Zhengyu Zhu

Outage Constrained Robust Beamforming for Secure Broadcasting Systems With Energy Harvesting

In this paper, we investigate simultaneous wireless information and power transfer systems for multiuser multiple-input single-output secure broadcasting channels. Considering imperfect channel state information, we introduce a robust secure beamforming design, where the transmit power is minimized subject to the secrecy rate outage probability constraint for legitimate users and the harvested energy outage probability constraint for energy harvesting receivers. The original problem is non-convex due to the presence of the probabilistic constraints. With the aid of Bernstein-type inequalities, we transform the outage constraints into the deterministic forms. Based on a successive convex approximation (SCA) method, we propose a low-complexity approach, which reformulates the original problem as a second-order cone programming problem. Also, we prove the convergence of the SCA-based iterative algorithm. Simulation shows that the proposed scheme outperforms the conventional method with lower complexity.

Robust Optimization for AN-Aided Transmission and Power Splitting for Secure MISO SWIPT System

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.

Robust Beamforming and Power Splitting Design in Distributed Antenna System with SWIPT under Bounded Channel Uncertainty

In this paper, we investigate a multiuser downlink distributed antenna system with simultaneous wireless information and power transmission under the assumption of imperfect channel state information at the distributed antenna (DA) port. To optimally design robust transmit beamforming vectors and receive power splitting factors, our design objective is to maximize the average worst-case signal-to-interference-plus-noise ratio while simultaneously achieving the individual energy harvesting (EH) constraint for each user and the per-DA port power constraint. We solve this non- convex problem by reformulating it into a two-stage problem. Simulation results are shown to validate the robustness and effectiveness of the proposed algorithms.

Robust transceiver designs in multiuser MISO broadcasting with simultaneous wireless information and power transmission

In this paper, we address a new robust optimization problem in a multiuser multiple-input single-output broadcasting system with simultaneous wireless information and power transmission, where a multi-antenna base station (BS) sends energy and information simultaneously to multiple users equipped with a single antenna. Assuming that perfect channel-state information (CSI) for all channels is not available at the BS, the uncertainty of the CSI is modeled by an Euclidean ball-shaped uncertainty set. To optimally design transmit beamforming weights and receive power splitting, an average total transmit power minimization problem is investigated subject to the individual harvested power constraint and the received signal-to-interference-plus-noise ratio constraint at each user. Due to the channel uncertainty, the original problem becomes a homogeneous quadratically constrained quadratic problem, which is NP-hard. The original design problem is reformulated to a relaxed semidefinite program, and then two different approaches based on convex programming are proposed, which can be solved efficiently by the interior point algorithm. Numerical results are provided to validate the robustness of the proposed algorithms.

Joint optimization of AN-aided beamforming and power splitting designs for MISO secrecy channel with SWIPT

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.

Sum Rate Maximizing in a Multi-User MIMO System with SWIPT

This paper studies the simultaneous wireless information and power transfer (SWIPT) in a multiuser broadcast (BC) multiple-input multiple-output (MIMO) system, in which a base station sends messages to several information decoding (ID) users, and transmits wireless power to multiple energy harvesting (EH) user at the same time. We aim to maximize the sum-rate of the ID users while maintaining a minimum EH constraint for each EH user. Firstly, an optimal rate-energy (R-E) boundary is characterized by using a BC-multiple access channel (MAC) duality derived from dirty paper coding (DPC). Since the complexity of the DPC is quite high due to continuously encoding and decoding at the transceivers, we then propose a sub- optimal algorithm using a weighted minimum mean square error (WMMSE) approach, which has lower complexity and iteratively converges a local optimal point. Finally, the performance comparisons and convergence properties are illustrated by simulation results.

Beamforming and Power Splitting Designs for AN-Aided Secure Multi-User MIMO SWIPT Systems

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.

Robust beamforming based on transmit power analysis for multiuser multiple-input–single-output interference channels with energy harvesting

In this study, the authors study the robust transmit beamforming and receive power splitting design for simultaneous wireless information and power transfer in multiuser multiple-input–single-output interference channel with imperfect channel-state information at the transmitter. Following the worst-case model, they minimise the average total transmit power subject to a set of energy harvesting constraints and signal-to-interference-and-noise ratio constraints. On the basis of the Lagrangian multiplier method, they propose a robust design method based on tight bounds that is able to achieve an approximate optimum. To reduce the complexity, they transform this original problem into a relaxed semi-definite programming problem based on loose bounds, which can be solved efficiently. It is shown from simulation results that their proposed methods outperform the non-robust scheme.

Robust Beamforming Design for MISO Secrecy Multicasting Systems with Energy Harvesting

In this paper, we study simultaneous wireless information and power transfer (SWIPT) for multiuser multiple-input- single-output (MISO) secrecy multicasting channels with imperfect channel state information. First, a robust secure beamfoming design is considered, where the transmit power is minimized subject to the secrecy rate outage probability constraint for legitimate users and the harvested energy outage probability constraint for energy harvesting receivers. The original problem is non-convex due to the presence of the probabilistic constraints. By utilizing Bernstein-type inequalities, we transform the outage constraints into the deterministic forms. In order to identify a local optimal rank-one solution, we propose an efficient approach based on a constrained concave convex procedure method to convert the original problem into a sequence of convex programming problems. Finally, simulation results are provided to validate the performance of our proposed design methods.

Robust beamforming and power splitting design in MISO SWIPT downlink system

In this study, the authors consider simultaneous wireless information and power transfer (SWIPT) in a multiple-input-single-output (MISO) downlink system, where power splitting scheme is considered for each user of this system. Since channel state information of each user cannot be available at the transmitter, robust beamforming for SWIPT in the MISO downlink system is presented by incorporating with different types of channel uncertainty models. The authors first formulate the robust power minimisation problem subject to the signal-to-inference-plus-noise ratio (SINR) and energy harvesting (EH) constraints by incorporating two Gaussian channel uncertainties. The original problem is not convex in terms of channel uncertainties, and cannot be solved efficiently. The authors employ the well-known Bernstein-type inequality and Gaussian error function to make probability based constraints tractable, respectively, in order to recast the original problem as the convex form. Moreover, the robust power minimisation problem with the probability based SINR and EH constraints is formulated by incorporating random distribution with known error mean and covariance matrix. By exploiting conditional value-at-risk functional and semi-definite relaxation, this optimisation problem is relaxed as the convex form. Finally, numerical results are provided to validate the performance of these proposed robust schemes.