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Rate Region of ISAC for Pinching-Antenna Systems

Chongjun Ouyang, Zhaolin Wang, Yuanwei Liu, Zhiguo Ding

arXiv:2505.10179v1eess.SP

TL;DR

Prior work on PASS for ISAC had not established fundamental performance limits or fully characterized the communication-sensing tradeoff. This paper derives CR-SR rate regions and bounds, finding that PASS achieves a larger region than conventional fixed-antenna systems.

  • Problem

    Prior PASS-in-ISAC work focused on beamforming optimization but had not established fundamental performance limits or fully characterized the communication-sensing tradeoff.

    Source: B. Motivation and Contributions · p. 2

  • Method

    For single-pinch PASS, the paper derives the rate region using rate-profile optimization and time sharing; for multiple pinches, it derives bounds using alternating optimization and relaxations.

    Source: §VI · p. 11

  • Results

    PASS achieves a larger CR-SR rate region and a more favorable tradeoff than conventional fixed-antenna systems.

    Source: §VI · p. 11

  • Takeaways & Limitations

    The reported PASS advantage persists with in-waveguide propagation loss and is amplified as the number of pinching antennas increases.

    Source: §VI · p. 11

Abstract

from arXiv · show

The Pinching-Antenna SyStem (PASS) reconstructs wireless channels through \emph{pinching beamforming}, wherein the activated positions of pinching antennas along dielectric waveguides are optimized to shape the radiation pattern. The aim of this article is to analyze the performance limits of employing PASS in integrated sensing and communications (ISAC). Specifically, a PASS-assisted ISAC system is considered, where a pinched waveguide is utilized to simultaneously communicate with a user and sense a target. Closed-form expressions for the achievable communication rate (CR) and sensing rate (SR) are derived to characterize the information-theoretic limits of this dual-functional operation. \romannumeral1) For the single-pinch case, closed-form solutions for the optimal pinching antenna location are derived under \emph{sensing-centric (S-C)}, \emph{communications-centric (C-C)}, and \emph{Pareto-optimal} designs. On this basis, the CR-SR trade-off is characterized by deriving the full CR-SR rate region, which is shown to encompass that of conventional fixed-antenna systems. \romannumeral2) For the multiple-pinch case, an antenna location refinement method is applied to obtain the optimal C-C and S-C pinching beamformers. As a further advance, inner and outer bounds on the achievable CR-SR region are derived using an element-wise alternating optimization technique and by invoking Cauchy-Schwarz and Karamata's inequalities, respectively. Numerical results demonstrate that: \romannumeral1) the derived bounds closely approximate the true CR-SR region; and \romannumeral2) PASS can achieve a significantly larger rate region than conventional-antenna systems.

I. INTRODUCTION … II. SYSTEM MODEL

The paper develops an information-theoretic analysis of PASS-assisted ISAC, deriving communication and sensing rates and characterizing their tradeoff for single- and multiple-pinch designs. It introduces the system architecture and its line-of-sight channel assumption.

I. INTRODUCTION

  • PASS uses independently activated dielectric particles along a waveguide to reconfigure antenna locations, and its waveguide can extend arbitrarily to place antennas near users.The introduction presents PASS as a flexible, scalable, cost-effective approach that can establish robust line-of-sight links.Source: §I · pp. 1–2

A. Prior Works

  • Prior PASS studies examined communication performance, propagation impairments, array gain, radiation modeling, blockage, localization, tracking, detection, and RCS sensing.The cited work reports PASS advantages in mitigating large-scale path loss and blockage, with sensing functions jointly optimized with communication performance.Source: A. Prior Works · p. 2

B. Motivation and Contributions

  • Existing PASS-ISAC studies primarily optimize dual-functional beamforming, leaving fundamental limits and the communication-sensing tradeoff insufficiently characterized.This paper addresses the gap by analyzing the achievable information-theoretic rate region as a function of pinching beamforming.Source: B. Motivation and Contributions · p. 2
  • For a single pinch, closed-form location solutions support sensing-centric, communications-centric, and Pareto-optimal designs, and the conventional-antenna rate region is nested within PASS's.Source: B. Motivation and Contributions · p. 2
  • For multiple pinches, location refinement optimizes communications-centric and sensing-centric designs, while alternating optimization with time sharing gives an inner bound and inequalities yield a closed-form outer bound.The outer bound uses Cauchy-Schwarz and Karamata's inequalities.Source: B. Motivation and Contributions · p. 2
  • The multiple-pinch inner and outer bounds closely approximate the true CR-SR region; PASS achieves a larger region than conventional-antenna systems, and adding pinching antennas can enlarge it.The simulations also report that PASS significantly outperforms conventional-antenna systems in both communication rate and sensing rate.Source: B. Motivation and Contributions · p. 2

Notations:

  • The notation subsection defines conventions for scalars, vectors, matrices, matrix operations, norms, sets, expectations, complex Gaussian distributions, convex hulls, and unions.Source: Notations · pp. 2–3

II. SYSTEM MODEL

  • The system has a base station communicating with one single-antenna user and sensing one target, using separate transmit and receive waveguides; the analysis assumes free-space LoS propagation.The transmit waveguide activates N pinching antennas for both tasks, while one receive-side pinching antenna is sufficient for collecting the single target's echo; multipath is out of scope.Source: §II · p. 3

A. Communication Model with PASS

The communication model defines the PASS waveguide geometry and user link, then evaluates communication performance assuming equal power allocation and negligible in-waveguide propagation loss.

A. Communication Model with PASS

  • The model places the transmit waveguide parallel to the x-axis at height d and specifies the user and pinching-antenna locations, with antenna deployment limited by tmax.The user is at uc = [xc, yc, 0]^T, and the nth antenna is at ψn = [tn, yt, d]^T.Source: A. Communication Model with PASS · p. 3
  • The received user signal, its SNR, and the resulting communication rate are defined for N active pinching antennas, with total transmit power P equally divided among them.Source: A. Communication Model with PASS · p. 3
  • The model neglects in-waveguide propagation loss because free-space path loss dominates, so its performance results are interpreted as upper bounds for PASS-based ISAC systems.The impact of in-waveguide loss is examined in the simulation section.Source: A. Communication Model with PASS · p. 3

Conventional Fixed-Antenna System: · B. Sensing Model with PASS

PASS’s pinching locations shape both communication and sensing performance, while sensing performance is modeled through target-RCS estimation. The paper compares PASS with fixed-antenna systems and frames the conflicting rate objectives through C-C, S-C, and Pareto-optimal designs.

Conventional Fixed-Antenna System:

  • The conventional fixed-antenna system uses one transmit antenna at [tf, yt, d]T, whereas PASS’s communication rate depends on its activated pinching locations.That spatial flexibility can establish a more stable and stronger line-of-sight link than the fixed-antenna system, which cannot dynamically reconfigure its channel.Source: Conventional Fixed-Antenna System · p. 4

B. Sensing Model with PASS

  • PASS’s sensing model uses a receive waveguide parallel to the x-axis at height d and a target response vector incorporating the target’s RCS.The base station uses the waveguide observation to estimate RCS, assuming the target location is perfectly tracked.Source: B. Sensing Model with PASS · p. 4
  • The sensing rate measures mutual information between the received observation and target RCS, conditioned on the transmitted signal, per unit time.Under the Swerling-I model, RCS is constant pulse-to-pulse with Rayleigh-distributed amplitude and βRCS ∼ CN(0, αs).Source: B. Sensing Model with PASS · p. 4
  • Maximizing sensing rate (SR) is equivalent to minimizing mean-squared error (MSE) when estimating the target’s radar cross section (RCS).The sensing model assumes the target location is perfectly tracked and focuses on estimating its RCS.Source: B. Sensing Model with PASS · p. 4
  • Aligning the receive pinching antenna with the target’s projection on the waveguide (r = xs) maximizes SR.The paper derives this location condition by comparing the SR expressions.Source: B. Sensing Model with PASS · p. 4
  • PASS’s SR depends on its pinching locations, and optimized PASS can outperform the conventional fixed-antenna system in sensing.The conventional comparison uses one fixed transmit antenna and one fixed receive antenna.Source: B. Sensing Model with PASS · p. 4
  • Because communication rate and sensing rate both depend on pinching beamformer t and their objectives conflict, the paper considers C-C, S-C, and Pareto-optimal designs to characterize the rate region.The conventional comparison assumes a single transmit antenna, citing deployment cost and the lack of PASS’s spatial flexibility.Source: B. Sensing Model with PASS · pp. 4–5

III. SINGLE-PINCH CASE · A. Communications-Centric Design · B. Sensing-Centric Design

The single-pinch analysis simplifies the CR and SR expressions to study PASS design, with communications-centric and sensing-centric placement optimizing different functions. The designs perform best when their channels are spatially aligned, while increasing separation can create a CR-SR trade-off.

III. SINGLE-PINCH CASE

  • With one active pinching antenna (N = 1), the CR and SR simplify, enabling analysis of PASS design despite coupled antenna locations and dual propagation phase shifts.Increasing the number of pinching antennas can enhance array gain and improve communication and sensing performance,.Source: §III · p. 5

A. Communications-Centric Design

  • The communications-centric design selects the activated location t1 to maximize Rc, with the resulting CR and SR specified for this design.The supplied passage does not expose the expressions for those rates.Source: A. Communications-Centric Design · p. 5

B. Sensing-Centric Design

  • The sensing-centric design selects the activated location t1 to maximize Rs, with the resulting CR and SR specified for this design.The supplied passage does not expose the expressions for those rates.Source: B. Sensing-Centric Design · p. 5
  • Under C-C and S-C designs, the optimal activated location is closest to the user and target, respectively, minimizing the corresponding path loss and maximizing that function’s rate.This characterization follows from the optimal-location results in the two designs.Source: B. Sensing-Centric Design · p. 5
  • When the user and target align along the waveguide axis (xc = xs), CR and SR simultaneously reach their respective maxima.The comparison of the C-C and S-C rates identifies this aligned case.Source: B. Sensing-Centric Design · p. 5
  • As the user-target offset |xc − xs| increases, optimizing one function can degrade the other; as the offset tends to infinity, C-C sensing rate approaches zero.The passage concludes that PASS-enabled ISAC yields greater mutual benefits when the communication and sensing channels are spatially aligned.Source: B. Sensing-Centric Design · p. 5

C. Pareto-Optimal Design · IV. MULTIPLE-PINCH CASE

For single-pinch PASS, a rate-profile method yields a closed-form Pareto design, and its achievable rate region contains that of conventional fixed-antenna systems. The multiple-pinch section frames the challenge of designing pinching beamformers for a favorable communication–sensing trade-off.

C. Pareto-Optimal Design

  • The rate-profile method traces the Pareto boundary across α ∈ [0, 1], and the non-convex optimization admits a closed-form optimal activated location.The boundary consists of rate pairs for which improving one rate requires decreasing the other.Source: C. Pareto-Optimal Design · p. 5
  • The optimal activated location lies on the waveguide-axis segment between the user’s and target’s projections, t⋆_α ∈ [x_c, x_s].This stated interval applies to the described case; the passage notes that a similar result holds when x_s ≤ x_c.Source: C. Pareto-Optimal Design · p. 5
  • Varying the activated location achieves rate pairs in a union set, while time-sharing among choices of t⋆_α, yields its convex hull as PASS’s complete rate region.The CR and SR are those achieved by setting t_1 = t⋆_α.Source: C. Pareto-Optimal Design · p. 5
  • Under optimized pinching locations, PASS achieves higher communication and sensing performance than conventional fixed-antenna systems by reducing large-scale path loss through antenna reconfiguration [18].Source: C. Pareto-Optimal Design · p. 6
  • The conventional fixed-antenna rate region is completely contained within the rate region achieved by PASS.The comparison attributes PASS’s higher communication and sensing performance under optimized pinching locations to reduced large-scale path loss through antenna reconfiguration [18].Source: C. Pareto-Optimal Design · p. 6

IV. MULTIPLE-PINCH CASE

  • For N > 1, designing the DFSAC pinching beamformer is challenging, and the section aims to characterize multiple-pinch PASS’s fundamental performance limits.The design objective is a favorable CR–SR trade-off.Source: §IV · p. 6

A. Communications-Centric Design … 2) Inner Bound:

The design characterizes the CR-SR trade-off through rate-profile optimization and develops an achievable inner bound using iterative antenna-location updates. It also specifies communications-centric and sensing-centric placement strategies.

A. Communications-Centric Design

  • The C-C design maximizes CR over locations separated by minimum spacing, using the antenna-location refinement method for its non-convex, NP-hard problem, with spacing constraint.Source: A. Communications-Centric Design · p. 6

B. Sensing-Centric Design

  • The S-C design maximizes SR by placing pinching antennas as close as possible to the sensing target while satisfying the minimum inter-antenna distance constraint,.Source: B. Sensing-Centric Design · p. 6

C. Pareto-Optimal Design

1) Rate Region:

  • The multiple-pinch CR-SR region is characterized using the communication and sensing rates achieved by the rate-profile-optimal beamformer for each α.Source: 1) Rate Region · p. 6

2) Inner Bound:

  • An element-wise alternating optimization method yields a suboptimal achievable inner bound, sequentially updating each antenna location while holding the others fixed.Source: 2) Inner Bound · p. 6
  • Each antenna location is updated by one-dimensional search, and iterations stop when the objective's fractional decrease falls below a predefined threshold.Source: 2) Inner Bound · p. 7
  • The element-wise algorithm's computational complexity scales as O(IiterNQ), where Iiter is the number of iterations until convergence.Source: 2) Inner Bound · p. 7

3) Outer Bound:

The section derives an outer bound for the rate region of PASS with multiple pinching antennas by relaxing the location constraints and reducing the bound to a scalar parameter. It establishes this bound alongside an inner bound and states a special-case treatment when the user and target positions coincide.

3) Outer Bound:

  • Cauchy–Schwarz and Karamata’s inequalities simplify an otherwise intractable search over the unit hypercube, yielding upper bounds that depend only on Zβ, the sum of the βn values.The derivation first relaxes the minimum inter-antenna distance and propagation-induced dual phase shifts, and constrains each activated location to [xc, xs].Source: 3) Outer Bound · pp. 7–8
  • The outer bound is the convex hull of regions indexed by Zβ varying from 0 to N, completing the multiple-pinch rate-region bounds alongside the inner bound.The section establishes both an inner bound and an outer bound for the rate region achieved by PASS with multiple pinching antennas.Source: 3) Outer Bound · p. 8
  • When Δx = 0, closed-form upper bounds for CR and SR are available in; their tightness was validated numerically, with derivations omitted here.The derived outer bound in this section applies when Δx ≠ 0.Source: 3) Outer Bound · p. 8

V. NUMERICAL RESULTS

The numerical section evaluates the analytical findings for a PASS-assisted ISAC system under specified deployment and simulation conditions. It considers ideal and lossy waveguides and compares PASS with a conventional fixed-antenna system.

Numerical setup

  • The user and target are uniformly distributed in a 20 m × 8 m region centered at the origin, with transmit and receive waveguides at height 3 m and y-coordinates −2 m and 2 m.The region dimensions are along the x- and y-axes, respectively.Source: §V · p. 8
  • Simulations use a 28 GHz carrier, effective refractive index 1.4, frame length 5, reflection strength 10, transmit power 10 dBm, and noise power −114 dBm.Other listed defaults include one-dimensional search precision Q = 104 and minimum inter-antenna distance ∆ = λ/2.Source: §V · p. 8
  • The evaluation compares an ideal waveguide without propagation loss and a practical waveguide with 0.08 dB/m loss against a conventional system with one fixed transmit and one fixed receive antenna.For the practical case, locations optimized under the ideal case are used and propagation loss is then incorporated; results are averaged over 10^3 independent channel realizations.Source: §V · pp. 8–9

A. Single-Pinch Case · 1) Achievable CR and SR:

In the single-pinch case, C-C and S-C designs trade off communication performance, while both can match or exceed the fixed-antenna system in sensing rate. The CR and SR respond differently to waveguide loss because sensing is affected by attenuation on both transmit and receive waveguides.

1) Achievable CR and SR:

  • C-C PASS achieves higher CR than S-C PASS regardless of in-waveguide propagation loss, which causes only marginal CR degradation for both designs.The subsequent discussion therefore focuses on the ideal waveguide scenario without in-waveguide propagation loss.Source: 1) Achievable CR and SR · p. 9
  • C-C activates the antenna at the user’s projection onto the waveguide axis, keeping CR invariant as Dx changes.This placement preserves the user’s path loss while moving along the waveguide axis.Source: 1) Achievable CR and SR · p. 9
  • As Dx increases, fixed-antenna and S-C PASS CR decline, while C-C PASS achieves higher CR than the fixed-antenna benchmark.The decline is attributed to growing average distance between the user and the waveguide center or the S-C activated location.Source: 1) Achievable CR and SR · p. 9
  • The S-C PASS CR disadvantage follows from user-target separation being triangular over [0, Dx], versus uniform user-to-center distance over [0, Dx/2] for fixed antennas.The triangular distribution yields a larger average transmission distance and thus reduced CR.Source: 1) Achievable CR and SR · p. 9
  • In-waveguide propagation loss affects SR more than CR because it attenuates signals on both transmit and receive waveguides, while CR depends only on transmit-waveguide loss.Source: 1) Achievable CR and SR · p. 9
  • Despite waveguide loss, S-C PASS achieves higher SR than the fixed-antenna system, while C-C PASS equals or exceeds its SR.Receive-side activation aligned with the target reduces degradation from mismatch with the C-C transmit-side activation.Source: 1) Achievable CR and SR · p. 9

2) Rate Region: … VI. CONCLUSION

The paper characterizes the CR-SR rate region of PASS-assisted ISAC and finds that PASS outperforms conventional fixed-antenna systems even with in-waveguide loss. Time sharing approximates the single-pinch region, while multiple-pinch systems require optimized pinching beamforming for a desirable trade-off.

2) Rate Region:

  • For single pinches, C-C/S-C time sharing suffices when xc is far from xs, but the full region requires rate-profile optimization plus time sharing as xc nears xs.The region becomes increasingly rectangular as the communication user and sensing target align along the transmit-waveguide axis.Source: 2) Rate Region · pp. 9–10
  • The average single-pinch PASS rate region exceeds the conventional fixed-antenna region despite in-waveguide loss, and S-C/C-C time sharing closely approaches the complete region.Propagation loss narrows the region and affects SR more than CR.Source: Figure 6 · p. 10, 2) Rate Region · p. 10

1) Achievable CR and SR:

  • Under C-C design, CR increases with pinching-antenna count and exceeds the conventional system; under S-C design, SR increases and exceeds it, while propagation loss affects SR more.In-waveguide loss has negligible impact on C-C CR; S-C CR is lower than conventional performance because its sensing-optimal beamformer mismatches the communication channel.Source: Figure 7 · p. 10, 1) Achievable CR and SR · p. 10

B. Multiple-Pinch Case — 2) Rate Region:

  • For multiple pinches, inner and outer bounds closely align, but C-C/S-C time sharing fails to approach the full region, making optimized beamforming necessary.The bounds converge further as xc approaches xs, and the region becomes increasingly rectangular.Source: Figure 8 · p. 10, 2) Rate Region · pp. 10–11
  • The average multiple-pinch PASS rate region is substantially larger than the conventional fixed-antenna region in both ideal and lossy scenarios.Increasing the number of pinching antennas further enlarges the achievable region.Source: Figure 9 · p. 11, 2) Rate Region · p. 11

VI. CONCLUSION:

  • The study derives single-pinch regions through rate-profile optimization and time sharing, and multiple-pinch bounds through alternating optimization and relaxation techniques.Its simulations find a more favorable CR-SR trade-off than conventional fixed-antenna systems, with the multiple-pinch case requiring careful beamformer design.Source: §VI · p. 11

APPENDIX · A. Proof of Lemma 1 · B. Proof of Lemma 2

The appendix derives the sensing mutual-information expression through a virtual SIMO channel and shows that maximizing sensing rate is equivalent to minimizing the target’s estimation error.

A. Proof of Lemma 1

  • The echo signal is modeled through the capacity of a virtual SIMO Gaussian channel with Gaussian-distributed RCS input β_RCS ∼ CN(0, α_s).Source: A. Proof of Lemma 1 · p. 11
  • The virtual channel vector is h(u_s, t)s^T, with the corresponding virtual noise defined using the receive phase φ_r and noise vector n^T.Source: A. Proof of Lemma 1 · p. 11
  • The sensing mutual information is given by; Sylvester’s identity and |φ_r|^2 = 1, L^-1∥s∥^2 = 1 yield the expression in (15).Source: A. Proof of Lemma 1 · p. 11

B. Proof of Lemma 2

C. Proof of Theorem 1 … Karamata’s inequality:

The proofs characterize the single-pinch Pareto-optimal rate profile, establish inclusion of fixed-antenna rate pairs in the PASS region, and use extreme-point and majorization arguments for Lemma 3.

C. Proof of Theorem 1

  • The Pareto-optimal activated location must lie between xc and xs, since reflecting a location outside that interval preserves one rate and improves the other.The proof rules out t1 < xc by reflecting it about xc, and t1 > xs by reflecting it about xs.Source: C. Proof of Theorem 1 · p. 12
  • Parameterizing t1 = xc + β∆x reduces the rate-profile search to endpoint cases or the intersection fc(β) = fs(β), found by bisection.The optimum is β = 1 when fc(1) ≥ fs(1), β = 0 when fc(0) ≤ fs(0), and otherwise occurs where the two functions intersect.Source: C. Proof of Theorem 1 · p. 12

D. Proof of Theorem 2

  • For any fixed-antenna location xf, its rate pair lies within the PASS region CS; the proof compares rates at xc, xs, or xf according to xf’s position.When xf < xc, choosing t1 = xc improves both rates; when xf > xs, choosing t1 = xs improves both; between them, t1 = xf matches the fixed-antenna pair.Source: D. Proof of Theorem 2 · p. 12

E. Proof of Lemma 3

  • Lemma 3 invokes Bauer’s maximum principle: a convex continuous function on a convex compact set attains its maximum at an extreme point.The proof applies this principle to the function and set under consideration.Source: E. Proof of Lemma 3 · p. 12
  • The resulting variables are set to 0 or 1, with at most one intermediate value when their total Sβ is not an integer.This describes the structure of the maximizing variables in the proof.Source: E. Proof of Lemma 3 · p. 12

Karamata’s inequality:

  • For a convex function, majorization implies that the sum over the majorizing vector is at least the sum over the other vector, given equal totals; strict convexity makes the inequality strict unless they match.Majorization requires partial-sum dominance through k − 1 and equality of the full sums.Source: Karamata’s inequality · p. 12
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