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International Conference on Communications

Amplify-and-forward relay beamforming for secrecy with cooperative jamming and imperfect CSI

Sanjay Vishwakarma, A. Chockalingam

Published Jun 1, 2013• 25 citations
Publisher

Abstract

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.

DOI
10.1109/icc.2013.6655008

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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 evaluate secrecy rates in cooperative relay beamforming in the presence of imperfect channel state information (CSI) and multiple eavesdroppers. A source-destination pair aided by k out of M relays, 1 ≤ k ≤ M, using decode-and-forward relay beamforming is considered. We compute the worst case secrecy rate with imperfect CSI in the presence of multiple eavesdroppers, where the number of eavesdroppers can be more than the number of relays. We solve the optimization problem for all possible relay combinations to find the secrecy rate and optimum source and relay weights subject to a total power constraint. We relax the rank-1 constraint on the complex semi-definite relay weight matrix and use S-procedure to reformulate the optimization problem that can be solved using convex semi-definite programming.
In this paper, we study beamforming techniques for secrecy with worst case signal-to-interference-plus-noise ratio (SINR) guarantees in cooperative communications with imperfect channel state information (CSI). The worst case SINRs are the minimum SINR at the intended destination and the maximum SINR at the eavesdroppers. We consider a norm bounded CSI error model. With the available imperfect channel estimates, we design beamformers such that the minimum SINR receivable by the intended destination is above a certain threshold, while the maximum value of SINRs receivable at the eavesdroppers are below another lower threshold. We consider amplify-and-forward (AF) and decode-and-forward (DF) relaying schemes. The relays do the worst case transmit beamforming and injection of artificial noise (AN). We jointly optimize the beamformers and the AN for the AF and DF schemes subject to the worst case SINR constraints at the destination and the eavesdroppers. We solve the corresponding optimization problems as semi-definite programming (SDP) problems by rank relaxation and S-procedure. Numerical results show that AN injection at the relays significantly reduces the average total transmit power required to meet the worst case SINR constraints, and improves the solution feasibility of the optimization problems.
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.
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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.
In this paper, we study the secrecy transmission in multi-antenna relay networks with multiple eavesdroppers. The relay employs the amplify-and-forward relaying protocol and simultaneously sends the artificial noise to interfere the eavesdroppers. It is assumed that only imperfect channel state information on the main and eavesdropping channels is available at the relay. We exploit the robust beam forming and jamming to maximize the worst-case secrecy rate under a total relay power budget. Because of the infinitely nonconvex constraints, the problem is difficult to solve. Therefore, we approximate the problem into several tractable semi definite programs by semi definite relaxation, S-procedure, and the successive convex approximation techniques. Simulation results show the effectiveness of the proposed scheme.