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IEEE Transactions on Vehicular Technology

Robust Secure Beamforming in MIMO Wiretap Channels With Deterministically Bounded Channel Errors

Miao Jiang, Yiqing Li, Qi Zhang, Quanzhong Li, Jiayin Qin

Published Aug 9, 2018• 9 citations
Publisher

Abstract

In this paper, a multiple-input multiple-output wiretap channel model is studied, where the information packet sent from the transmitter to the desired receiver is wiretapped by a potential eavesdropper. When ideal channel state information (CSI) is available, we design the secure beamforming using a proposed iterative closed-form updating scheme based on majorization-minimization approach. Numerical results demonstrate that the proposed scheme acquires the same secrecy rate as the existing algorithms whereas it has much lower complexity. When ideal CSI is not available and channel errors are modeled by deterministically bounded model, we investigate robust secure beamforming (RSB) optimization problem whose goal is worst-case secrecy rate maximization. In the formulated optimization problem, the objective function includes the expression of a logarithm of a determinant (log det) minus log det. Instead of approximating the log det expression as a trace, we propose to linearize two log det terms. After linearization, epigraph reformulation is used to deal with deterministically bounded channel errors and semi-infinite constraints are recast as linear matrix inequalities. Finally, an alternating optimization algorithm is utilized to find the RSB design. After obtaining the RSB design, we derive the worst-case secrecy rate. Numerical results illustrate that the proposed RSB design is superior to the nonrobust one.

DOI
10.1109/tvt.2018.2864542

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In this paper, a multiple-input multiple-output wiretap channel model is studied, where the information packet sent from the transmitter to the desired receiver is wiretapped by a potential eavesdropper. When ideal channel state information (CSI) is available, we design the secure beamforming using a proposed iterative closed-form updating scheme based on majorization-minimization approach. Numerical results demonstrate that the proposed scheme acquires the same secrecy rate as the existing algorithms whereas it has much lower complexity. When ideal CSI is not available and channel errors are modeled by deterministically bounded model, we investigate robust secure beamforming (RSB) optimization problem whose goal is worst-case secrecy rate maximization. In the formulated optimization problem, the objective function includes the expression of a logarithm of a determinant (log det) minus log det. Instead of approximating the log det expression as a trace, we propose to linearize two log det terms. After linearization, epigraph reformulation is used to deal with deterministically bounded channel errors and semi-infinite constraints are recast as linear matrix inequalities. Finally, an alternating optimization algorithm is utilized to find the RSB design. After obtaining the RSB design, we derive the worst-case secrecy rate. Numerical results illustrate that the proposed RSB design is superior to the nonrobust one.
This paper studies a cognitive multiple-input multiple-output (MIMO) network, in which a secondary transmitter aims to send confidential messages to its receiver in the presence of one multi-antenna eavesdropper, while has the interference temperature limit (ITL) for the primary user. Assuming that all the channels are imperfect and the errors are modeled by deterministically bounded model, we consider robust secure beamforming (RSB) design problem and our goal is to maximize the worst-case achievable secrecy rate subject to the total transmit power constraint and the ITL for the primary user. The formulated optimization problem is non-convex while the channel uncertainties make it more difficult to cope with. To address it, an inexact block coordinate descent (IBCD) approach is proposed to obtain the near-optimal solution, where we firstly linearize the two log-det terms of the objective function and then, the semi-infinite constraints with the bounded channel uncertainties are reformulated as linear matrix inequalities (LMIs). Finally, numerical results validate the performance of our proposed RSB algorithm.
In this paper, we investigate the robust secure transmit beamformming design for multiple-input single-output wiretap channels overheard by multiple non-collaborating single-antenna eavesdroppers. Assuming that at the transmitter, the instantaneous legitimate receiver's channel state information (CSI) is imperfect and only the statistical eavesdroppers' CSI is known, we seek to maximize the target secrecy rate R with the total transmit power constraint and the secrecy outage probability constraint. The resulting outage-constrained secrecy rate maximization (O-SRM) is non-convex and difficult to solve. Thus, we develop an efficient algorithm to solve it and determine the robust secure beamforming design. Specifically speaking, we first prove that the original O-SRM problem can be solved by an equivalent outage-constrained power minimization problem (O-PMP), which is easy to perform semi-definite relaxation (SDR) and can be solved by semi-definite program (SDP) consequently. Second, we transform the non-convex secrecy rate outage constraints into deterministic ones by resorting to Bernstein-type inequality II. Finally, by solving the convex approximation of the O-PMP with different Rs and bisection search over R, we convert the original O-SRM problem into a sequence of solvable SDPs. Simulation results are provided to verify the secrecy-rate performance improvement of the proposed robust beamforming compared with the existing worst-case design proposed by Li and Ma and the simple non-robust maximum-ratio transmission.
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 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.
This paper studies masked beamforming schemes for secure communication in broadcast multiple-input multiple-output (MIMO) systems with a passive multiple-antenna eavesdropper. Assuming no information about the eavesdropper is available at the transmitter, we aim to maximize the transmit power of the artificial noise while meeting mean square error (MSE) constraints at the legitimate receivers and the total power constraint at the transmitter. Based on imperfect channel state information (CSI) of the legitimate receivers at the transmitter, we present a worst-case robust masked beamforming algorithm. By exploiting alternating iterative optimization, the proposed algorithm recasts the non-convex optimization problem as two semidefinite program (SDP) based subproblems, which are solvable with interior-point methods. Simulation results are provided to illustrate the secrecy performance of the proposed algorithm.
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.