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Learning The Likelihood Test With One-Class Classifiers for Physical Layer Authentication

Francesco Ardizzon, Stefano Tomasin

TL;DR

This paper tackles physical-layer authentication (PLA) under the scenario where only legitimate-channel data is available for verification. It proposes LT-based OCC verifiers by training two-class models (NN and LS-SVM) on the legitimate dataset plus an artificial negative class generated from a uniform distribution over the legitimate domain, and shows that, under suitable conditions, these models converge to the LT. The authors prove that AE-based classifiers do not generally replicate LT and provide extensive numerical results in wireless AWGN and underwater acoustic settings, demonstrating near-LT performance for the LT-based OCCs. The work builds a principled link between statistical LT and ML-based OCC, offering practical guidelines for constructing secure PLA verifiers when the intruder distribution is unknown. The methods are applicable to both terrestrial and underwater channels and contribute to secure, low-overhead PLA in diverse communication scenarios.

Abstract

In physical layer authentication (PLA) mechanisms, a verifier decides whether a received message has been transmitted by a legitimate user or an intruder, according to some features of the physical channel over which the message traveled. To design the authentication check implemented at the verifier, typically either the statistics or a dataset of features are available for the channel from the legitimate user, while no information is available when under attack. When the statistics are known, a well-known good solution is the likelihood test (LT). When a dataset is available, the decision problem is one-class classification (OCC) and a good understanding of the machine learning (ML) techniques used for its solution is important to ensure security. Thus, in this paper, we aim at obtaining ML PLA verifiers that operate as the LT. We show how to do it with the neural network (NN) and the one-class least-squares support vector machine (OCLSSVM) models, trained as two-class classifiers on the single-class dataset and an artificial dataset. The artificial dataset for the negative class is obtained by generating channel feature (CF) vectors uniformly distributed over the domain of the legitimate class dataset. We also derive a modified stochastic gradient descent (SGD) algorithm that trains a PLA verifier operating as LT without the need for the artificial dataset. Furthermore, we show that the one-class least-squares support vector machine with suitable kernels operates as the LT at convergence. Lastly, we show that the widely used autoencoder classifier generally does not provide the LT. Numerical results are provided considering PLA on both wireless and underwater acoustic channels.

Learning The Likelihood Test With One-Class Classifiers for Physical Layer Authentication

TL;DR

This paper tackles physical-layer authentication (PLA) under the scenario where only legitimate-channel data is available for verification. It proposes LT-based OCC verifiers by training two-class models (NN and LS-SVM) on the legitimate dataset plus an artificial negative class generated from a uniform distribution over the legitimate domain, and shows that, under suitable conditions, these models converge to the LT. The authors prove that AE-based classifiers do not generally replicate LT and provide extensive numerical results in wireless AWGN and underwater acoustic settings, demonstrating near-LT performance for the LT-based OCCs. The work builds a principled link between statistical LT and ML-based OCC, offering practical guidelines for constructing secure PLA verifiers when the intruder distribution is unknown. The methods are applicable to both terrestrial and underwater channels and contribute to secure, low-overhead PLA in diverse communication scenarios.

Abstract

In physical layer authentication (PLA) mechanisms, a verifier decides whether a received message has been transmitted by a legitimate user or an intruder, according to some features of the physical channel over which the message traveled. To design the authentication check implemented at the verifier, typically either the statistics or a dataset of features are available for the channel from the legitimate user, while no information is available when under attack. When the statistics are known, a well-known good solution is the likelihood test (LT). When a dataset is available, the decision problem is one-class classification (OCC) and a good understanding of the machine learning (ML) techniques used for its solution is important to ensure security. Thus, in this paper, we aim at obtaining ML PLA verifiers that operate as the LT. We show how to do it with the neural network (NN) and the one-class least-squares support vector machine (OCLSSVM) models, trained as two-class classifiers on the single-class dataset and an artificial dataset. The artificial dataset for the negative class is obtained by generating channel feature (CF) vectors uniformly distributed over the domain of the legitimate class dataset. We also derive a modified stochastic gradient descent (SGD) algorithm that trains a PLA verifier operating as LT without the need for the artificial dataset. Furthermore, we show that the one-class least-squares support vector machine with suitable kernels operates as the LT at convergence. Lastly, we show that the widely used autoencoder classifier generally does not provide the LT. Numerical results are provided considering PLA on both wireless and underwater acoustic channels.
Paper Structure (16 sections, 3 theorems, 26 equations, 4 figures)

This paper contains 16 sections, 3 theorems, 26 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Related Literature and Main Contributions
  3. System Model and PLA Verification Problem
  4. Non-Separability and Decision Errors
  5. LT in the Statistical Framework
  6. occ in the ml Framework
  7. lt with Machine Learning Models
  8. lt as Hypothesis Test
  9. lt-Based occ
  10. On the Domain ${\mathcal{X}}$
  11. On the ae Classifier
  12. Numerical Results
  13. Channel Models
  14. Classifier's Architecture and Training
  15. Performance Evaluation
  16. ...and 1 more sections

Key Result

Lemma 1

When the pdf of the alternative hypothesis is constant on the domain of the null hypothesis, i.e., where $|\mathcal{X}|$ is the volume of ${\mathcal{X}}$, the lt myglrt is equivalent to the lrt lrt. This means that, for each threshold $\delta_1$ there exists a threshold $\delta_2$ such that

Figures (4)

  • Figure 1: Sampling pdf of the first entries of cf vectors in the datasets $\{[\bm{x}]_1\}$ in the wireless AWGN Scenario: the artificially generated dataset $\mathcal{D}^\star_1$ (red) for the training phase, the $\mathcal{T}_0$ dataset of the positive-class cf vectors (blue) for the test phase, and the $\mathcal{T}_1$ dataset of the alternative-class cf vectors (green) for the test phase.
  • Figure 2: Experimental (light) versus fitted gmm model (dark) for Alice (blue) and Trudy (red).
  • Figure 3: det curves for the awgn Scenario for various classifiers and the lt.
  • Figure 4: det curves for the Mixture Scenario for various classifiers and the lt.

Theorems & Definitions (3)

  • Lemma 1
  • Theorem 1
  • Theorem 2