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Secure Integrated Sensing and Communication Under Correlated Rayleigh Fading

Martin Mittelbach, Rafael F. Schaefer, Matthieu Bloch, Aylin Yener, Onur Günlü

Abstract

We consider a secure integrated sensing and communication (ISAC) scenario, in which a signal is transmitted through a state-dependent wiretap channel with one legitimate receiver with which the transmitter communicates and one honest-but-curious target that the transmitter wants to sense. The secure ISAC channel is modeled as two state-dependent fast-fading channels with correlated Rayleigh fading coefficients and independent additive Gaussian noise components. Delayed channel outputs are fed back to the transmitter to improve the communication performance and to estimate the channel state sequence. We establish and illustrate an achievable secrecy-distortion region for degraded secure ISAC channels under correlated Rayleigh fading. We also evaluate the inner bound for a large set of parameters to derive practical design insights for secure ISAC methods. The presented results include in particular parameter ranges for which the secrecy capacity of a classical wiretap channel setup is surpassed and for which the channel capacity is approached.

Secure Integrated Sensing and Communication Under Correlated Rayleigh Fading

Abstract

We consider a secure integrated sensing and communication (ISAC) scenario, in which a signal is transmitted through a state-dependent wiretap channel with one legitimate receiver with which the transmitter communicates and one honest-but-curious target that the transmitter wants to sense. The secure ISAC channel is modeled as two state-dependent fast-fading channels with correlated Rayleigh fading coefficients and independent additive Gaussian noise components. Delayed channel outputs are fed back to the transmitter to improve the communication performance and to estimate the channel state sequence. We establish and illustrate an achievable secrecy-distortion region for degraded secure ISAC channels under correlated Rayleigh fading. We also evaluate the inner bound for a large set of parameters to derive practical design insights for secure ISAC methods. The presented results include in particular parameter ranges for which the secrecy capacity of a classical wiretap channel setup is surpassed and for which the channel capacity is approached.
Paper Structure (14 sections, 6 theorems, 45 equations, 4 figures, 1 table)

This paper contains 14 sections, 6 theorems, 45 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model and Problem Definition
  3. Correlated-Fading AGN ISAC Channel Secrecy-Distortion Regions
  4. Secrecy-Distortion Region
  5. Bivariate Rayleigh Fading
  6. Achievable Rates for Gaussian Input
  7. Evaluation of Eq. \ref{['Eq:Achievable-Rate-a']}
  8. Evaluation of Eq. \ref{['Eq:Achievable-Rate-b']}
  9. Evaluation of Eq. \ref{['Eq:Achievable-Rate-c']}
  10. Numerical Results and Discussions
  11. Proof of Proposition \ref{['Prop:Part-A']}
  12. Proof of Proposition \ref{['prop:part-b-bound']}
  13. Proof of Proposition \ref{['Prop:Part-C']}
  14. Figures for Numerical Results

Key Result

Theorem 1

For physically-degraded ISAC channels, the secrecy-distortion region is the union w. r. t. all probability distributions $P_{X}$ of the rate-distortion tuples $(R,D_1,D_2)$ satisfying

Figures (4)

  • Figure 1: Secure ISAC model for $i~=~[1:n]$ and $j=1,2$, for which the message $M$ should be kept secret from the eavesdropper. We impose an average transmit power constraint on the channel input symbols $X_i$ and assume independent AGN components $N_{1,i}$ and $N_{2,i}$. We principally consider perfect channel output feedback with unit symbol time delay, i.e., $Z_{i-1}=(Y_{1,i-1},Y_{2,i-1})$ such that the function $f(\cdot,\cdot)$ is the identity function.
  • Figure 2: $R_{\alpha},R_{\alpha,\mathrm{ub}},\text{ and }R_{\beta}$ for power correlation coefficient $\rho^2=0.01$.
  • Figure 3: $R_{\alpha},R_{\alpha,\mathrm{ub}},\text{ and }R_{\beta}$ for power correlation coefficient $\rho^2=0.50$.
  • Figure 4: $R_{\alpha},R_{\alpha,\mathrm{ub}},\text{ and }R_{\beta}$ for power correlation coefficient $\rho^2=0.90$.

Theorems & Definitions (8)

  • Definition 1
  • Definition 2
  • Theorem 1: oursecureISACJSAIT
  • Corollary 1
  • Proposition 1
  • Proposition 2
  • Proposition 3
  • Proposition 4