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IEEE Communications Letters

A Minorization–Maximization Algorithm for Maximizing the Secrecy Rate of the MIMOME Wiretap Channel

Mudassir Masood, Ali Ghrayeb, Prabhu Babu, Issa M. Khalil, Mazen O. Hasna

Published Dec 7, 2016• 14 citations
Publisher

Abstract

We consider physical layer security in a multi-input multi-output multi-eavesdropper wiretap channel and present an exact solution to the problem of secrecy rate maximization. A system model with multiple multi-antenna eavesdroppers and multiple multi-antenna full-duplex receivers is considered, which is general enough such that models existing in the literature may be considered as special cases. In particular, we perform joint beamforming and artificial noise optimization in an effort to maximize the achievable secrecy rate. The optimization is performed in the presence of artificial noise generated by both transmitter and legitimate receivers. The resulting optimization problem is non-convex and difficult to solve. We develop a minorization-maximization algorithm to solve the problem exactly and the results can therefore be used to benchmark existing methods. Numerical results are presented to demonstrate the efficacy of the proposed approach.

DOI
10.1109/lcomm.2016.2628892

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We consider physical layer security in a multi-input multi-output multi-eavesdropper wiretap channel and present an exact solution to the problem of secrecy rate maximization. A system model with multiple multi-antenna eavesdroppers and multiple multi-antenna full-duplex receivers is considered, which is general enough such that models existing in the literature may be considered as special cases. In particular, we perform joint beamforming and artificial noise optimization in an effort to maximize the achievable secrecy rate. The optimization is performed in the presence of artificial noise generated by both transmitter and legitimate receivers. The resulting optimization problem is non-convex and difficult to solve. We develop a minorization-maximization algorithm to solve the problem exactly and the results can therefore be used to benchmark existing methods. Numerical results are presented to demonstrate the efficacy of the proposed approach.
We consider the problem of secrecy rate maximization in a multi-input multi-output multi-eavesdropper (MIMOME) wiretap channel and present an exact solution. A general system model with a multi-antenna eavesdropper and a multi-antenna full-duplex receiver is considered. In particular, we perform joint beamforming and artificial noise optimization in an effort to maximize the achievable secrecy rate. The optimization is performed in the presence of artificial noise generated by both transmitter and legitimate receiver. The resulting optimization problem is non-convex and difficult to solve. We develop a minorization-maximization algorithm to solve the problem. It is iterative in nature and guaranteed to converge to a locally optimal solution. The results can therefore be used to benchmark existing methods. Numerical results are presented to demonstrate the efficacy of the proposed approach.
In this paper, we study the energy-efficient secrecy precoding problem for a general multiple-input multiple-output multiple-eavesdropper (MIMOME) wiretap channel. The system model considered here consists of a common transmitter, a legitimate receiver, and multiple eavesdroppers, all mounted with multiple antennas. In order to improve the energy efficiency (EE) performance of the proposed system, an artificial noise (AN)-aided precoding scheme is adopted. Because the formulated EE maximization problem is of huge nonconvex complexity, we solve it by employing a two-tier optimization structure. Although the outer-tier optimization problem is quite simple and can be efficiently solved by the famous golden section searching method, the inner-tier optimization problem turns out to be nonconvex and cannot be easily solved. To solve it, we relax it to a secrecy rate maximization (SRM) problem, which naturally constitutes a difference convex (DC)-type programming problem and can be iteratively solved by employing a successive convex approximation (SCA) method. Numerical simulations are further provided to demonstrate the proposed algorithms. Results show that our algorithms can converge fast to a near-optimal solution.
In this paper, secure communication over a multi-input multi-output multi-eavesdropper (MIMÓME) wiretap channel is considered. We propose an enhanced MIMÓME artificial noise (AN) model in which the receiver (Bob) adopts the latest Full-Duplex MIMO Radio technique to emit AN jointly with the transmitter (Alice). An achievable secrecy rate is obtained for this model over an unfavorable noiseless eavesdropping channel. Optimization problem is formulated to solve the beamforming and power allocation for Alice and Bob's transmitting signals and to determine the dimension allocation between the information and AN signals. Simulations are carried out to illustrate the optimization process, and the results show that the enhanced MIMÓME model outperforms existing AN models for low self-interference regime.
This paper studies a secure communication over multiple-input multiple-output multi-antenna eavesdropper (MIMOME) channels which consist of legitimate parities, namely a transmitter and receiver, equipped with multi-antennas and a passive eavesdropper with multi-antennas. For securing the communication between the legitimate parties, we consider an artificial noise (AN) scheme in which the legitimate transmitter sends its secret messages and AN signal together. Meanwhile, it is assumed that the legitimate receiver has a full-duplex capability which enables it to capture the secret message from the transmitter and simultaneously generate a jamming signal to strengthen security. While there have been studies on similar setups, most of them focus on the design of the jamming signal with the assumption of full channel-state information (CSI) and/or system parameter optimization based on numerical evaluations. On the contrary, in this work, we instead introduce a tight lower bound on an achievable ergodic secrecy rate as a versatile analytic tool and derive a closed-form expressions for the bound. To confirm the analytic results, we carry out numerical evaluations of the ergodic secrecy rate which are compared with the proposed lower bound.
Joint transmit beamforming and cooperative jamming for MIMOME (multiple-input multiple-output multi-antenna-eavesdropper) wiretap channel is studied, where the model consists of a transmitter, a friendly jammer, a receiver and an eavesdropper. The optimization problem of finding transmit and jamming covariances to maximize the secrecy rate is non-convex, and blindly searching will result in local optima. Because of the transmit beamforming, the MIMOME channel can be related to an effective MISOSE channel. Using this relation, we propose an iterative algorithm that in each iteration: 1) searches the jamming covariance for the effective MISOSE channel and 2) updates the effective MISOSE channel. Numerical results show that our proposed algorithm achieves higher objective whereas blind search is trapped at local optima. The proposed algorithm achieves higher secrecy rate than the existing artificial noise scheme.
We consider a Gaussian multiple-input multiple-output (MIMO) wiretap channel model, where there exists a transmitter, a legitimate receiver and an eavesdropper, each node equipped with multiple antennas. We study the problem of finding the optimal input covariance matrix that achieves secrecy capacity subject to a power constraint, which leads to a non-convex optimization problem that is in general difficult to solve. Existing results for this problem address the case in which the transmitter and the legitimate receiver have two antennas each and the eavesdropper has one antenna. For the general cases, it has been shown that the optimal input covariance matrix has low rank when the difference between the Grams of the eavesdropper and the legitimate receiver channel matrices is indefinite or semi-definite, while it may have low rank or full rank when the difference is positive definite. In this paper, the aforementioned non-convex optimization problem is investigated. In particular, for the multiple-input single-output (MISO) wiretap channel, the optimal input covariance matrix is obtained in closed form. For general cases, we derive the necessary conditions for the optimal input covariance matrix consisting of a set of equations. For the case in which the transmitter has two antennas, the derived necessary conditions can result in a closed form solution; For the case in which the difference between the Grams is indefinite and has all negative eigenvalues except one positive eigenvalue, the optimal input covariance matrix has rank one and can be obtained in closed form; For other cases, the solution is proved to be a fixed point of a mapping from a convex set to itself and an iterative procedure is provided to search for it. Numerical results are presented to illustrate the proposed theoretical findings.