Deliverable D2.3 Final report on system level performance ... · v0.1 11.12.2019 Draft José...

D2.3 – Final report on system level performance evaluation by simulations

TERRANOVA Project of 75

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

Framework Programme for Research and Innovation, under grant agreement

No. 761794

Deliverable D2.3 Final report on system level

performance evaluation by simulations Work Package 2 - System Requirements, Concept and Architecture

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: 33 months

Ref. Ares(2020)2453895 - 08/05/2020



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 WP2

Number D2.3

Title Final report on system level performance evaluation by simulations

Version v1.0

Responsible unit ALB

Involved units UPRC, FhG, ICOM, UOULU, JCP-C, ALB, PIC

Type1 R

Dissemination level2 PU

Contractual date of

delivery

31.03.2020

Last update 30.04.2020

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

v0.1 11.12.2019 Draft José Machado (ALB) Initial version, first Tentative

version for the ToC

v0.2 19.02.2020 Draft Alexandros

Boulogeorgos (UPRC)

Contribution on chapter 4 (link

level simulations – Impact of

hardware imperfections in the

THz received signal)

v0.3 19.02.2020 Draft Joonas Kokkoniemi

(OULU)

Contribution on chapter 4 (link

level simulations – THz indoor

LOS and NLOS propagation and

channel estimation)

v0.4 20.02.2020 Draft José Machado (ALB) Contribution for chapter 2 -

Defined Key performance

Indicators for an optical/THz

system and minor changes on

remaining document content.


Boulogeorgos (UPRC)

Revision on 4.2 (Impact of

hardware imperfections in the

THz received signal)


(OULU)

Contribution on sections 3.4

(Pathloss Channel Modeling),

4.1 (THz indoor LOS and NLOS

propagation) and 4.4 (Channel

estimation)

v0.7 19.03.2020 Draft José Machado (ALB) Contribution for the “Executive

Summary” and “introduction”

(Chapter 1).


(OULU); Carlos Castro

(HHI); José Machado

(ALB)

Contribution for chapters 5.1

(Indoor Performance Evaluation

via Stochastic Geometry),

chapter 6.1 (Performance

feasibility by the demonstration

results) and corresponding

minor reviews.



v0.9 06.04.2020 Draft Carlos Castro (HHI); José

Machado (ALB)

Minor changes on 6.1

(Performance feasibility by the

demonstration results) and

contribution for 6.2

(Comparison of channel models

with measured data).


(OULU)

Contribution on sections 3.4

(Pathloss Channel Modeling),

4.1 (THz indoor LOS and NLOS

propagation) and 4.4 (Channel

estimation)


Boulogeorgos (UPRC)

Georgia Ntouni (ICOM)

Contribution on section 6.3

(Initial access performance

evaluation based on measured

data).

v0.12 17.03.2020 Draft José Machado (ALB) First edition of section 7

(Conclusions).


(OULU); Alexandros

Boulogeorgos (UPRC)

Contributions for Section 7

(Conclusions).

v0.14 28.04.2020 Draft Carlos Castro (HHI); José

Machado (ALB)

Contribution and revision of

Section 7 (Conclusions).

V1.0 30.04.2020 Final Angeliki Alexiou (UPRC),

Joonas Kokkoniemi

(OULU); José Machado

(ALB)

Final revision



Acronyms and Abbreviations

Acronym/Abbreviation Description

2G Second Generation

3G Third Generation

3GPP Third Generation Partnership Project

5G Fifth Generation

A-BFT Associate BeamForming Training

ACK Acknowledgement

ACO Analog Coherent Optics

ADC Analog-to-Digital Converter

AFC Automatic Frequency Correction

AFE Analogue FrontEnd

AGC Automatic Gain Control

AiP Antenna-in-Package

AM Amplitude Modulation

AMC Adaptive Modulation and Coding

AP Access Point

ASIC Application-Specific Integrated Circuit

ATDE Adaptive Time Domain Equalizer

ATI Announcement Transmission Interval

AWG Arrayed Waveguide Gratings

AWGN Additive White Gaussian Noise

AWV Antenna Weight Vector

BB BaseBand

BC Beam Combining

BER Bit Error Rate

BF BeamForming

BHI Beacon Header Interval

BI Beacon Interval



BOC BackOff Counter

BPSK Binary Phase Shift Keying

BRP Beam Refinement Protocol

BS Base Station

BTI Beacon Transmission Interval

CA Consortium Agreement

CAP Contention Access Period

CAUI 100 gigabit Attachment Unit Interface

CBAP Contention-Based Access Period

CapEx Capital Expenditure

CC Central Cloud

CCH Control CHannel

CDR Clock and Data Recovery

CFP C-Form Factor Pluggable

CMOS Complementary Metal–Oxide–Semiconductor

CoMP Coordination Multi-Point

COTS Commercial Off-The-Shelf

CPR Carrier Phase Recovery

CRC Cyclic Redundancy Code

CSI Channel State Information

CSMA/CA Carrier Sense Multiple Access with Collision Avoidance

CTA Channel Time Allocation

CTAP Channel Time Allocation Period

CTS Clear-To-Send

CTS-NI Clear-To-Send-Node-Information

CW Continuous Wave

D2D Device-to-Device

DAC Digital to Analog Converter

DC Direct Current

DCH Data CHannel

DDC Digital Down Conversion



DEMUX DE-MUltipleXer

DL DownLink

DMG Directional Multi-Gigabit

DMT Discrete Multi-Tone

DoA Direction of Arrival

DoF Degree of Freedom

DP Detection Probability

DP-IQ Dual Polarization In-phase and Quadrature

DPD Digital PreDistortion

DSB Dual-Side Band

DSP Digital Signal Processing

DTI Data Transfer Interval

DUC Digital Up Conversion

DWDM Dense Wavelength Division Multiplexing

EC European Commission

EDCA Enhanced Distributed Channel Access

EDMG Enhanced Directional Multi-Gigabit

E/O Electrical-Optical

ESE Extended Schedule Element

ETSI European Telecommunications Standards Institute

eWLB embedded Wafer Level Ball grid array

FAP False-Alarm Probability

FEC Forward Error Correction

FCS Frame Check Sequence

FD Full Duplex

FDD Frequency Division Duplexing

FDMA Frequency Division Multiple Access

FIFO First In First Out

FM Frequency Modulation

FPGA Field-Programmable Gate Array

FSO Free-Space Optics



FSPL Free Space Path Loss

FTTH Fiber To The Home

FWA Fixed Wireless Access

GA Grant Agreement

GaAs Gallium Arsenide

HEMT High Electron Mobility Transistor

HFT High Frequency Trading

HSPA High Speed Packet Access

HSPA+ evolved High Speed Packet Access

I/Q In-phase and Quadrature

I2C Inter-Integrated Circuit

IA Initial Access

ICF Intermediate Carrier Frequency

IEEE Institute of Electrical and Electronics Engineers

IF Intermediate Frequency

IoT Internet of Things

IM/DD Intensity Modulation/Direct Detection

IP Internet protocol layer

ISI InterSymbol Interference

ISM Industrial Scientific and Medical band

ITU International Telecommunication Union

ITU-R Radiocommunication sector of the International

Telecommunication Union

IQ COMP. In-phase and Quadrature impairments COMPensator

IQD Indoor Quasi Directional

KPI Key Performance Indicator

LDPC Low-Density Parity-Check

LO Local Oscillator

LoS Line of Sight

LTE-A Long Term Evolution Advanced

MAC Medium Access Control



MCE MAC Coordination Entity

MID Multiple sector IDentifier

MIMO Multiple Input Multiple Output

MMIC Monolithic Microwave Integrated Circuit

mmWave Millimeter Wave

MUE Mobile User Equipment

MUX MUltipleXer

MZI Mach-Zehnder Interferometer

NAV Network Allocation Vector

NETCONF NETwork CONFiguration

NI Node Information

NGPON2 Next-Generation Passive Optical Network 2

nLoS Non-Line Of Sight

NR New Radio

NRZ Non-Return to Zero

OFDM Orthogonal Frequency Division Modulation

OIF Optical Internetworking Forum

OLT Optical Line Terminal

ONUs Optical Network Units

OOK On-Off Keying

OpEx Operating Expenses

P2MP Point-to-Multi-Point

P2P Point-to-Point

PA Power Amplifier

PAM Pulse Amplitude Modulation

PBSS Personal Basic Service Set

PCB Printed Circuit Board

PCP Personal basic service set control point

PDM Polarization-Division Multiplexing

PDM-QAM Polarization Multiplexed Quadrature Amplitude

Modulation



PER Packet Error Rate

PFIS Point coordination Function Inter-frame Space

PHY PHYsical

PIN Positive-Intrinsic-Negative

PLL Phased Locked Loop

PNC Picocell Network Coordinator

PONs Passive Optical Networks

PSP Pulse Shaping Filter

PSF Primary Synchronization Signal

PtMP Point-to-Multi-Point

QAM Quadrature Amplitude Modulation

QoE Quality of Experience

QoS Quality-of-Service

QSFP Quad Small Form-Factor Pluggable

RA Random Access

RAT Radio Access Technology

RAR Random Access Response

RAU Remote Antenna Unit

RF Radio Frequency

RoF Radio over Fiber

RRM Radio Resource Management

RSRP Reference Signal Received Power

RSSI Received Signal Strength Indicator

RTS Request-To-Send

RTS-NI Request-To-Send-Node Information

RX Receiver

SC Small Cell

SD-FEC Soft-Decision Forward-Error Correction

SDM Space Division Multiplexing

SDMA Space Division Multiple Access

SDN Software Define Network



SFF Small Form Factor

SFP Small Form-Factor Pluggable

SiGe Silicon-Germanium

SINR Signal-to-Noise-plus-Interference Ratio

SISO Single Input Single Output

SLS Sector Level Sweep

SM Spatial Multiplexing

SME Small and Medium-sized Enterprise

SMF Single Mode Fiber

SNR Signal to Noise Ratio

SOTA State Of The Art

SP Service Period

SPI Serial Parallel Interface

SRC Sample Rate Conversion

SSB Single-SideBand

SSW Sector SWeep

SSW-FBCK Sector SWeep FeedBaCK

STA STAtion

STM-1 Synchronous Transport Module, level 1

STS Symbol Timing Synchronization

TAB-MAC Terahertz Assisted Beamforming Medium Access Control

TDD Time Division Duplexing

TDM Time Division Multiplexing

TDMA Time Division Multiple Access

TERRANOVA Terabit/s Wireless Connectivity by Terahertz innovative technologies to deliver Optical Network Quality of Experience in Systems beyond 5G

THz Terahertz

TIA TransImpedance Amplifier

TWDM Time and Wavelength Division Multiplexed

Tx Transmitter

TXOP Transmission Opportunity



UL Uplink

UE User Equipment

VCO Voltage Controlled Oscillator

VGA Variable Gain Amplifier

VLC Visible Light Communication

WLAN Wireless Local Area Network

WDM Wavelength Division Multiplexing

WiFi Wireless Fidelity

WiGig Wireless Gigabit alliance

WLBGA Wafer Level Ball Grid Array

WM Wireless Microwave

XG-PON 10 Gbit/s Passive Optical Network

XPIC Cross Polarization Interference Cancellation

YANG Yet Another Next Generation



Contents

1. Introduction ........................................................................................................................... 20

1.1 Scope ............................................................................................................................. 22

1.2 Structure ........................................................................................................................ 22

2. Defined Key performance Indicators and Physical System Limitations for an optical/THz

system ........................................................................................................................................... 23

2.1 Defined Key Performance Indicators (KPIs) ................................................................... 23

2.2 Physical System Limitations ........................................................................................... 23

3. Relevant THz channel modelling aspects for simulations ..................................................... 28

3.1 Molecular absorption loss ............................................................................................. 28

3.1.1 General absorption loss model.............................................................................. 28

3.1.2 Simplified molecular absorption loss model ......................................................... 28

3.1.3 FSPL and the total loss ........................................................................................... 30

4. Link Level simulation for the optical/THz System ................................................................. 31

4.1 THz indoor LOS and NLOS propagation ......................................................................... 31

4.1.1 Simulation model................................................................................................... 32

4.1.2 Simulation results .................................................................................................. 35

4.2 Impact of hardware imperfections in the THz received signal ...................................... 39

4.3 Antenna gain Vs antenna misalignment ........................................................................ 42

4.3.1 Gaussian distributed beam-steering ..................................................................... 42

4.3.2 Two-dimensional Gaussian movement of a single node ....................................... 44

4.4 General antenna misalignment loss .............................................................................. 46

4.4.1 Path loss model ..................................................................................................... 46

4.4.2 Antenna model ...................................................................................................... 46

4.4.3 Expected antenna gain .......................................................................................... 47

4.4.4 Numerical results ................................................................................................... 47

4.5 Channel Estimation ........................................................................................................ 50

4.5.1 System model ........................................................................................................ 50

4.5.2 Channel estimation ................................................................................................ 52


5. System level simulations for the optical/THz System ........................................................... 55



5.1 Indoor Performance Evaluation via Stochastic Geometry ............................................ 55

5.1.1 Antenna model ...................................................................................................... 57

5.1.2 Phase noise model ................................................................................................. 57

5.1.3 Channel model ....................................................................................................... 59

5.1.4 Stochastic phase noise model ............................................................................... 59

5.1.5 Stochastic indoor model ........................................................................................ 59


6. Comparative analysis of simulation and demonstration Results .......................................... 63

6.1 Performance feasibility by the demonstration results .................................................. 64

6.2 Comparison of channel models with measured data.................................................... 66

6.3 Initial access performance evaluation based on measured data .................................. 67

7. Conclusions ............................................................................................................................ 70

8. References ............................................................................................................................. 72



List of Figures

Figure 1: Individual loss components of the lower THz band LOS channel, as well as the expected

total losses under harsh weather conditions. The absorption losses and the FSPL were calculated

with the HITRAN-based line-by-line model and Friis equation, respectively. ............................... 24

Figure 2: A 3-dB Transmission window bandwidth at 342 GHz centre frequency as a function of

distance and relative humidity. ..................................................................................................... 25

Figure 3: Estimated upper net data rate bounds for small-sized THz sub-arrays (assuming a

forward error correction (FEC) threshold at BER = 2e-2). ............................................................. 26

Figure 4: Estimated data rates for small-sized THz sub-arrays ..................................................... 27

Figure 5: Error of the proposed simplified molecular absorption loss model. ............................. 30

Figure 6: An illustration of the simulation environment. The dark centre diamonds depict the Tx

grid, the green centre diamond in the corner depicts an access point, or the Rx. The red squares

are random reflection points representing objects in the environment. ..................................... 32

Figure 7: View of Figure 6 from above showing the distribution of the random reflection points.

....................................................................................................................................................... 32

Figure 8: Illustration of the system geometry; LOS path, deterministic reflections and random

reflections. ..................................................................................................................................... 34

Figure 9: Simulated and fitted path gain with about 30 dB total antenna gain as a function of

distance for LOS case. .................................................................................................................... 35


distance for NLOS case with all the objects and walls having refractive index of 1.5. ................. 37


distance for NLOS case with all the objects and walls having refractive index of 2.9. ................. 37


distance for NLOS case with all the objects and walls having random refractive. ........................ 39

Figure 13: Ergodic Capacity vs 𝝈𝒔 for different levels of 𝒌𝒕𝒓 and values of 𝝁. ............................. 41

Figure 14: Ergodic Capacity vs 𝒌𝒕𝒓 for different levels of 𝝈𝒔 and values of 𝝁. ............................. 41

Figure 15: Antenna misalignment in backhaul (a) and fronthaul (b) application scenarios. ........ 42

Figure 16: Beam-steering errors. ................................................................................................... 42

Figure 17: Directional gain vs angular misalignment standard deviation for different values of

antenna beam-width. .................................................................................................................... 43

Figure 18: Two-dimensional Gaussian shaking of (a) the UE, (b) the BS in fronthaul scenarios, and

(c) a single BS in backhaul scenarios. ............................................................................................ 44

Figure 19: RX’s effective area and transmitter’s beam footprint with 2D misalignment on the

horizontal and vertical axis of the receiver’s plane. ...................................................................... 45

Figure 20: Directional gain vs spatial jitter standard deviation for different values of antenna

gains. .............................................................................................................................................. 45

Figure 21: The expected antenna gain with and without antenna movement for 32-element

antenna array. ............................................................................................................................... 48


antenna array. ............................................................................................................................... 49




antenna array. ............................................................................................................................... 49

Figure 24: Comparison of the expected antenna gains for very small antenna movement

between 256-element antenna array and the 1024-element antenna array. .............................. 50

Figure 25: Multi-antenna receiver. ................................................................................................ 50

Figure 26: Radiation pattern of the patch antenna element. ....................................................... 52

Figure 27: Channel estimation accuracy with 4-element antenna array. ..................................... 54

Figure 28: Channel estimation accuracy with 6-element antenna array. ..................................... 54

Figure 29: Channel estimation accuracy with 12-element antenna array. ................................... 55

Figure 30: The indoor system model illustration, where the Rx is assumed to be in the upper

corner of the room in order to have maximum visibility to the room. ......................................... 56

Figure 31: An Illustration of the antenna gain of the ULA model with 128 antenna elements with

and without the phase noise. ........................................................................................................ 58

Figure 32: Simulated and theoretical antenna gains as a function of the phase noise standard

deviation. ....................................................................................................................................... 62

Figure 33: Simulated and theoretical received powers for the interfering links and the desired

link, as well as the noise floor as a function of the phase noise standard deviation. ................... 63

Figure 34: Theoretical SINR as a function of the phase noise standard deviation and number of

users. ............................................................................................................................................. 63

Figure 35: Summary of high-profile transmission experiments carried out within the scope of

TERRANOVA. The dotted and dashed reference curves for the various m-QAM formats depict

the maximum achievable distance for which error-free decoding is still possible assuming a soft-

decision FEC threshold of 3.4·10-2. Points in the diagram depict unidirectional SISO experiments

with offline DSP unless stated otherwise. ..................................................................................... 64

Figure 36: a) Received power (including 28 dB receiver conversion gain) vs. Time: Comparison

between theoretical results calculated with channel models for THz transmission (Simplified

model by the University of Oulu and the ITU-R P.676-12 model recommendations) and the

measured data at the receiver before DSP. b) Normalized received power variation between

measured data and the rain attenuation model based on actual weather conditions. Data

corresponds to a 500-km-long LOS THz system at a carrier frequency of 296.784 GHz with 55 dBi

Cassegrain antennas. Experiment was carried out in Berlin, Germany on March 3rd, 2020 from

8:30 to 18:30 CET. ......................................................................................................................... 66

Figure 37: Probability of correct detection vs number of samples for different values of θa. ...... 68



List of Tables

Table 1: Summary of the simulation parameters used to calculate the theoretical curves

according to an additive white Gaussian channel model. ............................................................. 64

Table 2: Scenarios under investigation. ........................................................................................ 68

Table 3: Average value and variance of the test statistics for the case in which Ns=2048. .......... 69



Executive Summary

The present deliverable “D2.3 - Final report on system level performance evaluation by

simulations,” reflects the relevant work that was carried out by the consortium partners in the

context of the performance evaluation by simulations that were mainly carried out during WP3

(THz wireless link design) and WP4 (wireless access and resource management) tasks. Section 2 is

based on the previously submitted deliverable “D2.1 TERRANOVA system requirements” and

summarises the defined Key Performance Indicators and physical system limitations that were

considered for the optical/THz TERRANOVA system developed within this project. Section 3 is

devoted to the relevant THz channel modelling simulation aspects while Sections 4 and 5 are

dedicated to link level and system level simulations respectively. In Section 6 a comparative

analysis between simulation and demonstration results is presented (outcome of “WP6 - THz

Demonstrator Implementation and Validation”) while in Section 7, conclusions are reported.

The main outcomes of the deliverable are:

• Evaluation of relevant THz channel modelling simulations,

• Evaluation of Link Level and System Level simulations of the Optical/THz TERRANOVA

communication system, and

• Assessment and comparative analysis between simulations and the demonstration

results stated as the main outcome of WP6 (THz Demonstrator Implementation and

Validation).



1. INTRODUCTION

Over the last years, the proliferation of wireless devices and the increasing number of bandwidth-

consuming internet services have significantly raised the demand for high data-rate transmission

with very low latency. While the wireless world moves towards the fifth generation (5G), several

technological advances, such as massive multiple-input multiple-output (MIMO) systems, full

duplexing, and millimeter wave (mmW) and visible light communications (VLCs) as well as free

space optics (FSOs), have been recognized as promising enablers. However, there is still limited

efficiency and flexibility when it comes to handling the huge amount of quality of service (QoS)

and experience (QoE) oriented data [1].

Since the used frequency spectrum for 5G has limited capacity, wireless THz became an attractive

complementing technology to the less flexible and more expensive optical-fibre connections as

well as to the lower data rate systems, such as VLCs, microwave links, and wireless fidelity (Wi-Fi)

[2], [3]. Motivated by this, the objective of the project TERRANOVA is to provide unprecedented

performance excellence, not only by targeting data rates in the Tbit/s regime, but also by

inherently supporting novel usage scenarios and applications, such as virtual reality, virtual office,

etc., which combine the extreme data rates with agility, reliability and almost-zero response time.

Additionally, in the near future, users in both rural and remote regions, in which the access is not

easily established (e.g., mountains and islands), should be able to connect with high data rates of

up to 10 Gbit/s per user, since it has been proven that access to high-speed internet for all is

crucial in order to guarantee equal opportunities in the global competitive landscape. Nowadays,

using solely optical fibre solutions is either infeasible or prohibitively costly. As a result, the use of

wireless THz transmission as backhaul extension of the optical fibre is an important building block

to bridge the ‘divide’ between rural areas and major cities and to guarantee high-speed internet

access everywhere, in the beyond 5G era. Finally, the increasing number of mobile and fixed end

users, as well as users in the industry and the service sector, will require hundreds of Gbit/s in the

communication to or between cell towers (backhaul) or between remote radio heads located at

the cell towers and centralized baseband units (fronthaul).

In all the above-mentioned scenarios, the proposed TERRANOVA system concept is expected to

be used for wireless access and backhaul networking; hence, it will influence the main technology

trends in wireless networks within the next ten years and beyond. Its implementation will have

to leverage breakthrough novel technological concepts. Examples are the joint design of

baseband digital signal processing (DSP) for the complete optical and wireless link, the

development of broadband and highly spectral efficient radio frequency (RF) frontends operating

at frequencies higher than 275 GHz, and new standardized electrical-optical (E/O) interfaces.

Additionally, to address the extremely large bandwidth and the propagation properties of the THz

regime, improved channel modelling and the design of appropriate waveforms, physical (PHY)

layer techniques, multiple access control (MAC) schemes and antenna array configurations are

required.

In this sense and with the vision to provide reliable and scalable connectivity of extremely high

data rates in the Tbit/s regime at almost ‘zero-latency’, TERRANOVA proposes to extend the fibre



optic systems’ QoS and QoE as well as performance reliability into the wireless domain, by

exploiting frequencies above 275 GHz for access and backhaul links.

In this context, this deliverable aims to reflect the work that was carried out by the consortium in

terms of the optical/THz TERRANOVA system performance evaluation by analytical and computer

simulations. It starts by providing an overview of the key performance indicators and physical

system limitations that were taken into consideration. Channel modelling aspects are also

addressed further with link and system level simulations. Finally, a reference comparison between

simulation and demonstration results is presented.



1.1 Scope

The goal of this deliverable, entitled “D2.3 Final report on system level performance evaluation

by simulations” (henceforth referred to as D2.3), is to reflect the work that was carried out by the

consortium partners in terms of theoretical and computer simulations of the TERRANOVA system

performance. Relevant channel modelling aspects as well as link and system level simulations are

presented together with a comparative analysis between the obtained simulation and

demonstration results.

1.2 Structure

The structure of this document is as follows:

• Section 2 (Defined Key performance Indicators and Physical System Limitations for an

optical/THz system) provides an overview of the key performance indicators (KPIs) and

the physical system limitations that were defined during “D2.1 TERRANOVA System

Requirements” and were taken into consideration for simulation purposes.

• Section 3 (Relevant THz channel modelling simulation aspects) discusses relevant SOTA

THz channel modelling considerations (e.g. pathloss). This work should be part of present

and future considerations for THz communication systems design.

• Section 4 (Link Level simulation for the optical/THz System) takes into consideration

several relevant aspects of the THz link level simulation in terms of: THz indoor LOS and

NLOS propagation, impact of hardware imperfections in the THz received signal, antenna

gain vs antenna misalignment and channel estimation.

• Section 5 (System level simulations for the optical/THz System) shows some simulation

results in terms of indoor performance evaluation by means of Stochastic Geometry.

• Section 6 (Comparative analysis of simulation and demonstration Results) combines the

simulation and demonstration results by means of a comparative analysis. This section

starts with a performance feasibility analysis from the demonstration results followed by

a selective comparison of channel models with measured data. Finally, an Initial Access

scheme performance evaluation based on measured data is performed.

• Section 7 (Conclusions) summarizes the main messages and findings of D2.3 and draws

the corresponding conclusions.



2. DEFINED KEY PERFORMANCE INDICATORS AND PHYSICAL

SYSTEM LIMITATIONS FOR AN OPTICAL/THZ SYSTEM

This section is devoted to briefly refer to the key performance indicators (KPIs) and the physical

system limitations that were derived from the previous project deliverables [4] and that are taken

into account for the simulation work carried out during WP2.

2.1 Defined Key Performance Indicators (KPIs)

Key performance indicators of the optical/THz link were defined, taking into account the relevant

use case scenarios that were targeted for the co-designed THz and fibre-optical network. The

relevant key performance indicators are:

• Aggregate throughput of wireless access for any traffic load/pattern [Tbit/s]

• Throughput of the point-to-point ‘fibre optic - THz wireless’ link [Tbit/s]

• Link latency of the ‘fibre optic - THz wireless’ [‘zero’ latency]

• Range of the ‘fibre optic - THz wireless’ link [tens of km optical, 1 km THz wireless]

• Reliable communications [probability of achieving a target BER and PER]

• Availability [‘Always’ available connectivity of ‘infinite’ number of devices]

Additionally to the above KPIs, energy efficiency, measured in terms of energy per information

bit, should also be taken into account when assessing the success of the THz networks

implementation (this is even more critical for mobile equipment).

2.2 Physical System Limitations

The reference THz link is defined as follows:

• Point-to-point LOS, single beam, single in-phase and quadrature (I/Q);

• Ideal transmitter, limited by output power;

• Ideal channel, only limited by loss;

• Ideal receiver, limited by additive white Gaussian noise (AWGN) thermal noise floor;

• M-QAM modulation and demodulation.

This reference link is based on the classic AWGN channel model and allows for the estimation of

the upper bounds on the THz link capacity and range, as a function of basic component and link

parameters. While this simplification neglects many known impairments, such as phase noise,

bandwidth limitations and nonlinearities, we assume that the use of digital impairments

correction and mitigation algorithms can efficiently idealize a real THz link, so that the calculated

upper bounds are still close enough to what will be achievable in reality.

The THz link suffers from several path loss mechanisms, including the free space path-loss (FSPL)

due to signal spreading, the effective antenna aperture, and the molecular absorption. The latter



is a distinguishing feature of the millimetre and sub-millimetre bands. The main difference

between the mmWave and the THz band is the progressively increasing molecular absorption loss.

Figure 1: Individual loss components of the lower THz band LOS channel, as well as the expected total losses under harsh weather conditions. The absorption losses and the FSPL were calculated

with the HITRAN-based line-by-line model and Friis equation, respectively.

The absorption losses were evaluated based on spectroscopic databases, i.e., high resolution

transmission (HITRAN) database, in conjunction with the Beer-Lambert law. They were calculated

for water vapour volume mixing ratios 0.01 and 0.02, at the earth’s surface level, representing

roughly the mean humidity in Europe and the equatorial regions in June 2016, respectively.

Because of the exponential nature of the molecular absorption and the volume mixing ratios of

the molecules, which is used to weight the total path-loss of the mixture, doubling the amount of

water vapour roughly doubles the loss on a dB scale. The Radio Communication Sector of

International Telecommunication Union (ITU-R) recommendations P.838-3 and P.840-6 were

used for evaluation of the attenuation caused by rain and fog, respectively.

Figure 1 compares the possible LOS losses per kilometre and their total contributions. As the distance between the transceiver nodes increases, the FSPL dominates the total loss below 370 GHz, whereas above 370 GHz, the molecular absorption loss dominates. Even below 370 GHz, we observe three absorption lines, which depend on the distance and humidity level. The curves for rain and fog correspond to a heavy rain of 50 mm/hr and a dense fog of 0.5 g/m3 liquid water content in air. Each of these conditions causes an additional approximately 10 dB loss at a carrier frequency around 300 GHz.

The path loss is severe at all distances due to high centre frequencies, but even more so at high

distance links. This is because the molecular absorption loss becomes more and more important

as the link distance is increased. The reason is that the FSPL is readily high because of the large

frequencies, but it increases with respect to square of the distance (d2), whereas the molecular

absorption loss increases exponentially (ed). As a result, the indoor short distance links do not

experience large molecular absorption losses, but, due to the high frequency, the FSPL remains

the cause of large path losses, even at short distances.



Below 1 THz, there are several transmission windows exhibiting minimum molecular absorption

(centred at about 260, 345, 415, 465, 495, 670, and 860 GHz) that can be utilized in long-distance

links, as shown later in Table 3. While the FSPL varies between about 140 dB to 150 dB per

kilometre in the 275 – 1000 GHz band, the molecular absorption loss varies at the same band from

about 1 dB to 80 dB at the transmission windows. The transmission window bandwidths further

depend on the distance and relative humidity as the molecular absorption loss increases as a

function of distance and the amount of water vapour in the atmosphere. This is illustrated in

Figure 2 at the centre frequency of 342 GHz.

From these calculations, we can conclude on the THz channel loss characteristics as follows: There

are several transmission windows between 275 GHz and 1 THz that could be potentially

aggregated for high-capacity transmission. Both the loss and bandwidth vary considerably among

the individual transmission windows and are additionally highly sensitive to environmental

parameters like humidity, rain or fog. Therefore, we expect outdoor link capacities that severely

vary over time (with weather conditions) as well as over geographical position (due to different

average humidity); especially for long distance links. In order to preserve a high link availability

(reliability key performance indicators - KPIs), highly flexible transmission schemes will be

required that can adapt spectral efficiency (e.g., QAM order), as well as modulation bandwidth

(e.g. symbol rate). Finally, this will impose challenges on the overall (‘end-to-end’) system

management.

Figure 2: A 3-dB Transmission window bandwidth at 342 GHz centre frequency as a function of distance and relative humidity.

Next, we use the results on channel loss in order to derive some upper bounds on the channel capacity of the above described reference THz link. In Figure 3, the estimated theoretical limits are shown for distances between 100 m and 1 km, which roughly apply to scenarios 1 and 2. The calculation assumes a single-channel frontend with a receiver noise figure of 10 dB over a



bandwidth of 64 GHz. The linear transmit power is set to 0 dBm. Note that these parameters are close to the ones derived from experimental demonstrators at 0.3 THz [5], [6]. The uncorrelated amplitude and phase mismatches are in the order of 1 dB and 1º, respectively [7]. The phase imbalance was estimated from on-chip measurements of the hybrid components used in the transceiver chip. A highly directive antenna with a gain of 55 dBi is assumed at both ends of the link. This corresponds to a physical antenna aperture size having a diameter of 225 mm and an aperture efficiency of 80%.

Figure 3 shows that the link capacity heavily depends on the transmission distance as well as on

the transmit power and the exponential absorption loss. We have plotted ideal cases without

absorption loss and with 5 dB loss (corresponding to a higher humidity, but otherwise good

weather conditions, i.e., no rain or fog). For 0 dBm transmit power (corresponding to the currently

state-of-the-art), a (capacity x distance) product of 300 Gb/s x 1000 m can be achieved with 64-

QAM modulation in the case with absorption loss, while this only approximately doubles for 10

dBm transmit power. Achieving a (Tb/s x 1000 m) product would therefore both need a further

>10x increase in transmit power well beyond 20 dBm and/or an increase of the used bandwidth

beyond 64 GHz. Due to the significant absorption loss, a maximum THz link distance beyond

several kilometres seems unlikely. To circumvent these challenges, a capacity increase using

spatial multiplexing, i.e. using a second polarization or several spatially separated antennas, as

well as relay stations to increase the maximum reach would be interesting options.

Figure 3: Estimated upper net data rate bounds for small-sized THz sub-arrays (assuming a forward error correction (FEC) threshold at BER = 2e-2).

Furthermore, it seems clear that very high-gain antennas will be needed to achieve a high

(capacity x distance) product. This in turn will lead to both large antenna arrays as well as to very

narrow beams.

In Figure 4, the maximum antenna opening angle for small-sized sub-arrays composed of NTX

antenna elements is depicted. The antenna opening angle corresponds to twice the maximum



beamspanning angle from broadside direction. The link distance is fixed to 10 m and the linear

transmit power to 0 dBm per antenna element. Apart from the antenna gain and spatial power

combining benefit all other assumptions are equivalent to the backhaul scenario, provided in

Figure 4. The calculations in Figure 4 assume that the array opening angle corresponds to the 3dB-

beamwidth of a single-antenna element, which amounts to an upper-bound of the array factor.

This figure predicts that data-rates up to 200 Gbps are possible with a maximum antenna opening

angle of 15 o, when using 4 elements. To make it practically useful, NTx needs to be increased to at

least 8 or 16, which allows for a data-rate increase or improves the trade-off between data-rate

and opening angle. A first experimental 4-channel platform was developed in [8], for verifying this

trade-off at 300 GHz. For the envisioned scenarios of limited number of antenna elements

between 4 and 16 and spanning angles of less than ~25 degrees, beamsteering can be achieved

by either time-shifting in the digital baseband, phase-shifting in the local oscillator (LO) path or in

combination, at relative bandwidths of 20%.

Generally, a large beam steering angle will limit the achievable (capacity x distance) product. This will be challenging in particular where both large beam steering angles as well as a large (capacity x distance) product is advantageous (please also refer to D2.1 - TERRANOVA system requirements). Here, several antenna arrays with hand-over might be needed for nomadic or mobile applications, where each antenna array only serves a smaller portion of the total required beam steering angle.

Figure 4: Estimated data rates for small-sized THz sub-arrays

0

5

10

15

20

25

30

35

40

45

50

0 5 10 15 20 25 30 35 40

Ava

ilab

le S

NR

(d

B)

Antenna Opening Angle (degree)

256QAM (400 Gb/s)

16QAM (200 Gb/s)

4QAM (100 Gb/s)

NTx = 32

NTx = 16

NTx = 8 NTx = 4

64QAM (300 Gb/s)



3. RELEVANT THZ CHANNEL MODELLING ASPECTS FOR

SIMULATIONS

This section looks through the last modifications to the channel models that were implemented

in the last phase of the project and that are used in many of the simulation models below. The

main change here from the previous work is an update to the simplified channel model and it

coefficients. This model is given below along with the line-of-sight (LOS) channel model based on

it.

3.1 Molecular absorption loss

Simplified channel models for LOS links were given for the low THz band (<500 GHz) in D3.2 and

D3.4. Here, we give the final version of the simplified model that comprises molecular absorption

loss and the free space path loss. This newest version of the LOS channel model covers frequency

range from 100 GHz to 450 GHz. A research paper describing this model has been submitted to

EURASIP Journal on Wireless Communication Networking [9].

As the LOS links are the most important links to be utilized in order to provide good

communication channel, those are also in major role in system performance analysis in this

deliverable. Thus, the basic LOS model along with the newest version of the simplified channel

model is given in this section.

3.1.1 General absorption loss model

The molecular absorption is given by the Beer-Lambert law. It describes the transmittance, i.e.,

the fraction of energy that propagates distance d through the medium. The molecular absorption

loss level is related to the link distance and absorption coefficient [11] [12].

𝜏(𝑓, 𝑑) =𝑃𝑟(𝑓)

𝑃𝑡(𝑓) = 𝑒𝛴𝑗𝜅𝑎

𝑗(𝑓)𝑑 ,

Where 𝜏(𝑓, 𝑑) is the transmittance, 𝑓 is the frequency, 𝑑 is the distance from transmitter (Tx) to

receiver (Rx) (in meters), 𝑃𝑡(𝑓) and 𝑃𝑟(𝑓) are Tx and Rx power, respectively, and 𝜅𝑎𝑗

(𝑓) is the

absorption coefficient of the jth absorbing species at frequency f. The absorption coefficient can

be calculated with spectroscopic databases, such as the HITRAN database [17]. The detailed

calculation of the absorption coefficient can be found, e.g., in [15] [16].

3.1.2 Simplified molecular absorption loss model

The polynomial absorption loss model is obtained by searching the strongest absorption lines on

the band of interest and extracting the parameters for those. The temperature and pressure

dependent coefficients are fixed. Since the absorption for frequencies above 100 GHz is mainly

caused by the water vapour in the air, the volume mixing ratio of water vapour is left floating. The

parametric model is characterized by the absorption coefficients 𝑦𝑖 at absorption lines i. The

above Beer-Lambert model becomes

𝑃𝐿𝑎𝑏𝑠(𝑓, 𝜇) = 𝑒𝑑(∑ 𝑦𝑖𝑖 (𝑓,𝜇)+ 𝑔(𝑓,𝜇)),



where f is the desired frequency grid, 𝑦𝑖 is an absorption coefficient for the ith absorption line,

𝑔(𝑓, 𝜇) is a polynomial to fit the expression to the actual response (see below for more details),

and 𝜇 is the volume mixing ratio of water vapour. It can be determined from the relative humidity,

e.g., as it was shown in the original paper [9] and also in the previous version of the model

presented in [11].

The six polynomials for the six major absorption lines at the 100 – 450 GHz band are given as:

𝑦1(𝑓, 𝜇) =𝐴(𝜇)

𝐵(𝜇) + (𝑓

100𝑐 − 𝑝1)2,

𝑦2(𝑓, 𝜇) =𝐶(𝜇)

𝐷(𝜇) + (𝑓

100𝑐− 𝑝2)

2,

𝑦3(𝑓, 𝜇) =𝐸(𝜇)

𝐹(𝜇) + (𝑓

100𝑐− 𝑝3)

2,

𝑦4(𝑓, 𝜇) =𝐺(𝜇)

𝐻(𝜇) + (𝑓

100𝑐− 𝑝4)

2,

𝑦5(𝑓, 𝜇) =𝐼(𝜇)

𝐽(𝜇) + (𝑓

100𝑐 − 𝑝5)2,

𝑦6(𝑓, 𝜇) =𝐾(𝜇)

𝐿(𝜇) + (𝑓

100𝑐− 𝑝6)

2,

𝑔(𝑓) =𝜇

0.0157(2 × 10−4 + 𝑎𝑓𝑏),

where c is the speed of light, and

𝐴(𝜇) = 5.159 × (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,

with 𝑝1 = 3.96 1/cm, 𝑝2= 6.11 1/cm, 𝑝3= 10.84 1/cm, 𝑝4= 12.68 1/cm, 𝑝5= 14.65 1/cm, 𝑝6= 14.94

1/cm, 𝑎 = 0.915 × 10−112, and 𝑏 = 9.42. The lines 𝑦1, 𝑦2, 𝑦3, 𝑦4, 𝑦5, and 𝑦6 correspond to

strong absorption lines at 119 GHz, 183 GHz, 325 GHz, 380 GHz, 439 GHz, and 448 GHz,

respectively. Those centre frequencies are also shown in the line expressions as the parameters

𝑝1 to 𝑝6 give the line center frequencies in wavenumbers. More details of the models are given

in [9]. The error of this model versus the exact response is given below in Figure 5. This shows that

the model very accurately predicts the fully theoretical model for molecular absorption loss.

Figure 5: Error of the proposed simplified molecular absorption loss model.

3.1.3 FSPL and the total loss

The FSPL of a LOS link is given by the common Friis transmission equation:

𝑃𝐿𝐹𝑆𝑃𝐿(𝑑, 𝑓) =(4𝜋𝑑𝑓)2

𝑐2,

Then the LOS channel loss is given by the FSPL and the molecular absorption loss as

𝑃𝐿(𝑑, 𝑓) =(4𝜋 𝑑 𝑓)2𝑒𝑥𝑝(𝜅𝑎(𝑓, 𝜇)𝑑)

𝑐2𝐺𝑅𝑥𝐺𝑇𝑥 ,

Where 𝐺𝑅𝑥 and 𝐺𝑇𝑥 are the antenna gains. When using the polynomial models above, the

absorption coefficient 𝜅𝑎(𝑓, 𝜇) is



𝜅𝑎(𝑓, 𝜇) = ∑ 𝑦𝑖

𝑖

(𝑓, 𝜇) + 𝑔(𝑓, 𝜇),

where the 𝑦𝑖(𝑓, 𝜇) are the above polynomial absorption lines, or subset of those depending on

the modelled frequency band within the frequency range from 100 – 450 GHz.

4. LINK LEVEL SIMULATION FOR THE OPTICAL/THZ SYSTEM

In the following sections several aspects of the link level simulations are described in the context

of the optical/THz TERRANOVA system design and development.

4.1 THz indoor LOS and NLOS propagation

In this section we study LOS and NLOS propagation in indoor location. We focus on statistical

modelling of the indoor THz propagation by Monte Carlo simulations. The advantage of the high

frequency, high antenna gain systems is the fact that the propagation phenomena are isolated

and those can be included into theoretical models that usually perfectly fit with the respective

real measurements. This is caused by the high gain antenna not being able to see the entire

environment similarly to what most omnidirectional antennas do at lower frequencies.

There are many papers about THz indoor channel and propagation modelling by measurements,

simulations, and theoretical works, such as [20], [21], [22], [23], [24], [25], [26]. The approach

here differs from the existing works in that nearly perfectly random indoor channel is created by

applying distributions for potential objects in the indoor space. Therefore, we can introduce

random reflection points representing objects in the environment, such as furniture, lamps,

decorations, etc. We also model the deterministic reflections from the walls, floor and ceiling

along with the line-of-sight (LOS) path between the Tx and Rx. Via utilizing Monte Carlo

simulations in random indoor environment, we can obtain some insights into the THz band system

operation in generic indoor locations. All the rooms are different, but they usually share certain

features, such as furniture placement in certain types of rooms, like living rooms or office spaces.

The random reflections in random room layout can originate from anywhere in the room and

ultimately the antenna patterns thin the number of the visible reflection points within the

environment as the higher is the gain, the narrower the radiation pattern of the antenna is. That

is, the less of the environment the antenna sees.

Here, we derive channel models for multipath channel with LOS path available, i.e., when the

primary communication path is the LOS path and the extra contribution is provided by the NLOS

paths. The second channel model is derived for a multipath NLOS model, where one of the NLOS

paths is the primary communications channel and the rest of the NLOS paths again sum to the

primary channel. It is shown that path loss of these NLOS models depend on the material

characteristics of the environment. The LOS channel is less sensitive to the multipath propagation

due to dominating LOS component decreasing the impact of the NLOS paths. The results herein

were partially presented in TERRANOVA deliverable D3.4 Section 2.3.2. However, the results

herein provide a complete version of those with fully random environment, in order to illustrate

the generic indoor propagation, and new estimates for the channel losses.



4.1.1 Simulation model

The simulation model utilized to study the signal multipath propagation in indoor locations is a

rectangular space limited by the walls, floor, and ceiling. An illustration of the assumed system

model is given in Figure 6 and Figure 7. The dark centre diamonds are the Txs and placing those

in a tight grid across the room gives a general overview of the path loss from any location in the

room. Those also represent a wide range of possible communication distances between the Tx

and the Rx. The single green centre diamond in the upper corner of the room is the Rx. The Rx is

assumed to be in the upper corner of the room, 20x20x20 cm3 away from the top corner. It depicts

an access point that has a good visibility over the room.

Figure 6: An illustration of the simulation environment. The dark centre diamonds depict the Tx grid, the green centre diamond in the corner depicts an access point, or the Rx. The red squares

are random reflection points representing objects in the environment.

Figure 7: View of Figure 6 from above showing the distribution of the random reflection points.



Given a position of a particular Tx with respect to the Rx, the walls are potential reflecting surfaces

for multipath propagation of the transmitted signals. The red squares in the figures are random

reflecting points caused, e.g., by people, furniture, objects, and other irregularities in the room.

Those are modelled by an exponential distribution with 40 cm mean to emphasize the fact that

most of the furniture and other objects are usually placed close to the walls. Therefore, it is less

likely that there would be reflection sources in the centre of the room. Notice that the

randomness of the objects and their locations in the environment is dependent on what type of

room is modelled. An office space, for instance might have more centred placement of the

furniture, however, with the larger furniture often still against the walls. Here, we focus on generic

artificial situation that would be depictive for a private home room.

In the Monte Carlo simulations the locations of the random reflection points and the number of

them are selected randomly. The walls cause a deterministic reflection points as there is one

single possible reflection point for each wall, and one for both the ceiling and the floor, dependent

on the positions of the Rx and Tx. It is highly unlikely that all the deterministic reflection points

would be available. Therefore, a blocking probability is employed for each of these paths. Finally,

all the available random and deterministic paths are summed at the receiver that causes

constructive and destructive summation based on the phase of the signals arriving through

different paths.

The availability of the randomly selected reflection points and the deterministic reflection points

is dependent on the selected antenna pattern and the position of the Rx and Tx. As an example,

isotropic antennas see the entire space and therefore all the reflection points. Very highly

directional antennas would only see each other and with very high certainty, no reflection points

at all. However, the antenna gain patterns are utilized to calculate the gains towards all reflection

points. We consider two scenarios in the numerical results, one with the LOS available, and one

where the primary communication path is selected among the reflection points by steering the

Rx and Tx antennas towards that reflection point.

Given the random and deterministic paths of the multipath signal, the total received power is

𝑃𝑅𝑥 = 𝑃𝑇𝑥𝛾(𝑟)𝐺𝑇𝑥(0)𝐺𝑅𝑥(0) + ∑ 𝑃𝑇𝑥𝛾(𝑅𝑖)𝐺𝑇𝑥(𝛼𝑇𝑥,𝑖)𝐺𝑅𝑥(𝛼𝑅𝑥,𝑖)

𝑁

𝑖=1

,

where 𝑃𝑅𝑥 is the received power, 𝑃𝑇𝑥 is the transmitted power, 𝐺𝑇𝑥 is the transmitter antenna

gain, 𝐺𝑅𝑥 is receiver antenna gain, N is the number of multipath components, 𝑅𝑖 is the length of

the ith multipath component, 𝛼𝑇𝑥,𝑖 is the angle of the ith multipath component to the primary

communication path, and 𝛼𝑅𝑥,𝑖 is the equivalent for the receiver. Notice that this is the

mechanism that rejects most of the random multipath components. The antenna pattern

determines how wide field of view it has, and the angle is dependent on where the reflection

point is with respect to the main communication path of the Rx and Tx. Path loss 𝛾(𝑥) is defined

as (similarly to the total loss in Section 3.1.3)

𝛾(𝑥) =𝑐2𝑒𝑥𝑝(−𝜅𝑎 𝑥)

(4𝜋𝑓𝑥)2,



where x is the distance, f is the frequency, and 𝜅𝑎 is the molecular absorption coefficient, which

can be estimated as it was shown above for the simplified model. An additional illustration of the

simulation system's geometry is given in Figure 8, where 𝑝𝑟 is the random reflection point, and

𝑝𝑏 is a blocking probability of a deterministic path.

Figure 8: Illustration of the system geometry; LOS path, deterministic reflections and random reflections.

The antennas in this work are assumed to be perfectly conical antennas with no side lobes. This

is a good approximation in the high mmWave and THz band as the large path loss requires very

high antenna gains where the main lobe gain can be tens of dBs higher that the side lobe levels

(depends on the antenna type and possible antenna element configurations). The ideal conical

antennas are also simple to handle in simulation models and in the theoretical calculations. Such

antennas would have a gain equivalent to

𝐺 =1

2𝜋 (1 − 𝑐𝑜𝑠 (𝜃12

))

due to geometry of a cone and constant total radiated power, where 𝜃1

2

is the antenna half

beamwidth. It can be seen that the gain for a full sphere, i.e., for an isotropic antenna is 1/4𝜋 to

all directions. This is due to the integration over the entire sphere equals 4𝜋. Then, the full

spherical integral over G is always unit, i.e., the full Tx power.



4.1.2 Simulation results

The simulations were run for a tight grid of Txs around the room, but with constant height of 120

cm to simulate a person holding the device. Nevertheless, the height is not a major issue here.

We ran the simulation model for a 400x600x240 cm3 room for this paper, but the results obtained

for other room sizes agree with the models produced in this reference room. That is, also in the

case we change the geometry. As a consequence, the absolute height of the device is not

important as the overall behaviour of the signal is dictated by the propagation paths and the

angles of arrival to those, i.e., the reflection losses, and the antenna gains. The antenna (full)

beamwidth was kept at 𝜋/16 radians in the numerical results, corresponding to antenna gain of

about 15 dB for rotationally symmetric antenna pattern assumed herein. The number of random

reflection points distributed exponentially about the sides of the room varied from 25 to 100. We

also simulated the results for two different bandwidths, 10 GHz and 100 GHz with centre

frequency being 300 GHz. However, the bandwidth did not have any impact on the results and

therefore the bandwidth is not considered below. Similarly, the antenna gains only scale the

below results without having impact on the behaviour of the path loss. Therefore, the actual

received power according to the above models becomes

𝑃𝑅𝑥 = 𝑃𝑅𝑥𝛾 𝐺𝑇𝑥(0)𝐺𝑅𝑥(0),

where 𝛾 is channel gain that is given below for the LOS and NLOS communication cases. Finally,

the blocking probability of the deterministic paths through walls, floor and ceiling was 0.5.

However, it should be noticed that the antenna gains render, e.g., the back wall invisible due to

the assumption of no side lobes.

Figure 9: Simulated and fitted path gain with about 30 dB total antenna gain as a function of distance for LOS case.



The simulations results show that if the LOS path is available, the NLOS paths are either very weak

compared to the LOS path or there are not available. This is natural due to large antenna gains to

maintain proper signal levels. As a consequence, the following free space path loss model with

path loss exponent 2 describes the loss very accurately:

𝛾𝐿𝑂𝑆 = 6.41 × 10−9𝑟−2,

where 𝛾𝐿𝑂𝑆 is the path gain of the channel and r is the distance in meters between Tx and Rx along

the primary signal path. Notice that this is not directly the free space path loss according to Friis

transmission equation, but it also takes into account molecular absorption loss. The simulated

path gains are shown in Figure 9. The above free space model is given as dashed line. This shows

a perfect fit between the simulation and proposed model.

Where things get more interesting is when there is no LOS path available. We model the reflected

power by basic Fresnel equations and by assuming circularly polarized radiation [26]

𝑅(𝜃𝑖) =1

2(𝑅𝑠(𝜃𝑖) + 𝑅𝑝(𝜃𝑖)),

where

𝑅𝑠(𝜃𝑖) =

|

|{𝑛1𝑐𝑜𝑠(𝜃𝑖) − 𝑛2√1 − (𝑛1𝑛2

𝑠𝑖𝑛(𝜃𝑖))

2

}

𝑛1𝑐𝑜𝑠(𝜃𝑖) + 𝑛2√1 − (𝑛1𝑛2


2|

|

2

and

𝑅𝑝(𝜃𝑖) =|

|𝑛1√1 − (𝑛1𝑛2


2

− 𝑛2𝑐𝑜𝑠(𝜃𝑖)

𝑛1√1 − (𝑛1𝑛2


2

+ 𝑛2𝑐𝑜𝑠(𝜃𝑖)|

|

2

are the reflectances of the perpendicular (𝑅𝑠(𝜃𝑖)) and the parallel (𝑅𝑝(𝜃𝑖)) signal components,

𝑅(𝜃𝑖) is the reflectance of circularly polarized signal, 𝜃𝑖 is the angle of incident, 𝑛1 is the refractive

index of air (assumed to be one), and 𝑛2 is the refractive index of the material.



Figure 10: Simulated and fitted path gain with about 30 dB total antenna gain as a function of distance for NLOS case with all the objects and walls having refractive index of 1.5.

Figure 11: Simulated and fitted path gain with about 30 dB total antenna gain as a function of distance for NLOS case with all the objects and walls having refractive index of 2.9.



The Fresnel equation's geometry is calculated based on the geometry of the room, locations of

the Rx and Tx, the respective deterministic reflection point locations and the random reflection

point locations. The simulations were run for three different refractive indices for reflective

materials. One case for refractive index of 1.5, one for 2.9 and one for random refractive index

varying between 1.5 and 2.9. These values were selected since our previous measurements have

shown that many common indoor materials fall between these refractive indices around 300 GHz,

but also around 1000 GHz [26]. For instance, medium density fiberboard (MDF) has a refractive

index of about 1.5 at 300 GHz. On the other hand, glass, as highly reflecting but weakly penetrating

material, has a refractive index of about 2.9 at 300 GHz.

Figure 9 to Figure 12 show the results for the above Fresnel equation assumptions. As expected,

high refractive index suggests high reflected power (Figure 11). The low end of the refractive

indices allows larger penetration and less reflected power (Figure 12). When the refractive index

is random, we obtain the most plausible picture of the random signal propagation. However, the

channel gains as well are random for any particular distance between the Tx and Rx. Notice that

the distance here is the distance via the reflected path, not the Euclidean distance.

Based on the simulations, we derived the following model for NLOS communications by fitting to

the simulation data:

𝛾𝑁𝐿𝑂𝑆 = 1.19 × 10−9𝑟−𝛼,

where 𝛼 are the path loss exponents obtained by simulations. Those were found as 𝛼 = 2.7, 2.17,

and 2.3 for the refractive indices 𝑛2 = 1.5, 2.9, and random, respectively. Figure 9 to Figure 12

also show a very good fit of the simulation data to the proposed models.

The results here are given for a room shown in Figure 6, but according to simulations on larger

rooms, the proposed models remain accurate. The most interesting case among these is the

random refractive index, as it gives the likely case with various materials present in a random

indoor location. This particular case shows that an average NLOS path causes about 15 dB of

additional loss to the LOS case. This is mainly attributed to the increased loss on the reflected

paths. This is an expected result as the reflections have less power than the LOS path.

The future work still requires some more estimation for proper random point distributions for

various environments. For instance, in office environment furniture are usually placed very much

differently than in a usual home. Also, the exact distribution parameters require attention.

Overall, simulations give a good overview of the general signal behaviour. Measurement

campaigns are also needed to further increase the credibility of the models.



Figure 12: Simulated and fitted path gain with about 30 dB total antenna gain as a function of distance for NLOS case with all the objects and walls having random refractive.

4.2 Impact of hardware imperfections in the THz received signal

A THz wireless fibre extender equipped with highly directional antennas at both the transmitter

(TX) and the receiver (RX) is considered, in order to mitigate the severe channel attenuation. The

employed system and channel model were initially presented in [4], where it is assumed that the

complex information signal 𝑥 is transmitted to the receiver over a complex flat fading channel ℎ

with complex additive noise 𝑛. The baseband equivalent received signal can be expressed as

𝑦𝑖 = ℎ 𝑥 + 𝑛,

where ℎ, 𝑥 and 𝑛 are statistically independent. Additionally, 𝑛 is modelled as a complex zero mean

additive white Gaussian process with variance 𝑁𝑜. Despite the fact that the received signal model

accommodates the impact of the wireless channel and noise, the effect of hardware RF

transceivers imperfections, namely in-phase and quadrature (IQI), phase noise (PHN), as well as

amplifier non-linearities (ANL), is detrimental in high data rate systems [10], [13]. These

imperfections generate a distortion between the intended signal 𝑥 and what is actually emitted

and distort the received signal during the reception processing. To accommodate their influence

at a given flat fading channel, we employ a generalized signal model [13], [14], which has been

both theoretically and experimentally validated [27], [19], [28], [29]. Based on this model, the

baseband equivalent received signal can be written as,

𝑦 = ℎ(𝑥 + 𝑛𝑡) + 𝑛𝑟,

where 𝑛𝑡 and 𝑛𝑟 are respectively the distortion noises from the hardware imperfections at TX and

RX [14], which can be modelled as [14], [30]



𝑛𝑡~𝐶𝑁(0, 𝑘𝑡2𝑃) and 𝑛𝑟~𝐶𝑁(0, 𝑘𝑟

2𝑃|ℎ|2),

where 𝑘𝑡 and 𝑘𝑟 are non-negative parameters that determine the level of hardware imperfections

at the TX and RX, respectively, while 𝑃 stands for the average transmitted power. The channel

coefficient, ℎ can be obtained as

ℎ = ℎ𝑙ℎ𝑝ℎ𝑓 ,

where ℎ𝑙 = ℎ𝑓𝑙ℎ𝑎𝑙 and ℎ𝑓𝑙, ℎ𝑎𝑙 model the propagation and molecular absorption gain

respectively. The term ℎ𝑓𝑙 is modelled by employing the Friis equation. Additionally, ℎ𝑎𝑙 denotes

the molecular absorption gain and can be evaluated as in [12], [31]. The molecular absorption

gain depends on the operational frequency, transmission distance and environmental conditions.

The antenna misalignment, |ℎ𝑝| can be modelled as a stochastic process with probability density

function (PDF) that can be obtained as [32]

𝑓ℎ𝑝(𝑥) =

𝛾2

𝐴𝑜𝛾2 𝑥𝛾2−1, 0 ≤ 𝑥 ≤ 𝐴𝑜,

where

𝛾 =𝑤𝑒𝑞

2𝜎𝑠,

with 𝑤𝑒𝑞 being the equivalent beam-width radius at the RX. Moreover, 𝐴𝑜 is the fraction of the

collected power when the TX and RX antennas are perfectly aligned. In order to accommodate

the multipath fading effect, we model |ℎ𝑓| as a generalized 𝛼 − 𝜇 distribution [33], with PDF that

can be expressed as

𝑓ℎ𝑓(𝑥) =

𝛼𝜇𝜇

ℎ̂𝑓𝛼𝜇

𝛤(𝜇)𝑥𝛼𝜇−1𝑒𝑥𝑝 (−𝜇

𝑥𝑎

ℎ̂𝑓𝑎

),

where 𝛼 > 0, 𝜇 and ℎ𝑓 stand for the fading parameter, normalized variance of the fading channel

envelope and the 𝛼-root mean value of the fading channel envelop, respectively.

Next, the joint effects of the deterministic and stochastic path-gain, i.e. misalignment and

multipath fading components as well as the impact of the transceiver hardware imperfections are

investigated. Accordingly, the ergodic capacity of the THz wireless fiber extender is defined as

𝐶 = 𝐸[𝑙𝑜𝑔2(1 + 𝜌)],

where 𝜌 represents the instantaneous signal-to-noise ratio (SNR) and 𝐸[·] returns the expected

value. In the following Monte Carlo simulation results, it is assumed that TX and RX gains are 𝐺𝑡 =

𝐺𝑟 = 55 dBi, 𝛼 = 2, 𝜇 = 1 (this value corresponds to Rayleigh multipath fading, which is

employed as a performance evaluation benchmark), 𝜇 = 4 and 𝑘𝑡𝑟 = 𝑘𝑡 = 𝑘𝑟, where (𝑘𝑡𝑟 = 0)

corresponds to the ideal RF-chain case (which is used here as a benchmark ). Moreover, standard

environmental conditions, i.e., 𝜑 = 50 %, 𝑝 = 101325 Pa and 𝑇 = 296 𝐾 are assumed.

Figure 13 illustrates the ergodic capacity as a function of 𝜎𝑠 for different levels hardware

imperfections and values of 𝜇. The transmission distance is 𝑑 = 30 m, the operational frequency



is set to 𝑓 = 275 GHz and the transmitted signal power over the noise at the RX is 𝑃/𝑁𝑜 = 25 dB.

As expected, for any given values of 𝜎𝑠 and 𝑘𝑡𝑟, the ergodic capacity for the curves having 𝜇 = 1

is always lower than the respective ones with 𝜇 = 4, because the latter represents multipath

fading with a strong line-of-sight path component. Furthermore, we observe that for a given value

of 𝜎𝑠 and μ and increasing 𝑘𝑡𝑟, the ergodic capacity significantly decreases. For example, for 𝜎𝑠 =

0.04 m and 𝜇 = 4 the ergodic capacity for 𝑘𝑡𝑟 = {0,0.1,0.2,0.8,1} equals to 6.68 (bits/sec/Hz),

5.04 (bits/sec/Hz), 3.57 (bits/sec/Hz), 0.83 (bits/sec/Hz) and 0.58 (bits/sec/Hz), respectively.

Additionally, for a given value of 𝜇 and 𝑘𝑡𝑟, as 𝜎𝑠 increases the ergodic capacity decreases. As an

example, for 𝜇 = 4 and 𝑘𝑡𝑟 = 0, changing 𝜎𝑠 = 0.01 m to 𝜎𝑠 = 0.1 m the ergodic capacity

degrades from 7.26 (bits/sec/Hz) to 4.15 (bits/sec/Hz).

In Figure 14, the ergodic capacity is depicted as a function of 𝑘𝑡𝑟 for different values of 𝜎𝑠 and 𝜇.

The transmission distance is set to 𝑑 = 20 m, the operational frequency is 𝑓 = 300 GHz and the

transmitted signal power over the noise at the RX is 𝑃/𝑁𝑜 = 20 dB. As expected, for any given

value of 𝜎𝑠 and 𝑘𝑡𝑟, the ergodic capacity for the curves having 𝜇 = 1 is always lower than the

respective ones with 𝜇 = 4. Also, we observe that for any given value of 𝜎𝑠 and 𝜇 as 𝑘𝑡𝑟 increases,

the ergodic capacity decreases. For example, for 𝜎𝑠 = 0.01 m and 𝜇 = 4 increasing 𝑘𝑡𝑟 = 0 to

𝑘𝑡𝑟 = 0.2 the ergodic capacity degrades from 7 (bits/sec/Hz) to 3.6 (bits/sec/Hz).

Figure 13: Ergodic Capacity vs 𝝈𝒔 for different levels of 𝒌𝒕𝒓 and values of 𝝁.

Figure 14: Ergodic Capacity vs 𝒌𝒕𝒓 for different levels of 𝝈𝒔 and values of 𝝁.



4.3 Antenna gain Vs antenna misalignment

(a) (b)

Figure 15: Antenna misalignment in backhaul (a) and fronthaul (b) application scenarios.

As shown in Figure 15, antenna misalignment may occur in both backhaul [34] and fronthaul [35]

use cases. In the former case, it is generated due to wind, small earthquakes and other

environmental phenomena, while, in the latter case, it may be the result of tracking estimation

errors and antenna array imperfections. Next, we present indicative antenna misalignment

models, and identify the advantages and disadvantages as well as the suitability of each model

for each use case. Finally, we discuss the most commonly used models and we report their impact

on transceiver antenna gains.

4.3.1 Gaussian distributed beam-steering

This model was introduced in [35] and accommodates the stochastic beam-steering error. In

particular, let us denote the beam-steering errors of the base station (BS) and the user equipment

(UE) as εz with z ∈ {B,U} (see Figure 16), where B stand for BS and U for UE, and assume that εB

and εU are independent and identical zero-mean Gaussian distributed random variables with

variance σB and σU, respectively.

Figure 16: Beam-steering errors.

To evaluate the effect of antenna misalignment in the link budget, we approximate the actual

beamforming pattern using the sectored model. This model has been employed in several



published works, including [35] and [36] due to the fact that it can capture the key particularities

of the beamforming pattern, such as the front-to-back ratio, and the half-power beam width.

According to this model, the antenna gain can be expressed as

where U (·) denotes the unit step function, and z ∈ {B,U}. Likewise, θz denotes the beam-width of

the node z ∈ {B,U} main lobe, φ represents the angle of the boresight direction, and γz is the

forward-to-backward power ratio that can be obtained as

with αz being an antenna-specific constant.

Next, we can extract the total directional gain between the BS and the UE as

,

where φB and φU are the error-free boresight directions of the BS and UE, respectively. Moreover,

the expected value of D can be obtained as

.

Figure 17: Directional gain vs angular misalignment standard deviation for different values of antenna beam-width.

In Figure 17, the expected value of the total directional gain is depicted against the misalignment

standard deviation, σ, for different values of antenna beam-width, θ. Note that, in this figure, it is

considered that σB = σU = σ and θB = θU = θ. Additionally, a = aB = aU = 1. As expected, for a given θ>



0.1σ, as σ increases, the expected value of the total directional antenna gain decreases, whereas,

for θ < 0.1σ, the beam-steering error falls within the half-beam width of both the Tx and Rx

antennas; hence, there is no effect on the system performance. Likewise, we observe that as θ

increases, the expected value of the total directional gain decreases; however, its tolerance to

antenna misalignment increases. Finally, this figure reveals the importance of considering the

angular misalignment when evaluating the system performance.

The Gaussian distributed beam-steering errors model is tractable and suitable for modelling

tracking estimation errors. Its main disadvantage is that it accommodates only the horizontal

angular error and it totally neglects the vertical one. In other words, it is an one dimensional (1D)

model.

4.3.2 Two-dimensional Gaussian movement of a single node

(a) (b)

(c)

Figure 18: Two-dimensional Gaussian shaking of (a) the UE, (b) the BS in fronthaul scenarios, and (c) a single BS in backhaul scenarios.

As illustrated in Figure 18, the 2D Gaussian movement of a single node model accommodates

scenarios in which either the BS or the UE experience antenna misalignment. For the sake of

simplicity and without loss of generality, we consider a downlink scenario where the UE shakes.

Additionally, we assume that the Rx antenna has a circular effective area of radius a and that the

Tx has a circular beam, which, at a transmission distance d, has a radius ρ, with ρ ∈ [0, wd] and wd

is the maximum radius of the beam at d. Moreover, as depicted in Figure 19, both beams are

considered in the x − y plane and r is the pointing error that can be expressed as the radial distance

of the centres of the Tx beam and Rx effective area.



Figure 19: RX’s effective area and transmitter’s beam footprint with 2D misalignment on the horizontal and vertical axis of the receiver’s plane.

We consider the backhaul scenario, in which both BSs are equipped with Cassegrain antennas. We

set d = 30 m, Gt = Gr = 45 dBi. Moreover, the transmission frequency is f = 275 GHz. Figure 20 plots

the expected value of the total directional gain as a function of σr, for different values of G = Gt =

Gr. We observe that, for a fixed G, as σr increases, the expected value of the total directional gain

decreases. Interestingly, for low values of σs, where the antenna misalignment is not quite

important, we observe a total directional gain loss, due to the beam-waist at the RX plain. Finally,

from this figure, we observe that, for a given σs, as G increases, the expected value of the total

directional gain also increases.

Figure 20: Directional gain vs spatial jitter standard deviation for different values of antenna gains.



This model can accommodate the impact of antenna misalignment that is caused by

environmental phenomena, such as wind, and small earthquakes. It is tractable; hence, it can be

used for theoretical analysis purposes. Another important characteristic of this model is that it

takes into account the TX beam-waist at the RX plane and therefore also the transmission

characteristics, namely transmission distance and frequency, as well as the type of the TX and RX

antennas.

4.4 General antenna misalignment loss

The previous section addressed the issue of antenna misalignment. This section extends the work

therein to give a generic stochastic model for antenna misalignment loss for any possible antenna

pattern. This is obtained by calculating the expected antenna gain in the presence of movement.

This work has also been presented in a journal publication in [37]. It should also be noted that

similar results were shown in our previous work in [38], which were also presented in TERRANOVA

Deliverable D4.2. Compared to those, we consider slightly different movement statistics and

address this problem where Gaussian motion is assumed at both ends of the link. The original

work had an incorrect distribution for this particular case. This is now fixed by independently

taking into account the distributions at both ends of the link.

4.4.1 Path loss model

We utilize the LOS model shown above. However, here we utilize the expected antenna gains that

follow from the statistical movement of the antennas. Thus, the expected channel gain becomes

𝐸[𝐻(𝑓, 𝑟)] =𝑐2

(4𝜋 𝑟𝑓)2𝑒−𝜅𝑎(𝑓)𝑟 𝐸Φ[𝐺𝑇𝑥(Θ)]𝐸Φ[𝐺𝑅𝑥(Θ)],

where 𝐸Φ[𝐺𝑇𝑥(Θ)] and 𝐸Φ[𝐺𝑅𝑥(Θ)] are the expected Tx and Rx antenna gains, respectively, over

certain antenna misalignment PDF Φ and with the random antenna directions Θ drawn from Φ.

The expected antenna gain in any link is formed by two components: the movement statistics and

the antenna gain. Those are discussed below.

4.4.2 Antenna model

For simplicity, we assume uniform linear array (ULA) antennas at both ends of the communication

link. The ULA assumption offers an easy way to compare the impact of antenna movement to the

expected antenna gain. The gain of ULA at a certain azimuth angle of observation 𝛼 is given as

𝐺(𝛼) = |𝐴𝐹(𝛼)|2,

where 𝐴𝐹(𝛼) is the array factor. The array factor provides the far-field radiation pattern of ULA

given as

𝐴𝐹(𝛼) = 1

√𝑁∑ 𝑒

𝑗2𝜋𝜆

𝑑𝑛(𝑠𝑖𝑛(𝛼)− 𝑠𝑖𝑛(Γ))

𝑁−1

𝑛=0

,

where 𝜆 and d (which is assumed to be 𝜆/2) are the carrier wavelength and spacing between the

antenna elements, respectively, and Γ is the desired beam steering direction.



4.4.3 Expected antenna gain

The expected antenna gain depends mostly on the movement statistics as without movement the

antenna pattern already provides the expected antenna gain. However, in the presence of

movement, the physical motion spreads the antenna pattern on average. The Gaussian and

double Gaussian (Rayleigh) movements were previously discussed. These types of movements

sway the antenna causing the misalignment to decrease the overall long-term antenna gain.

Temporal impact is quite slow compared with high frequency systems. However, on average, the

gain is decreased based on the average movement. Thus, the expected gain is obtained as

𝐸Φ[𝐺(Θ)] = ∫Φ(𝜃)𝐺(𝜃)𝑑𝜃𝜃

,

i.e., as an integral over the antenna pattern and the PDF Φ(𝜃) of the antenna movement. In this

context we utilize the above Gaussian and Rayleigh movement at one end, as well as composite

movements with Gaussian on the one end and Rayleigh movement on the other end, and

Gaussian movement on both ends of the link. The results for these movement scenarios are given

in the next section.

4.4.4 Numerical results

The impact of the antenna misalignment to the expected antenna gain is shown in this section.

The centre frequency of the transmission was 300 GHz. The antenna configurations were 32, 256,

and 1024 antenna element ULAs that correspond to single side antenna gains of about 15, 24, and

30 dBi, respectively. The ULAs have the half power beam widths of 3.2, 0.4, and 0.1 degrees for

the 32, 256, and 1024 antenna element arrays, respectively. The sizes of the ULAs are between

1.6 cm and 51.2 cm for 32 to 1024 antenna element arrays (given 300 GHz centre frequency and

𝜆/2 antenna spacing). The same antenna configurations were assumed to be at both ends of the

link. Here we only consider the impact of the antenna motion on the antenna gain. More complete

analysis in terms of SNR can be found in [37]. However, the expected total antenna gains give the

full statistics for the SNR calculation.

Figure 21 to Figure 23 show the expected antenna gains for 32, 256, and 1024 element antenna

arrays, respectively, for four movement cases (Gaussian single side, Rayleigh single side, Gaussian

both sides and Gaussian-Rayleigh) as a function of the movement variance. The losses correspond

to the combined Rx and Tx gains. The gains of the antenna arrays were kept equal at both sides.

The severity of the movement on the total antenna gain strongly depends on the antenna gain

itself, i.e., how narrow the main lobe beam is, and on the distance between Tx and Rx. The

narrower the beam, the higher the impact of the movement on the gain, as it could be expected.

As the distance increases, the relative motion becomes smaller and the impact of the movement

on the antenna gain is also smaller. From the antenna gain point of view, over longer distances,

the energy spreads more due to general path loss and the Tx illuminates larger area.

The antenna gain plays an important role in the gain degradation. The antenna arrays are strongly

focused towards the steered direction. We can see in Figure 22 and Figure 23 that the relative

gain loss is much higher in the case of the 1024-element array compared to the 256-element

array. Over a 100-meter link, the 1024-element array gives equal or lower gain compared to a

256-element array. This is because the 3-dB beamwidth of the larger array is four times smaller



(0.1 versus 0.4 degrees). We can see in Figure 24 how even a very small movement causes a severe

impact on the total antenna gain of the 1024-element array and especially when compared to a

256-element array. In particular, the Gaussian-Rayleigh is very sensitive to the movement with

the gain dropping very fast for high number of antenna elements.

For the 32-element array, the impact of the movement over long distances is negligible. This

follows the much higher 3-dB beamwidth of 3.2 degrees. In this case, similarly to the higher

antenna element cases, the movement causes larger loss for the shorter distances. Comparing

the worst-case scenarios, namely the Gaussian-Rayleigh cases for 20 meters at 0.2 m2 motion

variance, the total antenna gain losses for the link budget are 4, 25, and 40 dBs for the 32-, 256-,

and 1024-element arrays.

In general, it can be concluded that the 3-dB beamwidth plays an important role on how severe

loss the antenna movement causes. Very high gain antennas therefore suffer more from the

movement as it could be expected. It should be remembered that the 3-dB beamwidth does not

only depend on the antenna gain, but also on the antenna structure and the shape of the beam.

Thus, the possible impact of the movement on the link budget needs to be considered for each

application and the type of antennas that are utilized therein.

Figure 21: The expected antenna gain with and without antenna movement for 32-element antenna array.



Figure 24: Comparison of the expected antenna gains for very small antenna movement between 256-element antenna array and the 1024-element antenna array.

4.5 Channel Estimation

This section studies the effects of A/D conversion, quantized phase control and antenna element

radiation pattern on the channel estimation in multi-antenna receivers.

4.5.1 System model

Path 1

Path 2

Path L

...

...

A/D w1

A/D w2

A/D wN

φ1

φ2

φN

DSP

Figure 25: Multi-antenna receiver.



The system considered here is a link between two multi-antenna transceivers. The receiving node

is shown in Figure 25. Both transceivers are equipped with an N element antenna array. The

channel between the transceivers is composed of L independent scatterers and is defined as

𝐇 = ∑ ℎ𝑙𝐬RX(𝜗𝑙)𝐬TXH

𝐿

𝑙=1

(𝜃𝑙), (1)

where 𝜗𝑙, 𝜃𝑙 are the angle of arrival (AoA) at the receiver and angle of departure (AoD) at the

transmitter for path 𝑙, respectively, 𝐬TX, 𝐬RX are the array propagation vectors of the antenna

arrays at the transmitter and receiver, respectively, and ℎ𝑙 is the complex channel gain of the 𝑙th

path between the transceivers. When a uniform linear array with N antenna elements is used the

array propagation vector can be written as

𝐒 = [1 𝑒𝑗𝜅𝑑 sin 𝛼 ⋯ 𝑒(𝑁−1)𝑗𝜅𝑑 sin 𝛼]T

, (2)

where 𝑑 is the spacing between the antenna elements, 𝜅 =2𝜋

𝜆 is the wave number, 𝜆 is the wave

length of the signal, and 𝛼 is the angle between the direction of the plane wave and the antenna

array normal (𝛼 = 𝜗𝑙 at the receiver and 𝛼 = 𝜃𝑙 at the transmitter for path 𝑙).

The channel model (1) can be written in matrix format as

𝐇 = 𝐒RX�̃�𝐒𝐓𝐗𝐇 , (3)

where matrices 𝐒RX = [𝐬RX(𝜗1) ⋯ 𝐬RX(𝜗𝐿)], 𝐒TX = [𝐬TX(𝜃1) ⋯ 𝐬TX(𝜃𝐿)] contain the receiver

and transmitter propagation vectors, and �̃� = diag[ℎ1 ⋯ ℎ𝐿] is a diagonal matrix with channel

coefficients ℎ𝑙 as its diagonal elements.

In the simulations, the transmit antenna array consists of isotropic elements. For the receiver two

different antenna element models are considered, isotropic antennas and patch antenna type

elements, to compare the estimation performance with the theoretical isotropic model utilized

typically in signal processing publications and a more realistic antenna element radiation pattern.

The patch antenna radiation pattern is generated with the Antenna Designer application in Matlab

and is shown for AoA angles from -90⁰ to 90 in Figure 26 (0⁰ points to the direction of array

normal).



Figure 26: Radiation pattern of the patch antenna element.

The phase shifters between the antenna elements and analog-to-digital (A/D) in the receiver is

used for the beam steering. Phase shifters are controlled with quantized phase values. The A/D

converters are modelled with a staircase function. Only the effect of quantization is modelled,

other possible A/D converter non-ideal characteristics such as integral and differential

nonlinearity (INL, DNL) are not modelled, i.e., it is assumed that their effect on the performance

is negligible.

4.5.2 Channel estimation

It is assumed that the channel between the transmitter and receiver consists of separate

scatterers. In the estimation process, the channel is scanned by transmitting signals to 𝐾TX

directions with the direction of departure angles 𝛽𝑘TX (𝑘TX = 1 ⋯ 𝐾TX). While the transmitter is

transmitting the pilot signal 𝑑 to the direction 𝛽𝑘TX, the receiver collects signal samples from

directions 𝛾𝑘RX (𝑘RX = 1 ⋯ 𝐾RX). The received signal vector at the receiver antenna array before

the phase shifters is

𝐱RX = 𝐇𝐯(𝛽𝑘TX)𝑑, (4)

where 𝐯(𝛽𝑘TX

) is the steering vector used by the transmitter to transmit to direction 𝛽𝑘TX. The

receiver uses a steering vector 𝐰(𝛾𝑘RX) in order to receive a signal coming from the direction 𝛾.

The received signal is then

𝑦rx(𝛾𝑘RX) = 𝐰H(𝛾𝑘RX

)𝐇𝐯(𝛽𝑘TX)s + 𝑛, (5)



where 𝑛 is the additive Gaussian noise and 𝑠 is the transmitted signal. The received signals can be

collected to a vector as

𝐲RX = 𝐖H𝐇𝐕𝐬 + 𝐧, (6)

where the columns of the matrices 𝐖 and 𝐕 are the receiver and transmit steering vectors,

respectively and 𝐧 is a noise vector. The channel matrix can be estimated as

�̂� = (𝚽𝐇𝚽)−𝟏𝚽𝐇𝐲𝐑𝐗, (7)

where 𝚽 = 𝐕T⨂𝐖 (⨂ = Kronecker product).


In all the simulations the number of signal paths has been four (𝐿 = 4). The AoA and AoD angles

are uniformly distributed between -80⁰ and 80⁰. In Figure 27 - Figure 29, the Isotropic curves refer

to the cases where the elements of the antenna array are modelled as isotropic radiators, no

quantization is used, and the angle resolution of the phase shifters is 5⁰. Isotropic with b-bit ADC

curves shows the performance with isotropic elements, b-bit ADC converters and the angle

resolution of the phase shifters equal to 5⁰. The cases where the phase resolution of the phase

shifters has been 2⁰ are indicated with the marking (2⁰) in the legends. Patch curves show the

performance with the elements modelled as patch antennas with radiation patterns shown in

Figure 26. Different ADC and phase shifter control resolutions are indicated as in the isotropic

element cases. The antenna array is modelled as a uniform linear array with element spacing of

half wavelength.

In the four and six element cases the required ADC resolution to achieve the same performance

as without an ADC is 6 bits. In the 12-element case, 8-bit ADC is needed. When the quantization

is considered, the performance with patch antenna elements is worse than with isotropic ones.

When the phase shifter resolution is decreased from 5⁰ to 2⁰, the performance is improved by 4

dB, but the computational complexity is increased. When resolution of 5⁰ is used, both the

transmitter and receiver scan 33 different direction. With 2⁰ resolution, the number of scanned

directions increases to 81. The size of the matrix 𝚽 in (7) is 𝑥 × 𝑦, where 𝑥 = 𝐾2 + 1, where 𝐾 =

𝐾𝑅𝑋 = 𝐾𝑇𝑋 is the number of scanned directions and 𝑦 = 𝑁2 (𝑁 is the number of antenna

elements in both transmitter and receiver).



Figure 27: Channel estimation accuracy with 4-element antenna array.





5. SYSTEM LEVEL SIMULATIONS FOR THE OPTICAL/THZ SYSTEM

System level simulations will be described in the following sections aimed at the THz indoor

performance evaluation by stochastic geometry, especially focusing on relevant system, antenna,

phase noise, channel, stochastic phase noise and stochastic indoor models.

5.1 Indoor Performance Evaluation via Stochastic Geometry

In this section, we focus on analyzing indoor THz systems via stochastic geometry. The stochastic

geometry is a powerful tool for network analysis. In this deliverable, we use the stochastic

geometry to estimate the interference in the THz band indoor uplink scenario.

The stochastic geometry has been used in the past to study interference in various networks. For

instance, in [38] [39] [40], we have studied the THz specific interference modelling in generic

networks. The works in [41] [42] are also the only two works that we are aware of that considered

finite network size. To be specific, in [41], the authors used stochastic geometry to study

interference in indoor visible light communications and [42] studied interference in outdoor

mmWave systems. The limited network size is important in stochastic geometry since indoor

locations are limited. Especially in lower frequency ranges, the stochastic geometry is often

considered over infinite network sizes since the interference area of a single wireless network

entity is quite large because of lower losses. However, in the THz frequencies where the losses

are larger, the finite, and even small networks are easy to handle since the interference is local.

This is further illustrated as indoor simulations on interference levels match perfectly with the

results obtained with stochastic analysis.



While the relevance of stochastic geometry in the indoor locations is one advantage, a second

one is the possibility to obtain a closed-form stochastic expression for the phase noise and its

impact on the main antenna lobe gain. The derivation for the stochastic PHN is given below and

it is shown to be exact when compared with the simulation results. The work presented in the

following sections studies the PHN and the co-channel interference (CCI) in indoor uplink

situations. This work was also presented earlier in [43], where detailed analysis is given.

The system model is illustrated in Figure 30, where we consider an indoor uplink of a THz network

that consists of a Rx, or a THz access point (TAP), and a number of Txs. The network is assumed to

be deployed within a rectangular room. This is modelled as a three-dimensional rectangular space

(𝐴 × 𝐵 × 𝐶) m3. The Rx is set at certain coordinates (a,b,c) in the Cartesian space limited by the

above size of the room. The interfering Txs, on the other hand, are randomly distributed around

the room. The interference of the network is studied with respect to a desired Tx in order to

estimate the PHN impact on the signal-to-noise-plus-interference ratio (SINR). It is assumed that

all the transmit antenna beams are aligned towards the direction of the TAP. Therefore, the TAP

experiences interference from all the nodes in the network while communicating with the desired

user. The TAP antenna is pointed towards the desired Tx, which decreases the interference level

from the random interfering Txs because the TAP ‘sees’ the interference mostly through the

antenna side lobes. This is the main reason whythe analysis herein focuses on the uplink. In the

downlink direction the Rx (user) would experience interference on its side lobes from the side

lobes of the other users. On the other hand, in the downlink, there is added interference from the

TAP transmissions towards the other users (Rxs in this case). Therefore, the expected interference

level would be smaller in contrast to the uplink where on average the Rx sees the Txs' main lobe

antenna gains through its side lobes. Moreover, we assume ALOHA transmission scheme to

simplify the analysis. The ALOHA assumption mainly results in the Txs sending randomly on the

same channel without any specific resource allocation.

Figure 30: The indoor system model illustration, where the Rx is assumed to be in the upper corner of the room in order to have maximum visibility to the room.



5.1.1 Antenna model

We assume uniform linear array (ULA) antennas on all the nodes. Those consist of N identical

dipole antenna elements (isotropic/omnidirectional assumption in azimuth) equally spaced with

inter-element distance d. The complex far field radiation pattern, i.e., the array factor (AF), can

be obtained as

𝐴𝐹(𝛼) = 𝛽(Γ)𝑎(𝛼) = 1

√𝑁∑ exp (

𝑗2𝜋

𝜆𝑑𝑛 𝑠𝑖𝑛(Γ)) exp (

𝑗2𝜋

𝜆𝑑𝑛 𝑠𝑖𝑛(𝛼))

𝑁−1

𝑛=0

,

where 𝛽(Γ) is the steering vector, Γ is the beamforming direction, 𝑎(𝛼) is the antenna array

response, 𝛼 is the angle of observation, 𝑛 ∈ {0,1, … , 𝑁 − 1} is the antenna index, 𝜆 is the

wavelength, and d is the antenna element spacing, which is assumed to be 𝜆/2 in the following.

The array power gain is then given by

𝐺(𝛼) = |𝐴𝐹(𝛼)|^2,

that is, the maximum gain of a ULA antenna is equal to the number of the antenna elements due

to constructive summation of the antenna responses towards the beamforming direction

(𝐺𝑚𝑎𝑥(Γ) = 𝑁𝑇𝑥).

5.1.2 Phase noise model

The phase noise is assumed to influence the AF as

𝐴𝐹𝑝(𝛼) = 𝐴𝐹(𝛼)𝛾𝑝𝑚,

where 𝛾𝑝𝑚 is the complex PHN of the mth RF chain and is modelled as

𝛾𝑝𝑛 = 𝑒𝑗𝜃𝑘

𝑚,

where 𝜃𝑘𝑚 is the PHN angle of RF chain m. The phase noise is random and unique for each Rx

chain, and therefore 𝛾𝑝𝑚 corrupts each RF chain independently. In the numerical results, we

assume that the number of RF chains is equal to the number of antenna elements (to the analysis

simple). This basically means a fully digital antenna array although we do not utilize antenna gain

weights that would be used in a real optimized digital beamforming case. Cheaper choice in the

THz frequencies would be a hybrid antenna structure where a single RF chain controls a number

of analogue phase shifters.

The LOs in an antenna system can either be phased-locked or frequency-locked. When a phased-

locked loop (PLL) is employed, the PHN causes a small mismatch and is normally well modelled by

a Gaussian distribution. In case the frequency-locked case, the LO in the system is tuned to the

carrier frequency but it is free-running. The PHN in this case is modelled as a Wiener process [44]

𝜙𝑖 = 𝜙𝑘−1 + 𝑤𝑘 ,

where 𝑤𝑘 is Gaussian random variable. Assuming that the memory length of the Wiener process

is M, the experienced PHN becomes



𝜃𝑘 = ∑ 𝜙𝑖

𝑘−1

𝑖=𝑘−𝑀

+ 𝑤𝑘 .

When the phase noise is assumed to be zero-mean Gaussian, this can be written as

𝜃𝑘 ~ 𝑁(0, 𝑀𝜎𝑝2)

because of a sum of multiple Gaussian distributions. This expression is a zero mean normal

distribution with 𝜎𝑝2 PHN variance.

From the above expression for 𝐴𝐹𝑝(𝛼), it is can be seen that the PHN decreases the main antenna

lobe gain by mixing the beamformer phases that widens the main lobe and increases the side lobe

levels. If the PHN would be so high that it would make the phase of the antenna absolutely

random, the antenna gain would start to resemble to an omnidirectional antenna. Thus, the

higher the PHN standard deviation becomes, the higher the impact on the antenna phases. In

practical cases the PHN is small compared to the phase of the beamformer. An example of the

PHN impact on the antenna patterns is given in Figure 31, where an ULA antenna pattern with

128 antenna elements is shown with various PHN variances. From this figure, we can see that the

most evident impact of the PHN is on the side lobes. The impact of the phase noise on the main

lobe is derived and discussed in the next section.

Figure 31: An Illustration of the antenna gain of the ULA model with 128 antenna elements with and without the phase noise.



5.1.3 Channel model

We utilize a LOS channel in the analysis. The LOS channel without multipath components is a valid

choice in the THz band, and even in the indoor locations, since high gain antennas have actually

quite low side lobes. The LOS path gain utilized below is

𝑙(𝑟, 𝑓) =𝑐2𝑒𝑥𝑝(−𝜅𝑎(𝑓)𝑟)

(4𝜋 𝑟 𝑓)2,

which is the same LOS expression that was used previously in this deliverable.

5.1.4 Stochastic phase noise model

The stochastic impact of the PHN can be described by a mapping from the angular distribution

into a unit circle. This is because the real part of the complex PHN 𝛾𝑝 describes the power

degradation or amplification. This comes from the fact that the real part gives all the information

of the power fluctuations due to PHN, and it is directly linked to the imaginary part by the

Kramers-Kronig relation. An example would be that if the PHN angle 𝜃𝑘 is zero, PHN 𝛾𝑝 is unit. If

𝜃𝑘 is fully random (0 to 2𝜋), 𝛾𝑝 is also random and zero mean. Therefore, the PHN impact on the

main lobe gain can be evaluated by calculating the expected value of the real axis of the unit circle

by using the PDF of the PHN

𝐸 [√𝐺𝑝𝑛] = √𝑁𝑇𝑥 ∫𝑐𝑜𝑠(𝑥)

√2𝜋 𝜎𝑝2

exp (−𝑥2

2𝜎𝑝2) 𝑑𝑥

𝜋

−𝜋

,

where 𝐸[√𝐺𝑝𝑛] is the expected antenna amplitude gain, 𝑁𝑇𝑥 is the number of antennas and is

the maximum power gain as detailed above, and cos(x) maps the angles x on the real axis of the

unit circle. Solving this, yields

𝐸[𝐺𝑝𝑛] = 𝑁𝑇𝑥𝑒{−𝜎𝑝2}.

This expression is valid for small values of 𝜎𝑝. The details of the derivation are discussed in [43].

This expression is true if the phase variations are small enough to prevent the random phase from

rotating around the unit circle. That is, the PHN cannot make the antenna phases random, but the

control needs to be on the beamformer. This approximation will be demonstrated in the

numerical results providing the expected value of the antenna gain.

5.1.5 Stochastic indoor model

The indoor propagation environment is confined by walls, which limits the user distribution

around the so-called typical node of the network. This typical node is often assumed to be at the

origin of an infinite network experiencing the interference of the network as an average receiver

of the network. In the derivation of the stochastic model herein, we take the indoor assumption

into account by adjusting the integration bounds of the aggregated interference. Because of the

shape of a typical room, we use the Cartesian coordinate system rather than a spherical

coordinate system. The latter is a common assumption in random networks as the interference

may come from all directions. However, it is shown in the numerical results that the confined



space integration produces an exact interference estimate, while taking into account the

stochastic phase noise and realistic antennas.

The aggregate interference is given by the summation of the contributions of all the Txs of the

network [38] [39] [40]

𝐼𝑎𝑔𝑔𝑟 = ∑ 𝑙(𝑟𝑖)

𝑖∈Φ

,

where

𝑙(𝑟𝑖) = ∫𝑃𝑇𝑥

𝑊𝐸Θ[𝐺𝑇𝑥(Θ)]𝐸Θ[𝐺𝑅𝑥(Θ)]𝑙(𝑟𝑖, 𝑓)𝑑𝑓.

𝑊

where Φ is the set of active interfering nodes, 𝑃𝑇𝑥 is the transmit power of the Txs (assumed to

be same for all Txs), and W is the communication bandwidth. Moreover, 𝐸Θ[𝐺𝑇𝑥(Θ)] and

𝐸Θ[𝐺𝑅𝑥(Θ)] are the expected antenna gains of the Txs and the Rx, and Θ is the direction of the

antenna in the three dimensional space. The expected antenna gains in the context of this work

are the maximum transmit powers for all the Txs (desired and interference) due to the perfect

alignment assumption (with degradation by the phase noise included). The expected antenna gain

for the Rx is the maximum gain towards the desired Tx, and random with respect to the interfering

Txs since the Rx is pointed at the desired Tx.

The moments of the interference can be calculated from the Laplace transform of the aggregate

interference [45] [46]

𝔏𝐼𝑎𝑔𝑔𝑟(𝑠) = 𝐸Φ [exp (−𝑠 ∑ 𝑙(𝑟𝑖)

𝑖∈ 𝛷

)].

This expression is derived in detail in finite Cartesian coordinate system in [43]. The expected

aggregate interference level in the considered indoor scenario is given as

𝐸[𝐼𝑎𝑔𝑔𝑟] =𝑐2

8𝜋 𝑝𝜆 𝑁𝑇𝑥𝑒−𝜎𝑇𝑥

2∫ ∫ ∫ 𝑟−1 ∫

𝑃𝑇𝑥

𝑊𝑓2𝑊

𝐶−𝑐

0−𝑐

𝑒−𝜅𝑎(𝑓)𝑟𝑑𝑓𝑑𝑥𝑑𝑦𝑑𝑧,𝐵−𝑏

0−𝑏

𝐴−𝑎

0−𝑎

where 𝑁𝑇𝑥 is the number of Tx elements of the interfering Txs, 𝜆 is the density of the Txs, 𝑝 is the

probability of a Tx to transmit, 𝜎𝑇𝑥2 is the Tx PHN variance, 𝑟 = √𝑥2 + 𝑦2 + 𝑧2 is the Euclidian

distance. The desired Rx (or TAP) is located at coordinates (a,b,c), which are visible in the

integration interval corresponding to the room size (𝐴 × 𝐵 × 𝐶). Note that since the Rx is pointed

at the desired Tx, the Rx experiences random antenna gain from the interfering Txs. Therefore,

the expected antenna gain is 𝐸Θ[𝐺𝑅𝑥(Θ)] = 1. This follows the preservation of the transmit

energy. This behaviour is validated by running a simulation model with actual antenna gains and

random interfering Tx locations against the stochastic model with unit receiver gain according to

the above equation. The expression above is shown in the numerical results to give the exact

interference.




The Monte Carlo simulations were performed by dropping a Poisson distributed number of users

with mean 𝑁𝑢 in random locations in a three-dimensional rectangular space, which is limited in x,

y, and z axes by A, B, and C, respectively, that is, the size of the room. The main purpose of the

simulations is to check the validity of the antenna gain model herein as the stochastic geometry

itself has been proven accurate by numerous works. We assume that the random interfering Txs

point at the Rx at random angles determined by their locations per simulation run. The user

transmit beams are all perfectly pointed at the Rx, but the AP receive beam is pointed toward the

desired Tx.

The PHN variance is assumed to be the same for all the transceivers similarly to the memory length

of the Wiener processes. The centre frequency is set to 300 GHz and the Tx powers are equal to

0 dBm for all nodes. Moreover, the number of antenna elements for the Rx and all the Txs is 128,

the PHN variance per unit memory length is set to 0.017 rad^2, and the memory length of the

Wiener process is varied from 1 to 80. Furthermore, the Rx noise figure is assumed to be 10 dB,

the communication bandwidth is 5 GHz, and the probability of transmission p is 50%. The room is

assumed to be a typical small room sized 400 × 600 × 240 cm3 (𝐴 × 𝐵 × 𝐶). The desired user's

Tx is at 90 cm away from the Rx, and the number of interfering users is varied from 4 to 20 with

random x and y axis and 120 cm height. The desired Rx is located at coordinates (20 cm, 20 cm,

150 cm), i.e., 20 cm away from the walls and at 150 cm height from the floor. The Monte Carlo

simulations were performed over 10,000 network realizations for all the parameters.

Figure 32 shows the simulated and theoretical antenna gains as a function of the standard

deviation of the PHN with different numbers of antenna elements. We can see that as the PHN

standard deviation increases, the expected main lobe antenna gain decreases. As an example, for

128-element ULA, as the PHN total standard deviation (including the memory of the Wiener

process) shifts from 0.2 to 0.4 rad, we lose about 12.5% in antenna gain. Moreover, in the extreme

case, in which the PHN standard deviation changes from 0 to 1.2 rad, the antenna gain

degradation is 72.7%. On the other hand, the 32-element ULA is slightly less sensitive to the PHN.

It is shown that, with the PHN standard deviation increasing from 0.2 to 0.4 rad, about 6.67%

antenna gain reduction is observed. When the PHN standard deviation increases from 0 to 1.2

rad, the antenna gain degradation is approximately equal to 68.5%. In general, the same PHN

standard deviation increase causes more significant antenna gain degradation as the number of

antenna elements increases. We can also see how the phase noise fluctuates the antenna gains.

This is best shown in the simulated antenna gains where even the averaged antenna gains

fluctuate more and more as the PHN variance increases. This is caused by the uncertainty the PHN

introduces to the designed beamformer phases.



Figure 32: Simulated and theoretical antenna gains as a function of the phase noise standard deviation.

Figure 33 illustrates the impact of the PHN on the received signal powers as a function of the

number of interfering nodes with the noise floor shown as reference level. The markers show the

simulation results, whereas the continuous lines are the theoretical interference values. We can

see that the simulated and analytical results are identical. Therefore, this proves that the derived

stochastic phase noise expression is exact. Moreover, it is shown by the figure that for a fixed

number of interfering nodes the expected antenna gains decrease as the PHN standard deviation

increases. Thus, the received power also decreases due to corrupted antenna gains. The Rx has a

random antenna gain with respect to the interfering Txs. This causes slightly less impact of the

phase noise on the interference compared to the desired link with the main lobe gains at both

ends. This has a small impact on the expected SINR as a function of the PHN, which is also shown

in Figure 34 showing the stochastic SINR as a function of the PHN variance and the number of the

interfering users. The additional loss by PHN may drive the SNR/SINR below the operational region

depending on the bit error rate requirements. However, in general and for small phase noise

values, the impact of the phase noise on the system performance can be considered small. The

correct interpretation of the phase noise on the antenna gains is important, in order to be able to

model the system and its performance accurately. The results herein highlight the importance of

considering both the transceiver imperfections and the interference levels when analyzing and

designing indoor mmWave and THz wireless networks, and multi-antenna THz systems in general.

Those can have impact on the system performance that needs to be taken into account in the link

budget analysis.



Figure 33: Simulated and theoretical received powers for the interfering links and the desired link, as well as the noise floor as a function of the phase noise standard deviation.

Figure 34: Theoretical SINR as a function of the phase noise standard deviation and number of users.

6. COMPARATIVE ANALYSIS OF SIMULATION AND

DEMONSTRATION RESULTS

This chapter will focus on the comparative analysis between simulation and demonstration

results. It starts by presenting the THz link performance assessment of the demonstration

scenarios. It is followed by a comparison analysis between channel model estimations and

measured data and end with the initial access performance evaluation also evaluated over the

measured data.



6.1 Performance feasibility by the demonstration results

This section resumes the THz link performance evaluation as confirmed from the demonstrations

outcome.

Figure 35: Summary of high-profile transmission experiments carried out within the scope of TERRANOVA. The dotted and dashed reference curves for the various m-QAM formats depict the maximum achievable distance for which error-free decoding is still possible assuming a soft-decision FEC threshold of 3.4·10-2. Points in the diagram depict unidirectional SISO experiments with offline DSP unless stated otherwise.

Figure 35 depicts a comparison between the results of our most high-profile experiments and

reference curves for various m-QAM formats, whose simulation conditions are summarized in

Table 1. These theoretical curves represent the distance of the THz-wireless link corresponding to

a transmission performance (e.g. bit-error rate) at the SD-FEC limit of 3.4·10-2 (25% frame

overhead). In this diagram, there are two areas of interest for the comparison: the lower region

of the graph refers to lab experiments using 23 dBi horn antennas, and the upper region relates

to our long-haul outdoor experiments using high-gain (55 dBi) Cassegrain antennas.

Parameter Value

Transmitter output power -7 dBm

Carrier frequency 300 GHz

Atmospheric loss 5 dB/km

Antenna Gain (Tx/Rx) 23/23, 55/55

Noise figure (Rx) 8 dB

SD-FEC limit 3.4·10-2

Table 1: Summary of the simulation parameters used to calculate the theoretical curves according to an additive white Gaussian channel model.

30 40 50 60 70 80 90 100 110

0.1

1

10

100

1000D

ista

nce [m

]

Net data rate [Gb/s]

4-QAM

16-QAM

64-QAM

24 GBd16-QAM

32 GBd16-QAM

8 GBd64-QAM

MIMO Real-time 32 GBd 4-QAM

MIMO 32 GBd 4-QAM

32 GBd4-QAM

42 GBd4-QAM

28 GBd4-QAM

23 dBi

55 dBi



In the case of the 23 dBi horn antennas, by comparing our experimental data to the theoretical

expectations, we reveal that the maximum achievable distance for 32GBd 4-QAM is almost 4

times larger than the link measured in the lab. Nevertheless, this comes as no surprise since the

BER measured at this point was much lower than the SD-FEC threshold corresponding to the

theoretical curves. If we were to increase the transmission data, we could decrease the gap to the

reference 4-QAM curve until the BER performance of the experimental system reaches the SD-

FEC threshold. On the other hand, the theoretical curve for 16-QAM shows less than a twofold

increase in the total transmission distance compared to the experimental 32 GBd 16-QAM results.

In this scenario, where the BER performance of this experiment was close to the FEC threshold,

the difference comes mainly from the bandwidth limitations of the devices and some I/Q

imbalance from the THz frontends, which impairs high-order modulation formats.

Contrary to the 4-QAM lab experiment, the long-haul results depicted in Figure 35 have been

collected at BER values close to the SD-FEC threshold limit. Compared to the theoretical curves,

28 GBd 4-QAM and 42 GBd 4-QAM could still in perfect conditions achieve ~1.5 and ~2.6 times

larger distances, respectively. Following this, part of the limitations when transmitting high Baud

rate signals is the amount of bandwidth needed for broad spectra. In this regard, 42 GBd 4-QAM

requires more bandwidth than the transmitter THz frontend (~25 GHz) is capable of providing,

which is a major impairment that we have not compensated. Then, our data points corresponding

to 24 GBd 16-QAM and 8 GBd 64-QAM appear to deviate less than a factor of 2 in terms of

achievable distance from the theoretical curves. This difference can be attributed to the more

noticeable effects of phase noise in the higher-order modulation format and to the non-ideal

behaviour of the THz frontends.

Finally, in addition to the SISO results, we have plotted our first MIMO experiments in Figure 35.

By installing a second pair of Tx/Rx THz frontends, we are capable of virtually doubling the total

capacity of the THz-wireless link. In order to avoid distortions caused by crosstalk due to the close

proximity of the parallel links, we have adjusted the Tx-THz modules to radiate the signals into

free-space using orthogonal polarizations modes; thus, constructing an actual polarization-

multiplexed THz-wireless transmission system. Interestingly, the 32 GBd 4-QAM from the lab

experiment as well as the 32 GBd 4-QAM data from the outdoor experiment show similar

relations to the maximum achievable distance predicted by the theoretical analysis: ~2.6 and ~2.3

times longer links, respectively. In the lab experiment, the penalty arises from a real-time modem

applying a conventional DSP scheme that is not optimized to our particular experimental setup,

which results in a sub-par performance that limits the reach of our system. The outdoor system,

on the other hand, uses an offline DSP, where additional equalization and I/Q imbalance

correction stages have been built to better mitigate the impairments we perceive from the THz

frontends. This has allowed us to improve the overall performance of the link. However, the

transmission performance was impaired by non-ideal component characteristics and residual

polarization crosstalk, both reducing the potential achievable transmission distance of the link.



6.2 Comparison of channel models with measured data

A comparison between analytical channel models and measured data from the outdoor link

experiment is shown in Figure 36 (a). While the received power was measured at the oscilloscope,

in order to carry out calculations using the atmospheric attenuation model of the ITU-R P.676-12

recommendations [47] and the simplified model achieved by the University of Oulu [11], we have

relied on measurements from a weather station at Fraunhofer HHI’s premises. This station gives

us information regarding the water intensity in mm/hour and temperature in intervals of

30 seconds. The values for atmospheric pressure and relative humidity had to be estimated from

a weather portal, assuming them to be constant over the measurement period. This is something

that needs to be kept into consideration while analyzing the final results, since these inaccuracies

have slightly influenced the output of the analytical channel models.

a) b)

Figure 36: a) Received power (including 28 dB receiver conversion gain) vs. Time: Comparison between theoretical results calculated with channel models for THz transmission (Simplified model by the University of Oulu and the ITU-R P.676-12 model recommendations) and the

measured data at the receiver before DSP. b) Normalized received power variation between measured data and the rain attenuation model based on actual weather conditions. Data

corresponds to a 500-km-long LOS THz system at a carrier frequency of 296.784 GHz with 55 dBi Cassegrain antennas. Experiment was carried out in Berlin, Germany on March 3rd, 2020 from

8:30 to 18:30 CET.

Based on the data depicted in Figure 36 (a), our measured received power is ~1.5 dB lower than

estimated by the ITU-R P.676-12 model and ~3.5 dB lower than estimated by the model proposed

by the University of Oulu. This is consistent with the results that were presented in D6.2 for the

outdoor experiment that took place in Freiburg, Germany, where a 2 dB difference between both

channel models was observed. The previous considerations might point to the conclusion that the

ITU-R P.676-12 model fits slightly better to the experimental data. However, we must take into

account several measurement uncertainties that prevent us from categorically presenting a

channel model as final. Among them are uncertainties regarding the gain of the Cassegrain

antennas (55 dBi nominal value), uncertainties in the estimation of the transmitter output power

10 12 14 16 18

-10

-9

-8

-7

-6

-5

-4

-3

Rx p

ow

er

(dB

m)

Time of day (hh)

Simplified Oulu

ITU-R

Measured data

10 12 14 16 18-1.5

-1.2

-0.9

-0.6

-0.3

0.0

0.3

0.6

0.9

1.2

1.5

Rx p

ow

er

variation (

dB

)

Time of day (hh)

Rain attenuation model

Measured data



(-7 dBm), suboptimal antenna alignment in the measurement setup and the lack of precise

weather data in our test site. These limitations notwithstanding, models do provide a good picture

of how weather conditions affect the transmitted signals. This is more noticeable when we isolate

the rain-induced power variation at the receiver in Figure 36 (b), where the model fits pretty well

the measured data for most of the evaluation period. The small discrepancies are attributed to

the lack of accurate weather data, in particular with respect to the atmospheric pressure and

relative humidity, which had to be assumed as constant over the whole day as mentioned above.

6.3 Initial access performance evaluation based on measured data

The initial access (IA) procedure was presented and theoretically analysed in D4.2 as part of WP4.

In this deliverable, we present its performance evaluation based on measured data. From the

hardware point of view, the TX beamforming demonstrator was used, which is described in detail

in D6.3. Let θa be the physical direction of the TX beam from the RX point of view. The objective

of the IA algorithm is to determine the beam steering angle that maximizes the received energy.

In this direction, we propose Algorithm 1 that provides an estimation of the steering angle, θe,

which maximizes the received power.

Algorithm 1: IA algorithm.

Input: Ns: Number of samples Na: Number of training beam steering angles θ: a vector that contains all the training beam steering angles D: a matrix of data collected after the ADC. Each column of D contains data received with a different training steering angle. s: a vector that contains the modulation symbols

Output: θe: Beamsteering angle Step 1: For each beam steering angle θ(i) with i=1,…, Na

Calculate the test statistics of the D as

𝑇(𝑖) = ∑ 𝑫(𝑗, 𝑖)

𝑁𝑠

𝑗=1

End for each Step 2: Calculate the index that maximizes the value of T(i)

Index = max(T) Step 3: Return the beamsteering angle

θe= θ(Index)

In order to evaluate the efficiency of the proposed IA approach, we extract the probabilities of

correct detection and mis-detection for the scenarios described in the following Table 2.



Table 2: Scenarios under investigation.

Parameter Scenario 1 Scenario 2 Scenario 3 Scenario 4

θa (Degrees) -14 -8 0 15

θ (Degrees) [-14, -8, 0, 15]

Tx antenna beamwidth (Degrees)

10

Ns {2, 4, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 330, 512, 1024, 2048, 4096, 8192}

Total number of collected samples

163840

TX-RX distance (cm) 50

Figure 37: Probability of correct detection vs number of samples for different values of θa.

Figure 37 depicts the probability of correct detection as a function of the number of samples that

were used, for different values of θa, while Table 3 reports an indicative example of the average

and variance of the test statistics for the case in which the number of samples is set to 2048. As

expected, for a fixed θa, as Ns increases, the probability of correct detection increases. Moreover,

we observe that for approximately the same variance of the test statistics, as the average value

of the test statistics increases, the IA algorithm performance improves (see e.g., the cases in which

θa =-8⁰ and θa =-14⁰). However, when the variance values of the test statistics are quite different

(for example between 0⁰ and 15⁰), the necessity of taking into account both the average value

and the variance in order to determine the system performance is revealed. Finally, we observe



that the theoretical framework provides a good fit for the experimental results. This indicates that

the theoretical framework can be used in order to design IA approaches.

Table 3: Average value and variance of the test statistics for the case in which Ns=2048.

θa = θe 0 15 -8 -14

Average value of the test statistics

4.1112 1.4560 1.7975 1.5703

Variance of the test statistics

0.0098 0.0015 0.0031 0.0034



7. CONCLUSIONS

This deliverable presents and reflects the work that was carried out by the consortium partners

in terms of system and link level simulations mostly performed in the framework of WP3 and WP4

tasks. After providing an overview of the defined key performance indicators that were derived

in D2.1, relevant aspects of the THz channel modelling simulations are presented mostly focusing

on the molecular absorption loss in single link systems. These types of systems are the most likely

platforms for the upcoming THz communication systems due to very high requirements for the

antenna gains. Other loss mechanisms are therefore comprised by the spreading loss and

reflection losses in NLOS links.

At the link level simulations, some relevant aspects are also taken into account: THz indoor LOS

and NLOS propagation, impact of hardware imperfections on the THz received signal, antenna

gain Vs antenna misalignment, antenna misalignment losses and channel estimation. The THz

frequencies are predominantly suitable for LOS communications. Thus, the above link simulations

provided important results on the received power degradation in the presence of various

phenomena. It is very important to take into account the system imperfections as the pure Friis

transmission equation tends to give too optimistic results. In the design of practical link budgets,

the additional signal loss by hardware and environmental phenomena needs to be considered.

These are also true for the NLOS links that experience the same degradation and more due to

reflection and possible penetration losses. The link performance figures readily give sufficient

ground to estimate the THz performance and capacity in any possible system. The problem mainly

becomes more pronounced with resource allocation in different applications. However, the

general performance of any system falls into the performance collection of individual links.

On top of the link simulations, indoor systems were analysed with stochastic geometry. This gave

some interesting results on phase noise impact on system level SINR. The phase noise and other

link degrading phenomena decrease the received desired signal power. However, since the same

occurs for all the links, those also decrease the interference. Thus, the total SINR is affected by

the hardware imperfections, but if all the links experience the same, the total effective SINR is

more dependent on the number of the interferers. However, the unwanted link imperfections

decrease the SINR, which will degrade the overall system performance.

In the last part of this deliverable we compared theoretical/analytical results with corresponding

experimental measurements.

The first set of comparisons aimed at assessing the feasibility of long-range THz links and the

validity of channel models. The experimental work on THz-wireless communications has

demonstrated the potential for achieving high-capacity data transmission in the THz band. For

short-range links, we have implemented a real-time 4-QAM optic/THz-wireless MIMO system

operating at more than 100 Gb/s. Furthermore, by using offline DSP with an algorithm scheme

especially adapted for THz-transmission, we are even able to achieve 102.4 Gb/s 16-QAM, albeit

on a purely THz-wireless system. In a second step, we investigated the feasibility of THz-wireless

technologies to achieve long-range distances and still carry over the high data rates of the indoor

experiments. For this purpose, we set up two long-distance links: a 500-meter-long one in Berlin

(Germany) and a 1-kilometer-long one in Freiburg (Germany). For the longer link, we achieved a



maximum net data rate of 44.8 Gb/s 4-QAM in single-pol operation, which was mainly limited by

the SNR of the transmission link. For the link spanning 500 m, we achieved 76.8 Gb/s 16-QAM and

102.4 Gb/s 4-QAM for single-pol and MIMO configuration of the system; therefore,

demonstrating the possibility of extending THz-wireless links for realistic distances that are

required for the implementation of point-to-point links.

We then compared the measured received power to the results of simulations based on the

simplified channel model from the University of Oulu and the ITU-R676-12 recommendations for

channel modelling. Our results show a slight difference of ~1.5 dB and ~3.5 dB between our

measured data and the outcomes of the ITU channel model and the model proposed by the

University of Oulu. This is, however, acceptable since there is a small degree of uncertainty due

to variations from the nominal values (e.g. gains of the antennas) and a complicated estimation

of the transmitter power. Nevertheless, if we focus purely on in the power fluctuations caused by

changing weather conditions such as rain, we see how the attenuation models are capable of

predicting the overall behaviour of the power along the THz-wireless link.

Finally, we made comparison between the analytical and experimental results based on

measurements extracted from the TX beamforming demonstrator. Based on the comparison, it

became apparent that the analytical framework fully agrees with the experiments. Additionally,

this comparison indicated that the theoretical framework can also be a useful Initial Access

algorithm design tool.



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