{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:13:58Z","timestamp":1760148838494,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2023,6,10]],"date-time":"2023-06-10T00:00:00Z","timestamp":1686355200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>A split-aperture array (SAA) is an array of sensors or antenna elements in which the array is split into two or more sub-arrays (SAs). Recently proposed SAAs, namely coprime and semi-coprime arrays, offer to attain a small half-power beamwidth (HPBW) with a small number of elements, compared to most conventional unified-aperture arrays, at the cost of reduced peak-to-side-lobe ratio (PSLR). To reduce HPBW and increase PSLR, non-uniform inter-element spacing and excitation amplitudes have proven helpful. However, all the existing arrays and beam-formers suffer increased HPBW, degraded PSLR or both when the main beam is steered away from the broadside. In this paper, we propose staggered beam-steering of SAs, a novel technique for decreasing HPBW. In this technique, we steer the main beams of the SAs of a semi-coprime array to angles slightly different from the desired steering angle. In conjunction with staggered beam-steering of SAs, we have utilized Chebyshev weights to suppress the side lobes. The results show that the beam-widening effect of Chebyshev weights can be mitigated considerably by staggered beam-steering of the SAs. Ultimately, the unified beam-pattern of the whole array offers HPBW and PSLR better than the existing SAAs, uniform and non-uniform linear arrays, especially when the desired steering angle is away from the broadside direction.<\/jats:p>","DOI":"10.3390\/s23125484","type":"journal-article","created":{"date-parts":[[2023,6,12]],"date-time":"2023-06-12T02:28:42Z","timestamp":1686536922000},"page":"5484","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Semi-Coprime Array with Staggered Beam-Steering of Sub-Arrays"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7962-3232","authenticated-orcid":false,"given":"Waseem","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Electrical and Computer Engineering, Air University, Islamabad 44000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7610-9948","authenticated-orcid":false,"given":"Saleem","family":"Shahid","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Air University, Islamabad 44000, Pakistan"}]},{"given":"Waleed","family":"Iqbal","sequence":"additional","affiliation":[{"name":"Department of Avionics Engineering, Air University, Islamabad 44000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1014-3622","authenticated-orcid":false,"given":"Ahsan Sarwar","family":"Rana","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Air University, Islamabad 44000, Pakistan"}]},{"given":"Hijab","family":"Zahra","sequence":"additional","affiliation":[{"name":"School of Engineering, Faculty of Science and Engineering, Macquarie University, Sydney, NSW 2109, Australia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0647-5459","authenticated-orcid":false,"given":"Moath","family":"Alathbah","sequence":"additional","affiliation":[{"name":"College of Engineering, King Saud University, Riyadh 11451, Saudi Arabia"},{"name":"School of Engineering, Cardiff University, Cardiff CF24 3AA, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6390-0896","authenticated-orcid":false,"given":"Syed Muzahir","family":"Abbas","sequence":"additional","affiliation":[{"name":"School of Engineering, Faculty of Science and Engineering, Macquarie University, Sydney, NSW 2109, Australia"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,10]]},"reference":[{"key":"ref_1","unstructured":"Balanis, C.A. (2016). Antenna Theory, Wiley John & Sons."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1109\/TAP.1971.1139918","article-title":"Scanned directivity of linear arrays","volume":"19","author":"Langston","year":"1971","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"4867851","DOI":"10.1155\/2018\/4867851","article-title":"An antenna array sidelobe level reduction approach through invasive weed optimization","volume":"2018","author":"Sun","year":"2018","journal-title":"Int. J. Antennas Propag."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1007\/s10470-020-01612-1","article-title":"A novel algorithm in a linear phased array system for side lobe and grating lobe level reduction with large element spacing","volume":"104","author":"Khalilpour","year":"2020","journal-title":"Analog. Integr. Circuits Signal Process."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Khan, W., Saeed, S., and ur Rehman, A. (2019, January 12\u201315). Linear Antenna-Array with Log-increasing Inter-element Spacing and Non Uniform Weights. Proceedings of the 2019 1st Global Power, Energy and Communication Conference (GPECOM), Nevsehir, Turkey.","DOI":"10.1109\/GPECOM.2019.8778496"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"256759","DOI":"10.1155\/2012\/256759","article-title":"Nonuniformly Spaced Linear Antenna Array Design Using Firefly Algorithm","volume":"2012","author":"Zaman","year":"2012","journal-title":"Int. J. Microw. Sci. Technol."},{"key":"ref_7","first-page":"e21754","article-title":"To control the beamwidth of antenna arrays by virtually changing inter-distances","volume":"29","year":"2019","journal-title":"Int. J. RF Microw. Comput.-Aided Eng."},{"key":"ref_8","unstructured":"Ridwan, M., Abdo, M., and Jorswieck, E. (2011, January 13\u201316). Design of non-uniform antenna arrays using genetic algorithm. Proceedings of the 13th International Conference on Advanced Communication Technology (ICACT2011), Gangwon, Republic of Korea."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1515\/aee-2016-0001","article-title":"Optimum design of non-uniform symmetrical linear antenna arrays using a novel modified invasive weeds optimization","volume":"65","author":"Kenane","year":"2016","journal-title":"Arch. Electr. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1590\/2179-10742017v16i2913","article-title":"Analysis of linear antenna array for minimum side lobe level, half power beamwidth, and nulls control using PSO","volume":"16","author":"Rahman","year":"2017","journal-title":"J. Microw. Optoelectron. Electromagn. Appl."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1080\/09205071.2016.1268074","article-title":"Array pattern optimization for steerable linear isotropic antenna array using novel particle swarm optimization","volume":"31","author":"Banerjee","year":"2017","journal-title":"J. Electromagn. Waves Appl."},{"key":"ref_12","first-page":"317","article-title":"Antenna array synthesis using a newly evolved optimization approach: Strawberry algorithm","volume":"70","author":"Subhashini","year":"2019","journal-title":"J. Electr. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Enache, F., Deparateanu, D., and Popescu, F. (2017, January 25\u201327). Optimization of non-uniform linear antenna array with linear and parabolic parameters variations. Proceedings of the 2017 International Conference on Optimization of Electrical and Electronic Equipment (OPTIM) & 2017 Intl Aegean Conference on Electrical Machines and Power Electronics (ACEMP), Brasov, Romania.","DOI":"10.1109\/OPTIM.2017.7974965"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"185","DOI":"10.2528\/PIERM08072302","article-title":"Nonuniformly spaced linear array design for the specified beamwidth\/sidelobe level or specified directivity\/sidelobe level with coupling consideration","volume":"4","author":"Oraizi","year":"2008","journal-title":"Prog. Electromagn. Res. M"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"68","DOI":"10.25103\/jestr.041.10","article-title":"Phased Array Synthesis Using Modified Particle Swarm Optimization","volume":"4","author":"Zaman","year":"2011","journal-title":"J. Eng. Sci. Technol. Rev."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"37664","DOI":"10.1109\/ACCESS.2020.2976127","article-title":"Sidelobe Reductions of Antenna Arrays via an Improved Chicken Swarm Optimization Approach","volume":"8","author":"Liang","year":"2020","journal-title":"IEEE Access"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"5904018","DOI":"10.1155\/2020\/5904018","article-title":"Optimal Pattern Synthesis of Linear Array and Broadband Design of Whip Antenna Using Grasshopper Optimization Algorithm","volume":"2020","author":"Wang","year":"2020","journal-title":"Int. J. Antennas Propag."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"139601","DOI":"10.1109\/ACCESS.2019.2944109","article-title":"Design and Statistical Analysis of Tapered Coprime and Nested Arrays for the Min Processor","volume":"7","author":"Adhikari","year":"2019","journal-title":"IEEE Access"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1109\/JRPROC.1946.225956","article-title":"A Current Distribution for Broadside Arrays Which Optimizes the Relationship between Beam Width and Side-Lobe Level","volume":"34","author":"Dolph","year":"1946","journal-title":"Proc. IRE"},{"key":"ref_20","first-page":"11","article-title":"Adaptive Beam Formation in Smart Antenna Using Tschebyscheff Distribution and Variants of Least MeanSquare Algorithm","volume":"22","author":"Senapati","year":"2016","journal-title":"Mikrotalasna Rev."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"814","DOI":"10.1109\/LGRS.2019.2930817","article-title":"A Novel NLFM Waveform with Low Sidelobes Based on Modified Chebyshev Window","volume":"17","author":"Zhang","year":"2019","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"7905","DOI":"10.1109\/TAP.2020.3000575","article-title":"Compact Series-Fed Microstrip Patch Arrays Excited with Dolph\u2013Chebyshev Distributions Realized with Slow Wave Transmission Line Feed Networks","volume":"68","author":"Li","year":"2020","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_23","first-page":"333","article-title":"IFT and Chebyshev-based planar array thinning for adaptive interference suppression","volume":"22","author":"Agha","year":"2023","journal-title":"J. Comput. Electron."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Xu, S., Xu, H.X., Wang, Y., Xu, J., Wang, C., Pang, Z., and Luo, H. (2022). Circularly Polarized Antenna Array with Decoupled Quad Vortex Beams. Nanomaterials, 12.","DOI":"10.3390\/nano12173083"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1801479","DOI":"10.1002\/adom.201801479","article-title":"Chirality-Assisted High-Efficiency Metasurfaces with Independent Control of Phase, Amplitude, and Polarization","volume":"7","author":"Xu","year":"2019","journal-title":"Adv. Opt. Mater."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1797","DOI":"10.1109\/TAP.2017.2673814","article-title":"Dual-Mode Transmissive Metasurface and Its Applications in Multibeam Transmitarray","volume":"65","author":"Xu","year":"2017","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1109\/TSP.2010.2089682","article-title":"Sparse sensing with co-prime samplers and arrays","volume":"59","author":"Vaidyanathan","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Liu, Y., and Buck, J.R. (2015, January 8\u201311). Detecting Gaussian signals in the presence of interferers using the coprime sensor arrays with the min processor. Proceedings of the 2015 49th Asilomar conference on signals, systems and computers, Pacific Grove, CA, USA.","DOI":"10.1109\/ACSSC.2015.7421150"},{"key":"ref_29","first-page":"964","article-title":"Passive beamforming with coprime arrays","volume":"11","author":"Iodice","year":"2016","journal-title":"IET Radar Sonar Navig."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"614","DOI":"10.1049\/iet-spr.2018.5517","article-title":"Novel method for digital beamforming in co-prime sensor arrays using product and min processors","volume":"13","author":"Moghadam","year":"2019","journal-title":"IET Signal Process."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1186\/1687-6180-2014-148","article-title":"Extending coprime sensor arrays to achieve the peak side lobe height of a full uniform linear array","volume":"148","author":"Adhikari","year":"2014","journal-title":"EURASIP J. Adv. Signal Process."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Adhikari, K., Buck, J.R., and Wage, K.E. (2013, January 26\u201331). Beamforming with extended co-prime sensor arrays. Proceedings of the 2013 IEEE international conference on acoustics, speech and signal processing, Vancouver, BC, Canada.","DOI":"10.1109\/ICASSP.2013.6638447"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2841","DOI":"10.1121\/1.5100281","article-title":"Beamforming with semi-coprime arrays","volume":"145","author":"Adhikari","year":"2019","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"135","DOI":"10.2528\/PIERB09072309","article-title":"The multi-objective optimization of non-uniform linear phased arrays using the genetic algorithm","volume":"17","author":"Tokan","year":"2009","journal-title":"Prog. Electromagn. Res. B"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"785","DOI":"10.1109\/TAES.1973.309781","article-title":"Properties of Dolph-Chebyshev Weighting Functions","volume":"AES-9","author":"Ward","year":"1973","journal-title":"IEEE Trans. Aerosp. Electron. Syst."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/12\/5484\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:52:13Z","timestamp":1760125933000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/12\/5484"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,10]]},"references-count":35,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2023,6]]}},"alternative-id":["s23125484"],"URL":"https:\/\/doi.org\/10.3390\/s23125484","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2023,6,10]]}}}