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Characterization of a Geometrical Wireless Signal
Propagation Model for Indoor Ranging Techniques
Antonio Moschitta David Macii, Fabrizio Trenti Stefano Dalpez, Alessandro Bozzoli
DIEI – University of Perugia, DISI – University of Trento REET – Fondazione Bruno Kessler (FBK)
Perugia, Italy Trento, Italy Trento, Italy
E-mail: antonio.moschitta@diei.unipg.it
E-mail: macii@disi.unitn.it E-mail: sdalpez@fbk.eu
Abstract — Wireless positioning systems are interesting for a
variety of indoor applications such as security, home automation
and ambient assisted living (AAL) services. Unfortunately, the
accuracy of distance measurement techniques based on short-
range wireless communication transceivers is generally quite
poor, mainly because of multipath propagation phenomena. In
this paper an analytical model describing the effect of multipath
propagation on received signal power is presented. In particular,
both the case of pure sine wave indoor propagation and the more
involved scenario based on IEEE 802.15.4 Offset Quadrature
Phase-Shift keying (OQPSK) signals are analyzed. Several
experimental results collected in an anechoic chamber confirm a
reasonably good agreement with the proposed model, thus paving
the way to new strategies to improve indoor ranging accuracy
based on wireless techniques.
Keywords — Indoor positioning, ranging, radio frequency (RF),
multipath, wireless sensor networks (WSN).
I. INTRODUCTION
Indoor positioning systems have recently gained great
relevance in a lot of applications including home automation,
security, ambient assisted living (AAL), asset tracking and
logistics [1]. Even though many techniques based on different
types of sensors (e.g., video cameras [2], special inertial
platforms [3], infra-red sensors [4] or ultra-sound devices [5])
have been proposed, many researchers are still attracted by
purely Radio Frequency (RF) solutions. The reason of this
trend is basically twofold. First of all, in spite of the typical
vagaries and interference problems affecting electromagnetic
wave propagation [6], radio-based ranging tends to be
inherently cheaper and more robust to obstacles than
localization systems based on typical cameras, infrared or
ultra-sound sensors. Secondly, since nowadays almost any
portable electronic system is equipped with a radio
transceiver, this could be used not only for communication
purposes, but to support ranging techniques as well. Once the
distance between a moving wireless platform and a set of
fixed anchors is known, the position of the target within a
given reference frame could be easily estimated through
triangulation.
In general, the RF solutions for ranging can be roughly
classified in two groups, i.e. those based on Radio Signal
Strength (RSS) and those based on message Time of Flight
(ToF) measurements. The former techniques simply rely on
the RSS values estimated by the same radio chip used for
communication. If the amount of transmitted power and the
signal propagation model are known, the distance from the
transmitter can be estimated by inverting the propagation
model. Unfortunately, extensive studies proved that the
performance of this approach is quite poor in terms of
accuracy because of the limited resolution and the possible
nonlinearities of the on-chip RSS measurement circuitry
(which indeed is not conceived for metrological applications)
and, above all, because the RSS strongly depends on crucial
and unpredictable environmental factors such as reflections,
diffraction and scattering phenomena caused by other objects
located in the same environment [7],[8].
In ToF-based ranging solutions, the distance could be
measured by multiplying the speed of light by the time
interval that a message bit or a symbol spend in travelling
from the transmitter to the receiver. While conceptually very
simple, this measurement problem is quite complex in
practice, because the ToF of short-range radio signals is in the
order of a few ns, i.e. several orders of magnitude smaller than
the time spent to transmit or to receive any message.
Therefore, either both nodes are synchronized with sub-
nanosecond accuracy (Time of Arrival approach or ToA), or
the whole round-trip time must be measured by a single node,
which eventually divides the result by two after removing the
residence time spent by the message on either device [9]. In
both cases, it is essential that such time intervals are measured
at the lowest possible level (i.e., possibly next to the antenna)
and with sub-nanosecond resolution. Nowadays, this can be
done easily with suitable time-to-digital converters (TDC). In
addition, measurement accuracy can be greatly improved if the
pulses triggering the TDC have very short rising times. This is
one of the reasons why Ultra Wide Band (UWB) signals have
been successfully used in the implementation of indoor
ranging systems [10],[11]. In addition, UWB signals are more
robust to multipath phenomena because the radio pulses
reflected and scattered by other objects in the same
environment are not only delayed, but also smoothed by such
obstacles, thus enabling a better and easier detection of the
main pulse on the receiver. Unfortunately, UWB systems are
notoriously power-hungry and they are not commonly used for
short-range communication purposes despite of their inclusion
in the 2007 amendment to the standard IEEE 802.15.4 [12].
For these reasons, the objective of this work is to analyze how
the received power and the ToF values depend on the distance
from the transmitter when common Zigbee/IEEE 802.15.4
signals are subjected to multipath propagation. Such an
analysis could lead to new solutions to improve the ranging
accuracy of these systems [13],[14]. In this respect, super-
resolution techniques have been recently proposed to resolve
possible multipath components in indoor environments [15].
In section II the problem of multipath propagation of
monochromatic and Offset Quadrature Phase-Shift keying
(OQPSK) is modeled analytically. Then, in Section III some
experimental results validating the model are presented.
II.
MODEL DESCRIPTION
The adopted propagation model describes RF signal
propagation by means of the so-called ray-tracing technique
[16],[17]. This approach, based on an optical approximation,
is fairly accurate when the involved paths are several
wavelengths long. Initially, the transmission model between
two nodes was simulated under the assumption that simple
monochromatic signals propagate within a room. The room is
modeled as a box. The model allows the user to specify box
size, reflection coefficients of each box face, transmission
power, carrier frequency, nodes position, background noise at
the receiver input, and possible additional gain factors related
to antennas and front-end circuitry. Thus, if we assume that
the total length of the i-th path is d
i
, (with i=0 corresponding
to the LOS path) the signal at the receiver input is
)/(4)(,
6,...,1,2sin||)(
,0,2sin)(
)(
,)()(
0
0
0
000
6
0
iiii
i
i
iiitx
tx
i
i
i
dfcdF
i
c
d
tfGdFA
i
c
d
tfGdFA
ts
tsts
πϕ
ϕπ
π
=Γ∠=
⎪
⎪
⎩
⎪
⎪
⎨
⎧
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+
⎟
⎠
⎞
⎜
⎝
⎛
−Γ
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
⎟
⎠
⎞
⎜
⎝
⎛
−
=
=
∑
=
(1)
where
Γ
i
is the reflection coefficient of the i-th box face, f
0
is
the sinewave frequency, A
tx
is the signal peak value at the
transmitter output,
ϕ
i
is the angle of
Γ
i
, c is the speed of light
in vacuum, F(d
i
) is the free-space path loss at a distance d
i
from the transmitter, and G
i
keeps into account further gains
or attenuations, due, for example, to the antenna and to the
receiver front-end. Note that the received signal s(⋅) results
from the sum of several sine-waves of frequency f
0
and can be
reduced to a single sinewave given by
()
() ()
∑∑
==
−
==
⎟
⎠
⎞
⎜
⎝
⎛
=+=
+=
6
0
6
0
122
0
sin,cos
tan,
2sin)(
k
ii
i
ii
rxrx
rxrx
AA
A
tfAts
φβφα
α
β
ϕβα
ϕ
π
(2)
where A
i
is the amplitude at the receiver input of the signal
coming from the i-th path and it is defined as
⎩
⎨
⎧
=Γ
=
=
6,...,1,)(||
0,)(
00
iGdFA
iGdFA
A
iiitx
tx
i
(3)
while
φ
i
is the corresponding initial phase, that is
⎪
⎪
⎩
⎪
⎪
⎨
⎧
=+−
=−
=
6,...,1,2
0,2
0
0
0
i
c
d
f
i
c
d
f
i
i
i
ϕπ
π
φ
(4)
The developed model was validated through simulations in
two steps: at first in the case of free space propagation (i.e.,
with zero reflection coefficients for every face of the box).
Then, similar simulations were repeated assuming that one of
the surfaces of the box is a perfect mirror. The results of such
simulations are reported in Section III.A, where they are
compared with those related to various experiments conducted
in an anechoic chamber.
The proposed model has been also used to estimate the
received power variations as a function of the frequency in a
given environment. Eventually, the simulation model based on
(1) has been also extended to cover the case of IEEE 802.15.4
modulated waveforms at 2.4 GHz, using a Montecarlo
approach. Therefore, the new model can be rewritten as
()
),()(
6,...,0
,2sin)()(
)()(
0
6
0
tststs
i
c
d
tf
c
d
tsdFts
tsts
QIOQPSK
i
ii
OQPSKiii
i
i
+=
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+
⎟
⎠
⎞
⎜
⎝
⎛
−
⎟
⎠
⎞
⎜
⎝
⎛
−Γ=
=
∑
=
ϕπ
(5)
where s
OQPSK
(·) is the baseband OQPSK signal, obtained by
adding the in-phase component s
I
(·) and the quadrature
component s
Q
(·), given by
c
c
c
c
N
r
c
crQ
N
k
ckI
f
T
elsewhere
Ttt
f
tp
T
rTtpntskTtpnts
1
,
,0
0,
2
2sin
)(
,)
2
()(,)()(
1
0
1
0
=
⎪
⎩
⎪
⎨
⎧
<≤
⎟
⎠
⎞
⎜
⎝
⎛
=
−−=−=
∑∑
−
=
−
=
π
, (6)
f
c
=1 MHz is half of the IEEE 802.15.4 chip rate, equal to 2
Mchip/s, N=16 is the number of chips conveyed by the in-
phase and quadrature signals respectively and n
k
and n
r
are the
±1 chip values to be transmitted.
Notice that two simplifying assumption are introduced above.
The first one is that the path loss factor F is a function of the
2.4 GHz carrier frequency f
0
, and it does not vary significantly
in the 5 MHz band of an IEEE 802.15.4 channel. The second
assumption is that the reflection coefficients
Γ
i
will be
assumed as real, negative, and independent of the frequency.
III. EXPERIMENTAL RESULTS
A. Experimental setup description
In order to validate the model described in Section II,
several experiments were conducted in the anechoic chamber
of the “Fondazione Bruno Kessler” (FBK), Trento, Italy. The
chamber is about 20 m
2
in size and it is fully equipped for RF
and EMI testing procedures. All experiments were performed
in the Instrumentation, Scientific and Measurement (ISM)
band at 2.4 GHz, since it is the most widely used for short-
range wireless communications and sensor network
applications. Various types of experiments of increasing
complexity were conducted in the chamber. At first, the main
components used for the setup (e.g. cables, connectors and
antennas) were tested in fully anechoic conditions to estimate
and to compensate possible systematic uncertainty
contributions, e.g., due to unexpected attenuation phenomena
or significant antenna anisotropies. Afterwards, a thin 80x500
cm metal-coated plate was put on the floor of the chamber
between the transmitting and the receiving equipment to create
a multipath propagation environment with known geometric
characteristics. Two nominally isotropic Titanis swivel SMA
dipole antennas (one to transmit and the other one to receive
the radio signal) were placed vertically and parallel to each
other on top of two 1-meter wooden poles, as shown in Fig. 1.
The efficiency of such antennas is in the order of 80% with a
peak gain of 4 dBi on the XY plane of the dipole. A ruler was
drawn directly on the metal plate to adjust the distance
between antennas with negligible uncertainty. Using this
setup, different transmitters and receivers were connected to
the antennas in subsequent experimental sessions. All
experiments were performed with the receiver and the
transmitter placed at different distances, by increasing the
distance from 1 m to 4 m in steps of 5 cm at a time. In fact,
since the wavelength of RF signals at 2.4 GHz is about 12 cm,
the effect of multipath propagation with a significant LOS
component can be detected and analyzed properly, only if the
spatial resolution is smaller than the wavelength. Distances
shorter than 1 m were not taken into account because of the
near-field behavior of both antennas.
In the first session of experiments (in the following
referred to as Session 1 for brevity) an RF signal generator
HP8660C was used to produce a 0 dBm sine wave. A
spectrum analyzer Agilent E44070B was instead used to
measure the amount of received power. The spectrum analyzer
settings in terms of span, frequency resolution, windowing and
video bandwidth were properly adjusted to maximize
measurement accuracy according to instrument specifications.
Instrument configuration and data acquisition were managed
automatically through a NI Labview
TM
application.
In the second session of experiments (Session 2), a small
WSN node prototype (in the following simply referred to as
node A) made by Tretec S.r.L., Trento, Italy, was linked to one
of the antennas to generate a continuous stream of IEEE
802.15.4 packets at a nominal power of 0 dBm. The node
consists of an IEEE 802.15.4 Chipcon CC2520 radio
transceiver, an 8-bit Microchip PIC18LF46J50 micro-
controller (MCU) and a 3.7 V lithium-ion polymer (LiPo)
rechargeable battery. Again, the spectrum analyzer was used
to measure the amount of received power in 60 equally spaced
points from the transmitting node. In particular, since the
channels defined in the standard IEEE 802.15.4 at 2.4 GHz are
spaced 5 MHz apart to include some guard bands [18], the in-
channel total received power was measured over a 2-MHz
bandwidth [19].
Finally, in the third experimental session (Session 3) a twin
wireless receiving node, nominally identical to node A and
referred to as node B, was used to replace the spectrum
analyzer and it was configured to reply automatically to node
A IEEE 802.15.4 messages with an acknowledgement (ACK)
packet at 0 dBm. In addition, node A was programmed to
measure the amount of received power using its own on-chip
RSSI circuitry and it was also equipped with a time-to-digital
converter (TDC) Acam Mess Electronic TDC-GP2 able to
measure time intervals with a root mean square (rms)
resolution of 50 ps. The TDC is triggered by the Start of
Frame Delimiter (SFD) flag generated by the transceiver.
More precisely, the TDC starts counting anytime the first bit
of the SFD field of an IEEE 802.15.4 message is sent by node
A and it stops counting as soon as the SFD field of the ACK
response packet sent by node B is received. In this way, if no
packets are lost, the TDC retains the RTT values associated
with the exchange of any message-ACK pair. During the third
session of experiments, the RSS and RTT data streams were
transferred to a PC outside the anechoic chamber through a
USB link.
B. Measurement results
In Fig. 2(a) and 2(b) the experimental results of Session 1
for two different carriers, i.e. 2.405 GHz and 2.480 GHz
(dashed lines), respectively, are compared with the
corresponding received power values (solid lines) estimated
Fig. 1 – Snapshot of the experimental setup in the anechoic chamber of
the Fondazione Bruno Kessler (FBK).
on the basis of the model explained in Section II. In both cases
the amount of received power is plotted as a function of the
distance from the transmitter. The experimental patterns result
from the average of a few hundreds of repeated measurement.
The dotted lines refer to the ideal scenario (i.e., based on a
fully anechoic free-space propagation model), but they include
realistic efficiency and average gain values for both antennas.
It is worth noting that the chosen carrier frequencies
correspond to the center of channels 11 and 26 of the standard
IEEE 802.15.4 [18]. The attenuation due to the shielded
coaxial cables linking the transmitting antenna with the signal
generator (-8 dB) and the receiving antenna with the spectrum
analyzer (-3 dB), respectively, were properly estimated and
compensated. Observe that the experimental data are in
reasonable accordance with the simulation results, thus
confirming the general validity of the proposed model.
However, the position of minima and maxima does not always
correspond to the expected one. This is due to various
uncertainty contributions that are not explicitly included in the
model, such as the significant size and imperfect isotropy of
the antennas. Such non-idealities also justify the fluctuations
observed in the experimental data as well as the existence of
second-order multipath propagation phenomena, which have
been just roughly considered in the simulation results shown
in Fig. 2. It is worth noticing that switching the transmitter to a
different frequency (e.g., from 2.405 GHz to 2.48 GHz) may
lead to significant changes in the received power even at the
same distance. This is in accordance also with other
experimental results reported in the literature [8]. Hence, if the
on-chip RSSI detecting circuitry of an IEEE 802.15.4 device is
reasonably accurate and the entire transmission chain is
properly characterized, RSSI measurements at different
frequencies could be used to identify possible multipath
contributors. Fig. 3(a) and 3(b) show similar received power
patterns in the case of IEEE 802.15.4 messages transmitted
Fig. 2 – Measured (dashed lines) and simulated (solid lines) RF power
values received at different distances between 1 m and 4 m, under the
effect of a known amount of multipath fading. The transmitted signals are
0 dBm sine waves at 2.405 GHz (a) and 2.480 GHz (b). The dotted lines
refers to the ideal free-space propagation model.
1 1.5 2 2.5 3 3.5 4
-75
-70
-65
-60
-55
-50
-45
-40
-35
-30
Distance [m]
Received power [dBm]
1 1.5 2 2.5 3 3.5 4
-75
-70
-65
-60
-55
-50
-45
-40
-35
-30
Distance [m]
Received power [dBm]
(a)
(b)
Fig. 3 – Measured (dashed lines) and simulated (solid lines) RF power
values received in IEEE 802.15.4 channels 11 (a) and 26 (b), in semi-
anechoic conditions. The transmission power is about 0 dBm. The dotted
lines refers to the ideal free-space propagation model. The noisy patterns
refer to the values measured with the spectrum analyzer (point markers)
and with the on-chip RSSI circuitry (cross markers), respectively.
1 1.5 2 2.5 3 3.5 4
-75
-70
-65
-60
-55
-50
-45
-40
-35
-30
Distance [m]
Received power [dBm]
1 1.5 2 2.5 3 3.5 4
-75
-70
-65
-60
-55
-50
-45
-40
-35
-30
Distance [m]
Received power [dBm]
(
a
)
(
b
)
nominally at 0 dBm in channels 11 and 26, respectively.
Again, compared with the ideal fully anechoic case (dotted
lines), the received power values exhibit significant
oscillations in the order of several dBm because of the
multipath. Again, the solid lines correspond to the model-
based simulation results, while the dashed and dash-dotted
lines refer to the experimental results. In particular, the point-
shaped markers identify the values measured with the
spectrum analyzer in Session 2, while the cross-shaped
markers are related to the experiments of Session 3. In both
cases the random uncertainty contributions have been made
negligible through averaging and the systematic attenuation
terms (e.g., due imperfect matching between transceivers and
antennas) have been properly estimated and compensated. It
can be observed that in this case the agreement between
model-based simulations and experimental outcomes is better
than in the monochromatic case. This is probably due to the
larger bandwidth of the IEEE 802.15.4 signals, that may result
into a reduced impact of the aforementioned uncertainty
contributions.
Finally, Fig. 4 shows the average experimental ToF
patterns collected in Session 3 and associated with the
transmission of IEEE 802.15.4 messages in channels 11 (solid
line) and 26 (dashed line), respectively. In order to reduce the
total RTT latency as well as the random fluctuations due to the
higher layers of the protocol stack, the message payload size
was minimized and the automatic ACK feature was enabled
directly on the radio chip of node B. In addition, the carrier
sense multiple access with collision avoidance (CSMA-CA)
mechanism was disabled on both nodes to avoid random back-
off delays in the communication. Unfortunately, in spite of
such tricks in the implementation, we observed that even in
perfectly anechoic conditions the RTT data were affected by a
systematic offset of about 835 μs with random fluctuations in
the order of a few tens of ns. Fortunately, the systematic offset
is dominated by the time spent in receiving the data message
on node B before the ACK packet is sent. Therefore, if the
message size is fixed, this delay, as well as the systematic
latency introduced by both transceivers, can be easily
estimated and compensated at a chosen reference distance
(e.g., 1 m).
As far as the random fluctuations are concerned, they are
much larger than the pure ToF (which is in the order of a few
ns) and depend on the superimposition of multiple
independent effects including the finite symbol rate resolution
and the SNR at the receiver input. However, from several data
records collected at various distances in both anechoic and
semi-anechoic conditions, we discovered that, quite
surprisingly, they exhibit a stationary quasi-normal
distribution whose standard deviation (about 30 ns) is almost
independent of the environment. As a consequence, the jitter
can be made negligible simply by averaging a reasonable
amount of ToF values. The experimental patterns in Fig. 4
show the average of about 800 consecutive samples for each
position. Compared to the ideal ToF values (dotted line), both
experimental patterns exhibit relevant fluctuations around the
expected values. Such fluctuations are certainly correlated
with the received power patterns shown in Fig. 3. However, it
is quite hard to say whether they are dominated by multipath
fading or not. At the moment, a model describing the
relationship between received power and ToF is under
development. We expect to achieve more significant
information on this point in the next future.
IV. C
ONCLUSIONS
The main purpose of this paper is to understand how
multipath propagation affects the accuracy of radio-based
ranging techniques. A model based on ray-tracing has been
introduced to describe the influence of multipath on the
received power in semi-anechoic conditions. Model-based
simulations and experimental results are in fair agreement,
both for pure sine-waves and for IEEE 802.15.4-like signals.
Such results show that transmitting on different radio channels
leads to perceivable RSS variations, that are potentially useful
to resolve multipath components. ToF measurements have
been carried out as well, showing that repeated measurements
may lead to improved accuracy through averaging. Further
research activities are ongoing to find an analytical
relationship between ToF and RSS. In fact, some preliminary
experimental results show that, in semi-anechoic conditions,
the ToF pattern exhibits an oscillatory behavior, which is
related to the received SNR, as a consequence of the multipath
propagation.
A
CKNOWLEDGEMENTS
The research activities and the results described in this paper
are part of the PRIN 2008 project titled “Methodologies and
measurement techniques for spatio-temporal localization in
wireless sensor networks,” (N. 2008TK5B55_003) funded by
the Italian Ministry of University and Research. The authors
would like also to thank Dr. Michele Corrà and his
collaborators from Tretec S.r.l. for their constant support and
assistance.
Fig. 4 – Average Time of Flight (ToF) patters of IEEE 802.15.4 packets
transmitted in channel 11 (solid line) and channel 26 (dashed line),
respectively, under the effect of a known amount of multipath fading.
The dotted straight line refers to the ideal free-space propagation model.
1 1.5 2 2.5 3 3.5 4
-5
0
5
10
15
20
Distance [m]
Time of Flight (ToF) [ns]
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