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IET Communications

AN‐aided probabilistic robust and secure beamforming with imperfect LCSI and statistical ECSI

Jing Xu, Siwen Xu

Published Jan 9, 2020• 0 citations
Publisher

Abstract

The probabilistic robust beamforming with the help of artificial noise (AN) is investigated in this study, where a multiple‐input‐single‐output wiretap scenario with K single‐antenna eavesdroppers is considered. Based on a more practical assumption that the transmitter derives imperfect legitimate user's channel state information (LCSI) and statistical eavesdroppers' channel state information (ECSI), secrecy rate maximisation (SRM) under a total transmit power constraint and K probabilistic secrecy outage constraints are studied. To deal with it, the K probabilistic constraints are firstly approximated to the deterministic worst‐case ones by resorting to sphere bounding. Secondly, by introducing a slack variable the approximated worst‐case SRM can be further recast as a series of semi‐definite programmings. In this way, the jointly optimised robust beamforming vector and the AN covariance are determined in a tractable convex fashion. Moreover, the authors can prove that the derived AN‐aided secure robust beamforming actually is the optimal solution to the approximated worst‐case SRM problem. Numerical results reveal that the proposed AN‐aided probabilistic secure robust beamforming could achieve outage secrecy rate improvement in comparison with the existing optimal worst‐case robust beamforming without AN, optimal outage constrained robust beamforming without AN, the non‐robust isotropic AN transmission, and the non‐robust AN‐aided beamforming scheme.

DOI
10.1049/iet-com.2019.0768

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The probabilistic robust beamforming with the help of artificial noise (AN) is investigated in this study, where a multiple‐input‐single‐output wiretap scenario with K single‐antenna eavesdroppers is considered. Based on a more practical assumption that the transmitter derives imperfect legitimate user's channel state information (LCSI) and statistical eavesdroppers' channel state information (ECSI), secrecy rate maximisation (SRM) under a total transmit power constraint and K probabilistic secrecy outage constraints are studied. To deal with it, the K probabilistic constraints are firstly approximated to the deterministic worst‐case ones by resorting to sphere bounding. Secondly, by introducing a slack variable the approximated worst‐case SRM can be further recast as a series of semi‐definite programmings. In this way, the jointly optimised robust beamforming vector and the AN covariance are determined in a tractable convex fashion. Moreover, the authors can prove that the derived AN‐aided secure robust beamforming actually is the optimal solution to the approximated worst‐case SRM problem. Numerical results reveal that the proposed AN‐aided probabilistic secure robust beamforming could achieve outage secrecy rate improvement in comparison with the existing optimal worst‐case robust beamforming without AN, optimal outage constrained robust beamforming without AN, the non‐robust isotropic AN transmission, and the non‐robust AN‐aided beamforming scheme.
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 study considers a cellular multiple‐input single‐output system overheard by multiple eavesdroppers, in the presence of multiple pairs of single‐antenna device‐to‐device (D2D) nodes working as an underlay. All D2D nodes are permitted to access the cellular channel for their own communications. A novel eavesdropping scenario, termed as simultaneous eavesdropping, is studied, where the eavesdroppers intend to simultaneously overhear the cellular communication as well as D2D communications. Assuming imperfect channel state information (CSI) at the transmitter, the authors goal is to design the robust transmit covariance of confidential message and artificial noise, such that the worst‐case sum secrecy rate is maximised. This worst‐case sum secrecy rate maximisation problem is challenging to solve due to its non‐convexity and semi‐infiniteness incurred by the imperfect CSI. As a compromise, the authors develop a tractable approximation to its objective secrecy rate function for deriving a computationally efficient lower bound. Then a successive convex approximation (SCA) algorithm is proposed to solve the approximated problem in an iterative manner with provable convergence guarantee. Then it is proved that the SCA algorithm always yields a beam‐forming solution to the confidential message transmission. Numerical results illustrate that the proposed scheme outperforms the traditional one.
This paper investigates the joint robust beamforming and artificial noise design in two-user interference networks, where one of the two pairs is wiretapped by an external eavesdropper, and only imperfect eavesdropper's channel state information (ECSI) is available for the two pairs. Under individual transmission power constraint, our goal is to maximize the worst-case achievable secrecy rate of the wiretapped node and guarantee the signal-to-interference-plus-noise ratio (SINR) requirement at the wiretap-free node. In particular, considering the channel vectors and channel covariance matrices errors, we first model the imperfect ECSI in the sense of ellipsoidal uncertainties. In the sequel, our design goal is transformed into solving a non-convex optimization problem which can be further reformulated as a two-stage problem. With the help of rank relaxation and one dimensional line search, the considered two-stage problem is solved efficiently. Simulation results demonstrate the effectiveness of the proposed design in different scenarios.
This paper studies secure wireless transmission from a multi-antenna transmitter to a single-antenna intended receiver overheard by multiple eavesdroppers with considering the imperfect channel state information (CSI) of wiretap channel.To enhance security of communication link, the artificial noise (AN) is generated at transmitter.We first design the robust joint optimal beamforming of secret signal and AN to minimize transmit power with constraints of security quality of service (QoS), i.e., minimum allowable signal-to-interference-and-noise ratio (SINR) at receiver and maximum tolerable SINR at eavesdroppers.The formulated design problem is shown to be nonconvex and we transfer it into linear matrix inequalities (LMIs).The semidefinite relaxation (SDR) technique is used and the approximated method is proved to solve the original problem exactly.To verify the robustness and tightness of proposed beamforming, we also provide a method to calculate the worst-case SINR at eavesdroppers for a designed transmit scheme using semidefinite programming (SDP).Additionally, the secrecy rate maximization is explored for fixed total transmit power.To tackle the nonconvexity of original formulation, we develop an iterative approach employing sequential parametric convex approximation (SPCA).The simulation results illustrate that the proposed robust transmit schemes can effectively improve the transmit performance.
This paper studies the artificial noise (AN) aided beamforming design in the multiple-input, single-output, and multiple-eavesdropper wiretap channel from the perspective of secrecy outage. Unlike many existing works, which directly adopted the traditional null-space AN scheme, we start with a general assumption on the structure of the transmit signal, and seek to find the optimal structure by solving a secrecy outage probability (SOP) constrained secrecy rate maximization problem. By generalizing several existing conclusions regarding a single-antenna eavesdropper, we prove that the null-space AN scheme is indeed optimal for an arbitrary number of the eavesdropper’s antennas from the perspective of secrecy outage. Furthermore, the optimal power allocation between the information-bearing signal and the AN is found under both general conditions and the conservative assumption that the eavesdropper can be arbitrarily close to the transmitter or his receiver noise power can be arbitrarily low. It is also found that the increase in the eavesdropper’s antenna number is equivalent to requiring a smaller SOP under the conservative assumption. The results in this paper can help generalize existing design solutions for single-antenna eavesdroppers to multi-antenna eavesdroppers.
This paper considers an artificial noise (AN) aided secrecy rate maximization (SRM) problem for a multi-input single-output (MISO) channel overheard by multiple single-antenna eavesdroppers. We assume that the transmitter has perfect knowledge about the channel to the desired user but imperfect knowledge about the channels to the eavesdroppers. Therefore, the resultant SRM problem is formulated in the way that we maximize the worst-case secrecy rate by jointly designing the signal covariance W and the AN covariance Σ. However, such a worst-case SRM problem turns out to be hard to optimize, since it is nonconvex in W and Σ jointly. Moreover, it falls into the class of semi-infinite optimization problems. Through a careful reformulation, we show that the worst-case SRM problem can be handled by performing a one-dimensional line search in which a sequence of semidefinite programs (SDPs) are involved. Moreover, we also show that the optimal W admits a rank-one structure, implying that transmit beamforming is secrecy rate optimal under the considered scenario. Simulation results are provided to demonstrate the robustness and effectiveness of the proposed design compared to a non-robust AN design.