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IEEE Transactions on Vehicular Technology

Precoder Designs for MIMO Gaussian Multiple Access Wiretap Channels

Hoon Lee, Changick Song, Jihwan Moon, Inkyu Lee

Published Mar 6, 2017• 21 citations
Publisher

Abstract

This paper studies multiple-input multiple-output multiple access wiretap channels (MAC-WT) where an eavesdropper tries to tap the communication between multiple legitimate transmitters and a legitimate receiver. In this system, we propose precoder optimization methods at the transmitters in order to maximize the sum secrecy rate performance. Although this problem can be solved by the well-known difference of convex (DC) programming, we present a more efficient algorithm whose computational complexity is much lower than that of the conventional DC approach. By investigating the Karush-Kuhn-Tucker conditions, it is confirmed that the proposed low-complexity algorithm achieves the same performance as the conventional DC method. Our analysis also reveals that the proposed algorithm ensures global optimality for multiple-input single-output MAC-WT cases, while binary power control is optimal for single-input multiple-output scenarios. Simulation results demonstrate the efficacy of the proposed precoding methods.

DOI
10.1109/tvt.2017.2678601

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This paper studies multiple-input multiple-output multiple access wiretap channels (MAC-WT) where an eavesdropper tries to tap the communication between multiple legitimate transmitters and a legitimate receiver. In this system, we propose precoder optimization methods at the transmitters in order to maximize the sum secrecy rate performance. Although this problem can be solved by the well-known difference of convex (DC) programming, we present a more efficient algorithm whose computational complexity is much lower than that of the conventional DC approach. By investigating the Karush-Kuhn-Tucker conditions, it is confirmed that the proposed low-complexity algorithm achieves the same performance as the conventional DC method. Our analysis also reveals that the proposed algorithm ensures global optimality for multiple-input single-output MAC-WT cases, while binary power control is optimal for single-input multiple-output scenarios. Simulation results demonstrate the efficacy of the proposed precoding methods.
This paper considers a Gaussian multi-input multi-output (MIMO) multiple access wiretap (MAC-WT) channel, where an eavesdropper (Eve) wants to extract the confidential information of all users. Assuming that both the legitimate receiver and Eve jointly decode their interested messages, we aim to maximize the sum secrecy rate of the system by precoder design. Although this problem could be solved by first using the iterative majorization minimization (MM) based algorithm to get a sequence of convex log-determinant optimization subproblems and then using some general tools, e.g., the interior point method, to deal with each subproblem, this strategy involves quite high computational complexity. Therefore, we propose a simultaneous diagonalization based low-complexity (SDLC) method to maximize the secrecy rate of a simple one-user wiretap channel, and then use this method to iteratively optimize the covariance matrix of each user. Simulation results show that in contrast to the existing approaches, the SDLC scheme achieves similar secrecy performance but requires much lower complexity.
We consider the problem of finding secrecy rate of a multiple-input multiple-output (MIMO) wire-tap channel. A transmitter, a legitimate receiver, and an eavesdropper are all equipped with multiple antennas. The channel states from the transmitter to the legitimate user and to the eavesdropper are assumed to be known at the transmitter. In this contribution, we address the problem of finding the optimal precoder/transmit covariance matrix maximizing the secrecy rate of the given wiretap channel. The problem formulation is shown to be equivalent to a difference of convex functions programming problem and an efficient algorithm for addressing this problem is developed.
We consider the problem of finding secrecy rate of a multiple-input multiple-output (MIMO) wire-tap channel. A transmitter, a legitimate receiver, and an eavesdropper are all equipped with multiple antennas. The channel states from the transmitter to the legitimate user and to the eavesdropper are assumed to be known at the transmitter. In this contribution, we address the problem of finding the optimal precoder/transmit covariance matrix maximizing the secrecy rate of the given wiretap channel. The problem formulation is shown to be equivalent to a difference of convex functions programming problem and an efficient algorithm for addressing this problem is developed.
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.
MIMO wiretap channel consists of a multiple antenna transmitter, a legitimate multiple antenna receiver and a multiple antenna eavesdropper. Signaling strategy optimization for MIMO wiretap channel, including secrecy capacity maximization problem and power minimization problem with a secrecy rate constraint, are studied. We identify when the two problems are globally solvable. Further, iterative algorithms based on concave-convex procedure are proposed for the two problems, which can monotonically converge to a Karush-Kuhn-Tucker (KKT) point of the two problems. Numerical examples validate the effectiveness of the proposed algorithms.
In this paper, we investigate the secrecy rate of finite-alphabet communications over multiple-input-multiple-output-multiple-antenna eavesdropper (MIMOME) channels. Traditional precoding designs based on Gaussian input assumption may lead to substantial secrecy rate loss when the Gaussian input is replaced by practical finite-alphabet input. To address this issue, we investigate linear precoding designs to directly maximize the secrecy rate for MIMOME systems under the constraint of finite-alphabet input. By exploiting the theory of Karush-Kuhn-Tucker (KKT) analysis and matrix calculus, we first present necessary conditions of the optimal precoding design when instantaneous channel-state information (CSI) of the eavesdropper is known at the transmitter. In this light, an iterative algorithm for finding the optimal precoding matrix is developed, utilizing a gradient decent method with backtracking line search. Moreover, we find that the beamforming design in MIMONE systems, which is a secrecy-capacity-achieving approach for Gaussian signaling, no longer provides the maximum secrecy rate for finite-alphabet input data. This case is substantially different from the Gaussian input case. In addition, we derive the closed-form results on the precoding matrix, which maximizes the secrecy rate in the low signal-to-noise ratio (SNR) region, and reveal the optimal precoding structure in the high-SNR region. A novel jamming signal generation method that draws on the CSI of the eavesdropper to additionally increase the secrecy rate is further proposed. The precoding design with only statistical CSI of the eavesdropper available at the transmitter is also considered. Numerical results show that the proposed designs provide significant gains over recent precoding designs through a power control policy and the precoding design with the Gaussian input assumption in various scenarios.