Dual-Polarized Two-Dimensional Multibeam Antenna Array With Hybrid Beamforming and its Planarization

A feeding network crossing method is proposed to form an N <inline-formula> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> N dual-polarized two-dimensional multibeam antenna array (2D-MBAA) with analog-digital hybrid beamforming, which solves the problem of needing additional connection structure between the dual-polarized antenna array and analog feeding network for large-scale antenna arrays. The main design work is focused on the analog-beamformer (ABF) and two structures are proposed. One is vertical-crossed (VC) ABF and the other is parallel-crossed (PC) ABF, and the latter is a more complex design in exchange for a significantly reduced profile. As a verification, a <inline-formula> <tex-math notation="LaTeX">$4\times 4$ </tex-math></inline-formula> dual-polarized 2D-MBAA with PC-ABF has been fabricated and tested. It is operated at 3.45GHz with a bandwidth of about 10%, and it can realize a scanning angle of ±45°.


I. INTRODUCTION
Among the 5th generation mobile communication (5G) application technologies, multibeam antenna technology plays an important role [1], [2]. By controlling the amplitude and phase distribution of the antenna array to achieve ultra-high gain and beam scanning, it can overcome the space transmission loss and improve the signal-to-noise ratio and channel capacity. In a full digital antenna array, each antenna is connected to a digital radio frequency (RF) channel, and each digital RF channel includes an amplitude-phase control module, data acquisition module, low noise amplifier (LNA), power amplifier (PA), etc., whose complexity is very high. With the increase in the array scale, problems such as a large amount of data calculation and the heat dissipation of ultra-dense digital RF channels will be very tricky, which also limits the development of a full digital array to large-scale.
To solve the problem of the feeding network design for large-scale antenna arrays, the hybrid beamformer scheme has emerged, that is, the analog beamforming networks are used to feed a few antennas to form antenna subarrays, and The associate editor coordinating the review of this manuscript and approving it for publication was Yasar Amin . then the digital RF channels are used to feed the analog beamforming networks to achieve the hybrid feeding of the whole antenna array [3]. Since the existing digital RF channels are very mature, most of us focus on some problems of the analog beamforming networks.
In recent years, a variety of analog beamformers (ABFs) had been proposed. Most of them are based on structures such as the Butler matrix and the Rotman lens [4]- [7]. A two-dimensional (2D) multibeam array antenna is designed by cascading two stages of Rotman lenses [8]. A planar 2D multibeam array antenna is designed by cascading two stages of Butler matrix [9]. There are also 2D multibeam planar lenses designed by transmit-arrays [10]- [14]. In the existing literature, a large number of examples of large-scale antenna array systems with analog-digital hybrid beamforming have been designed [15]- [25]. They introduced many novel array layouts and algorithms, but most of them focused on the communication system and rarely described the characteristics of the actual multibeam antenna array. In 2005, a dual-polarized 2D multibeam antenna array with analog-digital hybrid beamforming is described in detail, but the processing of the dual-polarization antenna is too complex and there are installation errors [26]. There are VOLUME 9, 2021 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ also some single-polarized 2D multibeam array antennas with analog-digital hybrid beamforming, but the assembly method is complex and the profile is high [27], [28]. In recent years, some full-analog dual-polarized 2D multibeam antennas have been published, but due to the higher feeding network density of the dual-polarized 2D-MBAAs, the existing dual-polarized 2D-MBAAs with full-analog feeding networks are small arrays such as 2 × 2 [29], [30] and they are too difficult to scale up. Nowadays, in many scenarios, the antenna has dual-polarization requirements, such as communication base station, weather radar, and so on. Therefore, a low machining difficulty, low installation error and low profile dual-polarized 2D-MBAA with analog-digital hybrid beamforming needs to be proposed urgently.
In this paper, a hybrid beamformer structure of N × N dualpolarized 2D-MBAA is firstly proposed, which is a hybrid feeding structure including a stacked analog-beamformer (ABF) and digital-beamformers (DBFs). The stacked ABF consists of 2N one-dimensional analog-beamformers (1D-ABFs), which are stacked and crossed each other. Since the antenna and the 1D-ABF are integrated, the stacked ABF can feed the N × N dual-polarized antenna array directly without using the coaxial line connection. The DBFs consist of 2N digital RF channels and each digital RF channel is connected to a 1D-ABF. Thus, a dual-polarized 2D-MBAA with hybrid beamforming is formed. At almost the same scanning range and gain as the full-digital N × N dual-polarized antenna array, the analog-digital hybrid array require only 2N digital RF channels while the full-digital arrays require 2N × N channels.
According to the proposed hybrid beamformer structure, taking 4 × 4 antenna array as an example, a 4 × 4 dual-polarized 2D-MBAA with vertical-crossed analog-beamformer (VC-ABF) is designed. But the profile of this vertical cross structure is too high. To further planarize it, a parallel-crossed analog-beamformer (PC-ABF) is designed, with which a 4 × 4 dual-polarized 2D-MBAA with PC-ABF is designed, which greatly reduces the profile.
The rest of this paper is arranged as follows. In section II, the basic concept of hybrid beamforming is introduced and the hybrid beamformer structure for the dual-polarized 2D-MBAA is proposed. In section III, two kinds of dual-polarized 2D-MBAAs are designed, which are based on VC-ABF and PC-ABF respectively. In section IV, the simulation results of the two kinds of dual-polarized 2D-MBAAs are given and the advantages and disadvantages are compared. In section V, the measurements of the dual-polarized 2D-MBAA with PC-ABF are given. In section VI, a summary of the full text is given.  shown in Fig. 1(a). The hybrid beamformer is formed by a two-stage-beamformer. In the first stage, N digital RF channels are used to form digital beamformers (DBFs). M beam schemes are pre-stored in the digital domain and the beam deflection in the y-direction can be realized by adjusting the phase of the digital radio frequency (RF) channels. In the second stage, N one-dimensional analog-beamformers (1D-ABFs) are used to form a stacked analog-beamformer (ABF). N beams can be realized by the 1D-ABF and the beam deflection in the x-direction can be realized by switching the switches. Fig. 1(b) is the hybrid beam diagram, whose projection on the xoz-plane is the beam of the ABF, and projection on the yoz-plane is the beam of the DBF.

II. HYBRID BEAMFORMING FRAMEWORK
The DBFs are realized in the digital domain with some digital RF channels, and the feeding type of the digital RF channel is a coaxial connection, which can be simply achieved, and the design scheme of the digital-beam feeding network is the same whether it is single-polarized or dualpolarized, so this paper mainly introduces the design of the stacked ABF of the dual-polarized 2D-MBAA with hybrid beamforming.

B. ABF STRUCTURE OF SINGLE/DUAL-POLARIZED 2D-MBAA
To feed a dual-polarized 2D antenna array, the number of the 1D-ABFs will be doubled. Normally, to make the stacked ABF cascade well with the dual-polarized 2D antenna array, the placement direction of the 1D-ABFs should match the antenna polarization direction, that is, to place it in a crossed structure. Fig. 2 shows the conversion process of the stacked ABF structure of single/dual-polarized 2D-MBAA. To highlight the stacked ABF, the DBFs are not drawn. Fig. 2(a) shows the stacked ABF structure for the single-polarized 2D-MBAA with hybrid beamforming, which can be seen as the side view of Fig. 1 from the z-axis. The 1D-ABFs are placed along the y-direction, and the antenna is in x-polarization. Make a copy of the stacked ABF in Fig. 2 (a), rotate the copied part by 90 • , and cross the stacked ABF to the rotated one to form a grid-like network. Finally, a crossed ABF of the dual-polarized 2D-MBAA is formed. This grid-like structure can well match the dual-polarized antenna array, as shown in Fig. 2 Based on the proposed hybrid beamformer structure and taking a 4 × 4 antenna array as an example, two kinds of dual-polarized 2D-MBAAs are designed, named 4 × 4 dualpolarized 2D-MBAA with vertical cross-structured analogbeamformer (VC-ABF) and 4 × 4 dual-polarized 2D-MBAA with parallel cross-structured analog-beamformer (PC-ABF) respectively. Both of them are operated at 3.45GHz.

III. TWO KINDS OF DUAL-POLARIZED 2D-MBAAS
The DBFs of a 4 × 4 dual-polarized 2D-MBAA with hybrid beamforming needs eight digital RF channels and each 1D-ABF is excited by a digital RF channel simply. Since the digital RF channel has been relatively mature, the following two kinds of the 4 × 4 dual-polarized 2D-MBAAs do not describe the DBFs.

A. 4 × 4 DUAL-POLARIZED 2D-MBAA WITH VC-ABF
To design the 4 × 4 2D-MBAA as dual-polarization, four 1D-ABFs extending the output transmit-lines are stacked along the x-direction with stacking spacing d, which are called the y-polarized 1D-ABFs. Four 1D-ABFs extending the input transmit-lines are stacked along the y-direction, which are called the x-polarized 1D-ABFs. For the convenience of crossing, the extended length of the transmit-line is equal to the self-length of the 1D-ABF. The y-polarized 1D-ABF and x-polarized 1D-ABF resemble the shape of the left and right palms, crossing the fingertips of the left and right palms with each other to form a vertical cross structure. The formation process is shown in Fig. 3.
The 1D-ABF in the above structure is realized by a 4 × 4 Butler matrix. Fig. 4 shows the integration design of the 4 × 4 Butler matrix with 4 antennas. Fig. 4(a) is the block diagram. Each 4 × 4 Butler matrix consists of four 3dB-couplers, two cross-couplers, two 45 • phase shifters, and two 0 • phase shifters. Among them, the 3dB-coupler is a typical λ/4 branch-line 3dB-coupler. The cross-coupler is designed with the cross-transition structure of the microstripline to the coplanar-waveguide (CPW) and then to microstripline, similar to that in [31], which has the advantages of small area and low coupling. The phase shifter is designed with a microstrip-delay-line. The antenna is a traditional dipole  antenna designed on a substrate together with the 4×4 Butler matrix. Fig. 4(b) is the model diagram of the 4 × 4 Butler matrix with 4 antennas. The substrate material used here is a 0.762mm-thick Rogers RO 4350 (ε r = 3.66, tanδ = 0.004). Fig. 5 is the 4 × 4 dual-polarized 2D-MBAA with VC-ABF. The cross diagram of Butler matrices is shown in Fig. 5(a), and the Butler matrices crossed each other are also vertical to each other. The preliminary array with VC-ABF is shown in Fig. 5(b). Since the dual-polarized antenna unit does not form a centrosymmetric pattern, the cross-polarization level (CPL) of the antenna is high. To reduce the CPL, the x-polarized antenna is moved d/2 along the -x-direction (d is the stacking distance, also the distance between the antenna elements), so that the y-polarized antenna is on the central plane of the x-polarized antenna, as shown in Fig. 5(c). This greatly increases the polarization isolation and decreases the CPL. Since the motion of the translational antenna is only performed at the output end of the x-polarized 1D-ABF, the feasibility of this vertical cross structure will not be affected. Finally, a slit metal reflector plate is inserted below the antenna array, which not only improves the mechanical stability of the overall structure but also improves the front-to-back ratio of the array, as shown in Fig. 5(d). Fig. 6 shows the performance comparison of the dualpolarized antenna unit before and after moving. Fig. 6 (a) is the diagram before and after moving, and the red arrow represents the excitation of the antenna. Figure 6 (b) shows the comparison of polarization isolation. The polarization isolation after moving is 30dB, which is 13dB higher than that before moving. Figure 6 (c) shows the CPL comparison of the E plane. The CPL is as low as −25dB at ±45 • , which is 13dB lower than that before moving. Figure 6 (d) shows the CPL comparison of the H plane, which is also lower than that before moving. Since the profile of the 4 × 4 dual-polarized 2D-MBAA with VC-ABF is too high to be used in practice, we proposed a parallel cross structure, which planarizes the vertical cross structure. To feed the dual-polarized antenna array, a common idea is to feed the antenna in two layers [4]. Fig. 7 shows the formation process of the parallel cross structure. 1D-ABFs are distributed in the upper and lower layers of the antenna array by feeding on all sides to the middle. There are two kinds of 1D-ABF in PC-ABF. One type of 1D-ABF is that the output transmit-line is extended d (d is also the distance between antenna units) and transited to the other side of the ground for feeding, which is called L-1D-ABF (blue part in Fig. 7). The other type of 1D-ABF is to add a delay line of the same length at the input side to ensure that the total phase shift of the two feeding networks is the same, called S-1D-ABF (red part in Fig. 7). To achieve dual-polarization, two L-1D-ABFs and two S-1D-ABFs are placed in the upper and lower layers from the positive and negative directions of the x-axis to feed the 4 × 4 x-polarized planar array. The remaining two L-1D-ABFs and two S-1D-ABFs are placed in the upper and lower layers from the positive and negative directions of the y-axis, feeding a 4 × 4 y-polarized planar array.
The following is to design the actual model. The 1D-ABF is also the 4 × 4 Butler matrix, same with Fig. 4 (a). The two kinds of 1D-ABF, namely L-1D-ABF and S-1D-ABF, are designed as shown in Fig. 8, where the ground plane is hidden for the convenience of seeing the wiring. Fig. 8 (a) is L-1D-ABF and the design prototype of the 4×4 Butler matrix is shown in the blue section. The feeding network transition from the blue layer to the red layer and the interlayer transition structure of L-1D-ABF is shown in the red section. The elliptical patches are coupled through the ground plane hole to achieve radio frequency signal transmission without via. That is, the elliptical patchs and the hole on the ground plane make up a coupler. Fig. 8 (b) is S-1D-ABF. To ensure the same total phase shift as L-1D-ABF, a winding microstrip line is designed to the input side of S-1D-ABF to compensate for the feeding phase difference between L-1D-ABF and S-1D-ABF. The antenna unit is a dual-polarized patch antenna with a stacked structure which is similar to [32], as shown in Fig. 9 (The substrate is hidden here. Refer to Fig. 10 for the substrate). The top layer is a parasitic patch, which can increase the bandwidth. Two Y-shaped microstrip feeders are vertically distributed on both sides of the ground plane and feed the upper patch through a crossed slot on the ground plane. This structure can greatly increase the polarization isolation of the dual-polarized antenna and reduce the CPL of the dual-polarized antenna, and the 4×4 Butler matrix distributed in the upper and lower layers can be directly connected to the feeding points of the 4 × 4 dual-polarized antenna array.
The stacked structure of the 4 × 4 dual-polarized 2D-MBAA with PC-ABF is shown in Fig. 10, which consists of five substrate layers and five metal layers. From the bottom up, the 4th substrate layer is a 4mm-thick air, the 1st and 3rd metal layers are the feeding layers, the 2nd metal layer is the ground plane with crossed slots, the 4th metal layer is the dual-polarized patch antenna array, the 5th metal layer is the parasitic patch, and the eight 4 × 4 Butler matrices are distributed on both sides of the ground plane to feed the dual-polarized patch antenna array through the crossed slots. The substrate materials used here are Rogers RO 4350  (ε r = 3.66, tanδ = 0.004) with thickness of 0.508mm, 0.762mm and 1.524mm respectively.
Next, we will talk about how to realize dual-polarized 2D scanning. The following is the feeding diagram of the PC-ABF, as shown in Fig. 11. The eight 4 × 4 Butler matrices are named Butler1X, Butler2X, Butler3X, Butler4X, Butler1Y, Butler2Y, Butler3Y, Butler4Y, respectively from red to green.
We can divide the 4 × 4 dual-polarized patch antenna array into two single arrays, One is the x-polarized 4 × 4 patch antenna array, and the other is the y-polarized 4 × 4 patch antenna array. The feeding diagram of the x-polarized 4 × 4 patch antenna array is shown in Fig. 11 (a). It is fed by four 4 × 4 Butler matrices (Butler1X, Butler2X, Butler3X, But-ler4X), where Butler1X feeds the four red patches, Butler2X feeds the four black patches, Butler3X feeds the four blue patches, and Butler4X feeds the four green patches. Each 4×4 Butler matrix is excited by a digital RF channel. Adjusting the phase of the digital channel can adjust the beam deflection angle in the xoz-plane. Switching the excitation port of the VOLUME 9, 2021 Butler matrix through the switch can adjust the beam deflection angle in the yoz-plane, thus realizing the x-polarized 2D-MBAA with hybrid beamforming.
The feeding diagram of the y-polarized 4×4 patch antenna array is shown in Fig. 11 (b). In the same way above, the y-polarized 2D-MBAA can be realized. So, the dualpolarized 2D-MBAA with hybrid beamforming can be realized by exciting eight Butler matrices simultaneously, and the xand y-polarized beams can be independently deflected from each other. It is particularly important to note that the symmetrical Butlers here have 180 • phase difference because the feed direction is opposite, which needs to be corrected in the digital RF channel.
After the stack is fixed, the final design model of the 4 × 4 dual-polarized 2D-MBAA with PC-ABF is shown in Fig. 12. The structure is fixed with a copper column. In order to make the copper column not affect the performance of the array, the copper columns are kept away from the wiring and radiation patches as far as possible. Subsequent simulation verifies that the placement of copper columns does not affect the array function.

IV. SIMULATION RESULTS AND COMPARISON A. BEAM SIMULATION RESULTS
In the simulation, the digital RF channel is simulated directly by the amplitude and phase given by the excitation port. Since the 4 × 4 Butler matrix gives only ±45 • and ±135 • phase differences at the output, the phase differences of digital RF channels are also set to ±45 • and ±135 • to satisfy the symmetry of the beams. Finally, sixteen x-polarized and sixteen y-polarized beams with hybrid beamforming are realized. The directions of the thirty-two beams realized by the 4 × 4 dual-polarized 2D-MBAAs with VC-and PC-ABFs are little different, only slightly different in gain, so only the thirty-two beams realized by the 4 × 4 dual-polarized 2D-MBAAs with PC-ABF at 3.45 GHz are shown here, as Fig. 13. Each beam pattern is a top view from the -z-direction. For the x-polarized antenna array, the gain is between 14.38 and 16.51dBi, the 4 × 4 Butler matrix controls the beam deflects in the x-direction, the digital RF channel controls the beam deflects in the y-direction. For the y-polarized antenna array, the gain is between 13.97 and 16.61dBi, the digital RF channel controls the beam deflects in the y-direction, and the Butler matrix controls the beam deflects in the x-direction.

B. COMPARISON OF THE CPL
The simulation results show that the 4 × 4 dual-polarized 2D-MBAAs with VC-and PC-ABFs can both realize dualpolarized 2D multibeam. Next, we set the digital RF port to be of the same amplitude and phase, and observe the x-polarized beams excited by the Butler matrix in the yozplane and its CPL. The simulation results of the two kinds of 4 × 4 dual-polarized 2D-MBAAs are shown in Fig. 14, simulated at 3.45 GHz. Fig. 14 (a) shows the x-polarized four beams of the 4 × 4 dual-polarized 2D-MBAA with VC-ABF in the yoz-plane. The peak gain is 17dBi and the CPL is −20dB, meeting the basic requirements of the dual-polarization 2D multibeam.   Fig. 14 (b) shows the x-polarized four beams of the 4×4 dualpolarized 2D-MBAA with PC-ABF in the yoz-plane. The peak gain is 16.7dBi and the CPL is as low as −59dB, which is 39 dB lower than that of the vertical cross-structured one and can meet the requirements of high polarization purity. For both of the two kinds of MBAAs, the −3dB beamwidth of the total coverage of four beams is 90 • , the sidelobe level (SLL) is −10dB.

C. COMPARISON OF SCALABILITY
In many aspects, the 4 × 4 dual-polarized 2D-MBAA with PC-ABF has better performance than the 4 × 4 dualpolarized 2D-MBAA with VC-ABF. The profile of the 4 × 4 dual-polarized 2D-MBAA with PC-ABF is 0.08λ at 3.45 GHz, while the 4 × 4 dual-polarized 2D-MBAA with VC-ABF is 2.43λ at 3.45 GHz, which is 30 times that of the 4 × 4 dual-polarized 2D-MBAA with PC-ABF. If we don't have a high requirement for the bandwidth, the parasitic patch in PC-ABF can be removed, and the profile can be reduced to 0.3λ. Moreover, the 4 × 4 dual-polarized 2D-MBAA with VC-ABF is not centrally symmetrical and has low polarization purity.
From the aspect of array scale expansion, if we want to expand the array to a larger scale such as 8 × 8, 16 × 16, the 4 × 4 dual-polarized 2D-MBAA with VC-ABF can be easily achieved by increasing the number of ports and plates of the 1D-ABF. However, expanding with this structure will result in profiles that are comparable in size to the antenna array, such as the 8 × 8 antenna array shown in Fig. 15. While the large-scale expansion of antenna array with 4 × 4 dual-polarized 2D-MBAA with PC-ABF requires a more complex antenna feeding wiring structure and more layers of ABF, the profile will not increase significantly, but the design difficulty will be greatly increased because this will introduce more layers and thicker cross-layer coupling structure.
From the aspect of enlarging the scan range of the array, the 4 × 4 dual-polarized 2D-MBAA with PC-ABF can be joined into a circle with four identical arrays, and the digital RF channels can be placed inside so that each array is responsible for 90 • azimuth scanning and then the 360 • azimuth scanning can be realized, as shown in Fig. 16. If the same splicing is done for the 4 × 4 dual-polarized 2D-MBAA with VC-ABF, it will bring more volume. Moreover, it is very inconvenient to fix the multiple 4 × 4 dual-polarized 2D-MBAA with VC-ABF, so additional structures are needed to assist the fixation. In contrast, the 4 × 4 dual-polarized 2D-MBAA with PC-ABF can be easily mounted on the surface of digital RF channel equipment to form a compact hybrid beamforming device.  Some references describing antenna details are compared in Table 1. For the two array cases presented in this paper, the dual-polarized antenna array and ABF are both integrated, which is rare in previous articles, so they can avoid the installation error between antenna and ABF. For the references [26]- [28], it is troublesome to use additional card slots to fix the ABF.

V. EXPERIMENT AND VERIFICATION
The 4 × 4 dual-polarized 2D-MBAA with VC-ABF in this paper is only a preliminary design based on the feeding network structure we proposed, aiming to compare with the 4 × 4 dual-polarized 2D-MBAA with PC-ABF. The 4 × 4 dual-polarized 2D-MBAA with PC-ABF has better overall performance, and the purpose of this paper is to design a planar array, so only the 4×4 dual-polarized 2D-MBAA with PC-ABF is processed for verification test.

A. DIGITAL RF CHANNEL FEEDING SCHEME
Because of the symmetry of the feeding scheme and the symmetry of the dual-polarized patch antenna array in this paper, we only need to test the four beam patterns and their crosspolarization characteristics of a single dimension and a single polarization to get a general idea of the scan capability of the array. We set the digital RF channel to be equal amplitude and phase, that is, to feed four Butler matrices, Butler1X, Butler2X, Butler3X, Butler4X, using a 1/4 power divider (1/4 power divider used to simulate four digital RF channels). The power divider can provide four equal power signals with two phases of 0 • and two phases of 180 • . Four x-polarized beams on the yoz-plane are realized by switching the excitation port of the Butler matrix. The four beams are then tested for gain, pattern, and CPL, and the return loss of the 1/4 power divider input port is measured when each beam is generated. The test scenario of the 4 × 4 dual-polarized 2D-MBAA with PC-ABF is shown in Fig. 17. The test frequency is 3.3GHz, 3.45GHz, and 3.6 GHz.

B. MEASUREMENTS
The S11 measurement and simulation results of the Butler matrix input ports (also input ports of 4 × 4 dual-polarized 2D-MBAA with PC-ABF) are shown in Fig. 18. Since Butler matrix is self-symmetrical and is also placed symmetrically, we only test the return loss results of eight ports, including Butler1X, Butler2X, Butler1Y, and Butler2Y. Beam1 is the Butler matrix inner port and beam2 is the Butler matrix outer port. Due to the large area of the substrate and manual bonding, the measurement curve does not match the simulation curve very well. But almost all the S11s of all ports are less than −10dB between 3.3GHz and 3.6GHz.
The normalized measurement and simulation results of four x-polarized beams in the yoz-plane of the 4 × 4 dual-polarized 2D-MBAA with PC-ABF are shown in Fig. 19. The gain at the intersection of the beams is 4.1dB lower than the peak gain. At 3.3 GHz, 3.45 GHz and 3.6 GHz, the −4.1dB-coverage of the total coverage of four beams is 110 • , 90 • and 84 • respectively. The peak gain measured at 3.45GHz is 15.3dBi, which is 1.4dB lower than the simulated. After analysis, there are three possible causes for the decrease in gain. One is that there will be some warping after the large area substrate plate is processed, which may affect the characteristic impedance of the microstrip line. Secondly, the 4 × 4 dual-polarized 2D-MBAA with PC-ABF is made of four substrate plates through copper columns, which inevitably leads   to the gap between the substrate plates to reduces the actual gain of the antenna. Thirdly, the antenna may be inclined in the direction of the elevation angle, resulting in the peak gain not on the test plane.
The CPL of the 4 × 4 dual-polarized 2D-MBAA with PC-ABF shown in Fig. 19 is only −29dB, about 30dB upper than the simulated. After analysis, the main reasons may be as follows. Firstly, it is difficult to keep completely still in the test phase, and the CPL in the simulation is too low, reaching −59dB. Therefore, once the antenna is tilted a little, the CPL will be increased rapidly. Second, the warped substrate will result in the uneven surface of the antenna, which will also lead to the CPL increase.

VI. CONCLUSION
Based on the crossing method, a hybrid beamformer structure for dual-polarized 2D-MBAAs is proposed, which does not need an additional connection structure between dual-polarized antenna array and analog feeding network. The VC design is simple and easy to scale up, and the PC design is more troublesome but easy to extend the scan angle to omnidirectional. To obtain a lower CPL, the 4 × 4 dual-polarized 2D-MBAA with VC-ABF adopts the end-fire antenna array whose elements consist of two single-polarized antennas in a T-shaped pattern. The 4 × 4 dual-polarized 2D-MBAA with PC-ABF has a very low profile, and the dual-polarized antenna element can easily achieve a low CPL for its centrosymmetry. Since they can be simply extended and the installation error is reduced by the integrated structure, the two kinds of the proposed 4 × 4 dual-polarized 2D-MBAAs are of great reference value for the design of dual-polarized 2D-MBAAs with hybrid beamforming, whether in sub-6G or mm-Wave.