Artificial Noise Covariance Matrix Research Articles

Optimal coordinated beamforming with artificial noise for secure SWIPT in multi-cell networks

This paper investigates the multi-cell coordinated beamforming (MCBF) design for secure simultaneous wireless information and power transfer (SWIPT) in both centralized and distributed manners. In each cell, one transmitter serves multiple information receivers (IRs) and energy receivers (ERs) with the non-linear energy harvesting (EH) model. Meanwhile, several eavesdroppers (Eves) intend to intercept the confidential information transmitted for IRs. To achieve a secure transmission, the artificial noise (AN) is embedded in the transmit signals of each transmitter. The proposed design is formulated into a power-minimization problem to guarantee the IRs’ information and ERs’ energy requirements while avoiding the information being intercepted by Eves. Since the problem is non-convex and not easy to solve, a solution method based on semi-definition relaxation (SDR) is proposed and the global optimum is proved to be guaranteed with full channel state information (CSI). We further present a distributed AN-aided MCBF for the system by using alternating direction method of multipliers (ADMM), with which each transmitter is able to calculate its own beamforming vectors and AN covariance matrix based on its local CSI. Simulation results show that our proposed distributed design converges to the global optimum obtained by the centralized one. It is also shown that by employing AN, the total required power of the system is reduced and the effect of AN on the system performance decreases with increment of transmit antennas. Compared with traditional linear EH model, optimizing the system under the non-linear EH one avoids false output power at the ERs and saves power at the transmitter.

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.

Joint Transceiver Design for Secure Downlink Communications Over an Amplify-and-Forward MIMO Relay

This paper addresses joint transceiver design for secure downlink communications over a multiple-input multiple-output relay system in the presence of multiple legitimate users and malicious eavesdroppers. Specifically, we jointly optimize the base station (BS) beamforming matrix, the relay station (RS) amplify-and-forward transformation matrix, and the covariance matrix of artificial noise, so as to maximize the system worst-case secrecy rate in the presence of the colluding eavesdroppers under power constraints at the BS and the RS, as well as quality of service constraints for the legitimate users. This problem is very challenging due to the highly coupled design variables in the objective function and constraints. By adopting a series of transformation, we first derive an equivalent problem that is more tractable than the original one. Then, we propose and fully develop a novel algorithm based on the penalty concave-convex procedure (penalty-CCCP) to solve the equivalent problem, where the difficult coupled constraint is penalized into the objective and the resulting nonconvex problem is solved at each iteration by resorting to the CCCP method. It is shown that the proposed joint transceiver design algorithm converges to a stationary solution of the original problem. Finally, our simulation results reveal that the proposed algorithm achieves better performance than other recently proposed transceiver designs.

Transceiver Design to Maximize the Weighted Sum Secrecy Rate in Full-Duplex SWIPT Systems

This letter considers secrecy simultaneous wireless information and power transfer (SWIPT) in full duplex systems. In such a system, full duplex capable base station (FD-BS) is designed to transmit data to one downlink user and concurrently receive data from one uplink user, while one idle user harvests the radio-frequency (RF) signals energy to extend its lifetime. Moreover, to prevent eavesdropping, artificial noise (AN) is exploited by FD-BS to degrade the channel of the idle user, as well as to provide energy supply to the idle user. To maximize the sum of downlink secrecy rate and uplink secrecy rate, we jointly optimize the information covariance matrix, AN covariance matrix and receiver vector, under the constraints of the sum transmission power of FD-BS and the minimum harvested energy of the idle user. Since the problem is non-convex, the log-exponential reformulation and sequential parametric convex approximation (SPCA) method are used. Extensive simulation results are provided and demonstrate that our proposed full duplex scheme extremely outperforms the half duplex scheme.

An Effective Secure Transmission Scheme for AF Relay Networks with Two-Hop Information Leakage

In this letter, we propose a novel scheme to improve physical layer security for amplify-and-forward (AF) relay networks with two-hop information leakage. Unlike traditional joint cooperative beamforming (CB) and cooperative jamming (CJ) design, where mere artificial noise (AN) is exploited by the jammers to degrade eavesdroppers' channels, in our proposed scheme, the jammers send AN along with the confidential signal to simultaneously confuse the eavesdroppers and enhance the quality of received signals at the destination. In particular, the CB vectors and AN covariance matrix are jointly optimized for the relays and jammers under individual power constraints. By decoupling this resultant design problem, suboptimal solutions are obtained using the semidefinite relaxation technique. Simulation results are also provided to demonstrate that the proposed scheme has an obvious advantage in enhancing the secrecy rate.

Solutions for the MIMO Gaussian Wiretap Channel With a Cooperative Jammer

We study the Gaussian MIMO wiretap channel with a transmitter, a legitimate receiver, an eavesdropper and an external helper, each equipped with multiple antennas. The transmitter sends confidential messages to its intended receiver, while the helper transmits jamming signals independent of the source message to confuse the eavesdropper. The jamming signal is assumed to be treated as noise at both the intended receiver and the eavesdropper. We obtain a closed-form expression for the structure of the artificial noise covariance matrix that guarantees a secrecy rate larger or at least equal to the secrecy capacity of the wiretap channel with no jamming signal. We also describe how to find specific realizations of this covariance matrix expression that provide good secrecy rate performance, even when there is no nontrivial null space between the helper and the intended receiver. Unlike prior work, our approach considers the general MIMO case, and is not restricted to SISO or MISO scenarios.