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D3.2 – Channel and Propagation Modelling and Characterization

TERRANOVA Project of 63

This project has received funding from Horizon 2020, European Union’s

Framework Programme for Research and Innovation, under grant agreement

No. 761794

Deliverable D3.2 Channel and Propagation Modelling

and Characterization Work Package 3 - THz Wireless Link Design

TERRANOVA Project

Grant Agreement No. 761794

Call: H2020-ICT-2016-2

Topic: ICT-09-2017 - Networking research beyond 5G

Start date of the project: 1 July 2017

Duration of the project: 30 months



Disclaimer This document contains material, which is the copyright of certain TERRANOVA contractors, and

may not be reproduced or copied without permission. All TERRANOVA consortium partners

have agreed to the full publication of this document. The commercial use of any information

contained in this document may require a license from the proprietor of that information. The

reproduction of this document or of parts of it requires an agreement with the proprietor of

that information. The document must be referenced if used in a publication.

The TERRANOVA consortium consists of the following partners.

No. Name Short Name Country

1

(Coordinator)

University of Piraeus Research Center UPRC Greece

2 Fraunhofer Gesellschaft (FhG-HHI & FhG-IAF) FhG Germany

3 Intracom Telecom ICOM Greece

4 University of Oulu UOULU Finland

5 JCP-Connect JCP-C France

6 Altice Labs ALB Portugal

7 PICAdvanced PIC Portugal



Document Information

Project short name and number TERRANOVA (761794)

Work package WP3

Number D3.2

Title Channel and propagation modelling and

characterization

Version V1.0

Responsible unit UOULU

Involved units UOULU, UPRC, ICOM

Type1 R

Dissemination level2 PU

Contractual date of delivery 31.08.2018

Last update 31.08.2018

1 Types. R: Document, report (excluding the periodic and final reports); DEM: Demonstrator, pilot,

prototype, plan designs; DEC: Websites, patents filing, press & media actions, videos, etc.; OTHER:

Software, technical diagram, etc. 2 Dissemination levels. PU: Public, fully open, e.g. web; CO: Confidential, restricted under conditions set

out in Model Grant Agreement; CI: Classified, information as referred to in Commission Decision

2001/844/EC.



Document History

Version Date Status Authors, Reviewers Description

v0.01 08.08.2018 Draft Joonas Kokkoniemi

(UOULU)

Initial version (v0.01)

v0.02 20.08.2018 Draft Alexandros-Apostolos A.

Boulogeorgos (UPRC)

Corrections to the previous

version.

v0.03 22.08.2018 Draft Janne Lehtomäki

(UOULU)

Raytracing simulation model.

v0.04 23.08.2018 Draft Alexandros-Apostolos A.

Boulogeorgos (UPRC)

Fading literature review.

v0.05 24.08.2018 Draft Joonas Kokkoniemi

(UOULU)

Corrections to the previous

version and Geometrical

simulation model.

v0.06 29.08.2018 Draft Georgia Ntouni (ICOM) Corrections to the previous

version.

v1.0 31.08.2018 Final Markku Juntti (UOULU)

Janne Lehtomäki

(UOULU)

Joonas Kokkoniemi

(UOULU)

Angeliki Alexiou (UPRC)

Final Editorial Corrections



Acronyms and Abbreviations

Acronym/Abbreviation Description

BEP Bit error probability

BPSK Binary phase shift keying

EM Electromagnetic

FSPL Free space path loss

GEO Geostationary orbit

GPU Graphics processing unit

HITRAN High-resolution transmission molecular

absorption database

LEO Low Earth orbit

LOS Line-of-sight

MAC Medium access control

MDF Medium density fibreboard

NLOS Non-line-of-sight

PHY Physical layer

QAM Quadrature amplitude modulation

Rx Receiver

SINR Signal-to-interference-plus-noise ratio

SNR Signal-to-noise ratio

Tx Transmitter

UTD Uniform theory of diffraction



Contents

1. Introduction ............................................................................................................................... 11

2. THz band LOS channels ............................................................................................................ 12

2.1 Molecular absorption ..................................................................................................... 12

2.2 Path loss ......................................................................................................................... 12

2.3 Numerical results for the LOS paths ............................................................................. 13

2.4 Rain and fog attenuation ................................................................................................ 20

3. Generalized channel model ....................................................................................................... 22

4. Simplified channel models for 200 – 450 GHz band ................................................................ 32

4.1 Model for 200 – 400 GHz band ..................................................................................... 32

4.2 Model for 200 – 450 GHz band ..................................................................................... 35

5. Transmission windows below one terahertz .............................................................................. 38

5.1 Transmission windows in the 0.275 – 1 THz band ....................................................... 38

5.2 Simplified estimate for 200 – 400 GHz band ................................................................ 41

6. The channel measurements ........................................................................................................ 44

6.1 The Measurement setup ................................................................................................. 44

6.2 Theoretical reflection loss ............................................................................................. 46

6.3 Theoretical scattering loss ............................................................................................. 48

7. Noise in the THz band ............................................................................................................... 50

8. Fading in THz band ................................................................................................................... 52

9. Simulation for studying fading, interference, and multipath propagation ................................. 53

9.1 Ray-tracing approach..................................................................................................... 53

9.2 Geometric simulation model ......................................................................................... 56

10. Future work ............................................................................................................................. 59

11. Conclusions ............................................................................................................................. 60

References ..................................................................................................................................... 61



List of Figures

Fig. 1. Molecular absorption loss in the THz band. ...................................................................... 14 Fig. 2. Molecular absorption loss around the 300 GHz band. ....................................................... 14 Fig. 3. Losses as a function of frequency per 1 km link distance. ................................................. 15 Fig. 4. Total path loss in the THz band as a function of distance and frequency up to 100 meters.

....................................................................................................................................................... 16 Fig. 5. Total path loss around the 300 GHz as a function of distance and frequency up to 1 km. 16 Fig. 6. The distance after which the molecular absorption loss becomes the dominant loss

mechanism. .................................................................................................................................... 18 Fig. 7. The distance after which the molecular absorption loss becomes the dominant loss

mechanism around the 300 GHz band. .......................................................................................... 19 Fig. 8. Comparison of the molecular absorption loss and free space path loss as a function of the

distance and the frequency up to 10 km distance. ......................................................................... 19 Fig. 9. Comparison of the molecular absorption loss and free space path loss as a function of the

distance and the frequency up to 1 km distance. ........................................................................... 20 Fig. 10. Rain attenuation (dB/km) as a function of frequency for different precipitation levels... 21 Fig. 11. One possible terrestrial scenario for the generalized channel model. .............................. 22 Fig. 12. A path through the atmosphere where the plane parallel assumption fall short on properly

explaining the structure of the atmosphere (picture of the Earth from Nasa: NASA/NOAA/GOES

Project). ......................................................................................................................................... 24 Fig. 13. Geometry of a general path through the atmosphere (picture of the Earth from Nasa:

NASA/NOAA/GOES Project)......................................................................................................... 25 Fig. 14. Predicted distance through the atmosphere for the plane parallel approximation and for

the proposed model. ...................................................................................................................... 26 Fig. 15. Average water vapor mixing ratio and distribution on global scale, and the mean altitude

(m) of the corresponding value on the left-hand figure. ................................................................ 26 Fig. 16. Mean pressure and temperature of the atmosphere as a function of altitude (data from

1976 US Standard atmosphere [11]). ............................................................................................ 27 Fig. 17. Per-kilometer losses for different altitudes. ..................................................................... 29 Fig. 19. Path loss as a function of altitude and frequency for a 100 meter link. ........................... 30 Fig. 20. Path loss from ground to air as a function of frequency. ................................................. 31 Fig. 21. SNR bounds for BPSK and 64-QAM for BEP= . .................................................. 31

Fig. 22. Performance of the proposed simplified molecular absorption loss model. .................... 33 Fig. 23. Performance of the proposed simplified molecular absorption loss model compared to

other models. ................................................................................................................................. 34 Fig. 24. Close-up of Fig. 23 at 300 – 400 GHz band..................................................................... 35 Fig. 25. Absorption loss according to the extended simplified model detailed above. ................. 37 Fig. 26. Close up of Fig. 25 to better illustrate the error made in the absorption loss estimate by

the simplified model versus the fully accurate model. .................................................................. 37 Fig. 27. Path loss and transmission windows at 10 meter. ............................................................ 39 Fig. 28. Path loss and transmission windows at 100 meter. .......................................................... 39 Fig. 29. Available bandwidths at 10 meter. ................................................................................... 40 Fig. 30. Available bandwidths at 100 meter. ................................................................................. 40



Fig. 31. The predicted available bandwidths for three different distances and two different relative

humidity values at the transmission centre frequency 342 GHz. .................................................. 42 Fig. 32. Available bandwidth progression for two different relative humidity values at the

transmission centre frequency 342 GHz. ....................................................................................... 42 Fig. 33. Minimum bandwidth as a function of frequency and relative humidity at the transmission

centre frequency 342 GHz. ............................................................................................................ 43 Fig. 34. Maximum bandwidth as a function of frequency and relative humidity at the transmission

centre frequency 342 GHz. ............................................................................................................ 43 Fig. 35: TeraView TeraPulse measurement setup. ........................................................................ 45 Fig. 36: Measured materials. ......................................................................................................... 45 Fig. 37: Measured and fitted reflection loss for laminated medium density fibreboard (MDF) at

300 GHz. Red line represents an equivalent reflection loss for circularly polarized light with the

given refractive index. ................................................................................................................... 47 Fig. 38: Measured and theoretical scattering and reflection loss for plaster at 300 GHz at 45

degree incidence angle. ................................................................................................................. 49 Fig 39. Antenna brightness temperature as a function of frequency. ............................................ 51 Fig. 40. Flow of data in ray tracing calculations. .......................................................................... 53 Fig. 41. Office room (adapted from [30]) with four transmitters (in the corners close to roof) and

35 possible locations for a receiver. Different colours indicate different materials (concrete, glass,

painted wood, rubber floor, laminated MDF)................................................................................ 54 Fig. 42. Scatter points in the office room. ..................................................................................... 55 Fig. 43. Delay spread as a function of beam angle for receivers 1, 15, and 30. Center frequency is

equal to 300 GHz. .......................................................................................................................... 55 Fig. 44. An illustration of the simulation model with the desired and other users, and reflected and

random paths. ................................................................................................................................ 57

Fig. 45. Simulated average SINR and SINR thresholds for 16-QAM and BPSK for BEP.

....................................................................................................................................................... 57 Fig. 46. Simulated signal and interference powers and the noise power. ...................................... 58



List of Tables

Table 1. Tabled values for the LOS losses per 1 km link from 100 GHz to 880 GHz. ................. 17 Table 2: Fitted refractive indices to the measured reflection losses. ............................................. 47 Table 3: Parameters for the scattering loss of the measured materials. ......................................... 48



Executive Summary

This Deliverable, D3.2 – Channel and propagation modelling and characterization, focuses on the

channel modelling for the THz links. The knowledge of the channels is very important when

considering application and use case –specific communication solutions and most importantly,

when considering link budgets and theoretical capacities. The work consists of theoretical

channel models for arbitrary length line-of-sight (LOS) links, as well as measurement-based non-

line-of-sight (NLOS) link modelling. The derived models cover the needs of the TERRANOVA

communication scenarios. Based on the derived models, the TERRANOVA scenarios defined in

WP1 can be tested and analysed. The derived models are also useful beyond TERRANOVA in

generic THz research on arbitrary scale communication systems.



1. INTRODUCTION

The terahertz band (0.1 – 10 THz) communications systems have been under dense research

during the past few years. The obvious reasons are the vast frequency resources making it

possible to achieve very high data rates and/or enhance the spectrum sharing opportunities

among large numbers of users and devices. Due to challenges in implementation of the THz

capable transceivers, the utilization of the full THz band is demanding. A first step is to conquer

the below 1 THz frequencies, which is one of the fundamental objectives of the TERRANOVA

project.

Regardless of the application or the use-case of any frequency band, the knowledge of the

channel(s) is in focal point for understanding the signal behaviour in the medium. By proper

channel knowledge, an investigation of the potential communication solutions becomes

possible. Each frequency band has its own peculiarities and fading characteristics that have an

impact on the utilizable bandwidths, modulations, coding, etc. For this reason, great effort has

been put to studying and modelling the different THz bands. Intense channel investigation is

particularly important in these relatively poorly explored frequencies. Most of the existing

channel models focus on Beer-Lambert’s law with fixed absorption coefficient. This is a good

baseline model and also the starting point of the channel research for TERRANOVA. New

channel models are required because the TERRANOVA use cases vary from TERRANOVA

backhaul, i.e., a long distance (~1 km) backhaul for base station-to-base station links, to short

indoor communication links with other users and non-line-of-sight (NLOS) links. Off the shelf

models for all the TERRANOVA use cases do not exist, and thus, the channel modelling herein is

utilized to extend existing models and derive new ones to realistically model the propagation

environments.

In order to address the signal propagation in the various TERRANOVA scenarios and use cases,

the work in T3.1 of WP3 has been focusing on modelling the channel propagation characteristics

in various scales of communication. The main focus is on the below 1 THz frequency bands, but

since the channel models derived herein are valid over the entire THz band, some results are

given on the full 0.1 to 10 THz band. This document, Deliverable D3.2, describes the derived

channel models. Those include theoretical line-of-sight (LOS) models as well as NLOS modelling

via measurements. All the models herein are derived in a generic way, so that they can be

utilized and scaled based on the application, or use case in hand. The presented models have

been utilized in few publications during the TERRANOVA project [1] [2] [3] [4].

The work in this document is organized as follows. First the background on LOS channel

modelling is introduced, after which, the general and simplified LOS channel models are

reported. The measurements on NLOS paths are gone through next, followed by a short

discussion on the noise processes in the THz band. Finally, we discuss about fading on the THz

frequencies as well as simulation models utilized to study multipath and multiuser propagation

and fading.



2. THZ BAND LOS CHANNELS

The THz band signals experience fading even in the full LOS path because of the discrete

molecular absorption loss. The free space path loss, on the other hand, is always present due to

natural expansion of the electromagnetic waves in the medium. These phenomena are briefly

looked in this section serving as a background for most of the research done for TERRANOVA.

2.1 Molecular absorption

Molecular absorption is usually modelled by transmittance, i.e., the fraction of the energy

capable of propagating through the channel. It is calculated by Beer-Lambert’s law [5] [6] as

where is the frequency, is the distance from transmitter (Tx) to receiver (Rx), and

are transmitted and received power, respectively, is the absorption coefficient of

th absorbing species (molecule or its isotopologue) at frequency , and is the angle of

incident wave (not valid in homogenous spherically symmetric space). The absorption

coefficient is defined as

where is the number density of the molecules and is the absorption cross section of a

single molecule. The latter term is further defined by spectral line intensity and line shape

as

and thus, the molecular absorption coefficient depends on temperature , pressure , and

molecular composition of the channel. Further details on the absorption coefficient can be

found in the references herein and in the upcoming sections of this document, where the

detailed derivations of various propagation models are given.

2.2 Path loss

If we only consider LOS channel, molecular absorption loss and free space path loss (FSPL) are

the main loss mechanisms. Increased loss may be introduced by rain or fog discussed later, and



possibly scattering on impurities of the air [7]. However, in the general case we only have the

FSPL and the molecular absorption loss. The FSPL is defined as

where and are Rx and Tx antenna gains, and is the speed of light. The molecular

absorption loss is given as an inverse of (1). Therefore, the LOS path loss becomes (path gain in

the below form)

The numerical examples for the total loss below were calculated by using this expression, or its

inverse for path loss figures and are shown in the next section.

2.3 Numerical results for the LOS paths

Some numerical results for the molecular absorption loss and the FSPL are given below. Most of

them are calculated assuming isotropic antennas unless otherwise stated. As a consequence,

path losses are relatively high for long distance links. Molecular absorption loss values are

calculated at 296 K temperature, 101325 Pa pressure, and 50% relative humidity.

Fig. 1 shows the molecular absorption loss for the full THz band for one and five meter

distances. This figure shows the biggest problem in the higher THz band on long distance links: if

signals are not killed by the free space loss, then they are killed by the molecular absorption

loss, or the combination of both. Therefore, the full THz band is mainly useful for very short

distance links. It should be noticed that transmittance is usually given in linear scale (like below).

Thus, the total losses in Fig. 1 are not as severe as they appear. Regardless of this, the molecular

absorption loss increases exponentially and becomes an intense problem as the link distance

increases. This will be better shown below when free space loss is compared to the molecular

absorption loss.

Fig. 2 shows the transmittance for the 300 GHz region considering a variety of distances from 1

m to 2 km. It becomes obvious that the losses are considerably lower in the lower THz band, but

at the same time there are some deeply faded frequencies. Still, the distances are already very

reasonable for long distance communications compared with the full THz band. In particular,

frequencies around 300 GHz are modestly attenuated and most of the attenuation will come

from other sources, such the free space path loss.



Fig. 1. Molecular absorption loss in the THz band.

Fig. 2. Molecular absorption loss around the 300 GHz band.



Figs. 3 – 5 show the individual and total losses in the THz band as a function of distance and

frequency. Furthermore, Table 1 gives numerical values for the losses below 1 THz. As

mentioned above, these figures were calculated without antenna gains. Specifically, Fig. 3 shows

the general trend in the absorption pattern: below 1 THz, free space loss dominates the total

loss. Above 1 THz, molecular absorption loss becomes the major attenuation mechanism.

However, if we would add antenna gains, the molecular absorption loss would become more

important at the lower frequencies due to the relative degradation of the spreading loss. It

should be noticed that the axes in Fig. 3 are in logarithmic scale, which would not make the

difference of few tens of dBs total antenna gain visually large. However, with the antenna gains

added, the molecular absorption loss will be more prominent, especially at shorter distances.

This is better visualized in Figs. 6 - 7, where the boundary between these losses is shown.

Fig. 3. Losses as a function of frequency per 1 km link distance.



Fig. 4. Total path loss in the THz band as a function of distance and frequency up to 100 meters.

Fig. 5. Total path loss around the 300 GHz as a function of distance and frequency up to 1 km.



Table 1. Tabled values for the LOS losses per 1 km link from 100 GHz to 880 GHz.

Frequency (GHz)

100 120 140 160 180 200 220 240 260 280

Absorption loss (dB)

0.1 1.1 0.2 0.5 9.8 1.3 0.8 0.8 1.0 1.2

Free space loss (dB)

132.4 134.0 135.4 136.5 137.6 138.5 139.3 140.1 140.7 141.4

Total loss (dB)

132.5 135.1 135.6 137.0 147.3 139.8 140.0 140.8 141.7 142.6

Frequency (GHz)

300 320 340 360 380 400 420 440 460 480


1.8 9.1 4.2 7.6 231.0 11.2 10.5 65.5 29.1 31.5


142.0 142.6 143.1 143.6 144.0 144.5 144.9 145.3 145.7 146.1

Total loss (dB)

143.8 151.7 147.3 151.1 375.0 155.7 155.4 210.8 174.8 177.6

Frequency (GHz)

500 520 540 560 580 600 620 640 660 680


41.1 95.5 444.6 N/A /INF

313.9 102.1 230.2 41.5 39.9 35.0


146.4 146.8 147.1 147.4 147.7 148.0 148.3 148.6 148.8 149.1

Total loss (dB)

187.5 242.3 591.7 N/A /INF

461.7 250.1 378.5 190.1 188.7 184.0

Frequency (GHz)

700 720 740 760 780 800 820 840 860 880


47.4 98.7 595.2 1450 147.6 63.5 42.0 35.6 38.4 36.3


149.3 149.6 149.8 150.1 150.3 150.5 150.7 150.9 151.1 151.3

Total loss (dB)

196.8 248.3 745.0 1600 297.9 214 192.7 186.5 189.5 187.6



Figs. 6 and 7 show the boundary distance after which the molecular absorption becomes the

dominant loss, or putting it the other way, below which the free space loss is the dominant loss

mechanism. The antenna gain herein refers to the total combined gain, i.e. from Rx and Tx.

Furthermore, the maximum distance was set equal to 10 km because the molecular absorption

gain tends towards zero, as the distance tends to infinity. It is obvious that at frequencies above

1 THz the molecular absorption loss takes over quite fast, only after few meters to some tens of

meters, in general. Especially, in Fig. 7, we can observe that the molecular absorption becomes

the dominant loss at lower distance as the antenna gains increase. This is simply because the

molecular absorption loss only depends on distance and not on the angles.

Figs. 8 and 9 give some further comparisons of the molecular absorption loss to the FSPL around

the 300 GHz frequency band and up to 1 and 10 km, respectively. Indeed, in this band, the free

space loss is the most important loss, but depending on the target frequencies and bandwidths,

and ultimately, the target distances as seen in Figs. 6 and 7. In some bands, the FSPL is enough

to predict the total loss, whereas in other bands, or over very wide bandwidths, the molecular

absorption needs to be taken into account.

Fig. 6. The distance after which the molecular absorption loss becomes the dominant loss mechanism.



Fig. 7. The distance after which the molecular absorption loss becomes the dominant loss mechanism around the 300 GHz band.

Fig. 8. Comparison of the molecular absorption loss and free space path loss as a function of the distance and the frequency up to 10 km distance.



Fig. 9. Comparison of the molecular absorption loss and free space path loss as a function of the distance and the frequency up to 1 km distance.

2.4 Rain and fog attenuation

Other aspects of the outdoor propagation that should be considered are the rain and fog/mist

attenuations. These may become an issue in cases where long distance backhaul links are

studied. The rain attenuations for various precipitation rates are given in Fig. 10 in dB/km. The

attenuation curves in Fig. 10 are based on the ITU-R report P.838-3 [8]. Those are calculated for

a circular polarization, although, the vertical and the horizontal polarizations have nearly

identical attenuation curves as a function of frequency. More information on exact calculation

of the rain attenuation can be found in [8].

We can see that the rain attenuations for different precipitation levels below 1 THz frequencies

are rather modest. This is the case especially in northern countries. For instance, in Oulu,

Finland, average rainfall during the summer months is roughly speaking between 50 – 100 mm

per month. Of course, the situation changes quite a lot when moving south, where heavier rains

are more common. Furthermore, instantaneous rainfall can be very high, even if the monthly

means are low.

ITU-R also gives attenuation models for fog and clouds up to 1 THz frequency [9]. However, it

should be noted that both the fog and the rain attenuation models have some uncertainty. For

instance, in ITU-R recommendation P.838-2, they mention that the attenuation numbers are

tested and accurate up to 55 GHz. In P.838-3, this clause is missing and that particular document

does not justify the models very accurately. Regardless of this uncertainty, these models can be



held as a good baseline when considering loss in the long distance links and in adverse weather

conditions.

Fig. 10. Rain attenuation (dB/km) as a function of frequency for different precipitation levels.



3. GENERALIZED CHANNEL MODEL

The above well-known propagation models are very good if simple slant paths are considered.

However, if the molecular composition of the medium changes along the path from Tx to Rx,

more sophisticated models are needed. Such a case would be when communicating in vertical

direction. The atmosphere may also change in the case when the Tx (or Rx) is considerably

higher than its counterpart.

In this section, we give a general LOS channel model for the THz band. It is valid in all

temperatures, pressures, altitudes, and locations theoretically on any planetary environment. It

will, therefore, operate as a base model for all LOS paths as it is valid for all distances. The

reference cases herein are the communication paths of airplane to satellite links and ground to

air links as those offer the most extreme cases with atmosphere variability. However, as stated

above, the absorption coefficient may also change in a situation where Rx or Tx lie in different

altitudes, such as in the mountain scenario illustrated in Fig. 11. In TERRANOVA, the main

interest for this model is due to long distance links. The satellite-case gives the most general

derivation of the model which also ensures that the model is accurate for any communication

distance from any altitude to any altitude. Still, as stated above, the model is generally valid in

all altitudes.

Fig. 11. One possible terrestrial scenario for the generalized channel model.

The general absorption model is based on modelling the absorption in Beer-Lambert’s law

properly. The Beer-Lambert law is given as in Eq. (1) and shown in the following group of

equations.



The absorption coefficient depends on various parameters, such as pressure , temperature ,

molecular composition of the channel, line intensity , and line shape . Transmittance in plane

parallel atmosphere, i.e., assuming planar atmosphere with distance dependent absorption

coefficient (between points and ), is simply given by

The plane parallel atmosphere is a very good approximation up to certain limits, e.g., when

considering perfectly vertical paths, or perfectly horizontal paths in which the absorption

coefficient remains constant either locally or completely. Furthermore, the horizontal case

requires removal of the secant-term. However, longer links in arbitrary elevation angle require

more sophisticated geometry. When we consider vast distances through a realistic spherical

atmosphere, an equally spaced grid of altitude layers no longer accurately describe the

individual layer thicknesses (see Fig. 12). A layer here means a discrete grid of altitudes.

Discretisation of the altitude is necessary due to difficult representation of a continuous

absorption coefficient in computer simulations. That is, a layer describes a short distance,

over which the atmosphere remains in average constant and, thus, summation of the total path

is over this grid as in (7).



Fig. 12. A path through the atmosphere where the plane parallel assumption fall short on properly explaining the structure of the atmosphere (picture of the Earth from Nasa:

NASA/NOAA/GOES Project).

The general geometry of an arbitrary path on a curving surface is shown in Fig. 13. With rather

straightforward calculations we can calculate the true distance through the atmosphere, as

In order to obtain the meaningful altitude dependent distance, we need a derivative of , i.e.,

. Then, the transmittance can be written as



Fig. 13. Geometry of a general path through the atmosphere (picture of the Earth from Nasa: NASA/NOAA/GOES Project).

As mentioned above, the plane parallel approximation is relatively good, if the angle through

the atmosphere is vertical or horizontal. However, if we consider a horizontal path that, in the

extreme case, penetrates the entire atmosphere, the plane parallel approximation gives infinite

layer thickness due to the fact that Earth is approximated as a flat plane. The proposed model

fixes this by giving the Earth a radius and adjusting the layer thicknesses as a function of the

altitude (in the group of equations (8)). Below, in Fig. 14, there are some results for the angled

layer thicknesses with 500 m vertical grid resolution in the case of communication path to the

geostationary orbit from 11 km altitude. We can see that plane parallel model approximation

vastly over-estimates the distance through the atmosphere in the case of close to horizontal

directions. It should be noted that these correspond to penetrating the entire atmosphere, and

therefore, if the actual distance between Tx and Rx is known and the absorption coefficient is

constant between them, we can use the simpler plane parallel approximation.



Fig. 14. Predicted distance through the atmosphere for the plane parallel approximation and for the proposed model.

There is more to this general channel model than just geometrical issues on extremely long

distance links. Short and long distance links are all subject to atmospheric conditions that tend

to change, not only as a function of altitude, but they are also dependent on the location on

Earth. Remember that water vapor is the main cause of absorption loss in the THz band. The

amount of it varies globally due to temperature and altitude. The left-hand figure in Fig. 15 is

the mean water vapor mixing ratio and the right-hand figure is the corresponding altitude (data

from [10]).

Fig. 15. Average water vapor mixing ratio and distribution on global scale, and the mean altitude (m) of the corresponding value on the left-hand figure.

The amount of water vapor depends on the altitude via temperature, pressure, molecular

composition of the medium, all of which vary with altitude. The atmosphere is a dynamic



medium with roughly speaking decreasing temperature and pressure as a function of altitude.

Temperature in fact increases after certain altitude [11] (see Fig. 16).

Fig. 16. Mean pressure and temperature of the atmosphere as a function of altitude (data from 1976 US Standard atmosphere [11]).

Knowing the atmospheric parameters as a function of the altitude and the location on Earth, we

can calculate the generally valid absorption coefficient. The most important things to take into

account are the line intensity ( ) scaling and a proper line shape function .

The line intensity describes the intensity of the absorption line. It is scaled based on the

temperature of the surrounding medium. Most of the parameters can be obtained from, e.g.,

HITRAN catalogue [12].

Where things get interesting is the line shape. It tells the width of the absorption line and it is

dependent on the pressure of the atmosphere and there is no universal line shape that would

be valid in all atmospheric conditions. In Eq. (11) below, the most basic line shape, i.e., the

Lorentz line shape, which is very accurate at THz frequencies, is given.



In the high pressure conditions, pressure broadening of the line shape is the most important line

broadening mechanism (Eq. (12) is the pressure broadening half-width of the absorption line). In

the low pressure conditions, Doppler broadening becomes more important (Eq. (13)).

There is a variety of line shapes available, but our main concern is which one to choose. The

answer is that it does not matter much, as long as the Doppler and pressure broadenings are

separated properly. The first three equations of (14) are various forms of the Lorentz line shapes

and the last one is the Doppler line shape.

There is no strict rule whether to use Doppler or Lorentz line shapes, but in general when either

of the half-widths clearly dominates (5-10 times larger than the other one), we go with the

suggested line shape. When the line widths are comparable, we use the Voigt line shape that is

a convolution between the Lorentz and the Doppler line shapes [13]:

Considering the previously discussed phenomena, we can show some results in the degree of

absorption at different altitudes. Since satellite communication is considered as a reference

application about the general channel model, high gain parabolic antennas were utilized in the



following. Fig. 17 shows per kilometer losses for fixed absorption coefficients at the given

altitude. The path losses in this equation were calculated by (16) and the antenna gains by (17).

We can see that the absorption is considerably decreased in the case of the thinner atmosphere

as one could expect.

Fig. 17. Per-kilometer losses for different altitudes.

Fig. 18 shows the extreme cases of path loss through the entire atmosphere considering a path

from an airplane to satellite. Path losses become very large at long distances. However, the

numbers are decreased by the fact that airplane-to-satellite communication is considered in

contrast to the on Earth communications. The airplane altitude is 11 km. Antennas are parabolic

antennas with aperture efficiency 70%, and 1 m and 0.5 m diameter at the satellite and at the

airplane, respectively. GEO is 36,000 km away from earth, and thus, the angle is not so

important to the total distance or to the molecular absorption.



Fig. 18. Path losses to satellites at different altitudes and orientations.

Furthermore, Fig. 19 shows the path loss for a 100 meter link as a function of altitude. We can

see that it would be beneficial to transmit at higher altitudes due to very high molecular

absorption loss. This is the case in airplane-to-airplane communications, but it also shows

decreasing path loss if the THz links are placed on high altitudes, e.g., in mountain regions.

Fig. 19. Path loss as a function of altitude and frequency for a 100 meter link.

Fig. 20 illustrates the expected path loss in vertical direction from the surface of Earth. The path

losses are much larger in this case since the absorption is stronger close to Earth. This is also the

main limiting factor when considering very high distance on, or from, the surface of Earth.



Fig. 20. Path loss from ground to air as a function of frequency.

In the end, the THz band does theoretically support multigigabit-per-second links even at very

long links. Fig. 21 shows the SNRs for 500 km LEO satellite from 11 km altitude at 10 GHz with

10 mW total transmit power and target bit error probability (BEP) of . 64 QAM and BPSK

correspond to 60 and 10 Gbps (PHY). Note the high ideal antenna gains increase as a function of

frequency due to fixed physical aperture.

Fig. 21. SNR bounds for BPSK and 64-QAM for BEP= .



4. SIMPLIFIED CHANNEL MODELS FOR 200 – 450 GHZ BAND

The above absorption loss models give very accurate absorption estimates given any scale of

communications. However, implementing them is rather difficult and time consuming because

of the large numbers of tabulated values required from spectroscopic databases, such as

HITRAN. To address this problem, we developed a simplified molecular absorption loss model

that only requires straightforward polynomials to estimate the absorption loss, and therefore,

the path loss. The first version of the model covered the frequency range of 200 – 400 GHz and

is further detailed in [3]. The second version of the model is more complicated, but covers the

frequency range of 200 – 450 GHz, thus, completely covers the to-be-allocated frequency range

275 – 450 GHz at World Radio Conference in 2019 (WRC2019).

4.1 Model for 200 – 400 GHz band

As it was mentioned above, we have published a paper detailing the below simplified model. In

that paper, we give a simplified molecular absorption loss model for the frequency band 275 –

400 GHz. This model, however, is valid from about 200 GHz to 400 GHz. The model is given by an

exponential loss model as [3]

where

and is the distance, is the frequency, is the water vapor mixing ratio given by

in terms of the atmospheric pressure , relative humidity , and saturated water vapor partial

pressure given by [14]



where the temperature is given in Celsius degrees. Finally, the correction factor for the

molecular absorption loss is given by a polynomial

where for the coefficients it holds that , ,

, and . Utilizing this path loss model, we can see that it very

accurately predicts the path loss. There is some error in the peak absorption frequencies due to

simple Lorentz line shape utilized in the estimation. The difference to more complicated line

shapes suitable for the millimeter wave frequencies (such as van Vleck – Huber line shape) is

corrected with the -factor, but a small error remains regardless of this. However, the error

in between the absorption peaks is small. Fig. 22 shows the performance of the above model

when compared to the exact response by the line-by-line model (those presented in the

previous sections). We can see that the difference to the exact theory is almost non-existent

where the absorption is low. The error increases at the absorption lines due to simplification.

This is, however, not a big problem as the error correlated with the depth of the absorption loss

(and even tens of dBs of error) is not severe, if the total absorption is hundreds of dBs. We can

see that the model very accurately predicts the shape and the general absorption level.

Fig. 22. Performance of the proposed simplified molecular absorption loss model.



ITU-R has also presented simplified channel models for the millimeter wave frequencies [15].

However, those are not as accurate as the one presented here. They are also much more

complex, as they require at minimum 9 polynomials in comparison to the three in our model.

One of the reasons for poor accuracy of the ITU-models is the assumption of the (modified) full

Lorentz line shape that is not absolutely correct for the millimeter frequencies. Figs. 23 and 24

show the difference between different ITU models and our model, as well as to the exact model

presented by our HITRAN database –based line-by-line model. We can see that the proposed

model is very close to the actual response given by ‘Theoretical van Vleck – Weisskopf’ and, for

water, by ‘Theoretical VVH – water’. In fact, the ITU model fails in the so called transmission

windows (i.e., low loss windows between the absorption lines) by over-estimating the loss. This

is particularly important in the case of long distance links. More information about the

differences between the models is given in [3].

Fig. 23. Performance of the proposed simplified molecular absorption loss model compared to other models.



Fig. 24. Close-up of Fig. 23 at 300 – 400 GHz band.

4.2 Model for 200 – 450 GHz band

The above model was further enhanced to cover the frequency range of 200 – 450 GHz. This

required more polynomials. Thus, it is easier to use the model of Section 4.1, if frequencies

below 400 GHz are considered. Above 400 GHz, the number of absorption lines increases fast.

Above 450 GHz, it is already simpler to use database-based approaches rather than any

polynomial-based solutions.

The LOS path loss can be given as

where is the transmittance, is the frequency, is the distance, is the water vapor

mixing ratio, is the speed of light, and are the antenna gains. Transmittance can be

estimated based on the simplified model:



where ) is the absorption coefficient of the th absorption line in the simplified model,

and is the fitting function for the simplified model. The absorption coefficients are as

follows:

where

and 1/cm, 1/cm, 1/cm, 1/cm,

, . Figs. 25 and 26 give the comparison of the simplified model

(dashed green line) and the exact theory (blue line). We can see that as in the case of the

previous simplified model, this one is equally accurate and most of the error corresponds to the

highly absorbed frequencies. The model is in fact relatively accurate up to 500 GHz, but it is

missing a line at about 475 GHz and at about 485 GHz. Including these lines only adds to the

complexity of the overall model and as a result the full spectroscopic catalogue-based solutions

become more simple due to the very large number of polynomials.



Fig. 25. Absorption loss according to the extended simplified model detailed above.

Fig. 26. Close up of Fig. 25 to better illustrate the error made in the absorption loss estimate by the simplified model versus the fully accurate model.



5. TRANSMISSION WINDOWS BELOW ONE TERAHERTZ

As shown in the previous section, the molecular absorption coefficient causes strong signal loss

in certain deterministic frequencies. The low loss areas between the absorption lines are often

referred to as transmission windows. The molecular absorption loss increases as a function of

distance that causes these windows to shrink as the distance increases. This section considers

the available bands below one terahertz frequency. Furthermore, a model to estimate the

windows at the frequency band 200 – 400 GHz is given.

5.1 Transmission windows in the 0.275 – 1 THz band

The major transmission window centre frequencies in the 0.275 – 1 THz band are 290, 342, 410,

464, 482, 492, 651, 671, 850, and 870 GHz. However, it should be noted that due to the variable

strength of the molecular absorption loss, the specific bands may be chosen differently. The

particular centre frequencies are also subject to the considered application. The ones listed

above give a general view of the available bands in the 0.275 – 1 THz band.

Figs. 27 and 28 show the overall LOS path loss and illustrate the possible occupied bands with

given centre frequencies. Figs. 29 and 30 further give the actual available 3 dB bandwidths

(maximum loss deviation with respect to the loss at the center frequency). The figures are given

for 10 and 100 meter distances that show the impact of the molecular absorption to the

available band very well. As the distance increases, the available spectrum becomes more and

more scarce.

As stated above, the application specific centre frequencies and target link distances, as well as

the capabilities of the utilized transceivers, play a major role in band selection. Short distance

links do not require as much planning as long distance applications, such as backhaul links. As

the distance increases, the path loss increases vastly with the following decrease of utilizable

bandwidths. This introduces some limits on the link budgets depending on the requirements of

the system. In the next section, the bandwidth estimates are looked more closely for the

frequency band of 200 – 400 GHz.



Fig. 27. Path loss and transmission windows at 10 meter.

Fig. 28. Path loss and transmission windows at 100 meter.



Fig. 29. Available bandwidths at 10 meter.

Fig. 30. Available bandwidths at 100 meter.



5.2 Simplified estimate for 200 – 400 GHz band

In [3], we presented a simplified model to estimate the bandwidths within the transmission

windows between the peak absorption lines. These transmission windows refer to the low loss

spectrum between the strong absorption lines. The derived model is given in terms of the

frequency deviations from the peak absorption frequencies given certain path loss threshold ,

i.e., given a maximum tolerable loss with respect to the center frequency , we can

calculate the bandwidth based on the following model

In this model, and represent the frequency deviations from 325 and 380 GHz absorption

lines for the given loss threshold . Given the above frequency deviations, we can calculate the

available bandwidths as

where is the center frequency of the higher absorption line at 380 GHz,

is the center

frequency of the lower absorption line at 325 GHz.Moreover, gives the minimum

bandwidth when the loss is limited from a single side, i.e., the bandwidth is limited by the higher

wing loss with respect to the center frequency (note that the line center in hand depends on

) and gives the maximum available bandwidth given that the band is limited from

both sides, i.e., this gives the maximum bandwidth between two absorption lines. Detailed

description of the model can be found in [3].

Figs. 31 – 34 give some results for the available bandwidths assuming a transmit center

frequency of 342 GHz. This center frequency was chosen for these examples, because it lies

between the two absorption lines in the given band (275 – 400 GHz) and this particular

frequency gives the minimum loss between these lines. Fig. 31 gives the estimated bandwidths

for three different distances and two relative humidity values. Fig. 32 gives the bandwidth

progression as a function of the distance. We can see that as the distance increases, the

exponentially increasing path loss decreases the bandwidth that can be utilized. Furthermore,

the amount of water vapor in the atmosphere also has an impact on the progression; the more



water in the atmosphere, the larger the impact of the molecular absorption to the available

bandwidth. Figs. 33 and 34 give the full data for the bandwidths as a function of distance and

relative humidity.

Fig. 31. The predicted available bandwidths for three different distances and two different relative humidity values at the transmission centre frequency 342 GHz.

Fig. 32. Available bandwidth progression for two different relative humidity values at the transmission centre frequency 342 GHz.



Fig. 33. Minimum bandwidth as a function of frequency and relative humidity at the transmission centre frequency 342 GHz.

Fig. 34. Maximum bandwidth as a function of frequency and relative humidity at the transmission centre frequency 342 GHz.



6. THE CHANNEL MEASUREMENTS

The channel measurements in TERRANOVA were focused on the material characterisation,

namely, on reflection and scattering properties of various common indoor materials. The

measured values were fitted to Fresnel equations [16] and scattering theories presented by

Degli-Esposti [17]. The refractive indices below have been reported in a conference paper to be

presented in September 2018 [18].

The reflection properties of different materials are important with respect to multipath

propagation modelling. It has been shown in the past that the reflections are the most potential

and utilizable NLOS communication paths in THz frequencies [19]. Therefore, the reflected paths

can enable communications even if the LOS path is blocked. The scattered paths, on the other

hand, have far more severe path loss that reduces their usability in communications. However,

given large numbers of scattering points, they may introduce additional interference. Therefore,

they are also forth to study even if the expectedly highly direction antennas will reduce the

number of unpredicted paths.

6.1 The Measurement setup

The measurements were conducted with the TeraView TeraPulse 4000 time domain

spectroscopy platform. The measurement setup is shown in Fig. 35. This measurement device is

capable of measuring frequencies from 0.1 to 4.5 THz. However, in NLOS measurements, the

maximum measureable frequencies are around 2 THz due to usually increasing path loss as a

function of frequency. More information on the measurement setup can be found in [18].

The measured materials can be seen Fig. 36 and have been also listed in Tables 2 and 3. Those

include common materials found in indoor locations, such as different wood materials with

different surfaces (painted, laminated, non-finished). Based on the given materials, indoor

simulation models are possible as these (or similar materials) give quite a good overview of the

signal behaviour on reflected and scattered paths. More information on the materials can be

found in [18].



Fig. 35: TeraView TeraPulse measurement setup.

Fig. 36: Measured materials.



6.2 Theoretical reflection loss

The theoretical reflection loss on smooth surface is given by the Fresnel equations [16]. The

Fresnel equations can be found in [16] [18] and they depend on the refractive indices of the

surface material and the angle of incidence of the incoming radiation.

The measured reflection losses were fitted to those given by the Fresnel equations to find the

refractive indices of the materials. Those are listed in Table 2 for 300 and 1000 GHz frequencies.

An example of the fitting process is given in Fig. 37 for laminated medium density fibreboard at

300 GHz frequency. The measurement device quite strongly polarized the radiation. The best fit

was found weighting the Fresnel equations by 97% s-polarized and 3% p-polarized. Fig. 37 shows

a perfect fit between the measured and theoretical reflection loss. The red curve in the figure is

plotted in order to show the equivalent reflection loss of a circularly polarized source.

We were unable to fit the aluminium sample to the Fresnel equations due to very large reflected

power. Metals are almost like mirrors in the THz band, reflecting most of the incoming power.

Therefore, metals can be assumed to have very low reflection loss with most of the power

disappearing due to scattering on the surface imperfections.



Table 2: Fitted refractive indices to the measured reflection losses.

MATERIAL 300 GHz 1000 GHz

Concrete 2.1 1.8

MDF, painted 2.4 1.4

MDF, plaster 1.65 1.5

MDF, laminated 2.9 1.7

Floor, rubber 1.85 1.45

Glass 2.85 2.3

Metal N/A N/A

Fig. 37: Measured and fitted reflection loss for laminated medium density fibreboard (MDF) at 300 GHz. Red line represents an equivalent reflection loss for circularly polarized light with the

given refractive index.



6.3 Theoretical scattering loss

The theoretical scattering loss was modelled by the scattering model given by Degli-Esposti in

[17]. This model depends on the angle of incident radiation and the surface properties, such as

surface roughness and directivity of the outgoing radiation . Those are listed in Table 3

following the models in [17].

Fig. 38 shows an example of the scattering on plaster at 300 GHz at 45 degree angle of

incidence. It can be seen that the calculated values provide very accurate estimate of the

scattering power. It should be noted that the main lobe is wider in the measurements due to the

transmitted beam width that has been manipulated by mirrors. This causes the LOS paths to

exist at a few degrees offset between the transmitter and receiver. The theory, on the other

hand, assumed a small surface element that is evenly illuminated. As a consequence, the main

lobe appears narrower in the theoretical approach. It can be seen that the scattered power is

significantly lower than the reflected power (at minimum 30 dB). This causes the measured

scattering to be partly corrupted by thermal noise, which also shows that the scattering is not as

much a significant source of power as the reflected paths. However, the large number of

scattered rays, e.g., in the vicinity of the reflected path, may possibly cause some interference

due to the random phase of the scattering field. The corresponding equations for the considered

and fitted variables can be found in [17].

Table 3: Parameters for the scattering loss of the measured materials.

MATERIAL [cm]

Concrete 0.008 50

MDF, painted 0.004 40

MDF, plaster 0.008 50

MDF, laminated 0.001 40

Floor, rubber 0.002 40

Glass 0.002 170

Metal 0.002 170



Fig. 38: Measured and theoretical scattering and reflection loss for plaster at 300 GHz at 45 degree incidence angle.



7. NOISE IN THE THZ BAND

The noise present in the THz band is mostly due to the thermal noise of the receiver equipment.

However, theoretically, there is also increased noise due to the antenna brightness temperature

and re-radiation of the absorbed energy from own transmissions (self-induced noise). The

former is explained below in more detail. The self-induced noise has been predicted to cause

significant noise in the THz frequencies. However, we wrote a paper earlier analysing this noise

and concluded that it is most likely unmeasurable because it is so weak that regular thermal

noise dominates [20]. We have also tried to measure this type of noise, but the conclusions in

[20] seem to be correct and we have been unable to capture anything apart from the thermal

noise itself. For these reasons, we can safely utilize the regular thermal noise in estimating the

overall noise level in THz systems.

Antenna noise increases as a consequence of the emission of the absorbed energy. The

atmosphere radiates because it has a temperature and it radiates according to Planck’s law,

which causes the increased antenna noise. The antenna brightness temperature can be

expressed as [21]

and can be seen in Fig. 39. Due to the increasing absorption loss, the antenna brightness

temperature increases quickly and is mostly flat and saturated at the atmospheric temperature

and at frequencies around 1 THz and above. Below 500 GHz frequencies, the brightness

temperature varies due to weaker absorption, revealing that the real atmosphere is not a

perfect black body, but rather it is a gray body, i.e., partially transparent (as seen above).

The total noise level can be estimated from the temperature of the receiver as

where is the noise figure of the transmitter (in dB), is the Boltzmann constant, is the

bandwidth of the system (note that, in the general case, the noise power is an integral over the

frequencies), is the Planck constant, and is the frequency.

Thermal noise decreases as a function of frequency because the energy state population

probabilities are decreased when a quantum of energy becomes large compared to the kinetic

energy of the matter (hence the term in the above equation). Although looking slightly

complicated, this equation is in fact nearly identical to the thermal noise term in any

communication system, that is,



Fig 39. Antenna brightness temperature as a function of frequency.



8. FADING IN THZ BAND

The fading characteristics and models for the THz band will be investigated in TERRANOVA

project. The main work on those will be conducted by the simulation models, while the fading

will be investigated in future work. The utilized simulation models are discussed in the next

section and a short literature review will be given below.

The LOS and NLOS channel models were discussed above. All the channel effects can be

considered as part of the large and small scale fading. Especially, the molecular absorption loss

can be viewed as a deterministic fading process dependent on the distance. In general, the THz

channel particularities have been investigated in several works. In more detail, in [6], the

authors presented a deterministic propagation model for electromagnetic nanoscale

communications in the THz band, based on radiative transfer theory. In addition, in [3], a

simplified path-loss model for the 275-400 GHz band was introduced, which was employed in [4]

in order to evaluate the THz link performance in terms of average signal-to-noise ratio (SNR) and

capacity. Furthermore, in [1], a multi-ray THz propagation model was presented, whereas, in

[22], the authors reported a path-loss model for nano-sensor networks operating in the THz

band for plant foliage applications. In [23], a propagation model for intra-body nano-scale

communications was provided and in [24], a multi-ray THz propagation model was presented.

Although all the above mentioned contributions revealed the particularities of the THz medium,

they neglected the impact of fading. In [25], [26] and [27], the authors presented suitable

stochastic models that are able to accommodate the multipath fading effect in the THz band. In

particular, in [25], the authors introduced a multi-path THz channel model where the

attenuation factor was modelled as a Rayleigh or Nakagami-m distribution under the non-line-

of- sight condition and as a Rician or Nakagami-m distribution in LOS conditions. Moreover, in

[26] and [27], the authors proposed a two dimensional geometrical propagation model for

indoor THz communications. Based on this model, they developed a parametric reference model

for a THz multi-path Rician fading channel. In [28], the influence of antenna directivities on the

THz indoor channels for various antenna types was investigated assuming Rician fading,

whereas, in [29], the authors used a log-distance shadowing path-loss model for THz nano-

sensor networks communications in vegetation.

None of these models give definite answers on the nature of fading, and especially on the small

scale fading characteristics of the THz band. Therefore, the fading research is part of the

TERRANOVA project. As mentioned above, the fading is studied with the simulation models

presented in the next section, where also some very preliminary results on the received

multipath signals are given.



9. SIMULATION FOR STUDYING FADING, INTERFERENCE, AND

MULTIPATH PROPAGATION

The simulation models assist the study of mathematically difficult multipath and multiuser

models. In TERRANOVA project, two simulation approaches have been developed, a ray-tracing

model presented in Section 9.1 and a geometrical approach presented in Section 9.2. These

models incorporate the LOS and NLOS models presented in this document. Those include the

reflection and scattering models parameterized by the empirical measurements, the theoretical

LOS model, and the noise. Although the simulation models help understand the channel

behavior and limits placed by the large number of multipath signals from many Txs, they also

make it possible to study fading. An example on this is given in Section 9.2.

9.1 Ray-tracing approach

As a basic tool for implementing ray tracing on NVIDIA’s GPUs, OptiX framework has been used.

Rays are launched using OptiX ray generation programs, which are implemented for: different

transmitter types (point source, planar wavefront), diffraction simulation (Keller cone), and

scattering (LOS detection between scatter point and receiver). Rays are terminated at various

receiver points, diffraction edges, and scattering points. Output consists of path segments that

are passed to electromagnetic (EM) calculation.

Based on the paths from OptiX, MATLAB is used to calculate all the aspects of the ray output

field and receiver output. It is envisioned that eventually everything will be ported to

C++/C/Cuda C (outside the scope of TERRANOVA).

Fig. 40. Flow of data in ray tracing calculations.

Diffraction interactions are slightly problematic, because they cause paths to branch, from

which an exponential complexity arises (w.r.t. number of diffraction interactions along a path).

Fortunately, diffracted waves decay fast in most directions so one or two allowed diffractions



along a path are enough. The uniform theory of diffraction (UTD) is used for all the diffraction

field evaluations and classical Fresnel equations used for reflections.

Earlier solution from UOULU was developed further in TERRANOVA including support for diffuse

scatter simulation and improved geometry / material handling. Regarding scattering, the last

interaction point of a ray path before it hits a receiver will be considered as a significant

scattering interaction. The path may experience multiple reflections and/or some diffractions

before this scattering point. Scattering is modelled by Degli-Esposti’s model [17]. In

TERRANOVA, measurements were done to obtain the scattering model parameters for various

materials found in a typical office room.

Fig. 41. Office room (adapted from [30]) with four transmitters (in the corners close to roof) and 35 possible locations for a receiver. Different colours indicate different materials (concrete,

glass, painted wood, rubber floor, laminated MDF).



Fig. 42. Scatter points in the office room.

Fig. 43. Delay spread as a function of beam angle for receivers 1, 15, and 30. Center frequency is equal to 300 GHz.



Fig. 43 shows the delay spread as a function of beam angle for receivers in three different

positions. It can be seen that when beam angles are less than 20 degrees, channel is essentially

LOS. In this calculation, the best transmitter (out of the 4 possible in the room corners) and the

best beam pointing direction have been found for each receiver (not necessarily LOS direction

although almost always it was like this). It is emphasized that the results in Fig. 43 are based on

universally valid theories utilizing actual measured parameters for different materials at THz

frequencies.

9.2 Geometric simulation model

The geometric simulation model is based on modelling the environment as a set of deterministic

and random objects. In the early phase, the deterministic objects are walls, floor, and ceiling.

The random objects are furniture and other objects of the environment (coffee mugs, screens,

surface irregularities, etc.). The random objects and their locations are randomized on every

drop, as are the other users. The deterministic signal paths are calculated from the reflections

on the walls, floor, and ceiling, and the random objects operate as reflectors or scatterers. The

possible signal paths are shown in Fig. 44 for the desired user (left-hand figure) and for the other

users (right-hand figure). Furthermore, all the paths are subject to certain blocking probability as

it is unlikely that all the deterministic paths are available due to possible furniture or humans

blocking the signals.

The idea of the geometric simulator is similar to ray tracing, but the difference is due to the

random paths. They are different for all the drops of the simulation (one drop is one network

realization for which the channels are calculated). This gives variability to the received signals

due to movement of the user. The next step of the development is to determine the time

domain, which gives an opportunity to study, for instance, fading and medium access control

(MAC) solutions. The simulator has been developed to be as generic as possible, so that fixed

objects, channel models, antennas, etc. can easily be incorporated.

Figs. 45 and 46 give an example of simulation results for a situation similar to Fig. 44. This

simulation was run and averaged over 10 drops with 50 other users and 50 random objects

(both Poisson distributed) in a 10-by-10-by-3 room, ALOHA MAC with 50% transmit

probability, 50% blocking probability, and 45 degree wide conical shaped antenna patterns for

the Txs and Rxs (random directions). The test case is a very dense network, but it also shows the

impact of the interference very well. The fading over frequencies becomes large enough to

prevent the usage of even simple modulations with BPSK performance already struggling with

BEP target. This kind of results are required when estimating the fading (small and large

scale) in multipath and multiuser channels. However, as stated above, this simulator is still a

work in progress and will be documented and utilized in the future work.



Fig. 44. An illustration of the simulation model with the desired and other users, and reflected and random paths.

Fig. 45. Simulated average SINR and SINR thresholds for 16-QAM and BPSK for BEP.



Fig. 46. Simulated signal and interference powers and the noise power.



10. FUTURE WORK

Work on the WP3 T3.1 is scheduled to continue until the end of the 2018 (M18 of TERRANOVA

project). This deliverable is due in the end of August 2018 (M14). Therefore, the work on the

channel model continues beyond this document. The remaining four months of work will

include finalizing the derived channel models and gathering more data by measurements.

The main works to be concluded by the end of M18 are as follows:

Finalizing and submitting a journal article on the general LOS channel model presented

in Section 3.

Writing and submitting a journal article on the simplified channel model for the 200 –

450 GHz band presented in Section 4.2.

Measurements on the reflection and scattering coefficient for more materials in order

to form a more comprehensive database of material characteristics.

Develop the simulation tools to study and develop fading models for the THz band.

Further study on the noise processes and trying to capture the behaviour of the

molecular absorption noise by measurements.

On top of these tasks, the remaining time allows to study propagation and channel

characteristics identified by this or other work packages before the end of M18.



11. CONCLUSIONS

The main task of T3.1 has been to produce new and novel channel models to be utilized in the

TERRANOVA project. Those were presented in the document and include general theoretical

full-band LOS channel models as well as simplified LOS models for confined frequency bands.

The presented NLOS models, namely reflection and scattering coefficients for various materials,

can be utilized in multipath and NLOS propagation studies. By combining different models

presented herein, modelling of very complex propagation environments, such as indoor

locations, can be achieved. The backhaul links are easier, because they only require LOS channel

models along with possible rain and fog attenuation models. The average loss on LOS channels

can be estimated based on the location and altitude on Earth. The indoor locations usually have

many possible paths from Tx to Rx. These paths can be easily estimated by considering the

summation of multiple unique paths via reflection, scattering, and/or diffraction.

The interesting part of the THz communications is directional antennas. They are required due

to large path loss, but they also limit the number of possible paths from Tx to Rx. Therefore,

even closely related scenarios may have completely different propagation characteristics. For

example, indoor communication with LOS path is the most efficient. However, if it is blocked for

any reason, the NLOS paths become a viable option for communications. In any case, the

channels for all the paths can be constructed based on the channel models propagation

characteristics presented in this document.



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