Sector Unit-Cell Methodology for the Design of Sub-6 GHz 5G MIMO Antennas

A novel methodology based on the sectorization of multiple-port cavities with azimuthal symmetry into sector unit cells is presented to design 5G multiple-input multiple-output (MIMO) sub-6 GHz antennas. The methodology divides an N-port cavity antenna into N unit cells and predicts the performance of the N-port design with the analysis of two adjacent cells. This approximation reduces the time and complexity of the simulation of cavity antennas with a high number of ports. For the theoretical justification, cavity mode analysis of a closed cavity and characteristic modes analysis of open and sector cavities is addressed. With the use of the proposed methodology, five different cavity designs with circular, square, hexagonal, octagonal, and saw-tooth geometries are presented in this article. In addition, the fabrication of the 4-port circular shape design and its MIMO performance is also studied. Results show an impedance bandwidth of 130% (1.27-6 GHz), and an envelope correlation coefficient (ECC) lower than 0.1.

publications, there has been an enormous growth on the inter-30 est about MIMO compatible designs in size-limited devices 31 for smartphones applications [3], [4], [5], [6], [7], medi-32 cal applications [8] and for access point applications [9]. 33 The coexistence of several antennas in size-limited scenarios 34 produce highly coupled radiating elements, degrading their 35 performance. Isolation techniques are widely used to cope 36 with coupling issues, such as in [10] where a slotted stub is 37 used to increase to 20 dB the isolation of two ultra wide-band 38 stepped-shaped antennas ranging from 2 to 13.8 GHz. In [11] 39 a transmission-line-based decoupling method is presented to 40 increase 16-20 dB the isolation between co-polarized ele-41 ments for a MIMO antenna array working at 2.4 GHz. In addi-42 tion, an isolation structure is presented in [12] increasing 43 10-15.1 dB the isolation between elements providing connec-44 tion to the n78 band for smartphone applications. 45 The 5G infrastructure will include indoor access 46 points [13] to guarantee the 5G connection standards at 47 indoor environments with poor signal levels. Most of the 48 solutions are based on dual-polarized antennas due to its 49 orthogonal and low correlated radiation patterns which is 50 of the field distributions. Cavity modes and characteristic  In a previous article [28], the authors proposed a method-99 ology based on characteristic modes to decouple with an 100 x-shape block a 4-port cavity antenna with isolation issues. 101 In this article, a different methodology is proposed for the 102 design of similar N-port cavity antennas with a sector unit cell 103 approximation. The proposed methodology guarantees that 104 the analysis of two adjacent cells is enough for predicting the 105 performance of an N-cell antenna, simplifying the designing 106 process and reducing the time of simulations. For designs 107 with a higher number of ports, the decrease factor is consider-108 able, converting the proposed methodology in a proper candi-109 date for the simplification of the design of MIMO antennas. 110 The novelty of this article leans on the proposed methodology, 111 which has been successfully applied for the design of a 4-port 112 circular open-cavity, a 4-port square open cavity, a 6-port 113 hexagonal open cavity, an 8-port octagonal open cavity, and 114 an 8-port teeth-saw open cavity. For the octagonal design, the 115 use of the proposed methodology reduces their simulation 116 time by a factor of 26. The 4-port circular open-cavity has 117 been fabricated to demonstrate the viability of the methodol-118 ogy, and a MIMO compatibility study has also been provided 119 with the calculation of the channel capacity and the envelope 120 correlation coefficient (ECC). 121 The paper is organized as follows: In Section II, the study 122 of the first cavity modes of a closed coaxial cavity and the 123 characteristic modes analysis of an open coaxial cavity and its 124 sectorization is addressed. The study focuses on the effect of 125 reducing an open cavity into different angle sectors providing 126 information about the modes which are present and the modes 127 which are filtered. In Section III, the sector-unit cell method-128 ology is presented, and a coaxial four-port design is analyzed 129 for demonstration. Simulated and fabricated results are pre-130 sented, including a MIMO system performance evaluation. 131 In addition, three more designs are detailed with a system-132 atic design strategy with regular polygon geometry cavities 133 (square, hexagonal and octagonal) with the use of the sector 134 unit cell methodology. In Section IV, an 8-port saw-tooth 135 design with the use of the sector unit cell methodology with 136 x-axis replication is analyzed. Finally, Section V exposes the 137 conclusion of the paper.

139
In this section, the analysis of a closed coaxial cavity, an open 140 cavity, and 1/2, 1/4, 1/6, and 1/8 open cavity sectors is 141 addressed. Fig. 1(a) shows the coaxial closed cavity, that from 142 now on will be denominated as the coaxial cavity. Fig. 2(a) 143 presents the open coaxial cavity and its sectors. For the sake 144 of comparison, they all have dimensions of r1=108.5 mm, 145 r2=43.8 mm, and h1=34.2 mm, and the only difference is 146 that the closed cavity has a top cover enclosing the structure 147 and the open cavity has not.

148
Closed cavities are described in the electromagnetic lit-149 erature through the use of cavity modes, and the electric 150 and magnetic fields have been derived for canonical geome-151 tries [29] including the coaxial cavity, which is analytically 152 described in [30]. On the contrary, open cavities are not 153 analytically described, so we propose the use of characteristic 154 mode analysis to analyze open cavities and sectors. In the 155 following subsections, both analyses are addressed. In this subsection, the first five modes of a coaxial cavity 159 ( Fig. 1(a)) are analyzed. In cavity resonators, a three-symbol 160   The Theory of Characteristic Modes (TCM) [31], [32] 206 provides a basis set of currents on a structure with an arbitrary 207 geometry, which exhibits orthogonal radiation properties. 208 It provides a physical interpretation of the radiating mecha-209 nisms of the structure and helps to determine the optimum 210 feeding configuration. Characteristic modes are calculated 211 from the generalized impedance matrix of a structure [Z] 212 (calculated using the Method of Moments (MoM)) and the 213 resolution of the following eigenvalue problem: Eigenvalues (λ n ) are frequency-dependent and provide 216 radiation information about the associated current mode. The 217 mode stores electric energy (capacitive mode) when λ n is 218 negative and magnetic energy (inductive mode) when λ n is 219 positive. When λ n = 0, the mode is at resonance. Differ-220 ent modal attributes for the physical interpretation of the 221 eigenvalues have been proposed [33], [34]. In this paper, the 222 characteristic angle (α n ) has been selected for the analysis, 223 and it is derived as follows: When the mode is at resonance λ n = 0, α n = 180 • .

226
In this subsection, the characteristic modes analysis of an 227 open coaxial cavity and its 1/2, 1/4, 1/6 and 1/8 sectors is 228 addressed. Open coaxial cavity and sectors have equivalent 229 r1, r2 and h1 (as depicted in Fig. 2(a)). The open coaxial cav-230 ity has equivalent dimensions as the closed cavity analyzed in 231 the previous subsection but without the top cover enclosing 232 the cavity. The decision of analyzing sectors with different 233 sizes responds to the fact that the open cavity will be fed by N 234 excitations and will be divided into N identical subdivisions 235 or unit cells. The cavity then can be reinterpreted as a unit 236 cell which is replicated N times with azimuthal periodicity. 237 Commercial electromagnetic simulators are able to analyze 238 unit cells with periodic boundaries when Cartesian axes of 239 symmetry are used, but not when boundary conditions with 240   In Fig. 3 the modal electric field distribution at the corre-261 sponding resonance of the five first resonant modes of the 262 open coaxial cavity and the equivalent modes of the 1/2, 1/4, 263 1/6, and 1/8 sectors is represented in z=h1=34.2 mm plane. 264 Two types of modes are observed in Fig. 3, mode J 0 presents 265 an electric field distribution with only radial variation. The 266 rest of modes have both radial and azimuth variation in their 267 associated radiated field. Since the electric field distribution 268 of radial modes, like J 0 , is constant in azimuth variation, these 269 modes are always present in the cavity and in all the ana-270 lyzed sectors. Modes with azimuth variation (J 1 -J 4 ) exhibit 271 sinusoidal field distribution along the perimeter of the cavity. 272 They are at risk of vanishing if specific boundary conditions 273 are not satisfied when the open cavity is reduced to a sector. 274 Since an open circuit boundary condition is set through the 275 lines of symmetry when sectors are created, modes must 276 exhibit maximum field distribution where the cavity is cut. 277 Lines of symmetry that satisfy the previously specified con-278 ditions are depicted in black dashed lines in Fig. 3. Definitely, 279 if the cavity is split through the dashed lines, the mode will 280 still be present in the created sector.  The motivation of the analysis responds to the fact of 301 the future inclusion of feeding in the centre of the arc (d1) 302 of each sector (sector unit cell), creating an N-port design 303 if the sector unit cell is replicated N times. Distance d1 304 should guarantee a minimum distance between ports to avoid 305 coupling (λ/2 at f min approximately) and also defines the 306 resonance frequency of the azimuthal modes. If distance d1 307 between ports is respected, the size of the perimeter of the 308 cavity will be defined by N×d1. The higher N is, the higher 309 the cavity size is and, the first modes will resonate at lower 310 frequencies. The operating bandwidth will not be defined by 311 the first resonating modes of the cavity but by the bandwidth 312 of the excitation. The excited modes of high N cavities will 313 be higher-order modes of the cavity because the first modes 314 are far from the frequency which the feeding is operative.

315
In this study 1/2 (N=2), 1/4(N=4), 1/6(N=6) and 316 1/8(N=8) sectors of Fig. 4(a) with equivalent d1 are analyzed. 317 The first two azimuthal resonating modes of the sectors are 318 studied by representing the field distribution at resonance 319 ( Fig. 4(b)) and the characteristic angles ( Fig. 4(c)). It can 320 be observed that modes are resonant at approximately the 321 same frequency (because d1 is equivalent), but modes come 322 from different order modes of the complete cavity. It is then 323 confirmed that if the cavity is scaled up with N×d1, there 324 is always a mode that will be excited that comes from a 325 different order mode of the complete cavity depending on N. 326 The cavity size will not matter because d1 is respected and 327 first modes (for high values of N) resonate at a frequency out 328 of the bandwidth which the feeding is operative. The study 329 confirms the conservation of the modes if d1 is respected.

331
In this section, the information obtained from the previous 332 analysis is used to present a sector unit cell methodology. This 333 methodology predicts the performance of an N-port cavity-334 backed antenna by the analysis of only two of the N unit cells 335 in which the antenna is divided.

336
In Section II, the modes of the coaxial open cavity and 337 different angle sectors have been obtained. It has been demon-338 strated that radial modes are always present in both designs, 339 but azimuth modes are filtered if certain boundary conditions 340 are not satisfied when sectorization is applied.

341
Taking advantage of the obtained information regarding 342 the conservation of the modes, we propose to feed an open 343 cavity by N excitations arranged in a symmetric fashion and 344 divide the whole design into N sectors unit cells. The new 345 subdivision is called the sector unit cell and is composed of 346 a sector of the cavity fed in the centre of the arc length by a 347 T-shaped monopole.

348
The goal of the methodology is to simplify the analysis 349 of the N-port design to the study of only a sector unit cell 350 for impedance matching information and the study of two 351 adjacent unit cells for the study of isolation. In previous 352   for the design of regular polygon geometry cavities. For 376 demonstration, a wideband 4-port circular coaxial cavity, a 377 4-port square coaxial cavity, a 6-port hexagonal coaxial cav-378 ity, and an 8-port octagonal coaxial cavity have been designed 379 with the use of the proposed methodology. This designing 380 method decreases the time and complexity of the design and 381 simulation of multiple-fed open cavity solutions, especially 382 when the number of ports is high. The methodology is summarized at Fig. 5(a) higher than d1 = λ/2 to guarantee 15 dB of isolation level.

402
In Fig. 5(b), the S-parameters computed for the three stages  T-shaped monopoles ( Fig. 6(a)) on the aperture of cavity. 425 The cavity has been milled from a solid aluminum cylinder.  (Fig. 7(a)), 3 GHz (Fig. 7(b)), 4.5 GHz 443 (Fig. 7(c)) and 6 GHz (Fig. 7(d)). When the frequency is 444 low, the radiation pattern is composed of a single lobe. 445 When the frequency increases, the radiation pattern is slightly    [35] and the envelope correlation coefficient (ECC) 456 in a scenario with isotropic scattering (described by a uniform 457 distribution) is calculated. The proposed antenna, due to its 458 wide-band behavior, obtains a minimum isolation level of 459 15 dB. In order to guarantee that the MIMO performance is 460 not compromised by this parameter, the ideal (no coupling) 461 channel capacity and the channel capacity obtained with the 462 use of the proposed antenna at the lowest isolation level 463 frequency (f=3.1 GHz) are compared.

464
The channel capacity [35] is calculated with the use of 465 4 uncorrelated antennas as transmitting antennas, and the 466 four receiving antennas are the four antennas of the proposed 467 design. It is assumed isotropic scattering environment and 468 perfect channel state information (CSI) for the receiver but 469 not for the transmitter. Hence, the ergodic capacity can be 470 derived as (3) [35] where I is the 4 × 4 identity matrix, γ 0 471  described by different angular distributions (Uniform, Gaus-499 sian, Laplace) [36]. ECC values lower than 0.5 are expected 500 for uncorrelated radiation patterns [37]. In this article, the 501 ECC is calculated in an ideal scenario with isotropic scatter-502 ing. Hence Pa(θ,φ) is assumed to be described by a uniform 503 distribution (Pa(θ,φ)= 1), (4), as shown at the bottom of the 504 next page.

515
After the analysis of the channel capacity and the ECC 516 results, it can be stated that the proposed antenna is compati-517 ble and a good candidate for MIMO applications. In this section, the Unit Cell Methodology is applied for 521 the design of coaxial cavities with regular polygon geome-522 try. In the centre of each face of the polygon, a feeding is 523 connected; hence, the number of ports N of the designs is 524 equal to the number of faces of the polygon. A design with 525 four ports has then a square shape, six ports hexagonal, eight 526 ports octagonal, and so on. The distance d1, which describes 527 the arc sector of the unit cell of the circular design and the 528 distance between ports, in these designs, it is described more 529 intuitively by the side length (Lx) of the regular polygon 530 shape. 531 VOLUME 10, 2022 A systematic design process is presented for the optimiza-532 tion of the unit cell of an N port design with regular polygon 533 geometry. The equations detailed in Fig. 9 are meant to be 534 used with unit cells of any regular polygon geometry. The 535 distance between ports must be close to λ/2 at f min to guaran-536 tee a minimum isolation level of 15 dB, hence L x ≈ λ/2. The 537 angles β x of the base of the unit cell increases with N, and it 538 is defined by β x = π(N-2)/(2N). The top angle α x decreases 539 with N, and it is defined by α x = 2π/N. In Fig. 9 the unit 540 cell of an N=4 (square cavity-red), N=6 (hexagonal cavity-541 blue), and N=8 (octagonal-yellow) cavities are obtained with 542 the use of the proposed equations.  (Fig 12(a)).

579
In this case, the obtained design is not symmetric, and 580 it involves more complexity than the previous ones. The 581 methodology has been only used for the matching informa-582 tion prediction (S 11 (dB) dotted curve of Fig 12(b)). The unit 583 FIGURE 12. a) Scheme of the sector unit cell methodology for x-axis replication for the saw-tooth design, b) S-parameters of the unit cell, two contiguous cells and complete design and c) Port 1 simulated total efficiency and gain of the complete design. cell has been obtained from the octagonal open coaxial design 584 and has been slightly modified due to isolation problems 585 in the saw-tooth design disposition. The separation between 586 contiguous has been increased because the coupling between 587 contiguous cells experienced higher coupling values when 588 they were replicated through the x-axis. Fig 12(b) show the 589 S-parameters of the saw-tooth design with an impedance 590 bandwidth of 129% (1.46-6.85 GHz) and isolation higher 591 than 15dB. Furthermore, simulated gain and total efficiency 592 are represented in Fig 12(c) with values of an average 8 dBi 593 gain and a total efficiency higher than 82%. It is demonstrated that further distribution with different 595 geometries can also be obtained with the replication of the

634
Simulated results of the square, hexagonal, octagonal and 635 saw-tooth designs show an impedance bandwidth (S 11 (dB)< 636 −10 dB) of 126% (1.4-6.2 GHz), 130% (1.33-6.33 GHz), 637 128% (1.36-6.2 GHz) and 129% (1.46-6.85 GHz) respec-638 tively. Isolation between ports is always higher than 15 dB 639 because the minimum distance between ports of λ/2 is 640 always respected. Additionally, Table 5 compares the features 641 of the most relevant recent publications of MIMO access 642 point antennas and the proposed designs, highlighting the 643 impedance bandwidth, the size, the isolation, the number of 644 independent ports and the total efficiency.

645
The proposed sector unit cell methodology introduces a 646 great simplification of the simulation and design process 647 and a systematic strategy for designing complex and time-648 demanding cavity-based designs with a high number of ports. 649 As a reference, the simulation of the 8-port octagonal design 650 takes 4h 0m 14s, the simulation of two unit cells 8m 57s and 651 a unit cell 4m 6s in a computer with 16 GB of RAM and an 652 Intel Core i7-8700 CPU. It is then justified the benefits of 653 using the unit cell approximation methodology.