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IEEE Transactions on Vehicular Technology

Joint Design of Optimal Precoding and Cooperative Jamming for Multiuser Secure Broadcast Systems

Jae‐Mo Kang, Jun Yang, Jeongseok Ha, Il‐Min Kim

Published Aug 3, 2017• 9 citations
Publisher

Abstract

A multiuser secure broadcast system is considered, where there are one multiantenna base station (BS), multiple single-antenna legitimate users, one multiantenna friendly jammer (FJ), and one multiantenna eavesdropper (Eve). We jointly design the optimal precoding matrix at the BS and the jamming covariance matrix at the FJ by minimizing the total transmit power of the BS and FJ under the signal-to-interference-plus-noise ratio constraints at the users and Eve. To solve this challenging problem, when the FJ has more antennas than the users and Eve, we first find the optimal structure of the jamming covariance matrix and, then, convert the problem into its equivalentconvexform. Also, we propose an iterative algorithm to jointly design the precoding and jamming covariance matrices in all scenarios. The solution obtained by this algorithm is shown to be asymptotically optimal when the FJ has more antennas than the users and Eve. Numerical results show that the proposed schemes considerably outperform the existing schemes.

DOI
10.1109/tvt.2017.2735414

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A multiuser secure broadcast system is considered, where there are one multiantenna base station (BS), multiple single-antenna legitimate users, one multiantenna friendly jammer (FJ), and one multiantenna eavesdropper (Eve). We jointly design the optimal precoding matrix at the BS and the jamming covariance matrix at the FJ by minimizing the total transmit power of the BS and FJ under the signal-to-interference-plus-noise ratio constraints at the users and Eve. To solve this challenging problem, when the FJ has more antennas than the users and Eve, we first find the optimal structure of the jamming covariance matrix and, then, convert the problem into its equivalentconvexform. Also, we propose an iterative algorithm to jointly design the precoding and jamming covariance matrices in all scenarios. The solution obtained by this algorithm is shown to be asymptotically optimal when the FJ has more antennas than the users and Eve. Numerical results show that the proposed schemes considerably outperform the existing schemes.
Linear precoding and cooperative jamming for multiuser broadcast channel is studied to enhance the physical layer security. We consider the system where multiple independent data streams are transmitted from the base station to multiple legitimate users with the help of a friendly jammer. It is assumed that a normalized linear precoding matrix is given at the base station, whereas the power allocated to each user is to be determined. The problem is to jointly design the power allocation across different users for linear precoding and the cooperative jamming at the friendly jammer. The goal is to maximize a lower bound of the secrecy rate, provided that a minimum communication rate to the users is guaranteed. The optimal solution is obtained when the number of antennas at the friendly jammer is no less than the total number of antennas at the users and eavesdropper. Moreover, a suboptimal algorithm is proposed, which can be applied for all the scenarios. Numerical results demonstrate that the proposed schemes are effective for secure communications.
Cooperative jamming for multiuser multiple input multiple output (MIMO) broadcast channel is studied to enhance the physical layer security with the help of a friendly jammer. We assume the base station transmits multiple independent data streams to multiple legitimate users. During the transmission, however, there are multiple eavesdroppers with multiple antennas that have interests in the streams from the base station. In order to wiretap the desired streams, the eavesdroppers may collude or not, and maximize the signal-to-interference-plus-noise ratio (SINR) of the desired streams using receive beamforming. The optimal cooperative jammer is designed to keep the achieved SINR at eavesdroppers below a threshold to guarantee that the transmission from the base station to legitimate users is confidential. One main advantage of the proposed cooperative jamming scheme is that no modification is needed for the existing precoding schemes at the base station and decoding schemes at legitimate users. Thus, any existing practical precoding/decoding schemes for multiuser MIMO broadcast channel can be applied directly with the help of a friendly jammer using the proposed cooperative jamming.
Optimal cooperative jamming (CJ) is studied for multiuser multiple-input multiple-output (MU-MIMO) broadcast channel to enhance the physical layer security with the help of a friendly jammer (FJ). We first derive a necessary and sufficient condition to achieve the asymptotically perfect security and propose an optimal CJ scheme to minimize the maximum signal-to-interference-plus-noise ratio (SINR) at the eavesdropper subject to a power constraint at the FJ. Then we derive an achievable lower bound of the eavesdropper's SINR and propose an asymptotically optimal CJ scheme achieving the lower bound. Numerical results demonstrate that the proposed schemes are effective.
Robust quality-of-service (QoS)-based and secrecy rate-based secure transmission designs are investigated for a multiple-input single-output system with multiple eavesdroppers and a cooperative jammer. Two scenarios are considered: (a) eavesdroppers' channel state information (ECSI) is available and (b) ECSI is unavailable. In scenario (a), a QoS-based design is considered to minimize the worst case signal-to-interference-and-noise ratio at the eavesdroppers and to guarantee the QoS of the legitimate receiver. A secrecy rate-based design is also studied where the worst case secrecy rate is maximized. In scenario (b), a QoS-based design is considered to maximize the power of jamming signals under the QoS constraint of the legitimate receiver, and the secrecy rate-based design is not applicable. In all these designs, we jointly optimize the transmit beamforming vector and the covariance matrix of jamming signals under individual power constraints. As the optimization problems are non-convex, we propose an algorithm for each problem through semidefinite relaxation. Our analysis and simulation results show that, even though the linear precoding scheme in our designs is transmit beamforming rather than the general rank transmit covariance, this does not cause any loss of optimality.
This paper considers a Gaussian multi-input multi-output (MIMO) wiretap channel with a legitimate transmitter, a legitimate receiver (Bob), an eavesdropper (Eve), and a cooperative jammer. All nodes may be equipped with multiple antennas. Traditionally, the jammer transmits Gaussian noise (GN) to enhance the security. However, using this approach, the jamming signal interferes not only with Eve but also with Bob. In this paper, besides the GN strategy, we assume that the jammer can also choose to use the encoded jammer (EJ) strategy, i.e., instead of GN, it transmits a codeword from an appropriate codebook. In certain conditions, the EJ scheme enables Bob to decode the jamming codeword and thus cancel the interference, while Eve remains unable to do so even if it knows all the codebooks. We first derive an inner bound on the system’s secrecy rate under the strong secrecy metric, and then consider the maximization this bound through precoder design in a computationally efficient manner. In the single-input multi-output (SIMO) case, we prove that although non-convex, the power control problems can be optimally solved for both GN and EJ schemes. In the MIMO case, we propose to solve the problems using the matrix simultaneous diagonalization (SD) technique, which requires quite a low computational complexity. Simulation results show that by introducing a cooperative jammer with coding capability, and allowing it to switch between the GN and EJ schemes, a dramatic increase in the secrecy rate can be achieved. In addition, the proposed algorithms can significantly outperform the current state of the art benchmarks in terms of both secrecy rate and computation time.
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.