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Simultaneous Multi-Modal Covert Communications: Analysis and Optimization

Justin H. Kong, Terrence J. Moore, Fikadu T. Dagefu

Abstract

This paper investigates the problem of covert communications in a heterogeneous wireless network where multiple communication modalities are used simultaneously. In this setup, a legitimate transmitter sends confidential data to its receiver by selecting multiple modalities with the goal of maximizing communication covertness against a passive adversary (Willie) while satisfying a transmission rate requirement. We analyze two distinct scenarios for a given observation time by Willie. The two scenarios are: (i) Willie knows the modalities selected by the friendly transmitter, and (ii) Willie is unaware of the selected modalities. We first derive the optimal detector for Willie that minimizes the detection error probability (DEP) in both cases. For the first scenario, we derive an exact expression for the DEP and provide a computationally efficient approximation. For the second scenario, we introduce the DEP expressions in the low-signal-to-noise ratio (SNR) regime at Willie. Building on this analysis, we propose a novel low-complexity modality set selection technique designed to maximize the DEP subject to a rate constraint. Numerical simulations validate the derived analytical expressions and demonstrate that the proposed modality set selection technique achieves near-optimal performance, outperforming benchmark schemes.

Simultaneous Multi-Modal Covert Communications: Analysis and Optimization

Abstract

This paper investigates the problem of covert communications in a heterogeneous wireless network where multiple communication modalities are used simultaneously. In this setup, a legitimate transmitter sends confidential data to its receiver by selecting multiple modalities with the goal of maximizing communication covertness against a passive adversary (Willie) while satisfying a transmission rate requirement. We analyze two distinct scenarios for a given observation time by Willie. The two scenarios are: (i) Willie knows the modalities selected by the friendly transmitter, and (ii) Willie is unaware of the selected modalities. We first derive the optimal detector for Willie that minimizes the detection error probability (DEP) in both cases. For the first scenario, we derive an exact expression for the DEP and provide a computationally efficient approximation. For the second scenario, we introduce the DEP expressions in the low-signal-to-noise ratio (SNR) regime at Willie. Building on this analysis, we propose a novel low-complexity modality set selection technique designed to maximize the DEP subject to a rate constraint. Numerical simulations validate the derived analytical expressions and demonstrate that the proposed modality set selection technique achieves near-optimal performance, outperforming benchmark schemes.
Paper Structure (32 sections, 8 theorems, 56 equations, 9 figures, 1 table, 1 algorithm)

This paper contains 32 sections, 8 theorems, 56 equations, 9 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work and Motivation
  3. Contributions and Organization
  4. Network model
  5. Detection at Willie
  6. Communication Performance at Bob
  7. Optimization Problem
  8. Detection by a Fully-Aware Adversary
  9. Optimal Decision Rule
  10. Exact DEP analysis
  11. Closed-Form DEP Approximation
  12. Conventional DEP Metrics
  13. Detection under Modality Uncertainty
  14. Optimal Decision Rule under Uncertainty
  15. DEP Analysis in Low-SNR Regime
  16. ...and 17 more sections

Key Result

Theorem 1

When the selected subset of modalities ${\mathbf{s}}$ is known to Willie, the optimal decision rule at Willie that minimizes the DEP ${\texttt{P}}_{\text{DEP},{\mathbf{s}}}$ is where the SNR at Willie $\rho_{\text{W},m}$, weight $w_m$, received signal strength $E_m$, test statistic $T_{{\mathbf{s}}}$, and detection threshold $\delta_{{\mathbf{s}}}$ are respectively expressed as

Figures (9)

  • Figure 1: Network model for simultaneous multi-modal covert communications.
  • Figure 2: Performance trade-off: DEP and rate for individual modalities.
  • Figure 3: Validation of the derived exact DEP expression and approximation.
  • Figure 4: DEP performance for various active modality subsets.
  • Figure 5: Impact of modality uncertainty on the DEP.
  • ...and 4 more figures

Theorems & Definitions (14)

  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Lemma 1
  • proof
  • Corollary 1
  • Corollary 2
  • Theorem 3
  • proof
  • ...and 4 more