{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,14]],"date-time":"2026-07-14T18:19:09Z","timestamp":1784053149568,"version":"3.55.0"},"reference-count":26,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2022,9,26]],"date-time":"2022-09-26T00:00:00Z","timestamp":1664150400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Key Program of National Natural Science Foundations of China","award":["41930110"],"award-info":[{"award-number":["41930110"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In radar detection, in order to make the beam have variable directivity, a Capon beamformer is usually used. Although this traditional beamformer enjoys both high resolution and good interference suppression, it usually leads to high sidelobe and is sensitive to array steering vector (ASV) mismatch. To overcome such problems, this study devises a novel, robust adaptive beamformer that is robust to ASV mismatch under the constraint where the sidelobe is oriented to the ground. Moreover, to make full use of the transmit power, the constraint of a low peak-to-average power ratio (PAPR) is also taken into consideration. Accordingly, this robust adaptive beamformer is developed by optimizing a transmitting beamformer constrained by ASV mismatch and low PAPR. This optimization problem is transformed into a second-order cone programming (SOCP) problem which can be efficiently and exactly solved. The proposed transmit beamformer possesses not only adaptive interference rejection ability and robustness against ASV mismatch, but also direct sidelobe control and a low PAPR. Simulation results are presented to demonstrate the superiority of the proposed approach. The proposed method can make the peak sidelobe level (PSL) level on the ground side below \u221230 dB.<\/jats:p>","DOI":"10.3390\/s22197278","type":"journal-article","created":{"date-parts":[[2022,9,28]],"date-time":"2022-09-28T03:30:37Z","timestamp":1664335837000},"page":"7278","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Robust Adaptive Transmit Beamforming under the Constraint of Low Peak-to-Average Ratio"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8045-0073","authenticated-orcid":false,"given":"Hongtao","family":"Li","sequence":"first","affiliation":[{"name":"School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhoupeng","family":"Ding","sequence":"additional","affiliation":[{"name":"School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3601-6189","authenticated-orcid":false,"given":"Sirui","family":"Tian","sequence":"additional","affiliation":[{"name":"School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Songpo","family":"Jin","sequence":"additional","affiliation":[{"name":"China Electronics Technology Group Corp 54th Research Institute, Shijiazhuang 050081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,26]]},"reference":[{"key":"ref_1","first-page":"36","article-title":"Research on Broadband Transmission ADBF Based on Subband Maximum Signal to Noise Ratio Criterion","volume":"38","author":"Wang","year":"2019","journal-title":"Foreign Electron. Meas. Technol."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Day, D.A. (2009, January 4\u20138). Fast Phase-Only Pattern Nulling for Large Phased Array Antennas. Proceedings of the 2009 IEEE Radar Conference, Pasadena, CA, USA.","DOI":"10.1109\/RADAR.2009.4976945"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"8495","DOI":"10.1109\/TVT.2018.2849646","article-title":"Covariance Matrix Reconstruction with Interference Steering Vector and Power Estimation for Robust Adaptive Beamforming","volume":"67","author":"Zheng","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1049\/el.2015.3844","article-title":"Low-complexity variable loading for robust adaptive beamforming","volume":"52","author":"Zhuang","year":"2016","journal-title":"Electron. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1373","DOI":"10.1049\/el.2013.2070","article-title":"Interference covariance matrix reconstruction via steering vectors estimation for robust adaptive beamforming","volume":"49","author":"Lu","year":"2013","journal-title":"Electron. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1560","DOI":"10.1109\/TSP.2006.890820","article-title":"Adaptive detection with bounded steering vectors mismatch angle","volume":"55","author":"Besson","year":"2007","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1702","DOI":"10.1109\/TSP.2003.812831","article-title":"On robust Capon beamforming and diagonal loading","volume":"51","author":"Li","year":"2003","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1109\/TSP.2005.861052","article-title":"Finite sample size effect on minimum variance beamformers: Optimum diagonal loading factor for large arrays","volume":"54","author":"Mestre","year":"2006","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1109\/TAES.2010.5417174","article-title":"Fully Automatic Computation of Diagonal Loading Levels for Robust Adaptive Beamforming","volume":"46","author":"Du","year":"2010","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1083","DOI":"10.1007\/s11045-021-00775-y","article-title":"Steering vector optimization using subspace-based constraints for robust adaptive beamforming","volume":"32","author":"Zhang","year":"2021","journal-title":"Multidimens. Syst. Signal Process."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Vouras, P., and de Graaf, J. (2011, January 6\u20139). Robust Transmit Nulling in Phased Array Antennas. Proceedings of the 2011 Conference Record of the Forty Fifth Asilomar Conference on Signals, Systems and Computers (ASILOMAR), Pacific Grove, CA, USA.","DOI":"10.1109\/ACSSC.2011.6190399"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3706","DOI":"10.1109\/TSP.2014.2329653","article-title":"Robust Transmit Nulling in Wideband Arrays","volume":"62","author":"Vouras","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"108223","DOI":"10.1016\/j.sigpro.2021.108223","article-title":"Fast and robust adaptive beamforming algorithms for large-scale arrays with small samples","volume":"188","author":"Zhang","year":"2021","journal-title":"Signal Process."},{"key":"ref_14","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":"Yujie","year":"2012","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1099","DOI":"10.1109\/TVT.2017.2704610","article-title":"A Robust and Efficient Algorithm for Coprime Array Adaptive Beamforming","volume":"67","author":"Zhou","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2755","DOI":"10.1109\/TWC.2018.2803045","article-title":"MU-MIMO Communications with MIMO Radar: From Co-Existence to Joint Transmission","volume":"17","author":"Liu","year":"2018","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1109\/MSP.2020.2983832","article-title":"Joint Radar-Communication Strategies for Autonomous Vehicles: Combining Two Key Automotive Technologies","volume":"37","author":"Ma","year":"2020","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"252","DOI":"10.1109\/ACCESS.2016.2639038","article-title":"Survey of RF Communications and Sensing Convergence Research","volume":"5","author":"Paul","year":"2017","journal-title":"IEEE Access"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Catak, E., Catak, F.O., and Moldsvor, A. (2021, January 24\u201328). Adversarial Machine Learning Security Problems for 6G: mmWave Beam Prediction Use-Case. Proceedings of the 2021 IEEE International Black Sea Conference on Communications and Networking (BlackSeaCom), Bucharest, Romania.","DOI":"10.1109\/BlackSeaCom52164.2021.9527756"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3929","DOI":"10.1109\/TSP.2020.3004739","article-title":"Joint Transmit Beamforming for Multiuser MIMO Communications and MIMO Radar","volume":"68","author":"Liu","year":"2020","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"McCormick, P.M., Ravenscroft, B., Blunt, S.D., Duly, A.J., and Metcalf, J.G. (2017, January 8\u201312). Simultaneous Radar and Communication Emissions from a Common Aperture, Part II: Experimentation. Proceedings of the 2017 IEEE Radar Conference (RadarConf), Seattle, WA, USA.","DOI":"10.1109\/RADAR.2017.7944480"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"McCormick, P.M., Blunt, S.D., and Metcalf, J.G. (2017, January 8\u201312). Simultaneous Radar and Communications Emissions from a Common Aperture, Part I: Theory. Proceedings of the 2017 IEEE Radar Conference (RadarConf), Seattle, WA, USA.","DOI":"10.1109\/RADAR.2017.7944478"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Euziere, J., Guinvarc\u2019h, R., Lesturgie, M., Uguen, B., and Gillard, R. (2014, January 13\u201317). Dual function Radar Communication Time-Modulated Array. Proceedings of the 2014 International Radar Conference, Lille, France.","DOI":"10.1109\/RADAR.2014.7060416"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2168","DOI":"10.1109\/TSP.2015.2505667","article-title":"Dual-Function Radar-Communications: Information Embedding Using Sidelobe Control and Waveform Diversity","volume":"64","author":"Hassanien","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_25","unstructured":"Wang, Y.L., Li, R.F., and Ding, Q.J. (2009). Adaptive Array Processing, Tsinghua University Press."},{"key":"ref_26","unstructured":"Grant, M., and Boyd, S. (2022, September 25). CVX: Matlab Software for Disciplined Convex Programming. Available online: http:\/\/cvxr.com\/cvx."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/19\/7278\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:39:32Z","timestamp":1760143172000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/19\/7278"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,26]]},"references-count":26,"journal-issue":{"issue":"19","published-online":{"date-parts":[[2022,10]]}},"alternative-id":["s22197278"],"URL":"https:\/\/doi.org\/10.3390\/s22197278","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9,26]]}}}