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Secure Near-Field ISAC with Pinching-Antenna Systems: Exploiting Constructive-Destructive Interference

Dimitrios Bozanis, Vasilis K. Papanikolaou, Sotiris A. Tegos, Panagiotis D. Diamantoulakis, Christos Masouros, George K. Karagiannidis

arXiv:2609.32715v1eess.SP

TL;DR

Secure near-field ISAC with PASS must support communication and localization while preventing a sensing target from decoding confidential data. The paper jointly optimizes symbol-level precoding and antenna positions, using constructive and destructive interference alongside an exact PEB factorization. Simulations report sub-millimeter localization, erroneous target decisions, and gains over fixed-placement PASS and XL-MIMO benchmarks.

  • Problem

    Joint design of SLP and PA placement for secure Cartesian localization, including how the apertures contribute to localization and whether the combination expands feasibility, remains unexplored.

    Source: B. Motivation and Contributions · p. 2

  • Method

    The paper derives a PEB factorization and separates receive placement from joint transmit placement and per-symbol SLP design under CI and DI constraints.

    Source: E. CI and DI Regions · p. 4, §VI · p. 11

  • Results

    0.11 mm APEB for optimized PASS versus 1.17 mm for XL-MIMO, with optimized PASS feasible in each deployment up to 40 dB and in 90% of deployments at 45 dB.

    Source: §V · p. 10

  • Takeaways & Limitations

    PASS reconfigurability shapes receive geometry to achieve accurate localization with only a few RF chains, while the target made erroneous symbol decisions in every simulated sample.

    Source: §VI · p. 11

    Multiple pinching antennas per waveguide, imperfect target-position knowledge, and placement driven by global bounds accounting for ambiguities are left for future work.

    Source: §VI · p. 11

Abstract

from arXiv · show

This paper investigates secure near-field integrated sensing and communication (ISAC) with pinching-antenna systems (PASS), where a base station serves legitimate users while localizing a target that may also eavesdrop on the transmitted data. We jointly design symbol-level precoding (SLP) and the transmit and receive pinching-antenna positions to minimize the Cartesian position error bound (PEB) averaged over the data symbols. Constructive interference ensures reliable reception at the legitimate users, whereas destructive interference drives the target's observation toward incorrect symbol regions without sacrificing the illumination required for sensing. We derive the PEB for unknown complex target reflectivity and establish an exact factorization into transmit-illumination and receive-geometry terms. This decomposition reveals the distinct sensing roles of the two apertures, enables separate receive-placement and joint transmit-placement/SLP optimization, and provides analytical insights into local position identifiability, the range-information limitations of compact arrays, sensing-oriented receive placement, and in-waveguide attenuation. Building on these results, we develop an efficient algorithm by combining geometry-informed receive initialization, one-dimensional transmit-position searches, and convex per-symbol precoding. Numerical results demonstrate sub-millimeter localization, erroneous symbol decisions at the target, an expanded feasible operating region, and substantial gains over fixed-placement PASS and fully digital extremely large-scale MIMO (XL-MIMO) benchmarks.

I. INTRODUCTION

Secure ISAC must balance reliable communication, accurate sensing, and protection against a target that may eavesdrop. This paper combines PASS placement and symbol-level precoding to study secure Cartesian localization and the roles of the transmit and receive apertures.

I. INTRODUCTION

  • The target can be both the sensing object and an eavesdropper, making illumination a security concern alongside communication QoS and sensing accuracy.The paper frames these competing demands as a communication–sensing–security trade-off.Source: §I · p. 1

A. State of the Art

  • Earlier secure-ISAC studies use fixed-position arrays and do not examine antenna reconfiguration for joint direction and distance estimation under communication and security requirements.Prior PASS work addressed communication, sensing, or security separately, but joint SLP and PA placement for secure Cartesian localization remained unexplored.Source: A. State of the Art · p. 2, B. Motivation and Contributions · p. 2

B. Motivation and Contributions

  • The paper jointly designs SLP and transmit/receive PA positions for Cartesian PEB minimization, enforcing CI for legitimate users and DI toward the target/Eve.It derives the PEB for unknown complex reflectivity, studies receive-geometry and compact-array range-information limits, and characterizes attenuation effects.Source: B. Motivation and Contributions · p. 2
  • PEB factorization separates receive placement from joint transmit placement and SLP design, which the proposed method solves using geometry-informed initialization, one-dimensional searches, and convex per-symbol subproblems.The reported results include sub-millimeter localization and an expanded feasible operating region versus fixed-placement PASS and a compact array.Source: B. Motivation and Contributions · pp. 2–3

A. Pinching-Antenna Model and Network Topology

The indoor PASS topology uses separate transmit and receive waveguides with reconfigurable pinching-antenna positions. Those positions affect propagation through the transmit and receive channel vectors.

A. Pinching-Antenna Model and Network Topology

  • The BS connects to transmit and receive dielectric waveguides mounted parallel to the x-axis, with one RF chain per waveguide.The transmit and receive waveguides are separate, and the system serves multiple single-antenna users plus a point target that may eavesdrop.Source: A. Pinching-Antenna Model and Network… · p. 3
  • The channel model combines spherical-wave free-space propagation with waveguide phase shift and attenuation.Guided power decays as e^-αx along the waveguide.Source: A. Pinching-Antenna Model and Network… · p. 3
  • Each transmit and receive waveguide has a reconfigurable PA position that affects the corresponding channel vector.The transmit positions affect g(·), while the receive positions affect a(·).Source: A. Pinching-Antenna Model and Network… · p. 4

B. Communication Signal Model

The system sends symbol-dependent waveforms to legitimate users while a protected user's stream may be intercepted by the target. Its CI/DI requirements shape the users' and target's observations, while sensing uses the target echo.

B. Communication Signal Model

  • The BS generates a symbol-dependent transmit vector for the users' M-PSK symbols, subject to per-waveguide power limits.The noise-free Bob observation is expressed in a coordinate system rotated by the intended symbol's phase.Source: B. Communication Signal Model · p. 4

C. Eavesdropping Model

  • The target/Eve attempts to decode the protected Bob's stream, with the protected Bob taken as the user nearest the target.The index is set to k = 1 without loss of generality.Source: C. Eavesdropping Model · p. 4

D. Sensing Signal Model

  • The receive PAs collect the target echo, whose signal includes unknown complex target reflectivity; the target is modeled as a static point scatterer.The real and imaginary parts of reflectivity are treated as unknown nuisance parameters.Source: D. Sensing Signal Model · p. 4

E. CI and DI Regions

  • For M-PSK, CI keeps each Bob's observation inside its intended-symbol sector with an SNR-threshold margin, while DI places Eve's observation in a wrong-symbol region with detection margin Γe.The DI region is the union of decision regions for the M − 1 wrong symbols.Source: E. CI and DI Regions · p. 4

III. SENSING METRIC AND GEOMETRIC INSIGHTS

The single-snapshot Cartesian PEB accounts for unknown complex reflectivity and separates sensing information into receive geometry and target illumination. This factorization identifies distinct roles for the receive and transmit apertures.

A. Cartesian Position Error Bound

  • The derived single-snapshot PEB treats complex target reflectivity as a nuisance parameter in the equivalent Fisher information for target position.The PEB lower-bounds the root-mean-square error of any unbiased position estimate.Source: A. Cartesian Position Error Bound · p. 5

2 G(˜xR), (20)

  • The PEB factorizes into a receive-geometry term and a transmit-illumination term, separating the spatial information supplied by receive placement from illumination strength.The geometric term depends only on receive PA positions.Source: §2 · p. 5
  • For fixed receive positions, sensing performance depends on the target-observation magnitude, not its phase; increasing illumination can deepen Eve's observation in a wrong-symbol region.The receive geometry determines the structure of the position information, while transmit placement sets the PEB scale and governs sensing SNR and CI/DI feasibility.Source: §2 · p. 5

B. Geometric Insights

The receive-geometry term measures position information through the spread of power-weighted bearing vectors, yielding conditions for identifiability and revealing limitations of compact arrays. The section also characterizes sensing-oriented placement and the effect of waveguide attenuation.

Geometric information

  • The geometric term is κ² times the power-weighted covariance of receive bearing vectors, with position information coming from their centered spread.Because common phase shifts are indistinguishable from unknown target-reflectivity phase, only differences among receive-PA phase shifts carry position information.Source: B. Geometric Insights · p. 6

Identifiability

  • At least three receive waveguides with noncollinear bearing vectors are required to identify the two-dimensional target position; collinear bearings make the geometry matrix singular.The matrix rank is at most N_R − 1.Source: B. Geometric Insights · p. 6
  • With two receive PAs at different target distances, the amplitude term preserves position identifiability, but the PEB remains larger by order κr_m, making position practically unobservable.Compact arrays likewise provide very limited range information.Source: B. Geometric Insights · p. 6

Compact-array limitation

  • For a uniform aperture, range information is smaller than cross-range information by order A²/R², independently of SNR and snapshot count.For a 4-element λ/2-spaced array at 28 GHz and R = 4 m, range PEB is about 1700 times cross-range PEB.Source: B. Geometric Insights · p. 6

Waveguide attenuation

  • In-waveguide attenuation is paid on the transmit and receive paths, and the PEB doubles every ln 2/α meters.The optimal PA positions relative to the target do not depend on the transmit position x_t.Source: B. Geometric Insights · p. 6

IV. PROBLEM FORMULATION AND PROPOSED SOLUTION

The design jointly selects symbol-level precoding and transmit and receive PA positions, while fixed placements must serve all symbol vectors. Exact PEB factorization separates receive placement from the joint transmit-placement and precoding design.

Problem formulation

  • The design adds transmit- and receive-side PA positions as variables to secure symbol-level precoding, which previously optimized only the transmit vector.Constructive-interference constraints serve the Bobs, while destructive-interference constraints place the target/Eve observation in a wrong-symbol region.Source: §IV · pp. 6–7
  • Because PA positions are held fixed across symbol intervals, the objective minimizes PEB averaged over all equiprobable symbol vectors.Each symbol vector must satisfy the communication, target/Eve, power, and waveguide-placement constraints.Source: §IV · p. 7

Exact decomposition

  • Exact PEB factorization makes the joint problem equivalent to sequential receive-placement, per-symbol precoding, and transmit-placement subproblems.Receive placement is independent of the Bobs, symbols, and transmit side; per-symbol precoding is solved for each symbol vector and transmit placement.Source: §IV · p. 7
  • The factorization separates receive placement exactly and nests per-symbol precoding within transmit placement, avoiding block-iteration without loss of optimality.This differs from PASS designs that couple PA positions and beamformers through the objective and update them by alternating optimization.Source: §IV · p. 7

A. Receive Pinching-Antenna Placement

Receive placement minimizes a smooth geometric objective, with a closed-form characterization for a symmetric three-waveguide layout. The symmetric-layout offset balances range and cross-range information, while general-layout search can depend on initialization.

Arbitrary layout

  • The receive-placement objective is smooth and low-dimensional because channel phases cancel, but it is generally nonconvex and has no closed-form solution for arbitrary layouts.The initialization applies the symmetric-layout offset to each receive waveguide and searches all sign patterns, retaining the best solution.Source: A. Receive Pinching-Antenna Placement · pp. 7–8

Symmetric layout

  • For the symmetric three-waveguide layout, the PEB-optimal offset is a compromise: information on x_t is maximized at δ⋆_x > r⊥, while information on y_t is maximized at δ = 0.The communication-optimal zero offset is least informative about x_t because a small target displacement along the waveguide changes distance only to second order.Source: A. Receive Pinching-Antenna Placement · p. 7

Arbitrary layout

  • For arbitrary layouts, cyclic one-dimensional receive-PA searches converge to a coordinate-wise minimum that depends on the initial placement.Each coordinate update does not increase the geometric objective.Source: A. Receive Pinching-Antenna Placement · pp. 7–8

B. Symbol-Level Precoding for Fixed PA Positions

For fixed PA positions, the precoder maximizes sensing illumination while satisfying communication and wrong-symbol target constraints. Treating each wrong-symbol region separately yields convex subproblems and a bounded approximation to the per-symbol optimum.

Per-symbol precoding

  • The target's destructive-interference region is a union of M − 1 convex cones, so each wrong-symbol cone can be handled separately.Inside a cone, the illumination objective can be replaced by its projection onto the known direction of the candidate wrong symbol.Source: B. Symbol-Level Precoding for Fixed PA… · p. 8
  • Separating wrong-symbol cones makes the precoding subproblems convex and avoids repeated linearization iterations used in earlier secure SLP-ISAC designs.Each subproblem is a second-order cone program with a linear objective.Source: B. Symbol-Level Precoding for Fixed PA… · p. 8
  • The selected feasible precoder's illumination is within a worst-case factor cos Φ of the global optimum, and this factor tends to one as M grows.The method solves the convex problem for each wrong-symbol cone and chooses the solution with largest illumination.Source: B. Symbol-Level Precoding for Fixed PA… · p. 8
  • The target/Eve enters each convex precoding subproblem as a virtual (K + 1)-th Bob through two destructive-interference half-spaces.The constraints are half-spaces or discs, and the numerical solution uses consensus ADMM with closed-form projections.Source: B. Symbol-Level Precoding for Fixed PA… · p. 8

C. Transmit Pinching-Antenna Placement

Transmit placement is optimized through a cyclic candidate search that evaluates positions using a convex per-symbol problem, preserving feasibility. The method uses a surrogate illumination objective and terminates at a coordinate-wise minimum over candidate positions.

C. Transmit Pinching-Antenna Placement

  • The two-scale cyclic search evaluates each candidate transmit-antenna position through the optimal convex per-symbol problem, preserving feasibility of C1–C3 by construction.The transmit placement is the only non-convex block coupled with the symbols, and free-space phases vary on the wavelength scale.Source: C. Transmit Pinching-Antenna Placement · p. 9
  • Transmit antennas are initialized using the communication-optimal placement rule, with waveguide midpoints and a nearby feasible 1 m-grid layout as fallbacks.The nearest waveguide PA is placed relative to its Bob, while remaining PAs are placed at the corresponding target position.Source: C. Transmit Pinching-Antenna Placement · p. 9
  • The placement objective averages reciprocal illumination over symbol classes modulo common rotation, using the Proposition 4 illumination as a surrogate for the optimum.A common symbol rotation leaves illumination unchanged, reducing the expectation to M K−1 symbol vectors.Source: C. Transmit Pinching-Antenna Placement · p. 9
  • The surrogate objective bounds the original objective as J ≤ Ĵ ≤ J/cos Φ, and placements with any symbol vector lacking a feasible subproblem are rejected.Source: C. Transmit Pinching-Antenna Placement · p. 9
  • Accepted placements remain feasible and strictly decrease Ĵ, so the finite candidate search terminates at a coordinate-wise minimum.Each cycle tests Nc positions for each of NT transmit antennas, solving the per-symbol-class and wrong-symbol subproblems with ADMM.Source: C. Transmit Pinching-Antenna Placement · p. 9

V. NUMERICAL RESULTS

The numerical results show that optimized PASS combines sub-millimeter localization with wrong-symbol decisions at the target and expands the feasible QoS range. The conclusion attributes this performance to reconfigurable antenna placement and distinct transmit-illumination and receive-geometry roles.

V. NUMERICAL RESULTS

  • The target/Eve decided a wrong symbol in every simulated sample despite the strong illumination required for sensing.The observations lay deep inside wrong-symbol regions.Source: §V · pp. 9–10
  • Optimized PASS reaches APEB of 0.11 mm versus XL-MIMO’s 1.17 mm, is 29 times better than unoptimized PASS, and uses 64 times fewer RF chains.It is feasible in every deployment through 40 dB and in 90% at 45 dB, compared with 75% and 8% for unoptimized PASS.Source: Figure 3 · p. 10, §V · p. 10
  • With NR=2, APEB is 0.86 m; adding a third receive waveguide reduces it to 0.17 mm, while increasing NT from 2 to 8 halves APEB.The phase term is rank deficient at NR=2, and further receive-waveguide increases give more gradual improvement, reaching 0.075 mm at NR=8.Source: §V · p. 10, Figure 4 · p. 11
  • For receive placement, PEB diverges as δ approaches zero and the lossless minimum occurs near δ≈0.6r⊥; attenuation raises the curve and shifts the optimum slightly lower.With attenuation, in-waveguide losses are paid on both transmit and receive paths, so PEB grows with xt.Source: §V · p. 10, Figure 5 · p. 11
  • For K=2, optimized PASS is feasible in 90% of deployments at Γk=45 dB, and for K=2 or 3 remains below 0.17 mm APEB through 40 dB.With one Bob, it is feasible at every tested threshold and deployment, with APEB flat at 0.11 mm.Source: Figure 6 · p. 11, §V · p. 11

VI. CONCLUSION

  • The conclusion reports that exact PEB factorization separates receive placement from joint transmit placement and SLP, with convex per-symbol subproblems, and that PASS achieves sub-millimeter localization with few RF chains.It identifies multiple pinching antennas per waveguide, imperfect target-position knowledge, and global ambiguity-aware bounds as future work.Source: §VI · p. 11

APPENDIX A PROOF OF LEMMA 1

The appendices derive the Cartesian PEB with unknown complex reflectivity and express the receive-channel derivative through bearing and range-dependent terms.

APPENDIX A PROOF OF LEMMA 1

  • The PEB is the CRB on the root-mean-square error of the position estimate.Source: Appendix A · p. 11
  • The derivation accounts for unknown complex reflectivity through a Schur complement before obtaining the stated PEB expression.Source: Appendix A · p. 12

APPENDIX B PROOF OF LEMMA 2

  • The receive-channel derivative matrix is decomposed into a phase term and a range-dependent term, with the latter of relative order (κr_m)^-2.Source: Appendix B · p. 12

APPENDIX C PROOF OF COROLLARY 1

The appendices establish a unique PEB-minimizing receive offset and derive a convex dual formulation for the per-symbol precoding subproblem.

APPENDIX C PROOF OF COROLLARY 1

  • The PEB has a unique minimum at the offset corresponding to the unique positive root t⋆ of q(t), and δ⋆<r⊥.Source: Appendix C · p. 12

APPENDIX D PROOF OF LEMMA 3

  • For every waveguide with ζ_n≠0, the optimal power constraint is active; when ζ_n=0, feasibility and equalities determine x_n.Source: Appendix D · p. 13
  • Under the assumed Slater condition, the convex precoding subproblem and its convex dual have equal optimal values.Source: Appendix D · p. 13

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