Reactively Loaded Dielectric-Based Antenna Arrays With Enhanced Bandwidth and Flat-Top Radiation Pattern Characteristics

This paper presents an antenna array organized in sub-arrays and composed of densely spaced dielectric-based radiating elements. To reduce the number of active components required in the array beamforming network, each sub-array consists of a single active element, directly fed, and several passive reactively loaded elements. State-of-the-art implementations of such arrays are typically based on rectangular air-filled waveguide radiators which provide a limited bandwidth and support a single linear polarization only. By utilizing the dielectric-based radiators presented in this work, a significant increase in the operating bandwidth of the array can be achieved. In this case, the aforementioned reactive loading is implemented through short-circuited dielectric-filled waveguides. By optimizing the position of the short circuits, the radiation pattern of the sub-array can be controlled and synthesized according to a given mask. To create larger design flexibility, one can design the sub-array in the presence of the adjacent sub-arrays, achieving in this way their effective overlapping. By employing the considered design technique, a sub-array featuring flat-top radiation pattern characteristics in combination with low side-lobe levels and high gain was developed, manufactured, and thoroughly analyzed. An additional benefit of such a design choice is the possibility of supporting two orthogonal polarizations.


I. INTRODUCTION
Modern satellite and terrestrial communication networks require high flexibility and control in terms of radiation pattern reconfigurability. At the antenna level, this can be achieved by adopting active antenna array architectures with electronically controllable beam-steering and multibeam capabilities [1], [2]. The radiation characteristics of an antenna array depend on the position and excitation of The associate editor coordinating the review of this manuscript and approving it for publication was Lu Guo . the relevant radiating elements, as well as on the type of adopted antenna technology. Although active antenna arrays provide maximum performance flexibility, the relevant costs of implementation and the required power levels are prohibitive for most practical applications, even when arrays of moderate size are considered [3]. In order to deal with these limitations, various antenna array design architectures were proposed [4], [5], [6], [7], [8], [9], [10], [11], [12], [13].
In the case where the required field of view (FoV) is limited, a cost-effective antenna array solution can be realized by combining the radiating elements in sub-arrays and using one transmit/receive channel per sub-array. The disadvantage of such a configuration is the significant separation between the phase center of the various sub-arrays that is typically larger than half-wavelength at the frequency of operation, this leading to the appearance of grating lobes unless these are properly filtered by a flat-top radiation pattern at the level of individual sub-array. Many radiating structures have been proposed in the scientific literature to achieve flat-top radiation pattern characteristics [14], [15], [16], [17], [18], [19]; however, due to their specific geometries [15], [19] and large dimensions in combination with broad beamwidth [14], [16], [17], [18], there is no easy way to adopt those as radiating elements in an array structure, which is meant to deliver high gain and grating lobe free radiation even though in a limited scanning range.
To achieve effective control of the sub-array radiation characteristics while maintaining a large aperture of the radiating elements, the same radiating elements can be re-used in the adjacent sub-arrays achieving, in this way, a sub-array overlapping. A comprehensive overview of antenna arrays with sophisticated feeding structures enabling overlapping use can be found in [4]. Moreover, a recent example of a feeding network with overlapping functionality is presented in [7]. However, such a feeding network is very complex even for arrays with a small number of radiating elements; hence, this implementation concept has found limited application. The complexity of the feeding network can be simplified significantly by using array topologies consisting of both directly fed radiating elements and parasitic passive elements terminated on suitable loads. In such a configuration, the passive elements are fed via a free-space coupling mechanism. Examples of such a configuration can be found in [5] and [6] for dipole arrays whose beam-scanning characteristics are controlled by adjusting loads of suitable parasitic elements. In [10], [11], and [12], the radiated beam of waveguide antenna arrays is shaped by reactive loading of parasitic waveguiding elements. In a more recent study [13], complex magneto-electric dipoles have been used to enhance the antenna's directivity.
In [20], we designed and realized an array of subarrays composed of open-ended waveguide antenna elements. In the considered design, the reactive loads were implemented by parasitic waveguides terminated on short circuits and by properly selecting the relevant length. In this way, we were able to shape the radiation pattern of the individual sub-array and control the scattering parameters at the corresponding ports. The analysis of the radiation properties of a simplified version of such a structure, composed of identical passive metallic waveguide elements, is presented in [21], where multiple electromagnetic radiation regimes involving volume, surface, and leaky waves were identified for the considered class of antennas. The increased complexity of the radiating structure proposed in this study prevents the application of the analysis methodology used in [21]. On the other hand in [20], we have developed a coherent design methodology for reactively loaded overlapping sub-arrays design which is not constrained by the shape and type of the waveguides. The sub-array overlapping was also achieved by taking advantage of the mutual coupling process which occurs between adjacent waveguiding elements. The array structure detailed in [20], however, suffers from a limited operational bandwidth that reduces its practical use. To overcome the aforementioned limitation, we propose here to use reactively loaded dielectric-based radiating elements. As was shown in [22], an additional benefit of such a design choice is the possibility of supporting two orthogonal polarizations. This paper is organized as follows. Section II presents the framework of the semi-analytical design technique implemented for the design of the reactively loaded sub-array. Section III starts with the analysis of the performance of the radiating element and justifies its choice. Next, a linear array of 3-sub-arrays is designed and analyzed. Section III concludes with a theoretical analysis of the performance of a large array based on the previously designed subarray. In Section IV, the 3-sub-array prototype is presented, and its performance is compared with the theoretical study of Section III. Concluding remarks are summarized in Section V.

II. METHODOLOGY
A schematic of an antenna array of randomly distributed N a directly-fed active elements and N p reactively-loading passive elements is shown in Fig. 1. The optimization of the terminations of the various passive elements using a full-wave electromagnetic (EM) solver is extremely timeconsuming. Therefore, to reduce the development time, we exploit the semi-analytical design methodology developed by the authors in [20] that is summarized hereafter. According to [20], the frequency-domain distribution of the total electric field E(θ, ϕ) radiated by the array structure of Fig. 1 can be written as: with the superscript T denoting the matrix transposition and the subscripts a and p referring to the active and passive VOLUME 10, 2022 elements, respectively. Besides, θ and ϕ are the conventional spherical angles. In (1), the vector a a contains the excitation coefficients of the active, directly fed, radiators, whereas the vectors E a (θ, ϕ) and E p (θ, ϕ) are the electric fields radiated by the active and passive elements, respectively. Moreover, the matrices S p and S c denote the blocks of the complete array scattering matrix S that describe, respectively, the interaction between passive waveguides and the coupling process between passive and active waveguides. Lastly, p , γ p , and h p are diagonal matrices containing the reflection coefficients of the loads, the complex propagation coefficients, and lengths of the passive waveguides, respectively. In addition, the scattering matrix of the directly fed elements can be expressed as: Here, S a is the block, in the complete array scattering matrix S, that describes the interaction between directly fed radiating elements. By exploiting (1) and (2), the design of reactively loaded sub-arrays can be accomplished following the procedure hereafter: 1. Set the array topology and determine the minimum number N S of sub-arrays needed to approximate an infinitely large array environment for the central sub-array element and fix the number of elements per sub-array N E . 2. Determine the scattering matrix and the electric fields radiated by the N S × N E elements forming the array structure. 3. Choose a suitable optimization algorithm and set the proper optimization goals selecting from the set of available optimization parameters [ p , γ p , h p ].
4. Use the central sub-array pattern as the embedded element pattern for the design of arrays of any size. Utilizing the proposed design procedure, a reactively loaded array with a shaped radiation pattern and constrained scattering matrix characteristics can be developed and optimized. The proposed design procedure has been implemented in Matlab [23].

A. RADIATING ELEMENT
The choice of the radiating element plays a significant role during the antenna array design stage. First of all, in order to be able to shape the sub-array radiation pattern, the separation between array elements has to be smaller than λ 0 /2, with λ 0 being the free-space wavelength. In [20] and [24], we used, as radiating elements, air-filled rectangular waveguides operating on their fundamental TE 01 mode. This allowed us to keep one of the waveguide dimensions small to densely place the radiating elements and achieve efficient control of the sub-array radiation characteristics. Although we were able to design sub-arrays with nicely shaped radiation patterns and reduced active reflection coefficients at the selected working frequency, the radiation pattern stability over the frequency was rather limited. To overcome this limitation, in this study we propose to use dielectric radiators, terminated by dielectric-filled waveguides. The height of the dielectric radiator is optimized in such a way to achieve maximal radiation efficiency. For comparison reasons, the air-filled rectangular waveguide antenna array structure is shown in Fig. 2a, while in Fig. 2b an array of waveguides filled with extended dielectric rods is presented. In addition, in Fig. 2, the azimuth ϕ and elevation θ angles are defined. The rounding radius of the corners of the air-filled waveguide crosssections is adjusted to achieve the same cut-off frequency as obtained with the dielectric-filled waveguides. In both configurations, the elements are excited by the TE 01 waveguide mode. Table 1 presents the coupling levels between the central radiator, labeled as ''1'', and the adjacent elements on one side of each sub-array presented in Fig. 2. We can readily notice that the coupling levels achievable with the dielectric-based design are typically much larger than those obtained with the air-filled counterpart structure. Furthermore, the dielectric-based radiators are characterized by a reduced input reflection coefficient which translates into a smaller quality factor of the short-circuited ''resonators'' used as loading elements.

B. SUB-ARRAY DESIGN
In the present work, the sub-array design procedure detailed in [20] was utilized. Such a procedure starts with the choice of the number N S of integrated sub-arrays. To enable the overlapping between adjacent sub-arrays, we need to use N S ≥ 3. The simplest sub-array configuration which can be adopted is the one where an individual central directly-fed element is integrated with multiple passive elements symmetrically placed on both sides. In this study, we target an FoV of ±8.5 • around the broadside in combination with an operational bandwidth BW = 500 MHz (19.7-20.2 GHz) at a 10-dB return-loss level. To ensure that the grating lobes are outside the FoV for all the scan angles, the sub-array spacing has to be 3.42λ 0 or smaller wherein the roll-off of the relevant radiation pattern is properly accounted for [25]. Using the dimensions of the dielectric-based elements presented in the previous section while aiming for maximal subarray separation of about 2.5λ h , where λ h is the wavelength at the highest frequency of operation, we end up with a sub-array consisting of 11 elements and having a length L = 2.48λ h . The selected separation places the first grating lobe at ±23.8 • when the array is radiating along the broadside direction and at −15.3 • degrees for the maximum scan angle The scattering matrix S of the 3 × 11 elements array and the embedded radiated electromagnetic field distributions required for the application of the design algorithm were evaluated using a Finite Element Method (FEM) solver implemented in the commercial software CST Microwave Studio [26]. The numerical results collected in this way were then imported into a dedicated optimization tool, which relies on the numerical algorithm described in [20]. The lengths of the passive waveguide elements, h p , were chosen as the design parameters in the sub-array optimization procedure and the following objective function was built: where D denotes the array directivity function and S 11,a is the input reflection coefficient of the active element of the central sub-array when the adjacent sub-arrays are terminated with matched loads. In (3), the two terms in brackets control the optimization of the array radiation pattern in terms of sidelobe level (SLL) for θ ∈ [θ SL , 90 • ] with θ SL = 20 • and in terms of flatness within the FoV for θ ∈ [0 • , θ e ]. Since the considered array is symmetric, we can confine the analysis to the angular range θ ∈ [0, 90 • ] Upon focusing on the three (lower, middle, upper) frequencies f L = 19.7 GHz, f 0 = 20.0 GHz, and f H = 20.2 GHz, the design procedure is turned into the solution of the following minimization problem: where λ g = 10.1mm is the guided wavelength corresponding to the TE 01 mode of the dielectric-filled waveguide at the working frequency, f 0 = 20 GHz. Thanks to the symmetry of the sub-array structure, the number of design parameters is equal to half the number of passive waveguides.
The structure obtained by means of the presented design procedure is shown in Fig. 3, and the relevant optimized waveguide lengths are listed in Table 2, where the numbering starts from the element immediately adjacent to the central waveguide.  To assess the overlapping effect, the central sub-array was directly fed while the feeding waveguides of the adjacent subarrays were terminated to their characteristic impedances, as it is shown in Fig. 3, and the electric field distribution of the central sub-array was analyzed at different frequencies (see Fig. 4). Fig. 4 clearly shows a strong field coupling process occurring across neighboring sub-arrays, especially at the highest end of the operational band.   a pure TE 01 mode, without any feeding and holding structure included. One can notice that the designed antenna features a very low cross-polarization component with the XPD level being larger than 49 dB across the entire FoV.
The efficiency of the considered radiating structure is shown in Fig. 7. As it appears from Fig. 7, the designed sub-array features high radiation efficiency with a nearly flat distribution having a maximal fluctuation level of about 1.3%. For completeness, the sub-array performance has been evaluated, also, in the case of a lossless dielectric. By visual  inspection of Fig. 7, it is clear that the dielectric losses cause a degradation of the radiation efficiency of up to about 10%.

C. SUB-ARRAY PERFORMANCE
In Fig. 8, the input reflection coefficient of the central subarray and the coupling coefficients relevant to the optimized 3-sub-array configuration are shown. Thanks to the symmetry of the structure, the corresponding behavior can be characterized by means of a reduced number of scattering parameters. Fig. 8 shows that the coupling level between sub-arrays is lower than −20dB nearly across the entire band. On the other hand, the magnitude of S 11 is somehow larger than −10dB at low frequencies; however, it can be improved by integrating a suitable impedance matching circuit.
A feeding structure consisting of a pin integrated into a short-circuited waveguide parallel to the electric field of the TE 01 mode was adopted for the feeding of individual active elements. The position of the pin along the waveguide and its length were optimized in such a way as to enhance the impedance matching across the entire frequency band. The schematics of the feeding section is shown in Fig. 9, while the relevant dimensions are listed in Table 3.
Two additional 0.5-mm holes were realized in the waveguide structure so to make use of suitable tuning screws, in order to be able to adjust the input impedance characteristics after manufacturing. The distance between the waveguide  aperture and the center of the screw hole and the connector is 4.97 mm and 9.97 mm, respectively.
In Fig. 10 are presented the E-plane distributions of the directivity function obtained for 3-, 5-, and 7-sub-array configurations. One can readily observe that the integration of the first two sub-arrays next to the central one has a small but noticeable impact on the radiation characteristics. On the other hand, the integration of the additional subarrays produces rather marginal effects. In the light of this, the directivity function of the central sub-array in the 7-subarray configuration was selected as the embedded directivity function in the synthesis procedure of arrays of arbitrary size; the relevant main characteristics are reported in Table 4 for completeness.  In Fig. 11, the input reflection coefficient of the active element of the central sub-array and the relevant coupling coefficients to the adjacent sub-arrays are shown and VOLUME 10, 2022 compared when considering arrays of 3, 5, and 7 identical sub-arrays. As it can be noticed, a good impedance matching has been achieved across the entire frequency range of operation, with a slight degradation at the lower subband. Fig. 11 shows, also, that the input reflection coefficient remains practically unaffected when additional subarrays are integrated thanks to the low coupling level between sub-arrays. On the other hand, as the number of sub-arrays increases from 3 to 5, a reduced impact on the S 21 coefficient is observed. A further increase in the number of subarrays, however, does not cause any noticeable change in the coupling level between the central sub-array and the immediately adjacent one. Here it is worth mentioning that in the 7-sub-array configuration the coupling level to other sub-arrays which are further apart from each other is well below −35 dB. This clearly indicates that the surface wave component excited by the central active waveguide element does not propagate farther than the first adjacent sub-array.

D. CASE STUDY: ARRAY OF 57 SUB-ARRAYS
The use of the design sub-array in a large array configuration is presented in this section. The case study concerns the design of a linear array featuring a half-power beamwidth of 0.5 • around the broadside direction in the relevant E-plane, which requires an integration of N S = 57 sub-arrays. In order to properly account for the edge effects during the array  design stage, the technique implemented in [24] was adopted, and to this end, the considered 57-sub-array structure was segmented as illustrated in Fig. 12.
In Fig. 13, the radiation pattern of the designed array is shown for three relevant scan angles at the aforementioned frequencies f L = 19.7 GHz, f 0 = 20.0 GHz, and   f H = 20.2 GHz for three different scan angles. It is apparent that the grating lobes are filtered effectively in the case of broadside illumination for all three frequencies. However, as the scan angle moves away from the θ = 0 • direction, the first grating lobe moves closer to the boresight, this causing a   Table 5 summarizes the array characteristics at the considered frequencies. From Table 5, we can conclude that the boresight directivity is nearly constant over the entire frequency range of interest while having some decrease when scanning. In addition, the rejection level of the first grating VOLUME 10, 2022 lobe degrades while scanning to the edge of the FoV. In practical applications, the scan range can be limited so to ensure the required rejection level over the entire frequency band of operation.

IV. PROTOTYPE
To validate the design concept proposed in this research study, an array of three sub-arrays has been manufactured and thoroughly studied. The relevant model, inclusive of the mounting structure, is shown in Fig. 14.
The mounting structure consists of two metal pillars having a length of 108.95 mm and a tapered profile with thickness varying from 20 mm down to 2 mm. The feeding elements of the array are directly attached to the supporting pillars which, in turn, are fixed on a metal plate with dimensions of 97.85 mm × 106 mm × 5 mm. In order to increase reliability, holes with a radius of 1 mm were realized in the center of each short circuit wall, so to let air escape during the pressfilling process implemented for the fixation of the dielectric rods inside the passive waveguides.
During the manufacturing process, some deviations were noticed in the dimensions of the pins integrated in the connectors. In view of this, the array model was modified using the actual lengths for the pins (L 5 +L 8 ) and the dielectric cover of the pins (L 5 − L 13 ) indicated in Table 6.
The analysis with the new dimensions revealed that the aforementioned manufacturing errors primarily affect the impedance matching characteristics at the input ports (see Fig. 15), whereas the coupling coefficients and radiation patterns remain effectively unchanged. Fig. 16 shows different views of the manufactured prototype. The physical body of the array demonstrator is made of aluminum and machined through a computer numerical control (CNC) milling process. The feeding structures have been manufactured separately and then mounted on the main structure with screws. The supporting pillars have been realized out of aluminum as well, whereas the base plate is made out of stainless steel. The dielectric rods are milled out of a dielectric sheet with relative permittivity ε r = 10.0 (±5%).
The experimental measurements revealed a shift in the frequency response of the array demonstrator. The reason for such a shift is likely caused by the tolerance range of ±5% in the permittivity of the dielectric material used for the fabrication. By numerical fitting, we concluded that the actual relative permittivity is around ε r = 10.23.
The measured scattering parameters of the array demonstrator are shown in Fig. 17 and compared to those of the updated simulation model with the fitted relative dielectric constant. A residual deviation between measured and simulated S 11 , S 22 , and S 33 parameters can be observed. This is due to manufacturing inaccuracies which resulted in air gaps in the feeding structure. On the other hand, the reported in Fig. 18 measured and simulated radiation patterns successfully demonstrate the achievement of flat-top characteristics over almost the entire frequency band of operation.
The measured XPD is shown in Fig. 19 and it is compared to the equivalent figure of merit relevant to the complete array inclusive of feeding and holding structures as shown in Fig. 14 while accounting for the deviations between the simulated model and the manufactured prototype. As can be seen in Fig. 19, the inclusion of the feeding and the holding structures results in a reduced XPD level of about 30dB, in the worst-case scenario, across the main-beam region. The measured XPD results tend to match the simulated XPD behavioral trend, but are typically lower, although above 20dB across nearly the entire main-beam region with a small additional degradation at 19.5 GHz.

V. CONCLUSION
A reactively loaded antenna array with enhanced bandwidth characteristics was presented. The proposed design relies on dielectric-based radiating elements which support enhanced inter-element coupling which, in turn, translates into better control of the sub-array characteristics. The manufactured sub-array structure features a fairly stable flat-top radiation pattern over an operational bandwidth of about 500 MHz, from 19.7 GHz to 20.2 GHz. Relevant analyses revealed a strong overlapping effect, occurring between sub-arrays, which is instrumental to enhance the array directivity. A three-element array based on the designed sub-array was manufactured and characterized.
The flat-top radiation pattern behavior with low sidelobe levels across the operating frequency band has been successfully demonstrated. The measurements showed the importance of accurate manufacturing of the feeding structure to reduce performance deviations, especially in terms of input impedance matching characteristics. The Netherlands, where he is currently the Chief Technology Officer/the Vice-President of Engineering and is responsible for product development, program portfolio management, and technical direction of the engineering team. Since 2020, he has been an Associate Professor with the Group of Electromagnetics in Wireless Telecommunications, Eindhoven University of Technology, Eindhoven. He has authored or coauthored more than 200 publications in international peer-reviewed journals, book chapters, and conference proceedings. He holds 22 families of patents in antenna-related technologies and advanced computational techniques. His current research interests include the full-wave analysis and design of passive devices and antennas for satellite, wireless, and radar applications, the development of analytically-based numerical techniques devoted to the modeling of wave propagation and diffraction processes, the theory of special functions for electromagnetics, the deterministic synthesis of sparse antenna arrays, and the solution of boundary-value problems for partial differential equations of mathematical physics.
Dr. Caratelli is currently a member of the Applied Computational Electromagnetics Society (ACES), the Institution of Engineering and Technology (IET), the International Union of Radio Science (URSI), the Italian Electromagnetic Society (SIEm), and the Institute of GIOVANNI TOSO (Senior Member, IEEE) received the Laurea (cum laude) and Ph.D. degrees from the University of Florence, Italy, in 1992 and 1995, respectively. He received the Postdoctoral Fellowship from the University of Florence, in 1999. He spent more than one year as a Visiting Scientist at the Laboratoire d'Optique Electromagnétique, Marseille, France. In 1999, he was a Visiting Scientist at the University of California (UCLA) at Los Angeles. He received a scholarship from Alenia Spazio, Rome, Italy, and he has been appointed as a Researcher in a radio astronomy observatory of the Italian National Council of Researches (CNR). Since 2000, he has been with the Antenna and Submillimeter Waves Section, European Space Agency, ESA ESTEC, Noordwijk, The Netherlands. He has been initiating several research and development activities on satellite antennas based on arrays, reflectarrays, discrete lenses, and reflectors. In particular, in the field of onboard satellite antennas, he has been coordinating activities on multibeam antennas, active and passive, mainly at Telecom applications. In the field of terminal antennas for Telecom applications, he has been supporting the development of reconfigurable antennas with electronic, mechanical, and hybrid scanning. Some of these antennas, developed by Viasat, Airbus Italy, Satixfy UK, and Swissto12 are currently available as products. He has promoted the development of the commercial software tool QUPES by TICRA, also used worldwide, for the analysis and design of periodic and quasi-periodic surfaces, such as reflectarrays, frequency selective surfaces, transmitarrays, and polarizers. A. BART SMOLDERS (Senior Member, IEEE) was born in Hilvarenbeek, The Netherlands, in 1965. He received the M.Sc. and Ph.D. degrees in electrical engineering from the Eindhoven University of Technology (TU/e), in 1989 and 1994, respectively. From 1989 to 1991, he worked as an IC Designer at FEL-TNO, The Hague. From 1994 to 1997, he was a Radar System Designer with Thales, The Netherlands. From 1997 to 2000, he was the Project Leader of the Square Kilometer Array (SKA) with the Netherlands Foundation for Research in Astronomy (ASTRON). From 2000 to 2010, he was with NXP (formerly Philips) Semiconductors, The Netherlands, responsible for the innovation in the RF business line. Since 2010, he has been a fulltime Professor at the Electromagnetics Group, TU/e, with special interest in antenna systems and applications. He currently leads several research projects in the area of integrated antenna systems operating at frequencies up to 150 GHz for several application domains, including 5G/6G wireless communications, radar sensors, and radio-astronomy. He is the Junior-Past Chairman of the IEEE Benelux Section and the Past-Chair of the Nederlands Radio en Elektronica Genootschap (NERG). He is a Board Member of the Stichting Wetenschappelijke Activiteiten van het Nederlands URSI Committee (SWAN) and a member of the Advisory Board of ASTRON and PhotonDelta. Next to his research activities, he is the Dean of the Electrical Engineering Department, TU/e. He has published more than 150 papers. For more information visit the link: (https://www.tue.nl/en/research/researchers/ bart-smolders/). VOLUME 10, 2022