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Unified framework for outage-constrained rate maximization in secure ISAC under various sensing metrics

Hancheng Zhu, Zongze Li, Yik-Chung Wu

Abstract

Integrated sensing and communication (ISAC) is poised to redefine the landscape of wireless networks by seamlessly combining data transmission and environmental sensing. However, ISAC systems remain susceptible to eavesdropping, especially under uncertainty in eavesdroppers' channel state information, which can lead to secrecy outages. On the other hand, diverse and complex sensing performance requirements further complicate resource optimization, often requiring custom solutions for each scenario. To this end, this paper introduces a unified optimization framework that holistically addresses both the worst-case user secrecy rate and the sum secrecy rate across multiple users. Besides putting the two commonly used objectives into a single but flexible objective function, the framework accurately controls secrecy outage probabilities while accommodating a broad spectrum of sensing constraints. To solve such a general problem, we integrate the sensing requirements into the objective function through an auxiliary variable. This enables efficient alternating optimization and the proposed approach is theoretically guaranteed to converge to at least a stationary point of the original problem. Extensive simulation results show that the proposed framework consistently achieves higher optimized secrecy rates under various sensing constraints compared to existing methods. These results underscore the proposed unified framework's superiority and versatility in secure ISAC systems.

Unified framework for outage-constrained rate maximization in secure ISAC under various sensing metrics

Abstract

Integrated sensing and communication (ISAC) is poised to redefine the landscape of wireless networks by seamlessly combining data transmission and environmental sensing. However, ISAC systems remain susceptible to eavesdropping, especially under uncertainty in eavesdroppers' channel state information, which can lead to secrecy outages. On the other hand, diverse and complex sensing performance requirements further complicate resource optimization, often requiring custom solutions for each scenario. To this end, this paper introduces a unified optimization framework that holistically addresses both the worst-case user secrecy rate and the sum secrecy rate across multiple users. Besides putting the two commonly used objectives into a single but flexible objective function, the framework accurately controls secrecy outage probabilities while accommodating a broad spectrum of sensing constraints. To solve such a general problem, we integrate the sensing requirements into the objective function through an auxiliary variable. This enables efficient alternating optimization and the proposed approach is theoretically guaranteed to converge to at least a stationary point of the original problem. Extensive simulation results show that the proposed framework consistently achieves higher optimized secrecy rates under various sensing constraints compared to existing methods. These results underscore the proposed unified framework's superiority and versatility in secure ISAC systems.
Paper Structure (14 sections, 3 theorems, 38 equations, 7 figures, 1 table, 1 algorithm)

This paper contains 14 sections, 3 theorems, 38 equations, 7 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model and worst user secrecy rate maximization
  3. Extension to general sensing constraint in ISAC
  4. Proposed framework for solving the general max-min problem \ref{['eq:19']}
  5. Regularizing the inner minimization problem
  6. Finding an ascent point for the outer maximization problem
  7. Overall modified AO algorithm
  8. Solution quality analysis
  9. Solving \ref{['eq:16']} and \ref{['eq:17']} under different ISAC sensing metrics
  10. Obtaining the global optimal solution of \ref{['eq:16']}
  11. Obtaining the global optimal solution of \ref{['eq:17']}
  12. Computation of gradients in various ISAC scenarios
  13. Simulation Results and Discussions
  14. Conclusions

Key Result

Lemma 1

Yang:20 Suppose ${{\bm g}_{j}} \sim {\rm{{\cal C}{\cal N}}} ( {{\bm 0},\rho _{j}^2{{\bm I}_N}} ), \forall j$, the SOP constraint eq:8b can be equivalently transformed into where ${{\rho _j^2} \mathord{\left/ {\newline} \right. \nulldelimiterspace} {\varsigma _j^2}}$ is interpreted as the statistical signal-to-noise ratio (SNR) for the $j^{th}$ eavesdropper.

Figures (7)

  • Figure 1: Secure ISAC network model
  • Figure 2: Worst user secrecy rate performance with $I=5$, $J=8$, $N=20$, $M=5$, $P_{BS} = 20{\rm dBm}$. (a) $\Gamma = 10{\rm dB}$ under sensing SINR constraint, (b) $\gamma = 0.1$ under beampattern matching constraint, (c) ${P_{FA}} = 0.1$ and $\phi = 0.9$ under detection probability constraint
  • Figure 3: Worst user secrecy rate versus number of BS antennas under three different sensing metrics. Simulation settings: (a) $I=7$, $J=9$, $M=6$, $P_{BS} = 20{\rm dBm}$ and $\Gamma = 10{\rm dB}$ for sensing SINR constraint; (b)$I=5$, $J=7$, $M=4$, $P_{BS} = 20{\rm dBm}$ and $\gamma = 0.1$ for beampattern matching constraint; (c) $I=6$, $N=28$, $M=7$, $P_{BS} = 15{\rm dBm}$, $P_{FA}=0.1$ and $\phi = 0.85$ for detection probability constraint.
  • Figure 4: Worst user secrecy rate versus number of eavesdroppers under three different sensing metrics. Simulation settings: (a) $I=7$, $N=24$, $M=6$, $P_{BS} = 15{\rm dBm}$ and $\Gamma = 10{\rm dB}$ for sensing SINR constraint; (b) $I=5$, $N=24$, $M=4$, $P_{BS} = 10{\rm dBm}$ and $\gamma = 0.1$ for beampattern matching constraint; (c) $I=6$, $J=4$, $M=7$, $P_{BS} = 20{\rm dBm}$, $P_{FA}=0.1$ and $\phi = 0.9$ for detection probability constraint.
  • Figure 5: Realized sensing performance under different sensing constraint thresholds (a) $N=20$, $I=6$, $J=7$, $M=5$, $P_{BS} = 20{\rm dBm}$ with sensing SINR metric, (b) $N=16$, $I=5$, $J=4$, $M=6$, $P_{BS} = 20{\rm dBm}$ with beampattern matching metric, (c) $N=12$, $I=6$, $J=5$, $M=4$, $P_{BS} = 20{\rm dBm}$, ${P_{FA}} = 0.1$ with detection probability metric
  • ...and 2 more figures

Theorems & Definitions (4)

  • Lemma 1
  • Proposition 1
  • Definition 1
  • Proposition 2