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Performance Analysis of Pinching-Antenna Systems
Dimitrios Tyrovolas, Sotiris A. Tegos, Panagiotis D. Diamantoulakis, Sotiris Ioannidis, Christos K. Liaskos, George K. Karagiannidis
TL;DR
The paper addresses limited path-loss control and incomplete loss-aware evaluation of reconfigurable wireless systems. It develops closed-form PAS performance expressions and optimal-placement analysis under free-space and waveguide losses. Results show that losses increasingly affect longer waveguides, yet PASs consistently outperform conventional systems in reliability and data rate.
Problem
Existing reconfigurable technologies and prior PAS studies provide limited path-loss control or focus on lossless and specific configurations, leaving realistic waveguide-loss effects insufficiently evaluated.
Method
The paper derives closed-form outage-probability and average-rate expressions and analyzes pinching-antenna placement that maximizes performance under waveguide losses.
Results
PASs consistently outperform conventional systems in reliability and data rate, while waveguide losses significantly affect performance, especially as waveguide length increases.
Takeaways & Limitations
PASs can provide reliable, high-rate communication through dynamically repositionable antennas even when practical waveguide losses are present.
Abstract
from arXiv · showhide
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.
I. INTRODUCTION
6G wireless environments require adaptive, high-capacity communication, but existing reconfigurable technologies do not directly make path loss programmable. This paper introduces PASs and develops loss-aware analytical tools to evaluate their reliability, rate, and deployment advantages.
- 6G applications require ultra-reliable, high-capacity communications and wireless environments that adapt dynamically to users with different requirements.
- A. Motivation: Existing reconfigurable technologies primarily improve channel gain, while path loss remains a critical programmable parameter, especially at high frequencies.RISs incur double path loss, and fluid or moving antennas have position adjustments limited to a few wavelengths.
- A. Motivation: PASs use dielectric waveguides and dynamically activated radiating sites to make path loss programmable.
- B. Contribution: Prior PAS studies considered lossless waveguides or specific configurations, leaving realistic waveguide-loss effects insufficiently characterized.
- B. Contribution: The paper derives closed-form outage-probability and average-rate expressions and analyzes optimal antenna placement under waveguide losses.
- B. Contribution: Numerical results show that waveguide losses matter especially for longer waveguides, while PASs retain higher reliability and data-rate performance than conventional systems.
II. SYSTEM MODEL
The system models a downlink PAS serving a randomly located single-antenna user in a rectangular area. A pinching antenna moves along a dielectric waveguide, with the channel incorporating free-space propagation, guided-wave phase effects, and waveguide absorption.
- II. SYSTEM MODEL: The downlink consists of an access point and a single-antenna user randomly placed in a rectangular area with side lengths D_x and D_y.The user position is represented by ψ_m, with x_m uniformly distributed over [0, D_x] and y_m centered within the area.
- II. SYSTEM MODEL: The PAS dynamically adjusts the pinching antenna position along a dielectric waveguide to optimize link quality and radiate from a controlled point.The waveguide is parallel to the x-axis at height h and has length D_x.
- II. SYSTEM MODEL: The channel includes free-space path loss based on the Euclidean distance between the user and pinching antenna.The reference-distance path-loss factor is η = λ^2/(16π^2), where λ is the free-space wavelength.
- II. SYSTEM MODEL: The dielectric waveguide changes the signal phase through its effective refractive index and guided wavelength.The guided wavelength is λ_g = λ/n_eff.
- II. SYSTEM MODEL: Waveguide absorption is modeled with coefficient α and exponential power attenuation as the signal travels from the feedpoint to the pinching antenna.
III. PERFORMANCE ANALYSIS
The performance analysis derives outage-probability and average-rate expressions for PASs using a placement that minimizes antenna-user distance, then examines placement that maximizes received SNR. This exposes the trade-off between simple distance-based placement and performance-driven optimization.
- III. PERFORMANCE ANALYSIS: The analysis derives outage-probability and average-rate expressions for a PAS positioned to minimize the pinching-antenna distance from the user.
- III. PERFORMANCE ANALYSIS: The analysis also derives optimal pinching-antenna placement that maximizes received SNR under the modeled system conditions.
- III. PERFORMANCE ANALYSIS: The two placement strategies provide a trade-off between straightforward distance minimization and performance-driven optimization.
A. Outage Probability
The outage-probability analysis derives closed-form expressions for PASs under waveguide loss and its absence, including placement and multi-antenna cases.
- Placing the pinching antenna at xm minimizes path loss but does not guarantee uninterrupted communication.The paper therefore derives the outage probability for this placement rather than equating minimum path loss with zero outage.
- A closed-form outage expression is provided for a single pinching antenna at (xm, 0, h), with C = ηPtγthr/σ2.The result applies to a single-antenna user whose coordinates are xm and ym.
- The outage probability is obtained from the condition γr ≤ γthr by integrating over the feasible user-location region and the joint density of xm and ym.The derivation assumes independent xm and ym and uses an indicator function to represent the outage condition.
- The lossless-waveguide case is treated separately by setting α = 0, isolating the effect of the served area on outage probability.This idealized assumption removes waveguide attenuation from the analysis.
B. Average rate
The average-rate analysis derives a closed-form expression for PAS performance and extends the single-antenna result to multiple antennas and lossless waveguides.
- A closed-form expression is derived for the average rate Rp of a PAS with one pinching antenna and one single-antenna user.The expression uses A = ηPt/σ2 and includes the dilogarithm function Li2(·).
- The average rate is evaluated as the expectation of the system rate over user locations.Because the relevant expression is even in ym, the calculation can be written in integral form.
- The derivation rewrites the average-rate integral into components IA and IB before applying further algebraic simplifications.These steps lead to the stated closed-form result.
- For multiple pinching antennas, the average rate is closely approximated by the single-antenna expression with A = ηNPt/σ2.The approximation parallels the multi-antenna outage-probability treatment.
- For a lossless waveguide, the average-rate expression is given in prior work as a special case.This corresponds to the idealized no-attenuation setting considered for outage probability.
C. Optimal Position of Pinching Antenna
Waveguide attenuation can shift the best pinching-antenna position away from direct user alignment. The paper derives a closed-form, constrained optimizer and shows when alignment remains optimal.
- Motivation: Waveguide losses can shift the optimal antenna position away from direct alignment with the user, making performance-driven placement necessary.The objective is to maximize received SNR γr under the deployment constraints.
- Optimization formulation: The optimal placement maximizes f(xp), which combines waveguide attenuation with the free-space distance between the pinching antenna and user.The optimization is performed over the feasible waveguide interval [0, Dx].
- Critical-point analysis: Critical points are classified using derivative and second-derivative tests: xp2 is a local maximum, whereas xp1 is a local minimum.At critical points, the sign of f(xp)g′(xp) determines the second derivative because f′(xp)=0.
- Global optimization: The global optimum compares the valid local maximum with the feeding point xp = 0; if no valid interior maximum exists, xp = 0 is selected.The interior candidate must lie in [0, Dx] and outperform f(0).
- Practical placement: For typical indoor scenarios with small absorption, the optimum simplifies to x*p = xm, aligning the antenna horizontally with the user.The general expression remains important for understanding higher attenuation and varying waveguide conditions.
IV. NUMERICAL RESULTS
The numerical results evaluate PAS reliability and rate under varying deployment sizes, waveguide losses, and antenna counts. PASs generally outperform conventional systems, while increasing absorption degrades outage performance, especially for longer waveguides.
- Outage probability: Under Dx = 10 m and Dx = 30 m, a single-antenna PAS consistently achieves lower outage probability than a conventional single-antenna system at the same γt.The conventional system requires about 8 dB more transmit power at Dx = 30 m than Dx = 10 m to achieve an outage probability of 10^-5.
- Waveguide losses: Increasing the absorption coefficient α degrades outage performance, with stronger degradation as Dx increases because attenuation grows with waveguide distance.The study considers α = 0.01 for low-loss materials and α = 0.1 for moderate-loss dielectric waveguides.
- Waveguide losses: Placing the antenna at (xm, 0, h) minimizes path loss and remains a practical near-optimal strategy, although its divergence from the α-dependent optimum increases with α.The optimal placement depends on α under waveguide losses.
- Multiple pinching antennas: For multiple antennas, PAS outage performance improves with N and remains superior to a conventional access point with N feedpoint antennas.A PAS with N = 1 outperforms a conventional system with N = 2, while PAS N = 2 outperforms conventional N = 5.
- Average rate: A single-antenna PAS achieves higher average rate than a single-antenna conventional system for deployment areas with Dx = 10 m and Dx = 30 m.PAS rates remain nearly identical across the two areas, with only minor differences from waveguide losses, whereas the conventional system degrades significantly as Dx increases.
- Average rate: With multiple antennas, PAS consistently outperforms conventional systems in average rate, and PAS with two antennas matches the rate of a conventional system with five antennas.Dynamic repositioning along the waveguide provides additional degrees of freedom for compensating path loss.
V. CONCLUSION
The paper concludes that its analytical framework evaluates PAS reliability and rate under ideal and realistic waveguide conditions. It also supports analysis of single- and multiple-antenna configurations and informs placement and deployment strategies.
- Conclusion: The framework derives closed-form expressions for PAS outage probability and average rate with and without waveguide losses.These expressions cover both single and multiple pinching antenna scenarios.
- Conclusion: The resulting analysis provides insights into PAS scalability and deployment strategies across single- and multiple-antenna configurations.The conclusion presents the framework as a tool for evaluating PAS performance under ideal and realistic conditions.
APPENDIX A CALCULATION OF Ii AND Ij INTEGRALS
Appendix A derives the Ii and Ij integrals through successive algebraic transformations, concluding with the expressions used in the main analysis.
- Integral Ii: The appendix begins by incorporating I1 into Ii and rewriting the integral through successive algebraic manipulations.The derivation concludes when equation (35) is shown equivalent to equation (11).
- Integral Ij: The Ij derivation first states the integral and then applies algebraic manipulation to obtain equation (12).Equation (12) concludes the calculation of Ij.
APPENDIX B CALCULATION OF IA AND IB INTEGRALS
Appendix B derives the IA and IB integrals using substitutions, integration by parts, partial fractions, and algebraic transformations. The derivations conclude with equations (23) and (22), respectively.
- Integral IA: The IA calculation rewrites the integral through substitutions and algebraic manipulation before deriving equation (23).The appendix identifies equation (23) as concluding the calculation of IA.
- Integral IB: The IB calculation introduces intermediate variables, applies integration by parts and partial fraction decomposition, and uses cited integral identities to obtain equation (22).The derivation also uses complex-conjugate properties of dilogarithm-function arguments.
- Integral IB: The appendix proves intermediate relations involving I− and I+ before completing the IB derivation.These steps include rewriting expressions with cited identities and algebraic manipulations.
- Integral IB: The IB derivation concludes after establishing the final expression involving C = z(x, −h).This final step is explicitly identified as concluding the calculation of IB.