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National Doctoral Academic Forum on Information and Communications Technology

Robust secure transmission for Gaussian MISO wiretap channels with imperfect CSI

Tang Yanqun, Dongtang Ma, Wang Degang, Wei Jibo

Published Jan 1, 2013• 0 citations
Publisher

Abstract

We study robust secure transmit design in terms of input covariance matrix for Gaussian multiple-input single-output (MISO) wiretap channels in the presence of a single-antenna eavesdropper. Under the assumption that the transmitter knows partial channel state information (CSI) on the main and eavesdropper's channels, we jointly design the input covariance matrices of information-bearing signal and artificial noise (AN) to maximize the secrecy rate. Unfortunately, the secrecy rate maximization (SRM) problem is difficult to solve. We derive a safe approximation to the SRM problem and propose a tractable approach to solve it. To get more insights, we discuss the rank property of the input covariance matrix of the information-bearing signal. Finally, the simulation results are provided to verify the validity and robustness of our proposed transmit design.

DOI
10.1049/ic.2013.0223

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We study robust secure transmit design in terms of input covariance matrix for Gaussian multiple-input single-output (MISO) wiretap channels in the presence of a single-antenna eavesdropper. Under the assumption that the transmitter knows partial channel state information (CSI) on the main and eavesdropper's channels, we jointly design the input covariance matrices of information-bearing signal and artificial noise (AN) to maximize the secrecy rate. Unfortunately, the secrecy rate maximization (SRM) problem is difficult to solve. We derive a safe approximation to the SRM problem and propose a tractable approach to solve it. To get more insights, we discuss the rank property of the input covariance matrix of the information-bearing signal. Finally, the simulation results are provided to verify the validity and robustness of our proposed transmit design.
This paper studies robust transmission schemes for multiple-input single-output (MISO) wiretap channels. Both the cases of direct transmission and cooperative jamming with a helper are investigated with imperfect channel state information (CSI) for the eavesdropper links. Robust transmit covariance matrices are obtained based on worst-case secrecy rate maximization, under both individual and global power constraints. For the case of an individual power constraint, we show that the nonconvex maximin optimization problem can be transformed into a quasi-convex problem that can be efficiently solved with existing methods. For a global power constraint, the joint optimization of the transmit covariance matrices and power allocation between the source and the helper is studied. We also investigate the robust wiretap transmission problem for the case with a quality-of-service constraint at the legitimate receiver. Numerical results show the advantage of the proposed robust design. In particular, for the global power constraint scenario, although cooperative jamming is not necessary for optimal transmission with perfect eavesdropper's CSI, we show that robust jamming support can increase the worst-case secrecy rate and lower the signal to interference-plus-noise ratio at the eavesdropper in the presence of channel mismatches between the transmitters and the eavesdropper.
In this letter, we study the robust artificial noise (AN) aided transmit design for a multiple-input single-output (MISO) wiretap channel with a single-antenna eavesdropper. We consider two uncertainty models for the imperfect channel state information (CSI) on the main and eavesdropper's channels at the transmitter. For the deterministic uncertainty model, we solve the worst-case secrecy rate maximization (WC-SRM) problem via semidefinite program (SDP). For the stochastic uncertainty model, we propose a suboptimal solution to the outage probability constrained secrecy rate maximization (OP-SRM) problem based on the robust design for the WC-SRM problem. The simulation results demonstrate performance improvement of the proposed worst case robust design as compared to that based on the worst case method without usage of AN.
In this work, a robust artificial noise (AN) aided transmit method is proposed for a multicast multiple-input single-output (MISO) system in the presence of multiple single-antenna eavesdroppers. With the imperfect covariance-based channel state information (CSI), we aim to minimize the transmit power at the transmitter under the multicast secrecy rate constraint and the maximum transmit power constraint. The resulting optimization problem involves the joint optimization of the beamforming vector and AN covariance matrix. After using the semidefinite relaxation (SDR) technique, we derive the exact reformulation of the original optimization through the Lagrange duality. Then this non-convex problem is transformed into a one-variable optimization problem, which can be handled by solving a series of semidefinite programs (SDPs). Simulation results demonstrate the effectiveness of the proposed robust transmit method.
A Gaussian multiple-input single-output (MISO) secrecy channel is considered, where a transmitter is equipped with multiple antennas, and an intended receiver and an eavesdropper each equipped with a single antenna. This paper studies the robust beamforming design in the presence of uncertainty of channel state information (CSI) on the eavesdropper channel. Under the assumption that all possible states of the eavesdropper channel are in a given set, the problem of optimizing the transmit covariance for the worst-case secrecy capacity which is the maximum transmission rate at which the eavesdropper is unable to decode under any channel realization in the set, is cast as a max-min optimization problem. We propose to transfer the max-min problem into a convex optimization problem that can be solved efficiently. The optimal secrecy rate and transmit covariance are expressed in the form of the generalized eigenvalue and eigenvector, the same form as the conventional case of the perfect eavesdropper's CSI, which indicates our results is the generalization of the conventional case.
A multiple-input multiple-output (MIMO) wiretap channel in the presence of one multiple-antenna eavesdropper is considered. We assume that imperfect channel state information (CSI) on the legitimate link and only statistical CSI of the eavesdropper channel are available at the transmitter. This paper addresses the issue of optimal input covariance matrix design that maximizes the secrecy rate subject to the total power constraint. The secrecy rate maximization (SRM) is studied under a relaxed assumption on the perfect CSI.We reformulate the SRM problem and propose an alternating optimization (AO) algorithm to find the optimal input covariance matrix. Simulation results are presented to validate the effectiveness of the proposed approach. The impact of the channel estimation error is investigated.
In this paper, we study the achievable secrecy rate of the multiple input single output (MISO) wiretap channel, which consists of a transmitter, a legitimate receiver and multiple eavesdroppers. The transmitter is equipped with multiple antennas, while the receiver and all the eavesdroppers each have a single antenna. We assume that the transmitter has perfect channel state information (CSI) for their links to legitimate receiver, but it has only imperfect CSI for their channels to eavesdroppers. Optimal transmit covariance matrix is obtained based on worst-case secrecy rate maximization, under power constraints. The maximum secrecy rate computation can be formulated as a non-convex optimal problem, which cannot be solved directly. In this paper, we transform non-convex optimal problem into a quasi-convex optimal problem which can be efficiently solved with the bisection method. The simulation result and analysis demonstrate the effectiveness of our methods.