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IEEE Communications Letters

Distributionally Robust Optimization for Secure Transmission With Assisting Jammer in MISO Downlink Networks

Xiaochen Liu, Yuanyuan Gao, Lei Wang, Nan Sha, Shijie Wang

Published Dec 27, 2018• 8 citations
Publisher

Abstract

This letter investigates secure transmission with imperfect channel state information (CSI) in multi-input single-output downlink wireless networks that consist of a transmitter, a desired receiver, one eavesdropper, and an assisting jammer. Specifically, only rough first- and second-order moment information is obtained for the estimation errors of CSI. We aim to minimize the total transmit power by jointly designing the beamforming vector at transmitter and artificial noise covariance at jammer under the reliability and secrecy constraints for all the possible distributions of CSI errors. Since the chance-constrained optimization problem is non-convex, we reformulate it using a Lagrangian duality theory and semidefinite relaxation. The simulation results illustrate the validity of the proposed distributionally robust transmit scheme.

DOI
10.1109/lcomm.2018.2886025

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This letter investigates secure transmission with imperfect channel state information (CSI) in multi-input single-output downlink wireless networks that consist of a transmitter, a desired receiver, one eavesdropper, and an assisting jammer. Specifically, only rough first- and second-order moment information is obtained for the estimation errors of CSI. We aim to minimize the total transmit power by jointly designing the beamforming vector at transmitter and artificial noise covariance at jammer under the reliability and secrecy constraints for all the possible distributions of CSI errors. Since the chance-constrained optimization problem is non-convex, we reformulate it using a Lagrangian duality theory and semidefinite relaxation. The simulation results illustrate the validity of the proposed distributionally robust transmit scheme.
In this paper, we propose the distributionally robust secure transmit schemes in multi-input single-output (MISO) downlink wireless networks which consist of a transmitter, a desired receiver, multiple eavesdroppers and an assisting jammer. The imperfect channel state information (CSI) is considered and the CSI errors are only captured by the mean and covariance. We first study the transmit power minimization by jointly designing the beamforming vector at transmitter and artificial noise(AN) covariance at jammer, while the lower bound of connection probability at desired receiver and lower bound of outage probability at eavesdroppers are guaranteed simultaneously. Since the chance-constrained problem is non-convex, we derive two safe convex approximations by exploiting the Conditional Value-at-risk (CVaR) based method and Bernstein-type inequality (BTiE) based method, respectively. Specifically, we extend the application of BTiE originally proposed with the Gaussianity assumption to other possible distributions which satisfy the proposed sufficient condition. Furthermore, the secrecy rate maximization is exploited under the constraint of total transmit power. The original problem is non-convex and fractional, hence we design the Bilevel Quick Search (BQS) method to make it tractable. Finally, the simulation results verify the effectiveness and the robustness of the proposed transmit schemes.
Physical layer security has recently emerged as a promising approach to provide secure wireless communications. Physical layer security technology is the key means to achieve security and communication integration. The built-in security mechanism based on the characteristics of wireless channel provides a feasible idea for the realization of “one secret at a time”. It has important application prospects in integrity protection of service data, Internet of things (IoT) lightweight encryption and blockchain wireless security technology. In this paper, we consider the scenario of a unicast multiuser multiple-input single-output (MISO) downlink system in the presence of multiple single-antenna passive eavesdroppers. Instead of assuming perfect channel state information (CSI), we investigate the artificial noise (AN)-aided robust transmit beamforming scheme with imperfect CSI on legitimate receivers and no CSI regarding eavesdroppers at the transmitter. Under the fixed total transmit power, the information symbol and the AN are transmitted concurrently. We aim to guarantee each legitimate receiver's signal-to-interference-and-noise ratio(SINR) outage probability below a preset level with minimum power. Hence, as much power as possible can be allocated to AN to confuse the eavesdroppers. In order to reduce the negative impact on the legitimate receivers, the AN is transmitted in the null space of the estimated legitimate channels. To deal with this nonconvex optimization problem, a rank relaxed formulation is obtained by employing semidefinite relaxation (SDR). Then we propose two approaches by using Bernstein-type inequality and S-procedure, respectively, to transform the probabilistic constraints into deterministic constraints. The optimization problem is reformulated as a convex semidefinite program (SDP). Simulation results show that the proposed approaches have better performances than the non-robust approach.
A robust quality-of-service (QoS) based secure transmission design is investigated for a cooperative jamming aided multiple-input single- output system with unknown eavesdroppers. By assuming legitimate receiver's channel state information (CSI) is imperfect and eavesdroppers' CSI is unavailable, our system design goal is to maximize the power of artificial jamming signals, and to guarantee a minimum QoS at the legitimate receiver. The transmit beamforming vector and covariance matrix of jamming signals are jointly optimized under individual power constraints. As this optimization problem is non-convex, we propose a solution method by using the semidefinite relaxation approach. Numerical results show that, our design, in which the precoding scheme of information transmission is transmit beamforming, outperforms its transmit covariance based counterpart.
This paper addresses robust designs of secure simultaneous wireless information and power transfer for multiple-input single-output (MISO) multiuser systems. By using a bounded uncertainty model for the channel state information (CSI) from transmitters to legitimate receivers and under the assumption of only available statistic knowledge of the CSI to eavesdroppers, we consider the robust designs with both worst-case and chance-constrained optimizations. To jointly optimize transmit beamforming vectors and power splitting factors, we formulate three problems aiming at minimizing the system power, maximizing the sum secrecy rate, and maximizing the minimal secrecy rate, respectively, subject to both energy harvesting and secrecy outage constraints. These problems are intractable in their original forms due to the CSI models and their non-convexity. To reach computationally efficient solutions, we first rewrite the original problems by semi-definite relaxation, then transform the CSI uncertainty related constraints by S-procedure, and finally approximate the non-convex constraints by the first-order Taylor expansion. By the reformulations, we present iterative successive convex approximation algorithm for approaching the optimized solutions. Simulation results under various setups of system parameters are provided to examine the system performance and validate the effectiveness of the proposed schemes.
In this work, a robust artificial noise (AN) aided transmit method is proposed for a multicast multiple-input single-output (MISO) system in the presence of multiple single-antenna eavesdroppers. With the imperfect covariance-based channel state information (CSI), we aim to minimize the transmit power at the transmitter under the multicast secrecy rate constraint and the maximum transmit power constraint. The resulting optimization problem involves the joint optimization of the beamforming vector and AN covariance matrix. After using the semidefinite relaxation (SDR) technique, we derive the exact reformulation of the original optimization through the Lagrange duality. Then this non-convex problem is transformed into a one-variable optimization problem, which can be handled by solving a series of semidefinite programs (SDPs). Simulation results demonstrate the effectiveness of the proposed robust transmit method.
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.