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D2.3 – Final report on system level performance evaluation by simulations
TERRANOVA Project Page 1 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
D2.3 – Final report on system level performance evaluation by simulations
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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
D2.3 – Final report on system level performance evaluation by simulations
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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.
D2.3 – Final report on system level performance evaluation by simulations
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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.
v0.5 26.02.2020 Draft Alexandros
Boulogeorgos (UPRC)
Revision on 4.2 (Impact of
hardware imperfections in the
THz received signal)
v0.6 19.03.2020 Draft Joonas Kokkoniemi
(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).
v0.8 26.03.2020 Draft Joonas Kokkoniemi
(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.
D2.3 – Final report on system level performance evaluation by simulations
TERRANOVA Project Page 5 of 75
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).
v0.10 09.04.2020 Draft Joonas Kokkoniemi
(OULU)
Contribution on sections 3.4
(Pathloss Channel Modeling),
4.1 (THz indoor LOS and NLOS
propagation) and 4.4 (Channel
estimation)
v0.11 16.04.2020 Draft Alexandros
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).
v0.13 24.04.2020 Draft Joonas Kokkoniemi
(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
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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
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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
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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
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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
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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
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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
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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
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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
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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
4.5.3 Numerical results ................................................................................................... 53
5. System level simulations for the optical/THz System ........................................................... 55
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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
5.1.6 Numerical results ................................................................................................... 61
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
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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
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. ................. 37
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. ................. 37
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. ........................ 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
Figure 22: The expected antenna gain with and without antenna movement for 256-element
antenna array. ............................................................................................................................... 49
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Figure 23: The expected antenna gain with and without antenna movement for 1024-element
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
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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
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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).
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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
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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.
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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.
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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
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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.
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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
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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
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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)
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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)),
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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,
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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
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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.
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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.
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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,
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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.
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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.
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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
𝑠𝑖𝑛(𝜃𝑖))
2|
|
2
and
𝑅𝑝(𝜃𝑖) =|
|𝑛1√1 − (𝑛1𝑛2
𝑠𝑖𝑛(𝜃𝑖))
2
− 𝑛2𝑐𝑜𝑠(𝜃𝑖)
𝑛1√1 − (𝑛1𝑛2
𝑠𝑖𝑛(𝜃𝑖))
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.
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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.
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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.
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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]
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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
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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.
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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
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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>
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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.
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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.
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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.
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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
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(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.
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Figure 22: The expected antenna gain with and without antenna movement for 256-element antenna array.
Figure 23: The expected antenna gain with and without antenna movement for 1024-element antenna array.
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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.
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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).
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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)
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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).
4.5.3 Numerical results
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).
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Figure 27: Channel estimation accuracy with 4-element antenna array.
Figure 28: Channel estimation accuracy with 6-element antenna array.
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Figure 29: Channel estimation accuracy with 12-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.
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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.
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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
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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.
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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
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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.
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5.1.6 Numerical results
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.
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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.
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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.
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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
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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.
D2.3 – Final report on system level performance evaluation by simulations
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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
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(-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.
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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
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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
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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
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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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