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Power Angular Spectrum versus Doppler Spectrum
– Measurements and Analysis
Jan M. Kelner1, Cezary Ziółkowski1, Michał Kryk1, Jarosław Wojtuń1, Leszek Nowosielski1, Rafał Przesmycki1,
Marek Bugaj1, Aniruddha Chandra2, Rajeev Shukla2, Anirban Ghosh3, Aleš Prokeš4, Tomáš Mikulášek4
1 Institute of Communications Systems, Faculty of Electronics, Military University of Technology, Warsaw, Poland,
{jan.kelner, cezary.ziolkowski, michal.kryk, jaroslaw.wojtun, leszek.nowosielski, rafal.przesmycki, marek.bugaj}@wat.edu.pl
2 ECE Department, NIT Durgapur, Durgapur, India, niruddha.chandra@ieee.org, rs.20ec1103@phd.nitdgp.ac.in
3 Faculty of Engineering, Niigata University, Niigata-shi, Japan, aniz.ghosh@gmail.com
4 Department of Radio Electronics, Brno University of Technology, Brno, Czech Republic, prokes@vutbr.cz, mikulasekt@vut.cz
Abstract—In this paper, we present an empirical
verification of the method of determining the Doppler
spectrum (DS) from the power angular spectrum (PAS).
Measurements were made for the frequency of 3.5 GHz, under
non-line-of-sight conditions in suburban areas characteristic of
a university campus. In the static scenario, the measured PAS
was the basis for the determination of DSs, which were
compared with the DSs measured in the mobile scenario. The
obtained results show that the proposed method gives some
approximation to DS determined with the classic methods used
so far.
Index Terms— propagation, measurements, power angular
spectrum, Doppler spectrum, Doppler spread.
I. INTRODUCTION
The mobile network development that has been observed
for 40 years has contributed to a significant increase in their
coverage and user number, extending the scope and
improving the quality of provided services. The development
of new standards by international bodies (including 3GPP,
ITU, ETSI, and IEEE) and the implementation of new radio
and network technologies are crucial factors ensuring the
success of the next generation of networks. In the case of the
currently introduced fifth (5G) and the emerging sixth
generation (6G), the use of higher frequency ranges
(millimeter and terahertz waves) and angular-selectively
beamforming (along with the use of massive multiple-input-
multiple-output (MIMO) technology) are considered to be
one of the most important innovations in the physical layer,
which contribute to increasing the network performance
parameters and extending the possibilities of the provided
services [1].
Propagation measurements are the basis for the
performance analysis of new radio technologies, designing
radio links and mobile networks. On the other hand, these
measurements are fundamentals for the development of new
channel models necessary to conduct a broader analysis of
the designed networks and assess the possibilities of new
technologies using simulation studies [2].
Propagation measurements consist in determining various
parameters and transmission characteristics of real radio
channels. These characteristics are closely related to the
nature of propagation environments, used antenna systems,
frequency ranges, and bandwidths of transmitted signals. The
greatest network capacity, i.e., the density of users (or user
equipment (EU)) per area unit, is found in metropolitan and
urban areas. Hence, network capacity is related to the
number of base stations per area unit, which is the largest in
urbanized terrains. The higher density of base stations also
results from the need to ensure the appropriate quality of
radio signals necessary to provide services with appropriate
quality metrics. This is directly related to the fact that a
greater number of obstacles (i.e., mainly buildings) in
propagation paths from a transmitter (TX) to receiver (RX)
occur in urban areas. So, in these scenarios, non-line-of-sight
(NLOS) conditions are more common compared to the line-
of-sight (LOS) conditions that prevail in rural environments.
NLOS conditions are the main cause of dispersion
phenomena in the received signal. The introduction of
broadband systems contributed to a significant increase in
dispersion, especially in the time domain. To counteract this
negative phenomenon, MIMO technology, beamforming or
directional antenna systems, etc. are used in 5G and 6G
systems. Power delay profile (PDP), power angular spectrum
(PAS), and Doppler spectrum (DS) are transmission
characteristics that illustrate radio channel dispersion in time,
angle of arrival (AOA), and frequency domains, respectively
[3]. The RMS delay, angular, and Doppler spreads
parameters are usually used for the comparative evaluation
of the dispersion phenomenon, which is determined based on
PDP, PAS, and DS, respectively [4].
Assuming some condition stationarity in the selected
measurement area (e.g., no movement of the surrounding
elements), it can be said that the determined PAS and PDP,
RMS angular, and delay spreads unambiguously describe the
channel dispersion in the domain of the AOA and delay [5].
In the case of DS, the dispersion in the frequency domain
additionally depends on the direction of object (TX/RX)
movement with respect to the TX-RX direction. However, in
[6], it was shown that DS is directly related to PAS. Thus,
based on the measured single PAS, the DS can be
determined for a specific position and any movement
direction. It allows describing the dispersion in the frequency
domain in the full range of changes in the object movement
The paper has been presented at the 2023 17th European Conference
on Antennas and Propagation (EuCAP), Florence, Italy, 26–31 Mar. 2023
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.
https://doi.org/10.23919/EuCAP57121.2023.10133231
direction based on the PAS illustrating the dispersion in the
AOA domain.
The analysis presented in [6] is based on simulation
studies, while in this paper, we present this issue based on
empirical measurements. To the best of the authors'
knowledge, this is the first analysis of this problem, which
proves the originality and novelty of the presented issue. For
the purposes of this verification, we conducted PAS and DS
measurements on the university campus at the frequency of
3.5 GHz, i.e., in a typical sub-6 GHz band dedicated to 5G
systems [7].
The rest of the paper is organized as follows. Section II
presents the theoretical foundations of the relationship
between PAS and DS, which are contained in [6]. The
measurement scenario and test-bed are presented in Sections
III and IV, respectively. The measurement results are
included in Section V. Finally, a conclusion is presented.
II. RELATIONSHIP BETWEEN PAS AND DS
In [6], theoretical foundations and the method of DS
determination based on PAS are presented. Then, based on
the assumption that the PAS is modeled by Laplacian with
specific parameters [8], a numerical methodology of
determining DSs based on a single PAS for different
directions α of object movement (i.e., RX) and simulation
results are shown.
PAS, P(ϕ), can be represented by the probability density
function (PDF) of AOA, fϕ(ϕ), and the total power, P0, of the
received signal [9]
0
P P f
The relation fundamentals between DS and PAS is the
relationship between the Doppler shift, fD, and AOA, ϕ, [6]
max cos
D D
f f
hence, the inverse function is
max
arccos
D D D
f f f
where maxD
f v c
is the maximum Doppler shift,
max max
D D D
f f f , v and c are the velocity of the object
(e.g., RX) and light speed, respectively.
Naturally, DS, SD(fD), is a Doppler shift function. On the
other hand, considering the above formulas, DS can be
viewed as an AOA function. So [6]
J ,
D D D D
S f P f f
where the Jacobian J(ϕ, fD) between the AOA and Doppler
shift is defined for
max max
D D D
f f f [6]:
2 2
max
d1
J , d
D
D
D
D D
f
ff
f f
Hence, we can present the final relationship between DS
and PAS or PDF of AOA as follows [6]:
0
2 2 2 2
max max
D D
D D
D D D D
P f P f f
S f
f f f f
The numerical methodology of determining DS based on
PAS is described in detail in [6].
III. MEASUREMENT SCENARIOS
To empirically verify the concept presented in [6], we
conducted measurements on the campus of the Military
University of Technology in Warsaw. The propagation
environment can be classified as a suburban area with NLOS
conditions. The measurements were carried out for two
scenarios: static (see Fig. 1) and dynamic (see Fig. 2).
Situational maps were made using the Google Earth
application.
The PAS was determined based on measurements in the
static scenario, while the DSs were determined in the mobile
scenario for the four directions of mobile traffic of the
receiving station. The measurements were made for the
harmonic signal (to easy determining DS) for the frequency
of 3.5 GHz. Additionally, the PAS verification at 10 GHz
has been planned.
A. Static Scenario
Figure 1 illustrates the location of the transmitting (TX)
and receiving (RX) parts of the measuring test-bed on the
university terrain. Measurements were made near the
buildings of the Faculty of Electronics (i.e., no. 45, 47, and
75).
Fig. 1. Static measurement scenario.
In both scenarios, the transmitting part of the test-bed
was stationary and located in the same position. The
transmitting antenna was placed close to building no. 75, so
as to ensure NLOS conditions at the reception site. The
structure of the transmitting part is described in Section IV.A.
The receiving part of the measuring station was located
in the middle of the road intersection, near buildings no. 45
and 47. In the static scenario, we use a directional antenna
placed on a turn table. The direction of 0° for the PAS was
determined along the path between buildings no. 45 and 75.
The received power level was reading with a step 1°. In
Section IV.B, the static receiving part is presented.
B. Dynamic Scenario
The mobile measurement scenario in the top view is
illustrated in Fig. 2. In this case, the TX was located in the
same place as in the static scenario. The mobile receiving
part of the test-bed mounted in the vehicle moved through
the intersection center near buildings no. 45 and 47.
Fig. 2. Mobile measurement scenario.
Measurements involving the registration of IQ samples
by the mobile RX were made for four movement directions,
i.e., 0°, 90°, 180°, and 270°. The signal registration took
place over a short section of the route (about 40÷50 m). The
vehicle speed on the measuring section was constant and
about 30 km/h. For the analyzed scenarios, the direction to
the signal source (i.e., TX) relative to the direction of 0° and
the intersection center (i.e., RX position for the static
scenario) is about –25°. For the mobile measurement
scenario, the maximum Doppler shift was approximately
97 Hz. Section IV.C presents the structure of the mobile
receiving part.
IV. CONFIGURATION OF MEASURING TEST-BED
Section III describes two measurement scenarios that
were the fundamentals for the verification of the method
described in [6]. In both cases, the stationary transmitting
part of test-bed was equipped with an omnidirectional
antenna (see Fig. 3). In the static scenario, the receiving part
was also stationary and the RX was equipped with a
directional antenna mounted on the turn table (see Fig. 4). In
the mobile scenario, the RX was equipped with an
omnidirectional antenna that was mounted on the vehicle
roof (see Fig. 5).
A. Transmitting Part of Test-bed
Figure 3 shows a block diagram of the transmitting test-
bed part. The SMF100A signal generator by Rohde &
Schwarz (R&S) generated a 3.5 GHz signal, which was
additionally stabilized with an external rubidium standard.
The generator was connected to the input of the transmitting
antenna OMNI A0105 operating at the frequency of 3.5
GHz.
Fig. 3. Transmitting stationary part of measurement test-bed.
B. Static Receiving Part of Test-bed
Figure 4 depicts a block diagram of the stationary
receiving part of the measuring station.
Fig. 4. Receiving stationary part of measurement test-bed.
The R&S FSH20 spectrum analyzer was connected to the
inputs of two antennas:
Ultra Wide Band Parabolic Antenna by Technical
Antennas (gain 24 dBi, half-power beam width
(HPBW) 8°), used to receive the signal at the
frequency of 3.5 GHz,
High Gain Parabolic Antenna by Technical Antennas
(gain 27 dBi, HPBW 4°) used to receive the signal at
the frequency of 10 GHz.
These antennas were mounted on the turn table to
measure the received signal level as a function of the angle
(azimuth) in the range from 0° to 360° with the step of 1°.
C. Mobile Receiving Part of Test-bed
A block diagram of the mobile receiving part of the test-
bed is shown in Fig. 5.
Fig. 5. Receiving mobile part of measurement test-bed.
The R&S ESMD measurement RX with an active
receiving antenna, OMNI A0107, connected to its input, was
used to build the mobile receiving part of the test-bed. In this
case, a rubidium standard was also used as an external
reference signal source to stabilize the measurement RX.
V. EXPERIMENT RESULTS
A. Power Angular Spectra
Based on the performed measurements of the received
signal level using the test-bed for the static scenario, we
determine the PAS. The measurements were carried out for
the frequencies of 3.5 and 10 GHz, but for the higher
frequency, the antenna HPBW is about two times lower than
for 3.5 GHz. The normalized PASs obtained in the static
scenario for the two analyzed frequencies are shown in
Fig. 6. These characteristics are the basis for determining the
DSs for the analyzed movement directions in accordance
with the methodology presented in [6].
Fig. 6. Normalized PASs for 3.5 and 10 GHz.
Due to the NLOS conditions, the obtained PASs do not
show a maximum in the TX-RX direction (i.e., for
ϕ = 335°= –25°). The highest signal level occurs for the
direction of about 48° and 52° for 3.5 and 10 GHz,
respectively. This direction is related to building no. 45, from
where the main scattering of the transmitted signal comes to
the RX. For 10 GHz, we used an antenna with a lower
HPBW, so the obtained PAS extremum is more selective
angularly. On the other hand, the obtained graphs show PAS
differentiation versus frequency.
B. Doppler Spectra
In the experiment, DSs were determined based on
measurements performed for the mobile scenario. On the
other hand, according to the method presented in [6], we also
determined DSs based on the PAS for 3.5 GHz. The DSs
obtained by the two considered methods and for four
analyzed movement directions are shown in Fig. 7 (a)-(d).
Fig. 7. Normalized DSs for selected RX movement direction: (a) 0°,
(b) 90°, (c) 180°, and (d) 270°.
C. Results Analysis
Graphs in Fig. 7 can be used for subjective comparative
evaluation of DSs determined based on measurements and
the method described in [6]. In this case, we see some
discrepancies in the obtained channel characteristics. In the
authors' opinion, the main reason for the differences is the
fact that the PAS was determined pointwise, while the signal
registration for DSs determination was performed spatially
on the certain RX motion trajectory. Thus, the DSs obtained
from the measurements are spatially averaged, while the
PAS measurement was made for a specific location.
To compare the DSs obtained with the two analyzed
methods, we also used two scalar measures determined for
angular dispersion, i.e., average Doppler shift and RMS
Doppler spread defined as follows [10][11]
max
max
avg
0
1
d
D
D
f
D D D D D
f
f f S f f
P
max
max
2
avg
0
1
d
D
D
f
D D D D D D
f
f f S f f
P
Table 1 contains these parameters calculated for all
analyzed DSs.
TABLE I. TABLE STYLES
RX
movement
direction
TX direction
relative to
RX
movement
direction
Average Doppler
shift
Doppler spread
Based on
measure-
ments
Based on
PAS
Based on
measure-
ments
Based on
PAS
(deg) α (deg) fDavg (Hz) fDavg (Hz) σD (Hz) σD (Hz)
0
–
25
72
8
0
32
42
90
–
1
1
5
47
7
2
2
55
180
155
–
66
–
80
37
42
270
65
–
2
–
7
37
55
The largest discrepancy in results occurs for the
movement direction of 90°. The best fit was obtained for the
directions of 180° and 0°, and slightly worse for 270°. The
results show that the method proposed in [6] can be used,
e.g., in simulation studies, as a certain approximation of
classical methods (i.e., those used so far).
VI. SUMMARY
In this paper, we have made the empirical verification of
the DS determination method based on PAS, which is
presented in [6]. Measurements were made at 3.5 GHz in a
suburban environment on the university campus. The
obtained results show that the applied method can be used in
simulation studies as a certain approximation of the methods
of DS determination used so far. The fundamental
discrepancies result from the fact that the PAS was
determined pointwise, while the signal registration for DSs
determination was performed spatially on a certain RX
motion trajectory. Therefore, DSs based on measurements
are spatially averaged.
The authors plan an additional campaign in the 10 GHz
mobile scenario. Measurements with a lower-HPBW antenna
(i.e., for 10 GHz), show that the obtained PAS is more
accurate angularly. Moreover, to better reflect mobile
measurements, the PAS should be averaged over several
measurement points along the RX route. We assume that
these more accurate measurements will allow for a better fit
of the DSs obtained based on the two analyzed methods. If it
is confirmed, we would like to highlight that method [6]
allows determining the DS at a point, which is not possible in
the case of mobile measurements.
ACKNOWLEDGMENT
This work was developed within a framework of the
research grants: project no. 17-27068S sponsored by the
Czech Science Foundation, grant no. LO1401 sponsored by
the National Sustainability Program, grant MubaMilWave
no. 2021/43/I/ST7/03294 sponsored by the National Science
Center (NCN), grant no. UGB/22-740/2022/WAT sponsored
by the Military University of Technology, and grant no.
CRG/2018/000175 sponsored by SERB, DST, Government
of India.
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