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Physical Layer Location Privacy in SIMO Communication Using Fake Path Injection

Trong Duy Tran, Maxime Ferreira Da Costa, Linh Trung Nguyen

TL;DR

This work addresses location privacy in SIMO wireless links by injecting fake propagation paths and securely sharing their parameters with a legitimate receiver. The core method uses a CRB-based privacy margin, defined as the ratio of Eve’s minimum CRB eigenvalue to Bob’s maximum CRB eigenvalue, to quantify privacy gains, and leverages spectral properties of generalized Vandermonde matrices and the Dirichlet kernel to derive explicit bounds. The main contributions include two main theorems giving CRB bounds under AoA-only and joint AoA-channel estimation, revealing a quadratic scaling of privacy with the inverse angular separation between true and fake paths, and a corollary showing privacy gains scale with antenna counts and separation. Numerical experiments validate the theoretical bounds and illustrate practical benefits in BER for Bob and Eve, highlighting the potential of fake-path injection for physical-layer privacy in multi-user SIMO systems and suggesting extensions to MIMO scenarios.

Abstract

Fake path injection is an emerging paradigm for inducing privacy over wireless networks. In this paper, fake paths are injected by the transmitters into a single-input multiple-output (SIMO) communication channel to obscure their physical location from an eavesdropper. The case where the receiver (Bob) and the eavesdropper (Eve) use a linear uniform array to locate the transmitter's (Alice) position is considered. A novel statistical privacy metric is defined as the ratio between the smallest (resp. largest) eigenvalues of Eve's (resp. Bob's) Cramér-Rao lower bound (CRB) on the SIMO channel parameters to assess the privacy enhancements. Leveraging the spectral properties of generalized Vandermonde matrices, bounds on the privacy margin of the proposed scheme are derived. Specifically, it is shown that the privacy margin increases quadratically in the inverse of the angular separation between the true and the fake paths under Eve's perspective. Numerical simulations validate the theoretical findings on CRBs and showcase the approach's benefit in terms of bit error rates achievable by Bob and Eve.

Physical Layer Location Privacy in SIMO Communication Using Fake Path Injection

TL;DR

This work addresses location privacy in SIMO wireless links by injecting fake propagation paths and securely sharing their parameters with a legitimate receiver. The core method uses a CRB-based privacy margin, defined as the ratio of Eve’s minimum CRB eigenvalue to Bob’s maximum CRB eigenvalue, to quantify privacy gains, and leverages spectral properties of generalized Vandermonde matrices and the Dirichlet kernel to derive explicit bounds. The main contributions include two main theorems giving CRB bounds under AoA-only and joint AoA-channel estimation, revealing a quadratic scaling of privacy with the inverse angular separation between true and fake paths, and a corollary showing privacy gains scale with antenna counts and separation. Numerical experiments validate the theoretical bounds and illustrate practical benefits in BER for Bob and Eve, highlighting the potential of fake-path injection for physical-layer privacy in multi-user SIMO systems and suggesting extensions to MIMO scenarios.

Abstract

Fake path injection is an emerging paradigm for inducing privacy over wireless networks. In this paper, fake paths are injected by the transmitters into a single-input multiple-output (SIMO) communication channel to obscure their physical location from an eavesdropper. The case where the receiver (Bob) and the eavesdropper (Eve) use a linear uniform array to locate the transmitter's (Alice) position is considered. A novel statistical privacy metric is defined as the ratio between the smallest (resp. largest) eigenvalues of Eve's (resp. Bob's) Cramér-Rao lower bound (CRB) on the SIMO channel parameters to assess the privacy enhancements. Leveraging the spectral properties of generalized Vandermonde matrices, bounds on the privacy margin of the proposed scheme are derived. Specifically, it is shown that the privacy margin increases quadratically in the inverse of the angular separation between the true and the fake paths under Eve's perspective. Numerical simulations validate the theoretical findings on CRBs and showcase the approach's benefit in terms of bit error rates achievable by Bob and Eve.
Paper Structure (17 sections, 5 theorems, 28 equations, 4 figures)

This paper contains 17 sections, 5 theorems, 28 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Contributions and Organization of the Paper
  3. Mathematical Notation and Definitions
  4. Problem Statement
  5. SIMO Model with Fake Path Injection
  6. Statistical Privacy Metric
  7. Main Results
  8. Privacy on the Angle of Arrivals
  9. Channel Coefficients--AoAs Privacy
  10. Proofs of Theorem \ref{['theo:privacy_aoa']} and Theorem \ref{['theo:privacy_aoa_channel']}
  11. Numerical Bounds on the Dirichlet Kernel
  12. Proof of Theorem \ref{['theo:privacy_aoa']}
  13. Proof of Theorem \ref{['theo:privacy_aoa_channel']}
  14. Numerical Experiments
  15. Validation of the theorems
  16. ...and 2 more sections

Key Result

Theorem 2

Assume $\Delta_B \geq \frac{\pi^2}{N}$, and $\delta_E < \frac{\Delta_E}{2}$. Then there exist two numerical constants $C > 0$ and $C'>0$ such that

Figures (4)

  • Figure 1: SIMO communication model with fake path injection.
  • Figure 2: Theoretical and realized extremal values of Bob's and Eve's CRB, case of known channel coefficients.
  • Figure 3: Fake path separation needed to achieve a target secrecy margin $\gamma$, case of known channel coefficients.
  • Figure 4: BER of Bob and Eve after estimating the CSI

Theorems & Definitions (6)

  • Definition 1: Statistical privacy margin
  • Theorem 2
  • Corollary 3
  • Theorem 4
  • Corollary 5
  • Lemma 6