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Citation: Honda, K. Over-the-Air
Testing of a Massive MIMO Antenna
with a Full-Rank Channel Matrix.
Sensors 2022,22, 1240. https://
doi.org/10.3390/s22031240
Academic Editors: Naser Ojaroudi
Parchin, Chan Hwang See and Raed
A. Abd-Alhameed
Received: 23 December 2021
Accepted: 5 February 2022
Published: 6 February 2022
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sensors
Technical Note
Over-the-Air Testing of a Massive MIMO Antenna with a
Full-Rank Channel Matrix
Kazuhiro Honda
Graduate School of Engineering, Toyama University, 3190 Gofuku, Toyama 930-8555, Japan;
hondak@eng.u-toyama.ac.jp; Tel.: +81-76-445-6759
Abstract:
This paper presents an over-the-air testing method in which a full-rank channel matrix
is created for a massive multiple-input multiple-output (MIMO) antenna system utilizing a fading
emulator with a small number of scatterers. In the proposed method, in order to mimic a fading
emulator with a large number of scatterers, the scatterers are virtually positioned by rotating the
massive MIMO antenna. The performance of a 64-element quasi-half-wavelength dipole circular
array antenna was evaluated using a two-dimensional fading emulator. The experimental results
reveal that a large number of available eigenvalues are obtained from the channel response matrix,
confirming that the proposed method, which utilizes a full-rank channel matrix, can be used to assess
a massive MIMO antenna system.
Keywords:
massive multiple-input multiple-output (MIMO) antenna; over-the-air (OTA) testing;
channel matrix; full-rank; fading emulator
1. Introduction
Global commercial services for ultra-high speed fifth-generation (5G) mobile commu-
nication using multiple-input multiple-output (MIMO) systems are currently available [
1
,
2
].
One of the possible solutions to significantly enhance the channel capacity of MIMO sys-
tems is to utilize a large number of antenna elements for both the base station (BS) and the
mobile station (MS). Such a system is called a massive MIMO system [3].
Most of the activity so far undertaken in developing massive MIMO systems has been
directed toward providing large-scale MIMO antennas at the BS, with antennas comprising
more than 100 antenna elements [
4
,
5
], and there are few reports of doing something similar
at the MS [
6
]. The author is currently developing a method to achieve a large-scale MIMO
antenna system that maintains an invariable channel capacity over the full-azimuth at the
MS, such as, for example, a connected ground-based or flying car [7].
The usual technique for evaluating the performance of MIMO antennas with multipath
fading channels is to do Monte Carlo simulation where several scatterers are placed on a
circle [
8
,
9
]. This is known as the Clarke model or ring model. Using this model, the number
of scatterers required to simulate the full-rank property of the channel matrix for a massive
MIMO system is greater than the number of subchannels.
To analyze the capability of the developed antenna [
7
], the author proposed a Monte
Carlo simulation with randomly arranged scatterers [
10
]. A small number of differently
positioned scatterers were set for each BS antenna using random numbers, confirming
that the channel matrix created can achieve full-rank status similar to conventional Monte
Carlo simulation. However, a large number of scatterers are necessary to emulate a lot
of channels.
A legitimate manner of assessing the performance of a fabricated massive MIMO
antenna is to test it in the field [
11
]. However, with field testing, the measurements are
neither repeatable nor controllable, and, moreover, the measurement process is considerably
time-consuming and labor-intensive. Hence, over-the-air (OTA) testing, which evaluates
Sensors 2022,22, 1240. https://doi.org/10.3390/s22031240 https://www.mdpi.com/journal/sensors
Sensors 2022,22, 1240 2 of 12
the ability of a MIMO antenna by reproducing a realistic multipath radio propagation
environment in the laboratory, is essential.
A proper OTA testing method for massive MIMO antennas is required to accelerate the
development and optimization of the antenna [12]. As many massive MIMO BS antennas
have been developed, radiating evaluation methods for massive MIMO BS antennas using
fading emulators have also been investigated [
13
,
14
]. Many BS antennas comprise a
two-dimensional
planar array antenna with a number of patch antennas. Consequently,
a large number of scatterers are placed in a limited direction with respect to the OTA
apparatus and scatterers are selected from among them for the assessment.
On the other hand, an OTA testing method for massive MIMO MS antennas is not
currently available. A fading emulator with a small number of scatterers placed on a circle
has been adopted for proper OTA testing of a handset MS comprising a few MIMO antenna
elements [
15
,
16
]. In the standard method utilizing a fading emulator, the arrangement
of the scatterers depends on the number of subchannels, indicating that a large number
of scatterers are necessary to assess the performance of a massive MIMO system with a
full-rank channel matrix. Therefore, because of the size and cost of the equipment, the
standard method is not effective for massive MIMO MS antennas.
The author proposed an OTA evaluation method for a massive MIMO antenna that
creates a full-rank channel matrix [
17
]. The results of the Monte Carlo simulation, which
included simulation of the proposed OTA testing method, revealed that even though the
channel model comprised a limited number of scatterers, a full-rank channel matrix can be
created. However, an experimental verification of this has not been done.
This paper presents an experimental verification of the proposed method utilizing a
two-dimensional fading emulator with a small number of scatterers. In the OTA measure-
ments, the massive MIMO MS antenna is located at the center of the fading emulator and
is rotated depending on the measured channel response at the BS antenna, in such a way
that a small number of scatterers are equivalent to a much larger number of scatterers. The
experimental results showed that the number of available eigenvalues is greater than that
obtained with the previous method.
2. Measurement Method of the Full-Rank Channel
In a previous Monte Carlo simulation with a uniform arrangement of scatterers, which
represented the secondary wave source, N
×
Mchannel responses were calculated to form
Equation (1).
HS=
h11 h12 · · · h1Km· · · h1M
h21 h22 · · · h2Km· · · h2M
.
.
..
.
.....
.
.....
.
.
hN1hN2· · · hNKm· · · hN M
(1)
where K
m
indicates the number of actual scatterers. Mand Ndenote the number of
elements in the BS and MS, respectively. Furthermore, the author assumed that the number
of elements at the BS is equal to that at the MS, that is, M=N.
In Equation (1), because all the signals from the Melements at BS overlap with each
other at the same location, the number of columns that satisfy linear independence is equal
to K
m
in the channel model. Consequently, assuming that K
m
is less than M, Equation (1) is
transformed into Equation (2) using diagonalization.
HS=
h11 h12 · · · h1Km0· · · 0
h21 h22 · · · h2Km0· · · 0
.
.
..
.
.....
.
..
.
.....
.
.
hN1hN2· · · hNKm0· · · 0
(2)
Sensors 2022,22, 1240 3 of 12
Therefore, the eigenvalue vector obtained using singular value decomposition (SVD)
is denoted by Equation (3).
Λ=λ1λ2· · · λKm0· · · 0(3)
The rank of Equation (2) equals K
m
which is less than M, indicating a rank-deficient
status. Consequently, the number of eigenvalues, that is, the number of channels, observed
is only K
m
. Hence, a large number of scatterers, greater than M, are necessary to obtain
full-rank status with rank (HS) = M.
The method of randomly arranged scatterers, in which a limited number of scatterers
are arranged to simulate each BS element, was proposed [
10
]. The required number
of scatterers to generate the Rayleigh fading environment for one BS element is small.
However, the total number of scatterers is the product of Mand K
m
. Consequently, for
OTA testing of a massive MIMO system incorporating the method of randomly arranged
scatterers, a small number of scatterers must be selected from among the large number of
scatterers on the circle of the fading emulator. Otherwise, the actual scatterers need to be
relocated for each BS. Hence, the OTA testing implemented using the method of randomly
arranged scatterers is extremely labor-intensive process compared with the standard OTA
testing method.
The author proposed an OTA testing method in which the scatterers are virtually
formed emulating a large number of scatterers [
17
]. Figure 1shows the configuration of
the proposed fading emulator to enable a full-rank channel matrix for a massive MIMO
antenna. In Figure 1,K
m
, that is, the number of scatterers in the 1st set, is 14 which is
sufficient to produce a Rayleigh fading environment. The 2nd to S-th sets of scatterers are
virtually placed, where Sindicates the number of scatterer sets.
Sensors 2022, 22, 1240 3 of 12
11 12 1
21 22 2
12
00
00
00
m
m
m
K
K
S
NN NK
hh h
hh h
hh h
=
H
(2)
Therefore, the eigenvalue vector obtained using singular value decomposition (SVD)
is denoted by Equation (3).
12 00
m
K
λλ λ
=
Λ
(3)
The rank of Equation (2) equals Km which is less than M, indicating a rank-deficient
status. Consequently, the number of eigenvalues, that is, the number of channels, ob-
served is only Km. Hence, a large number of scatterers, greater than M, are necessary to
obtain full-rank status with rank (Hs) = M.
The method of randomly arranged scatterers, in which a limited number of scatterers
are arranged to simulate each BS element, was proposed [10]. The required number of
scatterers to generate the Rayleigh fading environment for one BS element is small. How-
ever, the total number of scatterers is the product of M and Km. Consequently, for OTA
testing of a massive MIMO system incorporating the method of randomly arranged scat-
terers, a small number of scatterers must be selected from among the large number of
scatterers on the circle of the fading emulator. Otherwise, the actual scatterers need to be
relocated for each BS. Hence, the OTA testing implemented using the method of randomly
arranged scatterers is extremely labor-intensive process compared with the standard OTA
testing method.
The author proposed an OTA testing method in which the scatterers are virtually
formed emulating a large number of scatterers [17]. Figure 1 shows the configuration of
the proposed fading emulator to enable a full-rank channel matrix for a massive MIMO
antenna. In Figure 1, Km, that is, the number of scatterers in the 1st set, is 14 which is suf-
ficient to produce a Rayleigh fading environment. The 2nd to S-th sets of scatterers are
virtually placed, where S indicates the number of scatterer sets.
Figure 1. Configuration of the scatterers for evaluating the massive MIMO system.
The angular intervals between the i-th and (i + 1)-th sets of scatterers, Δφ, as shown
in Figure 1, are the same. Therefore, each set of scatterers is formed by rotating the 1st set
of scatterers. Consequently, the placement of each of scatterer differs, and a large number
of scatterers can be emulated, with the expectation that measurement with a full-rank
property of the channel matrix can be achieved.
Scatterer #1
Scatterer #2
Scatterer #3
Scatterer #4
Scatterer #5
Scatterer #6
Scatterer #7
Scatterer #8
Scatterer #9
Scatterer #10
Scatterer #11 Scatterer #12
Scatterer #13
Scatterer #14
S-th set
2nd set
1st set
S-th set
2nd set
1st set
S-th set
2nd set
1st set
Δ
ϕ
Massive MIMO antenna
Figure 1. Configuration of the scatterers for evaluating the massive MIMO system.
The angular intervals between the i-th and (i+ 1)-th sets of scatterers,
∆ϕ
, as shown
in Figure 1, are the same. Therefore, each set of scatterers is formed by rotating the 1st set
of scatterers. Consequently, the placement of each of scatterer differs, and a large number
of scatterers can be emulated, with the expectation that measurement with a full-rank
property of the channel matrix can be achieved.
The most important parameter in the measurement is the number of scatterer sets
which depends on the number of actual scatterers. Independent paths via each BS antenna
are generated by orthogonal initial phase sets at the actual scatterers. Hence, the maximum
number of BS elements emulated in accordance with each set of scatterers is the same as
the number of actual scatterers. In order to achieve a full-rank matrix, Smust be adjusted
to be greater than Mdivided by K
m
. Another important parameter is
∆ϕ
. If
∆ϕ
is small,
Sensors 2022,22, 1240 4 of 12
the possibility of generating different paths from adjacent sets of scatterers is small. In this
paper, ∆ϕis set to equal angular intervals, and it is calculated as follows:
∆ϕ=
360
Km
1
S(4)
There are two ways to construct the fading emulator embodied using the proposed
method. One of the possible ways is to rotate the turn rail on which the actual scatterers
are located, as shown in the insert in Figure 2a, which is the same structure shown in
Figure 1. Another is that the massive MIMO antenna, which is placed at the center of
the turntable, is rotated, as illustrated on the left hand side of the inset in Figure 2b. In
this case, the rotation target, that is, the massive MIMO antenna, is different to that of
Figure 1, but
Figures 1and 2b
have the same benefit of achieving a full-rank channel matrix
measurement, as explained in below.
Sensors 2022, 22, 1240 4 of 12
The most important parameter in the measurement is the number of scatterer sets
which depends on the number of actual scatterers. Independent paths via each BS antenna
are generated by orthogonal initial phase sets at the actual scatterers. Hence, the maxi-
mum number of BS elements emulated in accordance with each set of scatterers is the
same as the number of actual scatterers. In order to achieve a full-rank matrix, S must be
adjusted to be greater than M divided by Km. Another important parameter is Δφ. If Δφ is
small, the possibility of generating different paths from adjacent sets of scatterers is small.
In this paper, Δφ is set to equal angular intervals, and it is calculated as follows:
360 1
m
K
S
ϕ
Δ= (4)
There are two ways to construct the fading emulator embodied using the proposed
method. One of the possible ways is to rotate the turn rail on which the actual scatterers
are located, as shown in the insert in Figure 2a, which is the same structure shown in
Figure 1. Another is that the massive MIMO antenna, which is placed at the center of the
turntable, is rotated, as illustrated on the left hand side of the inset in Figure 2b. In this
case, the rotation target, that is, the massive MIMO antenna, is different to that of Figure
1, but Figures 1 and 2b have the same benefit of achieving a full-rank channel matrix meas-
urement, as explained in below.
(a)
0 25.7 51.4 154.3 180 205.7 231.4 257.1 282.9 308.6 334.4 36077.1 102.9 128.6
Global Azimuth Angle [deg]
1st set (BS #1−#13)
2nd set (BS #14−#26)
3rd set (BS#27−#39)
4th set (BS #40−#52)
5th set (BS #53−#64)
1st set (BS #1−#13)
2nd set (BS #14−#26)
3rd set (BS#27−#39)
4th set (BS #40−#52)
5th set (BS #53−#64)
1st set (BS #1−#13)
2nd set (BS #14−#26)
3rd set (BS#27−#39)
4th set (BS #40−#52)
5th set (BS #53−#64)
…
MS #1
MS #2
MS #64
Locus of scatterer #1
#1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 #13 #14
Turnrail
x
y
Sensors 2022, 22, 1240 5 of 12
(b)
Figure 2. Massive MIMO OTA apparatus: (a) with the turn rail; (b) with the turntable.
It is known that with multiple probe antenna based methods, such as those with fad-
ing emulators, the repeatability and controllability of the radio propagation environment
are superior to those obtained with other OTA testing methods, such as reverberation
chamber based methods or two-stage methods [18]. In OTA assessment using a fading
emulator, the MIMO channel response between the m-th BS antenna element and n-th MS
antenna element is measured individually, taking advantage of the high time correlation
characteristics of the apparatus.
Figure 2 shows the relationship between the channel response measured, the azimuth
angle of the actual scatterers, and the azimuth angle of the massive MIMO antenna in the
case of a 64 × 64 MIMO system, with Km = 14, and S = 5. The symbols in Figure 2 are asso-
ciated with Figure 1. The circles indicate the positions of the scatterers, whereas the star
symbol denotes the azimuth angle of the massive MIMO antenna, which starts from 0° in
the measurements.
In Figure 2a, the massive MIMO MS antenna is fixed at the center of the fading emu-
lator, and the actual scatterers are moved by rotating the turn rail. Accordingly, the global
azimuth angle of the scatterers is varied depending on the measured channel response for
the m-th BS antenna. The black line indicates the locus of scatterer #1.
The channel responses from BS #1 to BS #13 are measured with the 1st set of scatterers
in place. Then, the turn rail is rotated by Δφ, and the channel responses from BS #14 to BS
#26 are measured with the 2nd set of scatterers in place. By repeating this procedure, the
channel responses of the n-th MS antenna are fulfilled. Moreover, this method applies to
all MS antennas, resulting in a full-rank channel response matrix.
In contrast, in Figure 2b, the actual scatterers remain stationary, and the turntable
with the massive MIMO MS antenna is rotated. Consequently, the local azimuth angle of
the massive MIMO MS antenna is changed corresponding to the measured channel re-
sponse for the m-th BS antenna. The black line shows the locus of the star symbol express-
ing the angle of the massive MIMO antenna. However, the global azimuth angle of the
MIMO antenna is fixed during OTA testing. When the local azimuth angle is transformed
so that the global azimuth angle is 0°, as shown on the right hand side of the inset in Figure
2b, it becomes the same as in Figure 2a. Eventually, the actual scatterers are virtually po-
sitioned in different locations.
1st set (BS #1−#13)
2nd set (BS #14−#26)
3rd set (BS#27−#39)
4th set (BS #40−#52)
5th set (BS #53−#64)
1st set (BS #1−#13)
2nd set (BS #14−#26)
3rd set (BS#27−#39)
4th set (BS #40−#52)
5th set (BS #53−#64)
1st set (BS #1−#13)
2nd set (BS #14−#26)
3rd set (BS#27−#39)
4th set (BS #40−#52)
5th set (BS #53−#64)
…
MS #1
MS #2
MS #64
Locus of symbol ★in the massive MIMO antenna
#1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 #13 #14
0 25.7 51.4 154.3 180 205.7 231.4 257.1 282.9 308.6 334.4 36077.1 102.9 128.6
Local Azimuth Angle [deg]
−25.7
Turntab le
Turnt able
=
y
’
y
x
’
x
Figure 2. Massive MIMO OTA apparatus: (a) with the turn rail; (b) with the turntable.
Sensors 2022,22, 1240 5 of 12
It is known that with multiple probe antenna based methods, such as those with fading
emulators, the repeatability and controllability of the radio propagation environment
are superior to those obtained with other OTA testing methods, such as reverberation
chamber based methods or two-stage methods [
18
]. In OTA assessment using a fading
emulator, the MIMO channel response between the m-th BS antenna element and n-th MS
antenna element is measured individually, taking advantage of the high time correlation
characteristics of the apparatus.
Figure 2shows the relationship between the channel response measured, the azimuth
angle of the actual scatterers, and the azimuth angle of the massive MIMO antenna in the
case of a 64
×
64 MIMO system, with K
m
= 14, and S= 5. The symbols in Figure 2are
associated with Figure 1. The circles indicate the positions of the scatterers, whereas the
star symbol denotes the azimuth angle of the massive MIMO antenna, which starts from 0
◦
in the measurements.
In Figure 2a, the massive MIMO MS antenna is fixed at the center of the fading
emulator, and the actual scatterers are moved by rotating the turn rail. Accordingly,
the global azimuth angle of the scatterers is varied depending on the measured channel
response for the m-th BS antenna. The black line indicates the locus of scatterer #1.
The channel responses from BS #1 to BS #13 are measured with the 1st set of scatterers
in place. Then, the turn rail is rotated by
∆ϕ
, and the channel responses from BS #14 to BS
#26 are measured with the 2nd set of scatterers in place. By repeating this procedure, the
channel responses of the n-th MS antenna are fulfilled. Moreover, this method applies to all
MS antennas, resulting in a full-rank channel response matrix.
In contrast, in Figure 2b, the actual scatterers remain stationary, and the turntable with
the massive MIMO MS antenna is rotated. Consequently, the local azimuth angle of the
massive MIMO MS antenna is changed corresponding to the measured channel response
for the m-th BS antenna. The black line shows the locus of the star symbol expressing the
angle of the massive MIMO antenna. However, the global azimuth angle of the MIMO
antenna is fixed during OTA testing. When the local azimuth angle is transformed so that
the global azimuth angle is 0
◦
, as shown on the right hand side of the inset in Figure 2b, it
becomes the same as in Figure 2a. Eventually, the actual scatterers are virtually positioned
in different locations.
The channel responses from BS #1 to BS #13 are measured. Then, the turntable is
rotated by
−∆ϕ
, and the channel responses from BS #14 to BS #26 are obtained. By repeating
this operation, the channel responses of the n-th MS antenna are satisfied. Furthermore,
this is done for all MS antennas, demonstrating that the channel matrix is full-rank status.
3. Results and Discussion
3.1. Analytical Results
To verify the proposed OTA method, Monte Carlo simulation of a massive MIMO
antenna was conducted. The massive MIMO antenna comprises a 64-element quasi-half-
wavelength dipole MIMO circular array antenna at 5 GHz to exclude the effect caused by
electromagnetic mutual coupling. The array antenna was arranged with equal angular
intervals. The radiation pattern of the massive MIMO antenna was calculated by the
method of moments.
Figure 3shows the number of channels as a function of the total number of scatterers
K
n
, that is the number of scatterers located to perform all measurements. In Figure 3, the
black circles represent the analytical outcome with the proposed method as a function of
S, whereas the blue rhombuses are those of the randomly arranged scatterers method, in
which the scatterers on each BS were randomly selected from among all the scatterers. The
red line represents the theoretical value, as expressed in Equation (3). Kmis set to 14.
Sensors 2022,22, 1240 6 of 12
Sensors 2022, 22, 1240 6 of 12
The channel responses from BS #1 to BS #13 are measured. Then, the turntable is ro-
tated by −Δφ, and the channel responses from BS #14 to BS #26 are obtained. By repeating
this operation, the channel responses of the n-th MS antenna are satisfied. Furthermore,
this is done for all MS antennas, demonstrating that the channel matrix is full-rank status.
3. Results and Discussion
3.1. Analytical Results
To verify the proposed OTA method, Monte Carlo simulation of a massive MIMO
antenna was conducted. The massive MIMO antenna comprises a 64-element quasi-half-
wavelength dipole MIMO circular array antenna at 5 GHz to exclude the effect caused by
electromagnetic mutual coupling. The array antenna was arranged with equal angular
intervals. The radiation pattern of the massive MIMO antenna was calculated by the
method of moments.
Figure 3 shows the number of channels as a function of the total number of scatterers
Kn, that is the number of scatterers located to perform all measurements. In Figure 3, the
black circles represent the analytical outcome with the proposed method as a function of
S, whereas the blue rhombuses are those of the randomly arranged scatterers method, in
which the scatterers on each BS were randomly selected from among all the scatterers.
The red line represents the theoretical value, as expressed in Equation (3). Km is set to 14.
It can be seen from Figure 3 that the proposed method has the same effect as the
method of randomly arranged scatterers. When Kn is greater than 64, the number of chan-
nels equals 64. In contrast, when Kn is less than 64, the number of channels is understood
to be just Kn. Hence, full-rank status can be achieved by rotating the actual scatterers mul-
tiple times, even with a small number of scatterers on the OTA apparatus.
Figure 3. Number of channels vs. number of total scatterers.
Figure 4 shows the average of the 64th eigenvalues through all snapshots as a func-
tion of the angular interval between the i-th and (i + 1)-th sets of scatterers with S as a
parameter [17]. The green, red, and blue curves indicate the cases where S is 3, 5, and 7,
respectively. Km is set to 14.
As can be seen in Figure 4, there is no green curve for S = 3 because the total number
of scatterers is only 42 (=14 × 3), indicating a rank-deficient status. In contrast, when S is
greater than 5, the average of the 64th eigenvalues is confirmed, indicating full-rank sta-
tus.
The average of the 64th eigenvalues is increased with increasing the angular interval.
This is because, when Δφ is small, there is high correlation coefficient between the incom-
ing waves due to the closely spaced arrangement of the scatterers. On the other hand, the
14 28 42 56 70 84 98
0
8
16
24
32
40
48
56
64
Total Number of Scatterers
K
n
Number of Channels
Proposed method
Randomly arranged
Eq. (3)
K
m
= 14
Figure 3. Number of channels vs. number of total scatterers.
It can be seen from Figure 3that the proposed method has the same effect as the method
of randomly arranged scatterers. When K
n
is greater than 64, the number of channels
equals 64
. In contrast, when K
n
is less than 64, the number of channels is understood to be
just K
n
. Hence, full-rank status can be achieved by rotating the actual scatterers multiple
times, even with a small number of scatterers on the OTA apparatus.
Figure 4shows the average of the 64th eigenvalues through all snapshots as a func-
tion of the angular interval between the i-th and (i+ 1)-th sets of scatterers with Sas a
parameter [
17
]. The green, red, and blue curves indicate the cases where Sis 3, 5, and 7,
respectively. Kmis set to 14.
Sensors 2022, 22, 1240 7 of 12
independence of the incoming wave is greater as Δφ is increased i.e., the eigenvalues are
larger. But the average of the 64th eigenvalues is reduced for more large angular intervals
such as Δφ = 6° with S = 5. In this case, the azimuth angle of scatterer #1 in the 5th set is
24°, which is close to that of scatterer #2 in the 1st set, 25.7°. Thus, all the scatterers includ-
ing the virtual scatterers should be set to equal angular intervals.
Figure 4. Average of the 64th eigenvalues.
3.2. Experimental Results
This subsection is devoted to verification of the proposed method utilizing the fading
emulator with a small number of scatterers. The channel response matrix of the 64 × 64
MIMO system was measured using a two-dimensional fading emulator with a uniform
incident wave distribution in azimuth. In millimeter wave 5G communications, the dis-
tance between the BS and MS is smaller than previous communication systems because
the path loss between the BS and MS is large, resulting in an environment in which line-
of-sight propagation or a cluster power distribution is assumed. In the sub-6 GHz fre-
quency bands, the propagation environment is like the cluster or uniform power distribu-
tions found in previous communication systems. In this paper, a uniform power distribu-
tion, with which a sufficient number of paths in a propagation environment are expected,
is considered.
Figure 5 shows the configuration of the massive MIMO-OTA apparatus that embod-
ies the proposed method using the turntable, as shown in Figure 2b. The inserted lower
right photo is a bird’s eye view of the fading emulator. A 64-element quasi half-wave-
length dipole MIMO circular array antenna was placed on a turntable located at the center
of the fading emulator. The radius of the massive MIMO antenna was 20 cm. Fourteen
scatterers, comprising vertically polarized half-wavelength sleeve dipole antennas, were
set at equal angular intervals on a circle of radius 120 cm. The frequency was set to 5 GHz.
1 2 3 4 5 6
10
-8
10
-7
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
Angular Intervals
Δφ
[deg]
Average of the 64th Eigenvalues
S= 3
S= 5
S = 7
Km= 14
Δ
ϕ
10−1
10−2
10−3
10−4
10−5
10−6
10−7
10−8
Figure 4. Average of the 64th eigenvalues.
As can be seen in Figure 4, there is no green curve for S= 3 because the total number
of scatterers is only 42 (=14
×
3), indicating a rank-deficient status. In contrast, when Sis
greater than 5, the average of the 64th eigenvalues is confirmed, indicating full-rank status.
The average of the 64th eigenvalues is increased with increasing the angular interval.
This is because, when
∆ϕ
is small, there is high correlation coefficient between the incoming
waves due to the closely spaced arrangement of the scatterers. On the other hand, the
independence of the incoming wave is greater as
∆ϕ
is increased i.e., the eigenvalues are
larger. But the average of the 64th eigenvalues is reduced for more large angular intervals
such as
∆ϕ
= 6
◦
with S= 5. In this case, the azimuth angle of scatterer #1 in the 5th set is 24
◦
,
which is close to that of scatterer #2 in the 1st set, 25.7
◦
. Thus, all the scatterers including
the virtual scatterers should be set to equal angular intervals.
Sensors 2022,22, 1240 7 of 12
3.2. Experimental Results
This subsection is devoted to verification of the proposed method utilizing the fading
emulator with a small number of scatterers. The channel response matrix of the 64
×
64
MIMO system was measured using a two-dimensional fading emulator with a uniform
incident wave distribution in azimuth. In millimeter wave 5G communications, the distance
between the BS and MS is smaller than previous communication systems because the path
loss between the BS and MS is large, resulting in an environment in which line-of-sight
propagation or a cluster power distribution is assumed. In the sub-6 GHz frequency bands,
the propagation environment is like the cluster or uniform power distributions found in
previous communication systems. In this paper, a uniform power distribution, with which
a sufficient number of paths in a propagation environment are expected, is considered.
Figure 5shows the configuration of the massive MIMO-OTA apparatus that embodies
the proposed method using the turntable, as shown in Figure 2b. The inserted lower right
photo is a bird’s eye view of the fading emulator. A 64-element quasi half-wavelength
dipole MIMO circular array antenna was placed on a turntable located at the center of the
fading emulator. The radius of the massive MIMO antenna was 20 cm. Fourteen scatterers,
comprising vertically polarized half-wavelength sleeve dipole antennas, were set at equal
angular intervals on a circle of radius 120 cm. The frequency was set to 5 GHz.
Sensors 2022, 22, 1240 8 of 12
Figure 5. Configuration of the massive MIMO-OTA apparatus.
Figure 6 shows the cumulative distribution function (CDF) of the instantaneous ei-
genvalues obtained through SVD for a measured channel response matrix utilizing a fad-
ing emulator with a small number of scatterers. Figure 6a,b show the results for the pre-
vious method without rotation of the massive MIMO antenna and for the proposed
method with rotation of the massive MIMO antenna, respectively. In the proposed
method, S is set to 5 and the incremental rotation angle, Δφ, as illustrated in Figure 1, is
5.1°, that is, the angular intervals between the scatterers are equal.
As shown in Figure 6a, there is a large interval between the 14th and 15th eigenval-
ues. Therefore, the previous OTA testing method can emulate only 14 channels with the
same K
m
. However, the 15th and subsequent eigenvalues are observed. This is due to the
fact that the measured channel matrix includes noise and that the time correlation is 0.999,
not absolutely 1. In contrast, in Figure 6b, an extremely dense eigenvalue distribution is
observed because five scatterer sets have the same effect as 70 scatterers. Consequently, a
full-rank channel matrix for a massive MIMO system can be implemented using the pro-
posed method.
Figure 5. Configuration of the massive MIMO-OTA apparatus.
Figure 6shows the cumulative distribution function (CDF) of the instantaneous eigen-
values obtained through SVD for a measured channel response matrix utilizing a fading
emulator with a small number of scatterers. Figure 6a,b show the results for the previous
method without rotation of the massive MIMO antenna and for the proposed method with
rotation of the massive MIMO antenna, respectively. In the proposed method, Sis set to 5
and the incremental rotation angle,
∆ϕ
, as illustrated in Figure 1, is 5.1
◦
, that is, the angular
intervals between the scatterers are equal.
Sensors 2022,22, 1240 8 of 12
Sensors 2022, 22, 1240 9 of 12
(a)
(b)
Figure 6. CDF characteristics of the eigenvalues: (a) previous method; (b) proposed method.
Figure 7a shows the average eigenvalue distribution with S as a parameter. The
green, red, and blue curves denote the cases where S is 3, 5, and 7, respectively. For com-
parison, the previous method is depicted by the black curve in the graph. When the actual
scatterers were rotated, Δφ was set to equal angular intervals between the i-th and (i + 1)-
th sets. As the angular interval between the scatterers is 25.7° with Km set to 14, Δφ is 5.1°
with S equal to 5.
As can be seen from Figure 7a, when S is smaller than 3, the number of channels is
less than 64 because Kn is less than M. Specifically, the number of available eigenvalues at
S = 1 and 3 is 14 (=14 × 1) and 42 (=14 × 3), respectively. These results agree well with those
in Figure 3. In contrast, when S is greater than 5, the number of channels is 64. Therefore,
the proposed method can achieve a full-rank channel matrix. Note that, the required num-
ber of scatterer sets is determined by the number of elements at BS, M, and the number of
actual scatterers, Km.
Figure 7b shows the average eigenvalue distribution with Δφ as a parameter. The
green, blue, and red curves indicate the cases where Δφ is 1°, 3°, and 5.1°, respectively. S
is set to 5.
It can be observed that the gap in the distribution of average eigenvalues is elimi-
nated and the distribution becomes more uniform with increasing Δφ. This is because,
when Δφ is small, the channels are insufficiently independent owing to the proximity be-
tween the i-th and (i + 1)-th sets, resulting in the characteristics of the measured results in
10
-5
10
0
10
5
0
10
20
30
40
50
60
70
80
90
100
Eige nvalue
λ
Cumulative Percentage [%]
14th eigenvalue
15th eigenvalue
10
−5
10
0
10
5
0
10
-5
10
0
10
5
0
10
20
30
40
50
60
70
80
90
100
Eige nvalue
λ
Cumulative Percentage [%]
10−5100105
0
Figure 6. CDF characteristics of the eigenvalues: (a) previous method; (b) proposed method.
As shown in Figure 6a, there is a large interval between the 14th and 15th eigenvalues.
Therefore, the previous OTA testing method can emulate only 14 channels with the same
K
m
. However, the 15th and subsequent eigenvalues are observed. This is due to the fact
that the measured channel matrix includes noise and that the time correlation is 0.999,
not absolutely 1. In contrast, in Figure 6b, an extremely dense eigenvalue distribution is
observed because five scatterer sets have the same effect as 70 scatterers. Consequently,
a full-rank channel matrix for a massive MIMO system can be implemented using the
proposed method.
Figure 7a shows the average eigenvalue distribution with Sas a parameter. The green,
red, and blue curves denote the cases where Sis 3, 5, and 7, respectively. For comparison,
the previous method is depicted by the black curve in the graph. When the actual scatterers
were rotated,
∆ϕ
was set to equal angular intervals between the i-th and (i+ 1)-th sets. As
the angular interval between the scatterers is 25.7
◦
with K
m
set to 14,
∆ϕ
is 5.1
◦
with Sequal
to 5.
Sensors 2022,22, 1240 9 of 12
Sensors 2022, 22, 1240 10 of 12
Figure 4. Eventually, the setting of S and Δφ depending on Km is one of the most important
issues for generating a radio propagation environment for a massive MIMO system with
a large number of channels.
(a)
(b)
Figure 7. Eigenvalue distribution: (a) with the number of scatterer sets as a parameter; (b) with the
rotation angle increment as a parameter.
Figure 8 shows the CDF of the instantaneous channel capacity of the 64 × 64 MIMO
array as a function of Δφ. The green, blue, and red curves describe the cases where Δφ is
1°, 3°, and 5.1°, respectively. S is set to 5. For comparison, the analytical outcome through
Monte Carlo simulation for the realization of a full-rank channel matrix is illustrated by
the purple curve in the graph. The values shown in the graph for each case are the average
channel capacity calculated from the following equation:
1
1S
s
s
CC
S=
= (5)
where Cs indicates the channel capacity of the s-th snapshot and S is the number of snap-
shots. The input signal-to-noise ratio (SNR), defined as the SNR for each incident wave
when a theoretical isotropic antenna is used for receiving the incident wave, is set to 30
dB. Therefore, the SNR is determined only by the received power of the isotropic antenna
and is not depended on the output power of the actual BS or the network analyzer used
14 28 42 56 64
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
10
1
10
2
10
3
10
4
10
5
Subchannel Number
Average Eigenvalue
Previous (
S
= 1)
S
= 3
S
= 5
S
= 7
14th eigenvalue
42th eigenvalue
K
m
= 14
10
5
10
4
10
3
10
2
10
1
10
0
10
−1
10
−2
10
−3
10
−4
10
−5
14 28 42 56 64
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
10
1
10
2
10
3
10
4
10
5
Subchannel Number
Average Eigenvalue
Previous
Δ
ϕ
= 1
°
Δ
ϕ
= 3
°
Δ
ϕ
= 5.1
°
K
m
= 14
10
5
10
4
10
3
10
2
10
1
10
0
10
−1
10
−2
10
−3
10
−4
10
−5
Figure 7.
Eigenvalue distribution: (
a
) with the number of scatterer sets as a parameter; (
b
) with the
rotation angle increment as a parameter.
As can be seen from Figure 7a, when Sis smaller than 3, the number of channels is less
than 64 because K
n
is less than M. Specifically, the number of available eigenvalues at S= 1
and 3 is 14 (=14
×
1) and 42 (=14
×
3), respectively. These results agree well with those in
Figure 3. In contrast, when Sis greater than 5, the number of channels is 64. Therefore, the
proposed method can achieve a full-rank channel matrix. Note that, the required number of
scatterer sets is determined by the number of elements at BS, M, and the number of actual
scatterers, Km.
Figure 7b shows the average eigenvalue distribution with
∆ϕ
as a parameter. The
green, blue, and red curves indicate the cases where
∆ϕ
is 1
◦
, 3
◦
, and 5.1
◦
, respectively. Sis
set to 5.
It can be observed that the gap in the distribution of average eigenvalues is eliminated
and the distribution becomes more uniform with increasing
∆ϕ
. This is because, when
∆ϕ
is small, the channels are insufficiently independent owing to the proximity between the
i-th and (i+ 1)-th sets, resulting in the characteristics of the measured results in Figure 4.
Eventually, the setting of Sand
∆ϕ
depending on K
m
is one of the most important issues
for generating a radio propagation environment for a massive MIMO system with a large
number of channels.
Figure 8shows the CDF of the instantaneous channel capacity of the 64
×
64 MIMO
array as a function of
∆ϕ
. The green, blue, and red curves describe the cases where
∆ϕ
is
Sensors 2022,22, 1240 10 of 12
1
◦
, 3
◦
, and 5.1
◦
, respectively. Sis set to 5. For comparison, the analytical outcome through
Monte Carlo simulation for the realization of a full-rank channel matrix is illustrated by the
purple curve in the graph. The values shown in the graph for each case are the average
channel capacity calculated from the following equation:
C=
1
S
S
∑
s=1
Cs(5)
where C
s
indicates the channel capacity of the s-th snapshot and Sis the number of
snapshots. The input signal-to-noise ratio (SNR), defined as the SNR for each incident wave
when a theoretical isotropic antenna is used for receiving the incident wave, is set to 30 dB.
Therefore, the SNR is determined only by the received power of the isotropic antenna and
is not depended on the output power of the actual BS or the network analyzer used in the
fading emulator. However, since an isotropic antenna does not exist, the received power
measured using other antennas must be compensated. In this paper, the power received by
an isotropic antenna REF is calculated as follows [15]:
REF =
Eh|S21|2i
Gd
(6)
where
Eh|S21|2i
indicates the average received power of the half-wavelength dipole an-
tenna, placed at the center of the fading emulator, measured using the network analyzer.
G
d
is the maximum radiation gain of half-wavelength dipole antenna in the horizontal
plane, i.e., 2.15 dBi. Therefore, the SNR is determined by
SN R =
REF
N(7)
where Nis the power of the noise.
Sensors 2022, 22, 1240 11 of 12
in the fading emulator. However, since an isotropic antenna does not exist, the received
power measured using other antennas must be compensated. In this paper, the power
received by an isotropic antenna REF is calculated as follows [15]:
2
21
d
ES
REF G
= (6)
where 2
21
ES
indicates the average received power of the half-wavelength dipole an-
tenna, placed at the center of the fading emulator, measured using the network analyzer.
Gd is the maximum radiation gain of half-wavelength dipole antenna in the horizontal
plane, i.e., 2.15 dBi. Therefore, the SNR is determined by
R
EF
SNR N
= (7)
where N is the power of the noise.
As shown in Figure 8, the average channel capacity increases with increasing Δφ.
These results can be understood from Figure 7b, because the channel capacity is calculated
using the eigenvalues of the channel matrix [7]. Moreover, the channel capacity measured
at Δφ = 5.1° achieves 97% of the analytical outcome; indicating that the observed result
corresponds to the simulation value. The channel capacity of about 450 bits/s/Hz at an
SNR of 30 dB, which is equivalent to 45 Gbps with a bandwidth of 100 MHz, is fully sat-
isfied, which is one of the most important performance goals of 5G mobile communication
[1]. It is concluded from these results that OTA testing incorporating the proposed method
is a valid approach for obtaining a full-rank channel matrix for a massive MIMO system.
Figure 8. CDF characteristics of a system with 64 × 64 MIMO channel capacity.
4. Conclusions
This paper presents an OTA evaluation method in which a full-rank channel matrix
is created for a massive MIMO MS antenna utilizing a fading emulator with a small num-
ber of scatterers. The massive MIMO MS antenna is placed at the center of a turntable
which is rotated; the total number of scatterers can be determined by controlling the rota-
tion of the massive MIMO antenna. The experimental results reveal that a full-rank chan-
nel matrix for a massive MIMO antenna system can be obtained embodying the proposed
method. This is a valuable tool for assessing the high MIMO channel capacity of a massive
MIMO antenna.
Future work may include verification of the proposed method for the cluster propa-
gation environment assumed in 5G mobile communication systems.
050 100 150 200 250 300 350 400 450 500
0
10
20
30
40
50
60
70
80
90
100
Channel Capacity [bits/s/Hz]
Cumulative Percentage [%]
206.7 321.2 416.8 463.8
477.9
SNR = 30 dB
f= 5 GHz
Previous
Δ
ϕ
= 1°
Δ
ϕ
= 3°
Δ
ϕ
= 5.1°
Monte Carlo
97%
Figure 8. CDF characteristics of a system with 64 ×64 MIMO channel capacity.
As shown in Figure 8, the average channel capacity increases with increasing
∆ϕ
.
These results can be understood from Figure 7b, because the channel capacity is calculated
using the eigenvalues of the channel matrix [
7
]. Moreover, the channel capacity measured
at
∆ϕ
= 5.1
◦
achieves 97% of the analytical outcome; indicating that the observed result
corresponds to the simulation value. The channel capacity of about 450 bits/s/Hz at an SNR
of 30 dB, which is equivalent to 45 Gbps with a bandwidth of 100 MHz, is fully satisfied,
which is one of the most important performance goals of 5G mobile communication [
1
]. It
Sensors 2022,22, 1240 11 of 12
is concluded from these results that OTA testing incorporating the proposed method is a
valid approach for obtaining a full-rank channel matrix for a massive MIMO system.
4. Conclusions
This paper presents an OTA evaluation method in which a full-rank channel matrix is
created for a massive MIMO MS antenna utilizing a fading emulator with a small number
of scatterers. The massive MIMO MS antenna is placed at the center of a turntable which is
rotated; the total number of scatterers can be determined by controlling the rotation of the
massive MIMO antenna. The experimental results reveal that a full-rank channel matrix for
a massive MIMO antenna system can be obtained embodying the proposed method. This is
a valuable tool for assessing the high MIMO channel capacity of a massive MIMO antenna.
Future work may include verification of the proposed method for the cluster propaga-
tion environment assumed in 5G mobile communication systems.
Funding: This research received no external funding.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: Not applicable.
Conflicts of Interest: The author declares no conflict of interest.
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Available via license: CC BY 4.0
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