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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-

tral with regard to jurisdictional clai-

ms in published maps and institutio-

nal afﬁliations.

Copyright: © 2021 by the authors. Li-

censee MDPI, Basel, Switzerland.

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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.

Sensors 2021,21, 597 7 of 17

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)

Sensors 2021,21, 597 8 of 17

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

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 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.

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 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

Sensors 2021,21, 597 12 of 17

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.

Sensors2021,21,xFORPEERREVIEW13of18

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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Sensors2021,21,xFORPEERREVIEW13of18

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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