ETSI TR 104 140 V1.1.1 (2025-05)

TECHNICAL REPORT
Propagation measurement and modelling for
PtP radio links in the E, W and D bands

2 ETSI TR 104 140 V1.1.1 (2025-05)

Reference
DTR/ATTMTMmWT-0030
Keywords
channel modelling, millimetre wave, mWT,
propagation
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3 ETSI TR 104 140 V1.1.1 (2025-05)
Contents
Intellectual Property Rights . 4
Foreword . 4
Modal verbs terminology . 4
Executive summary . 4
Introduction . 5
1 Scope . 7
2 References . 7
2.1 Normative references . 7
2.2 Informative references . 7
3 Definition of terms, symbols and abbreviations . 8
3.1 Terms . 8
3.2 Symbols . 8
3.3 Abbreviations . 9
4 Propagation features at mm-wave . 9
4.1 Tropospheric attenuation . 9
4.2 Gaseous attenuation . 9
4.3 Fog attenuation . 10
4.4 Rain attenuation . 11
5 Rain attenuation prediction: event-based analysis . 14
5.0 Introductory concepts . 14
5.1 Wet antenna effect . 15
5.2 Comparison of models . 16
6 Rain attenuation prediction: statistical analysis . 19
6.0 Introductory concepts . 19
6.1 Path reduction factor . 20
6.2 The SC EXCELL model . 23
6.3 Comparison of models . 24
7 Field trial measurements . 26
8 Implications to radio link budget evaluation . 28
9 Conclusion . 28
History . 30

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4 ETSI TR 104 140 V1.1.1 (2025-05)
Intellectual Property Rights
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Foreword
This Technical Report (TR) has been produced by ETSI Technical Committee Access, Terminals, Transmission and
Multiplexing (ATTM).
Modal verbs terminology
In the present document "should", "should not", "may", "need not", "will", "will not", "can" and "cannot" are to be
interpreted as described in clause 3.2 of the ETSI Drafting Rules (Verbal forms for the expression of provisions).
"must" and "must not" are NOT allowed in ETSI deliverables except when used in direct citation.
Executive summary
The present document deals with Electro-Magnetic (EM) wave propagation for terrestrial PtP links in the
millimetre-wave (mm-wave) range (30 - 300 GHz), where rain plays the most relevant role since rain drops absorb and
scatter electromagnetic energy inducing significant path losses, due to their size (about 1 - 5 mm) being comparable to
the EM wavelength.
When dealing with attenuation due to rain there are several factors to be considered:
• Specific attenuation due to rain γ (dB/km), which is dependent not only on frequency and rain rate but also on
R
the particular Drop Size Distribution (DSD).
• Total attenuation due to rain along the radio link (dB), which is dependent on the spatial variation of the
specific attenuation along the link.
• Attenuation due to rain but not related to the propagation path (dB), such as the wet antenna effect.
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5 ETSI TR 104 140 V1.1.1 (2025-05)
As for the specific attenuation, several models of DSD have been developed based on both experimental rain data and
analytical models of rain attenuation mechanisms. All the analyses converge on the fact that the DSD model is highly
dependent on the type of rain in the specific rain zone and in the specific season.
Recommendation ITU-R P.838-3 [i.3] is based on the Laws-Parsons drop size distribution model which describes
typical continental temperate rainfall of stratiform kind. When considering a convective type of rain, typical of tropical
regions, a different modelling of DSD is needed and different results would be obtained.
As for the total link attenuation, several models of the path reduction factor have been developed in order to take into
account the spatial inhomogeneity of rain along the link. All models describe a path reduction factor which decreases
below 1 with increasing link length, where the link length is much larger than the length over which the rain rate can be
considered homogeneous. Instead when dealing with short links, below about 1 km, where rain rate can be considered
constant along the path, the path reduction factor should be reasonably slightly less than or equal to 1.
Recommendation ITU-R P.530-18 [i.4] is based on a model which gives a path reduction factor increasing well over 1
with a decreasing link length, which seems to be not physically sound and gives as a consequence an overestimation of
the attenuation due to rain along the link. A proper adaptation of the model limiting the path reduction factor to 1 could
be a good way forward to have a more accurate prediction model for short links.
The wet antenna attenuation, due to the thin water film deposited by rain over the antenna of the radio equipment, is a
cause of attenuation that should be separated from the propagation loss due to rain along the link. This effect could be
the cause of some measurements apparently giving a path reduction factor much higher than unity with short links.
Finally it is important noting that there is no physical reason why the range of applicability of a terrestrial rain
attenuation prediction model for mmWave systems should be limited to 100 GHz, as it is currently the case in
Recommendation ITU-R P3530-18 [i.4]; as a matter of fact in the mmWave frequency range (30 - 300 GHz) the main
attenuation mechanisms are absorption and Mie scattering and only when going towards higher frequencies, well over
the mmWave range, the geometric optics scattering model becomes valid.
Introduction
The present document deals with Electro-Magnetic (EM) wave propagation at millimetre-wave (mm-wave) for
terrestrial PtP links, with particular consideration of frequencies about and over 100 GHz, in the:
• E (71 - 86 GHz);
• W (92 - 115 GHz); and
• D (130 - 175 GHz) bands.
In this frequency range propagation is subject to several atmospheric effects induced by:
• Gases (mainly oxygen and water vapour).
• Suspended water droplets (fog).
• Hydrometeors (rain, snow, hail).
Among them, at frequencies higher than 10 GHz rain plays the most relevant role since rain drops absorb and scatter
electromagnetic energy, thus inducing significant path losses; this effect becomes more and more relevant as long as the
wavelength is comparable to the rain drop size (about 1 - 5 mm), in particular in the mm-wave part of the EM spectrum
(30 - 300 GHz).
That is why it is of paramount importance to investigate atmospheric effects impairing millimeter-waves, specifically
rain attenuation, which is greatly dependent on the operational frequency, on the rain rate and on the rain drop
dimensions, described by the Drop Size Distribution (DSD).
As a matter of fact, there are two ITU-R Recommendations dealing with rain attenuation effects:
• Recommendation ITU-R P.838-3 [i.3], which provides specific attenuation as a function of the rain rate and
operational frequency.
• Recommendation ITU-R P.530-18 [i.4], which presents a rain attenuation model for terrestrial links.
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6 ETSI TR 104 140 V1.1.1 (2025-05)
Both theoretical analysis and field measurements highlight the importance of considering the microphysics of rain when
predicting specific attenuation due to rain, in particular the DSD that is function of the rain type and of the rain zone.
Moreover when considering short radio links (in the order of a few hundred meters and up to about 1 km), which would
be typical with systems at D band, a proper evaluation of the spatial variation of rain rate along the link length should be
performed; the effective path length over which the rain rate can be considered uniform is given by the link length
multiplied by the path reduction factor and is highly dependent on the rain rate; in case of high rain rate, typical of
convective events, the effective path length can be expected to be small, whilst for low rain rate, typical of stratiform
events, the effective path length would tend to be large.
Both theoretical analysis and field measurements highlight that in case of short radio links (less than 1 km) the path
reduction factor should be less than or equal to 1, according to the rain rate; this is not the case for the model currently
adopted in Recommendation ITU-R P.530-18 [i.4].
Finally it is important noting that there is no physical reason why the range of applicability of a terrestrial rain
attenuation prediction model for mmWave systems should be limited to 100 GHz, as it is currently the case in
Recommendation ITU-R P.530-18 [i.4].
The present document is structured in the following clauses:
• Clause 4 deals with the different atmospheric propagation phenomena impacting EM waves.
• Clause 5 deals with rain attenuation prediction based on the availability of rain data time series (event-based
analysis), considering the relevance of Drop Size Distribution in determining the specific attenuation due to
rain; it deals also with wet antenna attenuation.
• Clause 6 deals with rain attenuation prediction based on long term rain data collection (statistical analysis),
considering different empirical and analytical models and the relevance of path reduction factor with short
links.
• Clause 7 gives some information on measurements from field trials.
• Clause 8 summarizes some implications for link budget estimation.

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7 ETSI TR 104 140 V1.1.1 (2025-05)
1 Scope
The present document provides information about electromagnetic propagation at millimetre wave, considering the
available models, both derived from physical analysis and from real data fitting and comparing them with
measurements.
2 References
2.1 Normative references
Normative references are not applicable in the present document.
2.2 Informative references
References are either specific (identified by date of publication and/or edition number or version number) or
non-specific. For specific references, only the cited version applies. For non-specific references, the latest version of the
referenced document (including any amendments) applies.
NOTE: While any hyperlinks included in this clause were valid at the time of publication, ETSI cannot guarantee
their long term validity.
The following referenced documents are not necessary for the application of the present document but they assist the
user with regard to a particular subject area.
[i.1] Recommendation ITU-R P.676-12 (2019): "Attenuation by atmospheric gases and related effects".
[i.2] Recommendation ITU-R P.840-7 (2017): "Attenuation due to clouds and fog".
[i.3] Recommendation ITU-R P.838-3 (2005): "Specific Attenuation Model for Rain for Use in
Prediction Methods".
[i.4] Recommendation ITU-R P.530-18 (2021): "Propagation data and prediction methods required for
the design of terrestrial line-of-sight systems".
[i.5] 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". Proceeding of
EuCAP 2018, 9-13 April 2018, pp. 1-5, London, UK.
[i.6] Luini, L., Roveda, G., Zaffaroni, M., Costa, M., Riva, C. (2020): "The Impact of Rain on Short
E-band Radio Links for 5G Mobile Systems: Experimental Results and Prediction Models".
TM
IEEE Transactions on Antennas and Propagation, vol. 68, no. 4, Page(s): 3124-3134,
April 2020.
[i.7] Lin, S. H. (1977): "National Long Term Rain Statistics and Empirical Calculation of 11 GHz
Microwave Rain Attenuation". Bell Syst. Tech. J., 56, 1581–1604.
[i.8] H. J. Liebe, G. A. Hufford, M. G. Cotton, 1993: "Propagation modelling of moist air and
nd
suspended water/ice particles at frequencies below 1000 GHz", in Proc. AGARD 52 Spec.
Meeting EM Wave Propag.
[i.9] D. Ahrens, 1994: "Meteorology Today: an introduction to weather, climate and the environment",
th
9 edition Brooks/Cole, Belmont.
[i.10] E. J. McCartney: "Optics of the Atmosphere: Scattering by Molecules and Particles", New York:
Wiley, 1976.
[i.11] L. Luini, C. Capsoni: "A Unified Model for the Prediction of Spatial and Temporal Rainfall Rate
TM
Statistics", IEEE Transactions on Antennas and Propagation, vol. 61, no. 10, Page(s):
5249 - 5254, October 2013.
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8 ETSI TR 104 140 V1.1.1 (2025-05)
[i.12] T. Oguchi, 1983: "Electromagnetic wave propagation and scattering in rain and other
TM
hydrometeors", Proc. IEEE , vol. 71, pp. 1029-1077.
[i.13] H.Y. Lam, L. Luini, J. Din, C. Capsoni, A. D. Panagopoulos, 2012: "Investigation of Rain
TM
Attenuation in Equatorial Kuala Lumpur", IEEE Antennas and Wireless Propagation Letters,
volume 11, Page(s): 1002-1005.
[i.14] M. M. Z. Kharadly, Robert Ross: "Effect of Wet Antenna Attenuation on Propagation Data
TM
Statistics", IEEE Transactions on Antennas and Propagation, Vol. 49, No. 8, Page(s):
1183-1191, August 2001.
[i.15] M. Thurai, V. N. Bringi, A. B. Manić, N. J. Šekeljić, B. M. Notaroš, 2014: "Investigating raindrop
shapes, oscillation modes, and implications for radio wave propagation", Radio Sci., 49, 921-932.
[i.16] R. Gunn and G. D. Kinzer: "The terminal velocity of fall for water droplets in stagnant air",
J. Atmos. Sci., vol. 6, no. 4, pp. 243–248, 1949.
[i.17] M. Rashid, Jafri Din: "Effects of reduction factor on rain attenuation predictions over millimeter-
wave links for 5G applications", Bulletin of Electrical Engineering and Informatics, Vol. 9, No. 5,
October 2020, pp. 1907~1915.
[i.18] L. Luini and C. Capsoni: "The SC EXCELL model for prediction of rain attenuation on terrestrial
radio links," Electron. Lett., vol. 49, no. 4, pp. 307–308, Feb. 2013.
[i.19] A. Musthafa, L. Luini, C. Riva, S, Livieratos, G. Roveda: "A Long-Term Experimental
Investigation on the Impact of Rainfall on Short 6G D-Band Links", Radio Science, May 2023.
[i.20] Laws J.O., Parsons D.A.: "The relation of raindrop-size to intensity", Trans. AGU.
[i.21] Xin Zhang, Zhenwei Zhao, Zhensen Wu, Leke Lin, Changsheng Lu, Mingchen Sun, Qinglin Zhu:
"Rain attenuation prediction model for terrestrial links incorporating wet antenna effects",
IET Microwaves, Antennas & Propagation 2023; 1–8.
[i.22] Olsen, R., Rogers, D., Hodge, D.: "The aRb relation in the calculation of rain attenuation".
TM
IEEE Trans. Antennas Propagat. 26(2), 318–329 (1978). ®
[i.23] Ericsson Microwave outlook report 2023.
[i.24] O. Zahid, S. Salus, Long-Term Rain Attenuation Measurement for Short-Range mmWave Fixed
Link Using DSD and ITU-R Prediction Models, Radio Science, 57, e2021RS007307.
[i.25] A. Maitra, Rain attenuation modeling from measurements of rain drop size distribution in the
TM
Indian region, IEEE Antennas and Wireless propagation letters, January 2005.
[i.26] Recommendation ITU-R P.837-7: "Characteristics of precipitation for propagation modelling".
3 Definition of terms, symbols and abbreviations
3.1 Terms
Void.
3.2 Symbols
Void.
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9 ETSI TR 104 140 V1.1.1 (2025-05)
3.3 Abbreviations
For the purposes of the present document, the following abbreviations apply:
rd
3GPP 3 Generation Partnership Project
th
5G 5 Generation of Mobile Networks
CCDF Complementary Cumulative Distribution Function
DBSG3 Data Base Study Group 3 (ITU-R)
DSD Drop Size Distribution
EHF Extremely High Frequency
NOTE: 30 - 300 GHz range, mm-wave range.
EM ElectroMagnetic
MW MicroWave
P Pressure
PtP Point to Point
RH Relative Humidity
SC EXCELL Stratiform/Convective EXponential CELL
SHF Super High Frequency
NOTE: 3 - 30 GHz range (cm-wave range).
T Temperature
4 Propagation features at mm-wave
4.1 Tropospheric attenuation
The atmosphere is a thermodynamic system containing water in vapor, liquid and solid state, gases and aerosol,
surrounding the Earth up to 100 km. As for the propagation of millimeter-waves and microwaves along terrestrial paths,
only the lower layer close to the Earth surface is of concern. The atmosphere is commonly characterized through
temperature, pressure, relative humidity and density of its main components (gases and water).
4.2 Gaseous attenuation
Oxygen and water vapour are the gaseous components of the atmosphere influencing the electromagnetic wave
propagation in the frequency range from 10 up to 350 GHz. Other gases need to be taken into account only at higher
frequencies (e.g. CO2 for optical wavelengths). The weather condition with no fog is typically referred to as "clear sky"
condition.
The oxygen absorption is mainly due to the resonance of oxygen molecules as magnetic dipoles, which occurs in
specific bands: for example, oxygen attenuation is basically negligible up to 40 GHz, but it becomes important around
50 GHz and is dominant around 60 GHz.
The oxygen concentration depends on the air pressure and temperature. The former is characterized by a decreasing
exponential profile with the height, while the latter is highly influenced by daily, seasonal and geographical variations.
Oxygen absorption increases with the decrease in temperature.
The water vapour absorption, due to the molecular interaction with electromagnetic waves as electric dipole, can be
calculated as the sum of two terms, which are linear and quadratic functions of the water vapour density, respectively.
Water vapour absorption is linked to meteorological parameters like pressure, temperature and water vapour density.
In principle, the procedure to calculate the gaseous attenuation along terrestrial paths consists in two steps:
1) calculation of the specific attenuation due to gases γ (dB/km) at any point along the propagation path;
G
2) calculation of the total path attenuation due to gases A by integration of all the contributions.
G
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In practice, this approach is unfeasible because it would require the knowledge at any time of the complete spatial
distribution along the path of meteorological parameters like air pressure, temperature and gases concentration.
However, as the attenuation due to gases is very stable in space (tens of kilometers) and in time (hours), γ is typically
G
considered to be constant along terrestrial propagation paths, which is more and more true for short links (e.g. less than
1 km). In turn, this implies that the path attenuation can be simply calculated as:
A = γ L
G G
where L (km) is the length of the terrestrial link.
The most acknowledged methodology for the prediction of γ L is named MPM93 and was proposed by Liebe et al. in
G
[i.8]. The model, which is currently adopted in Annex 1 of Recommendation ITU-R P.676-12 [i.1], defines the intensity
and the width of oxygen and water vapor spectral absorption lines in the 1 - 1 000 GHz frequency range. The
contribution of each line, which depends on pressure P, relative humidity RH and temperature T, is summed up to yield
the overall specific attenuation due to gases.
The specific attenuation due to gases, calculated using the Liebe MPM93 model is shown in Figure 1, for the following
standard reference meteorological parameters: T = 15 °C, P = 1 013,25 mbar and water vapor content (which is tightly
linked to RH) ρ = 7,5 g/m .
V
As is clear from the figure, the contribution coming from oxygen is mainly limited to the frequency bands around
60 GHz and 120 GHz, where the specific attenuation can reach values as high as 15 dB/km. On the other hand, the
impact of water vapor is associated to three main absorption peaks (centered approximately around 22, 183 and
325 GHz), but it is also given by a linear term providing, in general, more attenuation than the one induced by oxygen
(see especially the 210 - 310 frequency range).

Figure 1: Specific attenuation due to gases as a function of frequency,
calculated using the Liebe MPM93 model [i.8]
4.3 Fog attenuation
Fog is a suspension of microscopic water droplets (in the order of microns) formed by condensation of the atmospheric
water vapor on the surface of suspended hygroscopic particles, named condensation nuclei. Fog is usually associated
with values of relative humidity close to saturation (100 %).
In meteorology, the term fog is used when the visibility is less than 1 km, whereas mist is an intermediate state where
the relative humidity is above 60 % and the visibility exceeds 1 km. Finally, haze is any suspension of dry solid
particles (smoke, dust, sand, salt, etc.) of microscopic size. Fog, produced by cooling of the air, can be classified into
[i.9]:
• Radiation fog: generated by radiational cooling of the Earth surface that lowers the air temperature enough to
reach saturation. It is usually observed at night during the cold season and in calm wind conditions and it is
typical of continental areas.
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• Advection fog: due to a wet and warm air mass moving over a cool surface. It is more frequent during spring
and requires moderate or fresh breeze blowing. It is further divided into marine fog (produced by advection of
marine air from warm to cold oceanic areas) and coastal or maritime fog (originated by warm air masses
migrating inland from the sea).
• Upslope or hill fog: due to adiabatic cooling of air masses moved up by wind along hill or mountain flanks.
The effect of suspended water droplets on EM waves is markedly different from the one induced by gases. Every
droplet has a twofold impact on the incoming EM wave: part of the electromagnetic energy is scattered in several
directions around the particle, while part of it is absorbed by the particle itself, causing an increase in its temperature. In
general, in the microwave and mm-wave region absorption prevails over scattering and the Rayleigh model applies
[i.10].
The dimension of the water droplets forming fog is very small: they are in the order of microns. When considering EM
waves in the 10 - 300 GHz, the shortest wavelength is λ = 1 mm (for f = 300 GHz), which is three order of magnitude
larger than the size of fog droplets.
The specific attenuation due to fog γ is shown in Figure 2 as a function of frequency, for different liquid water contents
F
(where T is fixed to 0 °C) [i.2].
The impact of fog increases continuously with frequency, reaching up to 7 dB/km at 300 GHz with w = 0,5 g/m , which
is considered as the limit value associated to extremely thick fog.

Figure 2: Specific attenuation due to fog (T = 0 °C) as a function of frequency and
for different liquid water content values
(Calculated according to Recommendation ITU R P.840 7 [i.2])
4.4 Rain attenuation
Rain is the prevailing phenomenon related to precipitating particles in the atmosphere and, depending on the site, it
occurs for a period of time approximately comprised between 1 % and 10 % in a year (the year is considered as the
basic repetition period for weather phenomena). Values as large as 3 % - 7 % are quite common in temperate climates
[i.11]. Rain affects the lower part of the atmosphere; specifically, making reference to temperate climates, rain develops
up to a few kilometers during winter because of the low height of the 0 °C isotherm layer (usually assumed as the
vertical limit for the presence of water particles during stratiform events) and up to 10 - 15 km during thunderstorms
(typical of summer periods) because of the strong updrafts/downdrafts which carry water/ice particles even to the
highest layers of the atmosphere.
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Rain consists of drops of spheroidal shape with equivolumetric diameters varying between few tenths of millimeters to
a maximum of 6 millimeters (larger drops are not common because the cohesive force is not as strong as the
aerodynamical force). In fact, the hydrometeor shape is far from being spherical if its dimension is large, because of the
balance between the internal and external forces acting on the lower surface of the drop in its falling path.
Measurements have shown that drops larger than about 1 mm in radius are of oblate spheroidal shape with flattened
base [i.12].
As an example, Figure 3 depicts the typical shape of a falling rain drop, for different sizes. The black line represents the
most probable shape derived from several drops within the same size class (figure extracted from [i.15]), which points
out that the oblateness increases with the drop dimension.

Figure 3: Typical shape of falling rain drops, for different sizes;
the black line represents the most probable shape derived
from several drops within the same size class
(Source: [i.15])
For what concerns the impact of hydrometeors on electromagnetic waves, rain represents the main drawback to their
propagation at frequencies above 10 GHz because the hydrometeor size is comparable with the wavelength of the
incident wave. Other types of precipitation such as hail and snow are not considered in the present document because
their effects on the propagation of the electromagnetic waves are marginal and their occurrence probability well below
the one of rain.
Each rain drop causes scattering and absorption (i.e. attenuation, overall) on EM waves, however, contrary to the water
droplets forming fog, the size of rain drops is of the same order of the wavelength considered in the 10 - 300 GHz range
(3 cm-1 mm range). This has a twofold effect: on one side, absorption and scattering are comparable and, on the other
side, the specific attenuation due to rain, γ , has a more complex expression compared to the case of fog. Indeed, γ
R R
depends on the size of each drop as follows [i.13]:
�
γ � 4,343 ∗ 10 � ��, ��������
�
� ���
�
where σext is the extinction cross section, taking care of both scattering and absorption, D is the rain drop diameter, N is
the number of drops with diameter D in unit volume, f is frequency.
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13 ETSI TR 104 140 V1.1.1 (2025-05)
This equation points out that the specific attenuation due to rain is obtained by weighting the fade induced by a rain
drop with given diameter D with the number of rain drops with that size. This latter information is provided by N(D)
(typically referred to as Drop Size Distribution (DSD)), which indicates the number of rain drops with given diameter D
3 -1 -3
contained in 1 m . The DSD, whose units are mm m , is typically measured by specific instruments, named
disdrometers, which count and classify drops according to their size; the DSD can be derived from the output of a
disdrometer as follows [i.13]:
�
�� �
�
� �
� � �
�
� �
�� � ���
� �
where n is the number of raindrops whose diameter falls in the i-th class (with mean diameter D ), ΔD (mm) represents
i i i
the width of each drop-size class, S (mm ) is the disdrometer sampling area, T (seconds) is the instrument integration
time, v(D ) (m/s) is the terminal velocity of rain drops, which, for example, can be extracted from the work of Gunn and
i
Kinzer [i.16] or derived directly from the disdrometer measurements.
Besides measured from a disdrometer, the DSD can also be modelled using analytical functions. According to the ratio
of the size of the drop to the wavelength inside the particle and to the shape of the drop, different electromagnetic
techniques can be used to compute the extinction cross section σ . In fact, if drops are small with respect to the
ext
wavelength, the Rayleigh scattering approach can be used; if they are of the same order of wavelength and spherical, the
exact Mie solution can be applied; in the most general case, including oblate spheroids, approximate numerical methods
have to be used.
As extensively shown in the literature [i.3], [i.13], the specific attenuation due to rain γ , obtained for different rain
R
intensity values R (mm/h), can be fitted with good accuracy using the following power law equation:
α
γ = kR
R
where k and α are coefficients that depend on the operational frequency f, the wave polarization (linear vertical for
terrestrial links) and link elevation (zero for terrestrial links); when deriving the power law equation from theoretical
analysis instead than from empirical fitting, it is found that k and α are also dependent on temperature and drop size
distribution [i.22].
The specific attenuation due to rain γ is shown in Figure 4 as a function of frequency, for different rain rates,
R
calculated according to Recommendation ITU-R P.838-3 [i.3]: while specific attenuation increases monotonically with
R, reaching even values as high as 50 dB/km for 200 mm/h (f ≈ 115 GHz), γ increases with frequency up to 100 GHz,
R
after which, depending on R, a stable or slightly decreasing trend emerges.

Figure 4: Specific attenuation due to rain as a function of frequency, for different rain rates,
calculated according to Recommendation ITU-R P.838-3 [i.3]
It is important to consider that the attenuation curves shown in Figure 4 are actually just a reference to give a hint about
how intense the fades caused by rain can be. Indeed, an accurate evaluation of the specific attenuation γ is to be done
R
not simply as a function of rain rate R but more precisely as a function of DSD.
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Several drop size distribution models have been developed depending on the different types of rain in the different rain
zones; in particular Recommendation ITU-R P.838-3 [i.3] is based on the Laws-Parsons drop size distribution model
[i.20] which describes typical continental temperate rainfall of stratiform kind.
As an example of the relevance of the DSD, the specific attenuation obtained in three locations in India [i.25] with
different DSD as compared with the Recommendation ITU-R P.838-3 [i.3] model are shown in Figure 5, where some
curves overestimate the ITU-R model whilst others underestimate it depending on location, frequency and rain rate.

Figure 5: Specific attenuation variability with DSD, f and R in three locations in India [i.25]
From the physical point of view as long as the wavelength is much larger than the rain drop size, as it is in the cm-wave
range, the Rayleigh scattering prevails and the rain attenuation is related to the total volume of water in the raindrops,
that is to the rain rate, with the distribution of drop size being hardly relevant; instead when the wavelength becomes
comparable with the drop size, as it is in the mm-wave range, Mie scattering becomes more relevant and the rain
attenuation gets more sensible to the actual distribution of drop size. When the wavelength is much shorter than the
drop size, well over the mmWave range, geometric optics scattering occurs.
A comparison among different models is shown in next clause on the base of experimental data.
5 Rain attenuation prediction: event-based analysis
5.0 Introductory concepts
This clause presents different methods that can be used to predict the time series of the rain attenuation starting from
information on precipitation.
As noted in clause 4.1.3, there are two models that can be applied to predict the rain attenuation:
• A model based on a power law equation which is employed in Recommendation ITU-R P.838-3 [i.3], where
the specific attenuation due to rain γ is function of rain rate R and frequency.
R
• A model considering the specific attenuation due to rain γ as a function of Drop Size Distribution.
R
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In order to compare the accuracy of the two models a propagation experiment has been carried out since 2016 at
Politecnico of Milan [i.5] considering a link with radios at E band (about 80 GHz) and D band (about 150 GHz)
co-sited. The link length is about 325 m and measurement instruments are present on site such as a disdrometer, which
allows to measure DSD, and a weather station, which allows to measure pressure P, temperature T and relative humidity
RH.
The attenuation due to rain can be derived by measuring the received power at one link side and by evaluating the
attenuation due to gases by means of Liebe MPM93 model (see clause 4.1.1) and from the measurement of P, T and
RH. The attenuation due to rain as measured by the radio link can be compared to the one predicted by
Recommendation ITU-R P.838-3 [i.3] and to the one predicted by disdrometric data for different rain events.
5.1 Wet antenna effect
When it is raining, a thin layer of water can be deposited over the surface of the antenna radome of the radio link,
provoking an attenuation that is not related to propagation. The attenuation due to wet antenna extends in time after the
end of the rain event, till the thin layer of water is dried. In order to perform the comparison of models with the
measured rain attenuation, the wet antenna attenuation has to be properly evaluated and distinguished from rain
attenuation along the propagation path.
This effect has been modelled in [i.14], where the attenuation grows with rain rate till a stationary value is reached
according to a simple exponential law:
���
�
� ���1�� )
��
where A is the total attenuation obtained from the received power (depending on rain rate), a and b are coefficients
T
depending on frequency and type of antenna radome and coating.
Other factors which affect the wet antenna attenuation are rainfall type, wind speed and direction.
In the propagation experiment at Politecnico of Milan [i.6], the wet antenna effect has been evaluated and filtered out
from measured rain attenuation by leveraging on data collected by the disdrometer during stratiform rain events, where
the rain rate can be assumed as constant over the link length. In Figure 6 the evaluated wet antenna attenuation on one
link at E band is reported.
Figure 6: Estimated wet antenna attenuation as a function of total link attenuation got
from disdrometer data (red line) and fitted by the power law coefficients at 73 GHz in Milan
(Source: [i.6])
It is important to consider that the wet antenna attenuation in Figure 6 is obtained only during the rain event along the
link (identified by means of the co-sited disdrometer) and the larger part of wet antenna attenuation occurring after the
end of the rain event is not considered.
The wet antenna attenuation has been evaluated also by China Research Institute of radio wave propagation and Xidian
University [i.21], by applying the exponential model to some radio links ranging in frequency between 37 and 137 GHz,
whose dataset are contained in the ITU-R DBSG3, with the results shown in Figure 7.
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Figure 7: Wet antenna attenuation of some terrestrial links in
the ITU‐R DBSG3 dataset (each link is 0,5 km long)
(Source: [i.21])
The wet antenna effect can be significantly reduced by using a suitable coverage and/or hydrophobic coating of the
radome.
5.2 Comparison of models
A first sample of comparison among rain attenuation models at E band is given by the propagation experiment at
Politecnico of Milan [i.5] and shown in Figure 8 considering:
• the data measured by the radio link as a reference;
• the data predicted by Recommendation ITU-R P.838-3 [i.3];
• the data predicted by the model based on DSD got by the disdrometer;
with respect to the measured rain rate reported in Figure 9.
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Figure 8: Rain attenuation on the E band link (73 GHz) in Milan: derived from the link (blue line
...