{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,29]],"date-time":"2025-12-29T18:59:21Z","timestamp":1767034761001,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,2,20]],"date-time":"2023-02-20T00:00:00Z","timestamp":1676851200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Nature Science Foundation of China","doi-asserted-by":"publisher","award":["62201580","2021JM-222","2023-JC-YB-553"],"award-info":[{"award-number":["62201580","2021JM-222","2023-JC-YB-553"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007128","name":"Natural Science Foundation of Shaanxi Province","doi-asserted-by":"publisher","award":["62201580","2021JM-222","2023-JC-YB-553"],"award-info":[{"award-number":["62201580","2021JM-222","2023-JC-YB-553"]}],"id":[{"id":"10.13039\/501100007128","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>This paper proposes two data-independent phase-only beamforming algorithms for frequency diverse array multiple-input multiple-output radar against swarm interference. The proposed strategy can form a deep null at the interference area to achieve swarm interference suppression by tuning the phase of the weight vector, which can effectively reduce the hardware cost of the receiver. Specifically, the first algorithm imposes constant modulus constraint and sidelobe level constraint, and the phase-only weight vector is solved. The second algorithm performs a constant modulus decomposition of the weight vector to obtain two phase-only weight vectors, and uses two parallel phase shifters to synthesize one beamforming weight. Both methods can obtain the phase-only weight to realize suppression for swarm interference. Simulation results demonstrate that our strategy shows superiority in beam shape, output signal-to-interference-noise ratio, and phase shifter quantization performance, and has the potential for use in many applications, such as radar countermeasures and electronic defense.<\/jats:p>","DOI":"10.3390\/rs15041159","type":"journal-article","created":{"date-parts":[[2023,2,21]],"date-time":"2023-02-21T01:39:28Z","timestamp":1676943568000},"page":"1159","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Data-Independent Phase-Only Beamforming of FDA-MIMO Radar for Swarm Interference Suppression"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0880-4404","authenticated-orcid":false,"given":"Geng","family":"Chen","sequence":"first","affiliation":[{"name":"School of Air Defense and Missile Defense, Air Force Engineering University, Xi\u2019an 710051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chunyang","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Air Defense and Missile Defense, Air Force Engineering University, Xi\u2019an 710051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jian","family":"Gong","sequence":"additional","affiliation":[{"name":"School of Air Defense and Missile Defense, Air Force Engineering University, Xi\u2019an 710051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9503-4910","authenticated-orcid":false,"given":"Ming","family":"Tan","sequence":"additional","affiliation":[{"name":"College of Information and Communication, National University of Defense Technology, Wuhan 430010, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1356-6196","authenticated-orcid":false,"given":"Yibin","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Air Defense and Missile Defense, Air Force Engineering University, Xi\u2019an 710051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3139","DOI":"10.1109\/TAES.2019.2899796","article-title":"Robust Adaptive Beamforming via Simplified Interference Power Estimation","volume":"55","author":"Zheng","year":"2019","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"4602","DOI":"10.1109\/TAP.2019.2911317","article-title":"Pattern Synthesis via Oblique Projection-Based Multipoint Array Response Control","volume":"67","author":"Zhang","year":"2019","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2594","DOI":"10.1109\/LCOMM.2020.3006506","article-title":"Multi-Constraint Adaptive Beamforming in the Presence of the Desired Signal","volume":"24","author":"Ge","year":"2020","journal-title":"IEEE Commun. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"664","DOI":"10.1109\/LCOMM.2019.2899874","article-title":"Middle Subarray Interference Covariance Matrix Reconstruction Approach for Robust Adaptive Beamforming with Mutual Coupling","volume":"23","author":"Li","year":"2019","journal-title":"IEEE Commun. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1018","DOI":"10.1109\/LAWP.2021.3069743","article-title":"Linear Arbitrary Array Pattern Synthesis with Shape Constraints and Excitation Range Control","volume":"20","author":"Zhang","year":"2021","journal-title":"IEEE Antennas Wirel. Propag. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1109\/TSP.2017.2760279","article-title":"Analysis and Design of Optimum Sparse Array Configurations for Adaptive Beamforming","volume":"66","author":"Wang","year":"2018","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"eabm5954","DOI":"10.1126\/scirobotics.abm5954","article-title":"Swarm of micro flying robots in the wild","volume":"7","author":"Zhou","year":"2022","journal-title":"Sci. Robot"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"eabq2215","DOI":"10.1126\/scirobotics.abq2215","article-title":"Swarms of flying robots in unknown environments","volume":"7","author":"Soria","year":"2022","journal-title":"Sci. Robot"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/j.sigpro.2014.11.009","article-title":"A linearly constrained minimum variance beamformer with a pre-specified suppression level over a pre-defined broad null sector","volume":"109","author":"Amar","year":"2015","journal-title":"Signal Process."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2135","DOI":"10.1109\/TSP.2015.2512527","article-title":"Average SINR Calculation of a Persymmetric Sample Matrix Inversion Beamformer","volume":"64","author":"Liu","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3881","DOI":"10.1109\/TSP.2012.2194289","article-title":"Robust Adaptive Beamforming Based on Interference Covariance Matrix Reconstruction and Steering Vector Estimation","volume":"60","author":"Gu","year":"2012","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1016\/j.sigpro.2013.10.009","article-title":"Robust adaptive beamforming based on interference covariance matrix sparse reconstruction","volume":"96","author":"Gu","year":"2014","journal-title":"Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1810","DOI":"10.1109\/TSP.2017.2649487","article-title":"A2RC: An Accurate Array Response Control Algorithm for Pattern Synthesis","volume":"65","author":"Zhang","year":"2017","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"4075","DOI":"10.1109\/TAP.2017.2718582","article-title":"Pattern Synthesis with Multipoint Accurate Array Response Control","volume":"65","author":"Zhang","year":"2017","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"108259","DOI":"10.1016\/j.sigpro.2021.108259","article-title":"MPARC: A fast beampattern synthesis algorithm based on adaptive array theory","volume":"189","author":"Ai","year":"2021","journal-title":"Signal Process."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"7053","DOI":"10.1109\/TAP.2021.3076505","article-title":"Beampattern Synthesis for Phased Array with Dual-Phase-Shifter Structure","volume":"69","author":"Zhuang","year":"2021","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"652","DOI":"10.1109\/TSP.2018.2885454","article-title":"OPARC: Optimal and Precise Array Response Control Algorithm\u2014Part I: Fundamentals","volume":"67","author":"Zhang","year":"2019","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"668","DOI":"10.1109\/TSP.2018.2885492","article-title":"OPARC: Optimal and Precise Array Response Control Algorithm\u2014Part II: Multi-Points and Applications","volume":"67","author":"Zhang","year":"2019","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3126","DOI":"10.1109\/TSP.2019.2912147","article-title":"Flexible Array Response Control via Oblique Projection","volume":"67","author":"Zhang","year":"2019","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"834","DOI":"10.1109\/TAP.2020.3016508","article-title":"Correction Analysis of Frequency Diverse Array Radar about Time","volume":"69","author":"Tan","year":"2021","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"280","DOI":"10.1016\/j.sigpro.2018.09.016","article-title":"Clutter Suppression for Airborne FDA-MIMO Radar using Multi-Waveform Adaptive Processing and Auxiliary Channel STAP","volume":"154","author":"Wen","year":"2019","journal-title":"Signal Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3705","DOI":"10.1109\/TAES.2021.3083591","article-title":"Single-Snapshot Angle and Incremental Range Estimation for FDA-MIMO Radar","volume":"57","author":"Lan","year":"2021","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1368","DOI":"10.1109\/TAES.2017.2785598","article-title":"FDA Radar Ambiguity Function Characteristics Analysis and Optimization","volume":"54","author":"Wang","year":"2018","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"973","DOI":"10.1109\/TSP.2016.2628340","article-title":"Robust adaptive beamforming for fast-moving target detection with FDA-STAP radar","volume":"65","author":"Xu","year":"2017","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1109\/TAES.2021.3098100","article-title":"Slow-Time FDA-MIMO Technique with Application to STAP Radar","volume":"58","author":"Wen","year":"2022","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/j.sigpro.2019.05.025","article-title":"Bistatic FDA-MIMO radar space-time adaptive processing","volume":"163","author":"Wen","year":"2019","journal-title":"Signal Process."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"8323","DOI":"10.1109\/JSEN.2020.3045757","article-title":"A Novel Deceptive Jamming Approach against Frequency Diverse Array Radar","volume":"21","author":"Tan","year":"2021","journal-title":"IEEE Sen. J."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"11584","DOI":"10.1109\/TVT.2020.3014689","article-title":"Suppression of Mainbeam Deceptive Jammer with FDA-MIMO Radar","volume":"69","author":"Lan","year":"2020","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"4145","DOI":"10.1109\/TGRS.2019.2961324","article-title":"Transceive Beamforming with Accurate Nulling in FDA-MIMO Radar for Imaging","volume":"58","author":"Lan","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2081","DOI":"10.1109\/LAWP.2019.2937682","article-title":"Phase-Only Control of Peak Sidelobe Level and Pattern Nulls Using Iterative Phase Perturbations","volume":"18","author":"Aslan","year":"2019","journal-title":"IEEE Antennas Wirel. Propag. Lett."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"6647","DOI":"10.1109\/TVT.2021.3089418","article-title":"Reconfigurable Sparse Array Synthesis with Phase-Only Control via Consensus-ADMM-Based Sparse Optimization","volume":"70","author":"Wen","year":"2021","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1049\/iet-map:20070256","article-title":"Phase-only adaptive nulling with neural networks for antenna array synthesis","volume":"3","author":"Ghayoula","year":"2009","journal-title":"IET Microw. Antennas Propag."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"3038","DOI":"10.1109\/LAWP.2017.2759318","article-title":"Interference suppression of ULA antennas by phase-only control using bat algorithm","volume":"16","author":"Luyen","year":"2017","journal-title":"IEEE Antennas Wireless Propag. Lett."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"6439","DOI":"10.1109\/TAP.2019.2923083","article-title":"Fast Array Response Adjustment with Phase-Only Constraint: A Geometric Approach","volume":"67","author":"Zhang","year":"2019","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"4154","DOI":"10.1109\/JSEN.2018.2820905","article-title":"Enhanced Three-Dimensional Joint Domain Localized STAP for Airborne FDA-MIMO Radar under Dense False-Target Jamming Scenario","volume":"18","author":"Wen","year":"2018","journal-title":"IEEE Sen. J."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"103811","DOI":"10.1016\/j.dsp.2022.103811","article-title":"DCFDA-MIMO: A dual coprime FDA-MIMO radar framework for target localization","volume":"133","author":"Chen","year":"2023","journal-title":"Digital Signal Process."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1109\/MSP.2010.936019","article-title":"Semidefinite Relaxation of Quadratic Optimization Problems","volume":"27","author":"Luo","year":"2010","journal-title":"IEEE Signal Process. Magazine"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"634","DOI":"10.1109\/TAP.2013.2290797","article-title":"Application of Convex Relaxation to Array Synthesis Problems","volume":"62","author":"Fuchs","year":"2014","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_39","unstructured":"(2012). MATLAB Software for Disciplined Convex Programming, CVX Res., Inc."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/4\/1159\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:37:19Z","timestamp":1760121439000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/4\/1159"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,20]]},"references-count":39,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2023,2]]}},"alternative-id":["rs15041159"],"URL":"https:\/\/doi.org\/10.3390\/rs15041159","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2023,2,20]]}}}