Artificial Noise Covariance Matrix Research Articles

Joint Precoding and Artificial Noise Design for MU-MIMO Wiretap Channels

Secure precoding superimposed with artificial noise (AN) is a promising transmission technique to improve security by harnessing the superposition nature of the wireless medium. However, finding a jointly optimal precoding and AN structure is very challenging in downlink multi-user multiple-input multiple-output wiretap channels with multiple eavesdroppers. The major challenge in maximizing the secrecy rate arises from the non-convexity and non-smoothness of the rate function. Traditionally, an alternating optimization framework that identifies beamforming vectors and AN covariance matrix has been adopted; yet this alternating approach has limitations in maximizing the secrecy rate. In this paper, we put forth a novel secure precoding algorithm that jointly and simultaneously optimizes the beams and AN covariance matrix for maximizing the secrecy rate when a transmitter has either perfect or partial channel knowledge of eavesdroppers. To this end, we first establish an approximate secrecy rate in a smooth function. Then, we derive the first-order optimality condition in the form of the nonlinear eigenvalue problem (NEP). We present a computationally efficient algorithm to identify the principal eigenvector of the NEP as a suboptimal solution for secure precoding. Simulations demonstrate that the proposed methods improve secrecy rate significantly compared to the existing methods.

Joint Secure Communication and Radar Beamforming: A Secrecy-Estimation Rate-Based Design

This paper considers transmit beamforming in dual-function radar-communication (DFRC) system, where a DFRC transmitter simultaneously communicates with a communication user and detects a malicious target with the same waveform. Since the waveform is embedded with information, the information is risked to be intercepted by the target. To address this problem, physical-layer security technique is exploited. By using secrecy rate and estimation rate as performance measure for communication and radar, respectively, three secrecy rate maximization (SRM) problems are formulated, including the SRM with and without artificial noise (AN) and robust SRM. For the SRM beamforming, we prove that the optimal beamformer can be computed in closed form. For the AN-aided SRM, by leveraging alternating optimization, similar closed-form solution is obtained for the beamformer and the AN covariance matrix. Finally, the imperfect CSI of the target is also considered under the premise of a moment-based random phase-error model on the direction of arrival at the target. Simulation results demonstrate the efficacy and robustness of the proposed designs.

Secrecy Rate Optimization in Nonlinear Energy Harvesting Model-Based mmWave IoT Systems With SWIPT

Secrecy rate (SR) optimization in millimeter wave (mmWave) Internet of Things (IoT) systems with simultaneous wireless information and power transfer (SWIPT) is studied in this article. Adopting the SWIPT architecture, energy-constrained devices get charged by the radio-frequency waves transmitted from a base station. The hybrid precoding technique is applied to reduce the implementation cost by separately designing a digital precoder and an analog precoder. Also, we adopt the artificial noise (AN)-assisted transmission method to maximize the SR. In this problem, we aim to jointly optimize the digital precoding vector, AN covariance matrix, and power-splitting ratio under the nonlinear energy harvesting (EH)-constraints. Then, we propose a semidefinite relaxation-based alternating optimization algorithm for the case of perfect channel state information (CSI) and imperfect CSI. Finally, simulation results show that the proposed algorithms are effective to improve the SR.

Intelligent Reflecting Surface Assisted Secure Transmission in UAV-MIMO Communication Systems.

This paper studies the intelligent reflecting surface (IRS) assisted secure transmission in unmanned aerial vehicle (UAV) communication systems, where the UAV base station, the legitimate receiver, and the malicious eavesdropper in the system are all equipped with multiple antennas. By deploying an IRS on the facade of a building, the UAV base station can be assisted to realize the secure transmission in this multiple-input multiple-output (MIMO) system. In order to maximize the secrecy rate (SR), the transmit precoding (TPC) matrix, artificial noise (AN) matrix, IRS phase shift matrix, and UAV position are jointly optimized subject to the constraints of transmit power limit, unit modulus of IRS phase shift, and maximum moving distance of UAV. Since the problem is non-convex, an alternating optimization (AO) algorithm is proposed to solve it. Specifically, the TPC matrix and AN covariance matrix are derived by the Lagrange dual method. The alternating direction method of multipliers (ADMM), majorization-minimization (MM), and Riemannian manifold gradient (RCG) algorithms are presented, respectively, to solve the IRS phase shift matrix, and then the performance of the three algorithms is compared. Based on the proportional integral (PI) control theory, a secrecy rate gradient (SRG) algorithm is proposed to iteratively search for the UAV position by following the direction of the secrecy rate gradient. The theoretic analysis and simulation results show that our proposed AO algorithm has a good convergence performance and can increase the SR by 40.5% compared with the method without IRS assistance.

Collaborative Optimization Model of Highway Network with Tourism Resources as the Target Node

In order to improve the collaborative optimization effect of tourism resources and highway network, this paper combines deep learning algorithm to construct a collaborative optimization model of tourism resources and highway network, and adopts an algorithm based on continuous convex approximation. By iterating the optimal solution obtained each time, a high-quality approximate beamforming matrix and artificial noise covariance matrix can finally be obtained, which eliminates the problem that the traditional algorithm cannot solve the noise. Moreover, this paper introduces artificial noise to prove that the rank relaxation is compact by considering the corresponding minimization power problem. The simulation results show that the proposed scheme and approximation algorithm can obtain better system security and speed than the existing literature, and there are certain improvements compared with the traditional method, so the effectiveness of the method in this paper is verified by simulation experiments.

Intelligent Reflecting Surface and Artificial-Noise-Assisted Secure Transmission of MEC System

Mobile-edge computing (MEC) and intelligent reflecting surface (IRS) have attracted much attention as promising technologies for the next-generation mobile networks and Internet of Things (IoT). In this article, we investigate how to improve the security of the MEC system with the assistance of IRS and artificial noise (AN) in the IoT. By adjusting the phase of the IRS, the users’ signals can be enhanced and the eavesdroppers’ signal can be weakened. In addition, the full-duplex base station (FD-BS) transmits AN to destroy the eavesdroppers’ signal and further enhance the users’ security. We minimize the users’ secure energy consumption by jointly optimizing the base station receive beamforming vectors, AN covariance matrix, IRS phase shifts, users’ offloading time, transmit power, and local computation tasks. The formulated problem is a nonconvex problem that is hard to solve directly, so we decompose it into tractable subproblems and develop an alternating optimization approach by combining the semidefinite relaxation (SDR) algorithm and Dinkelbach’s method. The results show that the proposed scheme can greatly reduce the secure energy consumption compared with other benchmark scheme.

Optimal design for the artificial‐noise‐aided IRS‐MIMO‐OFDM secure communications

This paper discusses an artificial noise-aided intelligent reflecting surface-MIMO–OFDM system physical layer secure communication, in which two cases for the intelligent reflecting surface reflection coefficient models are considered separately, that is unit modulus constraint for the reflection coefficients and the more practical situation of amplitude phase-shift dependence. Then the problem of joint optimisation for the precoding matrix, artificial noise covariance matrix and intelligent reflecting surface reflection coefficient matrix to maximise the sum secrecy rate under the power constraint at the transmitter is formulated, and then an alternate optimisation-based inexact block coordinate descent algorithm is proposed to tackle the formulated non-convexity problem. For the problem with unit modulus constraint for the intelligent reflecting surface reflection coefficients, closed-form solutions of the optimisation variables are obtained by utilising the Lagrange multiplier method and the complex circular manifold method. For the problem with intelligent reflecting surface reflection coefficient amplitude phase-shift dependence, alternate optimisation-based penalty method is used to obtain the intelligent reflecting surface optimal reflection matrix. Numerical results indicate that the algorithm for the intelligent reflecting surface reflection coefficient unit modulus constraint achieves the maximum secrecy rate, and the algorithm for the intelligent reflecting surface reflection coefficient of amplitude phase-shift dependence has the sub-optimal performance, and the benchmark schemes such as no intelligent reflecting surface and intelligent reflecting surface random phase shift strategies have the worst and similar performance.

Robust Secure Beamforming Design for Cooperative Cognitive Radio Nonorthogonal Multiple Access Networks

By the integration of cooperative cognitive radio (CR) and nonorthogonal multiple access (NOMA), cooperative CR NOMA networks can improve the spectrum efficiency of wireless networks significantly. Due to the openness and exposure of wireless signals, secure communication is an important issue for cooperative CR NOMA networks. In this paper, we investigate the physical layer security design for cooperative CR NOMA networks. Our objective is to achieve maximum secrecy rate of the secondary user by designing optimal beamformers and artificial noise covariance matrix at the multiantenna secondary transmitter under the quality-of-service at the primary user and the transmit power constraint at the secondary transmitter. We consider the practical case that the channel state information (CSI) of the eavesdropper is imperfect, and we model the imperfect CSI by the worst-case model. We show that the robust secrecy rate maximization problem can be transformed to a series of semidefinite programmings based on S-procedure and rank-one relaxation. We also propose an effective method to recover the optimal rank-one solution. Simulations are provided to show the effectiveness of our proposed robust secure algorithm with comparison to the nonrobust secure design and traditional orthogonal multiple access schemes.

Robust Transmission Design for Intelligent Reflecting Surface-Aided Secure Communication Systems With Imperfect Cascaded CSI

In this paper, we investigate the design of robust and secure transmission in intelligent reflecting surface (IRS) aided wireless communication systems. In particular, a multi-antenna access point (AP) communicates with a single-antenna legitimate receiver in the presence of multiple single-antenna eavesdroppers, where the artificial noise (AN) is transmitted to enhance the security performance. Besides, we assume that the cascaded AP-IRS-user channels are imperfect due to the channel estimation error. To minimize the transmit power, the beamforming vector at the transmitter, the AN covariance matrix, and the IRS phase shifts are jointly optimized subject to the outage rate probability constraints under the statistical cascaded channel state information (CSI) error model. To handle the resulting non-convex optimization problem, we first approximate the outage rate probability constraints by using the Bernstein-type inequality. Then, we develop a suboptimal algorithm based on alternating optimization, the penalty-based and semidefinite relaxation methods. Simulation results reveal that the proposed scheme significantly reduces the transmit power compared to other benchmark schemes.

Artificial-Noise-Aided Secure MIMO Wireless Communications via Intelligent Reflecting Surface

This article considers an artificial noise (AN)-aided secure MIMO wireless communication system. To enhance the system security performance, the advanced intelligent reflecting surface (IRS) is invoked, and the base station (BS), legitimate information receiver (IR) and eavesdropper (Eve) are equipped with multiple antennas. With the aim for maximizing the secrecy rate (SR), the transmit precoding (TPC) matrix at the BS, covariance matrix of AN and phase shifts at the IRS are jointly optimized subject to constrains of transmit power limit and unit modulus of IRS phase shifts. Then, the secrecy rate maximization (SRM) problem is formulated, which is a non-convex problem with multiple coupled variables. To tackle it, we propose to utilize the block coordinate descent (BCD) algorithm to alternately update the variables while keeping SR non-decreasing. Specifically, the optimal TPC matrix and AN covariance matrix are derived by Lagrangian multiplier method, and the optimal phase shifts are obtained by Majorization-Minimization (MM) algorithm. Since all variables can be calculated in closed form, the proposed algorithm is very efficient. We also extend the SRM problem to the more general multiple-IRs scenario and propose a BCD algorithm to solve it. Simulation results validate the effectiveness of system security enhancement via an IRS.

Robust and Secure Wireless Communications via Intelligent Reflecting Surfaces

In this paper, intelligent reflecting surfaces (IRSs) are employed to enhance the physical layer security in a challenging radio environment. In particular, a multi-antenna access point (AP) has to serve multiple single-antenna legitimate users, which do not have line-of-sight communication links, in the presence of multiple multi-antenna potential eavesdroppers whose channel state information (CSI) is not perfectly known. Artificial noise (AN) is transmitted from the AP to deliberately impair the eavesdropping channels for security provisioning. We investigate the joint design of the beamformers and AN covariance matrix at the AP and the phase shifters at the IRSs for maximization of the system sum-rate while limiting the maximum information leakage to the potential eavesdroppers. To this end, we formulate a robust non-convex optimization problem taking into account the impact of the imperfect CSI of the eavesdropping channels. To address the non-convexity of the optimization problem, an efficient algorithm is developed by capitalizing on alternating optimization, a penalty-based approach, successive convex approximation, and semidefinite relaxation. Simulation results show that IRSs can significantly improve the system secrecy performance compared to conventional architectures without IRS. Furthermore, our results unveil that, for physical layer security, uniformly distributing the reflecting elements among multiple IRSs is preferable over deploying them at a single IRS.

Secure beamforming design of SWIPT relay network with multiple users and eavesdroppers

This paper studies the secure beamforming design for simultaneous wireless information and power transfer (SWIPT) in a amplify-and-forward (AF) relay networks with multiple users and eavesdroppers. Each user node adopts the power splitting (PS) scheme to decode information and harvest energy simultaneously. Our objective is to minimize the total relay transmit power under the constraints of secure transmission rate and energy harvesting requirements by jointly optimizing the beamforming matrix, artificial noise covariance matrix and PS ratios. For this non-convex problem, we propose a two-stage optimization approach to convert the original problem into two sub-problems. The first subproblem uses semidefinite relaxation (SDR) technique to transform the original problem into a convex problem, and then finds the optimal solution of the second subproblem through k-dimensional exhaustive search algorithm. Furthermore, we also propose a low complexity suboptimal solution scheme based on particle swarm optimization (PSO) algorithm. Simulation results show that the proposed scheme saves transmitting power and achieves better performance than other schemes.

Secrecy Energy Efficiency in Multi-Antenna SWIPT Networks With Dual-Layer PS Receivers

This paper studies the secrecy energy efficiency (SEE) for MISO power-splitting (PS) SWIPT networks in the presence of multiple passive eavesdroppers (Eves), where the non-linear energy harvesting (EH) model and the dual-layer PS receiver architecture are employed. With only channel distribution information (CDI) of Eves known and the artificial noise (AN) embedded into the transmit signals at the transmitter, a SEE maximization problem is formulated under constraints of the minimal rate and EH requirements of legitimate receivers and the power budget at the transmitter. To tackle the difficulty caused by the fractional objective function and the probability constraints in solving the considered problem, the second-layer PS ratios are firstly optimized by bisection and sum-of-ratios maximization methods, and then the transmit beamforming vectors, the AN covariance matrix and the first-layer PS ratios are jointly optimized by using successive convex approximation (SCA) and Dinkelbach’s methods. The proposed solution approach is theoretically proved to converge to a stationary point of the SDR form of the considered problem, which is further shown to be the optimal one. Numerical results show that our proposed design achieves the highest SEE over traditional power minimization and secrecy rate maximization designs. Moreover, when the rate requirement is larger than a threshold or the available power is less than a threshold, traditional power minimization design or secrecy rate maximization design is able to achieve a similar SEE to our proposed design. Besides, the dual-layer PS receiver architecture is able to improve the EH efficiency and system SEE.

Transmit Antenna Selection and Beamformer Design for Secure Spatial Modulation With Rough CSI of Eve

The security of spatial modulation (SM) aided networks can always be improved by reducing the desired link's power at the cost of degrading its bit error ratio performance and assuming the power consumed to artificial noise (AN) projection (ANP). We formulate the joint optimization problem of maximizing the secrecy rate (Max-SR) over the transmit antenna selection and ANP in the context of secure SM-aided networks, which is mathematically a non-linear mixed integer programming problem. In order to solve this problem, we provide a pair of solutions, namely joint and separate solutions. Specifically, an accurate approximation of the SR is used for reducing the computational complexity, and the optimal AN covariance matrix (ANCM) is found by convex optimization for any given active antenna group (AAG). Then, given a large set of AAGs, simulated annealing mechanism is invoked for optimizing the choice of AAG, where the corresponding ANCM is recomputed by this optimization method as well when the AAG changes. To further reduce the complexity of the above-mentioned joint optimization, a low-complexity two-stage separate optimization method is also proposed. Furthermore, when the number of transmit antennas tends to infinity, the Max-SR problem becomes equivalent to that of maximizing the ratio of the desired user's signal-to-interference-plus-noise ratio to the eavesdropper's. Thus our original problem reduces to a fractional programming problem, hence a significant computational complexity reduction can be achieved for the optimization problem. Our simulation results show that the proposed algorithms outperform the existing leakage-based null-space projection scheme in terms of the SR performance attained, and drastically reduces the complexity at a slight SR performance reduction.

An Anti-Eavesdropping Strategy for Precoding-Aided Spatial Modulation With Rough CSI of Eve

In this paper, an anti-eavesdropping strategy is proposed for secure precoding-aided spatial modulation networks, under the assumption that the rough channel state information of eavesdropper can be obtained at the transmitter. Traditionally, artificial noise (AN) can be always projected into the null-space of the legitimate channel, however it may lead to some security loss since this strategy dispenses with a holistic consideration for secure transmissions. To reduce the computational complexity of our optimization problem, we derive a closed-form expression that is a loose bound of the approximate rate over the illegitimate channel. Then a concave maximization problem is formulated for optimizing the covariance matrix of AN. Simulation results show that our proposed low-complexity scheme performs closely to the method which directly maximizes the approximate secrecy rate expression, and harvests significant secrecy rate gains compared with the traditional null-space projection benchmark.

Energy-Efficient Wireless Powered Secure Transmission With Cooperative Jamming for Public Transportation

In this paper, wireless power transfer and cooperative jamming (CJ) are combined to enhance physical security in public transportation networks. First, a new secure system model with both fixed and mobile jammers is proposed to guarantee secrecy in the worst-case scenario. All jammers are endowed with energy harvesting (EH) capability. Following this, two CJ based schemes, namely B-CJ-SRM and B-CJ-TPM, are proposed, where SRM and TPM are short for secrecy rate maximization and transmit power minimization, respectively. They respectively maximize the secrecy rate (SR) with transmit power constraint and minimize the transmit power of the BS with SR constraint, by optimizing beamforming vector and artificial noise covariance matrix. To further reduce the complexity of our proposed optimal schemes, their low-complexity (LC) versions, called LC-B-CJ-SRM and LC-B-CJ-TPM are developed. Simulation results show that our proposed schemes, B-CJ-SRM and B-CJ-TPM, achieve significant SR performance improvement over existing zero-forcing and QoSD methods. Additionally, the SR performance of the proposed LC schemes are close to those of their original versions.

Robust Beamforming and Power Allocation in CR MISO Networks with SWIPT to Maximize the Minimum Achievable Rate

In this paper, a new method is presented to maximize the minimum achievable rate of the users in a cognitive radio multiple input single output network. The secondary system provides simultaneous wireless information and power transfer (SWIPT) for energy harvesting receivers. Considering random Gaussian vector for the estimation error of the channel state information (CSI), we impose some outage constraints to guarantee the quality of service of the network. Outage constraints on the received power and the information leakage at the energy harvesting users are imposed to assure SWIPT. We introduce new convex inequalities to replace the original non-convex constraints and write the objective function as the minimization of the maximum of some fractional functions. This new objective function and convex inequalities result in a new quasi-convex general fractional programming problem. The new quasi-convex optimization problem is written in such a way that the computational costs to solve this problem are as low as possible. We develop an algorithm to obtain the optimal beamforming weights and artificial noise covariance matrix. All stochastic constraints are rewritten for the special case that the covariance matrices of error in the estimation of CSI are a factor of identity matrix. This reformulation results in less computation costs to obtain optimal beamforming weights and AN covariance matrix. Simulation results confirm that, all stochastic constraints are satisfied with certain probability. In comparison with the previous robust related work, the proposed method achieves higher rates which confirms superiority of our method.

Global Energy Efficiency in Secure MISO SWIPT Systems With Non-Linear Power-Splitting EH Model

This paper considers an MISO simultaneous wireless information and power transfer (SWIPT) system, where one transmitter serves multiple authorized receivers in the presence of several potential eavesdroppers (idle receivers). To prevent the information interception by eavesdroppers, artificial noise (AN) is embedded into the transmit signals. The non-linear energy harvesting (EH) model is adopted and a novel power-splitting (PS) EH receiver architecture is proposed. Stochastic uncertainty channel model (SUM) is considered for the idle receivers due to outdated channel feedback. A global energy efficiency (GEE) maximization problem is formulated by jointly optimizing the transmit beamforming vectors, the AN covariance matrix, and the PS ratios, under the minimal rate and secure transmission constraints of authorized receivers, the EH requirement constraints of idle receivers, and the total available power constraint at the transmitter. Since the problem is non-convex with no known solution, it is solved based on the following solution framework. Firstly, the PS ratios are optimized by using the bisection method and successive convex approximation (SCA), and then, the transmit beamforming vectors and the AN covariance matrix are jointly optimized by using a Dinkelbach’s Algorithm based method, where SCA is applied to solve its inner subproblem. It is theoretically proved that by involving AN, the system GEE can be improved. Numerous results show that system GEE first increases and then keeps unchanged with the increment of the total available power, but it first keeps unchanged and then decreases with the increment of the minimal rate requirement. It is also observed that compared with traditional EH receiver architecture and linear EH model, our proposed PS EH receiver architecture is able to achieve higher GEE and avoid false output power at idle receivers.

Robust Energy Efficient Beamforming in MISOME-SWIPT Systems With Proportional Secrecy Rate

The joint design of beamforming vector and artificial noise covariance matrix is investigated for the multiple-input-single-output-multiple-eavesdropper simultaneous wireless information and power transferring (MISOME-SWIPT) systems. In the MISOME-SWIPT system, the base station delivers information signals to the legitimate user equipment and broadcasts jamming signals to the eavesdroppers. A secrecy energy efficiency (SEE) maximization problem is formulated for the considered MISOME-SWIPT system with imperfect channel state information, where the SEE is defined as the ratio of sum secrecy rate over total power consumption. Since the formulated SEE maximization problem is non-convex, it is first recast into a series of convex problems in order to obtain the optimal solution with a reasonable computational complexity. Two suboptimal solutions are also proposed based on the heuristic beamforming techniques that trade performance for computational complexity. In addition, the analysis of computational complexity is performed for the optimal and suboptimal solutions. Numerical results are used to verify the performance of proposed algorithms and to reveal practical insights.

Secure Full-Duplex Two-Way Relaying for SWIPT

This letter studies bi-directional secure information exchange in a simultaneous wireless information and power transfer system enabled by a full-duplex multiple-input multiple-output amplify-and-forward (AF) relay. The AF relay injects artificial noise (AN) in order to confuse the eavesdropper. Specifically, we assume a zeroforcing (ZF) solution constraint to eliminate the residual self-interference. As a consequence, we address the optimal joint design of the ZF matrix and the AN covariance matrix at the relay node as well as the transmit power at the sources. We propose an alternating algorithm utilizing semi-definite programming technique and 1-D searching to achieve the optimal solution. Simulation results are provided to demonstrate the effectiveness of the proposed algorithm.