Design of Parameter-Optimized Spiral Arrays with Ultra-Wideband Grating Lobe Suppression

An effective method is presented to design the layout of spiral array with ultra-wideband (UWB) grating lobe suppression. In this method, the general array factor expression of spiral array is formulated. Then, the synthesis problem of spiral array layout is converted to an optimization problem of t...

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Published inElectronics (Basel) Vol. 12; no. 7; p. 1664
Main Authors Liu, Siqi, Chen, Liyang, Liu, Yanhui
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.04.2023
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ISSN2079-9292
2079-9292
DOI10.3390/electronics12071664

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Abstract An effective method is presented to design the layout of spiral array with ultra-wideband (UWB) grating lobe suppression. In this method, the general array factor expression of spiral array is formulated. Then, the synthesis problem of spiral array layout is converted to an optimization problem of three geometric parameters: s, r and Δϕ. These parameters can determine the exact position of each element. The optimization problem is solved by particle swarm optimization (PSO) algorithm where the constraints of element spacing and array aperture are introduced. For different-sized spiral arrays, there are always only three variables that need to be optimized in the PSO algorithm, which allows the proposed method to handle the layout design of large-scale spiral arrays with UWB grating lobe suppression. Two examples with different synthesis requirements are conducted to verify the effectiveness and advantages of the proposed method.
AbstractList An effective method is presented to design the layout of spiral array with ultra-wideband (UWB) grating lobe suppression. In this method, the general array factor expression of spiral array is formulated. Then, the synthesis problem of spiral array layout is converted to an optimization problem of three geometric parameters: s, r and Δϕ. These parameters can determine the exact position of each element. The optimization problem is solved by particle swarm optimization (PSO) algorithm where the constraints of element spacing and array aperture are introduced. For different-sized spiral arrays, there are always only three variables that need to be optimized in the PSO algorithm, which allows the proposed method to handle the layout design of large-scale spiral arrays with UWB grating lobe suppression. Two examples with different synthesis requirements are conducted to verify the effectiveness and advantages of the proposed method.
Audience Academic
Author Liu, Yanhui
Liu, Siqi
Chen, Liyang
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Cites_doi 10.1049/iet-map.2015.0401
10.1109/TAP.2020.2969741
10.1109/TAP.2012.2220107
10.1109/TAP.2010.2078439
10.1109/TAP.2019.2947180
10.1002/mop.20894
10.23919/URSIGASS.2017.8105205
10.1109/TAP.2007.913145
10.1109/TAP.2018.2860044
10.1109/TAP.2013.2250232
10.1109/TAP.2008.927580
10.1002/mop.30655
10.1002/mop.23148
10.1109/TAP.2020.3016484
10.1109/LPT.2015.2492419
10.1109/TAP.2018.2867031
10.1155/2009/624035
10.1109/JSEN.2020.2971568
10.1109/TAP.2012.2196951
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References Perez (ref_17) 2008; 50
Tzanidis (ref_3) 2013; 66
Zhang (ref_4) 2018; 66
Spence (ref_12) 2008; 56
Fuchs (ref_7) 2012; 60
ref_14
Huang (ref_22) 2018; 66
Gong (ref_6) 2021; 69
Gregory (ref_13) 2013; 61
ref_20
Zhang (ref_1) 2017; 59
Lin (ref_8) 2020; 60
Liu (ref_21) 2020; 68
Oliveri (ref_10) 2020; 68
ref_19
ref_18
Garza (ref_5) 2016; 10
Eldek (ref_2) 2005; 46
ref_16
Gabrielli (ref_15) 2016; 28
Spence (ref_11) 2010; 58
Keizer (ref_9) 2008; 56
References_xml – volume: 10
  start-page: 347
  year: 2016
  ident: ref_5
  article-title: Synthesis of sparse circular antenna arrays applying a tapering technique over reconstructed continuous current distribution
  publication-title: IET Microw. Antennas Propag.
  doi: 10.1049/iet-map.2015.0401
– volume: 68
  start-page: 4406
  year: 2020
  ident: ref_21
  article-title: Synthesis of large unequally spaced planar arrays utilizing differential evolution with new encoding mechanism and cauchy mutation
  publication-title: IEEE Trans. Antennas Propag.
  doi: 10.1109/TAP.2020.2969741
– volume: 61
  start-page: 176
  year: 2013
  ident: ref_13
  article-title: Exploiting rotational symmetry for the design of ultra-wideband planar phased array layouts
  publication-title: IEEE Trans. Antennas Propag.
  doi: 10.1109/TAP.2012.2220107
– volume: 58
  start-page: 3931
  year: 2010
  ident: ref_11
  article-title: Generalized space-filling gosper curves and their application to the design of wideband modular planar antenna arrays
  publication-title: IEEE Trans. Antennas Propag.
  doi: 10.1109/TAP.2010.2078439
– volume: 68
  start-page: 2895
  year: 2020
  ident: ref_10
  article-title: Autocorrelation-driven synthesis of antenna arrays-the case of DS-based planar isophoric thinned arrays
  publication-title: IEEE Trans. Antennas Propag.
  doi: 10.1109/TAP.2019.2947180
– volume: 46
  start-page: 36
  year: 2005
  ident: ref_2
  article-title: Wideband 2D array of microstrip fed rectangular-slot antennas for radar applications
  publication-title: Microw. Opt. Technol. Lett.
  doi: 10.1002/mop.20894
– ident: ref_16
  doi: 10.23919/URSIGASS.2017.8105205
– volume: 56
  start-page: 76
  year: 2008
  ident: ref_12
  article-title: Design of broadband planar arrays based on the optimization of aperiodic tilings
  publication-title: IEEE Trans. Antennas Propag.
  doi: 10.1109/TAP.2007.913145
– volume: 66
  start-page: 5249
  year: 2018
  ident: ref_22
  article-title: Near-field pattern synthesis for sparse focusing antenna arrays based on Bayesian compressive sensing and convex optimization
  publication-title: IEEE Trans. Antennas Propag.
  doi: 10.1109/TAP.2018.2860044
– volume: 66
  start-page: 3017
  year: 2013
  ident: ref_3
  article-title: UWB low-profile tightly coupled dipole array with integrated balun and edge terminations
  publication-title: IEEE Antenna Wirel. Propag. Lett.
  doi: 10.1109/TAP.2013.2250232
– volume: 56
  start-page: 2757
  year: 2008
  ident: ref_9
  article-title: Linear array thinning using iterative FFT techniques
  publication-title: IEEE Trans. Antennas Propag.
  doi: 10.1109/TAP.2008.927580
– volume: 59
  start-page: 1962
  year: 2017
  ident: ref_1
  article-title: Wideband dual circularly polarized beam-scanning array for Ka-band satellite communications
  publication-title: Microw. Opt. Technol. Lett.
  doi: 10.1002/mop.30655
– volume: 50
  start-page: 627
  year: 2008
  ident: ref_17
  article-title: Particle swarm optimization with tournament selection for linear array synthesis
  publication-title: Microw. Opt. Technol. Lett.
  doi: 10.1002/mop.23148
– volume: 69
  start-page: 869
  year: 2021
  ident: ref_6
  article-title: Synthesis of sparse planar arrays with multiple patterns by the generalized matrix enhancement and matrix pencil
  publication-title: IEEE Trans. Antennas Propag.
  doi: 10.1109/TAP.2020.3016484
– volume: 28
  start-page: 209
  year: 2016
  ident: ref_15
  article-title: Aperiodic antenna array for secondary lobe suppression
  publication-title: IEEE Photon. Technol. Lett.
  doi: 10.1109/LPT.2015.2492419
– ident: ref_18
– ident: ref_19
– volume: 66
  start-page: 6382
  year: 2018
  ident: ref_4
  article-title: A wideband circularly polarized tightly coupled array
  publication-title: IEEE Trans. Antennas Propag.
  doi: 10.1109/TAP.2018.2867031
– ident: ref_14
  doi: 10.1155/2009/624035
– ident: ref_20
– volume: 60
  start-page: 5554
  year: 2020
  ident: ref_8
  article-title: Optimized design for sparse arrays in 3-D imaging sonar systems based on perturbed bayesian compressive sensing
  publication-title: IEEE Sens. J.
  doi: 10.1109/JSEN.2020.2971568
– volume: 60
  start-page: 3499
  year: 2012
  ident: ref_7
  article-title: Synthesis of sparse arrays with focused or shaped beampattern via sequential convex optimizations
  publication-title: IEEE Trans. Antennas Propag.
  doi: 10.1109/TAP.2012.2196951
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SubjectTerms Algorithms
Antenna arrays
Antennas
Arrays
Design and construction
Design optimization
Design parameters
Genetic algorithms
Layouts
Mathematical optimization
Methods
Optimization
Particle swarm optimization
Radiation
Synthesis
Ultra wideband technology
Ultrawideband
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