Available via license: CC BY 4.0
Content may be subject to copyright.
4th URSI AT-RASC, Gran Canaria, 19-24 May 2024
Spectral Efficiency for mmWave Downlink with Beam Misalignment in Urban Macro Scenario
Jarosław Wojtuń(1), Cezary Ziółkowski(1), Jan M. Kelner(1), Aniruddha Chandra(2), Rajeev Shukla(2), Anirban Ghosh(3),
Aleš Prokeš(4), Tomas Mikulasek(4), Radek Zavorka(4), and Petr Horký(4)
(1) Institute of Communications Systems, Military University of Technology, Warsaw, Poland
(2) Department of Electronics and Communication Engineering, National Institute of Technology, Durgapur, India
(3) Department of Electronics and Communication Engineering, SRM University AP, Andhra Pradesh, India
(4) Department of Radio Electronics, Brno University of Technology, Brno, Czech Republic
Abstract
In this paper, we analyze the spectral efficiency for
millimeter wave downlink with beam misalignment in
urban macro scenario. For this purpose, we use a new
approach based on the modified Shannon formula, which
considers the propagation environment and antenna system
coefficients. These factors are determined based on a multi-
ellipsoidal propagation model. The obtained results show
that under non-line-of-sight conditions, the appropriate
selection of the antenna beam orientation may increase the
spectral efficiency in relation to the direct line to a user.
1. Introduction
The spectral efficiency is based on Shannon–Hartley
theorem for the additive white Gaussian noise (AWGN)
channel. Generally, it can be referred to as free-space (FS)
conditions or, to put it simply, also to line-of-sight (LOS)
conditions [1]. Under non-LOS (NLOS) conditions, where
more complex propagation conditions occur, this approach
is insufficient. In addition, transmitting and receiving
antenna systems should be considered in estimating the
spectral efficiency. Therefore, we can conclude that the
spectral efficiency value is primarily determined by the
environment and antenna systems.
In this paper, we propose a spectral efficiency estimation
for a millimeter wave (mmWave) downlink (DL) under
beam mismatch conditions based on a modified Shannon
formula that considers the coefficients of the antenna
system and propagation environment. These coefficients
are determined by simulation using the 3D multi-
ellipsoidal propagation model (MPM) [2]. This approach is
based on [3], where spectral efficiency is determined for a
radio link with two directional horn antennas. This paper
analyzes beam orientations of the 5G gNodeB
beamforming antenna system and user equipment (UE)
antenna operating in the mmWave band on the spectral
efficiency. The studies included LOS and NLOS
conditions, which are defined based on 3GPP tapped-delay
line (TDL) model [4]. The results show a significant
influence of the misalignment of antenna beams on the
received power in NLOS conditions. Under LOS
conditions, spectral efficiency maximization is achieved
for gNodeB beam oriented to UE. Under NLOS conditions,
this direction does not maximize spectral efficiency. This
method of evaluating the impact of parameters and the
optimal choice of antenna orientation on the radio spectral
efficiency under beam mismatch conditions determines the
originality and novelty of the developed solution. The main
contributions in this paper are listed as follows.
• We use a novel spectral efficiency estimation
methodology based on the standard Shannon formula
that considers the coefficients of the antenna system and
propagation environment.
• Through extensive simulation, we analyze spectral
efficiency for a 28 GHz mmWave DL for urban macro
(UMa) scenario using the recommended 3GPP antenna
patterns.
• We put a recommendation to use optimal antenna
orientation for different propagation conditions to
maximize spectral efficiency.
The remainder of the paper is organized as follows. An
approach to determining channel spectral efficiency is
described in Section II. Section III presents the results of
spectral efficiency estimation for a 28 GHz mmWave DL
and UMa scenario using the MPM and recommended
3GPP antenna power radiation patterns. A summary is
provided in Section IV.
2. Influence of Propagation Environment and
Antenna System on Spectral Efficiency
The spectral efficiency of the radio channel depends on
its quality, defined by signal-to-noise ratio, . In the
case of FS propagation, can be described by the
Shannon’s formula
(1)
where
,
and
are the desired
signal power at a distance from the transmitter and noise
(interference) power, respectively.
Differences in propagation conditions in a real multipath
(MP) environment and the ability to concentrate energy
radiation by the antenna system significantly affect the
power level
of the received signal. This means that
The paper has been presented at the 2024 4th URSI Atlantic Radio
Science Meeting (ATRASC), Meloneras, Spain, 19–24 May 2024
https://doi.org/10.46620/URSIATRASC24/WVAQ4220
This research was funded in part by the National Science Center (NCN), Poland, grant no. 2021/43/I/ST7/03294
(MubaMilWave). For this purpose of Open Access, the author has applied a CC-BY public copyright license
to any Author Accepted Manuscript (AAM) version arising from this submission.
the spectral efficiency is determined by both the
environmental conditions and the pattern and orientation of
the antenna system. The radio wave propagation conditions
in the real environment and the antenna system parameters
are the reason for the different power values
and
i.e., and , respectively.
Let
be the desired signal power for an
omnidirectional antenna and MP environment. Therefore,
we can express and by the following relation
(2)
The expression describing the spectral efficiency
considering the real propagation conditions and influence
of the antenna system is [3]
(3)
where
and
represents antenna system and propagation
environment factors, respectively, and
are defined by path loss models for FS and MP conditions
(e.g., 3GPP, WINNER II, COST 2100, or MiWEBA),
respectively.
Equation (3) allows for a comparative assessment of the
impact of both the propagation environment and antenna
system on the radio spectral efficiency.
The main problem of the practical use of (3) to determine
the spectral efficiency boils down to the evaluation of the
coefficient , i.e., the relationship between the
received powers using the beamforming and
omnidirectional antenna systems. The MPM is used to
determine the received signal power in MP propagation
conditions. Figure 1 shows the MPM geometry [2]. A
detailed description of the MPM geometrical structure has
been presented in [2,3,5].
Figure 1. Scattering geometry of MPM.
The MPM-based methodology described in [5]
modifies the path loss and power balance for different
HPBWs and orientations of the antenna beams. A relative
power factor, , is its basis. It represents a relative power
for the analyzed beam mismatch and alignment conditions,
as follows
(4)
where
is the received power for the
and directions of the transmitting and receiving antenna
beams (determined with respect to the OX axe in Figure 1),
respectively, and the selected distance .
3. Spectral Efficiency Estimation for
mmWave DL with Beam Misalignment in
Urban Macro Scenario
The evaluation of the power losses resulting from the
misalignment of the antenna beams in the directional link
and the optimal selection of their orientation in LOS and
NLOS conditions is based on the simulation tests. In the
paper, all presented simulation studies were performed
based on the MPM implementation prepared in the
MATLAB environment.
In simulation studies, a spatial scenario was analyzed, as
shown in Figure 1, where the 5G NR gNodeB and UE
represent the transmitter (TX) and receiver (RX),
respectively. Therefore, the adopted scenario may
correspond to communications between the gNodeB and
UE operating in the mmWave band and UMa scenario.
To model the antenna power radiation patterns, we adopted
3GPP recommendations [6]. HPBWs of the 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°, Φ0 = 15° and
Φ0 = 30° are illustrated in Figure 2. In the gNodeB, we used
a vertical patch as an antenna array with a size of 12×8
elements, whereas the UE antenna consists of a single
element. In the rest of the paper, we will refer to these
antennas as directional.
Figure 2. Antenna beam patterns of 1×1 UE and 12×8
gNodeB for Φ0 = 0°, Φ0 = 15° and Φ0 = 30°.
Other assumptions are as follows:
• carrier frequency is equal to fc = 28 GHz;
• PDPs are based on TDL models from the 3GPP TR
38.901 standard [4], i.e., the TDL-B and TDL-D for
NLOS and LOS conditions, respectively; these TDLs
are adopted for analyzed fc and RMS delay spread, στ,
for so-called the normal-delay profile and UMa
scenario, i.e., στ = 266 ns;
• Rician factor defining the direct path component in the
scenario for LOS conditions is appropriate for TDL-D
[4], i.e.,
= 13.3 dB;
• distance between the TX and RX is equal to
50 m D 250 m with step ΔD = 25 m;
• gains of the transmitting and receiving antennas are
equal to GT = 25.68 dBi and GR = 3.75 dBi for the
transmitting and receiving antennas, respectively;
• low heights of the transmitting (7 m) and receiving
(1.5 m) antennas are based on measurement scenarios
[7];
• beam alignment is defined for α = 180° and β = 0° (see
Figure 1);
• analyzed ranges of beam directions are as follows:
90° α 270° and –90° β 90° with step
Δα = Δβ = 1°;
• to obtain average statistical results in the MPM, L = 10
paths are generated at the TX for each time-cluster
(semi-ellipsoid); on the other hand, M = 360 Monte-
Carlo simulations were run for each analyzed scenario;
in this case, the average resolution of generating the
angles of departure is about 0.1°.
In Figure 3, K(α, β) versus α and β directions of the
transmitting and receiving antenna beams is illustrated.
This graphs clearly show that when the beams are directed
at each other, a dominant received power is obtained. In the
analyzed LOS and NLOS conditions. Figure 3 (a) shows
that the maximum power is obtained for beam alignment,
which is obvious. The direction of the receiving antenna
has a decisive influence on the power level. Despite the
direction changes of the TX antenna, the extremum power
is ensured when the RX antenna is pointed at the TX.
Figure 3. Relative power factor K(α,β) versus α and β
directions of transmitting and receiving beams under (a)
LOS and (b) NLOS conditions for D = 100 m.
Under NLOS conditions, the MP propagation phenome-
non makes it necessary to search for optimal α and β
directions of the transmitting and receiving antenna beams,
which will ensure the maximization of the received signal
level. Figure 3 (b) shows that under NLOS conditions, the
received signal obtains the statistically highest power level
for the TX beam direction equal to α = 120°. However, in
this case, the beam direction of the receiving antenna to
achieve this power level should be equal β = 28°.
The lack of the direct path (
= 0 dB) under NLOS
conditions is the principal cause of the difference in results
concerning those obtained for LOS conditions. For NLOS
conditions, most of the received power comes from the
delayed components scattered on the semi-ellipsoids.
Therefore, the global maximum of the received power does
not appear for α = 180° and β = 0°.
The effects of using directional antenna systems are shown
in Figures 4 and 5.
Figure 4. Spectral efficiency versus SNR for directional
antenna pattern and under LOS and NLOS conditions.
Figure 5. Spectral efficiency versus SNR for βmax under
NLOS conditions.
Under LOS conditions, the use of directional antennas and
alignment of the transmitting and receiving antenna beams
(i.e., beams oriented to each other) provides statistically
multiple increases in the radio spectral efficiency (see
Figure 4). Of course, this increase depends on the gains of
the antennas. For the analyzed radio link with the
directional antennas whose gains are equal to GT = 25.68
dBi and GR = 3.75 dBi, the spectral efficiency is higher by
9.5 bit/s/Hz concerning the radio link with the
omnidirectional antenna systems and FS propagation
conditions. On the other hand, for LOS conditions, MP
propagation has a negligible effect on spectral efficiency
compared to FS propagation.
The NLOS conditions significantly reduce the spectral
efficiency even several times. The use of beamforming
antenna system is one way to minimize the adverse effects
of MP propagation under NLOS conditions.
The analysis results presented in Figures 4 and 5 show that
the radio spectral efficiency also depends on the distance
between the TX and RX. For NLOS conditions, the double
distance reduction increases the radio spectral efficiency by
about 0.2–1.2 bit/s/Hz in the whole analyzed range of SNR
variability.
Under NLOS conditions, the alignment of the transmitting
and receiving antenna beams does not provide to achieve
the maximum received power. Therefore, under these
propagation conditions, beamforming antenna system
should supply a beam steering mechanism to the direction
of the maximum level of the received signal. The
justification for applying such a solution is illustrated in
Figure 5.
It can be seen that using the direction of the maximum
signal level ensures an additional increase in the spectral
efficiency by 1 bit/s/Hz. The increment increases as the
TX–RX distance is greater.
The spectral efficiency change versus the distance between
the TX and RX. The comparison of the spectral efficiency
change for the straight (i.e., α = 180° and β = 0°) and
optimal (i.e., α = 180° and β = βmax) directions of the
antenna beams is shown in Figure 6.
Figure 6. Spectral efficiency versus TX–RX distance for
straight and optimal directions of antenna beams under
NLOS conditions.
The exemplary graphs are obtained assuming that the
received signal level provides the SNR = 20 dB. It is evident
that as the TX–RX distance increases, the level of the
desired signal decreases. Thus, the radio spectral efficiency
decreases. In the case of the optimal direction of the
antenna beams, a 4-fold increase in the distance (from 50
m to 200 m) causes only about a 4.5-fold reduction in the
spectral efficiency. On the other hand, with the increase in
the distance, maintaining the straight direction results in a
6-fold decrease in the spectral efficiency. It shows that
using steering and selecting the optimal beam direction in
the antenna system mitigates the degrading effect of
distance on the radio spectral efficiency.
4. Conclusions
This paper focuses on spectral efficiency analysis for
mmWave band and UMa scenario. The spectral efficiency
evaluation is based on a modified Shannon formula that
considers the coefficients of the antenna systems and the
propagation environment. The MPM was used to
determine these coefficients. Pointing the antennas at each
other under LOS conditions maximizes spectral efficiency.
However, the results obtained for NLOS conditions show
that the optimal selection of the gNodeB beam direction
can increase the spectral efficiency in relation to the
direction toward the user. These optimal directions are
determined based on the MPM. The conducted analysis
shows that beam misalignment can positively affect the
parameters of the radio link under NLOS conditions, which
is in accordance with the measurement results presented in
the literature.
6. Acknowledgements
This work was co-funded by the Czech Science Foundation
under grant no. 23-04304L, the National Science Centre,
Poland, under the OPUS call in the Weave program, under
research project no. 2021/43/I/ST7/03294 acronym
‘MubaMilWave’ and by the Military University of
Technology under grant no. UGB/22-863/2023/WAT, and
chip-to-startup (C2S) program no. EE-9/2/2021-R&D-E
sponsored by MeitY, Government of India.
References
[1] G. Miao, J. Zander, K. W. Sung, and S. B. Slimane,
Fundamentals of mobile data networks. United
Kingdom: Cambridge University Press, 2016.
[2] C. Ziółkowski and J. M. Kelner, “Statistical
evaluation of the azimuth and elevation angles seen
at the output of the receiving antenna,” IEEE Trans.
Antennas Propag., vol. 66, no. 4, pp. 2165–2169,
Apr. 2018, doi: 10.1109/TAP.2018.2796719.
[3] C. Ziółkowski, J. M. Kelner, J. Krygier, A. Chandra,
and A. Prokeš, “Radio channel capacity with
directivity control of antenna beams in multipath
propagation environment,” Sensors, vol. 21, no. 24,
Art. no. 24, Dec. 2021, doi: 10.3390/s21248296.
[4] 3GPP, “5G. Study on channel model for frequencies
from 0.5 to 100 GHz (3GPP TR 38.901 version 16.0.0
Release 16),” 3rd Generation Partnership Project
(3GPP), Technical Specification Group Radio Access
Network, Valbonne, France, Tech. Rep. 3GPP TR
38.901 V16.0.0 (2019-12), Release 16, Dec. 2019.
[5] J. M. Kelner and C. Ziółkowski, “Evaluation of angle
spread and power balance for design of radio links
with directional antennas in multipath environment,”
Phys. Commun., vol. 32, pp. 242–251, Feb. 2019, doi:
10.1016/j.phycom.2018.12.005.
[6] 3GPP, “Evolved Universal Terrestrial Radio Access
(E-UTRA) and Universal Terrestrial Radio Access
(UTRA; Radio Frequency (RF) requirement
background for Active Antenna System (AAS) Base
Station (BS),” 3rd Generation Partnership Project
(3GPP), Valbonne, France, Tech. Rep. 3GPP TR
37.842 V13.3.0 (2019-12), Release 13, Dec. 2019.
Accessed: Feb. 09, 2020. [Online]. Available:
https://portal.3gpp.org/desktopmodules/Specification
s/SpecificationDetails.aspx?specificationId=2625
[7] T. S. Rappaport, G. R. MacCartney, M. K. Samimi,
and S. Sun, “Wideband millimeter-wave propagation
measurements and channel models for future wireless
communication system design,” IEEE Trans.
Commun., vol. 63, no. 9, pp. 3029–3056, Sep. 2015,
doi: 10.1109/TCOMM.2015.2434384.
