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Variability of Radio Signal Attenuation by Single
Deciduous Tree Versus Reception Angle at 80 GHz
Jarosław Wojtuń1, Cezary Ziółkowski1, Jan M. Kelner1, Tomas Mikulasek2, Radek Zavorka2, Jiri Blumenstein2,
Petr Horký2, Aleš Prokeš2, Aniruddha Chandra3, Niraj Narayan3, Anirban Ghosh4
1 Institute of Communications Systems, Faculty of Electronics, Military University of Technology, Warsaw, Poland,
jaroslaw.wojtun@wat.edu.pl
2 Department of Radio Electronics, Brno University of Technology, Brno, Czech Republic
3 ECE Department, National Institute of Technology, Durgapur, India
4 ECE Department, SRM University AP, 522240 India
Abstract—Vegetation significantly affects radio signal
attenuation, influenced by factors such as signal frequency,
plant species, and foliage density. Existing attenuation models
typically address specific scenarios, like single trees, rows of
trees, or green spaces, with the ITU-R P.833 recommendation
being a widely recognized standard. Most assessments for single
trees focus on the primary radiation direction of the
transmitting antenna. This paper introduces a novel approach
to evaluating radio signal scattering by a single deciduous tree.
Through measurements at 80 GHz and a bandwidth of
approximately 2 GHz, we analyze how total signal attenuation
varies with the reception angle relative to the transmitter-tree
axis. The findings from various directional measurements
contribute to a comprehensive attenuation model applicable to
any reception angle and also highlight the impact of bandwidth
on the received signal level.
Index Terms— measurements, path loss model, propagation,
single tree, vegetation.
I. INTRODUCTION
The development of mobile networks and the increasingly
high requirements imposed on them necessitate the use of
increasingly larger radio resources [1]. In fifth-generation
(5G) and beyond networks, the potential of using millimeter
waves (mmWaves) (i.e., FR2, , formally
) has been recognized [2]. The mmWave frequency
band offers advantages such as high data rates [3] and a low
level of interference [4, 5]. On the other hand, the use of
mmWave frequencies in wireless communication systems has
to overcome challenges such as severe path loss, high
atmospheric absorption [6], sensitivity to precipitation (such
as rain, snow, and fog) [7, 8], and signal blocking [9],
especially in non-line-of-sight (NLOS) conditions.
Implementing new wireless communication systems in the
mmWave range significantly expands the possibilities and
diversity of telecommunications services, but it requires a
thorough understanding of the environment's transmission
properties. The propagation characteristics of mmWave
channels have been extensively studied in recent years [10,
11]. Numerous measurement campaigns have been conducted
to investigate the propagation characteristics of mmWave
channels in various scenarios, including indoor [12], outdoor
[13, 14], and vehicular [15, 16].
Electromagnetic wave attenuation is a crucial
characteristic that influences both the spatial design of
wireless networks and the assessment of received signal
quality in the presence of environmental interference. This
characteristic depends on a wide range of parameters related
to the environment – such as landform and cover, as well as
the type, shape, and size of obstacles – and the transmission
technology used, including frequency range, transmitted
power, and antenna systems. The phenomenon of
electromagnetic wave attenuation and scattering caused by a
single deciduous tree represents one of the simplest
propagation scenarios encountered in suburban areas. Despite
its spatial simplicity, this scenario has significant implications
for millimeter wave propagation.
Many studies have examined the influence of trees on
signal attenuation. In works [17–20], researchers analyzed the
attenuation caused by trees both with and without leaves. They
also investigated the effects of antenna polarization, line-of-
sight (LOS), and NLOS conditions, as well as the dependence
of attenuation on different parts of the tree crown.
Consequently, the ITU-R P.833 recommendation [21]
defines a propagation model that describes how attenuation
varies with distance, dimensions, vegetation type, and the
electrical parameters of obstacles. However, this
recommended model has several limitations related to the
positioning of the transmitter (TX), the single deciduous tree,
and the receiver (RX), which together define a straight-line
propagation path. This scenario does not allow for evaluating
scattering effectiveness in NLOS conditions when using a
single deciduous tree as a scattering element (broken
propagation path). Additionally, the model does not account
for the influence of the transmitted signal bandwidth, , on
the attenuation value.
In this paper, we propose an extension of the scenario to
include cases with varying scattering directions for wave
propagation in the range. Additionally, the results
consider the impact of the transmitted signal's bandwidth on
the attenuation caused by the single deciduous tree.
The relationship between the propagation path loss (PL)
attenuation, the reception angle, , and the signal bandwidth
was established based on an analysis of measurement data.
This data was obtained from a dedicated measurement testbed
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 paper will be presented at the 2025 19th European Conference
on Antennas and Propagation (EuCAP), Stockholm, Sweden, 30 Mar.–4 Apr. 2025
used in the experimental scenario. A description of both the
scenario and the components of the measurement testbed is
provided in Section II. The methodology for determining the
propagation path attenuation for various reception angles is
presented in Section III. Section IV contains the results of the
measurement data analysis, along with the interpolation
function that represents the relationship between propagation
path attenuation and reception angle while accounting for the
transmitted signal's bandwidth. Finally, we summarize the
paper.
II. MEASUREMENT SCENARIO
A detailed description of the measurement scenario can be
found in [22]. The measurement campaign was conducted at
various times throughout the year in the Orlické Mountains in
the Czech Republic.
In this paper, we focus on measurements taken in June
2023. We analyze the scenario involving a single deciduous
tree – a willow (Salix caprea) – which stands tall with
a diameter of . Figure 1 illustrates the relative positions of
the TX and RX during the measurements, highlighting the
angles and distances between them, as well as the distances
from both the TX and RX to the tree.
Fig. 1. Measurement scenario.
The measurement testbed consisted of Xilinx Zynq
UltraScale+ RFSoC ZCU111 boards, which transmitted the
baseband signal and acquired the I and Q components. A
simple frequency-modulated continuous wave (FMCW) with
a bandwidth of and a duration was
used as the baseband signal. Most of the energy of the signal
is within the range of ±980 MHz, therefore, the maximum
analyse bandwidth is equal 1960 MHz. The signal was up- and
down-converted to the mmWave band using the Sivers IMA
FC1003E/03 up/down converter. Agilent generators with a
rubidium reference clock served as the local
oscillators. The signal was transmitted at carrier frequency
. Additionally, a power amplifier (Filtronic
Cerus 4 AA015), a low-noise amplifier (LNF-
LNR55_96WA_SV), and horn or open-ended waveguide
antennas (OWGA) were employed.
In [22] the authors provide all details on the calibration of
the measurement system, raw data processing, and the
methods employed to eliminate crosstalk between the TX and
RX antennas.
III. PATH LOSS EVALUATION VERSUS RECEPTION ANGLE
To achieve the aim of this paper, i.e., determining how the
attenuation of a radio signal varies with the reception angle,
we propose a procedure for assessing this attenuation. Our
approach involves evaluating the changes in the power level
of the received signal in relation to the power level of a
reference signal, which is received at an angle of .
Additionally, we have considered the bandwidth of the
transmitted signal as a relevant parameter in our analysis.
The received signal is processed to estimate the PL. We
transform it to the frequency domain (by Fourier transform)
and determine its power
, ()
where is the value of the Fourier transform for a
specific spectrum bin, , and analysed impulse, is the
number of the Fourier transform coefficients, which
correspond directly with the analysed bandwidth of the signal,
and is the number of analysed impulses.
The mean power for all received impulses is calculated. In
our research, we average the power of =1000 impulses
. ()
We determine the attenuation correction coefficient, ,
for each reception angle in relation to the direct path, i.e.,
.
. ()
We determine the PL for the direct path.
, ()
where is the attenuation of the attenuator that was used
in the calibration procedure of the measuring testbed (see [22],
chapter III-B). is a gain of OWGA which was used in
this case.
For and , we determine PL as follows
()
Due to the smaller distance of the receiver from the tree
for compared to the other cases, we introduce an
additional attenuation correction factor defined
below
()
where FSPL is the free space path loss (
), where
represents the distance between the TX and RX antennas,
is the center frequency, and is the speed of light.
, (see Fig. 1).
Finally, for , the PL is equal to
()
IV. PATH LOSS MODEL FOR SELECTED SCENARIO
In this paper, we analyze the selected measurement sub-
scenario described in [22], i.e., for a tree with foliage. In this
case, for each analyzed receiver position illustrated in Fig. 1,
1000 measurements of the channel impulse response (CIR)
were performed. Based on them, we determined the received
signal spectra and calculated their powers. The empirical
cumulative distribution functions (ECDFs) of the relative
received power for the individual receiver positions and
maximum bandwidth (i.e., ) are shown in Fig. 2.
Fig. 2. ECDFs for different receiver positions and maximum bandwidth.
The power distributions for the three receiver positions are
close to normal with similar deviations, while for ,
the ECDF shape is similar to bimodal. This differentiation
may be due to diverse propagation conditions. For the
reception angle , the received signal may be partly
scattered by the tree and partly received directly from the
transmitter. In this case, the best line-of-sight (LOS)
conditions occur, and the average power is the highest (
, see Fig. 2). For the other reception directions, the
signal is primarily scattered by the tree.
Based on the measured powers and considering the
reference attenuation of
for the analyzed sub-
scenario (see [22, Tbl. 3]), we determined the path losses for
individual receiver positions, which are depicted in Fig. 3. For
the reception angle , an example PL distribution close
to normal is presented.
Fig. 3. PLs for different receiver positions and maximum bandwidth.
To determine the continuous PL model as a function of
reception angle (for ), we used third-degree
polynomial interpolation, which we can describe as follows:
, ()
where , , , and are coefficients of the interpolation
polynomial. For the maximum bandwidth, the obtained result
is depicted in Fig. 4.
Fig. 4. PL versus reception angle based on third-degree polynomial
interpolation for maximum bandwidth.
We can see that the interpolation curve considers the
measurement data well. The obtained PL model is in line with
intuition. The highest attenuation occurs for the reception
direction between and . In these cases, the radio
wave scattered by the tree must be reflected either back or
sideways. The maximum attenuation occurs in the middle of
this range, i.e., around . The smallest attenuation occurs
for a reception angle of around . As mentioned above,
LOS conditions can partially occur in this case. However, with
the increase of the reception angle to , the
attenuation increases again, which is caused by direct
scattering introduced by the tree and leaves.
We performed a similar analysis for different bandwidths
of the transmitted signal in the range from to .
For this purpose, bandpass filters with the appropriate
bandwidth are used to determine the received powers based
on the spectra. Next, the procedure described for the
maximum bandwidth is repeated for each case. The PL
models versus reception angle for different bandwidths are
presented in Fig. 5.
Fig. 5. PL versus reception angle based on third-degree polynomial
interpolation for different bandwidths.
We can see that PL increases with increasing bandwidth
. The third-degree polynomials described by (8) are again
used to model the shapes of the PL curves. The polynomial
coefficients of the PL models for the individual bandwidths
are given in Table I. The smallest variation in coefficient
values occurs for , which means that the attenuation of the
received signal that we would obtain near the transmitter is
approximately equal to and independent of the
bandwidth.
TABLE I. POLYNOMIAL COEFFICIENTS FOR PATH LOSS MODEL.
Bandwidth
B [MHz]
Polynomial coefficient
C
[dB/rad3]
D
[dB/rad2]
E
[dB/rad]
F
[dB]
200
5.14
–25.95
33.98
103.81
500
6.63
–34.28
45.25
104.31
1000
7.55
–38.47
51.09
104.35
1500
7.63
–38.87
51.55
105.43
1960
7.75
–39.45
52.55
105.32
The proposed PL models versus reception angle for
different bandwidths constitute a valuable extension of the
previously used vegetation attenuation models.
V. CONCLUSIONS
The propagation attenuation models introduced by
vegetation available in the literature consider various
scenarios, from a single tree, through a row of trees to an
environment such as a park, orchard, or forest. These models
usually consider the analysis of attenuation in the vertical
plane including the transmitter and the tree(s) as the scattering
element. The recommendation [21] introduces, i.a., modeling
different components diffracted around the vegetation.
However, the receiver is always located in the same plane. In
this paper, we propose a novel approach to modeling the
scattering introduced by a single tree. The proposed PL model
based on empirical measurements and third-degree
polynomial interpolation allows us to evaluate the signal
attenuation versus reception angle for different bandwidths.
In the near future, we want to extend this modeling method
for other weather conditions, i.e. for the remaining sub-
scenarios described in [22]. We aim to analyze how bandwidth
affects signal attenuation across different seasons.
Additionally, we plan to repeat the measurements for various
types of trees and evaluate the universality of the developed
model.
ACKNOWLEDGMENT
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/22-478/2024/WAT, and
chip-to-startup (C2S) program no. EE-9/2/2021-R&D-E
sponsored by MeitY, Government of India.
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