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ARCTAN: Arbitrary RF Containment Using Tactical Aerial Networks and Differentiable Ray Tracing

Samuel Rivera, Zhihui Gao, Yiming Li, Tingjun Chen

arXiv:2610.00752v1eess.SPcs.NI

TL;DR

Aerial base stations can leak usable signal beyond their intended service area, while prior cooperative-jamming defenses often depend on adversary-location assumptions or simplified channels. ARCTAN jointly optimizes base stations and jammers through differentiable ray tracing; across three target-zone geometries, it reports mean in-zone SINR near 10 dB and substantially lower signal-leakage ratios.

  • Problem

    Aerial base-station broadcasts can leak beyond the service area, and prior cooperative-jamming defenses often assume known adversary locations, simplified channels, or continuously repositioned jammers.

    Source: §I · p. 1

  • Method

    ARCTAN jointly optimizes ABS and CJ positions, orientations, and transmit powers using differentiable ray tracing and learnable CJ activation gates.

    Source: §I · p. 1

  • Results

    Across Circle/L-Shape/Square zones, mean in-zone SINR is 10.0/9.7/9.6 dB and signal-leakage ratios fall from 94.7%/94.9%/93.2% to 43.9%/42.4%/45.2%.

    Source: §I · p. 1

  • Takeaways & Limitations

    ARCTAN’s results support denying usable signal beyond a mission-defined boundary in realistic propagation environments through gradient-based optimization.

    Source: §VI · pp. 6–7

Abstract

from arXiv · show

Aerial base stations (ABSs) can rapidly establish connectivity in ad hoc, infrastructure-deprived environments, but their broadcast, line-of-sight transmissions leak far beyond the intended service area, exposing communications to passive eavesdropping and interference. Prior physical layer defenses based on cooperative jamming typically assume known eavesdropper locations, simplified statistical channels, or continuously repositioned jammers. We instead pose the problem as a radio frequency (RF) containment: confining usable signal to a user-defined, arbitrarily-shaped target zone while denying it elsewhere independent of eavesdropper location. We present ARCTAN, a gradient-based optimization framework that jointly optimizes the position, orientation, and transmit power of stationary ABSs and cooperative jammers (CJs) by backpropagating through site-specific, differentiable 3D ray traced channels. Evaluated in a high-fidelity digital twin across three target zone geometries, ARCTAN achieves a mean in-zone SINR of approximately 10 dB while reducing mean out-of-zone SINR from 13-16 dB to -3-5 dB, and suppressing signal-leakage ratios from over 93% to below 46% requiring at most 10 of 12 candidate CJs.

I. INTRODUCTION AND MOTIVATION

Aerial base stations provide rapid connectivity, but their broadcast signals can leak beyond the service area, while existing cooperative-jamming defenses often rely on known adversary locations, simplified channels, or repositioned jammers. ARCTAN frames this as RF containment and jointly optimizes aerial base stations and cooperative jammers to serve an arbitrary target zone while suppressing usable signal outside it.

I. INTRODUCTION AND MOTIVATION

  • Prior cooperative-jamming defenses often assume known or bounded adversary locations, simplified channel models, or continuous jammer repositioning.These constraints motivate a design that reasons over the environment and the whole target zone instead.Source: §I · p. 1
  • RF containment is defined as confining usable signal to an arbitrarily shaped, user-defined target zone while denying it elsewhere, independent of eavesdropper location.The operational goal is to drive outside-zone SINR below a conventional receiver’s decoding threshold, not to attenuate the radiated field.Source: §I · p. 1
  • ARCTAN jointly optimizes ABS and CJ configurations using differentiable ray tracing rather than statistical channel approximations, tailoring coverage to the physical environment.Learnable activation gates select a minimally viable set of CJs under sustained operation.Source: §I · p. 1
  • Across Circle/L-Shape/Square zones, ARCTAN achieves mean in-zone SINR of 10.0/9.7/9.6 dB and reduces signal leakage from 94.7%/94.9%/93.2% to 43.9%/42.4%/45.2%.The evaluation uses Sionna RT and a high-fidelity Geo2SigMap digital twin.Source: §I · p. 1

II. RELATED WORKS

Prior physical-layer security and secrecy-region approaches face constraints including adversary-location assumptions, simplified channel models, and limited zone geometries. ARCTAN combines site-specific ray tracing with operator-defined target zones, within a low-altitude aerial network of service ABSs and cooperative jammers.

II. RELATED WORKS

  • Earlier cooperative-jamming approaches commonly assume known or bounded adversary locations, continuously reposition jammers, or use statistical channels that miss multipath-rich propagation.Some low-probability-of-detection approaches also trade concealment for sustained high-throughput communication.Source: §II · p. 2
  • Prior spatial secrecy-region methods use rudimentary zones and simplified line-of-sight geometries, while ARCTAN supports arbitrary operator-defined zones with site-specific ray-traced channels.ARCTAN reframes the objective from concealing a transmission to denying its usability beyond the target zone.Source: §II · p. 2

A. Network Model and Node Roles

  • The network comprises low-altitude ABS service nodes and co-channel CJs, modeled as steerable point sources with shared location, steering-angle, and transmit-power parameters.ABSs use directional 3GPP TR 38.901 antenna patterns, whereas CJs use isotropic antennas as broad-area interferers.Source: A. Network Model and Node Roles · p. 2

B. Coverage Zones and Sampled Receiver (RX) Locations

The system defines an operator-bounded target zone within an outdoor operational area and evaluates sampled receiver locations inside and outside it. Its site-specific ray-traced channels model geometry-dependent multipath, with path powers combined incoherently for smoother optimization.

B. Coverage Zones and Sampled Receiver (RX) Locations

  • The operator-defined target zone Z may have any bounded shape and may overlap buildings, which are masked out before the outdoor area is split into interior and exterior zones.The sampled receiver set approximates integration over the target zone and its complement.Source: B. Coverage Zones and Sampled Receiver… · p. 2

C. Channel Model

  • Ray tracing resolves each airborne-to-receiver link into geometry-dependent paths with delay, attenuation, and phase, including site-specific multipath interactions.The received power combines path energies incoherently, making the objective less sensitive to sub-wavelength phase alignment and smoother for gradient-based optimization.Source: C. Channel Model · pp. 2–3
  • Figure 1 traces the workflow from the Duke Campus quad to a modeled operational area, initialized target zone and nodes, and optimized spatial coverage.The final panel provides the visual comparison with the initial deployment setup.Source: Figure 1 · p. 3

D. Best-Server SINR

The best-server formulation evaluates the strongest achievable ABS SINR at each receiver while accounting for interference from other ABSs and CJs. ARCTAN seeks high SINR inside the target zone and low SINR outside it, using jointly optimized ABSs and CJs.

D. Best-Server SINR

  • At each receiver, the serving ABS is the one with the highest SINR, modeling an idealized handoff that reports the best achievable SINR.CJ-induced interference and noise are common to all candidate serving links at that receiver.Source: D. Best-Server SINR · p. 3

IV. PROBLEM FORMULATION AND ALGORITHM

  • The containment objective raises SINR across Zin for intended users and lowers it across Zout to reduce wasted power, interference, and external observability.The formulation denies usable signal beyond the operator-defined zone without relying on a particular adversary location.Source: §IV · p. 3
  • ABSs control the desired-signal numerator while CJs raise the exterior interference floor, but each role can also degrade SINR in the other region.The coupled leakage and interference effects mean containment cannot be achieved by optimizing the two node roles separately.Source: §IV · p. 3
  • Noise-like CJs suppress exterior SINR by adding interference; unlike targeted nulling, they require no inter-platform coordination and can blanket broad, non-convex areas.The passage also contrasts this approach with adding an ABS outside the zone, which creates coverage rather than suppressing it.Source: §IV · p. 3

A. Optimization Problem

ARCTAN jointly optimizes airborne-node configurations and CJ activity to improve in-zone coverage, reduce exterior leakage, and promote uniform in-zone SINR. Its objective combines these goals through separate losses and operator-selected weights.

A. Optimization Problem

  • ARCTAN jointly optimizes airborne-node configurations Θ and CJ-selection parameters Ψ to maximize SINR coverage in Zin and suppress leakage in Zout, subject to physical limits.The objective includes in-zone coverage, outside leakage, in-zone uniformity, and CJ-activity terms.Source: A. Optimization Problem · p. 3
  • The in-zone loss rewards higher average SINR and penalizes locations below threshold γ, with extra weight on improving mean SINR.The softplus approximation supplies nonzero gradients near the threshold; µin = 3.0 weights increases in mean in-zone SINR.Source: A. Optimization Problem · p. 4
  • The outside loss penalizes locations above threshold γ and reduces average SINR across Zout, with µout = 1.0 controlling the trade-off.The two terms target above-threshold exterior locations and the overall exterior SINR level.Source: A. Optimization Problem · p. 4
  • The uniformity loss reduces spatial SINR variation within Zin and penalizes locations below the acceptable level η = 10 dB.The loss uses the variance across in-zone receiver samples and a penalty for SINR shortfalls.Source: A. Optimization Problem · p. 4
  • Learnable CJ activity indicators are encouraged to be sparse, then thresholded at νth = 0.5 to select active jammers for final SINR evaluation.The four objective weights are λin = 2.0, λout = 8.0, λu = 0.1, and λg = 3.0, reflecting operator priorities.Source: A. Optimization Problem · p. 4

B. The ARCTAN Algorithm

ARCTAN initializes ABSs and CJs from the target-zone geometry, then optimizes ABSs first and jointly optimizes ABSs and CJ activity. The figure shows deployment and SINR distributions across three zone geometries.

B. The ARCTAN Algorithm

  • The initialization procedure places nodes at geometrically suitable, unobstructed locations to give the optimizer a favorable starting basin.The available platform counts determine the numbers of ABSs and candidate CJs.Source: B. The ARCTAN Algorithm · p. 4
  • ABSs start at spatially separated points on the target-zone boundary, while candidate CJs form a uniformly spaced ring at a fixed standoff distance.The ABS seeds come from clustered random candidates projected to the boundary; their azimuths point toward the zone center.Source: B. The ARCTAN Algorithm · p. 4
  • The two-stage optimization first adjusts ABSs with CJs off, then jointly optimizes ABS configurations and CJ gates while seeking to preserve interior coverage.The first stage establishes uniform interior coverage; the second activates CJs that reduce exterior leakage.Source: B. The ARCTAN Algorithm · pp. 4–5
  • For Circle, L-shape, and Square zones, Fig. 2 compares initial ABS-only, optimized ABS-only, and jointly optimized ABS-and-CJ deployments, plus three SINR differences.The difference panels show ABS-driven uniformity improvement, CJ-induced exterior degradation, and the total coverage shift from initial to optimized configurations.Source: Figure 2 · p. 5

A. 3D Scene and Target Zone Generation

The evaluation scene is built from geographically accurate 3D environment geometry, while target zones and building footprints are represented as planar polygons. Differentiable ray tracing supplies propagation information for direct optimization of airborne-node configurations.

A. 3D Scene and Target Zone Generation

  • Geo2SigMap generates geographically accurate 3D environment geometry directly from target-area latitude-longitude coordinates.Scene geometry determines modeled reflection, diffraction, and other per-interaction behavior that affects coverage-prediction fidelity.Source: A. 3D Scene and Target Zone Generation · p. 5
  • The scene is exported in Mitsuba 3-compliant form and imported into Sionna RT for evaluation.The exported scene references triangle-mesh objects of the layout.Source: A. 3D Scene and Target Zone Generation · p. 5
  • Target zones are represented as ordered polygon vertices, with curved boundaries approximated by densifying vertices; building contours are unioned into A0.Zin and Zout are then constructed from the zone and building geometry.Source: A. 3D Scene and Target Zone Generation · p. 5
  • Differentiable traced paths let ARCTAN directly optimize Θ and Ψ over downlink propagation from each airborne node to sampled receiver locations.The samples lie in Zin or Zout, and ray calculations use Sionna’s point-to-point PathSolver.Source: A. 3D Scene and Target Zone Generation · p. 5

B. Monte Carlo Receiver Sampling

Receiver samples determine the accuracy of the Monte Carlo loss estimates across the in-zone and out-of-zone regions. ARCTAN uses proportional rejection sampling and Halton sequences to improve those estimates.

B. Monte Carlo Receiver Sampling

  • Receiver-sample placement and quantity determine the accuracy of Monte Carlo loss estimates across Zin and Zout.The receiver set is divided into independently initialized in-zone and out-of-zone subsets.Source: B. Monte Carlo Receiver Sampling · p. 5
  • Each receiver subset is independently initialized in proportion to area using rejection sampling and one sequence per coordinate dimension.Source: B. Monte Carlo Receiver Sampling · p. 5
  • Halton low-discrepancy sampling reduces variance in low-dimensional settings, improving approximations of L(Θ, Ψ) at each iteration,.Source: B. Monte Carlo Receiver Sampling · p. 6

C. Simulation Setup

The simulation evaluates three target-zone geometries on a campus digital twin, then compares ABS-only optimization with joint ABS–CJ optimization. Joint optimization suppresses out-of-zone SINR while keeping in-zone SINR near the target across all three geometries.

C. Simulation Setup

  • The propagation evaluator uses Sionna RT’s RadioMapSolver to generate smoothed coverage maps and distinct ray paths from the PathSolver, making it an unbiased evaluator.Source: C. Simulation Setup · p. 6
  • The evaluation uses the Duke University campus, two ABSs, 12 candidate CJs, and 500 in-zone receiver samples.The out-of-zone receiver count is calculated proportionally based on area.Source: C. Simulation Setup · p. 6
  • Each optimization stage uses 100 iterations and the predefined optimization hyperparameters.Source: C. Simulation Setup · p. 6
  • The 600 m × 600 m evaluation area is divided into 0.5 m × 0.5 m grid elements, with Circle, L-shape, and Square zones spanning up to 200 m from the center on each axis.Source: C. Simulation Setup · p. 6

D. Impact of ABS and CJ Optimization on SINR Distribution

  • Mean Zout SINR falls from 12.4/15.7/13.4 dB to −4.7/−3.1/−3.3 dB for Circle/L-shape/Square using 7/10/6 active CJs.Joint optimization yields mean Zin SINR of 10.0/9.7/9.6 dB, close to target η across the three geometries.Source: D. Impact of ABS and CJ Optimization… · p. 6
  • ABS-only optimization reduces mean Zin SINR from 22.1/23.29/23.94 dB to 14.9/18.0/16.3 dB for Circle/L-shape/Square as the uniformity objective is pursued.The corresponding σ values decrease from 13.1/15.6/14.2 to 11.9/13.1/12.5 dB.Source: D. Impact of ABS and CJ Optimization… · p. 6

E. Coverage and Leakage Performance Analysis

Across three zone geometries, ARCTAN reduces signal leakage while retaining in-zone coverage, with a modest signal-hole increase. Its conclusion frames containment as denying usable signal beyond a mission-defined boundary, and identifies static scenes and fixed candidate positions as current scope limits.

E. Coverage and Leakage Performance Analysis

  • Fig. 3 compares initial deployment, ABS-only optimization, and joint ABS–CJ optimization across mean SINR and threshold-based in-zone and out-of-zone percentages.Source: Figure 3 · p. 6
  • Signal-leakage ratios fall from 94.7%, 94.9%, and 93.2% to 43.9%, 42.4%, and 45.2% for circular, L-shaped, and square zones, respectively.Signal-hole ratios are 9.2%, 12.3%, and 11.4%, respectively; the authors describe the 9–12% increase as a tradeoff from boundary interference.Source: E. Coverage and Leakage Performance… · p. 6

VI. CONCLUSION

  • ARCTAN aims to deny usable signal beyond a mission-defined boundary rather than conceal or physically attenuate the transmission, and the authors report this is achievable in realistic propagation environments.Source: §VI · pp. 6–7
  • The current formulation assumes a static scene and fixed candidate positions; online reoptimization in dynamic or partially known environments is future work.Source: §VI · p. 7
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