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International Conference on Communications

Secrecy in MIMOME wiretap channels: Beamforming with imperfect CSI

Chenxi Liu, Nan Yang, Giovanni Geraci, Jinhong Yuan, Robert Malaney

Published Jun 1, 2014• 12 citations
Publisher

Abstract

We propose two beamforming schemes supporting multi-stream transmission in multi-input multi-output multi-antenna eavesdropper wiretap channels with imperfect channel state information of the eavesdropper. We first propose a generalized eigenvalue decomposition (GEVD)-based beamforming scheme by designing the beamforming matrix and determining the power allocation matrix. In particular, we determine a general power allocation matrix for arbitrary signal-to-noise ratio (SNR) and a simplified power allocation matrix for high SNR. We demonstrate that our GEVD-based beamforming scheme delivers a higher achievable secrecy rate than the existing beamforming schemes in the medium and high SNR regime. We also demonstrate that the simplified power allocation matrix delivers the same achievable secrecy rate as the general power allocation matrix at high SNRs. We then propose an easy-to-construct EVD-based beamforming scheme which reduces signal processing cost and eliminates power allocation. We demonstrate that our EVD-based beamforming scheme delivers a higher secrecy rate than the GEVD-based beamforming scheme and the existing beamforming schemes in the low SNR regime.

DOI
10.1109/icc.2014.6884065

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We propose two beamforming schemes supporting multi-stream transmission in multi-input multi-output multi-antenna eavesdropper wiretap channels with imperfect channel state information of the eavesdropper. We first propose a generalized eigenvalue decomposition (GEVD)-based beamforming scheme by designing the beamforming matrix and determining the power allocation matrix. In particular, we determine a general power allocation matrix for arbitrary signal-to-noise ratio (SNR) and a simplified power allocation matrix for high SNR. We demonstrate that our GEVD-based beamforming scheme delivers a higher achievable secrecy rate than the existing beamforming schemes in the medium and high SNR regime. We also demonstrate that the simplified power allocation matrix delivers the same achievable secrecy rate as the general power allocation matrix at high SNRs. We then propose an easy-to-construct EVD-based beamforming scheme which reduces signal processing cost and eliminates power allocation. We demonstrate that our EVD-based beamforming scheme delivers a higher secrecy rate than the GEVD-based beamforming scheme and the existing beamforming schemes in the low SNR regime.
In this paper, we propose a new beamforming scheme for multi-input multi-output (MIMO) Gaussian wiretap channels where the channel state information (CSI) from the eavesdropper is imperfectly known to the transmitter. A stochastic model is constructed to characterize the imperfect CSI of the eavesdropper, in which a factor 0 ≤ τ ≤ 1 is introduced to describe the degree of the available eavesdropper's channel knowledge at the transmitter. When τ varies from 0 to 1, the eavesdropper's channel knowledge available at the transmitter ranges from statistically known to perfectly known. We design the proposed beamforming scheme by maximizing a lower bound on the achievable secrecy rate. We first demonstrate that our scheme achieves higher secrecy rate than the existing eigenvalue decomposition-based beamforming scheme which is optimal for τ = 0. We then demonstrate that the proposed scheme achieves higher secrecy rate than the existing generalized eigenvalue decomposition-based beamforming scheme which is optimal for τ = 1. Furthermore, we derive tight approximations for the proposed beamforming scheme in the high signal-to-noise ratio (SNR) regime and the low SNR regime. The accuracy of these approximations is validated via numerical results. Finally, we demonstrate that our proposed scheme achieves almost the same secrecy performance as the optimal beamforming solution that is obtained through numerical search.
A Gaussian multiple-input multiple-output wiretap channel in which the eavesdropper and legitimate receiver are equipped with arbitrary numbers of antennas and the transmitter has two antennas is studied in this paper. The input covariance matrix that achieves the secrecy capacity is determined. In particular, it is shown that the secrecy capacity of this channel can be achieved by linear precoding. Precoding and power allocation schemes that maximize the achievable secrecy rate, and thus achieve the secrecy capacity, are developed. The secrecy capacity is then compared with the achievable secrecy rate of generalized singular value decomposition (GSVD)-based precoding, which is the best previously proposed technique for this problem. Numerical results demonstrate that substantial gain can be obtained in secrecy rate between the proposed and GSVD-based precodings.
This paper considers a multiple-input multiple-output (MIMO) Gaussian wiretap channel model, where there exists a transmitter, a legitimate receiver and an eavesdropper, each equipped with multiple antennas. Perfect secrecy is achieved when the transmitter and the legitimate receiver can communicate at some positive rate, while ensuring that the eavesdropper gets zero bits of information. In this paper, the perfect secrecy rate of the multiple antenna MIMO wiretap channel is maximized for arbitrary numbers of antennas under the assumption that the transmitter performs beamforming based on the generalized singular value decomposition (GSVD). More precisely, the optimal allocation of power for the GSVD-based precoder that maximizes the achievable secrecy rate is derived. Numerical results are presented to illustrate that the achievable secrecy rate of the GSVD-based precoding approach is nearly identical to that of the optimal scheme.
This paper considers a multiple-input multiple-output (MIMO) Gaussian wiretap channel model, where there exists a transmitter, a legitimate receiver and an eavesdropper, each equipped with multiple antennas. Perfect secrecy is achieved when the transmitter and the legitimate receiver can communicate at some positive rate, while ensuring that the eavesdropper gets zero bits of information. In this paper, the perfect secrecy capacity of the multiple antenna MIMO wiretap channel is found for aribtrary numbers of antennas under the assumption that the transmitter performs beamforming based on the generalized singular value decomposition (GSVD). More precisely, the optimal allocation of power for the GSVD-based precoder that achieves the secrecy capacity is derived. This solution is shown to have several advantages over prior work that considered secrecy capacity for the general MIMO Gaussian wiretap channel under a high SNR assumption. Numerical results are presented to illustrate the proposed theoretical findings.
We consider transmission of confidential data over multiple-input single-output multiple-eavesdropper (MISOME) Rayleigh-fading wiretap channels. The transmitter has access to full channel state information (CSI) of a legitimate link but only partial CSI of an eavesdropper link in forms of the average received signal-to-noise power ratio (SNR). In this location-aware scenario, we develop the optimal power allocation strategy that maximizes the secrecy rate achievable by beamforming. The optimal power control is regulated in an on-off fashion with the threshold depending only on the numbers of antennas and the average SNRs. By rescuing the vanishing high-SNR degree of freedom for secure communication from this optimal on-off beamforming with the artificial noise scheme, we further derive the achievable ergodic secrecy rate of MISOME wiretap channels in closed form.
This paper studies the achievable secrecy performance of multiple-input multiple-output wiretap channels in the presence of imperfect channel state information (CSI) with practical low-complexity transmission schemes. In particular, we propose a general order transmit antenna selection and power-efficient output-threshold maximal ratio combining scheme. Two separate cases depending on the availability of the eavesdropper's CSI at the transmitter are considered. New closed-form expressions of the secrecy outage probability and the average secrecy rate are obtained. In addition, the secrecy diversity order and array gains, high signal-to-noise ratio slope, and power offset are characterized through asymptotic analysis, which enables the characterization of the effect of imprecise transmit antenna selection, output-threshold, and imperfect CSI on the secrecy performance. Numerical results are presented to validate the main outcomes of this paper.