The principle of sequential rotation, a well-known method to arrange the radiating elements of antenna arrays, is briefly described, and the impact on the polarization of different antenna array configurations is presented. The influence of the number of rotations and rotation angles is investigated, and arrangements for optimized polarization quality of antenna arrays are shown, which are of significant importance for current and future communications systems.</p

K. Kuhlmann

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Adv. Radio Sci., 20, 17–21, 2023https://doi.org/10.5194/ars-20-17-2023© Author(s) 2022. This work is distributed underthe Creative Commons Attribution 4.0 License.Sequential Rotation of Antenna Array Elements –Rotation Angle for Optimum Array PolarizationKarsten KuhlmannDepartment 2.2, High Frequency and Electromagnetic Fields, Physikalisch-Technische Bundesanstalt (PTB),Bundesallee 100, 38116 Braunschweig, GermanyCorrespondence: Karsten Kuhlmann (karsten.kuhlmann@ptb.de)Received: 31 January 2022 – Revised: 9 September 2022 – Accepted: 12 September 2022 – Published: 21 March 2023Abstract. The principle of sequential rotation, a well-knownmethod to arrange the radiating elements of antenna arrays, isbriefly described, and the impact on the polarization of differ-ent antenna array configurations is presented. The influenceof the number of rotations and rotation angles is investigated,and arrangements for optimized polarization quality of an-tenna arrays are shown, which are of significant importancefor current and future communications systems.1 IntroductionThe principle of sequential rotation is an established methodto arrange the radiating elements of antenna arrays. Thoughthe design can become more complex compared to arrayswithout rotated elements, there are two main applications.The first one is to improve the AR (axial ratio) of CP (circu-lar polarization). AR defines the quality of CP as magnituderatio of a TEM (transverse electromagnetic) wave’s two or-thogonal and 90◦ phase shifted field vectors. Three cases aredistinguished:1. CP (Circular polarization): 1 < AR≤ 2,2. EP (Elliptical polarization): 2 < AR≤ 10,3. LP (Linear polarization): 10 < AR≤∞.In antenna arrays intended for CP the single elements oftenexhibit only EP. This is e.g. due to manufacturing cost reduc-tion or other design aspects. But the sequential rotation ofsuch elements still may improve the array performance sig-nificantly (Pozar and Schaubert, 1995; Smith, 1991).The second main application is the usage of sequentiallyrotated linearly polarized single elements to get a circularlypolarized antenna array (Huang, 1986; Hall et al., 1989). Thisapproach allows for a very simple antenna element design. Ifthe phase relations between the elements are adjustable likee.g. for phased arrays or in systems for DBF (digital beamforming), both left-handed and right-handed CP can be real-ized.In addition to the improved polarization quality, the prin-ciple of sequential rotation will also enhance the symmetryof antenna array radiation characteristics, as it introduces asort of averaging for the potential asymmetrical single el-ement radiation characteristic. Indeed, the only real draw-backs of this method are the potential excitation of gratinglobes (Kuhlmann, 2013) and a more complex design, espe-cially in highly integrated active antenna arrays like e.g. forsatellite communication (Kuhlmann and Jacob, 2010) or cur-rent and future communications standards 5G and 6G.The importance of sequential rotation in antenna arrays isfurther supported by more than 400 publications about theusage of this method, listed at IEEE Explore between 2010and 2022. The applications, frequency ranges, and array sizesvary a lot, but, to the author’s knowledge, no recent publica-tion investigates the topic presented here. Usually the arrayelements are rotated by 90◦ on rectangular grids to e.g. im-prove polarization quality, sometimes by 180◦. The latter, aswill be seen in the next section, might not have brought thedesired result.This paper investigates the fundamental building blocks ofpotentially large arrays. The questions it answers are:– What is theoretically the minimal required distributionof elements to achieve a perfect CP?– Which distributions do not improve the polarizationquality but unnecessarily increase the design complex-ity?Published by Copernicus Publications on behalf of the URSI Landesausschuss in der Bundesrepublik Deutschland e.V.18 K. Kuhlmann: Sequential Rotation of Antenna Array ElementsAs it would lead to too many combinations to investigate,this paper does not discuss:– Type of single element radiator (patch, horn, . . .),– Array type (linear, planar, spatial),– Grid (rectangular, triangular, . . .),– Element distance (determines grating lobes and scan-ning range).Further information on these four topics as well as mutualcoupling can be found in e.g. Kuhlmann and Jacob (2009)and Kuhlmann (2013). Here (Kuhlmann, 2021), only arraysconsisting of perfect isotropic radiators are considered, andthe AF (array factor) is calculated for the main direction. Asis known from antenna theory, a simple multiplication of theAF with a simulated or measured antenna yields a completeradiation diagram. There is basically no limit to complexity.E.g. if the application requires two different polarized an-tenna arrays, either using the same grid (dual-polarized el-ements) or on different grids (Jaschke, 2021), the result isgained by superposition.In Sect. 2 of this paper, the mathematical definitions forpolarization calculations and some examples are given, inSect. 3, several cases are studied, and in Sect. 4 some cur-rent and future applications are examined.2 Fundamentals of sequential rotationAt first, some definitions are introduced. For a referenceplane (here xy) which is orthogonal to the direction of radi-ation (here z) the four main polarizations have the followingnormalized field vectors:Left-handed CP: eLHCP =(1j)1√2, (1)Right-handed CP: eRHCP =(1−j)1√2, (2)Horizontal LP: eHP =(10), (3)Vertical LP: eVP =(01). (4)This is valid for transmit antennas. For receive antennas thevectors for RCHP and LCHP must be exchanged (Pozar,2005). For the principle of sequential rotation the elementsare usually rotated by 360◦/N , N being the number of ele-ments of the antenna array. E.g., for a two element array therotation angle is 180◦, and for a four element array it is 90◦.Both cases are depicted in Fig. 1. Also shown is an imperfectAR for each element represented as two orthogonal arrowswith unequal length.Large antenna arrays are usually assembled from severalsmaller sub arrays or subgroups, thus following a modularFigure 1. Subgroups for antenna arrays with two (a) and four (b) se-quentially rotated elements.principle, which enables to adapt the array size to applica-tions with different requirements. To get the AR of a sub-group, the vectorial AF must be calculated. In main directionof the array an electrical phase equal to the rotation angle ofthe element is added. A left-handed CP with AR= 2 leads to(no normalization)AF=(2j)+(−2−j)ej180◦=(42j)(5)for a two element subgroup and toAF=(2j)+(−j2)ej90◦+(−2−j)ej180◦+(j−2)ej270◦AF=(66j)(6)for a four element subgroup. As can be seen from Eq. (5), inany array with elements rotated by 180◦ the AR of the sin-gle antenna will not be improved. In Eq. (6) however, the ARis ideal. Indeed, this is true for any AR and any size of sub-group, as long as there are more than two elements, a rotationby 360◦/N , and the AR is identical for each element. This isexamplarily depicted in Fig. 2 for N = 1. . .4 elements and anAR of the single element between 1 and 4.If for some reasons (manufacturing tolerance, element po-sition, etc.) the AR is slightly different for each element, anearly ideal CP is still achievable, as long as the AR dif-ferences are equally distributed for many elements. Evenif the elements are linearly polarized (AR=∞), the polar-ization of the array is perfectly circular. Although depend-ing on the element distance, cross-polarized grating lobes(e.g. right-handed CP instead of left-handed CP) might oc-cur. This effect cannot be completely avoided, but it can bereduced by sequentially rotated subgroups (Hall and Smith,1993, 1994; Thiel and Dreher, 2004) or by introducing ran-dom techniques (Smolders and Visser, 2014).3 Case studiesIn Sect. 2 it has been shown, that the CP of a sequentiallyrotated antenna array is ideal for three or more elements perAdv. Radio Sci., 20, 17–21, 2023 https://doi.org/10.5194/ars-20-17-2023K. Kuhlmann: Sequential Rotation of Antenna Array Elements 19Figure 2. AR for antenna arrays with sequentially rotated elements.Figure 3. AR for antenna arrays with two sequentially rotated ele-ments vs. AR of single element.subgroup, and it is identical to the element’s AR for one el-ement or two elements per subgroup. In Fig. 3, the AR of atwo element subgroup with different rotation angles is pre-sented. For 0 and 180◦, the AR is not improved, while it isperfect (AR= 1) for 90◦, even with only two elements. Inbetween the AR changes gradually.Figure 4 shows the same study for a three element sub-group. For this case the polarization is perfectly circular forthe angles 45, 60, 120, and 135◦. Just as for the two elementsubgroup, the range from 180 to 360◦ is a repetition of therange 0 to 180◦.Figure 4. AR for antenna arrays with three sequentially rotated el-ements vs. AR of single element.To better investigate the rotation angle dependency itself,in Fig. 5 ARarray for the three element subgroup is plotted vs.the rotation angle instead of ARsingle. And in Fig. 6 the AR isplotted vs. the rotation angle for different subgroup sizes. Forthe rotation angle 180◦ (and 360◦) the AR of the array fol-lows the AR of the single element. All other rotation anglesimprove the AR. The range from 180 to 360◦ is symmetricalto the range 0 to 180◦ with 180◦ being the mirror plane ofsymmetry. The number of rotation angles which achieve per-fect CP increases with the number of subgroup elements. Foran infinite number of elements, the AR is one for all rotationsangles except for 0 and 180◦. Also, the AR is always one foran even number of subgroup elements and a rotation angle of90◦.4 ApplicationsIn the telecommunications standard 5G antenna arrays at mi-crowave and millimeter wave frequencies are introduced andof high importance for success (5G Lab, 2016). Especiallymultiple beam capabilities for base stations will be essentialto enable the required number of connections, the high band-width for each user, and the small latency (∼ 1 ms) in realtime applications.Apart from mobile phones, many smart devices like vehi-cles or buildings will be part of a large network (Internet ofThings – IoT). For autonomous systems the connection sta-bility is of outmost importance. Not all but many of thesenew applications are candidates for use of antenna arrays.https://doi.org/10.5194/ars-20-17-2023 Adv. Radio Sci., 20, 17–21, 202320 K. Kuhlmann: Sequential Rotation of Antenna Array ElementsFigure 5. AR for antenna arrays with three sequentially rotated el-ements vs. rotation angle, ARsingle = 4.Figure 6. AR for antenna arrays with sequentially rotated elementsvs. rotation angle, ARsingle = 4.While base station antenna arrays might be realized conven-tionally on rectangular grids, indoor antennas might utilizeother shapes, e.g. triangular or circular grids (Airrays GmbH,2016; see Fig. 7).Applying the results presented here, the rotation angles ofthe elements can be optimized. If e.g. a subgroup size withseven elements is chosen, there are eleven additional rotationangles aside from 360/7= 51.43◦, as is depicted in Fig. 8.A small subgroup might be the base for building largeplanar arrays on a triangular grid, which is shown in Fig. 9(left, no element rotation shown). For indoor communication,placing antennas in the upper room corners might be prefer-able, thus a triangular shape as depicted in Fig. 9 (center,no element rotation shown) could be advantageous. In lin-ear antenna array subgroups feeding all elements from oneside could be essential for the system design, e.g. to avoidFigure 7. Antenna array configurations for next generation mobilecommunication base stations (Airrays GmbH, 2016). Outdoor units:4× 16 and 8× 8 elements. Indoor unit: 16 elements arranged on acircle (ceiling mounted).Figure 8. AR for antenna arrays with seven sequentially rotatedelements vs. rotation angle (ARsingle = 4). Angles for ARarray = 1are indicated by circles and the numbers are given in the box.vias (electrical connection between layers) and subsequentlyunnecessary many layers in PCBs (Printed Circuit Boards).This might lead to choose the rotation angle as small as possi-ble. For a seven element subgroup the smallest rotation anglefor ideal CP is 15◦, as is shown in Fig. 9 (right).Several other scenarios for mobile communication (anten-nas on pillars, circle segments, conformal arrays) might alsoprofit from using non-standard rotation angles.5 ConclusionsIn antenna arrays perfect single radiators are not realizable.Unwanted differences between elements will further impedeefficient operation. It has been shown in this paper, that aAdv. Radio Sci., 20, 17–21, 2023 https://doi.org/10.5194/ars-20-17-2023K. Kuhlmann: Sequential Rotation of Antenna Array Elements 21Figure 9. Examples of antenna array subgroups.smart approach of placing and rotating the elements on asuitable grid will improve the radiation characteristics of theantenna array. This effect will be most efficient, if the sin-gle radiators show only medium polarization quality, like e.g.mass produced inexpensive devices used in IoT applications.This study gives advice to design sequentially rotated anten-nas with optimized rotation angles.Code and data availability. No software code or research data isavailable for the presented work, but all results can be reproducedwith the equations and parameters given here.Competing interests. The author has declared that there are nocompeting interests.Disclaimer. Publisher’s note: Copernicus Publications remainsneutral with regard to jurisdictional claims in published maps andinstitutional affiliations.Special issue statement. This article is part of the special issue“Kleinheubacher Berichte 2021”.Acknowledgements. The author would like to thankFrauke Gellersen and Thomas Kleine-Ostmann from PTB forvaluable discussions and checking the manuscript (proofreading).Financial support. This open-access publication was funded by thePhysikalisch-Technische Bundesanstalt.Review statement. This paper was edited by Ludger Klinkenbuschand reviewed by two anonymous referees.References5G Lab: 5G Summit, http://www.5gsummit.org/dresden-2016/ (lastaccess: 2 October 2022), 2016.Airrays GmbH: Smart basestation antenna for next generation mo-bile communication, http://www.airrays.com/ (last access: May2019), 2016.Hall, P. S. and Smith, M. S.: Reduction of Grating Lobes in Se-quentially Rotated Microstrip Patch Arrays, in: Eighth Interna-tional Conference on Antennas and Propagation, Edinburgh, UK,30 March–2 April 1993, 364–367, https://ieeexplore.ieee.org/abstract/document/224699 (last access: 2 October 2022), 1993.Hall, P. S. and Smith, M. S.: Sequentially Rotated Arrays with Re-duced Sidelobe Levels, IEE Proceedings: Microwaves, Anten-nas and Propagation, 141, 321–325, https://doi.org/10.1049/ip-map:19941193 , 1994.Hall, P. S., Huang, J., Rammons, E., and Roederer, A.: Gain of Cir-cularly Polarised Arrays Composed of Linearly Polarised Ele-ments, Electron. Lett., 25, 124–125, 1989.Huang, J.: A Technique for an Array to generate Circular Polariza-tion with Linearly Polarized Elements, IEEE T. Antenn. Propag.,34, 1113–1124, https://doi.org/10.1109/TAP.1986.1143953,1986.Jaschke, T.: Substrate integrated waveguide technology for Rx/Txintegrated array antennas, PhD thesis, Technische UniversitätHamburg, https://doi.org/10.15480/882.3648, 2021.Kuhlmann, K.: Hochintegrierte aktive Sendeantenne für denMillimeterwellenbereich, PhD thesis, Technische UniversitätHamburg-Harburg, https://doi.org/10.15480/882.1086 , 2013.Kuhlmann, K.: Sequential Rotation of Antenna Array Elements– Rotation Angle Optimum, in: Kleinheubacher Tagung, Mil-tenberg, 28–30 September 2021, https://www.kh2021.de/ (lastaccess: 2 October 2022), 2021.Kuhlmann, K. and Jacob, A. F.: Antenna Arrays on Rectangularand Triangular Grids for Polarization Multiplexing – a Compara-tive Study, in: Proc. German Microwave Conference, Munich,Germany, 1–4, https://doi.org/10.1109/GEMIC.2009.4815896 ,2009.Kuhlmann, K. and Jacob, A. F.: Active 30 GHz AntennaArray for Digital Beamforming and Polarization Mul-tiplexing, in: IEEE MTT-S International MicrowaveSymposium Digest, Anaheim, CA, USA, 1276–1279,https://doi.org/10.1109/MWSYM.2010.5514863 , 2010.Pozar, D. M.: Microwave Engineering, 3rd edn., John Wiley &Sons, Inc., ISBN: 9780471644514, 2005.Pozar, D. M. and Schaubert, D. H.: Microstrip Antennas:The Analysis and Design of Microstrip Antennas and Ar-rays, Electrical engineering, antennas and propagation, Wiley,ISBN: 9780780310780, 1995.Smith, M. S.: Grating Lobes of Sequentially Rotated AntennaArrays, in: Seventh International Conference on (IEE) Anten-nas and Propagation, York, UK, 15–18 April 1991, 217–220,https://ieeexplore.ieee.org/document/98215 (last access: 2 Octo-ber 2022), 1991.Smolders, A. B. and Visser, H. J.: Low Side-Lobe Circularly-Polarized Phased Arrays Using a Random Sequential RotationTechnique, IEEE T. Antenn. 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Sequential Rotation of Antenna Array Elements – Rotation Angle for Optimum Array Polarization

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Sequential Rotation of Antenna Array Elements – Rotation Angle for Optimum Array Polarization

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