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Joint Pinching-Antenna Position and Power Optimization for Dual-Waveguide ISAC Systems

Saeid Pakravan, Imene Trigui, Wessam Ajib, Wei-Ping Zhu

arXiv:2610.11987v1eess.SP

TL;DR

Fixed-position arrays constrain spatial reconfiguration for ISAC, and localization-aware joint design is less explored when the communication user is also the sensing target. This paper jointly optimizes transmit and receive PA positions and transmit power using an alternating approach. Its design achieves higher communication rates than the considered benchmarks, with more pronounced gains under stringent localization requirements.

Abstract

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Pinching-antenna (PA) systems provide spatial reconfigurability for integrated sensing and communication (ISAC) through controllable radiation locations along dielectric waveguides. This paper investigates a dual-waveguide PA-assisted ISAC system in which the communication user also serves as the sensing target, coupling the communication and sensing links through a common user/target geometry. Spatially separated transmit and receive waveguides provide separate spatial control over the forward and return sensing paths. We jointly optimize the transmit and receive PA positions and transmit power to maximize the aggregate communication rate subject to minimum sensing-SNR and two-dimensional localization Cramer-Rao bound (CRB) requirements, along with power, energy, and deployment constraints. To solve the resulting non-convex problem, we develop an alternating optimization algorithm that combines a bounded water-filling power update with a proximal first-order joint PA-position update. Numerical results show that the proposed design achieves higher communication rates than the considered benchmarks, with more pronounced gains under stringent localization requirements.

I. INTRODUCTION

Fixed-position antenna arrays limit spatial reconfiguration for ISAC, while localization-aware joint design with the communication user as target remains less explored. This paper develops a dual-waveguide framework and alternating optimization approach, reporting rate gains over considered benchmarks, particularly under stringent localization requirements.

I. INTRODUCTION

  • Fixed-position arrays limit spatial reconfiguration, while jointly meeting communication, sensing-SNR, and localization-CRB requirements with transmit power and both PA positions remains a coupled non-convex problem.The communication user itself also serves as the localization target, coupling communication and sensing through a common geometry.Source: §I · p. 1, B. Motivation and Main Contributions · p. 2

A. Related Works

  • Prior PA-assisted ISAC work spans communication–sensing trade-offs, resource allocation, multi-waveguide architectures, and CRB-based localization, but explicit localization requirements for a communication user as target remain less explored.The paper also identifies joint transmit/receive PA placement and transmit-power optimization under these requirements as a coupled design challenge.Source: A. Related Works · pp. 1–2, B. Motivation and Main Contributions · p. 2

B. Motivation and Main Contributions

  • The framework models communication and echo-based sensing, using sensing SNR and position CRB to characterize sensing quality and localization accuracy.The user is the shared communication endpoint and sensing target, while separated waveguides allow separate transmit- and receive-PA configuration.Source: B. Motivation and Main Contributions · pp. 2–3
  • The joint optimization maximizes achievable communication rate subject to sensing-SNR, localization-CRB, energy, antenna-spacing, and waveguide-deployment constraints.The paper uses alternating optimization with a water-filling-type power update and iterative PA-position optimization.Source: B. Motivation and Main Contributions · p. 3
  • The proposed design achieves communication-rate gains over fixed-position, partially optimized, and single-waveguide benchmarks, particularly under stringent localization requirements.The design jointly configures transmit and receive PA positions and transmit power.Source: B. Motivation and Main Contributions · pp. 2–3

II. SYSTEM MODEL AND PROBLEM FORMULATION

The system uses spatially separated transmit and receive waveguides, with the communication user also serving as the sensing target. PA locations are reconfigurable along each waveguide, and the channel model accounts for guided and free-space propagation.

II. SYSTEM MODEL AND PROBLEM FORMULATION

  • The transmit waveguide radiates the dual-functional communication–sensing signal, while the separated receive waveguide collects the reflection from the same user/target.The user/target is located on the ground plane in the stated three-dimensional coordinate system.Source: §II · p. 3, Figure 1 · p. 3

A. System Geometry and PA Deployment

  • Each PA location has a configurable coordinate along its waveguide, with the waveguide’s lateral position and height fixed.The waveguides extend along the x-axis, and their transmit and receive deployments are spatially separated.Source: A. System Geometry and PA Deployment · p. 3
  • PA positions can be reconfigured at the beginning of each time slot and remain fixed during that slot; each waveguide’s feed point is at its beginning.The waveguide deployments differ in their fixed lateral position and height.Source: A. System Geometry and PA Deployment · p. 3
  • The geometry distinguishes the free-space distance from the user/target to a PA from the guided distance between the feed point and that PA.These are separate propagation distances associated with the user link and waveguide deployment.Source: A. System Geometry and PA Deployment · p. 3

B. Waveguide-Aware Channel Model

  • The channel model is line-of-sight-dominated and spherical-wave-based, accounting for free-space and guided-wave propagation while neglecting small-scale fading and mutual coupling.The guided wavelength is defined as the free-space wavelength divided by the waveguide’s effective refractive index.Source: B. Waveguide-Aware Channel Model · p. 3
  • Transmit coupling coefficients are fixed and nonnegative, and transmit power denotes the budget at the waveguide input; receive coupling efficiencies are fixed rather than optimized.Equal transmit coupling is identified as a special case.Source: B. Waveguide-Aware Channel Model · pp. 3–4
  • Each PA contributes to the effective propagation response through a term whose phase accounts for both free-space and guided-wave propagation.The response model includes the waveguide’s amplitude attenuation coefficient.Source: B. Waveguide-Aware Channel Model · p. 4
  • The same effective response model is used for the base-station-to-user transmit link and the user/target-to-base-station receive link.The functional dependence is omitted when it is unambiguous.Source: B. Waveguide-Aware Channel Model · p. 4

C. Communication and Echo-Sensing Models

The model uses the same user as communication receiver and sensing target, with the transmitted waveform reflected back through a cascaded sensing link. Communication rate and echo quality are characterized separately, with spatially separated waveguides controlling the sensing paths.

C. Communication and Echo-Sensing Models

  • The received communication signal yields a communication SNR and an achievable rate, with system bandwidth denoted by B.The transmitted dual-functional waveform has unit average power, and P_t is the total transmit power.Source: C. Communication and Echo-Sensing Models · p. 4
  • The user is modeled as a point scatterer and sensing target; its effective sensing coefficient is assumed available from prior sensing or calibration and constant within each sensing interval.The localization CRB is evaluated conditionally on that coefficient.Source: C. Communication and Echo-Sensing Models · p. 4
  • The sensing echo follows a cascaded transmit–target–receive response, and its SNR characterizes received-echo quality for a minimum sensing-reliability requirement.Separate transmit and receive waveguides provide distinct configurable responses for the forward and reflected paths.Source: C. Communication and Echo-Sensing Models · p. 4

D. Localization Model

The localization model evaluates position information locally at a nominal target estimate and uses the CRB to quantify estimation accuracy beyond echo quality. The resulting design jointly maximizes communication rate subject to sensing, localization, power, energy, and deployment requirements.

D. Localization Model

  • The CRB complements sensing SNR by measuring localization accuracy, and for a nonsingular FIM it lower-bounds the sum of estimation-error variances in the two location coordinates.Configurations lacking sufficient information for two-dimensional localization receive an infinite localization-error bound.Source: D. Localization Model · p. 4
  • The two-dimensional target position is unknown, while the FIM and CRB are evaluated locally at a nominal location estimate obtained from prior localization or tracking.Transmit and receive PA positions jointly determine sensing-response spatial derivatives and thus the localization information in the echo.Source: D. Localization Model · pp. 4–5

E. Problem Formulation

  • The optimization maximizes aggregate achievable communication rate by jointly selecting transmit power and transmit/receive PA positions under sensing, localization, power, energy, and PA-deployment requirements.The constraints include minimum sensing SNR and a maximum localization CRB, as well as per-slot power, total energy, feasible intervals, and adjacent-PA spacing.Source: E. Problem Formulation · p. 5
  • The problem is non-convex because rate, sensing SNR, and localization CRB depend nonlinearly and jointly on PA positions and transmit powers.The sensing-SNR constraint depends on a product of transmit and receive channel gains, while localization uses the inverse of a configuration-dependent FIM.Source: E. Problem Formulation · p. 5

III. PROPOSED AO-BASED SOLUTION

The solution alternates between transmit-power and joint PA-position updates to address the coupled non-convex problem. For fixed PA positions, power allocation has a water-filling-type solution subject to sensing, localization, and energy feasibility.

III. PROPOSED AO-BASED SOLUTION

  • The AO framework successively updates transmit powers and PA positions because communication rate, sensing SNR, and localization CRB are coupled through both variable sets.The power update fixes positions, while the position update fixes powers.Source: §III · p. 5

A. Transmit-Power Optimization

  • For fixed PA positions, the transmit-power subproblem is convex and admits a closed-form water-filling-type solution.The power allocation respects the sensing-SNR and localization requirements.Source: §III · p. 5, A. Transmit-Power Optimization · p. 5
  • Power allocation is feasible only when the unit-power FIM is nonsingular in every slot and the minimum required powers fit the total-energy budget.Increasing power cannot remove localization degeneracy when the unit-power FIM is singular in any slot.Source: A. Transmit-Power Optimization · p. 5
  • When the total-energy constraint is active, KKT conditions determine a dual variable that can be found by bisection because allocated energy is nonincreasing in that variable.If maximum per-slot power already satisfies the energy budget, the optimum instead uses P_t = P_max in every slot.Source: A. Transmit-Power Optimization · p. 6

B. Joint PA-Position Optimization

With powers fixed, the method jointly refines transmit and receive PA positions, using their spatial degrees of freedom for communication and sensing/localization. A proximal first-order update is solved as a convex quadratic program and accepted only when original constraints and objective monotonicity are preserved.

B. Joint PA-Position Optimization

  • Transmit and receive PA positions are optimized jointly because receive-side positions affect sensing SNR and localization FIM even though they do not directly affect communication rate.The transmit positions can then be adjusted for communication performance while both PA sets support sensing and localization requirements.Source: B. Joint PA-Position Optimization · p. 6
  • The position update approximates sensing-SNR and CRB constraints around the current feasible configuration and uses proximal regularization to control displacement.Affine local constraints and quadratic regularization make the update a convex quadratic program; zero displacement remains feasible for the local constraints.Source: B. Joint PA-Position Optimization · p. 6
  • Backtracking checks each candidate against the original sensing-SNR and CRB constraints and accepts only feasible steps that do not decrease communication objective.If no acceptable step is found, the current PA configuration is retained; slot updates are separable and can be carried out in parallel.Source: B. Joint PA-Position Optimization · p. 6

C. Complexity and Convergence Analysis

The analysis gives the computational costs of the power and position updates and shows that the AO objective converges to a finite value. The position updates are separable across time slots, and each uses a convex QP.

C. Complexity and Convergence Analysis

IV. NUMERICAL RESULTS

The numerical study evaluates the communication–localization trade-off and the benefits of jointly optimizing transmit power and both PA deployments. Its setup uses separated 10 m waveguides and averages results over 500 user/target-location realizations unless otherwise specified.

IV. NUMERICAL RESULTS

  • The numerical results evaluate the communication–localization trade-off and joint optimization of transmit power and transmit and receive PA positions.The section assesses the proposed dual-waveguide PA-assisted ISAC framework.Source: §IV · p. 7

A. Simulation Setup

  • The transmit and receive waveguides are each 10 m long, positioned at yTx = −1 m and yRx = 1 m, with six PAs on each.The waveguide height is 3 m; the carrier frequency is 28 GHz and the effective refractive index is 1.4.Source: A. Simulation Setup · p. 7
  • Unless stated otherwise, results average 500 independent Monte Carlo realizations of user/target locations uniformly drawn from [−5, 5] × [8] m2.The effective sensing coefficient is normalized as |βt| = 1.Source: A. Simulation Setup · p. 7

B. Benchmark Schemes

Across the considered benchmarks, the proposed design achieves the highest communication rate, with more pronounced gains under stringent sensing and localization requirements. The results also show that transmit and receive PA resources affect rate differently, and that adaptive power allocation adds benefit.

B. Benchmark Schemes

  • The benchmark set includes shared-waveguide, Tx-Only, Rx-Only, Fixed-PA, and Equal-Power Allocation schemes.The schemes respectively constrain transmit/receive positions to coincide, fix receive PAs, fix transmit PAs, fix both PA deployments, or allocate energy equally across time slots.Source: B. Benchmark Schemes · p. 7
  • For all considered PA configurations, the achievable rate increases monotonically over AO iterations and approaches a stable value; more PAs improve the converged rate.Fig. 2 presents the algorithm's convergence behavior.Source: B. Benchmark Schemes · p. 7, Figure 2 · p. 8
  • The proposed design consistently achieves the highest rate, with more pronounced gains under stringent localization and sensing requirements.The rate-versus-localization-CRB and rate-versus-sensing-SNR comparisons support this overall result.Source: Figure 3 · p. 8, Figure 4 · p. 8, B. Benchmark Schemes · p. 8
  • As maximum transmit power increases, all schemes achieve higher rates, while the proposed design's advantage over Equal-Power Allocation grows.The Single-Waveguide and Tx-Only schemes have lower rates with reduced spatial flexibility; Rx-Only and Fixed-PA have more limited gains when transmit PAs cannot be jointly adapted.Source: Figure 5 · p. 8, B. Benchmark Schemes · p. 8
  • Increasing the number of transmit PAs substantially improves rate with diminishing incremental gains, while adding receive PAs yields a more moderate improvement.Transmit PAs directly shape the communication channel; receive PAs affect rate indirectly through sensing and localization constraints. Equal-Power Allocation remains slightly inferior as spatial resources increase.Source: B. Benchmark Schemes · pp. 8–9, Figure 6 · p. 9

V. CONCLUSION

  • Transmit and receive PA counts have distinct impacts: transmit PAs shape communication directly, whereas receive PAs provide sensing flexibility but smaller rate gains.The conclusion identifies independently reconfigurable transmit and receive deployments as having potential to enhance the communication–sensing trade-off.Source: B. Benchmark Schemes · p. 8, §V · p. 9

APPENDIX A

With PA positions fixed, the power-allocation subproblem is convex when the configuration admits feasible power. Its solution uses a dual variable found by bisection when the total-energy constraint is active.

APPENDIX A

  • For fixed PA positions, the power-allocation objective includes the per-slot rate term B log2(1 + atPt).The passage states that the subproblem is convex when the fixed PA configuration admits a feasible power allocation.Source: Appendix A · p. 9
  • When the total-energy constraint is active, the dual variable ν is selected to meet the energy budget and can be found efficiently by bisection.Allocated energy is nonincreasing in ν.Source: Appendix A · p. 9
  • If the per-slot maximum powers fit within the total-energy budget, that constraint is inactive and the optimal power is Pmax in every time slot.The objective is increasing in each Pt.Source: Appendix A · p. 9

APPENDIX B

Appendix B provides analytical derivatives used in the joint PA-position update. It covers channel, communication-rate, sensing-SNR, and CRB-gradient calculations.

APPENDIX B

  • The appendix supplies analytical derivatives for the joint PA-position update in (29).It begins with the channel coefficient associated with a PA on either the transmit or receive waveguide.Source: Appendix B · pp. 9–10
  • The communication-rate derivative is given for a real PA coordinate and is zero for a receive-PA coordinate.Source: Appendix B · pp. 9–10
  • The sensing-SNR derivative is formed for an arbitrary PA coordinate, with the other waveguide denoted by ¯i.Source: Appendix B · p. 10
  • For the CRB gradient, the appendix defines v_t from the derivative of µ_t with respect to ξ_t and expresses the FIM compactly.Source: Appendix B · p. 10
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