Semidefinite Relaxation Technique Research Articles

Accurate Semidefinite Relaxation Method for Elliptic Localization With Unknown Transmitter Position

Elliptic localization where a transmitter actively sending out a signal to locate an object from its echo appears in many practical systems including multiple-input-multiple-output (MIMO) radars and wireless communications. In this article, the elliptic localization problem when the transmitter position is not known is addressed. We propose an effective method for joint estimation of the object and transmitter positions. Using the range measurements from the direct paths between the transmitter and the receivers together with the indirect paths through the object, we formulate a non-convex weighted least squares (WLS) minimization problem. The non-convex nature of this problem makes it difficult for an iterative search algorithm to reach the optimal solution, implying that good estimate is not guaranteed. To handle this difficulty, we propose to solve the formulated WLS localization problem by applying the semidefinite relaxation (SDR) technique, resulting in a convex semidefinite program (SDP). The proposed SDR method is then extended to the more general case when multiple transmitters at unknown positions are used and the receiver positions are subject to errors. Simulation results show that the proposed method can attain the Cramer-Rao lower bound (CRLB) accuracy under Gaussian noise and has superior performance over the existing method.

Joint beamforming and power-splitting optimization for SWIPT-enabled MISO full-duplex two-way cooperative NOMA systems

In this paper, a multiple-input single-output (MISO) full-duplex two-way cooperative non-orthogonal multiple access (NOMA) system is considered. The relay is energy-restricted and may not accomplish the information exchange between two end users. To address this problem, simultaneous wireless information and power transfer (SWIPT) is proposed, which employs power splitting (PS) at the relay to harvest energy. To maximize the harvested energy of the relay under QoS and power constraints, a joint optimization problem of the beamforming vectors and the PS ratio is formulated. The problem is nonconvex, and the original problem is transformed into a tractable form by applying the semidefinite relaxation (SDR) technique. Then a bilevel programming (BLP) based method is proposed to obtain an approximately optimal solution. Moreover, to reduce the computational complexity, a successive convex approximation (SCA)-based iterative algorithm is developed to derive a suboptimal solution. Numerical results show that our proposed strategy significantly enhances the energy harvesting performance compared with the existing transmission strategies.

MIMO Dual-Functional Radar-Communication Waveform Design With Peak Average Power Ratio Constraint

In this paper, novel Dual-Functional Radar-Communication (DFRC) waveforms with peak average power ratio (PAPR) constraint are designed, which are under the multiple-input multiple-output (MIMO) radar-communication system. The DFRC waveforms transmitted by multiple antennas can send communication information to many downlink cellular users and detect radar targets simultaneously. An optimization model is established to minimize the downlink multi-user interference (MUI) under PAPR constraint. The model is non-convex quadratically constrained quadratic programs (QCQP) and can be derived into a convex problem and solved by using the semi-definite relaxation (SDR) technique with rank-one approximation. Numerical simulations demonstrate that our proposed waveforms can achieve a better radar performance in practical scenarios without sacrificing the communication performance.

Intelligent Reflecting Surface-Aided Joint Processing Coordinated Multipoint Transmission

This article investigates intelligent reflecting surface (IRS)-aided multicell wireless networks, where an IRS is deployed to assist the joint processing coordinated multipoint (JP-CoMP) transmission from multiple base stations (BSs) to multiple cell-edge users. By taking into account the fairness among cell-edge users, we aim at maximizing the minimum achievable rate of cell-edge users by jointly optimizing the transmit beamforming at the BSs and the phase shifts at the IRS. As a compromise approach, we transform the non-convex max-min problem into an equivalent form based on the mean-square error method, which facilities the design of an efficient suboptimal iterative algorithm. In addition, we investigate two scenarios, namely the single-user system and the multiuser system. For the former scenario, the optimal transmit beamforming is obtained based on the dual subgradient method, while the phase shift matrix is optimized based on the Majorization-Minimization method. For the latter scenario, the transmit beamforming matrix and phase shift matrix are obtained by the second-order cone programming and semidefinite relaxation techniques, respectively. Numerical results demonstrate the significant performance improvement achieved by deploying an IRS. Furthermore, the proposed JP-CoMP design significantly outperforms the conventional coordinated scheduling/coordinated beamforming coordinated multipoint (CS/CB-CoMP) design in terms of max-min rate.

NLOS Error Mitigation in Hybrid RSS-TOA-Based Localization Through Semi-Definite Relaxation

This letter focuses on the accurate target localization in non-line of sight (NLOS) environment through effective hybridization of time of arrival (TOA) and received signal strength (RSS) measurements. A non-linear weighted least square (NLWLS) problem is formulated from general approximation of hybrid maximum-likelihood (ML) estimation problem using balancing parameter i.e., mean NLOS effect. The NLWLS problem is then solved using semi-definite relaxation (SDR) technique which employs a novel convex hull constraint. The proposed method requires neither prior NLOS statistics nor NLOS path identification. The numerical simulations validate that the proposed method significantly outperforms the existing methods and achieves the performance comparatively closer to that of Cramer-Rao lower bound (CRLB).

Throughput Maximization for Intelligent Reflecting Surface-Aided Device-to-Device Communications System

Intelligent reflecting surface (IRS) is a promising technology for its capability of reflecting the incident signal towards the desired user. IRS can improve the efficiency of wireless communication systems. This paper introduces IRS into a device-to-device (D2D) communications system to improve the throughput of the D2D network. We adopt the block coordinate descent algorithm and semidefinite relaxation technique to optimize the beamforming vector, power allocation and phase shift matrix. Simulation results demonstrate that IRS is able to enhance the throughput of the D2D communications system, and the proposed algorithm significantly outperforms the other benchmark algorithms.

Joint optimization of SINR and maximum sidelobe level for hybrid beamforming systems with sub-connected structure

This paper considers jointly designing the digital beamformer (DBF) and analog beamformer (ABF) for multi-user downlink hybrid beamforming systems in order to enhance communication performance and reduce information leakage. Our goal is maximizing the minimum signal-to-interference-plus-noise ratio (SINR) while depressing the maximum sidelobe level (SLL) of all users. Since the problem is difficult to solve optimally due to its nonconvexity and the infinitely many sidelobe constraints, we analyze the upper bound of the power in the side lobe region and convert the infinite sidelobe level constraints into a finite number of constraints to reduce the complexity of the hybrid beamformer (HBF) design. Then we transform the DBF design and the ABF design problems into convex problems. Based on alternating optimization and semidefinite relaxation (SDR) techniques, we solve the problem effectively. Simulation results show that the proposed algorithm is envisioned to balancing the SINR of all users while effectively depressing the sidelobe level.

Joint design of the transmit and receive beamforming for multi-mission MIMO radar

This paper jointly designs the transmit and receive beamforming vectors for a multi-mission multiple-input multiple-output (MIMO) radar. The radar searches for potential targets within a prescribed region while tracking multiple targets with known locations. To improve the performance of search mission and track mission, we aim to maximize the transmit energy in the prescribed region and ensure that the received signal to interference plus noise ratio (SINR) of each target is not less than a preset threshold. To tackle the resulting NP-hard problem, we introduce an iterative algorithm based on the sequential optimization procedure. In each iteration, the receive beamforming vectors are first updated by resolving the unconstrained maximization problems. Then, a fractional quadratic constrained quadratic programming (QCQP) is developed for updating the transmit beamforming vector and is solved with semidefinite relaxation (SDR) technique. Numerical simulations verify the convergence performance of the proposed algorithm. The ability of the radar to simultaneously implement the required two tasks is also demonstrated through the synthesized transmit and receive beampatterns.

DCA approaches for simultaneous wireless information power transfer in MISO secrecy channel

This paper addresses the emerging practical requirement that wireless information and power transfer are employed simultaneously in a multiple-input single-output (MISO) secrecy channel. Transmit beamforming without artificial noise and that with artificial noise are considered. In addition, perfect and imperfect channel state information of both the legitimate receivers and eavesdroppers are investigated. These four scenarios correspond to four optimization problems. The considered problems aim to maximize the secrecy rate with constraints on the transmit power and the harvested energy at each receiver. Since these optimization problems are nonconvex, we propose the efficient algorithms based on Difference of Convex (DC) functions programming and DC Algorithm (DCA )—an innovative approach in nonconvex optimization. Exploiting the special structure of these problems, we utilize the semidefinite relaxation technique and S-procedure to reformulate them as general DC programs. The efficient algorithms based on general DCA are developed to solve the corresponding general DC programs. Numerical results are presented which illustrate the effectiveness of our proposed algorithms, they outperform the existing approaches in terms of both quality and rapidity.

Tight Semidefinite Relaxation for Interval Power Flow Model Based on Multi-Dimensional Holomorphic Embedding Method

In order to quantify the impact of uncertainties on power systems resulted from renewable energy, a novel interval power flow method based on multi-dimensional holomorphic embedding method (MDHEM) and tight semidefinite relaxation technique are proposed. First, the MDHEM is used to address the spatial correlation of renewable energy basis, and the analytical expressions of bus voltages and active branch flows are derived. Second, the general interval power flow (IPF) model can be cast as a box constrained polynomial optimization problem. Third, a tight semidefinite relaxation is designed to solve this special optimization problem. Simulation results on several large-scale test systems show the effectiveness and computational tractability of the proposed model.

Sum-Rate Optimization Constrained by Consumed Power for Multi- Antenna Non-Regenerative Relay Network

Background & Objective: This paper considers a multi-pair wireless network, which communicates peer-to-peer using some multi-antenna amplify-and-forward relays. Maximizing the throughput supposing that the total relay nodes’ power consumption is constrained, is the main objective of this investigation. We prove that finding the beamforming matrix is not a convex problem. Methods: Therefore, by using a semidefinite relaxation technique we find a semidefinite programming problem. Moreover, we propose a novel algorithm for maximizing the total signal to the total leakage ratio. Numerical analyses show the effectiveness of the proposed algorithm which offers higher throughput compared to the existing total leakage minimization algorithm, with much less complexity. Results and Conclusion: Furthermore, the effect of different parameters such as, the number of relays, the number of antennas in each relay, the number of transmitter/receiver pairs and uplink and downlink channel gains are investigated.

Pay-As-You-Go: A Wireless Power Transfer-Enabled Beamforming for Cooperative Communication Systems

This letter considers a wireless power transfer enabled cooperative communication system where the end-users (EUs) make use of WPT to send energy to intermediate RUs to receive information. In traditional cooperative communications systems, service provider provides the energy for cooperation and the networks are optimized from the service providers' perspectives. In the this system, EUs compensate for the energy requirements of RUs, and EUs should get a fair service back from RUs. To administrate EUs WPT and ensure the fair service policy, this proposes a novel beamforming technique named Pay-As-You-Go beamforming. This adapts data rates proportional to the amount of energy received from each EUs while optimizing the energy per bit cost of the overall system. Then formulated as an non convex optimization problem and solved with the semi-definite programming relaxation techniques.

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.

Optimizing a Secure Two-Way Network with Non-Linear SWIPT, Channel Uncertainty, and a Hidden Eavesdropper

In this paper, the optimization of downlink beamforming vectors, uplink transmission power, and power-splitting factors is investigated for a secure two-way SWIPT network in the presence of a hidden eavesdropper and non-linear energy harvesting circuits over both perfect and imperfect channels. The eavesdropper is inactive, so its channel information is not available at the base stations (BSs). The purpose of artificial noise is to create downlink interference with the hidden eavesdropper as much as possible, while satisfying the quality of service for two-way communications. For perfect downlink channels, the semidefinite relaxation (SDR) technique is exploited, and the optimal matrices are proven to satisfy rank-1 conditions, thus providing the optimal beamforming vectors. For imperfect downlink channel state information, we propose an iterative algorithm with a penalty function to obtain the approximate rank-1 matrices. On uplink, we attain the optimal transmission power for users receiving maximum ratio transmission beamforming at the BSs. Eventually, the numerical experiments show the superiority of the proposed scheme, compared to a conventional scheme, in terms of signal-to-interference-plus-noise ratio at the eavesdropper.

A TDOA-FDOA Passive Positioning Algorithm Based on the Semi-Definite Relaxation Technique

In the passive location of moving target, the closed-form solution can reach Cramer-Rao Lower Bound (CRLB) under the low noise level, but these algorithms often can not adapt to the large measurement noise condition. For this problem, this paper proposes a passive positioning algorithm based on the Semi-Definite Relaxation (SDR) using Time Difference Of Arrival (TDOA) and Frequency Difference Of Arrival (FDOA). Firstly, this method constructs the pseudo-linear equation of the typical closed-form solution. Secondly, the idea of Stochastic Robust Least Squares (SRLS) and the nonlinear relationship between the target parameters and the additional variables are used to transform the localization problem into the least squares problem with quadratic equality. Using Semi-Definite Programming (SDP) technique, constrained least squares problem is then converted into the SDP problem, which is finally solved by the optimization toolbox. The proposed method does not require an initial priori information and simulations show the effectiveness of the proposed method.

Robust Beamforming in Multibeam Satellite Systems With Non-Orthogonal Multiple Access

In this letter, we investigate the beamforming optimization problem in a non-orthogonal multiple access (NOMA) based multibeam satellite system. The design key is to minimize the transmit power on-board the multibeam satellite system with the perfect and imperfect channel state information (CSI), while meeting the quality of service (QoS) for satellite users. Owing to the intractability and non-convexity of the original optimization problem induced by the user’s CSI uncertainty, we consider the robust beamforming scheme to convert the original optimization problem into a tractable convex optimization problem by S-Procedure and semidefinite relaxation (SDR) techniques and obtain the optimal solutions. Finally, numerical simulations demonstrate the superiority and validity of the proposed beamforming optimization algorithms.

Multibeam Optimization for Joint Communication and Radio Sensing Using Analog Antenna Arrays

Multibeam technology enables the use of two or more subbeams for joint communication and radio sensing, to meet different requirements of beamwidth and pointing directions. Generating and optimizing multibeam subject to the requirements is critical and challenging, particularly for systems using analog arrays. This paper develops optimal solutions to a range of multibeam design problems, where both communication and sensing are considered. We first study the optimal combination of two pre-generated subbeams, and their beamforming vectors, using a combining phase coefficient. Closed-form optimal solutions are derived to the constrained optimization problems, where the received signal powers for communication and the beamforming waveforms are alternatively used as the objective and constraint functions. We also develop global optimization methods which directly find optimal solutions for a single beamforming vector. By converting the original intractable complex NP-hard global optimization problems to real quadratically constrained quadratic programs, near-optimal solutions are obtained using semidefinite relaxation techniques. Extensive simulations validate the effectiveness of the proposed constrained multibeam generation and optimization methods.

Robust and Secure Beamforming for Intelligent Reflecting Surface Aided mmWave MISO Systems

In this letter, we investigate the robust and secure beamforming (RSBF) in an intelligent reflecting surface (IRS) aided millimeter wave (mmWave) multiple input single output (MISO) system, where multiple single antenna eavesdroppers (Eves) are arbitrarily distributed nearby the legitimate receiver (Bob). Considering the channel state information (CSI) of cascaded wiretap channels is imperfectly known at the legitimate transmitter (Alice), the RSBF design problems to maximize the worst case of achievable secrecy rate (ASR) are formulated under the total transmission power and unit-modulus constraints. Since the problems are difficult to solve optimally due to their non-convexity and coupled variables, we substitute the wiretap channels by a weighted combination of discrete samples and propose a RSBF scheme based on alternating optimization and semidefinite relaxation (SDR) techniques, for both colluding and noncolluding eavesdropping scenarios. Simulation results show that the proposed RSBF scheme can effectively improve the ASR and also outperforms other benchmark schemes.

Optimal Beam Pattern Design for Hybrid Beamforming in Millimeter Wave Communications

Beamforming is an enabling technique for wireless communications over higher frequency band, e.g., mmWave frequency band. To enhance beam concentration and homogenization within any angle range, we propose a hybrid beamforming design in three steps. First, through analyzing radiation power ratio, we find the bases of beamforming vector to guarantee a satisfactory level of power radiated over the targeted angle range. Second, with the derived bases, we flat the response of the passband by solving a max-min optimization problem using semidefinite relaxation technique. Third, we perform hybrid decomposition to achieve compatibility with phased array antenna with hybrid structure. The proposed beamforming is verified through quantitative measurement of beam concentration and homogenization. Simulation results show that the beamform pattern designed by our method outperform other existing methods in multi-cell scenarios.

A distributionally robust stochastic optimization-based model predictive control with distributionally robust chance constraints for cooperative adaptive cruise control under uncertain traffic conditions

Motivated by connected and automated vehicle (CAV) technologies, this paper proposes a data-driven optimization-based Model Predictive Control (MPC) modeling framework for the Cooperative Adaptive Cruise Control (CACC) of a string of CAVs under uncertain traffic conditions. The proposed data-driven optimization-based MPC modeling framework aims to improve the stability, robustness, and safety of longitudinal cooperative automated driving involving a string of CAVs under uncertain traffic conditions using Vehicle-to-Vehicle (V2V) data. Based on an online learning-based driving dynamics prediction model, we predict the uncertain driving states of the vehicles preceding the controlled CAVs. With the predicted driving states of the preceding vehicles, we solve a constrained Finite-Horizon Optimal Control problem to predict the uncertain driving states of the controlled CAVs. To obtain the optimal acceleration or deceleration commands for the CAVs under uncertainties, we formulate a Distributionally Robust Stochastic Optimization (DRSO) model (i.e. a special case of data-driven optimization models under moment bounds) with a Distributionally Robust Chance Constraint (DRCC). The predicted uncertain driving states of the immediately preceding vehicles and the controlled CAVs will be utilized in the safety constraint and the reference driving states of the DRSO-DRCC model. To solve the minimax program of the DRSO-DRCC model, we reformulate the relaxed dual problem as a Semidefinite Program (SDP) of the original DRSO-DRCC model based on the strong duality theory and the Semidefinite Relaxation technique. In addition, we propose two methods for solving the relaxed SDP problem. We use Next Generation Simulation (NGSIM) data to demonstrate the proposed model in numerical experiments. The experimental results and analyses demonstrate that the proposed model can obtain string-stable, robust, and safe longitudinal cooperative automated driving control of CAVs by proper settings, including the driving-dynamics prediction model, prediction horizon lengths, and time headways. Computational analyses are conducted to validate the efficiency of the proposed methods for solving the DRSO-DRCC model for real-time automated driving applications within proper settings.