{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,25]],"date-time":"2026-01-25T04:57:08Z","timestamp":1769317028264,"version":"3.49.0"},"reference-count":35,"publisher":"MDPI AG","issue":"20","license":[{"start":{"date-parts":[[2021,10,19]],"date-time":"2021-10-19T00:00:00Z","timestamp":1634601600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41722404"],"award-info":[{"award-number":["41722404"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>A new stepwise and radially processed method for synthesizing uniformly distributed circular planar arrays with quantized weights is proposed in this paper. This method is based on a generalized analytical equation describing that for high directivity focusing arrays, minimizing the weighted mean square error between the reference pattern and the synthesized pattern is equivalent to minimizing the mean square error between the radial cumulative distributions of the reference distribution and the synthesized distribution. This principle has been successfully performed for designing large concentric ring arrays, and in this paper, we extend its use for synthesizing uniformly distributed planar circular arrays with quantized weights. Various numerical examples and comparisons with several reported statistical methods in terms of the lowest Maximum SideLobe Level (MSLL) demonstrate the effectiveness of the proposed method.<\/jats:p>","DOI":"10.3390\/s21206939","type":"journal-article","created":{"date-parts":[[2021,10,20]],"date-time":"2021-10-20T21:31:26Z","timestamp":1634765486000},"page":"6939","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Synthesis of Planar Circular Arrays with Quantized Amplitude Weights"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9549-5602","authenticated-orcid":false,"given":"Zhiqiu","family":"He","sequence":"first","affiliation":[{"name":"Electronic Information School, Wuhan University, Wuhan 430072, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6690-4024","authenticated-orcid":false,"given":"Gang","family":"Chen","sequence":"additional","affiliation":[{"name":"Electronic Information School, Wuhan University, Wuhan 430072, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2689","DOI":"10.1109\/JSTARS.2021.3057610","article-title":"Design of the New MST Radar in Chinese Meridian Project","volume":"14","author":"Chen","year":"2021","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1109\/MAP.2015.2397154","article-title":"Antenna Array Developments: A Perspective on the Past, Present and Future","volume":"57","author":"Haupt","year":"2015","journal-title":"IEEE Antennas Propag. Mag."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1109\/TAP.1962.1137887","article-title":"Space tapaering of linear and planar arrays","volume":"10","author":"Willey","year":"1962","journal-title":"IRE Trans. Antennas Propag."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"408","DOI":"10.1109\/TAP.1964.1138239","article-title":"Statistically designed density-tapered arrays","volume":"12","author":"Skolnik","year":"1964","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"993","DOI":"10.1109\/8.299602","article-title":"Thinned arrays using genetic algorithms","volume":"42","author":"Haupt","year":"1994","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_6","unstructured":"Chen, D., and Li, J. (2009, January 23\u201327). GA design of large thinned arrays. Proceedings of the 2009 3rd European Conference on Antennas and Propagation, Berlin, Germany."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"556","DOI":"10.1109\/TAP.2007.891552","article-title":"Advances in Particle Swarm Optimization for Antenna Designs: Real-Number, Binary, Single-Objective and Multiobjective Implementations","volume":"55","author":"Jin","year":"2007","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3359","DOI":"10.1109\/TAP.2009.2029382","article-title":"Large Planar Array Thinning Using Iterative FFT Techniques","volume":"57","author":"Keizer","year":"2009","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1555","DOI":"10.1109\/TAP.2013.2267194","article-title":"Synthesis of Thinned Planar Circular and Square Arrays Using Density Tapering","volume":"62","author":"Keizer","year":"2014","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1564","DOI":"10.1109\/TAP.2014.2302836","article-title":"Synthesis of Large Thinned Planar Arrays Using a Modified Iterative Fourier Technique","volume":"62","author":"Wang","year":"2014","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"4025","DOI":"10.1109\/TAP.2018.2842258","article-title":"Dynamic Programming Applied to Large Circular Arrays Thinning","volume":"66","author":"Tohidi","year":"2018","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"7320","DOI":"10.1109\/TAP.2019.2931959","article-title":"An Efficient Approach for the Synthesis of Large Sparse Planar Array","volume":"67","author":"Gu","year":"2019","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_13","first-page":"1","article-title":"Antenna Array Design by Artificial Bee Colony Algorithm With Similarity Induced Search Method","volume":"55","author":"Wang","year":"2019","journal-title":"IEEE Trans. Magn."},{"key":"ref_14","first-page":"234","article-title":"Synthesis of antenna arrays using artificial bee colony optimization algorithm","volume":"6","author":"Zaman","year":"2011","journal-title":"Int. J. Microw. Opt. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Zaman, M.A., and Matin, M.A. (2012). Nonuniformly Spaced Linear Antenna Array Design Using Firefly Algorithm. Int. J. Microw. Sci. Technol.","DOI":"10.1155\/2012\/256759"},{"key":"ref_16","unstructured":"Johnson, J., and Rahmat-samii, Y. (1994, January 20\u201324). Genetic algorithm optimization and its application to antenna design. Proceedings of the IEEE Antennas and Propagation Society International Symposium and URSI National Radio Science Meeting, Seattle, WA, USA."},{"key":"ref_17","first-page":"71","article-title":"Design and analysis of multi-step amplitude quantization weighted 2-D solid-state active phased array antennas","volume":"11","author":"Gao","year":"1994","journal-title":"J. Electron."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1157","DOI":"10.1109\/TAP.2011.2173119","article-title":"Amplitude-Only Low Sidelobe Synthesis for Large Thinned Circular Array Antennas","volume":"60","author":"Keizer","year":"2012","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1066","DOI":"10.1109\/TAP.1987.1144224","article-title":"An improved thinning method for density tapering of planar array antennas","volume":"35","author":"Numazaki","year":"1987","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_20","unstructured":"Ball, G.J. (1989, January 4\u20137). Statistical density and amplitude tapering. Proceedings of the 1989 Sixth International Conference on Antennas and Propagation, ICAP 89 (Conf. Publ. No.301), Coventry, UK."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1109\/8.81455","article-title":"Statistically thinned arrays with quantized element weights","volume":"39","author":"Mailloux","year":"1991","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_22","unstructured":"Shao, Z., Wang, J., and Luo, W. (2011, January 26\u201330). An improved method of designing of statically thinned arrays with quantized element weights. Proceedings of the 2011 Cross Strait Quad-Regional Radio Science and Wireless Technology Conference, Harbin, China."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"042078","DOI":"10.1088\/1755-1315\/252\/4\/042078","article-title":"Amplitude Quantization Techniques of Aperture Distribution in Phased Array Antennas","volume":"252","author":"Liu","year":"2019","journal-title":"IOP Conf. Ser. Earth Environ. Sci."},{"key":"ref_24","first-page":"79","article-title":"Multistep Sparse Technology in Arrays","volume":"27","author":"Li","year":"1999","journal-title":"Acta Electron. Sin."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"e2019JA027532","DOI":"10.1029\/2019JA027532","article-title":"A Case Study of the Daytime Intense Radar Backscatter and Strong Ionospheric Scintillation Related to the Low-Latitude E-Region Irregularities","volume":"125","author":"Chen","year":"2020","journal-title":"J. Geophys. Res. Space Phys."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"e2020GL090517","DOI":"10.1029\/2020GL090517","article-title":"Unexpected High Occurrence of Daytime F-Region Backscatter Plume Structures Over Low Latitude Sanya and Their Possible Origin","volume":"47","author":"Xie","year":"2020","journal-title":"Geophys. Res. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1029\/RS019i001p00441","article-title":"The mobile SOUSY Doppler radar: Technical design and first results","volume":"19","author":"Czechowsky","year":"1984","journal-title":"Radio Sci."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1125","DOI":"10.1029\/95RS00787","article-title":"Indian MST radar 1. System description and sample vector wind measurements in ST mode","volume":"30","author":"Rao","year":"1995","journal-title":"Radio Sci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1109\/MAP.2004.1374097","article-title":"Space-tapered circular (ring) array","volume":"46","author":"Milligan","year":"2004","journal-title":"IEEE Antennas Propag. Mag."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2852","DOI":"10.1109\/TAP.2011.2158783","article-title":"A Deterministic Two Dimensional Density Taper Approach for Fast Design of Uniform Amplitude Pencil Beams Arrays","volume":"59","author":"Bucci","year":"2011","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1627","DOI":"10.1109\/TAP.2013.2281519","article-title":"Array Antennas With Jointly Optimized Elements Positions and Dimensions Part II: Planar Circular Arrays","volume":"62","author":"Angeletti","year":"2014","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"217","DOI":"10.2528\/PIER10010104","article-title":"A Deterministic Approach to the Synthesis of Pencil Beams Through Planar Thinned Arrays","volume":"101","author":"Bucci","year":"2010","journal-title":"Prog. Electromagn. Res."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1109\/TAP.1960.1144807","article-title":"Design of circular apertures for narrow beamwidth and low sidelobes","volume":"8","author":"Taylor","year":"1960","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1386","DOI":"10.1109\/LAWP.2009.2039189","article-title":"Optimal Synthesis of Directivity Constrained Pencil Beams by Means of Circularly Symmetric Aperture Fields","volume":"8","author":"Bucci","year":"2009","journal-title":"IEEE Antennas Wirel. Propag. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1109\/MAP.2010.5525565","article-title":"APAS: An Advanced Phased-Array Simulator","volume":"52","author":"Keizer","year":"2010","journal-title":"IEEE Antennas Propag. 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