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Asilomar Conference on Signals, Systems and Computers (ACSSC)

Robust beamforming for MISO wiretap channel by optimizing the worst-case secrecy capacity

Wei Shi, James A. Ritcey

Published Nov 1, 2010• 32 citations
Publisher

Abstract

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.

DOI
10.1109/acssc.2010.5757521

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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.
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.
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.
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 the robust beamforming design problem for a multiple-input single-output (MISO) secrecy channel with a single-antenna eavesdropper. Due to the illegal nature, the eavesdropper may try to hide itself from being caught; thus, it could be difficult for the secrecy transmitter (S-Tx) to obtain accurate channel state information (CSI) of the eavesdropping link between S-Tx and the eavesdropper. Assuming that the CSI of the eavesdropping link belongs to a known uncertain set, this paper designs the optimal transmit strategy for the secrecy user to maximize the transmit rate under the condition that the eavesdropper cannot decode the secrecy message for all possible channel realizations of the eavesdropping link. This robust design problem is non-convex and cannot be solved by existing algorithms in the literature. By exploiting the relationship between the secrecy MISO channel and the cognitive radio (CR) MISO channel, this problem is transformed into a robust CR beamforming design problem, which can be solved efficiently by the interior point method. Numerical examples are provided to illustrate the effectiveness of the proposed algorithm.
We consider a multiple-input multiple-output (MIMO) Gaussian 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 that achieves secrecy capacity subject to a power constraint, which in general leads to a difficult non-convex optimization problem. For the Gaussian multiple-input single-output (MISO) wiretap channel where there exists a transmitter equipped with multiple antennas, a legitimate receiver and an eavesdropper each equipped with one antenna, the optimal input covariance is obtained in closed form. For the general case, we derive the necessary conditions for the optimal input covariance in the form of a set of equations. We show that for MISO case, the derived conditions guarantee the optimal input covariance. Numerical results are presented to illustrate the proposed theoretical findings.
This paper considers an energy-efficient transmit design in a multiple-input single-output (MISO) wiretap channel. In particular, a transmitter sends one confidential message to a legitimate receiver, which must be kept perfectly secure from multiple external eavesdroppers. Assuming partial eavesdroppers' channel state information (ECSI) at the transmitter, we aim to design the transmit beamformer such that the outage secrecy energy efficiency (SEE) is maximized. Two ECSI uncertainty scenarios are studied, i.e., statistical ECSI and imperfect ECSI. For the statistical ECSI case, only the distribution of ECSI is available at the transmitter. The SEE outage constraint admits a closed-form expression in this case, and an approximate solution can be obtained by solving a sequence of convex optimization problems. However, this does not apply to the imperfect ECSI case, where the channel lies in some uncertainty set centered at the true channel. We show that a conservative transmit scheme can be derived by invoking the Bernstein-type inequality. It is proved that our proposed methods always yield a solution of rank one, with either statistical or imperfect CSI. Numerical results are finally presented to confirm the efficacy of our proposed methods.