Comments on “A Three-Dimensional Geometrical Scattering Model for Cellular Communication Environment”

Abstract

Primarily, this comment first focuses on a critical review of a geometric channel model and incorrect formulas presented by M. Riaz, M. M. Khan, and Z. Ullah. The adopted solution is a simplified case of a model that has already presented in a literature. Next, we give a proposal to improve the analyzed problem and expected results for this model.

Full text

Vol.:(0123456789)
Wireless Personal Communications (2019) 108:1481–1491
https://doi.org/10.1007/s11277-019-06480-1
1 3
Comments on“A Three‑Dimensional Geometrical Scattering
Model forCellular Communication Environment”
JanM.Kelner1 · CezaryZiółkowski1
Published online: 10 May 2019
© The Author(s) 2019
Abstract
Primarily, this comment first focuses on a critical review of a geometric channel model and
incorrect formulas presented by M.Riaz, M.M.Khan, and Z.Ullah. The adopted solution
is a simplified case of a model that has already presented in a literature. Next, we give a
proposal to improve the analyzed problem and expected results for this model.
Keywords Three dimensional· Angle-of-arrival· Cellular mobile communications·
Channel modeling· Semi-ellipsoid
1 Introduction
A three dimensional (3D) geometric channel model proposed in [1] is a simplified case
of models presented in [2–4]. In previous models proposed by Riaz etal. [2–4], we may
notice an increase in their complexity. In contrast, the newest model presented in [1] is a
trivial simplification of these models. Although, the models in [2–4] concern a mobile-to-
mobile (M2M) scenario, while the models in [1] is dedicated to a fixed-to-mobile (F2M)
scenario. However, this fact does not justify the presentation of the simplified model.
In [1], numerous errors in the description, introduced symbols, and equations occur
there. Hence, the obtained results are erroneous and make it impossible to correctly inter-
pret a propagation phenomenon occurring in a real environment. A detailed analysis of the
models in [1] and [2–4] shows that most of the formulas presented in [1] are simplified
versions of equivalents of the previous works. However, the transformation of the models
from [2–4] is carried out negligently. Hence, many of the symbols used in [1] do not have
their counterparts in the analyzed solution. As a result, the presented formulas contain the
fundamental errors that undermine the credibility of this paper.
In Sect.2, a detailed list of the errors that occur in the model description and used for-
mulas is presented. A solution of the analyzed problem is the topic of the next section.
* Jan M. Kelner
jan.kelner@wat.edu.pl
Cezary Ziółkowski
cezary.ziolkowski@wat.edu.pl
1 Faculty ofElectronics, Institute ofTelecommunications, Military University ofTechnology, Gen.
Witold Urbanowicz Str. No. 2, 00-908Warsaw, Poland
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J.M.Kelner, C.Ziółkowski
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Section 4 includes summary, which shows a critical evaluation of using this model in a
practice.
2 Review ofCommented Paper
In this section, we present a justification for the critical assessment of [1]. For a clear pres-
entation of the objections, below, we list the most important errors. The fundamental errors
occurring among them are the reason for writing this comment. They are the following:
1. In abstract of [1], the authors wrote … expressions for the joint and marginal probabil-
ity density functions for angle-of-arrival and time-of-arrival in azimuth and elevation
planes are derived. …. However, in abstracts of [3] and [4], there are … expressions for
the joint probability density function of angle-of-arrival and time-of-arrival in azimuth
and elevation planes are derived. …. In [3] and [4], the expressions and analysis of time-
of-arrival really are presented, while in [1], this issue is not raised at all. Therefore, the
cited extracts show that [1] is an nonsolid copy of the previous work.
2. Admittedly, in [1, Sect.2], it is written … To model scattering environment around the
MS along roads, street and canyons, Riaz etal. introduced 3D spatial channel models
for M2M communication environment in [21,22,25]. …, where cited [21,22,25] are
[2, 4], and [3] in this paper, respectively. A detailed analysis of the models presented in
[1–4] shows their close dependences. However, the newest of these paper [1] represents
a trivial simplification of earlier work.
3. In [1, Sect.3], there is … This geometry and the work carried out for M2M communica-
tion environment in [21, 22, 25] motivated us to propose a 3D semiellipsoid geometrical
channel model for F2M communication scenario. Such geometrically-based scattering
channel modeling approach is useful in designing and modeling of wireless networks as
presented in [26]. …, where cited [26] is [5] in this paper. In [5], the wireless networks
concern mobile ad-hoc networks (MANETs). The authors of [1] do not indicate a strict
justification for using the presented model for MANET. Typically, MANET refers more
to M2M environments than F2M. Therefore, this conclusion is unjustified. Furthermore,
in [5], the issue of channel modeling is not at all brought up.
4. In [1, Sect.4], there is … Main research contributions in this paper are as follows; …
5. To validate our proposed model, we compare it with the existing models in the litera-
ture. …. In the topic related to a presentation of new channel models, the comparative
assessment of the proposed solution with models available in a literature is accepted as
standard, especially for probability density function (PDF) of angle of arrival (AoA)
models. In this case, measurement results available in a literature, e.g., [6–11], are com-
monly used for this evaluation. Examples of properly conducted comparative analysis
of the PDF of AoA models include in [12–15]. In this assessment, different measures
are used, e.g., the least-square error (LSE), standard deviation, Kolmogorov–Smirnov,
and Cramer–von Mises statistics. Furthermore, if a model is fitted to empirical data,
optimal parameters of this model should always be given. In [1], the model validation
and its comparison with other models are not presented.
6. In [1, Sect.5], in [1, Fig.2], the authors did not introduce the relevant symbols used in
the further description of the model, e.g.,:
• The orientation of the Cartesian coordinate system is not shown.
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• A sample scattering point, S, is marked in a wrong location. In this case, S is out-
side of the scattering area bounded by semi-ellipsoid. The position of analogous S
in [3] is presented correctly.
• Some symbols, i.e.,
𝜃
,
xm
,
ym
,
zm
,
𝜙t1
,
𝜙t2
,
𝛽t1
,
𝛽t2
,
rm
, P1, and P2, are not shown in the
figure, so understanding the model description is very difficult.
• BS is located at a ground level, no at
h
height.
7. In [1, Sect.5], the authors wrote … The model is made more flexible by introducing
rotation of the semi-ellipsoid around the vertical z-axis, this rotation is symbolized as
𝜃
.
…. The symbol,
𝜃
, does not appear in the model description anymore and this rotation is
not actually included! However, in the previous models [2–4], the possibility of rotating
the scattering area by using the appropriate angle,
𝜃
, is introduced.
8. In [1, Sect.5], in sentence … Let the MS is placed at the origin point in space and the
BS is placed some distance D from the MS at point (d,0,0) in the Cartesian coordinates
system. …, the authors introduce two symbols,
D
and
d
. In our opinion, these symbols
represent the same parameter.
9. In [1, Sect.5], below ([1], 1), there are three formulas, i.e.,
The first equation is incorrect. The other two are identities and contribute nothing.
10. In [1, Sect.5], the description from the paragraph … The scatterers that contribute
in the arriving of signals at the MS are confined in a scattering region and named
as partition P1. … to formula ([1], 5) is unrelated to this model. This may fit into the
description of the angular dispersion seen on the base station (BS) side rather than the
mobile station (MS). A similar description with partitions, P1, and P2, and adequate
equations are shown in the more complex models [3, 4]. In addition, this part of the
model description contains many errors, i.e.,:
• [1, Fig.3] is unnecessary because it does not bring anything new. In addition,
the case presented here only applies to case for
𝛽=0◦
. Otherwise, the position
of the scatterer, S, will be located outside of the scattering area bounded by the
semi-ellipsoid.
• There is written … This scattering partition is identified by looking at azimuth
angle,
𝜙
(i.e.,
𝜙t1≤𝜙≤𝜙t2
) and elevation angle,
𝛽t1
(i.e.,
𝛽≤𝛽t1
). … and next
in ([1], 3) and ([1], 4), relationship between
𝜙t1
and
𝜙t2
is completely different,
i.e.,
𝜙t2≤𝜙≤𝜙t1
.
• Formula ([1], 5) is unclear. Firstly, if
h2d2𝛺=d2h2𝛺
, so
2h2d2𝛺
should be
in formula instead of two the same elements. Secondly, the elements of this
formula have different dimensions (i.e.,
h2d2𝛺(
m
6)
,
𝛺2(
m
4)
, and
h2d2(
m
4)
), so
the argument of the arctan function is not dimensionless.
11. In [1, Sect.5], formula ([1], 6) is incorrect. According to [1, Fig.2], for corresponding
𝜙
and
𝛽
,
r1
should be equal to proper semi-axes of the semi-ellipsoid, i.e.,
r1=a
for
𝛽=0◦
and
𝜙∈{0◦, 180◦}
,
r1=b
for
𝛽=0◦
and
𝜙∈{90◦, 270◦}
,
r1=c
for
𝛽=90◦
and
0◦≤𝜙≤360◦
. As it shows, any conditions are not met based on ([1], 6).
12. In [1, Sect.6], the authors wrote … The joint PDF, of propagation distance
r1
, eleva-
tion
𝛽
and azimuth
𝜙
angles, can be usually be expressed as, … and then, in formula
([1], 7) and the continued description, they introduced the symbol
rm
instead of
r1
.
“…xm=xm+D,ym=ym,zm=zm…”.
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J.M.Kelner, C.Ziółkowski
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13. In [1, Sect.6], in formulas ([1], 7), ([1], 8), and ([1], 10) symbol
rm
is instead of
r1
.
14. In [1, Sect.6], formula ([1], 11) is incorrect, because this function is not normalized.
Each probability density function should be normalized. Considering the 10th note, if
we integrate ([1], 11) over
𝛽
and
𝜙
, we will not get value “1”.
15. In [1, Sect.6], it is written … If we integrate (11) over
𝛽
then we can find marginal
PDF of azimuth AoA as follows,
Similarly, PDF of elevation AoA can be found by integrating the joint PDF in (11)
over
𝜙
as given by,
…. In this case, the authors do not find marginal PDFs and these formulas show only
the properties of the marginal PDFs. According to cited sentence from abstract in
first above note, the expressions for the marginal PDFs should be given.
16. In [1, Sect.7], The authors should present the results and comparative analysis of
the proposed solution with other models. The proper methodology of presenting this
analysis is described in 4 note. To proper presenting results, values of model param-
eters should always be given. In previous models proposed by Riaz etal. [2–4], this
approach is used. In this case, values of
a
,
b
, and
c
are not known for the graphs shown
in [1, Figs.4–7].
17. In [1, Sect.7], the results shown in [1, Figs.4–6] are incorrect because the formula
([1], 11) on which they are based is incorrect (see 13 note). In [1, Figs.4–6], new
symbols,
𝛽1
and
𝜙1
, are used that are not explained in the paper. Additionally, the
graphs presented in [1, Figs. 5–6] do not represent PDFs, because
p
(
𝜙1,𝛽1=const.
)≠
π∕2
∫
0
p
(
𝜙1,𝛽1
)
d𝛽
1
. Additionally, the area under the PDF curve
should always be normalized, i.e., equals 1 for PDF support. These graphs are not all
the more the marginal PDFs. According the formulas ([1], 12) and ([1], 13), the mar-
ginal PDFs depend only on one selected angle. The legend in these figures shows
something else. These graphs represent the cross-sections of the 3D surface from [1,
Fig.4].
18. In [1, Sect.7], it is written … In order to validate the obtained results using the pro-
posed 3D geometrical channel model, we compare the spatial characteristics of our
model with the experimental data in [27] as shown in Fig.7. It can be seen from these
curves that the results obtained from our developed model are well-matched with the
experimental results. …, where cited [27] is [6] in this paper. In [1, Fig.7], the authors
show only one curve. Whereas, in [6], two measurement scenario, i.e., for Aarhus
and Stockholm, are presented. In this case, the selected scenario for empirical data is
not known. It is not possible to objectively evaluate the fit of the proposed model to
empirical data, and especially, to compare it with other models, if value of compara-
tive measure, e.g., LSE, is not given (see note 4). The authors also did not provide a
methodology for optimizing the model parameters while fitting it to empirical data.
p(𝜙)=
π∕2
∫
0
p(𝜙,𝛽)d𝛽([1], 12
)
p
(𝛽)=
2π
∫
0
p(𝜙,𝛽)d𝜙([1], 13
)
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Comments on“A Three‑Dimensional Geometrical Scattering Model…
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Additionally, it is not possible to obtain the presented graph for this model. Riaz etal.
[1, Fig.7] is a copy of [4, Fig.22], which is obtained for a case, where scattering occur
around a transmitting antenna, i.e., BS. The proposed model only considers scattering
occur around a receiving antenna, i.e., MS.
19. General remark. If the authors introduced the PDF abbreviation for the probability
density function, it is accepted that they should only use this abbreviation in the rest of
the paper. Whereas, they use interchangeably the PDF or pdf acronyms and full name.
Based on the analysis of [1], we can conclude that the proposed model is a trivial and
nonsolid simplification of the previous models proposed by Riaz etal. [2–4]. This trivial-
ity consists in the fact that this model considers only so-called local scattering around MS.
In this case, MS could represent only a receiver. As a result of so presented problem, the
PDFs of AOA seen at MS do not depend on the distance
D
between MS and BS and the BS
height,
h
. In the description, the PDF of AOA seen at BS is not presented at all.
3 Solution ofProblem forScenario Presented inCommented Paper
In this section, we present a proposal to improve the description of the model shown in [1].
Figure1 shows a geometry of the channel model proposed in [1]. MS and BS are located
in the origin of the coordinate system and at the point
(D, 0, h)
, respectively, where
h
and
D
are the BS height, and distance between MS and BS, respectively. Signal scattering occur only
around a MS antenna. A location of an exemplary scatterer S,
(
x
m
,y
m
,z
m)
, is bounded by a
semi-ellipsoid
where
a
,
b
, and
c
are semi-axes of the semi-ellipsoid, so-called the semi-major and semi-
minor axes, and height of the semi-ellipsoid, respectively.
(1)
x2
m
a
2+
y
2
m
b
2+
z
2
m
c
2
≤1
Fig. 1 Geometry of the proposed channel model
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J.M.Kelner, C.Ziółkowski
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The relations between the semi-axes of the semi-ellipsoid and
h
, and
D
, should be deter-
mined as
b≤a≤c<h≪D
.
Location of S can be expressed in Cartesian,
(
x
m
,y
m
,z
m)
, or spherical,
(
r
1
,𝜙,𝛽
)
, coordi-
nates, where
r1
,
𝜙
, and
𝛽
are radius, azimuth, and elevation angles, respectively. The Cartesian
and spherical coordinates are related as follows [16]
where variation ranges of the spherical coordinates are
r1∈⟨0, r1max⟩
,
𝜙∈⟨−π,π)
, and
𝛽∈⟨0, π∕2⟩
, respectively.
The maximum radius,
r1max
, can be determined on the basis of
Hence, for
𝛽=0
and
𝜙∈{0, π}
, we have
r1=a
, for
𝛽=0
and
𝜙∈{π∕2, 3π∕2}
, we have
r1=b
, and for
𝛽=π
∕2
and
𝜙∈⟨0, 2π⟩
, we have
r1=c
.
The authors of the proposed model assumed the uniform distribution of the scatterers
inside the semi-ellipsoid, so the density of the scatterers in Cartesian coordinates is equal
where
V
is the semi-ellipsoid volume, i.e., [16]
The joint PDF, p
(
r
1
,𝜙,𝛽
)
, of the radius, elevation, and azimuth is expressed as [17]
where
J(
x
m
,y
m
,z
m)
and
J(
r
1
,𝜙,𝛽
)
are the Jacobians of coordinate transformations, i.e.,
[16]
Thus, after substituting (4), (5), and (7) to (6), we obtain
If we integrate (8) over
r1
in range from 0 to
r1max
, we get the joint PDF for the elevation
and azimuth angles
(2)
xm
=r1cos 𝜙cos 𝛽,ym
=r1sin 𝜙cos 𝛽,zm
=r1sin 𝛽
(3)
r
1max =
abc
√
1
2
c2
[
a2+b2+
(
b2−a2
)
cos 2𝜙
]
cos2𝛽+a2b2sin2
𝛽
(4)
f
(
xm,ym,zm
)
=
1
V
(5)
V
=
2
3
π
abc
(6)
p
(r1,𝜙,𝛽)=
f
(
xm,ym,zm
)
|
|
|
J
(
xm,ym,zm
)|
|
|
=f(xm,ym,zm)|
|
|
J(r1,𝜙,𝛽)
|
|
|
(7)
J
(r1,𝜙,𝛽)=
1
J(xm,ym,zm)=
|
|
|
|
|
|
|
|
|
𝜕x
m
𝜕r1
𝜕x
m
𝜕𝜙
𝜕x
m
𝜕𝛽
𝜕ym
𝜕r1
𝜕ym
𝜕𝜙
𝜕ym
𝜕𝛽
𝜕zm
𝜕r
1
𝜕zm
𝜕𝜙
𝜕zm
𝜕𝛽
|
|
|
|
|
|
|
|
|
=r2
1cos
𝛽
(8)
p
(
r1,𝜙,𝛽
)
=
3r
2
1cos
𝛽
2πabc
(9)
p(𝜙,𝛽)=
r
1max
∫
0
p(r1,𝜙,𝛽)dr1=
r3
1max
cos
𝛽
2πabc
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where
r1max =r1max(𝜙,𝛽)
is given by (3).
Based on the marginal PDF properties and using numerical integrating (9) over
𝛽
or
𝜙
(10)
p(𝜙)=
𝜋∕2
∫
0
p(𝜙,𝛽)d
𝛽
(11)
p(𝛽)=
𝜋
∫
−𝜋
p(𝜙,𝛽)d
𝜙
Fig. 2 Joint PDF of AOA for a = 1.5b and c = 2b
Fig. 3 Joint PDF of AOA for a = 2b and c = 3b
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J.M.Kelner, C.Ziółkowski
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we can determined the PDFs of azimuth and elevation AOA, respectively. Exemplary
joint PDFs of AOA are determined for different parameters of the semi-ellipsoid. The
obtained results are shown in Figs.2, 3, 4 for
(
a=1.5b,c=2b
)
,
(
a=2b,c=3b
)
and
(
a=5b,c=10b
)
, respectively.
The characteristic feature of the joint PDFs is the presence of two maxima for
𝜙=0
and
𝜙=180◦
, respectively. Changing the semi-ellipsoid parameters causes modifications of a
height and width of these maxima.
The numerical calculations for (10) and (11) give the possibility of determining the
marginal PDFs of AOA shown in Figs.5 and 6 for the azimuth and elevation, respectively.
These graphs are presented for the selected semi-ellipsoid parameters.
Fig. 4 Joint PDF of AOA for a = 5b and c = 10b
Fig. 5 Marginal PDF of azimuth AOA for selected semi-ellipsoid parameters
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Based on the obtained results, we can conclude that the shapes of the joint and marginal
PDFs of AOA do not depend on the absolute value of the semi-ellipse parameters, but
only on their mutual relations. This means that graphs of
p(𝜙,𝛽)
,
p(𝜙)
, and
p(𝛽)
are the
same for, e.g.,
(
a=10 m, b=5 m, c=20 m
)
and
(
a=20 m, b=10 m, c=40 m
)
,
because relations between the parameters are constant, i.e.,
a=2b
and
c=4b=2a
.
Additionally, in the case of the marginal PDF of azimuth AOA, only the ratio between
a
and
b
influences on the shape of this characteristic. Thus, the parameter
c
can be
arbitrary. This results in overlapping the graphs in Fig. 5 for
(
a=2b,c=4b
)
and
(
a=2b,c=6b
)
, or
(
a=3b,c=4b
)
and
(
a=3b,c=6b
)
, respectively. For the same
values of the semi-ellipsoid parameters, i.e.,
a=b=c
, this distribution is uniform. This
effect results from (10), i.e., the integration
p(𝜙,𝛽)
over the elevation.
Analogously as in the case of the joint PDF, the marginal PDF of azimuth AOA has two
maxima for
𝜙=0
and
𝜙=180◦
, respectively. Hence, the proposed model in the azimuth
plane can only be used to map bimodal AOA distributions. So, such distributions can occur
in propagation environment for a typical street canyon. Whereas, empirical distributions
presented in [6–11] are unimodal, therefore they cannot be mapped by this model.
4 Conclusion
In this comments, we present the review of [1] and proposal to improve the proposed chan-
nel model. Although introducing appropriate changes in the analytical description of the
model, this model does not provide an opportunity to adequately reflect the propagation
properties of the environment.
The main reason for our comments on [1] is the presentation of the channel model,
which is the trivial and nonsolid simplification of the previous models proposed by Riaz
et al. [2–4]. This triviality consists in the fact that this model considers only the local
scattering around MS, which could represent only the receiver. Therefore, the PDFs of
AOA seen at MS do not depend on the distance between MS and BS and the BS height.
Fig. 6 Marginal PDF of elevation AOA for selected semi-ellipsoid parameters
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Additionally, this model does not depend on the absolute values of the semi-ellipsoid
parameters but only on the relations between these parameters.
This model incorrectly maps the propagation conditions that exist in the real environ-
ment. Proof of this is incorrect approximation of measurement data. Using the proposed
model, approximation of typical empirical distributions of AOA, presented in [6–11], is
not possible. It shows the distributions obtained from this model.
In addition, the numerous errors, especially in the entered formulas and symbols, are in
the model description. The erroneous application of mathematical rules makes it impos-
sible to assess the utility of the proposed model. In abstract of [1], the authors declare the
derivation of … expressions for the joint and marginal probability density functions for
angle-of-arrival and time-of-arrival in azimuth and elevation planes …, but only the equa-
tion on the joint PDF is given. In Sect.4 of [1], the authors promise to validate the model
on the basis of measurement data and compare it with other models, but these are also not
presented, although this approach is typical for papers describing new channel models.
The parameters for the obtained results and used optimization method for these param-
eters to match the model to empirical data also are not presented in the paper.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 Interna-
tional License (http://creat iveco mmons .org/licen ses/by/4.0/), which permits unrestricted use, distribution,
and reproduction in any medium, provided you give appropriate credit to the original author(s) and the
source, provide a link to the Creative Commons license, and indicate if changes were made.
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Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and
institutional affiliations.
Jan M. Kelner was born in Bystrzyca Kłodzka, Poland in 1977. He
received his M.Sc. degree in Applied Physics in 2001, his Ph.D. in Tel-
ecommunications in 2011, all from the Military University of Technol-
ogy (MUT) in Warsaw, Poland. In 2011 he won “The Winner Takes
All” contest on research grant of MUT Rector, and his Ph.D. Thesis
won the third prize in the Mazovia Innovator contest. He has authored
or co-authored more than seventy articles in peer-reviewed journals
and conferences. He is a reviewer for three scientific journals. He
works as a assistant professor in the Institute of Telecommunications,
in the Faculty of Electronics of MUT. His current research interests
include wireless communications, simulations, modelling, and meas-
urements of channels and propagation, signal-processing, navigation
and localization techniques.
Cezary Ziółkowski was born in Poland in 1954. He received M.Sc. and
Ph.D. degrees from the Military University of Technology (MUT),
Warsaw, Poland, in 1978 and 1993, respectively, all in telecommunica-
tion engineering. In 1989 he received M.Sc. degree from the Univer-
sity of Warsaw in mathematics, specialty-analysis mathematics appli-
cations. In 2013 he received the habil. degree (D.Sc.) in Radio
Communications Engineering from MUT. From 1982 to 2013 he was a
researcher and lecturer while since 2013 he has been a professor of
Faculty of Electronics with MUT. He was engaged in many research
projects, especially in the fields of radio communications systems
engineering, radio waves propagations, radio communication network
resources management and electromagnetic compatibility in radio
communication systems. He is an author or co-author of over eighty
scientific papers and research reports.
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