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1. Introduction
The World Radiocommunication Conference 2019 (ITUWRC,2019) identified several mmWave frequency
bands (24.25–27.5, 37–43.5, 45.5–47, 47.2–48.2, and 66–71GHz) for possible allocation for the International
Mobile Telecommunications (IMT2020) for 5G applications and 71–81GHz for nongeostationary fixedsatel
lite services. These higher frequency bands are largely affected by rainfall. The wavelength in the millimeter wave
band ranges from 11mm at 26GHz decreasing to 1mm at 300GHz (Hemadeh etal.,2017), while the diameter
of the raindrops is on the order of 1∼10mm. Since the water permittivity also differs from free space (complex
value; Durgin,2000) an electromagnetic wave incident on rain drops will suffer from scattering which causes
attenuation in the received signal strength (Nazar Elfadil etal.,2005).
Rain attenuation studies need longterm measurements and analysis over several years (Chandra Kestwal
etal.,2014; Lam etal.,2017) to provide telecommunication network providers with accurate and useful results
to plan and optimize reliable 5G radio links during precipitation events. Two rain attenuation prediction models
are generally used. These are the regression model, which uses rain rate and path attenuation statistics data for
rain attenuation modeling in a specific region; and the physical model (Crane,2003), which uses statistical infor
mation of rainfall and scattering caused by rain drops for providing accurate prediction that can be implemented
in different regions. It is recognized that the physical models depend mainly on precipitation conditions. Due to
the unpredictable behavior of rain distribution and weather conditions, this imposes significant challenges and
therefore a universal drop size distribution (DSD) is not feasible as it differs between regions: tropical region,
dry, polar, continental, and coastal region (Åsen & Gibbins,2002). Most of the rain attenuation studies report
measurements based on longrange line of sight fixed links. In Kvicera etal.(2011), a fixed link, which oper
ates at 93GHz over 850m is reported where the predicted attenuation using the ITUR model provides a lower
estimate than the measurements for high attenuation levels. In Schleiss etal.(2013), a link was set up at 38GHz
over 1.85km with the aim to study the rain attenuation and the wet antenna effect where 2.5dB maximum wet
antenna effect was found. Results in Luini etal.(2018) provide reliable rain attenuation values compared to the
DSD at 73, 83, 148, and 156GHz with a link distance of 325m. Results in Kim etal.(2013) show a significant
Abstract Several millimeter Wave (mmWave) bands, which suffer from rain attenuation, were identified in
the World Radiocommunication Conference 2019 (WRC19) for fifth generation (5G) radio networks. In this
paper, longterm attenuation is measured over typical building to building radio links in the built environment,
which constitute two 36m links along a direct link and an indirect side link at 25.84 and 77.54GHz and a
200m link at 77.125GHz. The attenuation was also estimated using precipitation data from a high end accurate
disdrometer weather station using the drop size distribution and the International Telecommunication Union
(ITU) models. The results indicate that attenuation using Mie theory is in agreement with the ITU model
for most of the rainfall events; with higher attenuation being measured than predicted when snow grains and
raindrops mix. Raindrops with diameter between 0.1 and 4mm indicate that the dominant raindrops have
considerable influence on the measured attenuation, especially at light and moderate rainfall events. The
maximum distance factor restriction of 2.5 in ITUR P.53017 is shown not to be suitable for shortrange fixed
links as it excessively underestimates attenuation.
Plain Language Summary Next generation mobile radio networks, 5G, are assigned several
frequencies in the millimeter wave band, which are likely to suffer from rain attenuation. This can lead to
outage in the communication link. This paper presents results of measurements and prediction models in the
millimeter wave band using weather statistical data and radio data.
ZAHID AND SALOUS
© 2022. The Authors.
This is an open access article under
the terms of the Creative Commons
Attribution License, which permits use,
distribution and reproduction in any
medium, provided the original work is
properly cited.
LongTerm Rain Attenuation Measurement for ShortRange
mmWave Fixed Link Using DSD and ITUR Prediction Models
O. Zahid1 and S. Salous1
1Department of Engineering, Durham University, Durham, UK
Key Points:
• Rain attenuation prediction in the
mmWave band using rain statistics
and fixed links radio data
• Longterm study through measured
and predicted rain attenuation
• Attenuation measurement as a
function of rainfall intensity, raindrop
distribution, dominant drops, and
drops diameter
Correspondence to:
S. Salous,
sana.salous@durham.ac.uk
Citation:
Zahid, O., & Salous, S. (2022). Long
term rain attenuation measurement for
shortrange mmWave fixed link using
DSD and ITUR prediction models. Radio
Science, 57, e2021RS007307. https://doi.
org/10.1029/2021RS007307
Received 1 MAY 2021
Accepted 29 MAR 2022
Author Contributions:
Conceptualization: O. Zahid
Data curation: O. Zahid
Formal analysis: O. Zahid
Investigation: O. Zahid, S. Salous
Methodology: O. Zahid
Resources: O. Zahid, S. Salous
Software: O. Zahid
Supervision: S. Salous
Validation: O. Zahid, S. Salous
Visualization: O. Zahid
Writing – original draft: O. Zahid
Writing – review & editing: S. Salous
10.1029/2021RS007307
Special Section:
The 33rd General Assembly and
Scientific Symposium (GASS)
of the International Union of
Radio Science (URSI)
RESEARCH ARTICLE
1 of 21
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difference between the International Telecommunication Union (ITU) model and the measured attenuation with
the conclusion that the ITU model is not suitable for rain intensity above 100mm/hr at 73 and 83GHz for 500m
links. In Juttula etal.(2019), the scattering effect and attenuation were reported at 100 and 500m at 60 and
300GHz where the difference between the DSD and the ITU model reaches 5dB.
Several works have reported rain attenuation prediction using rain statistics only. In Åsen and Gibbins(2002), a
DSD model is used to quantify rain attenuation at 57, 97, 135, and 210GHz at Chilbolton and Singapore. Their
results indicate that the DSD differs with climatic condition levels of pollution. At higher frequencies and high
rainfall rate, inconsistency and fluctuations were observed between the ITU model and the DSD attenuation
model, with lower attenuation values predicted by the ITUR model. In Tuhina etal.(2018), rain attenuation
measurements were conducted for 22GHz, 23GHz, and 31.4/30GHz in a tropical region: Kolkata in India and
Belem in Brazil for 2years. Results show good agreement between the DSD attenuation model and the ITUR
model for rainfall rate below 100mm/hr, with slight differences below 30mm/hr. In Saurabh etal.(2010), assum
ing a lognormal distribution for the DSD, both the DSD model and the ITUR model gave similar results for
frequencies below 30GHz with a maximum rainfall rate up to 30mm/hr in a tropical region.
In this paper, precipitation data are collected and used in the prediction models to estimate the rain attenu
ation in parallel with an mmWave channel sounder, which operates at two frequencies 25.84GHz (K band)
and 77.54GHz, over two 36m links: a direct link and an indirect link. Another link with a commercial radio
frequency (RF) head is set up for continuous wave (CW) transmission at 77.125GHz (E band) for attenuation
measurements. Measurements are conducted from October to December 2020, and January 2021 for all three
links. Since the rainfall rate is insufficient for the prediction of attenuation in the higher frequency bands, more
accurate precipitation data are needed which include: rainfall rate, rain drop diameter, DSD, rainfall velocity,
particle speed, and water permittivity. Such data can be obtained using a high end disdrometer station as used
in the present study. The results of the attenuation prediction and measurement can be applied for regions with
similar weather conditions. The ITUR P.53017 maximum distance factor restriction of 2.5 for shortrange links
is also investigated in addition to analyzing the effect of scattering of rain droplets.
This paper is organized as follows: the weather measurement system is presented in Section2 together with rain
statistics and raindrop distribution for the measurement period, followed in Section3 by a description of the fixed
link measurement setup for measuring attenuation and the ITU and the DSD prediction models. In Section4,
measurement results using the shortrange fixed link data sets and the PWS100 disdrometer precipitation data are
presented and compared for discussion; followed by raindrops induced scattering analyses in Section5. Conclu
sions and ongoing work are presented in Section6.
2. Precipitation Measurements for Rain Attenuation Modeling
2.1. Weather Station
A PWS100 Weather Sensor station was installed on the roof of the library at Durham University to record precip
itations data as shown in Figure1a. It is a laser based sensor capable of determining precipitation and visibility
parameters (Scientific,2015). Due to its developed measurement technique, the PWS100 can determine each
individual particle type from accurate size and velocity measurements. The technical specifications of the station
are listed in Table1. The PWS100 disdrometer covers a measurement area of 40cm
2. The station is controlled
remotely to store data through the campus wireless network and the CR1000 data acquisition as shown in the
block diagram of the measurement system in Figure1b over an internet protocol address once every minute.
Figure2a illustrates the rainfall intensity statistics between October 2020 and January 2021, with most of the
measured rain intensity being under 20mm/hr. In the results section, the rainfall intensity in mm/h is mapped
against the received signal in dBm to estimate the rain attenuation in (dB) over the measurement period. Five
types of rainfall intensities are used to investigate rain attenuation: light rainfall (R≤1mm/hr), Moderate (1mm/
hr<R≤4mm/hr), heavy (4mm/hr<R≤16mm/hr), very heavy (16mm/hr<R≤50mm/hr), and torrential
rainfall (R>50mm/hr).
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2.2. Drop Size Distribution
Raindrop Size Distribution (DSD), noted by N (D), plays a critical role in determining the microphysics of rain
(Marshall & Palmer,1948). It has a significant role in radio propagation performance links. The DSD varies
and depends on the location. For a given rainfall type, we could get two different types of DSDs which result in
different values of signal attenuation. Using the PWS100 disdrometer, the DSD is recorded with 300 values of
the number of drops corresponding to the diameter from 0.1 to 30mm with 0.1mm resolution. The DSD can be
calculated as:
N(D
i)=
300
∑
j=1
n
(
Di,vj
)
vj
⋅
1
S⋅Δt ⋅dD
i
(1)
where S=40cm
2 is the measurement surface of the laser beam of the PWS100 disdrometer, t=60s is the inte
gration time, n(Di, vj) is the number of particles registered within the classes with mean diameter Di(mm) and
mean speed vj(m/s), and dDi(mm) is the class width associated with the diameter Di. The PWS100 can determine
each individual particle type from accurate size. For each minute, we have the corresponding rain rate and number
of drops for each bin and the following steps take place for the average DSD:
1. The integration time intervals of disdrometer measurements are to be categorized according to the desired rain
rate classes, for example, 5 and 20mm/hr.
2. For each longterm mean (i.e., in each rain rate class) the disdrometer bin size classes are to be rearranged
according to the bin size classes (0.1, 0.2, and 30mm).
Figure 1. Weather measurement system installed on the roof of Durham University's library: (a) PWS100 weather station and (b) Block diagram.
Parameters Specifications
Particle diameter 0.1–30mm
Size accuracy 5% (for particles >0.3mm)
Particle velocity 0.16–30m/s
Velocity accuracy 5% (for particles >0.3mm)
Types of precipitation Drizzle, rain, snow grains, snowflakes, hail, ice pellets, graupel, and mixed
Rain rate intensity range 0–400mm/hr
Rain total accuracy Typically 10%
Table 1
Specifications of the PWS100 Weather Station
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3. The (longterm mean) drop count in each bin size class is to be divided by the measuring area (of the instru
ment 40cm
2) and by the column height (integration time multiplied by the mean fall velocity of this bin's
mean diameter). Thus the (longterm mean) drop counts per unit volume are obtained.
4. To obtain the required distribution density further in each bin size class the drop counts per unit volume are
to be divided by the bin size class width.
Appropriate unit conversions are implemented to deliver the result in (m
−3mm
−1). Figure2b reports the measured
DSD where the peak DSD occurs at around a raindrop diameter of 0.8–1.2mm for most of the rain events.
Figure 2. Precipitation measurement: (a) Continuous rain rate measurements between October 2020 and January 2021 in Durham, England and (b) the measured drop
size distribution from the PWS100 disdrometer.
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3. Prediction of Rain Attenuation
3.1. mmWave Fixed Link Channel Sounder Setup
The experimental fixed link setup described in Salous etal.(2019), Huang etal.(2019), and Zahid etal.(2020)
used for collecting fixed link data for real rain attenuation investigation is shown in Figure3. The first two links
are set up over a direct path and side path over 36m links and located on the rooftop of the Engineering depart
ment at Durham University (Latitude: 54.767396, Longitude: −1.570390) at 65m of sea level elevation. Two
antennas with vertical and horizontal polarizations are used for the E band and a dual polarized antenna is used
for the K band for the direct link. To study the effect of scattering and interference a second side link receiver was
installed. For the side link Rx, single vertically polarized antennas were used for both the K band and the E band.
Custom designed covers were installed for all the antennas to reduce the impact of the wet antenna effect on the
measured attenuation. The fixed link operates on CW transmission (building to building/lamppost to lamppost
scenario). The third link which operates at 77.125GHz is installed between Durham University Library roof
(Latitude: 54.768167, Longitude: −1.573418) at 62m of sea level and the engineering department roof which
gives a point to point 200m path. The Tx/Rx for the 200m link are commercial transceivers (Filtronic Orpheus
Eband modules) shown in Figure3d. The transceiver groups the Orpheus interface board, a NI USB8451, and
an electronic circuit power to supply the module. Once mated, the module can be powered up using standard lab
PSUs (−5V, +2.8V+3.3V, and +5.1V+18V). For the control of the module, a NI USB8451 is used with
the Filtronic Orpheus GUI software. The 200m pointtopoint link is named figuratively “Filtronic link.” The
three links are remotely controlled through the campus internet network and data are recorded for each minute,
simultaneously with the weather station data. The channel data are recorded for 1s every minute to relate with
the rain rate data. The sampling rate of the RF link is 80MHz and the attenuation per minute is an average of 1s,
as the baseband signal frequency is at 4, 12, and 31MHz, respectively.
3.2. Prediction Models
Rain attenuation affects the Quality of Service of radio links in the millimeter wave bands. It is therefore vital
to have accurate and reliable propagation models for predicting rain attenuation using precipitation data such as
rainfall rate, DSD, velocity, temperature, and water permittivity. The prediction models used in this study are the
ITUR P.8383 model and the DSD model, which use frequency parameters, wavelength, water permittivity, and
raindrop distributions (Shrestha & Choi,2017).
3.2.1. ITUR P.8383 Model
This model was validated theoretically and experimentally and is recommended for the frequency range from 1
to 1,000GHz. It is given by:
Figure 3. Fixed link radio frequency heads of the measurement setup, (a) transmitter box for 36m link, (b) receiver box for direct 36m link, (c) receiver box for side
36m link, (d) transceiver Filtronic box for 200m link.
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=
(2)
where R is the rainfall rate (mm/h), k and α are model parameters, which
depend on the frequency f(GHz), and γ is the specific attenuation in dB/
km. The ITU recommendation provides a lookup table of the values k and
α for different frequencies for both the vertical and horizontal polarization
(Recommendation ITUR P.8383,2005) are noted in Table2.
The total attenuation for a specific distance depends on the effective path
length deff, between the Tx and Rx antennas as:
=
(3)
where the effective path length, deff, of the link is obtained by multiplying the actual path length d by a distance
factor r, from ITUR P.53017 as
=
1
0.4770.6330.073
0.01
0.123 − 10.579(1 − exp(−0.024
))
(4)
where R0.01 is the rain rate exceeded for 0.01% of the time (with an integration time of 1min). In ITUR P.53017
it was recommended to use a maximum value of r equal to 2.5 while in the updated recommendation P.53018,
the restriction on the maximum value of r has been removed. For the present study, results with and without
the restriction of r=2.5 are compared with the measured attenuation for our shortrange fixed links for both
frequency bands.
3.2.2. Drop Size Distribution Model
The attenuation using the DSD model based on Mie theory in Bohren and Huffman(1998) is given as:
=4.343 × 103
∫∞
0
()()
(5)
where γ is the specific attenuation in dB/km,
𝛿
𝑒𝑥𝑡 =𝜋
(
𝐷
2)2
𝑄
𝑒𝑥𝑡
is the extinction cross section (m
2) for water drops
of diameter D (mm), and N(D) is the measured DSD value (m
−3 mm
−1) at diameter D from the sensor weather
station PWS100. The extinction efficiency Qext can be calculated from Mie scattering or Rayleigh scattering
theory depending on the size parameter X=πD/λ, where λ is the wavelength.
For the current rain attenuation prediction, we use the measured DSD from the PSW100 weather station. The
disdrometer records only fall velocity and not for each particle; hence, we use Equation6 given in Atlas and
Ulbrich(1977) and Atlas etal.(1973) for the calculation of particle speed. The DSD can also be calculated using
theoretical and analytical models such as: the MarshallPalmer (MP) distribution (Marshall & Palmer,1948)
and the Weibull distribution (Jürg & Enrico,1978). In this study, we use the measured raindrop distribution from
the PWS100 disdrometer. For comparison, we consider the widely used Gamma distribution, given by Ulbrich
(Carlton,1983) in Equation7.
()=
{
3.780.67
,
<0.89.65 − 10.3−0.6,
≥0.8
}.
(6)
𝑁(𝐷)=𝑁0𝐷𝜇exp(−𝜆𝐷) (0 ≤𝐷≤𝐷𝑚𝑎𝑥)
(7)
where D (mm) is the rain drop diameter, N0 is the intercept parameter, μ is the shape parameter, and λ is the
slope parameter, and the mean value of μ is 3 (Kumar etal.,2010; Nabangala,2016). Gamma distribution given
in Ulbrich model is applied to fit the rain DSD and used for comparison purpose only. The theoretical relation
between the terminal fall velocity and the drop dimension is taken for the DSD calculation because the velocity
of each particle is not measured.
0
=1.41 × 10
6
−0
.
52
(8)
=9
.
48 ×
−0.2
(9)
26GHz 77GHz
k (vertical) 0.1669 1.1276
k (horizontal) 0.1724 1.132
α (vertical) 0.9421 0.7073
α (horizontal) 0.9884 0.7177
Table 2
k and α Coefficients
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The type of scattering effect depends on the extinction efficiency which relies
on m the complex refractive index of water; which is related to temperature
and frequency (Schiebener & Straub,1990). Throughout the measurement
period, an average computation was used on the temperature. The average
temperature was 7° and the complex refractive index of water was calcu
lated according to Table3 for each frequency band. Figure4 presents the
extinction efficiency as a function of size parameter X, where Mie theory
calculations have been implemented to calculate the extinction efficiency. It
should be noted that X refers to Mie size parameter as a function of diameter
D, λ, and π. When the rain drop is much smaller than the wavelength X≪1, D<λ, the probability of scattering
increases and the wavelength decreases, that is, Rayleigh scattering. Mie scattering takes place when X≈1, while
geometric optics scattering occurs when X≫1.
The high capability measurement of the disdrometer provides for each minute the corresponding rain intensity,
number of recorded droplets for each diameter type, the temperature, the fall velocity, and humidity. For each
rainfall, the dominant number of drops is extracted. Figure5 displays the parameters that have significant impact
on the attenuation behavior computed from the collected precipitation data throughout the measurement period.
At each raindrop diameter, the figure displays the maximum number of drops found from the total rain statistics,
its speed in m/s, and the corresponding rain intensity. An exponential variation of particle speed up to 5mm drop
size is observed, beyond which the velocity flattens out. The number of drops is seen to be in the range of 25–250,
while most of the raindrops size falls between 0.1 and 2mm.
Because previous data sets in the paper we published in Huang etal.(2019) revealed a significant wet antenna
effect, the present study provides results following extensive updating of the measurement link setup along with
longer term measurement campaign than before, which reduces the antenna wetness effect by placing antenna
hoods and integrating the IF unit with the RF heads. In addition, longterm measurement disdrometer meteoro
logical data from the PWS100 of 3years are now available. The data are being submitted and used for the ITUR
Study Group 3 data sets bank.
4. Discussion of Measurement Results
This section presents the calculated attenuation at 25.84GHz (K band) and 77.54 GHz (E band) over the two
36m links between October 2020 and January 2021 and the 77.125GHz band over the 200m link from Novem
ber 2020 to January 2021 adopting the ITU and DSD models for comparison with the measured rain attenuation
for which the data availability ratio for direct and side 36m links is 82.55%
and 70.47% for the 200m link. Vertical to vertical polarization, which is
common to all the three links is selected for the two bands over 252hr of rain
data. The attenuation is calculated and referenced using sunny clear sky days
before and after the recorded data. We perform the following steps to meas
ure the attenuation: initially, a reference signal is obtained for sunny and clear
sky hours chosen before the rainfall event; then subtract from the reference
signal the received signal during the rain event. The data are verified each
minute to ensure reliability and to avoid loss in the signal due to the meas
urement system rather than rain. Measurement days where snow occurs are
compared to rainy days. The attenuation is mapped against the rain intensity.
The effects of raindrop diameter distribution, and diameter of the dominant
drops on the measured attenuation are presented. The measurements through
this period include some gaps of no rain hours and days while 218hr of light
rainfall data, 32hr of moderate rainfall data, 3.4hr of heavy rainfall data, and
around 25min of very heavy rainfall data were recorded. Predominant and
frequent rain events were identified for calculation and modeling of the rain
attenuation. For accurate and reliable rain attenuation study, minutes corre
sponding to equipment transient behavior (rising and drop of the received
power), the power flatness of the system, atmospheric attenuation, equipment
Frequency Water refractive index
26GHz 5.41+2.78i
77GHz 3.64+1.84i
Table 3
The Complex Refractive Index of Water
Figure 4. Extinction efficiency versus size parameter X for the selected
frequency bands.
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icing, humidity, and wind are not used in the analysis. For each link, the best
measured data sets and the most stable signal strength are used for the esti
mation of the attenuation.
4.1. Predicted Attenuation
The estimated rain attenuation using the disdrometer data is presented for
both the ITU and DSD model. The rain attenuation is classified into two
categories: (a) physical, which uses the measured radio link data for rain loss
calculation to integrate it into the radio channel parameters for link budget
calculation and (b) modeled attenuation, which predicts the attenuation
using the DSD model based on Mie scattering theory given by Equation5
using the disdrometer data and the ITUR prediction model given in Equa
tion2. When measuring and calculating rain attenuation with rain intensity
statistics, raindrop distributions, and particle size, various parameters such
as atmospheric conditions (Han & Duan,2019), scattering and interaction
between raindrops, and absorption (Mora Navarro & Costa, 2016; Surco
Espejo & Costa,2017) need to be considered. In this study, it is assumed that
the raindrops are spherical for Mie theory and scattering. The interactions
between raindrops are negligible. Other climatic conditions such as wind,
snow grains, snowflakes, and ice pellets are also not considered for rain atten
uation through snow events but will be presented to show their effect on the
signal strength. As shown in Figure4, the size parameter X is 5 and 16 for
26GHz, and 77GHz, respectively. At higher frequency, the extinction effi
ciency approaches 2.5 and the size parameter is greater than 10 (larger raindrops) almost near to geometric cross
section area, when Mie theory is applied.
Equations5 and2 are given for the specific calculation in dB/km, so the distance factor r should be taken into
consideration when converting to the specific path lengths of 36 and 200m. This factor was mainly derived from
longrange measurements. Using the ITU recommended maximum value of 2.5 raises the question regarding
its application for shortrange links less than 1km (Budalal etal.,2020; Huang etal.,2019; Olsen etal.,1978).
Hence, the suitability of the maximum r factor is further investigated for the current shortrange links.
Figures6 and7 show the calculated attenuation for the K and E bands using the ITU and DSD models for the
36 and 200m, respectively. The figures indicate good agreement for most of the rain events, whereas during the
snow events comparison with the DSD and the ITU is mainly derived from rain drops not snow grain and snow
flakes; therefore, the DSD model shows higher attenuation values up to 4dB than the ITU model since during the
snow events the raindrop distribution is formed of a mixture of raindrops and snow particles. Consecutive heavy
rainfall events show slightly higher attenuation using the ITU model at the E band for both links with 1.2 and
4dB recorded for maximum rainfall rate of 5mm/hr and 20mm/hr, respectively, for the direct E band link while
a maximum of 6dB loss for 20mm/hr for the 200m link.
4.2. Measured Attenuation
The results of the measured attenuation as a function of rainfall up to 25mm/hr are presented. Figures8, 10,
and11 show the received signal mapped against the rain intensity and snow particles for the three links: direct
36m, 200m, and side 36m, respectively, for the K and E band vertical to vertical polarization. The figures show
that the signal strength follows the rainfall trend. During snow events, the signal takes more time to recover to the
level following the end of rain/snow event due to antenna icing as can be seen in Figure9. This effect should be
differentiated from the measurement by eliminating from the analysis the icing events. Compared to the predict
edcalculated attenuation as shown in Figure12 (samples of dominant rainfall events through the measurement
period and matched attenuation) the measured attenuation for the direct 36m link during rain events without
snow and before mid of December 2020 shows an average of 0.8–1.5dB higher attenuation for heavy and very
heavy rainfall at 26GHz, while a difference of 0.4–1.3dB at 77GHz. However, higher losses up to 9.5dB are
recorded when a mixture between rain and snow occurs. The side link shows somewhat higher attenuation than
Figure 5. Particle velocity variation versus its diameter and the number of
maximum drops for each particle type for the measurement period of October
2020–January 2021.
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the direct link 0.5–2.3dB as the side link depends on nonLineofSight (NLOS) reflected paths to receive the
signal. Thus, the measured attenuation is affected by raindrops scattering mechanism. The K band side link exhib
its 1.7dB difference with respect to the predicted rain attenuation for light, moderate, and heavy rainfall events.
Measured rain attenuation for the 77GHz 200m link agrees well and follows the predicted attenuation for most
rainfall events where 6dB loss has been recorded for a maximum rain intensity of 20mm/hr.
It can also be observed that the measured attenuation values are not all uniform with the rain fall rate and the
calculated attenuation using the ITU and the DSD models using the disdrometer data. For instance, two similar
rain intensities may result in two different rain attenuation values. As an example 11mm/hr was recorded on
13 October 2020 at 10:17 and the 31 October 2020 at 12:58 result in 1.56 and 2.28dB at 77GHz, respectively.
This is also observed in other works (Aydin & Daisley,2002; Brazda & Fiser,2015; Sander,1975; Schönhuber
Figure 6. Predicted rain attenuation for K and E band over dominant recorded rainy days between October 2020 and January 2021 for 36m link.
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etal.,2015; Townsend etal.,2009). This instantaneous difference between the measured and the DSD/ITU calcu
lated attenuation values could be due to a number of factors:
1. Mie theory assumes that rain drops are spherical, whereas it is not always the case within a real rainfall event
since the DSD model uses real disdrometer data, which is subject to severe weather conditions that reduces
its collection capability.
2. For light rain rate, the disdrometer might not be able to count small raindrops in higher windy situations.
3. Other factors that may affect the collected radio data are the humidity (Tamošinait etal., 2011) where the
humidity continues its existence in the atmosphere in sunny clear days and temperature variability in space
and time (Setijadi etal.,2009). In the DSD model estimation, the average monthly value of temperature was
used and the humidity was neglected.
4. Successive rain events up to 10hr (moderate rainfall events). The signal takes more time to recover after this
longterm rain event.
5. The former method inherently assuming a constant analytical DSD for the derivation of the k and alpha coef
ficients in Equation2.
The raindrops size and rain event distributions are not uniform within space and time due to the variability of
raindrop distribution and the particle size, which corresponds to the number of each dominant raindrop diameter,
rainfall speed, and particle speed. Mostly, for all rainfall types, raindrops size between 0.1 and 3mm contribute to
the maximum attenuation which is λ/2 at 77GHz as shown in Figure16. This indicates that the number of domi
nant raindrops has a significant influence on the specific attenuation, which can result with up to 2dB difference
at the same rainfall type within two different dates at the range of 0.1–2mm drop size.
Figure 7. Predicted rain attenuation for E band over dominant recorded rainy days between November 2020 and January 2021 for 200m link.
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Figure 8. Longterm rain attenuation measurement for direct 36m link at K and E band through dominant recorded rainy days between October 2020 and January
2021.
Figure 9. Effect of snow and ice on hardware measurement.
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In Figure13 the measured CDFs are compared with the predicted CDFs from the ITU and DSD models. Good
agreement between measured and calculated attenuation is obtained at 77GHz for the direct, side, and Filtronic
links. A notable difference occurs at the lower frequency band at 26GHz between the measured and the theoret
ical values for the side link where the measured attenuation has larger values.
In addition, mmWave shortrange fixed links require accuracy and reliability of prediction. The ITUR P.53017
model uses the effective path length for estimating the rain fade and r distance factor which is derived from long
range measurements. It is recommended in the model to use a maximum value of r=2.5 whereas in the updated
recommendation, this restriction has been removed. The recommended value of r with and without the restricted
value are implemented into the calculation, and thereafter investigated for the three links within its correspond
ing frequency bands. Figures14 and 15 show a full and detailed comparison between the measured and ITU
predicted rain attenuation using the maximum recommended distance factor and without using it for the E and
K bands, respectively, where rain rate and attenuation were measured for each event in an instantaneous manner
within 1min interval. The results indicate that when the r value is restricted to 2.5, the predicted rain attenuation
exhibits higher differences with the measurements than when it is not used at both frequency bands for both the
36m and the 200m links.
To further examine the impact of other rain parameters on the link, Figure16 presents samples of measured
attenuation versus raindrop diameter from 0.1 to 7mm which were within different rainfall rates. The calculated
attenuation using Mie theory is correlated to the relevant amount and type of droplets collected at that minute,
thanks to the disdrometer's recording capabilities. The attenuation rises with the raindrop diameter. The highest
attenuation is illustrated for the events where raindrops' diameters range between 2 and 4mm. The analyzed
results indicate that very heavy and moderate rainfall rate lead to higher attenuation values for both frequencies
Figure 10. Longterm rain attenuation measurement for point to point 200m link at E band through dominant recorded rainy days between November 2020 and
January 2021.
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in the presence of large rain drops (above 2mm). Similar to the analyses in Figure6 in the previous section and
Figure16, when the particle speed is 9–10m/s even with a number of particles lower than 20 drops, it results in
higher and variable attenuation specially for very heavy rainfall higher than 20mm/hr where raindrops with the
size of 1–3mm lead up to 4.5dB higher attenuation. A diameter in the range of 4–7mm contributes occasionally
to the attenuation up to 2dB for both frequency bands. It should be highlighted that the computed rain attenu
ation value is matched for each rain rate event thanks to the weather station data measurement features, which
include the associated temperature, drop distribution per diameter for each minute, and humidity provided. We
can match the rain event to the matching raindrop size, which means that for example, if the event is 5mm/hr, we
can extract the number of drops for each drop size type and then select the dominant drop. This study found that
higher rainfall and a greater number of rain droplets of predominant diameter lead to higher attenuation than the
theoretical prediction with low rainfall.
Based on the computations, we identify the drop diameter region that contributes the most to overall attenuation.
The phrase (maximum attenuation) refers to the maximum value that is obtained with that number of drops.
The next section elaborates raindrops scattering mechanism using the recorded disdrometer data and Mie theory.
5. Raindrops Induced Scattering
Scattering due to raindrops has a significant effect because rain scattering is considered one of the main sources
of attenuation and interference (Olsen etal.,1993). Scattering can be governed as a function of wavelength (λ) of
the incident radiation, the size of the scattering particle, usually expressed as the nondimensional size parameter,
X, and the particle optical properties relative to the surrounding medium: the complex refractive index which
Figure 11. Longterm rain attenuation measurement for side 36m link at K and E band through dominant recorded rainy days between October 2020 and January
2021.
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Figure 12. Samples of measured rain attenuation compared to drop size distribution and International Telecommunication Union models over predominant rainfall
events for K and E band at direct and side 36m link and for E band at Filtronic 200 link: (a) E band 36m direct link, (b) K band 36m direct link, (c) E band 36m side
link, (d) K band 36m side link, and (e) E band 200m link.
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Figure 13. CDFs of the measured and the predicted rain attenuation for the three links: (a) K band 36m direct link, (b) E band 36m direct link, (c) K band 36m side
link, (d) E band 36m side link, and (e) E band 200m Filtronic link.
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depends on frequency and temperature. These parameters identify the scattering modeling which can be divided
into singlescattering or multiplescattering. Single scattering considers one interaction between the incident
wave and the precipitation field. When the density of scatterers or the scattering cross section increases multiple
scattering occurs. In the current analysis, the most common first order rain scattering approach is adopted. The
regular model which is considered widely to cause interference between fixed links (Capsoni etal., 2010) is
presented in Figure17.
Spherical raindrops, Mie theory, and bistatic radar equation given in Capsoni etal. (2010) and Capsoni and
D’Amico(1991) are considered for scattering functions calculations. The following functions are derived from
Mie theory and describe wave scattering through a common raindrops geometry:
Figure 14. Measured and International Telecommunication Union predicted rain attenuation for E band for the three links with and without using the maximum
distance factor restriction r of 2.5: (a) E band 36m direct link, (b) E band 36m side link, and (c) E band 200m link.
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1. Mie scattering amplitude function is given by:
1(cos)=
∞
∑
=1
2+1
(+ 1) (+
)
(10)
2(cos)=
∞
∑
=1
2+1
(+ 1) (+
)
(11)
the functions πn(cosθ) and τn(cosθ) describe the angular scattering patterns. an and bn are Mie coefficients
complex functions of drop diameter, refractive index, and wavelength.
2. Scattering cross section. It gives a conjectural definition of how much area is blocked out by the target during
the raindrops scattering event. It is given by:
𝜎
𝑠𝑐𝑎 =𝜋𝐷
2
𝑥
2
∞
∑
𝑛=1
(2𝑛+ 1)
(
𝑎𝑛

2+

𝑏𝑛

2
)
(12)
Figure18 shows the calculated scattering cross section as a function of scattering angle. The scattering cross
section reaches a value of 1.04×10
−4 (m
2/m
3) for a scattering angle of 0° at very heavy rainfall. Operating at
higher rain intensity will introduce superior scattering for both bands.
3. Bistatic scattering cross section η per unit volume which is a function of frequency and scattering geometry of
raindrops
𝜂
(𝜃𝑠)=
∫∞
0
𝑁(𝐷)𝜎𝑠𝑐𝑎(𝐷)𝑃(𝐷, 𝜃𝑠)𝑑𝐷
(13)
θsis the scattering angle, N(D) is the measured raindrops distribution. One significant element that defines the
prospect distribution of the scattered wave direction is the scattering phase function P(D, θs) defined by:
()= 1()
2
+2()
2
2
(14)
Figure 15. Measured and International Telecommunication Union predicted rain attenuation for K band for the two links with and without using the maximum distance
factor restriction r of 2.5: (a) K band 36m direct link and (b) K band 36m side link.
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where S1(θ) and S2(θ) terms are elements of the scattering amplitude matrix given by the Mie theory. Figure19
shows the scattering phase function versus the scattering angle for predefined raindrops diameter dominant in the
disdrometer measurements. It is noticed from the figure that the 77GHz band is considerably forward oriented
pattern while at 26GHz it is more inclined to Rayleigh, which explains the difference between the measured and
predicted attenuation for the K band side link presented in the previous section when Mie theory was applied for
all the calculations of both bands.
Figure20 displays the behavior of the bistatic scattering cross section for the E band versus the scattering angle
for the two different rainfall rates: 16 and 39mm/hr. The raininduced scattering is due to the beam angle falling
below 60°. It is the region where it is having significant effect but confined only to rainfall events higher than
10mm/hr and considerable raindrops diameter above 1mm.
6. Conclusions
Rain attenuation for millimeter wave 5G fixed link applications was investigated using longterm rain statistics
and radio data collected over three fixed links at Durham University. For most rain events, the signal level tends to
follow the trend of rainfall, and rain attenuation rises as the rain intensity increases. Predicted attenuation values
from the DSD and the ITU models have been analyzed and compared to measured data at 22.84 and 77.54GHz
for a direct and a side link over 36m together with a 200m point to point link at 77.125GHz. The DSD proves
that rainfall rates are insufficient to estimate rain attenuation values as other
factors are involved such as the raindrops shape and distribution, number of
dominant drops, diameter, and velocity. The drops diameter in the range of
0.1–2mm contributes to the overall attenuation within all frequencies for
particle speeds in the range between 1 and 5m/s. Larger raindrops contribute
irregularly to the attenuation when the rainfall velocity and particle speed is
in the range of (5–10m/s). Measurement results using the longterm meas
urements over the shortrange fixed links indicate that using recommenda
tion ITUR P.53018 without the restricted distance factor recommended in
P.53017 gives attenuation values closer to the measured values. In future
work, further measurements will be analyzed to better investigate the path
reduction factor value with specific consideration of the spatial homoge
neity of precipitation along the path and of any additional effects inducing
supplementary attenuation on the link such as wet antenna and/or due to the
system, which, as the path length decreases, are expected to be critical for
Figure 16. Calculated attenuation versus raindrop diameter in mm for (a) 25.84GHz and (b) 77.54GHz.
Figure 17. Geometry of rain scatter.
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the isolation of the impact solely due to rain. In this paper a simplified approach of raindrops induced scattering
was introduced to minimize the calculation complexity. Data indicate that the scattering cross section varies over
a wide range between 0° and 180° and symmetrically to 360°. Further work is ongoing to study the interference
between crosspolarization links, along with an evaluation of other precipitation effects such as snow grains,
snowflakes, hail, ice pellets, graupel, wind, and humidity on rain attenuation and scattering.
Figure 18. The scattering cross section calculated as a function of the scattering angle: (a) 25.84GHz and (b) 77.54GHz.
Figure 19. Normalized scattering phase function P(θ) at: (a) 25.84GHz and (b) 77.54GHz.
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Data Availability Statement
The data that support the findings of this study will be submitted to the ITUR Study Group 3 data bank (DBSG
3) and availability is subject to ITUR policy: https://www.itu.int/en/ITUR/studygroups/rsg3/Pages/dtbank
dbsg3.aspx.
References
Åsen, W., & Gibbins, C. J. (2002). A comparison of rain attenuation and drop size distributions measured in Chilbolton and Singapore. Radio
Science, 37(3). 61–615. https://doi.org/10.1029/2000RS002613
Atlas, D., Srivastava, R. C., & Sekhon, R. S. (1973). Doppler radar characteristics of precipitation at vertical incidence. Reviews of Geophysics
and Space Physics, 11(1), 1–35. https://doi.org/10.1029/RG011i001p00001
Atlas, D., & Ulbrich, C. W. (1977). Path and areaintegrated rainfall measurement by microwave attenuation in the 1–3 cm band. Journal of
Applied Meteorology, 16(20), 1322–1331. https://doi.org/10.1175/15200450(1977)016<1322:PAAIRM>2.0.CO;2
Aydin, K., & Daisley, S. E. A. (2002). Relationships between rainfall rate and 35GHz attenuation and differential attenuation: Modeling the
effects of raindrop size distribution, canting, and oscillation. IEEE Transactions on Geoscience and Remote Sensing, 40(11), 2343–2352.
https://doi.org/10.1109/TGRS.2002.805073
Bohren, C., & Huffman, D. R. (1998). Absorption and scattering of light by small particles. Wiley Science Paperback Series.
Brazda, V., & Fiser, O. (2015). Comparison of exact and approximate FSO rain attenuation formulas based on actual DSD. In 2015 9th European
Conference on Antennas and Propagation (EUCAP) (pp. 1–5). IEEE.
Budalal, A. A. H., Islam, M. R., Abdullah, K., & Abdul Rahman, T. (2020). Modification of distance factor in rain attenuation prediction
for shortrange millimeterwave links. IEEE Antennas and Wireless Propagation Letters, 19(6), 1027–1031. https://doi.org/10.1109/
LAWP.2020.2987462
Capsoni, C., & D’Amico, M. (1991). Prediction of effective transmission loss by hydrometeor scatter through a 3D rain cell model. In 1991 7th
International Conference on Antennas and Propagation, ICAP 91 (IEE) (Vol. 1, pp. 238–241).
Capsoni, C., Luini, L., & D’Amico, M. (2010). The MultiEXCELL model for the prediction of the radio interference due to hydrometeor scatter
ing. In Proceedings of the 4th European Conference on Antennas and Propagation (pp. 1–5). IEEE.
Carlton, W. U. (1983). Natural variations in the analytical form of the raindrop size distribution. Journal of Climate and Applied Meteorology,
22(10), 1764–1775. https://doi.org/10.1175/15200450(1983)022<1764:NVITAF>2.0.CO;2
Chandra Kestwal, M., Joshi, S., & Singh Garia, L. (2014). Prediction of rain attenuation and impact of rain in wave propagation at micro
wave frequency for tropical region (Uttarakhand, India). International Journal of Microwave Science and Technology, 2014, 1–6. https://doi.
org/10.1155/2014/958498
Crane, R. K. (2003). Propagation handbook for wireless communication system design (1st ed.). CRC Press.
Durgin, G. D. (2000). Theory of stochastic local area channel modeling for wireless communications (Doctoral dissertation). Retrieved from
http://hdl.handle.net/10919/29843
Han, C., & Duan, S. (2019). Impact of atmospheric parameters on the propagated signal power of millimeterwave bands based on real measure
ment data. IEEE Access, 7, 113626–113641. https://doi.org/10.1109/ACCESS.2019.2933025
Hemadeh, I. A., Satyanarayana, K., ElHajjar, M., & Hanzo, L. (2017). Millimeterwave communications: Physical channel models, design
considerations, antenna constructions, and linkbudget. IEEE Communications Surveys & Tutorials, 20(2), 870–913. https://doi.org/10.1109/
COMST.2017.2783541
Figure 20. Example of E band bistatic scattering cross section at two different rainfall: (a) 16mm/hr and (b) 39mm/hr.
Acknowledgments
The authors would like to acknowledge
the support of WaveComBE project,
under Horizon 2020 research and
innovation program with grant agreement
No. 766231, the support from Ofcom
under grant No. 1362, and the technicians
at Durham University for the setup of
the weather station and fixed links. The
200m radio link was set up with the
support of Filtronic who provided the
RF heads. The authors would also like
to acknowledge Mohamed Abdulali at
Durham University for developing C code
for automatic data acquisition.
Radio Science
ZAHID AND SALOUS
10.1029/2021RS007307
21 of 21
Huang, J., Cao, Y., Raimundo, X., Cheema, A., & Salous, S. (2019). Rain statistics investigation and rain attenuation modeling for millimeter
wave shortrange fixed links. IEEE Access, 7, 156110–156120. https://doi.org/10.1109/access.2019.2949437
ITUWRC. (2019). Final acts of the World Radiocommunication Conference (WRC19) (recommendation). International Telecommunication
Union (ITU).
Jürg, J., & Enrico, G. G. (1978). Shapes of raindrop size distributions. Journal of Applied Meteorology, 17(7), 1054–1061. https://doi.org/10.11
75/15200450(1978)017<1054:sorsd>2.0.co;2
Juttula, H., Kokkoniemi, J., Lehtomaki, J., Makynen, A., & Juntti, M. (2019). Rain induced cochannel interference at 60 Ghz
and 300 Ghz frequencies. In 2019 IEEE International Conference on Communications workshops (ICC workshops) (pp. 1–5).
https://doi.org/10.1109/ICCW.2019.8756966
Kim, J. H., Jung, M.W., Yoon, Y. K., & Chong, Y. J. (2013). The measurements of rain attenuation for terrestrial link at millimeter wave. In 2013
International Conference on ICT Convergence (ICTC) (pp. 848–849). https://doi.org/10.1109/ICTC.2013.6675497
Kumar, L. S., Lee, Y. H., & Ong, J. T. (2010). Truncated gamma drop size distribution models for rain attenuation in Singapore. IEEE Transac
tions on Antennas and Propagation, 58(4), 1325–1335. https://doi.org/10.1109/TAP.2010.2042027
Kvicera, V., Grabner, M., & Fiser, O. (2011). 4year hydrometeor attenuation statistics obtained at 93 Ghz on an 850 m terrestrial path. In
Proceedings of the 5th European Conference on Antennas and Propagation (EUCAP) (pp. 2501–2503). IEEE.
Lam, H. Y., Luini, L., Din, J., Alhilali, M. J., Jong, S. L., & Cuervo, F. (2017). Impact of rain attenuation on 5G millimeter wave communication
systems in equatorial Malaysia investigated through disdrometer data. In 2017 11th European Conference on Antennas and Propagation
(EUCAP) (pp. 1793–1797). https://doi.org/10.23919/EuCAP.2017.7928616
Luini, L., Roveda, G., Zaffaroni, M., Costa, M., & Riva, C. (2018). EM wave propagation experiment at E band and D band for 5G wireless
systems: Preliminary results. In 12th European Conference on Antennas and Propagation (EUCAP 2018) (pp. 1–5). https://doi.org/10.1049/
cp.2018.0378
Marshall, J. S., & Palmer, W. M. (1948). The distribution of raindrops with size. Journal of the Atmospheric Sciences, 5(4), 165–166. https://doi.
org/10.1175/15200469(1948)005<0165:TDORWS>2.0.CO;2
Mora Navarro, K. M., & Costa, E. (2016). Interference between millimeter wave radio links due to rain scatter. In 2016 USNCURSI Radio
Science Meeting (pp. 115–116). https://doi.org/10.1109/USNCURSI.2016.7588539
Nabangala, M. (2016). Determination of rainfall parameters for specific attenuation due to rain for different integration times for terrestrial line
ofsight links in South Africa (PhD thesis). University of KwaZuluNatal.
Nazar Elfadil, M., Zia, N., Salam, M. A., & Rao, J. (2005). Microwave attenuation studies due to rain for communication links operating in
Malaysia. Georgian Electronic Scientific Journal: Computer Science and Telecommunications, 5(1), 9–17.
Olsen, R. L., Rogers, D. V., & Hodge, D. B. (1978). The aR
b relation in the calculation of rain attenuation. IEEE Transactions on Antennas and
Propagation, 26(2), 318–329. https://doi.org/10.1109/TAP.1978.1141845
Olsen, R. L., Rogers, D. V., Hulays, R. A., & Kharadly, M. M. Z. (1993). Interference due to hydrometeor scatter on satellite communication links.
Proceedings of the IEEE, 81(6), 914–9229. https://doi.org/10.1109/5.257688
Recommendation ITUR P.8383. (2005). Specific attenuation model for rain for use in prediction methods (Technical Report). ITU.
Salous, S., Cao, Y., & Raimundo, X. (2019). Impact of precipitation on millimetre wave fixed links. In 2019 13th European Conference on Anten
nas and Propagation (EUCAP) (pp. 1–4). IEEE.
Sander, J. (1975). Rain attenuation of millimeter waves at λ = 5.77, 3.3, and 2 mm. IEEE Transactions on Antennas and Propagation, 23(2),
213–220. https://doi.org/10.1109/TAP.1975.1141059
Saurabh, D., Animesh, M., & Ashish, S. (2010). Rain attenuation modeling in the 10–100 GHz frequency using drop size distributions for
different climatic zones in tropical India. Progress in Electromagnetics Research B, 25(25), 211–224. https://doi.org/10.2528/PIERB10072707
Schiebener, P., Straub, E. J., Levelt Sengers, J. M. H., & Gallagher, J. S. (1990). Refractive index of water and steam as function of wavelength,
temperature and density. Journal of Physical and Chemical Reference Data, 19(3), 677–717. https://doi.org/10.1063/1.555859
Schleiss, M., Rieckermann, J., & Berne, A. (2013). Quantification and modeling of wetantenna attenuation for commercial microwave links.
IEEE Transactions on Geoscience and Remote Sensing, 10(5), 1195–1199. https://doi.org/10.1109/lgrs.2012.2236074
Schönhuber, M., Plimon, K., & Thurai, M. (2015). Statistical significance of specific rain attenuation dependence on geographic and climatic
conditions. In 2015 9th European Conference on Antennas and Propagation (EUCAP) (pp. 1–5). IEEE.
Scientific, C. (2015). Pws100 present weather sensor [Computer software manual]. Campbell Scientific.
Setijadi, E., Matsushima, A., Tanaka, N., Hendrantoro, G., & Elektro, J. T. (2009). Effect of temperature and multiple scattering on rain attenuation
of electromagnetic waves by a simple spherical model. Progress in Electromagnetics Research, 339–354, 339–354. https://doi.org/10.2528/
PIER09102609
Shrestha, S., & Choi, D.Y. (2017). Rain attenuation statistics over millimeter wave bands in South Korea. Journal of Atmospheric and SolarTer
restrial Physics, 152, 1–10. https://doi.org/10.1016/j.jastp.2016.11.004
Surco Espejo, T. M., & Costa, E. (2017). Scattering due to rain in Brazil for millimeter waves. In 2017 SBMO/IEEE MTTS International Micro
wave and Optoelectronics Conference (IMOC) (pp. 1–5). https://doi.org/10.1109/IMOC.2017.8121140
Tamošinait, M., Tamošinas, S., & Žilinskas, M. (2011). Atmospheric attenuation due to humidity. In P. V.Zhurbenko (Ed.), Electromagnetic
waves (pp. 158–169). In Tech.
Townsend, A. J., Watson, R. J., & Hodges, D. D. (2009). Analysis of the variability in the raindrop size distribution and its effect on attenuation
at 20–40 GHz. IEEE Antennas and Wireless Propagation Letters, 8(2), 1210–1213. https://doi.org/10.1109/LAWP.2009.2035724
Tuhina, H., Adhikari, A., & Maitra, A. (2018). Rain attenuation studies from radiometric and rain DSD measurements at two tropical locations.
Journal of Atmospheric and SolarTerrestrial Physics, 170, 11–20. https://doi.org/10.1016/j.jastp.2018.02.004
Zahid, O., Huang, J., & Salous, S. (2020). Long term rain attenuation measurements at millimeter wave bands for direct and side shortrange
fixed links. In 2020 33rd General Assembly and Scientific Symposium of the International Union of Radio Science (pp. 1–4). https://doi.
org/10.23919/URSIGASS49373.2020.9232024