High-Gain Planar Array of Reactively Loaded Antennas for Limited Scan Range Applications

electronics

Article High-Gain Planar Array of Reactively Loaded Antennas for Limited Scan Range Applications

Ronis Maximidis 1,* , Diego Caratelli 1,2 , Giovanni Toso 3 and A. Bart Smolders 1

1 Department of Electrical Engineering, Electromagnetics Group, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands; [email protected] (D.C.); [email protected] (A.B.S.) 2 Department of Research and Development, The Antenna Company, 5656 AE Eindhoven, The Netherlands 3 Antenna and Sub-Millimeter Waves Section, European Space Agency, ESA/ESTEC, 2200 AG Noordwijk, The Netherlands; [email protected] * Correspondence: [email protected]; Tel.: +31-40-247-2647

Received: 15 July 2020; Accepted: 18 August 2020; Published: 25 August 2020

Abstract: This paper proposes a novel high-gain antenna element that can be used in antenna arrays that only require a limited scan range. Each high-gain antenna element uses a linear sub-array of highly-coupled open-ended waveguides. The active central element of this sub-array is directly fed, while the remaining passive waveguides are reactively loaded. The loads are implemented by short-circuits positioned at various distances from the radiating aperture. The short-circuit positions control the radiation pattern properties and the scattering parameters of the array. The proposed sub-array antenna element is optimized in the presence of the adjacent elements and provides a high gain and a flat-top main lobe. The horizontal distance between the sub-array centers is large in terms of wavelengths, which leads to limited scanning capabilities in the E-plane. However, along the vertical axis, the element spacing is around 0.6 wavelength at the central frequency that is beneficial to achieve a wider scan range in the H-plane. We show that the sub-array radiation pattern sufficiently filters the grating lobes which appear in the array factor along the E-plane. To demonstrate the performance of the proposed array configuration, an array operating at 28.0 GHz is designed. The designed array supports scan angles up to 7.5 along the E-plane and 24.2 along the H-plane ± ◦ ± ◦ Keywords: phased arrays; high-gain array element; sub-array; mm-wave; flat-top pattern

1. Introduction To support the growing demand for high data rates, the telecommunication industry is constantly moving to higher frequencies where larger operational bandwidths are available [1]. However, the propagation loss of radio-wave signals also increases significantly at millimeter-wave frequencies, thus severely limiting the communication range. One way to deal with the increased path losses is to compensate them by increasing the directivity using antenna arrays with electronic beamforming [2,3]. An alternative solution consists in the use of multibeam antennas which reduce the overall system footprint and can enhance, significantly, the system capacity [4]. However, the cost of electronic components required for the development of such a complex antenna system increases dramatically as the frequency of operation becomes higher. Therefore, only small-size antenna arrays with moderate directivities have been developed until now. On the other hand, there are plenty of applications that require a very high antenna gain but only over a limited field of view (FoV). Examples in this respect are given by point-to-point or point-to-multipoint backhaul links and antennas for sub-urban coverage. For such applications, one can use array elements characterized by a large aperture and, therefore, high directivity [5].

Electronics 2020, 9, 1376; doi:10.3390/electronics9091376 www.mdpi.com/journal/electronics Electronics 2020, 9, 1376 2 of 15

This allows reducing the number of radiating elements needed to achieve the required gain levels. In turn, this translates into reduced design complexity and manufacturing costs of the feeding network. However, the use of radiating elements with large apertures leads to the appearance of grating lobes in the visible region. The distance between the main lobe and the grating lobes is inversely proportional to the distance between sub-array centers. Therefore, the inter-element spacing should be selected in such a way to keep the grating lobes outside the field of view for all scan angles. To this end, the aperture size should be restricted to certain dimensions. A useful design approach to overcome this drawback, and which is implemented in this research study, is based on the use of overlapping radiating apertures, i.e., the use of the same aperture for multiple feed points. In this way, we can achieve the required levels of gain while maintaining the overall array compactness. Even though overlapping techniques allow keeping grating lobes outside the FoV, the presence of grating lobes still has, per se, certain adverse effects on the side-lobe characteristics of the overall array. More specifically, in transmit mode, they can result in energy leakage along undesired directions that, in turn, can cause a waste of power and potential electromagnetic interferences. In the receive mode, grating lobes can cause the reception of spurious radio signals from undesired directions and, thereby, a degradation of the signal-to-interference ratio. Therefore, appropriate measures have to be taken so as to minimize the detrimental impact of grating lobes. The solution, adopted in this paper, is to filter the grating lobes by the proper shaping of the embedded radiation pattern featured by the individual array element [5,6]. A number of techniques have been developed to reduce the distance between radiating apertures. One can use a complex feeding network to distribute the energy of a port to multiple radiating apertures, enlarging, in this way, the size of each radiating element. Nonetheless, the feeding network becomes very complex even for a small number of array elements; therefore, this technique has found limited applications, mostly in space [7,8]. Another approach consists in using partially reflective surfaces placed above the array structure [9–11]. However, the reflective surfaces increase the height of the structure and reduce its mechanical robustness. In our previous work [6], we proposed a technique to reduce the separation between the phase centers of a one-dimensional array so as to avoid the use of complex overlapping networks or reflective surfaces. In the proposed design approach, each radiating aperture consists of a linear sub-array composed of one directly fed open-ended waveguide radiator and a large number of short-circuited highly-coupled waveguide elements. The energy is delivered to the passive waveguides by free-space coupling and the sub-array structure is designed in such a way to deliver energy to the passive elements of the adjacent sub-arrays as well. As a result, an effective overlapping between sub-arrays can be realized without the use of any additional power distribution network. The positions of the short circuits define the impedance experienced by the electromagnetic field coupled to the passive waveguides. Due to the low loss of the waveguides, said impedance is mainly reactive. Therefore, by optimizing the positions of short circuits, we can control the wave radiation process by the individual passive waveguide and, in this way, shape the embedded sub-array radiation pattern as well as control the active scattering parameters of the overall array structure. In the present research study, we apply the technique proposed in [6] to the design of a planar antenna array composed of linear sub-arrays. The embedded radiation pattern of the realized antenna sub-array provides a limited scan range along the sub-array main axis (E-plane) but a substantially larger coverage along the orthogonal axis (H-plane). The array presented in this paper operates at Ka-band at 28.0 GHz, where several emerging wireless applications are being developed [12] but can be easily scaled to any desired frequency. This paper presents the following new scientific contributions:

Extension of the overlapping technique based on free-space coupling to design a planar array. • The optimized array features high gain and requires a much smaller number of active elements as compared to traditional phased-array systems. A theoretical framework to optimize and analyze the proposed class of arrays for any • speciﬁc application. ElectronicsElectronics2020 2020, ,9 8,, 1376 x FOR PEER REVIEW 33of of 1515

The paper is organized as follows. In Section 2, we describe the design procedure, and introduce The paper is organized as follows. In Section2, we describe the design procedure, and introduce the mathematical model used for the array optimization; the interested reader can find a more the mathematical model used for the array optimization; the interested reader can ﬁnd a more detailed detailed derivation of the model in [6]. In Section 3.1, we present an overlapping sub-array structure derivation of the model in [6]. In Section 3.1, we present an overlapping sub-array structure featuring featuring an embedded flat-top radiation pattern. Next, in Section 3.2 we use the designed subarray an embedded ﬂat-top radiation pattern. Next, in Section 3.2 we use the designed subarray as a building as a building block for the development of a high-gain antenna array. The paper closes with the main block for the development of a high-gain antenna array. The paper closes with the main conclusions conclusions and future directions. and future directions.

2.2. MethodMethod

Figure 1 shows a schematic of a reactively loaded antenna array consisting of Na directly-fed Figure1 shows a schematic of a reactively loaded antenna array consisting of N a directly-fed waveguides and Np reactively loaded waveguides. The employed design procedure is general; waveguides and Np reactively loaded waveguides. The employed design procedure is general;

therefore,therefore,the the activeactive and and passive passive elements elements can can be be randomly randomly distributed distributed across across the the array. array.

h h

Γ 1

Np-1 - Na

1 Γ2

Na a a ΓNp Γ1 a y x Γ3 N +1 1 N +2 N +3 N +N -1 N -1 N +N N a a a a p a a p a FigureFigure 1.1. SchematicSchematic viewview ofof aa reactivelyreactively loadedloaded waveguidewaveguide antennaantenna array.array.

The total electric field →E(θ, ϕ) radiated by such a structure is given from [6]: The total electric field E(,) radiated by such a structure is given from [6]:   " # 1TT  1 1  T  2γ2  pphh 1 −   → Ee(,)(,))(,) Ta→ EE    S ( − p· p −  S   →    E(θ, ϕ) = a Ea(θap, ϕ) + Scc  (Γp pe ) Spp  Ep(θ, ϕ) ((1)1) · · · −   ·  with the superscript T denoting the matrix transposition; the subscripts a and p refer to active and T withpassive the elements superscript, respectively.denoting Besides the matrix, θ and transposition; φ are the conventional the subscripts sphericala and anglesp refer. to active and passiveIn elements,Equation respectively.(1), the vector Besides,a containsθ and ϕ theare excitation the conventional coefficients spherical of the angles. directly-fed array In Equation (1), the vector a contains the excitation coefficients of the directly-fed array elements, elements, and E (,) , E (,) are the vectors containing the electromagnetic field contributions → → a p and Ea(θ, ϕ), Ep(θ, ϕ) are the vectors containing the electromagnetic field contributions radiated by radiated by the active and passive elements, respectively. The matrices S p and S c are blocks of the the active and passive elements, respectively. The matrices Sp and Sc are blocks of the scattering matrix Sscattering, they are relevantmatrix S to, thethey entire are structurerelevant to and the describe entire structure the interaction and describe between the passiveinteraction waveguides between andthe thepassive coupling waveguides between the and passive the coupling and directly between fed waveguides,the passive respectively. and directly Finally, fed waveguidesΓ , γ , and, p p respectively. Finally,  ,  , and h are diagonal matrices containing the reflection coefficient of hp are diagonal matricesp containingp thep reflection coefficient of the load, the complex propagation constant,the load, andthe complex the length propagation of the passive constant waveguides,, and the respectively. length of the passive waveguides, respectively. InIn [[6]6],, itit hashas beenbeen demonstrateddemonstrated thatthat thethe scatteringscattering matrixmatrix ofof thethe activeactive elementselements cancan bebe calculatedcalculated asas follows:follows: " # 1 γ 1 − 22 hhp − 1 T S0 SSSSS= S + S ((Γ e −e p·pp))1 S  ST (2) a aa ac c· p·p − pp · c c (2) S wherewhereS a aisis the the block block matrix matrix of ofS describingS describing the the interaction interaction between between active active elements. elements. OnOn thethe basisbasis EquationsEquations (1)(1) andand (2),(2), thethe designdesign ofof thethe proposedproposed typetype ofof arraysarrays cancan bebe performedperformed usingusing thethe followingfollowing procedure:procedure:

1.1. Decide on the array topologytopology andand thethe minimumminimum numbernumber ofof sub-arrayssub-arrays NNSS usefuluseful toto approximateapproximate a large array environmentenvironment forfor thethe centralcentral sub-array.sub-array. 2.2. Decide on thethe number ofof elementselements perper sub-array,sub-array, NNEE.. 3.3. Obtain the scattering scattering matrix matrix and and th thee embedded embedded element element patterns patterns for for all allthe the elements elements of the of the(NS (N× NE) ×N (N) S ×(N NE) arrayN ). array. S × E × S × E 4. Choose an optimization algorithm and select the optimization parameters.

Electronics 2020, 9, 1376 4 of 15

Electronics 2020, 8, x FOR PEER REVIEW 4 of 15 4. Choose an optimization algorithm and select the optimization parameters. 5. DefineDeﬁne the objective function on the basis of Equaitons (1) and (2) (2).. 6. AfterAfter optimization, optimization, increase increase the the array array size by adding sub sub-arrays-arrays until there is no change in the embeddedembedded radiation radiation pattern of the central sub sub-array.-array. 7. UseUse the the obtained obtained pattern as the the embedded element pattern for the design of arraysarrays of any size.size.

As it is apparent from from E Equationsquations (1) (1) and and (2) (2),, the the main main optimization optimization parameters parameters are are (  (Γp , , γ p , hh p), p p p which), which deﬁne define the the electrical electrical length length of of the the passive passive waveguides waveguides and and their theirloading loading proﬁle.profile. The proposed design procedure hashas beenbeen implementedimplemented inin MatlabMatlab [[13]13]..

3. Design

3.1. Sub Sub-Array-Array Design In this paper,paper, wewe designdesign aa planarplanar arrayarray builtbuilt upup fromfrom linearlinear sub-arrays.sub-arrays. The sub-arrayssub-arrays have to support aawide wide scan scan range range in in the the H-plane H-plane with with a reduced a reduced scanning scan capabilityning capability in the E-plane.in the E- Theplane. design The startsdesign from starts the from structure the structure of Figure of Figure2a, where 2a, where a linear a linear antenna antenna sub-array sub-array of Nof EN=E =13 13 open-endedopen-ended waveguides is placed in an N = 9 3 array conﬁguration. waveguides is placed in an NAA = 9 ×× 3 array configuration.

27 25 26

24 22 23

21 19 20

18 16 17

3 1 2

6 4 5

9 7 8

12 10 11

15 13 14

(a)

t/2 wp wa t t/2

L (b)

Figure 2. 2. ((aa)) Planar NA == 99 × 33 array array configurationconﬁguration using high-gainhigh-gain sub-arrayssub-arrays of open-ended open-ended A × waveguides. The The central central sub-array sub-array is highlighted is highlighted in green, in whereas green, whereas the relevant the geometrical relevant geometrical parameters areparameters reported are in (reportedb). in (b).

The length of the sub-array,sub-array, LL= = 2.653λ00, with with λ0 denotingdenoting the the free free-space-space wavelength, was chosen in suchsuch aa wayway asas toto achieveachieve aa FoVFoV ofof aboutabout ±88◦°.. The choicechoice ofof thethe length,length,l wlw == 0.6λ0,, of of the the waveguides waveguides ± is governed by the the cut cut-o-offﬀ condition of of the the fundamental fundamental TE TE0101 modemode,, that that is islw l>w 0.5> 0.5λ0. λThe0. The width width of the of thepassive passive waveguides waveguides,, wp w= p0.12= 0.12λ0, λ the0, the thickness thickness of of the the wall walls,s, t t== 0.06790.0679λλ0,0 as, as well well as as the relevantrelevant rounding radius of 0.8 mm were chosen so as to simplify the manufacturing process. Finally, the width of the central waveguide, wa = 0.3λ0, is optimized in a way to achieve good impedance matching characteristics. At the initial design step, the length of all the waveguides is set to 0.1λg, where λg

Electronics 2020, 9, 1376 5 of 15 rounding radius of 0.8 mm were chosen so as to simplify the manufacturing process. Finally, the width of the central waveguide, wa = 0.3λ0, is optimized in a way to achieve good impedance matching characteristics. At the initial design step, the length of all the waveguides is set to 0.1λg, where λg denotes the guided wavelength of the fundamental TE01 mode of the passive waveguides. At the working frequency, f0 = 28.0 GHz, and for the speciﬁed waveguide dimensions, we get λg = 21.104 mm. In a linear array, the angular position of the grating lobes is a function of the separation d between antenna elements and the scan angle θ0, and is given by:

pλ0 sin θ = sin θ + (3) p 0 d where p = 1, 2, ... is chosen in such a way as to define an angle with real value, as per the condition ± ± |sinθp| 1. The maximum scan angle of the array factor before the appearance of the first grating lobe ≤ in the field of view is θp = θ . − 0 Using Equation (3), we can evaluate the maximum theoretical scan range in the two main planes of the array of sub-arrays in Figure2, which is 10.86 along the E-plane and 48.47 along the H-plane. ± ◦ ± ◦ Therefore, theoretically, in order to maximize the gain flatness and minimize the radiation to the undesired directions, the sub-array embedded radiation pattern has to have a high gain flat-top shape in the calculated scan range and should have a low gain outside this range. However, a radiation pattern with such a jump discontinuity in the relevant gain distribution cannot be synthesized using a limited-size array, unless we introduce a transition region which, however, reduces the maximum scan range. Therefore, on the basis of this observation, the flat-top region has been set to 8.0 and 40.0 ± ◦ ± ◦ along the E-plane and the H-plane, respectively. Additional design goals are enforced so as to achieve maximal directivity along the boresight, low side-lobe levels (SLL < 15 dB) along the E-plane, and − high return loss combined with low coupling coefficients at the active ports of the array at the central operating frequency. Equation (4) shows the objective function used for the optimization:

θ NPa R hh i Ψ f , h = S f , h D( f , h , θ , 0◦ ) + D( f , h , θ, 0◦ ) D( f , h , θ , 0◦ ) dθ O 0 p 01j,a 0 p 0 p 0 0 p 0 p 0 j=1 − 0 − ( Rθeh i + D( f , h , θ, 90◦ ) D( f , h , θ , 90◦ ) dθ 10 D( f , h , θ , 90◦ ) D( f , h , θ , 90◦ ) (4) 0 p 0 p 0 0 p c 0 p 0 0 − − − ) D( f ,h ,θ ,90◦ ) min 0 p e , −θ [θ ,90 ] D( f0,hp,θ,90◦ ) ∈ SL ◦ where the first term is to minimize S01j,a, j = 1,2, ... , Na, and, in this way, optimize the scattering parameters of the central sub-array. The second term maximizes the broadside directivity. The next two terms are introduced to maximize the flat-top regions, with θh = 40◦ and θe = 8◦, along the H-plane and E-plane, respectively. Finally, the last two terms are useful to minimize the directivity outside the field of view along the E-plane, the relative directivity at the critical angle θc = 14◦, and the SLL for θ [θ , 90 ] with θ = 20 . The designed sub-array is symmetrical with boresight radiation pattern ∈ SL ◦ SL ◦ characteristics along the z-axis. Therefore, we can confine the optimization process to the angular range ϕ [θ , 90 ]. Figure3 shows graphically the defined angular regions. ∈ SL ◦ Electronics 2020, 8, x FOR PEER REVIEW 5 of 15 denotes the guided wavelength of the fundamental TE01 mode of the passive waveguides. At the working frequency, f0 = 28.0 GHz, and for the specified waveguide dimensions, we get λg = 21.104 mm. In a linear array, the angular position of the grating lobes is a function of the separation d between antenna elements and the scan angle θ0, and is given by:

p0 sinp  sin 0 (3) d where p = ±1, ±2,… is chosen in such a way as to define an angle with real value, as per the condition |sinθp| ≤ 1. The maximum scan angle of the array factor before the appearance of the first grating lobe in the field of view is θp = −θ0. Using Equation (3), we can evaluate the maximum theoretical scan range in the two main planes of the array of sub-arrays in Figure 2, which is ±10.86° along the Ε-plane and ±48.47° along the H- plane. Therefore, theoretically, in order to maximize the gain flatness and minimize the radiation to the undesired directions, the sub-array embedded radiation pattern has to have a high gain flat-top shape in the calculated scan range and should have a low gain outside this range. However, a radiation pattern with such a jump discontinuity in the relevant gain distribution cannot be synthesized using a limited-size array, unless we introduce a transition region which, however, reduces the maximum scan range. Therefore, on the basis of this observation, the flat-top region has been set to ±8.0° and ±40.0° along the E-plane and the H-plane, respectively. Additional design goals are enforced so as to achieve maximal directivity along the boresight, low side-lobe levels (SLL < −15 dB) along the E-plane, and high return loss combined with low coupling coefficients at the active ports of the array at the central operating frequency. Equation (4) shows the objective function used for the optimization:

 Na h f,h  S f , h  D (,,,0) f ho  D (,,,0) f h  o  D (,,,0) f h  o d  O 0 p  1 j , a 0 p 0 p 0  0 p 0 p 0 j1 0 e  D( f ,h , ,90o )  D ( f , h ,  ,90 o ) d   10 D ( f , h ,  ,90 o )  D ( f , h ,  ,90 o )  0p 0 p 0 0 p c 0 p 0 (4) 0  o Df(0 ,h pe , ,90 )   min ,  ,90  o SL Df(0 ,h p , ,90 )  where the first term is to minimize S1,ja , j = 1,2,…, Na, and, in this way, optimize the scattering parameters of the central sub-array. The second term maximizes the broadside directivity. The next two terms are introduced to maximize the flat-top regions, with θh = 40° and θe = 8°, along the H- plane and E-plane, respectively. Finally, the last two terms are useful to minimize the directivity outside the field of view along the E-plane, the relative directivity at the critical angle θc = 14°, and the SLL for θ ∈ [θSL, 90°] with θSL = 20°. The designed sub-array is symmetrical with boresight radiation pattern characteristics along the z-axis. Therefore, we can confine the optimization process Electronicsto the angular2020, 9, range 1376 φ ∈ [θSL, 90°]. Figure 3 shows graphically the defined angular regions. 6 of 15

D (E-plane) D (H-plane)

θ θ o 90o θe θo θc θSL 90 θh θo (a) (b)

Figure 3. GraphicalGraphical representation representation of of the the array array radiation radiation pattern pattern mask mask along along the the(a) (Ea-)plane E-plane and and (b) (Hb-)plane. H-plane. Electronics 2020, 8, x FOR PEER REVIEW 6 of 15 Utilizing the objective function deﬁned in Equation (4), the design procedure is turned into the solutionUtilizing of the the following objective minimization function defined problem: in Equation (4), the design procedure is turned into the solution of the following minimization problem: argargmin minΨO ff0 ,,hh (5) Op 0 p (5) 00hh pg 0.50.5λg ≤ p≤ Due to the symmetry of the considered sub-array structure, the number of design parameters is Due to the symmetry of the considered sub-array structure, the number of design parameters is equal to half the number of passive waveguides embedded in each individual sub-array. equal to half the number of passive waveguides embedded in each individual sub-array. The optimization procedure starts with the calculation of the embedded element patterns and The optimization procedure starts with the calculation of the embedded element patterns scattering matrix of an array of 9 × (3 × 13) elements. To this end, a suitable full-wave electromagnetic and scattering matrix of an array of 9 (3 13) elements. To this end, a suitable full-wave solver is used [14]. The obtained results are× then× imported into an in-house developed dedicated electromagnetic solver is used [14]. The obtained results are then imported into an in-house developed software that implements the proposed design procedure. Next, using Equations (1) and (2), the dedicated software that implements the proposed design procedure. Next, using Equations (1) and (2), objective function of Equation (4) is implemented. Then, the Global Search Optimization routine the objective function of Equation (4) is implemented. Then, the Global Search Optimization routine embedded in Matlab [13] is adopted to address the minimization problem described by Equation (5). embedded in Matlab [13] is adopted to address the minimization problem described by Equation (5). The Global Search Optimization technique combines a global pattern-search-based optimizer with a The Global Search Optimization technique combines a global pattern-search-based optimizer with a local gradient-based optimization algorithm. Details of the Global Search Optimization algorithm can local gradient-based optimization algorithm. Details of the Global Search Optimization algorithm can be found in [15]. be found in [15]. The optimal positions of the short-circuits along the passive waveguides are listed in Table1, Table 1. Passive waveguides lengths of the optimized structure. where the waveguides have been numbered starting from the closest one to the central active element. A cross-section of theSection resulting Length array ish1 shown h2 in Figureh34 . h4 h5 h6 Value in λg 0.196 0.205 0.193 0.0000 0.098 0.206 Table 1. Passive waveguides lengths of the optimized structure. The optimal positions of the short-circuits along the passive waveguides are listed in Table 1, Section Length h1 h2 h3 h4 h5 h6 where the waveguides have been numbered starting from the closest one to the central active λ element. A crossValue-section in g of the resulting 0.196 array 0.205 is shown 0.193 in Figure 0.00004. 0.098 0.206

P3 P1 P2 FigureFigure 4. 4. CrossCross-section-section of of three three sub sub-arrays-arrays along along the the sub sub-array-array main axis axis.. The The waveguides waveguides are are shown shown inin blue. blue.

TheThe electromagnetic characteristics characteristics of of the the designed sub sub-array-array structure structure have been successfully validated byby usingusing a a full-wave full-wave solver solver [14 [14]]. After. After the the optimization optimization procedure, procedure the,number the number of sub-arrays of sub- arrayhas beens has gradually been gradually increased increased until the until radiation the radiation pattern pattern of the central of the centralsub-array sub does-array not does change not changesigniﬁcantly significantly any longer. any Figure longer5 .shows Figure the 5 threeshows main the cutsthree of main the embedded cuts of the radiation embedded pattern radiation of the central sub-array when integrated in 9 3, 11 5, and 15 9 array conﬁgurations. pattern of the central sub-array when integrated× × in 9 × 3, 11× × 5, and 15 × 9 array configurations.

Electronics 20202020,, 98,, 1376x FOR PEER REVIEW 7 of 15

Electronics 2020, 8, x FOR PEER REVIEW 7 of 15 (a) (b)

Figure 5.5. Embedded elementelement pattern pattern comparison comparison of of the the central central subarrays: subarrays: (a) ( 9a) 93 × and 3 and 11 115; × ( b5;) 11(b) 151 × × × and× 5 and 15 159 × at 9the at the design design frequency frequencyf = f028.0 = 28.0 GHz. GHz. × 0 In Figure5, one can notice a non-negligible change in the embedded radiation patterns along the E- and D-planes when the array size is increased from 9 3 to 11 5 sub-array elements. More specifically, × × even though the half-power beam-width does not vary along the H-plane, it differs significantly along the other planes, by 0.3◦ along the E-plane and by 1.3◦ along the D-plane. Furthermore, a large deviation of about 7.8 dB is observed in the sidelobe level along the E-plane. No meaningful performance variations occur for further increases of the array size, i.e., to 15 9 elements. As a matter of fact, × the maximal difference inside the half-power beam-width along the various planes is about 0.1 dB, whereas the deviation in terms of the sidelobe level is negligible. An additional investigation has been performed on the active reflection coefficient of the central sub-array element in the 9 3, 11 5, × × and 15 9 array topologies. As it appears in Figure 6, the active reflection coe fficients featured by × the central elements of the(a 11) 5 and 15 9 arrays show rather similar(b) behavior but differ quite × × significantly from the one obtained for the 9 3 array. On the basis of the reported results, the radiation Figure 5. Embedded element pattern comparison× of the central subarrays: (a) 9 × 3 and 11 × 5; (b) 11 pattern of the central element of the 11 5 array has been selected as the embedded sub-array pattern, × 5 and 15 × 9 at the design frequency× f0 = 28.0 GHz . whose main parameters are detailed in Table2. (a) (b)

Figure 6. Active reflection coefficient versus scan angle θ0 of the central element for (a) φ = 0° and

(b) φ = 90° at the design frequency f0 = 28.0 GHz.

In Figure 5, one can notice a non-negligible change in the embedded radiation patterns along the E- and D-planes when the array size is increased from 9 × 3 to 11 × 5 sub-array elements. More specifically, even though the half-power beam-width does not vary along the H-plane, it differs significantly along the other planes, by 0.3° along the E-plane and by 1.3° along the D-plane. Furthermore, a large deviation of about 7.8 dB is observed in the sidelobe level along the E-plane. No meaningful performance variations occur for further increases of the array size, i.e., to 15 × 9 elements. As a matter of fact, the maximal difference inside the half-power beam-width along the various planes is about 0.1 dB, whereas the deviation in terms of the sidelobe level is negligible. An additional investigation has been performed on the active reflection coefficient of the central sub-array element in the 9 × 3, 11 × 5, and 15 × 9 array topologies . As it appears in Figure 6, the active reflection coefficients featured by (thea) central elements of the 11 × 5 and 15 ( ×b )9 arrays show rather similar behavior but differ quite significantly from the one obtained for the 9 × 3 array. On the basis of the FigureFigure 6.6. Active reflection reﬂection coefficient coeﬃcient versus scan angle angle θθ00 ofof the the central central elementelement forfor (a(a))ϕ φ= = 00◦° andand reported results, the radiation pattern of the central element of the 11 × 5 array has been selected as ((bb)) ϕφ == 90◦° at the design frequency f0 = 28.028.0 GHz GHz.. the embedded sub-array pattern, whose main parameters are detailed in Table 2. In Figure 5, one can notice a non-negligible change in the embedded radiation patterns along the E- and D-planes when the array size is increased from 9 × 3 to 11 × 5 sub-array elements. More specifically, even though the half-power beam-width does not vary along the H-plane, it differs significantly along the other planes, by 0.3° along the E-plane and by 1.3° along the D-plane. Furthermore, a large deviation of about 7.8 dB is observed in the sidelobe level along the E-plane. No meaningful performance variations occur for further increases of the array size, i.e., to 15 × 9 elements. As a matter of fact, the maximal difference inside the half-power beam-width along the various planes is about 0.1 dB, whereas the deviation in terms of the sidelobe level is negligible. An additional investigation has been performed on the active reflection coefficient of the central sub-array element in the 9 × 3, 11 × 5, and 15 × 9 array topologies. As it appears in Figure 6, the active reflection coefficients featured by the central elements of the 11 × 5 and 15 × 9 arrays show rather similar behavior but differ quite significantly from the one obtained for the 9 × 3 array. On the basis of the reported results, the radiation pattern of the central element of the 11 × 5 array has been selected as the embedded sub-array pattern, whose main parameters are detailed in Table 2.

Electronics 2020, 9, 1376 8 of 15

Electronics 2020, 8, x FOR PEER REVIEW 8 of 15 Table 2. Embedded radiation pattern characteristics of the 11 5 array. × CutsTable 2. D(0Embedded) (dBi) radiation BW( p3attern dB) (characteristics) BW( 0.5 of dB) the (11) × 5 array SLL. (dB) ◦ − ◦ − ◦ H-plane 15.7 25.7 14.9 18.2 Cuts D(0°) (dBi) BW(−±3 dB) (°) BW(−0.5± dB) (°) SLL (dB)− E-plane 15.7 9.3 5.9 17.8 H-plane 15.7 ±±25.7 ±14.9± −18.2− D-plane 15.7 12.9 8.5 17.8 E-plane 15.7 ±±9.3 ±5.9± −17.8− D-plane 15.7 ±12.9 ±8.5 −17.8 From Figure5b and Table2, it can be concluded that the scan range along the E-plane is close to the optimizationFrom Figure objective, 5b and Table whereas 2, it can a gap be isconcluded observed that in relation the scan to range the scan along range the alongE-plane the is H-plane. close to Thethe optimization sub-array directivity objective for, whereasθ0 = 0◦ ais gap 15.7 is dBi,observed which in is relation 2.3 dB higherto the scan than range the nominal along the directivity H-plane. A calculatedThe sub-array on the directivity basis of thefor physicalθ0 = 0° is aperture 15.7 dBi area, whichap isof 2.3 the dB individual higher than sub-array, the nominal that is: directivity calculated on the basis of the physical aperture area Aap of the individual sub-array, that is: 4π Dap = 4Aap = 13.4 dBi (6) λ2 DAap02 ap 13.4 dBi (6) 0 WeWe cancan conclude conclude that that the the sub-array sub-array directivity directivity has has been been enhanced enhanced thanks thanks to the to overlapping the overlapping with adjacentwith adjacent sub-arrays. sub-arrays. This increase This increase in directivity in directivity can be translatedcan be translated in a 41% in reduction a 41% reduction of the required of the transmitrequired powertransmit or, power equivalently, or, equivalently, a 23% reduction a 23% reduction in the number in the of number required of sub-arrays.required sub In-arrays. order toIn provideorder to anprovide insight an into insight the process into the that process is responsible that is responsible for the enhancement for the enhancement of the directivity, of the directivity, the electric ﬁeld distribution over the radiating aperture of the 11 5 array is reported in Figure7 when only the the electric field distribution over the radiating aperture× of the 11 × 5 array is reported in Figure 7 centralwhen only sub-array the central is active sub- andarray the is otheractive sub-arrays and the other are terminatedsub-arrays onare matchedterminated loads. on matched loads.

FigureFigure 7.7. CalculatedCalculated electricelectric fieldfield distribution of the centralcentral sub-arraysub-array when all otherother sub-arrayssub-arrays are matchedmatched inin thethe 1111 × 5 array at the design frequency ff0 = 28.028.0 GHz GHz.. × 0 FromFrom FigureFigure7 7,, itit can can be be seen seen that that thethe electric electric fieldfield propagatespropagates inin aa veryvery eeffectiveffective wayway towardstowards adjacentadjacent sub-arrays sub-arrays virtually virtually in in all all directions. directions. Eff ectively, Effectively, all the all sub-arrays the sub-arrays contribute, contribute, to some to extent, some toextent, the electromagnetic to the electromagn field radiationetic field process. radiation This process. mechanism This enables mechanism the sub-array enables overlapping the sub-array and, fromoverlapping there, the and, mentioned from there, directivity the mentioned enhancement directivity and enhancement capability of synthesizingand capability complex-shaped of synthesizing radiationcomplex-shaped pattern. radiation It should pattern. be noted It however should that,be noted while however propagating, that, the while electromagnetic propagating, field the graduallyelectromagnetic decays field and gradually eventually decays displays and a eventually limited intensity displays along a limited the edge intensity elements along of thethe array.edge Thiselements is the of reason the array. why This a further is the increase reason why in the a numberfurther increase of sub-arrays in the (beyond number theof sub size-arrays of 11 (beyond5) does × notthe significantlysize of 11 × a5)ff ectdoes the not central significantly sub-array affect characteristics.In the central sub Figure-array8, the characteristics. embedded radiationIn Figure pattern 8, the ofembedded the central radiation sub-array pattern of the of 11 the5 central element sub array-array is presentedof the 11 × in 5 theelement uv-plane, array where is presented u = sin θincos theϕ × anduv-plane v = sin, whereθsinϕ .u = sinθcosφ and v = sinθsinφ.

ElectronicsElectronics 20202020,, 89,, x 1376 FOR PEER REVIEW 99 of of 15 15 Electronics 2020, 8, x FOR PEER REVIEW 9 of 15

Figure 8. Embedded element pattern of the optimized sub-array at the center of the 11 × 5 array, displayedFigure 8. inEmbedded the uv-plane, element where pattern u = sinθcosφ of the optimized and v = sub-arraysinθsinφ. atThe the black center and of white the 11 solid5 array,lines Figure 8. Embedded element pattern of the optimized sub-array at the center of the 11 × 5 array, encircledisplayeddisplayed areas inin thethe with uv-plane,uv a- plane, level wherehigherwhere u thanu == sinsinθcosφ −1θ5cos dBϕ andand v−v3 = =dB sinsinθ compareθsinsinφ.ϕ. Thed to blackb lack the maximum andand whitewhite value solidsolid . lines linesAll presentedencircle areas result withs are a level obtained higher at than the design15 dB frequency and 3 dB comparedf0 = 28.0 GHz to the. maximum value. All presented encircle areas with a level higher than− −15 dB− and −3 dB compared to the maximum value. All resultspresented are result obtaineds are at obtained the design at frequencythe design ffrequency0 = 28.0 GHz. f0 = 28.0 GHz. Figure 8 shows that the areas where the SLL is larger than −15 dB are outside the region defined Figure8 shows that the areas where the SLL is larger than 15 dB are outside the region by theFigure vertical 8 shows dotted that lines the. This areas region where identifies the SLL isthe larger angular than sector −15 dB −where are outside the grating the region lobes definedwould occurdefinedby the assuming vertical by the verticaldotted that the lines dotted considered. This lines. region Thissub- identifiesa regionrray is identifiesused the angularin a the uniform angular sector planar where sector array the where grating configuration the grating lobes would. lobes The performancewouldoccur assuming occur assuming of suchthat the an that considered array the considered can besub estimated-array sub-array is used by is analyzingin used a uniform in a uniform the planar embedded planar array array subconfiguration-array configuration. pattern. The presentedTheperformance performance in Figure of such of 8 such. Along an an array arraythe canH can-plane, be be estimated estimatedthe grating by by lobes analyzing analyzing are outside the the embedded the visible sub-arraysub region-array over pattern pattern the entirepresentedpresented scan inrange.in FigureFigure However,8 8.. AlongAlong along thethe H-plane,theH-plane, E-plane thethe, the gratinggrating grating lobeslobes lobes areare are outsideoutside inside the the visiblevisiblevisible regionregion.region overInover order thethe toentireentire achieve scanscan a range.range. 10 dB However,grating-lobe alongalong rejection thethe E-plane,E- levelplane, ,we thethe have gratinggrating to limitlobeslobes the areare scan insideinside range thethe visible visibleto ±8.7 region.region.°. On the In other order to achieve a 10 dB grating-lobe rejection level, we have to limit the scan range to 8.7 . On the other hand,to achieve if a 15 a dB10 dBgrating grating-lobe-lobe rejection rejection level level is enforced,, we have the to limitscan rangethe scan shrinks range further to± ±8.7 ◦to°. On±6.5 the°. other hand, if a 15 dB grating-lobe rejection level is enforced, the scan range shrinks further to 6.5 . hand,The if aactive 15 dB voltage grating standing-lobe rejection wave levelratio is(VSWR) enforced, versus the scan frequency range shrinksand scan further angle toof± ±6.5the ◦°central. sub-arrayTheThe activeactiveof the voltage11voltage × 5 array standingstanding configuration wavewave ratioratio is shown (VSWR)(VSWR) in versus Figure frequency 9. and scan angle ofof thethe centralcentral sub-array of the 11 5 array configuration is shown in Figure9. sub-array of the 11 ×× 5 array configuration is shown in Figure 9.

(a) (b) (a) (b) FigureFigure 9. 9. ActiveActive voltage voltage standing standing wave wave ratio ratio (VSWR) (VSWR) versus versus frequency frequency and and scan scan angle angle for for ( (aa)) H H-plane-plane andandFigure ( (bb)) E9. E-plane- planeActive of ofvoltage the the central central standing sub sub-array- arraywave ofratio of the the (VSWR) 11 11 × 55 array. array. versus frequency and scan angle for (a) H-plane × and (b) E-plane of the central sub-array of the 11 × 5 array. FigureFigure 99 shows shows that that the designedthe designed sub-array sub-array is intrinsically is intrins matched,ically matched, though the though relevant the impedance relevant impedancematchingFigure band matching 9 shows shifts withband that the shifts the scan dewith angle.signed the The scan sub maximum- angle.array Theis scanning intri maximumnsically range scanning matched, can be obtainedrange though can on thebe the obtained relevant basis of onapplication-speciﬁcimpedance the basis matching of application requirements band- shiftsspecific forwith requirements active the scan VSWR angle. andfor activeThe bandwidth. maximum VSWR In and case,scanning bandwidth. where range broadband canIn case be behaviorobtained, where on the basis of application-specific requirements for active VSWR and bandwidth. In case, where

Electronics 2020, 8, x FOR PEER REVIEW 10 of 15 broadband behavior is needed, the integration of a suitable impedance matching network can be explored. The design of such a matching network is outside the scope of this work.

3.2. Array Design In this section, we use the designed sub-array to realize an antenna array that features a rotationally symmetric mainbeam with a high directivity level of at least 46 dBi. To achieve these goals, a planar array of 65 × 19 elements is required. The simplest approach to the design of such an array would be to adopt the same embedded radiation pattern of the central sub-array analyzed in Electronics 2020, 9, 1376 10 of 15 the previous section for all the array elements. However, this approach would not account for the fact that the edge elements experience different surroundings and, therefore, are characterized by diffiserent needed, embedded the integration radiation of patterns a suitable. A impedance more accurate matching design network approach can consists be explored. in the The use design of the of embeddedsuch a matching radiation network pattern isof outside the edge the elements scope of of this the work. small array as an approximation of the one relevant to the edge elements of the large array, as illustrated schematically in Figure 10. 3.2.The Array transformation Design from the 11 × 5 to the 65 × 19 array configuration is performed as follows: 1. TheIn radiation this section, pattern we use of thethe designedcentral element sub-array of the to realize 11 × 5 anarray antenna (red element array that in featuresFigure 10 a rotationallya is used symmetricto synthesize mainbeam the central with 55 a high× 15 sub directivity-array ( levelhighlighted of at least in red 46 dBi.in Figure To achieve 10b). these goals, a planar array of 65 19 elements is required. The simplest approach to the design of such an array would 2. The elements× highlighted in orange in a are used to synthesize the corresponding domains with be55 to × adopt 1 sub the-arrays same highlighted embedded in radiation orange in pattern Figure of 10 theb. central sub-array analyzed in the previous 3. sectionSimilar forly all to the step array 2, the elements. blue elements However, in Figure this approach 10a are wouldused to not synthesize account forthe thedomains fact that of the1 × edge15 elementssub-arrays experience highlighted diﬀerent in blue surroundings in Figure 10 and,b. therefore, are characterized by diﬀerent embedded 4. radiationFinally, patterns.the remaining A more green accurate elements design in Figure approach 10a consistsare used in as the is to use complete of the embedded the 65 × 19 radiation array patternin Figure of the 10 edgeb. elements of the small array as an approximation of the one relevant to the edge elements of the large array, as illustrated schematically in Figure 10.

L2U5 L1U5 U5 (1x15) R1U5 R2U5 L2U5 L1U5 U5 R1U5 R2U5 L2U4 L1U4 U4 (1x15) R1U4 R2U4 L2U4 L1U4 U4 R1U4 R2U4 L2U3 L1U3 U3 (1x15) R1U3 R2U3 L2U3 L1U3 U3 R1U3 R2U3 L2U2 L1U2 U2 (1x15) R1U2 R2U2 L2U2 L1U2 U2 R1U2 R2U2 L2U1 L1U1 U1 (1x15) R1U1 R2U1 L2U1 L1U1 U1 R1U1 R2U1 L2 L1 R1 R2 L2 L1 C R1 R2 C (55×15) (55× 1) (55× 1) (55× 1) (55× 1) L2D1 L1D1 D1 R1D1 R2D1 L2D2 L1D2 D2 R1D2 R2D2 L2D1 L1D1 D1 (1x15) R1D1 R2D1 L2D3 L1D3 D3 R1D3 R2D3 L2D2 L1D2 D2 (1x15) R1D2 R2D2 L2D4 L1D4 D4 R1D4 R2D4 L2D3 L1D3 D3 (1x15) R1D3 R2D3 L2D5 L1D5 D4 R1D5 R2D5 L2D4 L1D4 D4 (1x15) R1D4 R2D4 L2D5 L1D5 D4 (1x15) R1D5 R2D5 (a) (b)

FigureFigure 10.10. SchematicSchematic representation representation of the of the transformation transformation from from (a) (smalla) small array array with with 11 11× 5 sub5 sub-array-array × elementselements to ( tob) (ab large) a large array array of 65 of × 6519 elements19 elements.. In (a) In each (a) b eachlock blockrepresent representss a sub- aarray sub-array placed placed in the in × specificthe speciﬁc location. location. In (b) Inthe (b various) the various blocks blocks represent represent sub- sub-domainsdomains (with (with dimensions dimensions indicated indicated into into brackets)brackets) synthesized synthesized using using the therelevant relevant embedded embedded sub sub-array-array patterns patterns in (a in). (Thea). Thegreen green blocks blocks are 1 are × 11 sub1-arrays. sub-arrays. × TheThe scan transformation characteristics from along the 11the 5two to theprincip 65 al19 planes array conﬁguration of the resulting is performed 65 × 19 asarray follows: are × × illustrated in Figure 11. The achieved boresight directivity level is 46.5 dBi, which is 0.1 dBi smaller 1. The radiation pattern of the central element of the 11 5 array (red element in Figure 10a is used than that displayed by the 65 × 19 array when the embedded× radiation pattern of the central sub- to synthesize the central 55 15 sub-array (highlighted in red in Figure 10b). array is used for all the elements and,× therefore, the edge effect is neglected. It is worth noting, also, 2. The elements highlighted in orange in a are used to synthesize the corresponding domains with that the edge effect causes faster decay of the array mainbeam with the scanning angle, as it can be 55 1 sub-arrays highlighted in orange in Figure 10b. observed in× Figure 11. In the absence of the edge effect, the array mainbeam would follow the profile 3. Similarly to step 2, the blue elements in Figure 10a are used to synthesize the domains of 1 15 of the central sub-array pattern. This non-ideality is responsible for a reduced scan range, which can× sub-arrays highlighted in blue in Figure 10b. be quantified as 7.5° in the E-plane, and 24.2° in the H-plane. 4. Finally, the remaining green elements in Figure 10a are used as is to complete the 65 19 array × in Figure 10b.

The scan characteristics along the two principal planes of the resulting 65 19 array are illustrated × in Figure 11. The achieved boresight directivity level is 46.5 dBi, which is 0.1 dBi smaller than that displayed by the 65 19 array when the embedded radiation pattern of the central sub-array is used × for all the elements and, therefore, the edge effect is neglected. It is worth noting, also, that the edge effect causes faster decay of the array mainbeam with the scanning angle, as it can be observed in Figure 11. In the absence of the edge effect, the array mainbeam would follow the profile of the central Electronics 2020, 9, 1376 11 of 15 sub-array pattern. This non-ideality is responsible for a reduced scan range, which can be quantified Electronics 2020, 8, x FOR PEER REVIEW 11 of 15 as 7.5Electronics◦ in the 2020 E-plane,, 8, x FOR and PEER 24.2 REVIEW◦ in the H-plane. 11 of 15

(a) (b) (a) (b) Figure 11. The radiation pattern of the 65 × 19 array for various scan angles along the (a) H-plane and FigureFigure 11. The 11. The radiation radiation pattern pattern of of the the 65 65 × 1919 array for for various various scan scan angles angles along along the the(a) H (a-plane) H-plane and and (b) E-plane. The figure also includes the× embedded radiation pattern of the central sub-array of the (b) E-plane.(b) E-plane. The The figure figure also also includes includes the the embedded embedded radiation pattern pattern of ofthe the central central sub sub-array-array of the of the 11 × 5 array, sub-array factor (SF). 11 511 array, × 5 array sub-array, sub-array factor factor (SF). (SF). × To show the impact of the edge effect on the side-lobe level characteristics, the array radiation To showTo show the impactthe impact of theof the edge edge e ffeffectect on on the the side-lobeside-lobe level level characteristics, characteristics, the thearray array radiation radiation pattern evaluated using the proposed design approach for the scan angles of 25° and 7.5° along the patternpattern evaluated evaluated using using the the proposed proposed design design approachapproach for for the the scan scan angles angles of of25° 25 andand 7.5° 7.5alongalong the the H- and E-plane, respectively, has been compared against the corresponding one obtained◦ when◦ the H- and E-plane, respectively, has been compared against the corresponding one obtained when the H- andradiation E-plane, pattern respectively, of the central has beensub-array compared is used againstfor all elements the corresponding of the array; onetherefore, obtained the whenedge the radiation pattern of the central sub-array is used for all elements of the array; therefore, the edge radiationeffects pattern are neglected of the central(see Figure sub-array 12). is used for all elements of the array; therefore, the edge effects are neglectedeffects are (see neglected Figure (see 12 ).Figure 12).

(a) (b) (a) (b) Figure 12. Comparison of the radiation pattern of the 65 × 19 calculated by the proposed approach Figure 12. Comparison of the radiation pattern of the 65 × 19 calculated by the proposed approach Figure(solid 12. line)Comparison versus an approach of the radiation that assum patternes identical of the embedded 65 19 calculated radiation (dotted by the line) proposed for the (a approach) H- (solid line) versus an approach that assumes identical embedded× radiation (dotted line) for the (a) H- (solidplane line) and versus (b) E- anplane. approach The figure that also assumes includes identical the embedded embedded radiation radiation pattern of (dotted the central line) sub for- the plane and (b) E-plane. The figure also includes the embedded radiation pattern of the central sub- (a) H-planearray of andthe 11 (b ×) 5 E-plane. array (SF) The. ﬁgure also includes the embedded radiation pattern of the central array of the 11 × 5 array (SF). sub-array of the 11 5 array (SF). As it can be noticed× in Figure 12, neglecting the edge effect leads to an overestimation of the As it can be noticed in Figure 12, neglecting the edge effect leads to an overestimation of the Asmain it-beam can be directivity, noticed by in 0.7 Figure dB in 12 the, neglecting H-plane, and the by edge 1.6 dB eﬀ iectn the leads E-plane to, an respectively overestimation. The of main-beam directivity, by 0.7 dB in the H-plane, and by 1.6 dB in the E-plane, respectively. The deviation along the E-plane is more noticeable because of the smaller number, 19, of sub-arrays in the main-beamdeviation along directivity, the E-plane by is 0.7 more dB noticeable in the H-plane, because andof the by smaller 1.6 dB number in the, 19, E-plane, of sub-array respectively.s in The deviation along the E-plane is more noticeable because of the smaller number, 19, of sub-arrays

Electronics 2020, 9, 1376 12 of 15

in thatElectronics direction, 2020, 8 as, x FOR compared PEER REVIEW to the number of elements, 65, along the H-plane. Another12 of e ff15ect of the edge elements that can be observed in Figure 12 is relevant for the increase of the sidelobe levels, by aboutthat direction, 14.6 dB for as θcompared25.0 toalong the number the H-plane, of elements, and by 65, about along 7.5 the dB H- forplane.θ Another7.5 along effect the of the E-plane. '− ◦ '− ◦ The performededge elements comparison that can be clearly observed shows in Figure the importance12 is relevant of for including the increase the of edge the sidelobe effects in levels, the analysis by about 14.6 dB for 휃 ≃−25.0° along the H-plane, and by about 7.5 dB for 휃 ≃−7.5° along the E-plane. of the array performance. The performed comparison clearly shows the importance of including the edge effects in the analysis The filtering effect of the sub-array factor for various scan angles is visualized in Figure 13e–h. of the array performance. For comparison, the array factor of a 65 19 array is presented in Figure 13a–d. Figure 13a–d shows The filtering effect of the sub-array× factor for various scan angles is visualized in Figure 13e–h. the array factor of a 65 19 array for various representative scanning angles. The array elements are For comparison, the× array factor of a 65 × 19 array is presented in Figure 13a–d. Figure 13a–d shows excitedthewith array uniform factor of amplitude,a 65 × 19 array whereas for various the represe phase taperingntative scanning is optimized angles. soThe to array steer elements the array are beam alongexcited the desired with uniform direction. amplitude, Because whereas of the the large phase distance tapering between is optimized array so elementsto steer the along array thebeam u-axis, gratingalong lobes the appear.desired Ondirection. the other Because hand, of thethe arraylarge distance element between separation array along elements the v-axisalong isthe smaller u-axis, than grating lobes appear. On the other hand, the array element separation along the v-axis is smaller than 0.6λ0 that is instrumental in keeping the grating lobes outside the visible region, as per Equation (3), for the0.6λ targeted0 that is instrumental scanning range. in keeping Figure the 13 gratinge–h shows lobes outside the filtering the visible effect region on the, as per sub-array Equation radiation (3), for the targeted scanning range. Figure 13e–h shows the filtering effect on the sub-array radiation pattern that is useful in the suppression of undesired grating lobes. It is worth mentioning that even pattern that is useful in the suppression of undesired grating lobes. It is worth mentioning that even thoughthough the sidelobethe sidelobe level level of of the the embedded embedded sub-arraysub-array pattern pattern is isvery very high high in some in some specific specific directions, directions, as is shown in Figure8, the radiation pattern of the total array has a sidelobe level below 30 dB, at the as is shown in Figure 8, the radiation pattern of the total array has a sidelobe level below −30− dB, at specifiedthe specified directions. directions. This performance This performance is achieved is achieved thanks thanks to the to fact the that fact the that array the array scanning scanning is restricted is to therestricted angular to region the angular defined region by thedefined contour by the line contour at 3 lin dBe at level. −3 dB Therefore, level. Therefore, it has it been has been shown shown that the − requirementthat the requirement on the sub-array on the side sub- lobearray level side canlobe belevel relaxed can be for relaxed certain for directionscertain directions which arewhich defined are by the scandefined range by ofthe the scan full range array. of the Finally, full array. due toFinally, the uniform due to the amplitude uniform amplitude excitation, excitation, the side-lobe the side level- of the totallobe radiation level of the pattern total isradiation about pattern13.27 dB. is about If further −13.27 sidelobe dB. If further level reduction sidelobe levelis required, reduction a suitable is − amplituderequired, tapering a suitable scheme amplitude of the tapering array excitation scheme of hasthe array to be excitation adopted has [16 ].to be adopted [16].

(a) (b)

Figure 13. Cont.

Electronics 2020,, 98,, 1376x FOR PEER REVIEW 13 of 15

(e) (f)

(g) (h)

Figure 13. Array factor ( a–d)) and the radiation pattern ( e–h) of thethe 6565 × 19 array for various scan × angles, where u == sinθcosϕφ and vv == sinθsinϕφ. The −33 dB contour of the central sub-arraysub-array radiation − pattern of the 11 × 5 array is also shown. × 4. Conclusions In this work, we have proposed a novel antenna array architecture based on high-gainhigh-gain linear sub-arrays.sub-arrays. An arrayarray structurestructure has has been been designed designed so so to to achieve achieve a directivitya directivity of of 46.5 46.5 dBi, dBi, which which is 2.2 is 2.2 dB higherdB higher than than the the corresponding corresponding 100% 100% aperture aperture effi efficiencyciency limit. limit. This This performance performance hashas beenbeen obtainedobtained by exploiting the the overlapping overlapping of of multiple multiple linear linear sub sub-arrays.-arrays. The The individual individual sub sub-array-array has has a length a length of of2.653 2.653λ0 λwhich0 which might might lead lead to to the the appearance appearance of of grating grating lobes lobes while while scanning. scanning. This This non non-ideality,-ideality, however, has has been been properly properly taken taken into into account account during during the design the design stage. stage. As a matter As a matter of fact, of the fact, grating the lobesgrating are lobes filtered are byfiltered a proper by a shaping proper ofshaping the embedded of the embedded element patternelement of pattern the sub-array. of the sub It has-array. been, It also,has been, demonstrated also, demonstrated that, for an that, accurate for an predictionaccurate prediction of the array of the characteristics, array characterist it is keyics,to it properlyis key to model the edge effects. The inclusion of the edge effect limited the array scan range from 9.3 to properly model the edge effects. The inclusion of the edge effect limited the array scan range± from◦ 7.5 along the E-plane and from 25.7 to 24.2 along the H-plane, respectively. We have shown ±±9.3°◦ to ±7.5° along the E-plane and± from◦ ±25.7± ° to◦ ±24.2° along the H-plane, respectively. We have thatshown the that antenna the antenna array is array intrinsically is intrinsically matched, matched, though though the relevant the relevant impedance impedance matching matching band shiftsband withshifts the with scan the angle. scan To angle. mitigate To mitigate this drawback, this drawback, the integration the integration of an external of an impedance external impedance matching networkmatching can network be considered. can be considered. The proposed The design proposed supports design a supports single linear a single polarization. linear polarization. Although thisAlth mightough bethis su mightfficient be in several sufficient operative in several scenarios, operative there scenarios, are a large there number are of a applications large number where of simultaneousapplications wheresupport simultaneous of two polarizations support is required. of two To polarizations achieve dual-polarization is required. operation,To achieve suitable dual- radiatingpolarization elements operation, have suitableto be utilized. radiating One elements example of have such to an be element utilized. is the One square example dielectric-filled of such an waveguideelement is the operating square indielectric TE01 and-filled TE10 waveguidemodes simultaneously. operating in AnotherTE01 and area TE10 for modes further simultaneously. improvement isAnother the extension area for of further the bandwidth improvement of the is proposed the extension design. of the One bandwidth way to achieve of the suchproposed an extension design. isOne to way to achieve such an extension is to investigate alternative choices for the radiating elements.

Electronics 2020, 9, 1376 14 of 15 investigate alternative choices for the radiating elements. Another option, especially if a wide-band operation is required, is to use active non-foster loads as waveguides terminations [17,18]. By enabling dual polarization and broadband behavior, one can develop multibeam/multicolor arrays based on the proposed reactively loading approach. In this case, the coloring can be performed on the basis of polarization and frequency separation [19]. Some general properties and implementation schemes for linear and planar arrays organized in overlapped subarrays can be found in [20].

Author Contributions: Conceptualization, R.M., D.C., G.T., and A.B.S.; methodology, R.M., D.C., G.T., and A.B.S.; software, R.M.; supervision, D.C., G.T., and A.B.S.; validation, R.M., D.C., G.T., and A.B.S.; writing—original draft preparation, R.M.; writing—review and editing, R.M., D.C., G.T., and A.B.S. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Acknowledgments: This study was conducted in the framework of a Network/Partnering Initiative between the European Space Agency, The Antenna Company, and the Eindhoven University of Technology, under the contract 4000114668/15/NL/MH. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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