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Radio Channel Capacity with Directivity Control of Antenna Beams in Multipath Propagation Environment

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The basic technology that will determine the expansion of the technical capabilities of fifth generation cellular systems is a massive multiple-input-multiple-output. Therefore, assessing the influence of the antenna beam orientations on the radio channel capacity is very significant. In this case, the effects of mismatching the antenna beam directions are crucial. In this paper, the methodology for evaluating changes in the received signal power level due to beam misalignment for the transmitting and receiving antenna systems is presented. The quantitative assessment of this issue is presented based on simulation studies carried out for an exemplary propagation scenario. For non-line-of-sight (NLOS) conditions, it is shown that the optimal selection of the transmitting and receiving beam directions may ensure an increase in the level of the received signal by several decibels in relation to the coaxial position of the beams. The developed methodology makes it possible to analyze changes in the radio channel capacity versus the signal-to-noise ratio and distance between the transmitter and receiver at optimal and coaxial orientations of antenna beams for various propagation scenarios, considering NLOS conditions. In the paper, the influence of the directional antenna use and their direction choices on the channel capacity versus SNR and the distance between the transmitter and receiver is shown.
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sensors
Article
Radio Channel Capacity with Directivity Control of Antenna
Beams in Multipath Propagation Environment
Cezary Ziółkowski 1, Jan M. Kelner 1, * , Jarosław Krygier 1, Aniruddha Chandra 2and Aleš Prokeš 3


Citation: Ziółkowski, C.; Kelner,
J.M.; Krygier, J.; Chandra, A.; Prokeš,
A. Radio Channel Capacity with
Directivity Control of Antenna Beams
in Multipath Propagation
Environment. Sensors 2021,21, 8296.
https://doi.org/10.3390/s21248296
Academic Editor: Peter Han
Joo Chong
Received: 11 November 2021
Accepted: 8 December 2021
Published: 11 December 2021
Publisher’s Note: MDPI stays neutral
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Copyright: © 2021 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
1Institute of Communications Systems, Faculty of Electronics, Military University of Technology,
00908 Warsaw, Poland; cezary.ziolkowski@wat.edu.pl (C.Z.); jaroslaw.krygier@wat.edu.pl (J.K.)
2Department of Electronics and Communication Engineering, National Institute of Technology,
Durgapur 713209, India; aniruddha.chandra@ieee.org
3Department of Radio Electronics, Brno University of Technology, 61600 Brno, Czech Republic;
prokes@vutbr.cz
*Correspondence: jan.kelner@wat.edu.pl; Tel.: +48-261-839-517
Abstract:
The basic technology that will determine the expansion of the technical capabilities of
fifth generation cellular systems is a massive multiple-input-multiple-output. Therefore, assessing
the influence of the antenna beam orientations on the radio channel capacity is very significant.
In this case, the effects of mismatching the antenna beam directions are crucial. In this paper, the
methodology for evaluating changes in the received signal power level due to beam misalignment
for the transmitting and receiving antenna systems is presented. The quantitative assessment of this
issue is presented based on simulation studies carried out for an exemplary propagation scenario.
For non-line-of-sight (NLOS) conditions, it is shown that the optimal selection of the transmitting
and receiving beam directions may ensure an increase in the level of the received signal by several
decibels in relation to the coaxial position of the beams. The developed methodology makes it
possible to analyze changes in the radio channel capacity versus the signal-to-noise ratio and distance
between the transmitter and receiver at optimal and coaxial orientations of antenna beams for various
propagation scenarios, considering NLOS conditions. In the paper, the influence of the directional
antenna use and their direction choices on the channel capacity versus SNR and the distance between
the transmitter and receiver is shown.
Keywords:
wireless communications; radio propagation; multi-elliptical propagation model; direc-
tional antennas; radio channel capacity; beam misalignment; non-line-of-sight (NLOS) conditions
1. Introduction
The effective increase in the capacity of wireless networks in relation to long term
evolution networks is one of the main goals in the development of fifth generation (5G)
systems. This results from the dynamic increase in the number of users, both people and
devices in relation to the Internet of Things [
1
,
2
], and the growing demand for the number
of provided telecommunications services. On the other hand, network capacity is directly
related to the channel capacity (i.e., spectral efficiency) of the individual radio links, which
is directly proportional to the bandwidth of the transmitted signals. Thus, increasing the
capacity of radio channel conditions is necessary for achieving the above-mentioned aim.
Fifth generation systems will also operate in millimeter-wave bands in addition to
the lower frequency ranges of microwaves used so far, i.e., decimeter and centimeter
waves [
2
6
]. Generally, a path loss between a transmitter (TX) and receiver (RX) increases
with frequency. The fundamental way to compensate for this increase in attenuation is to
increase the energy gain of the antenna system, which is inversely proportional to the width
of the radiation pattern. For this reason, in 5G systems, especially for millimeter-wave
ranges, directional antennas or multi-antenna systems, including those based on a massive
multiple-input-multiple-output (massive-MIMO) technology, will be used [
6
8
]. These
Sensors 2021,21, 8296. https://doi.org/10.3390/s21248296 https://www.mdpi.com/journal/sensors
Sensors 2021,21, 8296 2 of 20
types of antenna systems enable beamforming [
6
,
9
], which makes a spatial multiplexing
technique more effective.
In the transmitting antenna systems, a significant part of the energy is radiated in a
specific direction associated with an antenna power pattern direction, i.e., the direction of
the main lobe beam. To maximize a received signal power, i.e., minimizing the path loss for
the directional link, the direction of the receiving antenna beam should be appropriately
selected. Therefore, obtaining the maximum throughput in the directional wireless link
requires the implementation of an additional procedure that will ensure the optimal
orientation of the antenna beams.
Under line-of-sight (LOS) conditions, the beam directions of the transmitting and
receiving antennas are usually directed to each other to maximize the received signal
strength. However, in some cases, a beam alignment for LOS conditions is not possible.
For example, a base station beam (e.g., as the TX) is oriented in a specific sector direction,
while a mobile station (e.g., as the RX) moves along a street canyon, which does not match
the transmitting beam direction.
In non-LOS (NLOS) conditions characteristic for urban environments, the effect of a
beam misalignment is more visible and important for radio transmission achievement. In
this case, the orientation of the antenna beams on each other usually does not guarantee
minimizing the path loss. It may result from the occurrence of field obstacles, e.g., buildings,
in the TX–RX direction. Therefore, ensuring proper matching of the beam directions of the
transmitting and receiving antennas is necessary to maximize the received signal power. It
will allow obtaining the optimal capacity in the given propagation conditions.
The main aim of this paper is to evaluate the impact of parameters and the optimal
selection of antenna orientation on the radio channel capacity under NLOS conditions.
Minimizing the power losses resulting from the mismatch of the antenna beams and optimal
choice of their direction is the basis for the radio link quality analysis defined by the SNR.
The obtained results have a statistical nature and make it possible to assess the degradation
degree of channel capacity, considering the multipath environment propagation. This is
the basis for the effectiveness evaluation of the procedures for determining the optimal
orientation of both the transmitting and receiving antennas, ensuring maximum capacity
under specific propagation conditions. To assess changes in the received signal strength
for different antenna beam directions, a geometry-based multi-ellipsoidal propagation
model (MPM) [
10
,
11
] was used. This model is a three-dimensional (3D) version of the
multi-elliptical propagation model which takes into account only the azimuth plane [
11
].
The MPM considers the influence of the width and directions of beam patterns of the
transmitting and receiving antenna systems. It allows modifying the path loss model [
12
]
or received signal strength [
13
] of the directional link with beam misalignment. As a
result, the impact of the transmission parameters of the environment, antenna patterns,
and their spatial orientation on the channel capacity can be evaluated. This is the basis for
optimizing the antenna beam directions (e.g., in massive-MIMO systems), which ensures
the maximization of wireless link capacity under specific environmental conditions. Such
an approach to the analyzed problem, which takes into account the influence of a wide
range of environmental factors and factors related to the technical parameters of antenna
systems, determines the originality of the presented method for the assessment of the
channel capacity. The results presented in this paper refer to a strictly determined research
scenario, which is defined by the mutual position of the objects (i.e., TX and RX), beam
parameters [
14
], and the transmission properties of the propagation environment described
by the power delay profile (PDP) [
15
]. It is worth highlighting that this methodology used
for assessing the channel capacity, which considers the influence of parameters and patterns
of antenna beams, is universal and can be applied to various propagation environments
and scenarios.
Sensors 2021,21, 8296 3 of 20
2. Related Works
The channel capacity concept and subsequently formulated complete theory of infor-
mation and its transmission were developed by C.E. Shannon [
16
,
17
], based on the earlier
works of H. Nyquist and R. Hartley. Currently, this concept of communication channel ca-
pacity is called the Shannon–Hartley theorem (or Shannon capacity theorem) and is meant
as the theoretical upper bound on the information rate of data that can be transmitted at
an arbitrarily low error rate for the set signal-to-noise ratio (SNR). The analyzed channel
is classified as an additive white Gaussian noise (AWGN) and memoryless channel. In
the wireless link case, it should refer to the LOS and free space propagation conditions, an
isotropic antenna, so it does not consider the patterns and parameters of real antennas.
Later works defined capacities for channels with non-dispersive fading and then
parallel channels, which also provided an introduction to MIMO channels and spatial
diversity systems for dispersive propagation environments. The first works on the ergodic
capacity for the MIMO systems took into account Rayleigh fading and different types of
MIMO channels [
18
], e.g., uncorrelated, spatially correlated, double scattering, and keyhole.
On the other hand, in the literature, some papers focus on the capacity of channels with
Nakagami [19], Rician, Hoyt, or Weibull/log-normal fading [20].
For a few years, two (2D) or 3D geometry-based channel models have been used
to evaluate the channel capacity in multipath propagation environments characterized
by dispersion in time, frequency, and reception angle domains, e.g., [
21
]. This research
direction shows the influence of the patterns and parameters of antenna systems and the
angular dispersion occurring in the real multipath propagation environment on the channel
capacity determination. Recently, most of the research on capacity has been devoted to 5G
technologies (e.g., [
22
26
]), networks, and systems [
2
,
9
,
27
,
28
]. In particular, the analysis
of the signal propagation directions from the TX to the RX is crucial for systems based
on beamforming and massive-MIMO technologies [
25
,
26
]. The use of these technologies
in macro and micro-cells, as well as the creation of smaller, i.e., nano-, pico-, and femto-
cells (i.e., ultra-dense networks [
29
]) with the simultaneous use of spectral resources in
mm-wave bands [
5
,
30
] allows to significantly increase (about 10-fold [
29
]) not only the
spectral efficiency of individual channels and links, but also the capacity of the entire
network [
2
,
9
,
27
,
28
]. This aspect was accurately summarized in [
2
]: “
. . .
capacity for wireless
communication depends on spectral efficiency and bandwidth. It is also related to cell size
. . .
Cell sizes are becoming small and physical layer technology is already at the boundary of Shannon
capacity . . . ”.
Antenna beam misalignment in emerging 5G systems, especially in NLOS conditions,
is a significant issue from the viewpoint of effective beamforming and tracking procedures,
which ensure the achievement of the maximum capacity. Numerous papers, i.a., [
31
33
],
presenting both the effects and methods of reducing mismatch, testify to the importance
of this topic. The direction mismatch of the transmitting and receiving beams is the
reason for the increase in path loss. This fact is demonstrated in [
31
] by the results of
practically performed measurements. The effect of the increase in attenuation is the loss
of the received signal power, which results in a significant decrease in the throughput of
the directional link. Power losses have a significant impact on reducing the transmission
data rate. Examples of solutions that minimize the effects of mismatches for MIMO and
hybrid systems, non-orthogonal access systems based on the beamforming technique, are
presented in [32,33].
Hence, it may be seen that the analyzed area fits well with the current research trends.
In the novel relationship of the channel capacity proposed in Section 3, two impact factors
of multipath propagation environment and antenna systems, respectively, were introduced.
These factors ensure the appropriate modification of the capacity for the selected single-
channel defined by Shannon [
16
,
17
]. In the case of MIMO channels, the obtained results
should be adequately diversified. This approach is innovative and original in relation to the
above-presented methods of channel capacity estimation. In this capacity evaluation, the
MPM [
11
] as a geometry-based channel model, which is based on any PDP, and consider
Sensors 2021,21, 8296 4 of 20
the parameters of antenna beams, was used. It allows for the analysis of the influence of
the angular spread of the received signals on the capacity in time-varying channels. On the
other hand, the MPM was verified based on empirical results, which provides the basis
for the correctness of the presented analyses. Often, the channel capacity is represented in
an analytical form and as a graph as a function of SNR, the number of antenna elements
in MIMO systems, or environmental parameters (e.g., for different fading distributions).
However, from a practical point of view, it is worth illustrating capacity as a function of the
TX–RX distance at a given SNR for the reference distance, which was done in this work too.
The remainder of this paper is organized as follows. Section 3includes the novel
approach to express the relationship between the channel capacity and the environmental
factors and antenna beam parameters. In Section 4, the MPM description and power
angular spectrum (PAS) estimation based on it is shown in short. Next, in Section 5, the
impact of the antenna beam directions on the received total power under LOS and NLOS
conditions is analyzed. Section 6depicts the influence of the antenna beam orientation
on the radio channel capacity. The results shown in Sections 5and 6were obtained based
on simulation studies for the selected spatial scenarios using the MPM and MATLAB
environment. Finally, a summary of the paper is contained in Section 7.
3. Capacity and Antenna Beam Parameters
The Shannon-Hartley theorem [
16
,
17
] introduces the fundamental relationship that
describes the relative capacity of the transmission channel,
Cf
, in particular, for the radio link
Cf(bit/s/Hz)=log2(1+SNR), (1)
where
SN R =Pf/Pn
is the ratio of the desired signal power
Pf
to the additive interference
power
Pn
in the AWGN form induced in the omnidirectional antenna. In this paper, the
above relationship is treated as a reference, which describes the capacity of the radio
channel with an omnidirectional antenna system under free-space propagation conditions.
In a multipath propagation environment, especially in NLOS conditions, the level
of the desired signal is significantly reduced. It is the cause of the SNR reduction and
consequently of the channel capacity. Based on the Friis transmission equation [
34
], it can
be written
Pf(D)1/PL f(D)and Pm(D)1/PLm(D),(2)
where
Pf(D)
and
Pm(D)
are the desired signal powers received in free-space and multipath
propagation conditions versus distance
D
between the TX and RX, respectively, while
PL f(D)
and
PLm(D)
are environmental path loss under free-space and multipath propa-
gation conditions, respectively. For free-space propagation, the path loss in LOS conditions
has the form [34]
PL f(D)(dB)=20 log10 (4πD/λ), (3)
where
λ=c/fc
and
fc
are the wavelength and carrier frequency of the transmitted signal,
respectively, and cis the lightspeed.
For multipath propagation environments, the path loss may be represented by mul-
tiple propagation models. As examples of such models, MiWEBA (Millimetre-Wave
Evolution for Back-haul and Access) [
35
], METIS (Mobile and wireless communications
Enablers for the Twenty-twenty Information Society) [
36
], and 3GPP TR (3rd Generation
Partnership Project Technical Report) 38.901 [
15
] can be pointed out. The radio channel
capacity analysis presented in the remainder of the paper is based on the close-in (CI) free-
space reference distance path loss model [
14
], which does not affect the general character
of the proposed approach. The CI path loss model is shown in the following form:
PLm(D)(dB)=PLm(D0)+10PLE log10(D/D0), (4)
where
PLE
means a path loss exponent (PLE) and
D0
is the reference distance (for mm-
wave, usually
D0=
1
m
). In this case, the propagation conditions are defined by the
Sensors 2021,21, 8296 5 of 20
appropriate selection of PLE values, which were determined based on empirical measure-
ments. For example, these coefficient values for millimeter-waves and selected scenarios
are presented in [
14
]. The main drawback of this path loss determination approach for
radio links with narrow-beam antenna patterns is the fact that the measurement data used
for the
PLE
estimation are obtained for strictly determined parameters of the test-bed
antennas.
For the purposes of further analysis, the concept of the environmental factor
Ke(D)
is
introduced. It describes the relationship between the received signal powers in a multi-
path environment
Pm(D)
and in free-space conditions
Pf(D)
, considering omnidirectional
antenna systems. Based on Equation (2), this coefficient can be expressed as
Ke(D)=Pm(D)
Pf(D)=PL f(D)
PLm(D). (5)
Therefore, assuming the same level of environmental interference (i.e., noise), the
channel capacity in the conditions of multipath propagation can be presented in the form
Cm=log2(1+KeSN R). (6)
To consider the influence of antenna system parameters on the channel capacity, the
antenna system factor is introduced
Ka(D)=Ps(D)
Pm(D), (7)
where
Ps(D)
represents the received signal power in the link with the narrow-beam antenna
system. This factor describes the relationship between the received signal powers in a mul-
tipath propagation environment using narrow-beam antenna systems and omnidirectional
antennas.
Introducing the coefficients
Ke(D)
and
Ka(D)
makes it possible to determine the func-
tional relationship between the signal powers
Ps(D)
and
Pf(D)
received in the links with
narrow-beam and omnidirectional antennas in the multipath and free-space propagation
environments, respectively,
Ps(D)=Ka(D)Ke(D)Pf(D). (8)
Hence, the channel capacity
Cs
considering the multipath propagation environment
and the narrow-beam antenna system can be expressed by the following formula:
Cs=log2(1+KeKaSN R). (9)
Equation (5) shows that the propagation models for free-space and for multipath
conditions are the basis for determining the environmental factor
Ke(D)
. On the other
hand, the evaluation of the average received power is necessary for determining the
antenna system factor,
Ka(D)
. The proposed assessment method of channel capacity uses
the MPM to determine
Ps(D)
in the radio link with the narrow-beam antenna system,
considering the multipath propagation conditions. Thanks to this, the influence of both the
antenna parameters and the transmission properties of the propagation environment on
the channel capacity can be mapped.
In further analysis, as references, Shannon measures of the channel capacities,
Cf
and
Cd
, defined for free-space conditions, omnidirectional and directional antennas, respec-
tively, are used.
Cf
is defined by Equation (1), whereas based on the Friis transmission [
34
],
Cd
considers the change in gains (in linear measure) of the transmitting
GT
and receiving
GRantennas relative to the omnidirectional antennas
Cd=log2(1+GTGRSN R), (10)
Sensors 2021,21, 8296 6 of 20
where
SN R
is determined for the omnidirectional antennas according to the above defini-
tion. In the case of Cd, the antenna beams are oriented to each other.
4. Multi-Elliptical Propagation Model and Power Angular Spectrum Estimation
The MPM provides the estimation of a PAS,
p(θR,ϕR)
, or probability density function
(PDF),
f(θR,ϕR)
, of angle of arrival (AOA),
(θR,ϕR)
where
θR
and
ϕR
are the angles in the
elevation and azimuth planes, respectively. This model is a 3D geometry-based statistical
approach to modeling the spatial scattering of the received signal [
10
,
11
]. Figure 1shows
the MPM geometry, i.e., potential scattering areas represented by confocal semi-ellipsoids
or ellipses in 3D or 2D model versions, respectively [
11
]. This geometry results from a
PDP defining transmission properties of the analyzed channel. On the other hand, powers
defined in the PDP are the basis for determining the power of each propagation path. This
solution was firstly used by J.D. Parsons and A.S. Bajwa [
37
], and next by C. Oestges, V.
Erceg, and A.J. Paulraj [
38
]. In the MPM, it is assumed that the received signal is a sum of
delayed components related to the scatterers occurring on the appropriate semi-ellipsoids.
Sensors 2021, 21, 8296 7 of 22
Figure 1. Scattering geometry of MPM.
The geometric structure parameters of the MPM are closely related to the transmis-
sion properties of the propagation environment described by the PDP. In the case of en-
vironments with multipath propagation, the presence of several or a dozen local extremes
of the PDP function can be observed. This means that as a result of scattering on obstacles,
the electromagnetic wave reaches the RX through various propagation paths. This is the
reason why many components of the received signal arrive at the RX with different delays.
In practice, the components derived from the single scatterings determine the received
signal level. Thus, the semi-ellipsoids can be used to map the most likely positions of the
scattering elements. Obviously, the number of ellipsoids is equal to the number of PDP
extremes that come from the components of the received signal that form time-clusters
with similar delay. If the TX–RX distance is equal to ,D then the major xn
a and minor
,
yn
b zn
c half-axes of the nth semi-ellipsoid have the form [39]:
() ()
=+ == +
11
and 2 ,
22
xn n yn zn n n
acτDbccτcτD (11)
where n
τ is the delay of the nth time-cluster. These delays are determined as arguments
of the PDP local extrema. Each of such extremum represents the time-cluster of the reach-
ing propagation paths.
The geometric structure of the MPM has been described in detail in [10,11,39]. The
3D MPM model can be reduced to a 2D multi-elliptical model, in which the propagation
phenomena dominate in the azimuth plane [11]. This modeling approach in relation to
other geometry-based channel models ensures the minimization of the PAS estimation
Figure 1. Scattering geometry of MPM.
The geometric structure parameters of the MPM are closely related to the transmission
properties of the propagation environment described by the PDP. In the case of environ-
ments with multipath propagation, the presence of several or a dozen local extremes of
the PDP function can be observed. This means that as a result of scattering on obstacles,
the electromagnetic wave reaches the RX through various propagation paths. This is the
reason why many components of the received signal arrive at the RX with different delays.
In practice, the components derived from the single scatterings determine the received
signal level. Thus, the semi-ellipsoids can be used to map the most likely positions of the
scattering elements. Obviously, the number of ellipsoids is equal to the number of PDP
extremes that come from the components of the received signal that form time-clusters
Sensors 2021,21, 8296 7 of 20
with similar delay. If the TX–RX distance is equal to
D
, then the major
axn
and minor
byn
,
czn half-axes of the nth semi-ellipsoid have the form [39]:
axn =1
2(cτn+D)and byn =czn =1
2pcτn(cτn+2D),(11)
where
τn
is the delay of the nth time-cluster. These delays are determined as arguments of
the PDP local extrema. Each of such extremum represents the time-cluster of the reaching
propagation paths.
The geometric structure of the MPM has been described in detail in [
10
,
11
,
39
]. The
3D MPM model can be reduced to a 2D multi-elliptical model, in which the propagation
phenomena dominate in the azimuth plane [
11
]. This modeling approach in relation to
other geometry-based channel models ensures the minimization of the PAS estimation
error as shown in [
40
]. The efficiency of channel modeling using multi-ellipsoidal geometry
is also shown in [
41
] for the real vehicular-to-infrastructure scenario in the 60 GHz band
described in [42].
Estimation of
p(θR,ϕR)
consists in determining the trajectories of the propagation
paths coming from the TX and reaching the RX. These paths consider the multi-ellipsoidal
geometry of the scatterer positions. As mentioned, the geometric structure of the MPM
maps the potential locations of the scattering elements. Thus, the intersection of the
radiated propagation path with the individual semi-ellipses indicates the positions of the
scattering elements. Based on the angle of departure (AOD),
(θT,ϕT)
, where
θT
and
ϕT
are
the angles in the elevation and azimuth planes, respectively, the radial coordinate of the
scatterer in the spherical system with the origin in the TX can be determined [39]
rT=1
2ab2
yDsin θTcos ϕT+1
2asb2
yDsin θTcos ϕT2+4ab2
ya2
xD2
4, (12)
where
a=bysin θTcos ϕT2+a2
xcos2θT+(sin θTsin ϕT)2
,
ax=axn
, and
by=byn
.
Equation (12) is the result of solving the equation system describing the selected semi-
ellipsoid and the propagation path line from the TX for the analyzed AOD, (θT,ϕT)[39].
The coordinate transformation involving the translation of the coordinate system
origin to the RX allows for the AOA determination of individual propagation paths [39]
θR=arctan q(rTsin θTcos ϕT+D)2+(rTsin θTsin ϕT)2
rTcos θT
, (13)
ϕR=arctan rTsin θTsin ϕT
rTsin θTcos ϕT+D. (14)
In the simulation procedure for estimating
p(θR,ϕR)
, the normalized radiation pattern
of the transmitting antennas,
|gT(θT,ϕT)|2
, is used to generate the AODs, (
θT
,
ϕT
). Since
these patterns meet the probability density axioms [
43
], the PDF of AOD can be written
as [39]
fT(θT,ϕT)=1
4π|gT(θT,ϕT)|2sin θT
for θTh0, π/2)and ϕThπ,π).(15)
In the MPM, the local scattering phenomenon that occurs in the vicinity of the trans-
mitting and receiving antennas is also taken into account. In this case, the two-dimensional
von Mises distribution is used to describe the AOA statistical properties [11,39]
f0(θR,ϕR)=C0exp(γθcos(π/2θR))
2πI0(γθ)·exp(γϕcos ϕR)
2πI0(γϕ)
for θRh0, π/2)and ϕRhπ,π),
(16)
where
γθ
and
γϕ
define the angular dispersion of the local scattering components in
the elevation and azimuth planes, respectively,
I0(·)
is the zero-order modified Bessel
Sensors 2021,21, 8296 8 of 20
function of an imaginary argument, and
C0
represents the normalizing constant such that
(C0/2πI0(γθ))
π/2
R0
exp(γθcos(π/2 θR))dθR=1.
In the simulation procedure, the powers of the received signal components that are
associated with the individual propagation paths are determined from the PDP. To generate
these powers, an exponential distribution whose parameters (i.e., mean values
pn
) are the
local extremes of the PDP is adopted
fp(e
p)=(1/pn)exp(e
p/pn)for e
p0,
0 for e
p<0, (17)
where
pn
is the nth local extreme of the PDP that corresponds to the propagation paths
from the nth semi-ellipsoid.
As a result of the simulation, an ordered set of AOAs,
(θR,ϕR)
, and the corresponding
powers
~
p
are obtained. This set is the basis for the estimation the PAS,
pR(θR,ϕR)
in the
vicinity of the receiving antenna [
39
]. To obtain the PAS at the output of the receiving
antenna,
p(θR,ϕR)
, spatial filtering of
pR(θR,ϕR)
using the normalized pattern of the
receiving antenna,
|gR(θR,ϕR)|2
, should be realized [
10
,
11
]. A similar procedure of spatial
filtering is described in [
15
]. A detailed description of the practical implementation of
the estimation procedure can be found in [
11
]. The PAS at the output of the receiving
antenna,
p(θR,ϕR)
, are the basis for determining the received power
Ps(D)
according to
the relationship [11]
Ps=
π
Z
π
π/2
Z
0
p(θR,ϕR)dθRdϕR=
π
Z
π
π/2
Z
0
pR(θR,ϕR)|gR(θR,ϕR)|2dθRdϕR. (18)
Equations (7) and (18) show that the calculation of the antenna system factor,
Ka(D)
,
comes down to the determination of p(θR,ϕR).
The above description shows that many factors related to electromagnetic wave prop-
agation, which significantly affect the received signal level, are included in the proposed
method of the PAS estimation. The transmission properties of the propagation environment
characterizing the PDP determine the geometrical structure of the MPM and its spatial
parameters. The mapping of the spatial filtration phenomenon by the antenna systems is
realized by the utilization of their normalized radiation/reception patterns in the genera-
tion procedure of AODs, AOAs, and powers of the propagation paths. This approach to the
analyzed problem allows to consider the influence of antenna parameters (i.e., directions
of maximum radiation/reception, half-power beamwidths (HPBWs), pattern shape) on the
received signal level and, as a result, on the radio channel capacity. This is important in
NLOS conditions especially.
5. Antenna Orientation and Received Power for LOS/NLOS Conditions
The MPM does not directly provide path loss prediction and only gives us the pos-
sibility of assessing the PAS as a normalized function. In practice, many models derived
from statistically averaged measurement data can be used to evaluate the path loss. How-
ever, these models are defined for the beams directed on each other and selected HPBWs,
e.g., [
14
,
44
]. Presented in [
12
,
13
], the MPM-based methodology provides the modification
of the path loss and power balance for different HPBWs and orientations of the antenna
beams. A relative power factor,
K
, is its basis. It represents a relative power for the analyzed
beam mismatch and alignment conditions, as follows
K(α,β,D)(dB)=10 log10
Ps(α,β,D)
Ps(α=180,β=0,D), (19)
Sensors 2021,21, 8296 9 of 20
where
Ps(D)Ps(α,β,D)
is the received power for the
α
and
β
directions of the trans-
mitting and receiving antenna beams (determined with respect to the OX axe in Figure 1),
respectively, and the selected distance
D
. This power is calculated based on Equation (18)
and the PAS obtained in the MPM.
5.1. Assumptions for Simulation Studies
The evaluation of the power losses resulting from the mismatch of the antenna beams
in the directional link and optimal selection of their orientation especially in NLOS condi-
tions, is based on the simulation tests. Additionally, simulation results for LOS conditions
to verify the simulation procedure correctness and to show the more complex nature of
the propagation phenomenon under NLOS conditions are presented. In the paper, all
presented simulation studies were performed based on the MPM implementation prepared
in the MATLAB environment.
In simulation studies, a spatial scenario as shown in Figure 1was analyzed. The
adopted scenario may suit communications in microcell between the 5G New Radio
gNodeB base station and user equipment operating in the millimeter-wave band. The
following assumptions were considered:
carrier frequency is equal to fc=28 GHz;
PDPs are based on tapped-delay line (TDL) models from the 3GPP TR 38.901 stan-
dard [
15
], i.e., the TDL-B and TDL-D for NLOS and LOS conditions, respectively;
these TDLs are adopted for analyzed
fc
and rms delay spread,
στ
, for so-called the
normal-delay profile and urban macro (UMa) scenario, i.e., στ=266 ns;
Rician factor defining the direct path component in the scenario for LOS conditions is
appropriate for TDL-D [15], i.e., κ=13.3 dB;
intensity coefficients of the local scattering components, i.e., the 2D von Mises distri-
bution parameters, are equal to γθ=γϕ=60;
distance between the TX and RX is equal to D=50 m;
beam power patterns consider only the main lobe of the antenna systems. These
patterns are modeled by a Gaussian model [
43
] for the appropriate beam parameters,
i.e., HPBWs and gain.
HPBWs of the transmitting and receiving antennas are the same in the azimuth and
elevation planes, i.e.,
HPBWTθ,Rθ=HPBWTϕ,Rϕ=
10
based on the real antenna
parameters used in [14,44];
gains of the transmitting and receiving antennas are calculated based on the following
formula [45,46]:
GT,R=41253η
HPBWTθ,RθHPBWTϕ,Tϕ
, (20)
where
η=
0.7 is a typical average antenna efficiency. By extension, the gains are equal
to GT=GR=24.6 dBi for the transmitting and receiving antennas, respectively.
Low heights of the transmitting (7 m) and receiving (1.5 m) antennas are based on
measurement scenarios [14];
beam alignment is defined for α=180and β=0(see Figure 1);
analyzed ranges of beam directions are as follows: 90
α
270
and
90
β
90
;
steps of changing the antenna directions in simulation studies are α=β=1;
to obtain average statistical results in the MPM,
L=
10 paths are generated at the
TX for each time-cluster (semi-ellipsoid). On the other hand,
M=
360 Monte-Carlo
simulations were run for each analyzed scenario; in this case, the average resolution
of generating the AODs is about 0.1.
In accordance with the purpose of simulation tests, the mismatch effects of direc-
tions between the transmitting and receiving beams are presented. As a measure of the
power loss of the received signal, which results from the beam misalignment, the factor
K(α,β,D)K(α,β)defined by Equation (19) was used.
These studies relied on the Gaussian model [
43
] for the main lobe of the antenna
pattern. However, it should be highlighted that the MPM may consider any pattern
Sensors 2021,21, 8296 10 of 20
shape. For example, in [
47
,
48
], the actual pattern of 5G New Radio gNodeB base station
antenna system based on the massive-MIMO technology was implemented in the MPM
for downlink and uplink inter-beam interference analysis.
5.2. LOS Conditions
First, the effects of beam direction mismatch for LOS conditions (i.e., for TDL-D [15])
are presented. In Figures 2and 3,
K(α,β)
as a function of
α
and
β
directions of the
transmitting and receiving antenna beams is illustrated.
Sensors 2021, 21, 8296 11 of 22
analyzed ranges of beam directions are as follows: 90 270α°≤ ° and
90 90 ;
β
−°≤≤ °
steps of changing the antenna directions in simulation studies are ΔΔ1;αβ==°
to obtain average statistical results in the MPM, =10L paths are generated at the
TX for each time-cluster (semi-ellipsoid). On the other hand, 360
M
= Monte-
Carlo simulations were run for each analyzed scenario; in this case, the average res-
olution of generating the AODs is about 0.1 .°
In accordance with the purpose of simulation tests, the mismatch effects of directions
between the transmitting and receiving beams are presented. As a measure of the power
loss of the received signal, which results from the beam misalignment, the factor
()()
,,KαβDKαβ defined by Equation (19) was used.
These studies relied on the Gaussian model [43] for the main lobe of the antenna
pattern. However, it should be highlighted that the MPM may consider any pattern shape.
For example, in [47,48], the actual pattern of 5G New Radio gNodeB base station antenna
system based on the massive-MIMO technology was implemented in the MPM for down-
link and uplink inter-beam interference analysis.
5.2. LOS Conditions
First, the effects of beam direction mismatch for LOS conditions (i.e., for TDL-D [15])
are presented. In Figures 2 and 3,
()
,
Kαβ as a function of α and
β
directions of the
transmitting and receiving antenna beams is illustrated.
Figure 2. Relative power factor K(α,β) versus α and β directions of transmitting and receiving beams
under LOS conditions (3D graph).
Figure 2.
Relative power factor K(
α
,
β
) versus
α
and
β
directions of transmitting and receiving beams
under LOS conditions (3D graph).
Sensors 2021, 21, 8296 12 of 22
Figure 3. Relative power factor K(α,β) versus α and β directions of transmitting and receiving beams
under LOS conditions (2D graph).
These graphs clearly show that when the beams are directed at each other, a domi-
nant received power is obtained. In addition, it may be seen that if the transmitting beam
is not directed at the RX (i.e., 180α≠± °), the occurring power losses can be partially com-
pensated by the optimal selection of the receiving beam direction .
β
The compensation
efficiency of the receiving beam direction is depicted in Figure 3. Additionally, in Figure
4, the power losses that occur while maintaining a constant receiving angle 0
β
(red
dashed line) are shown.
Figure 4. Received signal power losses due to mismatch of transmitting beam direction under LOS
conditions.
In the analyzed LOS conditions, the Rician factor is equal to 13.3 dB. This means that
the first time-cluster in the PDP is dominant. Thus, the direct path (i.e., 00τ=) signifi-
cantly determines the received power for beam misalignment as well, which results from
the Friis equation [34]. Figures 2 and 3 show that the maximum power is obtained for
beam alignment, which is obvious. The direction of the receiving antenna has a decisive
influence on the power level. Despite the direction changes of the transmitting antenna,
the extremum power is ensured when the RX antenna is pointed at the TX.
For individual ,α the graph of the optimal reception angle (i.e., the optimal direc-
tion of the receiving beam), max ,β which ensures the maximization of the received signal
power, i.e.,
Figure 3.
Relative power factor K(
α
,
β
) versus
α
and
β
directions of transmitting and receiving beams
under LOS conditions (2D graph).
These graphs clearly show that when the beams are directed at each other, a dominant
received power is obtained. In addition, it may be seen that if the transmitting beam
is not directed at the RX (i.e.,
α6=±
180
), the occurring power losses can be partially
compensated by the optimal selection of the receiving beam direction
β
. The compensation
efficiency of the receiving beam direction is depicted in
Figure 3.
Additionally, in
Figure 4,
the power losses that occur while maintaining a constant receiving angle
β=
0
(red
dashed line) are shown.
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Sensors 2021, 21, 8296 12 of 22
Figure 3. Relative power factor K(α,β) versus α and β directions of transmitting and receiving beams
under LOS conditions (2D graph).
These graphs clearly show that when the beams are directed at each other, a domi-
nant received power is obtained. In addition, it may be seen that if the transmitting beam
is not directed at the RX (i.e., 180α≠± °), the occurring power losses can be partially com-
pensated by the optimal selection of the receiving beam direction .
β
The compensation
efficiency of the receiving beam direction is depicted in Figure 3. Additionally, in Figure
4, the power losses that occur while maintaining a constant receiving angle 0
β
(red
dashed line) are shown.
Figure 4. Received signal power losses due to mismatch of transmitting beam direction under LOS
conditions.
In the analyzed LOS conditions, the Rician factor is equal to 13.3 dB. This means that
the first time-cluster in the PDP is dominant. Thus, the direct path (i.e., 00τ=) signifi-
cantly determines the received power for beam misalignment as well, which results from
the Friis equation [34]. Figures 2 and 3 show that the maximum power is obtained for
beam alignment, which is obvious. The direction of the receiving antenna has a decisive
influence on the power level. Despite the direction changes of the transmitting antenna,
the extremum power is ensured when the RX antenna is pointed at the TX.
For individual ,α the graph of the optimal reception angle (i.e., the optimal direc-
tion of the receiving beam), max ,β which ensures the maximization of the received signal
power, i.e.,
Figure 4.
Received signal power losses due to mismatch of transmitting beam direction under LOS
conditions.
In the analyzed LOS conditions, the Rician factor is equal to 13.3 dB. This means
that the first time-cluster in the PDP is dominant. Thus, the direct path (i.e.,
τ0=
0)
significantly determines the received power for beam misalignment as well, which results
from the Friis equation [
34
]. Figures 2and 3show that the maximum power is obtained for
beam alignment, which is obvious. The direction of the receiving antenna has a decisive
influence on the power level. Despite the direction changes of the transmitting antenna,
the extremum power is ensured when the RX antenna is pointed at the TX.
For individual
α
, the graph of the optimal reception angle (i.e., the optimal direction
of the receiving beam),
βmax
, which ensures the maximization of the received signal power,
i.e.,
Kmax =K(α,βmax)=max
90β90K(α,β), (21)
is presented in Figure 5.
Sensors 2021, 21, 8296 13 of 22
() ()
max max 90 90
,
max , ,
β
KKαβ Kαβ
−°≤°
== (21)
is presented in Figure 5.
Figure 5. Optimal reception angle for different transmitting beam direction under LOS conditions.
The charts in Figures 4 and 5 prove the obvious conclusion graphically. For LOS con-
ditions, the optimal direction of the receiving beam is generally constant and equal
max 0.β≅°
Practically, it means that in this case it has no way of compensating the effects
of mismatching the direction of the transmitting beam by proper selection of the receiving
beam direction. This is due to the presence of the delayed components (i.e., time-clustes
for 0
n
τ>) in addition to the dominant direct path occurring under LOS conditions. In
free space conditions, the direct path appears only. In this case, the graph in Figure 5
would have a constant value for max 0.β
5.3. NLOS Conditions
Under NLOS conditions (i.e., for TDL-B [15]), the multipath propagation phenome-
non makes it necessary to search for optimal α and
β
directions of the transmitting and
receiving antenna beams, which will ensure the maximization of the received signal level.
Figures 6 and 7 illustrate the mismatch effects between the TX and RX beam directions.
Figure 5. Optimal reception angle for different transmitting beam direction under LOS conditions.
The charts in Figures 4and 5prove the obvious conclusion graphically. For LOS
conditions, the optimal direction of the receiving beam is generally constant and equal
βmax
=
0
. Practically, it means that in this case it has no way of compensating the effects
of mismatching the direction of the transmitting beam by proper selection of the receiving
beam direction. This is due to the presence of the delayed components (i.e., time-clustes
for
τn>
0) in addition to the dominant direct path occurring under LOS conditions. In free
space conditions, the direct path appears only. In this case, the graph in Figure 5would
have a constant value for βmax =0.
Sensors 2021,21, 8296 12 of 20
5.3. NLOS Conditions
Under NLOS conditions (i.e., for TDL-B [
15
]), the multipath propagation phenomenon
makes it necessary to search for optimal
α
and
β
directions of the transmitting and receiving
antenna beams, which will ensure the maximization of the received signal level. Figures 6
and 7illustrate the mismatch effects between the TX and RX beam directions.
Sensors 2021, 21, 8296 13 of 22
() ()
max max 90 90
,
max , ,
β
KKαβ Kαβ
−°≤°
== (21)
is presented in Figure 5.
Figure 5. Optimal reception angle for different transmitting beam direction under LOS conditions.
The charts in Figures 4 and 5 prove the obvious conclusion graphically. For LOS con-
ditions, the optimal direction of the receiving beam is generally constant and equal
max 0.β≅°
Practically, it means that in this case it has no way of compensating the effects
of mismatching the direction of the transmitting beam by proper selection of the receiving
beam direction. This is due to the presence of the delayed components (i.e., time-clustes
for 0
n
τ>) in addition to the dominant direct path occurring under LOS conditions. In
free space conditions, the direct path appears only. In this case, the graph in Figure 5
would have a constant value for max 0.β
5.3. NLOS Conditions
Under NLOS conditions (i.e., for TDL-B [15]), the multipath propagation phenome-
non makes it necessary to search for optimal α and
β
directions of the transmitting and
receiving antenna beams, which will ensure the maximization of the received signal level.
Figures 6 and 7 illustrate the mismatch effects between the TX and RX beam directions.
Figure 6.
Relative power factor K(
α
,
β
) versus
α
and
β
directions of transmitting and receiving beams
under NLOS conditions (3D graph).
Sensors 2021, 21, 8296 14 of 22
Figure 6. Relative power factor K(α,β) versus α and β directions of transmitting and receiving beams
under NLOS conditions (3D graph).
Figure 7. Relative power factor K(α,β) versus α and β directions of transmitting and receiving beams
under NLOS conditions (2D graph).
The graphs presented in Figure 8 show that in NLOS conditions for a limited range
of changes 90α
and for assumed parameters of antennas and propagation environ-
ments, a 6 dB increase in the received power can be achieved by optimal selection of the
TX and RX beam angles. This means that under these propagation conditions the mutual
coaxiality of the beams does not provide the highest received signal level.
Figure 8. Compensation effectiveness for beam misalignment under NLOS conditions.
Furthermore, Figure 8 shows that for the analyzed scenario, in the absence of coaxi-
ality of the transmitting beam direction, which exceeds ±15°, the optimal selection of the
receiving beam direction provides the possibility of increasing the received power in re-
lation to the beam alignment. Therefore, in systems using the massive-MIMO and beam-
forming technologies, the optimal selection of the antenna beam directions should be pro-
vided.
The statistical evaluation of an optimal direction of the receiving beam corresponding
to the transmitting beam misalignment is presented in Figure 9.
Figure 7.
Relative power factor K(
α
,
β
) versus
α
and
β
directions of transmitting and receiving beams
under NLOS conditions (2D graph).
The graphs presented in Figure 8show that in NLOS conditions for a limited range of
changes
|α|<
90
and for assumed parameters of antennas and propagation environments,
a 6 dB increase in the received power can be achieved by optimal selection of the TX and
RX beam angles. This means that under these propagation conditions the mutual coaxiality
of the beams does not provide the highest received signal level.
Furthermore, Figure 8shows that for the analyzed scenario, in the absence of coaxiality
of the transmitting beam direction, which exceeds
±
15
, the optimal selection of the
receiving beam direction provides the possibility of increasing the received power in
relation to the beam alignment. Therefore, in systems using the massive-MIMO and
beamforming technologies, the optimal selection of the antenna beam directions should be
provided.
Sensors 2021,21, 8296 13 of 20
Sensors 2021, 21, 8296 14 of 22
Figure 6. Relative power factor K(α,β) versus α and β directions of transmitting and receiving beams
under NLOS conditions (3D graph).
Figure 7. Relative power factor K(α,β) versus α and β directions of transmitting and receiving beams
under NLOS conditions (2D graph).
The graphs presented in Figure 8 show that in NLOS conditions for a limited range
of changes 90α
and for assumed parameters of antennas and propagation environ-
ments, a 6 dB increase in the received power can be achieved by optimal selection of the
TX and RX beam angles. This means that under these propagation conditions the mutual
coaxiality of the beams does not provide the highest received signal level.
Figure 8. Compensation effectiveness for beam misalignment under NLOS conditions.
Furthermore, Figure 8 shows that for the analyzed scenario, in the absence of coaxi-
ality of the transmitting beam direction, which exceeds ±15°, the optimal selection of the
receiving beam direction provides the possibility of increasing the received power in re-
lation to the beam alignment. Therefore, in systems using the massive-MIMO and beam-
forming technologies, the optimal selection of the antenna beam directions should be pro-
vided.
The statistical evaluation of an optimal direction of the receiving beam corresponding
to the transmitting beam misalignment is presented in Figure 9.
Figure 8. Compensation effectiveness for beam misalignment under NLOS conditions.
The statistical evaluation of an optimal direction of the receiving beam corresponding
to the transmitting beam misalignment is presented in Figure 9.
Sensors 2021, 21, 8296 15 of 22
Figure 9. Optimal reception angle for different transmitting beam direction under NLOS conditions.
Figures 7 and 8 show that under NLOS conditions, the received signal obtains the
statistically highest power level for the TX beam direction equal to 90 .α ° However,
in this case, the beam direction of the receiving antenna to achieve this power level should
be equal max 23 .β≅°
The lack of the direct path (i.e., the Rician factor equal to 0) under NLOS conditions
is the principal cause of the difference in results in relation to those obtained for LOS con-
ditions. For NLOS conditions, the majority of the received power comes from the delayed
components scattered on the semi-ellipsoids. Therefore, the global maximum of the re-
ceived power does not appear for 180α
and 0
β
(see Figures 6–8).
6. Antenna Orientation and Radio Channel Capacity
The results presented in Section 5 show that under NLOS propagation conditions, to
obtain the maximum received signal level on the radio link with directional antennas, it
is necessary to determine the optimal orientation of the antenna beams. Of course, in LOS
conditions, this problem does not arise since the direction determined by the TX and RX
positions is the direction of the maximum received signal level. In this section, an assess-
ment of the impact of both environmental transmission properties and antenna orienta-
tions on the channel capacity under NLOS conditions is presented. As reference data, the
Shannon channel capacities f
C and d
C with the omnidirectional and directional an-
tenna systems under free-space propagation conditions, respectively, were assumed.
The assessment of the received signal level, and consequently the SNR, which di-
rectly determines the channel capacity, is based on the MPM use in the simulation test
procedure, considering antennas with narrow radiation/reception beams. These studies
are carried out for the assumptions described in Section 5, taking into account the changes
in the distance .D The transmission properties of the propagation environment are re-
flected in the adopted CI path loss model [14] described by Equation (4).
This influence maps the channel capacity variation with the omnidirectional antenna
systems as a function of the reference SNR, which corresponds to free-space propagation
conditions. In this case, the SNR is directly proportional to the emitted signal level. For
free-space LOS (blue line), multipath LOS (red line), and multipath NLOS (black line)
propagation conditions, the graphs of capacity as an SNR function are shown in Figure
10.
Figure 9.
Optimal reception angle for different transmitting beam direction under NLOS conditions.
Figures 7and 8show that under NLOS conditions, the received signal obtains the
statistically highest power level for the TX beam direction equal to
α=±
90
. However, in
this case, the beam direction of the receiving antenna to achieve this power level should be
equal βmax
=23.
The lack of the direct path (i.e., the Rician factor equal to 0) under NLOS conditions
is the principal cause of the difference in results in relation to those obtained for LOS
conditions. For NLOS conditions, the majority of the received power comes from the
delayed components scattered on the semi-ellipsoids. Therefore, the global maximum of
the received power does not appear for α=180and β=0(see Figures 68).
6. Antenna Orientation and Radio Channel Capacity
The results presented in Section 5show that under NLOS propagation conditions,
to obtain the maximum received signal level on the radio link with directional antennas,
it is necessary to determine the optimal orientation of the antenna beams. Of course, in
LOS conditions, this problem does not arise since the direction determined by the TX
and RX positions is the direction of the maximum received signal level. In this section,
an assessment of the impact of both environmental transmission properties and antenna
Sensors 2021,21, 8296 14 of 20
orientations on the channel capacity under NLOS conditions is presented. As reference
data, the Shannon channel capacities
Cf
and
Cd
with the omnidirectional and directional
antenna systems under free-space propagation conditions, respectively, were assumed.
The assessment of the received signal level, and consequently the SNR, which directly
determines the channel capacity, is based on the MPM use in the simulation test procedure,
considering antennas with narrow radiation/reception beams. These studies are carried
out for the assumptions described in Section 5, taking into account the changes in the
distance
D
. The transmission properties of the propagation environment are reflected in
the adopted CI path loss model [14] described by Equation (4).
This influence maps the channel capacity variation with the omnidirectional antenna
systems as a function of the reference SNR, which corresponds to free-space propagation
conditions. In this case, the SNR is directly proportional to the emitted signal level. For
free-space LOS (blue line), multipath LOS (red line), and multipath NLOS (black line)
propagation conditions, the graphs of capacity as an SNR function are shown in Figure 10.
Sensors 2021, 21, 8296 16 of 22
Figure 10. Capacity versus SNR for omnidirectional antenna pattern and different propagation con-
ditions.
The obtained results are a graphical representation of Equations (1) and (6). For mul-
tipath propagation, the e
K coefficient is determined based on Equations (4) and (5),
where LOS and NLOS propagation conditions are determined by the PLE values equal to
2.1PLE = and 3.4,PLE = respectively [14]. These graphs show that the radio channel
capacity under LOS conditions in relation to free-space is only 0.5 bit/s/Hz less. On the
other hand, the NLOS conditions significantly reduce the channel capacity even several
times.
The use of antenna systems with narrow-beam radiation/reception patterns is one
way to minimize the negative effects of multipath propagation under NLOS conditions.
The effects of using spatially selective antenna systems are shown in Figure 11.
Figure 11. Capacity versus SNR for directional antenna pattern and under NLOS conditions.
Figure 10.
Capacity versus SNR for omnidirectional antenna pattern and different propagation
conditions.
The obtained results are a graphical representation of Equations (1) and (6). For
multipath propagation, the
Ke
coefficient is determined based on Equations (4) and (5),
where LOS and NLOS propagation conditions are determined by the PLE values equal to
PLE =
2.1 and
PLE =
3.4, respectively [
14
]. These graphs show that the radio channel
capacity under LOS conditions in relation to free-space is only 0.5 bit/s/Hz less. On the
other hand, the NLOS conditions significantly reduce the channel capacity even several
times.
The use of antenna systems with narrow-beam radiation/reception patterns is one
way to minimize the negative effects of multipath propagation under NLOS conditions.
The effects of using spatially selective antenna systems are shown in Figure 11.
For LOS conditions, the alignment of the transmitting and receiving antenna beams
(i.e., beams oriented to each other) provides statistically multiple increases in the radio chan-
nel capacity. Of course, this increase depends on the gains of the antennas. For the analyzed
radio link with the directional antennas whose gains are equal to
GT=GR=24.6 dBi,
the
capacity is higher by 1.5
÷
3.5 bit/s/Hz in relation to the radio link with the omnidi-
rectional antenna systems and free-space propagation conditions. The analysis results
presented in Figure 11 show that the radio channel capacity also depends on the distance
between the TX and RX. The double distance reduction increases the radio channel capacity
by about 1.5 bit/s/Hz in the whole analyzed range of SNR variability.
Sensors 2021,21, 8296 15 of 20
Sensors 2021, 21, 8296 16 of 22
Figure 10. Capacity versus SNR for omnidirectional antenna pattern and different propagation con-
ditions.
The obtained results are a graphical representation of Equations (1) and (6). For mul-
tipath propagation, the e
K coefficient is determined based on Equations (4) and (5),
where LOS and NLOS propagation conditions are determined by the PLE values equal to
2.1PLE = and 3.4,PLE = respectively [14]. These graphs show that the radio channel
capacity under LOS conditions in relation to free-space is only 0.5 bit/s/Hz less. On the
other hand, the NLOS conditions significantly reduce the channel capacity even several
times.
The use of antenna systems with narrow-beam radiation/reception patterns is one
way to minimize the negative effects of multipath propagation under NLOS conditions.
The effects of using spatially selective antenna systems are shown in Figure 11.
Figure 11. Capacity versus SNR for directional antenna pattern and under NLOS conditions.
Figure 11. Capacity versus SNR for directional antenna pattern and under NLOS conditions.
Under NLOS conditions, the alignment of the transmitting and receiving antenna
beams does not provide to achieve the maximum received power. Therefore, under
these propagation conditions, the massive-MIMO system should supply a beam steering
mechanism to the direction of the maximum level of the received signal. The justification
for the application of such a solution is illustrated in Figure 12.
Sensors 2021, 21, 8296 17 of 22
For LOS conditions, the alignment of the transmitting and receiving antenna beams
(i.e., beams oriented to each other) provides statistically multiple increases in the radio
channel capacity. Of course, this increase depends on the gains of the antennas. For the
analyzed radio link with the directional antennas whose gains are equal to
24.6 dBi,
TR
GG== the capacity is higher by 1.5 ÷ 3.5 bit/s/Hz in relation to the radio link
with the omnidirectional antenna systems and free-space propagation conditions. The
analysis results presented in Figure 11 show that the radio channel capacity also depends
on the distance between the TX and RX. The double distance reduction increases the radio
channel capacity by about 1.5 bit/s/Hz in the whole analyzed range of SNR variability.
Under NLOS conditions, the alignment of the transmitting and receiving antenna
beams does not provide to achieve the maximum received power. Therefore, under these
propagation conditions, the massive-MIMO system should supply a beam steering mech-
anism to the direction of the maximum level of the received signal. The justification for
the application of such a solution is illustrated in Figure 12.
Figure 12. Capacity versus SNR for βmax under NLOS conditions.
It can see that the use of the direction of the maximum signal level ensures an addi-
tional increase in the capacity by 2 ÷ 3 bit/s/Hz. The increment increases as the TX–RX
distance is greater. For 50 m,D= the selection of the direction of the maximum level en-
sures a statistical increase in the channel capacity by about 2 bit/s/Hz, while for
200 m,D=this increase is reduced to 3 bit/s/Hz.
The channel capacity change versus the distance between the TX and RX, considering
the stability of the emitted power (i.e., its constant value), makes it possible to practically
assess the reception effectiveness for max.β However, changing the TX/RX position makes
it necessary to search for the reception direction of the maximum signal level. Changes in
max
β as a function of D for 90α
are shown in Figure 13.
Figure 12. Capacity versus SNR for βmax under NLOS conditions.
Sensors 2021,21, 8296 16 of 20
It can see that the use of the direction of the maximum signal level ensures an addi-
tional increase in the capacity by 2
÷
3 bit/s/Hz. The increment increases as the TX–RX
distance is greater. For
D=
50
m,
the selection of the direction of the maximum level en-
sures a statistical increase in the channel capacity by about 2 bit/s/Hz, while for
D=
200
m,
this increase is reduced to 3 bit/s/Hz.
The channel capacity change versus the distance between the TX and RX, considering
the stability of the emitted power (i.e., its constant value), makes it possible to practically
assess the reception effectiveness for
βmax
. However, changing the TX/RX position makes
it necessary to search for the reception direction of the maximum signal level. Changes in
βmax as a function of Dfor α=90are shown in Figure 13.
Sensors 2021, 21, 8296 18 of 22
Figure 13. Statistical value of βmax versus TX–RX distance under NLOS conditions.
The presented result of max
β versus D has a statistical nature because the simula-
tion studies using the MPM are based on the statistical transmission characteristics of the
channel (i.e., TDLs from the 3GPP standard [15]). On the other hand, this statistical nature
arises from averaging the results over several simulation cycles. As can be seen, as the
distance increases, the reception directions for the maximum signal level converge to
max 0.β→°
Determining the radio channel capacity for optimal receiving beam direction makes
it possible to evaluate the system effectiveness for selecting the signal reception direction.
The comparison of the capacity change for the straight (i.e., 180α
and 0
β
) and
optimal (i.e., 90α
and max
ββ=) directions of the antenna beams is shown in Figure
14.
Figure 14. Channel capacity versus TX–RX distance for straight and optimal directions of antenna
beams under NLOS conditions.
Figure 13. Statistical value of βmax versus TX–RX distance under NLOS conditions.
The presented result of
βmax
versus
D
has a statistical nature because the simulation
studies using the MPM are based on the statistical transmission characteristics of the
channel (i.e., TDLs from the 3GPP standard [
15
]). On the other hand, this statistical nature
arises from averaging the results over several simulation cycles. As can be seen, as the
distance increases, the reception directions for the maximum signal level converge to
βmax 0.
Determining the radio channel capacity for optimal receiving beam direction makes it
possible to evaluate the system effectiveness for selecting the signal reception direction.
The comparison of the capacity change for the straight (i.e.,
α=
180
and
β=
0
) and
optimal (i.e.,
α=
90
and
β=βmax
) directions of the antenna beams is shown in Figure 14.
The exemplary graphs are obtained assuming that, at
D=
50
m,
the level of the
received signal provides the
SN R =
20
dB
. It is obvious that as the TX–RX distance
increases, the level of the desired signal decreases. Thus, the radio channel capacity
decreases. In the case of the optimal direction of the antenna beams, a six-fold increase
in the distance causes only about a 2.5-fold reduction in the capacity. On the other hand,
with the increase in the distance, maintaining the straight direction results in a 4.4-fold
decrease in the capacity. This shows that the use of steering and selection of the optimal
beam direction in the antenna system (e.g., massive-MIMO) mitigate the degrading effect
of distance on the radio channel capacity.
Sensors 2021,21, 8296 17 of 20
Sensors 2021, 21, 8296 18 of 22
Figure 13. Statistical value of βmax versus TX–RX distance under NLOS conditions.
The presented result of max
β versus D has a statistical nature because the simula-
tion studies using the MPM are based on the statistical transmission characteristics of the
channel (i.e., TDLs from the 3GPP standard [15]). On the other hand, this statistical nature
arises from averaging the results over several simulation cycles. As can be seen, as the
distance increases, the reception directions for the maximum signal level converge to
max 0.β→°
Determining the radio channel capacity for optimal receiving beam direction makes
it possible to evaluate the system effectiveness for selecting the signal reception direction.
The comparison of the capacity change for the straight (i.e., 180α
and 0
β
) and
optimal (i.e., 90α
and max
ββ=) directions of the antenna beams is shown in Figure
14.
Figure 14. Channel capacity versus TX–RX distance for straight and optimal directions of antenna
beams under NLOS conditions.
Figure 14.
Channel capacity versus TX–RX distance for straight and optimal directions of antenna
beams under NLOS conditions.
7. Conclusions
This paper focuses on the influence assessment of the antenna system parameters,
with particular emphasis on their orientation, on the radio channel capacity under NLOS
propagation conditions. The need to take up such topics is related to implementing new
technologies in antenna systems with beamforming and tracking technologies, e.g., massive-
MIMO. The performed evaluation has a statistical nature and is based on simulation studies.
In this case, the MPM was used to map the effects of propagation phenomena. The obtained
results show that under NLOS conditions, it is desirable to use directional antennas as this
provides significant compensation for signal attenuation. The effect of this is as follows:
a dozen or so times increase in the radio channel capacity compared to the omnidirec-
tional antenna;
the direction selection of the maximum received signal level increase by about 2 bit/s/Hz
the channel capacity regardless of the TX–RX distance;
the control system for selecting the reception direction of the maximum signal level
increases the capacity of the link, and its efficiency increases with increasing distance.
The issues presented in this article are of significant practical importance. The pro-
posed procedure provides a quantitative assessment of the efficiency of using beam-steering
antenna systems under NLOS conditions. The use of the geometry-based MPM in the
simulation tests presents the possibility to consider not only the parameters and patterns
of the antenna system, but also the type of propagation environment. Thanks to this, the
method of analyzing the capacity of the directional radio links enables the evaluation of
the spatial range of the implementation of complex telecommunication services. This is
important in the process of planning the area covered by base stations. This determines
the originality of the radio channel capacity analysis method described in this paper in
comparison to the methods presented so far in the literature.
In the future, the authors plan to conduct empirical research for selected scenarios
that will allow to verify the approach presented in this paper. Additionally, the authors
also want to compare the impact of utilizing a simplified antenna pattern (i.e., Gaussian
model for the main lobe) with a real pattern (i.e., considering the side-lobes) on various
Sensors 2021,21, 8296 18 of 20
parameters of the directional radio link, including throughput, interference, energy balance,
and angular spread.
Author Contributions:
Conceptualization, C.Z. and J.M.K.; methodology, C.Z., J.M.K., J.K., A.C.
and A.P.; software, J.M.K. and J.K.; validation, C.Z., J.M.K., J.K, A.C. and A.P.; formal analysis, C.Z.
and J.M.K.; investigation, C.Z., J.M.K., J.K, A.C. and A.P.; resources, J.M.K.; data curation, J.M.K.;
writing—original draft preparation, C.Z., J.M.K., J.K, A.C. and A.P.; writing—review and editing,
C.Z., J.M.K., J.K., A.C. and A.P.; visualization, J.M.K.; supervision, C.Z., J.M.K., J.K., A.C. and A.P.;
project administration, J.M.K., A.C. and A.P.; funding acquisition, J.M.K., A.C. and A.P. All authors
have read and agreed to the published version of the manuscript.
Funding:
This work was developed within a framework of the research grants: grant no. GBMON/
13996/2018/WAT sponsored by the Polish Ministry of Defense, grant no. UGB/22-854/2021/WAT
sponsored by the Military University of Technology, Poland, grant no. CRG/2018/000175 spon-
sored by SERB, DST, Government of India, project no. 17-27068S sponsored by the Czech Science
Foundation, grant no. LO1401 sponsored by the National Sustainability Program, the Czech Republic.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement:
The data presented in this study are available on request from the
corresponding author. The data are not publicly available due to project restrictions.
Acknowledgments:
The authors would like to express their great appreciation to the Sensors jour-
nal Editors and anonymous Reviewers for their valuable suggestions, which have improved the
manuscript quality.
Conflicts of Interest: The authors declare no conflict of interest.
Abbreviations
2D two dimensional
3D three dimensional
3GPP 3rd Generation Partnership Project
5G fifth-generation
AOA angle of arrival
AOD angle of departure
AWGN additive white Gaussian noise
CI close-in free-space reference distance (path loss model)
HPBW half-power beamwidth
LOS line-of-sight
METIS Mobile and wireless communications Enablers for the Twenty-twenty Information Society
MIMO multiple-input-multiple-output
MiWEBA Millimetre-Wave Evolution for Back-haul and Access
MPM multi-elliptical propagation model
NLOS non-line-of-sight
PAS power angular spectrum
PDF probability density function
PDP power delay profile
PL path loss
PLE path loss exponent
RX receiver
SNR signal-to-noise ratio
TDL tapped-delay line
TR technical report
TX transmitter
UMa urban macro
Sensors 2021,21, 8296 19 of 20
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