In this letter, secure beamforming designs are investigated in a multiple-input multiple-output secrecy channels with simultaneous wireless information and power transfer. In order to achieve fairness among different multiple energy harvesting receivers, the minimum harvested energy is maximized under the secrecy rate requirements. In particular, in order to reduce the computational complexity of the semidefinite programming problem, a successive convex approximation (SCA) iterative algorithm is proposed in the perfect channel state information (CSI) case to obtain a near-optimal rank-one solution. Moreover, the original problem is extended to the imperfect CSI case by incorporating a norm-bounded error model, where an SCA-based iterative algorithm is also proposed. Simulation results reveal that the SCA-based iterative algorithm achieves the same performance as the semidefinite relaxation method with reduced complexity.
In this letter, secure beamforming designs are investigated in a multiple-input multiple-output secrecy channels with simultaneous wireless information and power transfer. In order to achieve fairness among different multiple energy harvesting receivers, the minimum harvested energy is maximized under the secrecy rate requirements. In particular, in order to reduce the computational complexity of the semidefinite programming problem, a successive convex approximation (SCA) iterative algorithm is proposed in the perfect channel state information (CSI) case to obtain a near-optimal rank-one solution. Moreover, the original problem is extended to the imperfect CSI case by incorporating a norm-bounded error model, where an SCA-based iterative algorithm is also proposed. Simulation results reveal that the SCA-based iterative algorithm achieves the same performance as the semidefinite relaxation method with reduced complexity.
This paper studies the secure transmission issue for simultaneous wireless information and power transfer in a multiuser multiple-input-multiple-output system with multiple external eavesdroppers, where the transmitter broadcasts independent confidential messages to different legitimate receivers. Each receiver can be seen as an internal eavesdropper intended by other receivers. Our objective is to achieve the robust beamforming design under imperfect channel state information, in which the total transmission power is minimized with constraints on the achievable secrecy rate and the energy harvesting. Since the problem is nonconvex, we propose a two-level optimization scheme. For the inner problem, we investigate two conservative relaxation approaches, large-deviation inequality and Bernstein-type inequality (BTI), to reformulate the outage secrecy rate constraints into some convex ones, yielding a convex optimization by semidefinite programming (SDP) relaxation. For the outer problem, it is a K-variable optimization problem, which can be solved via the novel line-dimensional-like search method. Moreover, we characterize the rank profile of SDP relaxed solution for these two approaches. Specifically, the optimal solution is proved to be rank-one. Numerical results are provided to verify the performance of the proposed algorithms, where the LDI-based scheme outperforms the BTI-based scheme in terms of energy efficiency.
In this article, we study a robust beamforming design for multiuser multiple-input–multiple-output secrecy networks with simultaneous wireless information and power transfer (SWIPT). In this system, an access point, multiple Internet-of-Things (IoT) devices under the nonlinear energy harvesting (EH) model with a help of one cooperative jammer (CJ). We employ artificial noise (AN) generation to facilitate efficient wireless energy transfer and secure transmission. To achieve EH fairness, we aim to maximize the minimum harvested energy among users subject to secrecy rate constraint and total transmit power constraint in the presence of channel estimation errors. By incorporating a norm-bounded channel uncertainty model, the original robust problem is transformed into a two-layer optimization problem, where the inner layer problem is reformulated as semidefinite programming (SDP) and the outer layer problem is solved by a one-dimensional (1-D) line search algorithm. In addition, in order to reduce computational complexity, we propose an algorithm based on sequential parametric convex approximation (SPCA). Finally, simulation results show that the proposed SPCA method achieves the same performance as the two-layer algorithm with much lower complexity.
In this paper, an energy harvesting scheme for a multi-user multiple-input-multiple-output secrecy channel with artificial noise (AN) transmission is investigated. Joint optimization of the transmit beamforming matrix, the AN covariance matrix, and the power splitting ratio is conducted to minimize the transmit power under the target secrecy rate, the total transmit power, and the harvested energy constraints. The original problem is shown to be non-convex, which is tackled by a two-layer decomposition approach. The inner layer problem is solved through semi-definite relaxation, and the outer problem, on the other hand, is shown to be a single-variable optimization that can be solved by 1-D line search. To reduce computational complexity, a sequential parametric convex approximation method is proposed to find a near-optimal solution. This paper is then extended to the imperfect channel state information case with norm-bounded channel errors. Furthermore, tightness of the relaxation for the proposed schemes is validated by showing that the optimal solution of the relaxed problem is rank-one. Simulation results demonstrate that the proposed SPCA method achieves the same performance as the scheme based on 1-D but with much lower complexity.
In this letter, we consider a multiple-input-multiple-output (MIMO) downlink system with simultaneous wireless information and power transfer (SWIPT), where the information sent to the desired receiver (DR) may be wiretapped by the malicious energy harvesting (EH) receivers (potential eavesdroppers). Assuming the channel state information (CSI) of the EH receivers is not perfectly known at the transmitter, we aim to maximize the worst-case secrecy rate by jointly designing the precoding matrix, AN covariance matrix and power splsplitting ratio, under the constraints of total transmit power and harvested energyitting ratio, under the constraints of total transmit power and harvested energy at receivers. The formulated problem is non-convex and semi-infinite, which is hard to tackle. To solve it, we first deal with the non-convexity caused by CSI errors with the aid of the S-Procedure, and then employ the Taylor series approximation techniques to transfer the nonconvex problem into a convex optimization problem. Based on that, we propose an iterative algorithm with proved convergence to solve the original problem. Simulation results are finconvex optimization problem. Based on that, we propose an iterative algorithmally provided to show the effectiveness of our proposed robust transmit design.
In this paper, we consider a multiuser multiple-input multiple-output (MIMO) downlink communication system with simultaneous wireless information and power transfer (SWIPT). In particular, we focus on a realistic and efficient multi-receiver multi-eavesdropper MIMO SWIPT system, in which the channel state information (CSI) of each legitimate receiver and energy receiver (i.e., potential eavesdropper) is partially known to the transmitter. Based on this, we propose a robust artificial noise (AN)-aided secure transmission scheme for the system, where the channel uncertainties are modeled by the worst-case model. In the proposed scheme, we aim to maximize the worst-case achievable secrecy rate under the transmit power constraint and the energy harvesting (EH) constraint, by jointly optimizing the transmit precoding matrix and the AN covariance matrix. We utilize the S-Procedure and Taylor series approximation to transform the non-convex problem. Then, we apply the interior point method to tackle the transformed convex problem, obtaining the approximate optimal matrices and the corresponding maximum worst-case secrecy rate. Simulation results show that our proposed scheme achieves significant performance improvements in terms of convergence and the worst-case achievable secrecy rate.
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.