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On the Secrecy Rate of In-Band Full-duplex Two-way Wiretap Channel

Navneet Garg, Haifeng Luo, Tharmalingam Ratnarajah

TL;DR

This work tackles a two-way MIMOME wiretap channel with in-band full-duplex operation and keyless security. It introduces an artificial-noise design that injects AN into both the signal and null spaces and develops a two-step, ergodic-rate–based power allocation to maximize the sum secrecy rate under transmit-power constraints, accounting for imperfect CSI and partial Eve knowledge. By modeling Eve’s precoder knowledge through chordal distance and selecting between known and unknown AN scenarios, the approach yields fast coarse and fine adjustments (via SCA/Newton steps) that closely track true secrecy rates under practical conditions. The results reveal that IBFD can enhance secrecy when AN knowledge is present, while limited information at Eve or CSI imperfections can further improve performance, highlighting a practical, adaptable design for secure two-way wireless links.

Abstract

In this paper, we consider a two-way wiretap Multi-Input Multi-Output Multi-antenna Eve (MIMOME) channel, where both nodes (Alice and Bob) transmit and receive in an in-band full-duplex (IBFD) manner. For this system with keyless security, we provide a novel artificial noise (AN) based signal design, where the AN is injected in both signal and null spaces. We present an ergodic secrecy rate approximation to derive the power allocation algorithm. We consider scenarios where AN is known and unknown to legitimate users and include imperfect channel information effects. To maximize secrecy rates subject to the transmit power constraint, a two-step power allocation solution is proposed, where the first step is known at Eve, and the second step helps to improve the secrecy further. We also consider scenarios where partial information is known by Eve and the effects of non-ideal self-interference cancellation. The usefulness and limitations of the resulting power allocation solution are analyzed and verified via simulations. Results show that secrecy rates are less when AN is unknown to receivers or Eve has more information about legitimate users. Since the ergodic approximation only considers Eves distance, the resulting power allocation provides secrecy rates close to the actual ones.

On the Secrecy Rate of In-Band Full-duplex Two-way Wiretap Channel

TL;DR

This work tackles a two-way MIMOME wiretap channel with in-band full-duplex operation and keyless security. It introduces an artificial-noise design that injects AN into both the signal and null spaces and develops a two-step, ergodic-rate–based power allocation to maximize the sum secrecy rate under transmit-power constraints, accounting for imperfect CSI and partial Eve knowledge. By modeling Eve’s precoder knowledge through chordal distance and selecting between known and unknown AN scenarios, the approach yields fast coarse and fine adjustments (via SCA/Newton steps) that closely track true secrecy rates under practical conditions. The results reveal that IBFD can enhance secrecy when AN knowledge is present, while limited information at Eve or CSI imperfections can further improve performance, highlighting a practical, adaptable design for secure two-way wireless links.

Abstract

In this paper, we consider a two-way wiretap Multi-Input Multi-Output Multi-antenna Eve (MIMOME) channel, where both nodes (Alice and Bob) transmit and receive in an in-band full-duplex (IBFD) manner. For this system with keyless security, we provide a novel artificial noise (AN) based signal design, where the AN is injected in both signal and null spaces. We present an ergodic secrecy rate approximation to derive the power allocation algorithm. We consider scenarios where AN is known and unknown to legitimate users and include imperfect channel information effects. To maximize secrecy rates subject to the transmit power constraint, a two-step power allocation solution is proposed, where the first step is known at Eve, and the second step helps to improve the secrecy further. We also consider scenarios where partial information is known by Eve and the effects of non-ideal self-interference cancellation. The usefulness and limitations of the resulting power allocation solution are analyzed and verified via simulations. Results show that secrecy rates are less when AN is unknown to receivers or Eve has more information about legitimate users. Since the ergodic approximation only considers Eves distance, the resulting power allocation provides secrecy rates close to the actual ones.
Paper Structure (33 sections, 2 theorems, 52 equations, 8 figures, 1 algorithm)

This paper contains 33 sections, 2 theorems, 52 equations, 8 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Contributions
  3. Orgnization
  4. Notations
  5. System Model
  6. Channel model
  7. Legitimate and eavesdropping channels
  8. Residual self-interference channels
  9. Precoding and transmitted signals
  10. Eve's knowledge about the precoder
  11. Received signals
  12. Secrecy rates
  13. Two-step secrecy power allocation
  14. Rate approximation
  15. Coarse power allocation
  16. ...and 18 more sections

Key Result

Lemma 1

For the received signal equation $\mathbf{y}=\mathbf{H}\mathbf{x}+\mathbf{z},$ where $\mathbf{z}\sim\mathcal{CN}\left(\mathbf{0},\mathbf{C}_{z}\right)$ and $\mathbf{x}\sim\mathcal{CN}\left(\mathbf{0},\mathbf{C}_{x}\right)$, the rate approximation can be obtained as

Figures (8)

  • Figure 1: Two-way wiretap channel model with Alice and Bob operating in IBFD manner.
  • Figure 2: Rates at Alice $(0,0)$, Bob $(0,1)$ and Eve $(0.5,5)$ with approximations for $P_{s,i}=1-P_{w,i}-P_{\underline{w},i}$, $P_{w,i}=P_{\underline{w},i}$, $P_{i}=25$ dB, $\kappa_{iE}=0.1$, $N_{A}=N_{B}=\frac{N_{E}}{2}=2b=4$.
  • Figure 3: Secrecy rate regions for Alice and Bob streams with known and unknown artificial noise $\theta=0,1$.
  • Figure 4: Sum secrecy rates with $P_{s,i}=1-P_{w,i}-P_{\underline{w},i}$, $P_{w,i}=P_{\underline{w},i}$.
  • Figure 5: Averaged sum secrecy rates versus strength of residual self-interference channels for different cases.
  • ...and 3 more figures

Theorems & Definitions (6)

  • Lemma 1
  • proof
  • Corollary 1
  • proof
  • proof
  • proof