Semidefinite Relaxation Technique Research Articles

IRS-Based Wireless Jamming Attacks: When Jammers Can Attack Without Power

This paper proposes to use Intelligent Reflecting Surface (IRS) as a green jammer to attack a legitimate communication without using any internal energy to generate jamming signals. In particular, the IRS is used to intelligently reflect the signals from the legitimate transmitter to the legitimate receiver (LR) to guarantee that the received signals from direct and reflecting links can be added destructively, which thus diminishes the Signal-to-Interference-plus-Noise Ratio (SINR) at the LR. To minimize the received signal power at the LR, we consider the joint optimization of magnitudes of reflection coefficients and discrete phase shifts at the IRS. Based on the block coordinate descent, semidefinite relaxation, and Gaussian randomization techniques, the solution can be obtained efficiently. Through simulation results, we show that by using the IRS-based jammer, we can reduce the signal power received at the LR by up to 99\%. Interestingly, the performance of the proposed IRS-based jammer is even better than that of the conventional active jamming attacks in some scenarios.

Optimal secure transmit design for wireless information and power transfer in V2X vehicular communication systems

Simultaneous wireless information and power transfer (SWIPT) in vehicle to everything networks is a perspective technology which helps prolong the lifetime of sensors installed on roadside devices and vehicles. In this study, we consider a secure vehicular communication system with SWIPT under a non-linear EH model where the energy vehicular receivers are able to collect energy from the radio frequency signals as they are idle. We formulate the secure transmit signal design as an optimization problem which aims to maximize the minimum fairness energy power at the energy vehicular users. In addition, the considered optimization problem also considers different quality of service requirements: a maximum tolerable capacity at energy vehicular receivers and a minimum needed signal-to-interference-ratio at information vehicular receivers. To obtain a manageable solution, we reexpress the referred problem by variable substitutions and replacing a non-convex constraint with a convex form. Then, we adopt the semidefinite relaxation (SDR) technique to obtain the optimal solution of the original problem. To decrease calculational complexity, we also propose a suboptimal secure beamforming scheme for facilitating wireless energy transfer and providing physical layer security. Simulation results indicate that the developed secure transmit signal algorithm can obtain better performance gains than other algorithms.

Robust Power Optimization for Downlink Cloud Radio Access Networks with Physical Layer Security.

Since the cloud radio access network (C-RAN) transmits information signals by jointly transmission, the multiple copies of information signals might be eavesdropped on. Therefore, this paper studies the resource allocation algorithm for secure energy optimization in a downlink C-RAN, via jointly designing base station (BS) mode, beamforming and artificial noise (AN) given imperfect channel state information (CSI) of information receivers (IRs) and eavesdrop receivers (ERs). The considered resource allocation design problem is formulated as a nonlinear programming problem of power minimization under the quality of service (QoS) for each IR, the power constraint for each BS, and the physical layer security (PLS) constraints for each ER. To solve this non-trivial problem, we first adopt smooth -norm approximation and propose a general iterative difference of convex (IDC) algorithm with provable convergence for a difference of convex programming problem. Then, a three-stage algorithm is proposed to solve the original problem, which firstly apply the iterative difference of convex programming with semi-definite relaxation (SDR) technique to provide a roughly (approximately) sparse solution, and then improve the sparsity of the solutions using a deflation based post processing method. The effectiveness of the proposed algorithm is validated with extensive simulations for power minimization in secure downlink C-RANs.

Cooperative Multiple Target Nodes Localization Using TOA in Mixed LOS/NLOS Environments

In this paper, the time-of-arrival based cooperative localization problem under mixed line-of-sight/non-line-of-sight (LOS/NLOS) conditions is addressed. Under the conditions of unknown statistics of NLOS errors and unknown path status, we formulate a non-convex robust weighted least squares (RWLS) problem to locate the multiple stationary target nodes. In this problem, we introduce some “balancing parameters” to alleviate the possible improper upper bounds problem of the existing robust localization methods, and jointly estimate the target node positions and the balancing parameters. With the aid of the semidefinite relaxation technique, the RWLS problem is transformed into a convex mixed semidefinite and second order cone programming problem, which can be solved efficiently. The idea is then extended to the moving target nodes localization problem, where the velocity is assumed to be fixed within a short time period. Both simulated and real experimental data are used to verify the performance of the proposed method. The results show that the proposed method works well for both the sparse and dense NLOS environments, and also confirm the superior performance of the proposed method over the existing methods.

Robust adaptive beamforming against large steering vector mismatch based on minimum dispersion

Many efforts have been recently devoted to adaptive beamformers based on the minimum dispersion (MD) criterion for non-Gaussian signals, which results in improved signal-to-noise ratio performance. However, large steering vector mismatch and inappropriate choice of uncertainty set will cause performance degradation to the existing MD-based methods. To address these issues, we develop a robust MD-based beamformer against large steering vector mismatch, which utilizes multiple small uncertainty sets to cover the whole uncertainty region. The ℓp−norm (p≥1) minimization problem turns to be nonlinear and nonconvex because of these multi-uncertainty-set constraints. To solve the problem, a projected gradient algorithm is utilized to transform the original problem into a nonconvex quadratically constrained quadratic programming (QCQP) problem. The semidefinite programming relaxation technique is then employed in each iteration to deal with the nonconvex QCQP problem. Numerical results demonstrate that the proposed beamformer offers a significant performance improvement in case of large steering vector mismatch for non-Gaussian signals compared with the conventional schemes.

Unsupervised Learning for Passive Beamforming

Reconfigurable intelligent surface (RIS) has recently emerged as a promising candidate to improve the energy and spectral efficiency of wireless communication systems. However, the unit modulus constraint on the phase shift of reflecting elements makes the design of optimal passive beamforming solution a challenging issue. The conventional approach is to find a suboptimal solution using the semi-definite relaxation (SDR) technique, yet the resultant suboptimal iterative algorithm usually incurs high complexity, hence is not amenable for real-time implementation. Motivated by this, we propose a deep learning approach for passive beamforming design in RIS-assisted systems. In particular, a customized deep neural network is trained offline using the unsupervised learning mechanism, which is able to make real-time prediction when deployed online. Simulation results show that the proposed approach maintains most of the performance while significantly reduces computation complexity when compared with SDR-based approach.

Backscatter Then Forward: A Relaying Scheme for Batteryless IoT Networks

In this letter, we introduce a novel relaying scheme together with a joint energy beamforming (EB) and time allocation optimization to meet requirements about energy efficiency and hardware constraints of batteryless IoT networks. First, we propose an intelligent relaying scheme using RF-powered gateways as relay nodes to deliver information from batteryless IoT devices to a hybrid access point (HAP). The HAP can also transfer energy to the gateways and batteryless devices using EB techniques. The energy from HAP will be then used to supply power for gateways and as a communications means to transmit data for batteryless devices. We then formulate a sum-rate maximization problem by jointly optimizing the EB vectors, time scheduling, and power allocation. Since the optimization problem is non-convex, we exploit EB characteristics for data backscattering and employ variable substitutions and semidefinite relaxation techniques to transform it into a convex one. After that, a low-complexity method is proposed to obtain the optimal solution in a closed-form. Simulation results confirm that the proposed scheme can achieve significant sum-rate gain.

Localisation algorithm based on weighted semi-definite programming

In order to improve the performance of reduced complexity positive semi-definite programming (RCSDP) algorithm based on time difference of arrival (TDOA), a weighted positive semi-definite programming (WSDP) scheme is proposed in this paper. Based on the squared distance differences between the target node to one anchor node and to the other anchor node, the location of the target node is described as the optimal solution of a non-convex optimisation problem. The semi-definite relaxation technique is used to transform the original non-convex problem into a weighted convex problem, which takes the measurement noise into consideration, and then the estimated location of the target node is obtained. The simulation results show that the localisation performance of WSDP algorithm is better than that of RCSDP algorithm, regardless of whether the target node is located inside or outside the area surrounded by anchor nodes.

On fractional quadratic optimization problem with two quadratic constraints

In this paper, we study the problem of minimizing the ratio of two quadratic functions subject to two quadratic constraints in the complex space. Using the classical Dinkelbach method, we transform the problem into a parametric nonlinear equation. We show that an optimal parameter can be found by employing the S-procedure and semidefinite relaxation technique. A key element to solve the original problem is to use the rank-one decomposition procedure. Finally, within the new algorithm, semidefinite relaxation is compared with the bisection method for finding the root on several examples. For further comparison, the solution of fmincon command of MATLAB also is reported.

Weighted Sum-SINR and Fairness Optimization for SWIPT-Multigroup Multicasting Systems With Heterogeneous Users

The development of next generation wireless communication systems focuses on the expansion of existing technologies, while ensuring an accord between various devices within a system. In this article, we target the aspect of precoder design for simultaneous wireless information and power transmission (SWIPT) in a multi-group (MG) multicasting (MC) framework capable of handling heterogeneous types of users, viz., information decoding (ID) specific, energy harvesting (EH) explicit, and/or both ID and EH operations concurrently. Precoding is a technique well-known for handling the inter-user interference in multi-user systems, however, the joint design with SWIPT is not yet fully exploited. Herein, we investigate the potential benefits of having a dedicated precoder for the set of users with EH demands, in addition to the MC precoding. We study the system performance of the aforementioned system from the perspectives of weighted sum of signal-to-interference-plus-noise-ratio (SINR) and fairness. In this regard, we formulate the precoder design problems for (i) maximizing the weighted sum of SINRs at the intended users and (ii) maximizing the minimum of SINRs at the intended users; both subject to the constraints on minimum (non-linear) harvested energy, an upper limit on the total transmit power and a minimum SINR required to close the link. We solve the above-mentioned problems using distinct iterative algorithms with the help of semi-definite relaxation (SDR) and slack-variable replacement (SVR) techniques, following suitable transformations pertaining the problem convexification. The main novelty of the proposed approach lies in the ability to jointly design the MC and EH precoders for serving the heterogeneously classified ID and EH users present in distinct groups, respectively. We illustrate the comparison between the proposed weighted sum-SINR and fairness models via simulation results, carried out under various parameter values and operating conditions.

Localization of a Moving Source by Frequency Measurements

This paper investigates the localization of a moving source in position and velocity, by observing the emitted frequency from the source that is subject to the Doppler shift effect at a number of stationary sensors. Previous attempts rely on exhaustive grid search or numerical polynomial optimization to obtain a solution. We shall propose a constrained optimization to formulate the localization problem, which enables the problem to be solved efficiently using the linear optimization method to reach a closed-form solution or the semi-definite relaxation technique to achieve a noise resilient estimate. The algorithms are developed for the single-time and multiple-time observations. The presence of errors in the source frequency and the sensor positions are considered. The non-cooperative scenario where the source frequency is completely not known is also addressed. Analysis validates the proposed closed-form solution in reaching the Cramer-Rao Lower Bound accuracy under Gaussian noise over the small error region. Simulations support the performance of the proposed solutions.

Three-Dimensional Rigid Body Localization in the Presence of Clock Offsets

This letter develops a novel approach to determinethepose of a rigid body in an asynchronous network using the range measurements. While the sensors on the rigid body share one clock, the synchronization between distant anchors is often unavailable. The pose parameters of the rigid body are estimated in the presence of clock offsets by applying the semi-definite relaxation (SDR) technique. Then, the clock offsets are obtained by utilizing the rigid body pose information acquired in the previous step. Perturbation analysis is conducted to examine the performance of the proposed method theoretically. Simulations validate that the proposed method achieves the Cramer-Rao lower bound (CRLB) performance at low noise levels.

Symbiotic Radio: A New Communication Paradigm for Passive Internet of Things

In this article, a symbiotic radio (SR) system is proposed to support passive Internet of Things (IoT), in which a backscatter device (BD), also called IoT device, is parasitic in a primary transmission. The primary transmitter (PT) is designed to assist both the primary and BD transmissions, and the primary receiver (PR) is used to decode the information from the PT as well as the BD. The symbol period for BD transmission is assumed to be either equal to or much greater than that of the primary one, resulting in parasitic SR (PSR) or commensal SR (CSR) setup. We consider a basic SR system which consists of three nodes: 1) a multiantenna PT; 2) a single-antenna BD; and 3) a single-antenna PR. We first derive the achievable rates for the primary and BD transmissions for each setup. Then, we formulate two transmit beamforming optimization problems, i.e., the weighted sum-rate maximization (WSRM) problem and the transmit power minimization (TPM) problem, and solve these nonconvex problems by applying the semidefinite relaxation (SDR) technique. In addition, a novel transmit beamforming structure is proposed to reduce the computational complexity of the solutions. The simulation results show that for CSR setup, the proposed solution enables the opportunistic transmission for the BD via energy-efficient passive backscattering without any loss in spectral efficiency, by properly exploiting the additional signal path from the BD.

Simultaneous Lightwave Information and Power Transfer in Visible Light Communication Systems

In this paper, we investigate a novel simultaneous lightwave information and power transfer (SLIPT) in visible light communication (VLC) systems, where a photo diode (PD) and a solar panel are utilized as the information receiver and the energy harvester, respectively. By systematically analyzing both the information receiver and the energy harvester, we obtain the explicit expressions to characterize the illumination-rate-energy region. Based on the derived expressions, we investigate the downlink unicast transmission of multi-LED multi-user SLIPT VLC networks, and study the total transmit power minimization problem under the rate requirements, the minimum energy harvesting requirements, and dimming control constraints. To solve such non-convex problem, we exploit the semidefinite relaxation (SDR) technique and relax the problem into a convex problem, which can be efficiently solved via interior-point methods. Moreover, for the sake of users’ fairness, we further investigate the beamformer design to maximize the minimal rate under both minimum energy harvesting and dimming control constraints. Finally, the numerical results are provided to evaluate the proposed SLIPT system.

User-centric harvested energy-efficiency maximisation for secure SWIPT transmissions

ABSTRACTIn this paper, simultaneous wireless information and power transfer (SWIPT) transmissions with multiple-input single-output transceiver pairs are considered. In each pair, a multi-antenna transmitter sends data and energy to a single-antenna receiver with a signal-splitting structure and a non-linear energy harvesting model. Each transceiver pair tries to achieve high individual harvested energy efficiency, and uses artificial noise (AN) to protect the information from being overheard by other users that cooperate like a virtual eavesdropper. The weighted sum user-centric harvested energy-efficiency maximisation problem is formulated under constraints on the required signal-to-interference-plus-noise ratio (SINR) at each receiver, plus a limited SINR for virtual eavesdroppers and limited transmit power at each transmitter. The optimal precoding beamforming, AN, and signal-splitting factors are obtained by two proposed algorithms. The first solution exploits semidefinite relaxation and sequential parametric convex approximation techniques to convert the non-convex problem to a series of convex subproblems with matrix variables. We obtain optimal beamforming vectors along with an optimal covariance matrix for AN. The second solution directly utilizes beamforming approximation and obtains a low complexity solution for the convex subproblem. Moreover, we need to apply the feasible point pursuit method. Finally, numerical evaluations are provided in comparison with some benchmark schemes.

Robust secrecy energy efficiency optimisation in heterogeneous networks with simultaneous wireless information and power transfer: centralised and distributed design

With the ellipsoid-bounded channel state information (CSI) errors, this study investigates the robust secrecy energy efficiency (SEE) optimisation in a wireless powered heterogeneous network. Specifically, the authors consider the network where multiple femtocell base stations (FBSs) are deployed under the coverage of one macrocell base station (MBS). Meanwhile, the MBS serves multiple macrocell users in the presence of a malicious multiple-antenna eavesdropper (Eve) while each FBS serves a pair of information receiver (IR) and energy receiver (ER) with multiple antennas, where the ER attempts to wiretap the information of IR in the same femtocell. To promote the secrecy performance, artificial noise (AN) is aided into the downlink signal at the MBS and FBSs, and the problem of maximising SEE is formed in a cross-tier multi-cell AN-aided transmit beamforming design. This problem is non-convex while containing infinite constraints caused by CSI errors, which cannot be solved directly. In this regard, the authors resort to the successive convex approximation, semi-definite relaxation techniques and Lagrange duality theory to acquire its solvable form. Moreover, to reduce the overhead of information exchange among coordinated BSs, they further propose a distributed approach based on alternative direction multiplier method. Finally, simulation results validate the effectiveness of the proposed design.

Nature‐inspired waveform optimisation for range spread target detection in cognitive radar

The waveform optimisation problem in cognitive radar is non-convex and will have sub-optimal solutions when solved by the semi-definite relaxation (SDR) technique. Here, a novel nature-inspired waveform optimisation framework is proposed for range-spread target detection in cognitive radar. First, the waveform optimisation problem is formulated using maximum a posteriori probability and Kalman filtering to estimate the target scattering coefficients. To solve this problem more accurately and efficiently, three nature-inspired algorithms (modified particle swarm optimisation algorithm, Bat Algorithm, and Beetle Antennae Search algorithm), as a nature-inspired waveform optimisation (NIWO) approach is proposed. It is demonstrated through computer simulations that the proposed NIWO approach significantly outperforms the SDR approach, showing a promising tool for waveform optimisation in cognitive radar.

The Optimization of Transcostal Phased Array Refocusing Using the Semidefinite Relaxation Method.

Tumors in organs partially obscured by the rib cage represent a challenge for high-intensity focused ultrasound (HIFU) therapy. The ribs distort the HIFU beams in a manner that reduces the focusing gain at the target, which could result in treatment-limiting collateral damage. In fact, skin burns are a common complication during the ablation of hepatic tumors. This problem can be addressed by employing optimal refocusing algorithms that are designed to achieve a specified focusing gain at the target while controlling the exposure to the ribs in the path of the HIFU beam. However, previously proposed optimal refocusing algorithms did not allow for the controlled transmission through the ribs. In this article, we introduce a new approach for refocusing that can more efficiently steer power toward the target while limiting the power deposition on the ribs. The approach utilizes the semidefinite relaxation (SDR) technique to approximate the original (nonconvex) optimization problem. An important advantage of the SDR-based method over previously proposed optimization methods is the control of the side lobes in the focal plane. The method also allows for specifying an acceptable level of exposure to the ribs. Simulation results using a 1-MHz spherical concave phased array focused on an inhomogeneous medium are presented to demonstrate the performance of the SDR refocusing approach. A finite-difference time-domain propagation model was used to model the propagation in the inhomogeneous tissues, including the ribs. Temperature simulations based on the inhomogeneous transient bioheat transfer equation (tBHTE) demonstrate the significance of the improvements in the focusing gain when using the limited power deposition (LPD) method. The results also demonstrate that the LPD method yields well-behaved array excitation vectors, realizable by currently existing drivers.

Secrecy energy efficiency optimization in heterogeneous networks with simultaneous wireless information and power transfer

In this paper, we investigate the secrecy energy efficiency (SEE) optimization for a heterogeneous network with simultaneous wireless information and power transfer, where multiple femtocell base stations (FBSs) are deployed under the coverage of one macrocell base station (MBS). Meanwhile, the MBS serves multiple macrocell users (MUs) in the presence of a malicious multiple-antenna eavesdropper (Eve) while each FBS serves a pair of information receiver (IR) and energy receiver (ER), where the ER with multiple antennas acts as a potential Eve to wiretap the information transmitted to IR in the same femtocell. Then, to promote the secrecy performance, artificial noise (AN) is injected into the downlink transmit signal at the MBS and FBSs. Furthermore, with the aim of achieving green and secure communications in 5G, the problem of maximizing average SEE performance of the whole network is reformulated while considering cross-tier multi-cell transmit beamforming (TBF) design. To obtain the optimal design, we resort to the successive convex approximation (SCA) and semi-definite relaxation (SDR) techniques to reformulate this nonconvex max–min fractional program problem into a series of solvable forms. Subsequently, an iterative algorithm is proposed to arrive at provably convergent design. Finally, simulation results validate the effectiveness and security of the proposed AN-aided TBF design.

Grating-Lobe Clutter Suppression in Uniform Subarray for Airborne Radar STAP

This paper aims to address grating-lobe clutter suppression in a uniform subarray (US) for the airborne radar system. Due to the sparsity at the subarray level and different scanning angles between the inner subarray and the subarray, grating lobes are produced. The grating-lobe clutter then enters the main lobe, defined as main grating-lobe clutter (MGLC). When the target falls into the MGLC with the same Doppler frequency, the clutter cannot be effectively suppressed by the conventional space-time adaptive processing (STAP) algorithm. Hence, we design a transmit beamforming (TB)-STAP algorithm based on a modified phased array (MPA) radar system, where TB suppresses the MGLC, while STAP suppresses the main-lobe and sidelobe clutter; the goal is to maximize the output signal-to-clutter-plus-noise ratio (SCNR). The optimal solution of TB-STAP can be obtained through several iterations, and in each iterative algorithm, the TB is a quadratically constrained quadratic problem (QCQP) solved via the semidefinite relaxation (SDR) technique, and the STAP can obtain a closed solution by the minimum variance distortionless response (MVDR) algorithm. The simulation results show that compared with traditional STAP in PA and multiple-input multiple-output (MIMO) radars, the proposed algorithm in MPA radar greatly improves the output SCNR.