Multi Beam Dielectric Lens Antenna for 5G Base Station

sensors

Letter Multi Beam Dielectric Lens Antenna for 5G Base Station

Farizah Ansarudin 1,2,* , Tharek Abd Rahman 1,3, Yoshihide Yamada 4, Nurul Huda Abd Rahman 5 and Kamilia Kamardin 4

1 School of Electrical Engineering, Universiti Teknologi Malaysia, Johor 81310, Malaysia; [email protected] 2 Department of Electrical, Electronic & Systems Engineering, Faculty of Engineering & Built Environment, Universiti Kebangsaan Malaysia, Bangi, Selangor 43650, Malaysia 3 Wireless Communication Centre, Universiti Teknologi Malaysia, Johor 81310, Malaysia 4 Malaysia-Japan International Institute of Technology, Universiti Teknologi Malaysia, Kuala Lumpur 54100, Malaysia; [email protected] (Y.Y.); [email protected] (K.K.) 5 Faculty of Electrical Engineering, Universiti Teknologi MARA, Shah Alam, Selangor 40450, Malaysia; [email protected] * Correspondence: [email protected]; Tel.: +603-8911-8393

Received: 15 September 2020; Accepted: 13 October 2020; Published: 16 October 2020

Abstract: In the 5G mobile system, new features such as millimetre wave operation, small cell size and multi beam are requested at base stations. At millimetre wave, the base station antennas become very small in size, which is about 30 cm; thus, dielectric lens antennas that have excellent multi beam radiation pattern performance are suitable candidates. For base station application, the lens antennas with small thickness and small curvature are requested for light weight and ease of installation. In this paper, a new lens shaping method for thin and small lens curvature is proposed. In order to develop the thin lens antenna, comparisons of antenna structures with conventional aperture distribution lens and Abbe’s sine lens are made. Moreover, multi beam radiation pattern of three types of lenses are compared. As a result, the thin and small curvature of the proposed lens and an excellent multi beam radiation pattern are ensured.

Keywords: lens antenna; lens shaping method; straight-line condition; multi beam radiation pattern; wide angle range

1. Introduction Nowadays, the 5G mobile system is rapidly developing to achieve fast rate transmission, low latency, extremely high traffic volume density, super-dense connections and improved spectral energy, as well as cost efficiencies [1–3]. With the introduction of 5G, the mobile technology has new features such as millimetre wave operation, small cell size and multi beam base station antenna to meet massive multiple-input multiple-output (MIMO) requirements [4–6]. At millimetre wave, the base station antenna size is expected to be less than 30 cm, and due to the massive MIMO usage in 5G technology, the antenna system shall have excellent multi beam radiation patterns. Aperture antennas such as a dielectric lens and reflector can be among the alternatives proposed to replace the present array antenna system. Based on recent studies [7,8], the dielectric lens antenna is known to produce excellent multi beam patterns as compared to the reflector antenna. A Luneburg lens that is composed of spherical layered material has achieved a good multi beam radiation pattern in very wide-angle region [9]. However, having a Luneburg lens with continuously varying material permittivity as a function of the lens radius is quite difficult to accomplish in practice. As a result, many methods for these non-uniform geometries have been studied to simplify the lens geometry for various communication applications as well as its feeding network [10–12]. However, in those works, the capabilities of performing wide angular scanning for multi beam applications were not discussed in detail.

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As for the case of a homogenous lens, the shaped lens, designed based on Abbe’s sine condition, has achieved good wide-angle multi beam characteristics [13]. In achieving excellent radiation patterns, lens surfaces were shaped by ray tracing based on the Geometrical Optics (GO) method [14–17], where, typically, lens shaping can be done by the aperture distribution method or Abbe’s sine method [18,19]. Shaped dielectric lens antennas were developed for the low side lobe radiation pattern and multi beam radiation pattern [20–22]. For low side lobe and multi beam shaping, different lens forming equations were employed. However, to satisfy the installation requirement, the previous lens shaping methods were not suitable. Furthermore, it was used for single beam radiation pattern synthesis only, and the applications were limited to airborne radar and vehicle’s collision avoidance system. In [23], multi beam radiation characteristics are studied sufficiently with Abbe’s sine case. However, for a practical base station usage, this lens shape was not suitable due to the large diameter of the circular lens and because it was operating at low frequency. In addition to that, the scanning angle was limited to 30◦ of angular range. Therefore, small lens thickness and small curvature are requested in a 5G lens antenna system to meet the requirements of multi beam scanning, ease-of-installation on a thin pole and lightweight structure. Furthermore, the 5G antenna system shall incorporate a massive multiple-input multiple-output (MIMO) feature; thus, an antenna with a wide angle beam scanning ability shall be designed. In this paper, a new lens shaping method for thin and small lens curvature is proposed. Multi beam characteristics are compared by designing shaped lens antenna using the aperture distribution condition, Abbe’s sine condition and the newly proposed shaping method based on the straight-line concept. At first, lens shape design equations for three methods are shown. Three types of lens shapes are obtained by the Matrix Laboratory (MATLAB) program. Next, the multi beam radiation pattern is calculated by a commercial electromagnetic simulator FEKO.

2. Materials and Methods

2.1. Lens Antenna Structure and Parameter The design concept and lens antenna parameters are shown in Figure1. The ray tracing method based on Geometrical Optics (GO) is employed in the lens design. The lens is rotationally symmetrical around the z-axis, and the x-axis corresponds to the radial direction of the lens. The lens is composed of two surfaces, the inner surface (S1) and outer surface (S2). Radiated radio waves from the feed horn are expressed by rays diverging from the feed horn. Rays coming to the lens are refracted at the inner and outer surfaces. The ray emitted from the feed at an angle, θ, reaches S1 at the point indicated by (r,θ). After the ray is refracted at S1 by an angle φ, the ray reaches S2 at the point indicated by (z,x). All rays passing through the lens beam become parallel to the z-axis, which indicates that a flat wave 2 front is formed. On the aperture plane, an illumination distribution, Ed (x), is achieved depending on 2 the feed horn radiation pattern, Ep (θ). Refraction conditions on the lens surfaces and the aperture distribution condition are given by differential equations as shown in the next sub-section. By solving the simultaneous differential equations, shaped lens surfaces are obtained.

2.2. Lens Surface Design Equations In order to clarify the proposed lens design method, conventional design methods such as aperture distribution condition and Abbe’s sine condition are explained. This section shows the equations used in designing the lens shape based on all three methods. Sensors 2020, 20, 5849 3 of 17 Sensors 2020, 20, x FOR PEER REVIEW 3 of 17

Figure 1.1. Design concept of lens shaping method.

2.2.1.2.2. Lens Fundamental Surface Design Ray Equations Equations ThereIn order are to three clarify important the proposed expressions lens todesign represent method, the ray conventional tracing principle, design whichmethods are derivedsuch as basedaperture on thedistribution Snell’s Law condition [24]. The and Snell’s Abbe’s Law sine on thecondition inner surface are explained. (S1) is given This by section Equation shows (1): the equations used in designing the lens shape based on all three methods. dr nr sin(θ φ) = − . (1) dθ n cos(θ φ) 1 2.2.1. Fundamental Ray Equations − − TheThere Snell’s are three Law important on the outer expressions surface (S2), to isrepresent given by the Equation ray tracing (2), where principle,n is the which refractive are derived index ofbased the lenson the and Snell’sφ is the Law refracted [24]. The angle Snell’s of theLaw lens. on the inner surface (S1) is given by Equation (1): The expression for slope dz can be derived from the condition that all exit rays after refraction are dx 𝑑𝑟 𝑛𝑟 𝑠𝑖𝑛(𝜃 −ɸ) parallel to the z-axis. The dz and dx shown= in Equation (2) for. variable change from dx to dθ. (1) dx dθ 𝑑𝜃 𝑛𝑐𝑜𝑠(𝜃−ɸ) −1

dz n sin φ dz n sin φ dx The Snell’s Law on the outer surface= (S2), is, given= by Equation (2), where n is the refractive index(2) of the lens and ɸ is the refracteddx angle1 ofn thecos lens.φ d θ 1 n cos φ dθ − − The expression for slope can be derived from the condition that all exit rays after refraction In the ray tracing calculation, the constant condition of the total electric path length, Lt, is given are parallel to the z-axis. The and shown in Equation (2) for variable change from dx to dθ. by expression (3): Lt = r + nr + Zo Z, (3) ɸ 1 − ɸ = , = (2) ɸ Z r cosθ ɸ r = − , (4) 1 cos φ In the ray tracing calculation, the constant condition of the total electric path length, Lt, is given whereby expressionZo is the (3): aperture plane position and Z is the distance from inner surface at the edge to aperture plane, respectively. Equation (4) determines the φ value for a given θ value. Then, Equations (1) and 𝐿 =𝑟+ 𝑛𝑟 +𝑍 −𝑍, (3) (2) can be solved for the variable θ, if dx is known, which can be calculated from Equation (5). dθ 𝑍−𝑟𝑐𝑜𝑠𝜃 2.2.2. Aperture Distribution Condition 𝑟 = , (4) 𝑐𝑜𝑠 ɸ The following electric power conservation condition is given to obtain the diﬀerential dx equation. where Zo is the aperture plane position and Z is the distance from inner surface at the edged toθ aperture plane, respectively. Equation (4) determines the ɸ2 value for a given θ value. Then, Equations (1) and dx Ep(θ) D (2) can be solved for the variable θ, if is known,= which can be calculated from Equation (5). (5) dθ P 2( ) Ed x

2.2.2.Here, Aperture the total Distribution horn power, ConditionP, is given by Equation (6). The following electric power conservationZ condition is given to obtain the differential P = E2(θ)dθ (6) equation. p 𝑑𝑥 𝐸(𝜃) 𝐷 (5) = 𝑑𝜃 𝑃 𝐸 (𝑥) Here, the total horn power, P, is given by Equation (6).

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(6) 𝑃=𝐸 (𝜃)𝑑𝜃 (6) The total aperture power, D, is given𝑃=𝐸 by Equation (𝜃)𝑑𝜃 (7). The total aperture power, D, is given by Equation (7). The total aperture power, D, is given by EquationZ (7). D = E2(x)dx (7) d (7) 𝐷=𝐸 (𝑥)𝑑𝑥 (7) 𝐷=𝐸 (𝑥)𝑑𝑥 The fundamental parameters in lens shaping are the feed radiation, Ep22(θ), and aperture The fundamental parameters in lenslens shapingshaping areare thethe feedfeed radiation,radiation, EEpp2(θ), and apertureaperture distribution, Ed2(x). The values of Ep22(θ) and Ed2(2x) are given as follows: distribution, Ed2((xx).). The The values values of of EEpp2(θ(θ) )and and EEd2d(x()x are) are given given as as follows: follows: 𝐸 (𝜃) =𝑐𝑜𝑠 (𝜃), (8) 𝐸2(𝜃) =𝑐𝑜𝑠 m(𝜃), Ep(θ) = cos (θ), (8) 1 𝑥 ( ) 11 𝑥x p 𝐸2(𝑥 )=1−1−= , (9) 𝐸Ed(𝑥x) =1−1−1 1 𝐶𝑋 , , (9) − −𝐶C 𝑋Xm where C is the edge illumination of an aperture distribution. The value p determines the aperture where C isis thethe edgeedge illuminationillumination ofof anan apertureaperture distribution.distribution. The value p determinesdetermines the aperture distribution taper and Xm is the maximum radius of the aperture. Differential Equations (1), (2) and distribution tapertaper andandX Xmm isis thethe maximummaximum radius radius of of the the aperture. aperture Di. Differentialﬀerential Equations Equations (1), (1), (2) (2) and and (5) (5) can be solved based on the constant path length condition of Equations (3) and (4). The can(5) can be solved be solved based based on the constanton the constant path length path condition length ofcondition Equations of (3) Equations and (4). The (3) performance and (4). The of performance of this method is determined based on the calculated or designed aperture2 distribution, thisperformance method is of determined this method based is dete onrmined the calculated based on or designedthe calculated aperture or designed distribution, apertureEd (x distribution,), for a given Ed2(x), for a given horn radiation2 pattern, Ep2(θ). An example of a designed lens shape is shown in hornEd2(x), radiation for a given pattern, hornE radiationp (θ). An pattern, example E ofp2( aθ). designed An example lens shapeof a designed is shown lens in Figure shape2 .is The shown newly in Figure 2. The newly developed MATLAB program will be discussed in Section 2.3, and the antenna developedFigure 2. The MATLAB newly developed program willMATLAB be discussed program in will Section be discussed 2.3, and the in Section antenna 2.3, parameters and the antenna will be parameters will be described in Section 2.4. The shapes of the inner and outer lens surfaces have describedparameters in will Section be described 2.4. The in shapes Section of the2.4. innerThe shapes and outer of the lens inner surfaces and outer have speciallens surfaces curvatures. have special curvatures. During transmitting mode, all rays go into the aperture plane and become parallel Duringspecial curvatures. transmitting During mode, transmitting all rays go into mode, the all aperture rays go plane into the and aperture become plane parallel and to become the horizontal parallel to the horizontal axis. The spacing of rays is observed to be gradually increased towards the lens edge axis.to the Thehorizontal spacing axis. of raysThe spacing is observed of rays to is be observed gradually to increasedbe gradually towards increased the towards lens edge the in lens order edge to in order to achieve the aperture distribution taper. achievein order theto achieve aperture the distribution aperture distribution taper. taper.

Figure 2. Lens shape based on the energy conservation law. Figure 2. Lens shape based on the energy conservation law.

The aperture distribution calculated by Equation (9) shows that the maximum radius of outer The aperture distribution calculated by Equati Equationon (9) shows that the maximum radius of outer surface,surface, Xm == 51.7951.79 mm, mm, for for tapered tapered must must be be larger larger than than 1 1(C (C > >1).1). Here, Here, C Cis the is the edge edge illumination illumination (C surface, Xm = 51.79 mm, for tapered must be larger than 1 (C > 1). Here, C is the edge illumination (C (C= 6),= 6),and and the the edge edge level level of the of the aperture aperture electric electric field ﬁeld is − is8.638.63 dB dBas shown as shown in Figure in Figure 3. 3. = 6), and the edge level of the aperture electric field is −8.63− dB as shown in Figure 3.

FigureFigure 3.3. Aperture distribution onon x-zx-z plane.plane. Figure 3. Aperture distribution on x-z plane.

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Sensors 2020, 20, x FOR PEER REVIEW 5 of 17 2.2.3. Abbe’s Sine Condition 2.2.3. Abbe’s Sine Condition dx Another method of obtaining the dθ expression is through the Abbe’s sine condition as explained in [18Another], where themethod coma of free obtaining condition the is found expression for a limited is through scan. The thecondition, Abbe’s sine as expressedcondition byas Equation (10), is called Abbe’s sine condition. explained in [18], where the coma free condition is found for a limited scan. The condition, as expressed by Equation (10), is called Abbe’s sine condition. x = Fs sin θ (10)

𝑥=𝐹 𝑠𝑖𝑛 𝜃 (10)

The meaning of this equation is shown in Figure4 . Based on this ﬁgure and by employing the Abbe’sThe sine meaning condition, of this the equation crossing is point shown of the in Figure incoming 4. Based and the onrefracted this figure rays and should by employing exist on thethe circleAbbe’s of sine radius, condition,Fs. The ditheﬀ erentialcrossing form point of of Equation the incoming (10) if givenand the by refracted the next equation. rays should The exist lens on shape the showncircle of in radius, Figure Fs4 is. The solved differential by Equations form of (1), Equation (2) and (11),(10) if respectively. given by the next equation. The lens shape shown in Figure 3 is solved by Equations (1), (2) and (11), respectively. dx 𝑑𝑥 = F =𝐹 s𝑐𝑜𝑠cos 𝜃 θ (11)(11) d𝑑𝜃θ

FigureFigure 4.4. Abbe’sAbbe’s sinesine conditioncondition lens.lens. 2.2.4. Proposed Lens by Straight-Line Condition 2.2.4. Proposed Lens by Straight-Line Condition dx As explained in Section 2.2.3, the diﬀerential equation dθ of Abbe’s sine is derived from the As explained in Section 2.2.3, the differential equation of Abbe’s sine is derived from the condition that the refraction point is on the circle. As for the straight-line condition, small lens curvaturecondition andthat thin the lensrefraction thickness point are required;is on the thus, circle. the As refraction for the pointstraight-line is expected condition, to be better small on lens the straight-linecurvature and for thin a wide lens scanning thickness beam. are required; thus, the refraction point is expected to be better on the straight-line for a wide scanning beam. dx By taking into account the radius of the circle in obtaining dθ in the Abbe’s sine condition, the dx straight-lineBy taking condition into account can also the be radius obtained of the by circle the d θinequation. obtaining The straight-line in the Abbe’s condition sine condition, of the lens the shape is shown in Figure5, and the equation is given by Equation (12). straight-line condition can also be obtained by the equation. The straight-line condition of the lens shape is shown in Figure 5, and the equationx = Listan givenθ by Equation (12). (12)

The diﬀerential equation form is expressed𝑥 =by Equation𝐿 𝑡𝑎𝑛 𝜃 (13), where L is the distance from the(12) feed to theThe straight-line differential curve equation on the form lens. is expressed by Equation (13), where L is the distance from the dx feed to the straight-line curve on the lens. = L sec2 θ (13) dθ 𝑑𝑥 From the developed MATLAB program,=𝐿 Equations 𝑠𝑒𝑐 𝜃 (1), (2) and (13) have been solved, which(13) has 𝑑𝜃 resulted in smaller lens thickness, T, and smaller curvature. Thus, this shape is suitable for a base stationFrom application. the developed MATLAB program, Equations (1), (2) and (13) have been solved, which has resulted in smaller lens thickness, T, and smaller curvature. Thus, this shape is suitable for a base station application.

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Figure 5. Straight-lineStraight-line condition condition lens. lens. Figure 5. Straight-line condition lens. 2.3. MATLAB Program for Solving Differential Equations 2.3. MATLAB Program for Solving Differential Equations In2.3. order MATLAB to solve Program the for three Solving diff erentialDifferential equations, Equations a MATLAB program is developed. The flow In order to solve the three differential equations, a MATLAB program is developed. The flow of of the developedIn order to program solve the is three explained differential by theequation flows, chart a MATLAB shown program in Figure is developed.6. The parameter The flow ofof the the developed program is explained by the flow chart shown in Figure 6. The parameter of the initial initialthe condition developed as program shown in is Figureexplained7 is by determined. the flow char Here,t shownθ oinis Figure an important 6. The parameter parameter of the influencing initial condition as shown in Figure 7 is determined. Here, θo is an important parameter influencing the lens the lenscondition thickness. as shown In accordance in Figure 7 is with determined. the ∆θ, changesHere, θo is of an r important and z are parameter given by influencing Equations the (1) lens and (2), thickness. In accordance with the Δθ, changes of r and z are given by Equations (1) and (2), respectively.thickness. The In changeaccordance of x withis determined the Δθ, changes by Equations of r and (5), z are (11) given and (13)by Equations for the design (1) and method (2), of respectively. The change of x is determined by Equations (5), (11) and (13) for the design method of aperturerespectively. distribution, The change Abbe’s of sine x is conditiondetermined and by Equations straight-line (5), condition,(11) and (13) respectively. for the design As method a result, of the apertureaperture distribution, distribution, Abbe’s Abbe’s sine sine condition condition and and straight-line straight-line condition,condition, respectively. respectively. As Asa result, a result, the the inner surface (θ,r) and the outer surface (z,x) are determined to design the lens surfaces and rays are inner surfaceinner surface (θ,r) (andθ,r) andthe theouter outer surface surface (z,x) (z,x) are are determined determined toto designdesign the the lens lens surfaces surfaces and and rays rays are are plotted on the structure. plottedplotted on the on structure. the structure.

FigureFigure 6. Flow 6. Flow chart chart of of ray ray tracing tracing programprogram for for lens lens antenna antenna shaping. shaping.

Figure 6. Flow chart of ray tracing program for lens antenna shaping.

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FigureFigure 7. 7. InitialInitial condition condition of of lens lens shaping. shaping. 2.4. Structural Parameters for Lens Designing 2.4. Structural Parameters for Lens Designing In designing lens shapes shown in Figures2,4 and5, the optimum antenna parameters used In designing lens shapes shown in Figures 2, 4 and 5, the optimum antenna parameters used are are shown in Table1. As for common parameters, the lens diameter, D, is set to 100 mm and the shown in Table 1. As for common parameters, the lens diameter, D, is set to 100 mm and the feed feed radiation pattern is fixed. Other structural parameters of aperture distribution condition (ADC), radiation pattern is fixed. Other structural parameters of aperture distribution condition (ADC), Abbe’s sine condition (ASC) and straight-line condition (SLC) are independently determined based on Abbe’s sine condition (ASC) and straight-line condition (SLC) are independently determined based the different design methods. on the different design methods. Table 1. Dielectric lens antenna configuration. Table 1. Dielectric lens antenna configuration. Antenna Parameter Dimension Lens Shape Dimension Antenna Parameter Dimension Lens Shape Dimension General Specification Aperture Distribution (ADC) OperatingGeneral Frequency, Specification fo 28.21 GHz Aperture Focal Length, DistributionF (ADC) 106 mm OperatingMax. angle, Frequency,θm fo 26.56 28.21◦ GHzLength from horn Focal to lens Length, edge, rm F 111.78106 mm mm Refractive index, n 2 Maximum radius of S2, Xm 51.79 mm Lens Diameter,Max. angle, D (10 λ θ)m 100 mm 26.56° Total Length electrical from length, horn Ltto lens edge, rm 266.98111.78 mm mm Initial conditionRefractive of normal index, vector, nθ o 10◦ 2 Lens Maximum Thickness, radiusT of S2, Xm 17.0051.79 mm mm 2 Initial conditionLens Diameter, at lens edge, D (10 do λ) 5 mm 100 mm Aperture Total distribution, electricalE d (x)length, LtEquation (9)266.98 and Figure mm3 Abbe Sine Condition (ASC) InitialFeed condition Horn {Ep of2 normal(θ)} vector, θo 10° Radius Lensof circle, Thickness,Fs T 111.8217.00 mm mm Equation (8) and Figure 10 Maximum radius of S2, Xm 50.13Equation mm (9) Initial condition at lens edge, do 5 mm Aperture distribution, E2d(x) Total electrical length, Lt 252.84and mm Figure 3 Lens Thickness, T 14.80 mm StraightAbbe Line Sine Condition Condition (ASC) Feed Horn {Ep2(θ)} (SLC)—Proposed Radius of circle, Fs 111.82 mm Distance to lens, L 97.34 mm Equation (8) and Figure 8 Maximum radius of S2, Xm 50.13 mm Maximum radius of S2, Xm 50.36 mm Total electricalTotal electrical length, Lt length, Lt 253.89252.84 mm mm Lens Thickness,Lens Thickness,T T 13.8314.80 mm mm Straight Line Condition (SLC)—

Proposed In order to clarify the feature of SLC, smaller focal length structures are shown in Figure8. Distance to lens, L 97.34 mm Calculation parameters are summarised in Table2. From the figure, the lens thickness and area ratio of Maximum radius of S2, Xm 50.36 mm SLC become the smallest. In order to make clear the difference, the lens area and thickness are shown Total electrical length, Lt 253.89 mm in Figure9. It is clarified that SLC achieves the smallest lens area and thickness. Lens Thickness, T 13.83 mm

Table 2. Lens antenna parameter for F = 40 mm and F = 60 mm. In order to clarify the feature of SLC, smaller focal length structures are shown in Figure 8. CalculationAntenna parameters Parameter are summarised ADC in Table 2. From the ASC figure, the lens thickness SLC and area ratio of SLC become the smallest.F = In40 order to F =make60 clear F the= 40 difference, F = 60the lens Farea= 40 and thickness F = 60 are shownMax. in Figure angle, θ9.m It is clarified57.5 that SLC 49.5 achieves the 59.1 smallest lens 43.4 area and thickness. 47.4 37.7 m of Equation (8) 5 10 5 10 5 10 p of Equation (9) 1 1 1 1 1 1

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ADC ASC SLC

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ADC ASC SLC

(a) F = 40 mm

(b) F = 60 mm

Figure 8. Lens structure for ADC, ASC and SLC at a focal length of (a) F = 40 mm, (b) F = 60 mm.

Table 2. Lens antenna parameter for F = 40 mm and F = 60 mm.

Antenna Parameter ADC ASC SLC

F = 40 F = 60 F = 40 F = 60 F = 40 F = 60 Max. angle, θm 57.5( b) F49.5 = 60 mm59.1 43.4 47.4 37.7 m of Equation (8) 5 10 5 10 5 10 FigureFigure 8.8. LensLens structurestructure forfor ADC,ADC, ASCASC andand SLCSLC atat aa focalfocal lengthlength ofof ((aa)F) F= = 4040 mm,mm, ((bb)F) F == 60 mm. p of Equation (9) 1 1 1 1 1 1 Table 2. Lens antenna parameter for F = 40 mm and F = 60 mm.

Antenna Parameter ADC ASC SLC F = 40 F = 60 F = 40 F = 60 F = 40 F = 60 Max. angle, θm 57.5 49.5 59.1 43.4 47.4 37.7 m of Equation (8) 5 10 5 10 5 10 p of Equation (9) 1 1 1 1 1 1

FigureFigure 9. 9.Lens Lens area area ratio ratio and and thickness thickness at at focal focal length length F F= =40 40 mm,mm, FF= = 6060 mmmm andand FF == 100 mm.

2.5.2.5. RadiationRadiation PatternPattern ofof aa FeedFeed HornHorn The feed horn radiation, E 2(θ), employed in MATLAB is expressed by Equation (8) with radiation The feed horn radiation,p Ep2(θ), employed in MATLAB is expressed by Equation (8) with coeradiationﬃcient, coefficient, m = 17, and m the= 17, maximum and the maximum angle from angl thee feedfrom horn the isfeed according horn is toaccording the lens to shapes the lens as tabulated in Table1. The maximum power for lens illumination is about 10.17 dB, as shown in shapes as tabulated in Table 1. The maximum power for lens illumination− is about −10.17 dB, as Figure 10. Based on the focal length to lens diameter ratio, F/D, the maximum angle from feed to lens shown inFigure Figure 9. Lens10. Based area ratio on theand focalthickness length at focal to lens length diameter F = 40 mm, ratio, F = F/D, 60 mm the and maximum F = 100 mm. angle from edge is calculated to be about θ = 26.56 . feed to lens edge is calculated tom be about◦ θm = 26.56°. 2.5. Radiation Pattern of a Feed Horn

The feed horn radiation, Ep2(θ), employed in MATLAB is expressed by Equation (8) with radiation coefficient, m = 17, and the maximum angle from the feed horn is according to the lens shapes as tabulated in Table 1. The maximum power for lens illumination is about −10.17 dB, as shown in Figure 10. Based on the focal length to lens diameter ratio, F/D, the maximum angle from feed to lens edge is calculated to be about θm = 26.56°.

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2 17 FigureFigure 10. 10. FeedFeed horn horn radiation radiation pattern, pattern, EEp2p(θ(θ) )== coscos17θθ, ,on on x-z x-z plane.

2.6. Parameters of Electromagnetic Simulations 2.6. Parameters of Electromagnetic Simulations For validation,validation, the the shaped shaped lenses lenses developed developed in MATLAB in MATLAB are simulated are bysimulated using an electromagneticby using an electromagnetictool called FEKO tool to recognize called FEKO its electrical to recognize performance. its electrical The performance. numerical analysis The numerical in FEKO analysis software in is FEKObased onsoftware the Method is based of Momenton the Method (MoM) of technique Moment (MoM) [25], and technique the antenna [25], system and the consists antenna of system a horn consistsantenna asof thea horn feeding antenna element as andthe feeding a dielectric elemen lenst antenna. and a dielectric The use oflens the antenna. multilevel The fast use multipole of the multilevelmethod (MLFMM) fast multipole becomes method inevitable; (MLFMM) thus, the surfacebecomes equivalent inevitable; principle thus, (SEP)the surface is employed equivalent for the principlefeed horn (SEP) and the is dielectricemployed lens for body. the feed The detailshorn and of the the simulation dielectric parameters lens body. are The shown details in Tableof the3. simulationMoM is an parameters accurate solver are shown because in itTable performs 3. MoM full is wave an accurate analysis solver to derive because rigorous it performs solution full for wave the analysiscomplex to model. derive rigorous solution for the complex model.

Table 3. Simulation parameters of horn feed and dielectric lens antenna. Table 3. Simulation parameters of horn feed and dielectric lens antenna.

ParameterParameter Specification Speciﬁcation ComputerComputer ProcessorProcessor Xeon Xeon2.10 GHz 2.10 GHz RandomRandom Access Access Memory Memory 512 GB 512 GB ElectromagneticElectromagnetic Software Software FEKO FEKO 2019.2 2019.2 DielectricDielectric Lens Lens Antenna Antenna RefractiveRefractive index, index, n n 2 2 Tan δ 0.0004 Tan δ 0.0004 Mesh size λ/8 Mesh size λ/8 Number of meshes 66,112 Number of meshes 66,112 FeedFeed Horn Horn MaterialMaterial PEC PEC Mesh size λ/12 NumberMesh of meshes size λ/12 18,532 Number of meshes 18,532 Simulation Time (MoM) 3H Simulation Time (MoM) 3H

3. Simulation Simulation Results Results and and Discussion Discussion 3.1. Feed Horn Design 3.1. Feed Horn Design 2 In order to achieve the Ep (θ) radiation pattern as shown in Figure 10, a pyramidal horn antenna In order to achieve the Ep2(θ) radiation pattern as shown in Figure 10, a pyramidal horn antenna is employed in FEKO. The horn structure and size are shown in Figure 11a. The simulated radiation is employed in FEKO. The horn structure and size are shown in Figure 11a. The simulated radiation pattern for the E-plane and H-plane is shown in Figure 11b, which shows the obtained gain of 15.13 dBi pattern for the E-plane and H-plane is shown in Figure 11b, which shows the obtained gain of 15.13 with an edge level of 9.11 dB and 7.23 dB at the E-plane and H-plane, respectively. dBi with an edge level− of −9.11 dB and− −7.23 dB at the E-plane and H-plane, respectively.

SensorsSensors 2020 2020, 20, ,20 x ,FOR x FOR PEER PEER REVIEW REVIEW 10 10of 17of 17 Sensors 2020, 20, 5849 10 of 17

(a)( a) (b()b )

FigureFigureFigure 11. 11. 11.(a )( (aDimensiona)) Dimension Dimension of offeed of feed feed horn horn horn antenna antenna antenna and and and (b )( (bradiationb)) radiation radiation pattern pattern pattern (y-z (y-z (y-z plane). plane). plane).

FigureFigure 1212 showsshows that that the the reflection reﬂection coefficient coeﬃcient of ofa feed a feed horn horn antenna antenna is about is about −44.4644.46 dB. The dB. Figure 12 shows that the reflection coefficient of a feed horn antenna is about −44.46 −dB. The pyramidal feed horn is simulated from 25.2 GHz to 30.8 GHz, and the operating frequency, fo, is at pyramidalThe pyramidal feed horn feed is horn simulated is simulated from from25.2 GHz 25.2 GHzto 30.8 to 30.8GHz, GHz, and andthe theoperating operating frequency, frequency, fo, fiso, at is at 28.2128.2128.21 GHz. GHz. GHz.

FigureFigureFigure 12. 12. 12.Reflection ReflectionReflection coefficient coefficient coefficient of ofa of 28.21 a a 28.21 28.21 GHz GHz GHz feed feed feed horn horn horn antenna. antenna. antenna. 3.2. Radiation Characteristics of the Centre Beam 3.2.3.2. Radiation Radiation Characteristics Characteristics of ofthe the Centre Centre Beam Beam The radiation patterns of all three lens antennas (ADC, ASC, SLC) are shown in Figure 13. All lenses The radiation patterns of all three lens antennas (ADC, ASC, SLC) are shown in Figure 13. All haveThe achieved radiation the patterns same main of all beam three patterns lens antennas and almost (ADC, similar ASC, sidelobe SLC) are levels. shown In order in Figure to examine 13. All the lenses have achieved the same main beam patterns and almost similar sidelobe levels. In order to lensesaccuracy have ofachieved the radiation the same patterns main shown beam inpatterns Figure and10, thealmost theoretical similar values sidelobe of antennalevels. In gain order and to the examine the accuracy of the radiation patterns shown in Figure 10, the theoretical values of antenna examinebeamwidth the accuracy of uniform of the aperture radiation distribution, patterns shown as shown in Figure by Equations 10, the (14)theoretical and (15) values [26], areof antenna calculated gaingain and and the the beamwidth beamwidth of ofuniform uniform aperture aperture distribution, distribution, as asshown shown by by Equations Equations (14) (14) and and (15) (15) [26], [26], and compared. Here, D indicates the antenna diameter and θBT is the half-power beamwidth (HPBW). are calculated and compared. Here, D indicates the antenna diameter and θBT is the half-power areThe calculated comparisons and compared. of the theoretical Here, D values indicates and the the antenna simulation diameter results and are summarisedθBT is the half-power in Table 4. beamwidth (HPBW). The comparisons of the theoretical values and the simulation results are beamwidthBased on the(HPBW). data, the The simulated comparisons beam widthsof the theore are slightlytical values increased and for the all lensessimulation as compared results toare the summarisedsummarised in inTable Table 4. 4.Based Based on on the the data, data, the the simu simulatedlated beam beam widths widths are are slightly slightly increased increased for for all all theoretical beam width, θBT = 6.25◦, due to the tapered aperture distributions of the designed lens. lenses as compared to the theoretical beam width, θBT = 6.25°, due to the tapered aperture lensesThe increasedas compared value to of the tapertheoretical aperture beam distribution width, θ hasBT = resulted 6.25°, indue an to increase the tapered of the beamaperture width. distributions of the designed lens. The increased value of the taper aperture distribution has resulted distributionsIn this paper, of the taperdesigned aperture lens. distribution,The increased p, valu is 1; thus,e of the the taper values aperture of the beam distribution width for has all resulted lenses are in an increase of the beam width. In this paper, the taper aperture distribution, p, is 1; thus, the values in increasedan increase as of compared the beam to width. the beam In this width paper, of uniform the taper aperture aperture distribution. distribution, In p, addition is 1; thus, to that,the values the gain of ofthe the beam beam width width for for all all lenses lenses are are increased increased as as compared compared to tothe the beam beam width width of ofuniform uniform aperture aperture reduction from the theoretical value GT = 29.34 dBi is produced by the tapered aperture distributions distribution. In addition to that, the gain reduction from the theoretical value GT = 29.34 dBi is distribution.when ADC, In ASC addition and SLC to that, gain arethe 27.56gain dBi,reduction 27.74 dBifrom and the 27.69 theoretical dBi, respectively. value GT Furthermore,= 29.34 dBi is the produced by the tapered aperture distributions when ADC, ASC and SLC gain are 27.56 dBi, 27.74 producedaperture by effi theciencies tapered of 66.37%aperture to distributions 69.20% are also wh achieved.en ADC, ASC and SLC gain are 27.56 dBi, 27.74 dBidBi and and 27.69 27.69 dBi, dBi, respectively. respectively. Furthermore, Furthermore, the the aperture aperture efficiencies efficiencies of of66.37% 66.37% to to69.20% 69.20% are are also also achieved. achieved. πD2 G = (14) T λ

Sensors 2020, 20, x FOR PEER REVIEW 11 of 17

𝜋𝐷 Sensors 2020, 20, 5849 𝐺 = 11(14) of 17 𝜆

𝜆λ θ𝜃BT =58.4= 58.4 (15) 𝐷D

FigureFigure 13.13. RadiationRadiation patternpattern forfor ADC,ADC, ASCASC andand SLCSLC lenslens withwith theoreticaltheoreticalgain gainvalue, value,G GTT = 29.34 dBi.

Table 4. Lens antenna performance for ADC, ASC and SLC. Table 4. Lens antenna performance for ADC, ASC and SLC. Antenna Parameter ADC ASC SLC Antenna Parameter ADC ASC SLC

Gain of uniformGain of aperture uniform distribution, aperture distribution,GT (dBi) GT (dBi) 29.34 29.34 Theoretical beam width, θ 6.25 Theoretical beamBT width, θBT ◦ 6.25° Simulated Beam Width, θBS 6.55◦ 6.40◦ 6.54◦ Simulated Beam Width, θBS 6.55° 6.40° 6.54° Simulated Gain, Gs (dBi) 27.56 27.74 27.69 Gain diffSimulatederence Gain, Gs (dBi) 1.78 27.561.60 27.74 1.65 27.69 − − − Efficiency, ηGain difference 66.37%− 69.20%1.78 −1.60 68.39%−1.65 Efficiency, η 66.37% 69.20% 68.39% 3.3. Radiation Characteristics of Multi Beam 3.3. Radiation Characteristics of Multi Beam The multi beam antennas are capable of generating a number of synchronised and independent The multi beam antennas are capable of generating a number of synchronised and independent directive beams to cover the predefined angular and to provide a solution to overcome the shortcomings directive beams to cover the predefined angular and to provide a solution to overcome the of the antenna with a single-directive beam. In this section, the radiation mode is explained for shortcomings of the antenna with a single-directive beam. In this section, the radiation mode is determining each of the feed coordinates at a specific angular range. explained for determining each of the feed coordinates at a specific angular range. 3.3.1. Feed Positions for Multi Beams 3.3.1. Feed Positions for Multi Beams The off-focus radiation patterns are investigated in the y-z plane. The relation of the feed positions withThe respect off-focus to the radiation shift angles patterns is shown are in investigated Figure 14. Thein the feed y-z positions plane. The of F4 relation and F5 of seem the tofeed be approachingpositions with the respect inner to surface the shift of theangles lens. is The shown locus in ofFigure the feed 14. The position, feed positionsF(y,z), is determinedof F4 and F5 below seem withto beR approaching= 100 [27,28 ].the inner surface of the lens. The locus of the feed position, F(y,z), is determined below with R = 100 [27,28]. 2 F (y, z) = R cos θF (16) (𝑦, 𝑧) = 𝑅 𝑐𝑜𝑠𝜃 The feed coordinates are expressedF by Equations (17) and (18). (16) The feed coordinates are expressed by Equations (17) and (18). 2 z = R cos θF cos θF + R (17) 𝑧=𝑅 𝑐𝑜𝑠 𝜃 cos 𝜃 +𝑅 (17)

2 x = R cos θF sin θF (18) 𝑥=𝑅 𝑐𝑜𝑠 𝜃 sin 𝜃 (18) Based on the equations, the feed coordinates are calculated and shown in Table5 for θF of the 10◦ step angle.Based on the equations, the feed coordinates are calculated and shown in Table 5 for θF of the 10° step angle.

Sensors 2020, 20, x FOR PEER REVIEW 12 of 17

Table 5. Feed Coordinate.

Feed Angle (θF) Feed Coordinate y z F1 = 10° 4.49 16.84 F2 = 20° 17.03 30.20 F3 = 30° 35.06 37.50 F4 = 40° 55.05 37.72 Sensors 2020, 20, 5849 12 of 17 Sensors 2020, 20, x FOR PEER REVIEW F5 = 50° 73.45 31.65 12 of 17

Table 5. Feed Coordinate.

Feed Angle (θF) Feed Coordinate y z F1 = 10° 4.49 16.84 F2 = 20° 17.03 30.20 F3 = 30° 35.06 37.50 F4 = 40° 55.05 37.72 F5 = 50° 73.45 31.65

Figure 14. Locus of feed position.

3.3.2. Aperture Distribution Condition Table 5. Feed Coordinate. The design parameters of the aperture distribution condition (ADC) are tabulated in Table 1, Feed Angle ( ) Feed Coordinate which is shown in Section 2.4. TheθF ADC lens structure and multi beam radiation characteristic are y z shown in Figure 15a,b, respectively. The ADC lens produces a good multi beam pattern in the angle F1 = 10◦ 4.49 16.84 range of 40° (F1 to F4). It shows a slight drop in gain at the scanning angle θF of 50° (F5). Moreover, F2 = 20 17.03 30.20 the deterioration of the half power◦ beam width is not significant with a difference of about 1.43° as F3 = 30◦ 35.06 37.50 compared to the on-focusF4 feed= 40 (F0). 55.05 37.72 ◦ Figure 14. Locus of feed position. F5 = 50◦ 73.45 31.65 3.3.2. Aperture Distribution Condition 3.3.2. Aperture Distribution Condition The design parameters of the aperture distribution condition (ADC) are tabulated in Table 1, whichThe is shown design in parameters Section 2.4. of The the ADC aperture lens distribution structure and condition multi beam (ADC) radiation are tabulated characteristic in Table are1, shownwhich isin shownFigure 15a,b, in Section respectively. 2.4. The ADCThe ADC lens lens structure produces and a multi good beam multi radiation beam pattern characteristic in the angle are shown in Figure 15a,b, respectively. The ADC lens produces a good multi beam pattern in the angle range of 40° (F1 to F4). It shows a slight drop in gain at the scanning angle θF of 50° (F5). Moreover, therange deterioration of 40◦ (F1 toof F4).the half It shows power a slightbeam dropwidth in is gain not atsignificant the scanning with angle a differenceθF of 50 of◦ (F5). about Moreover, 1.43° as comparedthe deterioration to the on-focus of the half feed power (F0). beam width is not signiﬁcant with a diﬀerence of about 1.43◦ as compared to the on-focus feed (F0).

(a) (b)

Figure 15. (a) ADC structure; (b) Multi beam radiation patterns for ADC lens shape.

Table 6 summarizes the multi beam radiation characteristics and feed angles. The relation between the feed angle, θF, and the beam shift angle, θS, can be expressed as θF = aθS. The value of a is changed from 1.14 to 1.33 depending on the feed angles of 10° to 50°.

(a) (b)

FigureFigure 15. 15. (a(a) )ADC ADC structure; structure; ( (bb)) Multi Multi beam beam radiation radiation patterns patterns for for ADC ADC lens lens shape. shape.

TableTable 66 summarizes summarizes the the multi multi beam beam radiation radiation characteristics characteristics and feed and angles. feed angles. The relation The betweenrelation betweenthe feed angle,the feedθF angle,, and the θF, beam and the shift beam angle, shiftθS ,angle, can be θ expressedS, can be expressed as θF = aθ asS. TheθF = a valueθS. The of valuea is changed of a is changedfrom 1.14 from to 1.33 1.14 depending to 1.33 depending on the feed on anglesthe feed of angles 10◦ to of 50 ◦10°. to 50°.

Sensors 2020, 20, x FOR PEER REVIEW 13 of 17

Table 6. Multi beam characteristics of ADC lens.

Sensors 2020, 20, 5849 13 of 17 Feed Angle θF Shifted Beam θs Gain Difference Feed Position HPBWθBS Gain (dBi) (°) (°) (dBi)

F0 0 Table 6. Multi 0 beam characteristics6.54 of ADC27.55 lens. 0 F1 10 8.7 6.66 27.22 -0.33 Feed Position Feed Angle θF (◦) Shifted Beam θs (◦) HPBWθBS Gain (dBi) Gain Diﬀerence (dBi) F2 20 16.8 7.00 27.25 -0.30 F0 0 0 6.54 27.55 0 F3F1 30 10 24.6 8.77.57 6.66 26.65 27.22 -0.90 0.33 − F4F2 40 20 31.8 16.8 8.00 7.00 25.23 27.25 -2.32 0.30 − F5F3 50 30 37.5 24.6 8.03 7.57 23.03 26.65 -4.52 0.90 − F4 40 31.8 8.00 25.23 2.32 − F5 50 37.5 8.03 23.03 4.52 3.3.3. Abbe’s Sine Condition −

3.3.3.In optics, Abbe’s Abbe’s Sine Condition sine condition is well known for designing a collimating lens for a limited scan. This ASC lens structure and multi beam radiation characteristic for on-focus (F0) and off-focus feeds (F1–F5) Inare optics, shown Abbe’s in Figure sine 16a,b, condition respectively. is well known A similar for trend designing with athe collimating ADC lens lenshas been for a discussed limited scan. in SectionThis ASC 3.3.2, lens which structure shows and a multigood beamradiation radiation pattern characteristic produced by for the on-focus ASC lens (F0) for and angle oﬀ-focus range feedsof 40°.(F1–F5) are shown in Figure 16a,b, respectively. A similar trend with the ADC lens has been discussed in Section 3.3.2, which shows a good radiation pattern produced by the ASC lens for angle range of 40◦.

(a) (b)

FigureFigure 16. 16.(a) ASC(a) ASC structure; structure; (b) (Multib) Multi beam beam radiation radiation pattern pattern for forASC ASC lens. lens.

TheThe multi multi beam beam characteristics characteristics of ASC of ASC are aretabulated tabulated in Table in Table 7, which7, which specifies speciﬁes the the shifted shifted beam beam directiondirection (θS (),θ HPBW(S), HPBW(θBSθ) andBS) and gain gain for each for each feed feed angle. angle. Based Based on the on thetable, table, a clear a clear correlation correlation between between thethe feed feed angle, angle, θF,θ andF, and shifted shifted beam beam direction, direction, θS,θ isS, observed is observed and and it can it can be beexpressed expressed as asθFθ =F b=θSb, θS, wherewhere the the b valueb value is determined is determined to be to befrom from 1.11 1.11 to 1.27. to 1.27. It can It can be clearly be clearly seen seen that that there there are areno nochanges changes in gainin gain for forfeed feed position, position, F1, F1, but but a slight a slight decremen decrementt is observed is observed from from F2 F2to toF4. F4. Slight Slight deterioration deterioration occursoccurs in the in the main main beam beam for forF5 F5as the as thegain gain is dropped is dropped to 23.03 to 23.03 dBi dBi from from F0 F0with with a gain a gain difference diﬀerence of of aboutabout −4.684.68 dBi. dBi. The The maximum maximum shifted shifted beam beam direction direction is 39.3° is 39.3 whenwhen the thefeed feed angle angle is at is 50°. at 50 . − ◦ ◦

TableTable 7. Multi 7. Multi beam beam characteristics characteristics of ASC of ASC lens. lens.

Feed PositionFeed Feed Angle Angle θθF F (◦)Shifted Shifted Beam Beam θs θs (◦) HPBWθBS Gain (dBi) GainGain Di Differenceﬀerence (dBi) Feed Position HPBWθBS Gain (dBi) F0(°) 0(°) 0 6.40 27.77(dBi) 0 F0 F10 10 0 96.40 6.5027.77 27.77 0 0 F2 20 17.4 6.83 27.68 0.09 F1 10 9 6.50 27.77 −0 F3 30 25.8 7.33 26.92 0.85 F2 20 17.4 6.83 27.68 −0.09− F4 40 33.3 7.89 25.31 2.46 − F3 F530 50 25.8 39.37.33 8.5526.92 23.09 −0.854.68 F4 40 33.3 7.89 25.31 −2.46− F5 50 39.3 8.55 23.09 −4.68 3.4. Proposed Lens by Straight-Line Condition

The detailed lens parameters and structures calculated based on the newly proposed SLC method are tabulated in Table1 and are shown in Figure 17a. This lens shape provides the lowest thickness as compared to the ADC and ASC lenses. The multi beam radiation characteristic for SLC is shown in Figure 17b, which is calculated for feed angle of θF = 0◦ to 50◦. From the ﬁgure, it is clearly seen that Sensors 2020, 20, x FOR PEER REVIEW 14 of 17

3.4. Proposed Lens by Straight-Line Condition The detailed lens parameters and structures calculated based on the newly proposed SLC method are tabulated in Table 1 and are shown in Figure 17a. This lens shape provides the lowest thickness as compared to the ADC and ASC lenses. The multi beam radiation characteristic for SLC Sensors 2020, 20, 5849 14 of 17 is shown in Figure 17b, which is calculated for feed angle of θF = 0° to 50°. From the figure, it is clearly seen that the tilt angle of 40° can also produce a good multi beam radiation pattern. At the beam directionthe tilt of angle θs = 42.6°, of 40◦ thecan beam also producedeformation a good becomes multi beamlarge. radiation pattern. At the beam direction of θs = 42.6◦, the beam deformation becomes large.

(a) (b)

FigureFigure 17. ( 17.a) SLC(a) SLCstructure; structure; (b) Multi (b) Multi beam beam radiation radiation pattern pattern for SLC for SLClens. lens.

TheThe details details of the of the SLC SLC multi multi beam beam characteristics characteristics are shown inin TableTable8. 8. It isIt foundis found that that F1 isF1 similar is similarto the to ASCthe ASC lens lens where where there there is no is reduction no reduction in gain in but gain it showsbut it shows a slightly a slightly wider HPBW.wider HPBW. It also has It an alsoalmost has an similar almost relationship similar relationship to the ADC to andthe ADC ASC, whereand ASC, the feedwhere angle, the feedθF, and angle, shifted θF, and beam shifted direction, beamθS direction,, can be expressed θS, can be as expressedθF = cθS as. The θF = range cθS. The value range of valuec varies of c from varies 1.07 from to 1.17.1.07 to It 1.17. can beIt can seen be that seenthe that feed the angle,feed angle,θF, is θ largerF, is larger than than the shiftedthe shifted beam beam direction, direction,θS, θ forS, for all all lenses lenses (ADC, (ADC, ASC ASC and and SLC). SLC).This This condition condition is demonstratedis demonstrated based based on theon the principle principle of Snell’s of Snell’s Law Law when when the wavesthe waves are passingare passingthrough through between between two boundariestwo boundaries from from free space free space to a dielectric to a dielectric material. material. However, However, gain reduction gain reductionbecomes becomes large for large both for feeds both at feeds F4 and at F4 F5, and respectively. F5, respectively.

TableTable 8. Multi 8. Multi beam beam characteristics characteristics of SLC of SLClens. lens. Feed Position Feed Angle ( ) Shifted Beam s ( ) HPBW Gain (dBi) Gain Diﬀerence (dBi) Feed Angle θFθ F ◦ Shifted Beam θs θ ◦ θBS Gain Difference Feed Position HPBWθBS Gain (dBi) F0(°) 0(°) 0 6.54 27.69(dBi) 0 F0 F10 10 0 9.36.54 6.6327.69 27.69 0 0 F2 20 18 7.00 27.38 0.31 F1 10 9.3 6.63 27.69 0− F3 30 26.7 7.83 26.41 1.28 − F2 F420 40 18 35.17.00 9.1327.38 24.35 −0.313.34 − F3 F530 50 26.7 42.67.83 14.3326.41 21.00 −1.286.69 − F4 40 35.1 9.13 24.35 −3.34 F5 50 42.6 14.33 21.00 −6.69 In order to understand the beam shapes more in detail, 2D radiation patterns are shown in Figure 18. At a feed angle of θ = 0 and 20 , the symmetrical main beam shapes in the theta (θ) and In order to understand the beamF ◦ shapes ◦more in detail, 2D radiation patterns are shown in Sensorsphi (φ 2020) directions, 20, x FOR are PEER achieved. REVIEW In θF = 40◦, the main beam shape is not symmetrical. This beam15 shape of 17 Figure 18. At a feed angle of θF = 0° and 20°, the symmetrical main beam shapes in the theta (θ) and deformation is caused by the aperture phase aberration in the oﬀ-focus feed. phi (ɸ) directions are achieved. In θF = 40°, the main beam shape is not symmetrical. This beam shape deformation is caused by the aperture phase aberration in the off-focus feed.

(a) θF = 0° (b) θF = 20° (c) θF = 40°

FigureFigure 18. 18.SLC SLC 2D2D radiationradiation patternpattern atat feedfeed angleangle (a(a))θ θFF == 00°,◦,( (b) θF == 20°,20◦ ,((cc) )θθF F= =40°.40 ◦.

AccordingAccording to Tables6 –6–8,8, the the beam beam directions directions of of ADC, ADC, ASC ASC and and SLC SLC from from the the feed feed angles angles 0 ◦ to 0° 50 to◦ 50°are are shown shown in Table in Table9. The 9. usefulness The usefulness of the SLCof the design SLC methoddesign method is clariﬁed, is clarified, as maximum as maximum beam direction beam direction obtained is at θs = 42.6° as compared to ADC and ASC, where the beam directions are θs = 37.5° and θs = 39.3°, respectively. The correlation between the feed angle and the beam direction for all lenses is shown in Figure 19.

Table 9. Beam direction of ADC, ASC and SLC lenses.

Feed Angle, θF Beam Direction, θs ADC ASC SLC 0 0 0 0 10 8.7 9 9.3 20 16.8 17.4 18 30 24.6 25.8 26.7 40 31.8 33.3 35.1 50 37.5 39.3 42.6

Figure 19. Feed angle and beam direction of ADC, ASC and SLC.

The correlation between the gain reduction and the shifted beam directions is shown in Figure 20. At beam directions of less than θS = 40°, the gain reduction of ADC, ASC and SLC become similar. At θS = 42.6°, the gain reduction increases to −6.69 dBi. From this figure, it is concluded that the proposed SLC achieves good multi beam radiation patterns as compared to the ADC and ASC lenses.

Sensors 2020, 20, x FOR PEER REVIEW 15 of 17

(a) θF = 0° (b) θF = 20° (c) θF = 40°

Figure 18. SLC 2D radiation pattern at feed angle (a) θF = 0°, (b) θF = 20°, (c) θF = 40°.

SensorsAccording2020, 20, 5849 to Tables 6–8, the beam directions of ADC, ASC and SLC from the feed angles15 0° of to 17 50° are shown in Table 9. The usefulness of the SLC design method is clarified, as maximum beam direction obtained is at θs = 42.6° as compared to ADC and ASC, where the beam directions are θs = obtained is at θs = 42.6◦ as compared to ADC and ASC, where the beam directions are θs = 37.5◦ and 37.5° and θs = 39.3°, respectively. The correlation between the feed angle and the beam direction for θs = 39.3◦, respectively. The correlation between the feed angle and the beam direction for all lenses is all lenses is shown in Figure 19. shown in Figure 19.

Table 9. Beam direction of ADC, ASC and SLC lenses. Table 9. Beam direction of ADC, ASC and SLC lenses.

Feed Angle, θF Beam Direction, θs Feed Angle, θ Beam Direction, θs F ADC ASC SLC ADC ASC SLC 0 0 0 0 010 08.7 9 09.3 0 1020 8.716.8 17.4 918 9.3 20 16.8 17.4 18 30 24.6 25.8 26.7 30 24.6 25.8 26.7 40 31.8 33.3 35.1 40 31.8 33.3 35.1 5050 37.537.5 39.3 39.3 42.6 42.6

FigureFigure 19. 19. FeedFeed angle angle and and beam beam direction direction of of ADC, ADC, ASC ASC and and SLC. SLC.

TheThe correlation correlation between thethe gaingain reductionreduction and and the the shifted shifted beam beam directions directions is is shown shown in in Figure Figure 20 . 20.At At beam beam directions directions of of less less than thanθS θ=S =40 40°,◦, thethe gaingain reductionreduction of ADC, ASC ASC and and SLC SLC become become similar. similar. At θ = 42.6 , the gain reduction increases to 6.69 dBi. From this ﬁgure, it is concluded that the At θS = 42.6°,◦ the gain reduction increases to −−6.69 dBi. From this figure, it is concluded that the proposedSensorsproposed 2020 ,SLCSLC 20, x achievesFOR achieves PEER goodREVIEW good multi multi beam beam radiation radiation patterns patterns as as compared compared to to the the ADC ADC and and ASC ASC lenses.16 lenses. of 17

FigureFigure 20. 20. GainGain difference diﬀerence of each each shifted beam for ADC, ASC and SLC.

4. Conclusions 4. Conclusions The new thin lens antenna has been designed by applying a straight-line condition. Multi beam The new thin lens antenna has been designed by applying a straight-line condition. Multi beam radiation patterns are achieved and, as compared to the conventional lens antenna designed based on radiation patterns are achieved and, as compared to the conventional lens antenna designed based Abbe’s sine condition (ASC) and aperture distribution condition (ADC), this method also produced on Abbe’s sine condition (ASC) and aperture distribution condition (ADC), this method also good results. For wide-angle beam scanning operation of up to 30 from the centre beam, good multi produced good results. For wide-angle beam scanning operation ◦of up to 30° from the centre beam, good multi beam radiation patterns with small beam shape distortion are achieved. The usefulness of the newly developed shaped lens is ensured for multi beam radiation pattern characteristics in which an aperture efficiency of approximately 68.39% is achieved.

Funding: This work was funded by the HICOE research grant with vote number [4J411], and the Universiti Teknologi Malaysia with research grant vote number [00L68].

Acknowledgments: The authors would like to thank the Ministry of Higher Education (MoHE) for the HLP scholarship and the HICOE research grant.

Conflicts of Interest: The authors declare no conflict of interest.

References

Sensors 2020, 20, 5849 16 of 17 beam radiation patterns with small beam shape distortion are achieved. The usefulness of the newly developed shaped lens is ensured for multi beam radiation pattern characteristics in which an aperture eﬃciency of approximately 68.39% is achieved.

Author Contributions: F.A. made an extensive contribution of the conceptualization, design, analysis and original draft preparation. T.A.R. contributed in funding, supervising and reviewing the manuscript. Y.Y. participated in funding, supervising and validating the analysis critically for important intellectual contents. N.H.A.R.: technical consultation, reviewing and editing and K.K.: reviewing and editing. All authors have read and agreed to the published version of the manuscript. Funding: This work was funded by the HICOE research grant with vote number [4J411], and the Universiti Teknologi Malaysia with research grant vote number [00L68]. Acknowledgments: The authors would like to thank the Ministry of Higher Education (MoHE) for the HLP scholarship and the HICOE research grant. Conﬂicts of Interest: The authors declare no conﬂict of interest.

References

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