Diagnosis of subarray‐structured base station antennas in a compact setup based on solving linear equations

Abstract

Since the total number of the antenna elements can be up to hundreds in a massive multiple‐input multiple‐output (MIMO) system, subarray‐structured base station (BS) array configurations are widely adopted to achieve a good cell coverage and to reduce the required number of radio frequency chains at the same time. It is crucial for any BS product to ensure that the antenna elements perform correctly as expected. Therefore, the necessity of array diagnosis is evident, especially for large BS arrays. Furthermore, it is essential that the diagnosis can be achieved in a compact and cost‐effective setup with high measurement efficiency (i.e. only a few measurement samples are required). The principle of the diagnosis method presented in this article is to obtain the S‐parameters between the subarrays and the probe via solving linear equations. In the simulation, a BS array composed of 16 subarrays with each containing 3 elements is used to validate the diagnosis method at 3.5 GHz. An array composed of 4 subarrays with each containing 3 elements was used in the measurements to verify the diagnosis method with two different phase tuning matrices at 3 GHz. Successful diagnosis results have been achieved in both the simulations and the measurements.

Full text

Received: 11 November 2022
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Revised: 26 June 2023
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Accepted: 1 July 2023
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IET Microwaves, Antennas & Propagation
DOI: 10.1049/mia2.12390
ORIGINAL RESEARCH
Diagnosis of subarray‐structured base station antennas in a
compact setup based on solving linear equations
Mengting Li
1
|Fengchun Zhang
1
|Wei Fan
2
1
Antennas Propagation and Millimetre‐wave Systems
Section, Aalborg University, Aalborg, Denmark
2
National Mobile Communications Research
Laboratory, School of Information Science and
Engineering, Southeast University, Nanjing, China
Correspondence
Wei Fan.
Email: fwlovethisworld@gmail.com
Funding information
European Partnership on Metrology MEWS, Grant/
Award Number: 21NRM03
Abstract
Since the total number of the antenna elements can be up to hundreds in a massive
multiple‐input multiple‐output (MIMO) system, subarray‐structured base station (BS)
array congurations are widely adopted to achieve a good cell coverage and to reduce the
required number of radio frequency chains at the same time. It is crucial for any BS
product to ensure that the antenna elements perform correctly as expected. Therefore,
the necessity of array diagnosis is evident, especially for large BS arrays. Furthermore, it is
essential that the diagnosis can be achieved in a compact and cost‐effective setup with
high measurement efciency (i.e. only a few measurement samples are required). The
principle of the diagnosis method presented in this article is to obtain the S‐parameters
between the subarrays and the probe via solving linear equations. In the simulation, a BS
array composed of 16 subarrays with each containing 3 elements is used to validate the
diagnosis method at 3.5 GHz. An array composed of 4 subarrays with each containing 3
elements was used in the measurements to verify the diagnosis method with two different
phase tuning matrices at 3 GHz. Successful diagnosis results have been achieved in both
the simulations and the measurements.
KEYWORDS
antenna arrays, antenna testing, MIMO systems
1
|
INTRODUCTION
Massive multiple‐input multiple‐output (MIMO) equipped
with a great number of antenna elements is one of the key
technologies in the fth generation (5G) communication sys-
tem and will continue to play a vital role in the future
communication system [1]. The massive MIMO system could
typically have up to hundreds of antennas in one base station
(BS) [2, 3]. However, the cost and the power consumption
caused by the radio frequency (RF) chains connected to each
antenna element become extremely high as the array size be-
comes larger. A good solution to this problem is to divide the
whole array into several subarrays and each subarray is con-
nected to one RF chain [4]. This subarray‐structured BS an-
tenna array can achieve good cell coverage for different
scenarios by wisely selecting the subarray conguration and
implementing the beamforming technique [5]. However, the
prerequisite for achieving high performance of the massive
MIMO system is that every antenna element should work
properly as expected. Faulty antenna elements, that is, antennas
which cannot radiate as normal ones due to the disconnection
or the damaged antenna structure, could have signicant ef-
fects on the array performance in terms of beam steering ac-
curacy, nulling operation etc. Thus, there is no doubt that array
diagnosis is a necessary step before BS products are put into
use in the real world.
It is non‐trivial to achieve array diagnosis for large‐scale
arrays with subarray‐structured conguration. Firstly, the
subarray‐structured BS antennas are designed to provide high
antenna gain and exible beamforming capability which typi-
cally contain more antenna elements than the common BS
antennas, resulting in extremely large array dimensions and
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is
properly cited.
© 2023 The Authors. IET Microwaves, Antennas & Propagation published by John Wiley & Sons Ltd on behalf of The Institution of Engineering and Technology.
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IET Microw. Antennas Propag. 2023;17:920–930. wileyonlinelibrary.com/journal/mia2

far‐eld distance. Therefore, it is crucial that the diagnosis of
subarray‐structured BS antennas can be conducted in the near‐
eld of the array. Secondly, a subarray composed of several
antenna elements is considered as one radiation unit, which
provides no access to the individual antenna element. The el-
ements within one subarray work as a whole with the same
excitation settings. Finally, it is preferred that the diagnosis
method does not require a dedicated measurement environ-
ment. That is, the measurement campaigns could be conducted
in a typical indoor scenario with a compact setup, for example,
an indoor laboratory environment with possible scatterings
from surroundings. This requirement is essential for cost
saving of massive BS testing in production testing environ-
ments since a dedicated measurement scenario such as
anechoic chamber will signicantly increase the measurement
complexity and the cost.
In the state of the arts, many researchers made contribu-
tions on solving the array diagnosis problem. Array diagnosis
methods based on eld transformation using near‐eld mea-
surement data have been proposed in refs [6, 7]. The principle
is to use the eld data sampled on a planar or cylindrical
surface to obtain the far‐eld pattern of the impaired array and
reconstruct the eld distribution on the array aperture. A large
number of near‐eld measurement samples with around 0.5
wavelength spacing are required to achieve good reconstruc-
tion accuracy, leading to intolerable measurement time for large
arrays. For arrays with more complex geometries, matrix
methods [8, 9] have been implemented to detect the failures in
the array by solving an ill‐conditioned matrix inverse problem
using the Landweberone or pseudo‐inversion strategies.
However, matrix methods also require a large number of
samples to ensure the sufcient accuracy. To shorten the
measurement time, several techniques are investigated to
reduce the required measurement samples. Genetic algorithms
have been employed in refs [10, 11] to detect the faulty ele-
ments based on a small number of amplitude‐only array
pattern samples although the computation complexity is rela-
tively high. Recently, the compressed sensing (CS)‐based
techniques [12–15] have been successfully adopted in the array
diagnosis with much reduced measurement samples in the
near‐eld or far‐eld of the array. Nevertheless, an important
requirement of using CS is the signal sparsity, meaning that the
number of the failed elements should be much smaller than the
total antenna number.
In ref. [16], different phase tuning is applied on the array
elements and the excitations of the elements are calculated by
solving linear equations. A single probe is employed to receive
the complex array signals in the far‐eld of the antenna under
test (AUT). Based on the method proposed in ref. [16], the
estimation errors have been further reduced by introducing
more phase tuning settings in ref. [17]. To date, only a few re-
searchers focus on the diagnosis of subarray‐structured BS
antennas. In ref. [18], the detection of failure elements within a
subarray is achieved by comparing the received power level
between the faulty‐free subarray and subarray with faulty ele-
ments based on solving linear equations. However, some key
questions, such as the requirements on the probes, the selection
of the phase tuning matrix, and the error sources are not well
answered.
In this paper, the diagnosis of subarray‐structured BS an-
tennas is achieved by tuning phase shift values of different
subarrays and solving the linear equations based on the com-
plex array signals received by the probes. Compared with the
work in ref. [18], two different kinds of phase tuning matrices
and more discussions about the probes, error sources etc. are
provided. Moreover, the method is extensively validated by
numerical simulations with a BS array containing 16 subarrays
with each composed of 3 elements as well as measurements
with an array containing 4 subarrays with each composed of 3
elements. In the following, the signal model of the diagnosis
system for subarray‐structured BS antennas is given in Sec-
tion 2. The diagnosis method is detailed in Section 3. The
effectiveness of the method is evaluated and veried with
numerical simulations and measurements provided in Sec-
tions 4and 5respectively. Finally, a conclusion is drawn in
Section 6.
2
|
SIGNAL MODEL
The diagram of the diagnosis system for a subarray‐structured
BS antenna is shown in Figure 1. Note that the proposed
diagnosis method is not limited to a specic array congura-
tion. Assume the AUT consists of Nsubarrays with Pantenna
elements included in one subarray. Nphase shifters are
employed to adjust the phase shift values fed into the corre-
sponding subarrays. Assume that Qprobes and Msets of pre‐
designed phase shift settings are required in the diagnosis
system. The requirements on the number and the location of
the probes will be discussed later in Section 3.2. The signal
model can be written as
Φ⋅X¼Y;ð1Þ
FIGURE 1 Diagram of the diagnosis system for subarray‐structured
BS antennas. BS, base station.
LI ET AL.
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Φ¼
ejϕ1;1…ejϕ1;N
⋮ ⋱ ⋮
ejϕM;1…ejϕM;N
2
43
5;ð2Þ
X¼
x1;1…x1;Q
⋮ ⋱ ⋮
xN;1…xN;Q
2
43
5;ð3Þ
Y¼
y1;1…y1;Q
⋮ ⋱ ⋮
yM;1…yM;Q
2
43
5;ð4Þ
where the matrices Φ∈CMN,X∈CNQand Y∈CMQare
specically explained in the following:
Matrix Φ={ejϕm;n} is the phase tuning matrix, which
decides the phase shift assigned to each subarray. Element
ϕ
m,n
denotes the phase shift value fed into the nth
subarray for the mth set of pre‐designed phase shift
setting, as illustrated in Figure 1(n∈[1, N], m∈[1, M]).
The design of the phase tuning matrix will be discussed in
Section 3.3.
Matrix X={x
n,q
} is the complex signal received by the qth
probe from the nth subarray. The working status of the
elements within the subarrays will be revealed by the
received signal powers of the selected probes, as detailed in
Section 3.
Matrix Y={y
m,q
} is the array response received by the qth
probe for mth set of phase shift settings. It can be recorded
as the complex transmission coefcient S
21
using a vector
network analyser (VNA) in practical measurements.
3
|
DIAGNOSIS METHOD
The basic principle of our diagnosis method is to solve (1) and
compare the received signal powers obtained from matrix Xto
reveal the working status of the antenna elements in the sub-
arrays. The detailed diagnosis procedures are summarised
below:
1) Determine the required number of the probes and loca-
tions according to the AUT conguration and the available
laboratory conditions;
2) Design the phase tuning matrix Φwhich contains the
values set in the phase shifters;
3) Set the value of the phase shifters according to the rst row
of the phase tuning matrix and employ VNA to record the
array response received by the individual probes in turns;
4) Repeat the step 3) for Msets of phase shift settings and
obtain in total MQarray responses to construct the
matrix Y;
5) Solve the linear equations and analyse the data to achieve
faulty element(s) detection.
3.1
|
Faulty detection
With the measured array response Yand the known pre‐
designed phase tuning matrix Φ,Xcan be solved by con-
ducting an inverse operation on matrix Φ:
X¼Φ−1⋅Y:ð5Þ
In the following, we will explain in detail how the relative
signal power of x
n,q
reveals the working status of the antenna
elements within the subarrays.
We rst derive the complex signal received by a probe from
one antenna element in the subarray. Since the probe is typi-
cally placed in the far‐eld of the subarray, the view angle and
distance from a specic probe to any antenna element within
the subarray are assumed to be the same. The antenna element
patterns in an array are very similar in their main beam di-
rections, thus the element patterns can be approximately
considered as the same in this case. Then, the complex signal
received by the qth probe from the pth element in the nth
subarray, that is, wðqÞ
n;pcan be derived as
wðqÞ
n;p¼cn;pe0θEle
n;q;ϕEle
n;q
 eqθPro
n;q;ϕPro
n;q
 λe−jkdn;q
4πdn;q;ð6Þ
where c
n,p
represents the complex excitation for the pth element
in the nth subarray. λis the wavelength and k¼2π
λis the angular
wavenumber in free space at the working frequency.
e0θEle
n;q;ϕEle
n;q
 and eqθPro
n;q;ϕPro
n;q
 are antenna eld patterns for
the antenna element within the nth subarray (in the direction of
the qth probe, that is, θEle
n;q;ϕEle
n;q
 ) and the qth probe antenna
(in the direction of the nth subarray, that is, θPro
n;q;ϕPro
n;q
 )
respectively. d
n,q
denotes the distance between the qth probe and
the nth subarray. The received signal by the qth probe from the
nth subarray x
n,q
is the superposition of signals from all the
subarray elements, which can be obtained by
xn;q¼X
P
p¼1
wðqÞ
n;p
¼e0θEle
n;q;ϕEle
n;q
 eqθPro
n;q;ϕPro
n;q
 λe−jkdn;q
4πdn;qX
P
p¼1
cn;p;
¼an;qX
P
p¼1
cn;p;
ð7Þ
where a
n,q
describes the transmission coefcient between the
qth probe and any antenna element in the nth subarray. For a
faulty‐free antenna array, the array is uniformly excited,
meaning that the complex excitations for all the array elements
are the same (which can be denoted as I
0
). The excitation for
the faulty antenna element is close to 0 since the connection is
disrupted whereas the excitations for elements which work
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LI ET AL.

correctly in the subarray remain the same. Note that the power
delivered to the faulty element(s) will not be radiated anymore,
resulting in power loss in the antenna system.
Assume all the elements in the nth
1subarray work properly
whereas the nth
2subarray has ifaulty elements. xn1;q1and xn2;q2
are the received signals from the solved matrix X.xn;q
rep-
resents the amplitude of the complex signal. Then, the relative
received power level can be obtained by
D½dB ¼ −10log10
xn2;q2
2
xn1;q1
2
!
¼−10log10
P−ið Þ2jI0j2an2;q2
2
P2jI0j2an1;q1
2
!
≈ −10log10
P−i
P
 2
:
ð8Þ
The relative received power level can directly show whether
there are failed antenna elements in a specic subarray when
jan2;q2j
jan1;q1japproximates 1. The condition that an2;q2
j j
an1;q1
j j≈1 can be
achieved by properly selecting the number and the locations of
the probes, which will be discussed later.
By comparing the relative received power levels of the sub-
arrays dened in Equation (7), the location of the faulty subarray
and the number of the faulty element(s) within this subarray can
be detected. For example, assuming one subarray is composed of
3 antenna elements, Daround 3.5 dB indicates there is one faulty
element within the subarray. If the whole subarray is faulty, the
value of Dbecomes an innite number in principle. The
detection becomes easier as the value of Dincreases. Therefore,
the detection of the one failure element case is the most chal-
lenging task. Detecting a single faulty element within a subarray
composed of more elements would be more difcult since the
deviation of the received power level will be insufcient or
marginal. Besides the failure caused by the antenna element itself,
loose cable connections, bad performance of the amplier or
phase shifter connected to the subarray or antenna element
could also be detected by the proposed method. However, we
cannot know the specic locations of the failures. This might be
further detected by conducting additional RF testings (i.e.
measuring the return loss or voltage standing wave ratio [VSWR]
etc.) at different points of the RF path which contains the
detected faulty subarray.
3.2
|
The probe number and location
The determination of the number and the locations of the
probes are critical for the diagnosis method. As mentioned
before, the jan2;q2j
jan1;q1jshould be close to 1 for achieving accurate
diagnosis results. When one probe is employed in the diagnosis
system, the probe should be typically placed in the far‐eld or
at least mid‐eld of the AUT to full the condition. It is true
that a large measurement distance could denitely reduce the
unexpected effects caused by the differences in pathloss and
view angles between the probe and different subarrays. How-
ever, it requires a demanding measurement environment for
large‐scale BS arrays. To tackle this issue, a multi‐probe strat-
egy, that is, with the probes properly distributed around the
boresight directions of different subarrays, can be employed to
make jan2;q2j
jan1;q1jclose to 1. The multi‐probe strategy is important
for ensuring that the relative power level of the received signals
could correctly reveal the working status of the antenna ele-
ments in the subarrays, especially for measurements with a very
short distance between the AUT and the probes.
For AUTs with different congurations, the required probe
array conguration might be different. The employment of a
probe wall could be a possible solution. A similar strategy has
been widely used in performance testing of MIMO devices [3,
19]. The basic idea is to constitute a probe wall by introducing
sufcient probe antennas with a uniform distribution. For a
specic AUT, the required probe conguration can be
approximated by activating the selected probes on the probe
wall whereas the other parts of the probe wall can be covered
by absorbers to reduce the reections. Another possible so-
lution is to achieve a virtual probe array with the help of a
mechanical positioner. However, long measurement time might
be needed due to the slow mechanical movement, especially
for the virtual probe array with a large size.
To summarise, the required number and the arrangement
of probes should be properly designed according to the AUT
conguration. The criterion is that the errors introduced by the
differences in the pathloss and the view angles between the
probes and the subarrays of AUT should be negligible. For
different AUTs, the required probe array can be practically
achieved by employing a probe wall or virtual probe array.
3.3
|
Phase tuning matrix
Since Xis solved via taking inversion of matrix Φas shown in
Equation (5), we need to design the phase tuning matrix. Two
different ways of generating matrix Φare given in the
following. For the rst one, a 180° phase shift is assigned to
one subarray whereas 0° phase shift is set to the others for one
measurement. The phase tuning procedure is completed when
the phase of every subarray has been inverted. The phase
tuning matrix can be expressed as
Φ¼
1 1 1 … 1
−1 1 1 … 1
1−1 1 … 1
⋮ ⋮ ⋮ ⋱ ⋮
1 1 1 … −1
2
6
6
6
6
4
3
7
7
7
7
5ð9Þ
The other way is to generate the phase shift setting matrix
based on the Hadamard matrix. An example of Φfor AUT
composed of 4 subarrays can be given as
LI ET AL.
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Φ¼
1 1 1 1
1−1 1 −1
11−1−1
1−1−1 1
2
6
6
43
7
7
5:ð10Þ
As can be seen in Equations (8) and (9), both methods
require only two phase states, that is, 0° and 180°, which can be
achieved by 1‐bit phase shifters. The rst ‘inverse’ way for
generating Φrequires M=Nþ1 sets of phase shift settings
whereas M=Nsettings are required for the Hadamard matrix‐
based method. Therefore, the measurement time will be similar
for these two methods. Nevertheless, there are also differences
between these two methods. The rst ‘inverse’ method does
not have a limitation on the number of the subarrays. However,
the second method can only be directly implemented when the
total number of the subarrays Nfulls the condition: N,N/12,
or N/20 is a power of 2.
A condition number for a matrix (Φin our discussion)
gives an indication of the accuracy of the results from matrix
inversion and the associated linear equation solution. The
condition number can be considered as an amplication factor
of the noise/error in the system. Its minimum value is 1,
representing no error amplication in the system. The extreme
case is that Φis singular (i.e. with an innite condition num-
ber), in which case the linear equation has no unique solution.
Thus, it is of key importance to consider the condition number
when designing the phase tuning matrix Φsince measurement
uncertainties (limited phase tuning accuracy, scattering in the
environments etc.) are inevitable, resulting in possible errors in
the measured data. If the condition number of matrix Φis
large, we cannot guarantee valid solutions of the linear equa-
tions with practical measurement data. The condition number
of any Hadamard matrix is 1 due to the orthogonality between
any two columns of the matrix. The condition number of the
matrix Φgenerated by the inverse method for AUT with
different number of subarrays is shown in Figure 2. It becomes
larger as the number of the subarrays increases. It can be
observed that the condition number approximates N/2, that is,
half of the number of the subarray and exceeds 10 when the
total number of the subarrays is larger than 20. Therefore, the
Hadamard matrix‐based method is preferred especially for
AUT with a large number of subarrays.
3.4
|
Error sources
In addition to the errors caused by the directive antenna pat-
terns as well as the deviations of the pathloss (from the
selected probe to the different antenna elements) discussed in
Section 3.2, there are also other error sources in a practical
measurement. Phase shifters will be employed in practical
measurements to implement phase tuning of each subarray.
The uncertainties in terms of both amplitude and phase exist in
practical phase shifters. The use of high performance phase
shifters with small uncertainties would be benecial for
reducing these errors. Besides, the complex array signals
received by the probes are measured by S
21
parameters using
VNA in practical measurements. The scatterings from the
surrounding environments and the mutual couplings within the
AUT and probe array will also contribute to the measured S
21
,
which can be considered as noise components. The effects of
the noise will be discussed in Section 4.
4
|
SIMULATIONS
The AUT used in the numerical simulation is composed of 16
subarrays with 3 antenna elements in each subarray. The BS
antenna element is a 45° polarised cross dipole antenna
working from 3.2 to 3.9 GHz with 80° 5° HPBW in hori-
zontal and vertical planes. More detailed information can be
referred to ref. [20]. Only the simulated results at 3.5 GHz for
one polarisation are provided for simplicity. The radiation
patterns of the total 48 elements at 3.5 GHz are simulated by
CST Microwave Studio, as shown in Figure 3. In this simula-
tion, one additional BS antenna is used as the probe and it is
placed in the boresight of the AUT array with a distance of
0.5 m. The complex array signals recorded by the probe are
calculated using the simulated antenna patterns and Friss
transmission equation [21].
The locations of the probe and AUT elements can be seen
in Figure 4. The boresight direction of the AUT elements is
FIGURE 2 Condition number of matrix Φ using the ‘inverse’ method.
FIGURE 3 The model of the BS arrays in CST Microwave Studio. BS,
base station.
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LI ET AL.

along þx‐axis whereas the probe radiates towards the inverse
direction. The element spacing in the AUT array is 0.5 λalong
the z‐axis and 2
3λalong the y‐axis respectively. Since the dif-
ferences of view angles from the probe to different subarrays
are small in this case, multiple probes are not necessary in this
simulation setup. The amplitude and phase uncertainties
caused by phase shifters are set within the range of 0.2 dB
and 2° respectively. Moreover, the noise effects on the
measured complex array signals are also investigated in the
simulations. The phase shift setting matrix Φis designed based
on a Hadamard matrix with 16 sets of phase shift settings in
total. Two faulty cases are considered here for illustrations, that
is, the faulty subarray and faulty element cases. All the elements
in one subarray fail for the faulty subarray case whereas only
one antenna element fails for the faulty element case.
The location of the faulty subarray is marked in red as
shown in Figure 5a and the diagnosis results without
FIGURE 4 The locations of the probe and AUT used in the
simulation. AUT, antenna under test.
FIGURE 5 (a) The location of the faulty subarray and the estimated signal powers of different subarrays (b) without noise effects, (c) with 30 dB SNR, and
(d) with 20 dB SNR respectively. SNR, signal to noise ratio.
LI ET AL.
-
925

considering noise effects, with 30 dB signal to noise ratio (SNR)
and with 20 dB SNR are plotted in Figure 5b–d respectively. As
discussed in Section 3.1, the power of the faulty subarray should
be innitely low theoretically. However, the amplitude of the
signal from the faulty subarray obtained by solving linear
equations cannot be zero with the existence of phase shifter
implementation errors or/and the noise effects. The deviations
of the signal powers of the normal subarrays are within
0.25 dB, 1.0 dB and 1.8 dB for diagnosis systems with no
noise, 30 dB SNR and 20 dB SNR respectively. It can be
observed the power difference between the faulty subarray and
the normal subarrays decreases from around 36.5 dB to around
27 dB when noise effects are considered. Nevertheless, the
faulty subarray can be easily recognised even with 20 dB SNR.
Note that with a compact measurement setup in practice, high
SNR can typically be achieved.
For the second case, the location of the faulty element is
marked in red in Figure 6. The value of parameter Dis 3.5 dB
when one element is faulty in a subarray containing 3 elements.
Therefore, the estimated signal power of the faulty subarray
with one failed element should be 3.5 dB lower than the power
of the normal subarrays in the ideal case. The estimated signal
powers of normal subarrays without noise effects are within the
range from 9.4 to 11.2 dB whereas the signal power of the
subarray with one faulty element is 5.6 dB as shown in Figure 6a.
Similar diagnosis results can be seen in Figure 6b with a bit larger
deviation in the received signal powers of normal subarrays. The
faulty element can be clearly detected in Figure 6b,c due to
sufcient power difference between the normal subarrays and
the subarray with one faulty element. However, it can be found
in Figure 6d that the deviation of the signal powers between
different normal subarrays reaches more than 3 dB with 20 dB
FIGURE 6 (a) The location of the faulty element in the array and the estimated signal powers of different subarrays (b) without noise effects, (c) with 30 dB
SNR, and (d) with 20 dB SNR respectively. SNR, signal to noise ratio.
926
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SNR making the faulty element detection more difcult
compared to the previous two results. The faulty element case is
more challenging than the faulty array case since the value of
parameter Dis much smaller. However, successful diagnosis can
still be achieved when the SNR is higher than 20 dB.
5
|
MEASUREMENTS
The proposed diagnosis method was also experimentally vali-
dated using an AUT composed of 4 subarrays with each sub-
array containing 3 elements. The measurements were
conducted in a typical indoor laboratory environment at Aal-
borg University.
5.1
|
Measurement system
The schematic of the measurement system and a photo of the
measurement scenario are given in Figures 7and 8a respectively.
The AUT used in the measurements is an array consisting of 4
subarrays with each subarray containing 3 elements. The AUT is
selected from a 3 16 antenna array, as marked in Figure 8b.
Either one or three probes are used in the measurements. The
element spacing is 5 and 10 cm along the horizontal direction and
vertical direction respectively. The digital phase shifters are
controlled by a laptop. For each measurement, we assign the
designed phase shift values to the phase shifters according to the
phase tuning matrix Φ. The specications of the components of
our measurement system are detailed in Table 1. The complex
array signals received by the probe are measured as S
21
parameter
at 3 GHz for each measurement.
5.2
|
Measurement campaigns
The effectiveness of the diagnosis method is validated by two
different groups of measurements. In the rst group of
measurements, the phase tuning matrix Φis generated by both
the ‘inverse’ and Hadamard matrix‐based methods. The mea-
surement distance is 50 cm and only a single probe placed in the
boresight of the AUT is implemented. The purpose is to validate
the array diagnosis method using the Φdetermined by both
FIGURE 8 Photos of the (a) diagnosis system and (b) AUT. AUT,
antenna under test.
TABLE 1Specications of the components of the measurement
system.
System component Specications
Antenna Type: Horn antenna of Vivaldi type
Operating frequency: 2.5–4 GHz
Polarisation: Vertical
Gain: 9 dBi at 3 GHz
HPBW: 54° in the horizontal plane
Phase shifters Phase adjustment range: 0–360°
Phase adjustment resolution: 1°
Phase adjustment accuracy: 2.5°
Power splitter Operating frequency: 0.25–6 GHz
Phase unbalance (max.): 6°
Amplitude unbalance (max.): 0.6 dB
FIGURE 7 The schematic of the measurement system.
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‘inverse’ and Hadamard matrix‐based approaches. Both the
faulty subarray and the faulty element cases are considered here.
The second group of measurements aims to investigate the
diagnosis accuracy in a short measurement distance with
multiple probes employed in the system. Therefore, the mea-
surement distance is set as 10 cm and three probes are placed
towards AUT, as shown in Figure 7. Only the faulty element
case is considered in the second group of measurements since
this faulty type is more challenging and requires higher diag-
nosis accuracy. The phase tuning matrix Φis generated based
on the Hadamard matrix.
5.3
|
Measurement results
Figure 9depicts the diagnosis results of the rst group of
measurements. The normalised signal powers obtained by us-
ing ‘inverse’ and Hadamard matrix‐based methods when sub-
array 1 is faulty are shown in Figure 9a. The powers of the
subarray 1 obtained using ‘inverse’ and Hadamard matrix‐
based method are around 35 and 27 dB lower than the
powers of the other subarrays respectively. Better agreement
between these two methods can be seen in Figure 9b when
subarray 2 is faulty. As discussed before, the signal power of
the faulty subarray cannot be zero due to the existence of
noise. The noise level and the measurement uncertainties will
both have an effect on the received signal power of the faulty
subarray. Nevertheless, it is obvious that two faulty subarray
cases are both successfully detected. The diagnosis results for
two faulty element cases, that is, one faulty element in subarray
1 and one faulty element in subarray 2 are given in Figure 9c,
drespectively. The deviation of the signal powers between the
normal subarrays is within 0.8 and 1 dB for ‘inverse’ and
Hadamard matrix‐based methods respectively. In principle, the
signal power of the faulty subarray with one failed element
should be 3.5 dB lower than the other normal subarrays. The
relative signal power of different subarrays shown in Figure 9d
are closer to the theoretical value than the results shown in
Figure 9c. For diagnosis using Φgenerated by the Hadamard
matrix, the errors introduced by the RF components used in
the system would accumulate on the rst subarray, resulting
more errors than the other subarrays [17]. However, the faulty
element can be clearly detected in Figure 9c,d using both the
‘inverse’ and Hadamard matrix‐based methods.
FIGURE 9 The diagnosis results for the cases that (a) subarray 1 is faulty, (b) subarray 2 is faulty, (c) one element in subarray 1 is faulty and (d) one element
in subarray 2 is faulty respectively.
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Multiple probes strategies are mentioned in Section 3.2 for
improving the diagnosis accuracy when the measurement dis-
tance is constrained. In the second group of measurements, the
measurement distance is reduced to 10 cm. In this setup, the
differences of the view angles from the probe to different
subarrays are not negligible. Therefore, three probes are
employed to reduce the estimation errors. The diagnosis results
with a single probe and multiple probes for the faulty element
case (one failed element in subarray 2) are compared in
Figure 10. The deviation of the signal powers between the
normal subarrays is up to 3 dB with the single probe setup. The
signal power of subarray 1 is around 3 dB lower than the power
of subarray 3, which might lead to false detection. However, the
deviation of the signal powers between the normal subarrays is
reduced to 1.1 dB when three probes are used. Thus, subarray 2
with a single faulty element can be clearly recognised.
6
|
CONCLUSION
An array diagnosis method based on solving linear equations
for subarray‐structured BS antennas in a compact and non‐
anechoic scenario is comprehensively presented and its
effectiveness has been validated by both the numerical simu-
lations with a BS array composed of 16 subarrays and mea-
surements using an array composed of 4 subarrays. The probe
number and locations are rstly determined by the AUT
conguration and the available laboratory conditions. Two
different ways of generating the phase tuning matrix Φ are
provided with their respective pros and cons discussed. The
detection of the faulty elements in the AUT is achieved by
comparing the relative received signal powers from different
subarrays with the assistance of a dened parameter D. The
simulation results demonstrate that the diagnosis for the faulty
subarray (all the elements in one subarray are faulty) and faulty
element (only one element is faulty in one subarray) cases can
be clearly achieved when the SNR is higher than 20 dB. Two
groups of measurements were conducted to further verify the
diagnosis method. In the rst group of measurements, the
diagnosis results using the phase shift setting matrix generated
by the ‘inverse’ and Hadamard matrix‐based methods are
provided and successful detection can be achieved by both
‘inverse’ and Hadamard matrix‐based methods. In the second
group of measurements, multiple probes were employed to
improve the diagnosis accuracy in a short measurement dis-
tance. The power deviation between the normal subarrays is
up to 3 dB with a single probe and reduced to 1.1 dB with
three probes.
AUTHOR CONTRIBUTIONS
Mengting Li: Data curation; investigation; methodology;
validation; writing – original draft. Fengchun Zhang: Meth-
odology; validation; writing – review & editing. Wei Fan:
Conceptualisation; supervision; writing – review & editing.
ACKNOWLEDGEMENTS
European Partnership on Metrology MEWS (21NRM03).
CONFLICT OF INTEREST STATEMENT
The authors declare that there is no conict of interest.
DATA AVAILABILITY STATEMENT
The data that support the ndings of this study are available
from the corresponding author upon reasonable request.
ORCID
Mengting Li
https://orcid.org/0000-0002-0144-870X
Wei Fan https://orcid.org/0000-0002-9835-4485
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How to cite this article: Li, M., Zhang, F., Fan, W.:
Diagnosis of subarray‐structured base station antennas
in a compact setup based on solving linear equations.
IET Microw. Antennas Propag. 17(12), 920–930 (2023).
https://doi.org/10.1049/mia2.12390
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