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Array Gain for Pinching-Antenna Systems (PASS)

Chongjun Ouyang, Zhaolin Wang, Yuanwei Liu, Zhiguo Ding

arXiv:2501.05657v2eess.SP

TL;DR

PASS addresses flexible-antenna deployment by analyzing how array gain depends on antenna number and inter-antenna spacing. The paper derives an upper bound and position-refinement method, incorporates mutual coupling, and finds optimal values for both parameters, with numerical results showing higher gain than conventional-antenna systems.

  • Problem

    The paper investigates whether PASS array gain increases monotonically with antenna number or as inter-antenna spacing decreases.

  • Method

    The paper derives a closed-form array-gain upper bound, develops a position-refinement method, and analyzes spacing with mutual coupling.

  • Results

    PASS has an optimal antenna number and inter-antenna spacing that maximize array gain, and numerical results show higher gain than conventional-antenna systems.

  • Takeaways & Limitations

    Practical PASS deployment requires optimizing both the number of pinching antennas and their inter-antenna spacing.

Abstract

from arXiv · show

Pinching antennas is a novel flexible-antenna technology, which can be realized by employing small dielectric particles on a waveguide. The aim of this letter is to characterize the array gain achieved by pinching-antenna systems (PASS). A closed-form upper bound on the array gain is derived by fixing the inter-antenna spacing. Asymptotic analyses of this bound are conducted by considering an infinitely large number of antennas, demonstrating the existence of an optimal number of antennas that maximizes the array gain. To approach this bound, an antenna position refinement method is introduced. The relationship between the array gain and inter-antenna spacing is further explored by incorporating the effect of mutual coupling. It is proven that there also exists an optimal inter-antenna spacing that maximizes the array gain. Numerical results demonstrate that by optimizing the number of antennas and inter-antenna spacing, PASS can achieve a significantly larger array gain than conventional-antenna systems.

I. INTRODUCTION

PASS addresses limitations of conventional flexible-antenna systems by enabling scalable antenna deployment along an arbitrarily long waveguide. This paper analyzes array-gain behavior and finds that both antenna number and spacing have non-monotonic optima.

  • Motivation: Conventional flexible-antenna movements are typically limited to apertures of several wavelengths, reducing their effectiveness against large-scale path loss.Such systems can also be costly and have limited flexibility to add or remove antennas.
  • PASS concept: PASS activates dielectric-waveguide antennas at arbitrary points, enabling highly flexible and scalable deployment near the user.Unlike conventional flexible-antenna systems, the waveguide length can be arbitrarily long.
  • Research questions: The paper asks whether array gain increases monotonically with antenna number or decreases monotonically with inter-antenna spacing, and answers both questions negatively.The analysis challenges the intuition that more antennas or smaller spacing always improves gain.
  • Contributions: A closed-form upper bound, a position-refinement method, mutual-coupling analysis, and numerical optimization characterize PASS array gain.The analysis identifies optimal antenna number and spacing and compares PASS with conventional-antenna systems.
  • System model: The theoretical investigation adopts a free-space line-of-sight channel model for a single-antenna downlink user.Multipath fading is left for future work.

B. Pinching-Antenna System

PASS uses multiple activated pinching antennas on a waveguide to jointly serve a user. Array gain is the performance metric because received SNR and communication rate are proportional to it.

  • System configuration: PASS activates N pinching antennas on a waveguide aligned parallel to the x-axis at height d.The antennas jointly serve the single-antenna user, with N assumed even for notational simplicity.
  • Antenna locations: The nth pinching antenna is located at ψ_n = [x_n, 0, d]^T, with antenna positions ordered along the waveguide.The index set is defined symmetrically around the waveguide center.
  • Signal model: The received signal combines the waveguide-transmitted symbol across the activated pinching antennas in the downlink model.The transmitted symbol s is normalized, and additive Gaussian noise is included at the user.
  • Propagation effects: Each pinching antenna experiences an in-waveguide phase shift determined by its distance from the waveguide feed point.The model neglects waveguide propagation loss because prior work indicates its overall impact is limited.
  • Performance metric: Array gain is the PASS performance metric because both received SNR and communication rate are proportional to it.The model distributes total transmit power equally among the N active antennas.

A. Array Gain Versus Antenna Number

For fixed inter-antenna spacing, the paper analyzes how PASS array gain scales with antenna number while neglecting mutual coupling through a minimum spacing constraint.

  • A. Array Gain Versus Antenna Number: The antenna-number analysis neglects mutual coupling by maintaining a minimum inter-antenna spacing of ∆pλ, where ∆p ≥ 1.This spacing constraint simplifies the analysis of array-gain scaling with N.
  • A. Array Gain Versus Antenna Number: To maximize single-user PASS array gain, the antenna array center is positioned directly above the user.This symmetry gives x_n + x_−n over 2 equal to x_u and pairs offsets around the user.

1) Array Gain with Equal Spacing:

With equally spaced antennas, the analysis expresses antenna offsets using the minimum spacing and approximates the resulting summation by a definite integral.

  • 1) Array Gain with Equal Spacing:: Because ε ≪ 1, the summation in the array-gain expression is accurately approximated using a definite integral.This approximation supports the subsequent analytical bound.

2) An Upper Bound of the Array Gain:

The analysis derives an upper bound for PASS array gain and shows that adding antennas indefinitely eventually reduces the gain. This establishes an optimal antenna number under the stated spacing and coupling assumptions.

  • The closed-form upper bound is constructed by replacing inter-antenna spacings with their minimum and simplifying the array-gain expression.
  • As N →∞, the array gain of equally spaced antennas converges to 0.
  • As N increases, power per antenna decreases, leaving most power-carrying antennas too far from the user to deliver appreciable energy.
  • Therefore, increasing the number of pinching antennas does not guarantee continuous array-gain growth; an optimal antenna number exists.
  • The same optimal-number conclusion applies to non-uniformly spaced PASS when mutual coupling is ignored and minimum spacing is maintained.

3) A Method to Approach the Upper Bound:

The paper refines antenna positions to make received signals combine constructively while preserving minimum spacing. The resulting locations closely track the derived upper bound under the stated large-height condition.

  • The refinement method adjusts each antenna location to enforce constructive combination of received signals at the user.
  • Each antenna is shifted by a positive wavelength-scale distance, which has negligible impact on large-scale path loss when d is large.
  • Subsequent antennas are positioned sequentially while maintaining inter-antenna spacing of at least ∆pλ.
  • Equation (13) shows that the refined positions closely track the upper bound when d ≫λ.

4) Optimal Antenna Number and Array Gain Limits:

The upper-bound function has a finite maximizer, yielding an optimal antenna number and corresponding aperture. Both the optimal number and maximum gain decrease as minimum spacing increases.

  • The upper-bound function is maximized at x⋆≈3.32, where fub(x⋆)≈1.105.
  • For d=1 m, the optimal antenna aperture is approximately 6.64 m; for d=3 m, it increases to 19.92 m.
  • The upper-bound function increases for x∈(0,x⋆), so adding antennas improves gain only while N≤N⋆.
  • The optimal antenna number and maximum array gain decrease as the minimum inter-antenna spacing ∆p increases.
  • For two closely spaced antennas, the maximum array gain is bounded by 2ηfub(x⋆)dλ.

B. Array Gain Versus Antenna Spacing

PASS array gain is not guaranteed to improve as antennas become closer: mutual coupling can make the spacing relationship non-monotonic and create an optimal spacing.

  • Array-gain modeling: Mutual coupling (MC) must be incorporated because it alters the spatial channel and can reduce or enhance PASS array gain.The channel is modeled using an MC matrix, with evenly spaced antennas simplifying the analysis.
  • Analytical case: For two closely spaced antennas, the MC matrix admits an eigendecomposition that yields an analytical array-gain expression.The two-antenna case is analyzed because the general MC matrix is typically complex and position-dependent.
  • Effect of mutual coupling: Mutual coupling reduces array gain in one comparison, while the MC-aware analysis also identifies configurations where coupling enhances gain.The reported gain difference is obtained by comparing the MC-aware expression with the model that neglects MC.
  • Spacing dependence: Reducing inter-antenna spacing does not always improve array gain because the MC-aware gain varies non-monotonically with spacing.A one-dimensional search over ∆∈[0, λ] is used to identify the maximum.
  • Spacing dependence: An optimal inter-antenna spacing exists that maximizes array gain when mutual coupling is considered.This conclusion contrasts with the unphysical infinite-gain implication of setting certain spacing terms to zero under simplified equations.
  • Scope: The generalization beyond two antennas remains open because the MC matrix has a complex structure that strongly depends on antenna positions.The authors anticipate that these results will motivate future MC-aware PASS designs.

IV. NUMERICAL RESULTS

Numerical simulations evaluate PASS array gain against antenna number and spacing under propagation-loss and mutual-coupling settings. They show optimal antenna-number and spacing choices, close agreement between bounds and optimized results, and advantages over conventional systems.

  • Simulation setup: The simulations use fc = 28 GHz, d = 3 m, xu = 0 m, xf = 0 m, x0 = x−N/2, and neff = 1.44.Two configurations are considered: no waveguide propagation loss and 0.08 dB/m loss.
  • Array gain versus antenna number: PASS and its upper bound vary non-monotonically with antenna number, with an optimal number maximizing array gain.The optimized array gain closely tracks the upper bound, while propagation loss has an insignificant effect in this setting.
  • Maximum gain versus minimum spacing: Increasing minimum inter-antenna spacing decreases PASS maximum array gain in both propagation-loss configurations.The approximated bound closely matches simulated results obtained by searching over N ∈[0, 10^4].
  • Comparison with conventional systems: Optimized and uniformly spaced PASS outperform, or at least match, conventional fluid- and fixed-location antenna systems.The reported comparison includes two fluid-antenna configurations and conventional fixed-location antennas.
  • Mutual-coupling results: With mutual coupling, array gain oscillates with spacing and an optimal spacing maximizes gain; without coupling, the maximum occurs at ∆ = 0.The two-antenna simulation aligns closely with the analytical approximation, and PASS outperforms conventional fixed-location antennas for the considered values of N.

V. CONCLUSION

The paper concludes that PASS array gain is maximized by jointly optimizing antenna number and inter-antenna spacing. Propagation loss has a minor overall effect, while mechanical deployment complexity remains unresolved.

  • Main conclusion: PASS array gain is maximized at an optimal number of pinching antennas and an optimal inter-antenna spacing.The conclusion emphasizes optimizing both parameters for practical PASS deployments.
  • Main conclusion: Waveguide propagation loss has only a minor effect on overall PASS performance.
  • Open issue: The mechanical complexity of dynamically adding or removing dielectric materials remains an open issue for future research.
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