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arXiv:1701.03383 · IEEE Transactions on Vehicular Technology

Secure Communications With Cooperative Jamming: Optimal Power Allocation and Secrecy Outage Analysis

Kanapathippillai Cumanan, George C. Alexandropoulos, Zhiguo Ding, George K. Karagiannidis

Published Jan 24, 2017• 91 citations
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Abstract

This paper studies the secrecy rate maximization problem of a secure wireless communication system in the presence of multiple eavesdroppers. The security of the communication link is enhanced through cooperative jamming with the help of multiple jammers. First, a feasibility condition is derived to achieve a positive secrecy rate at the destination. Then, we solve the original secrecy rate maximization problem, which is not convex in terms of power allocation at the jammers. To circumvent this nonconvexity, the achievable secrecy rate is approximated for a given power allocation at the jammers, and the approximated problem is formulated into a geometric programming one. Based on this approximation, an iterative algorithm has been developed to obtain the optimal power allocation at the jammers. Next, we provide a bisection approach, based on 1-D search, to validate the optimality of the proposed algorithm. In addition, by assuming Rayleigh fading, the secrecy outage probability (SOP) of the proposed cooperative jamming scheme is analyzed. More specifically, a single-integral form expression for the SOP is derived for the most general case, as well as a closed-form expression for the special case of two cooperative jammers and one eavesdropper. Simulation results have been provided to validate the convergence and the optimality of the proposed algorithm, as well as the theoretical derivations of the presented SOP analysis.

DOI
10.1109/tvt.2017.2657629

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This paper studies the secrecy rate maximization problem of a secure wireless communication system in the presence of multiple eavesdroppers. The security of the communication link is enhanced through cooperative jamming with the help of multiple jammers. First, a feasibility condition is derived to achieve a positive secrecy rate at the destination. Then, we solve the original secrecy rate maximization problem, which is not convex in terms of power allocation at the jammers. To circumvent this nonconvexity, the achievable secrecy rate is approximated for a given power allocation at the jammers, and the approximated problem is formulated into a geometric programming one. Based on this approximation, an iterative algorithm has been developed to obtain the optimal power allocation at the jammers. Next, we provide a bisection approach, based on 1-D search, to validate the optimality of the proposed algorithm. In addition, by assuming Rayleigh fading, the secrecy outage probability (SOP) of the proposed cooperative jamming scheme is analyzed. More specifically, a single-integral form expression for the SOP is derived for the most general case, as well as a closed-form expression for the special case of two cooperative jammers and one eavesdropper. Simulation results have been provided to validate the convergence and the optimality of the proposed algorithm, as well as the theoretical derivations of the presented SOP analysis.
This paper investigates cooperative security in wireless networks, where a source (Alice) intends to transmit a confidential message to a legitimate destination (Bob), with the help of a cooperative jammer (Charlie), coexisting with multiple passive eavesdroppers (Eves). In particular, by assuming knowledge of Bob's perfect channel state information (CSI) but only Eves’ statistical CSIs, secrecy beamforming with artificial noise (AN) is utilized for secure transmission, and cooperative jamming (CJ) is explored to further enhance secrecy. We first derive an accurate closed-form expression for the secrecy outage probability (SOP), and establish the condition under which positive secrecy rate is achievable. Then, we provide a secure transmit design for maximizing the SOP constrained secrecy rate. Moreover, based on a strict mathematical analysis, we characterize the impact of the main channel quality and the number of Eves on transmit design and secrecy performance. Specifically, optimal power allocation ratio between the information-bearing signal and the AN signal increases as the main channel quality improves, and decreases with the number of Eves. Numerical results confirm that our design achieves performance improvement in terms of both secrecy rate and secure energy efficiency, as compared to the approach without CJ.
A cooperative jamming system is investigated to enhance security of wireless communications in the presence of eavesdroppers. Different from traditional wireless security strategies that maximize secrecy capacity, a novel strategy based on the minimization of compromised secrecy region (CSR) is proposed. The secrecy region with a given secrecy outage probability is derived by considering path-loss and fading channel effects. Through numerical approximation of the outage probability, the optimal location and allocated power of the jammer are calculated to minimize the CSR which exhibits high secrecy outage probability. Without knowing the exact location of the randomly-distributed eavesdropper, our proposed scheme provides a new optimization criterion based on this compromised area minimization, thereby increasing the security level in cooperative jamming systems. Numerical results further validate the proposed CSR minimization scheme for cooperative jamming.
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.
In this paper, we investigate cooperative security in wireless networks, where a source (Alice) intends to transmit a confidential message to a legitimate destination (Bob), with the help of a cooperative node (Charlie), in the presence of multiple independent eavesdroppers (Eves). In particular, cooperative jamming (CJ) is explored to enhance secure communication between Alice and Bob. We provide a transmit design to maximize the secrecy rate, subject to a secrecy outage probability (SOP) constraint. Specifically, we establish a condition under which positive secrecy rate can be guaranteed. In addition to secrecy rate performance, we also pay attention to the secure energy efficiency, defined as the ratio of secrecy rate to total power consumption. Numerical results validate the effectiveness and energy efficiency of our proposed CJ scheme.
The problem of power allocation with uncoordinated cooperative jamming is addressed in this paper to enhance the physical layer security of the single-input-single-output wiretap channel with single-antenna jammers. Differing from the existing works concerning the secrecy rate maximization, this paper studies the problem of minimizing the secrecy outage probability with fixed secrecy rate, where the channel state information concerning the eavesdropper is only known statistically. This problem is formulated as an optimization problem of power allocation for the jamming signals. We prove that the optimization problem is convex in essence, and the optimal solution is thus conveniently obtained by using the methods of golden section search and bi-section search. Simulation results show that the proposed approach is very efficient and can significantly enhance the physical layer security by reducing the secrecy outage probability.
A novel secrecy scenario of uplink non-orthogonal multiple access (NOMA) along with cooperative jammer(s) to improve secrecy performance is studied in this work. We first characterize secrecy performance in terms of positive secrecy rate probability, secrecy outage probability (SOP) and effective secrecy throughput (EST), and derive the closed-expressions of individual secrecy performance. The analytical results not only show an improvement on secrecy performance with the aid of cooperative jamming, but also clearly illustrate how each jammer affects the secrecy performance. We then continue the study of the individual secrecy performance for its asymptotic behaviors, and reveal it is only dependent on its relative distance to the eavesdropper over the desired receiver in a high signal-to-noise ratio (SNR) regime. Finally, the maximization of overall secrecy performance is covered by investigating two optimization problems: 1) optimal selection of jammer(s) under the same transmit power; 2) optimal power allocation to each transmitter, including jammers, under the constraint of limited total transmit power. The solutions to these two problems are presented and demonstrated by an appropriate case.