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Multi-User Covert Communication in Spatially Heterogeneous Wireless Networks

Jinyoung Lee, Hyeonsik Yeom

Abstract

This paper investigates an uplink multi-user covert communication system with spatially distributed users. Unlike prior works that approximate channel statistics using averaged parameters and homogeneous assumptions, this study explicitly models each user's geometric position and corresponding user-to-Willie and user-to-Bob channel variances. This approach enables an accurate characterization of spatially heterogeneous covert environments. We mathematically prove that a generalized on-off power control scheme, which jointly accounts for both Bob's and Willie's channels, constitutes the optimal transmission strategy in heterogeneous user configurations. Leveraging the optimal strategy, we derive closed-form expressions for the minimum detection error probability and the minimum number of cooperative users required to satisfy a covert constraint. With the closed-form expressions, comprehensive theoretical analyses are conducted, which are validated by Monte-Carlo simulations. One important insight obtained from the analysis is that user spatial heterogeneity can enhance covert communication performance. Building on these findings, a piecewise search algorithm is proposed to achieve exact optimality with significantly reduced computational complexity. We demonstrate that optimization considering user's spatial heterogeneity achieves substantially improved covert communication performance than that based on the assumption of spatial homogeneity.

Multi-User Covert Communication in Spatially Heterogeneous Wireless Networks

Abstract

This paper investigates an uplink multi-user covert communication system with spatially distributed users. Unlike prior works that approximate channel statistics using averaged parameters and homogeneous assumptions, this study explicitly models each user's geometric position and corresponding user-to-Willie and user-to-Bob channel variances. This approach enables an accurate characterization of spatially heterogeneous covert environments. We mathematically prove that a generalized on-off power control scheme, which jointly accounts for both Bob's and Willie's channels, constitutes the optimal transmission strategy in heterogeneous user configurations. Leveraging the optimal strategy, we derive closed-form expressions for the minimum detection error probability and the minimum number of cooperative users required to satisfy a covert constraint. With the closed-form expressions, comprehensive theoretical analyses are conducted, which are validated by Monte-Carlo simulations. One important insight obtained from the analysis is that user spatial heterogeneity can enhance covert communication performance. Building on these findings, a piecewise search algorithm is proposed to achieve exact optimality with significantly reduced computational complexity. We demonstrate that optimization considering user's spatial heterogeneity achieves substantially improved covert communication performance than that based on the assumption of spatial homogeneity.

Paper Structure

This paper contains 19 sections, 8 theorems, 67 equations, 7 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. System Model
  4. Detection at Willie
  5. Optimization Problem
  6. Optimal Transmit Power Profile
  7. Analysis of Detection at Willie
  8. Optimization of System Parameters
  9. Reformulation of the Optimization Problem
  10. Optimization of Transmit Power for Alice
  11. Numerical Results
  12. Simulation Setup
  13. Willie's Detection Performance
  14. Impact of Covertness Level and Spatial Parameters
  15. Performance Comparison with Existing Work
  16. ...and 4 more sections

Key Result

Proposition 1

For sufficiently large $M$, the optimal transmit power profile for non-covert users under spatial heterogeneity is an on–off scheme for a given $P_a$, i.e.,

Figures (7)

  • Figure 1: System model of multi-user cooperation for covert communication.
  • Figure 2: Spatial configuration of the spatially adverse scenario.
  • Figure 3: DEP $\zeta$ as a function of the detection threshold $\gamma$ for various combinations of $K$ and $P_a$.
  • Figure 4: Minimum DEP $\zeta_{\min}$ versus the number of cooperative users $K$ for different transmit powers $P_a$.
  • Figure 5: Minimum number of cooperative users $K_{\min}$ versus covert constraint $1-\epsilon$ for $P_a = 25~\mathrm{mW}$.
  • ...and 2 more figures

Theorems & Definitions (20)

  • Proposition 1
  • proof
  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • ...and 10 more