Long Term Rain Attenuation Measurement for short‐range mmWave Fixed Link using DSD and ITU‐R Prediction Models

Abstract

Several millimeter Wave (mmWave) bands, which suffer from rain attenuation, were identified in the World Radiocommunication Conference 2019 (WRC‐19) for fifth generation (5G) radio networks. In this paper, long‐term attenuation is measured over typical building to building radio links in the built environment, which constitute two 36 m links along a direct link and an indirect side link at 25.84 and 77.54 GHz and a 200 m link at 77.125 GHz. 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 4 mm 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 ITU‐R P.530‐17 is shown not to be suitable for short‐range fixed links as it excessively underestimates attenuation.

Full text

1. Introduction
The World Radiocommunication Conference 2019 (ITU-WRC,2019) identified several mmWave frequency
bands (24.25–27.5, 37–43.5, 45.5–47, 47.2–48.2, and 66–71GHz) for possible allocation for the International
Mobile Telecommunications (IMT-2020) for 5G applications and 71–81GHz for non-geostationary fixed-satel-
lite services. These higher frequency bands are largely affected by rainfall. The wavelength in the millimeter wave
band ranges from 11mm at 26GHz decreasing to 1mm at 300GHz (Hemadeh etal.,2017), while the diameter
of the raindrops is on the order of 1∼10mm. 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 etal.,2005).
Rain attenuation studies need long-term measurements and analysis over several years (Chandra Kestwal
etal.,2014; Lam etal.,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 long-range line of sight fixed links. In Kvicera etal.(2011), a fixed link, which oper-
ates at 93GHz over 850m is reported where the predicted attenuation using the ITU-R model provides a lower
estimate than the measurements for high attenuation levels. In Schleiss etal.(2013), a link was set up at 38GHz
over 1.85km with the aim to study the rain attenuation and the wet antenna effect where 2.5dB maximum wet
antenna effect was found. Results in Luini etal.(2018) provide reliable rain attenuation values compared to the
DSD at 73, 83, 148, and 156GHz with a link distance of 325m. Results in Kim etal.(2013) show a significant
Abstract Several millimeter Wave (mmWave) bands, which suffer from rain attenuation, were identified in
the World Radiocommunication Conference 2019 (WRC-19) for fifth generation (5G) radio networks. In this
paper, long-term attenuation is measured over typical building to building radio links in the built environment,
which constitute two 36m links along a direct link and an indirect side link at 25.84 and 77.54GHz and a
200m link at 77.125GHz. 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 4mm 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 ITU-R P.530-17 is shown not to be suitable for short-range 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.
Long-Term Rain Attenuation Measurement for Short-Range
mmWave Fixed Link Using DSD and ITU-R 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
• Long-term 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
short-range mmWave fixed link using
DSD and ITU-R 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 100mm/hr at 73 and 83GHz for 500m
links. In Juttula etal.(2019), the scattering effect and attenuation were reported at 100 and 500m at 60 and
300GHz where the difference between the DSD and the ITU model reaches 5dB.
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 210GHz 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 ITU-R model. In Tuhina etal.(2018), rain attenuation
measurements were conducted for 22GHz, 23GHz, and 31.4/30GHz in a tropical region: Kolkata in India and
Belem in Brazil for 2years. Results show good agreement between the DSD attenuation model and the ITU-R
model for rainfall rate below 100mm/hr, with slight differences below 30mm/hr. In Saurabh etal.(2010), assum-
ing a log-normal distribution for the DSD, both the DSD model and the ITU-R model gave similar results for
frequencies below 30GHz with a maximum rainfall rate up to 30mm/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 25.84GHz (K band)
and 77.54GHz, over two 36m 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 77.125GHz (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 ITU-R P.530-17 maximum distance factor restriction of 2.5 for short-range 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 Section2 together with rain
statistics and raindrop distribution for the measurement period, followed in Section3 by a description of the fixed
link measurement setup for measuring attenuation and the ITU and the DSD prediction models. In Section4,
measurement results using the short-range fixed link data sets and the PWS100 disdrometer precipitation data are
presented and compared for discussion; followed by raindrops induced scattering analyses in Section5. Conclu-
sions and ongoing work are presented in Section6.
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 Figure1a. 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 Table1. The PWS100 disdrometer covers a measurement area of 40cm
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 Figure1b over an internet protocol address once every minute.
Figure2a illustrates the rainfall intensity statistics between October 2020 and January 2021, with most of the
measured rain intensity being under 20mm/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≤1mm/hr), Moderate (1mm/
hr<R≤4mm/hr), heavy (4mm/hr<R≤16mm/hr), very heavy (16mm/hr<R≤50mm/hr), and torrential
rainfall (R>50mm/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 30mm with 0.1mm 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=40cm
2 is the measurement surface of the laser beam of the PWS100 disdrometer, t=60s 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 20mm/hr.
2. For each long-term 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 30mm).
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 0.1–30mm
Size accuracy 5% (for particles >0.3mm)
Particle velocity 0.16–30m/s
Velocity accuracy 5% (for particles >0.3mm)
Types of precipitation Drizzle, rain, snow grains, snowflakes, hail, ice pellets, graupel, and mixed
Rain rate intensity range 0–400mm/hr
Rain total accuracy Typically 10%
Table 1
Specifications of the PWS100 Weather Station

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3. The (long-term mean) drop count in each bin size class is to be divided by the measuring area (of the instru-
ment 40cm
2) and by the column height (integration time multiplied by the mean fall velocity of this bin's
mean diameter). Thus the (long-term 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). Figure2b reports the measured
DSD where the peak DSD occurs at around a raindrop diameter of 0.8–1.2mm 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 etal.(2019), Huang etal.(2019), and Zahid etal.(2020)
used for collecting fixed link data for real rain attenuation investigation is shown in Figure3. The first two links
are set up over a direct path and side path over 36m links and located on the rooftop of the Engineering depart-
ment at Durham University (Latitude: 54.767396, Longitude: −1.570390) at 65m 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 77.125GHz is installed between Durham University Library roof
(Latitude: 54.768167, Longitude: −1.573418) at 62m of sea level and the engineering department roof which
gives a point to point 200m path. The Tx/Rx for the 200m link are commercial transceivers (Filtronic Orpheus
E-band modules) shown in Figure3d. The transceiver groups the Orpheus interface board, a NI USB-8451, and
an electronic circuit power to supply the module. Once mated, the module can be powered up using standard lab
PSUs (−5V, +2.8V+3.3V, and +5.1V+18V). For the control of the module, a NI USB-8451 is used with
the Filtronic Orpheus GUI software. The 200m point-to-point 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 1s every minute to relate with
the rain rate data. The sampling rate of the RF link is 80MHz and the attenuation per minute is an average of 1s,
as the baseband signal frequency is at 4, 12, and 31MHz, 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
ITU-R P.838-3 model and the DSD model, which use frequency parameters, wavelength, water permittivity, and
raindrop distributions (Shrestha & Choi,2017).
3.2.1. ITU-R P.838-3 Model
This model was validated theoretically and experimentally and is recommended for the frequency range from 1
to 1,000GHz. It is given by:
Figure 3. Fixed link radio frequency heads of the measurement setup, (a) transmitter box for 36m link, (b) receiver box for direct 36m link, (c) receiver box for side
36m link, (d) transceiver Filtronic box for 200m 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 look-up table of the values k and
α for different frequencies for both the vertical and horizontal polarization
(Recommendation ITU-R P.838-3,2005) are noted in Table2.
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 ITU-R P.530-17 as

=
1
0.4770.6330.073
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 1min). In ITU-R P.530-17
it was recommended to use a maximum value of r equal to 2.5 while in the updated recommendation P.530-18,
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 short-range 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 Equation6 given in Atlas and
Ulbrich(1977) and Atlas etal.(1973) for the calculation of particle speed. The DSD can also be calculated using
theoretical and analytical models such as: the Marshall-Palmer (M-P) 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 Equation7.

()=
{
3.780.67

,
<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 etal.,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)
26GHz 77GHz
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 Table3 for each frequency band. Figure4 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. Figure5 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 5mm 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 2mm.
Because previous data sets in the paper we published in Huang etal.(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, long-term measurement disdrometer meteoro-
logical data from the PWS100 of 3years are now available. The data are being submitted and used for the ITU-R
Study Group 3 data sets bank.
4. Discussion of Measurement Results
This section presents the calculated attenuation at 25.84GHz (K band) and 77.54 GHz (E band) over the two
36m links between October 2020 and January 2021 and the 77.125GHz band over the 200m 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 36m links is 82.55%
and 70.47% for the 200m link. Vertical to vertical polarization, which is
common to all the three links is selected for the two bands over 252hr 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 218hr of light
rainfall data, 32hr of moderate rainfall data, 3.4hr of heavy rainfall data, and
around 25min 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
26GHz 5.41+2.78i
77GHz 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 Equation5
using the disdrometer data and the ITU-R prediction model given in Equa-
tion2. 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 Figure4, the size parameter X is 5 and 16 for
26GHz, and 77GHz, 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.
Equations5 and2 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 200m. This factor was mainly derived from
long-range measurements. Using the ITU recommended maximum value of 2.5 raises the question regarding
its application for short-range links less than 1km (Budalal etal.,2020; Huang etal.,2019; Olsen etal.,1978).
Hence, the suitability of the maximum r factor is further investigated for the current short-range links.
Figures6 and7 show the calculated attenuation for the K and E bands using the ITU and DSD models for the
36 and 200m, 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 4dB 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
4dB recorded for maximum rainfall rate of 5mm/hr and 20mm/hr, respectively, for the direct E band link while
a maximum of 6dB loss for 20mm/hr for the 200m link.
4.2. Measured Attenuation
The results of the measured attenuation as a function of rainfall up to 25mm/hr are presented. Figures8, 10,
and11 show the received signal mapped against the rain intensity and snow particles for the three links: direct
36m, 200m, and side 36m, 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 Figure9. This effect should be
differentiated from the measurement by eliminating from the analysis the icing events. Compared to the predict-
ed-calculated attenuation as shown in Figure12 (samples of dominant rainfall events through the measurement
period and matched attenuation) the measured attenuation for the direct 36m link during rain events without
snow and before mid of December 2020 shows an average of 0.8–1.5dB higher attenuation for heavy and very
heavy rainfall at 26GHz, while a difference of 0.4–1.3dB at 77GHz. However, higher losses up to 9.5dB 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 0.5–2.3dB as the side link depends on non-Line-of-Sight (NLOS) reflected paths to receive the
signal. Thus, the measured attenuation is affected by raindrops scattering mechanism. The K band side link exhib-
its 1.7dB difference with respect to the predicted rain attenuation for light, moderate, and heavy rainfall events.
Measured rain attenuation for the 77GHz 200m link agrees well and follows the predicted attenuation for most
rainfall events where 6dB loss has been recorded for a maximum rain intensity of 20mm/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 11mm/hr was recorded on
13 October 2020 at 10:17 and the 31 October 2020 at 12:58 result in 1.56 and 2.28dB at 77GHz, 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 36m link.

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etal.,2015; Townsend etal.,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 etal., 2011) where the
humidity continues its existence in the atmosphere in sunny clear days and temperature variability in space
and time (Setijadi etal.,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 10hr (moderate rainfall events). The signal takes more time to recover after this
long-term rain event.
5. The former method inherently assuming a constant analytical DSD for the derivation of the k and alpha coef-
ficients in Equation2.
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 3mm contribute to
the maximum attenuation which is λ/2 at 77GHz as shown in Figure16. This indicates that the number of domi-
nant raindrops has a significant influence on the specific attenuation, which can result with up to 2dB difference
at the same rainfall type within two different dates at the range of 0.1–2mm drop size.
Figure 7. Predicted rain attenuation for E band over dominant recorded rainy days between November 2020 and January 2021 for 200m link.

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Figure 8. Long-term rain attenuation measurement for direct 36m 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 Figure13 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 77GHz for the direct, side, and Filtronic
links. A notable difference occurs at the lower frequency band at 26GHz between the measured and the theoret-
ical values for the side link where the measured attenuation has larger values.
In addition, mmWave short-range fixed links require accuracy and reliability of prediction. The ITU-R P.530-17
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. Figures14 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 1min 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
36m and the 200m links.
To further examine the impact of other rain parameters on the link, Figure16 presents samples of measured
attenuation versus raindrop diameter from 0.1 to 7mm 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 4mm. The analyzed
results indicate that very heavy and moderate rainfall rate lead to higher attenuation values for both frequencies
Figure 10. Long-term rain attenuation measurement for point to point 200m 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 2mm). Similar to the analyses in Figure6 in the previous section and
Figure16, when the particle speed is 9–10m/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 20mm/hr where raindrops with the
size of 1–3mm lead up to 4.5dB higher attenuation. A diameter in the range of 4–7mm contributes occasionally
to the attenuation up to 2dB 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 5mm/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 etal.,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. Long-term rain attenuation measurement for side 36m 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 36m link and for E band at Filtronic 200 link: (a) E band 36m direct link, (b) K band 36m direct link, (c) E band 36m side
link, (d) K band 36m side link, and (e) E band 200m link.

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Figure 13. CDFs of the measured and the predicted rain attenuation for the three links: (a) K band 36m direct link, (b) E band 36m direct link, (c) K band 36m side
link, (d) E band 36m side link, and (e) E band 200m Filtronic link.

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depends on frequency and temperature. These parameters identify the scattering modeling which can be divided
into single-scattering or multiple-scattering. 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 etal., 2010) is
presented in Figure17.
Spherical raindrops, Mie theory, and bistatic radar equation given in Capsoni etal. (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 36m direct link, (b) E band 36m side link, and (c) E band 200m 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)
Figure18 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 36m direct link and (b) K band 36m 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. Figure19
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 77GHz band is considerably forward oriented
pattern while at 26GHz 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.
Figure20 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 39mm/hr. The rain-induced 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
10mm/hr and considerable raindrops diameter above 1mm.
6. Conclusions
Rain attenuation for millimeter wave 5G fixed link applications was investigated using long-term 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 77.54GHz
for a direct and a side link over 36m together with a 200m point to point link at 77.125GHz. 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
0.1–2mm contributes to the overall attenuation within all frequencies for
particle speeds in the range between 1 and 5m/s. Larger raindrops contribute
irregularly to the attenuation when the rainfall velocity and particle speed is
in the range of (5–10m/s). Measurement results using the long-term meas-
urements over the short-range fixed links indicate that using recommenda-
tion ITU-R P.530-18 without the restricted distance factor recommended in
P.530-17 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) 25.84GHz and (b) 77.54GHz.
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 cross-polarization 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) 25.84GHz and (b) 77.54GHz.
Figure 19. Normalized scattering phase function P(θ) at: (a) 25.84GHz and (b) 77.54GHz.

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Data Availability Statement
The data that support the findings of this study will be submitted to the ITU-R Study Group 3 data bank (DBSG-
3) and availability is subject to ITU-R policy: https://www.itu.int/en/ITU-R/study-groups/rsg3/Pages/dtbank-
dbsg3.aspx.
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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
200m 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.

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