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Hybrid sparse array design using Delaunay Triangulation and Convex optimization for wide beam steering

INTERNATIONAL JOURNAL OF MICROWAVE AND WIRELESS TECHNOLOGIES 2025年

作者： Gao, Pan Chen, Zhongquan Eindhoven Univ Technol Elect Engn Dept Eindhoven Netherlands Eindhoven Univ Technol Math & Comp Sci Dept Eindhoven Netherlands

In this paper, we propose a hybrid sparse array design utilizing Delaunay Triangulation algorithm for element positioning and Convex algorithm for element excitation optimization. This Delaunay Triangulation algorithm yields a radiation pattern devoid of grating lobes. Then Convex algorithm is used to optimize the element excitations to further decrease side-lobe-level. The minimum inter-element distance is as large as 8 times of wavelength. The peak-side-lobe-level can be -17.3 dB. Furthermore, beam steering can be achieved with good performance within 80 degrees field-of-view range.

关键词： beam steering Convex Delaunay Triangulation grating lobes hybrid sparse array side-lobe-level

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A Novel Planar sparse array Design for Two-Dimensional Direction Estimation with Increased Degrees of Freedom

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CIRCUITS SYSTEMS AND SIGNAL PROCESSING 2025年第2期44卷 1214-1238页

作者： Goel, Kretika Agrawal, Monika Kar, Subrat Indian Inst Technol Delhi SeNSE Dept New Delhi 110016 India Indian Inst Technol Delhi CARE Dept New Delhi 110016 India Indian Inst Technol Delhi Dept Elect Engn New Delhi 110016 India

Developing a novel category of 2-D sparse arrays to improve information resolution with a minimum of possible actual sensors has proven to be a notable and persistent demanding objective. This study introduces a new layout for planar sparse arrays to estimate signal arrival angles in both azimuth and elevation dimensions. By introducing this new category of two-dimensional arrays, we strive to improve existing planar geometries. Specifically, our method's principle involves strategically positioning sensors to maximize spatial diversity and enhance the array's ability to resolve incoming signals from different angles. This optimization results in a higher DoF compared to traditional planar arrays, offering improved performance in signal processing tasks such as direction finding and beamforming. Furthermore, the intended design of the array aims to reduce the occurrence of gaps within the difference coarray and make it hole-free to enhance its suitability for DoA estimation algorithms. To assess the effectiveness of the suggested array, numerical simulations were conducted, demonstrating the achieved RMSE (Root Mean Square Error) value in the proposed RCPA is the least, i.e., less than 0.1%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document}, as compared to other existing planar arrays. The reduced RMSE achieved with the proposed RCPA array could significantly enhance the accuracy of existing applications such as radar and sonar systems, leading to improved target detection, tracking, and localization capabilities. The detailed explanation of our approach and the rationale behind its improved DoF serves to provide readers with a comprehensive understanding and motivation for adopting this innovative array design.

关键词： sparse array DoA (Direction of Arrival Estimation) Difference coarray DoF (Degrees of Freedom)

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Research on the fusion imaging method of sign coherence and time reversal for Lamb wave sparse array

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ULTRASONICS 2025年 145卷 107489页

作者： Sun, Liu-Jia Han, Qing-Bang Yin, Cheng Jin, Qi-Lin Ge, Kao Hohai Univ Coll Informat Sci & Engn Changzhou 213200 Peoples R China

Time-reversal imaging struggles to detect plate-like structures due to interference from Lamb wave mode conversion and the processing demands, leading to less effective outcomes. This paper proposes a sign coherence factor and time reversal fusion (SCF-TR) imaging method based on amplitude and phase estimation. This method removes the coherence of array signals during signal reversal and refocusing. It reintroduces the sign coherence component to reduce interference from non-target scattered waves and partially overcome the constraints imposed by the Rayleigh criterion. The method allows imaging at a resolution smaller than the wavelength of Lamb and enhances the quality of the resulting images. In addition, a sparse array design utilizing the White Shark Optimisation Algorithm (WSO) is proposed to streamline the SCF-TR calculation process. This design utilizes sparse full matrix data to improve imaging efficiency. The experimental results show that for single blind hole defects, the SCF-TR method improves the array performance metrics and signal-to-noise ratio by 22.46% and 42.50%, respectively, compared to the TR method. For multiple asymmetric blind hole defects, when the defect size exceeds the resolution threshold, SCF-TR accurately reflects the position and morphology of defects smaller than the wavelength. When the defect size is below the resolution threshold, SCF-TR achieves superresolution imaging. The sparse array designed using the White Shark Optimization algorithm demonstrates good sidelobe characteristics, effectively reducing sidelobe noise without reducing the array aperture. Moreover, the SCF-TR imaging time is reduced by approximately half while maintaining imaging accuracy.

关键词： Lamb waves Amplitude-phase estimation SCF-TR sparse array Super-resolution imaging

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Multi-source DOA tracking with an adaptive superposition model for sparse array

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SIGNAL PROCESSING 2025年 230卷

作者： Cao, Jinke You, Mingyi Li, Dawei Zhang, Xiaofei Zhou, Fuhui Nanjing Univ Aeronaut & Astronaut Coll Elect & Informat Engn Nanjing Peoples R China Nanjing Univ Aeronaut & Astronaut Key Lab Dynam Cognit Syst Electromagnet Spectrum S Minist Ind & Informat Technol Nanjing 211106 Peoples R China 36 Res Inst CETC Jiaxing 314000 Peoples R China Natl Key Lab Electromagnet Space Secur Jiaxing 314000 Peoples R China

Tracking the direction of arrival (DOA) with a passive sensor array is a well-known problem in signal processing. Traditional methods, such as subspace tracking and super-resolution techniques, struggle with data association and trajectory crossing. Although Kalman filter-based methods are excellent for tracking, they are difficult to apply to DOA tracking due to complex nonlinear transformations and unknown source signals in the array-received signals. To overcome these limitations, we propose two adaptive tracking methods using a sparse array (SA): one based on the extended Kalman filter (SA-AEKF) and the other on the unscented Kalman filter (SA-AUKF). Tracking is implemented using an adaptive superposition model that adapts to changes in signal and noise intensity. Moreover, it avoids the presence of multiple measurements at the same tracking time by superimposing multiple snapshot measurements into a single measurement. Finally, we analyze the Cram & eacute;r- Rao bound (CRB) and posterior Cram & eacute;r-Rao bound (PCRB) for the proposed algorithms. Simulation results show that our methods outperform conventional techniques in challenging scenarios with low signal-to-noise ratios, limited snapshots, trajectory crossovers, and fewer array elements than signal sources.

关键词： DOA tracking Multi-source tracking sparse array Extended Kalman filter Unscented Kalman filter Adaptive tracking Superposition model CRB PCRB

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Optimal sparse array Design for Airborne Weather Radar With Integrated Communications

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IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS 2025年第2期61卷 4238-4254页

作者： Wang, Xiangrong Huang, Jiayi Wang, Xianghua Huang, Tianyao Amin, Moeness Beihang Univ Sch Elect & Informat Engn Beijing 100191 Peoples R China Beijing Univ Posts & Telecommun Sch Intelligent Engn & Automation Beijing 100876 Peoples R China Univ Sci & Technol Beijing Sch Comp & Commun Engn Beijing 100083 Peoples R China Villanova Univ Ctr Adv Commun Villanova PA 19085 USA

A close and continuous observation of typhoon can be accomplished by a phased array weather radar mounted on an airborne ship platform. The precise typhoon inner structure can be assimilated from the data obervations, thus envisioning a significant accuracy improvement in the prediction of typhoon intensity and travelling path. The requirement of high-resolution meteorological observation, against the limited power supply and payload weight imposed by the airborne platform, renders the deployment of sparse phased arrays essential to achieve tangible solutions. Integrated communications in the weather radar enable conveying the information to the ground control station without impacting radar beam scanning. This is completed by embedding the information symbols via the complex transmit beampattern modulation. As typhoon is a volume target spanning multiple range gates and angular bins, the focus of this work is a joint design of the optimal sparse array and associated beamforming weights for a well-controlled beam scanning in a wide angular range with integrated downlink communications. The constant modulus constraint of beamforming weights are imposed to maximize the radar transmit power efficiency, and an extension to discrete weight amplitudes is further considered for performance improvement. The simulation results demonstrate that the proposed sparse phased array weather radar can achieve an improved meteorological observation and a satisfied communication quality, especially in the scenarios of interferences.

关键词： Radar Meteorological radar Phased arrays Meteorology Airborne radar array signal processing Antenna arrays Tropical cyclones Radar antennas Doppler radar Beamforming integrated communications sparse array spatial resolution weather radar

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Pattern-reconfigurable sparse array synthesis with minimum element spacing constraint

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JOURNAL OF ELECTROMAGNETIC WAVES AND APPLICATIONS 2025年第7期39卷 810-821页

作者： Wang, Zhongyuan Xu, Min Shen, Mingwei Shen, Yipin Hohai Univ Coll Informat Sci & Engn Nanjing Peoples R China Sci & Technol Elect Informat Control Lab Chengdu Peoples R China Hohai Univ Coll Comp & Software Nanjing Peoples R China Zhejiang Gongshang Univ Coll Comp Sci & Technol 18 Xuezheng StXiasha Higher Educ Pk Hangzhou Peoples R China

Due to the coupling effects caused by closely spaced array elements, the minimum spacing constraint is introduced into the synthesis of a multiple-pattern sparse array, and a low-complexity off-grid sparse reconstruction algorithm is applied to achieve precise array element position. The auxiliary weighted vector with spacing constraint is incorporated into the off-grid synthesis problem, transforming the initial l0-norm optimization into the mixed l0/l1-norm optimization, and a sequential alternating iteration (SAI) method has been presented to approach the optimization problems. In addition, convex optimization is employed to simultaneously obtain offsets to decrease reconstruction errors in different beam patterns. The experimental results show that the SAI method achieves the desired antenna patterns for multiple scanning angles through the optimal arrangement of sparse array elements while ensuring sufficient array element spacing. Compared to the previous method, the pattern error is reduced by 16.67% and the sparsity is increased by 20%.

关键词： Minimum spacing constraint off-grid reconfigurable multiple patterns sparse array

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Improved Sparrow Search Algorithm for sparse array Optimization

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MODELLING AND SIMULATION IN ENGINEERING 2025年第1期2025卷

作者： Ji, Juanjuan Su, Jie Zhang, Lanfang Zhang, Liuying Jiang, Julang Ma, Hongliang Anqing Normal Univ Sch Elect Engn & Intelligent Mfg Anqing Peoples R China

The synthesis problem of the number of array elements, array element spacing, and array formation is widely concerned in sparse array optimization. The local optimum problem is still an urgent problem to be solved in the existing optimization algorithms. A sparse array optimization algorithm on improved sparrow search algorithm (ISSA) is proposed in this paper. Firstly, a probabilistic following strategy is proposed to optimize the following strategy of the sparrow search algorithm (SSA), and it can improve the global search capability of the algorithm. Secondly, the adaptive local search and Cauchy-Gaussian mutation are used to avoid falling into the local optimum situation, and more high-quality areas are searched to improve the local extremum escape ability and convergence performance of the algorithm. Finally, the peak sidelobe level (PSLL) is used as the fitness function to adaptively optimize the position of the array elements. Experimental simulations show that the proposed approach has good main lobe response and low sidelobe response. In the sparse planar array, the sidelobe level decreases by -1.41 dB compared with the genetic algorithm (GA) and 0.69 dB lower than the SSA. In sparse linear array, the sidelobe level decreases by -1.09 dB compared with differential evolution algorithm and 0.40 dB lower than the SSA. The optimization of sparse arrays significantly enhances the accuracy and robustness of antenna array error estimation.

关键词： array antenna ISSA sparse array sparse planar array

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sparse array for Beamforming in Wireless Communication Systems

JOURNAL OF ENGINEERING

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JOURNAL OF ENGINEERING 2025年第1期2025卷

作者： Ossa-Molina, Oscar Guerra, Juan Felipe Betancur, Andres Felipe Inst Univ ITM Sch Engn Dept Elect & Telecommun Medellin Colombia

The usefulness of smart antennas lies in enhancing the received signal from a particular direction while suppressing unwanted interfering signals and noise from other directions. This process is known as beamforming. In this paper, we study beamforming using different antenna array geometries to improve performance. We explore sparse arrays, including coprime and nested arrays, and employ a beamforming technique. The design of the antenna elements includes a half-wavelength dipole and a rectangular patch antenna. Crucial array parameters such as the envelope correlation coefficient, spatial gain diversity, and mutual coupling are evaluated. The array pattern after beamforming is presented for each array antenna, and it was demonstrated that the sparse array achieves superior results compared to the uniform linear array. This work contributes to the intelligent management of the wireless channel, addressing requirements such as higher capacity, frequency reuse, low delay, and reliability in new mobile technologies such as 5G and beyond.

关键词： antenna arrays beamforming mutual coupling sparse array spatial resolution

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In-situ monitoring of μ m-sized electrochemically generated corrosion pits using Lamb waves managed by a sparse array of piezoelectric transducers

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ULTRASONICS 2025年 147卷 107527页

作者： Nicard, C. Rebillat, M. Devos, O. El May, M. Letellier, F. Dubent, S. Thomachot, M. Fournier, M. Masse, P. Mechbal, N. Arts & Metiers Inst Technol PIMM CNAM CNRS Paris France Univ Bordeaux Arts & Metiers Inst Technol CNRS I2M Bordeaux France Cedrat Technol Meylan France RESCOLL Talence France

Corrosion is a major threat in the aeronautic industry, both in terms of safety and cost. Efficient, versatile, and cost affordable solutions for corrosion monitoring are thus needed. Ultrasonic Lamb Waves (LW) appear to be very efficient for corrosion monitoring and can be made cost effective and versatile if emitted and received by a sparse array of piezoelectric elements (PZT). A LW solution relying on a sparse PZT array and allowing to monitor mu m-sized corrosion pit growth on stainless 316L grade steel plate is here evaluated. Experimentally, the corrosion pit size is electrochemically controlled by both the imposed electrical potential and the injection of a corrosive NaCl solution through a capillary located at the desired pit location. In parallel, the corrosion pit growth is monitored in-situ every 10 s by sending and measuring LW using a sparse array of 4 PZTs bonded to the back of the steel plate enduring corrosion. As a ground truth information, the corrosion pit volume is estimated as the dissolved volume balancing the electronic charges exchanged during corrosion. The corrosion pit radius is additionally checked post-experiment precisely with an optical measurement. Measured LW signals are then post-processed in order to compute a collection of synthetic damage indexes (DIs). After dimension reduction steps, obtained DI values correlates extremely well with the corrosion pit radius. Using a linear model relating those DI values to corrosion pit radius, it is demonstrated that corrosion pit from 30 mu m to 150 mu m can be reliably detected, located, and their upcoming size extrapolated. Two independent experiments were achieved in order to ensure the repeatability of the proposed approach. LW managed by a sparse PZT array thus appears to be reliable and efficient to monitor growth of mu m-sized corrosion pits on 316L steel plates. If embedded in aeronautical structure, such an approach could be a versatile and cost-effective alternative to actual non-d

关键词： Piezoelectric Transducers sparse array Pitting Corrosion Structural Health Monitoring Ultrasonic Lamb Waves Controlled Electrochemical Experiments

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sparse array Beampattern Synthesis via Alternating Direction Method of Multipliers

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2018年第5期66卷 2333-2345页

作者： Liang, Junli Zhang, Xuan So, Hing Cheung Zhou, Deyun Northwestern Polytech Univ Sch Elect & Informat Xian 710068 Shaanxi Peoples R China City Univ Hong Kong Dept Elect Engn Hong Kong Hong Kong Peoples R China

In this paper, we devise beampattern synthesis algorithms for sparse arrays using the alternating direction method of multipliers (ADMM). Unlike the usual weighted lp norm, we utilize the l p norm of the array weight vector, where 0 < p < 1, as the objective function to enhance its sparsity for arbitrary array configurations. To solve the resultant nonconvex and nonlinear optimization problem, we introduce auxiliary variables to decouple the array weight vector in the objective function from the complicated constraints on main lobes and sidelobes, and then, the array weight vector and auxiliary variables are updated alternately via ADMM. To determine the array weight vector with the lp norm, we analyze the convexity or concavity of the subfunction related to each weight element using its derivatives. On the other hand, we divide the objective function of auxiliary variables into multiple nonlinear subfunctions, each of which is only dependent of the magnitude of the corresponding auxiliary variable and is calculated in parallel via analyzing simplified two-sided constraints. Furthermore, we extend our methodology to the symmetric excitation case with symmetric array configurations. Numerical examples show that the proposed methods can obtain satisfactory radiation pattern with fewer antennas than the existing techniques and are applicable for arbitrary or symmetric array configurations.

关键词： Alternating direction method of multipliers (ADMM) beampattern synthesis nonconvex and nonlinear optimization sparse array

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