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Physical Layer Anomaly Detection via Adaptive Gaussian Mixture Model

Mamady Delamou, Luan Chen, Arsenia Chorti

arXiv:2610.18946v1cs.CRcs.LG

TL;DR

Wireless localization can be compromised by physical-layer spoofing, and noise and complex dependencies in measured signals make legitimate and adversarial transmissions difficult to distinguish. The paper proposes calibrated adaptive GMM detection from joint AoA and RSS patterns; it reports superior detection versus baseline methods, with 1% false alarm rate.

  • Problem

    Noisy, distorted physical-layer measurements and dependencies among localization metrics make it difficult to distinguish legitimate transmissions from spoofed signals.

    Source: §I · p. 1

  • Method

    The framework calibrates CSI and uses an adaptive GMM to detect anomalies in jointly analyzed AoA and RSS measurements.

    Source: §I · pp. 1–2

  • Results

    The adaptive GMM achieves superior detection rate to conventional GMM, LOF, SVM, and k-NN while maintaining 1% FAR.

    Source: §V · p. 6

  • Takeaways & Limitations

    The framework detects CSI spoofing through deviations from learned legitimate spatial patterns without requiring prior knowledge of the attack trajectory or displacement.

    Source: §II · p. 2

Abstract

from arXiv · show

Physical-layer spoofing attacks pose a critical threat to wireless localization systems by manipulating channel state information (CSI). Detecting such attacks becomes particularly challenging when the attacker and the legitimate node are spatially proximate, as their CSI characteristics become increasingly similar. To address this challenge in indoor scenarios, we propose an adaptive Gaussian mixture model (GMM)-based detection framework that learns legitimate CSI patterns and detects spatial inconsistency through statistical anomaly detection. Using a massive multiple-input multiple-output (MIMO) experimental dataset with 64 uniform linear array (ULA) antenna and 5 mm spatial resolution, we evaluated our detector against CSI spoofing attacks with spatial displacements ranging from 50 mm to 450 mm. The adaptive GMM achieves 95-98% detection rate for displacements above 150 mm while maintaining 1% false alarm rate. We benchmark our approach against conventional GMM, local outlier factor (LOF), one-class support vector machine (SVM) and k-nearest neighbors (k-NN) classifiers, demonstrating overall superior detection performance of our proposed classifier.

I. INTRODUCTION

Wireless localization is vulnerable because noisy, interdependent physical-layer measurements make legitimate transmissions difficult to distinguish from spoofed signals. The paper proposes calibrated, adaptive GMM detection using joint AoA and RSS patterns, and frames the system and attack as learning legitimate measurements before detecting spatially displaced CSI.

I. INTRODUCTION

  • Wireless localization is vulnerable to physical-layer attacks, while noise, distortion, and dependencies among AoA, ToF, and RSS complicate distinguishing legitimate from corrupted signals.Localization supports applications including indoor navigation, asset tracking, autonomous vehicles, and emergency services.Source: §I · p. 1
  • The proposed framework learns legitimate joint AoA–RSS patterns and treats deviations caused by spatially displaced spoofed CSI as anomalies.The introduction describes adaptive thresholding as part of the probabilistic approach.Source: §I · p. 1
  • The adaptive GMM is reported to achieve 95–98% detection for spatial displacements from 150 mm, and the benchmark comparison includes conventional GMM, LOF, SVM, and k-NN.The framework jointly analyzes AoA and RSS measurements.Source: §I · p. 2

II. SYSTEM MODEL AND PROBLEM STATEMENT

  • The system model considers an indoor LoS massive MIMO setup with a ULA, and represents the channel as a spatial steering vector and frequency steering vector combined with noise.The array spacing is 0.07 m, carrier frequency 2.61 GHz, and bandwidth 20 MHz.Source: §II · p. 2
  • The attacker injects prerecorded CSI from another spatial location, and detection uses observed AoA and RSS to distinguish learned legitimate measurements from spoofed transmissions without knowing the attack trajectory or displacement.The measurement vector contains estimated AoA and measured signal power.Source: §II · p. 2

III. ADAPTIVE GMM-BASED SPOOFING DETECTION

Legitimate measurements follow consistent statistical patterns in the joint AoA–RSS feature space, shaped by wireless propagation and user mobility. The adaptive GMM learns these patterns from attack-free data and detects deviations without requiring prior knowledge.

III. ADAPTIVE GMM-BASED SPOOFING DETECTION

  • Spatially displaced spoofed measurements violate the learned legitimate distribution, creating detectable anomalies.The underlying patterns arise from physical constraints on propagation and user mobility.Source: §III · p. 2
  • Joint AoA–RSS patterns provide the feature space in which legitimate measurements are modeled and spoofed deviations are identified.The passages describe the patterns as statistically consistent and linked to propagation and mobility constraints.Source: §III · pp. 2–3
  • The adaptive GMM learns legitimate measurement patterns from attack-free training data and detects deviations without prior knowledge.The passage does not specify the prior knowledge that is unnecessary.Source: §III · p. 3

A. CSI Calibration and Feature Extraction

The framework calibrates raw CSI to address hardware impairments, then extracts calibrated AoA and RSS features for detection. Calibration sharply reduces measurement errors; ToF is excluded because its delay resolution is too limited for the dataset’s spatial resolution.

A. CSI Calibration and Feature Extraction

  • A joint nonlinear least-squares calibration estimates hardware impairment parameters, including IQ imbalance, unknown time offset, and antenna-specific phase errors.It is initialized once using approximately Ncal reference measurements; standard sequential methods do not account for these impairments.Source: A. CSI Calibration and Feature… · p. 3
  • The system extracts calibrated AoA and RSS from each channel matrix using Root-MUSIC with spatial smoothing and average received power, respectively.The calibration corrects the CSI before feature extraction.Source: A. CSI Calibration and Feature… · p. 3
  • Over 90% of calibrated AoA errors fall below 3°, versus approximately 50% of uncalibrated samples exceeding 25°; calibration also improves the RSS error distribution.The figure presents CDFs of estimation MAE before and after calibration for AoA and RSS.Source: A. CSI Calibration and Feature… · p. 3, Figure 2 · p. 3
  • ToF is omitted because, at 20 MHz bandwidth, its 15 m spatial resolution is far coarser than the dataset’s 5 mm spatial resolution.Such delay resolution allows only coarse localization.Source: A. CSI Calibration and Feature… · p. 3

B. Adaptive GMM Detection Model

The detector models calibrated AoA and RSS as a two-dimensional feature vector and represents legitimate operation with a Gaussian mixture model. The mixture provides a flexible probability model for variability and correlations in the joint feature space.

B. Adaptive GMM Detection Model

  • Each time step is represented by calibrated AoA and RSS, whose joint distribution is modeled for legitimate operation with a GMM.The model is described as capturing natural variability and correlations in the feature space.Source: B. Adaptive GMM Detection Model · pp. 3–4
  • The legitimate-user density is a mixture of K Gaussian components, with weights summing to one and full covariance matrices capturing AoA–RSS correlations.Each component has a mean vector and a full covariance matrix.Source: B. Adaptive GMM Detection Model · p. 4

1) Component Selection and Training:

The component-selection procedure weighs model fit against detection performance across different GMM component counts. The GMM is trained on attack-free data using EM, with features standardized from training-set statistics.

1) Component Selection and Training:

  • Fig. 3 compares BIC and maximum detection performance across GMM component counts, framing component selection as a model-fit versus detection trade-off.Lower BIC indicates better fit, while higher detection rate indicates better attack detection.Source: Figure 3 · p. 4
  • EM estimates GMM parameters on attack-free training data from multiple trajectories by alternating responsibility calculation with parameter updates until convergence.The E-step computes component responsibilities; the M-step updates parameters to maximize expected log-likelihood.Source: 1) Component Selection and Training · p. 4
  • Features are standardized using the training-set mean and standard deviation before GMM training.The same scaling is applied to all features.Source: 1) Component Selection and Training · p. 4

2) Adaptive Detection Framework:

The adaptive GMM smooths windowed log-likelihoods and adjusts its detection threshold using local measurement statistics. An attack is declared when the smoothed likelihood falls below that threshold.

2) Adaptive Detection Framework:

  • Exponential smoothing reduces sensitivity to instantaneous measurement fluctuations, while adaptive thresholding adjusts the cutoff using local window statistics.The threshold is constrained to remain at least 0.9 times the validation-calibrated base threshold.Source: 2) Adaptive Detection Framework · p. 4
  • The detector smooths a windowed log-likelihood over W samples before comparing it with the adaptive threshold.The smoothed value is δΛ(t) + (1 − δ)Λsmooth(t − 1).Source: 2) Adaptive Detection Framework · p. 4
  • An attack is declared when the exponentially smoothed likelihood falls below κadapt(t).The local mean and standard deviation are computed over an adaptive window; β controls threshold sensitivity.Source: 2) Adaptive Detection Framework · p. 4

A. Experimental Setup

The evaluation uses densely sampled measurements from a controlled massive-MIMO testbed and tests spoofing across spatial offsets. Training, validation, and test trajectories are separated, with validation used to calibrate the target false-alarm rate.

A. Experimental Setup

  • The testbed uses a 64-element ULA in a controlled laboratory with predominantly LoS propagation and 5 mm spatial sampling.It includes parallel trajectories with 251 measurement points each.Source: A. Experimental Setup · p. 4
  • Training uses trajectories 1–50, validation 51–60, and testing 65–70; attacks span samples 175–225 in test trajectories.Validation calibrates thresholds for a target 1% false alarm rate.Source: A. Experimental Setup · p. 4
  • Spoofed CSI is drawn from trajectories offset by 5–450 mm, and the detector uses a three-component GMM with W = 10 and Wadapt = 20.The reported parameters are β = 1.5 and δ = 0.3; the validation threshold is set at the first percentile of windowed likelihoods to achieve 1% FAR.Source: A. Experimental Setup · p. 5

B. Detection Performance and Analysis

Adaptive GMM performs best in the reported low-displacement comparison, where spoofed CSI closely resembles legitimate patterns. Detection is also illustrated for a 250 mm attack, and all evaluated algorithms exceed 95% detection above 300 mm.

B. Detection Performance and Analysis

V. CONCLUSION

The conclusion presents calibrated joint AoA and RSS analysis with an adaptive GMM for CSI spoofing detection. It reports improved estimation accuracy and detection performance, while identifying non-line-of-sight multipath and complementary security mechanisms as future work.

V. CONCLUSION

  • The proposed framework detects CSI spoofing in massive-MIMO localization through joint analysis of calibrated AoA and RSS measurements.The conclusion reports superior detection rate at 1% FAR relative to conventional GMM, LOF, SVM, and k-NN.Source: §V · p. 6
  • Calibration reduces AoA MAE from 22.74° to 1.27° and RSS MAE from 62.66 dBm to 1.77 dBm.The conclusion states that these reductions enable highly accurate parameter estimation.Source: §V · p. 6
  • Future work will investigate non-line-of-sight multipath environments and integration with complementary security mechanisms.Source: §V · p. 6

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