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978-1-5386-3498-1/18/$31.00 © 2018 IEEE
2018 Moscow Workshop on Electronic and Networking Technologies (MWENT)
Abstract— WiFi positioning techniques based on signal angle-
of-arrival measure ments have good accuracy and are promising.
In such systems, several antennas receive the signal and an angle-
of-arrival is computed by comparison of signal phases. Existing
algorithms use a simple geometric angle-to-phase model:
geometric ray paths cause corresponding phase differences and
the differences are a trigonometric function of the angle-of-
arrival. The model considers the receiver antennas as
independent. However, the assumption is rough for WiFi antenna
systems. Distances between the receiver antennas are small, the
antennas influence to each other. The antennas are coupled.
In this paper, we study the impact of the WiFi antennas
mutual coupling to angle-of-arrival estimations. Electromagnetic
simulations and hardware experiments were performed for this
purpose. Commercial-of-the-shelf modules were used for the
experiments. It is shown by simulations and experiments that the
antenna mutual coupling offsets the angle of arrival estimations
about 5-10 degrees. Considering of the mutual coupling can
reduce angle estimation errors and, as consequence, increase
positioning accuracy.
Index Terms—WiFi, angle of arrival, indoor positioning,
mutual antenna influence.
I. INTRODUCTION
NDOOR positioning is an actual problem for modern location
based services. Any WiFi utilization for this purpose has
many advantages. The standard is widespread and
implemented already in the vast majority of user devices.
The simplest way to determine a user position is to
compare an access point (AP) identification number with a
database. If the device receives the signal, the user is near the
AP. Results of the approach are inaccurate (tens of meters).
The better accuracy can be achieved by special signal
processing of the WiFi signals. Signals parameters (signal-to-
noise ratio, delay [1] and others) are in close dependence on
the user position relatively to APs. Resulting accuracy
depends on a geometric factor value, propagation conditions
and utilized parameters of the signals.
The estimations based on signal strength allow to achieve
about 10 m accuracy under good conditions [2], [3].
This work was supported by the Ministry of Education and Science of the
Russian Federation (project no. 8.9615.2017/BCh)
Ilya V. Korogodin is with National Research University “Moscow Power
Engineering Institure”, Moscow, Russia (e-mail: korogodiniv@gmail.com).
Vladimir V. Dneprov is with National Research University “Moscow
Power Engineering Institure”, Moscow, Russia (e-mail:
vvdneprov@gmail.com).
The next step of the accuracy improvement is angular
measurements based on phase differences. In this case, the
user position is calculated on the basis of mutual angles to
beacons: Angles of Arrival (AoA) or Angles of Departure
(AoD). The mutual angles measurements are formed by a
phase comparison for several spaced antennas.
As it will be shown below, existing algorithms use a
simple geometric angle-to-phase model. In the model, the
phase differences are caused by the difference in the path of
the rays to each antenna (see Fig. 1). The path difference and,
consequently, the phase difference are in proportion to the
trigonometric function of AoA:
() ()
1
,1
sin
m
geom m
c
−
=
ω
ψθ θ
rr , (1)
where
θ
is AoA,
,1geom m
ψ
is the phase difference between the
m-th and the 1-st antennas,
ω
is the carrier frequency, c is
speed of light,
m
r
is the radius vector for the m-th antenna, m
is the antenna index from 1 to M.
The phase difference method achieves up to 10 cm
accuracy [4], [5] under laboratory conditions.
Combinations of positioning methods increase reliability
of results. Commercial solutions from Cisco (Aironet
Hyperlocation) use the WiFi angular approach integrated with
Bluetooth measurements [6], [7]. As result, good resolution
about 1-3 m can be achieved under practice propagation
conditions and it is seems like the best result for widespread
commercial systems.
Angular measurements are basis of such precise WiFi
positioning. Any improvements in angle accuracy improve the
performance, so it is a subject for many contemporary
researches. Let’s observe the relevant articles.
Tzur [8] used the phase differences between two WiFi
antennas to calculate the AoA (just as inverse transform for
phase difference). A commercial of the shelf (COTS) network
interface card (NIC) was used to obtain the phases. Some
improvements concerning hardware inaccuracies were
presented in the work. They achieve an AoA accuracy of 8
degrees under good propagation conditions.
Impact of Antenna Mutual Coupling on WiFi
Positioning and Angle of Arrival Estimation
Ilya V. Korogodin, Vladimir V. Dneprov
I
Fig. 1. The path difference as the sinus function of the AoA.
2018 Moscow Workshop on Electronic and Networking Technologies (MWENT)
SpotFi [9] uses a similar NIC with three antennas. A
modified MUSIC algorithm is applied for AoA calculations
and a multipath rays mitigation. Under line of sight (LoS)
conditions, a median error of 5 degrees is claimed.
The MUSIC multipath mitigation performance increases
for bigger amount of antennas. It is shown by Phaser [10] and
in a paper of Xiong et al [11]. Phaser combines several NICs
to get a five antennas setup. Xiong built a FPGA-based
wireless radio with an eight antennas setup.
Normally APs are equipped with up to three antennas. For
such configuration, Shussel [12] does not find a significant
difference between applying MUSIC and a simple calculation
AoA as inverse function of the phase differences between the
antennas. In their test scenario, they achieve the accuracy with
9 degrees medium error.
There is a common curious peculiarity in the errors graphs
in these articles. The error depends on certain AoA value
significantly. Authors achieved good resolution for low AoA
values (then a LOS is perpendicular to the antennas line). The
AoA estimation has shifts for big angle values.
We have a hypothesis of a systematic shift origin:
The described above simple geometric model is
inaccurate for close located WiFi antennas. A mutual
electromagnetic influence of the antennas to each over and to
AP body distorts phase radiation patterns (RP). It causes
additional errors on the phase-to-angle transform stage.
In the following sections, we perform an electromagnetic
simulation and experiments to check the hypothesis and
decrease angle estimation errors.
II.
E
LECTROMAGNETIC SIMULATION
It is too rough to consider the AP’s antennas as
independent. They influence to each over. The dependence of
the phase difference from AoA is complex; it is different from
the similar function for independent antennas in the geometric
model. It is possible to estimate this offset
EM geom
=−
ψ
εψ ψ
by means of a simulation.
The expected mutual influence degree depends on the
particular antenna system configuration. We chose the
configuration accordingly to the next requirements:
- The antenna system should be similar to ones in described
above research to compare results.
- The antenna system should be similar to usual MIMO AP
antennas.
- The antenna system should be easy representable in
simulation programs.
- The antenna system should be made for mockup.
As result, we considered a simple linear antenna array of 3
elements (see Fig. 2). An electromagnetic model (EM) of the
antenna system was developed into CST Microwave Studio
(see Fig. 3). The model is close to the experimental setup,
which will be described in the relevant section. There is a
ground plane, three dipoles and coaxial cables in the model.
The ground plane is a 15x15 cm perfect electric conductor
plate. The plate simulates the AP body. The antennas are
continued cores of relevant cables. The pin length is
4
λ
.
Their diameter is 1.1 mm. The distance between close pairs is
2
λ
. The dielectric parts of the cables diameter is 3.92 mm.
Braids of the cables have 6 mm diameter and are connected to
the ground plane. There are three ports at a distance of 1 cm
from the plate.
The model is not perfect match to usual 3 dBi WiFi-
dipoles. However, it is easy to implement the antenna system
for real world tests. Besides, the degree of mutual influence
for the modeled antenna is expected similar to the WiFi
dipoles.
Simulation results contain power and phase radiation
patterns for each port. Due to the symmetry of the model
results for the first and the third antennas (ports) are same, so
we should discuss differences between the middle and any
side antenna. Similarly, it suffices to consider phase
differences
,31
EM
ψ
and
,21
EM
ψ
for the third and for the second
antennas with respect to the first one.
Power radiation patterns in the horizontal plane for the vertical
polarization are presented in Fig. 4. The patterns both are not
circular and are not equal. The difference between them
reaches about 2 dB. An irregularity of the side antenna
radiation pattern is about 5 dB.
Fig. 2. SolidWorks antenna model.
Fig. 3. CST Microwave Studio antenna model.
Fig. 4. Power radiation patterns in the horizontal plane for the vertica
l
p
olarization.
2018 Moscow Workshop on Electronic and Networking Technologies (MWENT)
Although the amplitude depends on the direction, this
dependence is weak in comparison with same dependence for
phases. Phase radiation patterns are presented in Fig. 5. The
patterns are significantly different in the horizontal plane. The
difference allows estimating AoA/AoD by means of the phase
comparison. The fact is the basis of all interferometry
approaches.
Let’s compare the phase differences obtained through
simulation and calculated by means of the geometric angle-to-
phase model (1). The phase differences as the function of the
angle in the horizontal plane are presented in Fig. 6.
The CST phase differences functions are close to the
geometric angle-to-phase model (1) of independent antennas.
There is a little offset, up to 10-20 degrees (see Fig. 7).
The offset causes relevant shifts in the AoA calculated on
the basis of the phase differences. The shift is depictured in
Fig. 8.
III.
M
OCKUP
We made a mockup of a WiFi angle determination device to
check the EM results with experiments. The mockup includes
a WiFi signal transmitter (TX), a WiFi receiver (RX) and a
laptop.
Both the TX and the RX are based on COTS Intel 5300
WiFi 802.11n cards. The cards mounted into Lenovo Q180
PCs, controlled by Kubuntu 14.04.
Daniel Halperin has made custom drivers Linux CSI Tool
for the modules [13]. The drivers allow to initiate signal
transmission by TX and to obtain the amplitudes and phases of
subcarriers gotten by RX. The measurements are quantized,
i.e., each of real and imaginary parts is represented using 8
bits. The WiFi cards operate in 5 GHz WiFi spectrum, the
speed rate is 6 Mb/s, and an injection mode is used.
Fig. 5. Phase radiation patterns for the theta-component of the field: a)
antenna 1; b) antenna 2.
Fig. 6. Phase differences for the EM model and for the geometric angle-to-
phase antennas model.
Fig. 7. The offset between the phase differences for EM and geometric
angle-to-phase models.
Fig. 8. The offset in AoA estimations caused by the antenna coupling:
simulation result
Fi
g
. 9. The WiFi receiver with the hand-made antenna s
y
stem.
2018 Moscow Workshop on Electronic and Networking Technologies (MWENT)
Both the TX and RX got a hand-made antenna system (see
Fig. 9). The system is an implementation of the model used for
the electromagnetic simulation above.
IV.
E
XPERIMENTAL RESULTS
The mockup measurements are shifted by delays in the
branches of the receiver front-end. It causes relevant shifts in
phase differences which have to be compensated by any
calibration procedure. We used the procedure described in
[14].
The EM predicts the divergences in phases which cause
errors in resulting AoA estimations. We need an AoA error
estimation methodology to check the prediction. Our
methodology described below.
We placed both the TX and RX on tripods in an open area
to prevent any multipath. RX was mounted through a time-
lapse head (see Fig. 10). The REVO EPH-6 was used as the
head. The head allows to rotate the RX evenly and very slowly
(180 degrees per 15 minutes).
In the beginning of any iteration we align the receiver
antennas and TX to achieve initial AoA of -90 degrees (see
Fig. 11). The laptop initiates transmission of data packets by
the TX. Evenly each 3 seconds the TX broadcasts 50 packets
with 512 bit payloads. RX processes signals, stores subcarriers
amplitudes and phases, and redirects the data to the laptop.
The data acquisition is stopped when the RX did a half-turn
and the antennas are aligned again.
As result, we get measurements signed by the true angle
value: the first observation corresponds to -90 degrees, the last
one corresponds to +90 degrees, and the middle observations
are uniformly distributed from -90 to +90 degrees. So, we can
compare true and estimated values.
In accordance with the methodology, we performed
several iterations for different distances between the RX and
TX. The each iteration results were processed and the AoA
estimations were obtained.
We used an algorithm described in [14] to compute the
AoA. The algorithm transforms subcarrier measurements to
AoA with the consideration of any particular angle-to-phase
model. For example, on the first stage we used the geometric
model (1).
The estimation offset
θ
ε
was calculated as the mean
difference between the estimated and true AoA. The EM
simulation predicted the significant offset in the AoA
estimations in the case of simple geometric model utilization
(see Fig. 8). We get a very similar curve as the result of
experiments processing (see Fig. 12). It confirms the mutual
antenna influence hypothesis. The simulation curve on Fig. 12
was very close to the experimental one except its amplitude.
We multiplied it by a factor of 2 in order to fit experimental
curve.
The unconsidered mutual antenna influence significant
reduces the AoA estimation accuracy. We repeated the
processing utilizing the EM angle-to-phase model. It allowed
to decrease estimation errors in a wide span of angles (see Fig.
13).
Fig. 10. The TX and RX with hand-made antenna systems.
Fig. 11. The experiment methodology: even rotation from -90 degrees to
+90 degrees allows to know true AoA (purple) and to compare it wit
h
measured AoA (blue).
Fig. 12. AoA estimation offset: simulation vs experiment
2018 Moscow Workshop on Electronic and Networking Technologies (MWENT)
V.
C
ONCLUSION
The WiFi positioning based on angular methods is an
interesting and perspective technique as the indoor navigation.
Relevant contemporary researches are focused on the signal
processing: multipath mitigation, subcarrier utilization,
ambiguity resolution. They have achieved impressing results
and get accuracy about 5-10 degrees. In the conditions,
electromagnetic properties of antennas begin to have a
meaning. Developers should take into account mutual
influence of the WiFi antennas to achieve better results. It is
shown by the simulation and experiments that the influence
causes offsets about 5-10 degrees in the angle of arrival
estimations.
In our tests, we achieve accuracy about of 5 degree.
Obviously, it is possible to get better results with particular
RPs obtained by means of anechoic chamber tests.
The conclusions of this study are equally applicable to the
problem of the angle of departure estimating.
A
CKNOWLEDGMENT
The authors are grateful to Igor Tsarik (Amungo
Navigation) for his assistance in the electromagnetic
simulation and useful recommendations.
R
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Ilya V. Korogodin
received the B.S. and
M.S. degrees in radio physics from
National Research University “Moscow
Power Engineering Institute” (MPEI) in
2010 and the Ph.D. degree in radio
navigation in 2013.
From 2006 to 2010, he was a
Researcher with Radionavigation
Fig. 13. AoA estimation offset (absolute value): geometric model vs E
M
model.
2018 Moscow Workshop on Electronic and Networking Technologies (MWENT)
Laboratory. From 2010 to 2013, he was an Assistant with
Radio system department. Since 2013, he has been an
Associate Professor. He is the author more than 20 articles and
4 patents. His research interests include digital GNSS signal
processing, GLONASS evaluation, constellation simulation,
multiantenna systems and ASICs. He is a head maintainer in a
research GNSS receiver/simulator project. His teaching
interests include the estimation theory, the mathematic
simulation, and the receiver design.
Vladimir V. Dneprov
received the M.S.
degree in radiotechnics from National
Research University “Moscow Power
Engineering Institute” in 2014.
From 2014 till now he is a Researcher
with Radionavigation Laboratory at
MPEI. Also he is a postgraduate at the
Radio Engineering Systems Department at
the same university. His research interests
are GNSS signal processing and attitude determination.
