In this letter, we investigate the secure beamforming design for multiuser multiple-input single-output interference channel with an eavesdropper. The robust secrecy rate optimization problem is studied with the imperfect channel state information. We consider the beamforming design to maximize the minimum worst case secrecy rate subject to the transmit power constraints with norm-bounded channel uncertainty. The problem is non-convex and hard to solve. We propose an effective method to reformulate this non-convex problem as a series of tractable convex program problems with linear matrix inequality and second-order cone constraints by exploiting the conservative approximation and the sequential convex approximation methods. The simulation results demonstrate the effectiveness of the proposed algorithm.
In this letter, we investigate the secure beamforming design for multiuser multiple-input single-output interference channel with an eavesdropper. The robust secrecy rate optimization problem is studied with the imperfect channel state information. We consider the beamforming design to maximize the minimum worst case secrecy rate subject to the transmit power constraints with norm-bounded channel uncertainty. The problem is non-convex and hard to solve. We propose an effective method to reformulate this non-convex problem as a series of tractable convex program problems with linear matrix inequality and second-order cone constraints by exploiting the conservative approximation and the sequential convex approximation methods. The simulation results demonstrate the effectiveness of the proposed algorithm.
In this paper, we consider max-min fairness for a downlink two-user multi-input single-output (MISO) system with imperfect channel state information available at transmitter (CSIT) taking into account the total power constraint and the physical layer security. Considering the worst-case channel uncertainty for a potential eavesdropper (PE), we study the robust secure beamforming algorithm design which maximizes the minimum achieved worst-case secrecy rate among single-antenna legitimate users. In contrast to existing schemes adopted in the literatures, we propose a rather unorthodox rate splitting (RS) scheme which advocates the dual use of a common message serving both as a desired message and artificial noise (AN) for legitimate users and the PE, respectively. The algorithm design is formulated as a non-convex optimization problem which is generally intractable. As a compromise approach, we apply the successive convex approximation (SCA) method which facilitates the design of a low-complexity suboptimal iterative algorithm. In each iteration, a rank-constrained semi-definite program (SDP) is solved optimally by SDP relaxation (SDR). Simulation results demonstrate that our proposed robust secure beamforming scheme in the MISO-RS secure transmission system outperforms that of the non-robust counterpart. Moreover, our results also unveil that the proposed RS scheme can achieve a superior performance compared to the existing non-orthogonal multiple access (NOMA) schemes and the traditional scheme.
This letter addresses the robust optimization problem of downlink coordinated beamforming over the multiple-input single-output (MISO) interference channel with confidential messages (IFC-CM) exploiting imperfect channel state information (CSI) at the transmitters. Our aim is to minimize the total transmitted power subject to the worst-case individual signal-to-interference-plus-noise-ratio (SINR) and equivocation rates. To model the imperfect CSI, bounded ellipsoidal uncertainties for channel vector and covariance are both considered. By deriving the equivalent forms for the SINR and secrecy constraints, the worst-case robust problem can be reformulated as a semi-definite programming (SDP) with the help of rank relaxation. Simulation results show the effectiveness of the proposed algorithm.
This paper investigates secrecy rate optimization problems for a multiple-input-single-output (MISO) secrecy channel in the presence of multiple multiantenna eavesdroppers. Specifically, we consider power minimization and secrecy rate maximization problems for this secrecy network. First, we formulate the power minimization problem based on the assumption that the legitimate transmitter has perfect channel state information (CSI) of the legitimate user and the eavesdroppers, where this problem can be reformulated into a second-order cone program (SOCP). In addition, we provide a closed-form solution of transmit beamforming for the scenario of an eavesdropper. Next, we consider robust secrecy rate optimization problems by incorporating two probabilistic channel uncertainties with CSI feedback. By exploiting the Bernstein-type inequality and S-Procedure to convert the probabilistic secrecy rate constraint into the determined constraint, we formulate this secrecy rate optimization problem into a convex optimization framework. Furthermore, we provide analyses to show the optimal transmit covariance matrix is rank-one for the proposed schemes. Numerical results are provided to validate the performance of these two conservative approximation methods, where it is shown that the Bernstein-type inequality-based approach outperforms the S-Procedure approach in terms of the achievable secrecy rates.
Robust quality-of-service (QoS)-based and secrecy rate-based secure transmission designs are investigated for a multiple-input single-output system with multiple eavesdroppers and a cooperative jammer. Two scenarios are considered: (a) eavesdroppers' channel state information (ECSI) is available and (b) ECSI is unavailable. In scenario (a), a QoS-based design is considered to minimize the worst case signal-to-interference-and-noise ratio at the eavesdroppers and to guarantee the QoS of the legitimate receiver. A secrecy rate-based design is also studied where the worst case secrecy rate is maximized. In scenario (b), a QoS-based design is considered to maximize the power of jamming signals under the QoS constraint of the legitimate receiver, and the secrecy rate-based design is not applicable. In all these designs, we jointly optimize the transmit beamforming vector and the covariance matrix of jamming signals under individual power constraints. As the optimization problems are non-convex, we propose an algorithm for each problem through semidefinite relaxation. Our analysis and simulation results show that, even though the linear precoding scheme in our designs is transmit beamforming rather than the general rank transmit covariance, this does not cause any loss of optimality.
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 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.