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On the Robustness of AoA as an Authentication Feature Under Spoofing: Fundamental Limits from Misspecified Cramer Rao Theory

Sotiris Skaperas, Arsenia Chorti

Abstract

The robustness of angle of arrival (AoA) as a physical layer authentication (PLA) feature under spoofing attacks is studied, assuming a digital uniform linear array verifier. The verifier estimates the AoA assuming a legitimate user's single source model, whereas the received signal is generated by a multi antenna adversary at a different angle, leading to a model mismatch. Closed form expressions are derived for the misspecified Cramer Rao bound, the PLA decision threshold, the spoofing detection, false alarm and misdetection probabilities. Simulation results validate the theoretical findings and highlight the impact of the signal to noise ratio, array geometries, spoofing precoding and number of snapshots on authentication robustness.

On the Robustness of AoA as an Authentication Feature Under Spoofing: Fundamental Limits from Misspecified Cramer Rao Theory

Abstract

The robustness of angle of arrival (AoA) as a physical layer authentication (PLA) feature under spoofing attacks is studied, assuming a digital uniform linear array verifier. The verifier estimates the AoA assuming a legitimate user's single source model, whereas the received signal is generated by a multi antenna adversary at a different angle, leading to a model mismatch. Closed form expressions are derived for the misspecified Cramer Rao bound, the PLA decision threshold, the spoofing detection, false alarm and misdetection probabilities. Simulation results validate the theoretical findings and highlight the impact of the signal to noise ratio, array geometries, spoofing precoding and number of snapshots on authentication robustness.
Paper Structure (14 sections, 36 equations, 3 figures)

This paper contains 14 sections, 36 equations, 3 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Assumed (Legitimate) Model
  4. True (Spoofed) Model
  5. Misspecified Cramér Rao Bound
  6. Cramér Rao Bound
  7. MCRB Under Model Mismatch
  8. Pseudo-True Parameter $\theta_0$
  9. PLA Binary Hypothesis Test
  10. Asymptotic behavior of AoA-based authentication
  11. Variance sensitivity of AoA-PLA under spoofing
  12. Simulation Results
  13. Conclusions and Future Directions
  14. Derivation of $\eta(\theta)$ and $D(\theta)$

Figures (3)

  • Figure 1: $P_{SD}$ and $P_{FA}$ for $M=16$, $L=1$, $K=20$.
  • Figure 2: $P_{SD}$ and $P_{FA}$ for: a) $K=10$, and, b) $M=32$. SNR$=0$ dB.
  • Figure 3: $P_{\mathrm{SD}}$ versus $L$ (log scale) for the equal-gain ($\phi_{\max}=0^\circ$) and the phase-impaired case ($|\phi_\ell|\leq 10^\circ$). $M=8$, $K=2$, and SNR$=5$ dB.