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INTL JOURNAL OF ELECTRONICS AND TELECOMMUNICATIONS, 2020, VOL. 66, NO. 1, PP. 11-16
Manuscript received November 16, 2019; revised January, 2020. DOI: 10.24425/ijet.2019.130259
© The Author(s). This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0,
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Abstract—Radio environment maps (REMs) are beginning to be
an integral part of modern mobile radiocommunication systems
and networks, especially for ad-hoc, cognitive, and dynamic
spectrum access networks. The REMs will use emerging military
systems of tactical communications. The REM is a kind of database
used at the stage of planning and management of the radio
resources and networks, which considers the geographical features
of an area, environmental propagation properties, as well as the
parameters of radio network elements and available services. At
the REM, for spatial management of network nodes, various
methods of propagation modeling for determining the attenuation
and capacity of wireless links and radio ranges are used. One
method of propagation prediction is based on a numerical solution
of the wave equation in a parabolic form, which allows considering,
i.a., atmospheric refraction, terrain shape, and soil electrical
parameters. However, the determination of a current altitudinal
profile of atmospheric refraction may be a problem. If the
propagation-prediction model uses a fixed refraction profile, then
the calibration of this model based on empirical measurements is
required. We propose a methodology for calibrating the analyzed
model based on an example empirical research scenario. The paper
presents descriptions of the propagation model, test-bed and
scenario used in measurements, and obtained signal attenuation
results, which are used for the initial calibration of the model.
Keywords—calibration of propagation model, empirical
measurements, path loss model, propagation, parabolic equation
method, radio environment map
I. INTRODUCTION
ROPAGATION models might be divided into small-,
medium- and large -scale models. The small-scale models,
also known as channel models, describe propagation
phenomena occurring in signals into a small-scale, i.e.,
primarily fast fading and Doppler effect. The medium-scale and
large-scale models describe shadowing, i.e., slow fading, and
path loss, i.e., signal attenuation, respectively [1–4]. An
example of the separation of propagation-phenomena on the
three discussed types of the models is presented in Fig. 1 (based
on [4]).
Individual types of propagation models find different
applications. In the case of the large-scale models, they are used,
i.a., to assess the distance-range of radio systems in various
types of environments. Attenuation models may generally be
classified into two groups, i.e. statistical and deterministic
Jan M. Kelner, Michał Kryk, Jerzy Łopatka, and Piotr Gajewski with the
Military University of Technology, Faculty of Electronics, Institute of
Communications Systems, Gen. Sylwester Kaliski Str. No. 2, 00-908 Warsaw,
models. The statistical models illustrating the average path loss
in the analyzed propagation environment. In the case of the
deterministic models, attenuation for specific points of space
can be determined considering landforms, existing buildings, or
vegetation, etc. While the statistical models will allow
determining the coarse radio range of the analyzed
communication system, the deterministic models allow
estimating this range depending on a propagation direction. This
is schematically illustrated in Fig. 2 (based on [5]) for a
hypothetical transmitter (TX).
Fig. 1. Separation of propagation phenomena into large-, medium- and small-
scale.
Fig. 2. Example ranges of hypothetical TX determined using statistical and
deterministic path loss models.
Poland (e-mail: jan.kelner@wat.edu.pl, michal.kryk@wat.edu.pl,
jerzy.lopatka@wat.edu.pl, piotr.gajewski@wat.edu.pl).
A Statistical Calibration Method of Propagation
Prediction Model Based on Measurement
Results
Jan M. Kelner, Michał Kryk, Jerzy Łopatka, and Piotr Gajewski
P
12 J. M. KELNER, M. KRYK, J. ŁOPATKA, P. GAJEWSKI
The range evaluation of wireless systems is used for designing
radio networks, e.g., in cellar telephony. Then, terrain locations
of wireless network nodes, e.g., base stations, is an important
issue for providing different services for mobile users, i.e.,
providing coverage of an area with network access. In the first
stage of designing such a network, simulation analyzes are
performed in which statistical or deterministic models, e.g.,
ray-tracing methods [6,7] can be used. In the next approach,
measurements are usually made in the real environment.
When planning mobile ad-hoc networks (MANETs), the
approach to design the cellular networks cannot be used. On the
one hand, the statistical models are too coarse to assess the radio
range of MANET nodes. On the other hand, the deterministic
ray-tracing methods require a lot of time, high computing
power, and accurate spatial digital maps containing information
about types of building materials. In addition, it is not possible
to perform dedicated propagation measurements due to the
dynamically changing situation in such a network. Therefore,
different approaches are used in this case. For the radio range
assessment, simpler and less accurate deterministic models are
usually used than those based on the ray-tracing. In the case of
evaluating the real situation between the MANET nodes, results
of spectrum sensing [8–13], implemented in modern cognitive
networks [14–18] may be utilized. These solutions are used in
so-called radio environment maps (REMs) [19–24].
The REM is a kind of database used at the stage of planning
and management of the radio resources and networks, which
considers the geographical features of an area, environmental
propagation properties, as well as the parameters of radio
network elements and available services [20,24]. At the REM,
for spatial management of network nodes, various methods of
propagation modeling for determining the attenuation and
capacity of wireless links and radio ranges are used. We propose
a propagation prediction method based on a numerical solution
of the wave equation in a parabolic form, so-called a parabolic
equation method (PEM) [25–28]. The PEM allows considering,
i.a., atmospheric refraction, terrain shape, and soil electrical
parameters. However, the determination of a current altitudinal
profile of atmospheric refraction may be a problem. If the
propagation-prediction model uses a fixed refraction profile,
then the calibration of this model based on empirical
measurements is required. We propose a methodology for
calibrating the analyzed model based on an example empirical
research scenario. The paper presents descriptions of the
propagation model, test-bed and scenario used in measurements,
and obtained signal attenuation results, which are used for the
initial calibration of the model.
The purpose of this paper is showing the calibration
methodology of the propagation prediction model based on
sample empirical results. In this case, a path loss model based
on the PEM is used to create a propagation awareness in the
REM for the needs of planning the MANETs with low antenna-
heights of the network nodes.
The remainder of the paper is organized as follows. Section II
gives a brief description of the PEM. In Section III, a test-bed,
measurement scenario, and obtained empirical results are
shown. The calibration methodology of the path loss model
based on the PEM is presented in Section IV. The final part of
the paper contains a summary.
II. PARABOLIC EQUATION METHOD
The propagation prediction model used to create the REM is
based on the PEM, i.e., the numerical solution of the differential
parabolic equation for the electric field strength E (x, z) along an
assumed azimuth direction (radius), i.e., a corresponding
terrain-profile (generalized x coordinate) and for determined
height above this terrain (z coordinate) [25,26]
( ) ( )
( )
( )
222
00
2
,,
2j 1 , 0
E x z E x z
k k n E x z
x
z
− + − =
(1)
where
j1=−
, k0 = 2π / λ is a wave number, λ is a wavelength,
rr
n
=
is an air refractive index, μr and εr are relative
magnetic and electric permeabilities of air, respectively.
The PEM allows to consider the following physical
phenomena [25,26]:
• air refraction, i.e., atmospheric refractivity, and its
influence on radio wave propagation;
• terrain diffraction, i.e., radio wave diffraction on a terrain
ruggedness, which allows considering the terrain profile in
determining the radio range of the TX;
• impact of soil electrical parameters, i.e., ground
conductivity and permeability, on wave propagation in a
lower part of a troposphere.
Additionally, the proposed solution gives the opportunity to
consider the phenomenon of radio wave diffraction in built-up
areas. In this case, the height profile of the terrain in a given
cross-section should also consider the heights of buildings and
other infrastructure [25,26].
In practice, two methods of numerical solution of the parabolic
equation are used [25,26], i.e., a finite difference method (FDM)
and split-step Fourier method (SSFM). Due to the lower
calculation speed of the FDM algorithm, we decided to
implement the SSFM method for the PEM solution. In this case,
the fast Fourier transform algorithm (FFT) is not implemented
in the time and frequency domain, but in the space domain.
The main advantages of the PEM include [25]:
• frequency range of the analysis from 30 MHz to 100 GHz;
• propagation-prediction range from far-field of a
transmitting antenna (~1÷30 m) to several hundred
kilometers (~300 km);
• considering the terrain profile, i.e., landform, and the radio
wave diffraction (terrain diffraction);
• considering the air-refraction phenomena and refractive-
index changes along the terrain profile;
• considering the electrical parameters of the soil and their
changes along the terrain profile;
• considering a beamwidth of the transmitting antenna in the
elevation plane and the vertical or horizontal polarization
of the receiving antenna.
The PEM model is used in the REM in two ways. For
estimation of the path loss for wireless links, i.e., the point-to-
point attenuation between the TX and receiver (RX), and
determining propagation attenuation maps around the TXs.
These maps are the basis for determining radio-ranges for the
individual nodes of the MANET.
Figure 3 shows an exemplary result obtained based on the
PEM, i.e., the signal attenuation determined along the analyzed
terrain profile and heights above the ground, for a given
transmitting antenna hight, hT. The terrain profiles are
determined from digital terrain elevation data (DTED) [29]. The
DTED maps are represented by matrices of integers containing
information about the ground level measured in meters above
mean sea level (AMSL). In this matrix, the desirable terrain
profile representing the height component (z coordinate) along
the given azimuth direction (generalized x coordinate) should be
A STATISTICAL CALIBRATION METHOD OF PROPAGATION PREDICTION MODEL BASED ON MEASUREMENT RESULTS 13
Fig. 3. Sample result of PEM as attenuation distribution for given terrain profile
and height of transmitting antenna.
determined. In our analysis, we use DTED2 with a raster
resolution of 30 m and we assume hT = 2 m.
Based on the attenuation distribution, L (x, z), in the XZ plane,
where x represents the distance from the TX along the given
azimuth direction, while z corresponds to the height, we
determine the path loss L for the defined height of the receiving
antenna, hR. Figure 4 depicts the path loss for hR = 2 m.
Fig. 4. Sample path loss for given terrain profile and height of receiving antenna.
For the same hR, we determined the propagation attenuation
map illustrated in Fig. 5. This map was generated based on the
losses of the paths determined for 360 terrain profiles with a 1°
angular step in the azimuth plane. The shown attenuation map
corresponds to an area of 40 km × 40 km.
Fig. 5. Exemplary propagation attenuation map for chosen TX and defined
height of receiving antenna.
The propagation attenuation map is the basis of the radio range
map determined for the individual wireless network nodes
(TXs). Figure 6 presents an example of the radio range map
obtained for several types of modulation. In this case, detailed
information about the TX/RX parameters of the node (e.g.,
radiated power, antennas gain, noise characteristics of the
analyzed modulation and coding schemes, boundary values of
signal-to-noise ratio, receiver sensitivity) is required.
Fig. 6. Exemplary radio range map for chosen TX and defined height of
receiving antenna.
III. EMPIRICAL MEASUREMENTS
A. Measurement test-bed
To calculate the attenuation correctly from the proposed PEM,
the initial calibration should be carried out. Therefore, a
measuring campaign was realized to obtain the actual data. The
conception of the electromagnetic field strength measurement
system is shown in Figs. 7 and 8 for transmitting and receiving
parts, respectively.
Fig. 7. Block diagram of reference transmitter station.
The reference transmitting station (Fig. 7) is equipped with the
signal generator Rohde&Schwarz (R&S) SMIQ02b, which
emitted a harmonic signal at a fixed frequency equal to
289.3 MHz. The signal was fed through a 50 W amplifier to an
omnidirectional transmitting antenna. The frequency ranges of
signal generator, amplifier and antenna are equals
0.3÷2200 MHz, 20÷512 MHz, and 100÷600 MHz, respectively.
14 J. M. KELNER, M. KRYK, J. ŁOPATKA, P. GAJEWSKI
Fig. 8. Block diagram of monitoring station.
During measurements, it was a requirement that the generated
signal power was equal to 1 or 10 W. As a result, the signal
power level set at the generator was –11 or –5 dBm,
respectively.
Both parts of the test-bed can be stationary or mobile.
Therefore, scenarios in different places may be proposed. Each
of the measurement stations was equipped with a GPS receiver
and computer that recorded current time and location.
The main element of the monitoring station (Fig. 8) is the
wideband receiver R&S ESMD with a frequency range from
20 MHz to 3.6 GHz. This device was specially developed for
signal search, radio monitoring, detection, and spectrum
monitoring task.
Fig. 9. Mobile reference transmitter station.
Fig. 10. Mobile monitoring station.
For empirical measurements, the receiver worked in FFM
mode with the build-in RMS detector on a 1 kHz frequency
range. The receiving antenna used at the monitoring station is
the D220R Diamond Antenna and it has a frequency range from
10 to 1600 MHz.
All elements are managed by a computer PC, which enables
time and location registration. In addition, it initiates the R&S
ESMD and records power levels from detectors.
All stations are installed on mobile platforms that are
presented in Figs. 9 and 10.
B. Measurement Scenario
The measurement scenario for the initial calibration of the
PEM model was located at the Military University of
Technology in Warsaw. A position of the monitoring station
(RX) and a movement trajectory of the reference transmitting
station (TX) are presented in Figs. 11 (based on [5]) and 12
(based on [30]).
Fig. 11. Empirical measurement scenario.
Fig. 12. Spatial placement of initial (a) and final (b) sections of measuring route
where LOS conditions occur.
A STATISTICAL CALIBRATION METHOD OF PROPAGATION PREDICTION MODEL BASED ON MEASUREMENT RESULTS 15
The sections of the TX motion trajectory with line-of-sight
(LOS) propagation conditions are marked in yellow. The red
lines are means non-LOS conditions between the reference
transmitting station (TX) and receiving monitoring (RX)
station. We assumed that the RX was stationary and TX was
mobile.
C. Measurement Results
During the measurements, log files are created at each station.
These files contain information about the system time and
current position. Additionally, the received power is recorded in
the log file of the monitoring station. After measurements,
distance calculation and correlations of both files are required.
The results are the relationships between the received power and
TX-RX distance or TX movement time.
Figure 13 illustrates the recorded location of both stations.
The blue and red lines correspond to LOS and NLOS conditions
on the TX movement trajectory, respectively. These results are
consistent with the planned scenario depicted in Fig. 11.
Fig. 13. Monitoring station (RX) location and reference transmitting station
(TX) movement trajectory.
The attenuation of the reference signal versus the TX
movement time with the region selection for LOS (blue) and
NLOS (red) conditions is presented in Fig. 14.
Fig. 14. Attenuation of the reference signal versus TX movement time.
IV. CALIBRATION OF PROPAGATION MODEL
The utilization of the recorded measurement data for the PEM
calibration required their preparation. First, we determined the
measuring route sections, i.e., signal recording time intervals,
corresponding to LOS and NLOS conditions. Next, based on the
recorded positions of the transmitting and receiving parts of the
test-bed, the distances, D, between the TX and RX were
calculated. Finally, by correlating the GPS system times for the
data recorded at the transmitting and receiving parts, it was
possible to assign the measured attenuations for LOS and NLOS
conditions and the distance D. These results are shown in
Fig. 15. The data for LOS and NLOS conditions were marked
with blue and red, respectively.
Fig. 15. Empirical path loss models versus TX-RX distance for LOS and NLOS
conditions.
For grouped data, we determined empirical close-in free space
reference distance path loss (CI) models. The CI model is
defined as follows [31–34]:
( )
( ) ( )
0 10 0
dB 10logL D L D n D D X
= + +
(2)
where L(D0) = 39,6 dB is a free-space path loss (FSPL) for a
reference distance equal to D0 = 10 m, n is a path loss exponent,
Xσ is a zero-mean normal random variable with a deviation equal
to σ, which represents the shadowing phenomena.
Using the least-squares method [35,36], linear regression was
determined for measurement data separately for LOS and NLOS
conditions. In these cases, the path loss exponents are
nLOS = 2.97 and nNLOS = 3.79, respectively.
Due to the close distances between the TX and RX, and flat
terrain, we adopted the flat terrain profile for modeling the
analyzed scenario in the PEM. Attenuation was determined for
these conditions, which is shown in black in Fig. 15. For the
PEM data, the path loss exponent of the CI model is equal to
nPEM = 2.53. Therefore, we recommended using correction and
calibration factors in the PEM for LOS and NLOS conditions,
respectively
Δ 0.44
LOS LOS PEM
n n n= − =
(3)
Δ 1.26
NLOS NLOS PEM
n n n= − =
(4)
On their basis, the attenuation L (D) determined in the PEM
should be corrected in accordance with the relationship
( ) ( ) ( )
10 0
Δ 10logL D L D n D D= +
(5)
where Δn = ΔnLOS or Δn = ΔnNLOS for LOS and NLOS
conditions, respectively.
V. CONCLUSIONS
This paper presents the calibration methodology of the
propagation model based on the PEM, which allows considering
the terrain diffraction and atmospheric refractivity. The basis for
model calibration is empirical data obtained for the described
measurement scenario. The presented model calibration was
aimed at introducing correction factors for the attenuation
determined by the analyzed PEM model separately for LOS and
16 J. M. KELNER, M. KRYK, J. ŁOPATKA, P. GAJEWSKI
NLOS conditions. This approach required the separation of
measurement data. The presented attenuation correction
methodology can also be applied to other propagation prediction
models and other measurement scenarios.
The chosen measurement scenario was for the initial PEM
model calibration. The current version of the PEM model does
not include buildings and vegetations, hence, it is necessary to
introduce correction factors for various types of environments,
so-called clutters. On the other hand, the PEM model will be
used in the REM mainly to assess the radio ranges of the
MANET nodes. Therefore, we will ultimately plan to carry out
measurement campaigns for significant distances between the
TX and RX, in order of 10÷20 km, which will also allow its
calibration for such propagation conditions.
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