Robust transmit design for secure AF relay networks with imperfect CSI

Lingxiang Li,Jun Fang,Zhi Chen,Yu Xu

doi:10.1186/s13638-016-0641-1

Abstract

This paper studies robust transmit design for secure AF relay networks with imperfect channel state information (CSI). Two CSI error models, deterministically bounded error model and stochastic error model, are considered. In order to use the power at relays more efficiently, a joint cooperative relaying and jamming scheme is considered, where relays cooperate to forward the source signal and simultaneously they cooperate to send jamming signals to confuse the eavesdroppers. In this joint cooperative relaying and jamming framework, we address the robust joint optimization of the relay weights and the input covariance matrix of jamming signals for secrecy rate maximization (SRM), under both total and individual relay power constraints. Specifically, for the case of deterministically bounded error model, where the CSI error can be specified by an uncertainty set, we maximize the worst-case secrecy rate. While for the case of stochastic error model, where the probability distribution of the CSI error is Gaussian, we maximize the outage constrained secrecy rate. The challenge of these considered SRM-based optimizations lies in their non-convexity. This paper shows that such SRM-based optimization can be solved in a convex fashion and via solving a sequence of semidefinite programs (SDPs). Numerical results are presented to show the efficacy of the proposed scheme.

Highlights

In the classical three-node wiretap channel, secrecy capacity is typically zero when the source-destination link is weaker than the source-eavesdropper link [1, 2]
When the power budget at relays is large enough, the secrecy rate achieved by the proposed scheme approaches the maximal achievable rate of the SRD link
It can be observed that both the secrecy rate achieved by the proposed scheme and that achieved by the relaying without jamming scheme decline with the increasing number of eavesdroppers

Summary

Introduction

In the classical three-node wiretap channel, secrecy capacity is typically zero when the source-destination link is weaker than the source-eavesdropper link [1, 2]. 1. Robust joint optimization of the relay weights and the input covariance matrix of jamming signals for secrecy rate maximization (SRM) is addressed, under both total and individual relay power constraints. Robust joint optimization of the relay weights and the input covariance matrix of jamming signals for secrecy rate maximization (SRM) is addressed, under both total and individual relay power constraints The challenge of these SRM-based optimizations lies in their non-convexity. We prove that the optimal relay weights and input covariance matrix of jamming signals in the SRC power minimization problem constitute an optimal solution to our inner problem In this way, we provide a tight convex relaxation of our inner problem. For a given relaying weight vector v and input covariance matrix of jamming signals QJ , the received signal-to-noise (SNR) at the destination and the mth eavesdropper are, respectively, γD.

Robust joint relaying and jamming design with norm-bounded CSI error

Worst-case secrecy rate constrained power minimization

Robust joint relaying and jamming design with stochastic CSI error

Conclusions