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On Stochastic Performance Analysis of Secure Integrated Sensing and Communication Networks

Marziyeh Soltani, Mahtab Mirmohseni, Rahim Tafazolli

TL;DR

This work analyzes the stochastic security performance of a downlink MIMO ISAC system facing both a communication eavesdropper and a sensing eavesdropper under Rayleigh fading. It introduces an artificial-noise aided transmit structure and derives exact expressions for the secrecy ergodic rate $C_s=(E[R]-E[R_e])^+$ and the ergodic CRBs $E[\text{CRB}(\theta)]$ and $E[\text{CRB}(\phi)]$, treating the CRB as a random variable and employing CLT-based PDFs for tractability. The CRB analysis yields closed-form and bounded expressions for the CCDFs $P(\text{CRB}(\theta) > \epsilon)$ and $P(\text{CRB}(\phi) > \epsilon)$, along with exact ergodic CRBs and their common-approximation bounds, enabling precise evaluation of target localization privacy in stochastic ISAC networks. Numerical results corroborate the theory, showing positive secrecy rates for a range of power allocations and illustrating the distinct behavior of CRBs for the BS and the sensing eavesdropper, thereby highlighting the impact of AN-based beamforming on ISAC security and privacy.

Abstract

This paper analyzes the stochastic security performance of a multiple-input multiple-output (MIMO) integrated sensing and communication (ISAC) system in a downlink scenario. A base station (BS) transmits a multi-functional signal to simultaneously communicate with a user, sense a target angular location, and counteract eavesdropping threats. The system includes a passive single-antenna communication eavesdropper and a multi-antenna sensing eavesdropper attempting to infer the target location. The BS-user and BS-eavesdroppers channels follow Rayleigh fading, while the target azimuth angle is uniformly distributed. To evaluate the performance, we derive exact expressions for the secrecy ergodic rate and the ergodic Cramer-Rao lower bound (CRB) for target localization at both the BS and the sensing eavesdropper. This involves computing the probability density functions (PDFs) of the signal-to-noise ratio (SNR) and CRB, leveraging the central limit theorem for tractability. Numerical results validate our findings.

On Stochastic Performance Analysis of Secure Integrated Sensing and Communication Networks

TL;DR

This work analyzes the stochastic security performance of a downlink MIMO ISAC system facing both a communication eavesdropper and a sensing eavesdropper under Rayleigh fading. It introduces an artificial-noise aided transmit structure and derives exact expressions for the secrecy ergodic rate and the ergodic CRBs and , treating the CRB as a random variable and employing CLT-based PDFs for tractability. The CRB analysis yields closed-form and bounded expressions for the CCDFs and , along with exact ergodic CRBs and their common-approximation bounds, enabling precise evaluation of target localization privacy in stochastic ISAC networks. Numerical results corroborate the theory, showing positive secrecy rates for a range of power allocations and illustrating the distinct behavior of CRBs for the BS and the sensing eavesdropper, thereby highlighting the impact of AN-based beamforming on ISAC security and privacy.

Abstract

This paper analyzes the stochastic security performance of a multiple-input multiple-output (MIMO) integrated sensing and communication (ISAC) system in a downlink scenario. A base station (BS) transmits a multi-functional signal to simultaneously communicate with a user, sense a target angular location, and counteract eavesdropping threats. The system includes a passive single-antenna communication eavesdropper and a multi-antenna sensing eavesdropper attempting to infer the target location. The BS-user and BS-eavesdroppers channels follow Rayleigh fading, while the target azimuth angle is uniformly distributed. To evaluate the performance, we derive exact expressions for the secrecy ergodic rate and the ergodic Cramer-Rao lower bound (CRB) for target localization at both the BS and the sensing eavesdropper. This involves computing the probability density functions (PDFs) of the signal-to-noise ratio (SNR) and CRB, leveraging the central limit theorem for tractability. Numerical results validate our findings.

Paper Structure

This paper contains 17 sections, 9 theorems, 40 equations, 2 figures.

Table of Contents

  1. Introduction
  2. System Model and Transmission Strategy
  3. CRB analysis
  4. CCDF of $\text{CRB}(\theta)$ at the BS
  5. CCDF of $\text{CRB}(\phi)$ at the sensing eavesdropper
  6. Target Ergodic CRB at the BS and Sensing Eavesdropper
  7. Secrecy Ergodic Rate
  8. Numerical Results
  9. Proof of Lemma \ref{['lemma4']}
  10. Proof of Lemma \ref{['forsummery']}
  11. Proof of Lemma \ref{['forsummery2']}
  12. Proof of Lemma \ref{['forsummery3']}
  13. Proof of Lemma \ref{['exactderivationlemma']}
  14. Proof of Lemma \ref{['crbsensingeav']}
  15. Ergodic CRB at the BS and Sensing eavesdropper
  16. ...and 2 more sections

Key Result

Lemma 1

$\text{CRB}(\theta)$ is equal to: where $\mathbf{b}'$ is the derivation of $\mathbf{b}(\theta)$ with respect to $\theta$. ${r}_i\triangleq \mathcal{R}(e^{jf_i}{h}_i)=|{h}_i|\cos(f_i+{{\phi}}_i)$, ${t}_i\triangleq \mathcal{I}(e^{jf_i}{h}_i)=|{h}_i|\sin(f_i+{{\phi}}_i)$, ${{k}}_i\triangleq |{h}_i|^2$, ${R}\triangleq \sum_{i=1}^{N}{r}_

Figures (2)

  • Figure 1: System model.${\mathbf{Y}_{sr}}_{i}$ and $h_{ei}$ denotes the $i$-th row and element of $\mathbf{Y}_{sr}$ and $\mathbf{h}_{e}$, respectively
  • Figure 2: Ergodic rate, Ergodic CRB, and CCDF of CRB

Theorems & Definitions (10)

  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Lemma 4
  • Lemma 5
  • proof
  • Lemma 6
  • Lemma 7
  • Lemma 8
  • Lemma 9