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sensors
Article
Modeling of Downlink Interference in Massive MIMO 5G
Macro-Cell †
Kamil Bechta 1, Cezary Ziółkowski 2, Jan M. Kelner 2, * and Leszek Nowosielski 2
Citation: Bechta, K.; Ziółkowski, C.;
Kelner, J.M.; Nowosielski, L.
Modeling of Downlink Interference in
Massive MIMO 5G Macro-Cell.
Sensors 2021,21, 597. https://
doi.org/10.3390/s21020597
Received: 12 December 2020
Accepted: 12 January 2021
Published: 16 January 2021
Publisher’s Note: MDPI stays neu-
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Copyright: © 2021 by the authors. Li-
censee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and con-
ditions of the Creative Commons At-
tribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
1Nokia Solutions and Networks, 54-130 Wrocław, Poland; kamil.bechta@nokia.com
2Institute of Communications Systems, Faculty of Electronics, Military University of Technology,
00-908 Warsaw, Poland; cezary.ziolkowski@wat.edu.pl (C.Z.); leszek.nowosielski@wat.edu.pl (L.N.)
*Correspondence: jan.kelner@wat.edu.pl; Tel.: +48-261-839-517
† The paper is an extended version of our paper published in Bechta, K.; Ziółkowski, C.; Kelner J.M.;
Nowosielski, L. Downlink interference in multi-beam 5G macro-cell. In Proceedings of the 2020 23rd
International Microwave and Radar Conference (MIKON), Warsaw, Poland, 5–8 October 2020; pp. 140–143,
doi:10.23919/MIKON48703.2020.9253919.
Abstract:
Multi-beam antenna systems are the basic technology used in developing fifth-generation
(5G) mobile communication systems. In practical implementations of 5G networks, different ap-
proaches are used to enable a massive multiple-input-multiple-output (mMIMO) technique, including
a grid of beams, zero-forcing, or eigen-based beamforming. All of these methods aim to ensure
sufficient angular separation between multiple beams that serve different users. Therefore, ensuring
the accurate performance evaluation of a realistic 5G network is essential. It is particularly crucial
from the perspective of mMIMO implementation feasibility in given radio channel conditions at
the stage of network planning and optimization before commercial deployment begins. This paper
presents a novel approach to assessing the impact of a multi-beam antenna system on an intra-cell
interference level in a downlink, which is important for the accurate modeling and efficient usage of
mMIMO in 5G cells. The presented analysis is based on geometric channel models that allow the
trajectories of propagation paths to be mapped and, as a result, the angular power distribution of
received signals. A multi-elliptical propagation model (MPM) is used and compared with simulation
results obtained for a statistical channel model developed by the 3rd Generation Partnership Project
(3GPP). Transmission characteristics of propagation environments such as power delay profile and
antenna beam patterns define the geometric structure of the MPM. These characteristics were adopted
based on the 3GPP standard. The obtained results show the possibility of using the presented novel
MPM-based approach to model the required minimum separation angle between co-channel beams
under line-of-sight (LOS) and non-LOS conditions, which allows mMIMO performance in 5G cells to
be assessed. This statement is justified because for 80% of simulated samples of intra-cell signal-to-
interference ratio (SIR), the difference between results obtained by the MPM and commonly used
3GPP channel model was within 2 dB or less for LOS conditions. Additionally, the MPM only needs
a single instance of simulation, whereas the 3GPP channel model requires a time-consuming and
computational power-consuming Monte Carlo simulation method. Simulation results of intra-cell
SIR obtained this way by the MPM approach can be the basis for spectral efficiency maximization in
mMIMO cells in 5G systems.
Keywords:
5G; downlink; interference; signal-to-interference ratio (SIR); massive MIMO; multi-beam
antenna system; multi-elliptical propagation model; 3GPP standard
1. Introduction
Achieving greater transmission capacity for wireless links is the main goal of the
currently developed fifth-generation (5G) mobile communication system [
1
,
2
]. The use of
new spectral resources that cover frequency ranges exceeding 3 GHz provides an increase
in the performance and capacity of next generation networks. However, propagation
Sensors 2021,21, 597. https://doi.org/10.3390/s21020597 https://www.mdpi.com/journal/sensors
Sensors 2021,21, 597 2 of 17
phenomena that occur in the centimeter-wave (cmWave) and millimeter-wave (mmWave)
ranges cause numerous problems in the practical implementation of radio transmission
equipment solutions [
3
,
4
]. The increase in propagation environment attenuation at higher
frequencies makes it necessary to reduce the size of cells and sectors served by individual
network base stations (BS). Hence, obtaining full coverage forces increased density of BSs
in a given deployment area. The dominant amount of mobile users’ equipment (UEs) of
wireless networks occurs in urban areas, where the phenomenon of multipath propagation
significantly limits the transmission capabilities of radio links. In combination with the
Doppler effect, resulting from user motions, this phenomenon leads to signal dispersion in
time, frequency, and reception angle domains [5].
A multi-antenna system is one of the basic solutions used in the currently implemented
5G systems that minimize adverse propagation phenomena. A massive multiple-input-
multiple-output (mMIMO) technique plays a special role [
6
,
7
]. It uses a beamforming
technique [
8
,
9
], which allows for the possibility of practical implementation of spatial
multiplexing for radio resources. This multiplexing improves spectral efficiency by using
the same frequency sub-bands in angularly separated beams (spatially orthogonal beams).
In urban areas, multipath propagation is the cause of the angular dispersion of the received
signals [
10
]. It is the reason for receiving signal components from unwanted beams that
significantly interfere with the signal from the serving (i.e., useful, reference) beam. A level
of this interference is directly connected with spatial orthogonality between reference and
interfering beams. If a signal-to-interference ratio (SIR), i.e., the ratio between received
powers of reference and interfering signals, is higher, then the spatial orthogonality between
these beams is better. Therefore, at the mMIMO 5G network planning and optimization
stages, it is important to assess spatial orthogonality in realistic propagation conditions
accurately. This allows achievable performance for a given deployment scenario to be
estimated. One of the metrics that can help estimate mMIMO cell performance is the
relation between the SIR and angular separation between the reference and interfering
beams. Since UEs are distributed mostly on a horizontal plane, rather than a vertical one, in
the typical cells of a mobile network, in the majority of cases is enough to consider angular
separation only on a horizontal plane to make an accurate estimation of the SIR. In other
words, accurate modeling of the relation between the angular separation of reference and
interfering beams on a horizontal plane and the SIR helps to estimate many parameters
of mMIMO cells. For example, we may determine a minimum distance between UEs that
can be served by simultaneous mMIMO beams with an assumed interference level or
maximum number of uniformly distributed UEs, which can be served by simultaneous
mMIMO beams with the assumed level of the SIR.
In the literature, an interference subject concerns interfering signals in a wide-sense.
The nature of their formation may be diverse. In most cases, when we talk about interfer-
ences, we mean so-called non-intentional interferences, i.e., those arising from the operation
of radio, electronic, or mechatronic devices, networks, or whole systems during their work.
The second group is the so-called intentional interference (i.e., jamming) mainly used
in the military or security to disrupt enemy communication systems or counteract radio
systems in a protected area (i.e., electromagnetic curtain [
11
]), e.g., in airports, buildings,
and infrastructure of strategic importance. Examples of jamming 5G systems are presented
in [12,13]. The remainder of the paper focuses on non-intentional interferences.
The interference subject in communication systems, in particular in 5G systems, is
widely represented in the literature. Works in this area focus on the three following topics:
•interference cancelation, mitigation, awareness, and management methods,
•interference modeling and assessment methods,
•interference estimation and measurement methods.
Software-based algorithms and hardware solutions that are implemented in BS and
UE belong to the first method group. Papers focusing on this topic present novel solutions,
usually based on simulation analysis, e.g., [
14
–
19
]. The purpose of these methods is to
increase the efficiency of devices and networks and make better use of radio resources.
Sensors 2021,21, 597 3 of 17
Various modeling methods are used in interference evaluation. They are usually based
on energetic assessment of the received signals. However, interference level analysis may
take different aspects into account. In this case, the important aspects influencing the
received signal form have a crucial value in the faithful reflection of the modeled issue in
relation to the real situation. These aspects include, first of all, the channel model, as well
as the parameters and characteristics of antenna systems. The possibility of considering
environment nature and propagation conditions, as well as the appropriate reflection of
angular dispersions affecting the received signal powers, should be taken into account
when choosing a channel model. On the other hand, considering the parameters and
patterns of antenna systems is of crucial importance, especially in the analysis of 5G
spatially multiplexing systems, including those ensuring beamforming (e.g., with the
mMIMO system).
Modeling methods are used to evaluate existing systems or new solutions (e.g., new
mitigation algorithm) and, in particular, to evaluate inter- and intra-system electromagnetic
compatibility, coexistence of 5G with other systems (e.g., fixed satellite services (FSS) [
20
,
21
],
radars [
22
], long term evolution (LTE) [
23
], etc.) or to assess 5G network/system efficiency
under occurring interference [
24
]. For 5G systems, intra-system interference (also called
self-interference) analysis concerns, i.e., inter-cell [
16
–
19
] or inter-beam (or intra-cell) [
17
,
24
]
interferences. In this case, we would like to note that most of the works available in the
literature focus on inter-cell rather than inter-beam interference analysis. These methods
are usually used in the network design and planning stages. This paper focuses on this
group method for modeling and evaluating inter-beam interference in 5G massive-MIMO
systems.
The last group of research and scientific works focuses on interference measurements
in real environments for existing systems and networks, e.g., [23,25,26].
In this paper, we present a novel approach for assessing the interference level in a
downlink (DL) that arises as a result of using a multi-beam antenna system in 5G BS
(gNodeB), which is based on a multi-elliptical propagation model (MPM) [
27
]. Simulation
results of the DL SIR obtained with the use of the MPM were compared with simula-
tion results of the commonly used 3rd Generation Partnership Project (3GPP) channel
model [
28
]. Simulations have been performed for realistic beam patterns of mMIMO
antenna systems [
29
] and parameters of 5G networks determined by the 3GPP and Interna-
tional Telecommunication Union (ITU) [
30
]. These assumptions indicate the originality of
the obtained results and the MPM approach for determining the interference level from
undesirable beams, i.e., interfering beams of the antenna system.
Joint modeling of beamforming and angular spread is required to obtain an accurate
estimation of realistic interference levels. Used spatial filtering of multipath components by
the antenna pattern is sensitive to time-variant radio channel conditions. Such an approach
to the modeling of 5G systems performance is gaining more attention. For example, in [
31
],
the results of link budget calculations in the real propagation environment of the mmWave
system can be found, whereas the corresponding impact on the efficiency of antenna array
tapering is described in [
32
]. The study presented in this article follows the same modeling
principles. Therefore, it can be considered as valuable input to the current state of the art.
The rest of the paper is organized as follows. Section 2describes practical ways of using
multi-beam antenna systems. Section 3presents the basis for assessing the interference level
in the DL based on the use of the MPM and 3GPP channel model. Assumptions, obtained
results, and conclusions from the performed simulations are presented in
Sections 4and 5
,
respectively.
2. Multi-Beam Antenna System—Practical Aspects
One of the key differentiators of 5G is the ability to utilize the benefits of the mMIMO
technique, especially the simplification of multiple-user access [
1
,
2
]. Due to a large number
of antenna elements connected to multiple transmission-reception radio chains, fast fading,
as seen by the gNodeB, gradually disappears, and the radio channel becomes flat in
Sensors 2021,21, 597 4 of 17
the frequency domain. This effect, called channel hardening, causes that in orthogonal
frequency division multiplexing (OFDM) access each subcarrier has a similar channel
gain. Therefore, different UEs from the same cell can be allocated to the whole available
frequency bandwidth [6,7].
On top of this, mMIMO allows cell capacity in reference to conventional MIMO to
increase significantly. Due to the spatial multiplexing of available resources obtained
through energy focusing using large antenna arrays, i.e., beamforming, mMIMO allows
the same frequency bandwidth to be reused by multiple UEs at the same time. However,
such a multi-user scenario is only possible in the case of favorable propagation conditions,
i.e., when propagation channel responses from the gNodeB are sufficiently different to
simultaneously serve UEs (UEs are considered to be spatially orthogonal). From this
viewpoint, the number of available resources in the cell are multiplied by the number of
UEs. In less favorable propagation conditions, i.e., when the spatial orthogonality between
UEs is not sufficient, the available radio resources have to be appropriately distributed.
Usually, if different UEs are served by other beams, they can be allocated with full available
bandwidth in different time slots to avoid intra-cell interference. In cases where the same
beam serves multiple UEs, the available bandwidth is split between these UEs accordingly.
It may also be possible that only a single UE will be under the coverage of two neighboring
beams. This would result in a doubling of the resources available from a single beam, i.e.,
UE can be served in two consecutive time slots.
Even though, due to beamforming, mMIMO significantly limits inter-cell interference
in reference to legacy MIMO, the problem of unavoidable re-use of training sequences,
i.e., pilot contamination, by UEs in different cells still exists, and the inter-cell interference
grows along with the number of base stations in the network [
19
]. Therefore, it is crucial
that inter-cell interference, on top of intra-cell interference, is accurately modeled in the
network planning and optimization stages, as well as accurately estimated and limited
during network operation through sufficient precoding.
3. Interference Evaluation in Downlink
3.1. Fundamentals of the Multi-Elliptical Propagation Model
Dispersion in the angular domain is characteristic of areas where multipath propaga-
tion occurs, e.g., urbanized areas with non-line-of-sight (NLOS) or even line-of-sight (LOS)
conditions [
10
]. In such propagation environments, the basis for power assessment is a
power angular spectrum (PAS),
p(θ,φ,D)
, where
θ
and
φ
are the angles of arrival (AOA) in
the elevation and azimuth planes, respectively, and
D
is the distance between a transmitter
(Tx) and receiver (Rx). This function allows the received power
PR(D)
to be determined
according to the relationship [33]
PR(D)=x
Ω
p(θ,φ,D)dθdφ. (1)
where Ω={(θ,φ):θ∈[0◦, 90◦),φ∈[−180◦, 180◦)}.
Thus, knowing the PAS for signals for useful (i.e., reference, serving) and unwanted
(i.e., interfering) beams allows the energy relation between them to be assessed. In this
paper, we analyze the transmission of signals in a frequency range from 3 to 4 GHz and
with receiving point distances at 100, 200, and 500 m. For these conditions, we can assume
that the dispersion phenomenon of the received power dominates in the azimuth plane.
This fact is shown in [
27
,
33
]. In this case, the SIR between the useful signal strength
PR0(D)
Sensors 2021,21, 597 5 of 17
and the power of the interfering signal
PRI (D)
that comes from the unwanted beam has
the following form [5]:
SI R(D)(dB)=10 log10
PR0(D)
PRI (D)=10 log10
180◦
R
−180◦
p0(φ,D)dφ
180◦
R
−180◦
pI(φ,D)dφ
, (2)
where
p0(φ,D)=
90◦
R
0
p0(θ,φ,D)dθ
and
pI(φ,D)=
90◦
R
0
pI(θ,φ,D)dθ
represent the PASs of
the serving and interfering signals in the azimuth plane, respectively.
Equation (2) reduces the SIR evaluation to determine
p0(φ,D)
and
pI(φ,D)
in the case
when the MPM is used. The geometry of this model describes the most probable locations
of scatterers. Its structure consists of a set of confocal ellipses whose foci determine the
positions of the Tx and Rx, i.e., the gNodeB and UE for the DL scenario, respectively. The
scattering geometry of the MPM in the azimuth plane is illustrated in Figure 1[
27
], whereas
Figure 2depicts the simplified MPM simulation procedure.
Sensors2021,21,xFORPEERREVIEW5of18
withreceivingpointdistancesat100,200,and500m.Fortheseconditions,wecanassume
thatthedispersionphenomenonofthereceivedpowerdominatesintheazimuthplane.
Thisfactisshownin[27,33].Inthiscase,theSIRbetweentheusefulsignalstrength
0R
PD
andthepoweroftheinterferingsignal
RI
PD
thatcomesfromtheunwanted
beamhasthefollowingform[5]:
180
0
0180
10 10 180
180
,
dB 10 log 10 log ,
,
R
RI
I
pDd
PD
SIR D PD pDd
(2)
where
90
00
0
,,,pD pθDdθ
and
90
0
,,,
II
pD pθDdθ
representthePASsof
theservingandinterferingsignalsintheazimuthplane,respectively.
Equation(2)reducestheSIRevaluationtodetermine
0
,
pD
and
,
I
pD
inthe
casewhentheMPMisused.Thegeometryofthismodeldescribesthemostprobablelo‐
cationsofscatterers.Itsstructureconsistsofasetofconfocalellipseswhosefocidetermine
thepositionsoftheTxandRx,i.e.,thegNodeBandUEfortheDLscenario,respectively.
ThescatteringgeometryoftheMPMintheazimuthplaneisillustratedinFigure1[27],
whereasFigure2depictsthesimplifiedMPMsimulationprocedure.
Figure1.Scatteringgeometryofthemulti‐ellipticalpropagationmodel(MPM)intheazimuth
plane.
Basedonconsideredassumptions,i.e.,theTx‐Rxdistance—spatialscenario(step1)
andachosenpowerdelayprofile(PDP)forLOS/NLOSconditions(step2),instep3,we
calculateparametersofscatteringgeometrystructure.Forthenthellipse(time‐cluster),
themajor,
,
xn
aandminor,,
yn
baxesaredefinedbasedonthePDPaccordingtothefol‐
lowingrelationships[27,34]:
1
,
2
xn n
acτD
(3)
12,
2
yn n n
bcτcτD
(4)
Figure 1. Scattering geometry of the multi-elliptical propagation model (MPM) in the azimuth plane.
Based on considered assumptions, i.e., the Tx-Rx distance—spatial scenario (step 1)
and a chosen power delay profile (PDP) for LOS/NLOS conditions (step 2), in step 3, we
calculate parameters of scattering geometry structure. For the nth ellipse (time-cluster), the
major,
axn
, and minor,
byn
, axes are defined based on the PDP according to the following
relationships [27,34]:
axn =1
2(cτn+D), (3)
byn =1
2qcτn(cτn+2D), (4)
where
c
denotes the speed of light,
τn
is a delay for which the PDP takes the nth local
extreme,
n=
1, 2,
. . .
,
N
, and
N
is the number of time-clusters (i.e., the local extremes) in
the PDP.
Sensors 2021,21, 597 6 of 17
Sensors2021,21,xFORPEERREVIEW6of18
wherecdenotesthespeedoflight,n
τisadelayforwhichthePDPtakesthenthlocal
extreme,1,2, ..., ,nNandNisthenumberoftime‐clusters(i.e.,thelocalextremes)in
thePDP.
TheadoptedwayofcreatingtheMPMgeometricstructureenablesmappingofthe
transmissionpropertiesofpropagationenvironments.Detaileddescriptionsofthisstruc‐
tureareprovidedin[27,33–35].
Figure2.SimplifiedsimulationprocedureoftheMPM.
Instep4,wechoosetheTxandRxantennaparameters,i.e.,theirpatternshapes,
gains,directionsofmaximumradiation/reception,andhalf‐power‐beamwidths(HPBWs).
Inthesimulationtestingprocedure,themappingofdirectionalantennasisobtainedusing
theirnormalizedradiationpattern[35],whichisrealizedinstep5.Sincethesecharacter‐
isticsmeetthedefinitionpropertiesofprobabilitydensity[36],inthesimulationproce‐
dure,thedirectionsofdepartureofpropagationpathsaregeneratedontheirbasis.Ade‐
taileddescriptionofdeterminingtheradiationangledistributionisgivenin[35].Instep
6,basedontheMPMgeometrystructure,AOAsarecalculatedforeachangleofdeparture
(AOD).ThesetsoftheobtainedAOAsforeachtime‐clusterarethebasisfordetermining
thehistogramsinstep7.Foreachtime‐cluster,wechooseappropriatepowersdefinedin
theanalyzedPDP(step8).Next,instep10,wemultiplytheAOAhistogramswiththe
properpowerstoobtainthePASseenaroundtheRx[33,35].Atthisstage,thelocalscat‐
teringcomponentsanddirectpathforLOSconditionsarealsoconsidered(step9).Using
spatialfilteringbytheRxantennapattern,wecalculatethePASseenonthisantennaout‐
put(steps11and12)[33].Duringinterferenceanalysis,welaunchtheMPMsimulation
proceduretwicefortheservingandinterferenceTxbeams,respectively.
3.2.Fundamentalsof3GPPChannelModel
Forlink‐levelanddetailedsystem‐levelsimulations,the3GPPhasprovidedinstruc‐
tionsonhowtogeneratestatisticalthree‐dimensional(3D)channelmodels,asshownin
Figure3[28].Itincludesallthenecessaryradiopropagationphenomenathatmustbe
consideredduringacomprehensivesimulationtoprovideanestimationoftheradiolink
budget(includinginterference)andperformance.
Itshouldbenotedthataccordingto[28],dispersionintheangulardomainismod‐
eledinsteps4,6,7,and8ofFigure3.Instep4,whentheangularspread(AS)foragiven
Figure 2. Simplified simulation procedure of the MPM.
The adopted way of creating the MPM geometric structure enables mapping of the
transmission properties of propagation environments. Detailed descriptions of this struc-
ture are provided in [27,33–35].
In step 4, we choose the Tx and Rx antenna parameters, i.e., their pattern shapes, gains,
directions of maximum radiation/reception, and half-power-beamwidths (HPBWs). In the
simulation testing procedure, the mapping of directional antennas is obtained using their
normalized radiation pattern [
35
], which is realized in step 5. Since these characteristics
meet the definition properties of probability density [
36
], in the simulation procedure,
the directions of departure of propagation paths are generated on their basis. A detailed
description of determining the radiation angle distribution is given in [
35
]. In step 6,
based on the MPM geometry structure, AOAs are calculated for each angle of departure
(AOD). The sets of the obtained AOAs for each time-cluster are the basis for determining
the histograms in step 7. For each time-cluster, we choose appropriate powers defined
in the analyzed PDP (step 8). Next, in step 10, we multiply the AOA histograms with
the proper powers to obtain the PAS seen around the Rx [
33
,
35
]. At this stage, the local
scattering components and direct path for LOS conditions are also considered (step 9).
Using spatial filtering by the Rx antenna pattern, we calculate the PAS seen on this antenna
output (
steps 11 and 12
) [
33
]. During interference analysis, we launch the MPM simulation
procedure twice for the serving and interference Tx beams, respectively.
3.2. Fundamentals of 3GPP Channel Model
For link-level and detailed system-level simulations, the 3GPP has provided instruc-
tions on how to generate statistical three-dimensional (3D) channel models, as shown in
Figure 3[
28
]. It includes all the necessary radio propagation phenomena that must be
considered during a comprehensive simulation to provide an estimation of the radio link
budget (including interference) and performance.
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Sensors2021,21,xFORPEERREVIEW7of18
scenarioandnetworklayoutisgenerated,i.e.,basedontheassumedstatisticalmodel,the
followingparametersaregenerated:
azimuthspreadofdeparture(ASD),
zenith(i.e.,elevation)spreadofdeparture(ZSD),
azimuthspreadofarrival(ASA),
zenithspreadofarrival(ZSA).
Figure3.Blockdiagramofstatisticalchannelmodelreconstructionaccordingto3GPP.
Instep6,thepowerforallraysofallclusters(whichariseduetomultipathpropaga‐
tion)isgenerated,whereasinstep7,theanglesofdepartureandarrivalaredetermined
foralltheserays.Finally,instep8,randomcouplingisperformedbetweendepartureand
arrivalanglesforraysinsideagivencluster,inbothazimuthandelevation.Ascanbe
noticed,accordingtothe3GPPchannelmodel[28],thePAS,
,
,,pθD
obtainedatthe
endofstep8doesnotdependontheassumedantennapattern.Itisconsideredonlyin
step11,wherechannelcoefficientsforeachclusterandeachTxandRxelementofantenna
arraysaregenerated.Onlyattheendofstep11areresultsofthespatialfilteringofmul‐
tipathcomponents(clustersandrays)bytheTxandRxnominalantennapatternsknown.
Therefore,tocorrectlycalculatethereceivedpowerofeitherreferenceorinterferingsig‐
nal,itisrequiredtodeterminetheeffectiveantennagainsfortheTxandRx.Theseeffec‐
tiveantennagainsaredefinedasanintegralpartofthemultipliednominalantennapat‐
tern(fortheTxorRx)andPAS,whichisequivalenttospatialfiltering,asshownbelow
[37]:
Ω
,
,, ,
Eff Nom
GD g θpθDdθd
(5)
where
,
Nom
gθ
indicatesnominal3Dantennapattern,eitherfortheTxorRx,ineither
thereferenceorinterferinglink.Similarly,
Eff
GD
indicatestheeffectivegainoftheTx
orRxineitherthereferenceorinterferinglink.FollowingthenotationofEquation(2),the
SIRcalculatedaccordingtothe3GPPchannelmodel[28]maybepresentedasfollows:
Figure 3. Block diagram of statistical channel model reconstruction according to 3GPP.
It should be noted that according to [
28
], dispersion in the angular domain is modeled
in steps 4, 6, 7, and 8 of Figure 3. In step 4, when the angular spread (AS) for a given
scenario and network layout is generated, i.e., based on the assumed statistical model, the
following parameters are generated:
•azimuth spread of departure (ASD),
•zenith (i.e., elevation) spread of departure (ZSD),
•azimuth spread of arrival (ASA),
•zenith spread of arrival (ZSA).
In step 6, the power for all rays of all clusters (which arise due to multipath propaga-
tion) is generated, whereas in step 7, the angles of departure and arrival are determined
for all these rays. Finally, in step 8, random coupling is performed between departure and
arrival angles for rays inside a given cluster, in both azimuth and elevation. As can be
noticed, according to the 3GPP channel model [
28
], the PAS,
p(θ,φ,D)
, obtained at the
end of step 8 does not depend on the assumed antenna pattern. It is considered only in
step 11, where channel coefficients for each cluster and each Tx and Rx element of antenna
arrays are generated. Only at the end of step 11 are results of the spatial filtering of multi-
path components (clusters and rays) by the Tx and Rx nominal antenna patterns known.
Therefore, to correctly calculate the received power of either reference or interfering signal,
it is required to determine the effective antenna gains for the Tx and Rx. These effective
antenna gains are defined as an integral part of the multiplied nominal antenna pattern
(for the Tx or Rx) and PAS, which is equivalent to spatial filtering, as shown below [37]:
GE f f (D)=x
Ω
gNom (θ,φ)p(θ,φ,D)dθdφ, (5)
where
gNom (θ,φ)
indicates nominal 3D antenna pattern, either for the Tx or Rx, in either
the reference or interfering link. Similarly,
GE f f (D)
indicates the effective gain of the Tx or
Rx in either the reference or interfering link. Following the notation of Equation (2), the
SIR calculated according to the 3GPP channel model [28] may be presented as follows:
SI R(D)(dB)=10 log10
PR0(D)
PRI (D)=10 log10
GE f f
T0(D)·GE f f
R0(D)
GE f f
TI (D)·GE f f
RI (D), (6)
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where
GE f f
T0(D)
,
GE f f
R0(D)
,
GE f f
TI (D)
, and
GE f f
RI (D)
indicate the effective gains of the Tx and
Rx in reference and interfering links, respectively.
4. Simulation Studies
4.1. Assumptions
In the simulation studies, we considered a scenario illustrated in Figure 4[
38
]. In this
case, the macro-cell gNodeB (Tx) with the mMIMO antenna array generates two beams in
the selected sector, i.e., reference and interfering beams marked in green and red colors,
respectively. Their directions determined the angle of beam separation,
∆α
. The UE (Rx)
is in an area of the reference beam at distance
D
. Directions of the UE (purple color) and
reference gNodeB beams provide their alignment. We assessed the DL SIR versus
∆α
between the serving and unwanted beams for various distances
D
in an urban macro
(UMa) deployment scenario.
Sensors2021,21,xFORPEERREVIEW8of18
000
10 10
dB 10 log 10 log ,
Eff Eff
RTR
Eff Eff
RI TI RI
PD GDGD
SIR D PD GDGD
(6)
where
0
,
Eff
T
GD
0
,
Eff
R
GD
,
Eff
TI
GD
and
Eff
RI
GD
indicatetheeffectivegainsoftheTx
andRxinreferenceandinterferinglinks,respectively.
4.SimulationStudies
4.1.Assumptions
Inthesimulationstudies,weconsideredascenarioillustratedinFigure4[38].Inthis
case,themacro‐cellgNodeB(Tx)withthemMIMOantennaarraygeneratestwobeamsin
theselectedsector,i.e.,referenceandinterferingbeamsmarkedingreenandredcolors,
respectively.Theirdirectionsdeterminedtheangleofbeamseparation,Δ.αTheUE(Rx)
isinanareaofthereferencebeamatdistance.DDirectionsoftheUE(purplecolor)and
referencegNodeBbeamsprovidetheiralignment.WeassessedtheDLSIRversusΔα
betweentheservingandunwantedbeamsforvariousdistancesDinanurbanmacro
(UMa)deploymentscenario.
Figure4.Spatialscenarioofsimulationstudies[38].
Formorerealisticresults,weusedpracticalpatternsfortheUEandgNodeBbeams,
andsimulationassumptionsdevelopedbythe3GPPandITUin[29,30].ThegNodeBwas
equippedwithanantennaarrayof8×8elementsthatgeneratetwoanalyzedbeamsin
theselectedsector.TheUEbeamwithHPBWsequalto90°and65°onthehorizontaland
verticalplanes,respectively,isgeneratedbyasingleantennaelement.Figure5depicts
the3Dpatternofthereferencebeam[38].ThepatternsoftheUE(purpledashedline),
reference(greenline),andinterference(reddottedline)beamsintheazimuthplaneare
showninFigure6[38].Inthiscase,theexemplaryinterferingbeamispresentedfor
Δ30 .α
Figure 4. Spatial scenario of simulation studies [38].
For more realistic results, we used practical patterns for the UE and gNodeB beams,
and simulation assumptions developed by the 3GPP and ITU in [
29
,
30
]. The gNodeB was
equipped with an antenna array of 8
×
8 elements that generate two analyzed beams in
the selected sector. The UE beam with HPBWs equal to 90
◦
and 65
◦
on the horizontal and
vertical planes, respectively, is generated by a single antenna element. Figure 5depicts the
3D pattern of the reference beam [
38
]. The patterns of the UE (purple dashed line), reference
(green line), and interference (red dotted line) beams in the azimuth plane are shown in
Figure 6[38]. In this case, the exemplary interfering beam is presented for ∆α=30◦.
Sensors 2021,21, 597 9 of 17
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Figure5.3Dpatternofreferencebeam[38].
Figure6.Patternsofusers’equipment(UE),reference,andexemplaryinterferingbeamsinthe
azimuthplane[38].
ThemainsimulationparametersaresummarizedinTable1,whereasdetailsofas‐
sumedchannelmodelsareasfollows:
incaseoftheMPM:
o PDPsarebasedontapped‐delayline(TDL)modelsfromthe3GPPstandard
[28](pp.77–78,Tables7.7.2–2,7.7.2–4),i.e.,TDL‐DandTDL‐BforLOSand
NLOSconditions,respectively;
o theseTDLscorrespondanUMascenarioandnormal‐delayprofile,i.e.,rms
delayspread(DS)isequalto363ns
τ
σ[28](pp.80,Table7.7.3–2);
o intheTDL‐DforLOSconditions,theRicianfactorisdefinedas13.3dBκ
[28](pp.78,Table7.7.2–4);
o localscatteringdescribedbythevonMisesdistribution[39]withanintensity
coefficientequalto60;γ
incaseofthe3GPPmodel:
o NewRadio(NR)UMaLOSandNLOSstatisticalchannelmodelswithparam‐
etersfrom[28](Section7.5);
Figure 5. 3D pattern of reference beam [38].
Sensors2021,21,xFORPEERREVIEW9of18
Figure5.3Dpatternofreferencebeam[38].
Figure6.Patternsofusers’equipment(UE),reference,andexemplaryinterferingbeamsinthe
azimuthplane[38].
ThemainsimulationparametersaresummarizedinTable1,whereasdetailsofas‐
sumedchannelmodelsareasfollows:
incaseoftheMPM:
o PDPsarebasedontapped‐delayline(TDL)modelsfromthe3GPPstandard
[28](pp.77–78,Tables7.7.2–2,7.7.2–4),i.e.,TDL‐DandTDL‐BforLOSand
NLOSconditions,respectively;
o theseTDLscorrespondanUMascenarioandnormal‐delayprofile,i.e.,rms
delayspread(DS)isequalto363ns
τ
σ[28](pp.80,Table7.7.3–2);
o intheTDL‐DforLOSconditions,theRicianfactorisdefinedas13.3dBκ
[28](pp.78,Table7.7.2–4);
o localscatteringdescribedbythevonMisesdistribution[39]withanintensity
coefficientequalto60;γ
incaseofthe3GPPmodel:
o NewRadio(NR)UMaLOSandNLOSstatisticalchannelmodelswithparam‐
etersfrom[28](Section7.5);
Figure 6. Patterns of users’ equipment (UE), reference, and exemplary interfering beams in the azimuth plane [38].
The main simulation parameters are summarized in Table 1, whereas details of as-
sumed channel models are as follows:
•in case of the MPM:
o
PDPs are based on tapped-delay line (TDL) models from the 3GPP stan-
dard [
28
] (pp. 77–78, Tables 7.7.2-2, 7.7.2-4), i.e., TDL-D and TDL-B for LOS
and NLOS conditions, respectively;
o
these TDLs correspond an UMa scenario and normal-delay profile, i.e., rms
delay spread (DS) is equal to στ=363 ns [28] (pp. 80, Table 7.7.3-2);
o
in the TDL-D for LOS conditions, the Rician factor is defined as
κ=
13.3
dB
[
28
]
(pp. 78, Table 7.7.2-4);
o
local scattering described by the von Mises distribution [
39
] with an intensity
coefficient equal to γ=60;
•in case of the 3GPP model:
o
New Radio (NR) UMa LOS and NLOS statistical channel models with parame-
ters from [28] (Section 7.5);
o
Monte Carlo simulation methodology with 1000 repetitions of statistical chan-
nel model realizations.
Sensors 2021,21, 597 10 of 17
Table 1. Main simulation parameters.
Parameter Value
carrier frequency 3.5 GHz
distance Dbetween gNodeB (Tx) and UE (Rx) {100, 200, 500} m
height of gNodeB (Tx) antenna 25 m
height of UE (Rx) antenna 1.5 m
gain of single antenna element 6.4 dBi
HPBW of single antenna element 90◦for H, 65◦for V
spacing between antenna elements 0.5 of wavelength for H, 0.7 of wavelength
for V
front to back ratio 30 dB
antenna array of gNodeB (Tx) 8 ×8
antenna array for UE (Rx) 1 ×1
range of angular separation ∆αin horizontal
plane between reference and interfering beams
from 0◦to 60◦, with step of 1◦
The angular spread characteristics for the UMa channel are determined by the 3GPP [
28
]
using the inverse Gaussian and Laplacian functions for the azimuth and zenith spreads,
respectively. The mean and standard deviation values for these distributions are given
in [
28
] (pp. 42–44, Table 7.5-6 Part-1). Therefore, the Monte Carlo simulation methodology
is required to obtain a statistically representative set of results.
Two separate simulation tools have been used to obtain results for the MPM and
3GPP model. In the MPM’s case, we use our own simulator developed in a MAT-
LAB environment. It is based on analysis of propagation paths between the Tx and
Rx, scattered on the multi-elliptical geometry, according to the block diagram depicted in
Figure 2
. Since 2015, the MPM and its simulator are developing [
27
,
34
]. In the first version,
isotropic/omnidirectional pattern antennas were considered [
34
]. Next, we introduced
the Gaussian pattern for the transmitting [
35
] and then for the receiving antennas [
33
]. In
this case, the transmitting pattern is used to determine the path direction probability. In
contrast, the receiving pattern is using for spatial filtering of the paths reaching to the Rx,
similarly to the 3GPP model. In the last version of the simulator used in this research, we
replaced the Gaussian patterns with realistic patterns based on3GPP recommendation [
30
].
In this case, we use the same approach as in the second simulator for the 3GPP model. The
MPM simulator was validated at every stage of its evolution. In many of our papers, we
showed its verification based on measurement data and comparison with other propaga-
tion models, e.g., [
34
,
35
,
40
]. Generating a huge number of propagation paths, we obtained
an average result for the MPM based on only one simulation run. In this case, analysis
of the confidence intervals of the obtained results is not possible. To achieve this aim, we
have to follow an approach similar to that used in the 3GPP simulator, i.e., we must run
multiple simulations for a small number of random propagation paths in accordance with
the Monte Carlo process. We want to highlight that the calculation time for the Monte
Carlo approach is definitely shorter for the MPM than the 3GPP simulator.
Simulation results for the 3GPP channel model have been obtained by a proprietary
system-level simulator, also implemented in a MATLAB environment according to the
block diagram depicted in Figure 3. A crucial part of this simulator is the implementation of
the full 3D statistical channel model, as defined by the 3GPP in [
28
]. From the perspective of
the results presented in this paper, the essential parts of the simulator used are the antenna
model and fast fading models, based on Sections 7.3 and 7.5 of [
28
], respectively. As a
UMa scenario has been assumed in this study, the most important statistical parameters
of angular spread can be found in Table 7.5-6 Part-1 of [
28
]. This simulator is maintained
and used to provide system-level simulation results as contributions to current 3GPP
standardization works, as well as research studies, e.g., [37].
Sensors 2021,21, 597 11 of 17
4.2. Results for LOS Conditions
For the above assumptions, we carried out simulation studies. Results obtained for
LOS conditions are depicted in Figures 7and 8. Graphs in Figure 7present the SIRs
versus the angle of beam separation for the various distances between the UE and gNodeB,
obtained for the MPM and 3GPP model. Figure 8shows the corresponding cumulative
distribution functions (CDFs) of SIR.
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maintainedandusedtoprovidesystem‐levelsimulationresultsascontributionstocur‐
rent3GPPstandardizationworks,aswellasresearchstudies,e.g.,[37].
4.2.ResultsforLOSConditions
Fortheaboveassumptions,wecarriedoutsimulationstudies.Resultsobtainedfor
LOSconditionsaredepictedinFigures7and8.GraphsinFigure7presenttheSIRsversus
theangleofbeamseparationforthevariousdistancesbetweentheUEandgNodeB,ob‐
tainedfortheMPMand3GPPmodel.Figure8showsthecorrespondingcumulativedis‐
tributionfunctions(CDFs)ofSIR.
Figure7.Signal‐to‐interferenceratios(SIRs)versusangleofbeamseparationforline‐of‐sight
(LOS)conditionsanddifferentUE–gNodeBdistancesobtainedforthemulti‐ellipticalpropagation
model(MPM)and3GPPmodel.
Figure8.Cumulativedistributionfunctions(CDFs)ofSIRforLOSconditionsandselecteddis‐
tancesobtainedfortheMPMand3GPPmodel.
Figure 7.
Signal-to-interference ratios (SIRs) versus angle of beam separation for line-of-sight (LOS) conditions and different
UE–gNodeB distances obtained for the multi-elliptical propagation model (MPM) and 3GPP model.
Sensors2021,21,xFORPEERREVIEW11of18
maintainedandusedtoprovidesystem‐levelsimulationresultsascontributionstocur‐
rent3GPPstandardizationworks,aswellasresearchstudies,e.g.,[37].
4.2.ResultsforLOSConditions
Fortheaboveassumptions,wecarriedoutsimulationstudies.Resultsobtainedfor
LOSconditionsaredepictedinFigures7and8.GraphsinFigure7presenttheSIRsversus
theangleofbeamseparationforthevariousdistancesbetweentheUEandgNodeB,ob‐
tainedfortheMPMand3GPPmodel.Figure8showsthecorrespondingcumulativedis‐
tributionfunctions(CDFs)ofSIR.
Figure7.Signal‐to‐interferenceratios(SIRs)versusangleofbeamseparationforline‐of‐sight
(LOS)conditionsanddifferentUE–gNodeBdistancesobtainedforthemulti‐ellipticalpropagation
model(MPM)and3GPPmodel.
Figure8.Cumulativedistributionfunctions(CDFs)ofSIRforLOSconditionsandselecteddis‐
tancesobtainedfortheMPMand3GPPmodel.
Figure 8.
Cumulative distribution functions (CDFs) of SIR for LOS conditions and selected distances obtained for the MPM
and 3GPP model.
As can be expected, an increase in
∆α
reduces the DL interference between the refer-
ence beam (providing services to the UE) and the interference beam. However, the nature
of the SIR graphs is not uniform. For
∆α∼
=
15
◦
, 30
◦
, and 48
◦
, there are local maxima. They
are visible for both assumed channel models and result from considering side lobes in
the realistic patterns of gNodeB beams. For the 3GPP channel model, the magnitudes of
local maxima are noticeably higher than in the MPM. High maxima in the 3GPP model are
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caused by the significant difference between powers of direct and reflected multipath com-
ponents, which is typical for the 3GPP LOS channel models. However, for the remaining
ranges of angular separation
∆α
, where local maxima are not present, the results obtained
for the MPM and 3GPP model are comparable. The CDFs of SIR (see Figure 8) illustrate that
for 80% of the analyzed range of angular separation, the results obtained by both models
are within 2 dB, with half of these results within 1 dB of difference. This comparison of the
LOS scenario clearly indicates that estimation of intra-cell interference and SIR with the
use of the MPM demonstrates accuracy comparable with the 3GPP channel model.
To estimate intra-cell interference and SIR, the MPM only needs a single simulation
instance. In contrast, the 3GPP statistical channel model requires computational power-
and time-consuming Monte Carlo simulations. Taking the above facts into account, the
MPM seems to be a reasonable alternative to the commonly used channel model of the
3GPP, especially if obtained simulation results are comparable.
4.3. Results for NLOS Conditions
Due to modeling of the transmission properties of the propagation environment, the
3GPP simulation test procedure is strictly statistical. On the other hand, the procedure used
in the MPM is based on the PDP, which provides the creation of a geometric structure for the
determined analysis of propagation paths. The DS (
στ=
363
ns
) is the only joint parameter
that describes the transmission properties of the environment. Under LOS conditions, the
signal arriving at the Rx via the direct path is the dominant component of the received
signal. Hence, according to 3GPP and MPM procedures, simulation tests give us results
with a similar set of values and the nature of changes. Under NLOS conditions, the 3GPP
approach gives a statistical estimate of the SIR as a function of the beam separation angle
and the distance from the gNodeB. In contrast, the MPM procedure is associated with
specific transmission properties of the propagation environment, which define the PDP
and constitute one random set of parameters in the 3GPP procedure.
For NLOS conditions, we carried out the simulation tests based on the assumptions
described in Section 4.1. The obtained results are shown in Figures 9and 10. Charts in
Figure 9depict the SIRs versus
∆α
for various
D
obtained for (a) the MPM and (b) the
3GPP model, respectively. The corresponding CDFs of SIR are illustrated in Figure 10.
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Figure9.SIRsversusangleofbeamseparationfornon‐line‐of‐sight(NLOS)conditionsanddiffer‐
entdistancesbetweenUEandgNodeBobtainedforthe(a)MPMand(b)3GPPmodel.
Figure10.CDFsofSIRforNLOSconditionsandselecteddistancesobtainedfor(a)theMPMand
(b)the3GPPmodel.
Ascanbeexpected,anincreaseinΔαreducestheDLinterferencebetweentheref‐
erencebeam(providingservicestotheUE)andtheinterferencebeam.However,the
spreadingeffectofthepropagationenvironmentcausessignificantangulardispersionin
thepowerofthereceivedsignals.Thisisthereasonforanincreaseinthelevelofco‐
channelinter‐beaminterference,i.e.,adecreaseintheSIRbyabout15dBinreferenceto
correspondingLOSresults.Theresultsobtainedinthe3GPPsimulationtestprocessshow
littledifferentiationinrelationtotheEUposition.Thiseffectisduetothemultipleuses
ofaveraginginthe3GPPprocedure.Itconsistsofarandomselectionofthetransmission
parametersofthepropagationenvironmentinthenextsimulationstep.Theselectionran‐
domnessoftheseparametersislimitedonlybytheconditionofensuringaconstantthe
DSvalue.
Figure 9.
SIRs versus angle of beam separation for non-line-of-sight (NLOS) conditions and different distances between UE
and gNodeB obtained for the (a) MPM and (b) 3GPP model.
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Figure9.SIRsversusangleofbeamseparationfornon‐line‐of‐sight(NLOS)conditionsanddiffer‐
entdistancesbetweenUEandgNodeBobtainedforthe(a)MPMand(b)3GPPmodel.
Figure10.CDFsofSIRforNLOSconditionsandselecteddistancesobtainedfor(a)theMPMand
(b)the3GPPmodel.
Ascanbeexpected,anincreaseinΔαreducestheDLinterferencebetweentheref‐
erencebeam(providingservicestotheUE)andtheinterferencebeam.However,the
spreadingeffectofthepropagationenvironmentcausessignificantangulardispersionin
thepowerofthereceivedsignals.Thisisthereasonforanincreaseinthelevelofco‐
channelinter‐beaminterference,i.e.,adecreaseintheSIRbyabout15dBinreferenceto
correspondingLOSresults.Theresultsobtainedinthe3GPPsimulationtestprocessshow
littledifferentiationinrelationtotheEUposition.Thiseffectisduetothemultipleuses
ofaveraginginthe3GPPprocedure.Itconsistsofarandomselectionofthetransmission
parametersofthepropagationenvironmentinthenextsimulationstep.Theselectionran‐
domnessoftheseparametersislimitedonlybytheconditionofensuringaconstantthe
DSvalue.
Figure 10. CDFs of SIR for NLOS conditions and selected distances obtained for (a) the MPM and (b) the 3GPP model.
As can be expected, an increase in
∆α
reduces the DL interference between the ref-
erence beam (providing services to the UE) and the interference beam. However, the
spreading effect of the propagation environment causes significant angular dispersion
in the power of the received signals. This is the reason for an increase in the level of
co-channel inter-beam interference, i.e., a decrease in the SIR by about 15 dB in reference to
corresponding LOS results. The results obtained in the 3GPP simulation test process show
little differentiation in relation to the EU position. This effect is due to the multiple uses
of averaging in the 3GPP procedure. It consists of a random selection of the transmission
parameters of the propagation environment in the next simulation step. The selection
randomness of these parameters is limited only by the condition of ensuring a constant the
DS value.
On the other hand, use of the MPM makes it possible to assess the impact of the UE
position on SIR changes. In this case, the PDP unambiguously defines the transmission
environment parameters that are the basis for determining the MPM spatial structure.
Thanks to this, it is possible to map the Rx position in relation to scattering element
locations, which determines the individual propagation path trajectories. The simulation
test results clearly indicate that estimation of the intra-cell interference and SIR with MPM
use demonstrates greater detail in comparison to the 3GPP channel model [
27
]. Therefore,
the MPM seems to be a reasonable alternative to the commonly used 3GPP channel model,
especially if we want to obtain an assessment for strictly determined PDP.
It should be highlighted that the 3GPP model is currently considered a standard in
the analysis of 5G systems and beyond. However, this does not mean that the results
obtained by this model always faithfully reflect the simulated scenario. This may be due
to differences between the modeling approaches, i.e., statistical, stochastic, geometric, or
deterministic. Many models in the literature also show divergence from the 3GPP model,
e.g., [
41
–
44
]. The authors of [
41
,
42
] propose models based on empirical measurements
carried out in Vienna and New York, respectively, whereas ray-tracing approaches are
described in [
43
,
44
]. In the last, differences in the CDFs of the received interference power
are shown.
4.4. Analysis of SIR Confidence Intervals
To analyze simulation result variability, we determined the confidence intervals
against the average SIRs,
SI Ravg
, presented in Sections 4.2 and 4.3. The obtained confidence
intervals are depicted in Figures 11 and 12 for LOS and NLOS conditions, respectively. In
Sensors 2021,21, 597 14 of 17
this case, considering the similarity of the results for various distances, we show the results
only for D=100 m.
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Ontheotherhand,useoftheMPMmakesitpossibletoassesstheimpactoftheUE
positiononSIRchanges.Inthiscase,thePDPunambiguouslydefinesthetransmission
environmentparametersthatarethebasisfordeterminingtheMPMspatialstructure.
Thankstothis,itispossibletomaptheRxpositioninrelationtoscatteringelementloca‐
tions,whichdeterminestheindividualpropagationpathtrajectories.Thesimulationtest
resultsclearlyindicatethatestimationoftheintra‐cellinterferenceandSIRwithMPMuse
demonstratesgreaterdetailincomparisontothe3GPPchannelmodel[27].Therefore,the
MPMseemstobeareasonablealternativetothecommonlyused3GPPchannelmodel,
especiallyifwewanttoobtainanassessmentforstrictlydeterminedPDP.
Itshouldbehighlightedthatthe3GPPmodeliscurrentlyconsideredastandardin
theanalysisof5Gsystemsandbeyond.However,thisdoesnotmeanthattheresultsob‐
tainedbythismodelalwaysfaithfullyreflectthesimulatedscenario.Thismaybedueto
differencesbetweenthemodelingapproaches,i.e.,statistical,stochastic,geometric,orde‐
terministic.Manymodelsintheliteraturealsoshowdivergencefromthe3GPPmodel,
e.g.,[41–44].Theauthorsof[41,42]proposemodelsbasedonempiricalmeasurements
carriedoutinViennaandNewYork,respectively,whereasray‐tracingapproachesare
describedin[43,44].Inthelast,differencesintheCDFsofthereceivedinterferencepower
areshown.
4.4.AnalysisofSIRConfidenceIntervals
Toanalyzesimulationresultvariability,wedeterminedtheconfidenceintervals
againsttheaverageSIRs,avg ,SIR presentedinSections4.2and4.3.Theobtainedconfi‐
denceintervalsaredepictedinFigures11and12forLOSandNLOSconditions,respec‐
tively.Inthiscase,consideringthesimilarityoftheresultsforvariousdistances,weshow
theresultsonlyfor100m.D
Figure11.ExemplarySIRswithconfidenceintervalsversusangleofbeamseparationforLOScon‐
ditions,D=100m,obtainedfor(a)theMPMand(b)the3GPPmodel.
Figure 11.
Exemplary SIRs with confidence intervals versus angle of beam separation for LOS conditions, D= 100 m,
obtained for (a) the MPM and (b) the 3GPP model.
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Figure12.ExemplarySIRswithconfidenceintervalsversusangleofbeamseparationforNLOS
conditions,D=100m,obtainedfor(a)theMPMand(b)the3GPPmodel.
TheconfidenceintervalsoftheSIRgraphswereillustratedas
avg ΔΔ,
SIR
SIR ασ α
where
Δ
SIR
σα
isastandarddeviationfortheselectedseparationangle,calculated
basedon1000valuesoftheSIRsetobtainedduringeachMonteCarlorun.Usingthe
MonteCarloapproachinthe3GPPsimulatorallowstheseconfidentialintervalstobeob‐
tainedsimultaneously.AverageresultsfortheMPMsimulator,illustratedinprevious
sections,wereobtainedbasedontheso‐calledsingle‐simulationmode.Inthiscase,we
usedahugenumberofpropagationpaths.Toanalyzetheconfidenceintervalsforthese
averageresults,wealsohadtoruntheMPMsimulatorinMonteCarlomodewithasmall
numberofrandompropagationpaths.
Generally,wemayseethattheMPMresultsfallwithintheambitofthe3GPPconfi‐
denceintervals.UnderLOSconditions,bothmodels’resultsareveryconvergent,asde‐
scribedindetailinSection4.2.Theobtainedresultsoftheconfidenceintervalsfurther
increasetheirsimilarity.Inthiscase,acharacteristicfeatureisaslightincreaseinthede‐
viationwiththeincreaseinΔ.αUnderNLOSconditions,theSIRresultsfortheMPM
fallwhollywithintheambitoftheconfidenceintervalsobtainedforthe3GPPmodel.For
thesepropagationconditions,itischaracteristictokeeptheconstantSIR
σregardlessof
theseparationangle.
Tocompareerrordistributionofthesimulationresults,wecalculatedthemean
standarddeviation,
,
σfortheMPM:0.84dB
MPM
LOS
σand1.83dB,
MPM
NLOS
σand3GPP:
30.94dB
GPP
LOS
σand
3
8.91dB,
GPP
NLOS
σunderLOSandNLOSconditions,respectively.In
thiscase,SIRvariabilitymaybemodeledasaGaussianrandomvariablewithastandard
deviationdeterminedbytheappropriate.σConversely,theaveragevalueofthisran‐
domvariableshouldbemodeledusingtheaveragedSIRdescribedinSections4.2or4.3.
Ontheotherhand,wecanseethesimilarityofbothsimulatorsintheirσvaluesforLOS
conditions.UnderNLOSconditions,thevaluesofσaredefinitelydifferent.Thismay
resultfromthefactthatintheMPM,thescattererlocationsarelimitedtothedefined
multi‐ellipticalstructurerelatedtothePDP.However,inthestatistical3GPPchannel
model,thepotentialpositionsofthescatterersarecharacterizedbymorespatialvariation.
Figure 12.
Exemplary SIRs with confidence intervals versus angle of beam separation for NLOS conditions, D= 100 m,
obtained for (a) the MPM and (b) the 3GPP model.
The confidence intervals of the SIR graphs were illustrated as
SI Ravg (∆α)±σSI R(∆α)
,
where
σSIR (∆α)
is a standard deviation for the selected separation angle, calculated based
on 1000 values of the SIR set obtained during each Monte Carlo run. Using the Monte
Carlo approach in the 3GPP simulator allows these confidential intervals to be obtained
simultaneously. Average results for the MPM simulator, illustrated in previous sections,
were obtained based on the so-called single-simulation mode. In this case, we used a huge
number of propagation paths. To analyze the confidence intervals for these average results,
we also had to run the MPM simulator in Monte Carlo mode with a small number of
random propagation paths.
Sensors 2021,21, 597 15 of 17
Generally, we may see that the MPM results fall within the ambit of the 3GPP con-
fidence intervals. Under LOS conditions, both models’ results are very convergent, as
described in detail in Section 4.2. The obtained results of the confidence intervals further
increase their similarity. In this case, a characteristic feature is a slight increase in the
deviation with the increase in
∆α
. Under NLOS conditions, the SIR results for the MPM
fall wholly within the ambit of the confidence intervals obtained for the 3GPP model. For
these propagation conditions, it is characteristic to keep the constant
σSIR
regardless of the
separation angle.
To compare error distribution of the simulation results, we calculated the mean
standard deviation,
σ
, for the MPM:
σMPM
LOS =
0.84
dB
and
σMPM
NLOS =
1.83
dB,
and 3GPP:
σ3GPP
LOS =
0.94
dB
and
σ3GPP
NLOS =
8.91
dB,
under LOS and NLOS conditions, respectively. In
this case, SIR variability may be modeled as a Gaussian random variable with a standard
deviation determined by the appropriate σ. Conversely, the average value of this random
variable should be modeled using the averaged SIR described in Section 4.2 or
Section 4.3
.
On the other hand, we can see the similarity of both simulators in their
σ
values for LOS
conditions. Under NLOS conditions, the values of
σ
are definitely different. This may
result from the fact that in the MPM, the scatterer locations are limited to the defined multi-
elliptical structure related to the PDP. However, in the statistical 3GPP channel model, the
potential positions of the scatterers are characterized by more spatial variation.
5. Conclusions
This paper focused on modeling the interference of radio DLs arising in multi-beam
antenna systems, which helps to assess the performance of the mMIMO in 5G cells at
network planning and optimization stages. Furthermore, we presented the comparison
of two modeling methodologies that allow the DL intra-cell interference and SIR to be
estimated. The presented methods of SIR evaluation were based on simulation studies.
In this case, the MPM and 3GPP channel model, combined with realistic beam patterns
and simulation parameters of the 3GPP/ITU, were used. The obtained results shown the
effectiveness of the novel approach using the MPM in determining the minimum angular
separation in multi-beam antenna arrays that provided an acceptable interference level
compared with the simulation results obtained by the 3GPP channel model. Unlike the
methods of inter-beam interference assessment used so far, the MPM solution proposed in
this paper considers the phenomenon of the angular dispersion of received power. The
ability to adapt the MPM geometric structure to actual transmission conditions minimizes
SIR evaluation errors. In this, the presented novel MPM approach’s utilization for assessing
the interference level at the receiving point could be considered as an efficient method
for the determination of the required minimum angular separation between co-channel
beams of mMIMO cells. Therefore, the MPM approach might help maximize spectral
efficiency in 5G networks under deployment. This statement is justified as for 80% of
simulated samples of the intra-cell SIR the difference between results obtained by the
MPM and commonly used 3GPP model was within 2 dB or less for LOS conditions of the
UMa network operating in a 3.5 GHz band. In the case of NLOS, the difference between
both channel models is more visible. This may result from the fact that in the MPM, the
scatterer locations are limited to the defined multi-elliptical structure related to the PDP.
Conversely, in the statistical 3GPP channel model, the potential positions of the scatterers
are characterized by more spatial variation. Further studies are being conducted in which
the MPM effectiveness is assessed in mmWave simulation scenarios with both DL and
uplink.
Author Contributions:
Conceptualization, K.B., J.M.K. and C.Z.; methodology, K.B., J.M.K. and C.Z.;
software, K.B. and J.M.K.; validation, K.B. and J.M.K.; formal analysis, C.Z.; investigation, K.B. and
J.M.K.; resources, K.B. and J.M.K.; data curation, K.B. and J.M.K.; writing—original draft preparation,
K.B., J.M.K., C.Z. and L.N.; writing—review and editing, K.B., J.M.K., C.Z. and L.N.; visualization,
J.M.K.; supervision, C.Z.; project administration, J.M.K. and C.Z.; funding acquisition, J.M.K. All
authors have read and agreed to the published version of the manuscript.
Sensors 2021,21, 597 16 of 17
Funding:
This research was funded by the POLISH MINISTRY OF DEFENSE, grant number
GBMON/13-996/2018/WAT on “Basic research in sensor technology field using innovative data
processing methods” and grant number UGB/22-730/2020/WAT on “Impact of various propagation
conditions on effectiveness of wireless communication and electronic warfare systems”.
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 Remote Sensing
Editors and anonymous Reviewers for their valuable suggestions, which have improved the quality
of the paper.
Conflicts of Interest: The authors declare no conflict of interest.
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