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Entropy

Secure Communication for Two-Way Relay Networks with Imperfect CSI

Cong Sun, Ke Liu, Dahu Zheng, Wenbao Ai

Published Sep 29, 2017• 8 citations
Publisher

Abstract

This paper considers a two-way relay network, where two source nodes exchange messages through several relays in the presence of an eavesdropper, and the channel state information (CSI) of the eavesdropper is imperfectly known. The amplify-and-forward relay protocol is used and the relay beamforming weights are designed. The model is built up to minimize the total relay transmit power while guaranteeing the quality of service at users and preventing the eavesdropper from decoding the signals. Due to the imperfect CSI, a semi-infinite programming problem is obtained. An algorithm is proposed to solve the problem, and the iterative points are updated through the linesearch technique, where the feasibility are preserved during iterations. The optimality property is analyzed. The obtained subproblems are quadratic constrained quadratic programming problems, either with less than $4$ constraints or with only one variable, which are solved optimally. Simulation results demonstrate the importance of the proposed model, and imply that the proposed algorithm is efficient and converges very fast, where more than 85% of the problems are solved optimally.

DOI
10.3390/e19100522

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This paper considers a two-way relay network, where two source nodes exchange messages through several relays in the presence of an eavesdropper, and the channel state information (CSI) of the eavesdropper is imperfectly known. The amplify-and-forward relay protocol is used and the relay beamforming weights are designed. The model is built up to minimize the total relay transmit power while guaranteeing the quality of service at users and preventing the eavesdropper from decoding the signals. Due to the imperfect CSI, a semi-infinite programming problem is obtained. An algorithm is proposed to solve the problem, and the iterative points are updated through the linesearch technique, where the feasibility are preserved during iterations. The optimality property is analyzed. The obtained subproblems are quadratic constrained quadratic programming problems, either with less than 444 constraints or with only one variable, which are solved optimally. Simulation results demonstrate the importance of the proposed model, and imply that the proposed algorithm is efficient and converges very fast, where more than 85% of the problems are solved optimally.
This paper considers a physical layer security model in wireless communications. Two legitimate users communicate through several relays with the presence of an eavesdropper. We jointly design the relay beamforming weights and minimize the total relay transmit power, while ensuring users' Quality of Services and preventing the information being eavesdropped at the same time. The problem is a robust optimization problem, because of the imperfect channel state information from users and relays to the eavesdropper. First the original problem is simplified, where the high order robust terms are omitted. Then we design an iterative algorithm based on line search, by solving two Quadratically Constrained Quadratic Programming subproblems and a one-dimensional subproblem. Simulation results indicate that the proposed algorithm outperforms the state of the arts.
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.
We consider an amplify-and-forward (AF) relay network with multiple source-destination pairs in the presence of an eavesdropper. This paper studies the robust artificial noise (AN) assisted joint transceiver optimization for secure communication with imperfect channel state information (CSI) of legitimate users and no CSI regarding the eavesdropper. The goal is to design the linear precoding matrix of the relay and the linear equalizer of each destination, such that the transmit power for the information-bearing signals and forwarded background noises at the relay can be minimized subject to the quality of service (QoS) constraints at the destinations. The remainder of the constrained total power is used to generate the AN for jamming the eavesdropper. Although such a power minimization problem is nonconvex, we recast it into two semidefinite programming (SDP) subproblems which can be solved using interior-point methods. Then this problem can be solved with the alternating iterative optimization algorithm. Simulations demonstrate that the proposed algorithm can significantly reduce the sensitivity to imperfect CSI, while degrading the eavesdropper's capability of intercepting.
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.
We address a robust beamforming design and power allocation problem for a one-way multi-antenna relay network, where the multi-antenna source implements communication with the multi-antenna destination via a decode-and-forward (DF) relay in the presence of the multiple single-antenna eavesdroppers. The eavesdroppers can only overhear the information flowed from the relay to the destination in the second hop. We aim to maximize the worst-case secrecy rate in the condition that the global channel state information (CSI) is imperfect. To this end, we propose the joint beamforming and power allocation design for the worst-case secrecy rate maximization. However, our proposed design constitutes a non-convex problem, which involves an infinite number of constraints because of the imperfect CSI. To make the problem more tractable, we approximate the problem into several tractablesemidefinite programs by semidefinite relaxation, successive convex approximation, and S-procedure techniques, and we propose an iterative algorithm to solve the problem. Furthermore, we show that the proposed algorithm is also applicable for the case the Gaussian wiretap model, where only the eavesdroppers' CSI is imperfect. Simulation results validate the effectiveness of the proposed algorithm.
In this paper, we study the physical layer security in a two-way relay system consisting of two transceivers, one eavesdropper, and multiple relays. We study the system in case of the channel state information (CSI) of the eavesdropper is unknown, and hence artificial noise is used to degrade the signal to noise ratio at the eavesdropper. In order to reserve the maximum possible power for artificial noise, we consider the problem of minimizing the total power of the information signal transmitted by the relays, under quality of service constraints at the legitimate transceivers. This problem has been solved using semidefinite programming (SDP) and second order cone programming (SOCP) methods. Here, aiming to significantly decrease the complexity, we propose a novel approach to find the optimal solution using the generalized eigenvalue. We show that in most cases, we can provide a closed-form expression of the optimal solution. In addition, our proposed solution can be used for all quadratically constrained quadratic programs (QCQPs) with positive definite objective function and two constraints. Simulation results demonstrate the effectiveness of our algorithm in terms of optimality and low complexity compared to SDP.