IEICE TRANS. COMMUN., VOL.E99–B, NO.1 JANUARY 2016167

PAPER

Three-Dimensional Over-The-Air Assessment for VerticallyArranged MIMO Array Antennas

Kun LI†a), Student Member, Kazuhiro HONDA†, and Koichi OGAWA†, Members

SUMMARY This paper presents a new methodology of the over-the-air (OTA) assessment for vertically arranged multiple-input multiple-output(MIMO) array antennas. Particular emphasis is placed on how well handsetMIMO antennas with a vertically arranged structure are characterized usingthe limited number of scatterers implemented in a fading emulator. First westudied the mechanism of the arrangement of scatterers on the variation ofchannel responses using a proposed three-dimensional analytical model. Itis shown that the condition of a 3D-OTA with the prescribed parametersallows the correlation to be reduced, which permits the channel capacity toincrease in the same manner that sufficient scatterers are distributed overthe entire solid angle. Then the appropriate scatterers arrangement for a3D-OTA instrument considering the number of DUT antenna elements andmultipath characteristics is investigated. The analytical results show thata suitable scatterers arrangement can be determined for various conditionsof multipath environments and numbers of array elements, and that thearrangement can be employed for designing an actual 3D-OTA apparatus.key words: MIMO-OTA, fading emulator, vertically arranged array an-tenna, three-dimensional channel model

1. Introduction

The development of simple and appropriate over-the-air (OTA) testing apparatus for mobile terminals with amultiple-input multiple-output (MIMO) system is indis-pensable to the success of upcoming LTE-Advanced and 5Gcellular systems [1]–[6]. The method of OTA testing canbe classified into two categories: the reverberation cham-ber and the spatial fading emulator. Several studies for OTAevaluation using the reverberation chamber have been re-ported [7]–[11]. These studies examine a simple structurefor an OTA apparatus at low cost. However, the appara-tus has some drawbacks in terms of difficulties in control-ling the angular spread of incident waves and the cross-polarization power ratio (XPR), and in generating clusterand uniform spectra environments because all of the re-flected waves coming from one signal source are uncon-trolled.

A fading emulator is one of the other solutions to di-rectly producing a radio multipath environment with highcontrollability and high accuracy [12]–[15]. In the litera-tures [14], [15], a spatial fading emulator was successfullyimplemented to evaluate the channel capacity of MIMO an-tennas. The fading emulator is created based on a two-dimensional channel model in which incident waves com-

Manuscript received April 7, 2015.Manuscript revised August 21, 2015.†The authors are with Toyama University, Toyama-shi, 930-

8555 Japan.a) E-mail: d1471007@ems.u-toyama.ac.jp

DOI: 10.1587/transcom.2015EBP3148

ing from a base station are confined to a horizontal plane.Hence, in the apparatus, a number of uncorrelated wavesthat ensure parallel transmission using MIMO streamingchannels exist only in the azimuth angles. This means thata vertically aligned MIMO array cannot be evaluated usinga conventional fading emulator [15] because adjacent ele-ments in the array located in the vertical direction exhibit aunity correlation owing to an absence of uncorrelated inci-dent waves in the elevation angles. This eventually degradesthe channel capacity.

In future MIMO standardization, a MIMO array imple-mented in a handset is anticipated to be in commercial usein a system with an increasing number of array elements,such as 4 × 4 and 8 × 8 MIMO systems to achieve giga-bit high-speed communications. Thus, the evaluation of aMIMO antenna arranged in the column direction is neces-sary because a two-dimensional array is advantageous formulti-element compactness.

Another important topic is the diversity of applications.We have studied an eight-element MIMO antenna mountedon the wrist for the purpose of gigabit transmission of wear-able applications in body area networks (BANs) [16]. Wear-able antennas have a remarkable feature different from con-ventional antennas used in cellular handsets: their directionsmounted on the human body cannot be determined as a spe-cific value, which means that a MIMO antenna fabricatedas a linear array located horizontally may change as a ver-tical array at the time of a practical use. In order to eval-uate the vertically arranged MIMO array antenna, a three-dimensional OTA test method needs to be developed.

In previous research, several methods for 3D-OTA as-sessment have been proposed [17]–[19]. Previous litera-ture [19] provides an analytical model for the assessmentof a 3D spatial channel emulator for OTA tests, where theimpact of the installation range and interval of probe ringson the spatial correlation characteristics between receptionpoints is presented. However, the variation of MIMO chan-nel capacity caused by different scatterers arrangement isnot analyzed. Further, the index for designing an OTA ap-paratus considering multipath environments and DUT arrayelements is not advanced.

This paper presents a new methodology for OTA as-sessment of vertically arranged MIMO array antennas. Thehandset MIMO with a vertically arranged structure is eval-uated with a limited number of scatterers implemented in afading emulator [20]. Moreover, the number of DUT an-tenna elements and multipath characteristics are considered

Copyright c© 2016 The Institute of Electronics, Information and Communication Engineers

168IEICE TRANS. COMMUN., VOL.E99–B, NO.1 JANUARY 2016

as parameters for determining the appropriate scatterers ar-rangement in an actual 3D-OTA apparatus.

In Sect. 2, a three-dimensional channel model for eval-uating N-element vertically arranged MIMO array antennasis proposed. The number of scattering units is assumed tobe arranged in the entire space for creating a multipath radiowave environment. In Sect. 3, an analytical method using aMonte Carlo simulation is presented. The calculation of thechannel response matrix will be introduced in detail.

Section 4 shows the numeral analytical results usingthe proposed channel model. First, we clarified the mecha-nism of the scatterers arrangement on variations in channelresponses using the proposed three-dimensional analyticalmodel. Then the appropriate scatterers arrangement consid-ering the number of DUT antenna elements and multipathcharacteristics is investigated. The analytical results showthat a suitable scatterers arrangement considering variousmultipath environments and the number of array elementscan be determined as desired for designing an actual 3D-OTA apparatus.

Finally, Sect. 5 summarizes some conclusions derivedfrom this paper and also discusses possible future extensionof these studies.

2. 3D-OTA Channel Model for Vertical MIMO Array

In previous studies of MIMO-OTA testing [14], [15], it wasdetermined that the array elements of a DUT antenna ar-ranged in the row direction is related to the scatterers placedin the azimuth direction. Therefore, in this paper, we focuson a discussion of the scatterers arrangement in the elevationdirection, which is related to the array elements arranged inthe column direction.

Figure 1 shows the three-dimensional channel modelfor assessing a vertically arranged MIMO array antenna. InFig. 1(a), the MIMO antenna with N-element is arranged inone column in the z-direction, which is comprised of verti-cally oriented half-wavelength dipole antennas. The antennaelement spacing ds is set to 9 cm, while the frequency for theanalysis is 2 GHz. The radiation characteristics of each ele-ment are calculated using the method of moments [21].

In Fig. 1(b), the vertically arranged MIMO antenna

Fig. 1 Three-dimensional channel model for OTA assessment of verti-cally arranged MIMO array antenna.

shown in Fig. 1(a) is located at the center of the channelmodel where a number of scatterers are distributed in spacein a three-dimensional manner. The angular power distribu-tion of the incident wave in the channel model is assumedto be a uniform in azimuth and a Gaussian in elevation [21],where ms represents the average elevation angle of the in-cident wave, and σs signifies the standard deviation. In theelevation direction, the scatterers used in an actual fadingemulator are distributed within a limited angular range be-tween pl and ph in a symmetrical manner with respect to ms.The number of scatterers is set to nh in azimuth and nv in el-evation at an equal interval. The phase of the radio wavesfrom each scatterer is randomly distributed to realize the un-correlated condition among all paths between the scatterersand the array elements.

Figure 2 shows an example of the incident wave dis-tribution and the scatterers arrangement in an OTA appara-tus. The red circles indicate the scatterers placement. Fig-ures 2(a) and (b) show the scatterers arrangement in the az-imuth and elevation directions, respectively. The averageelevation angle ms = 20◦, and the standard deviation of in-cident waves σs = 20◦. The number of scatterers is set to nh= 7 in azimuth and nv = 5 in elevation. Five scatterers in theelevation direction are arranged from pl = −10◦ to ph = 50◦,indicating that Δα = ph − pl = 60◦, where Δα is defined asthe separation between ph and pl shown in Fig. 2(b).

Fig. 2 Incident wave distribution and scatterers arrangement ph = 50◦,pl =−10◦, nv = 5, nh = 7.

LI et al.: THREE-DIMENSIONAL OVER-THE-AIR ASSESSMENT FOR VERTICALLY ARRANGED MIMO ARRAY ANTENNAS169

In order to obtain useful knowledge of the requiredconditions of a 3D-OTA channel model, we focus on thekey parameters of ph, pl, nv, ms, σs, and N, which may de-termine the channel capacity of MIMO array antennas, aswill be presented in Sect. 4.

3. Analytical Method

In the literature [15], the authors investigated the radius ofa two-dimensional fading emulator in a cluster environmentin which incident waves with a small angular spread exist inthe azimuth direction. To do this, they analyzed the averagereceived power ratio between two MIMO antenna elements.Their investigation corresponds to the scenario where theincident waves of the three-dimensional channel model, de-scribed in Fig. 1, have a small angular spread in the eleva-tion direction. Hence, we can estimate the required radiusof the 3D-OTA apparatus discussed in this paper on the ba-sis of the outcomes given in [15]. The estimation resultsshow that the error of the received power can be suppressedwithin 1 dB when the radius is larger than 1.0 m, 1.5 m, and2.0 m at 2 GHz, where the element spacing between the twoquasi-dipole arrays is less than 10 cm, 17 cm, and 30 cm, re-spectively (see Fig. 9 in [15]).

These element spacings correspond to the total arraysize when N = 2, 3, and 4 for the MIMO array antenna illus-trated in Fig. 1(a), where the total array size is defined as thedistance between the exciting port of element #1 and that ofelement #N. From the quantitative relationship between theradius and the element spacing, the required radius for thearray with N = 8 (total array size of 60 cm) is estimated tobe 2.8 m by means of the extrapolation method. On the basisof this knowledge, the analysis hereafter is performed underthe condition that the criterion for the radius of the emula-tor mentioned above is satisfied, which results in a situationwhere incoming waves emitted from the emulator scatter-ers arriving at a DUT terminal can be assumed to be planewaves [19].

Figure 3(a) shows the channel model of an M × NMIMO system in a three-dimensional scatterers arrange-ment, in which the MIMO array at the MS side is arrangedin the vertical direction [22]. The number of array elementsin a base station (BS) and a handset antenna are defined asM and N, respectively. In this paper, an NLOS situationbetween the base station and terminal antenna is assumed.M BS antennas create a set of M uncorrelated waves whereeach wave comprises Km scatterers as shown in Fig. 3(a),which surround N handset antennas, constructing second-wave sources around the moving terminal. Thus, M un-correlated waves are subject to independent identically dis-tributed (i.i.d.) complex Gaussian processes. Note that Km

scatterers share M waves coming from M BS antennas, butthe uncorrelated conditions among the M waves is achievedby giving random phases to the scatterers [22]. Figure 3(b)shows the coordinate of the k-th scatterer with the handsetmoving toward the azimuth direction φv. The channel re-sponse of the n-th handset antennas can be expressed as the

Fig. 3 Channel model in a three-dimensional scatterers arrangement: (a)Channel model of an M × N MIMO. (b) Coordinate of scatterers.

sum of the Km paths under the nearby m-th scatterers groups,as follows:

hnm=

Km∑k=1

hk,nm exp

{j2πdλ

cos(φk,m−φv) sin(θk,m)

}(1)

where λ is the carrier wavelength in free space, and d is thedistance travelled by the handset antenna toward the azimuthdirection φv shown in Fig. 3(b).

hk,nm in Eq. (1) is determined by the combination of thecomplex electric field directivity of the antenna element forthe θ and φ polarization components, which can be calcu-lated by the method of moments. Hence, we can analyze anarbitrary DUT antenna by replacing hk,nm in Eq. (1) in accor-dance with the type of antenna to be investigated [21], indi-cating that the DUT antenna shown in Fig. 1(a) is separatedfrom the channel model illustrated in Fig. 1(b). This meansthat the three-dimensional channel model presented in thispaper possesses broad generalities in analyzing 3D-OTA re-sponses of different types of DUT antennas treated in thisarticle. The phases of different polarization components areindependent of each other to realize the uncorrelated char-acteristics among all the paths between the scatterers andhandset antennas.

hnm in Eq. (1) indicates the channel response betweenthe m-th base station antennas and n-th terminal antennas.Therefore, the channel response of the arrays at the s-thsnapshots can be calculated by the following matrix:

170IEICE TRANS. COMMUN., VOL.E99–B, NO.1 JANUARY 2016

Hs = [hnm] =

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

h11 h12 · · · h1M

h21 h22 · · · h2M...

.... . .

...hN1 hN2 · · · hNM

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦(2)

The eigenvalues λi are obtained based on the singularvalue decomposition derived from Eq. (2) and can be used toinfer the instantaneous Shannon capacity (without feedback)in the s-th snapshots as follows:

Cs =

L∑i=1

log2

(1 +γλi

M

)[bits/s/Hz] (3)

where L = min (N, M), and γ denotes the input signal-to-noise ratio (SNR). Here, the SNR is defined as an averagevalue of instantaneous SNRs when an isotropic antenna (an-tenna gain is 0 dBi) is used for receiving the coherent inci-dent waves with vertical polarization (XPR =∞), which areassumed to be radiated from a single antenna at the base sta-tion. The analysis is executed successively until the handsetantenna arrives at the end point of the moving direction. Theaverage value of the channel capacity when the terminal an-tenna moving in a distance can be obtained by the followingequation:

C =1S

S∑s=1

Cs (4)

where S signifies the number of samples.

4. Analytical Results

Based on the channel model and analytical method men-tioned in Sects. 2 and 3, some analyses for 3D-OTA tests arecarried out. We focus on two viewpoints: mechanism anal-ysis and determination of scatterers arrangement, which arepresented in Sects. 4.1 and 4.2, respectively.

4.1 Mechanism Analysis

Figure 4 shows the cumulative distribution function (CDF)of the eigenvalue and channel capacity of a 4 × 4 MIMOantenna in the vertically arranged array configuration, asshown in Fig. 1.

In Fig. 4(b), the curves shown on the left side indi-cate the single-input single-output (SISO) channel capacity,while the black curve on the right side shows the MIMOchannel capacity. The symbols Cmimo and Csiso drawn inthe figure indicate the calculated values of MIMO and SISOchannel capacity, respectively. A vertically polarized inci-dent wave with an SNR of 30 dB is considered. The averageelevation angle is assumed to be ms = 20◦ with an angularspread of σs = 20◦. The scatterers are distributed with theparameters of ph = 90◦, pl = −90◦, nv = 37, and nh = 30.Hence, the total amount of 1,110 scatterers is arranged inthe entire space.

As shown in Fig. 4, dense eigenvalues and a large ca-pacity are observed when distributing a large number of

Fig. 4 Eigenvalue and channel capacity of the 4 × 4 MIMO array (ph =90◦, pl = −90◦, nv = 37, nh = 30).

scatterers over the entire solid angle. The 4 × 4 MIMOachieves a large channel capacity of 36.1 bits/s/Hz, whichis equivalent to a channel capacity of 3.6 Gbps when a 100-MHz bandwidth is considered.

Figure 5 shows the CDF of the eigenvalue and chan-nel capacity when ph = 25◦, pl = 15◦ (Δα = ph − pl =10◦), nv = 5, and nh = 7. The average elevation angle isassumed to be ms = 20◦ with an angular spread of σs = 20◦.As shown in Fig. 5, sparse eigenvalues and a small capac-ity are given when distributing a small number of scatterersover a small angular range. The eigenvalue has a sparsedistribution, which is different from that in Fig. 4. Specif-ically, compared with the first and second eigenvalues, thethird eigenvalue is 1/100 or less, while the fourth eigenvaluecannot even be observed on the graph. This yields a smallchannel capacity of 24.1 bits/s/Hz.

The abovementioned phenomenon seen in Fig. 4 andFig. 5 can be understood very clearly by considering the cor-relation coefficient. Table 1 shows the correlation coefficientbetween the i-th and j-th elements, where the element indexis defined in Fig. 1(a). Tables 1 (a) and (b) show the analyti-cal results corresponding to the key parameters described inFig. 4 and Fig. 5, respectively.

We can find a small correlation of less than 0.66 inTable 1(a) throughout the entire results. By contrast, Ta-ble 1(b) indicates that the correlation between the two ele-ments aligned in column is higher than 0.9. This fact pro-vides a physical picture for explaining why Fig. 5(a) shows asparse eigenvalue. It also indicates that, if the angular rangeof the scatterers is confined to a narrow angle such as Δα =10◦, the OTA assessment cannot be carried out. Therefore,

LI et al.: THREE-DIMENSIONAL OVER-THE-AIR ASSESSMENT FOR VERTICALLY ARRANGED MIMO ARRAY ANTENNAS171

Fig. 5 Eigenvalue and channel capacity of the 4 × 4 MIMO array (ph =25◦, pl = 15◦, nv = 5, nh = 7)

Table 1 Absolutes of complex correlation coefficient between elements.

the angular range of the scatterers needs to be extended.Figure 6 shows the eigenvalue and channel capacity

when ph = 50◦, pl = −10◦ (Δα = 60◦), nv = 5, and nh =7. The average elevation angle is set to ms = 20◦ with anangular spread of σs = 20◦. In Fig. 6, we have dense dis-tribution of the eigenvalues, resulting in a large capacity of35.1 bits/s/Hz, which is very close to the idealized value inFig. 4. Thus, the limited number of scatterers of the 3D-OTAapparatus has a good ability to assess a vertically arrangedMIMO array antenna.

Table 2 shows the correlation coefficients correspond-ing to the parameters described in Fig. 6. As shown in Ta-

Fig. 6 Eigenvalue and channel capacity of the 4 × 4 MIMO array (ph =50◦, pl = −10◦, nv = 5, nh = 7).

Table 2 Absolutes of complex correlation coefficient between elements.

ph = 50 deg, pl = -10 deg, nv = 5, nh = 7

ble 2, we have very small correlations between the elementsaligned in the vertical direction, which is the same behav-ior that was observed in Table 1(a). This supports the hy-pothesis that correlations are reduced owing to uncorrelatedwaves in the vertical plane.

Figure 7 shows the average channel capacity as a func-tion of the angular region of scatterers, defined as Δα = ph −pl, as shown in Fig. 2(b), with the number of scatterers nv asparameters when the number of vertical arrays N = 4. Theaverage elevation angle is set to ms = 20◦ with an angularspread of σs = 20◦.

In Fig. 7, it can be seen that Δα of 80◦ with nv = 5 or 7is found to be suitable for 3D-OTA, as shown by position P2,because almost the same performance can be achieved asthat observed when distributing over the entire solid angle,as indicated by the diamond-shaped symbol plotted on theright axis.

However, considering practicability and cost of manu-facture, the size of the instruments needs to be as small aspossible. Therefore, nv = 3 with Δα of 50◦ is another choicefor the realization of an OTA apparatus, as shown by posi-

172IEICE TRANS. COMMUN., VOL.E99–B, NO.1 JANUARY 2016

Fig. 7 Channel capacity vs. number of scatterers and angular region.

tion P1 in Fig. 7, because 89.8% of the target value of thechannel capacity can be obtained there.

Since in this paper we focus on the scatterers arrange-ment in the elevation direction, nv = 3, 5, and 7 have beeninvestigated as key parameters. Here, only odd numbers areused because the scatterer is required at the peak position ofthe Gaussian distribution in the elevation direction, as shownin Fig. 2(b). Further, the odd number of scatterers is suitablefor the symmetrical arrangement on the left and right sidesof the peak position.

On the other hand, the number of scatterers in the az-imuth direction nh is fixed at seven. The reason is that in atwo-dimensional channel model, the sum of more than six orseven waves is sufficient to realize the Rayleigh distributionin the azimuth direction [23].

The SNR is set to 30 dB. The diamond mark on theright axis in Fig. 7 indicates the average channel capacityvalue calculated with the parameters of ph = 90◦, pl = −90◦,nv = 37, and nh = 30, which means that a total of 1,110scatterers are arranged throughout the entire space, as shownin Fig. 4. Hence, the goal of the OTA apparatus developmentis to obtain a capacity that is close to the value analyzedbased on these parameters.

Additionally, MIMO channel capacity may be changedwhen a different number of DUT antenna arrays N is em-ployed in different multipath environments, such as variousms and σs. Thus, the multipath characteristics and the num-ber of arrays need to be considered as the parameters fordetermining an appropriate scatterers arrangement (nv, Δα)in the design of an OTA apparatus, as will be introduced inSect. 4.2.

4.2 Determination of Scatterers Arrangement

Since the idealized value of the channel capacity may bechanged because of different conditions (N, ms, or σs), inorder to describe the effective degree to which the MIMOchannel capacity is evaluated, we define the channel capac-ity ratio rc, which indicates the percentage of the channelcapacity as compared with the target value, as follows:

rc =C

Ct

(5)

where C indicates the average channel capacity calculatedusing Eq. (4), while Ct indicates the idealized value calcu-lated with the parameters of ph = 90◦, pl = −90◦, nv = 37,and nh = 30, as shown in Fig. 4.

Figure 8 shows the variations in the channel capacityratio rc when the number of arrays N is increased from 2to 8 considering σs, ms, and Δα = ph − pl as parameters.nh is 7, while the SNR is set to 30 dB with XPR = 50 dB.Figures 8(a) and (b) represent the two cases when nv = 3and 5, respectively. In Fig. 8, the angular spread σs is setto 10◦, 20◦, and 30◦. The figures (1) (2) (3) on the upperside indicate when ms = 20◦, while the figures (4) (5) (6)on the lower side indicate the case of ms = 40◦. These areselected as examples that represent the general characteris-tics of incident waves in the elevation direction in multipathenvironments in an urban macro cellular environment [24].The results rc calculated by Eq. (5) are represented by sym-bol •. Based on these data, the approximate curved surfacesare created using the least-mean-square (LMS) method.

In Fig. 8, an obvious fluctuation of rc is observed owingto various σs and ms. Thus, the suitable scatterers arrange-ment (nv, Δα) based on the desired (σs, ms) for evaluatingdifferent numbers of array N needs to be determined. Theuseful information from the raw data in Fig. 8 will be ab-stracted and reorganized.

As shown in Figs. 8(a)-(1) and (4), nv = 3 is sufficientto evaluate the array with N = 2 because more than 80%of channel capacity ratio rc is obtained in most part of en-tire data. However, with the number of arrays N increasingfrom 2 to 8, a significant reduction of the entire rc can beobserved.

In particular, when N = 8, as shown in Figs. 8(a)-(3)and (6), the entire rc are almost less than 60%, indicating thatthe number of scatterers nv = 3 is not sufficient to evaluatethe MIMO array with a large number of elements arrangedin the vertical direction. Thus, nv needs to be increased forthe case when N is very large.

In Fig. 8(b), when nv = 5 is used, the entire rc are in-creased compared with the rc for nv = 3 in Fig. 8(a) evenwhen N = 8. This indicates that nv = 5 is necessary to en-sure the evaluation of the channel capacity when N = 8.

However, Figs. 8(a)-(1), (a)-(2), and (b)-(3) show thatrc can be maintained at a high level only when Δα is fixedin a certain range, as shown by the vertical dotted arrows.Thus, an appropriate scatterers arrangement Δα needs to bedetermined for different conditions. The mechanism wasillustrated in Sect. 4.1, where the positions of P1 and P2 inFig. 7 can be found in Figs. 8(a)-(2) and (b)-(2), respectively.

Table 3 shows how to determine the appropriate scatter-ers arrangement (nv, Δα) using the data of channel capacityratio rc exhibited in Fig. 8 in different situations of σs whenms = 20◦. Tables 3(a), (b), and (c) list three cases: N = 2and nv = 3, N = 4 and nv = 3, and N = 8 and nv = 5. Thesecorrespond to Figs. 8(a)-(1), (a)-(2), and (b)-(3), which are

LI et al.: THREE-DIMENSIONAL OVER-THE-AIR ASSESSMENT FOR VERTICALLY ARRANGED MIMO ARRAY ANTENNAS173

Fig. 8 Channel capacity ratio vs. number of array elements and scatterers angular region.

determined in order to cover the optimum (nv, Δα) consider-ing the possibility and commonality in different conditionsof N and σs.

In Table 3(a) where N = 2 and nv = 3, a large rangeof Δα from 10◦ to 60◦ can be selected because more than80% of rc is obtained in any case of σs corresponding toFig. 8(a)-(1). However, in Table 3(b) where N = 4 and nv= 3, Δα where the channel capacity is evaluated with morethan 80% of rc is reduced to a range from 30◦ to 50◦. More-over, in Table 3(c) where N = 8 and nv = 5, the optional Δα

is changed to a range from 50◦ to 70◦. These appropriateranges of Δα are indicated by the dotted boxes in Table 3,which correspond to the separation of the vertical dotted ar-rows in Fig. 8.

As mentioned in Fig. 7, considering the manufacture ofthe actual OTA assessment apparatus, the number of scat-terers in the elevation direction nv needs to be as small aspossible. Moreover, the scatterers angular region Δα is alsoanticipated to be smaller as possible to reduce the size ofthe device. In addition, it is convenient for the design of the

174IEICE TRANS. COMMUN., VOL.E99–B, NO.1 JANUARY 2016

Table 3 Determination of scatterers arrangement (nv, Δα) for various N and σs when ms = 20◦.

Fig. 9 Channel capacity ratio vs. the number of array elements and scat-terers angular region when Δα = 50◦: (a) ms = 20◦ and (b) ms = 40◦.

actual apparatus if the scatterers angular region Δα is fixedat a certain value.

Thus, it can be concluded that Δα = 50◦ is the mostsuitable scatterers arrangement, because in any conditionsof N and σs, at least 80% of the channel capacity ratio canbe achieved even when N is increased to 8, as shown bythe horizontal arrow in Table 3. In Fig. 8, it can be seen thatwhen Δα is fixed at 50◦, as indicated by the two-way arrows,rc is maintained at the mountain ridge of the approximatecurved surfaces in each case of σs. This indicates that avalid proposed scatterers arrangement has Δα = 50◦.

Figure 9 shows the channel capacity ratio rc as a func-tion of nv and σs when Δα = 50◦. Figures 9(a) and (b) showthe cases when ms = 20◦ and 40◦, respectively. The solidcurve shows that nv = 3, while the dotted line shows that nv= 5. The curve with symbols �, •, and � indicates the casewhen σs = 10◦, 20◦, and 30◦, respectively.

In Fig. 9(a), it can be seen that when Δα is fixed at 50◦,if N is less than 4, nv = 3 is sufficient to evaluate the channelcapacity because these parameters can yield an rc of morethan 80%. However, if a large number of array elementssuch as N = 8 is used, nv = 5 is needed to ensure an rc ofmore than 80%.

Furthermore, when a high incident wave angle ms =

40◦ is considered as shown in Fig. 9(b), nv = 5 with Δα =50◦ is found to be necessary for evaluating the case whenN = 8. This conclusion can be observed in Fig. 8(b)-(6),where the two-way arrow representing the position of Δα =50◦ passes through the mountain ridge of the approximatecurved surface when N = 8 with ms = 40◦ and various σs.

We conclude from the above investigations that whenthe number of DUT antenna arrays N is less than 4, nv =3 is adequate to realize a 3D-OTA assessment, while if Nis increased to 8, nv = 5 is necessary. Further, it is foundthat Δα = 50◦ is the optimum parameter for a convenientapparatus design because the scatterers can be fixed in eachcase of ms = 20◦ and 40◦.

Since a small-cell era is coming for future wirelesscommunication systems, the approach between the mobileterminal and base station will lead to variations in the ms

and σs of incident waves in the elevation direction, while thenumber of arrays N will be increased to realize ultra-high-capacity. The proposed scatterers arrangement (nv, Δα) fora 3D-OTA apparatus can be applied to evaluate the multi-element MIMO antenna in various multipath conditions (σs,ms) as desired.

5. Conclusion

This paper presents a new methodology of OTA assessmentfor vertically arranged MIMO array antennas. The appro-

LI et al.: THREE-DIMENSIONAL OVER-THE-AIR ASSESSMENT FOR VERTICALLY ARRANGED MIMO ARRAY ANTENNAS175

priate scatterers arrangement considering multipath charac-teristics and the number of DUT antenna elements requiredfor evaluating vertically arranged MIMO array antennas hasbeen studied. Useful knowledge has been obtained that canbe employed in the design of an actual 3D-OTA apparatus.

A great quantity of analytical data for the appropriatescatterers arrangement are proposed. The arrangement canbe determined based on the actual conditions of multipathcharacteristics and the number of DUT antenna elements asdesired. We also provide a choice of scatterers arrangementssuch that when we test the vertically arranged MIMO arrayantenna, the angular range of 50◦ is found to be suitablefor 3D-OTA testing. Based on this investigation, when thenumber of vertically arranged antenna arrays N is less than4, the number of scatterers nv = 3 is adequate to realize a3D-OTA assessment, while if N is increased to 8, nv = 5 isnecessary.

In the view of the analytical results presented in this pa-per, it is anticipated to obtain the optimization of the struc-ture of the OTA device. An actual 3D-OTA is currently be-ing designed using the knowledge obtained in this paper, andit will be presented in separate papers.

Acknowledgments

This work was supported by the SCOPE 2014 grant number145005101.

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176IEICE TRANS. COMMUN., VOL.E99–B, NO.1 JANUARY 2016

Kun Li was born in Nanjing, China, onFebruary 13, 1989. He received a B.E. degree inCommunication Engineering from the NanjingUniversity of Posts and Telecommunications in2011, and an M.E. degree in Electrical and Elec-tronic Engineering from Toyama University, To-yama, Japan, in 2014. He is currently a D.E. stu-dent at Toyama University, where he is studyingan over-the-air testing methodology for body-area networks and MIMO systems. His studiesalso include an on-body wearable antenna with

a low-profile structure. He is a student member of the IEEE.

Kazuhiro Honda was born in Ishikawa onJuly 29, 1972. He received his B.E. and M.E.degrees in Electrical and Electronic Engineer-ing from Toyama University, Toyama, Japan, in1996 and 1998, respectively. Since 1998, he hasbeen a member of the technical staff at the To-yama University, Toyama, Japan. His currentresearch interests include electromagnetic inter-action between antennas and the human body.Mr. Honda was the recipient of the ResearchAward from the Japan Society for Simulation

Technology in 2005, based on the estimation of the electric charge dis-tribution in a cloud. He is a member of the IEEE.

Koichi Ogawa was born in Kyoto in 1955.He received his B.S. and M.S. degrees in Elec-trical Engineering from Shizuoka University in1979 and 1981, respectively. He received aPh.D. degree in Electrical Engineering from theTokyo Institute of Technology in 2000. Hejoined Matsushita Electric Industrial Co., Ltd.,in Osaka in 1981. Since 2003, Dr. Ogawa hasbeen engaged as a Guest Professor at the Centerfor Frontier Medical Engineering, Chiba Uni-versity, Chiba, Japan. In 2005, he was also

a Visiting Professor with the Antennas and Propagation Division, De-partment of Communication Technology, Aalborg University, Denmark.Dr. Ogawa is currently a Professor at Toyama University, Japan. From2007 to 2010, he was the Chair of the IEEE AP-S Kansai Chapter, Japan.From 2013 to 2014, he was the Chair of the IEEE AP-S Nagoya Chapter,Japan. He is a senior member of the IEEE and is listed in Who’s Who in theWorld.