A Design Approach of Optical Phased Array with Low Side Lobe Level and Wide Angle Steering Range

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Article A Design Approach of Optical Phased Array with Low Side Lobe Level and Wide Angle Steering Range

Xinyu He, Tao Dong *, Jingwen He and Yue Xu

State Key Laboratory of Space-Ground Integrated Information Technology, Beijing Institute of Satellite Information Engineering, Beijing 100095, China; [email protected] (X.H.); [email protected] (J.H.); [email protected] (Y.X.) * Correspondence: [email protected]

Abstract: In this paper, a new design approach of optical phased array (OPA) with low side lobe level (SLL) and wide angle steering range is proposed. This approach consists of two steps. Firstly, a nonuniform antenna array is designed by optimizing the antenna spacing distribution with particle swarm optimization (PSO). Secondly, on the basis of the optimized antenna spacing distribution, PSO is further used to optimize the phase distribution of the optical antennas when the beam steers for realizing lower SLL. Based on the approach we mentioned, we design a nonuniform OPA which has 1024 optical antennas to achieve the steering range of ±60◦. When the beam steering angle is 0◦, 20◦, 30◦, 45◦ and 60◦, the SLL obtained by optimizing phase distribution is −21.35, −18.79, −17.91, −18.46 and −18.51 dB, respectively. This kind of OPA with low SLL and wide angle steering range has broad application prospects in laser communication and lidar system.

Keywords: optical phased array; antenna array; low side lobe; wide angle steering range

1. Introduction Citation: He, X.; Dong, T.; He, J.; Xu, Optical phased array (OPA) is an array operating at optical frequency that achieves Y. A Design Approach of Optical beam steering by controlling the phase distribution of the optical antennas. OPA has the Phased Array with Low Side Lobe abilities of fast beam steering and beam agility, and it has the advantages of small size, Level and Wide Angle Steering light weight, high resolution and good security. OPA has broad application prospects Range. Photonics 2021, 8, 63. https:// in laser communication, lidar and other fields [1–3]. At present, silicon-based OPA is a doi.org/10.3390/photonics8030063 common OPA design [4]. Arc dielectric grating antenna is mostly used in silicon-based OPA to realize light radiation. In order to realize effective radiation, the size of the arc Received: 28 January 2021 grating antenna is relatively large. In [5], the width of the arc grating antenna designed Accepted: 22 February 2021 µ µ Published: 25 February 2021 by Sun et al. is 2.8 m, which is much larger than the wavelength 1.55 m commonly used in optical communication. OPAs with equal antenna spacings and equal excitation amplitudes have been proposed and demonstrated many times [6–8]. Due to the large Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in size of the antenna, the antenna spacing between two adjacent antennas is larger than one published maps and institutional affil- wavelength. Therefore, there are grating lobes in the far field pattern of the OPA, which iations. results in a small beam steering range. The grating lobes cannot be effectively suppressed by weighting the amplitudes and the phases of the array excitation. A lot of research literatures have proved that the grating lobes can be suppressed by using nonuniform arrays [9–12]. In [12], a nonuniform OPA with 128 antennas is proposed and fabricated by CMOS (complex metal oxide semiconductor) technology compatible with silicon photonic Copyright: © 2021 by the authors. technology. The beam steering range of ±40◦ is achieved, and the side lobe level (SLL) is Licensee MDPI, Basel, Switzerland. − ◦ This article is an open access article 10 dB when the beam direction is 0 . However, in order to meet the wider application, distributed under the terms and we need to further suppress the SLL and achieve wider beam steering range. conditions of the Creative Commons In this paper, a design approach is proposed to realize the low SLL and wide angle Attribution (CC BY) license (https:// steering of OPA by optimizing the antenna spacing distribution and the antenna phase creativecommons.org/licenses/by/ distribution, respectively. Firstly, the particle swarm optimization (PSO) is used to optimize 4.0/). the antenna spacing distribution to achieve the grating lobes and side lobes suppression.

Photonics 2021, 8, 63. https://doi.org/10.3390/photonics8030063 https://www.mdpi.com/journal/photonics Photonics 2021, 8, x FOR PEER REVIEW 2 of 9

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optimize the antenna spacing distribution to achieve the grating lobes and side lobes suppression. Secondly, after obtaining the antenna spacing distribution, we further Secondly, after obtaining the antenna spacing distribution, we further optimize the phase distributionoptimize the ofphase the distribution designed nonuniform of the designed antenna nonuniform array by antenna PSO under array different by PSO under beam steeringdifferent anglesbeam steering to suppress angles the to side suppress lobes inthe the side beam lobes steering in the beam state. steering After two state. steps After of optimization,two steps of optimization, the SLL lower the than SLL− lower17.91 dBthan under −17.91 the dB beam under steering the beam and steering a wide angleand a steeringwide angle range steering±60◦ rangeof the ±60° OPA of are the realized. OPA are realized.

2. Design A Approachpproach of Optical Phased Array Figure1 1 displays displays thethe schematicschematic diagramdiagram ofof OPA.OPA. Light Light from from a a tunable tunable laser laser is is fed fed into into the waveguide through a gratinggrating coupler, andand thenthen isis evenlyevenly distributeddistributed toto NN waveguideswaveguides through thethe opticaloptical distributiondistribution network.network. The phase of light in each waveguide isis controlledcontrolled by a tunable phase shifter. As shown in FigureFigure1 1,, the the waveguide waveguide arrayarray isis connected connected toto thethe grating antenna array, and the light light is is radiated radiated by by these these grating grating antennas. antennas.

Figure 1. Schematic diagram of optical phased array (OPA).(OPA).

The far ﬁeldfield pattern of a nonuniformnonuniform arrayarray isis [[13]13]::

N−1N −1 2 2πjx(sin− sin ) j xn(sinnsθ−sin θs) E(θ) = Ane λ  (1) E() ∑= An e (1) =  n 1n=1

n−1 n−1 xn = ∑ dk (2) xdnk=k=1 (2) k=1 where An is the excitation amplitude of the n-th optical antenna, N is the number of

antennas,where An andis theλ, θ excitationand θs denote amplitude the operating of the n wavelength,-th optical antenna, the observation N is the direction number and of theantenna specifieds, and beam λ, θ and steering θs denote angle, the respectively. operating wavelength, In our design, the the observation excitation direction amplitude and is equal,the specified i.e., An beam= 1. The steering parameter angle,d respectivelyk is the distance. In our between design, the thek +excitation 1-th antenna amplitude and the is kequal,-th antenna, i.e., An and= 1. Thexn is parameter the position dk coordinateis the distance of the betweenn-th antenna. the k + 1-th antenna and the k- th antenna,The expression and xn is ofthe SLL position is: coordinate of the n-th antenna. E2 The expression of SLL is: SLL = max−sidelobe (3) E2 Emainlobe2 2 max− sidelobe 2 where E max−sidelobe is the intensity of theSLL maximum= 2 side lobes and E mainlobe is the intensity(3) of the main lobe. Emainlobe Due to the restriction of the optical antenna size, the antenna spacing of the OPA is where E2max−sidelobe is the intensity of the maximum side lobes and E2mainlobe is the intensity of difficultthe main to lobe be suppressed. to less than one wavelength. The grating lobes will appear in the far field pattern, which limits the steering range of the array. Therefore, the nonuniform arrangement of the antenna array is adopted to design the OPA.

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Due to the restriction of the optical antenna size, the antenna spacing of the OPA is difficult to be suppressed to less than one wavelength. The grating lobes will appear in Photonics 2021, 8, 63 3 of 9 the far field pattern, which limits the steering range of the array. Therefore, the nonuniform arrangement of the antenna array is adopted to design the OPA.

2.1.2.1. Optimizing Optimizing the theSpacing Spacing Distri Distributionbution of the of theAntennas Antennas In In order order to to achieve achieve the the grating grating lobes lobes and and side side lobes lobes suppression, suppression, the global the optimiza- global optimizationtion algorithm algorithm PSO [ 14PSO] is [14] used is to used ﬁnd to the find optimal the optimal antenna antenna spacing spacing distribution. distribution. PSOPSO is a is bionic a bionic optimization optimization algorithm, algorithm, and and it is it a is stochastic a stochastic opt optimizationimization algorithm algorithm developeddeveloped by byimitating imitating the the foraging foraging behavior behavior of birds. of birds. In the In the algorithm, algorithm, each each of the of the birds birds is takenis taken as a as particle, a particle, and and it only it only has has two two attributes attributes of velocity of velocity and and position. position. PSO PSO has has been been widelywidely used used because because of its of itssimple, simple, less less constraints constraints and and strong strong global global optimization optimization ability. ability. TheThe flow ﬂow chart chart of PSO of PSO algorithm algorithm is shown is shown in inFigure Figure 2. 2.

FigureFigure 2. Flow 2. Flow chart chart of particle of particle swarm swarm optimization optimization (PSO (PSO)) algorithm algorithm..

TheThe steps steps involved involved in PSO in PSO are are as asfollows. follows. (i) (i)InitializationInitialization of particle of particle swarm. swarm. First First of all, of all,appropriate appropriate search search space space range range and and flight flight velocityvelocity range range should should be beset. set. After After that, that, a set a setof random of random initialization initialization velocities velocities and and positionspositions are are given given in inthe the preset preset velocity velocity range range and and space space range. range. Meanwhile, Meanwhile, the the numbernumber of particles of particles is set. is set. (ii)(ii) CalculationCalculation of particles of particles fitness fitness value. value. It is It necessary is necessary to set to setup upa fitness a fitness function function for for evaluatingevaluating the theperformance performance of the of theparticles. particles. In our In our study, study, the the SLL SLL is used is used for for fitness fitness evaluation. evaluation. (iii) Searching for global optimal solution. Firstly, the historical optimal solution found (iii) Searching for global optimal solution. Firstly, the historical optimal solution found by each particle is regarded as the individual optimal solution pbest. Secondly, an by each particle is regarded as the individual optimal solution pbest. Secondly, an optimal solution is found from these individual optimal solutions as the global optimal solution is found from these individual optimal solutions as the global optimal solution gbest. optimal solution gbest. (iv) Updating the velocities and positions. The velocity and position for i-th particle are (iv) Updating the velocities and positions. The velocity and position for i-th particle are obtained by the following equations: obtained by the following equations: + j+j1 1 jj jj j j V = ω × V + c1 × rand() × (pbest − X ) Vii =  V i +i c1  rand()  ( pbest i −i X i )i (4) j j (4) +c2 × rand()jj× (gbest − Xi ) +c2  rand()  (g best − X i ) j+1 j j+1 Xi = Xi + Vi (5) j+1 j j+ 1 where V and X represent the velocityXXV andi=+ position i of i the particle, respectively. The subscript(5) i is the particle number, and the superscript j is the number of iterations. The function rand() represents a random number between 0 and 1. The parameters c1 and c2 are learning factors, and ω is called inertia factor.

After the positions and velocities of particles are updated, it is necessary to judge whether the positions and velocities of the particles exceed the constraint conditions. In Photonics 2021, 8, 63 4 of 9

the process of optimization, the absorption boundary is adopted for the problem of cross- border. That is, if Xi < Xmin, then Xi = Xmin, and if Xi > Xmax, then Xi = Xmax. It is the same way for the cross-boundary processing of particle velocity. (v) Termination condition. If the difference of four consecutive results is smaller than the preset value, the optimization is terminated. In this step, the optimization can be expressed as to ﬁnd the spacing distribution to minimize the SLL by: min SLL s.t. min(d1, d2, ··· , dN−1) ≥ dmin (6) max(d1, d2, ··· , dN−1) ≤ dmax

where the antenna spacing di is variable, which corresponds to Xi in Equations (4) and (5). The parameter dmin is the minimum antenna spacing, and dmax is the maximum antenna spacing. In our design, the optimization is terminated when the difference of four consecutive results is less than 0.01 dB. In PSO algorithm, the number of particles is an important parameter, which depends on the number of the optimization variable. A smaller number of particles will reduce the global searching ability of the algorithm, while a large number of particles will employ too many computing resources and reduce the efﬁciency of the algorithm. For an optical phased array with 1024 antennas, 200 particles can be used to obtain a better optimization result with less computing time. The learning factor c1 and c2 are set as 2. In [15], Xu et al. proposed a plasmonic optical antenna with a subwave- length footprint, which is helpful to achieve antenna spacing smaller than one wavelength. Considering the size of the optical antenna and the mutual couplings between the optical antennas, the minimum antenna spacing dmin is set as 0.8λ, and the maximum antenna spacing dmax is set as 3λ. The operating wavelength is 1.55 µm. The minimum value of particle velocity vdmin is equal to (dmin − dmax)/2, and the maximum value vdmax is equal to (dmax − dmin)/2. The array we designed contains 1024 optical antennas, and the antenna distribution is set to symmetric distribution, and the SLL calculated at the steering angle ◦ ◦ of 0 , i.e., the steering angle θs is set as 0 . After optimization, a set of antenna spacings (d1, d2,..., dN−1) is obtained.

2.2. Optimizing the Antenna Phase Distribution under Beam Steering By optimizing the antenna spacing distribution, both the grating and side lobes can be suppressed effectively. Based on the designed spacing distribution of the antennas, the far field pattern with steering angles of 20◦, 30◦, 45◦ and 60◦ also can be calculated by (1). When the beam steers, the SLL becomes significantly higher than that of the beam pointing to 0◦ [16]. For a given OPA, the antenna spacing distribution is fixed, but the phase of light in each antenna can be changed in real time. Therefore, we further optimize the antenna phase distribution under different steering angles by utilizing PSO, so as to make the SLL as low as possible during the beam steering. When the phase of the array is no longer linearly distributed as in equation (1), it is a variable. The far field pattern of the array is expressed as: N−1 2π j( xn sin θ+αn) E(θ) = ∑ Ane λ (7) n=1

where the parameter αn represents the phase of the n-th antenna. In this step, the optimization can be expressed as to ﬁnd the antenna phase distribution to minimize the SLL by min SLL s.t. min(α1, α2, ··· , αN−1) ≥ αmin (8) max(α1, α2, ··· , αN−1) ≤ αmax

where the antenna spacing αi is variable, which corresponds to Xi in Equations (4) and (5). The parameter αmin is the minimum phase, and αmax is the maximum phase. Photonics 2021, 8, x FOR PEER REVIEW 5 of 9

Photonics 2021, 8, 63 5 of 9 min SLL

st. . min(1 ,  2 , , N − 1 )   min (8) In the phase optimization process. The optimization is terminated when the difference max( ,  , ,  )   of four consecutive results is less than 0.011 dB, 2 the numberN − 1 of max particles is 200. The learning factor c and c are set as 2. The antenna spacing distribution of the OPA is the result where the1 antenna2 spacing 훼i is variable, which corresponds to Xi in Equations (4) and (5). optimized by PSO in the previous step. The minimum phase α , and the maximum The parameter 훼min is the minimum phase, and 훼max is the maximummin phase. π phaseIn αthemax phaseare set optimization to 0 and 2 ,process respectively.. The optimization Similarly, the is minimum terminated velocity when thevαmin differenceis equal − v − ofto four (αmin consecutiveαmax)/2, results and the is l maximumess than 0.01 velocity dB, the numberαmax is equalof particles to (αmax is 200.α Themin)/2. learning After optimization, a set of phase distribution (α1, α2, ... , αN−1) is obtained when the beam factor c1 and c2 are set as 2. The antenna spacing distribution of the OPA is the result steers to a speciﬁc angle. optimized by PSO in the previous step. The minimum phase 훼min, and the maximum phase In a word, the optimization is performed twice to achieve wide angle steering and low 훼max are set to 0 and 2π, respectively. Similarly, the minimum velocity v훼min is equal to (훼min SLL of the OPA. Firstly, a nonuniform antenna array is designed to suppress the grating − 훼max)/2, and the maximum velocity v훼max is equal to (훼max − 훼min)/2. After optimization, a set and side lobes. The antenna spacing distribution of the OPA is optimized by using the PSO. of phase distribution (훼1, 훼2, … , 훼N-1) is obtained when the beam steers to a specific angle. Secondly, on the basis of the optimized antenna spacing distribution, the SLL is further In a word, the optimization is performed twice to achieve wide angle steering and reduced by optimizing the phase distribution of the antennas for different beam steering low SLL of the OPA. Firstly, a nonuniform antenna array is designed to suppress the angle by PSO. grating and side lobes. The antenna spacing distribution of the OPA is optimized by using the3. ResultsPSO. Secondly, and Discussions on the basis of the optimized antenna spacing distribution, the SLL is further reduced by optimizing the phase distribution of the antennas for different beam In this Section, the design approach mentioned above is utilized to realize low SLL steeringand wide angle angle by steering PSO. range of an OPA with 1024 antennas.

3.3.1. Results Simulation and Di Resultsscussion Obtaineds by Optimizing the Spacing Distribution of the Antennas InFigure this Section3 shows, the the design antenna approach spacing mentioned distribution above of the is utilized nonuniform to realize 1024-antenna low SLL andarray wide obtained angle steering by PSO. range It shows of an that OPA the with antenna 1024 distribution antennas. is sparse at both ends and dense in the middle. The aperture of the whole array is 1267.5 λ. We calculate the far field 3.1.pattern Simulation of the Results nonuniform Obtained array by whoseOptimizing antenna the Spacing spacing Distribution distribution of is the shown Antennas in Figure 3 by (1).Figure Figure 3 shows4a,b shows the antenna the far field spacing patterns distribution of the nonuniform of the nonuniform antenna array 1024 when-antenna the ◦ ◦ arraybeam obtained steering by angle PSO. is 0It showsand 20 that, respectively. the antenna distribution is sparse at both ends and denseFor in the comparative middle. The analysis, aperture far of field the whole pattern array of a uniformis 1267.5 1024-antennaλ. We calculate array the far with field the psameattern aperture of the nonuniform as the designed array nonuniform whose antenna array spacing is calculated. distribution The antenna is shown spacing in Figure of the 3 byuniform (1). Figure array 4a is,b 1.24showλs. the Figure far 5fielda,b showspatterns the of far the field nonuniform patterns antenna of the uniform array when antenna the ◦ ◦ beamarray steering when the angle beam is steering0° and 20°, angle respectively. is 0 and 20 , respectively.

FigureFigure 3. 3. OptimizedOptimized antenna antenna spacing spacing distribution distribution of of an an array array with with 1024 1024 antennas antennas..

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(a) (b)

Figure 4. The far field patterns of the nonuniform array with 1024 antennas, when the steering angle θs is (a) 0° and (b) 20°, respectively.

For comparative analysis, far field pattern of a uniform 1024-antenna array with the same( aaperture) as the designed nonuniform array is calculated.(b) The antenna spacing of the uniform array is 1.24 λ. Figure 5a,b shows the far field patterns of the uniform antenna Figure 4. The far field patterns of the nonuniform array with 1024 antennas, when the steering angle θs is (a) 0° and◦ (b) Figure 4. The far ﬁeld patternsarray of when the nonuniform the beam steering array with angl 1024e is antennas, 0° and 20°, when respectively. the steering angle θs is (a) 0 and (b20°,) 20 respectively◦, respectively..

For comparative analysis, far field pattern of a uniform 1024-antenna array with the same aperture as the designed nonuniform array is calculated. The antenna spacing of the uniform array is 1.24 λ. Figure 5a,b shows the far field patterns of the uniform antenna array when the beam steering angle is 0° and 20°, respectively.

(a) (b)

s ◦ FigureFigure 5. 5. TheThe farfar ﬁeldfield patternspatterns of the uniform array array with with 1024 1024 antennas, antennas, when when the the beam beam steering steering angle angle θ θ iss is(a) ( a0°) 0andand (b) (b20°,) 20 respectively◦, respectively..

ItIt cancan bebe seenseen fromfrom FiguresFigure s4 4and and5 that5 that for for the the antenna antenna arrays arrays with with the the same same aperture aperture andand thethe(a) samesame numbernumber ofof antennas,antennas, thethe gratinggrating lobeslobes( appearbappear) inin thethe farfar ﬁeldfield patternpattern ofof thethe uniformuniform array, array, while while the the grating grating lobes lobes are are obviously obviously suppressed suppressed by by nonuniform nonuniform antenna antenna Figure 5. The far field patterns of the uniform array with 1024 antennas, when the beam steering angle θs is (a) 0° and (b) spacing distribution. At the same time, we also calculate the far field pattern of uniform OPA 20°, respectively. spacing distribution. At the same time, we also calculate the far ﬁeld pattern of uniform OPAof the of same the sameaperture aperture size with size spacing with spacing of 0.45λ of between 0.45λ between the antennas the antennas,, when the when beam the steering beam ◦ ◦ steeringangleIt is can angle0°, be the seen is SLL 0 ,from theis − SLL 1Figure3.30 is dB−s 13.30,4 andand dB, the5 that andhalf for thepower the half antenna beamwidth power arrays beamwidth (HPBW with the (HPBW)) is same 0.04°. aperture is For 0.04 the. For the designed nonuniform antenna array, the SLL reaches −20.50 dB when the beam and the same number◦ of antennas, the grating◦ lobes appear in the far field pattern of the steeringuniform angle array, is while 0 , and the the grating HPBW lobes is 0.05 are. obviously After comparison, suppressed it can by be nonuniform found that antenna for the antenna array without grating lobes, the SLL of the array can be reduced by optimizing the spacing distribution. At the same time, we also calculate the far field pattern◦ of uniform OPA spacingof the same distribution aperture size of the with antennas spacing when of 0.45λ the between beam steering the antennas angle, iswhen 0 . the beam steering angle is 0°, the SLL is −13.30 dB, and the half power beamwidth (HPBW) is 0.04°. For the

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designed nonuniform antenna array, the SLL reaches −20.50 dB when the beam steering angle is 0°, and the HPBW is 0.05°. After comparison, it can be found that for the antenna array Photonics 2021, 8, 63 without grating lobes, the SLL of the array can be reduced by optimizing the spacing7 of 9 distribution of the antennas when the beam steering angle is 0°.

3.2. Simulation Results Obtained by Optimizing the Antenna Phase Distribution under Beam Steering3.2. Simulation Results Obtained by Optimizing the Antenna Phase Distribution under Beam Steering To further reduce the SLL of the nonuniform array when the beam steers, the phase distributionTo further of the reduce optical the antennasSLL of the is nonuniform further optimized array when by PSO. the beamFigure steers, 6a shows the phase the distribution of the optical antennas is further optimized by PSO. Figure6a shows the antenna phase distribution without optimization when the beam steering angle θs is 30°,◦ Figureantenna 6b phaseshows distributionthe antenna withoutphase distribution optimization with when optimization the beam when steering the beam angle stθseeringis 30 , Figure6b shows the antenna phase distribution with optimization when the beam steering angle θs is 30°.◦ Figure 7 is the far field pattern at different beam steering angles. The results inangle Figureθs is 7a 30 are. Figure directly7 is calculated the far ﬁeld by pattern (1) and at differentthe results beam in Figure steering 7b angles. are obtained The results by in Figure7a are directly calculated by (1) and the results in Figure7b are obtained by optimizing the phase distribution of the antennas. optimizing the phase distribution of the antennas.

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Figure 6. The antenna phase distribution (a) without and (b) with optimization when the beam steering angle θs is 30°.◦ Figure 6. The antenna phase distribution (a) without and (b) with optimization when the beam steering angle θs is 30 .

(a) (b)

FigureFigure 7.7. FarFar ﬁeldfield beambeam steeringsteering patternspatterns ofof thethe nonuniformnonuniform antennaantenna arrayarray ((aa)) withoutwithout andand ((bb)) withwith optimizingoptimizing phasephase atat differentdifferent steeringsteering angles.angles.

TableTable1 1 shows shows the far far field ﬁeld radiation radiation characteristics characteristics of the of the nonuniform nonuniform 1024 1024-antenna-antenna array arrayat the atbeam the steering beam steering angle of angle0°, 20°, of 30°, 0◦ ,45° 20 ◦and, 30 60°◦, 45 obtained◦ and 60 with◦ obtained different with approache differents. It can be found that compared with the approach without phase optimization, when the beam steering angle is 0°,20°, 30°, 45° and 60°, the SLL obtained by optimizing phase distribution is reduced by 0.85, 3.43, 2.55, 3.05 and 3.10 dB, respectively, and the HPBW is basically the same. Therefore, further optimizing the phase distribution of antennas under beam steering by PSO can effectively reduce the SLL of a nonuniform antenna array.

Table 1. Far field radiation characteristics of nonuniform array.

Approach Parameter 0° 20° 30° 45° 60° SLL (dB) −20.50 −15.36 −15.36 −15.41 −15.41 Without phase optimization HPBW (°) 0.05 0.05 0.05 0.07 0.09 SLL (dB) −21.35 −18.79 −17.91 −18.46 −18.51 With phase optimization HPBW (°) 0.05 0.05 0.05 0.06 0.09

4. Conclusions In summary, a design approach for realizing the OPA with low SLL and wide angle steering range is proposed. The approach includes two optimization processes. In the first optimization process, a nonuniform antenna array is designed by optimizing the antenna spacings with PSO, which helps to suppress the grating lobes and achieve wide angle steering. In the second optimization process, the SLL is further reduced when the beam steers by optimizing the antenna phase distribution. Utilizing the approach, an OPA with nonuniform 1024-antenna array is designed and a wide steering range of ± 60° is achieved. When the beam steering angle is 0°, 20°, 30°, 45° and 60°, the SLL is −21.35, −18.79, −17.91, −18.46 and −18.51 dB, respectively.

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approaches. It can be found that compared with the approach without phase optimization, when the beam steering angle is 0◦, 20◦, 30◦, 45◦ and 60◦, the SLL obtained by optimizing phase distribution is reduced by 0.85, 3.43, 2.55, 3.05 and 3.10 dB, respectively, and the HPBW is basically the same. Therefore, further optimizing the phase distribution of antennas under beam steering by PSO can effectively reduce the SLL of a nonuniform antenna array.

Table 1. Far ﬁeld radiation characteristics of nonuniform array.

Approach Parameter 0◦ 20◦ 30◦ 45◦ 60◦ Without phase SLL (dB) −20.50 −15.36 −15.36 −15.41 −15.41 optimization HPBW (◦) 0.05 0.05 0.05 0.07 0.09 With phase SLL (dB) −21.35 −18.79 −17.91 −18.46 −18.51 optimization HPBW (◦) 0.05 0.05 0.05 0.06 0.09

4. Conclusions In summary, a design approach for realizing the OPA with low SLL and wide angle steering range is proposed. The approach includes two optimization processes. In the ﬁrst optimization process, a nonuniform antenna array is designed by optimizing the antenna spacings with PSO, which helps to suppress the grating lobes and achieve wide angle steering. In the second optimization process, the SLL is further reduced when the beam steers by optimizing the antenna phase distribution. Utilizing the approach, an OPA with nonuniform 1024-antenna array is designed and a wide steering range of ± 60◦ is achieved. When the beam steering angle is 0◦, 20◦, 30◦, 45◦ and 60◦, the SLL is −21.35, −18.79, −17.91, −18.46 and −18.51 dB, respectively.

Author Contributions: Conceptualization, T.D.; methodology, X.H., T.D. and J.H.; investigation, X.H.; formal analysis, X.H., J.H. and Y.X.; writing—original draft preparation, X.H.; writing—review and editing, X.H. and J.H.; supervision, T.D. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Innovation Funds of China Aerospace Science and Technology, grant number No. Y-Y-Y-GJGXKZ-18 and No. Z-Y-Y-KJJGTX-17, and National Natural Science Foundation of China, grant number 62005020. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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