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A line‑of‑sight channel model forthe100–

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

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RESEARCH

Kokkoniemietal. 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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Kokkoniemietal. 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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Kokkoniemietal. 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 Simplied 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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Kokkoniemietal. 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 Simplied 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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Kokkoniemietal. J Wireless Com Network (2021) 2021:88

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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Kokkoniemietal. J Wireless Com Network (2021) 2021:88

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. Figure1 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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Kokkoniemietal. 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 andthetotal 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 anddiscussion

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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Kokkoniemietal. J Wireless Com Network (2021) 2021:88

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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Kokkoniemietal. J Wireless Com Network (2021) 2021:88

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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Kokkoniemietal. J Wireless Com Network (2021) 2021:88

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 ofthemodel withreduced 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

. Figures6

and 7 compare the performance of the proposed model with reduced terms against

the exact theory. Figure6 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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Kokkoniemietal. 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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Kokkoniemietal. J Wireless Com Network (2021) 2021:88

Telecommunications Administrations (CEPT) Electronic Communications Commit-

tee (ECC) Recommendation 18(01) [21]. ose are detailed in Table1. 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 Table2. 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 Table2 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 Tables1 and 2. e average path losses per

band (indexed in Tables1 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)

Content courtesy of Springer Nature, terms of use apply. Rights reserved.

Page 13 of 15

Kokkoniemietal. 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 Table2 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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Page 14 of 15

Kokkoniemietal. 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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Page 15 of 15

Kokkoniemietal. J Wireless Com Network (2021) 2021:88

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