A Millimeter-Wave 2D Beam Steering Antenna Using Extended Hemispherical Dielectric Lens Antenna Subarrays

Recent work has proposed that millimeter-wave beam steering antennas consisting of lens antenna subarrays (LASs) reduce hardware complexity. This manuscript extends the concept to 2D beam steering with extended hemispherical dielectric lenses (EHDLs). To accomplish this, we introduce a design process to maximize scan range and side lobe level (SLL) performance. The design process first employs the solution of the geometric disk covering problem to identify the initial positions of the feed antennas such that the subarray size, <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula>, is minimized. This process is followed by systematic 3D full-wave simulation-based parametric sweeps of lens geometry and feed antenna positions to maximize scan range and minimize SLL. Finally, we demonstrate this process with a 38 GHz antenna consisting of <inline-formula> <tex-math notation="LaTeX">$L$ </tex-math></inline-formula> = 7 LASs and <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> = 17 feed antennas per LAS. The resulting antenna has a ±36° field of view, −9.5 dB SLL, 5° half-power beamwidth, and ~20 dBi maximum realized gain. Compared to the existing literature on subarray-based beam-steering antennas, this antenna performs with a more extensive scan range while offering a comparable SLL performance.

rate of such a system by utilizing a hybrid multiple-input-23 multiple-output (MIMO) architecture. These are formed by 24 linearly scaling up the phased array electronics with the 25 number of desired signal chains and corresponding analog- 26 to-digital/digital-to-analog converters [2], [3]. However, the 27 drive to include many antenna elements and multiple signal 28 The associate editor coordinating the review of this manuscript and approving it for publication was Tutku Karacolak . chains makes hybrid MIMO architectures very complex to 29 implement, high in operating cost, and hungry in DC power 30 consumption [4]. For large arrays, DC power consumption 31 of control components such as phase shifters (through their 32 loss compensating or variable gain amplifiers) becomes a sig-33 nificant issue that motivates researchers to investigate alter-34 native architectures [5]. Researchers have also recognized 35 phase shifter-associated hardware complexity and cost as a 36 challenge due to many control and bias signals that need rout-37 ing per the included phase shifters. There have been recent 38 improvements in reducing this complexity as one can incor-39 porate entire transmit/receive modules on a single BiCMOS 40 chip [6], yet, difficulty in integration of large antenna arrays 41 continues. subarray elements [10], [11]. While these improvements 57 show it is possible to reduce the SLL down to ≈=15 dB, 58 they achieve scan ranges on the order of ±10 • to ±20 • .

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The 1D LAS antenna design presented in [16] is based on 103 maximizing the gain of the center feed antenna under a single 104 lens. This approach was unsuitable for carrying out the pre-105 sented 2D LAS design as it led to both a small scan range and 106 high SLL. An essential need in 2D LAS design is to consider 107 the beam steering and SLL performance when one positions 108 the feed antenna out of the x and y axes to steer the beam 109 towards different elevation and azimuth directions. The possibility that side lobes appear out of the beam steering 112 plane of the primary lobe presents a critical design challenge. 113 For example, when the feed antenna is translated away from 114 the center of an EHDL (20 mm diameter and 12 mm height) 115 by 7 mm while making a 30 • angle with the x-axis, the 116 maximum of the radiation pattern manifests in the φ ==150 • 117 cut (see Fig.2a). However, this pattern does not accurately 118 represent the SLL. As seen in the 3D radiation pattern plot 119 in Fig.2b, the peaks of the side lobes are not necessarily in 120 the same azimuth cut of the main beam. To capture the side 121 lobe behavior in the design process, we extract beamwidth 122 contours from the 3D radiation pattern and plot the con-123 tours in a polar plot where radial distance represents the 124 elevation angle θ and angular position corresponds to the 125 azimuth angle φ. One can create contours for absolute gain 126 values or relative values normalized to the maximum gain. 127 The =7 dB contours in Fig.2c Fig.3 illustrates the proposed design process for the 2D 138 LAS-based antenna. The procedure is iterative in adjusting 139 the lens' geometry and spacing based on specific design cri-140 teria such as scan range, SLL, and gain variations by utilizing 141 the beamwidth contours extracted from full-wave simulated 142 3D radiation patterns.    Although the manufacturing capability allows for complex 151 lens shapes, the lens surface is kept spherical for its enhanced 152 off-axis steering ability [22]. Identifying and selecting the 153 best material for realizing the lens is beyond the scope of 154 this manuscript. As such, we selected acrylonitrile butadiene 155 styrene (ABS) for its wide availability in 3D printing and well 156 known dielectric properties (ε r = 2.4, tan δ = 0.006) from 157 recent research [23].

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For the feeding antenna, we utilized an aperture-coupled 159 patch antenna which we designed as described in [16] within 160 the presence of a semi-infinite ABS material. This decision 161 is a departure from most traditional lens antenna designs, 162 where the feed antenna type and its characteristics are con-163 sidered carefully in terms of efficiently illuminating the lens 164 surface while minimizing the side lobes. Such feed antennas 165 are physically large, which prevents dense packing on the 166 focal plane. Therefore, these feeds cannot provide beams 167 intersecting at their half-power beamwidth (HPBW) contours 168 when packed next to each other. This strategy contrasts with 169 our case, in which it is a design goal to pack many feeds on 170 the focal plane. Additionally, the small size of our lens further 171 complicates feed optimization as radiation characteristics are 172 affected by the lens surface and internal reflections. Still, 173 prior works ( [24]) show that patch antennas form simple 174 and effective feeds for small lenses, motivating their use 175 in this work. We designed the patch as in [16], but to be 176 well-matched when placed directly under the dielectric lens 177 without any air gaps. The substrate material was chosen as 178 RO4003C with ε r = 3.35 and tan δ = 0.0027. The design 179 exhibits a 7 % |S 11 |<=10 dB bandwidth which is well-suited 180 for operation in the 37 to 40 GHz mm-wave band with geom-181 etry detailed in Fig.4.

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The primary design parameters for the EHDL are diam-183 eter and extension length. We select the initial subarray 184 size to equally subdivide the 2D planar aperture of a half-185 wavelength (λ 0 /2)-spaced phased array. For example, if we 186 were to replace an N = 64 element square λ 0 /2 spaced phased 187 antenna array aperture with a LAS-based antenna, a potential 188 choice could be to pick L = 4 with M = 16 feed antennas 189 to subdivide the array by four. The lens diameter can be 190 approximated from which at a center frequency of 38 GHz leads to 15.8 mm. 193 Note that this is a diameter of 2λ 0 , which makes the lens 194 box optimization from [26]. In this work, we used black-box 228 optimization to solve the constrained non-linear optimization 229 problem. The implementation follows [26] in that we first gives the radial component of the polar position of the feeds 249 on the focal plane. However, there are several issues with this 250 simple solution, such as changes in HPBW shape [24] for off-251 axis elements, as well as complexities from the electrically 252 small lens. Hence, after obtaining an initial mapping from 253 GDC to positions via this relation, we still carry out several 254 full-wave simulations to adjust the feed antenna positions 255 until the simulated scan coverage matches the prediction.

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We carry out the presented LAS-based antenna design with 258 the assistance of programs written in the Julia programming 259 language [29]. Julia is a free, high-performance, open-source 260 programming language designed specifically for scientific 261 computing. Binaries are available on the Julia Language web-262 site. We have packaged many calculations for following the 263 design flowchart into a general-purpose Julia library freely 264 available on GitHub, Antennas.jl, that provides an easy-to-use 265 interface for working with antenna and antenna array pattern 266 data. Antennas.jl can ingest exported pattern data from HFSS 267 via a comma-separated value (CSV) file. Then, using the 268 Plots.jl library and Contour.jl library, the beamwidth contours 269 can be plotted at the desired level.

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The goal is to produce a 2D beam steering LAS-based 271 antenna with at least ±37.5 • scan range and SLL below 272 =9 dB. Meeting this goal will produce an antenna that meets 273 or exceeds the performance of the previous design presented 274 in [16] while achieving beam steering in 2D. We first start 275 with the initial lens geometry detailed in the previous section.  Fig.6a and Fig.6b, respectively. The single-lens 329 performance for the center excitation is depicted in Fig.7.

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The lens has a maximum gain of 12.6 dBi and directivity of   An SPM T switch network will select a feed antenna under 344 each LAS, which will be identical to all other LASs within 345 the antenna. Feed antennas will be excited equally in ampli-346 tude. Consequently, the array factor (i.e., AF s based on the 347 description given in the introduction) will steer the main beam 348 within the HPBW contour of the selected feed antenna by 349 applying proper phase shifts. In creating the array, we assume 350 there is a small gap between the lenses such that the lenses do 351 not touch each other. This spacing is necessary to avoid the 352 meshing issues encountered in the EM solver, which results 353 in significantly longer simulation times for the entire LAS-354 based antenna. A gap of 0.1 mm (noted as G in Fig.4) was 355 found not to impact the performance of the antenna while 356 avoiding the aforementioned issue.

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The Julia package Antennas.jl includes an array factor tool 358 that implements the array factor analysis. First, we import the 359 3D pattern data exported from HFSS for each feed antenna 360 element excitation. Then, we identify the direction of max-361 imum radiation for each feed antenna. We approximate the 362 HPBWs of all feed antennas to be identical to that of the 363 center-fed antenna from previous simulations. For each feed 364 antenna, we generate array factors to steer the L = 7 ele-365 ment array to the direction of the feed's maximum radia-366 tion along with directions that trace out its HPBW contour. 367 Subsequently, we multiply these array factors by the single 368 lens radiation pattern generated by the excited feed antenna. 369 The HPBW and SLL contours of these patterns can be plotted 370 VOLUME 10,2022 in the same fashion as the single lens to observe performance.

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One may need to adjust element spacing if the design is not 372 performing well. However, we needed no such adjustment for 373 the presented design as we achieved ±36 • scan range in every 374 azimuth cut and up to ±42 • in some azimuth cuts with SLL 375 better than =9 dB, as desired in design specifications. The 376 HPBW contours for the L = 7 element LAS-based antenna 377 are depicted in Fig.8.    when subarrays are excited in equal phase and amplitude, 426 resulting in broadside radiation. The ports at the connectors 427 can also be excited with relative phase delays to simulate 428 the beam steering performance when subarrays are excited 429 with equal amplitude but with the proper relative phase differ-430 ences. The experimental setup also follows this model, where 431 we individually measure radiation from each subarray and 432 sum the patterns in software with the desired relative phase 433 differences. Section III explains that the experimental setup 434 also employs a calibration process before the pattern summa-435 tion to remove uncertainties associated with measurements. 436 beam steering results that are consistent with those obtained 438 from the array factor analysis with ±36 • coverage and SLL 439 better than =10 dB. The maximum realized gain is 19.8 dBi 440 (including connector loss) with a directivity of 22.8 dBi. Due 441 to the similarity with array factor analysis (Fig.8), we chose to 442 omit the full-wave HPBW contour plot from this manuscript.  these phase offsets, we added the phase shifts from the ana-492 lytical array factor formula to individual patterns measured 493 from each lens to generate the radiation pattern.

494
Our far-field measurement capability limits us only to take 495 2D radiation pattern measurements. Hence, several azimuth 496 cuts are needed to validate the design process, simulated 497 radiation pattern, and realized gain performance. Four dif-498 ferent physical configurations of the lenses are measured. 499 These configurations correspond to the various feed anten-500 nas' excitation and are indicated in Fig.6. The considered feed 501 antennas are the center element (with accompanying cross-502 polarization measurement) (A), the elements furthest from the 503 lens center in the E and H planes (B and C), and the element 504 located on the 45 • diagonal (D). We used a different stand 505 for each lens configuration to properly rotate the antenna 506 to measure the azimuth cut that contains the direction of 507 maximum radiation. 508 Fig.12 depicts the broadside E-Plane radiation perfor-509 mance of the antenna along with its cross-polarization. The 510 measured and simulated realized gains match closely up to 511 ±50 • . There is a ≈5 dB difference in the side lobe patterns 512 corresponding to the direction of the horizon (90 • ). This 513 discrepancy is generally seen in the other radiation pattern 514 measurements as well. This difference may be due to the 515 large ground plane introduced by the feeding network and 516 the 3D printed test stand or the phase errors introduced via 517 VOLUME 10, 2022    simulated performance. Steering within the HPBW of the 541 associated single-lens beam drops the traces in power by 3 dB 542 as expected. The outer beam (from patch B) is steered to ±34 • 543 in Fig.13. This beam can be steered further to ±36 • while 544 not exceeding an SLL of =9.5 dB. These results match the 545 expectation of a ±36 • scan range from full-wave simulations. 546 To observe pattern differences in the E and H-plane scans, 547 the two patches in the φ = 0 • and φ = 90 • positions were 548 measured and compared in Fig.14. These patches correspond 549 with patch B and C in Fig.6. Both patches steer to ±30 • with 550 varying sidelobe behaviors. The E-plane cut has a higher SLL 551 of =10.5 dB while the H-plane has a lower SLL of =12.7 dB. 552 However, as both SLLs are under =9 dB, both feed antennas 553 are equally suited to be used within the LAS-based antenna 554 context. The measured data matches reasonably well with the 555 simulated data, with noteworthy features well represented.

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The measurements presented demonstrate the challenging 557 cases of the LAS-based antenna in steering far off-axis. While 558 these measurements differ slightly from simulated results, 559 the general behavior is consistent. The broadside behav-560 ior matches very well, while off-axis behavior approaches 561 expected performance. Therefore, the measurements show 562 success in demonstrating this antenna's ability to steer to 563 ±34 • covering ±36 • while maintaining a low SLL.

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In this work, we introduced a 2D LAS-based antenna using 566 EHDLs. To facilitate the design, we presented a system-567 atic approach to achieving good performance in scan range 568 and side lobe level. The concept is demonstrated with an 569 antenna consisting of L = 7 LAS and M = 17 feed antennas 570 per LAS. The antenna operates at 38 GHz with a realized 571 gain of 19.8 dBi and worst case SLL of =9.5 dB while 572 exhibiting a coverage of ±36 • . The measured performance 573 corresponds well with simulation-based predictions. Table 1 574 outlines the performance of the presented LAS-based antenna 575 within the context of subarray-based antennas reported to 576 date. The proposed design operates in the 38 GHz band, pro-577 vides 2D beam-steering capability, and exhibits the highest 578 beam-steering range with nearly =10 dB SLL performance. 579 Additionally, this design remains low profile through small, 580 efficient lenses, allowing for incorporation in large, spectrum-581 efficient phased arrays.

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He is currently a Professor with the Elec-704 trical Engineering Department, University of 705 South Florida. His research interests include reconfigurable antennas and 706 RF circuits with mm-wave applications, additive manufacturing of structural 707 antennas and phased array antennas, microfluidics for highly reconfigurable 708 RF devices and new concepts (e.g. metamaterials, volumetric 3D reactive 709 loading, polymers) for designing conformal, miniature, and multifunctional 710 antennas. He was a recipient of the 2014 CAREER Award from the U.S.