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Delay-Angle Information Spoofing for Channel State Information-Free Location-Privacy Enhancement

Jianxiu Li, Urbashi Mitra

TL;DR

Numerical results show that the proposed DAIS strategy results in more than 15 dB performance degradation for the eavesdropper as compared with that for the legitimate localizer at high signal-to-noise ratios, and provides more effective location-privacy enhancement than the prior art.

Abstract

In this paper, a delay-angle information spoofing (DAIS) strategy is proposed to enhance the location privacy at the physical layer. More precisely, the location-relevant delays and angles are artificially shifted without the aid of channel state information (CSI) at the transmitter, such that the location perceived by the eavesdropper is incorrect and distinct from the true one. By leveraging the intrinsic structure of the wireless channel, a precoder is designed to achieve DAIS while the legitimate localizer can remove the obfuscation via securely receiving a modest amount of information, i.e., the delay-angle shifts. A lower bound on eavesdropper's localization error is derived, revealing that location privacy is enhanced not only due to estimation error, but also by the geometric mismatch introduced by DAIS. Furthermore, the lower bound is explicitly expressed as a function of the delay-angle shifts, characterizing performance trends and providing the appropriate design of these shift parameters. The statistical hardness of maliciously inferring the delay-angle shifts by a single-antenna eavesdropper as well as the challenges for a multi-antenna eavesdropper are investigated to assess the robustness of the proposed DAIS strategy. Numerical results show that the proposed DAIS strategy results in more than 15 dB performance degradation for the eavesdropper as compared with that for the legitimate localizer at high signal-to-noise ratios, and provides more effective location-privacy enhancement than the prior art.

Delay-Angle Information Spoofing for Channel State Information-Free Location-Privacy Enhancement

TL;DR

Numerical results show that the proposed DAIS strategy results in more than 15 dB performance degradation for the eavesdropper as compared with that for the legitimate localizer at high signal-to-noise ratios, and provides more effective location-privacy enhancement than the prior art.

Abstract

In this paper, a delay-angle information spoofing (DAIS) strategy is proposed to enhance the location privacy at the physical layer. More precisely, the location-relevant delays and angles are artificially shifted without the aid of channel state information (CSI) at the transmitter, such that the location perceived by the eavesdropper is incorrect and distinct from the true one. By leveraging the intrinsic structure of the wireless channel, a precoder is designed to achieve DAIS while the legitimate localizer can remove the obfuscation via securely receiving a modest amount of information, i.e., the delay-angle shifts. A lower bound on eavesdropper's localization error is derived, revealing that location privacy is enhanced not only due to estimation error, but also by the geometric mismatch introduced by DAIS. Furthermore, the lower bound is explicitly expressed as a function of the delay-angle shifts, characterizing performance trends and providing the appropriate design of these shift parameters. The statistical hardness of maliciously inferring the delay-angle shifts by a single-antenna eavesdropper as well as the challenges for a multi-antenna eavesdropper are investigated to assess the robustness of the proposed DAIS strategy. Numerical results show that the proposed DAIS strategy results in more than 15 dB performance degradation for the eavesdropper as compared with that for the legitimate localizer at high signal-to-noise ratios, and provides more effective location-privacy enhancement than the prior art.

Paper Structure

This paper contains 26 sections, 5 theorems, 39 equations, 7 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Delay-Angle Information Spoofing for Location-Privacy Enhancement
  4. Delay-Angle Information Spoofing
  5. Precoder Design
  6. Eve’s Localization
  7. Bob’s Localization
  8. Localization Accuracy with Delay-Angle Information Spoofing
  9. Effective Fisher Information for Channel Estimation
  10. Bob's Localization Error
  11. Eve's Localization Error
  12. Degraded Localization Accuracy
  13. Impact of Parameter Design
  14. Robustness of Delay-Angle Information Spoofing
  15. Hardness of Delay-Angle Shifts Estimation
  16. ...and 11 more sections

Key Result

Lemma 1

Given the true and mismatched distributions of the estimated parameters $\widehat{\bm\eta}_{\text{Eve}}$ in Equations eq:truemodel and eq:mismatchmodel, the pseudo-true locations of Alice and scatterers are given by where $k_{\min}\triangleq\arg\min_k\bar{\tau}_k$ and with $k=1,2,\cdots,K$.

Figures (7)

  • Figure 1: System model.
  • Figure 4: (a) Lower bounds for the RMSE of Eve’s localization with different choices of $\bm\Delta$, where $k_{\min}=k$ means that the $k$-th path with the smallest shifted TOA is assumed to be the LOS path for localization due to phase wrapping according to Equation \ref{['eq:ptrue']}; (b) The associated values of $\|\bar{\bm p}^{\star}-\bar{\bm p}\|$; (c) The associated values of $\cos^2(\bar{\theta}_{\mathrm{Tx},k_{\min}})$.
  • Figure 5: Lower bounds for the RMSE of Eve’s localization with more choices of $\bm\Delta$.
  • Figure 6: Lower bounds for the RMSE of localization with different choices of $\Delta_\theta$, where $\Delta_\tau=T_s$.
  • Figure 7: Lower bounds for the RMSE of localization with different choices of $\Delta_\tau$, where $\Delta_\theta=0.25\pi$.
  • ...and 2 more figures

Theorems & Definitions (10)

  • Lemma 1
  • Proposition 1
  • Corollary 1
  • Remark 1: Interpretation of the simplified MCRB
  • Remark 2: Distinction from the analysis in li2023fpi
  • Proposition 2
  • Remark 3: Impact of Angle Shift
  • Remark 4: Impact of Delay Shift
  • Remark 5: Knowledge of the CSI
  • Proposition 3