Channel Modeling and Performance Analysis of Airplane-Satellite Terahertz Band Communications

Abstract

Wireless connectivity in airplanes is becoming more important, demanded, and common. One of the largest bottlenecks with the in-flight Internet is that the airplane is far away from both the satellites and the ground base stations during most of the flight time. Maintaining a reliable and high-rate wireless connection with the airplane over such a long-range link thus becomes a challenge. Microwave frequencies allow for long link distances but lack the data rate to serve up to several hundreds of potential onboard customers. Higher bands in the millimeter-wave spectrum (30 GHz - 300 GHz) have, therefore, been utilized to overcome the bandwidth limitations. Still, the per-user throughput with state-of-the-art millimeter-wave systems is an order of magnitude lower than the one available with terrestrial wireless networks. In this paper, we take a step further and study the channel characteristics for the terahertz band (THz, 0.3 THz - 10 THz) in order to map the feasibility of this band for aviation. We first propose a detailed channel model for aerial THz communications taking into account both the non-flat Earth geometry and the main features of the frequency-selective THz channel. We then apply this model to estimate the characteristics of aerial THz links in different conditions. We finally determine the altitudes where the use of airplane-to-satellite THz connection becomes preferable over the airplane-to-ground THz link. Our results reveal that the capacity of the airborne THz link may reach speeds ranging from 50 - 150 Gbps, thus enabling cellular-equivalent data rates to the passengers and staff during the entire flight.

Full text

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 70, NO. 3, MARCH 2021 2047
Channel Modeling and Performance Analysis of
Airplane-Satellite Terahertz Band Communications
Joonas Kokkoniemi , Member, IEEE, Josep M. Jornet , Senior Member, IEEE, Vitaly Petrov , Member, IEEE,
Yevgeni Koucheryavy, Senior Member, IEEE, and Markku Juntti , Fellow, IEEE
Abstract—Wireless connectivity in airplanes is becoming more
important, demanded, and common. One of the largest bottlenecks
with the in-flight Internet is that the airplane is far away from
both the satellites and the ground base stations during most of the
flight time. Maintaining a reliable and high-rate wireless connec-
tion with the airplane over such a long-range link thus becomes
a challenge. Microwave frequencies allow for long link distances
but lack the data rate to serve up to several hundreds of potential
onboard customers. Higher bands in the millimeter-wave spectrum
(30 GHz–300 GHz) have, therefore, been utilized to overcome the
bandwidth limitations. Still, the per-user throughput with state-
of-the-art millimeter-wave systems is an order of magnitude lower
than the one available with terrestrial wireless networks. In this
paper, we take a step further and study the channel character-
istics for the terahertz band (THz, 0.3 THz–10 THz) in order to
map the feasibility of this band for aviation. We first propose a
detailed channel model for aerial THz communications taking into
account both the non-flat Earth geometry and the main features of
the frequency-selective THz channel. We then apply this model
to estimate the characteristics of aerial THz links in different
conditions. We finally determine the altitudes where the use of
airplane-to-satellite THz connection becomes preferable over the
airplane-to-ground THz link. Our results reveal that the capacity of
the airborne THz link may reach speeds ranging from 50–150 Gbps,
thus enabling cellular-equivalent data rates to the passengers and
staff during the entire flight.
Index Terms—Airplane communications, satellite
communications, THz channel modeling, THz communications.
I. INTRODUCTION
TODAY, terahertz (THz, 0.3 THz–3 THz) communication
is widely considered to be one of the next frontiers for
Manuscript received September 13, 2020; revised January 2, 2021; accepted
January 28, 2021. Date of publication February 10, 2021; date of current version
April 2, 2021. This work was supported in part by the Horizon 2020, European
Union’s Framework Programme for Research and Innovation, under Grant
Agreement Nos. 761794 (TERRANOVA) and 871464 (ARIADNE), in part by
the Academy of Finland 6Genesis Flagship under Grant 318927, and in part by
the US Air Force Research Laboratory Grant FA8750-20-1-0200. The review of
this article was coordinated by Prof. J. Joung. (Corresponding author: Joonas
Kokkoniemi.)
Joonas Kokkoniemi and Markku Juntti are with the Centre for Wire-
less Communications, University of Oulu, Oulu 90014, Finland (e-mail:
joonas.kokkoniemi@oulu.fi; markku.juntti@oulu.fi).
Josep M. Jornet is with the Department of Electrical and Computer
Engineering, Northeastern University, Boston, MA 02115 USA (e-mail:
jmjornet@northeastern.edu).
VitalyPetrov was with the Tampere University, Tampere 33720, Finland. He is
now with Nokia Bell Labs, Espoo 02610, Finland (e-mail: vitaly.petrov@tuni.fi).
Yevgeni Koucheryavy is with the Unit of Electrical Engineering, Tampere
University, Tampere 33720, Finland (e-mail: yk@cs.tut.fi).
Digital Object Identifier 10.1109/TVT.2021.3058581
future wireless systems. Data transmission over the THz band
offers at least an order of magnitude higher rates than emerging
millimeter-wave (mmWave, 30 GHz–300 GHz) communication
systems and two orders of magnitude when compared to state-
of-the-art microwave solutions [1], [2]. Hence, THz communi-
cation cannot only exceed the performance requirements for the
fifth-generation (5G) networks, but also enable many tempting
applications in the area of holographic communications, aug-
mented and virtual reality, and tactile internet [3]. While the
first prototypes of point-to-point connections over the low THz
frequencies are already appearing [4], the research community
is slowly switching its focus on studying the features of THz
links in prospective application-specific setups.
One of the attractive usage scenarios in the area is enabling
THz connectivity with flying airplanes. The aviation industry
has been growing by over 6% a year over the recent decades,
reaching an incredible figure of 4.3 billion passengers carried
in 2018 [5]. Although the current COVID-19 pandemic is mo-
mentarily slowing down the development, in the long run the
trend is expected to continue. While the average duration of
a flight is less than 3 hours, a substantial amount of flights
are longer than 7 hours. Some flights between the continents
take the even longer time up to enormous 18 hours 45 minutes
with a recently introduced route between Singapore and Newark,
USA, by Singapore Airlines. Despite the continuously increased
popularity of long haul flights, the airplane is one of the few
typical locations where the average person is used to not have
high-rate Internet connectivity.
Aiming to address this limitation, modern aircrafts are al-
ready equipped with satellite-based solutions operating in Ku
(12–18 GHz) and, recently, Ka (26.5–40 GHz) frequency bands.
Still, these systems can provide only limited service to restricted
numbers of passengers, as the aggregated traffic from over
400 users (e.g., in a Airbus A350-1000) cannot be efficiently
multiplexed into a single mmWave link. Here, the use broadband
THz spectrum provides decisive advantages, rapidly increasing
the data rate of the airplane connectivity and thus allowing all the
passengers and crew members to stay continuously connected to
their common applications and services. However, the high-rate
airborne connectivity in the THz band requires not only the
evolution in the transceiver and antenna design. Importantly,
it also demands a better understanding of the properties of
the THz signal when propagating through the atmosphere at
a high altitude. Potentially high losses at a multi-kilometer THz
link between the airplane and a satellite may even question the
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/

2048 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 70, NO. 3, MARCH 2021
feasibility of the airborne THz communications. It will be shown
in the numerical results that the THz bands have very potential
for high altitude satellite communications. However, those re-
quire very large antenna gains and terrestrial communications
benefits from lower losses at mmWave bands. In the case of, e.g.,
handheld applications where antenna gain at the user end is very
low, the low frequency solutions are most likely the only feasible
solution. That is, the feasibility of the high frequency systems
depend on the application. High bandwidth applications will
always benefit from the higher bandwidths offered by mmWave
and THz communications with the latter having potential to
provide the extreme data rates, but only in low loss situations.
Related Work
A general model for free-space wireless communications in
the THz band was first presented in [6]. The model enables esti-
mating the path loss over a direct THz link, properly accounting
for the specific effects present in THz communications, such as
molecular absorption. The properties of the THz propagation
in complex environments have been extensively studied via
ray-based simulations [7]–[10]. For this purpose, deterministic
channel models are first built following the exact geometry of the
scenario. Then, the impact of multipath propagation is modeled
following either ray-tracing or ray-launching approach. The
approach is featured by high accuracy but limited scalability, as
even the minor modifications in the modeled scenario requires
a restart of the computationally complex ray-based simulations.
In response to this issue, mathematical approaches to model
multi-path THz communications have been proposed in [11]
and [12]. These stochastic models primarily target indoor THz
systems, where the signal can reflect from walls and other
obstacles multiple times before reaching the target receiver.
Despite the progress in understanding the key features of the
THz signal propagation, the airborne nature of the THz links
between an airplane and a satellite has its own specifics that
must be taken into account in channel modeling. The topic has
been partially covered in prior works. A simulation-based model
for THz band satellite links has been proposed in [13]. Later,
a review of weather impact on outdoor THz links has been
presented in [14]. The latter study has been complemented by
Y. Balal and Y. Pinhasi in [15], where effects of the atmosphere
non-homogeneous refractivity on mmWave and THz band satel-
lite links has been explored.
In parallel to academic research, some initial steps towards
characterizing the airborne THz links have been made by In-
ternational Telecommunication Union (ITU). Specifically, the
approach to estimate the signal attenuation by atmospheric gases
has been presented in ITU-R P.676-9 [16] while the noise levels
for different frequencies (including the THz band) have been
estimated in ITU-R P.372-13 [17].
Finally, one of the closest models to our approach – the
am atmospheric model – has been presented by S. Paine from
Smithsonian Astrophysical Observatory in [18]. The model first
characterizes the absorption losses at different altitudes and then
allows the estimation of the average effect when propagating
through several atmospheric layers by integrating the obtained
data. There are also other models suitable for THz band line-
by-line absorption loss calculations, such as MODTRAN [19]
and ATM [20]. However, as these have not been designed for
wireless communications, they are not very agile for dynamic
loss calculations as a function of a position of a moving network
nodes. Still, these models are very accurate, but best suited
for static link calculations. For dynamic environments and user
nodes, it is more efficient to create a model that automatically
calculates the path losses and the link budget based on the
positions of the network elements.
Our Motivation and Contribution
Summarizing the related work survey, no model has been
proposed to date for airborne THz band communications that
takes into account: (i) the curvature of the atmosphere and,
consequently, (ii) the non-uniformity of atmospheric absorption
losses. Simultaneously, there has not yet been presented a de-
tailed numerical study investigating the feasibility of airborne
wireless communications via the THz band while accounting
for the above-mentioned specifics. We aim to partially fill the
gap in this article.
The main contributions of this article are thus:
1) The mathematical model to characterize the airborne THz
band communications is proposed, taking into account (i)
the features of the target use case and the deployment
geometry, (ii) the peculiarities of the signal propagation
through the atmosphere, as well as (iii) the prospective
characteristics of THz radio equipment to operate in the
airborne scenarios.
2) The illustrative numerical study is performed estimating
the performance of the data exchange between an airplane
and a satellite over the THz frequencies. Particularly, the
signal-to-noise ratio (SNR) and the mean capacity of the
airborne THz link are estimated. Our numerical study
allows to conclude that capacities of 50–150 Gbps in air-
borne THz links can be achieved using certain sub-bands
in the THz spectrum.
The remainder of this paper is organized as follows. In
Section II we detail the system model used in our study. The
specifics of the THz signal propagation are discussed in detail in
Section II-B. The channel model for airborne wireless commu-
nications in the THz band is introduced in Section III. We later
apply the contributed model in Section IV for the received signal
quality and performance evaluation of prospective airborne THz
links. The obtained analytical results are numerically elaborated
in Section V. The concluding remarks are drawn in the last
section.
II. SYSTEM MODEL
A. Scenario Description
The general system concept is to provide high data rate
fronthaul connection to an airplane, which furthermore serves
the passengers on board and in general provides Internet con-
nection to the airplane. However, as a side product, the channel
models derived in this paper cover several use cases for aerial

KOKKONIEMI et al.: CHANNEL MODELING AND PERFORMANCE ANALYSIS OF AIRPLANE-SATELLITE TERAHERTZ BAND COMMUNICATIONS 2049
Fig. 1. An illustration of the system model considered in this paper and
the several wireless links in it. Picture of Earth by NASA/NOAA’s GOES
Project [21].
vehicle communications, as illustrated in Fig. 1. The consid-
ered application scenarios for the channel models in this paper
include: (i) airplane-to-satellite (A2S) or satellite-to-airplane
(S2A), (ii) Earth-to-airplane (E2A) or airplane-to-Earth (A2E),
and (iii) Earth-to-Satellite (E2S) or satellite-to-Earth (S2E). The
satellite-to-satellite (S2S) case is not considered in this paper due
to strong focus on modeling the molecular absorption and the
atmosphere in general. Even the low Earth orbit (LEO) satellites
lie in nearly empty space where any atmospheric effects will
be small. Therefore, the channel mainly comprises free space
loss and the antenna systems. Furthermore, although not deeply
analysed, the E2S/S2E use case is equivalent to models required
for possible THz band remote area communications.
The target scenario for the A2S and S2A channel modeling
is shown in Fig. 2. The target scenario for channel modeling
consists of an airplane at an altitude haand a satellite at an
altitude hsfrom the Earth and distance ras from the airplane.
The boundary of the atmosphere is ratm away from the airplane.
As the separation distance between the considered airplane
and satellite is significant, the relative speed of the airplane
is considered negligible for the channel modeling. The most
important parameters and variables are given in Table I.
B. Atmospheric Propagation in the Terahertz Band
The main phenomena affecting the propagation of THz signals
in the target scenarios are went through in the following. Those
include free space path loss and the molecular absorption loss.
Some additional loss mechanism include rain, cloud, fog, and
possible scattering losses that are briefly discussed below.
1) Spreading Loss: The spreading loss measures the fraction
of the power radiated by an isotropic transmitter at a frequency
fthat an isotropic receiver at a distance rcan detect. Under the
assumption of spherical propagation, the spreading loss is given
by
PLspr(f, r)=4πr24π
(c/f)2=4πfr
c2,(1)
where cis the speed of light in the medium, fis the frequency,
and ris the distance from Tx to Rx. In our system, directional
antennas (e.g., horn lens antennas, Cassegrain parabolic anten-
nas or beamforming antenna arrays) will expectedly be utilized
TAB LE I
THE MOST IMPORTANT CONSTANTS,VARIABLES,AND PARAMETERS USED IN
THE PAPER
at the transmitter and the receiver to counter the high channel
losses. In that case, their directivity gain D(θ, γ)with respect to
an ideal isotropic emitter and detector (commonly given in dBi)
needs to be accounted for.
2) Molecular Absorption Loss: The molecular absorption
loss measures the fraction of electromagnetic energy that is
converted into kinetic energy internal to vibrating molecules [6],
[18], [22]. For an homogeneous medium with thickness r,this
is given by the Beer-Lambert law and can be written as:
PLabs(f, r)=eΣiκi
a(f)r,(2)
where κi
a(f)is the absorption coefficient of ith absorbing
species (molecule or its isotopologue) at frequency f. We de-
note the total summed absorption coefficient with κa(f), i.e.,
κa(f)≡iκi
a(f).
In our system, the medium is not homogeneous, as the den-
sity of different absorbing molecules (particularly water vapor
molecules) changes drastically with altitude. In the case of
vertical paths, the absorption coefficient κadepends on distance
κa(f,r)and its variations need to be accurately computed along
the signal propagation path.
3) Scattering Loss on Aerosols: One possible loss mecha-
nism comes from the aerosol scattering. The aerosols are small
particles suspended by air, such as dust, ice particles, pollution,
etc. Those are modelled by the Beer-Lambert law and therefore
can theoretically cause significant losses over long distance
links [23]. However, as it was shown in [23], the THz frequencies
require rather large particles to cause significant losses. On Earth
this is possible, e.g., in very dusty conditions, but in general this
is not a problem at higher altitudes. The possible losses on clouds
can be handled as shown below. For the sake of tractability, we
ignore these losses in the further study.
4) Rain and Cloud Losses: Additional attenuation may be
caused by adverse weather conditions in A2A, A2S, and S2A

2050 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 70, NO. 3, MARCH 2021
Fig. 2. The system geometry for the angles and distances in the airplane to satellite system. Picture of Earth by NASA/NOAA’s GOES Project [21].
scenarios. The ITU-R provides rain [24] and cloud/fog [25]
attenuation models. Those are detailed in Section III-C. It should
be noted that the cloud attenuation is formally valid only up to
200 GHz frequencies [25]. Furthermore, the cloud densities,
cloud thicknesses and rain rates vary greatly depending on the
type of the cloud, and the probability of different types of clouds
vary geographically. However, in any case the Earth to airplane
or satellite paths experience added path losses ranging from few
decibels up to tens of decibels in the presence of clouds and
depending on the weather in general. In the further, we note
the rain and cloud losses with the distance-dependant variables
δRain(rr)and δCloud (rc), respectively.
III. ATMOSPHERIC PAT H LOSS MODELING
In this section, we derive the path loss for the above aerial
use cases. As highlighted in the previous section, the main
challenge arises from the non-uniform molecular absorption
coefficient through the atmosphere. The density, temperature,
and molecular composition of the atmosphere depend on the
altitude. This section gives the dynamic molecular absorption
loss coefficient valid at any altitude by taking into account
the impact of atmospheric parameters on the absorption line
calculations. After that, we go through the transmission path
geometry of slant paths through the atmosphere. Table I gives
the most important constants, variables, and parameters utilized
in this paper.
A. Non-Homogeneous Molecular Absorption Loss
Traditionally the channel modeling for the THz frequencies
has been considered for terrestrial communications. When mov-
ing to higher altitudes, the homogeneous assumption for the
line shape functions is no longer valid. We can also utilize
meteorological data to take into account the global variations
in water vapor content as a function of latitude, longitude, and
altitude. Those will be discussed briefly in conjunction with the
numerical results. Similarly, when moving to higher altitudes,
mixing ratios of the molecular species change and this has to be
taken into account for accurate molecular absorption modeling.
The line-by-line absorption model and the parameters re-
quired for different altitudes is presented in Appendix. Putting
the absorption loss model therein together, the altitude depen-
dent absorption coefficient becomes
κi
a(f,p(hatm),T(hatm))
=p(hatm)μiNA
RgT(hatm)Si(T(hatm ))Fi(f,p(hatm),T(hatm)),(3)
where p(hatm)is the pressure, NAis the Avogadro constant, Rg
is the gas constant, Si(T(hatm)) is the line intensity, T(hatm)
is the temperature, Fi(f,p(hatm),T(hatm)) is the absorption
line width. The altitude hatm is directly having impact on
the pressure and temperature and it is indirectly affecting
on the line-by-line parameters presented in Appendix depending
on the altitude. The distance through the atmosphere is handled
by the integration over the total molecular loss in the atmosphere
and is given in the next section. The line width in the above
equation is
Fi(f,p(hatm),T(hatm))
=⎧
⎨
⎩
Fi
VVH(f,p(hatm),T(hatm)),if˜αi
L>> αi
D,
Fi
D(f,T(hatm )),if˜αi
L<< αi
D,
Fi
V(f,p(hatm),T(hatm)),if˜αi
L≈αi
D,
(4)
where Fi
VVH(f,p(hatm),T(hatm)),Fi
D(f,T(hatm )), and
Fi
V(f,p(hatm),T(hatm)) are the Van Vleck-Weisskopf, Doppler,
and Voigt line shape functions, respectively, and αi
Land αi
D
are Lorentz and Doppler line half widths (half width at half

KOKKONIEMI et al.: CHANNEL MODELING AND PERFORMANCE ANALYSIS OF AIRPLANE-SATELLITE TERAHERTZ BAND COMMUNICATIONS 2051
Fig. 3. System geometry on the angles of the transmission path through the
atmosphere. Picture of Earth by NASA/NOAA’s GOES Project [21].
maximum). The Lorentz line shapes are utilized in high
pressure environment and the Doppler line shapes in low
pressure environment. These are explained more deeply in
the Appendix. Notice that the altitude defines the pressure,
temperature, and other parameters utilized in the calculation
of the absorption coefficient. As a consequence, the line shape
function requires a dynamic algorithm that defines the correct
line shape for every possible set of pressure, temperature, and
absorption line center frequency. This can easily be done in
the line-by-line algorithm by calculating and comparing the
Doppler and Lorentz absorption line half-widths.
B. Transmission Path Geometry
The general system geometry is shown in Fig. 2. The usual
way to model the atmosphere is to assume plane parallel atmo-
sphere. By assuming flat surface, the geometry of the system
is significantly simplified. However, when talking about appli-
cations where the entire atmosphere is penetrated, the plane
parallel assumption overestimates the thickness of the atmo-
sphere. The impact is the higher the lower is the angle to the
surface. In order to rectify the problems with the plane parallel
model, in this work we model realistic curving atmosphere. In
such setting, the problem becomes with ever-changing angle to
the zenith (and to the elevation angle ψ) as shown in Fig. 3.
This problem can be modeled geometrically by utilizing the
geometry shown in Fig. 2. In this figure, Ris the Earth’s radius,
hais the altitude of the airplane, bis the Earth’s radius plus
the total thickness of the atmosphere, hsis the altitude of the
satellite, φais the elevation of the airplane, φsis the elevation of
the satellite, ras is the distance from the airplane to satellite,
and ratm is the most interesting parameter, i.e., the distance
through the atmosphere from the airplane to the boundary of
the atmosphere. This latter distance is important because of
the molecular absorption that depends on the altitude and the
constantly evolving line parameters as the altitude changes. It
should be noted that the elevation herein means an arbitrary angle
that is used to define the geometry between the Earth, airplane,
and the satellite. Herein, it is bound to the latitude to illustrate
the angles easily. However, in the case of moving airplanes,
the angular differences have to be bound to both latitude and
longitude based on the real locations of the network elements.
The main difference of the curving atmosphere to the plane
parallel atmosphere comes from the dynamically changing at-
mospheric parameters depending on the altitude. This is shown
in Fig. 3. Distance from the airplane to satellite is given by the
law of cosines
ras =(R+ha)2+(R+hs)2−2(R+ha)(R+hs)cos(ρ),
(5)
where Ris the radius of Earth, hais the altitude of the airplane,
hsis the altitude of the satellite, and ρis the angle between
the airplane and satellite looked from the center of the Earth.
This angle is obtained as subtraction of the elevation angles,
i.e., ρ=|φa−φs|, where φais the elevation of the airplane and
φsis the same for the satellite. See details on these variables in
Fig. 2. The distance from airplane to imaginary line from Earth’s
core to satellite is calculated as
a=(R+ha)sin(ρ).(6)
Then the angle between the satellite and the airplane, looked
from the satellite, is obtained from the two as
α=sin
−1a
ras .(7)
The angle between line from Earth to airplane and the line from
airplane to satellite is give simply by
=180◦−α−ρ, (8)
which is also equivalent to =ψ+90◦where ψis the elevation
angle of transmissions path from airplane to satellite. These
angles also directly give the transmission angle with respect
to zenth as θ=180◦−=90◦−ψ. Now we have everything
we need in order to calculate the distance from airplane through
the atmosphere ratm. This can be calculated from the triangle
suspended by R+ha, distance from the core of the Earth to
boundary of the atmosphere b, and ratm. Let us first calculate the
corner angles of this triangle. We can obtain angle δfrom law
of sines
δ=sin
−1(R+ha)cos()
b.(9)
Then we can obtain last angle as η=180◦−−δ. Finally we
can obtain the distance through the atmosphere ratm with the law
sines as
ratm =bsin(η)
sin().(10)
On the other hand, we could also solve ratm with the law of
cosines and the quadratic formula as
ratm =(R+ha)cos()
+1
2(−2(R+ha)cos())2−4((R+ha)2−b2).
(11)
Both of these expressions for ratm are equal, but the former gives
perhaps a bit more compact way to calculate the angles and the

2052 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 70, NO. 3, MARCH 2021
Fig. 4. Comparison of the layer thickness of the plane parallel atmosphere and
a round atmosphere as a function of altitude.
Fig. 5. A comparison of the total distance through the atmosphere according to
the plane parallel assumption and the model herein as a function of the elevation
angle.
distances. Finally, in order to fit this new approximation for the
length of the atmosphere to the transmittance, we need to take
a derivative of it. The reason is that the absorption coefficient
changes as a function of the altitude, but does not depend on the
total distance. Therefore, we need to manipulate the space over
which the total absorption is calculated. That is, we multiply the
absorption coefficient by d/dr(ratm)instead of sec(θ)as in the
case of plane parallel atmosphere. Then,
τ(f,r)=e−
r2

r1
κa(f,r)d
dr ratmdr
=e−
r2

r1
κa(f,ratm)dratm
.(12)
The difference between the plane parallel assumption and
the proposed model is shown in Figs. 4 and 5. In computer
simulations/models, we are forced to discretize the parameters
due to utilization of the data bases to obtain the parameters
and since the computer inherently handles only discrete data.
Then we also have to discretize the atmosphere into equally
spaced layers. In the plane parallel atmosphere, the distance
through each layer is same at all altitudes due to the simple
geometry. In the geometry given above, the discretization leads
into non-equal propagation distance through the layer depending
on the altitude and the angle of penetration due to curvature of the
atmosphere. It can be seen in Figs. 4 and 5 that the vertical path
through the atmosphere is exactly the same for both model as
they should be. Notice that the atmosphere has been calculated
up to 500 km altitude where it is already very thin and does
not contribute much on the propagation anymore. Fig. 4 shows
the propagation distance through a single 500 m layer (500 m
resolution accuracy) at 38.2◦angle from the ground. As stated
above, the layer altitude has impact on the dynamic distance
through the atmosphere. Thus, the plane parallel assumption
tends over estimate the layer thickness. The problem is the worse
the lower is the angle through the atmosphere. This is well visible
in Fig. 5, which shows the total distance through the atmosphere.
As the molecular absorption is dependent on the propagation
through molecular medium, the plane parallel assumption may
greatly overestimate the total absorption loss. The next section
looks into derivation of the absorption coefficient κa(f,r)as
the geometry of the propagation is one important issue, and the
second important aspect are the parameters fed into the model.
C. Total Path Loss
By combining (1) with (12), the total path loss can be written
as
PL(f,r)= (4πrasf)2δRain (rr)δCloud (rc)
c2GTx(θTx )GRx(θRx)er2
r1κa(f,ratm)dratm ,
(13)
where GTx(θTx )and GRx(θRx)are the Tx and Rx antenna gains
towards directions θTx and θRx, respectively, and δRain(rr)and
δCloud(rc)are the channel gains due to rain and cloud losses,
where rris the distance through the rain and rcis the distance
through the cloud/fog.
The rain loss is given by [24]
δRain,dB(rr)=kRα
rreff,(14)
where kand αare parameters tabulated in [24], Rris rain rate
(mm/hr), and reff is the effective distance that is a multiplication
between the actual distance rrand a distance scaling factor. This
scaling factor is detailed in [26, Sec. 2.4.1]. The cloud loss is
given by [25]
δCloud,dB(rc)=KlMrc,(15)
where Klis the specific attenuation coefficient and Mis the liq-
uid water density (g/m3) in cloud or fog. It should be noticed that
the above losses are specified in the ITU-R recommendations in
decibel scale (hence the dB-subscript in the above equations).
More details on the parameters for these models can be found
in [24] and [25].
IV. RECEIVED SIGNAL POWER
In order to calculate the SNR and subsequently the channel
capacity of the links under study, this section studies the prop-
erties of the received signal including the noise.

KOKKONIEMI et al.: CHANNEL MODELING AND PERFORMANCE ANALYSIS OF AIRPLANE-SATELLITE TERAHERTZ BAND COMMUNICATIONS 2053
A. Total Received Signal Power
The received signal power spectral density Yat the receiver
is given by
Y(f,r)=X(f)PL(f, r)+N(f, r),(16)
where X(f)is the transmitted signal power spectral density with
total power PTx =WX(f)df and Wis the signal bandwidth,
PL(f,r)is the total path loss given by (13), and N(f,r)refers
to the total noise power spectral density. As we discuss next,
the calculation of the noise at THz frequencies is a non-trivial
process.
B. Noise
The last piece of the puzzle before calculating the SNR is
the noise. The noise is an interesting problem in THz band
since the molecular absorption process introduces additional
antenna noise due to atmosphere acting as black body radiator,
i.e., the atmosphere emits radiation according to the Planck’s
law. At regular atmospheric temperatures, the atmospheric black
body radiation begins to contribute significantly around sub-THz
frequencies. This can be modelled via antenna brightness tem-
perature. There are two options: at lower frequencies, where
hf kBT, the Rayleigh-Jeans law can be utilized [27]. At
higher frequencies, this model suffers from so called ultraviolet
catastrophe, i.e., it gives infinite overall black body energy due
to ever-increasing energy as a function of frequency. The second
option is to use Planck’s law, which is accurate everywhere, and
is given as [27]
Bf(f,T)= 2hf 3
c2(ehf
kBT−1)
.(17)
Then the brightness temperature becomes
Tb=hf
kB
ln 1+ehf
kBT(d)−1
1−exp(−r2
r1κa(f,ratm,p,T)dratm)−1
,
(18)
where Tis the average temperature, or temperature profile
of the atmosphere and the last term comes from the derived
channel model and 1 −exp(−r2
r1κa(f,ratm,p,T)dratm)gives
the emissivity of the atmosphere. Though the Raleigh-Jeans law
can be used in the low THz band, our model used the more
accurate Planck’s law to determine the brightness temperature
of the atmosphere.
Besides the atmospheric noise, the thermal noise at the re-
ceiver needs to be taken into account. The thermal noise begins
to decrease at the THz frequencies due to quantum effects at
very low temperatures, or very high frequencies, i.e., when
hf kbT. At this region, the probabilities of the higher en-
ergy states of the molecules/atoms become smaller and smaller,
making the thermal noise smaller and smaller with respect to
the one predicted by simple kBT[28]. Taking into account the
total noise power degradation, the thermal noise power density
with receiver noise figure Nf(in dB) becomes
NT(f,Nf)=kBTη(f)10Nf/10
=kBThf/kBT
exp(hv/kBT)−110Nf/10
=hf
exp(hv/kBT)−110Nf/10 ,(19)
where function η(f)takes into account the noise power re-
duction. However, η(f)does not play crucial role in the THz
communications, since the transition when quantum of energy
exceeds per Hertz thermal noise power occurs at 6.168 THz
at 296 K temperature, i.e., when kBT=hv. Therefore, the
noise reduction is modest, up to few dBs at 10 THz frequency.
Considering the fact that the THz band systems are envisioned
to be extremely wide band systems, there is far more noise than
in the conventional systems, mainly contributed by the large
thermal energy of the wide band systems.
Finally, the total noise power spectral density at the receiver
becomes:
N(f)=Bf(f,T )+NT(f, Nf).(20)
The total noise power can be then obtained by integrating N
over the receiver bandwidth, Win our model.
C. The System SNR and Capacity
Taking into account the noise and the path loss from above,
the SNR becomes
SNR(f,r)= X(f)PL(f, r)
N(f),(21)
and the corresponding Shannon capacity is
C(r)=W
log2(1+SNR(f,r))df . (22)
V. N UMERICAL RESULTS
In this section, we evaluate the expected path losses and link
performances based on the above channel models.
A. Parameters for the Channel Model
One important factor in modeling the atmosphere is to model
the altitude dependent parameters correctly. Those are mainly
the temperature and pressure, and volume mixing ratios of
different molecules. All these vary quite a bit as a function
of altitude. For this work, we utilized the 1976 US Standard
Atmosphere [29]. The corresponding temperature and pressure
as a function altitude is given in Fig. 6. The volume mixing
ratios of common molecules is given in Fig. 7. Interestingly, the
volume mixing ratios of the molecules remain roughly the same
to the sea level up until 86 km altitude, after which they start to
vary to each other. The pressure, temperature, volume mixing
ratios, and ground level humidities are shown in Figs. 6 to 8.
If one is interested modeling applications close to ground
level, the global average humidities and the ground height has an
impact on the molecular absorption loss. This mostly depends
on the elevation angle, but also in the exact location in some
cases. Fig. 8 shows the average humidity around the world (left)
and the ground height (right). The data for these were obtained

2054 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 70, NO. 3, MARCH 2021
Fig. 6. Atmospheric pressure and temperature as a function of altitude.
Fig. 7. Volume mixing ratios of different molecules as a function of altitude.
from NASA/GMAO MERRA2 reanalysis data [30]. From [30],
one can find large datasets of atmospheric data, including global
humidity data at different time scales and much more related to
global weather and climate.
The rain and fog attenuations were shortly discussed above.
In the real atmosphere, we do not always have clear weather and
additional losses by clouds and rain impair the link performance.
These are the mostly affecting low altitude communications,
below few kilometer heights. As such, they have small impact
on A2S and communications while at the typical flight heights.
However, some losses by clouds can also exist at very high
altitudes. For the take off and landing phases these may have
an impact, and also in the G2A use case.
In the below example shown in Fig. 9, we assume a typical
nimbostratus cloud, which is roughly one kilometer thick and
has a cloud bottom height of 0.7 km [31]. The cloud density
isassumedtobe0.5g/m
3, which is close to a typical density
of a nimbostratus cloud [31]. The rain rate is assumed to be
5 mm/hr, which corresponds to a moderate rain. Figure 9 shows
the impact of the clouds and rain with the above assumptions
for a slant path and path angled at 45 degrees. The angled path
therefore increases the path lengths inside the rain and clouds by
sec(θ=45◦),or√2. We can see that the losses vary from few
decibels to few tens of decibels. Depending on the frequency
and other losses, this may cause problems in signal reception
and should be taken into account in the link budget consider-
ations. However, as mentioned above, the rain and cloud/fog
attenuations are mostly affecting low altitude communications,
such as E2A communication scenario.
TAB L E I I
THE SIMULATION PARAMETERS USED IN THE NUMERICAL RESULTS
The simulation parameters for the rest of the numerical results
are given in Table II unless otherwise stated. The antenna gains
are calculated with a parabolic antenna equation
G(f)=AeπdA
λ2
,(23)
where Aeis the aperture efficiency, and dAis the diameter of the
antenna. We can see that the antenna gain increases to square
of frequency for fixed size dish when increasing the frequency.
Adding dishes at both ends of the link, the ideal gain of the
antenna gain can be very large and even overcome the electric
size of the antenna visible in free space path loss equation
(λ2/4π). In the low absorption loss region, for fixed distance,
the SNR can therefore theoretically get better when increasing
the frequency. This is also shown later in the SNR calculations.
The parabolic antennas have advantage of providing a lot gain
in relatively compact package than can be mounted on fuselage
of the airplane. Such antennas require an aerodynamic cover
to protect the antenna and to interfere as little as possible with
the overall aerodynamics of the airplane. The downside is the
need for physical beaforming that limits visibility of all the paths
and restricts the maximum beamforming angles to at most the
horizon with respect to the antenna mount, but most likely less
to keep the antenna profile low. If there is a downward link, a
separate antenna is required at the bottom of the fuselage.
The transmission power was chosen to be modestly low to take
into account the fact that at the moment generating a lot of power
in the THz band is difficult. The bandwidth is chosen to be rather
low to decrease the noise bandwidth, which is very important de-
sign aspect for the prospective long range THz communications.
What is the large enough bandwidth that justifies the THz band,
but keeps the noise floor small enough. The antennas are typical
parabolic antennas with 70% aperture efficiency. To show the
impact of the angular differences between the satellite and the
airplane, we utilize 0◦,6.25
◦, and 12.5◦elevation differences
between the two. At GEO orbit being at 35 786 km height and
LEO orbit at 500 km height, those correspond to 0–14.7◦angle
(14.7◦at 0–20 km altitude for 12.5◦elevation difference) from
the zenith at airplane to GEO satellite and 0–78◦degree angle
for the LEO orbits (58.5–77.2◦zenith angle at ground level and
59.6–78.0◦at 20 km altitude). These correspond to angles from
the horizon of the airplane to satellite varying from 12-90◦. These
elevation differences correspond to link distances in S2A to vary

KOKKONIEMI et al.: CHANNEL MODELING AND PERFORMANCE ANALYSIS OF AIRPLANE-SATELLITE TERAHERTZ BAND COMMUNICATIONS 2055
Fig. 8. The surface volume mixing ratio of water vapor (left) and the surface height from the sea level (right).
Fig. 9. Rain and cloud attenuations for slant paths as well as for 45◦angled
paths from zenith.
Fig. 10. Path loss from airplane to satellite for LEO and GEO orbits as a
function of frequency. The airplane altitude is 11 km.
from about 500 to 1526 km for the LEO orbit at 500 km altitude
depending on the airplane altitude (that is rather small compared
to the total link distance), and 35 786 – 35 964 km for the GEO
orbit.
B. Path Losses
Figure 10 shows the path loss from airplane to satellite for
an airplane at 11 km altitude as a function of frequency. The
path losses are shown for a geostationary Earth orbit (GEO,
Fig. 11. Path loss from airplane to satellite for 500 km LEO satellite as a
function of frequency and airplane altitude.
∼36 000 km) and for a low Earth orbit (LEO) at 500 km altitude.
The path losses have been calculated for zenith path and for
elevation differences 6.25–12.5◦through the atmosphere for the
LEO orbit, and 12.5◦elevation difference for the GEO due to
smaller differences between the path losses between different
angles. The LEO connection suffers more from the angled paths
due to the path loss by absorption has more relatively higher
impact on the shorter paths. The GEO path loss is dominated
by the FSPL and the absorption does not have a that large
impact on the total path loss. We can see that the path losses
are considerable. Those range from about 190 to 260 dBs
disregarding the absorption peaks that are much higher. This
means that the required antenna gains need to be very high,
but at the same time, the bandwidths need to be low enough
to keep the noise level down and to avoid the absorption peaks.
Considering fixed aperture antennas, the antenna diameters need
to be in the order of 0.5–1 meters to provide enough gain in
the ideal case. Furthermore, LEO path loss towards zenith as
a function of distance and frequency is given in Fig. 11. This
figure shows that the FSPL dominates vast majority of the high
altitude links with molecular absorption loss increasing towards
the high frequencies and the lower altitudes. This implies that
the A2S/S2A links provide the best performance at the higher
flight altitudes as it will be shown later.
The path losses from Earth to airplane as a function of airplane
altitude are shown in Figs. 12 and 13 for a frequency range from
100 GHz to 1000 GHz. The latter figure assumes LEO height
of 500 km. Any frequencies above 1000 GHz are effectively

2056 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 70, NO. 3, MARCH 2021
Fig. 12. Path loss from Earth to airplane as a function of airplane altitude and
frequency.
Fig. 13. Path loss from Earth to satellite as a function of frequency.
blocked due to high absorption loss close to Earth. We can
see that the below 380–450 GHz frequencies are utilizable
for airplane communications from the ground. However, the
losses remain high and partially so due to high FSPL at high
frequencies. This also means a certain type of a bottle neck
for feeding the satellites. The airplane to satellite links suffer
less from the atmospheric loss and could theoretically utilize
higher frequencies that than the Earth to airplane, or Earth
to satellite links. This potentially opens a door for frequency
division between ground to satellite and air to satellite links.
However, this is also dependent on the capacity requirements,
and hardware limitations. The latter is a major problem at the
THz frequencies and potentially considerable losses have to be
expected from inefficiency of them. In this paper we do not
consider those, as the development of the THz band hardware
is still a major research topic and relatively poorly understood
from the viewpoint of realistic system and link performance.
It should still be kept in mind that more losses are expected
compared to pure atmospheric losses due to rain, clouds/fog,
and other possible mechanism, such as the scattering loss.
Airplane to airplane path loss for a 100 m link is shown in
Fig. 14 as a function of altitude and frequency. As expected, the
path loss decreases with altitude and makes the communications
more simple. Above 10 km height, the loss is mostly comprised
of the FSPL disregarding some spikes in the spectrum. This is
also shown in Fig. 15, which shows the path losses per kilometer
link on ground level and at 11 km height. As a reference,
the antenna gains for 0.5 m diameter dish antenna (’airplane
antenna’) and 1 m diameter dish antenna (’satellite antenna’)
Fig. 14. Path loss from airplane to airplane (common altitude) for a 100 m
link as a function of airplane altitude and frequency.
Fig. 15. Comparison of path losses per kilometer for FSPL, molecular absorp-
tion loss at sea level and 11 km altitude, and antenna gains of 0.5 and 1 m ideal
dish antennas.
are also shown. It should be noticed that the airplanes in general
fly far away from each other and 100 m distance would be
considered very dangerous. The airplane to airplane links do not
have many use cases in civil aircrafts, but would be potential for
military applications and in drone-to-drone applications. Also,
these figures are applicable to on Earth communications due to
varying land height. On a general note on the high frequency
links, the THz band offers a natural protection against third
parties to listen to the data traffic as the FSPL and atmospheric
losses kill the signals over long distances in the lower atmosphere
as seen in Fig. 12 and 14.
C. SNR and Capacity
Based on the path losses, we can estimate the performance
of the extremely long links. Figure 16 shows the path losses
from A2G and S2A (or G2A and A2S) as a function of the
airplane altitude for 660 GHz and 940 GHz center frequencies.
The satellite is on LEO orbit at 500 km height and we show
results also for 12.5◦elevation difference. As it can be expected,
there is a crossover altitude for the lower loss connection di-
rection. This crossover point depends on the frequency and the
elevations of the airplane and the satellite, but suggests that the
best way to provide THz connectivity would be to have both
links available. During the mid-flight, the satellite link provides
better connectivity. Considering that the use of electronic devices

KOKKONIEMI et al.: CHANNEL MODELING AND PERFORMANCE ANALYSIS OF AIRPLANE-SATELLITE TERAHERTZ BAND COMMUNICATIONS 2057
Fig. 16. Comparison of A2G and A2S path losses at 660 and 940 GHz center
frequencies as a function of the airplane altitude for zenith paths and inclined
paths with crossover altitudes where of the minimum loss path.
Fig. 17. Comparison of A2G and A2S capacities at 660 and 940 GHz center
frequencies as a function of the airplane altitude for zenith paths and inclined
paths. The shown capacity is for the minimum path loss path from Fig. 16.
is not allowed during the take off and landing, the satellite link
alone would be enough for the passenger use. These crossover
altitudes are approximately 1.85 km (at ρ=0◦) and 3.3 km (at
ρ=12.5◦) for 940 GHz frequency and 2.5 km (at ρ=0◦) and
4.15 km (at ρ=12.5◦) for 660 GHz. It should also be noticed that
the calculation herein does not take into account the movement
of the airplane that would have more severe impact towards
ground since the link distance is much lower that towards the
satellites. The true path loss towards the ground would therefore
also depend on the available ground stations and their locations,
which would increase the distance and the path loss, most likely
very significantly rendering the low altitude communications
challenging. Especially with physical beam steering that is not
as agile for handovers as electronic beamsteering techniques.
Figure 17 provides the capacity figures for the calculated
minimum path losses in Fig. 16 assuming 1 W transmit power,
5GHz bandwidth, 10 dB noise figure, and 0.5 m dish antenna
at airplane and 1 m dish antenna at satellite and ground. With
these figures, The link budget is formed of the 30 dBm transmit
power, -67 dBm noise floor, uplink antenna gains of 69.2 dBi
72.3 dBi for 660 GHz and 940 GHz frequencies, respectively,
and downlink gains of 75.2 dBi and 78.3 dBi for 660 GHz
and 940 GHz frequencies, respectively. Combined with the path
losses in Fig. 16, the resultant SNR figures on some specific
points are given in Fig. 17. The capacities can exceed 150 Gbps
at close proximity to Earth station. Mid-flight capacities ranging
from 55–70 Gbps can be achieved. Interestingly, whereas the
940 GHz band performs worse close to Earth, it gives increased
capacity at higher frequencies compared to 660 GHz band. This
is attributed to the higher antenna gains at higher frequencies.
This is an interesting results that shows good potential of very
high frequencies for A2S scenarios even if usability of close
to 1 THz frequencies and beyond are difficult on surface level
due to very high path loss. The capacity and SNR figures
herein are remarkably good considering the high path losses.
Theoretically, the calculated SNRs would be able to support very
high modulation orders. In the reality though, additional losses
should be expected and combined with possible adverse weather
conditions, the real average SNRs would be lower. However,
these are very promising figures for the future ultra-high distance
THz communications.
The expected SNR as a function of altitude and frequency for
A2S link to GEO orbit is given in Fig. 18. As a consequence of the
fixed apertures, the effective antenna gain increases to the square
of the frequency per antenna. This is seen as one of the potential
source to compensate the high losses in the channel; It will be
easier to make electrically large antennas at THz frequencies
that significantly increase the antenna gains [32]. As the antenna
gains at both ends of the link increase to square of the frequency
according to (23), this translates into increasing SNR as a
function frequency in Fig. 18 as the free space path loss increases
to the square of frequency. The SNR is further increased by the
altitude of the plane due to before mentioned lower absorption
loss at high altitudes. In the real world, the antenna losses
and power generation become more difficult when moving to
higher frequencies. This can be expected to decrease the overall
transmission performance at higher frequencies. However, the
ideal results herein have shown great potential with room to
move even with higher expected losses. Figure 18 also shows
the SNR limits of some modulation methods for 10−6target BEP
values for 1 GHz bandwidth signal. Namely, for 16-QAM and
BPSK. As expected of the long distance links in the THz band,
the usable modulation orders remain modest to ensure good BEP
performance. It should be noted that the BER values are pure
physical layer BEPs and do not take into account coding. Thus,
the actual BERs would be better with lower overall throughput
due to coding overhead.
Whereas the overall picture favor the higher frequencies be-
cause of theoretically higher achievable antenna gains, the reality
is that the hardware imperfections would most likely decrease
the performances as the frequency is increased. However, the
results herein show great potential for the THz frequency band
for long distance communications. There are many obstacles
ahead to realize these types of systems. Most notably in the
hardware side, but with time and leaps the THz communications
has taken during the past few years, these frequencies will truly
be conquered in the near future. This also then opens doors
for wide range of multiple scales of communications on these
frequencies. As an example, to provide high speed satellite
communications for the airplanes.

2058 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 70, NO. 3, MARCH 2021
Fig. 18. SNR from satellite to airplane as a function of airplane altitude and frequency for GEO orbit. Figure also shows boundaries for square gray coded
16-QAM and BPSK for target BEP probability of 10−6.
VI. CONCLUSION
We presented a channel model for airplane communications
in the THz band in this paper. The results show that the path
losses in airborne links are very high, as it can be expected
from an extremely high distance links operating at very lossy
THz frequencies. However, if the antenna apertures are high,
potentially very large antenna gains can be achieved. Regardless
of the very high path loss, airplane to satellite, and airplane
to airplane communications are perfectly possible on rather
wide spectrum. The Earth to satellite or airplane case is more
demanding due to high absorption loss close to Earth. This may
limit the Earth communications to below 380 GHz frequencies.
In practice, the 100–300 GHz frequency bands are in any case the
first frequencies to be commercially utilized in the near future.
Possible weather impacts will decrease the signal levels, and
increasingly so at higher end of the THz band. The frequency
regulation, on the other hand, will limit the full utilization of the
THz frequencies in the space applications due to protection of the
passive Earth observation services. Although it is often said that
the THz frequencies are only for short distance communications,
they also have great potential in long distance applications. This
is especially the case in space where the atmosphere causes
less channel losses. The numerical results herein showed that
the THz band is a very promising platform for high capacity
links, especially when the applied in high atmosphere. The main
outcome of this paper were the LOS channel model for high
distance THz communication links and a feasibility analysis of
the THz band for those. The future work will leverage the results
by studying real flight paths in simulation models with cloud
coverage and global weather. Based on the results in this paper,
the real flight paths will offer very good performance during the
mid-flight at high altitudes. The take-off and landing are the most
challenging parts of the flight to provide feasible capacity, but on
the other hand those are the times when electronic devices need
to be in offline mode. Therefore, the future of high frequency
communications to bring maximum capacity for the airplanes
looks really bright.
APPENDIX
We give the derivation of the molecular absorption coefficient
in different atmospheric conditions below. The absorption loss
was described Section II-B and it depends on the link distance
and absorption coefficient. The latter depends on pressure, tem-
perature and molecular composition as
κi
a(f)=Niσi(f),(24)
where Niis the number density and σi(f)is the absorption cross
section of the ith absorbing species. The number density Nifor
the absorbing species ican be estimated by the ideal gas law [6],
[18]
Ni=p
p0
T0
Tμin0=p
p0
T0
T
p0
RgT0
μiNA=p
RgTμiNA,(25)
where p0and T0are the standard pressure and temperature
(101 325 Pa and 296 K, respectively), pis the pressure, Tis
the temperature, μiis the volume mixing ratio of absorbing
species i,Rgis gas constant (Rg=kBNA), kBis the Boltzmann
constant, NAis the Avogadro constant and n0=p0NA/(RgT0)
the number density of the molecules in standard pressure and
temperature.
Different molecules have specific abundances in atmosphere.
In addition, the different isotopologues of the molecules have
their natural abundances [6], [18]. We have included all the abun-
dances of molecules and their subspecies into the variable μi.
The abundances of atmospheric molecules and the other parame-
ters for line-by-line calculations can be found in high-resolution
transmission molecular absorption database (HITRAN) [33].
Other similar models to HITRAN, such as GEISA [34] and
JPL [35], also exist.

KOKKONIEMI et al.: CHANNEL MODELING AND PERFORMANCE ANALYSIS OF AIRPLANE-SATELLITE TERAHERTZ BAND COMMUNICATIONS 2059
The absorption cross section σi(f)is calculated as a prod-
uct of spectral line intensity Si(T)and spectral line shape
Fi(p, f, T )(σi(f)=Si(T)Fi(p, f, T )). The absorption cross
section gives the effective absorption area for a single particle.
The spectral line intensity gives the absorption strength of the
spectral lines and spectral line shape gives the shape of the
absorption lines. The line shape is normalized so that the inte-
gration over the line shape equals unity [36]. It should be noticed
that line intensity depends only on temperature and line shape
depends on frequency, pressure and temperature. For simplicity,
we will use notation Fi(f)for line shape, as the line shape is
calculated for each line center fi
0. In order to calculate the line
shape Fi(f), the resonance frequencies fi
cof the line centers
fi
0must be calculated first. The resonance frequencies increase
from zero-pressure position fi
0according to [6], [22]
fi
c=fi
0+δi
p
p0
,(26)
where δiis the linear pressure shift.
Even though the absorption process is discrete in frequency
domain, the individual absorption lines are spread due to colli-
sions between the molecules (Lorentz broadening), as well as
because of the velocity of the molecules (Doppler broadening).
The pressure broadening can be expressed with Lorentz half-
width αi
L(at pressures higher than 10 kPa [22]). This can be
obtained from foreign and self-broadened half-widths αf
0and
αi
0respectively by [18], [22]
αi
L=[(1−μi)αf
0+μiαi
0]p
p0T0
Tγ
,(27)
where γis temperature broadening coefficient. Self-broadening
is caused by the collisions between molecules of the same
species, while foreign-broadening is due to the inter-molecular
collisions. The coefficients γ,αf
0and αi
0can be obtained from
the line catalogues.
At high air pressure, Lorentzian line shapes are utilized [37].
The most familiar of those is the Lorentz line shape [18], [38]
Fi
L(f±fi
c)= 1
π
αi
L
(f±fi
c)2+(αi
L)2.(28)
This was enhanced by Van Vleck and Weisskopf in 1945 [38]
and the Van Vleck-Weisskopf asymmetric line shape is defined
as [38]–[40]
Fi
VVW(f)=f
fi
c2
[Fi
L(f−fi
c)+Fi
L(f+fi
c)].(29)
The Van Vleck-Weisskopf line shape with far end adjustments
can be obtained as in [22]
Fi
VVH(f)= f
fi
c
tanh( hf
2kBT)
tanh( hfi
c
2kBT)[Fi
L(f−fi
c)+Fi
L(f+fi
c)],
(30)
where his Planck constant. This line shape has also been referred
to as Van Vleck-Huber line shape due to derivation by Van Vleck
and Huber [39]. In reality, the differences between these line
shapes are rather small in the THz band and the choice of one
over another does not produce large error.
At low pressures (below one kPa), i.e., in the higher altitudes,
the Doppler broadening becomes the most significant broaden-
ing mechanism and it causes a Gaussian line shape [22]. The
Doppler broadening half-width can be expressed as
αi
D=fi
c
c2log(2)kBT
mic2,(31)
where miis the molar mass of the absorbing species i.The
Doppler line shape can be obtained as
Fi
D(f)=log(2)
παi
D
exp (f−fi
c)2log(2)
cαi
D.(32)
The important thing here is which line shape to choose in
the case of paths that penetrate vast vertical distances in the
atmosphere. As we move from lower altitudes to higher alti-
tudes, we need to decide which line shape is the appropriate
one for calculating the line shape. In the transition zone, i.e.,
where Doppler and Lorentz half widths are comparable, one
should utilize Voigt line shape [37]. This can be obtained as a
convolution of the Lorentz and Doppler line shapes by
Fi
V(f)= 1
√παD
1
π
αi
L
αD±∞
exp(−t2)
[f−fc
αD−t]2+(αi
L
αD)
dt. (33)
In our calculation, we utilize Voigt line shape for those lines that
have Doppler and Lorentz half widths within five times of each
other. Otherwise, the dominant line shape is utilized, i.e., the
one that produces larger line width.
The line intensity Si
0can be obtained from HITRAN database
for reference temperature T0=296 K, but it has to be scaled for
the other temperatures with [41]
Si(T)=Si
0
Q(T0)
Q(T)
e(−hcEi
L
kBT)
e(−hcEi
L
kBT0)⎛
⎝
1−e(−hfi
c
kBT)
1−e(−hfi
c
kBT0)⎞
⎠(34)
where Ei
Lis the lower state energy of the transition of absorbing
species i. Notice that we utilize HITRAN database where the
lower state energies have been given in the units 1/cm. Thus, the
multiplication of Ei
Lwith hc. The partition function Q(T)and
its definitions can be found in [41, Appendix A].
REFERENCES
[1] R. Piesiewicz et al., “Short-range ultra-broadband terahertz communica-
tions: Concepts and perspectives,” IEEE Antennas Propag. Mag., vol. 49,
no. 6, pp. 24–39, Dec. 2007.
[2] I. F. Akyildiz, J. M. Jornet, and C. Han, “Teranets: ultra-broadband
communication networks in the terahertz band,” IEEE Wireless Commun.,
vol. 21, no. 4, pp. 130–135, Aug. 2014.
[3] M. Giordani, M. Polese, M. Mezzavilla, S. Rangan, and M. Zorzi, “Toward
6g networks: Use cases and technologies,” IEEE Commun. Mag., vol. 58,
no. 3, pp. 55–61, Mar. 2020.
[4] T. S. Rappaport et al., “Wireless communications and applications above
100 GHz: Opportunities and challenges for 6G and beyond,” IEEE Access,
vol. 7, pp. 78 729–78 757, 2019.
[5] ICAO, “The world of air transport in 2018,” International Civil Aviation
Organization Report, Tech. Rep., 2018. [Online]. Available: https://
www.icao.int/annual-report-2018/Pages/the- world-of- air-transport-in-
2018.aspx
[6] J. M. Jornet and I. F. Akyildiz,“Channel modeling and capacity analysis for
electromagnetic nanonetworks in the terahertz band,”IEEE Trans. Wireless
Commun., vol. 10, no. 10, pp. 3211–3221, Oct. 2011.

2060 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 70, NO. 3, MARCH 2021
[7] B. Peng and T. Kürner, “Three-dimensional angle of arrival estimation in
dynamic indoor terahertz channels using a forward-backward algorithm,”
IEEE Trans. Veh. Technol., vol. 66, no. 5, pp. 3798–3811, May 2017.
[8] V. Petrov, J. Kokkoniemi, D. Moltchanov, J. Lehtomaki, Y. Koucheryavy,
and M. Juntti, “Last meter indoor terahertz wireless access: Performance
insights and implementation roadmap,” IEEE Commun. Mag., vol. 56,
no. 6, pp. 158–165, 2018.
[9] S. Priebe, M. Kannicht, M. Jacob, and T. Kürner, “Ultra broadband indoor
channel measurements and calibrated ray tracing propagation modeling at
thz frequencies,” J. Commun. Netw., vol. 15, no. 6, pp. 547–558, 2013.
[10] V. Petrov et al., “On unified vehicular communications and radar sensing
in millimeter-wave and low terahertz bands,” IEEE Wireless Commun.,
vol. 26, no. 3, pp. 146–153, Jun. 2019.
[11] C. Han, A. O. Bicen, and I. F. Akyildiz, “Multi-ray channel modeling and
wideband characterization for wireless communications in the terahertz
band,” IEEE Trans. Wireless Commun., vol. 14, no. 5, pp. 2402–2412,
May 2015.
[12] S. Priebe and T. Kürner, “Stochastic modeling of thz indoor radio chan-
nels,” IEEE Trans. Wireless Commun., vol. 12, no. 9, pp. 4445–4455,
Sep. 2013.
[13] J. Y. Suen, M. T. Fang, S. P. Denny, and P. M. Lubin, “Modeling of terabit
geostationary terahertz satellite links from globally dry locations,” IEEE
Trans. Terahertz Sci. Technol., vol. 5, no. 2, pp. 299–313, Mar. 2015.
[14] J. F. Federici, J. Ma, and L. Moeller, “Reviewof weather impact on outdoor
terahertz wireless communication links,” Nano. Commun. Netw., vol. 10,
pp. 13–26, 2016, terahertz Communications. [Online]. Available: http://
www.sciencedirect.com/science/article/pii/S1878778916300394
[15] Y. Balal and Y. Pinhasi, “Atmospheric effects on millimeter and sub-
millimeter (thz) satellite communication paths,” J. Infrared, Millimeter,
Terahertz Waves, vol. 40, pp. 219–230, Mar. 2019.
[16] ITU, “Attenuation by atmospheric gases and related effects,” Recommen-
dation ITU-R P.676-12, Tech. Rep., Aug. 2019.
[17] ITU, “Radio noise,” Recommendation, Tech. Rep. ITU-R P.372-14, Aug.
2019.
[18] S. Paine, “The am atmospheric model,” Smithsonian Astrophysical Obser-
vatory, Cambridge, MA, USA, Tech. Rep. w152, version 11.0, Sep. 2019.
[19] A. Berk, P.Conforti, R. Kennett, T. Perkins, F. Hawes, and J. van den Bosch,
“MODTRAN6: A major upgrade of the MODTRAN radiative transfer
code,” in Algorithms Technol. Multispectral, Hyperspectral, and Ultra-
spectral Imagery XX, M. Velez-Reyes and F. A. Kruse, Eds., vol. 9088,
Int. Soc. Opt. Photon. SPIE, 2014, pp. 113–119. [Online]. Available:
https://doi.org/10.1117/12.2050433
[20] J. R. Pardo, J. Cernicharo, and E. Serabyn, “Atmospheric transmission at
microwaves (ATM): An improved model for millimeter/submillimeter ap-
plications,”IEEE Trans. Antennas Propag.,vol. 49, no. 12, pp. 1683–1694,
Dec. 2001.
[21] “NASA/NOAA’s GOES Project,” Mar. 2014. [Online]. Available:
https://www.nasa.gov/content/three-atmospheric-dragons- low-pressure-
areas-around- the-us/
[22] “Calculation of molecular spectra with the spectral calculator,” [Online].
Available: https://www.spectralcalc.com/info/CalculatingSpectra.pdf
[23] J. Kokkoniemi, J. Lehtomäki, K. Umebayashi, and M. Juntti, “Frequency
and time domain channel models for nanonetworks in terahertz band,”
IEEE Trans. Antennas Propag., vol. 63, no. 2, pp. 678–691, Feb. 2015.
[24] ITU, “Specific attenuation model for rain for use in prediction methods,”
Recommendation, Tech. Rep. ITU-R pp. 838.3, Mar. 2005.
[25] ITU, “Attenuation due to clouds and fog,” Recommendation, Tech. Rep.
ITU-R P.840.8, Aug. 2019.
[26] ITU,“Propagation data and prediction methods required for the design
of 979 of terrestrial line-of-sight systems,” Recommendation, Tech. Rep.
ITU-R P.530-17, Dec. 2017.
[27] T. L Wilson, “Introduction to millimeter/sub-millimeter astronomy,” vol.
38. M. Dessauges-Zavadsky and D. Pfenniger Eds. Berlin, Heidelberg,
Germany: Springer, Mar. 2018. [Online]. Available: https://doi.org/10.
1007/978-3-662- 57546-8_1ps://doi.org/10.1007/978-3- 662-57546-8_1
[28] H. Nyquist, “Thermal agitation of electric charge in conductors,” Phys.
Rev., vol. 32, pp. 110–113, Jul. 1928.
[29] “U.S. standard atmosphere 1976,” NASA, Tech. Rep., NOAA-S/T-76-
1562 Oct. 1976.
[30] “NASA EarthData GES DISC,”[Online]. Available: https://disc.gsfc.nasa.
gov/
[31] S. D. Slobin, “Microwave noise temperature and attenuation of clouds:
Statistics of these effects at various sites in the United States, Alaska, and
Hawaii,” Radio Sci., vol. 17, no. 6, pp. 1443–1454, Nov. 1982.
[32] S. U. Hwu, K. B. deSilva, and C. T. Jih, “Terahertz (THz) wireless systems
for space applications,” in Proc. IEEE Sens. Appl. Symp. Proc., 2013, pp.
1–5,
[33] L. S. Rothman et al., “The HITRAN 2008 molecular spectroscopic
database,” J. Quant. Spectrosc. Radiat. Transfer, vol. 110, no. 9–10,
pp. 533–572, Jun.–Jul. 2009.
[34] N. Jacquinet-Husson et al., “The 2009 edition of the GEISA spectro-
scopic database,” J. Quant. Spectrosc. Radiat. Transfer, vol. 112, no. 15,
pp. 2395–2445, Oct. 2011.
[35] H. M. Pickett, E. A. Cohen, B. J. Drouin, and J. C. Pearson, “Submil-
limeter, millimeter, and microwave spectral line catalog,” 2003. [Online].
Available: http://spec.jpl.nasa.gov/ftp/ pub/catalog/ doc/catdoc.pdf
[36] R. T. Pierrehumbert, Principles of Planetary Climate. Cambridge, U.K.:
Cambridge Univ. Press, 2010.
[37] X. Huang and Y. L. Yung, “A common misunderstanding about the voigt
line profile,” J. Atmos. Sci., vol. 61, pp. 1630–1632, Jul. 2004.
[38] J. H. Van Vleck and V. F. Weisskopf, “On the shape of collision-broadened
lines,” Rev. Mo.d. Phys., vol. 17, no. 2–3, pp. 227–236, 1945.
[39] J. H. Van Vleck and D. L. Huber, “Absorption, emission, and linebreadths:
A semihistorical perspective,” Rev.Mod. Phys., vol. 49, no. 4, pp. 939–959,
1977.
[40] I. Halevy, R. T. Pierrehumbert, and D. P. Schrag, “Radiative transfer
in CO2-rich paleoatmospheres,” J. Geophys. Res., vol. 114, no. D18,
pp. 1–18, Sep. 2009.
[41] L. S. Rothman et al., “The HITRAN molecular spectroscopic database and
HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant.
Spectrosc. Radiat. Transfer, vol. 60, no. 5, pp. 665–710, Nov. 1998.
Joonas Kokkoniemi (Member, IEEE) received the
B.Sc. (Tech.), M.Sc. (Tech.), and Dr.Sc. (Tech.) de-
grees in communications engineering from the Uni-
versity of Oulu, Oulu, Finland, in 2011, 2012, and
2017, respectively. He is currently a Postdoctoral
Research Fellow with Centre for Wireless Commu-
nications, the University of Oulu. From September to
November 2013, he was a Visiting Researcher with
the Tokyo University of Agriculture and Technology,
Tokyo, Japan. From March to October 2017, he was
a Visiting Postdoctoral Researcher with the State
University of New York at Buffalo, Buffalo, NY, USA. His research interests
include THz band and mmWave channel modeling and communication system’s
analysis.
Josep M. Jornet (Senior Member, IEEE) received
the B.S. in telecommunication engineering, the M.Sc.
in information and communication technologies in
2008 from Universitat Politecnica de Catalunya,
Barcelona, Spain, and the Ph.D. degree in electrical
and computer engineering from the Georgia Institute
of Technology (Georgia Tech), Atlanta, GA, USA,
in 2013. Between August 2013 and August 2019,
he was a Faculty with the Department of Electrical
Engineering, the University at Buffalo, The State
University of New York, Buffalo, NY, USA. Since
2019, he has been an Associate Professor with the Department of Electrical
and Computer Engineering, the Director of the Ultrabroadband Nanonetworking
Laboratory and a Member of the Institute for the Wireless Internet of Things and
the SMART Center, Northeastern University, Boston, MA, USA. He is currently
the Lead PI on multiple grants from U.S. federal agencies, including the National
Science Foundation, the Air Force Office of Scientific Research, and the Air
Force Research Laboratory. He has authored or coauthored more than 160 peer-
reviewed scientific publications, one book, and has also been granted four US
patents in his research areas, which include terahertz communication networks,
wireless nano-bio-communication networks, and the Internet of Nano-Things.
Since July 2016, he has been a Editor-in-Chief of the Nano Communication
Networks Journal (Elsevier). He was the recipient of the National Science
Foundation CAREER Award and several other awards from IEEE, ACM, UB,
and Northeastern University.

KOKKONIEMI et al.: CHANNEL MODELING AND PERFORMANCE ANALYSIS OF AIRPLANE-SATELLITE TERAHERTZ BAND COMMUNICATIONS 2061
Vitaly Petrov (Member, IEEE) received the Special-
ist degree in information systems security from the
Saint Petersburg State University of Aerospace In-
strumentation, Saint Petersburg, Russia, the M.Sc. de-
gree in IT and communications engineering, and the
Ph.D. degree in communications engineering from
the TampereUniversity of Technology,Tampere, Fin-
land, in 2011, 2014, and 2020, respectively. Since
2020, he has been a Senior Standardization Specialist
and a 3GPP RAN1 delegate with Nokia Bell Labs,
Helsinki, Finland. In 2018, he was a Visiting Re-
searcher with The University of Texas at Austin, Austin, TX, USA, in 2016 and
2019, a Visiting Researcher with University at Buffalo, The State University of
New York, Buffalo, NY, USA, and in 2014, a Visiting Scholar with the Georgia
Institute of Technology, Atlanta, GA, USA. His current research interests include
mmWave and THz band communications, softwarized networks, cryptology,and
network security. He was the recipient of the Best Student Paper Award at IEEE
VTC-Fall 2015, the Best Student Poster Award at IEEE WCNC 2017, and the
Best Student Journal Paper Award from IEEE Finland in 2019.
Yevgeni Koucheryavy (Senior Member, IEEE) re-
ceived the Ph.D. degree from the Tampere University
of Technology, Tampere, Finland, in 2004. He is
currently a Professor and the Lab Director with the
Unit of Electrical Engineering, Tampere University
of Technology. He has authored or coauthored nu-
merous publications in the field of advanced wired
and wireless networking and communications. His
current research interests include various aspects in
heterogeneous wireless communication networks and
systems, the Internet of Things and its standardiza-
tion, and nanocommunications. He is an Associate Technical Editor of the
IEEE Communications Magazine and the Editor of the IEEE COMMUNICATIONS
SURVEYS AND TUTORIALS.
Markku Juntti (Fellow, IEEE) received the M.Sc.
(EE) and Dr.Sc. (EE) degrees from the University
of Oulu, Oulu, Finland, in 1993 and 1997, respec-
tively.
From 1992 to 1998, he was with the University of
Oulu. From 1994 to 1995, he was a Visiting Scholar
with Rice University, Houston, TX, USA. From 1999
to 2000, he was a Senior Specialist with Nokia Net-
works, Oulu, Finland. Since 2000, he has been a Pro-
fessor of communications engineering with the Uni-
versity of Oulu, Centre for Wireless Communications
(CWC), where he leads the Communications Signal Processing Research Group.
He is also the Head of CWC Radio Technologies (RT) Research Unit. He is also
an Adjunct Professor with Department of Electrical and Computer Engineering,
Rice University, Houston, TX, USA. He has authored or coauthored almost
500 papers published in international journals, conference records, and books
Wideband CDMA for UMTS in 2000–2010, Handbook of Signal Processing
Systems in 2013 and 2018 and 5G Wireless Technologies in 2017. His research
interests include signal processing for wireless networks and communication
and information theory.
He was the Editor of IEEE TRANSACTIONS ON COMMUNICATIONS and an
Associate Editor for IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY.He
was the Secretary of IEEE Communication Society Finland Chapter in 1996–97
and the Chairman for years 2000–2001. He has been Secretary of the Technical
Program Committee (TPC) of the 2001 IEEE International Conference on
Communications (ICC), and the Chair or Co-Chair of the Technical Program
Committee of several conferences including 2006 and 2021 IEEE International
Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC),
the Signal Processing for Communications Symposium of IEEE Globecom
2014, Symposium on Transceivers and Signal Processing for 5G Wireless and
mmWave Systems of IEEE GlobalSIP 2016, ACM NanoCom 2018, and 2019
International Symposium on Wireless Communication Systems (ISWCS). He
was also the General Chair of 2011 IEEE Communication Theory Workshop
(CTW 2011) and 2022 IEEE Workshop on Signal Processing Advances in
Wireless Communications (SPAWC).