A line-of-sight channel model for the 100–450 gigahertz frequency band

Abstract

This paper documents a simple parametric polynomial line-of-sight channel model for 100–450 GHz band. The band comprises two popular beyond fifth generation (B5G) frequency bands, namely, the D band (110–170 GHz) and the low-THz band (around 275–325 GHz). The main focus herein is to derive a simple, compact, and accurate molecular absorption loss model for the 100–450 GHz band. The derived model relies on simple absorption line shape functions that are fitted to the actual response given by complex but exact database approach. The model is also reducible for particular sub-bands within the full range of 100–450 GHz, further simplifying the absorption loss estimate. The proposed model is shown to be very accurate by benchmarking it against the exact response and the similar models given by International Telecommunication Union Radio Communication Sector. The loss is shown to be within ±2 dBs from the exact response for one kilometer link in highly humid environment. Therefore, its accuracy is even much better in the case of usually considered shorter range future B5G wireless systems.

Full text

A line‑of‑sight channel model forthe100–
450 gigahertz frequency band
Joonas Kokkoniemi* , Janne Lehtomäki and Markku Juntti
1 Introduction
e high-frequency communications aim at finding large contiguous bandwidths to
serve high data rate applications and services. Especially the millimeter wave (mmWave)
frequencies (30–300 GHz) are among the most prominent to provide high data rate
connectivity in fifth generation (5G) and beyond (B5G) systems [1–4]. In this context,
the 5G systems will utilize the below 100 GHz frequencies, whereas the B5G systems,
including the visioned sixth generation (6G) systems, will look for spectral resources
also above 100 GHz [3]. ese frequencies would theoretically allow very large band-
widths, but there are still many challenges to reach the above 100 GHz band efficiently
with compact and portable devices. To overcome the challenges in conquering these fre-
quencies, there have been and are ongoing a lot of research efforts towards understand-
ing the propagation channels, beamforming challenges, and transceiver hardware. For
instance, EU Horizon 2020 projects TERRANOVA [5] for the low THz frequencies 275–
325 GHz, and ARIADNE [6] for the D band (110–170 GHz). Also, the first standards for
the THz communications are appearing, such as IEEE 802.15.3d [7]. us, the utilization
Abstract
This paper documents a simple parametric polynomial line-of-sight channel model for
100–450 GHz band. The band comprises two popular beyond fifth generation (B5G)
frequency bands, namely, the D band (110–170 GHz) and the low-THz band (around
275–325 GHz). The main focus herein is to derive a simple, compact, and accurate
molecular absorption loss model for the 100–450 GHz band. The derived model relies
on simple absorption line shape functions that are fitted to the actual response given
by complex but exact database approach. The model is also reducible for particular
sub-bands within the full range of 100–450 GHz, further simplifying the absorption
loss estimate. The proposed model is shown to be very accurate by benchmarking it
against the exact response and the similar models given by International Telecommu-
nication Union Radio Communication Sector. The loss is shown to be within ±2 dBs
from the exact response for one kilometer link in highly humid environment. Therefore,
its accuracy is even much better in the case of usually considered shorter range future
B5G wireless systems.
Keywords: Absorption loss, THz channel modeling, THz communications, THz
propagation
Open Access
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RESEARCH
Kokkoniemietal. J Wireless Com Network (2021) 2021:88
https://doi.org/10.1186/s13638‑021‑01974‑8
*Correspondence:
joonas.kokkoniemi@oulu.fi
Centre for Wireless
Communications (CWC),
University of Oulu, P.O.
Box 4500, 90014 Oulu,
Finland
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Kokkoniemietal. J Wireless Com Network (2021) 2021:88
of the +100 GHz frequencies for the near future wireless communication systems looks
very promising.
One of the most important research topics on new frequency bands, knowledge of the
operational channels is in the focal point to understand the fundamental physical limits
of the transmission platform. is paper considers the line-of-sight (LOS) propagation
in the sub-THz and low-THz frequencies at frequency range from 100 to 450 GHz.1 e
main goal of this paper is to give tools to model the molecular absorption loss with a
simple model that has minimal loss in accuracy to full line-by-line models. e molecu-
lar absorption loss is caused by the energy of the photons being absorbed by the free
energy states of the molecules [9]. e absorption loss is described by the Beer–Lambert
law, and it causes exponential frequency selective loss on the signals as a function the
frequency. e lowest absorption lines lie at low mmWave frequencies [10], but the first
major absorption lines appear above 100 GHz.
e molecular absorption loss is most often modeled by line-by-line models for
which the parameters are obtained from spectroscopic databases, such as high-resolu-
tion transmission molecular absorption database (HITRAN) [10]. e work herein uti-
lizes the spectroscopic databases by obtaining the parameters for the major absorption
lines, and we simplify those by simple polynomials that only depend on the water vapor
content in the air. ese are then applied to the Beer–Lambert’s law to obtain distance
dependent absorption loss. e free space propagation is modeled by the square-law free
space path loss (FSPL). us, the produced model is a simple and a relatively compact
way to estimate the total free space loss on the above 100 GHz frequencies. e main
use case of the produced model is to be able to omit the complicated spectroscopic data-
bases that take efforts to implement and use flexibly. is is especially the case with the
common wireless communications problems where detailed information on the source
of the loss is not required, but just an easy way to model it.
Starting from the 100 GHz frequency, we model six absorption lines at about 119 GHz,
183 GHz, 325 GHz, 380 GHz, 439 GHz, and 448 GHz. is adds two lines at 119 GHz
and 183 GHz to our previous model ([8]) in order to address the D band propagation.
Water vapor is the main cause of the absorption losses in the above 100 GHz frequencies
and all but one of the above six lines are caused by it. Absorption at 119 GHz is caused
by oxygen, and it is comparably weak. Although weak, it has been included in the model,
since it is part of the D band and it causes a small attenuation on long distance links.
ere exist a lot of research on the line-by-line models and models for calculating the
absorption spectrum, such as [9, 11–14]. ere are also some existing works on para-
metric absorption loss models. International Telecommunication Union Radio Com-
munication Sector (ITU-R) has provided a model to calculate gaseous attenuation up
to 1000 GHz in ITU-R P.676-8 [15]. is model is line-by-line based, and its output is
therefore matched with those of the full spectroscopic databases. ere is, however, a
difference to the proposed model in this paper: ITU-R uses a modified full Lorentz line
shape function that is not in general recommended for the millimeter frequencies [11]
due to heavy tailed frequency domain absorption distribution. A better choice is a model
1 is paper is an invited extended version of the conference paper presented in the EuCNC’19 conference [8].
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Kokkoniemietal. J Wireless Com Network (2021) 2021:88
that takes into account lower wing absorption by using line shape such as van Vleck–
Weisskopf or van Vleck–Huber [11]. Furthermore, the full model by ITU-R still requires
large numbers of tabulated parameters (553) that render its utilization similarly slow as
the full databases. In [15], a polynomial-based approximation is also given. It is valid
up to 350 GHz, but it is somewhat usable up to about 450 GHz. Newer version of this
model, ITU-R 676-11, also exists but that version does not have a polynomial model. We
use the older version in this paper as we present a similar (but more simpler) polynomial
model.
Compared to the proposed model, the ones presented in [15] have several weaknesses.
e ITU-R models [15] include lines even up to 1780 GHz, but it is only specified to be
valid for frequencies up to 350 GHz. e simplified model in the newer version is also
limited to 350 GHz. e model also includes nine polynomials. If some of these terms
are removed, they may also affect frequencies in different bands due to additive nature
of the absorption lines. For example, the term involving 1780 GHz has to be kept or
the attenuation levels between the peaks absorption frequencies at lower frequencies is
incorrect. However, the ITU-R models are still fairly accurate below 450 GHz. Because
of the Full Lorentz line shape model, they overestimate the absorption line wing absorp-
tion. As detailed above, we will give a model with the extended frequency range and
more accurate estimate for the absorption loss in simple form. is model can also be
reduced to a simpler one (due to utilization of a fit parameter) for a desired sub-band
within the full range of the model (100–450 GHz).
We have given a simplified molecular absorption loss model in the past in [16]. It was
intended for the 275–400 GHz band. We also gave an extended version of that in [8] for
frequencies from 200–450 GHz. is paper is an extended version of [8] with new lines
focusing on the D band. As mentioned above, the main goal of this paper is to provide
easy and accurate tools to estimate the LOS path loss above 100 GHz. e proposed
model is shown to be very accurate by numerical results in Sect.3, where it is bench-
marked against the line-by-line models as well as the ITU-R parametric models.
e rest of this paper is organized as follows: Sect.2 derives the proposed absorption
loss model, Sect.3 gives some numerical examples, and Sect.4 concludes the paper.
2 Simplied molecular absorption loss model
2.1 Molecular absorption loss
e main goal of this paper is to provide a tool to easily model the molecular absorption
loss. It is formally described by the Beer–Lambert law, which gives the transmittance,
i.e., the fraction of energy that propagates through the medium at link distance d. is
exponential power law depends on the link distance and absorption coefficient by [9, 11]
where
τ(f,d)
is the transmittance, f is the frequency, d is the distance from transmitter
(Tx) to receiver (Rx),
Pt(f)
and
Pr(f)
are the Tx and Rx powers, respectively, and
κj
a(f)
is the absorption coefficient for the jth type of molecule or its isotope at frequency f.
e absorption coefficient is usually calculated with databases of spectroscopic param-
eters, such as the HITRAN database [10], GEISA [17], or JPL [18]. Detailed calculation
(1)
τ(
f,d)=
P
r(
f
)
Pt(f)
=e−�jκj
a(f)d
,
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Kokkoniemietal. J Wireless Com Network (2021) 2021:88
of the absorption coefficient with line-by-line models can be found, e.g., in [9, 11, 16]. To
summarize the line-by-line models based on the spectroscopic databases, the molecu-
lar absorption coefficient is calculated by calculating the effective cross-sectional area of
the individual molecules for absorption. is area depends on the absorption line shape
functions for which the parameters are obtained from the spectroscopic databases.
Finally, the cross-sectional areas of different types of molecules are multiplied with the
respective number densities to obtain the total absorption loss coefficient. We derive the
simplified absorption loss coefficient expressions based on the theory described above.
2.2 Simplied absorption loss model
e polynomial absorption loss model is obtained by searching the strongest absorp-
tion lines on the band of interest and extracting the parameters for those from the spec-
troscopic databases. e temperature and pressure dependent coefficients are fixed. As
the absorption on the frequencies above 100 GHz is mainly caused by the water vapor,
the volume mixing ratio of water vapor is left floating. e parametric model is charac-
terized by the absorption coefficients
yi
at absorption lines i. e above Beer–Lambert
model becomes
where f is the desired frequency grid,
yi
is an absorption coefficient for the ith absorp-
tion line,
g(f,µ)
is a polynomial to fit the expression to the actual theoretical response
(detailed below), and
µ
is the volume mixing ratio of water vapor. It is determined from
the relative humidity
φ
at temperature T and pressure p by
where
φp∗
w
(
T,p
)/
100
is the partial pressure of water vapor and
p∗
w
is the saturated water
vapor partial pressure, i.e., the maximum partial pressure of water vapor in the air. is
can be obtained, e.g., from the Buck equation [19]
where the pressure p is given in hectopascals and T is given in degrees of centigrade.
e six polynomials for the six major absorption lines at the 100–450 GHz band are
the following2:
(2)
PLabs(f,µ)
=
e
d

i
yi(f,µ)+g(f,µ)
,
(3)
µ
=
φ
100
p∗
w(
T,p
)
p,
(4)
p∗
w=6.1121(1.0007 +3.46 ×10−6p)exp
17.502T
240.97
+
T,
(5)
y1(f,µ) =
A(µ)
B(µ) +

f
100c−p1

2
,
2 Please note that in our conference version [8], to which this paper is an extension to, there was a typo that is rectified
in this paper. e terms
(f/
100
c
−
px)2
were not squared therein. is causes the model therein to give an incorrect
output. However, this happens at so notable level that it should be obvious if one tries to implement the model and com-
pares to our results. e numerical results in [8] were made with correct expressions.
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where, c is the speed of light (m/s), the frequency f is given in Hertz, and
where
p1=3.96
cm
−1
,
p2=6.11
cm
−1
,
p3=10.84
cm
−1
,
p4=12.68
cm
−1
,
p5=14.65
cm
−1
,
p6
=
14.94
cm
−1
,
a=0.915 ×10−112
,
b=9.42
. e lines
y1
,
y2
,
y3
,
y4
,
y5
, and
y6
correspond to strong absorption lines at center frequencies 119 GHz, 183 GHz,
325 GHz, 380 GHz, 439 GHz, and 448 GHz, respectively. is is also visible in the line
expressions as the parameters
p1
to
p6
give the line center frequencies in wavenumbers.
ese parameters are accurate for the whole frequency band 100–450 GHz. However,
slightly improved performance between the absorption lines below 200 GHz can be
achieved by using value
2×10−5
in the place of
2×10−4
in (11). is only has minor
impact on very long link distances, such as one kilometer and beyond link distances.
(6)
y2(f,µ) =
C(µ)
D(µ) +

f
100c−p2

2
,
(7)
y3(f,µ) =
E(µ)
F(µ) +

f
100c−p3

2
,
(8)
y4(f,µ) =
G(µ)
H(µ) +

f
100c−p4

2
,
(9)
y5(f,µ) =
I(µ)
J(µ) +

f
100c−p5

2
,
(10)
y6(f,µ) =
K(µ)
L(µ) +

f
100c−p6

2
,
(11)
g(f,µ) =
µ
0.0157
(2×10−4+af b)
,
A(µ) =5.159 ×10−
5
(1−µ)(−6.65 ×10−
5
(1−µ) +0.0159)
,
B(µ) =(−2.09 ×10−4(1−µ) +0.05)2,
C(µ) =0.1925µ(0.1350µ+0.0318),
D(µ) =(0.4241µ+0.0998)2,
E(µ) =0.2251µ(0.1314µ+0.0297),
F(µ) =(0.4127µ+0.0932)2,
G(µ) =2.053µ(0.1717µ+0.0306),
H(µ) =(0.5394µ+0.0961)2,
I(µ) =0.177µ(0.0832µ+0.0213),
J(µ) =(0.2615µ+0.0668)2,
K(µ) =2.146µ(0.1206µ+0.0277),
L(µ)
=
(0.3789µ
+
0.0871)
2
,
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e above absorption lines were estimated based on the simple Lorentz line shape.
e reason is the simpler form as compared to more accurate, but at the same time
more complex line shapes, such as the van Vleck–Huber line shape [12, 20]. is
produces an error as the Lorentz line shape over estimates the absorption line wing
absorption. erefore, the fit polynomial
g(f,µ)
is introduced. is fit polynomial
also takes care of the wing absorption in the case the model is only utilized partially.
at is, if one only utilizes some of the lines to model a sub-band within the full 100–
450 GHz band, the fit polynomial in (11) as in full model should always be included.
It was obtained by curve fitting to the difference between the exact response and the
response of the above
yi
lines. It would be possible to calculate the exact difference
theoretically, but would only apply to the in-band absorption lines and this would
not consider the out-of-band wing absorption, mainly from lines above 450 GHz. e
total absorption loss with the above model is shown to produce very accurate esti-
mate of the loss in the numerical results.
e water vapor volume mixing ratio is taken into account in the fit polynomial
g(f,µ)
based on the volume mixing ratio calculated from water vapor according to
(3). Whereas it is highly accurate, this estimate will cause some error that is depend-
ent on the water vapor level. Figure1 shows the error of the absorption coefficient to
the exact one based on the above absorption loss model and before applying the fit
polynomial. is error was calculated at 25 degrees centigrade and in various volume
mixing ratios of water vapor
µ
= [0.0031 0.0094 0.0157 0.0220 0.0282] that corre-
spond to relative humidities
φ
= [10% 30% 50% 70% 90%], respectively, at 298.15 K
(25 degrees centigrade) temperature and at standard pressure 101,325 Pa. In this fig-
ure, taking into account the exponential y-axis, the error is small. However, the error
increases as a function of frequency. is is due to the increasing and accumulating
wing absorption from the higher frequency lines. is is the error the fit polynomial
g
(
f,µ)
rectifies by adjusting the absorption lines shapes. e value 0.0157 in
g
(
f,µ)
100 150 200 250 300 350 400 450
Frequency [GHz]
10-6
10-5
10-4
10-3
10
-2
Difference to exact absorption coefficient
RH = 90%
RH = 70%
RH = 50%
RH = 30%
RH = 10%
Fig. 1 An error of the proposed absorption coefficient. An error of the absorption coefficient of the
proposed model to the exact one as a function of the frequency for different humidity levels before adding
the fit polynomial
g(f,µ)
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Kokkoniemietal. J Wireless Com Network (2021) 2021:88
comes from the design atmospheric conditions of 25 degrees centigrade and 50% rela-
tive humidity at standard pressure. It should be noticed that the error is the smallest
for lower humidities due to the fact that there is less water in the air, and thus, the
overall difference between the exact and estimated absorption coefficient is small.
2.3 FSPL andthetotal loss
e total loss in pure LOS path requires the molecular absorption loss and the loss
due to free space expansion of the waves. e FSPL is given by the Friis transmission
equation:
We focus herein only on the free space propagation and thus the total LOS path loss is
given by the FSPL and the molecular absorption loss as
where
GRx
and
GTx
are the antenna gains. When using the polynomial models above, the
absorption coefficient
κa(f,µ)
is
where the
yi(f,µ)
are the above polynomial absorption lines (and as also shown in (2)),
or subset of those depending on the modeled frequency band within the frequency
range from 100–450 GHz. For instance, a D band propagation model would only require
lines
y1
(
f,µ)
and
y2
(
f,µ)
. Another popular band for high-frequency communications is
the 275–325 GHz band. en, only the line
y3(f,µ)
would be enough. e fit polynomial
g(f,µ)
is always required and because of it we can use very low complexity models for
the possible sub-bands, further pronouncing the complexity benefits as compared to the
ITU-R polynomial model. It will be shown in the numerical results that these subsets
give very accurate estimate of the loss also in partial bands without a need to implement
all the lines in the model.
3 Numerical results anddiscussion
In this section, we first present some performance analysis for the proposed molecular
absorption loss model. is is done by analyzing the error produced by the model to
the exact model, as well as comparing it to the ITU-R parametric and full models. After
that, we analyze the accuracy of the model with reduced polynomials. Lastly, we give
link budget calculations for some common +100 GHz frequency bands.
3.1 Error performance analysis
We compare the path loss values of the proposed molecular absorption loss model ver-
sus the ITU-R models in Figs.2, 3 and 4 for the relative humidity levels from 10% to 90%,
respectively, at 25 degree centigrade for a one-kilometer link. A high link distance was
(12)
PL
FSPL(d,f)=
(4πdf )
2
c
2
.
(13)
PL
(d,f)=
(4πdf )
2
exp(κa(f,µ)d)
c
2GRxGTx
,
(14)
κ
a(f,µ) =

i
yi(f,µ) +g(f,µ)
,
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used to emphasize the differences between the models. is is because the impact of the
molecular absorption loss decreases for short distances due to exponential power law.
As it was predicted above, the Lorentz line shape (along with the full Lorentz line
shape) overestimates the wing absorption. is is not a major issue at higher parts of
the THz band due to more lines and line mixing. However, at the lower frequencies this
is a problem because the Lorentz line shape does not attenuate the absorption wing
response fast enough towards the zero frequency. As a consequence, the ITU-R models
give higher path loss figures in general for below 500 GHz frequencies. e difference
to the actual response varies from few dBs to tens of dBs depending on the link distance
and humidity level. Notice that the simplified reduced version of the ITU-R model does
not include all the lines leading to incorrect results.
Fig. 2 Molecular absorption loss at 1 km distance and 10% relative humidity. Molecular absorption loss at 1
km distance at 25 degrees centigrade and 10% relative humidity (
µ
=
0.0031
)
Fig. 3 Molecular absorption loss at 1 km distance. Molecular absorption loss at 1 km distance at 25 degrees
centigrade and 50% relative humidity (
µ
=
0.0157
)
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ere are a couple of further observations to be made. e ITU-R models are
based on the full Lorentz model, but the database specific one does overestimate the
response even more. is is due to reason that the ITU-R model is a modified version
of the full Lorentz model that increases its accuracy. Second observation is that the
proposed model is rather accurate, but not perfect. In Figs.2 to 4, the difference is the
largest below 200 GHz. However, the large part of the apparent difference comes from
the logarithmic y-axis. Figure 5 gives the true worst case error herein. is figure
shows the error of the path loss for one kilometer link at 25 degrees centigrade and at
90% relative humidity. It can be seen that the error is very good across the band, but
the lower frequencies do give comparably slightly larger error due to in general lower
absorption loss. However, the figures herein are for one kilometer link and the error
Fig. 4 Molecular absorption loss at 1 km distance and 90% relative humidity. Molecular absorption loss at 1
km distance at 25 degrees centigrade and 90% relative humidity (
µ
=
0.0282
)
100 150 200 250 300 350 400 450
Frequency [GHz]
0
5
10
15
20
25
30
Error to exact for 1 km link [dB]
ITU full model
Proposed model
Fig. 5 Error of the model and comparison with ITU-R model. Absolute errors given by the ITU-R full model
and the proposed model to the exact theory for a one kilometer link
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will decrease with decreasing distance due to exponential behavior of the absorption
loss. us, the resultant error of roughly ±2 dB is very good for such extremely high
link distances considering the high frequencies and their general applicability to low
range communications. Furthermore, the error also decreases in less humid environ-
ment and this is in general true for ITU-R models as well. For instance at 10% relative
humidity at 25 degrees centigrade, the differences are rather modest. Regardless of
this, in more humid environments there is a notable difference between the models,
especially above the 200 GHz frequencies.
As a last note on the error performance, all the models herein are rather accurate and
it is an application specific issue how accurately the absorption loss needs to be calcu-
lated. If the link distance is high or the communications band is in the vicinity of the
absorption line, the importance of the correct loss is high. However, on low distance
links and in the middle of the low loss regions of the spectrum the absorption loss is
modest and large error is not made if the absorption loss is omitted altogether.
3.2 Performance ofthemodel withreduced terms
If one targets only some sub-band within the 100–450 GHz band, the proposed
model can be further simplified by only using subset of the polynomials
yi
. Figures6
and 7 compare the performance of the proposed model with reduced terms against
the exact theory. Figure6 shows performance of the proposed model when using the
first two lines at about 119 GHz and 183 GHz separately and jointly (shown as lines 1
and 2 in the figure). In the other words, one should utilize the absorption coefficient as
κa(f,µ)
=
y1(f,µ)
+
g(f,µ)
or
κa(f,µ)
=
y1(f,µ)
+
y2(f,µ)
+
g(f,µ)
for lines 1 and 1
and 2 jointly, respectively. is reduction corresponds roughly to the frequency range
of the D band. It can be seen that the proposed model with reduced terms performs
very well on estimating the absorption loss. e same occurs in the case of Fig.7 that
shows the performance of the next two lines (lines 3 and 4) corresponding to frequen-
cies 325 GHz and 380 GHz. ese two line alone gives a very good estimate of the loss
100 120 140 160 180 200
Frequency [GHz]
-20
0
20
40
60
80
Absorption loss for one kilometer link [dB]
Exact theory
Proposed model, lines 1 and 2
Proposed model, line 1
Error to exact, lines 1 and 2
Error to exact, line 1
Fig. 6 Performance of the proposed model with reduced terms, low band. Reduced versions of the
proposed model giving absorption losses up to about 160 GHz (1 term) and 200 GHz (2 terms)
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Kokkoniemietal. J Wireless Com Network (2021) 2021:88
up to about 330 GHz and 390 GHz for the line 3 and joint lines 3 and 4, respectively.
ese correspond to utilizing an absorption coefficient as
κa(f,µ)
=
y3(f,µ)
+
g(f,µ)
and
κa
(
f,
µ) =
y3
(
f,
µ) +
y4
(
f,
µ) +
g
(
f,µ)
. As such, the line 3 would be mostly enough
for the popular transition frequencies between the mmWave and THz bands. Namely
275–325 GHz. However, with these two lines, the model remains accurate from about
200 GHz up to the above-mentioned 390 GHz. erefore, the proposed model is flexible
and easily reducible for multiple frequency bands within the full range from 100 to 450
GHz for some specific applications that occupy only certain sub-band.
3.3 Link budget calculations
To show some examples on use cases for simple channel model, we give link budget
calculations for the D band and THz band below. We assume long distance backhaul
connection, a one kilometer LOS link. For the D band, we have chosen the free bands
for wireless communications therein according to European Conference of Postal and
280 300 320 340 360 380400 420440
Frequenc
y
[GHz]
0
50
100
150
Absorption loss for one kilometer link [dB]
Exact theory
Proposed model, lines 3 and 4
Proposed model, line 3
Error to exact, lines 3 and 4
Error to exact, line 3
Fig. 7 Performance of the proposed model with reduced terms, high band. Reduced versions of the
proposed model giving absorption losses up to about 330 GHz (3rd line only) and 390 GHz (lines 3 and 4
only)
Table 1 Link budget calculations for the D band channels. Values in brackets are the exact
theoretical values
Parameter
D1
D2
D3
D4
Center frequency (GHz) 132.00 144.75 157.75 170.90
Bandwidth (GHz) 3 7.5 12.5 7.8
Transmit power (dBm) 0
Tx/RX antenna gain (dBi) 48.3 49.1 49.9 50.6
Noise figure (dB) 10
Noise floor (dBm)
−69.2
−65.2
−63.0
−65.0
Link distance (m) 1,000
Path loss (dB) 135.1 (135.2) 136.0 (136.1) 137.0 (137.1) 139.4 (139.4)
Rx power (dBm)
−38.5
(
−38.5
)
−37.8
(
−37.8
)
−37.3
(
−37.4
)
−38.2
(
−38.2
)
SNR (dB) 30.6 (30.6) 27.4 (27.3) 25.6 (25.6) 26.8 (26.8)
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Kokkoniemietal. J Wireless Com Network (2021) 2021:88
Telecommunications Administrations (CEPT) Electronic Communications Commit-
tee (ECC) Recommendation 18(01) [21]. ose are detailed in Table1. For the THz
band, we utilize every second channel of 802.15.3d standard with 8.64 GHz channeli-
zation [7]. ese channels are given in Table2. e transmit powers at the high-fre-
quency bands have not been regulated other than by maximum radiation intensities
[22] that are typically in the range of 55 f−
0.177
G
W/m
2
depending on the source and
application, where
fG
is frequency in GHz. us, we use 0 dBm transmit power for all
bands in order to have rather conservative radiated power with respect to the radia-
tion limits and what the current THz capable devices are able to output. A one kilo-
meter link at +100 GHz frequencies requires very large antenna gains. We assume
parabolic reflector antennas to provide very large gain. e gain of such antenna is
given by
where
Ae
is the aperture efficiency,
da
is the diameter of the parabolic reflector, and

is
the wavelength. We assume aperture efficiency of 70% herein and a 225 mm diameter
for the parabolic antenna. is diameter is equivalent to that of the Cassegrain antennas
developed in TERRANOVA project [23]. is size parabolic antenna gives about 55 dBi
gain at 300 GHz frequency [23] and as also shown below in Table2 based on (15) with
the above parameters. e antenna gains per band, average path loss per channel, and
the received powers and SNRs are given in Tables1 and 2. e average path losses per
band (indexed in Tables1 and 2) compared to the theoretical path losses from theoreti-
cal path loss given by molecular absorption loss in (1) and FSPL given in (12) are given in
Fig.8. For these calculations, no other losses, such as antenna feeder losses, are assumed.
e main aim here is to estimate performance of the simplified path loss model.
Based on the link budget calculations, the proposed simplified model gives a very
good performance without a need for complex line-by-line models. e link budget
calculations are among the most important applications for estimating the required
antenna gains and transmit powers for novel wireless systems. A simple channel gain
estimate helps to quickly calculate the expected channel loss within the overall link
(15)
G
a=Ae

πda

2
,
Table 2 Link budget calculations for the THz band channels. Values in brackets are the exact
theoretical values
Parameter
T1
T2
T3
T4
Center frequency (GHz) 265.68 282.96 300.24 317.52
Bandwidth (GHz) 8.64
Transmit power (dBm) 0
Tx/RX antenna gain (dBi) 54.4 54.9 55.5 55.9
Noise figure (dB) 10
Noise floor (dBm) -64.6
Link distance (m) 1,000
Path loss (dB) 142.2 (142.4) 142.9 (143.2) 144.2 (144.7) 153.6 (154.7)
Rx power (dBm) -33.4 (-33.7) -33.0 (-33.4) -33.3 (-33.8) -41.7 (-42.9)
SNR (dB) 31.2 (30.9) 31.6 (31.2) 31.3 (30.8) 22.9 (21.7)
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Kokkoniemietal. J Wireless Com Network (2021) 2021:88
budget. We can see that the expected accuracy of the proposed simplified model gives
SNR values that are at most 1.2 dB off the real value. is level of difference in the real
systems is insignificant due to all the other loss mechanisms, and, the link distance
here is quite large for high-frequency communications. Although these link distances
are very much possible as shown, e.g., in [23, 24], where 1 km link distance with the
above-mentioned 55 dBi Cassegrain antennas was demonstrated.eir total loss with
antenna gains at 300 GHz was about 40 dBs, whereas in Table2 we see a loss of about
33 dBs. is shows that even with very simple calculations, one can get very close to
real-life measurements even without taking into account feeder losses, or other possi-
ble atmospheric losses, such as fog loss and small particle scattering in the air. ere-
fore, the proposed simplified loss model can very reliably estimate the atmospheric
losses and the accuracy of the total link budget mostly falls into properly modeling all
the parts of the wireless system that have impact on the total received power.
3.4 Discussion
As a summary and discussion from above, the higher mmWave and low THz frequen-
cies are among the most potential frequencies to utilize ultrahigh rate communications in
the future wireless systems. e proper modeling of the channel behavior therein is very
important due to absorption loss and how it behaves in comparison with the FSPL. In short
distance communications (few meters) below 300 GHz, it is not absolutely crucial to model
the absorption due to dominating FSPL. Its importance increases with link distance, but
also with frequency. In the other words, the link budget and the components in it are appli-
cation dependent. e tools provided herein give and easy way to model the absorption loss
and estimate its impact on the link budget.
100 150 200 250 300 350
Frequency [GHz]
120
130
140
150
160
170
Path Loss [dB]
Theoretical path loss
D1
D2
D4
D3
T1
T2
T3
T4
Fig. 8 Path losses for the bands considered in the link budget calculations. The exact path loss as a function
of frequency versus the average losses per band given in Tables 1 and 2
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Kokkoniemietal. J Wireless Com Network (2021) 2021:88
4 Conclusion
We derived a LOS channel model for 100–450 GHz frequency range in this paper. e
main goal was to find a simple and easy to use model for the molecular absorption loss.
e derived model was shown to be very accurate and predict the channel loss very well
in the target frequency regime. is model can be reduced to simpler forms in the case of
limited frequency range within 100–450 GHz. Considering the upcoming B5G systems, the
interesting frequency bands include the D band (110 GHz to 170 GHz) and the low THz
frequencies (275 GHz to 325 GHz). e molecular absorption loss is an important part of
the link budget considerations at +100 GHz bands. erefore, the model presented here
gives a simple tool to estimate the total link loss in various environmental conditions and
link distances. As it was shown in the numerical results, the derived model can be used to
predict the expected SNR within D band and THz band with below 2 dB error compared to
the exact theoretical model. erefore, this simple tool gives high enough accuracy for any
LOS system analysis, but also in the broader sense, analysis of the large scale fading in the
sub-THz regime.
5 Methods/experimental
is paper is a purely theoretical model on simple way to estimate the absorption loss.
Although theoretical, the original data obtained from the HITRAN database [10] are based
on experimental data. e goal in this article is to simplify the complex database approach
into simple polynomial equations with only few floating parameters, such as humidity and
frequency. As such, the model produced in this paper is suitable for LOS channel loss esti-
mation for various wireless communications systems. ose include back- and fronthaul
connectivity and general LOS link channel estimation. e work is heavily based on the
HITRAN database and the theoretical models for absorption loss as well as simple LOS free
space path loss models.
Abbreviations
5G: Fifth generation; 6G: Sixth generation; B5G: Beyond fifth generation; FSPL: Free space path loss; HITRAN: High-resolu-
tion transmission molecular absorption database; ITU-R: International Telecommunication Union Radio Communication
Sector; LOS: Line-of-sight; mmWave: Millimeter wave; Rx: Receiver; Tx: Transmitter.
Authors’ contributions
JK derived the molecular absorption loss model. All the authors participated in writing the article and revising the manu-
script. All authors read and approved the final manuscript.
Funding
This work was supported in part by the Horizon 2020, European Union’s Framework Programme for Research and Inno-
vation, under Grant Agreement No. 761794 (TERRANOVA) and No. 871464 (ARIADNE). It was also supported in part by
the Academy of Finland 6Genesis Flagship under Grant No. 318927.
Data availability
Not applicable.
Declarations
Competing interests
The authors declare that they have no competing interests.
Received: 7 January 2020 Accepted: 30 March 2021
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Kokkoniemietal. J Wireless Com Network (2021) 2021:88
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