[Paper Review] Sum Secrecy Rate in Full-Duplex Wiretap Channel with Imperfect CSI

Sanjay Vishwakarma, A. Chockalingam|arXiv (Cornell University)|Nov 15, 2013

Wireless Communication Security Techniques16 references3 citations

TL;DR

This paper investigates the sum secrecy rate in a full-duplex wiretap channel with single-antenna users and an eavesdropper under imperfect channel state information (CSI). It formulates a semidefinite programming (SDP) problem to maximize the sum secrecy rate by jointly optimizing message and artificial jamming signal powers, showing that CSI errors reduce the achievable secrecy rate region, with performance degrading as error bounds increase.

ABSTRACT

In this paper, we consider the achievable sum secrecy rate in full-duplex wiretap channel in the presence of an eavesdropper and imperfect channel state information (CSI). We assume that the users participating in full-duplex communication and the eavesdropper have single antenna each. The users have individual transmit power constraints. They also transmit jamming signals to improve the secrecy rates. We obtain the achievable perfect secrecy rate region by maximizing the sum secrecy rate. We also obtain the corresponding optimum powers of the message signals and the jamming signals. Numerical results that show the impact of imperfect CSI on the achievable secrecy rate region are presented.

Motivation & Objective

• To characterize the achievable sum secrecy rate region in a full-duplex two-way wiretap channel with imperfect CSI.
• To optimize the transmit powers of both message signals and artificial jamming signals to maximize secrecy rate under individual power constraints.
• To analyze the impact of bounded CSI errors on the secrecy rate region and system performance.
• To derive a semidefinite programming formulation that ensures perfect secrecy under CSI uncertainty.

Proposed method

• Formulates a full-duplex two-user wiretap channel with single-antenna transmitters, receivers, and an eavesdropper.
• Introduces artificial jamming signals at both transmitters to degrade the eavesdropper’s channel and enhance secrecy.
• Models CSI errors as bounded absolute deviations around estimated channel gains, with error bounds denoted by ε.
• Derives a semidefinite programming (SDP) problem to maximize the sum secrecy rate under perfect secrecy constraints.
• Uses S-lemma and Schur complement to transform probabilistic constraints into convex SDP constraints for tractable optimization.
• Applies bisection search to solve the resulting SDP problem for the minimum feasible secrecy rate threshold.

Experimental results

Research questions

• RQ1 How does imperfect CSI affect the achievable sum secrecy rate region in a full-duplex two-way wiretap channel?
• RQ2 What is the optimal power allocation strategy for message and jamming signals that maximizes the sum secrecy rate under power constraints and CSI uncertainty?
• RQ3 How do bounded CSI errors in the legitimate and eavesdropper channels impact the secrecy rate performance?
• RQ4 Can semidefinite programming be effectively used to compute the secrecy rate region under imperfect CSI with guaranteed perfect secrecy?

Key findings

• The achievable secrecy rate region shrinks as the magnitude of CSI errors increases, demonstrating a direct performance degradation due to channel uncertainty.
• Increasing the transmit power from 3 dB to 6 dB results in a larger achievable secrecy rate region, confirming the benefit of higher power under imperfect CSI.
• The proposed SDP-based optimization framework successfully computes the optimal power allocation for message and jamming signals under perfect secrecy constraints.
• Numerical results show that even small CSI errors (e.g., ε = 0.04) significantly reduce the sum secrecy rate, highlighting the sensitivity of secrecy performance to CSI accuracy.
• The secrecy rate region is bounded by the minimum feasible value of the secrecy rate threshold obtained via bisection search on the SDP problem.
• The use of artificial jamming signals improves secrecy by degrading the eavesdropper’s channel, especially under imperfect CSI conditions.