Full-Azimuth Beam Steering MIMO Antenna Arranged in a Daisy Chain Array Structure

micromachines

Article Full-Azimuth Beam Steering MIMO Antenna Arranged in a Daisy Chain Array Structure

Kazuhiro Honda 1,*, Taiki Fukushima 2 and Koichi Ogawa 1

1 Graduate School of Engineering, Toyama University, 3190 Gofuku, Toyama 930-8555, Japan; [email protected] 2 Panasonic System Networks R&D Lab. Co., Ltd., Technology Center, 2-5 Akedori, Izumi-ku, Sendai, Miyagi 981-3206, Japan; [email protected] * Correspondence: [email protected]; Tel.: +81-76-445-6759

Received: 28 August 2020; Accepted: 18 September 2020; Published: 19 September 2020

Abstract: This paper presents a multiple-input, multiple-output (MIMO) antenna system with the ability to perform full-azimuth beam steering, and with the aim of realizing greater than 20 Gbps vehicular communications. The MIMO antenna described in this paper comprises 64 elements arranged in a daisy chain array structure, where 32 subarrays are formed by pairing elements in each subarray; the antenna yields 32 independent subchannels for MIMO transmission, and covers all communication targets regardless of their position relative to the array. Analytical results reveal that the proposed antenna system can provide a channel capacity of more than 200 bits/s/Hz at a signal-to-noise power ratio (SNR) of 30 dB over the whole azimuth, which is equivalent to 20 Gbps for a bandwidth of 100 MHz. This remarkably high channel capacity is shown to be due to two signiﬁcant factors; the improved directivity created by the optimum in-phase excitation and the low correlation between the subarrays due to the orthogonal alignment of the array with respect to the incident waves. Over-the-air (OTA) experiments conﬁrm the increase in channel capacity; the proposed antenna can maintain a constant transmission rate over all azimuth angles.

Keywords: daisy chain multiple-input multiple-output (MIMO) antenna; beam steering array; large-scale MIMO; over-the-air (OTA) testing; Monte Carlo simulation; connected car

1. Introduction One of the most straightforward approaches for improving the capacity of multiple-input multiple-output (MIMO) systems is to use a large number of antenna elements. The concept of large-scale MIMO or massive MIMO systems with more than 100 antenna elements has been proposed for both fifth and sixth generation (5G and 6G) mobile communications [1,2]. Figure1 shows a conceptual illustration of a massive MIMO system. In massive MIMO systems, investigations are mostly based on the development of a large-scale antenna at a base station, in which a planar array antenna with a number of patch antennas arranged in a two-dimensional manner on a column-row alignment basis is commonly developed [3–6], as depicted in Figure1. The primary objective of these antennas is, using a beam forming technique, to illuminate respective mobile stations distributed in a specific confined region of the service area in a cell, known as a hot-spot. Thus, a large-scale MIMO antenna used for massive MIMO systems is capable of communicating with mobile stations in the hemispherical spatial region perpendicular to the surface of the patch array. With regard to a mobile station antenna, on the other hand, one of the most important performance goals in MIMO systems is the ability to communicate with the target over the full azimuth, i.e., full-azimuth beam steering, as illustrated in Figure1.

Micromachines 2020, 11, 871; doi:10.3390/mi11090871 www.mdpi.com/journal/micromachines Micromachines 2020, 11, 871 2 of 25 Micromachines 2020, 11, x 2 of 25

Large-scale MIMO antenna

MIMO transmission Patch array Mobile station

Full-azimuth beam steering

Base station

Figure 1. Conceptual illustration of a massive MIMO system.

One of the possible solutions to fulfilling fulfilling this requirement is the use of a circular array in which a number of patch antennas are arranged in a cylindrical manner [7,8]. [7,8]. However, However, there is a certain drawback to this configuration configuration in that each patch antenna radiates in a direction normal to the surface of thethe patch,patch, resulting resulting in in a situationa situation in whichin which not not all ofall the of radiationthe radiation beams beams contribute contribute to MIMO to MIMO spatial spatialmultiplexing multiplexing when an when incident an wave incident comes wave from comes a particular from azimuthal a particular direction. azimuthal Consequently, direction. weConsequently, cannot obtain we full-rank cannot obtain channel full matrices-rank channel corresponding matrices to corresponding the number of patchesto the number due to theof patches limited dueavailability to the limited of the receivedavailability signals, of the which received leads signals, to a reduction which leads in channel to a reduction capacity. in channel capacity. There has been a great deal of intere interestst in the development of connected car systems with greater than a gigabit gigabit transmission transmission rates [ [9].9]. It It is is anticipated anticipated that that the the MIMO antennas implemented in automobiles willwill bebe usedused in in systems systems with with a relativelya relatively small small cell cell radius radius involving involving a street a street microcell microcell [10]. [10].In such In such an environment, an environment, the the various various objects objects in in the the surrounding surrounding area—such area—such asas trees,trees, signboards, buildings, and numerous vehicles—resultvehicles—result in complex radio radio propagation propagation phenomena. phenomena. In In a street microcell environment, it is known that the spatial angular pow powerer spectrum (APS) is small compared with thatthat inin the the conventional conventional macrocell macrocell counterpart counterpart [11 ].[11]. This This is because is because the incidentthe incident waves waves from thesefrom thesescatterers scatterers are not are uniformly not uniformly distributed, distributed, but occur but occur in clusters, in clusters, with with strong strong contributions contributions from from a few a fewdirections. directions. In addition, In addition, the radiation the radiation pattern pattern of a vehicular of a vehicular antenna antenna changes changes greatly greatly due to thedue mutual to the mutualelectromagnetic electromagnetic coupling coupling between between the antenna the antenna and the and dynamic the dynamic motion ofmotion the car, of especiallythe car, especially when it whenturns rightit turns or leftright at or an left intersection. at an intersection. This indicates This thatindicates the mutual that the influence mutual ofinfluence the incident of the waves incident and wavesthe car’s and antennas the car’s could antennas result could in a complicatedresult in a complicated MIMO channel MIMO response. channel response. Based on the above above-mentioned-mentioned phenomena, the characteristics of a vehicular MIMO antenna are summarized as follows:

(1) AnticipatedAnticipated changes changes in in receiv receiveded power power when when the the position position of of the the car changes relative to the incidentincident waves. waves. (2) IncreaseIncrease in in spatial spatial fading fading correlation correlation between between the the array array branches branches due to the narrow APS. (3) Changes in both the received power and correlation, which may be encountered at the same (3) Changes in both the received power and correlation, which may be encountered at the same time, time, as the car moves in different directions relative to the incident waves. as the car moves in diﬀerent directions relative to the incident waves. (4) A possible increase or decrease in the MIMO channel capacity caused by (1), (2), or (3). (4) A possible increase or decrease in the MIMO channel capacity caused by (1), (2), or (3). These phenomena may occur simultaneously in an actual connected car system. Hence, all the These phenomena may occur simultaneously in an actual connected car system. Hence, all the solutions with regard to the above issues must be integrated into one unit in the developed MIMO solutions with regard to the above issues must be integrated into one unit in the developed MIMO antenna. Considering this technical background, we have developed new technologies in an ongoing antenna. Considering this technical background, we have developed new technologies in an ongoing project with the following objectives: project with the following objectives: (A) Development of higher order MIMO arrays, such as 8 × 8 [12], 16 × 16 [13], and 32 × 32 [14,15] MIMO antenna systems, suitable for implementation in an automobile.

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(A) Development of higher order MIMO arrays, such as 8 8 [12], 16 16 [13], and 32 32 [14,15] × × × MIMO antenna systems, suitable for implementation in an automobile. (B) Development of radiation pattern steering capability to achieve a large signal-to-noise power ratio (SNR) that can direct the peak radiation toward the communication target. (C) Realization of low correlation between the MIMO channels established by the orthogonal relationship between the array alignment and the incident waves over the full azimuth. (D) Development of an angle of arrival (AOA) estimation antenna that obtains bearing information from radio waves incident on the MIMO antenna, using an RF-based interferometric monopulse technique with reduced hardware complexity. To realize these objectives simultaneously, we are currently developing a 32 32 MIMO antenna × system that utilizes circular array beam steering technology. Great emphasis is placed on a way of achieving a large-scale vehicle borne MIMO antenna that provides full-azimuth coverage. The new array configuration proposed in this paper yields the full availability of the received signals, which results in a channel capacity of several tens of gigabits owing to the effective operation of the MIMO multiplexing transmission. This paper, which is part of the extensive R&D activities we have performed so far in this field, is devoted to a comprehensive description of the development work undertaken for a 32 32 MIMO × antenna system, including Monte Carlo simulations and over-the-air (OTA) testing to investigate how the developed 32 32 MIMO array performs in a propagation environment where it is anticipated the × forthcoming 5G and 6G connected car systems will be used. In order to tackle the four challenges—(A), (B), (C), and (D), listed above—we start by describing the methodology and the basic characteristics of MIMO antennas. We first present a brief explanation of the configuration of the whole antenna system. Studies on the AOA antenna are presented in separate papers [16,17].

(B) Development of radiation pattern steering capability to achieve a large signal-to-noise power ratio (SNR) that can direct the peak radiation toward the communication target. (C) Realization of low correlation between the MIMO channels established by the orthogonal relationship between the array alignment and the incident waves over the full azimuth. (D) Development of an angle of arrival (AOA) estimation antenna that obtains bearing information from radio waves incident on the MIMO antenna, using an RF-based interferometric monopulse technique with reduced hardware complexity. To realize these objectives simultaneously, we are currently developing a 32 × 32 MIMO antenna system that utilizes circular array beam steering technology. Great emphasis is placed on a way of achieving a large-scale vehicle borne MIMO antenna that provides full-azimuth coverage. The new array configuration proposed in this paper yields the full availability of the received signals, which results in a channel capacity of several tens of gigabits owing to the effective operation of the MIMO multiplexing transmission. This paper, which is part of the extensive R&D activities we have performed so far in this field, is devoted to a comprehensive description of the development work undertaken for a 32 × 32 MIMO antenna system, including Monte Carlo simulations and over-the-air (OTA) testing to investigate how the developed 32 × 32 MIMO array performs in a propagation environment where it is anticipated the forthcoming 5G and 6G connected car systems will be used. In order to tackle the four challenges—(A), (B), (C), and (D), listed above—we start by describing the methodology and the basic characteristics of MIMO antennas. We first present a brief explanation of the configuration of the whole antenna system. Studies on the AOA antenna are presented in separate papers [16,17].

2. New Concept of a Large-Scale MIMO Antenna In Figure 2 an illustrated overview of our ongoing project, conducting research and development work toward a full-azimuth beam steering MIMO array, is shown [18]. We have taken on the big challenge of achieving a 100 Gbps channel capacity on a moving vehicle for the forthcoming sixth- generation (6G) mobile communications. To this end, we have devised effective means of constructingMicromachines 2020 a large-scale, 11, 871 MIMO array antenna, with distinct features that cannot be achieved using4 of 25 previous technologies commonly aimed at enhancing the channel capacity at a base station; the objective of our project is accomplished by the emergence of a new technology named “Daisy Chain categorized in the family in Figure2A, this paper focuses on a detailed description of the design and MicromachinesMIMO Antenna”. 2020, 11, x 4 of 25 performance of a daisy chain 32 32 MIMO antenna. Figure 2a shows a family of ×daisy chain MIMO antennas, which comprises a plurality of 4 × 4 MIMO antennas, as a basic component module, arranged in a variety of two-dimensional geometrical configurations. The term “4 × 4 MIMO” means that the1200 number of elements at the base station (former number) is four and that at the mobile station (latter number) is four. Therefore,PIERS2019 we have four 1000 subchannels for MIMO transmission in this case. This new approach100Gbps enables @100MHz us to construct a high- order MIMO antenna with great ease since the same fabrication process used to fabricate 4 × 4 MIMO antennas is used for each configuration. For example,800 as shown in Figure 2a, the 32 × 32 MIMO antenna(a) 4 × 4 hasMIMO a circular(b) 8 × 8 MIMOarray of (c)eight 16 × 164 MIMO× 4 MIMO antennas, resembling a daisy chain with eight pink 600 EMTS2019 flowers, forming a 32 × 32 MIMO array as a whole. Hence, we have named this type of antenna “Daisy Chain MIMO Antenna”. This Paper 400 Figure 2b shows the history of the development of the daisy chain MIMOEMTS2019 antenna. The figure APMC2018 illustrates the channel capacity achieved using the different[bits/s/Hz] Capacity Channel 200 size arrays, together with the abbreviated PIERS2018 name of the international conference where the correspondingAPMC2017 paper was presented. As shownSNR=30dB in the figure, we have accomplished a twofold increase in channel0 capacity as the size of the array doubles. 4×4 8×8 16×16 32×32 64×64 128×128 Consequently,(d) 32 × 32 MIMO we have(e) 64 achieved × 64 MIMO a(f) channel 128 × 128 MIMO capacity greater than 100 Gbps for a bandwidth of 100 MHz by means of a 128 × 128 MIMO array, as indicated in Figure 2b. Among the various configurations categorized(A) in the family in Figure 2a, this paper focuses on(B a) detailed description of the design and performance of a daisy chain 32 × 32 MIMO antenna. FigureFigure 2. 2. AA big big challenge challenge toward toward 100 100 Gbps Gbps channel channel capacity. capacity. (A (A) )A A family family of of daisy daisy chain chain MIMO MIMO antennas.antennas. (B (B) )History History of of the the development. development. 3. Daisy Chain 32 × 32 Multiple-Input Multiple-Output (MIMO) Antenna 3. Daisy Chain 32 32 Multiple-Input Multiple-Output (MIMO) Antenna Figure 3 shows× the configuration of a beam steering MIMO antenna arranged in a daisy chain array Figurestructure3 shows [14]. theFigure conﬁguration 3a shows ofthe a beamwhole steering structure MIMO of th antennae MIMO arranged antenna in sys a daisytem. chainFigure array 3b showsstructure a 4 × [14 4 ].MIMO Figure circular3a shows array the [19], whole which structure is used of theas a MIMO component antenna module system. to form Figure the3b 32 shows × 32 MaIMO 4 4 array. MIMO As circular shown in array Figure [19], 3a which, the developed is used as MIMO a component antenna module comprises to form 64 elements the 32 arranged32 MIMO × × inarray. a daisy As chain shown array in Figure structure,3a, the forming developed a dual MIMO-rin antennag configuration comprises; one 64 elementsring is formed arranged by the in a 4 daisy × 4 MIMOchain arrayarray, structure, and the other forming ring a is dual-ring constructed conﬁguration; from eight one sets ring of 4 is × formed 4 MIMO by arrays, the 4 arranged4 MIMO array,in a × circleand thewith other radius ring r at is constructedequal angular from intervals eight sets of 45°, of 4 constructing4 MIMO arrays, the 32 arranged× 32 MIMO in aarray circle as with a whole. radius × r at equal angular intervals of 45 , constructing the 32 32 MIMO array as a whole. ◦ × Subarray 9-12 4 Subarrays Creation of Subarray 13-16 Subarray 5-8 #3 #2 #2 + #3 Beam

 jkd1 E0 E0e Beam1 MIMO Array d1 Subarray1 (1) Large SNR #4 #1 #1 + #4 E  jkd2 Cluster AOA Antenna 0 d2 E0e Subarray 17-20 Subarray 1-4 Beam2 Incident Wave Subarray2 y  Subarray18 Subarray2 x 2 #9 z #5 + #8  jkd2 r E0e Beam3 Orthogonal to Subarray 21-24 Subarray 29-32 Subarray3 d2 a #5 #8 MIMO Array Subarray4 #6 + #7 Subarray 25-28 d 1  jkd1 Beam4 E0 E0e (2) Low 4×4 MIMO #6 #7 Correlation System

(a) (b)

FigureFigure 3. 3. BeamBeam steering steering MIMO MIMO antenna antenna arranged arranged in in a a daisy daisy chain chain array array structure. structure. (a ()a )The The whole whole structurestructure of of a a32 32 × 3232 MIMO MIMO system. system. (b ()b 4) 4× 4 MIMO4 MIMO system. system. × × 32 subarrays are created by pairing elements in each 4 × 4 MIMO array; the antenna yields 32 independent subchannels for MIMO transmission, and covers all communication targets regardless of their position relative to the array, as mentioned below. As illustrated in Figure 3b, four pairs of the eight elements form four subarrays (Elements #2–3, #1–4, #5–8, and #6–7). All the elements are half-wavelength dipole antennas. These subarrays create four independent radiation patterns

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32 subarrays are created by pairing elements in each 4 4 MIMO array; the antenna yields × 32 independent subchannels for MIMO transmission, and covers all communication targets regardless Micromachinesof their position 2020, 11 relative, x to the array, as mentioned below. As illustrated in Figure3b, four pairs5 of 25 of the eight elements form four subarrays (Elements #2–3, #1–4, #5–8, and #6–7). All the elements (Beam1are half-wavelength–Beam4), each dipoleof which antennas. acts as a Thesesubchannel subarrays for the create MIMO four array independent by enabling radiation excitation patterns of the four(Beam1–Beam4), subarrays which each achieves of which an acts in as-phase a subchannel state toward for thethe MIMOtarget direction array by enablingof communication. excitation ofAs the a result,four subarrays the peak whichgain of achieves the beam an is in-phaselarger than state that toward of an theordinary target dipole direction antenna, of communication. which results Asin a a largeresult, SNR. the peak gain of the beam is larger than that of an ordinary dipole antenna, which results in a largeIn SNR. Figure 3b, k represents the wave number, d1 and d2 denote the distance between Elements #2 and #3, and Elements #1 and #4, respectively. E0 signifies the amplitude of the electric field, and j In Figure3b, k represents the wave number, d1 and d2 denote the distance between Elements #2 indicates the complex unit. Using these parameters, the excitation conditions for the four subarrays and #3, and Elements #1 and #4, respectively. E0 signifies the amplitude of the electric field, and j toindicates establish the an complex in-pha unit.se state Using for these the formation parameters, of the a beam excitation toward conditions the communication for the four subarrays target are to describedestablish anin in-phaseSection 5. state for the formation of a beam toward the communication target are described in SectionAnother5. unique feature of the 4 × 4 MIMO antenna is the realization of low correlation. When an incidentAnother wave unique with feature a narrow of the APS 4 arrives4 MIMO from antenna the right is the side realization of the figure, of low the correlation. four subarrays When are an × arrangedincident waveperpendicular with a narrow to the APSincident arrives wave. from In thegeneral, right sidein a ofcluster the figure,propagation the four environment, subarrays are a MIMOarranged array perpendicular parallel to an to incident the incident wave wave. results Inin general,high correlation in a cluster between propagation the branches environment, [20]. In contrast,a MIMO a arrayMIMO parallel array ort tohogonal an incident to an wave incident results wave in yields high correlationlow correlation. between Hence, the the branches orthogonal [20]. arrangementIn contrast, a between MIMO array the subarray orthogonal and to anthe incident cluster inci wavedent yields wave, low as correlation. shown in Figure Hence, 3b the, results orthogonal in a smallerarrangement correlation between coefficient, the subarray which and is beneficial the cluster for incident the enhancement wave, as shownof the MI inMO Figure channel3b, results capacity, in a togethersmaller correlationwith the creation coefficient, of a large which SNR is beneficial due to the for four the enhancementsubarrays mentioned of the MIMO above. channel capacity, togetherIn Figure with 3b the, as creation the eight of aelements large SNR form due a tocircular the four arrangement subarrays mentionedwith 45° intervals, above. the subarrays can be rotated every 45° in the azimuth plane. Figure 4 shows the four combinations of subarrays In Figure3b, as the eight elements form a circular arrangement with 45 ◦ intervals, the subarrays according to the angle of the incident wave [19]. The yellow zone shows the angular range of the can be rotated every 45◦ in the azimuth plane. Figure4 shows the four combinations of subarrays incidentaccording wave to the applicable angle of to the MIMO incident communications. wave [19]. The Therefore, yellow zone when shows an automobile the angular turns range right of theor leftincident at an intersect wave applicableion, which to results MIMO in communications.a situation where an Therefore, incident wave when arrives an automobile from other turns azimuth right angles,or left at we an can intersection, select other which appropriate results in combinations a situation where from among an incident the possible wave arrives combinations from other of subarrays.azimuth angles, This function we can select can also other be appropriate applied effectively combinations to the from 32 × among 32 MIMO the possible beam steering combinations array antenna,of subarrays. by performing This function synchronized can also be switching applied e ffofectively all the to32 the subarray 32 32 beams. MIMO This beam unique steering feature array × allowsantenna, the by SNR performing of the 32 subarray synchronized beams switching to be large, of and all the simultaneously, 32 subarray beams. the correlation This unique to be featuresmall, whichallows keeps the SNR the of channel the 32 subarray capacity beams in a hi togh be-bit large, rate and condition, simultaneously, even with the considerable correlation to dynamic be small, motionwhich keepsof the thecar. channel capacity in a high-bit rate condition, even with considerable dynamic motion of the car.

y y 67.5deg 112.5deg y 112.5deg y 67.5deg #3 #3 #3 #3 #2 #2 #2 #2 157.5deg #4 22.5deg #4 #4 #4 22.5deg #1 #1 #1 157.5deg #1 x x x x #5 #5 202.5deg #5 #5 337.5deg #8 202.5deg #8 337.5deg #8 #8 #6 #6 #6 #7 #6 #7 #7 #7 247.5deg 247.5deg 292.5deg 292.5deg (a) (b) (c) (d)

FigureFigure 4. 4. CombinationsCombinations of of the the subarrays. subarrays. (a) (Combination1.a) Combination1. (b) (Combination2b) Combination2.. (c) Combination3. (c) Combination3. (d) Combination4.(d) Combination4.

FigFigureure 5 showsshows a aschematic schematic diagram diagram of a of beam a beam forming forming network network for full for-azimuth full-azimuth steering, steering, which compriseswhich comprises switches, switches, phase phase shifters, shifters, and andpower power dividers dividers [15]. [15 Using]. Using this this network, network, the the four four combinationscombinations of of subarrays, subarrays, as as shown shown in in Figure Figure 44,, can be chosen according to the angle of the incident wavewave to to deliver deliver signals signals to to Elements Elements #1 #1–8–8 for for achieving achieving an an in in-phase-phase state state between a pair of elements.

MicromachinesMicromachines 20202020, 11,,11 x , 871 6 of6 25 of 25 Micromachines 2020, 11, x 6 of 25 #1 #2 #3 #8 #1 #2 #3 #8 Switch Switch

1 2 3 4 Phase shifter 1 2 3 Power4 Phase divider shifter Power divider ch1 ch2 ch3 ch4 ch ch ch ch 1 2 3 4 Figure 5. Beam forming network for full-azimuth steering. FigureFigure 5. 5. BeamBeam forming forming network network for for full full-azimuth-azimuth steering. steering. 4. 4.Formulation Formulation of ofMonte Monte Carlo Carlo Simulation Simulation 4. Formulation of Monte Carlo Simulation ThisThis section section is is devoted devoted to the the formulation formulation of of a Monte a Monte Carlo Carlo simulation simulation used used to analyze to analyze the channel the This section is devoted to the formulation of a Monte Carlo simulation used to analyze the channelresponses responses of the of daisy the daisy chain chain MIMO MIMO antenna. antenna. As shownAs shown in Figure in Figure6a, the6a, the concept concept of clustersof cluster [ s21 ] channel responses of the daisy chain MIMO antenna. As shown in Figure 6a, the concept of clusters [21is] employedis employed to to simulate simulate a seta set of discreteof discrete waves waves with with narrow narrow APS AP arrivingS arriving at aat mobile a mobile station station (MS). [21] is employed to simulate a set of discrete waves with narrow APS arriving at a mobile station (MS)In Figure. In Figure6, the 6, bell-shaped the bell-shaped blue blue curves curves represent represent a cluster a cluster incident incident wave. wave. We have We have developed developed Monte (MS). In Figure 6, the bell-shaped blue curves represent a cluster incident wave. We have developed MonteCarlo Carlo simulation simulation software software using MATLAB, using MATLAB, in which in a which cluster a channel cluster model channel suitable model for suitable simulating for a Monte Carlo simulation software using MATLAB, in which a cluster channel model suitable for simulatinglarge-scale a large MIMO-scale antenna MIMO at theantenna mobile at sidethe mobile is formulated. side is formulated. The developed The softwaredeveloped is software an improved is simulating a large-scale MIMO antenna at the mobile side is formulated. The developed software is anversion improved of the version channel of the modeling channel used model foring simulating used for handsetsimulating adaptive handset and adaptive MIMO arraysand MIMO with a an improved version of the channel modeling used for simulating handset adaptive and MIMO arrayuniforms with azimuthal a uniform APS azimuth [22,23al]. APS [22,23]. arrays with a uniform azimuthal APS [22,23].

m=1 M q z BS m=1 M q z BS Cluster q=1 Cluster q=1 Mobile q = p /2 StationMobile q = p /2 MS n=1 N Station y MS v y n=1 N k=1 v q k,m k=1  q k-th scatterer k,m k-th scatterer Q for q-th cluster c for q-th cluster Qc Km Incident wave k Km Moving directionIncident wave k x scatterer Moving direction x Moving direction scatterer Moving direction (a) (b) (a) (b) FigureFigure 6. Channel 6. Channel model model used used for for performing performing the the Monte Monte Carlo Carlo simulation. simulation. (a)( Clustera) Cluster channel channel model model ofFigure ofM M× N 6.MIMO.N ChannelMIMO. (b) ( modelCoordinatesb) Coordinates used for of theperforming of the k-thk-th scatterer scatterer. the Monte. Carlo simulation. (a) Cluster channel model of M ×× N MIMO. (b) Coordinates of the k-th scatterer. In Inorder order to to simulate simulate a a small cellcell scenario,scenario, each each cluster cluster is is assumed assumed to haveto have a large a large number number of arrival of arrivalpaths,In paths, ensuringorder ensuring to thesimulate full-rank the afull small status-rank cell of status ascenario, channel of a matrixeach channel cluster created matrix is byassumed created a large-scale to by have a MIMO large a large-scale antenna. number MIMO Here, of antennaarrivalthe term. Here, paths, ‘path’ the ensuring is term used ‘ topath the represent’ isfull used-rank independent to representstatus of subchannels independent a channel matrixfor subchannels MIMO created transmission for by MIMO a large which transmission-scale are MIMOcreated whichantennaby reflecting are. Here,created or the di byff termraction reflecting ‘path points’ is or used from diffraction to surrounding represent points independent objects from insurrounding a cell,subchannels such objectsas buildings, for MIMO in a cell, trees, transmission such and ascars. buiwhichHence,ldings, are in trees, ancreatedactual and by cars. cellular reflecting Hence, system, or in andiffraction the actual number cellular points of paths system,from may surrounding the change number greatly, objects of paths depending in a may cell, change such on the as greatly,buipropagationldings, depending trees, environment andon the cars. propagation arising Hence, from in environment an congested actual cellular urban arising or system, non-crowdedfrom congestedthe number rural urban areas. of pathsor Consideringnon may-crowded change this ruralgreatly,fact, areas. the depending prime Considering objective on thethis of propagation thefact, channel the prime modelenvironment objective used in ofarising this the paper channe from is congestedl to model assess used the urban theoreticalin thisor non paper- limitationcrowded is to assessruralof the the areas. channel theoretical Considering capacity limitation achieved this fact, of the by the thechannel prime daisy objectivecapacity chain MIMO achievedof the antenna channe by the whenl model daisy a su usedchainfficiently inMIMO this large paper antenna number is to whenassessof paths a sufficientlythe are theoretical available large limitation in number a cell where of pathsthe a channel relevant are available capacity antenna in achievedoperates.a cell where by thea relevant daisy chain antenna MIMO operates. antenna when a sufficiently large number of paths are available in a cell where a relevant antenna operates. MM basebase station station (BS) (BS) ant antennasennas create create a set a set of ofQcQ clusters,c clusters, each each of ofwhich which comprise comprisess M Muncorrelateduncorrelated M base station (BS) antennas create a set of Qc clusters, each of which comprises M uncorrelated waves,waves, forming forming KmK mscatterersscatterers surrounding surrounding N NMSMS antennas. antennas. Thus, Thus, the the M Muncorrelateduncorrelated waves waves are are subjectwaves,subject to toformingan an independent independent Km scatterers and and identically surroundingidentically distributed distributed N MS antennas.(i.i.d) (i.i.d) complex complex Thus, Gaussian theGaussian M uncorrelatedprocess. process. Furthermore, Furthermore, waves are thesubjectthe correlation correlation to an independentcharacteristics characteristics and of of theidentically the BS BS and and MSdistributed MS sides sides are are (i.i.d) taken taken complex to to be be independent independent Gaussian process. of eacheach other, otherFurthermore,, based based on the correlation characteristics of the BS and MS sides are taken to be independent of each other, based on the Kronecker assumption [24]. MS antennas are assumed to be surrounded by Km scatterers, on the Kronecker assumption [24]. MS antennas are assumed to be surrounded by Km scatterers,

MicromachinesMicromachines 20202020,, 1111,, x 871 77 of of 25 25 created by Qc clusters. The Km scatterers belonging to the q-th cluster are Gaussian distributed in azimuththe Kronecker in two assumption-dimensional [24 ].coordinates MS antennas. Figure are assumed 6b depicts to be the surrounded coordinate bys Kofm thescatterers, k-th scatterer created, in by whicQc clusters.h the MS The is Kmovingm scatterers toward belonging the azimuth to the directionq-th cluster, ϕv are. Using Gaussian the above distributed-mentioned in azimuth channel in modeling,two-dimensional we carried coordinates. out a Monte Figure Carlo6b depicts simulation the coordinates according to of the followingk-th scatterer, procedure in which: the MS is moving toward the azimuth direction, φv. Using the above-mentioned channel modeling, we carried 4.1.out S atep Monte 1: Generation Carlo simulation of Km-Path according to the following procedure: The multipath property is modeled by the angular power spectrum. The spectrum of the 4.1. Step 1: Generation of Km-Path Gaussian distribution for the q-th cluster is shown in Figure 7a, and given below. The multipath property is modeled by the angular power spectrum. The spectrum of the Gaussian 2 distribution for the q-th cluster is shown in Figure7a, and givenp below. q p XPR 2 PA( , )= exp n o2  (1) HHqq π2  2π 1 XPRXPR  φ 22q µq  P ( , φ) = A exp − −  (1) Hθ Hθ  2  2 1 + XPR  2σq 

ppπ 11 π (2) PPPHHq((,)(,), φ)= = P ( , φ) (2) Hφ 222 XPRXPR Hθ 2 wherewhere µµqq isis the the azimuth azimuth angle angle of of the the mean mean of of the the incident incident wave, wave, σσqq isis the the standard standard deviation deviation of of the the powerpower spectrum, spectrum, and and XPR XPR is is the the cross cross-polarization-polarization power power ratio, ratio, given given as as the the propagation propagation parameter, parameter, andand is is assumed assumed to to b bee the the average average value value [25] [25].. The The channel channel responses responses of of the the s signalsignals for for a a particular particular snapshotsnapshot of of fading fading are are generated generated using using random random numbers numbers,, which which ensures ensures orthogonality orthogonality between between subchannelssubchannels for for the the purpose purpose of of ideal ideal MIMO MIMO transmission transmission with with a a full full-rank-rank channel channel matrix.

hq Average Power V,k nm q hH,k nm

n-th antenna Eq n 2q E n

output 0 q Azimuth Angle 180deg hq k, nm (a) (b)

FigureFigure 7. 7. IncidentIncident wave wave model model for for the the Monte Monte Carlo Carlo simulation. simulation. (a ()a )Gaussian Gaussian incident incident wave wave in in azimuth. azimuth. ((bb)) Two Two polarization polarization components.

4.2.4.2. S Steptep 2 2:: Generation Generation of of Polarization Polarization and and Summation Summation of of All All Clusters Clusters ItIt is is assumed assumed that that the the kk--thth path path for for the the qq--thth cluster cluster has has a a transfer transfer function function with with vertical vertical and and horizontalhorizontal components components,, as as shown shown in in Fig Figureure 77bb.. The vertical and horizontal components of the transfer functionfunction of of the the kk--thth path path for for the the qq--thth cluster cluster at at the the nn--thth antenna antenna are are given given by r q qXPRXPR qq p π qq q q h hVk , nm== h kh ,m EqE nθ(n( ,, kφ , m )exp) exp j j Vϕ k , m  (3(3)) Vk,nm 121+XPRXPR k,m 2 k,m Vk,m r q q11 qq p π qq q q h = h Eφ n( , φ ) exp jϕ (4(4)) Hhk,nmHk , nm= + h k ,mk,m E n( , k , m )expk,m  j H k , mHk, m 121 XPRXPR 2 q q where Eθn (π/2, φ k,m) and Eφn (π/2, φ k,m) are the complex electric ﬁeld directivities of the n-th antenna where Eθn (π/2, ϕqk,m) and Eϕn (π/2, ϕqk,m) are the complex electric field directivities of the n-th antenna element in the xy-plane for the θ and φ components, respectively, which are deﬁned at the origin element in the xy-planeq for the θ and ϕ components, respectively, which are defined at the origin of of the coordinates. h k,m represents the equivalent amplitude of the incident waves and can be set the coordinates. hqk,m represents the equivalent amplitude of the incident waves and can be set to an to an arbitrary value; thus, it is assumed to have unity amplitude. XPR is the cross-polarization arbitrary value; thus, it is assumed to have unity amplitude. XPR is the cross-polarization power

Micromachines 2020, 11, 871 8 of 25

q q power ratio. The phases of the vertical and horizontal polarization components, ϕ Vk,m and ϕ Hk,m, are independent of each other, and are uniformly distributed from 0 to 2π. For each path, the two polarization components are combined with reference to the schematic diagram shown in Figure7b, as the complex sum of the vertical and horizontal components, and we have

q q q h = h + h k,nm Vk,nm Hk,nm (5) where the transfer function of the k-th path is evaluated by summing all the cluster responses, and is given by Qc X q h = h k,nm k,nm (6) q=1

4.3. Step 3: Generation of the Resultant Channel Response Using the transfer function represented by Equation (6), the resultant channel response at the n-th antenna is calculated using the equation

Km ( ) X 2πd hnm = h exp j cos(φ φ v) (7) k,nm λ k,m − k=1 where λ is the wavelength in free space, and d is the distance traveled by a mobile station moving toward the azimuth direction φv, as shown in Figure6b. This scheme is applied repeatedly to generate the following channel response matrix at the s-th snapshot    h11 h12 h1m   ···   h h h m   21 22 ··· 2  Hs = [hnm] =  . . .  (8)  . . .. .   . . . .    h hn h n1 2 ··· NM The distance traveled by the mobile station between two successive points, ∆d, in the simulation is changed according to the angular spread of the incident waves, because a narrow spread results in a long fading period. For each value of d, fading is assumed to be quasi-static, i.e., the channel response is kept constant. The complex correlation coeﬃcient between two channel responses is deﬁned as

h1∗h2 ρc = h i (9) √ h h √ h h h 1∗ 1i h 2∗ 2i where h1 and h2 represent the two distinct channel responses in the matrix of Equation (8), and denotes the ensemble average of X where Y* represents the complex conjugate of Y. Using this deﬁnition, the absolute value of the complex correlation coeﬃcient can be obtained from

ρa = ρc (10)

Here, the absolute value of the complex correlation coeﬃcient ρa in Equation (10) is used as a general description of the correlation behavior of the MIMO antenna performance throughout this paper, as mentioned in Section5.

4.4. Step 4: Evaluation of the Channel Capacity The eigenvalues and eigenvectors are obtained using the following SVD (singular value decomposition) operation H Hs = UsDsVs (11) Micromachines 2020, 11, 871 9 of 25

Us = [e , , e ] (12) r1 ··· rL Vs = [e , , e ] (13) t1 ··· tL h p p i Ds = diag λ , , λ (14) 1 ··· L where L = min (N, M). Us and Vs are the singular vectors of the receiving (mobile station) and transmitting (base station) antennas, respectively. Ds represents the singular values, where λi denotes the eigenvalue of the i-th subchannel for spatial multiplexing transmission in the MIMO system. Using these eigenvalues, the instantaneous channel capacity and its average value are ﬁnally evaluated by L ! X γ λi C = log 1 + (15) s 2 M i=1 S 1 X C = Cs (s = 1 S) (16) S ··· s=1 where γ is the input SNR (signal-to-noise power ratio), deﬁned as the SNR for each incident wave when an isotropic antenna is used for receiving the incident wave, permitting the performance of the antenna elements used in the MIMO array to be included in the simulation results.

5. Theoretical Investigation

5.1. Design of 4 4 MIMO Antenna × As described in Section3, the 4 4 MIMO antenna depicted in Figure3b is used as a basic × component module or a fundamental functional unit cell to construct the 32 32 MIMO antenna array. × Hence, in the ﬁrst step of our investigation, we considered the design of the 4 4 MIMO antenna [19]. × Two of the eight antenna elements arranged in the circle form a subarray that receives a subchannel of the MIMO communication, where the number of subarrays in the 4 4 MIMO antenna is four. × The radius of the circle, a, was set to 4.9 cm so that the distance between adjacent elements (d1 shown in Figure3b) was a quarter-wavelength at 2 GHz. In this case, the directivity of Subarray1 is expected to have a cardioid radiation pattern in the absence of mutual electromagnetic coupling between antenna elements. Figure8 shows the fundamental principle of the cardioid radiation pattern created by two isotropic point sources corresponding to Elements #2 and #3 in Figure3b, in which there is no electromagnetic mutual coupling between the two sources. As shown in Figure8a, the distance between the two sources is set to d1 = λ/4. Furthermore, the received signal from Element #2 is delayed by φp = π/2 using a phase shifter. The total received signal, Et, is given by summing the received signals from Elements #2 and #3 using a signal combiner, and calculated from the equation

π Et = Ea 1 + exp j (cos φ 1) (17) 2 − where φ represents the azimuthal angle deﬁned in Figure8. Ea denotes the amplitude of excitation of each element. Using this circuit topology shown in Figure8a, an actual signal processing unit was fabricated, as described in Section6 (see Figure 18a). Figure8b illustrates the radiation pattern normalized to its peak value, calculated by the absolute value of Equation (17). As can be seen from Figure8b, the radiation pattern directs its maximum towards φ = 0◦ and exhibits a deep null towards φ = 180◦. Therefore, the array works as a phased array antenna that yields a strong radiation intensity in the direction of the line between the two sources. MicromachinesMicromachines 20202020,, 11,, x 871 1010 of of 25 25

#3φ #2 1 0.8 λ − jπ /2 E = Ee 0.6 a d1 a 4 π 0.4 Phase shifter φ = 0.2 φ p φ =°180 φ =°0 2 0

-0.2

-0.4 + Signal combiner -0.6

-0.8 E -1 t -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 (a) (b)

FigureFigure 8.8. PrinciplePrinciple of of the the cardioid cardioid radiation radiation pattern pattern created bycreated two isotropic by two point isotropic sources. point (a) Configurationsources. (a) Configurationof the array. (b )of Cardioid the array. radiation (b) Cardioid pattern. radiation pattern.

WhenWhen thethe subarrayssubarrays described described in Figurein Figure3b are 3b investigated, are investigated, the electromagnetic the electromagnetic mutual coupling mutual couplingbetween thebetween dipole the antenna dipole elements antenna must elements be considered. must be considered. The signals The received signals by tworeceived elements by two are elementsmultiplied are by multiplied the weight by functions the weight and function phase controls and phase between control the twobetween elements. the two In Subarray1elements. In in Subarray1Figure3b, the in weightFigure functions3b, the weight of each functions element (ofw each2 and elementw3) and the(w2 phaseand w shift3) and value the (phaseτ2) are shift optimized value (byτ2) Equationare optimized (18) using by Equation the two (18) electric using field the directivities two electric ( Efield2 and directivitiesE3) of the angle(E2 and of E the3) of incident the angle wave of the(φ) incident when the wave antenna (ϕ) when elements the areantenna excited elements individually. are excited individually. − τ wE()φφ ej 2 + wE () w22E (φ)e jτ2 + w 33E (φ) E ()φ = 2 2 − 3 3 Es1s1(φ) = p ()+ (18)(18) 6060(PPP223+ P3) where P2 andand PP33 areare the the input input power power at at the the feed feed point point of of Elements Elements #2 #2 and and #3, #3, respectively. respectively. The The phase phase ofof one one element element shifts shifts to to an an in-phase in-phase state state with with resp respectect to to the the other other element element at at the the angle angle of of the the incident incident wave in consideration of the mutual electromagne electromagnetictic coupling. The The weight weight functions functions are are determined determined inin such such a a way way that that the the gain gain in in the the communication communication direction of the combined radiation pattern yields yields thethe maximum maximum value. value. In In Subarray2, Subarray2, the the same same procedure procedure is is applied applied to to optimize optimize the the radiation radiation pattern. pattern. InIn Section Section 66,, wewe willwill introduceintroduce aa microwavemicrowave circuitcircuit forfor realizingrealizing weightweight functionsfunctions inin anan experimentalexperimental way (see Figure 18a). SinceSince the the maximum maximum radiation radiation gain gain of of each each elemen elementt is is approximately approximately 0 0 dBd, dBd, in in order order to to further enhanceenhance the the radiation radiation gain, gain, we we examined examined placing placing a a parasitic parasitic or or unexcited unexcited element, element, Element Element #9 #9 shown shown inin Figure Figure 33bb atat thethe centercenter ofof thethe circle.circle. FigureFigure9 9 shows shows the the radiation radiation gain gain at at 0 0°◦ asas a a function of of the lengthlength of the parasitic elementelement [[19].19]. TheThe parasiticparasitic ElementElement #9 #9 works works as as a a reflector reflector or or director, director, similar similar to toa Yagi–Udaa Yagi–Uda array array antenna, antenna, when when its lengthits length is long is lo orng short, or short, respectively. respectively. The blueThe blue and redand solidred solid lines linesindicate indicate the radiation the radiation gain at gain 0◦ of at Elements 0° of Elem #2 andents #1,#2 respectively,and #1, respectively, which are which the most are influentialthe most influentialelements on elements the directivities on the directivities of Subarray1 of Subarray1 and Subarray2, and Subarray2, when the when incident the incident wave comes wave from comes 0◦ . fromThe black 0°. The line black shows line the shows average the value average of the value radiation of the gainradiation of Elements gain of #1Elements and #2at #1 0 ◦and. The #2 starat 0°. marks The starplotted marks on plotted the right on axis the representright axis therepresent radiation the gainsradiation of each gains element of each (#1, elem #2,ent #3, (#1, and #2, #4) #3, when and #4) the whenparasitic the elementparasitic #9 element was not #9 in was place. not Figure in place.9 shows Figure that 9 shows when thethat lengthwhen ofthe the length parasitic of the element parasitic is elementshorter thanis shorter a half than wavelength a half wavelength (0.5 λ = 7.5 cm),(0.5 λ the = radiation7.5 cm), the gains radiation of Elements gains #1of andElements #2 are #1 enhanced. and #2 areWhen enhanced. the length When of the the parasitic length of element the pa israsitic set to element 6.2 cm(0.41 is setλ to), the6.2 averagecm (0.41 radiation λ), the average gain of radiation Elements gain#1 and of #2Elements at 0◦ is #1 at itsand maximum #2 at 0° is value.at its maximum value.

Micromachines 2020, 11, 871 11 of 25 Micromachines 2020, 11, x 11 of 25

5 #1 (main element of Subarray2) 2.5 0 #2 (main element of Subarray1) -2.5 Ave. (#1, #2) [dBd]

[dBd] #3 0 0 -5 -7.5 Gain g Gain g Gain -10 Max #4 -12.5 without parasitic element -15 5.5 6 6.5 7 7.5 8 8.5 9 Length of Parasitic Element [cm] FigureFigure 9. 9.Radiation Radiation gain gain of of each each element. element.

TheThe excitation excitation conditions conditions forfor SubarraysSubarrays 1–41–4 areare summarizedsummarized inin TableTable1 ,1, which which is is obtained obtained by by searchingsearching for for the the optimum optimum amplitude amplitude and and phase phase from from among among the the possible possible weight weight functions functions of of each each elementelement using using Equation Equation (18). (18) Furthermore,. Furthermore, Element Element #9 #9 is usedis used as as a parasitic a parasitic or non-excitingor non-exciting element element to enhanceto enhance the directivity.the directivity. From From the analytical the analytical results results given ingiven Figure in9 Figure, the length 9, the of length the parasitic of the elementparasitic iselement set to 6.2 is cmset (0.41to 6.2λ cm). As (0.41 shown λ). As in shown Figure4 in, the Figure subarray 4, the combinations subarray combinations are the same are when the same the angle when ofthe the angle incident of the wave incident is 0◦ and wave 180 is◦. 0° However, and 180°. the However, optimized the weight optimized function weight and phase function shift and values phase of eachshift element values of at eachφ = 0 element◦ are diff aterent ϕ = from0° are those different at φ =from180 ◦those. In Combination1, at ϕ = 180°. In sinceCombination1, the subarray since has the a symmetricalsubarray has configuration a symmetrical with configuration respect to the withy-axis, respect the optimum to the y-axis, value the of elementoptimum #2 value at φ = of0◦ elementis that of#2 #3 at at ϕ φ= 0°= 180is that◦, whereas of #3 at ϕ the = 180°, optimum whereas value the of optimum #3 at φ = value0◦ is thatof #3 of at #2 ϕ at= 0°φ is= that180◦ of. Thus, #2 at ϕ we = 180°. can selectThus, other we appropriatecan select other combinations appropriate from combinatio among thens possible from among combinations the possible of subarrays. combinations of subarrays. Table 1. Excitation conditions of each element. Table 1. Excitation conditions of each element Frontward for Incident Wave Backward for Incident Wave Subarray1 #2 1 V,Frontward160 for Backward#3 0.72 V,for 0 − ◦ ◦ Subarray2 #1 1 V,Incident330 Wave Incident#4 0.38 Wave V, 0 − ◦ ◦ Subarray3Subarray1 #8 1 V,#2 330 1 V, −160° #3 #5 0.72 0.38 V, V, 0° 0 − ◦ ◦ Subarray4 #7 1 V, 160 #6 0.72 V, 0 Subarray2 #1− 1 ◦V, −330° #4 0.38 V, 0° ◦ Subarray3 #8 1 V, −330° #5 0.38 V, 0° Figure 10 shows the θ-polarized radiation patterns in the xy-plane of Subarray2 as a function Subarray4 #7 1 V, −160° #6 0.72 V, 0° of the angle of the incident wave [19]. The angle of the incident wave is changed from 0◦ to 135◦ in 45◦ intervals. The black arrows in the figure indicate the angle of the incident wave. The radius of Figure 10 shows the θ-polarized radiation patterns in the xy-plane of Subarray2 as a function of the circle, a, is set to 4.9 cm. The frequency used in the analysis is 2 GHz. As shown in Figure 10, the angle of the incident wave [19]. The angle of the incident wave is changed from 0° to 135° in 45° the radiation patterns vary depending on the angle of the incident wave, which is in accordance with intervals. The black arrows in the figure indicate the angle of the incident wave. The radius of the the subarray combination, as illustrated in Figure4. Furthermore, a radiation gain of 4.1 dBd at the circle, a, is set to 4.9 cm. The frequency used in the analysis is 2 GHz. As shown in Figure 10, the angle of the incident wave is achieved and is larger than an ordinary dipole antenna, which results radiation patterns vary depending on the angle of the incident wave, which is in accordance with the in a large SNR. The directivities of the other three subarrays also control the direction of the beam. subarray combination, as illustrated in Figure 4. Furthermore, a radiation gain of 4.1 dBd at the angle Therefore, high signal levels can be maintained even though the direction of the incoming wave varies of the incident wave is achieved and is larger than an ordinary dipole antenna, which results in a due to the dynamic motion of the automobile in connected car applications. large SNR. The directivities of the other three subarrays also control the direction of the beam. Therefore, high signal levels can be maintained even though the direction of the incoming wave varies due to the dynamic motion of the automobile in connected car applications.

MicromachinesMicromachines 20202020, ,1111, ,x 871 1212 of of 25 25

XY Plane XY Plane XY Plane XY Plane 10 y 10 y 10 y 10 y 0 0 0 0

-10 -10 -10 -10

-20 -20 -20 -20 x x x x -10 -10 -10 -10

0 0 0 0 Eθ Eθ Eθ Eθ 10 10 10 10 10 0 -10 -20 -10 0 10 10 0 -10 -20 -10 0 10 10 0 -10 -20 -10 0 10 10 0 -10 -20 -10 0 10 [dBd] [dBd] [dBd] [dBd] (a) (b) (c) (d)

FigureFigure 10. 10. RadiationRadiation pattern pattern of of Subarray2 Subarray2 when when the the 4 4× 44 MIMO MIMO antenna antenna is is used. used. (a ()a )ϕφ == 00 deg deg × (Combination1).(Combination1). (b ()b )ϕφ == 4545 deg deg (Combination2). (Combination2). (c ()c )ϕφ == 9090 deg deg (Combination3). (Combination3). (d ()d )ϕφ == 135135 deg deg (Combination4).(Combination4).

5.2. Performance Evaluation of 32 32 MIMO Antenna 5.2. Performance Evaluation of 32 ×× 32 MIMO Antenna TableTable 22 listslists the the analytical analytical conditions conditions used used for performingfor performing the Monte the Mont Carloe simulation.Carlo simulation. The number The numberof clusters of clusters and number and number of scatterers of scatterers were setwere to set 1 and to 1 30, and respectively. 30, respectively. The numberThe number of samples of samples was wasassumed assumed to be to 5000.be 5000. In theIn the Monte Monte Carlo Carlo simulation, simulation, the the mobile mobile station station was was moved moved by by a distancea distance of of100 100λ λto to 1000 1000λ,λ which, which was was changed changed depending depending on on the the angular angular spread, spread, with with the the distance distance between between two twosuccessive successive points points in the in the simulation simulation being being∆d =Δd0.02 = 0.02λ toλ 0.2 to λ0.2. λ.

TableTable 2. 2. AnalyticalAnalytical conditions. conditions.

FrequencyFrequency 20002000 MHz MHz NumberNumber of elements of elements (M, N (M) , N) MM= N= =N 32= 32 Number of clusters (Qc) 1 Number of clusters (Qc) 1 Number of scatterers (Km) 30 Number of scatterers (Km) 30 Initial phase for scatterers Random Initial phase for scatterers Random Traveling distance (d) 1000λ for σ = 10◦ Traveling distance (d) 1000λ for σ = 10° (dependent on angular spread) 100λ for σ = 100◦ (dependentNumber on ofangular samples spread) (S) 100λ 5000 for σ = 100°

NumberSampling of samples interval (S) (∆d = d/S) 0.2λ for5000σ = 10 ◦ λ Sampling(dependent interval on (Δ angulard = d/S) spread) 0.020.2forλ forσ = σ100 = 10°◦ (dependentMoving on direction angular (φspread)V) 0.02λ 5for◦ σ = 100° XPR 50 dB (Vertical Pol.) Moving direction (ϕV) 5° Antenna element Half-wavelength dipole XPR 50 dB (Vertical Pol.) Method of EM analysis Method of moments Antenna element Half-wavelength dipole Method of EM analysis Method of moments One of the most important considerations in the development of the 32 32 MIMO antenna is × that the desired directivities of the 32 subarrays are varied via electromagnetic (EM) coupling due to One of the most important considerations in the development of the 32 × 32 MIMO antenna is the proximity of the antenna elements. In particular, the radiation patterns of the 16 elements that are that the desired directivities of the 32 subarrays are varied via electromagnetic (EM) coupling due to closest to the AOA antenna located at the center of the circle, exhibit a signiﬁcant reduction. This fact the proximity of the antenna elements. In particular, the radiation patterns of the 16 elements that are allows the channel capacity to be reduced because the directivity of the subarray, which is mainly closest to the AOA antenna located at the center of the circle, exhibit a significant reduction. This fact composed of these elements, cannot lead the beam in the direction of the incoming wave. allows the channel capacity to be reduced because the directivity of the subarray, which is mainly Figure 11 shows the radiation patterns of two subarrays, Subarray2 and Subarray18, as functions composed of these elements, cannot lead the beam in the direction of the incoming wave. of the radius r of the array when the angle of the incident wave φ is 0 [14]. These two subarrays are Figure 11 shows the radiation patterns of two subarrays, Subarray2◦ and Subarray18, as functions depicted in Figure3a by the two red broken rectangles. The excitation conditions listed in Table1 are of the radius r of the array when the angle of the incident wave ϕ is 0° [14]. These two subarrays are used for all the subarray groups in the 32 32 MIMO antenna. depicted in Figure 3a by the two red broken× rectangles. The excitation conditions listed in Table 1 are used for all the subarray groups in the 32 × 32 MIMO antenna.

Micromachines 2020, 11, x 13 of 25 Micromachines 2020, 11, 871 13 of 25

10 y 10 y 0 0

-10 -10

-20 x -20 x -10 -10

0 r = 30cm 0 r = 30cm r = 15cm r = 15cm 4 4MIMO 4 4MIMO 10 10 10 0 -10 -20 -10 0 10 10 0 -10 -20 -10 0 10 [dBd] [dBd]

(a) (b)

FigureFigure 11.11. RadiationRadiation patternspatterns ofof Subarray2Subarray2 andand Subarray18Subarray18 whenwhen thethe 3232 × 32 MIMO antenna is used. × ((aa)) Subarray2.Subarray2. ((bb)) Subarray18.Subarray18.

InIn FigureFigure 11 11,, the the black black and and red red solid solid lines lines indicate indicate the the radiation radiation patterns patterns at r at= 30r = cm 30 andcm andr = 15 r = cm, 15 respectively.cm, respectively. The blueThe blue broken broken line indicatesline indicates the radiation the radiation pattern pattern of the of 4 the4 4 MIMO × 4 MIMO array array without without EM × couplingEM coupling caused caused by other by other 4 4 4 MIMO × 4 MIMO arrays arrays [19]. The[19]. black The black arrows arrows in the in figure the figure show theshow angle the ofangle the × incidentof the incident wave. Aswave. shown As inshown Figure in 11 Figure, the radiation 11, the radiation gains at an gains incident-wave at an incident-wave angle of 0◦ anglefor Subarray2 of 0° for isSubarray2 constant regardlessis constant ofregardless the radius ofr ,the while radius the radiationr, while the gain radiation at φ = 0 gainfor theat ϕ32 = 0°32 for MIMO the 32array × 32 ◦ × agreesMIMO well array with agrees that well for thewith 4 that4 MIMO for the array. 4 × 4 MIMO This is array. because This the is radiation because beamthe radiation from Subarray2 beam from is × directedSubarray2 to theis directed outside ofto thethe whole outside antenna of the system whole andantenna is less system affected and by theis less EM affected coupling by caused the EM by thecoupling other 4caused4 MIMO by the arrays. other 4 × 4 MIMO arrays. × InIn contrast,contrast, thethe radiationradiation gainsgains atat φϕ == 00°◦ forfor Subarray18Subarray18 areare significantlysignificantly degradeddegraded byby thethe EMEM couplingcoupling whenwhen r = 1515 cm. cm. This This is is due due to to the the fact fact that that Subarray18 Subarray18 directs directs its itsradiation radiation beam beam toward toward the theAOA AOA antenna antenna and and is significantly is significantly affected affected by byEM EM coupling coupling with with the theAOA AOA antenna. antenna. However, However, the theradiation radiation gain gain at r at =r 30= 30cm cm is isimproved improved considerably considerably and and is isclose close to to that that of of the the 4 4 × 44 MIMO MIMO array. × TheseThese resultsresults showshow thatthat thethe radiationradiation gaingain atat thethe angleangle ofof thethe incidentincident wavewave increasesincreases withwith increasingincreasing radiusradius duedue toto smallersmaller EMEM coupling.coupling. TheThe finalfinal targettarget ofof ourour studystudy isis toto obtainobtain transmissiontransmission ratesrates greatergreater thanthan aa gigabitgigabit toto ensureensure thethe successsuccess ofof thesethese arraysarrays inin upcomingupcoming connectedconnected carcar systems.systems. Hence,Hence, toto investigateinvestigate thethe optimumoptimum radiusradius forfor thisthis purpose,purpose, thethe channelchannel capacitycapacity isis calculatedcalculated throughthrough MonteMonte CarloCarlo simulations,simulations, withwith aa singlesingle clustercluster GaussianGaussian spectrumspectrum comingcoming fromfrom azimuthazimuth angleangleφ ϕ,, as as depicted depicted in in Figure Figure3 b.3b. FigureFigure 12 12 showsshows thethe averageaverage channelchannel capacity,capacity, calculatedcalculated fromfrom EquationEquation (16),(16), asas aa functionfunction ofof thethe radiusradius rr atat 22 GHzGHz [[14].14]. TheThe blackblack andand redred curvescurves correspondcorrespond toto incident-waveincident-wave anglesangles φϕ ofof 00°◦ and 4545°.◦. Half-wavelengthHalf-wavelength dipoledipole antennas antennas are are used used for for the the 64 64 elements. elements. The The radius radius of of the the 4 4 × 44 MIMOMIMO antennaantenna × aa isis setset toto 4.94.9 cm.cm. TheThe cross-polarizationcross-polarization powerpower ratio,ratio, XPR,XPR, isis setset toto 5050 dB,dB, whichwhich isis equivalentequivalent toto aa verticallyvertically polarizedpolarized propagationpropagation environment.environment. TheThe standardstandard deviationdeviation ofof thethe incidentincident wavewaveσ σ( (σσ11 forfor thethe cluster1cluster1 inin FigureFigure7 a)7a) is is set set to to 30 30°.◦. TheThe SNRSNR ofof thethe incidentincident wavewave isis setset toto 3030 dB.dB. FigureFigure 1212 showsshows thatthat aa channelchannel capacitycapacity ofof overover 220220 bitsbits/s/Hz/s/Hz isis achievedachieved whenwhen rr isis greatergreater thanthan 3030 cm,cm, whichwhich isis equivalentequivalent toto 2222 GbpsGbps forfor aa bandwidthbandwidth ofof 100100 MHz.MHz. TheThe channelchannel capacitycapacity increasesincreases byby 5252 bitsbits/s/Hz/s/Hz whenwhenr r= = 3030 cm,cm, comparedcompared withwith thethecase casewhere wherer r= = 1515 cm.cm. Furthermore,Furthermore, thethe channelchannel capacitycapacity remainsremains constantconstant afterafterr r= = 3030 cmcm,, meaningmeaning that,that, consideringconsidering thethe sizesize ofof thethe array,array,r r= = 3030 cmcm isis oneone ofof the the best best possible possible solutions solutions for obtainingfor obtaining the maximumthe maximum channel channel capacity capacity with an with array an of array limited of size.limited Note size. that Note the that black the and black red and curves red curves at angles at angles of 0◦ and of 0° 45 and◦ closely 45° closely overlap. overlap. This This is due is due to the to factthe that,fact that, as described as described in Figure in 4Figure, the 32 4, the32 MIMO32 × 32 array MIMO uses array different usescombinations different combinations of subarrays, of × Combination1subarrays, Combination1 and Combination2, and Combination2, at φ = 0◦ and 45at ◦ϕ, which= 0° and enables 45°, which the radiation enables gain the in radiation these directions gain in tothese be enhanced directions with to be equal enhanced intensity. with Consequently, equal intensity. we Consequently, have the same we level have of channelthe same capacity level of atchannel these

Micromachines 2020, 11, x 14 of 25 MicromachinesMicromachines2020 2020, 11,, 11 871, x 1414 of of 25 25 capacity at these angles, which confirms that the beam steering function operates correctly, regardless ofcapacity the size at of these the array. angles, which confirms that the beam steering function operates correctly, regardless angles,of the whichsize of conﬁrmsthe array. that the beam steering function operates correctly, regardless of the size of the array. 240 240 230 230 220 220 210 52 bits/s/Hz 52 bits/s/Hz 210  = 30deg 200 σ 200 a == 4.9cm 30deg 190 fa= =2GHz 4.9cm 190 180 XPRf = 2GHz = 50dB 180 SNRXPR = = 30dB 50dB 170 SNR = 30dB 170  = 0deg Channel Capacity [bits/s/Hz] 160 φ== 45deg 0deg

Channel Capacity [bits/s/Hz] 160 150 φ = 45deg 15010 15 20 25 30 35 40 45 50 10 15 20 25 30 35 40 45 50 Radius of Array r [cm] Radius of Array r [cm] Figure 12. Channel capacity as a function of the radius of the array. FigureFigure 12. 12.Channel Channel capacity capacity as as a functiona function of of the the radius radius of of the the array. array. To understand the mechanism for the radius-channel capacity relationship more specifically, we performedToTo understand understand an analysis the the mechanismof mechanism the channel for for gain. thethe radius-channelradius-channe Figure 13 showsl capacity capacity the channel relationship relationship gain moreas more a function specifically, speciﬁcally, of the we wenumberperformed performed of the an an subarray analysis analysis withof of the the the channel radius as gain. a parame Figure ter 1313 when showsshows a single thethe channelchannel Gaussian gain gain wave as as a a functionwith function a standard of of the the numberdeviationnumber of of theof the σ subarray =subarray 30° comes with with thefrom the radius anradius angle as as a parameterofa parameter ϕ = 0°. The when when channel a singlea single gain Gaussian Gaussian is defined wave wave as with thewith aratio standarda standard of the deviationreceiveddeviation ofpower ofσ =σ 30 =of 30°◦ thecomes comes signal from from at each an an angle subarrayangle of ofφ =ϕto 0= ◦that 0°.. The Theof channela channelsingle gainisotropic gain is is deﬁned definedantenna. as as theThus, the ratio ratio a channel of of the the receivedgainreceived exceeding power power of 2.15 theof dBthe signal meanssignal at each thatat each subarraythe subarray to that hasto ofthat more a single of gaina single isotropic than isotropic an antenna.ordinary antenna. Thus,dipole aThus, antenna. channel a channel gain Note exceedingthatgain we exceeding obtained 2.15 dB 2.15 meansthe dBchannel thatmeans the gain that subarray in the such subarray hasa way more thathas gain morethe thanaverage gain an than ordinaryoperation an ordinary dipole is performed dipole antenna. antenna. with Note respect that Note wetothat obtainedall we32 incidentobtained the channel waves. the channel gain in gain such in a waysuch thata way the that average the average operation operation is performed is performed with respect with respect to all 32to incident all 32 incident waves. waves.

1010 1010 Subarrays 1-4 Subarrays 1-4 55 Subarrays 17-20 55 Subarrays 17-20

00 00

--55 -5-5 9-12 13-16 9-12 5-8 -10 -10 13-16 5-8  = 0deg -10-10 17-20 1-4 2 φ== 30deg 0deg σ 17-20 1-4 2σ r == 30cm 30deg Average of Channel- Gain [dB] 15-15 21-24 29-32 Incident rr== 20cm 30cm AverageChannelof Gain [dB] 25-28 Average of Channel Gain [dB] Gain Channel of Average -15-15 21-24 29-32 WaveIncident 25-28 rr== 15cm 20cm Average of Channel Gain [dB] Channel of Average Wave -20-20 r = 15cm 1 2 3 4 5 6 7 8 9 1011121314151617181920212223242526272829303132 -20-20 1 2 3 4 5 6 7 8 9 1011Number12131415 of16 17Subarray181920212223242526272829303132 Number of Subarray FigureFigure 13. 13.Channel Channel gain gain as as a a function function of of the the number number of of each each subarray. subarray. Figure 13. Channel gain as a function of the number of each subarray. In Figure 13, we calculated three cases; r = 30 cm, r = 20 cm, and r = 15 cm. The inset in the ﬁgure In Figure 13, we calculated three cases; r = 30 cm, r = 20 cm, and r = 15 cm. The inset in the figure shows the geometrical relationship between the array structure and the incident wave. The blue and showsIn the Figure geometrical 13, we calculated relationship three between cases; ther = 30array cm, structure r = 20 cm, and and the r = incident15 cm. The wave. inset The in theblue figure and red subarrays indicate that these subarrays, Subarrays 1–4 and Subarrays 17–20, are located in the redshows subarrays the geometrical indicate thatrelationship these subarrays, between Subarraysthe array structure 1–4 and andSubarrays the incident 17–20 ,wave. are located The blue in theand red subarrays indicate that these subarrays, Subarrays 1–4 and Subarrays 17–20, are located in the

Micromachines 2020, 11, x 15 of 25 Micromachines 2020, 11, 871 15 of 25 forward and backward directions with respect to the incident wave, as shown in the inset. The blue and red arrows included in the upper part of Figure 13 indicate the locations of Subarrays 1–4 and forward and backward directions with respect to the incident wave, as shown in the inset. The blue Subarrays 17–20 on the lateral axis. and red arrows included in the upper part of Figure 13 indicate the locations of Subarrays 1–4 and Figure 13 shows that, regardless of the radius, Subarrays 1–4, which face the incident wave, Subarrays 17–20 on the lateral axis. provide a large channel gain of more than 2.15 dB, meaning that these subarrays operate more Figure 13 shows that, regardless of the radius, Subarrays 1–4, which face the incident wave, effectively than a conventional dipole antenna. On the other hand, for Subarrays 17–20, the channel provide a large channel gain of more than 2.15 dB, meaning that these subarrays operate more effectively gains exhibit a significant reduction as the radius decreases. In particular, when r = 15 cm the channel than a conventional dipole antenna. On the other hand, for Subarrays 17–20, the channel gains exhibit a gain is reduced to −10 dB, implying that these subarrays do not yield a useful subchannel for MIMO significant reduction as the radius decreases. In particular, when r = 15 cm the channel gain is reduced transmission. This phenomenon for the reduction in channel gain can also be understood from the to 10 dB, implying that these subarrays do not yield a useful subchannel for MIMO transmission. radiation− patterns, as described in Figure 11. It is concluded from these results that the reduction in This phenomenon for the reduction in channel gain can also be understood from the radiation patterns, channel capacity with decreasing radius r, as described in Figure 12, is caused by a decrease in the as described in Figure 11. It is concluded from these results that the reduction in channel capacity channel gains of the subarrays, particularly that situated at the back with respect to the incident wave, with decreasing radius r, as described in Figure 12, is caused by a decrease in the channel gains of the as illustrated in Figure 13. subarrays, particularly that situated at the back with respect to the incident wave, as illustrated in Figure 14 shows the channel capacity of the 32 × 32 MIMO array as a function of the angle ϕ Figure 13. when r = 30 cm. The angular spread σ and SNR were set to 30° and 30 dB, respectively. For Figure 14 shows the channel capacity of the 32 32 MIMO array as a function of the angle φ when comparison, the channel capacity of a 32 × 32 MIMO× dipole array is included in the graph. The dipole r = 30 cm. The angular spread σ and SNR were set to 30 and 30 dB, respectively. For comparison, array comprises eight groups of four-element dipole linear◦ arrays with a spacing of 3 cm arranged at the channel capacity of a 32 32 MIMO dipole array is included in the graph. The dipole array equal 45-degree angles aligned× along the y-axis, situated at the same locations as Subarrays 1–4 to comprises eight groups of four-element dipole linear arrays with a spacing of 3 cm arranged at equal 29–32, as indicated by the inset in the figure. As shown in Figure 14, when the proposed antenna is 45-degree angles aligned along the y-axis, situated at the same locations as Subarrays 1–4 to 29–32, used, the channel capacity remains constant regardless of the angle of the incident wave. In contrast, as indicated by the inset in the figure. As shown in Figure 14, when the proposed antenna is used, in the case of the dipole array antenna, more than 32-bits/s/Hz degradation in the channel capacity is the channel capacity remains constant regardless of the angle of the incident wave. In contrast, in the observed when the angle of the incident wave is 90° or 270°, in which the dipole array is parallel to case of the dipole array antenna, more than 32-bits/s/Hz degradation in the channel capacity is observed the incident wave. The dipole array gives a channel capacity of less than 205 bits/s/Hz because of low when the angle of the incident wave is 90 or 270 , in which the dipole array is parallel to the incident SNR or high correlation. In contrast, the◦ 32 × 32◦ MIMO array achieves a constant channel capacity of wave. The dipole array gives a channel capacity of less than 205 bits/s/Hz because of low SNR or high 220 bits/s/Hz regardless of the direction of the incoming wave owing to the full-azimuth beam correlation. In contrast, the 32 32 MIMO array achieves a constant channel capacity of 220 bits/s/Hz steering function. × regardless of the direction of the incoming wave owing to the full-azimuth beam steering function.

240

230

220 210 32bits/s/Hz

200

190

180 Dipole Array r = 30cm σ = 30deg Channel Capacity [bits/s/Hz] Capacity Channel r 170 f = 2GHz Proposed SNR = 30dB Dipole 160 0 45 90 135 180 225 270 315 360 Angle of Incident Wave φ [deg]

FigureFigure 14. 14.Channel Channel capacity capacity as as a functiona function of of the the angle angle of of the the incident incident wave. wave. 5.3. Antenna–Propagation Mutual Interactions 5.3. Antenna–Propagation Mutual Interactions As mentioned in the introduction, the MIMO antenna for a connected car system, implemented in As mentioned in the introduction, the MIMO antenna for a connected car system, implemented the framework for the ﬁfth and sixth generation (5G and 6G) mobile communications, is anticipated in the framework for the fifth and sixth generation (5G and 6G) mobile communications, is to be used in a system where the distance between the base station and the mobile station is small, anticipated to be used in a system where the distance between the base station and the mobile station compared with the conventional macrocell counterpart. In a small cell system, there are two signiﬁcant is small, compared with the conventional macrocell counterpart. In a small cell system, there are two

MicromachinesMicromachines2020 2020, 11, 11, 871, x 1616 of of 25 25

significant factors to be considered that affect the channel capacity of a MIMO system; the signal-to- factorsnoise topower be considered ratio (SNR) that and aﬀ theect spatial the channel angular capacity power of spread a MIMO of the system; incoming the signal-to-noise waves. The interaction power ratiobetween (SNR) these and thetwo spatial physical angular quantities power is spread complex of theand incoming there might waves. be a The tradeoff interaction relationship between because, these twofor physicalexample, quantities when a mobile is complex station and is situated there might in close be aproximity tradeoﬀ relationshipto a base station because, the received for example, power whenof the a mobilemobile stationstation is increases situated indue close to the proximity large SNR to a but base the station angular the receivedpower spread power of of the the received mobile stationsignal increasesdecreases due owing to the to largethe line-of-sight SNR but the (LOS angular) property power of spread the radio of the propagation received signal mechanism. decreases owingOn to thethe line-of-sightbasis of the (LOS)above-mentioned property of thebackground radio propagation, we carried mechanism. out a Monte Carlo simulation to investigateOn the basishow ofthe the developed above-mentioned 32 × 32 MIMO background, array performs we carried in a out propagation a Monte Carlo environment simulation where to investigate how the developed 32 32 MIMO array performs in a propagation environment where forthcoming 5G and 6G connected× car systems are anticipated to be used. Figure 15 shows the channel forthcomingcapacity as 5Ga function and 6G of connected the angular car systemspower spread are anticipated of an incident to be used.wave Figurewith the 15 SNR shows as thea parameter. channel capacityIn Figure as 15, a function the solid of lines the angular denote the power cases spread where of the an incidentradius of wave the array with r the is 30 SNR cm as and a parameter. the dashed Inlines Figure represent 15, the the solid cases lines of denote r = 20 cm. the We cases assume where a thesingle radius incident of the wave array comingr is 30 from cm and ϕ = the 0° along dashed the linesx-axis. represent the cases of r = 20 cm. We assume a single incident wave coming from φ = 0◦ along the x-axis.

300 r = 30cm r = 20cm 250 φ = 0deg SNR = 30dB 200

150 SNR = 20dB 100

50 SNR = 10dB Channel Capacity [bits/s/Hz]

0 0 20 40 60 80 100 Angular Spread σσ [deg]

Figure 15. Channel capacity vs. the angular power spread. Figure 15. Channel capacity vs. the angular power spread. It can be seen from Figure 15 that the 32 32 MIMO array achieves a maximum channel capacity It can be seen from Figure 15 that the 32× × 32 MIMO array achieves a maximum channel capacity of 277 bits/s/Hz when SNR = 30 dB, r = 30 cm, and σ = 100 . Moreover, Figure 15 shows that the of 277 bits/s/Hz when SNR = 30 dB, r = 30 cm, and σ = 100°.◦ Moreover, Figure 15 shows that the channel capacity decreases significantly as the angular power spread of the incoming wave decreases. channel capacity decreases significantly as the angular power spread of the incoming wave decreases. Specifically, when SNR = 30 dB and r = 30 cm the channel capacity is 268 bits/s/Hz in the case of Specifically, when SNR = 30 dB and r = 30 cm the channel capacity is 268 bits/s/Hz in the case of σ = σ = 60 . In contrast, the channel capacity reduces to 135 bits/s/Hz in the case of σ = 10 , which is 60°. In◦ contrast, the channel capacity reduces to 135 bits/s/Hz in the case of σ = 10°, which is◦ equivalent equivalent to a 50% reduction. In [10], the channel model parameters for various cellular systems to a 50% reduction. In [10], the channel model parameters for various cellular systems are are summarized, and the angular spread at the mobile station is found to vary between 30 and 80 summarized, and the angular spread at the mobile station is found to vary between 30° and◦ 80° (see◦ (see Table 2 in [10]). Judging from this fact, Figure 15 indicates that the developed antenna has good Table 2 in [10]). Judging from this fact, Figure 15 indicates that the developed antenna has good performance in situations encountered in typical application scenarios. performance in situations encountered in typical application scenarios. To clarify the mechanism responsible for the observations described in Figure 15, the channel gain To clarify the mechanism responsible for the observations described in Figure 15, the channel and correlation characteristics were investigated. gain and correlation characteristics were investigated. Figure 16 shows the channel gain and correlation coefficient of each subarray of the 32 32 MIMO Figure 16 shows the channel gain and correlation coefficient of each subarray of× the 32 × 32 array as a function of the number of the subarray. The black lines with round symbols denote the MIMO array as a function of the number of the subarray. The black lines with round symbols denote case where σ = 10 , whereas the red lines with square symbols represent the case where σ = 60 . the case where σ ◦= 10°, whereas the red lines with square symbols represent the case where σ = 60°.◦ The correlation coefficient is defined as the absolute value of the complex correlation coefficient between The correlation coefficient is defined as the absolute value of the complex correlation coefficient Subarray1 and the other subarrays, defined as ρa in Equation (10). Note that we obtained the correlation between Subarray1 and the other subarrays, defined as ρa in Equation (10). Note that we obtained the coefficient in such a way that the average operation is performed with respect to all 32 incident waves. correlation coefficient in such a way that the average operation is performed with respect to all 32 As described in Figure6, and Equations (3) and (4) in Section4, the incident waves from the base incident waves. As described in Figure 6, and Equations (3) and (4) in Section 4, the incident waves from the base station are assumed to be plane waves, i.e., far-field assumption, and thus the channel

Micromachines 2020, 11, x 17 of 25 model does not include the effects of the distance between the base and mobile stations on the correlation. It can be seen from Figure 16a that a channel gain of more than 2 dB is obtained for the subarrays numbered 1–8 and 29–32 for both σ = 10° and 60°. Particularly, the channel gain for σ = 10° exceeds 4 dB and is larger than that for σ = 60°. This is due to the fact that when σ = 10° the peak gain at ϕ = 0° results in a large channel gain due to in-phase excitation of the array, as depicted in Figure 11. In contrast, the channel gain for the subarrays numbered 13–24 is small in magnitude because of the shadowing effects caused by the subarrays located in front of them. Figure 16b shows that the correlationMicromachines coefficients2020, 11, 871 for σ = 10° are larger than those for σ = 60°. Especially, the correlations between17 of 25 Subarrays 1 and 2, 1 and 3, and 1 and 4, which belong to the same 4 × 4 MIMO array group, are more than 0.6. In contrast, when σ = 60° the correlation is less than 0.5 over the entire array. station are assumed to be plane waves, i.e., far-ﬁeld assumption, and thus the channel model does not include the eﬀects of the distance between the base and mobile stations on the correlation.

9 1 8  = 10deg 0.9  = 10deg  = 60deg  = 60deg 7 0.8 r = 30cm r = 30cm 6 0.7 SNR = 30dB SNR = 30dB 5  = 0deg 0.6  = 0deg 4 0.5 3 0.4 2 0.3 1 0.2

Average Channel of Gain [dB] Average 0 0.1 Absolute of of Absolute Correlation Complex -1 1 2 3 4 5 6 7 8 9 1011121314151617181920212223242526272829303132 01 2 3 4 5 6 7 8 9 1011121314151617181920212223242526272829303132 Number of Subarray Number of Subarray

(a) (b)

FigureFigure 16. ChannelChannel gain gain and and correlation correlation characteristics characteristics of each of subarray. each subarray. (a) Channel (a) gain.Channel (b) Correlation. gain. (b) Correlation. It can be seen from Figure 16a that a channel gain of more than 2 dB is obtained for the subarrays numberedThe changes 1–8 and in 29–32the channel for both gainσ = and10◦ correlationand 60◦. Particularly, coefficients thementioned channel above gain for resultσ = 10in ◦a exceedsvariety of4 dBdistribut and isions larger of eigenvalues. than that for Figureσ = 60 ◦17a,b. This show is due the to cumulative the fact that distribution when σ = functions10◦ the peak (CDF) gain of attheφ eigenvalues= 0◦ results when in a large σ = 60 channel° and σ gain = 10 due°. The to in-phaseeigenvalues excitation are obtained of the from array, Equation as depicted (14) inthrough Figure an11 . SVDIn contrast, operation. the channel gain for the subarrays numbered 13–24 is small in magnitude because of the shadowingIn Figure 17a eff,ects the presence caused by of the 32 subarraysdensely distributed located in eigenvalues front of them. in the Figure graph 16 meansb shows that that there the arecorrelation 32 effective coeffi subchannelscients for σ = for10 ◦MIMOare larger transmission. than those This for σ indicates= 60◦. Especially, that the thechannel correlations matrix betweendefined bySubarrays Equation 1 and(8) has 2, 1 a and full 3,-rank and 1property and 4, which corresponding belong to theto the same number 4 4 MIMOof subarrays array group,because are all more the × subarraysthan 0.6. In can contrast, receive when signalsσ =from60◦ the communication correlation is less target than owing 0.5 over to the the entire beam array.steering function of the proposedThe changes antenna. in the This channel feature gain is quite and correlation different from coeffi acients conventional mentioned circular above array result antenna in a variety with aof number distributions of patch of eigenvalues.antennas arranged Figure in17 aa,b cylindrical show the manner cumulative [7,8], distribution as described functions in the introduction. (CDF) of the Micromachines 2020, 11, x 18 of 25 Consequently,eigenvalues when the developedσ = 60◦ and antennaσ = 10◦ operates. The eigenvalues normally areand obtained effectively from as a Equation 32-element (14) MIMO through array an antenna.SVD operation. In contrast, the sparsely distributed 18 eigenvalues, shown in Figure 17b, indicate that the developed100 array works as a MIMO antenna with a small100 number of elements. More specifically, a 90 r = 30cm 90 large channelSNR gain = 30dB in the case of σ = 10° provides large first and second eigenvalues, as indicated by 80 80 the symbol “A” = 0deg on the right side of Figure 17b. Moreover, a high correlation coefficient for σ = 10° 70 70 creates small60 eigenvalues distributed on the left side of60 Figure 17b, asB indicated by the symbolA “B”. Eventually,50 when σ = 10° these two observations result50 in a small channel capacity, as described in Figure 15.40 40 30 30

20 20 Cumulative Percentage [%] Cumulative Percentage Cumulative Percentage [%] 10 10

0 0 10-4 10-2 100 102 104 10-4 10-2 100 102 104 Eigenvalue  Eigenvalue 

(a) (b)

FigureFigure 17.17. CDF characteristics ofof eigenvalues.eigenvalues. (a) σ = 60°60◦..( (bb)) σσ == 1010°.◦ .

FromIn Figure the 17 extensivea, the presence analytical of 32 investigations densely distributed performed eigenvalues in this in paper, the graph we meansconclude that that there a remarkablyare 32 eﬀective high subchannels channel capacity for MIMO of more transmission. than 200 bits/s/Hz This indicates achieved that by the the channel beam steering matrix deﬁned32 × 32 MIMOby Equation array— (8)as has depicted a full-rank in Figure propertys 12, 14, corresponding and 15—can tobe theattributed number to of two subarrays significant because factors; all the the improvedsubarrays can directivity receive signals due to from in-phase the communication excitation of the target array owing and to the the lowbeam correlation steering function between of subarrays caused by the orthogonal alignment of the array with respect to the incident waves.

6. Experimental Verification To confirm the validity of the proposed antenna, this section presents experiments carried out to evaluate the 4 × 4 and 32 × 32 MIMO arrays. We performed two types of measurements; radiation pattern measurements in an anechoic chamber and over-the-air (OTA) testing using a two- dimensional fading emulator in a cluster propagation environment [26].

6.1. Impedance and Radiation Measurements Figure 18 shows the setup for measuring the radiation pattern of a 4 × 4 MIMO array in an anechoic chamber [15]. The signal processing unit was designed using the circuit topology depicted in Figure 8a, including a phase shifter and a signal combiner. Figure 18a shows a fabricated microwave circuit for the weight functions of Subarry2 (w1 and w4) using a double-sided printed circuit board with a thickness of 1 mm and a relative permittivity of 4.2 (FR4). The phase shift of the received signal for each element was realized using different lengths of microstrip transmission lines. The 30° phase difference between #1 and #4 is equivalent to a difference in length of 7.6 mm. The phase difference of the produced network was 34°, indicating that the phase difference was achieved. Furthermore, to get the correct weight function, the difference in power loss between the microstrip lines, which was 0.21 dB, was considered.

/2-dipole Coaxial cable

Element #4 Input port

Phase shifter Subarray2

Power divider Element #1 Microwave circuit Attenuators

(a) (b)

Figure 18. Radiation pattern measurement setup of a 4 × 4 MIMO array in an anechoic chamber. (a) Fabricated microwave circuit. (b) Prototype of a 4 × 4 MIMO array.

Micromachines 2020, 11, x 18 of 25

100 100 90 r = 30cm 90 SNR = 30dB 80 80 Micromachines 2020 = 0deg, 11, 871 18 of 25 70 70 60 60 B A 50 50 the proposed40 antenna. This feature is quite diﬀerent from40 a conventional circular array antenna with a number30 of patch antennas arranged in a cylindrical manner30 [7,8], as described in the introduction.

Consequently,20 the developed antenna operates normally20 and eﬀectively as a 32-element MIMO Cumulative Percentage [%] array antenna. Cumulative Percentage [%] 10 10

0 0 In contrast,10-4 the10-2 sparsely100 distributed102 10 184 eigenvalues,10-4 shown10-2 in Figure100 17b,102 indicate104 that the developed array works asEigenvalue a MIMO  antenna with a small number of elements.Eigenvalue More  specifically, a large channel gain in the case of σ = 10◦ provides large first and second eigenvalues, as indicated by the (a) (b) symbol “A” on the right side of Figure 17b. Moreover, a high correlation coefficient for σ = 10◦ creates small eigenvalues distributedFigure 17. CDF on the characteristics left side of Figureof eigenvalues. 17b, as indicated(a) σ = 60°. by (b) the σ = symbol10°. “B”. Eventually, when σ = 10◦ these two observations result in a small channel capacity, as described in Figure 15. From the the extensive extensive analytical analytical investigations investigations performed performed in this inpaper, this we paper, conclude we that conclude a remarkably that a highremarkably channel high capacity channel of more capacity than 200of more bits/s /thanHz achieved 200 bits/s/Hz by the achieved beam steering by the 32 beam32 MIMO steering array—as 32 × 32 × depictedMIMO array in Figure—as depicted12, Figure in 14 Figure, and Figures 12, 14, 15—can and 15 be— attributedcan be attributed to two significant to two significant factors; the factors; improved the directivityimproved due directivity to in-phase due excitation to in-phase of the excitation array and of the the low array correlation and the between low correlation subarrays caused between by thesubarrays orthogonal caused alignment by the orthogonal of the array alignment with respect of the to thearray incident with respect waves. to the incident waves.

6. Experimental Verification Veriﬁcation To conﬁrmconfirm the the validity validity of of the the proposed proposed antenna, antenna, this this section section presents presents experiment experimentss carried carried out out to evaluate the 4 4 and 32 32 MIMO arrays. We performed two types of measurements; to evaluate the 4 × 4 and× 32 × 32 MIMO× arrays. We performed two types of measurements; radiation radiationpattern measurements pattern measurements in an anechoic in an anechoic chamber chamber and over and-the over-the-air-air (OTA) (OTA) testing testing using using a two a- two-dimensionaldimensional fading fading emulator emulator in a cluster in a cluster propagation propagation environment environment [26]. [ 26].

6.1. Impedance and Radiation Measurements Figure 18 shows the setup for measuring the radiation pattern of a 4 4 MIMO array in an Figure 18 shows the setup for measuring the radiation pattern of a 4 ×× 4 MIMO array in an anechoic chamberchamber [[15].15]. TheThe signalsignal processingprocessing unit unit was was designed designed using using the the circuit circui topologyt topology depicted depicted in Figurein Figure8a, including 8a, including a phase a phaseshifter shifterand a signal and acombiner. signal combiner. Figure 18 aFigure shows 18a a fabricated shows a microwave fabricated circuit for the weight functions of Subarry2 (w and w ) using a double-sided printed circuit board microwave circuit for the weight functions of1 Subarry24 (w1 and w4) using a double-sided printed withcircuit a thicknessboard with of a 1 thickness mm and a of relative 1 mm permittivityand a relative of permittivity 4.2 (FR4). The of phase4.2 (FR4). shift The of the phase received shift signalof the forreceived each elementsignal for was each realized element using was direalizedfferent using lengths different of microstrip lengths transmission of microstrip lines. transmission The 30◦ phase lines. diThefference 30° phase between difference #1 and between #4 is equivalent #1 and #4 to is a diequivalentfference in to length a difference of 7.6 mm. in length The phase of 7.6 dimm.fference The ofphase the produceddifference networkof the produced was 34 ◦network, indicating was that34°, theindicating phase dithatfference the phase was difference achieved. was Furthermore, achieved. toFurther get themore correct, to get weight the correct function, weight the di function,fference in the power difference loss between in power the lo microstripss between lines, the whichmicrostrip was 0.21lines, dB, which was was considered. 0.21 dB, was considered.

/2-dipole Coaxial cable

Element #4 Input port

Phase shifter Subarray2

Power divider Element #1 Microwave circuit Attenuators

(a) (b)

Figure 18. RadiationRadiation pattern pattern measurement measurement setup setup of of a 4 a × 4 4 MIMO4 MIMO array array in an in anechoic an anechoic chamber. chamber. (a) × (Fabricateda) Fabricated microwave microwave circuit. circuit. (b) (Prototypeb) Prototype of a of 4 a× 44 MIMO4 MIMO array. array. ×

An attenuator was used for realizing the weight function. Since w1 = 1.0 and w4 = 0.38 for Subarray2, as listed in Table1, the received signal of #4 had to be synthesized by attenuating 8.40 dB compared to that of #1. Since the power loss for #4 due to the microstrip line was 0.21 dB larger than Micromachines 2020, 11, x 19 of 25

An attenuator was used for realizing the weight function. Since w1 = 1.0 and w4 = 0.38 for MicromachinesSubarray2,2020 as listed, 11, 871 in Table 1, the received signal of #4 had to be synthesized by attenuating 8.4019 of dB 25 compared to that of #1. Since the power loss for #4 due to the microstrip line was 0.21 dB larger than that for #1, a power loss of 8.19 dB had to be realized by the attenuator. 0 dB and 8 dB attenuators that for #1, a power loss of 8.19 dB had to be realized by the attenuator. 0 dB and 8 dB attenuators were were connected to the terminals of #1 and #4 of the fabricated microwave circuit, respectively. The 0 connected to the terminals of #1 and #4 of the fabricated microwave circuit, respectively. The 0 dB dB attenuator was used for realizing the retention of the phase of the received signals of #1 and #4. attenuator was used for realizing the retention of the phase of the received signals of #1 and #4. Hence, Hence, the difference in the received power between #1 and #4 was 8.50 dB, indicating that the weight the diﬀerence in the received power between #1 and #4 was 8.50 dB, indicating that the weight function function had been achieved. had been achieved. The radiation pattern of a 4 × 4 MIMO array antenna was measured in an anechoic chamber. The radiation pattern of a 4 4 MIMO array antenna was measured in an anechoic chamber. Figure 18b shows the measurement× setup of a 4 × 4 MIMO antenna, which comprises eight half- Figure 18b shows the measurement setup of a 4 4 MIMO antenna, which comprises eight wavelength dipole antennas designed at 2 GHz. Two× attenuators and the fabricated microwave half-wavelength dipole antennas designed at 2 GHz. Two attenuators and the fabricated microwave circuit were located under the antenna and connected to the antenna using coaxial cables. As shown circuit were located under the antenna and connected to the antenna using coaxial cables. As shown in in Figure 18b, the prototype of a 4 × 4 MIMO antenna was mounted on a turntable for sampling Figure 18b, the prototype of a 4 4 MIMO antenna was mounted on a turntable for sampling signals signals of the radiation patterns× at azimuth angles in the xy-plane using a vector network analyzer. of the radiation patterns at azimuth angles in the xy-plane using a vector network analyzer. Figure 19 exhibits the impedance characteristics of Subarray2 drawn on a Smith chart measured Figure 19 exhibits the impedance characteristics of Subarray2 drawn on a Smith chart measured at the input port of the microwave circuit, as indicated in Figure 18a, using a network analyzer [15]. at the input port of the microwave circuit, as indicated in Figure 18a, using a network analyzer [15]. In Figure 19, the black broken circle represents the impedance locus corresponding to a voltage In Figure 19, the black broken circle represents the impedance locus corresponding to a voltage standing standing wave ratio (VSWR) of 2. It can be seen from Figure 19 that a good matching condition with wave ratio (VSWR) of 2. It can be seen from Figure 19 that a good matching condition with a VSWR of a VSWR of less than 2 was achieved in the frequencies between 1.8 GHz and 2.2 GHz, where existing less than 2 was achieved in the frequencies between 1.8 GHz and 2.2 GHz, where existing MIMO-based MIMO-based cellular systems are being operated. cellular systems are being operated.

0.5

2 GHz 1.8 GHz 0

2.2 GHz VSWR = 2 -0.5

-1 -1 -0.5 0 0.5 1

Figure 19. Measured impedance of Subarray2. Figure 19. Measured impedance of Subarray2. Figure 20 presents the measured and calculated θ-polarized radiation patterns of Subarray1 and Subarray2Figure 20 presents in the horizontal the measured (xy) planeand calculated when the θ-polarized angle of the radiation incident patterns wave is of 0 Subarray1◦ [27]. In theand measurement,Subarray2 in wethe performedhorizontal a(xy calibration) plane when to compensate the angle for of thethe power incident loss. wave The redis 0° line [27]. indicates In the themeasurement, measured results, we performed while the a calibration blue line represents to compensate the calculated for the power results. loss. The The frequency red line indicates for the measurementsthe measured wasresults, 2 GHz. while the blue line represents the calculated results. The frequency for the measurementsAs shown inwas Figure 2 GHz. 20 , there are some appreciable discrepancies between the measured and calculatedAs shown results, in particularly Figure 20, inthere the are sidelobe some and appreciable backlobe angulardiscrepancies regions. between A possible the measured cause of these and discrepanciescalculated results, is the particularly electromagnetic in the distortion sidelobe arisingand backlobe from coaxial angular feed regions. cables A connected possible cause between of these the dipolediscrepancies elements is andthe theelectromagnetic microwave circuit, distortion as shown arising in from Figure coaxial 18b. Nevertheless,feed cables connected good agreement between betweenthe dipole the measuredelements resultsand the and microwave the analytical circuit, outcome as shown can be observedin Figure in the18b. direction Nevertheless, of the x -axisgood indicatedagreement by between the black the arrows, measured conﬁrming results that and thethe weightanalytical functions outcome and can the be phase observed shift valuesin the direction listed in Tableof the1 workx-axis well indicated according by the to black the angle arrows, of the confirming incident wave. that the weight functions and the phase shift values listed in Table 1 work well according to the angle of the incident wave.

MicromachinesMicromachines 2020 2020, 11,, 11x , x 2020 of 25of 25 Micromachines 2020, 11, 871 20 of 25

10 10 10 y y 10 y y 0 0 0 0

-10-10 -10-10

-20-20 -20-20 x x x x -10-10 -10-10 0 0 0 MeasuredMeasured 0 MeasuredMeasured Calculated Calculated Calculated Calculated 1010 1010 1010 0 0 -10-10-20-20-10-10 0 0 1010 1010 0 0 -10-10-20-20-10-10 0 0 1010 [dBd] [dBd] [dBd] [dBd] (a)( a) (b)( b) Figure 20. Measured and calculated results of radiation patterns. (a) Subarray1. (b) Subarray2. FigureFigure 20. 20.Measured Measured andand calculated calculated results results of of radiation radiation patterns. patterns. (a(a)) Subarray1. Subarray1. ((bb)) Subarray2.Subarray2.

6.2.6.2.6.2. Over Over-the-AirOver-the-Air-the-Air Testing TestingTesting TheTheThe channel channelchannel capacity capacitycapacity was waswas measured measuredmeasured using using using a two aa two-dimensionaltwo-dime-dimensionalnsional fading fading fading emulator emulatoremulator [26 [ [26],26], ],as as asillustrated illustratedillustrated inin inFigure Figure Figure 21 21 .21. .

#5 #4 #3 Scatterer #6 14 Scatterers (Sleeve Dipole) #7 #2 32×32 MIMO

1.2m #8 2 #1 0.3m Gaussian #9 Wave #14

#10 #13 #11 #12

(a)( a) (b)( b) FigureFigure 21. 21. OTAOTA testing testing of ofa 32 a 32× 32 32daisy daisy chain chain MIMO MIMO antenna. antenna. (a) (Twoa) Two-dimensional-dimensional fading fading emulator. emulator. Figure 21. OTA testing of a 32 ×× 32 daisy chain MIMO antenna. (a) Two-dimensional fading emulator. (b()b( Externalb)) External External view. view. view.

InIn In [28], [[28],28 ], the thethe appropriate appropriateappropriate number numbernumber of of of probe probeprobe antennas antennasantennas for forfor a a fadinga fadingfading emulator emulatoremulator was waswas investigated investigatedinvestigated theoretically.theoretically.theoretically. The TheThe results resultsresults show showshow that thatthat 11 11–15–11–1515 scatterers scatterersscattere rsneed needneed to to tobe be beimplemented implementedimplemented for forfor achieving achievingachieving a agooda goodgood multimulti-clustermulti-cluster-cluster propagation propagationpropagation environment. environment. environment. On OnOn the thethe basis basisbasis ofof ofthis thisthis knowledge, knowledge,knowledge, we wewe have havehave developed developeddeveloped a fading aa fadingfading emulatoremulatoremulator with withwith 14 14 14scatterers. scatterers.scatterers. FourteenFourteenFourteen scatterers scatterersscatterers with with with equal equal equal angular angular angular intervals intervals intervals were were were arranged arranged arranged on on a circlea circle withwith with aa radius radiusa radius ofof 1.2of1.2 m.1.2 m.Them. The The scatterers scatterers scatterers comprise comprise comprise vertically vertically vertically polarized polarized polarized half-wavelength half half-wavelength-wavelength sleeve sleeve dipolesleeve dipole antennas. dipole antennas antennas. The beam. The The steeringbeam beam steeringMIMOsteering MIMO array MIMO antennaarray array antenna isantenna located is locatedis at located the centerat atthe the center of center the of emulator, ofthe the emulator, emulator, as shown as asshown in shown Figure in inFigure 21 Figure. This 21. 21. fadingThis This fadingemulatorfading emulator emulator has the has functionhas the the function function of an operatingof ofan anoperating operatin algorithm algorithmg algorithm on the basison on the ofthe basis the basis same of ofthe formulation the same same formulation formulation described describedindescribed Section in4 .inSection To Section change 4. To4. theTo change anglechange the of the theangle angle incident of ofthe th waveincidente incident from wave 0wave◦ tofrom 360from ◦0,° the0°to to360 beam 360°,°, the steering the beam beam arraysteering steering was arraymountedarray was was mounted on mounted a turntable on on a to turntablea rotateturntable at to 45 to◦ rotatesteps rotate atin at azimuth45 °45° steps steps while in in azimuth maintainingazimuth while while a maintaining power maintaining spectrum a powera withpower a

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spectrum with a fixed Gaussian distribution generated on the scatterers, as depicted by the blue curve ﬁxed Gaussian distribution generated on the scatterers, as depicted by the blue curve in Figure 21a. in Figure 21a. The experiments were performed in a cluster propagation environment, which had an The experiments were performed in a cluster propagation environment, which had an angular power angular power spectrum with a Gaussian distribution with an incident wave angle of µ = 0° and a spectrum with a Gaussian distribution with an incident wave angle of µ = 0 and a standard deviation standard deviation of σ = 30°. The frequency was 2 GHz. The SNR was set◦ to 30 dB and 40 dB. of σ = 30 . The frequency was 2 GHz. The SNR was set to 30 dB and 40 dB. Figure◦ 22 shows the measured channel capacity of the 4 × 4 MIMO antenna, as illustrated in Figure 22 shows the measured channel capacity of the 4 4 MIMO antenna, as illustrated in Figure 18b, as a function of the angle of the incident wave. Half-wavelength× dipole antennas were Figure 18b, as a function of the angle of the incident wave. Half-wavelength dipole antennas were used used for the array elements. In the experiments, using the microwave circuit in Figure 18a, we for the array elements. In the experiments, using the microwave circuit in Figure 18a, we manually manually switched the RF ports to set the amplitude and phase appropriate for each subarray, in switched the RF ports to set the amplitude and phase appropriate for each subarray, in accordance accordance with Table 1. The development of a switching network, as depicted in Figure 5, for with Table1. The development of a switching network, as depicted in Figure5, for conducting conducting time-independent measurements is a subject for our future studies. time-independent measurements is a subject for our future studies.

Dipole Array 25 Ver. Pol. OTA (4×4 MIMO) OTA (Dipole) Channel Capacity [bits/s/Hz] SNR = 30dB 3cm Cal. (4×4 MIMO) f = 2GHz Cal. (Dipole) 20 0 45 90 135 180 225 270 315 360 φ Angle of Incident Wave [deg] FigureFigure 22. 22.Channel Channel capacity capacity of of a a 4 4 ×4 4 MIMO MIMO array array antenna antenna measured measured by by OTA OTA testing. testing. × InIn Figure Figure 22 22,, The The black black round round symbols symbols denote denote the the measured measured results results of of the the 4 4 ×4 4 MIMO MIMO antenna, antenna, × whereaswhereas the the blue blue curve curve represents represents the the analytical analytical results results using using Monte Monte Carlo Carlo simulations. simulations. The The red red curve curve depictsdepicts the the measured measured results results of of a a four-element four-element linear linear dipole dipole array array comprising comprising vertically vertically polarized polarized half-wavelengthhalf-wavelength dipole dipole antennas antennas with with a a spacing spacing of of 3 3 cm, cm as, as denoted denoted by by the the inset inset in in Figure Figure 22 22,, in in which which thethe entire entire array array size size is is the the same same as as the the 4 4 ×4 4 MIMO MIMO antenna. antenna. Figure Figure 22 22 shows shows that that there there is is good good × agreementagreement between between the the measured measured and and calculated calculated results results for for the the 4 4 ×4 4 MIMO MIMO antenna. antenna. Furthermore, Furthermore, × thethe proposed proposed antenna antenna maintains maintains a a constant constant transmission transmission rate rate over over 360 360 degrees degrees of of azimuthal azimuthal angle, angle, whereaswhereas the the dipole dipole array array yields yields heavy heavy ﬂuctuations fluctuations with with deep deep nulls nulls at anglesat angles of 90of◦ 90°and and 270 ◦270°,, which which is similaris similar to the to the result result for thefor the 32 3232 × MIMO32 MIMO array array antenna antenna described described in Figure in Figure 14. 14. × FigureFigure 23 23 shows shows the the channel channel capacity capacity of of a a prototype prototype of of the the 32 32 ×32 32 daisy daisy chain chain MIMO MIMO antenna antenna as as × aa function function of of the the angle angle of of the the incident incident wave wave [15 [15].]. The The radius radius of of the the array array was was set set to tor =r =30 30 cm. cm. The The SNR SNR waswas set set to to 30 30 dB dB and and 40 dB.40 dB. The The red roundred round and squareand squa symbolsre symbols denote denote the measured the measured results. results. The black The curvesblack representcurves represent the analytical the analytical results fromresults Monte from Carlo Monte simulations. Carlo simulations. Figure 23 Figure shows 23 that shows there that is goodthere agreement is good agreement between the between measured theand measured calculated and results. calculated Furthermore, results. Furthermore, the proposed the antenna proposed can maintainantenna acan constant maintain transmission a constant transmission rate over 360 rate degrees over in 360 azimuth. degrees Interestingly,in azimuth. Interestingly, the red round the and red squareround symbols and square corresponding symbols corresponding to angles of 22.5 to angles◦ and 337.5 of 22.5°◦ are and situated 337.5° at are the situated borders betweenat the borders two adjacentbetween sectors, two adjacent as illustrated sectors, inas illustrated Figure4. These in Figu measuredre 4. These data measured do not data show do appreciable not show appreciable changes, comparedchanges, withcompared 0◦ and with 360 ◦0°, indicating and 360°, thatindicating the proposed that the antenna proposed works antenna well, works even on well, the even borders on ofthe theborders sectors, of owingthe sectors, to the owing good beamto the steeringgood beam ability steering of the ability array. of the array.

Micromachines 2020, 11, x 22 of 25

Micromachines 2020,, 11,, x 871 2222 of of 25 25 400

350400

300350

250300

200250

150200

100150 Cal. (SNR = 40dB) r = 30cm OTA (SNR = 40dB)

Channel Capacity [bits/s/Hz] Capacity Channel Cal. (SNR = 40dB) 10050  = 30deg Cal. (SNR = 30dB) f r= =2GHz 30cm OTA (SNR = 40dB)

Channel Capacity [bits/s/Hz] OTA (SNR = 30dB) σ 500 = 30deg Cal. (SNR = 30dB) 0 45 90 f135= 2GHz180 225OTA270 (SNR 315= 30dB)360 0 Angle of Incident Wave  [deg] 0 45 90 135 180 225 270 315 360 Angle of Incident Wave φ [deg] Figure 23. Channel capacity of a 32 × 32 MIMO array antenna measured by OTA testing. Figure 23. ChannelChannel capacity capacity of of a a 32 × 3232 MIMO MIMO a arrayrray antenna antenna measured measured by by OTA OTA testing. testing. In Section 5.3, the channel gain and correlation× were obtained from a theoretical investigation using Monte Carlo simulation, as shown in Figure 16. In this section, to investigate the mechanism InIn Section 5.3,5.3, the channel gain and correlation were obtained from a theoretical investigation for achieving a large channel capacity in an empirical way, we took an experimental approach by using Monte CarloCarlo simulation,simulation, asas shown shown in in Figure Figure 16 16.. In In this this section, section, to to investigate investigate the the mechanism mechanism for means of OTA testing to evaluate the channel gain and correlation. forachieving achieving a large a large channel channel capacity capacity in an empiricalin an empirical way, we way, took we an took experimental an experimental approach approach by means by of Figure 24 shows the channel gain and correlation coefficient of each subarray of the 32 × 32 meansOTA testing of OTA to testing evaluate to theevaluate channel the gain channel and correlation.gain and correlation. MIMO array as a function of the number of the subarray [15]. The black curves indicate the analytical Figure 2424 showsshows the the channel channel gain gain and and correlation correlation coe ﬃcoefficientcient of each of subarrayeach subarray of the 32of the32 32 MIMO × 32 results using Monte Carlo simulation, while the red curves indicate the measured results× through MIMOarray as array a function as a function of the number of the number of the subarray of the subarray [15]. The [15]. black The curves black curves indicate indicate the analytical the analytical results OTA testing, depicted in Figure 21. The blue and red subarrays, indicated by the inset in Figure 24a, resultsusing Monte using CarloMonte simulation, Carlo simulation, while the while red curves the red indicate curves the indicate measured theresults measured through results OTA through testing, represent that these subarrays. Subarrays 1–4 and Subarrays 17–20 are located in the forward and OTAdepicted testing, in Figure depicted 21. Thein Figure blue and21. The red subarrays,blue and red indicated subarrays, by theindicated inset in by Figure the inset 24a, in represent Figure 24a, that backward directions with respect to the incident wave. The blue and red arrows included in the upper representthese subarrays. that these Subarrays subarrays. 1–4 and Subarrays Subarrays 1–4 17–20 and areSubarrays located in17–20 the forwardare located and backwardin the forward directions and part of Figure 24a indicate the locations of Subarrays 1–4 and Subarrays 17–20 on the lateral axis. backwardwith respect directions to the incident with respect wave. to The the blueincident and wave. red arrows The blue included and red in arrows the upper included part of in Figure the upper 24a partindicate of Figure the locations 24a indicate of Subarrays the locations 1–4 and of Suba Subarraysrrays 1–4 17–20 and on Subarrays the lateral 17–20 axis. on the lateral axis.

10 1 Subarrays 1-4 r = 30cm r = 30cm 9 0.9 8 SNR = 30dB 1 SNR = 30dB 710  = 0deg 0.8 9 Subarrays 1-4 r = 30cm r== 0deg 30cm 6  = 30deg 0.9  = 30deg 5 8 SNR = 30dB 0.7 SNR = 30dB 7 φ 0.8 φ 4 Subarrays 17=- 200deg 0.6 = 0deg 6 σ 3 = 30deg 0.7 σ = 30deg 2 5 0.5 Subarrays 17-20 1 4 9-12 0.6 0 3 13-16 5-8 0.4 0.5 -1 2 0.3 117-20 9-12 1-4 2 -2 0.4 -3 0 13-16 5-8 0.2 -1 21-24 29-32 2σ Average Channel of Gain [dB] Average -4 Incident 0.3 17-20 25-28 1-4 OTA Testing 0.1 OTA Testing -5-2 of Absolute Correlation Complex -3 Wave Monte Carlo 0.2 Monte Carlo -6 21-24 29-32 0

Average of Channel Gain [dB]Average Incident 1 2 3 4 5 6 7 8 9 1011121314151617181920212223242526272829303132 -41 2 3 4 525-286 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25OTA26 27 28 Testing29 30 31 32 0.1 OTA Testing -5 NumberWave of Subarray Monte Carlo Correlation Complex of Absolute Number of Subarray Monte Carlo -6 0 1 2 3 4 5 6 7 8 9 10 111213 14 15 161718 19 20 212223 24 25 262728 29 30 31 32 1 2 3 4 5 6 7 8 9 1011121314151617181920212223242526272829303132 Number(a) of Subarray Number(b) of Subarray

FigureFigure 24. 24. ChannelChannel gain(a) and and correlation correlation of of a 32 a 3232 × MIMO 32 MIMO array array measured measured by( OTAb ) by testing. OTA testing. (a) Channel (a) × Channelgain. (b gain.) Correlation. (b) Correlation. Figure 24. Channel gain and correlation of a 32 × 32 MIMO array measured by OTA testing. (a) FChanneligureFigure 24a 24 gain. ashows shows (b) Correlation.that that Subarrays Subarrays 1– 1–4,4, which which face face the the incident incident wave, wave, provide provide a alarge large channel channel gain gain ofof more more than than 2.15 dB,dB, meaningmeaning that that these these subarrays subarrays operate operate more more eﬀectively effectively than than a conventional a conventional dipole Figure 24a shows that Subarrays 1–4, which face the incident wave, provide a large channel gain dipoleantenna. antenna. On the On other the hand,other hand, for Subarrays for Subarrays 17–20, 1 the7–20 channel, the channel gain is signiﬁcantlygain is significantly reduced reduced to less than to of more than 2.15 dB, meaning that these subarrays operate more effectively than a conventional dipole antenna. On the other hand, for Subarrays 17–20, the channel gain is significantly reduced to

Micromachines 2020, 11, 871 23 of 25

0 dB. This implies that these subarrays do not contribute to the formation of subchannels available for MIMO transmission. It is worth noting that, in Figure 24a, there is an appreciable discrepancy between the OTA measurements and the analytical outcomes. This is due to the fact that Subarrays 1–4, 5–8, and 29–32, located in the forward direction with respect to the incident wave, receive strong signals from the scatterers because of the small distance between these subarrays and the scatterers emitting a cluster wave, as shown in Figure 21a. In contrast, Subarrays 13–16, 17–20, and 21–24, located at the back with respect to the direction of the incident wave, receive weak signals because of the large distance between these subarrays and the scatterers. Figure 24b shows that, in the OTA measurements, the correlation coefficient increases in a periodic manner, which is not observed in the analytical outcome from the Monte Carlo simulations. A possible cause of this phenomenon is the insufficient orthogonality between the incident waves coming from the scatterers, because, in the current experiment, the number of scatterers in the emulator is 14, which is considerably smaller than the number of subarrays, i.e., 32. Nevertheless, it can be seen from Figure 24b that except for the correlation between those particular subarray numbers showing a periodic increase, the correlation coefficients are less than 0.5 over the entire array because of the orthogonal alignment between the MIMO array and the incident waves.

7. Conclusions This paper presents a 32 32 MIMO antenna system with the ability to perform full-azimuth × beam steering. Analyses revealed that the proposed antenna system can provide a maximum channel capacity of 277 bits/s/Hz at an SNR of 30 dB when the radius of the array is 30 cm, which is equivalent to 27.7 Gbps with a bandwidth of 100 MHz. It was clariﬁed that this remarkably high channel capacity is due to two signiﬁcant factors; the improved directivity due to the optimum in-phase excitation and the low correlation between the subarrays due to the orthogonal alignment of the array with respect to the incident waves. We further performed an experimental validation of the channel capacity using over-the-air (OTA) testing. The results show that the proposed antenna can maintain a constant channel capacity over 360 degrees in azimuth. The developed technology can be applied to the achievement of a 64 64 MIMO array [29] and × a 128 128 MIMO array [18] in pursuit of much larger transmission rates in the 5 GHz frequency × band. Thereby, the daisy chain array structure proposed in this paper provides a strong solution for realizing a much higher order MIMO array antenna at higher frequencies, such as in the 5.9 GHz band, where the emerging vehicle-to-everything (V2X) and cellular-V2X (C-V2X) technologies are anticipated to be operated for future connected cars [30–32].

Author Contributions: Conceptualization, K.O.; Funding acquisition, K.H.; Investigation, K.H.; Methodology, K.H.; Validation, T.F.; Writing—original draft, K.H. All authors provided critical feedback and helped shape the research, analysis, and manuscript. All authors have read and agreed to the published version of the manuscript. Funding: This research and development work was supported by the MIC/SCOPE #205005002. Acknowledgments: The authors acknowledge the funding from the MIC/SCOPE #205005002. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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