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Anti-Localization Uplink Communications in Satellite-Terrestrial Systems
Ranran Sun, Bin Yang, Yulong Shen, Yuanyu Zhang, Xiaohong Jiang
TL;DR
Satellite uplinks can expose a transmitter to adversarial satellites that detect signals and localize their source, while physical-layer location protection remains underexplored. The paper proposes cooperative jamming with a joint LEP-based design under communication and power constraints. Its numerical results report higher LEP with jamming than without it, alongside the stated aim of reliable uplink communication.
Problem
Physical-layer protection against satellites that directly detect uplinks and use TDOA to localize transmitters remains largely unexplored.
Source: §I · p. 1Method
Alice superposes information and jamming signals while Bob combines the received signal, and the paper models LEP and jointly optimizes jamming coding and power under reliability and transmit-power constraints.
Source: §I · p. 2Results
The reported LEP is consistently higher with cooperative jamming than without it across the evaluated numbers of adversarial satellites.
Source: §VI · p. 10Takeaways & Limitations
The paper concludes that joint transmitter coding and power allocation with receiver combining can support reliable uplink communication while resisting adversarial localization.
Source: §I · p. 2, §VII · p. 12
Abstract
from arXiv · showhide
This paper investigates the anti-localization uplink communication in a satellite-terrestrial system, where a ground transmitter Alice communicates with a legitimate satellite receiver Bob in the presence of multiple cooperative adversarial satellites attempting to localize Alice with the time difference of arrival (TDOA) technique. Specifically, we propose a cooperative jamming-based scheme for such anti-localization communication,in which Alice exploits the superposition coding with power allocation to simultaneously transmit information/jamming signals for communication with Bob and for confusing signal detection/TDOA measurement at adversarial satellites, while Bob employs the combining vector technique to enhance the desired information signal and also suppress the jamming. We define a localization error probability (LEP) metric to jointly depict both the impacts of signal detection and TDOA measurement on localization performance, and then develop a theoretical framework for the LEP modeling under the proposed scheme. We further explore the joint optimal design of jamming coding and power for LEP maximization, subject to the constraints of AliceBob communication reliability and Alice's transmit power. An effective sample average approximation method is also provided to tackle this non-convex optimization problem. Finally, extensive numerical results are illustrated to validate our theoretical models and demonstrate how the cooperative jamming helps to provide an anti-localization guarantee while ensuring communication reliability
I. INTRODUCTION
The paper addresses physical-layer localization of satellite uplinks, proposing cooperative jamming and a joint LEP-based design to protect Alice while maintaining reliable communication with Bob. It situates this problem against existing location-protection and TDOA-localization work, then outlines the satellite monitoring setting.
I. INTRODUCTION
- Physical-layer protection remains largely unexplored, although adversarial satellites can detect uplinks and use TDOA to infer a transmitter’s location.Such exposure may lead to persistent tracking, targeted strikes, and privacy leakage.Source: §I · p. 1
- Alice superposes information and jamming signals to confuse satellite detection and TDOA measurement, while Bob combines signals to enhance information and suppress jamming.The design jointly optimizes jamming coding and power for LEP maximization under communication-reliability and transmit-power constraints.Source: §I · p. 2
II. RELATED WORKS
- The paper classifies existing location-protection approaches into network-layer routing obfuscation and application-layer anonymity or fake-source construction.It also reviews localization-performance work, including TDOA accuracy under measurement and system uncertainties.Source: §II · p. 2, C. Localization Performance Analysis · p. 3
A. Network-Layer Routing Obfuscation
- Routing-based protection introduces path uncertainty or traffic dispersion, but addresses traffic-analysis adversaries rather than satellites that localize from physical-layer measurements.The cited examples include routing randomness and cloud-based protection against hotspot-locating attacks.Source: A. Network-Layer Routing Obfuscation · p. 2
B. Application-layer Anonymity/Fake-source Construction
- Anonymity clouds, multiple sinks, and probabilistic forwarding conceal sources through routing changes, but do not prevent direct satellite signal detection and TDOA localization.The cited examples include,,, and.Source: B. Application-layer… · p. 2
C. Localization Performance Analysis
- Prior work analyzes TDOA accuracy under measurement uncertainty, while the paper identifies gaps in modeling detection, auxiliary participation, estimation error, and final localization error together.The paper’s setting also conditions localization on successful detection by a primary Willie.Source: C. Localization Performance Analysis · p. 3
III. SYSTEM MODEL
- The system comprises ground transmitter Alice, intended receiver Bob, and co-orbiting adversarial satellites that detect uplinks and attempt to localize Alice.Alice’s location is unknown to the adversaries and modeled as a random point in a suspicious ground region.Source: §III · p. 3
- A primary Willie monitors for Alice; after detection, auxiliary Willies detect independently and use generalized cross-correlation TDOA measurements to localize her.If the primary Willie declares no transmission, auxiliary satellites do not continue detection or localization.Source: §III · p. 3
A. Transmission at Alice
Alice transmits information and random-power jamming together, while the model represents the satellite links as Rician fading channels. The jamming is intended to disrupt Willie detection and TDOA estimation, subject to Alice’s power constraint.
A. Transmission at Alice
- Alice transmits an information-bearing signal and a jamming vector, with fixed information power, a unit-norm information beamformer, and a normalized jamming precoder.Jamming power is uniform on [0, Pj,max], and Alice’s peak-power constraint is Ps + Pj,max ≤ Pmax.Source: A. Transmission at Alice · p. 4
B. Channel Model
- The Alice–Bob and Alice–Willie links are modeled as MIMO Rician fading channels with distance-dependent path loss and line-of-sight and scattered components.Alice’s information and jamming signals share each Willie’s channel matrix but have different effective spatial directions.Source: B. Channel Model · p. 4
C. Received Signal at Bob
Bob combines his received signal and must meet a minimum SINR threshold. Willies use energy detection to decide whether Alice transmits, then use participating satellites’ noisy TDOA measurements to estimate her location.
C. Received Signal at Bob
- Bob applies a unit-norm receive combining vector, and the Alice–Bob link must satisfy the minimum SINR requirement γB ≥ γth.The combining vector is used to form Bob’s combined signal.Source: C. Received Signal at Bob · p. 4
D. Received Signal at Willies
- Each Willie uses energy detection and a constant-false-alarm-rate threshold to test whether Alice is transmitting.The detection model distinguishes missed detections and false alarms; the threshold fixes the false-alarm probability at a predefined value.Source: D. Received Signal at Willies · pp. 4–5
- Willies with successful detections combine received signals through generalized cross-correlation to estimate TDOA, then use the measurements in the Chan algorithm to estimate Alice’s location.Receiver noise and random jamming contribute to TDOA estimation error.Source: D. Received Signal at Willies · p. 5
IV. LOCALIZATION PERFORMANCE AT WILLIES
The LEP model accounts for coupled uncertainty in which satellites participate and how accurately they measure TDOA. It averages localization failure over participating Willie sets and underlying random factors.
IV. LOCALIZATION PERFORMANCE AT WILLIES
- Unlike conventional models with available adversarial nodes and deterministic geometry, this setting has uncertain auxiliary participation and TDOA accuracy.Participation depends on successful signal detection; measurement accuracy varies with Alice’s unknown location, satellite geometry, Rician fading, and random jamming power.Source: §IV · p. 5
- The final LEP averages over all possible participating Willie sets and the random factors underlying detection and measurement.The metric captures cases where too few auxiliaries participate or localization error exceeds the prescribed threshold.Source: §IV · p. 5
A. Performance Metric
The localization error probability (LEP) jointly captures missed detection and localization failure after the primary satellite triggers localization. A higher LEP indicates stronger protection against cooperative localization.
A. Performance Metric
- LEP is the primary metric for Alice’s protection against cooperative detection and TDOA localization.It jointly captures detection and localization effects on the Willies’ ability to infer Alice’s location.Source: A. Performance Metric · pp. 5–6
- After detection, localization failure includes auxiliary miss detections, too few participating satellites, TDOA errors, or unfavorable geometry; fewer than two TDOAs cannot support 2D localization.The failure event is defined by localization error exceeding the prescribed threshold d_th.Source: A. Performance Metric · pp. 5–6
- LEP combines primary Willie miss detection with post-trigger localization failure; a higher value indicates stronger location protection.The post-trigger term reflects the primary satellite’s detection probability multiplied by the probability of localization failure.Source: A. Performance Metric · p. 6
B. Average Missed Detection Probability
The missed-detection analysis models each Willie’s energy statistic under transmission and uses that model to obtain missed-detection probability.
B. Average Missed Detection Probability
- Under H1, the analysis derives the energy statistic’s mean and variance from the received-signal covariance matrix.These moments support the distributional approximation used for detection analysis.Source: B. Average Missed Detection Probability · p. 6
- Because the energy statistic is a weighted sum of correlated quadratic terms, its exact distribution is intractable, so the analysis moment-matches it to a Gamma distribution.The approximation matches the statistic’s first two moments.Source: B. Average Missed Detection Probability · p. 6
- The missed-detection probability is obtained from the Gamma model using the regularized lower incomplete Gamma function, and detection probability is its complement.The analysis defines average missed-detection probability for each Willie before taking the complement.Source: B. Average Missed Detection Probability · pp. 6–7
C. TDOA Measurement
The paper models TDOA estimation through generalized cross-correlation and analyzes how channel and jamming conditions affect its error variance.
C. TDOA Measurement
- Willies estimate TDOA through generalized cross-correlation, with the estimate given by the cross-correlation peak.The function compares processed received signals at an auxiliary Willie and the primary Willie.Source: C. TDOA Measurement · p. 7
- Under nonideal but sufficiently regular conditions, TDOA estimation error is modeled as a zero-mean Gaussian random variable.The error variance is based on the CRLB for time-delay estimation and depends on effective SINR and signal bandwidth.Source: C. TDOA Measurement · p. 7
- Alice’s jamming increases TDOA error variance by reducing effective SINR at both the auxiliary and primary Willies.The variance is also random from the Willies’ perspective because Alice’s location, channels, and jamming power are random.Source: C. TDOA Measurement · p. 7
D. Localization Error Probability
The localization-failure model uses participating satellites’ TDOA measurements to estimate Alice’s position and evaluates whether the resulting error exceeds a threshold.
D. Localization Error Probability
- The Chan algorithm estimates Alice’s position from available TDOA measurements because directly solving the nonlinear TDOA equations is difficult and computationally costly.The paper describes Chan as a closed-form estimator with low computational complexity and favorable localization accuracy in practical TDOA systems.Source: D. Localization Error Probability · p. 7
- Average localization failure is the expected probability that the location error exceeds d_th, evaluated over Alice’s location, channels, and jamming power.The localization error is approximated as isotropic Gaussian, yielding a Rayleigh-distributed error magnitude.Source: D. Localization Error Probability · p. 7
- The LEP has no closed-form expression because its component expressions are too complex, so numerical results are used to validate the theoretical analysis.Two-dimensional localization requires at least two independent TDOA measurements; fewer participating satellites are treated as unable to localize effectively.Source: D. Localization Error Probability · p. 8
E. Case Study
The case study shows that jamming increases localization error through both reduced Willie participation and less accurate TDOA measurements. The two effects apply whether jamming leaves too few auxiliary Willies for localization or enough Willies to attempt it.
E. Case Study
- With equal average detection probabilities and approximately equal failure probabilities for sets of the same size, the case study models participation as binomial and combines both jamming effects in LEP.Stronger jamming decreases detection probability and increases localization failure probability; together these raise LEP.Source: E. Case Study · p. 8
- As jamming increases, lower detection probability shifts the number of participating auxiliary Willies downward, making it more likely that fewer than two participate and 2-D localization fails.This protects Alice both by degrading measurement accuracy and by preventing sufficient localization geometry.Source: E. Case Study · p. 8
- Even with at least two participating auxiliary Willies, stronger jamming increases localization failure by enlarging TDOA estimation error variance.The reduced effective SINR at the primary and auxiliary Willies increases the error variance and the probability that localization error exceeds the threshold.Source: E. Case Study · p. 8
V. LOCALIZATION ERROR PROBABILITY MAXIMIZATION
The optimization jointly selects jamming power and direction to maximize LEP subject to Alice’s power budget and Bob’s communication reliability. The approach uses sample average approximation and alternating optimization, while the detector model affects how jamming changes missed detection.
V. LOCALIZATION ERROR PROBABILITY MAXIMIZATION
- The design maximizes LEP over maximum jamming power and a normalized jamming precoder, subject to Alice’s peak-power budget and Bob’s minimum-SINR reliability constraint.The robust communication constraint uses the worst-case SINR at maximum jamming power.Source: §V · p. 8
- Sample average approximation evaluates LEP across channel and jamming-power samples because Alice’s exact location is unknown to the Willies and the objective is non-convex.Each sample evaluates missed detection, auxiliary-Willie participation, and localization failure probabilities.Source: §V · p. 8
- When Alice can steer jamming into Bob’s effective null space, Bob’s SINR constraint does not limit jamming power; otherwise, jamming should be directed toward Willies while limiting leakage to Bob.In the null-space case, the peak-power constraint alone limits maximum jamming power.Source: §V · p. 9
- Alternating optimization searches jamming power for fixed covariance and updates the jamming covariance for fixed power using projected gradient ascent.The covariance update is projected onto the positive-semidefinite, trace, and Bob-SINR feasible set.Source: §V · p. 9
- With energy detection on total received emission, increasing jamming may reduce missed detection, so location protection mainly comes from larger TDOA errors and degraded localization accuracy.The effect on missed detection depends on the detector model.Source: §V · p. 9
VI. NUMERICAL RESULTS
The simulations validate the analysis and show that cooperative jamming degrades the adversaries’ localization while its feasible power is constrained by Alice’s power budget and Bob’s SINR requirement.
VI. NUMERICAL RESULTS
- Theoretical missed-detection probabilities match simulations for all four Willies and increase with the detection threshold.At small thresholds, missed detection is close to zero; it rises as received energy under H1 is more likely to fall below the threshold.Source: §VI · p. 10, Figure 2 · p. 10
- Bob’s average SINR decreases as maximum jamming power increases, motivating jamming-power design under Bob’s SINR constraint.The theoretical SINR results closely match simulations across the considered information-signal powers.Source: §VI · p. 10, Figure 3 · p. 10
- LEP falls as the number of Willies increases, but remains higher with jamming than without it across the tested range.The results attribute the decline to more available TDOA measurements and better localization geometry; the jamming advantage persists as the number of adversarial satellites grows.Source: §VI · p. 10, Figure 4 · p. 11
- With jamming, LEP increases as maximum jamming power rises and stays above the no-jamming baseline; without jamming, it is nearly unchanged.The reported mechanism is stronger interference at adversarial satellites, which reduces the effective SINR for TDOA estimation and enlarges localization error.Source: §VI · p. 11, Figure 5 · p. 11
- LEP decreases as the localization-error threshold increases in both cases, but remains higher with jamming, with a larger gap at higher thresholds.The authors report that jamming reduces effective TDOA-estimation SINR, increasing TDOA and localization errors.Source: §VI · p. 11, Figure 6 · p. 12
- Optimal maximum jamming power decreases as Bob’s minimum SINR requirement rises and is nearly unchanged across localization-error thresholds.At loose SINR requirements, Alice’s power budget limits jamming; at stricter requirements, Bob’s SINR constraint dominates, while the optimizer uses the largest feasible jamming power.Source: §VI · p. 12
VII. CONCLUSION
The paper presents an initial study of anti-localization uplink communication against cooperative TDOA localization. Its conclusions identify a protection–reliability tradeoff and the importance of jamming design.
VII. CONCLUSION
- The work is presented as an initial attempt at anti-localization uplink communication against cooperative TDOA-based localization.Source: §VII · p. 12
- Joint transmitter coding and power allocation with receiver combining can support reliable uplink communication while resisting adversarial localization.Alice's cooperative jamming is designed to confuse signal detection and TDOA measurement while Bob enhances the information signal and suppresses jamming.Source: §VII · p. 12
- Adversarial localization error probability is sensitive to maximum jamming power and the jamming precoding matrix, making careful jamming design important.Source: §VII · p. 12
- A stringent minimum SINR requirement at Bob restricts feasible jamming power and achievable localization error probability, creating a protection–reliability tradeoff.Source: §VII · p. 12, Figure 7 · p. 12