In this paper, we study an energy harvesting scheme for a multiple-input-single-output secrecy channel under imperfect channel state information case with either deterministic and statistical channel uncertainties. The system consists of one multi-antenna transmitter, several multi-antenna energy receivers (ERs) and one single-antenna co-located receiver (CR) who adopts a power splitter to decode information and harvest power simultaneously. We consider the artificial noise (AN) embedded information-bearing signal to interfere potential eavesdroppers (i.e., ERs) and capture the harvested power. We perform joint optimization for the masked beamforming matrix, the AN covariance matrix and the power splitting ratio, such that the transmit power is minimized to satisfy the target secrecy rate of the CR, the total transmit power and the energy harvesting constraints for the CR and the ERs. By incorporating norm-bounded channel uncertainty model, we propose a robust joint design method to obtain the optimal solution. Also, a suboptimal algorithm for the outage constrained robust optimization problem is proposed by adopting the Bernstein-type inequality. Furthermore, the tightness of the relaxation for the proposed schemes are verified by showing that the optimal solution of the relaxed problem is rank-one. Finally, simulation results are presented to validate the performance of our proposed schemes.
In this paper, we study an energy harvesting scheme for a multiple-input-single-output secrecy channel under imperfect channel state information case with either deterministic and statistical channel uncertainties. The system consists of one multi-antenna transmitter, several multi-antenna energy receivers (ERs) and one single-antenna co-located receiver (CR) who adopts a power splitter to decode information and harvest power simultaneously. We consider the artificial noise (AN) embedded information-bearing signal to interfere potential eavesdroppers (i.e., ERs) and capture the harvested power. We perform joint optimization for the masked beamforming matrix, the AN covariance matrix and the power splitting ratio, such that the transmit power is minimized to satisfy the target secrecy rate of the CR, the total transmit power and the energy harvesting constraints for the CR and the ERs. By incorporating norm-bounded channel uncertainty model, we propose a robust joint design method to obtain the optimal solution. Also, a suboptimal algorithm for the outage constrained robust optimization problem is proposed by adopting the Bernstein-type inequality. Furthermore, the tightness of the relaxation for the proposed schemes are verified by showing that the optimal solution of the relaxed problem is rank-one. Finally, simulation results are presented to validate the performance of our proposed schemes.
Considering simultaneous wireless information and power transfer (SWIPT), we study a multiple-input- single-output (MISO) secrecy channel which consists of a multi-antenna trans- mitter and a cooperative jammer (CJ), multiple multi-antenna energy receivers (ERs), i.e., potential eavesdroppers, and multiple single-antenna co-located receivers (CRs). Both transmitter and CJ send the intend signal with artificial noise (AN) and jamming signal to interfere with the ERs. All receivers (CRs and ERs) adopt a power splitter to decode information and harvest power simultaneously. We exploit AN and CJ to facilitate efficient wireless energy transfer and secure transmission. Our aim is to maximize the minimum harvested energy among all ERs and CRs subject to the total power constraints at the transmitter and CJ while guaranteeing the minimum secrecy rate for each CR above its requirement. By incorporating norm-bounded channel uncertainty model, we propose a joint design of robust secure transmission. The original problem is solved by a two- step approach. In the first step, the proposed problem is reformulated as a sequence of semidefinite programs (SDPs). In the second step, the proposed problem can be handled by one-dimensional search to attain the optimal solution. Simulation results indicate that the performance of the proposed scheme outperforms that of separated AN-aided or CJ-aided scheme.
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.
This letter investigates a multiple-input single-output secrecy channel, where the legitimate user and the eavesdroppers employ a power splitting scheme for information decoding and energy harvesting (EH), simultaneously. An artificial noise is embedded to the information bearing signal to interfere the eavesdroppers and to harvest power by all receivers (i.e., legitimate user and eavesdroppers). We consider the robust secrecy rate maximization problem subject to the transmit power and the EH constraints by incorporating the norm-bounded channel uncertainty. This robust optimization problem is not convex, and thus, it can be reformulated as a convex one along with matrix transformations and convex conic optimization techniques, which is iteratively solved based on constrained concave-convex procedure-based algorithm. Finally, numerical results are provided to validate our proposed algorithm.
This paper studies the secure beamforming design for simultaneous wireless information and power transfer in a multiple-input single-output broadcast channel with confidential messages and external eavesdroppers, where each receiver adopts the power splitting (PS) scheme to decode information and harvest energy concurrently, and it is also seen as a potential eavesdropper for messages not intended for it. Our objective is to minimize the total transmit power while guaranteeing the individual secrecy rate and energy harvesting constraints at each receiver by jointly optimizing transmit beamforming vectors, artificial noise covariance, and receive PS ratios. Both scenarios of perfect and imperfect channel state information (CSI) at the transmitter are considered. For the perfect CSI case, we propose a two-stage optimization approach to solve the original non-convex problem global optimality, and also provide a low-complexity suboptimal solution based on the particle swarm optimization algorithm. Furthermore, we also extend the above result to the colluding eavesdroppers scenario. For the imperfect CSI case, we propose a worst-case-based robust formulation, where the CSI errors are norm-bounded. With the aid of S-Procedure, we derive the equivalent forms for constraints and then transform the non-convex robust design into a convex optimization problem. Simulation results are finally presented to demonstrate the performance of our proposed schemes.
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.
In this paper, we investigate multiple-input single-output (MISO) simultaneous wireless information and power transfer (SWIPT) broadcast channels with confidential messages (BCC) scenario, in which a multiple-antenna transmitter simultaneously transmits confidential messages and power to multiple single-antenna receivers. Considering the imperfect channel state information (CSI), we study the joint optimization of transmit beamforming vectors, covariance of artificial noise, and power splitting ratios so as to minimize the total transmit power while satisfying the worst-case conservative secrecy rate and energy harvesting constraints. The original optimization is non-convex and intractable in general. To handle this challenge, in this paper, we first derive the exact upper or lower bounds of the constraints in original optimization problem by using the Lagrangian approach, and then convert the corresponding non-convex problem into a convex one with the aid of the rank relaxation technique. Finally, we provide simulation results to illustrate the robustness of the proposed design.