nearly constant over the wavelength-scale search region.Source: B. Statistical Characterization of the… · p. 5

C. Relationship Between the SNR and SIR

The single-user SNR analysis also applies to a PASS with one interferer. Under the stated independent-shadowing model, the SIR problem has the same correlation structure as the SNR case.

C. Relationship Between the SNR and SIR

  • The paper extends its SNR analysis to the SIR of a single-PA PASS serving one UE in the presence of an interfering UE.The long-term SIR is defined for positions along the waveguide.Source: C. Relationship Between the SNR and SIR · p. 5
  • For independent shadowing at the desired UE and interferer, their shadow difference is Gaussian with variance 2.The model also relates the desired-UE and interferer distances to the PA position.Source: C. Relationship Between the SNR and SIR · p. 5
  • The SIR and SNR cases have the same correlation structure, making the single-user SNR analysis directly applicable to SIR with one interferer.This conclusion follows for the stated simple model with independent shadowing processes.Source: C. Relationship Between the SNR and SIR · p. 5

III. ANALYSIS FOR EXPONENTIALLY CORRELATED LARGE-SCALE FADING

For exponentially correlated large-scale fading, the analysis represents the shadow-fading process using Brownian motion and derives a highly accurate approximation to the optimal long-term SNR distribution. It also derives the mean total SNR and identifies conditions that affect the approximation’s accuracy.

A. Optimal Long-Term SNR Distribution

  • The Brownian-motion representation yields a highly accurate approximation to the optimal long-term SNR distribution, which combines with small-scale-fading results to approximate total-SNR performance.The resulting distribution is expressed using a normal CDF and a single integral that is smooth, bounded, and quick to compute.Source: §III · p. 5, A. Optimal Long-Term SNR Distribution · p. 6
  • The optimal-SNR exceedance probability is separated into starting above the threshold and starting below it but crossing the threshold along the waveguide.The second event is treated as a curved-boundary crossing problem, with a tangent approximation used to estimate its probability.Source: A. Optimal Long-Term SNR Distribution · pp. 5–6
  • The exponential correlation model makes the shadow-fading process a Markovian Ornstein–Uhlenbeck process, enabling its representation as a transformation of standard Brownian motion.The passage contrasts this closed-form representation with non-Markovian correlation functions, which require knowledge of previous states to reproduce covariance.Source: A. Optimal Long-Term SNR Distribution · p. 6
  • The tangent approximation is most accurate when the waveguide is shorter, the user is near its end, and the path loss exponent is low.Its accuracy depends on how well the threshold boundary can be approximated by a line.Source: A. Optimal Long-Term SNR Distribution · p. 6

B. Mean SNR

The mean-SNR analysis combines the mean optimal long-term SNR with the mean maximum small-scale-fading contribution. It derives the optimal long-term mean by evaluating the component terms and then combines the results for an approximation to the mean total SNR.

B. Mean SNR

  • The mean-SNR derivation takes the expectation of total SNR using independence between long-term SNR and the fading channels.Source: B. Mean SNR · p. 6
  • The mean total SNR is approximated by combining the mean optimal long-term SNR with the mean maximum small-scale-fading contribution.The small-scale-fading result uses the derived PDF under the assumption that N sampled fading channels are sufficiently separated to be uncorrelated.Source: 1) Mean Optimal Long-Term SNR · p. 7

1) Mean Optimal Long-Term SNR:

  • The mean optimal long-term SNR expression is obtained by combining the derived component terms with the earlier long-term SNR result.The integrals for two terms are evaluated in appendices, while the integral for the first term is described as straightforward.Source: 1) Mean Optimal Long-Term SNR · p. 7

2) Mean SSF Maximum:

For smoothly correlated shadow fading, the paper approximates the optimal long-term SNR distribution using fade-sojourn duration. The mean total-SNR approximation combines the long-term mean with the small-scale-fading maximum under an uncorrelated-sampling assumption.

2) Mean SSF Maximum:

  • The mean total SNR is accurately approximated by combining the optimal long-term SNR result with the maximum small-scale-fading result.The maximum-fading mean uses the derived PDF when N fading channels are sampled far enough apart to be uncorrelated.Source: 2) Mean SSF Maximum · p. 7

IV. ANALYSIS FOR SMOOTHLY CORRELATED LARGE-SCALE FADING

  • For smoothly correlated shadow fading, the optimal long-term SNR distribution is approximated by modeling fade-sojourn distance with an exponential distribution whose mean is the average fade duration.The method derives the expected number of threshold crossings to obtain the average fade duration, then combines the long-term distribution with fading results for the overall SNR distribution.Source: §IV · p. 7

A. Optimal Long-Term SNR Distribution

  • For the smooth-correlation model, the expected crossing count and derivative variance are used to obtain an accurate approximation to the full SNR distribution.The derivative variance is 2a, and the crossing-count expression comprises two integrals that permit simple numerical integration.Source: A. Optimal Long-Term SNR Distribution · p. 8

V. PA POSITION SELECTION VIA REMS

The paper proposes radio environment map strategies for selecting pinching-antenna positions using long-term channel power. It considers opportunistic random-look construction and an idealized grid-based approach, with nearest-neighbor selection and interpolation options.

V. PA POSITION SELECTION VIA REMS

  • REM-based position selection remains valid without channel stationarity on small-scale-fading timescales, provided the large-scale propagation environment remains sufficiently stable during construction and use.Source: §V · p. 8
  • Random-look REMs estimate long-term channel power by spatially averaging opportunistic measurements, while a perfect grid-based REM provides an idealized upper-bound comparison.Random samples are accumulated within discretized regions, with averages converging toward the region’s true large-scale fading value as samples accrue.Source: §V · p. 8, A. Random Look-based Construction · p. 8

A. Random Look-based Construction

  • Random-look measurements can be collected during normal operation, and each sample update requires only a low-complexity O(1) computation.The update uses a weighted running average rather than reprocessing earlier samples.Source: A. Random Look-based Construction · p. 9
  • The random-look approach selects the nearest grid point to the user as the pinching-antenna position.The paper considers nearest-neighbor selection as well as interpolation-based selection and localization error.Source: §V · p. 8, A. Random Look-based Construction · p. 9

B. Perfect Grid-based Construction

The ideal grid-based REM maps each environment location to the PA position with the highest estimated channel power. Its perfect spatial coverage provides an upper-bound reference for comparing random-look construction and position-selection strategies.

B. Perfect Grid-based Construction

  • The idealized grid REM covers the environment uniformly, but assumes exact grid-point measurements and omits channel-estimation overhead.It serves as a bound, not a realistic deployment.Source: B. Perfect Grid-based Construction · p. 9
  • The grid-based REM discretizes the environment into Nx × Ny points and the waveguide into Np sample positions.The environment grid spans its full area, while the PA samples span the waveguide length.Source: B. Perfect Grid-based Construction · p. 9
  • At each environment grid point, the REM selects the PA sample with maximum estimated long-term SNR.Channel power is measured across the user-location and PA-position grid, then reduced to a map of best PA positions.Source: B. Perfect Grid-based Construction · p. 9
  • In the illustrated 10 × 10 m2 environment, each point is spaced 0.5 m apart and colored by its best position on a 10 m PA.The PA lies along the x-axis.Source: Figure 2 · p. 10
  • The perfect grid REM supports nearest-neighbor and interpolation-based PA selection, including a pragmatic bilinear interpolation method.The methods are compared with the ideal REM so selection strategy can be isolated from REM accuracy.Source: B. Perfect Grid-based Construction · p. 10

VI. NUMERICAL RESULTS

The numerical results examine maximum-SNR behavior under exponential and smoothly correlated shadow fading, then assess REM construction and position-selection settings. They show gains from longer waveguides, alongside trade-offs involving fading, reliability, and carrier frequency.

A. Exponentially Correlated LSF

  • As the UE moves toward the WG end, the SNR distribution shifts slightly left because fewer nearby PA positions are available, increasing average distance and path loss.The effect grows with WG length but remains small, even for long WGs.Source: A. Exponentially Correlated LSF · p. 10

1) SNR distribution:

  • 7.7 dB median SNR improvement comes from adding a 1 m PA to the traditional fixed-antenna system; extending the PA from 1 m to 2 m adds 1.5 dB, versus 0.8 dB from 10 m to 20 m.The reported gains diminish with WG length and are larger when the scattered component is stronger.Source: 1) SNR distribution · pp. 10–11

2) Mean SNR:

  • The mean-SNR expression is virtually indistinguishable from simulations; increasing Ricean K reduces mean SNRTS, while increasing carrier frequency also reduces it.Higher K suppresses fluctuations and yields more stable SNR; higher carrier frequency offers more bandwidth at the cost of lower mean SNR.Source: 2) Mean SNR · p. 11, Figure 4 · p. 11
  • For the mean-SNR results, the expression closely matches simulations across the considered Ricean K-factors and carrier frequencies.The plotted horizontal quantity η represents the proportion of the channel that is LoS.Source: 2) Mean SNR · p. 11

1) SNR Distribution:

  • Higher shadow-fading standard deviation raises the distribution’s upper tail but can also increase outage probability under spatial correlation.With shorter decorrelation distance, high shadow-fading variance can benefit the entire SNRTS distribution.Source: 1) SNR Distribution · p. 11, Figure 5 · p. 11

B. Smoothly Correlated Large-Scale Fading

C. REM Performance

  • The numerical evaluation uses an exponential shadow-fading correlation model and compares random-look and grid-based REM settings against random and near-optimal references.The REM scenario uses a 20 m WG, 100 selectable PA positions, and a 10-by-10 environment grid; localization-error and interpolation variants are included.Source: C. REM Performance · pp. 11–12

1) Comparison of Construction Methods:

The comparison finds that grid-based nearest-neighbor selection performs best for both α values, while localization errors have little effect on long-term SNR. The conclusion reports near-optimal, error-robust REM positioning and identifies position-dependent K-factor modeling and multi-interferer SIR analysis as future work.

1) Comparison of Construction Methods:

  • Grid-based nearest-neighbor selection performs best for both α values, followed by random-look selection with 100,000 samples.With fewer samples, random-look performance is closer to random positioning; increasing samples moves it toward optimal performance.Source: 1) Comparison of Construction Methods · p. 12, Figure 6 · p. 12

2) Impact of Positioning Error:

3) Comparison with Benchmarks:

  • Random-look REM positioning outperforms nearest-to-UE positioning, while continuous PASS outperforms discrete PASS, especially under optimal placement.The authors report that adding typical WG attenuation has negligible effect on nearest-to-UE positioning.Source: 3) Comparison with Benchmarks · p. 13, Figure 9 · p. 13

A. Conclusion

  • The paper presents the first analytical study of PASSs under Ricean fading with spatially correlated shadowing, and reports accurate SNR distribution and mean analyses verified by simulation.The conclusion also reports a low-complexity two-stage REM approach that achieves near-optimal performance and is robust to localization errors.Source: A. Conclusion · p. 13

B. Topics for Future Work

  • Position-dependent Ricean K-factor modeling is identified as future work to represent variation in LoS strength across the waveguide.The stated motivation includes obstacles and waveguide geometry that can vary LoS-path strength.Source: 1) Position-Dependent K-Factor Modeling · p. 13

2) Multi-Interferer SIR Analysis:

  • For multiple interferers, the SIR is not analytically tractable in the discussed formulation; an approximate lognormal sum may require an equivalent shadowing/distance representation.The text presents this as a possible extension of the work.Source: 2) Multi-Interferer SIR Analysis · p. 14

APPENDIX A DERIVATION OF g′(s, x)

The appendices derive intermediate expressions by differentiating g(s, x) and evaluating integrals used in the preceding analysis. They use product and chain rules, completing the square, substitutions, and integration by parts.

APPENDIX A DERIVATION OF g′(s, x)

  • The derivative derivation combines product-rule terms with equation (63) to obtain equation (34).The preceding steps apply logarithm rules and the chain rule.Source: Appendix A · p. 14

APPENDIX B INTEGRAL OVER u IN P2

  • The integral over u is split into components, with I1 expressed using a normal CDF and I2 evaluated with a similar substitution before combining terms into equation (36).The derivation completes the square using bI and cI.Source: Appendix B · p. 14

APPENDIX C INTEGRAL OVER x IN T2

  • For T2 in (41), completing the square rewrites the exponential argument; integration by parts solves IT2,1,1, and combining (79), (80), (82), (83), and (84) with (77) gives (44).Source: Appendix C · pp. 14–15

APPENDIX D INTEGRAL OVER x IN T3

The appendix evaluates the integral terms for T3 by relating one term to T2 and applying the preceding T2 procedure. It then combines intermediate results to obtain equation (45).

APPENDIX D INTEGRAL OVER x IN T3

  • The appendix writes T3 as an expression and notes that IT3,1 has the same form as T2.It follows the procedure given for T2.Source: Appendix D · p. 15
  • For IT3,2, the derivation substitutes y = log(x) and expresses the result using Ψ and Ω(s).Source: Appendix D · p. 15
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