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arXiv:1310.7158 · IEEE Transactions on Wireless Communications

Outage Constrained Robust Secure Transmission for MISO Wiretap Channels

Shuai Ma, Mingyi Hong, Enbin Song, Xiangfeng Wang, Dechun Sun

Published May 22, 2014• 85 citations
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Abstract

In this paper, we consider the robust secure beamformer design for multiple-input-single-output wiretap channels. Assuming that the eavesdroppers' channels are only partially available at the transmitter, we seek to maximize the secrecy rate under the transmit power and the secrecy rate outage probability constraint. The outage probability constraint requires that the secrecy rate exceed certain thresholds with high probability. Therefore, including such constraint in the design naturally ensures the desired robustness. Unfortunately, the presence of the probabilistic constraints makes the problem nonconvex and, hence, difficult to solve. In this paper, we investigate the outage probability constrained secrecy rate maximization problem using a novel two-step approach. Under a wide range of uncertainty models, our developed algorithms can obtain high-quality solutions, sometimes even exact global solutions, for the robust secure beamformer design problem. Simulation results are presented to verify the effectiveness and robustness of the proposed algorithms.

DOI
10.1109/twc.2014.2326415

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In this paper, we consider the robust secure beamformer design for multiple-input-single-output wiretap channels. Assuming that the eavesdroppers' channels are only partially available at the transmitter, we seek to maximize the secrecy rate under the transmit power and the secrecy rate outage probability constraint. The outage probability constraint requires that the secrecy rate exceed certain thresholds with high probability. Therefore, including such constraint in the design naturally ensures the desired robustness. Unfortunately, the presence of the probabilistic constraints makes the problem nonconvex and, hence, difficult to solve. In this paper, we investigate the outage probability constrained secrecy rate maximization problem using a novel two-step approach. Under a wide range of uncertainty models, our developed algorithms can obtain high-quality solutions, sometimes even exact global solutions, for the robust secure beamformer design problem. Simulation results are presented to verify the effectiveness and robustness of the proposed algorithms.
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.
This letter designs a robust beamformer for correlated multiple-input-single-output wiretap channels with multiple noncollaborating passive single-antenna eavesdroppers under channel uncertainty. Assuming that the source has only partial main channel information and statistical wiretap channel information, we seek to maximize the secrecy rate under the transmit power and secrecy outage constraints. To enhance security, the correlation between the main and wiretap channels, as a resource, is fully utilized to optimize the secure beamformer. Simulation results show that the secrecy rate is improved significantly under the transmit power and secrecy outage constraints.
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 single-antenna eavesdroppers. Assuming statistical 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, subject to the outage-constrained secrecy rate and transmit power constraints. The resultant problem is intractable to solve even after introducing a semidefinite relaxation (SDR) reformulation. To handle it, an equivalent parametric reformulation, based on the fractional programming and difference-of-concave programming theories, is proposed to recast this problem as a convex problem. By this means, the maximum outage SEE can be found in an iterative fashion. Moreover, we also give an approach to constructing a rank-one covariance matrix from our proposed method, implying the feasibility of transmit beamforming to achieve the obtained SEE performance. Numerical results are presented to show the effectiveness of our proposed method.
This letter designs a correlation-based secure beamformer for correlated multiple-input-single-output wiretap channels with multiple noncollaborating passive single-antenna eavesdroppers. The outage-probability-constrained secrecy rate maximization problem is investigated under the assumption that the source has accurate main channel information and statistical wiretap channel information. As the correlation provides some useful information, a more precise statistical distribution of the wiretap channel can be obtained, with which a closed-form expression for the secrecy outage probability is derived and a specific secure beamformer is designed. Simulation results show that the secrecy rate under the transmit power and secrecy outage constraints is improved.
This article studies robust artificial noise-aided beamforming for correlated multiple-input-single-output eavesdropping channels under Gaussian channel uncertainties. In the case of high reception correlation, under a secrecy outage probability constraint, the achievable secrecy rate is very small and does not satisfy the requirements of some high-rate applications. In view of this, optimization designs on the premise of quality-of-service (QoS) assurance are considered. By exploiting the correlation and employing a novel QoS criterion of the signal-to-noise ratio (SNR) outage probability, two optimization problems, namely minimization of the target SNR at eavesdroppers and maximization of the loose secrecy rate, are formulated. Despite less rigorous secrecy, a much lower target SNR at eavesdroppers and a higher loose secrecy rate are achieved. Compared with the conventional SNR-QoS, SNR-outage-QoS is a more flexible criterion that can be applied to Gaussian channel uncertainties, although challenging probabilistic constraints are introduced into the optimization problems. To make the optimization problems feasible, two approaches, namely, the Bernstein-type inequality approach and ellipsoid bounding approach, are applied to approximate the probabilistic constraints. Simulation results show that the robust transmit designs contribute to a secrecy performance gain from the perspective of SNR-outage-QoS.
In this letter, we investigate the simultaneous wireless information and power transfer in a multiple-input-single-output downlink system which consists of one multi-antenna transmitter, one single-antenna desired receiver, and multiple single-antenna eavesdroppers. Specifically, we investigate the outage-constrained secrecy rate maximization by jointly designing the transmit beamforming vector and the power splitting ratio with statistical channel uncertainties. To handle the formulated non-convex problem, we resort to semi-definite relaxation (SDR) and the Bernstein-type inequality to transform the outage constraints into a deterministic form. Then, the original problem can be efficiently solved by alternately optimizing two convex subproblems. In addition, we testify that the SDR can obtain the rank-one optimal solution. Finally, our proposed algorithm is validated by some representative numerical results.