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IEEE Transactions on Vehicular Technology

Secrecy Rate Optimizations for a MIMO Secrecy Channel With a Cooperative Jammer

Zheng Chu, Kanapathippillai Cumanan, Zhiguo Ding, Martin Johnston, Stéphane Y. Le Goff

Published Oct 6, 2014• 205 citations
Publisher

Abstract

In this paper, we study different secrecy rate optimization techniques for a multiple-input–multiple-output (MIMO) secrecy channel, where a multiantenna cooperative jammer is employed to improve secret communication in the presence of a multiantenna eavesdropper. Specifically, we consider two optimization problems, namely, power minimization and secrecy rate maximization. These problems are not jointly convex in terms of the transmit covariance matrices of the legitimate transmitter and the cooperative jammer. To circumvent these nonconvexity issues, we alternatively design the transmit covariance matrix of the legitimate transmitter and the cooperative jammer. For a given transmit covariance matrix at the cooperative jammer, we solve the power minimization and secrecy rate maximization problems based on a Taylor series expansion. Then, we propose two iterative algorithms to solve these approximated problems. In addition, we develop a robust scheme by incorporating channel uncertainties associated with the eavesdropper. By exploitingS-Procedure, we show that these robust optimization problems can be formulated into semidefinite programming. Moreover, we consider the secrecy rate maximization problem based on game theory, where the jammer introduces charges for its jamming service based on the amount of the interference caused to the eavesdropper. This secrecy rate maximization problem is formulated into aStackelberggame where the jammer and the transmitter are the leader and the follower of the game, respectively. For the proposed game,Stackelbergequilibrium is analytically derived. Simulation results have been provided to validate the convergence and performance of the proposed algorithms. In addition, it is shown that the proposed robust scheme outperforms the nonrobust scheme in terms of the achieved secrecy rate and the worst-case secrecy rate. Finally, theStackelbergequilibrium solution has been validated through numerical results.

DOI
10.1109/tvt.2014.2336092

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In this paper, we study different secrecy rate optimization techniques for a multiple-input–multiple-output (MIMO) secrecy channel, where a multiantenna cooperative jammer is employed to improve secret communication in the presence of a multiantenna eavesdropper. Specifically, we consider two optimization problems, namely, power minimization and secrecy rate maximization. These problems are not jointly convex in terms of the transmit covariance matrices of the legitimate transmitter and the cooperative jammer. To circumvent these nonconvexity issues, we alternatively design the transmit covariance matrix of the legitimate transmitter and the cooperative jammer. For a given transmit covariance matrix at the cooperative jammer, we solve the power minimization and secrecy rate maximization problems based on a Taylor series expansion. Then, we propose two iterative algorithms to solve these approximated problems. In addition, we develop a robust scheme by incorporating channel uncertainties associated with the eavesdropper. By exploitingS-Procedure, we show that these robust optimization problems can be formulated into semidefinite programming. Moreover, we consider the secrecy rate maximization problem based on game theory, where the jammer introduces charges for its jamming service based on the amount of the interference caused to the eavesdropper. This secrecy rate maximization problem is formulated into aStackelberggame where the jammer and the transmitter are the leader and the follower of the game, respectively. For the proposed game,Stackelbergequilibrium is analytically derived. Simulation results have been provided to validate the convergence and performance of the proposed algorithms. In addition, it is shown that the proposed robust scheme outperforms the nonrobust scheme in terms of the achieved secrecy rate and the worst-case secrecy rate. Finally, theStackelbergequilibrium solution has been validated through numerical results.
This paper proposes an alternating optimization algorithm for addressing the secrecy rate optimization problem for a multi-input-multi- output (MIMO) secrecy channel in the presence of a multiantenna eavesdropper, where a multiantenna cooperative jammer will be employed to confuse the eavesdropper by introducing jamming signal. We investigate the secrecy rate maximization problem, which is a non-convex problem in terms of transmit covariance matrices of the legitimate transmitter and the cooperative jammer. In order to circumvent this issue, we develop an optimization algorithm by alternating optimizing the transmit covariance matrices of the legitimate transmitter and the cooperative jammer where each transmit covariance matrix is optimized while other is fixed. Based on this algorithm, we develop a robust scheme by incorporating channel uncertainties associated with the eavesdropper. By exploiting S-Procedure, we show that these robust optimization problems can be formulated into semidefinite programming (SDP). Simulation results have been provided to validate the convergence and the performance of the alternating algorithm.
In this paper, we study the secrecy rate maximization (SRM) problem for a multiple-input-multiple-output (MIMO) secrecy channel, where a multi-antenna cooperative jammer is employed to improve secret communication in the presence of multiple multi-antenna eavesdroppers. The SRM problem are not jointly convex in terms of the transmit covariance matrices of the legitimate transmitter and the cooperative jammer. To solve the non-convexity issues, we propose an alternating optimization (AO) approach to design the transmit covariance matrix of the legitimate transmitter and the cooperative jammer. Simulation results validated the performance of the proposed algorithms.
This paper studies different secrecy rate optimization problems for a multiple-input–multiple-output (MIMO) secrecy channel. In particular, we consider a scenario where a communication through a MIMO channel is overheard by a multiple-antenna eavesdropper. In this secrecy network, we first investigate two secrecy rate optimization problems: 1) power minimization and 2) secrecy rate maximization. These optimization problems are not convex due to the nonconvex secrecy rate constraint. However, by approximating this secrecy rate constraint based on Taylor series expansion, we propose iterative algorithms to solve these secrecy rate optimization problems. In addition, we provide the convergence analysis for the proposed algorithms. These iterative optimization approaches are developed under the assumption that the transmitter has perfect channel state information. However, there are practical difficulties in having perfect channel state information at the transmitter. Hence, robust secrecy rate optimization techniques based on the worst-case secrecy rate are considered by incorporating channel uncertainties. By exploiting theS-Procedure, we show that these robust optimization problems can be formulated into semidefinite programming at low signal-to-noise ratios (SNRs). Simulation results have been provided to validate the convergence of the proposed algorithms. In addition, numerical results show that the proposed robust optimization techniques outperform the nonrobust schemes in terms of the worst-case secrecy rates and the achieved secrecy rates.
This paper studies different secrecy rate optimization problems for a multiple input multiple output (MIMO) secrecy channel. In particular, we consider a scenario where a communication through a MIMO channel is overheard by a multiple-antenna eavesdropper. In this secrecy network, we first investigate two secrecy rate optimization problems: a) power minimization, b) secrecy rate maximization. These optimization problems are not convex due to the non-convex secrecy rate constraint. However, by approximating this secrecy rate constraint based on Taylor series expansion, we propose iterative algorithms to solve these secrecy rate optimization problems. In addition, we provide the convergence analysis for the proposed algorithms. These iterative optimization approaches are developed under the assumption that the transmitter has the perfect channel state information. However, there are practical difficulties to have the perfect channel state information at the transmitter. Hence, robust secrecy rate optimization techniques based on the worstcase secrecy rate are considered by incorporating the channel uncertainties. By exploiting the S-Procedure, we show that these robust optimization problems can be formulated into semidefinite programming at low signal to noise ratios (SNRs). Simulation results have been provided to validate the convergence of the proposed algorithms. In addition, numerical results show that the proposed robust optimization techniques outperform the nonrobust schemes in terms of the worst-case secrecy rates and the achieved secrecy rates.
© 2014 EURASIP.In this paper, we consider a multi-input-multi-output (MIMO) wiretap channel with a multi-antenna eavesdropper, where a private cooperative jammer is employed to improve the achievable secrecy rate. The legitimate user pays the legitimate transmitter for its secured communication based on the achieved secrecy rate. We first approximate the legitimate transmitter covariance matrix by employing Taylor series expansion, then this secrecy rate problem can be formulated into a Stackelberg game based on a fixed covariance matrix of the transmitter, where the transmitter and the jammer try to maximize their revenues. This secrecy rate maximization problem is formulated into a Stackelberg game where the jammer and the transmitter are the leader and follower of the game, respectively. For the proposed game, Stackelberg equilibrium is analytically derived. Simulation results are provided to show that the revenue functions of the legitimate user and the jammer are concave functions and the Stackelberg equilibrium solution has been validated.
This paper investigates secrecy rate optimization problems for a multiple-input-single-output (MISO) secrecy channel in the presence of multiple multiantenna eavesdroppers. Specifically, we consider power minimization and secrecy rate maximization problems for this secrecy network. First, we formulate the power minimization problem based on the assumption that the legitimate transmitter has perfect channel state information (CSI) of the legitimate user and the eavesdroppers, where this problem can be reformulated into a second-order cone program (SOCP). In addition, we provide a closed-form solution of transmit beamforming for the scenario of an eavesdropper. Next, we consider robust secrecy rate optimization problems by incorporating two probabilistic channel uncertainties with CSI feedback. By exploiting the Bernstein-type inequality and S-Procedure to convert the probabilistic secrecy rate constraint into the determined constraint, we formulate this secrecy rate optimization problem into a convex optimization framework. Furthermore, we provide analyses to show the optimal transmit covariance matrix is rank-one for the proposed schemes. Numerical results are provided to validate the performance of these two conservative approximation methods, where it is shown that the Bernstein-type inequality-based approach outperforms the S-Procedure approach in terms of the achievable secrecy rates.