Inter-Beam Co-Channel Downlink and Uplink Interference for 5G New Radio in mm-Wave Bands

Abstract

This paper presents a methodology for assessing co-channel interference that arises in multi-beam transmitting and receiving antennas used in fifth-generation (5G) systems. This evaluation is essential for minimizing spectral resources, which allows for using the same frequency bands in angularly separated antenna beams of a 5G-based station (gNodeB). In the developed methodology, a multi-ellipsoidal propagation model (MPM) provides a mapping of the multipath propagation phenomenon and considers the directivity of antenna beams. To demonstrate the designation procedure of interference level we use simulation tests. For exemplary scenarios in downlink and uplink, we showed changes in a signal-to-interference ratio versus a separation angle between the serving (useful) and interfering beams and the distance between the gNodeB and user equipment. This evaluation is the basis for determining the minimum separation angle for which an acceptable interference level is ensured. The analysis was carried out for the lower millimeter-wave band, which is planned to use in 5G micro-cells base stations.

Full text

sensors
Article
Inter-Beam Co-Channel Downlink and Uplink Interference for
5G New Radio in mm-Wave Bands †
Kamil Bechta 1, Jan M. Kelner 2, * , Cezary Ziółkowski 2and Leszek Nowosielski 2


Citation: Bechta, K.; Kelner, J.M.;
Ziółkowski, C.; Nowosielski, L.
Inter-Beam Co-Channel Downlink
and Uplink Interference for 5G New
Radio in mm-Wave Bands. Sensors
2021,21, 793. https://doi.org/
10.3390/s21030793
Academic Editors: Waqas Khalid,
Heejung Yu, Rehmat Ullah and
Rashid Ali
Received: 19 December 2020
Accepted: 20 January 2021
Published: 25 January 2021
Publisher’s Note: MDPI stays neutral
with regard to jurisdictional claims in
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iations.
Copyright: © 2021 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
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:
This paper presents a methodology for assessing co-channel interference that arises in multi-
beam transmitting and receiving antennas used in fifth-generation (5G) systems. This evaluation
is essential for minimizing spectral resources, which allows for using the same frequency bands in
angularly separated antenna beams of a 5G-based station (gNodeB). In the developed methodology,
a multi-ellipsoidal propagation model (MPM) provides a mapping of the multipath propagation
phenomenon and considers the directivity of antenna beams. To demonstrate the designation
procedure of interference level we use simulation tests. For exemplary scenarios in downlink and
uplink, we showed changes in a signal-to-interference ratio versus a separation angle between the
serving (useful) and interfering beams and the distance between the gNodeB and user equipment.
This evaluation is the basis for determining the minimum separation angle for which an acceptable
interference level is ensured. The analysis was carried out for the lower millimeter-wave band, which
is planned to use in 5G micro-cells base stations.
Keywords:
wireless mobile communications; 5G; millimeter-wave; multi-beam antenna system;
wireless downlink and uplink; co-channel interference; signal-to-interference ratio; multi-ellipsoidal
propagation model; simulation studies
1. Introduction
This paper focuses on a methodology for assessing co-channel interference occur-
ring in fifth-generation (5G) networks, in which a directional wireless link is one of the
key techniques [
1
,
2
]. To this aim, especially in frequency bands below 6 GHz, 5G new
radio (NR) base stations (gNodeBs) use multi-beam antenna systems based on massive
multiple-input-multiple-output (massive-MIMO) technology, which is enabled by digital
beamforming [
3
,
4
]. This solution reduces the energy expenditure due to the high gain and
narrow width of the beams. The needed increase in the radio link capacity is obtained
thanks to an energy balance improvement. On the other hand, massive-MIMO ensures the
efficient use of spectral resources. An appropriate angular separation between individual
beams makes it possible to use the same frequency channels. However, the minimization
of spectral resources offered by this technology is associated with the need to assess the
interplay of signals received by individual beams. In the millimeter-waves (mmWaves)
frequency range, where early implementations of 5G are based on analog beamforming, the
multi-beam transmissions inside a single cell sector are obtained by multiple sub-arrays,
which constitute the full antenna array. Each of these sub-arrays is connected to individ-
ual transmission–reception chain and enables the simultaneous generation of multiple
beams. Hitherto, evaluation methodologies of co-channel interference mainly concerned
Sensors 2021,21, 793. https://doi.org/10.3390/s21030793 https://www.mdpi.com/journal/sensors

Sensors 2021,21, 793 2 of 20
omnidirectional and sectoral antennas and homogeneous environments, e.g., [
5
–
7
]. From
the viewpoint of 5G systems that use mmWaves, massive-MIMO, and beamforming, such
analysis should consider narrow beams of antenna systems. Examples of such studies
are presented in [
8
–
11
]. On the other hand, the analysis of co-channel interference is es-
sential to assessing the coexistence and compatible functioning of different radio systems.
The importance of this problem is presented in [
9
]. Besides, many new procedures in
massive-MIMO and beamforming systems that increase the efficiency of 5G require assess-
ing the level of interference between the antenna beams to and from individual users. The
partial-nulling based statistical beamforming is an example of such a procedure, the use of
which is based on the division of all users into two groups with a significantly different
degree of spatial correlation [
12
]. The solution presented in [
13
] is another example that
increases the spectral efficiency in massive-MIMO systems. These selected examples show
the importance of assessing the level of interference between the beams of the antenna
system from other users in developing and implementing new solutions.
The utilization of narrow beams and the dominance of the multipath propagation
phenomenon in urban areas significantly change interference analysis methods. In this
case, the practical used method of the interference assessment is based on simulation tests.
Parameters of transmitted and received signals as well as their statistical properties for
various types of propagation environments are input for these studies. The 3rd Generation
Partnership Project (3GPP) standard [
14
] is commonly used for this aim. This approach
recommends using deterministic cluster delay lines (CDLs) for link-level simulations,
where average angles of departure (AODs) and arrival (AOAs), in addition to tapped delay
line (TDL), are defined. For system-level simulations, where a statistical approach is more
appropriate, the 3GPP standard [
14
] recommends the full three-dimensional (3D) modeling
of a radio channel.
The interference topic is widely represented in the literature. On the one hand, there
are works on counteracting interference in the emerging and future systems. Examples
include software algorithms and hardware solutions aimed at interference cancellation [
15
],
mitigation [
16
], or awareness [
17
,
18
]. In this case, the currently proposed solutions are
mainly dedicated to multi-antenna systems. On the other hand, papers focusing on the
interference evaluation and measurement [
19
] methodologies are presented. In general,
the interference analysis can be performed at any distance from the signal source antenna.
In the case of a near-field, the influence between the individual elements of the multi-
antenna system can be investigated [
20
–
24
]. In the case of a far-field, inter-beam [
25
,
26
],
inter-cell [
18
,
26
,
27
], or inter-system interferences, i.e., the coexistence of different systems
and networks [
9
,
11
,
28
], might be studied. In the literature, the vast majority of scientific
works concern coexistence topic and the inter-cell interference assessment, rather than
inter-beam interference.
In this paper, we present a methodology for assessing co-channel interference that
is resulting from the utilization of the same frequency channels in different beams of
the gNodeB antenna system. To evaluate the signal-to-interference ratio (SIR), we use
simulation tests that are based on a 3D multi-ellipsoidal propagation model (MPM) [
29
–
31
].
However, the proposed methodology differs from the simulation approach recommended
by the 3GPP standard for link-level evaluations. In our methodology, using the MPM as
a geometry-based model (GBM) provides a statistical SIR metric in contrast to the 3GPP
approach with the pre-determined AODs and AOAs. In our solution, the knowledge
of spatial parameters such as the average AODs and AOAs of propagation paths is not
required to obtain results and the use of any power delay profile (PDP) or the TDL makes
it possible to adapt this model to any propagation scenarios. The use of the MPM and
antenna radiation patterns allow determining a power angular spectrum (PAS) of the
received signals. The obtained PASs are the basis for the SIR assessment in the multi-beam
antenna system. The MPM geometry is constructed based on the PDP or TDL, which
describe the transmission properties of a propagation environment. This original way
of mapping the effects of propagation phenomena enables obtaining a fully statistical

Sensors 2021,21, 793 3 of 20
SIR evaluation. It ensures a relationship of simulation results with the analyzed type
of propagation environment. The presented analysis is an extension of the paper [
32
],
which focused only on the downlink (DL) interference in multi-beam 5G macro-cell for
3.5 GHz band and under non-line-of-sight (NLOS) conditions. In that case, we used a two-
dimensional multi-elliptical model [
31
]. In this study, based on the 3D MPM, we discuss
the inter-beam co-channel interference in DL and additionally uplink (UL) for 28 GHz
band, under line-of-sight (LOS) and NLOS conditions. Using the 3D MPM to modeling
the inter-beam interference level testifies to the novelty of the presented approach. In this
case, an original approach to the UL interference assessment was proposed, taking path
loss corrections into account, compared to the DL scenario [32] shown previously.
The mutual configuration of the transmitting and receiving antenna beams is not only
the factor considered in our methodology. The presented solution of the SIR determination
also provides a mapping of the propagation environment influence on the PAS of the
received signals. The 3GPP methodology also takes this impact into account. However, it
is limited to well-defined types of environments that are defined based on the determined
channel characteristics and distributions of channel parameters. In the case of the MPM
methodology presented in this paper, we have the option to assess the SIR for any type of
propagation environment, whose transmission properties are defined by an appropriate
PDP. This fact significantly distinguishes the developed method and proves its originality.
The remainder of the paper is organized as follows: Section 2shows the construction
way of the MPM geometry based on the transmission properties of the propagation envi-
ronment, i.e., the TDL. The essence of the PAS determination procedure and then the SIR
assessment is presented in Section 3. In Sections 4and 5, the description of the analyzed
scenarios for the DL and UL transmissions and the results of simulation studies are drawn.
Section 6contains conclusions.
2. Multi-Ellipsoidal Propagation Model
In 5G networks, designing wireless links with narrow beams and beamforming tech-
nology enforces the use of GBMs. It is particularly important in relation to urbanized
areas. In this case, there is a large directional variation in the received powers. The use
of GBMs ensures the spatial power distribution in the vicinity of the receiving antenna.
In combination with the narrow beam patterns, this approach gives the possibility of a
statistical evaluation of the transmission properties of the wireless link. The MPM is one
of the GBMs. The set of confocal ellipsoids forms its geometrical structure representing
the potential locations of the scattering elements for an emitted radio wave. In the foci of
the ellipsoids, a transmitter (Tx) and receiver (Rx) are located. In propagation scenarios,
where the Tx and Rx are on the Earth’s surface, the MPM structure is represented by a set
of semi-ellipsoids, as shown in Figure 1[31].
Sensors 2021, 21, x FOR PEER REVIEW 4 of 23
Figure 1. MPM geometrical structure considering Earth surface.
The MPM geometrical structure is closely related to the transmission properties of
the propagation environment, which may be described by the PDP or TDL. In multipath
environments, we can observe the occurrence of several or a dozen taps or local extremes
in the TDLs or PDPs, respectively. It means that as a result of scattering on terrain obsta-
cles, the electromagnetic wave reaches the Rx by different propagation paths but with the
same delays
n
τ
for
1,2,...,nN
[33]. Thus, based on the properties of geometrical fig-
ures, the most probable locations of the scattering elements form an ellipsoid. Of course,
the number of ellipsoids is equal to the number
N
of time-clusters representing the taps
or local extremes in the TDL or PDP, respectively. If the distance between the Tx and Rx
is equal to
,D
then the parameters of individual ellipsoids such as a major, axn, and minor
semi-axes byn, czn describe the following relationships:
 

1,
2
xn n
acτD
(1)
 
  
12,
2
yn zn n n
b c cτ cτ D
(2)
where c denotes the speed of light.
The geometrical structure of the MPM is described in detail in [29–31]. The 3D MPM
may be reduced to the 2D multi-elliptical model, where propagation phenomena in the
azimuth plane are dominant [31]. For this modeling procedure in relation to other GBMs,
minimizing the estimation error of the PAS is shown in [34]. In the MPM, the phenomenon
of local scattering around the transmitting and receiving antennas is also included. In this
case, the AOAs of propagation paths are generated based on the 2D von Mises distribution
[29,35]:
   
 
 
 
 
 
00
00
exp cos 90 exp cos
,2πI 2πI
for 0, 90 and 180 , 180 ,
fC 

     


   
 

(3)
where
 

,θ
is AOA in the elevation and azimuth planes, respectively,
θ
γ
and

γ
de-
fine the angular dispersion of the components in the elevation and azimuth planes, re-
spectively,
 

0
I
is the zero-order modified Bessel function of the imaginary argument,
Figure 1. MPM geometrical structure considering Earth surface.

Sensors 2021,21, 793 4 of 20
The MPM geometrical structure is closely related to the transmission properties of
the propagation environment, which may be described by the PDP or TDL. In multipath
environments, we can observe the occurrence of several or a dozen taps or local extremes
in the TDLs or PDPs, respectively. It means that as a result of scattering on terrain obstacles,
the electromagnetic wave reaches the Rx by different propagation paths but with the same
delays
τn
for
n=
1, 2,
. . .
,
N
[
33
]. Thus, based on the properties of geometrical figures,
the most probable locations of the scattering elements form an ellipsoid. Of course, the
number of ellipsoids is equal to the number
N
of time-clusters representing the taps or
local extremes in the TDL or PDP, respectively. If the distance between the Tx and Rx is
equal to
D
, then the parameters of individual ellipsoids such as a major, a
xn
, and minor
semi-axes byn,czn describe the following relationships:
axn =1
2(cτn+D), (1)
byn =czn =1
2qcτn(cτn+2D), (2)
where cdenotes the speed of light.
The geometrical structure of the MPM is described in detail in [
29
–
31
]. The 3D
MPM may be reduced to the 2D multi-elliptical model, where propagation phenomena
in the azimuth plane are dominant [
31
]. For this modeling procedure in relation to other
GBMs, minimizing the estimation error of the PAS is shown in [
34
]. In the MPM, the
phenomenon of local scattering around the transmitting and receiving antennas is also
included. In this case, the AOAs of propagation paths are generated based on the 2D von
Mises distribution [29,35]:
f0(θ,φ)=C0exp(γθcos(90◦−θ))
2πI0(γθ)·exp(γφcos φ)
2πI0(γφ)
for θ∈h0, 90◦)and φ∈h−180◦, 180◦),
(3)
where
(θ,φ)
is AOA in the elevation and azimuth planes, respectively,
γθ
and
γφ
define
the angular dispersion of the components in the elevation and azimuth planes, respec-
tively,
I0(·)
is the zero-order modified Bessel function of the imaginary argument, and
C0
represents the normalizing constant such that C0
2πI0(γθ)
90◦
R0
exp(γθcos(90◦−θ))dθ=1.
3. Evaluation of Co-Channel Interference in Multi-Beam Antenna
The co-channel interference assessment is based on the SIR measure defined as:
SI R =PS
PIW
W↔SI R(dB)=PS(dBm)−PI(dBm), (4)
where
PS
and
PI
are the powers of the serving and interfering signal, respectively, which
occur at the output of the receiving antenna. In the multi-beam receiving antenna, the
interference signal is from a wireless link whose receiving antenna beam is formed in the
same frequency band as the serving beam. From the SIR definition, it follows that the main
problem of assessing this measure relies on determining
PS
and
PI
. Note that these powers
can be calculated based on the appropriate PASs,
pS,I(θ,φ)
, which are seen at the output of
the receiving antenna, namely:
PS,I=x
(θ,φ)
pS,I(θ,φ)dθdφ. (5)
However, these distributions depend on the power pattern of the serving beam [30]:
pS,I(θ,f)=e
pS,I(θ,f)|g(θ,f)|2, (6)

Sensors 2021,21, 793 5 of 20
where
e
pS,I(θ,φ)
represent the PASs in the vicinity of the receiving antenna and
|g(θ,φ)|2
is
the normalized power pattern of the receiving antenna.
Hence, it follows that the problem of the SIR assessment boils down to determining
e
pS,I(θ,φ)
. The developed methodology uses simulation tests to determine these PASs. The
input data for simulation procedures that condition the estimation of
e
pS,I(θ,φ)
is a set of
the following parameters and characteristics:
•
normalized power patterns
|gS(θT,φT)|2
,
|gI(θT,φT)|2
, and
|g(θ,φ)|2
, of the serving
and interfering transmitting and receiving beams, respectively, where
(θT,φT)
denotes
AOD in the elevation and azimuth planes, respectively;
•
gains
GS
,
GI
, and
G
of the serving and interfering transmitting and receiving beams,
respectively;
•
the Tx-Rx distances, i.e.,
DS
and
DI
between the serving and interfering mobile stations
(user equipment, i.e., UE-S and UE-I) and gNodeB for the UL scenario, respectively, or
DS=DI=Dfor the DL scenario;
•
the type of propagation environment defined by the TDL or PDP and rms delay
spread.
•
Estimation of
e
pS,I(θ,φ)
consists in the generation of a set of propagation paths de-
parting from the transmitting antennas of the serving and interfering links and their
transformation in a system composed of the semi-ellipsoid set. The generation pro-
cedure of AODs,
(θT,φT)
, uses the properties of the normalized power radiation
patterns [36]:
1
4πx
(θT,φT)
|gS,I(θT,φT)|2sin θTdθTdφT=1. (7)
The function under integral is non-negative. Therefore, the normalized power radia-
tion patterns meet the axioms of a probability density function. Hence, we can express the
distribution of AOD as [36]:
fS,I(θT,φT)=1
4π|gS,I(θT,φT)|2sin θT. (8)
The geometry structure of the MPM represents the statistical locations of the scattering
elements. Thus, the intersection of the radiated path with individual semi-ellipses indicates
the scattering places of this path. Knowing the AODs,
(θT,φT)
, of radiated propagation
paths, we can determine for each of them the radial coordinate
rT
in a spherical system with
an origin in the Tx (UE-S or UE-I). For the selected time-cluster (ellipsoid), this coordinate
is described by [29]:
rT=−1
2ab2
yDsin θTcos φT+1
2asb2
yDsin θTcos φT2+4ab2
ya2
x−D2
4, (9)
where a=bysin θTcos φT2+a2
xcos2θT+(sin θTsin φT)2.
Appropriate coordinate transformation resulting from translation the system origin to
the Rx allows determining AOA, (θ,φ), for propagation paths reaching the Rx [29]:
θ=arctan q(rTsin θTcos φT+D)2+(rTsin θTsin φT)2
rTcos θT
, (10)
φ=arctan rTsin θTsin φT
rTsin θTcos φT+D. (11)
In addition to the AOAs of propagation paths reaching the Rx with delays, the local
scattering paths are also included. In this case, the AOAs are generated using the von
Mises distribution described by Equation (3).

Sensors 2021,21, 793 6 of 20
Powers
e
p
of individual paths are determined based on the PDP or TDL. To generate
these powers, we use exponential distributions,
f(e
p)
, whose parameters (i.e., mean values
pn
for
n=
1, 2,
. . .
,
N
) are equal to powers of the taps or local extremes occurring in the
TDL or PDP, respectively:
f(e
p)=(1
pnexpe
p
pnfor e
p≥0,
0 for e
p<0, (12)
where
pn
is the nth local extreme of the PDP (or nth tap value of the TDL), which cor-
responds to the propagation paths reaching from the nth semi-ellipsoid, i.e., with the
delay τn.
As a simulation result, we get the set of
{(θ,φ,e
p)}
that enables estimating
e
pS,I(θ,φ)
[
29
].
Additional multiplication of each
e
p
value by the appropriate value of
|g(θ,φ)|2
gives us
the set of
{(θ,φ,p)}
, which is the basis for estimating
pS,I(θ,φ)
. A detailed description of
the practical implementation of the estimation procedure is provided in [
30
]. As a result,
we can determine PSand PIbased on Equation (5).
For the DL scenario, the SIR may be calculated based on Equation (4), because the
serving and interfering beams are generated by the same gNodeB, i.e.,
DS=DI=D
.
However, for the UL scenario, the SIR assessment requires additional consideration of
attenuation resulted from a difference in the distances between the gNodeB and UE-S or
UE-I. Considering this fact, we have:
SI R =PS
PI
∆PL ↔S IR(dB)=PS(dBm)−PI(dBm)+∆PL(dB)(13)
where:
∆PL =P L(DS)
PL(DI)↔∆PL(dB)=PL(DS)(dB)−PL(DI)(dB)(14)
represents the relationship between attenuation of propagation environment for different
distances,
PL(DS)
and
PL(DI)
are path losses for the wireless links between the UE-S or
UE-I and gNodeB, respectively. For assessing
∆PL
, we use a close-in free space reference
distance path loss model presented in [
37
]. To take the influence of variable weather
conditions into account that are related to atmospheric precipitation, the used path loss
model should be corrected based on ITU-R recommendations [
38
,
39
] or other approaches
proposed in the literature, e.g., [40,41].
Generally, the proposed methodology of the interference evaluation consists of the
following stages:
•defining the scenario parameters,
•determining the MPM parameters,
•
determining the PASs for the serving and interfering links based on simulation studies,
•calculating the powers for the determined PASs,
•calculating the SIR finally.
4. Assumptions and Scenarios of Simulation Studies
The aim of the simulation tests is to present a method of modeling and assessing the
co-channel interference that arises in the radio link with a multi-beam antenna system.
The studies focused on determining the SIR relationship on the separation angle
∆α
and
changes in the distance
D
(or distances
DS
and
DI
) between the UEs and gNodeB. The
simulations were carried out for carrier frequency of 28 GHz, typical for the 5G micro-
and pico-cells, where multiple sub-arrays and beamforming technologies are planned for
implementation. Besides, we considered two scenarios for the DL and UL, which are
illustrated in Figures 2and 3, respectively.

Sensors 2021,21, 793 7 of 20
Sensors 2021, 21, x FOR PEER REVIEW 8 of 23
Figure 2. DL spatial scenario of simulation studies [32].
Figure 3. UL spatial scenario of simulation studies.
In the DL scenario, we assumed that the gNodeB was generating two beams (serving
and interfering) in the selected sector that were operating in the same sub-band (frequency
channel). Thus, the SIR assessment came down to determining
S
P
and
I
P
powers in-
Figure 2. DL spatial scenario of simulation studies [32].
Sensors 2021, 21, x FOR PEER REVIEW 8 of 23
Figure 2. DL spatial scenario of simulation studies [32].
Figure 3. UL spatial scenario of simulation studies.
In the DL scenario, we assumed that the gNodeB was generating two beams (serving
and interfering) in the selected sector that were operating in the same sub-band (frequency
channel). Thus, the SIR assessment came down to determining
S
P
and
I
P
powers in-
Figure 3. UL spatial scenario of simulation studies.
In the DL scenario, we assumed that the gNodeB was generating two beams (serving
and interfering) in the selected sector that were operating in the same sub-band (frequency
channel). Thus, the SIR assessment came down to determining
PS
and
PI
powers induced
in the UE antenna that come from the signals generated by the serving and interfering
beams of the gNodeB, respectively. The distances between the gNodeB (Tx) and UE (Rx)
was equal to
D
. Besides, the serving (reference) gNodeB and UE beams were aligned, i.e.,

Sensors 2021,21, 793 8 of 20
directed to each other (
αTS =
0 and
αR=
0, see Figure 1). In relation to the direction of the
cell sector center, the reference and interfering gNodeB beams are oriented in
ΦS
and
ΦI
directions, respectively (see Figure 2). Thus, the separation angle of the beams is defined as:
∆α=ΦS−ΦI, (15)
Then the interfering beam orientation in relation to the Tx-Rx direction was equal to
αTI =∆α.
A similar scenario was taken into account for the UL transmission depicted in
Figure 3
.
In this case, the analyzed gNodeB beam served one subscriber (UE-S) in its area, while
another subscriber (UE-I) generated interferences towards this gNodeB beam. The UE-S
and UE-I beams (Tx) were oriented to the gNodeB (Rx), i.e.,
αTS =αT I =
0 (see
Figure 1
).
Whereas the gNodeB beam directions to the UE-S and UE-I were equal to
αRS =
0 and
αRI =∆α
, respectively. So, in both scenarios, the separation angle,
∆α
, was always
related with the direction of the gNodeB beam for the interfering link. In relation to the
direction of the cell sector center, the gNodeB beam direction was equal to
Φ0
(see
Figure 3
).
The distances between the gNodeB (Rx) and UE-S or UE-I (Tx) were equal to
DS
or
DI
,
respectively.
In our tests, the direction of the reference gNodeB beam overlapped with the cell
sector center, i.e.,
Φ0=ΦS=
0. Hence, we considered the change in separation angle in
the ranges of 0◦÷60◦. When analyzing the SIR changes in relation to the beam separation
angle, we considered discrete distance values between the gNodeB and UE (or UE-I in
the UL scenario), i.e.,
DS=
100
m
and
D=DI∈{50, 100, 150}(m)
. In this case,
∆α
was
changed from 0 to 60
◦
, which corresponds to half of a 120
◦
sector. Analyzing the SIR versus
D
or
DI
(for the DL or UL scenarios, respectively), we considered a continuous change of
the distance in the ranges of 10
÷
250 m, whereas the separation angle has discrete values
15
◦
, 20
◦
, and 30
◦
. For the UL scenario, we additionally used the close-in free space reference
distance propagation models with path loss exponents equal to 1.9 and 4.5 for LOS and
NLOS conditions, respectively [37].
To model the antenna power radiation patterns, we adopted 3GPP recommenda-
tions [
42
]. Half-power beamwidths of main-lobes of the antenna beams were 90
◦
for the UE
and about 12
◦
for the gNodeB, respectively. Single antenna beam patterns of the UE and
gNodeB for direction
Φ0=
0
◦
and
Φ0=
30
◦
are illustrated in Figure 4[
32
]. In the gNodeB,
we used a vertical patch as an antenna array with a size 12
×
8 of elements, whereas the
UE antenna consists of a single element.
Sensors 2021, 21, x FOR PEER REVIEW 10 of 23
Figure 4. Antenna beam patterns of 1 × 1 UE and 12 × 8 gNodeB for Φ0 = 0° and Φ0 = 30° [32].
The simulations were carried out for an urban macro (UMa) environment that is char-
acterized by a normal delay profile with the rms delay spread equal to 266 ns [14]. To
model the channel transmission properties, we adopted the TDLs with the 3GPP standard
[14], i.e., TDL-D and TDL-B for LOS and NLOS conditions, respectively. To estimate
 
,,,
SI
pθ

we used the averaging PASs obtained in 3600 Monte-Carlo simulations. In
each Monte-Carlo run, the PAS was obtained based on the generation of 10 random prop-
agation paths for each time-cluster (ellipsoid). Figure 5 presents averaged PAS examples
of the UE-S and UE-I in the azimuth plane for the UL scenario,
100 m,
SI
DD
Δ 30 ,α
LOS and NLOS conditions.
Figure 5. PASs of UE-S and UE-I in azimuth plane for ∆α = 30°, DS = DI = 100 m, under (a) LOS
(TDL-D) and (b) NLOS (TDL-B) conditions.
The presented results show the diversity of
 
,
S
pθ

and
 
,
I
pθ

both due to the
relationship between the beam lobes and surface areas under the graphs that correspond
Figure 4. Antenna beam patterns of 1 ×1 UE and 12 ×8 gNodeB for Φ0= 0◦and Φ0= 30◦[32].

Sensors 2021,21, 793 9 of 20
The simulations were carried out for an urban macro (UMa) environment that is char-
acterized by a normal delay profile with the rms delay spread equal to 266 ns [
14
]. To model
the channel transmission properties, we adopted the TDLs with the 3GPP standard [
14
], i.e.,
TDL-D and TDL-B for LOS and NLOS conditions, respectively. To estimate
pS,I(θ,φ)
, we
used the averaging PASs obtained in 3600 Monte-Carlo simulations. In each Monte-Carlo
run, the PAS was obtained based on the generation of 10 random propagation paths for
each time-cluster (ellipsoid). Figure 5presents averaged PAS examples of the UE-S and
UE-I in the azimuth plane for the UL scenario,
DS=DI=
100
m
,
∆α=
30
◦
, LOS and
NLOS conditions.
Sensors 2021, 21, x FOR PEER REVIEW 10 of 23
Figure 4. Antenna beam patterns of 1 × 1 UE and 12 × 8 gNodeB for Φ0 = 0° and Φ0 = 30° [32].
The simulations were carried out for an urban macro (UMa) environment that is char-
acterized by a normal delay profile with the rms delay spread equal to 266 ns [14]. To
model the channel transmission properties, we adopted the TDLs with the 3GPP standard
[14], i.e., TDL-D and TDL-B for LOS and NLOS conditions, respectively. To estimate
 
,,,
SI
pθ

we used the averaging PASs obtained in 3600 Monte-Carlo simulations. In
each Monte-Carlo run, the PAS was obtained based on the generation of 10 random prop-
agation paths for each time-cluster (ellipsoid). Figure 5 presents averaged PAS examples
of the UE-S and UE-I in the azimuth plane for the UL scenario,
100 m,
SI
DD
Δ 30 ,α
LOS and NLOS conditions.
Figure 5. PASs of UE-S and UE-I in azimuth plane for ∆α = 30°, DS = DI = 100 m, under (a) LOS
(TDL-D) and (b) NLOS (TDL-B) conditions.
The presented results show the diversity of
 
,
S
pθ

and
 
,
I
pθ

both due to the
relationship between the beam lobes and surface areas under the graphs that correspond
Figure 5.
PASs of UE-S and UE-I in azimuth plane for
∆α
= 30
◦
,D
S
=D
I
= 100 m, under (
a
) LOS (TDL-D) and (
b
) NLOS
(TDL-B) conditions.
The presented results show the diversity of
pS(θ,φ)
and
pI(θ,φ)
both due to the
relationship between the beam lobes and surface areas under the graphs that correspond
to the received powers,
PS
and
PI
, respectively. This fact indicates the dependence of the
received power on the main lobe orientation of the gNodeB beam pattern in relation to the
UE-I. This directly influences the determined SIR value. We observe the same situation in
the DL scenario. A detailed analysis of the simulation test results is described in the next
section.
5. Simulation Results
For the assumptions described in Section 4, we carried out simulation studies using
the MATLAB environment. The results for the DL and UL scenarios are discussed in
Section 5.1 and Section 5.2, respectively. Section 5.3 contains the comparison of inter-beam
interference evaluation obtained based on the MPM and 3GPP statistical model [
14
]. In
this case, we chose the DL scenario to present exemplary results.
5.1. DL Scenario
The simulation results for the DL scenario are presented in Figures 6–10.
Figures 6and 7
show the SIR graphs versus separation angles for selected distances between the gNodeB
and UE, under LOS and NLOS conditions, respectively. Based on these charts, we also
determined cumulative distribution functions (CDFs) of SIR,
F(SI R)
, presented in
Figure 8
.

Sensors 2021,21, 793 10 of 20
Sensors 2021, 21, x FOR PEER REVIEW 11 of 23
to the received powers,
S
P
and
,
I
P
respectively. This fact indicates the dependence of
the received power on the main lobe orientation of the gNodeB beam pattern in relation
to the UE-I. This directly influences the determined SIR value. We observe the same situ-
ation in the DL scenario. A detailed analysis of the simulation test results is described in
the next section.
5. Simulation Results
For the assumptions described in Section 4, we carried out simulation studies using
the MATLAB environment. The results for the DL and UL scenarios are discussed in Sec-
tions 5.1 and 5.2, respectively. Section 5.3 contains the comparison of inter-beam interfer-
ence evaluation obtained based on the MPM and 3GPP statistical model [14]. In this case,
we chose the DL scenario to present exemplary results.
5.1. DL Scenario
The simulation results for the DL scenario are presented in Figures 6–10. Figures 6
and 7 show the SIR graphs versus separation angles for selected distances between the
gNodeB and UE, under LOS and NLOS conditions, respectively. Based on these charts,
we also determined cumulative distribution functions (CDFs) of SIR,
 
,F SIR
presented
in Figure 8.
Figure 6. SIR versus separation angle for DL scenario, selected D = {50, 100, 150} m, and LOS
(TDL-D) conditions.
Figure 6. SIR versus separation angle for DL scenario, selected D= {50, 100, 150} m, and LOS (TDL-D) conditions.
Sensors 2021, 21, x FOR PEER REVIEW 12 of 23
Figure 7. SIR versus separation angle for DL scenario, selected D = {50, 100, 150} m, and NLOS
(TDL-B) conditions.
Figure 8. CDFs of SIR for DL scenario, selected D = {50, 100, 150} m, under (a) LOS (TDL-D) and
(b) NLOS (TDL-B) conditions.
The increase in the separation angle reduces the downlink interference between the
reference beam providing services to the UE and the interference beam. However, the
nature of the SIR graphs is not uniform. For
 
   Δ 15 ,30 , 48 ,α
there are local maxima.
We may observe this effect both for LOS and NLOS conditions. It results from considering
side lobes in the realistic patterns of the base station beams. As the distance
D
increases,
these maxima are less and less significant. We obtain the similar results in [32] for the
carrier frequency of 3.5 GHz.
On the other hand, the obtained results differ significantly from those presented in
[43], where some stabilization may be seen in the SIR graphs. In [43], two simplifications
are assumed. Firstly, the Gaussian main lobe pattern without side lobes is modeling as the
beam. Secondly, the beam gain is constant regardless of its radiation direction. Whereas,
Figure 7. SIR versus separation angle for DL scenario, selected D= {50, 100, 150} m, and NLOS (TDL-B) conditions.
Sensors 2021, 21, x FOR PEER REVIEW 12 of 23
Figure 7. SIR versus separation angle for DL scenario, selected D = {50, 100, 150} m, and NLOS
(TDL-B) conditions.
Figure 8. CDFs of SIR for DL scenario, selected D = {50, 100, 150} m, under (a) LOS (TDL-D) and
(b) NLOS (TDL-B) conditions.
The increase in the separation angle reduces the downlink interference between the
reference beam providing services to the UE and the interference beam. However, the
nature of the SIR graphs is not uniform. For
 
   Δ 15 ,30 ,48 ,α
there are local maxima.
We may observe this effect both for LOS and NLOS conditions. It results from considering
side lobes in the realistic patterns of the base station beams. As the distance
D
increases,
these maxima are less and less significant. We obtain the similar results in [32] for the
carrier frequency of 3.5 GHz.
On the other hand, the obtained results differ significantly from those presented in
[43], where some stabilization may be seen in the SIR graphs. In [43], two simplifications
are assumed. Firstly, the Gaussian main lobe pattern without side lobes is modeling as the
beam. Secondly, the beam gain is constant regardless of its radiation direction. Whereas,
Figure 8.
CDFs of SIR for DL scenario, selected D= {50, 100, 150} m, under (
a
) LOS (TDL-D) and (
b
) NLOS (TDL-B)
conditions.

Sensors 2021,21, 793 11 of 20
Sensors 2021, 21, x FOR PEER REVIEW 13 of 23
in the real beamforming antenna array, the beam gain depends on its direction. This sec-
ond fact influences importantly on the differences in the presented results.
The comparison of the CDFs (see Figure 8) shows that for 80% of the results of the
LOS simulation tests, we obtain up to 20 dB better beam separation compared to NLOS
conditions. In the absence of a direct propagation path, we can observe an increase in the
SIR value by 5 dB in over 80% of the results, whereas this increase is below 1 dB for LOS
conditions. Figure 9 illustrates the SIR versus the gNodeB-UE distance for selected
Δ,α
under LOS and NLOS conditions.
Figure 9. SIR versus distance for DL scenario, selected ∆α = {15°, 20°, 30°}, under (a) LOS (TDL-D)
and (b) NLOS (TDL-B) conditions.
Analyzing the obtained results, we can see that as the distance increases, the SIR is
reduced. The rationale for this effect is as follows. In the simulation study scenarios, we
assume that the environment is homogeneous in terms of propagation properties. This
means that the PDP is constant in all directions of electromagnetic wave emission. This
assumption complies with the conditions of the propagation phenomena analysis de-
scribed and recommended by 3GPP [14]. In relation to the model MPM, this means that
an increase in the gNodeB-UE distance causes an apparent increase in large and a decrease
in small semi-axes of all half-ellipsoids. As a result, the reception of the propagation paths
which originate from the main lobe of the interfering beam is focused on the direction of
maximum reception of the UE antenna. This causes an increase in the interference level
relative to the power of the useful signal by about 7 dB. However, for
Δ 20 ,α
we see
an evident influence of the side lobes on the increase of the interference level, which re-
sults in the reduction of the SIR to 13 dB in LOS simulations. The concentration of the
interfering paths on the direction of maximum reception also occurs in the NLOS condi-
tions. In this case, the uniformity of the spreading of all propagation paths lowers the
range of SIR variation about 10 dB and reduces the differentiation of the side lobes’ influ-
ence.
For LOS conditions, we can also observe that, despite the larger separation angle for
Δ 20 ,α
we obtain a lower useful beam resistance to interference compared to
Δ 15 .α
This effect is the result of the concentration of the received power on the side-
lobe direction and the first minimum of the useful Rx beam, respectively. Figure 10 shows
that this phenomenon does not occur under NLOS propagation conditions. The scattering
phenomenon of electromagnetic waves under these conditions makes it impossible to con-
centrate the received power in the Tx-Rx direction.
Figure 9.
SIR versus distance for DL scenario, selected
∆α
= {15
◦
, 20
◦
, 30
◦
}, under (
a
) LOS (TDL-D) and (
b
) NLOS (TDL-B)
conditions.
Sensors 2021, 21, x FOR PEER REVIEW 14 of 23
Figure 10. SIR versus separation angle for UL scenario, selected DI = {50, 100, 150} m, DS = 100 m,
and LOS (TDL-D) conditions.
5.2. UL Scenario
In Figures 10–13, the simulation results are depicted for the UL scenario. Figures 10
and 11 present the SIR curves versus separation angles for selected distances between the
gNodeB and UE-I, under LOS and NLOS conditions, respectively. Figure 12 shows the
CDFs of SIR for the UL scenario, which were obtained based on curves in Figures 10 and
11.
Figure 11. SIR versus separation angle for UL scenario, selected DI = {50, 100, 150} m, DS = 100 m,
and NLOS (TDL-B) conditions.
Figure 10.
SIR versus separation angle for UL scenario, selected D
I
= {50, 100, 150} m, D
S
= 100 m, and LOS (TDL-D)
conditions.
The increase in the separation angle reduces the downlink interference between the
reference beam providing services to the UE and the interference beam. However, the
nature of the SIR graphs is not uniform. For
∆α={15◦, 30◦, 48◦}
, there are local maxima.
We may observe this effect both for LOS and NLOS conditions. It results from considering
side lobes in the realistic patterns of the base station beams. As the distance
D
increases,
these maxima are less and less significant. We obtain the similar results in [
32
] for the
carrier frequency of 3.5 GHz.
On the other hand, the obtained results differ significantly from those presented in [
43
],
where some stabilization may be seen in the SIR graphs. In [
43
], two simplifications are
assumed. Firstly, the Gaussian main lobe pattern without side lobes is modeling as the
beam. Secondly, the beam gain is constant regardless of its radiation direction. Whereas, in
the real beamforming antenna array, the beam gain depends on its direction. This second
fact influences importantly on the differences in the presented results.
The comparison of the CDFs (see Figure 8) shows that for 80% of the results of the
LOS simulation tests, we obtain up to 20 dB better beam separation compared to NLOS
conditions. In the absence of a direct propagation path, we can observe an increase in the

Sensors 2021,21, 793 12 of 20
SIR value by 5 dB in over 80% of the results, whereas this increase is below 1 dB for LOS
conditions. Figure 9illustrates the SIR versus the gNodeB-UE distance for selected
∆α
,
under LOS and NLOS conditions.
Analyzing the obtained results, we can see that as the distance increases, the SIR
is reduced. The rationale for this effect is as follows. In the simulation study scenarios,
we assume that the environment is homogeneous in terms of propagation properties.
This means that the PDP is constant in all directions of electromagnetic wave emission.
This assumption complies with the conditions of the propagation phenomena analysis
described and recommended by 3GPP [
14
]. In relation to the model MPM, this means that
an increase in the gNodeB-UE distance causes an apparent increase in large and a decrease
in small semi-axes of all half-ellipsoids. As a result, the reception of the propagation paths
which originate from the main lobe of the interfering beam is focused on the direction of
maximum reception of the UE antenna. This causes an increase in the interference level
relative to the power of the useful signal by about 7 dB. However, for
∆α=
20
◦
, we see an
evident influence of the side lobes on the increase of the interference level, which results in
the reduction of the SIR to 13 dB in LOS simulations. The concentration of the interfering
paths on the direction of maximum reception also occurs in the NLOS conditions. In this
case, the uniformity of the spreading of all propagation paths lowers the range of SIR
variation about 10 dB and reduces the differentiation of the side lobes’ influence.
For LOS conditions, we can also observe that, despite the larger separation angle
for
∆α=
20
◦
, we obtain a lower useful beam resistance to interference compared to
∆α=
15
◦
. This effect is the result of the concentration of the received power on the side-
lobe direction and the first minimum of the useful Rx beam, respectively. Figure 10 shows
that this phenomenon does not occur under NLOS propagation conditions. The scattering
phenomenon of electromagnetic waves under these conditions makes it impossible to
concentrate the received power in the Tx-Rx direction.
5.2. UL Scenario
In Figures 10–13, the simulation results are depicted for the UL scenario.
Figures 10 and 11
present the SIR curves versus separation angles for selected distances between the gNodeB
and UE-I, under LOS and NLOS conditions, respectively. Figure 12 shows the CDFs of SIR
for the UL scenario, which were obtained based on curves in Figures 10 and 11.
Sensors 2021, 21, x FOR PEER REVIEW 14 of 23
Figure 10. SIR versus separation angle for UL scenario, selected DI = {50, 100, 150} m, DS = 100 m,
and LOS (TDL-D) conditions.
5.2. UL Scenario
In Figures 10–13, the simulation results are depicted for the UL scenario. Figures 10
and 11 present the SIR curves versus separation angles for selected distances between the
gNodeB and UE-I, under LOS and NLOS conditions, respectively. Figure 12 shows the
CDFs of SIR for the UL scenario, which were obtained based on curves in Figures 10 and
11.
Figure 11. SIR versus separation angle for UL scenario, selected DI = {50, 100, 150} m, DS = 100 m,
and NLOS (TDL-B) conditions.
Figure 11.
SIR versus separation angle for UL scenario, selected D
I
= {50, 100, 150} m, D
S
= 100 m, and NLOS (TDL-B)
conditions.

Sensors 2021,21, 793 13 of 20
Sensors 2021, 21, x FOR PEER REVIEW 15 of 23
Figure 12. CDFs of SIR for UL scenario, selected DI = {50, 100, 150} m, DS = 100 m, (a) LOS (TDL-D)
and (b) NLOS (TDL-B) conditions.
The obtained results are evident because the SIR graphs correspond to the inversion
of the gNodeB beam pattern for the useful link. This testifies the correctness of the devel-
oped simulation procedure. The comparison of graphs in Figures 10 and 11 shows the
smoothing effect of a multipath propagation environment on changes in the SIR as a func-
tion of
Δ.α
Figure 11 shows that as the distance between the UE-I and gNodeB increases,
the shape of the analyzed graph becomes similar as to the graph for LOS conditions. In
this case, the distance increase contributes to the convergence of the signal reception di-
rections to the distribution concentrated around the UE-I-gNodeB direction. Similar as to
the DL scenario, the comparative analysis of the CDFs (see Figure 12) shows better beam
separation with respect to the NLOS conditions. In this case, for 80% of the simulation test
results, the SIR value may be about 25 dB greater. The graphs illustrated in Figures 10 and
11 also show that under both LOS and NLOS conditions, to ensure the desired quality of
the received signal, i.e., a given value of the SIR, the separation angle decreases with in-
creasing the distance. From a practical viewpoint, this conclusion is obvious. However,
the possibility of quantitative SIR assessment in multi-beam radio links operating under
NLOS conditions determines the originality of the presented solution. This fact is a prem-
ise for the practical use of the developed method in the process of planning and power
control in radio links with multi-beam antenna systems.
Figure 13 displays the SIR charts versus
I
D
for
100 m,
S
D
selected
Δ,α
under
LOS and NLOS conditions. The presented results are obtained for
Δα
equal to 15°, 20°,
and 30°. For these values, the gNodeB beam pattern of the serving link reaches the first
minimum, maximum of the first side-lobe, and second minimum, respectively (see Figure
10).
Figure 12.
CDFs of SIR for UL scenario, selected D
I
= {50, 100, 150} m, D
S
= 100 m, (
a
) LOS (TDL-D) and (
b
) NLOS (TDL-B)
conditions.
Sensors 2021, 21, x FOR PEER REVIEW 16 of 23
Figure 13. SIR versus distance DI for UL scenario, selected ∆α = {15°, 20°, 30°}, DS = 100 m, under
(a) LOS (TDL-D) and (b) NLOS (TDL-B) conditions.
Analyzing the results for LOS conditions, we can see the same effect as for the DL
simulation study scenario. Despite the larger separation angle for
Δ 20 ,α
we obtain a
lower useful beam resistance to interference compared to
Δ 15 .α
Of course, the reason
for this effect is the same as in the DL scenario. For NLOS conditions, the scattering phe-
nomenon of electromagnetic waves under these conditions makes it impossible to concen-
trate the received power in the Tx-Rx direction. Therefore, we do not see this effect in
Figure 13b. The obtained results show the possibility of the SIR evaluation for various
propagation conditions enabling optimal management of co-channel beams, which is the
basis for interference mitigation, minimizing energy and spectral resources of wireless
networks.
5.3. Exemplary Comparison of MPM with 3GPP Approach for DL Scenario
In this section, we provide an example comparison of the proposed MPM-based ap-
proach with another solution. In our opinion, choosing a different propagation model that
can be the basis for a similar analysis of the inter-beam interference level is not easy. It
results from the fact that only a few propagation models make it possible to consider the
parameters and patterns of antennas and the environmental scattering of signals occur-
ring in a radio channel. The statistical model based on the 3GPP standard [14] is one of
them. Moreover, the choice of the 3GPP model was dictated by three reasons. Firstly, the
analysis carried out in this paper with the use of the MPM is based on TDLs defined in
the same standard [14]. Secondly, in both simulators we considered the same antenna pat-
terns created according to the 3GPP recommendation [42]. Thirdly, we were able to use a
proprietary simulator of the 3GPP statistical model, which was developed in the MATLAB
environment and is used for generating the results contributed to the 3GPP, as an input
to 5G standardization or research studies (e.g., [9,44]).
Exemplary interference comparison determined based on the MPM and 3GPP model
was carried out for the DL scenario and the distance
100 mD
. To obtain the average
SIR,
avg ,SIR
the Monte Carlo method with 1000 repetitions of statistical channel model
realizations was used in the 3GPP simulator. Based on the set of obtained results, confi-
dence intervals for
avg
SIR
with the standard deviation
SIR
σ
were also determined. The
same parameters as in Section 5.1 were adopted in the research.
Figure 13.
SIR versus distance D
I
for UL scenario, selected
∆α
= {15
◦
, 20
◦
, 30
◦
}, D
S
= 100 m, under (
a
) LOS (TDL-D) and (
b
)
NLOS (TDL-B) conditions.
The obtained results are evident because the SIR graphs correspond to the inversion of
the gNodeB beam pattern for the useful link. This testifies the correctness of the developed
simulation procedure. The comparison of graphs in Figures 10 and 11 shows the smoothing
effect of a multipath propagation environment on changes in the SIR as a function of
∆α
.
Figure 11 shows that as the distance between the UE-I and gNodeB increases, the shape of
the analyzed graph becomes similar as to the graph for LOS conditions. In this case, the
distance increase contributes to the convergence of the signal reception directions to the
distribution concentrated around the UE-I-gNodeB direction. Similar as to the DL scenario,
the comparative analysis of the CDFs (see Figure 12) shows better beam separation with
respect to the NLOS conditions. In this case, for 80% of the simulation test results, the SIR
value may be about 25 dB greater. The graphs illustrated in Figures 10 and 11 also show

Sensors 2021,21, 793 14 of 20
that under both LOS and NLOS conditions, to ensure the desired quality of the received
signal, i.e., a given value of the SIR, the separation angle decreases with increasing the
distance. From a practical viewpoint, this conclusion is obvious. However, the possibility
of quantitative SIR assessment in multi-beam radio links operating under NLOS conditions
determines the originality of the presented solution. This fact is a premise for the practical
use of the developed method in the process of planning and power control in radio links
with multi-beam antenna systems.
Figure 13 displays the SIR charts versus
DI
for
DS=
100
m
, selected
∆α
, under LOS
and NLOS conditions. The presented results are obtained for
∆α
equal to 15
◦
, 20
◦
, and 30
◦
.
For these values, the gNodeB beam pattern of the serving link reaches the first minimum,
maximum of the first side-lobe, and second minimum, respectively (see Figure 10).
Analyzing the results for LOS conditions, we can see the same effect as for the DL
simulation study scenario. Despite the larger separation angle for
∆α=
20
◦
, we obtain
a lower useful beam resistance to interference compared to
∆α=
15
◦
. Of course, the
reason for this effect is the same as in the DL scenario. For NLOS conditions, the scattering
phenomenon of electromagnetic waves under these conditions makes it impossible to
concentrate the received power in the Tx-Rx direction. Therefore, we do not see this effect
in Figure 13b. The obtained results show the possibility of the SIR evaluation for various
propagation conditions enabling optimal management of co-channel beams, which is the
basis for interference mitigation, minimizing energy and spectral resources of wireless
networks.
5.3. Exemplary Comparison of MPM with 3GPP Approach for DL Scenario
In this section, we provide an example comparison of the proposed MPM-based
approach with another solution. In our opinion, choosing a different propagation model
that can be the basis for a similar analysis of the inter-beam interference level is not easy. It
results from the fact that only a few propagation models make it possible to consider the
parameters and patterns of antennas and the environmental scattering of signals occurring
in a radio channel. The statistical model based on the 3GPP standard [
14
] is one of them.
Moreover, the choice of the 3GPP model was dictated by three reasons. Firstly, the analysis
carried out in this paper with the use of the MPM is based on TDLs defined in the same
standard [
14
]. Secondly, in both simulators we considered the same antenna patterns
created according to the 3GPP recommendation [
42
]. Thirdly, we were able to use a
proprietary simulator of the 3GPP statistical model, which was developed in the MATLAB
environment and is used for generating the results contributed to the 3GPP, as an input to
5G standardization or research studies (e.g., [9,44]).
Exemplary interference comparison determined based on the MPM and 3GPP model
was carried out for the DL scenario and the distance
D=
100
m
. To obtain the average
SIR,
SI Ravg
, the Monte Carlo method with 1000 repetitions of statistical channel model
realizations was used in the 3GPP simulator. Based on the set of obtained results, confidence
intervals for
SI Ravg
with the standard deviation
σSIR
were also determined. The same
parameters as in Section 5.1 were adopted in the research.
To compare the MPM and 3GPP approaches, we ran the MPM simulator also in Monte
Carlo mode for 1000 runs. Thus, the mean results,
SI Ravg
, with the confidence intervals,
SI Ravg ±σSIR
, were determined. The results of the MPM and 3GPP comparison for the
DL scenario and the distance
D=
100
m
between the gNodeB and UE are illustrated in
Figures 14 and 15 for LOS and NLOS conditions, respectively.

Sensors 2021,21, 793 15 of 20
Sensors 2021, 21, x FOR PEER REVIEW 17 of 23
To compare the MPM and 3GPP approaches, we ran the MPM simulator also in
Monte Carlo mode for 1000 runs. Thus, the mean results,
avg ,SIR
with the confidence
intervals,
avg ,
SIR
SIR σ
were determined. The results of the MPM and 3GPP comparison
for the DL scenario and the distance
100 mD
between the gNodeB and UE are illus-
trated in Figures 14 and 15 for LOS and NLOS conditions, respectively.
Figure 14. SIR comparison between (a) MPM and (b) 3GPP model for DL scenario, D = 100 m, and
LOS conditions.
Figure 15. SIR comparison between (a) MPM and (b) 3GPP model for DL scenario, D = 100 m, and
NLOS conditions.
Overall, we might conclude that the results are similar. The SIR results are more sim-
ilar for LOS conditions (see Figure 14), where we may see characteristic extremes resulting
from the use of the same gNodeB antenna pattern. In this case, both the maxima and the
minima fall for the same separation angles. This is due to the presence of a direct path that
enhances or reduces the influence of the pattern side lobes in certain directions relative to
Figure 14. SIR comparison between (a) MPM and (b) 3GPP model for DL scenario, D= 100 m, and LOS conditions.
Sensors 2021, 21, x FOR PEER REVIEW 17 of 23
To compare the MPM and 3GPP approaches, we ran the MPM simulator also in
Monte Carlo mode for 1000 runs. Thus, the mean results,
avg ,SIR
with the confidence
intervals,
avg ,
SIR
SIR σ
were determined. The results of the MPM and 3GPP comparison
for the DL scenario and the distance
100 mD
between the gNodeB and UE are illus-
trated in Figures 14 and 15 for LOS and NLOS conditions, respectively.
Figure 14. SIR comparison between (a) MPM and (b) 3GPP model for DL scenario, D = 100 m, and
LOS conditions.
Figure 15. SIR comparison between (a) MPM and (b) 3GPP model for DL scenario, D = 100 m, and
NLOS conditions.
Overall, we might conclude that the results are similar. The SIR results are more sim-
ilar for LOS conditions (see Figure 14), where we may see characteristic extremes resulting
from the use of the same gNodeB antenna pattern. In this case, both the maxima and the
minima fall for the same separation angles. This is due to the presence of a direct path that
enhances or reduces the influence of the pattern side lobes in certain directions relative to
Figure 15. SIR comparison between (a) MPM and (b) 3GPP model for DL scenario, D= 100 m, and NLOS conditions.
Overall, we might conclude that the results are similar. The SIR results are more
similar for LOS conditions (see Figure 14), where we may see characteristic extremes
resulting from the use of the same gNodeB antenna pattern. In this case, both the maxima
and the minima fall for the same separation angles. This is due to the presence of a direct
path that enhances or reduces the influence of the pattern side lobes in certain directions
relative to its main lobe (see Figures 4and 5). Therefore, the optimal directions’ selection
for the adjacent beams in the gNodeB based on the MPM and 3GPP approaches will be
identical or very similar. In this case, we would like to emphasize that the MPM approach
gives the possibility to obtain an average result from a single simulation, while the 3GPP
statistical model requires the time-consuming Monte Carlo methodology.
Under NLOS conditions (see Figure 15), the dynamics of SIR changes is lower than
for LOS conditions. The results for the MPM and the 3GPP model show that the multipath

Sensors 2021,21, 793 16 of 20
propagation environment for NLOS conditions and the lack of a direct path provide to
minimize the impact of the transmitting antenna pattern lobes. Thus, the selection of
optimal directions for the adjacent gNodeB beams should be made based on an analysis
for LOS conditions. On the other hand, we would like to highlight that other propagation
models available in the literature also indicate result differences with the 3GPP model,
e.g., [45–48].
With regard to the presented above comparative analysis, it is also worth providing the
mean values of the standard deviation,
σModel
LOS/N LOS
, obtained for the MPM:
σMPM
LOS =
0.58
dB
and
σMPM
NLOS =
1.69
dB
, and 3GPP model:
σ3GPP
LOS =
0.97
dB
and
σ3GPP
NLOS =
7.51
dB
under LOS
and NLOS conditions, respectively. The differentiation of the obtained results is related
to the different spatial nature of scatterings (i.e., spatial dispersion) in the two analyzed
propagation models. In the MPM, we use a multi-ellipsoidal geometric structure which
is defined based on the TDL of the 3GPP standard [
14
]. On the other hand, the 3GPP
statistical model has greater flexibility in the spatial location of potential scatterers. A more
detailed comparison of the MPM and 3GPP model will be presented in the prepared next
paper focusing on the 3.5 GHz band used in 5G massive-MIMO systems. A more detailed
description of the 3GPP model and simulator will be presented there.
6. Conclusions
This paper is devoted to assessing the limitations that exist in multi-beam antenna
systems. Here, the SIR is the primary metric that is used to evaluate the level of interference
between the intra-cell beams. The presented procedure for assessing this parameter is
based on the PAS analysis, which is determined by simulation tests. By using the channel
transmission characteristics (i.e., TDL or PDP) to create the geometric MPM structure, the
results of assessing the received power are closely related to the different propagation envi-
ronment type. Using the MPM allows mapping the impact of the antenna beam radiation
patterns on the PAS. The presented methodology allows evaluating changes in the PAS as a
function of antenna beam shape and parameters such as the maximum radiation direction,
main and side-lobes beamwidths. Additionally, the ability to evaluate the SIR under both
LOS and NLOS conditions justifies using this method in the network planning process
of energy and spectral management of 5G system with the multi-beam antenna systems.
In the multipath propagation environment, in most cases to evaluate fluctuations in the
received signal level, the Rician and Rayleigh distributions are used for LOS and NLOS
conditions, respectively. The SIR assessment is the basis for determining the parameters of
these characteristics. Due to the association of the SIR with the propagation properties of
the environment, it is justified to use the presented SIR assessment methodology in the 5G
network planning. The ability to adapt the developed model to any environment, weather
conditions, and multi-beam antenna system distinguishes this SIR determination method
from among the methods used so far. The comparison of the mean results for the proposed
methodology with a similar approach based on the 3GPP statistical model shows that the
same optimal directions for the adjacent gNodeB beams might be determined faster based
on the MPM approach. A more detailed comparison of the two solutions with regard to
the interference level assessment in the 3.5 GHz band will be presented in the authors’ next
work [
49
]. In the future, we also plan to conduct empirical research for selected scenarios
that will allow us to verify the approach presented in this paper.
Author Contributions:
Conceptualization, 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, 793 17 of 20
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 Sensors jour-
nal Editors and anonymous Reviewers for their valuable suggestions, which have improved the
manuscript quality.
Conflicts of Interest: The authors declare no conflict of interest.
Abbreviations
3D three-dimensional
3GPP 3rd Generation Partnership Project
5G fifth-generation
AOA angle of arrival
AOD angle of departure
CDF cumulative distribution function
DL downlink
GBM geometry-based model
gNodeB 5G base station
ITU International Telecommunication Union
LOS line-of-sight
MIMO multiple-input-multiple-output
mmWave millimeter-wave
MPM multi-ellipsoidal propagation model
NLOS non-line-of-sight
NR New Radio
PAS power angular spectrum
PDP power delay profile
Rx receiver
SIR signal-to-interference ratio
TDL tapped delay line
Tx transmitter
UE user equipment
UE-I interfering UE
UE-S serving UE
UMa urban macro
UL uplink
Symbols
(θ,φ)AOA of individual propagation path
(θT,φT)AOD of individual propagation path
|g(θ,φ)|2normalized power pattern of receiving antenna
|gI(θT,φT)|2normalized power pattern of interfering transmitting antenna
|gS(θT,φT)|2normalized power pattern of serving transmitting antenna
αRdirection of receiving beam
αRI direction of interfering receiving beam
αRS direction of serving receiving beam
αTdirection of transmitting beam
αTI direction of interfering transmitting beam

Sensors 2021,21, 793 18 of 20
αTS direction of serving transmitting beam
∆αseparation angle between serving and interference beams
∆PL path loss correction coefficient (relationship between attenuation of
propagation environment for different distances)
γθangular dispersion of local scattering components in elevation plane
γφangular dispersion of local scattering components in azimuth plane
θelevation AOA of individual propagation path
θTelevation AOD of individual propagation path
Φ0direction of receiving (gNodeB) beam in relation to direction of cell sector
center in UL scenario
ΦI
direction of interfering transmitting (gNodeB) beam in relation to direction of
cell sector center in DL scenario
ΦS
direction of serving transmitting (gNodeB)beam in relation to direction of cell
sector center in DL scenario
φazimuth AOA of individual propagation path
φTazimuth AOD of individual propagation path
σSIR standard deviation of SIR for confidence interval analysis
σ3GPP
LOS standard deviation of SIR for 3GPP model and LOS conditions
σ3GPP
NLOS standard deviation of SIR for 3GPP model and NLOS conditions
σModel
LOS/N LOS standard deviation of SIR for Model and LOS/NLOS conditions
σMPM
LOS standard deviation of SIR for MPM and LOS conditions
σMPM
NLOS standard deviation of SIR for MPM and NLOS conditions
τndelay of nth time-cluster in PDP/TDL
aauxiliary variable used to compute rT
axn major semi-axis of nth ellipsoid along x-axis
byn minor semi-axis of nth ellipsoid along y-axis
C0normalizing constant
clightspeed
czn minor semi-axis of nth ellipsoid along z-axis
Ddistance between Tx and Rx or between gNodeB (Rx) and UE (Tx) in DL
DIdistance between UE-I (Tx) and gNodeB (Rx) in UL
DSdistance between UE-S (Tx) and gNodeB (Rx) in UL
F(SI R)CDF of SIR
f(e
p)distribution of path power
f0(θ,φ)2D von Mises distribution describing local scattering components
fI(θT,φT)distribution of AOD for interfering link
fS(θT,φT)distribution of AOD for serving link
Ggain of receiving beam
GIgain of interfering transmitting beam
GSgain of serving transmitting beam
I0(·)zero-order modified Bessel function of imaginary argument
Nnumber of all time-clusters in analyzed PDP/TDL
nnumber of analyzed time-cluster in PDP/TDL
PIpower of interfering signal
PSpower of serving signal
PL path loss
PL(DI)path loss for wireless links between UE-I and gNodeB at distance DI
PL(DS)path loss for wireless links between UE-S and gNodeB at distance DS
e
ppower of individual propagation path
pn
mean power of nth time-cluster in PDP/TDL (nth local extreme of PDP/TDL)
pI(θ,φ)PAS seen at the output of receiving antenna for interfering link
pS(θ,φ)PAS seen at the output of receiving antenna for serving link
e
pI(θ,φ)PAS in vicinity of receiving antenna for interfering link
e
pS(θ,φ)PAS in vicinity of receiving antenna for serving link
rTradial coordinate in spherical system with origin in Tx
SI R SIR
SI Ravg average SIR for confidence interval analysis
SI Ravg ±σSI R confidence intervals of SIR

Sensors 2021,21, 793 19 of 20
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