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EURASIP Journal on Wireless Communications and Networking

Robust transmit design for secure AF relay networks with imperfect CSI

Lingxiang Li, Yu Xu, Zhi Chen, Jun Fang

Published Jun 2, 2016• 4 citations
Publisher

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.

DOI
10.1186/s13638-016-0641-1

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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.
This paper studies robust transmit design to maximize the worst-case secrecy rate in AF networks under both total and individual relay power constraints. Channel state information (CSI) in the network is assumed to be perfectly known except for that associated with the eavesdroppers whose imperfection is modeled as deterministic bounded errors. To use the power at the relay nodes more efficiently, a joint cooperative relaying and jamming scheme is considered. Through some matrix manipulations, we recast the original nonconvex optimization problem as a sequence of semidefinite programs (SDPs), which enables us to obtain the optimal relay weights and the optimal covariance matrix of the jamming signal. Numerical results are presented to show the efficacy of the proposed scheme.
In this paper, we compute worst case secrecy rates in amplify-and-forward (AF) relay beamforming with cooperative jamming (CJ) in the presence of imperfect channel state information (CSI). A source-destination pair aided by M relays is considered. Number of eavesdroppers J can be more than the number of relays. Out of the M relays, k1relays (1 ≤ k1≤ M) act as data relays and the remaining k2= M - k1relays act as jamming relays. Data relays aid the communication by relaying data in AF mode, and jamming relays cooperate by transmitting jamming signals (artificial noise). The jamming signals are created such that they degrade the eavesdroppers' channels but do not significantly affect the intended receiver's channel, thereby improving secrecy rate. Imperfection in the CSI is modeled using a norm-bounded error model. We solve for the optimum (k1, k2) and the weights of data relays and jamming relays that maximize the secrecy rate subject to a total relay power constraint. We relax the rank-one constraint on the complex semi-definite data relays and jamming relays weight matrices and reformulate the optimization problem into a form that can be solved using convex semi-definite programming. Numerical results on the secrecy rate that illustrate the effect of cooperative jamming, imperfect CSI, and number of eavesdroppers are presented.
In this paper, we study robust joint beamforming and cooperative jamming (CJ) in a secure decode-and-forward (DF) relay system in the presence of multiple eavesdroppers, in which a multi-antenna DF relay employs transmit beamforming to help the source deliver information to the destination and simultaneously generates Gaussian artificial noise to confuse these eavesdroppers. We assume that all the channel state information (CSI) is imperfectly known at the relay subject to norm-bounded CSI errors. Our objective is to maximize the achievable secrecy rate at the destination by jointly optimizing the transmit beamforming vector of information signals and the covariance matrix of jamming signals at the relay subject to its total transmit power constraint. Although this problem is non-convex and in general difficult to be solved, we obtain its optimal solution via the technique of semi-definite relaxation (SDR) together with a one-dimensional (1-D) search. Specifically, we prove that the SDR is tight for the problem of our interest. Finally, numerical results are provided to validate our proposed scheme.
We study the transmit design at relay nodes for secure amplify-and-forward (AF) networks. Two joint cooperative relaying and jamming schemes, namely Secrecy Rate Maximization Scheme and Null-Space Jamming Scheme, are proposed. In the first scheme, optimal relaying weight vector and optimal covariance matrix associated with the artificial noise (AN) are obtained, which involves doing a one-dimensional search and solving a sequence of semidefinite programs(SDPs). In the second scheme, which is suboptimal but computationally much cheaper, AN is designed to decrease the rate at the eavesdropper while the relaying weight vector is determined to increase the rate at the destination. In addition, Power Allocation based on secrecy rate maximization provides a balance between these two goals. Numerical results show that the proposed Secrecy Rate Maximization Scheme outperforms the existing cooperative relaying without jamming scheme. Especially, when the power is large enough, the secrecy rate achieved by the proposed schemes approaches the maximal achievable rate for the no-eavesdropper case.
This letter studies the secure cooperative transmission for an amplify-and-forward (AF) relay network in the presence of multiple multi-antenna eavesdroppers. Since the perfect channel state information (CSI) of the eavesdroppers are not available, we propose a robust joint distributed beamforming and artificial noise scheme to maximize the worst-case secrecy rate of the network, under the total power constraint of all the relay nodes. With the semidefinite relaxation (SDR) technique, the design can be solved by a one-dimension search which involves a sequence of semidefinite programming (SDP). Simulation results demonstrate the validity of the proposed strategy.
This paper investigates a joint robust scheme in a secrecy relay network where distributed relays perform cooperative beamforming and a friendly jammer transmits jamming signal to enhance the information security. Specifically, we consider the outage constraint secrecy rate maximization design with imperfect channel state information. Through semidefinite relaxation and one-dimensional search, we propose a two-layer optimization method to solve the nonconvex problem. In addition, the Bernstein-type inequality and large deviation inequality are utilized to convert the probabilistic constraint. Simulation results demonstrate the performance of the proposed design.