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Multi-User Cooperation for Covert Communication Under Quasi-Static Fading

Jinyoung Lee, Duc Trung Dinh, Hyeonsik Yeom, Si-Hyeon Lee, Jeongseok Ha

TL;DR

It will be proved that the optimal strategy for the non-covert users is an on-off scheme with equal transmit power and the theoretical results derived in this work are confirmed by comparing them with numerical results obtained with exhaustive searches.

Abstract

This work studies a covert communication scheme for an uplink multi-user scenario in which some users are opportunistically selected to help a covert user. In particular, the selected users emit interfering signals via an orthogonal resource dedicated to the covert user together with signals for their own communications using orthogonal resources allocated to the selected users, which helps the covert user hide the presence of the covert communication. For the covert communication scheme, we carry out extensive analysis and find system parameters in closed forms. The analytic derivation for the system parameters allow one to find the optimal combination of system parameters by performing a simple one-dimensional search. In addition, the analytic results elucidate relations among the system parameters. In particular, it will be proved that the optimal strategy for the non-covert users is an on-off scheme with equal transmit power. The theoretical results derived in this work are confirmed by comparing them with numerical results obtained with exhaustive searches. Finally, we demonstrate that the results of work can be utilized in versatile ways by demonstrating a design of covert communication with energy efficiency into account.

Multi-User Cooperation for Covert Communication Under Quasi-Static Fading

TL;DR

It will be proved that the optimal strategy for the non-covert users is an on-off scheme with equal transmit power and the theoretical results derived in this work are confirmed by comparing them with numerical results obtained with exhaustive searches.

Abstract

This work studies a covert communication scheme for an uplink multi-user scenario in which some users are opportunistically selected to help a covert user. In particular, the selected users emit interfering signals via an orthogonal resource dedicated to the covert user together with signals for their own communications using orthogonal resources allocated to the selected users, which helps the covert user hide the presence of the covert communication. For the covert communication scheme, we carry out extensive analysis and find system parameters in closed forms. The analytic derivation for the system parameters allow one to find the optimal combination of system parameters by performing a simple one-dimensional search. In addition, the analytic results elucidate relations among the system parameters. In particular, it will be proved that the optimal strategy for the non-covert users is an on-off scheme with equal transmit power. The theoretical results derived in this work are confirmed by comparing them with numerical results obtained with exhaustive searches. Finally, we demonstrate that the results of work can be utilized in versatile ways by demonstrating a design of covert communication with energy efficiency into account.
Paper Structure (15 sections, 9 theorems, 82 equations, 8 figures, 1 table)

This paper contains 15 sections, 9 theorems, 82 equations, 8 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. System Model
  4. Detection Error at Willie
  5. Problem Formulation
  6. Optimal Power Profile for Cooperative Users
  7. Detection Performance for Willie
  8. Optimization of Legitimate Users' Parameters
  9. Numerical results
  10. Conclusions
  11. Proof of Proposition \ref{['prop:power_profile']}
  12. Proof of Lemma \ref{['lemma:DEP']}
  13. Proof of Lemma \ref{['lemma:connection_prob']}
  14. Proof of Theorem \ref{['theorem:Opt_R']}
  15. Proof of Cross Point

Key Result

Proposition 1

The on-off scheme with the maximum transmit power is the optimal power allocation of the users for given $R$ and $P_a$. That is, The activation threshold, $\tau$ is decided to make the inequality, $\zeta_{\min} \ge 1 - \epsilon$ hold while minimizing $\Omega = \sum_m P^2_m$.

Figures (8)

  • Figure 1: System model of multi-user cooperation for covert communication.
  • Figure 2: Detection error probability, $\zeta$, versus the detection threshold, $\gamma$, with $K = 25$ and $K = 15$, and $P_a = P_{\max}$.
  • Figure 3: Minimum detection error probability, $\zeta_{\min}$, versus the number of cooperative users, $K$, when $\epsilon=0.05$.
  • Figure 4: Throughput, $\eta$, versus the covert rates, $R$, for $M=500$, $P_a = 0.83$, $\epsilon=0.03$, and $\epsilon=0.025$.
  • Figure 5: The peak maximum throughput, $\eta^*_{\max}$, versus the covert constraint, $\zeta \geq 1 - \epsilon$, for $M=1000$, $M=500$, and $M=200$ when $P_{\max} = 1$.
  • ...and 3 more figures

Theorems & Definitions (19)

  • Proposition 1
  • proof
  • Remark 1
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Theorem 3
  • proof
  • Theorem 4
  • ...and 9 more