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On Achievable Covert Communication Performance under CSI Estimation Error and Feedback Delay

Jiaqing Bai, Ji He, Yanping Chen, Yulong Shen, Xiaohong Jiang

TL;DR

This work analyzes covert communications in a two‑hop DF relay under realistic CSI impairments caused by channel estimation error (CEE) and feedback delay (FD). It develops a MMSE/Gauss–Markov based CSI model, couples it with a channel inversion power control (CIPC) scheme, and derives closed‑form expressions for detection error probability (DEP) and covert rate (CR). An alternating optimization framework optimizes the channel inversion parameter $Q_c$ and data symbol length $L_d$ to maximize the long‑term CR while satisfying a DEP constraint, with dedicated algorithms for power control and symbol scheduling. Numerical results validate the theory and show how imperfect CSI degrades covert performance, while the proposed joint design mitigates these effects and enables practical covert operation in two‑hop networks.

Abstract

Covert communication's effectiveness critically depends on precise channel state information (CSI). This paper investigates the impact of imperfect CSI on achievable covert communication performance in a two-hop relay system. Firstly, we introduce a two-hop covert transmission scheme utilizing channel inversion power control (CIPC) to manage opportunistic interference, eliminating the receiver's self-interference. Given that CSI estimation error (CEE) and feedback delay (FD) are the two primary factors leading to imperfect CSI, we construct a comprehensive theoretical model to accurately characterize their effects on CSI quality. With the aid of this model, we then derive closed-form solutions for detection error probability (DEP) and covert rate (CR), establishing an analytical framework to delineate the inherent relationship between CEE, FD, and covert performance. Furthermore, to mitigate the adverse effects of imperfect CSI on achievable covert performance, we investigate the joint optimization of channel inversion power and data symbol length to maximize CR under DEP constraints and propose an iterative alternating algorithm to solve the bi-dimensional non-convex optimization problem. Finally, extensive experimental results validate our theoretical framework and illustrate the impact of imperfect CSI on achievable covert performance.

On Achievable Covert Communication Performance under CSI Estimation Error and Feedback Delay

TL;DR

This work analyzes covert communications in a two‑hop DF relay under realistic CSI impairments caused by channel estimation error (CEE) and feedback delay (FD). It develops a MMSE/Gauss–Markov based CSI model, couples it with a channel inversion power control (CIPC) scheme, and derives closed‑form expressions for detection error probability (DEP) and covert rate (CR). An alternating optimization framework optimizes the channel inversion parameter and data symbol length to maximize the long‑term CR while satisfying a DEP constraint, with dedicated algorithms for power control and symbol scheduling. Numerical results validate the theory and show how imperfect CSI degrades covert performance, while the proposed joint design mitigates these effects and enables practical covert operation in two‑hop networks.

Abstract

Covert communication's effectiveness critically depends on precise channel state information (CSI). This paper investigates the impact of imperfect CSI on achievable covert communication performance in a two-hop relay system. Firstly, we introduce a two-hop covert transmission scheme utilizing channel inversion power control (CIPC) to manage opportunistic interference, eliminating the receiver's self-interference. Given that CSI estimation error (CEE) and feedback delay (FD) are the two primary factors leading to imperfect CSI, we construct a comprehensive theoretical model to accurately characterize their effects on CSI quality. With the aid of this model, we then derive closed-form solutions for detection error probability (DEP) and covert rate (CR), establishing an analytical framework to delineate the inherent relationship between CEE, FD, and covert performance. Furthermore, to mitigate the adverse effects of imperfect CSI on achievable covert performance, we investigate the joint optimization of channel inversion power and data symbol length to maximize CR under DEP constraints and propose an iterative alternating algorithm to solve the bi-dimensional non-convex optimization problem. Finally, extensive experimental results validate our theoretical framework and illustrate the impact of imperfect CSI on achievable covert performance.
Paper Structure (15 sections, 6 theorems, 62 equations, 12 figures, 3 algorithms)

This paper contains 15 sections, 6 theorems, 62 equations, 12 figures, 3 algorithms.

Table of Contents

  1. INTRODUCTION
  2. SYSTEM MODEL AND PRELIMINARIES
  3. System Model
  4. The Modeling of Imperfect CSI
  5. Two-Hop Covert Transmission
  6. Willie's Detection Strategy
  7. PERFORMANCE ANALYSIS
  8. End-to-End Successful Transmission Probability
  9. Derivation of Detection Error Probability
  10. Optimal Problem of Maximal CR
  11. NUMERICAL RESULTS
  12. Simulation Settings and Model Validation
  13. Minimum DEP $\xi^*$ Analysis
  14. Optimal CR $\bar{R}_{ab}$ Analysis
  15. CONCLUSIONS

Key Result

Theorem 1

In the considered two-hop covert relaying system with the imperfect CSI, the E2E successful transmission probability is determined as here $\mathcal{P}_{su}^r$ and $\mathcal{P}_{su}^b$ are respectively given by where $\phi_1\overset{\Delta}=\frac{Q_c}{P_{max}}$, $\phi_2\overset{\Delta}=\frac{Q_c\rho _{ar}^2}{4^{R_{ab}} - 1}-N_0$, $\phi_3\overset{\Delta}=\frac{Q_c\rho _{rb}^2}{4^{R_{ab}} - 1}-N_0

Figures (12)

  • Figure 1: The illustration of two-hop covert relaying system.
  • Figure 2: Overall transmission scheduling of the concerned system.
  • Figure 3: Overall transmission scheduling of the concerned system.
  • Figure 4: Successful transmission probability $\mathcal{P}_{su}$ vs. $\rho_{ar}^2$ with $P_{max}=20$dBm, $N_0=0$dBm.
  • Figure 5: Successful transmission probability $\mathcal{P}_{su}$ vs. design parameter $Q_c$ with $P_{max}=20$dBm, $N_0=0$dBm.
  • ...and 7 more figures

Theorems & Definitions (6)

  • Theorem 1
  • Corollary 1
  • Theorem 2
  • Theorem 3
  • Lemma 1
  • Theorem 4