ArticlePDF Available

Abstract and Figures

This paper presents a connectivity analysis of reconfigurable intelligent surface (RIS) assisted terahertz (THz) wireless systems. Specifically, a system model that accommodates the particularities of THz band links as well as the characteristics of the RIS is reported, accompanied by a novel general end-to-end (e2e) channel attenuation formula. Based on this formula, we derive a closed-form expression that returns the optimal phase shifting of each reflection unit (RU) of the RIS. Moreover, we provide a tractable e2e channel coefficient approximation that is suitable for analyzing the RIS-assisted THz wireless system performance. Building upon the aforementioned approximation as well as the assumption that the user equipments are located in random positions within a circular cluster, we present the theoretical framework that quantifies the coverage performance of the system under investigation. In more detail, we deliver a novel closed-form expression for the coverage probability that reveals that there exists a minimum transmission power that guarantees 100% coverage probability. Both the derived channel model as well as the coverage probability are validated through extensive simulations and reveal the importance of taking into account both the THz channel particularities and the RIS characteristics, when assessing the system's performance and designing RIS-assisted THz wireless systems.
Content may be subject to copyright.
>REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER <1
Coverage analysis of reconfigurable intelligent surface assisted THz
wireless systems
Alexandros–Apostolos A. Boulogeorgos, Senior Member, IEEE, and
Angeliki Alexiou, Member, IEEE
This paper presents a connectivity analysis of reconfigurable intelligent surface (RIS) assisted terahertz (THz) wireless systems.
Specifically, a system model that accommodates the particularities of THz band links as well as the characteristics of the RIS is
reported, accompanied by a novel general end-to-end (e2e) channel attenuation formula. Based on this formula, we derive a closed-
form expression that returns the optimal phase shifting of each reflection unit (RU) of the RIS. Moreover, we provide a tractable
e2e channel coefficient approximation that is suitable for analyzing the RIS-assisted THz wireless system performance. Building
upon the aforementioned approximation as well as the assumption that the user equipments are located in random positions within
a circular cluster, we present the theoretical framework that quantifies the coverage performance of the system under investigation.
In more detail, we deliver a novel closed-form expression for the coverage probability that reveals that there exists a minimum
transmission power that guarantees 100% coverage probability. Both the derived channel model as well as the coverage probability
are validated through extensive simulations and reveal the importance of taking into account both the THz channel particularities
and the RIS characteristics, when assessing the system’s performance and designing RIS-assisted THz wireless systems.
Index Terms—Channel modeling, Connectivity analysis, Coverage probability, Reconfigurable intelligent surfaces, Terahertz
wireless systems.
NOMENCLATURE
3D Three Dimensional
6G Sixth Generation
AF Amplify-and-Forward
AHBF Azimuth Half-Power Beamwidth
AP Access Point
CDF Cumulative Distribution Function
e2e End-to-End
EHPB Elevation Half-Power Beamwidth
HITRAN HIgh Resolution TRansmission AbsorptioN
ITU International Telecommunication Union
LoS Line-of-Sight
PDF Probability Density Function
PL Path-Loss
RIS Reconfigurable Intelligent Surface
RU Reflection Unit
RX Receiver
SNR Signal-to-Noise-Ratio
THz Terahertz
TX Transmitter
UE User Equipment
I. INTRODUCTION
ACCORDING to the international telecommunication
union (ITU), the global mobile traffic is expected to
continue its exponential growth, reaching 5zettabytes per
month by 2020 [1]. This increase is driven by emerging data
rate hungry applications, like virtual, augmented and extended
reality, virtual presence by means of holographic projection,
autonomous vehicles, and others [2]–[4]. Looking forward
The authors are with the Department of Digital Systems, University
of Piraeus Piraeus 18534 Greece (e-mails: al.boulogeorgos@ieee.org, alex-
iou@unipi.gr).
This work has received funding from the European Commission’s Horizon
2020 research and innovation programme (ARIADNE) under grant agreement
No. 871464.
to the sixth generation (6G) era, two main approaches have
been identified as candidate technology enabler to support
these unprecedented traffic demands [5], [6]. The first one
is to exploit higher-frequency bands, with emphasis to the
terahertz (THz) [7]–[14], while the second one lies to the
use of reconfigurable intelligent surfaces (RISs) capable of
alternating their electromagentic properties and thus devising
a beneficial wireless propagation environment [15]–[20].
Scanning the technical literature, we can observe a fast
growing research effort on analyzing, optimizing, designing,
developing and demonstrating wireless THz systems [21]–
[38]. In more detail, in [21] and [22], Jornet et. al used
radiative transfer theory to extract a propagation model for
nano-scale THz communications, while, in [23], Yang et.
al presented a channel model for body-centric THz nano-
scale networks. Moreover, in [25], the authors reported a
simplified path-loss (PL) model for the 275 400 GHz band.
This work was extended in [26], in order to include the
impact of secondary reflections, and it was used as a basic
propagation model for several works that analyze the wireless
THz system performance, such as [27]–[30], and propose
physical and/or medium access control strategies, like [31]–
[33]. Meanwhile, in [34], the authors introduced a PL model
for nano-sensor THz networks for plant foliage applications,
while, in [35], a propagation model for intra-body nano-scale
communications was proposed. Moreover, in [36], the au-
thors presented a multi-ray THz propagation model. Likewise,
in [37], the authors revealed and quantified the detrimental
effect of blockage in THz wireless systems, whereas, in [38],
the authors presented a testbed for THz communications in
the 275 to 325 GHz. Additionally, in [39], the impact of
human blockage in low-THz wireless systems was discussed.
Similarly, in [40], the authors performed coverage analysis
in THz wireless systems that experience blockage. Finally,
in [41], the authors evaluated the effect of blockage in the
association process in THz wireless systems.
>REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER <2
All the aforementioned contributions agree that line-of-sight
(LoS) channel attenuation and blockage are the main limiting
factors of THz wireless systems. To break the barriers set
by blockage, recently, some research works proposed the use
of RIS [6], [16]–[19], [42]–[47]. In particular, in [6], [18],
and [19], the authors explained how RIS can be used to
mitigate the impact of blockage and introduced the idea of
reflected LoS links. In this direction, in [42], the authors
conducted an asymptotic uplink ergodic capacity study, as-
suming that the transmitter (TX)-RIS and RIS-receiver (RX)
channels follow Rician distribution, whereas, in [16] and [17],
the optimization framework for the maximization of the RX
received power was presented. Similarly, in [43] the joint
maximization of the sum-rate and energy efficiency was stud-
ied for a multi-user downlink scenario, in which connectivity
was established by means of reflected LoS. Additionally,
in [44], an error analysis was performed for RIS-assisted
non-orthogonal multiple access networks. Moreover, in [45],
di Renzo et. al highlighted the fundamental similarities and
differences between RISs and relays. In the same direction,
in [46], the authors compared the performance of RIS-assisted
systems against decode-and-forward relaying ones in terms
of energy efficiency, while, in [47], the authors conducted
a performance comparison between RIS and amplify-and-
forward (AF) relays in terms of average received signal-to-
noise-ratio (SNR), outage probability, diversity order and gain,
symbol error rate and ergodic capacity, which revealed that,
in general, RIS-assisted wireless systems can outperform the
corresponding AF relaying ones. Finally, in [48], the impact of
hardware imperfections in RIS-assisted wireless systems was
quantified in terms of outage probability and diversity order.
To the best of the authors knowledge, there are only a few
published works that examine the use of RIS in THz wireless
systems [49]–[52]. In [49] and [50], although the directional
nature of the THz links was taken into account, the PL
characteristics of the transmission path were neglected, while,
in [52], the design characteristics of the RIS as well as its
functionality were not taken into account. Finally, in [51], the
impact of molecular absorption loss was ignored, despite of its
paramount importance in the THz band, which was highlighted
in several previous contributions (see e.g., [27], [33], [53], [54]
and reference therein). The main reason behind this is the lack
of tractable channel model for RIS-assisted systems operat-
ing in the THz band that accommodates both the building
blocks of such systems and the particularities of the THz
band. In more detail, this model should take into account
the transceivers’ antenna gains as well as their position in
respect to the RIS position, the transmission frequency, the
characteristics of the reflection units (RUS), namely number
and dimensions of reflection elements, reflection coefficients,
antenna patterns and phase shifts of each one of the RU, as
well as the environmental conditions, while being tractable in
order to become a useful tool for analyzing the performance of
such systems. Motivated by this, this paper focuses on cover-
ing this gap by providing a low-complexity channel model that
takes into account the particularities of the THz propagation
medium as well as the physical characteristic of the RIS.
Building upon this model, we present a comprehensive system
model for RIS-assisted THz wireless systems that support
broadcasting and we conduct coverage analysis that reveals
their limitations. Specifically, the contribution of this paper is
as follows:
We provide a system model for RIS-assisted THz wireless
communications and we employ electromagnetic theory
tools to derive a general expression for the end-to-end
(e2e) channel attenuation. This expression takes into
account not only the access point (AP)-RIS and RIS-
user equipment (UE) distances, but also the RIS size, the
radiation pattern and the reflection coefficient of the RIS
unit cell, the AP and UE antenna gain, the transmission
frequency, as well as the environmental conditions. Note
that they have been two already published contributions
that provided the e2e pathloss in RIS-assisted wireless
sytsems [55], [56]. However, both [55] and [56] refer to
low frequency band communications; thus, they neglect
the impact of molecular absorption loss.
Building upon the channel attenuation expression, we
provide a simple closed-form expression that determines
the phase shift that each RIS element should impose in
order to steer the beam radiated from the RIS towards a
desired direction.
Next, we present a tight channel coefficient approxima-
tion that enables the performance analysis of the RIS-
assisted THz wireless system.
Based on the channel coefficient approximation, we
present the theoretical framework that returns the cumula-
tive distribution function (CDF) of the e2e channel coef-
ficient of the RIS-assisted THz wireless system. In more
detail, we consider a RIS-assisted downlink scenario in
which a single AP broadcasts to a number of UEs that
are located in random positions within a circular cluster
of radius equals to the one of the RIS to center of the
cluster footprint, and we obtain closed-form expressions
for the e2e channel coefficient CDF.
Finally, we use the e2e channel statistics to extract
an insightful closed-form expression for the coverage
probability.
The rest of the paper is structured as follows: Section II
focuses on presenting the system and channel model accom-
panied by the latter’s tight approximation, while Section III
presents the statistical analysis of the e2e channel coefficient
as well as the closed-form expression for the coverage prob-
ability. Numerical results verified by respective simulations
and accompanied by quantitative assessment are reported in
Section IV. Finally, closing remarks and key observations of
this work are summarized in Section V.
Notations: The operator |·|respectively denotes the absolute
value, whereas exp (x)stands for the exponential function.
Additionally, xreturns the square root of x, while sin (·),
cos (·),sin1(·),cos1(·)and sinc (·)respectively denote the
sine, cosine, arc sine, arc cosine, and sinc functions.
II. SY ST EM & CHA NN EL MO DE L
In this section, we present the system model and we extract
general formulas and approximations for the e2e channel
>REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER <3
Microcontroller
Varactor
RIS
AP
re
Nu UEs cluster
d1d
UE 1
UE nu
UE Nu
y
xz
dx
dy
1
n
N
.
.
.
.
.
.
1m
. . . . . . . . . M
φθ
UE 2
x’
y’
r
θnu
Fig. 1. System model.
coefficient. It is organized as follows: Section II-A presents the
system model, while Section II-B reports the channel model.
A. System model
As illustrated in Fig. 1, we consider the downlink scenario
of a RIS-assisted wireless THz system, in which a single AP
serves NuUE, that form a circular cluster with center O0(0,0)
and radius re, through a RIS. Moreover, it is assumed that, due
to blockage, no direct link between the AP and UEs can be es-
tablished. The AP and the nuth UE, with nu∈ {1,·· · , NU}
are equipped with high directional antennas of gains GAP and
Gnu, respectively, which point at the center of the RIS. The
RIS consists of M×Northogonal unit cells of dimensions dx
and dyand it is assumed that it has knowledge concerning the
position of the center of the cluster and its radius. Moreover,
the AP can use different codebooks in order to adjust its
beamwidth and focusing point in the RIS. Based on the the
used codebook different size of the RIS, i.e., different number
of RUs are employed. This allows the system to adjust the RIS
main lobe footprint in order to equal the cluster radius. Notice
that this functionality require that the cluster size is known to
the AP. A three dimensional (3D) Cartesian system is defined
with its center being at the center of the RIS and the RIS to
be at its x-y plane. Hence, the position of the RU, Um,n can
be obtained as
dm,n =n1
2dxxo+m1
2dyyo+ 0 zo,(1)
with n1N
2,N
2and m1M
2,M
2. Also, xo,
yo, and zostand for the unitary vectors at the x,y, and z
direction, respectively. Let, θt
m,n and θr
m,n,nube the elevation
angle from the (m, n)RU, Um,n, to the AP and to the
nuth UE, respectively, while φt
m,n and φr
m,n,nustand for
the corresponding azimuth angle. Finally, we use lt
m,n and
lm,n,nuto respectively define the distances from AP to the
Um,n RU and the one from the Um,n RU to the nuth UE.
B. Channel model
In this section, we assume that the distance between the
center of the RIS and the nuth UE is known, and we
evaluate the received power at the nuth, we identify the
optimal phase shift of each Um,n in order to steer the RIS-
generated beam to a desired direction, and we obtain the
channel coefficient as a function of the RIS specifications and
THz-specific characteristics.
For a given nuth UE position, the following theorem
returns the received power at the nuth UE.
Theorem 1: The received power at the nu-th UE can be
evaluated as
Pr=LnuPAP ,(2)
where Lnucan be expressed as in (3), given at the top of the
following page. In (3),
ζ1n1
2dx+ζ2m1
2dy=λφm,n
2π,(4)
and
Gt=GAP GGnu.(5)
Additionally, φm,n and |R|are respectively the controllable
phase shift and the absolute value of the reflection coefficient
introduced by the (m, n)RU, while Ur(θ, φ),Ut(θ, φ)and G
are the normalized received, the normalized transmitted power
ratio patterns and the unit cell gain, respectively. Moreover,
d1and dnurepresents the AP to the center of the RIS
distance and the one from the center of the RIS to the nu-
th UE. Meanwhile, θiand φiare respectively the elevation
and the azimuth angles from the center of the RIS to the AP,
while θrand φrrespectively denotes the elevation and the
azimuth angles from the center of the the RIS to the center
of the cluster. Finally, in (3), κ(f)stands for the molecular
absorption coefficient and can be obtained as in (6), given at
the top of the next page[54]1. In (6),
A(µ) = a1(1 µ) (a2(1 µ) + a3),(7)
B(µ) = (b1(1 µ) + b2)2,(8)
C(µ) = c1µ(c2µ+c3),(9)
E(µ) = (e1µ+d2)2,(10)
F(µ) = f1µ(f2µ+f3),(11)
G(µ)=(g1µ+g2)2,(12)
I(µ) = i1µ(i2µ+i3),(13)
J(µ)=(j1µ+j2)2,(14)
K(µ) = k1µ(k2µ+k3),(15)
L(µ)=(l1µ+l2)2,(16)
M(µ) = m1µ(m2µ+m3),(17)
N(µ)=(n1µ+n2)2,(18)
R(µ, f ) = µ
r1
(r2+r3fr4),(19)
with a1= 5.159 ×105,a2=6.65 ×105,a3= 0.0159,
b1=2.09 ×104,b2= 0.05,c1= 0.1925,c2= 0.135,
c3= 0.0318,e1= 0.4241,e2= 0.0998,f1= 0.2251,f2=
0.1314,f3= 0.0297,g1= 0.4127,g2= 0.0932,i1= 2.053,
i2= 0.1717,i3= 0.0306,j1= 0.5394,j2= 0.0961,k1=
1In order to compute the molecular absorption coefficient, radiative trans-
fer theory [57] and the high resolution transmission molecular absorption
(HITRAN) database [58] are widely used. However, since, in practice THz
wireless systems are expected to operate in the 100 500 GHz band, we
employ a simplified model for this band, which was introduced in [25] and
then extended in [54]. Note that this model, although it is a theoretical one,
is heavily based on the HITRAN database, which contains experimental data.
In other words, it has been verified by experimental data.
>REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER <4
Lnu=M2N2dxdyλ2|R|2Ur(θi, φi)Ut(θr, φr)Gt
64π3d2
1d2
nu
sinc2
λ(sin (θi) cos (θi) + sin (θr) cos (φr) + ζ1)dx
sinc2π
λ(sin (θi) cos (θi) + sin (θr) cos (φr) + ζ1)dx
×sinc2
λ(sin (θi) sin (φi) + sin (θr) sin (φr) + ζ2)dy
sinc2π
λ(sin (θi) sin (φi) + sin (θr) sin (φr) + ζ2)dyexp (κ(f) (d1+dnu)) (3)
κ(f) = A(µ)
B(µ) + f
100cq12+C(µ)
E(µ) + f
100cq22+F(µ)
G(µ) + f
100cq32
+I(µ)
J(µ) + f
100cq42+K(µ)
L(µ) + f
100cq52+M(µ)
N(µ) + f
100cq62+R(µ, f )(6)
0.177,k2= 0.0832,k3= 0.0213,l1= 0.2615,l2= 0.0668,
m1= 2.146,m2= 0.1206,m3= 0.0277,n1= 0.3789,n2=
0.0871,r1= 0.0157,r2= 2 ×104,r3= 0.915 ×10112,
r4= 9.42,q1= 3.96,q2= 6.11,q3= 10.84,q4= 12.68,
q5= 14.65, and q6= 14.94. Moreover, cis the speed of light,
and µis the volume mixing ratio of the water vapor and can
be obtained as
µ=p1(p2+p3P) exp p4(Tp6)
T+p5p6,(20)
where p1= 6.1121,p2= 1.0007,p3= 3.46 ×108,
p4= 17.502,p5= 240.97 oK, and p6= 273.15 oK.
Furthermore, Tstands for the air temperature, and Pis the
atmospheric pressure.
Proof: Please refer to Appendix A.
Remark 1: To steer the beam at the desired direction θr=θo
and φr=φo, the parameters ζ1and ζ2should be
ζ1=(sin (θi) cos (φi) + sin (θo) cos (φo)) (21)
and
ζ2=(sin (θi) sin (φi) + sin (θo) sin (φo)) .(22)
In this case, based on (4), the phase shift of the (m, n)element
can be obtained as in (23), given at the top of the following
page. In this case, according to (3), the maximum path-gain
is
Lmax
nu=M2N2dxdyλ2|R|2Ur(θo, φo)Ut(θo, φo)Gt
64π3d2
1d2
nu
×exp (κ(f) (d1+dnu)) .(24)
From (24), the channel gain of the received signal at the nu
UE at a specific distance dnucan be expressed as
hnu=MN pdxdyλ|R|pUr(θi, φi)Ut(θr, φr)Gt
8π3/2d1dnu
×exp 1
2κ(f) (d1+dnu).(25)
The following Lemma returns a tight approximation of the
channel coefficient.
Lemma 1: For realistic scenarios, the channel coefficient can
be tightly approximated as
hnuhl
nuX,(26)
where
hl
nu=MN pdxdyλ|R|pUt(θo, φo)Ur(θi, φi)Gtκ(f)
16π3/2d1
×exp 1
2κ(f)d1.(27)
and
X=2
κ(f)dnu1.(28)
Proof: From (25), the equivalent e2e channel coefficient
can be rewritten as
hnu=hl
nuY,(29)
where
Y=exp 1
2κ(f)dnu
1
2κ(f)dnu
.(30)
Next, by taking into account that, in practice, κ(f)<< 0.1
and by applying the Maclaurin series of the exponential
function [59] in (30), Ycan be tightly approximated as
Y ≈ X.(31)
Finally, by substituting (31) into (29), we obtain (26). This
concludes the proof.
III. PERFORMANCE ANALYSIS
This section is focused on presenting the theoretical frame-
work for the quantification of the coverage performance of the
RIS-assisted THz wireless system. In particular, Section III-A
present a closed-form expressions for the CDF of the e2e
channel coefficient, whereas, Section III-B, builds upon this
expression and extract a novel closed-form formula for the
coverage probability.
>REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER <5
φo
m,n =2π
λn1
2(sin (θi) cos (θi) + sin (θo) cos (φo)) dx2π
λm1
2(sin (θi) sin (θi) + sin (θo) sin (φo)) dy
(23)
A. Statistical analysis of the channel coefficient
We assume that the RIS is placed at height LRfrom the
nuth UE and that it targets at (φo, θo). In the far-field, the
euclidean distance between the center of the RIS and the nu
UE can be approximated as
dnudrnucos (θnu),(32)
where dis the euclidean distance between the center of the
RIS and the center of the cluster, rnuis the distance of the
nuUE from the center of the cluster and θnuis the physical
direction of the nuUE with respect to the coordination system
defined by the center of the cluster. Note that the UE location
is uniformly distribution in a disc of radius re; hence, the
probability density function of rnucan be obtained as
frnu(r) = 2r
r2
e
,with r[0, re].(33)
Moreover, θnucan be modeled as a uniform distribution with
probability density function (PDF) that can be expressed as
fθnu(x) = 1
2π,with x[0,2π].(34)
Finally, note that rnuand θnuare independent.
The following theorem returns the PDF and the CDF of the
random variable
Z=rnucos (θnu).(35)
Theorem 2: The PDF and CDF of Xcan be respectively
obtained as
fZ(x) = 2pr2
ex2
πr2
e
,with x[re, re](36)
and
FZ(x) =
0, x ≤ −re
1
2+1
π
xr2
ex2
r2
e+ 2 sin1x
re,re< x < re
1, x re
.
(37)
Proof: Please refer to Appendix B.
The following theorem returns the CDF of dnu.
Theorem 3: The CDF of dnucan be expressed as in (38),
given at the top of the next page.
Proof: Please refer to Appendix C.
The following theorem returns the CDF of the e2e channel
coefficient, assuming that the UE is located within the maxi-
mum path-gain region2.
Theorem 4: Assuming that the UE is located within the
maximum path-gain region, the CDF of the e2e channel
coefficient can be obtained as in (39), given at the top of the
next page.
Proof: Please refer to Appendix D.
2As maximum path-gain region, we define the area in which the following
condition holds: |Lnu/Lmax
nu|< , where stands for the maximum
acceptable path-gain reduction in comparison with Lmax
nu.
B. Coverage probability
As coverage probability, we define the probability that the
received power at the nuth UE that is within the maximum
path-gain region, to be above a predetermined threshold Pth,
i.e.,
Pc= Pr (PrPth |re=rth ),(40)
where rth denotes the radius of the maximum path-gain region.
Note that different applications require different levels of
minimum achievable spectral efficiency, which can be defined
as
C= log21 + Pr
No,(41)
where Nostands for the noise power. Thus, for a spectral
efficiency requirement, Cth, the received power should be at
least equal to Pth. Hence, (41) can be rewritten as
Cth = log21 + Pth
No,(42)
or equivalently
Pth =2Cth 1No.(43)
The following theorem returns a closed-form expression for
the coverage probability.
Theorem 5: The coverage probability can be obtained as
in (44), given at the top of the following page. In (44),
rth <2
κ(f)d, (45)
otherwise, Pc= 0.
Proof: Please refer to Appendix E.
Remark 2: From Theorem 5, it becomes evident that in order
to achieve a coverage probability that equals 1, a minimum
transmission power, which can be evaluated as
Pmin
AP =Pth hl
nu22
κ(f) (d+rth)12
,(46)
should be used.
IV. NUMERICAL RES ULT S & DISCUSSION
In this section, we report numerical results, accompanied
by related discussions, which highlight the effectiveness of
RIS-assisted THz wireless systems, reveals their limitations
as well as the relationship with the system parameters and
performance. In this direction, unless otherwise stated, we
investigate the following insightful scenario. We consider
standard environmental conditions, i.e., relative humidity 50%,
atmospheric pressure 101325 Pa, and temperature 296oK. The
AP transmission antenna gain is 50 dBi, which according
to [30], [60], [61] is a realistic value for THz wireless systems,
>REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER <6
Fdnu(x) =
0, x < d re
1
21
π
(dx)r2
e(dx)2
r2
e2 sin1dx
re, d rexre+d
1, x d+re
(38)
Fhnu(x) =
0, x < hl
nu2
κ(f)(d+re)1
1
2+1
π
d2hl
nu
κ(f)(x+hl
nu)!sr2
e(d2hl
nu
κ(f)(x+hl
nu))2
r2
e+ 2 sin1
d2hl
nu
κ(f)(x+hl
nu)
re
,
hl
nu2
κ(f)(d+re)1xhl
nu2
κ(f)(dre)1
1, x hl
nu2
κ(f)(dre)1
(39)
Pc=
1, Pth <hl
nu22
κ(f)(d+rth)12PAP
1
21
π
d2hl
nu
κ(f)rPth
PAP +hl
nu
v
u
u
u
tr2
th
d2hl
nu
κ(f)rPth
PAP +hl
nu
2
r2
th 2 sin1
d2hl
nu
κ(f)rPth
PAP +hl
nu
rth
,
hl
nu22
κ(f)(d+rth)12PAP Pth hl
nu22
κ(f)(drth)12PAP
0, Pth hl
nu22
κ(f)(drth)12PAP
(44)
while the UE received antenna gains are 20 dBi. The antenna
pattern of the RUs is described by [62], [63]
U(θ, φ) = cos (θ), θ [0,π
2]and φ[0,2π]
0,otherwise.(47)
Thus, Gcan be obtained as
G=Z2π
0Zπ
2
0
U(θ, φ) sin (θ) dθdφ, (48)
which by substituting (47) and performing the integration
returns G= 4. Moreover, |R|is set to 0.9, which is in-line
with [64]. The cluster radius can be obtained as
re=dsin 1
2θHP,(49)
where θHP stands for the azimuth half-power beamwidth
(AHPB) of the RIS. Finally, without loss of generality, we
assume that Nu= 1. Of note, in what follows, we use
continuous lines and markers to respectively denote theo-
retical and simulation results. Additionally, we employ the
finite element method (FEM) in order to verify the channel
model. Notice that this approach has been previously used
in several published contributions (see e.g., [65],[66] and
reference therein), due to its capability to accurate model
electromagnetic propagation mechanisms. Finally, respective
Monte Carlo simulations are employed to verify the coverage
probability theoretical framework.
In Fig. 2, the PL is demonstrated as a function of the
RU to the center of cluster distance for different values of
transmission frequency and M=N, assuming that d1= 1 m
Fig. 2. PL vs dfor different values of M=Nand f.
and that the optimal phase shifts are performed by each RU of
the RIS. In this figure, continuous lines are used to represent
the PL derived by (24), while dashed lines are employed to
denote the PL approximation, which is evaluated according
to (26). Finally, markers denotes FEM-based simulations.
We observe that the PL approximation perfectly match the
analytical frameworks; thus, the approximation framework
is verified. Moreover, both the analytical and approximated
results concise with the simulations, which verifies the PL
evaluation framework. As expected, for fixed fand M=N,
>REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER <7
as dincreases, the PL also increases. For instance, for f=
300 GHz and M=N= 100, the PL increases by about
20 dB, as dchanges from 1to 10 m. Moreover, for given
dand M=N, as fincreases, the PL also increases. For
example, for M=N= 10 and d= 10 m, the PL increased
by approximately 10 dB, as fincreases from 100 to 300 GHz.
Finally, we observe that, for fixed fand d, the PL decreases
as the number of RUs increases. For instance, for d= 10 m,
and f= 100 GHz, the PL decreases by approximately 40 dB,
as the M=Nincreases from 10 to 100.
Figure 3 demonstrates the e2e PL as a function of the
nuth UE direction, for different size of RIS, assuming that
d1=dnu = 1 m, the transmission frequency, f= 100 GHz,
dx=dy= 0.3 mm,|R|= 0.9,GAP = 50 dBi,Gnu =
20 dBi,θi=π
4,φi=π, and no phase shifting is introduced
by any RU. Of note the results presented in this figure has been
verified by FEM-based simulations. However, for the sake
of readability no markers have been placed. Notice that this
special case can be considered as RIS performance benchmark
and it represents scenarios in which the direction of the nuth
UE is unknown to the RIS. Figure 3.a illustrates the e2e PL
as a function of φr, for different number of M=N, and
θr=π
4. From this figure, we observe that, for given M=N,
the PL is minimized for φr= 0o. This is in-line with (3)
and (4), where, for the special case in which φm,n = 0, it
can be extracted that ζ1=ζ2= 0 and that, for θi6= 2,
φi6= 2, and θr6= 2kπ, with kinteger, the path-gain is
maximized for φr= 2. Moreover, it becomes apparent
that as M=Nincreases, the minimum PL decreases. For
example, for M=N= 10, the minimum e2e PL equals
42.83 dB, while, for M=N= 10, it is 2.83 dB. However,
as the RIS size increases, the azimuth AHPB decreases. For
instance, for M=N= 10, the AHPB is approximately equal
to 74o, which results to a cluster with radius that is equal
to 0.6 m whereas, for M=N= 100, it is about 8o, which
result to a cluster radius of 7 cm. This indicates that as the RIS
size increases, or equivalently as the number of the used RUs
increases, the size of the cluster that can be served, decreases.
Of note, from (49), it becomes evident that as dincreases,
realso increases. For example, for d= 10 m, in the case in
which M=N= 100, the cluster radius becomes equal to
0.7 m, while, in the case in which M=N= 10, it is equal
to 6 m. Similarly, Fig. 3.b depicts the e2e PL as a function
of θr, for different number of M=N, and φr=π
4. Again,
as the RIS size increases, the minimum PL and the elevation
half-power beamwidth (EHPB) decrease. Meanwhile, Fig. 3.c
presents the PL as a function of φrfor θr=π
4, assuming
that θo=π/6,φo=π/3and that the phase shifting of each
element is provided according to (23), whereas, in Fig. 3.d,
the corresponding PL against θr, for φr=π
4is depicted. By
comparing Fig. 3.a with Fig. 3.c and Fig. 3.b with Fig. 3.d,
we observe that by imposing appropriate phase shifting to
each RIS RU, the PL pattern is rotated in order to achieve
the minimum PL at the desired direction.
In Fig. 4, the PL is presented as a function of the nuth
UE direction, for different transmission frequencies, assuming
that d1=dnu = 1 m,dx=dy= 0.3 mm,|R|= 0.9,
GAP = 50 dBi,Gnu = 20 dBi,θi=π
4,φi=π,
θo=π/6, and φo=π/3. As expected the minimum PL
is observed for φr=π/3. Moreover, it is apparent that for
a fixed φr, as the transmission frequency increases, the PL
also increases. Finally, we observe that as the transmission
frequency increases, the AHPB decreases.
Figure 5 depicts the PL as a function of ffor different
values of M=N, assuming that θi=θr=θo=
φr=φo=π
4,φi=3π
4,d1=dnu= 10 m, and
dx=dy= 0.3 mm. The theoretical results perfectly match
the simulations, verifying the proposed channel model. From
this figure, it is revealed that there exists two frequency
regions, the first one from 370 to 390 GHz and the second one
from 430 to 455 GHz, in which the PL is maximized. This
is due to water molecules resonance. In other words, from
100 to 500 GHz, there exists three transmission windows;
the first one from 100 to 365 GHz, the second one from
375 to approximately 430 GHz, and the third one from 460
to 500 GHz. Outside these regions, for fixed Mand N, as
the transmission frequency increases, the PL also increases.
For example, for M=N= 20, as fincreases from 100
to 300 GHz, the PL increases for about 10 dB. Finally, it is
observed that, for a given transmission frequency, as the RIS
size increases, the PL decreases. For example, as M=N
increases from 10 to 100, the PL decreases for about 40 dB.
In Fig. 6, the PL is plotted as a function of the atmospheric
temperature and relative humidity, for different values of f,
assuming M=N= 100,d1= 1 m,dnu= 10 m,dx=dy
0.3 mm,θi= 45o,φi= 180o, and θr=θo=φr=φo= 45o.
In more detail, in Fig. 6.a, fis set to 100 GHz, while,
in Fig. 6.b, it equals 200 GHz. Likewise, in Fig. 6.c, fis
300 GHz, whereas, in Fig. 6.d, the transmission frequency is
set to 380 GHz, which is one of the worst scenarios, since
it is one of the resonant frequencies of water molecules.
Furthermore, in Fig. 6.e, the transmission frequency is equal
to 400 GHz, while, in Fig. 6.f, it is set to 450 GHz that is one
of the worst scenarios, due to the fact that in this frequency
the molecular absorption in maximized. Notice that, according
to [67]–[69], the frequencies 100,200,300 and 400 GHz
are within the THz transmission windows. As expected, for
a fixed atmospheric temperature, as the humidity increases,
the water molecules increases; thus, the molecular absorption
and the PL increase. For instance, in the worst case scenario
in which f= 380 GHz, for an atmospheric temperature of
273oK, the PL increases by approximately 2 dB as relative
humidity increases from 10% to 90%. On the other hand,
for f= 100 GHz, for the same atmospheric temperature,
the PL increase does not surpass 0.25 dB as the relative
humidity changes from 10% to 90%. The aforementioned ex-
amples reveals the importance of taking into account both the
transmission frequency and the atmospheric conditions, when
evaluating the link budget of of RIS-assisted THz systems.
Similarly, for a given relative humidity, as the atmospheric
temperature increases, the PL also increases. For example, for
f= 380 GHz and a relative humidity equals 50%, the PL
increases by 2 dB as the atmospheric temperature increase
from 270oKto 290oK. On the contrary, for f= 100 GHz,
the same relative humidity, the PL increases by approximately
0.01 dB as the atmospheric temperature increase from 270oK
>REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER <8
(a) (b)
(c) (d)
Fig. 3. a) PL vs φr, for θr=π
4and φm,n = 0o, for all mand n, b) PL vs θr, for different φr=π
4and φm,n = 0o, for all mand n. c) PL vs φr, for
θr=π
4,θo=π/6, and φo=π/3. d) PL vs θr, for φr=π
4,θo=π/6, and φo=π/3.
Fig. 4. PL vs φr, for θr=π
4,θo=π/6,φo=π/3, and different values
of f.
to 290oK. Moreover, for f= 200 GHz, the same temperature
variation causes a PL increase in the range of 0.05 dB,
while, for f= 400 GHz, it results to 0.5 dB. This indicates
that as the frequency increases the impact of environmental
Fig. 5. PL vs ffor different RIS sizes.
conditions to the PL become more severe. Finally, from this
figure, it becomes evident that neglecting the absorption loss
would lead to a frequency-dependent PL error in the range of
[0.1,22.7 dB]. This highlights the importance of taking into
account the molecular absorption loss when evaluating the PL
and the performance of RIS-assisted THz systems.
>REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER <9
(a) (b) (c)
(d) (e) (f)
Fig. 6. PL vs temperature and relative humidity, for (a) f= 100 GHz, (b) f= 200 GHz, (c) f= 300 GHz, (d) f= 380 GHz, (e) f= 400 GHz, and
(f) f= 450 GHz.
Fig. 7. PL vs temperature and frequency.
Figure 7 illustrates the PL as a function of the air tempera-
ture and the transmission frequency, assuming M=N= 100,
d1= 1 m,dnu= 10 m,dx=dy0.3 mm,θi= 45o,
φi= 180o, and θr=θo=φr=φo= 45o. As expected, for a
given transmission frequency, as the air temperature increases,
the PL also increases. For example, for f= 250 GHz, the PL
increases by about 0.1 dB, as the air temperature increases
from 270 to 320oK. Moreover, from this figure, it is verified
that there exist two frequency regions in which the PL is
maximized. In these regions, temperature variations cause a
more severe impact on PL. For instance, increasing the air tem-
perature from 270 to 280oKresults in 0.02 dB PL increase,
if the transmission frequency is equal to 280 GHz, while, the
same temperature increase cause a 0.5 dB PL increase, when
the transmission frequency is set to 383 GHz. This indicates
the importance of taking into account the air temperature and
its variations, when selecting the transmission frequency.
Figure 8 presents the coverage probability as a function
of PAP /Pth, for different values of f,M=Nand d,
assuming that φi=π,φr= 0, and θi=θr=π
4. From
this figure, we observe that the analytical results coincide with
the simulations, verifying the derived expressions. Moreover,
for given f,M=Nand d, as PAP
Pth increases, the coverage
probability also increases. For example, for f= 200 GHz,
M=N= 10 and d= 5 m,Pcincreases from 12.6% to
60.5%, as PAP /Pth increases from 50 to 55 dB. Meanwhile,
for fixed dand PAP
Pth , although, as the RIS size increase,
rth decreases, the path-gain increases; hence, the Pcalso
increases. For instance, for f= 200 GHz,d= 5 m and
PAP
Pth = 40 dB, as M=Nincreases from 10 to 50,rth
decreases from approximately 6.02 to 2.59 m; however, Pc
increases from 0to 1. Additionally, we observe that for given
RIS size and PAP
Pth , as dincreases, Pcdecreases. Finally, by
comparing Figs. 8a-c, it becomes apparent that for given PAP
Pth ,
M=Nand d, as fincreases, the Pcdecreases. For example,
for M=N= 50,d= 15 m, and PAP
Pth = 25 dB,Pcreduces
from 1to 0as the transmission frequency changes from 100
to 300 GHz.
Figure 9 depicts the coverage probability as a function of the
transmission frequency, for different values of PAP
Pth , assuming
M=N= 100,φi=π,φr= 0,θi=θr=π
4and d= 15 m.
As expected, for a given PAP
Pth , as the transmission frequency
increases, the PL increases; thus, the coverage probability
decreases. Likewise, for a fixed transmission frequency, as
PAP
Pth increases, the received power increases; as a result,
>REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER <10
(a) (b) (c)
Fig. 8. Pcvs PAP /Pth for different RIS sizes and d, assuming a) f= 100 GHz, b) f= 200 GHz, and c) f= 300 GHz.
Fig. 9. Pcvs frequency for different PAP /Pth.
the coverage probability also increases. For example, for a
transmission frequency that is equal to 250 GHz, as PAP
Pth
increases from 40 to 50 dB, the coverage probability increases
from 0to 1. Finally, from this figure, it becomes evident that as
PAP
Pth increases, the range of frequencies for which the coverage
probability equals 1increases.
Figure 10 presents the coverage probability as a function
of d, for different values of PAP /Pth, RIS size, and a)
f= 100 GHz, b) f= 200 GHz, and c) f= 300 GHz,
assuming φi=π,φr= 0, and θi=θr=π
4. As
expected, for given transmission frequency, RIS size and PAP
Pth ,
as dincreases, the average PL increases; thus, the cover-
age probability decreases. For example, for f= 200 GHz,
M=N= 50 and PAP
Pth = 30 dB, the coverage probability
reduces from 1to 0, as dincreases from 5to 10 m. Similarly,
for f= 100 GHz,M=N= 50 and PAP
Pth = 30 dB,
Pcchanges from 1to 0, as dincreases from 10 to 15 m.
Moreover, we observe that by increasing the RIS size, we
can counterbalance the transmission distance restriction. For
instance, for f= 200 GHz,PAP
Pth = 30 dB, and d= 20 m,
Pcincreases from 0to 1as M=Nchanges from 50
to 100. Likewise, it is observed that for fixed transmission
frequency, RIS size and d, as PAP /Pth increases, the coverage
probability also increases. For example, for f= 200 GHz,
d= 10 m and M=N= 100, as PAP /Pth increases
from 20 to 30 dB, the coverage probability changes from
approximately 40% to 100%. This indicates that another ap-
proach to countermeasure the transmission distance restriction
is to increase the AP transmission power. Finally, within the
same transmission window, for fixed PAP
Pth ,M=N, and
d,Pcincreases as the transmission frequency decreases. For
example, for PAP
Pth = 30 dB,M=N= 100, and d= 40 m,
Pcchanges from 0to 1, as fdecreases from 200 to 100 GHz.
This reveals that another approach to increase the transmission
distance is to decrease the transmission frequency.
Figure 11 depicts the coverage probability as a function
of PAP /Pth and air temperature for different values of f,
assuming M=N= 100,φi=π,φr= 0, and θi=θr=π
4.
As expected, for a given temperature as PAP /Pth increases,
the coverage probability increases. Moreover, for a fixed
PAP /Pth, as the air temperature increases, the PL increases;
hence, the coverage probability decreases. For example, for
f= 380 GHz and PAP /Pth = 60 dB, the coverage probabil-
ity decreases from 1to 0, as the air temperature increases
from 270 to 300oK. Similarly, for f= 100 GHz and
PAP /Pth = 5 dB, as the temperature changes from 270 to
280 oK,Pcdecreases from 1to 0. Finally, from this figure it
becomes evident that the minimum transmission power that is
required to achieve a coverage probability that is equal to 1,
increases as the air temperature increases.
V. CONCLUSIONS
This contribution presented a theoretical framework for RIS-
assisted THz wireless system coverage performance evalu-
ation. In more detail, we described the system model and
we employed electromagnetic theory tools in order to extract
a generalized formula for the e2e path-gain. This formula
revealed the relationships between the RIS specifications,
namely size, number of RIS RUs, RU size and reflection
coefficient, RU’s radiation patterns, as well as phase shift of
each RU, the transmission parameters, such as transmission
frequency AP to center of RIS and center of RIS to UE
distance, AP transmission and UE reception antenna gains,
azimuth and elevation angles from the AP to the center of the
>REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER <11
(a) (b) (b)
Fig. 10. Pcvs dfor different values of PAP /Pth and RIS size, assuming a) f= 100 GHz, b) f= 200 GHz, and c) f= 300 GHz.
(a) (b) (c)
(d) (e) (f)
Fig. 11. Pcvs Tand PAP /Pth , assuming a) f= 100 GHz, b) f= 200 GHz, c) f= 300 GHz, d) f= 380 GHz, e) f= 400 GHz and f)
f= 450 GHz.
RIS as well as from the center of the RIS to the UE, and THz-
specific parameters, like the environmental conditions that
affect the molecular absorption. Building upon this expression,
we determined the optimal phase shift of each RU in order to
steer the RIS-generated beam to a desired direction. Next, we
obtained an exact expression for the e2e channel coefficient
as well as a tight approximation that allows us to quantify
the system performance. Based on this expression, we first
obtained the statistics of the e2e channel, we defined the
coverage probability of the RIS-assisted THz wireless system
and derived a novel closed-form and insightful expression for
its quantification. This expression revealed that there exists
a minimum AP transmission power that can guarantee a
coverage probability of 100%. This minimum AP transmission
power depends not only on the system’s characteristics, but
also on the environmental conditions. Finally, we verified
the accuracy of the theoretical framework through respective
simulations, which highlighted the dependency between the
transmission power and maximum bandwidth that can be
used in RIS-assisted THz systems. The results highlight the
importance of taking into account the molecular absorption
loss when evaluating the PL and the performance of RIS-
assisted THz wireless systems. Therefore, this work is ex-
pected to contribute on analyzing, simulating, and designing
RIS-assisted THz systems. Moreover, it is expected to play a
key role on devising physical layer and medium access control
algorithms in RIS-assisted THz systems.
The performance analysis of RIS-assisted THz wireless
systems were conducted under the assumptions that (i) the
center of the cluster is perfectly known to the RIS controller,
>REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER <12
and (ii) the cluster radius is perfectly known to the AP. It
would be interesting to relax the aforementioned assumptions
and present new evaluation investigation assuming partial
knowledge of the cluster center and radius. Moreover, the
fading characteristics should be taken into account. Motivated
by this, our future effort will focus on the study of RIS-assisted
THz system performance in fading environments under partial
cluster position and radius knowledge. Finally, inspired by the
fact that in several realistic scenarios the users are mobile and
since the proposed path-loss model can be also applied in this
scenario, we intend to provide the theoretical framework for
quantifying the performance of RIS-assisted THz systems that
operate in dynamic environments in which the UEs are mobile.
APPENDICES
APPENDIX A
PROO F OF T HE OR EM 1
Since lt
m,n >> λ, where λis the wavelength of the
transmission signal, the power of the incident signal into the
Um,n can be obtained as
Pi
m,n = exp κ(f)lt
m,nGAP PAP
4πlt
m,n2
×Urθt
m,n, φt
m,nSU,(50)
where SUstand for the aperture of the RIS unit cell and can
be expressed as
SU=dxdy.(51)
By substituting (51) into (50), we can express the power of
the incident signal as
Pi
m,n = exp κ(f)lt
m,nUrθt
m,n, φt
m,n
×GAP PAP
4πlt
m,n2dxdy.(52)
Hence, the electric field of the incident signal into Um,n can
be written as
Ei
n,m =s2ZoPi
m,n
dxdy
exp j2πlt
m,n
λ,(53)
where Zois the air characteristic impedance.
Based on the energy conversation law, the total reflected
signal power by the Umn unit cell can be obtained as
Pr
m,n =R2
m,nPi
m,n.(54)
or equivalently
Pr
m,n = exp κ(f)lt
m,ndxdy
4πlt
m,n2|Rm,n |2
×Urθt
m,n, φt
m,nGAP PAP .(55)
By assuming that lm,n,nu>> λ, we can obtain the power
of the received signal at the nuUE from the Um,n RIS unit
cell as
Pm,n,nu= exp κ(f)lt
m,n +lm,n,nu
×G Ur(θi, φi)Pr
m,n
4π(lm,n,nu)2Ut(θr, φr)Sr
nu,(56)
where Sr
nuis the aperture of the nu-th UE receive antenna
and can be obtained as
Sr
nu=Gnuλ2
4π.(57)
With the aid of (57), (56) can be rewritten as
Pm,n,nu=dxdyλ2Ur(θi, φi)Ut(θr, φr)G|Rm,n|2GAP Gnu
(4π)3(lm,n,nu)2lt
m,n2
×exp κ(f)lt
m,n +lm,n,nuPAP .(58)
As a result, the electrical field of the received signal at the nu
UE from the Um,n RIS unit cell can be expressed as
Em,n,nu=s2Zo
Pm,n,nu
Sr
nu
exp j2π
λlt
m,n +lm,n,nu,
(59)
which, based on (58), can be equivalently written as
Em,n,nu=Rm,np2ZodxdyUr(θi, φi)Ut(θr, φr)GGAP PAP
4πlm,n,nult
m,n
×exp 1
2κ(f) + j2π
λlt
m,n +lm,n,nu.(60)
Then, the total electric field at the nuUE can be evaluated as
Er
nu=
M
2
X
m=M
2+1
N
2
X
n=N
2+1
Em,n,nu,(61)
which, by substituting (60) and taking into account that in
the far-field |Rm,n|≈|R|, can be equivalently expressed as
in (62), given at the top of the following page.
The AP position can be obtained as
rt=d1sin (θi) cos (φi)xo+d1sin (θi) sin (φi)yo
+d1cos (θi)zo.(63)
Thus, by employing (1) and (63), the distance between the AP
and the Um,n can be obtained as in (64), given at the top of
the following page. By employing the Taylor expansion in (64)
and keeping only the first term, the distance between the AP
and the Um,n can be approximated as
lt
m,n d1sin (θi)cos (φi)n1
2dx
sin (θi)sin (φi)m1
2dy(65)
Following the same steps, we can prove that
lm,n,nudnusin (θr)cos (φr)n1
2dx
sin (θr)sin (φr)m1
2dy.(66)
By substituting (65) and (66) into (62), and taking into
account that in practice dxand dyare at the order of λ/10,
while d1, dnu >> λ, we can tightly approximate the electric
field at the nuUE as in (67), given at the top of the following
page. In (67),
>REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER <13
Er
nu=|R|p2ZodxdyUr(θi, φi)Ut(θr, φr)GGAP PAP
4π
M
2
X
m=M
2+1
N
2
X
n=N
2+1
exp 1
2κ(f) + j2π
λlt
m,n +lm,n,nu+m,n
lm,n,nult
m,n
(62)
lt
m,n = d1sin (θi) cos (φi)n1
2dx2
+d1sin (θi) sin (φi)m1
2dy2
+d2
1cos2(θi)!1/2
(64)
Er
nu|R|p2ZodxdyUr(θi, φi)Ut(θr, φr)GGAP PAP
4πd1dnu
exp 1
2κ(f) (d1+dnu)
×
M
2
X
m=M
2+1
N
2
X
n=N
2+1
exp j2π
λd1+dnuβm,n +λ
2πφm,n (67)
βm,n =d1sin (θi) cos (θi)n1
2dx
sin (θi) sin (θi)m1
2dy
+dnusin (θr)cos (φr)n1
2dx
sin (θr)sin (φr)m1
2dy.(68)
The received signal power at the nuUE can be evaluated as
Pr=|Er
nu|2
2Zo
Sr
nu,(69)
which, with the aid of (57) and (67), can be written as
Pr=dxdyλ2|R|2Ur(θt, φt)Ut(θr, φr)GGAP GnuPAP
64π3d2
1d2
nu
×exp (κ(f) (d1+dnu)) |γ|2.(70)
In (70), γcan be evaluated as in (71), given at the top of the
following page, or equivalently
γ=γ1γ2,(72)
where γ1and γ2respectively obtained as in (73) and (74),
given at the top of the following page. In (73) and (74), ζ1
and ζ2are defined in (4). By taking into account the sum of
geometric progression theorem, (73) can be rewritten as
γ1=exp j
λδ1exp j
λδ1
exp jπ
λδ1exp jπ
λδ1,(75)
or equivalently γ1=sin(
λδ1)
sin(π
λδ1),or
γ1=Nsinc
λδ1
sinc π
λδ1,(76)
where
δ1= (sin (θi) cos (θi) + sin (θr) cos (φr)) dx+ζ1.(77)
By substituting (77) into (76), we get
γ1=Nsinc
λ(sin (θi) cos (φi) + sin (θr) cos (φr) + ζ1)dx
sinc π
λ(sin (θi) cos (φi) + sin (θr) cos (φr) + ζ1)dx.
(78)
Similarly, (74) can be expressed as
γ2=Msinc
λ(sin (θi) sin (φi) + sin (θr) sin (φr) + ζ2)dy
sinc π
λ(sin (θi) sin (φi) + sin (θr) sin (φr) + ζ2)dy.
(79)
Finally, by substituting (78) and (79) into (72) and then to (70),
we obtain (2). This concludes the proof.
APPENDIX B
PROO F OF TH EO RE M 2
Since θnuis uniformly distributed with lower and upper
bounds 0and 2π, respectively, cos (θnu)follows arc sine
distribution with lower and upper bounds 1and 1. Thus,
the PDF of D= cos (θnu)can be expressed as
fD(y) = (1
π1y2,1< y < 1
0,otherwise .(80)
According to [70], since Dand rnuare independent, the PDF
of Zcan be evaluated as
fZ(x) = Zre
|x|
frnu(r)fDz
r1
rdr.(81)
By substituting (33) and (80) into (81), we can rewrite the
PDF of Xas
fZ(x) = 2
πr2
eZre
x
r
r2x2dr,(82)
which, after performing the integration, can be expressed
as (36).
The CDF of Xcan be evaluated as
FZ(x) = Zx
re
fZ(y) dy,(83)
>REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER <14
γ=
M
2
X
m=M
2+1
N
2
X
n=N
2+1
exp j2π
λd1+dnuβm,n +λ
2πφm,n (71)
γ1=
N
2
X
n=N
2+1
exp j2π
λsin (θi) cos (θi)n1
2dx+ sin (θr)cos (φr)n1
2dx+ζ1 (73)
γ2=
M
2
X
m=M
2+1
exp j2π
λsin (θi) sin (θi)m1
2dy+ sin (θr)sin (φr)m1
2dy+ζ2 (74)
which, with the aid of (36) and after some algebraic manipu-
lations, can be rewritten as
FZ(x) = 2
πZx
re
1p1u2du.(84)
By employing [71], (84) can be written as (37). This concludes
the proof.
APPENDIX C
PROO F OF TH EO RE M 3
From (32), we can obtain the CDF of dnuas
Fdnu(x) = Pr (dnux),(85)
or equivalently
Fdnu(x) = Pr (Z ≥ dx),(86)
or
Fdnu(x) = 1 FZ(dx),(87)
which, with the aid of (37), returns (38).
APPENDIX D
PROO F OF TH EO RE M 4
The CDF of the e2e channel coefficient is defined as
Fhnu(x) = Pr (hnux),(88)
which, based on (26), can be rewritten as
Fhnu(x) = Pr X ≤ x
hl
nu.(89)
By employing (28), (89) can be expressed as
Fhnu(x) = Pr dnu2hl
nu
κ(f)x+hl
nu!,(90)
or equivalently
Fhnu(x)=1Pr dnu2hl
nu
κ(f)x+hl
nu!,(91)
or
Fhnu(x)=1Fdnu 2hl
nu
κ(f)x+hl
nu!,(92)
which, with the aid of (38), returns (39). This concludes the
proof.
APPENDIX E
PROO F OF TH EO RE M 5
From (40), with the aid of (2) and (26), we can evaluate the
coverage probability as
Pc= Pr hnurPth
PAP
re=rth!,(93)
or
Pc=Fhnu rPth
PAP
re=rth!,(94)
which, by employing (39) gives (44). This concludes the proof.
REFERENCES
[1] F. Tariq, M. Khandaker, K.-K. Wong, M. Imran, M. Bennis, and
M. Debbah, “A speculative study on 6g,” ArXiV, Aug. 2019.
[2] A.-A. A. Boulogeorgos and G. K. Karagiannidis, “Low-cost cognitive
radios against spectrum scarcity,IEEE Technical Committee on Cogni-
tive Networks Newsletter, vol. 3, no. 2, pp. 30–34, Nov. 2017.
[3] A.-A. A. Boulogeorgos, “Interference mitigation techniques in modern
wireless communication systems,” Ph.D. dissertation, Aristotle Univer-
sity of Thessaloniki, Thessaloniki, Greece, Sep. 2016.
[4] C. Zhang, K. Ota, J. Jia, and M. Dong, “Breaking the blockage for big
data transmission: Gigabit road communication in autonomous vehicles,”
IEEE Commun. Mag., vol. 56, no. 6, pp. 152–157, Jun. 2018.
[5] S. Dang, O. Amin, B. Shihada, and M.-S. Alouini, “What should 6G
be?” Nature Electronics, vol. 3, no. 1, pp. 20–29, Jan. 2020.
[6] L. Bariah, L. Mohjazi, S. Muhaidat, P. C. Sofotasios, G. K. Kurt,
H. Yanikomeroglu, and O. A. Dobre, “A prospective look: Key enabling
technologies, applications and open research topics in 6g networks.”
[7] I. F. Akyildiz, J. M. Jornet, and C. Han, “Terahertz band: Next frontier
for wireless communications,” Phys. Commun., vol. 12, pp. 16–32, Sep.
2014.
[8] Z. Xu, X. Dong, and J. Bornemann, “Design of a reconfigurable mimo
system for thz communications based on graphene antennas,” IEEE
Trans. THz Sci. Technol., vol. 4, no. 5, pp. 609–617, Sep. 2014.
>REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER <15
[9] R. Zhang, K. Yang, Q. H. Abbasi, K. A. Qaraqe, and A. Alomainy,
“Analytical characterisation of the terahertz in-vivo nano-network in the
presence of interference based on TS-OOK communication scheme,”
IEEE Access, vol. 5, pp. 10 172–10 181, Jun. 2017.
[10] A.-A. A. Boulogeorgos, A. Alexiou, T. Merkle, C. Schubert,
R. Elschner, A. Katsiotis, P. Stavrianos, D. Kritharidis, P. K. Chartsias,
J. Kokkoniemi, M. Juntti, J. Lehtom¨
aki, A. Teixeir´
a, and F. Rodrigues,
“Terahertz technologies to deliver optical network quality of experience
in wireless systems beyond 5G,” IEEE Commun. Mag., vol. 56, no. 6,
pp. 144–151, Jun. 2018.
[11] T. S. Rappaport, Y. Xing, O. Kanhere, S. Ju, A. Madanayake, S. Mandal,
A. Alkhateeb, and G. C. Trichopoulos, “Wireless communications and
applications above 100 GHz: Opportunities and challenges for 6g and
beyond,” IEEE Access, vol. 7, pp. 78 729–78 757, Jun. 2019.
[12] A.-A. A. Boulogeorgos, A. Alexiou, D. Kritharidis, A. Katsiotis,
G. Ntouni, J. Kokkoniemi, J. Lethtomaki, M. Juntti, D. Yankova,
A. Mokhtar, J.-C. Point, J. Machodo, R. Elschner, C. Schubert,
T. Merkle, R. Ferreira, F. Rodrigues, and J. Lima, “Wireless terahertz
system architectures for networks beyond 5G,” TERRANOVA CON-
SORTIUM, White paper 1.0, Jul. 2018.
[13] C. Lin and G. Y. L. Li, “Terahertz communications: An array-of-
subarrays solution,” IEEE Commun. Mag., vol. 54, no. 12, pp. 124–131,
Dec. 2016.
[14] A. Leuther, T. Merkle, R. Weber, R. Sommer, and A. Tessmann,
“THz frequency HEMTs: Future trends and applications,” in Compound
Semiconductor Week (CSW), May 2019.
[15] A. C. Tasolamprou, A. Pitilakis, S. Abadal, O. Tsilipakos, X. Timoneda,
H. Taghvaee, M. Sajjad Mirmoosa, F. Liu, C. Liaskos, A. Tsioliaridou,
S. Ioannidis, N. V. Kantartzis, D. Manessis, J. Georgiou, A. Cabellos-
Aparicio, E. Alarcn, A. Pitsillides, I. F. Akyildiz, S. A. Tretyakov, E. N.
Economou, M. Kafesaki, and C. M. Soukoulis, “Exploration of intercell
wireless millimeter-wave communication in the landscape of intelligent
metasurfaces,” IEEE Access, vol. 7, pp. 122 931–122 948, Aug. 2019.
[16] Q. Wu and R. Zhang, “Intelligent reflecting surface enhanced wireless
network: Joint active and passive beamforming design,” in IEEE Global
Communications Conference (GLOBECOM), Dec 2018, pp. 1–6.
[17] ——, “Beamforming optimization for intelligent reflecting surface with
discrete phase shifts,” in IEEE International Conference on Acoustics,
Speech and Signal Processing (ICASSP), May 2019, pp. 7830–7833.
[18] E. Basar, M. Di Renzo, J. De Rosny, M. Debbah, M. Alouini, and
R. Zhang, “Wireless communications through reconfigurable intelligent
surfaces,” IEEE Access, vol. 7, pp. 116 753–116 773, 2019.
[19] M. D. Renzo, M. Debbah, D.-T. Phan-Huy, A. Zappone, M.-S.
Alouini, C. Yuen, V. Sciancalepore, G. C. Alexandropoulos, J. Hoydis,
H. Gacanin, J. d. Rosny, A. Bounceur, G. Lerosey, and M. Fink, “Smart
radio environments empowered by reconfigurable ai meta-surfaces: An
idea whose time has come,” EURASIP Journal on Wireless Communi-
cations and Networking, vol. 2019, no. 1, pp. 1–20, May 2019.
[20] S. V. Hum and J. Perruisseau-Carrier, “Reconfigurable reflectarrays and
array lenses for dynamic antenna beam control: A review,” IEEE Trans.
Antennas Propag., vol. 62, no. 1, pp. 183–198, Jan. 2014.
[21] J. M. Jornet and I. F. Akyildiz, “Channel modeling and capacity analysis
for electromagnetic wireless nanonetworks in the terahertz band,” IEEE
Trans. Wireless Commun., vol. 10, no. 10, pp. 3211–3221, Oct. 2011.
[22] P. Boronin, V. Petrov, D. Moltchanov, Y. Koucheryavy, and J. M. Jornet,
“Capacity and throughput analysis of nanoscale machine communication
through transparency windows in the terahertz band,Nano Commun.
Networks, vol. 5, no. 3, pp. 72–82, Sep. 2014.
[23] K. Yang, A. Pellegrini, M. O. Munoz, A. Brizzi, A. Alomainy, and
Y. Hao, “Numerical analysis and characterization of THz propagation
channel for body-centric nano-communications,” IEEE Trans. THz Sci.
Technol., vol. 5, no. 3, pp. 419–426, May 2015.
[24] C. Han, A. O. Bicen, and I. F. Akyildiz, “Multi-ray channel modeling
and wideband characterization for wireless communications in the
terahertz band,” IEEE Trans. Wireless Commun., vol. 14, no. 5, pp.
2402–2412, May 2015.
[25] J. Kokkoniemi, J. Lehtom¨
aki, and M. Juntti, “Simplified molecular
absorption loss model for 275-400 gigahertz frequency band,” in 12th
European Conference on Antennas and Propagation (EuCAP), London,
UK, Apr. 2018.
[26] E. N. Papasotiriou, J. Kokkoniemi, A.-A. A. Boulogeorgos,
J. Lehtom¨
aki, A. Alexiou, and M. Juntti, “A new look to 275 to
400 ghz band: Channel model and performance evaluation,” in IEEE
International Symposium on Personal, Indoor and Mobile Radio
Communications (PIMRC), Bolonia, Italy, Sep. 2018.
[27] A.-A. A. Boulogeorgos, E. N. Papasotiriou, J. Kokkoniemi,
J. Lehtom¨
aki, A. Alexiou, and M. Juntti, “Performance evaluation of
THz wireless systems operating in 275-400 GHz band,” IEEE Vehicular
Technology Conference (VTC), 2018.
[28] A. Afsharinejad, A. Davy, B. Jennings, and C. Brennan, “An initial
path-loss model within vegetation in the thz band,” in 9th European
Conference on Antennas and Propagation (EuCAP), Lisbon, Portugal,
May 2015, pp. 1–5.
[29] A.-A. A. Boulogeorgos, E. N. Papasotiriou, and A. Alexiou, “Analytical
performance assessment of THz wireless systems,” IEEE Access, vol. 7,
pp. 11 436–11 453, 2019.
[30] A.-A. A. Boulogeorgos and A. Alexiou, “Error analysis of mixed THz-
RF wireless systems,” IEEE Commun. Lett., vol. 24, no. 2, pp. 277–281,
Feb. 2020.
[31] A.-A. A. Boulogeorgos, E. N. Papasotiriou, and A. Alexiou, “A distance
and bandwidth dependent adaptive modulation scheme for THz commu-
nications,” in 19th IEEE International Workshop on Signal Processing
Advances in Wireless Communications (SPAWC), Kalamata, Greece, Jul.
2018.
[32] A.-A. A. Boulogeorgos, S. Goudos, and A. Alexiou, “Users association
in ultra dense THz networks,” in IEEE International Workshop on Signal
Processing Advances in Wireless Communications (SPAWC), Kalamata,
Greece, Jun. 2018.
[33] A.-A. A. Boulogeorgos and A. Alexiou, “Performance evaluation of the
initial access procedure in wireless THz systems,” in 16th International
Symposium on Wireless Communication Systems (ISWCS). IEEE, aug
2019.
[34] A. Afsharinejad, A. Davy, B. Jennings, S. Rasmann, and C. Brennan,
“A path-loss model incorporating shadowing for THz band propagation
in vegetation,” in IEEE Global Communications Conference (GLOBE-
COM), San Diego, CA, USA, Dec. 2015, pp. 1–6.
[35] H. Elayan, R. M. Shubair, J. M. Jornet, and P. Johari, “Terahertz channel
model and link budget analysis for intrabody nanoscale communication,”
IEEE Trans. Nanobioscience, vol. 16, no. 6, pp. 491–503, Sep. 2017.
[36] M. A. Akkas, “Terahertz channel modelling of wireless ultra-compact
sensor networks using electromagnetic waves,IET Commun., vol. 10,
no. 13, pp. 1665–1672, 2016.
[37] A.-A. A. Boulogeorgos and A. Alexiou, Next Generation Wireless
Terahertz Communication Networks. to be published by CRC Press,,
2020, ch. Antenna misalignment and blockage in THz communications.
[38] T. Merkle, A. Tessmann, M. Kuri, S. Wagner, A. Leuther, S. Rey,
M. Zink, H.-P. Stulz, M. Riessle, I. Kallfass, and T. Kurner, “Testbed
for phased array communications from 275 to 325 GHz,” in IEEE Com-
pound Semiconductor Integrated Circuit Symposium (CSICS). IEEE,
Oct. 2017.
[39] O. Erturk and T. Yilmaz, “A hexagonal grid based human blockage
model for the 5g low terahertz band communications,” in IEEE 5G World
Forum (5GWF). IEEE, Jul. 2018.
[40] A. Shafie, N. Yang, Z. Sun, and S. Durrani, “Coverage analysis for 3d
terahertz communication systems with blockage and directional anten-
nas,” in IEEE International Conference on Communications Workshops
(ICC Workshops). IEEE, Jun. 2020.
[41] Y. Wu, J. Kokkoniemi, C. Han, and M. Juntti, “Interference and coverage
analysis for terahertz networks with indoor blockage effects and line-
of-sight access point association,” IEEE Trans. Wireless Commun., pp.
1–1, 2020.
[42] M. Jung, W. Saad, Y. R. Jang, G. Kong, and S. Choi, “Performance
analysis of large intelligence surfaces (LISs): Asymptotic data rate and
channel hardening effects,CoRR, vol. abs/1810.05667, 2018. [Online].
Available: http://arxiv.org/abs/1810.05667
[43] C. Huang, A. Zappone, G. C. Alexandropoulos, M. Debbah, and
C. Yuen, “Reconfigurable intelligent surfaces for energy efficiency in
wireless communication,” IEEE Trans. Wireless Commun., vol. 18, no. 8,
pp. 4157–4170, Aug 2019.
[44] V. C. Thirumavalavan and T. S. Jayaraman, “BER analysis of recon-
figurable intelligent surface assisted downlink power domain NOMA
system,” in International Conference on COMmunication Systems &
NETworkS (COMSNETS), Jan. 2020.
[45] M. D. Renzo, K. Ntontin, J. Song, F. H. Danufane, X. Qian, F. Lazarakis,
J. de Rosny, D.-T. Phan-Huy, O. Simeone, R. Zhang, M. Debbah,
G. Lerosey, M. Fink, S. Tretyakov, and S. Shamai, “Reconfigurable in-
telligent surfaces vs. relaying: Differences, similarities, and performance
comparison,” IEEE Open Journal of the Communications Society, pp.
1–1, 2020.
[46] E. Bjornson, O. Ozdogan, and E. G. Larsson, “Intelligent reflecting
surface versus decode-and-forward: How large surfaces are needed to
beat relaying?” IEEE Wireless Commun. Lett., vol. 9, no. 2, pp. 244–
248, Feb. 2020.
>REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER <16
[47] A.-A. A. Boulogeorgos and A. Alexiou, “Performance analysis of recon-
figurable intelligent surface-assisted wireless systems and comparison
with relaying,” IEEE Access, vol. 8, pp. 94463–94 483, May 2020.
[48] ——, “How much do hardware imperfections affect the performance of
reconfigurable intelligent surface-assisted systems?” IEEE Open Journal
of the Communications Society, vol. 1, pp. 1185–1195, Aug. 2020.
[49] X. Ma, Z. Chen, W. Chen, Z. Li, Y. Chi, C. Han, and S. Li, “Joint
channel estimation and data rate maximization for intelligent reflecting
surface assisted terahertz MIMO communication systems,” IEEE Access,
vol. 8, pp. 99 565–99 581, May 2020.
[50] J. Qiao and M.-S. Alouini, “Secure transmission for intelligent reflecting
surface-assisted mmWave and terahertz systems,” IEEE Wireless Com-
mun. Lett., vol. 9, no. 10, pp. 1743–1747, Oct. 2020.
[51] K. Tekbyk, G. K. Kurt, A. R. Ekti, A. Grin, and H. Yanikomeroglu,
“Reconfigurable intelligent surface empowered terahertz communication
for leo satellite networks,” ArXiV, Jul. 2020.
[52] S. P. Maruthi, T. Panigrahi, and M. Hassan, “Improving the reliability
of pulse-based terahertz communication using intelligent reflective sur-
face,” in IEEE International Conference on Communications Workshops
(ICC Workshops). IEEE, Jun. 2020.
[53] E. N. Papasotiriou, J. Kokkoniemi, A.-A. A. Boulogeorgos,
J. Lehtom¨
aki, A. Alexiou, and M. Juntti, “A new look to 275 to
400 GHz band: Channel model and performance evaluation,” in IEEE
International Symposium on Personal, Indoor and Mobile Radio
Communications (PIMRC), Bolonia, Italy, Sep. 2018.
[54] J. Kokkoniemi, J. Lehtomki, and M. Juntti, “A line-of-sight channel
model for the 100-450 gigahertz frequency band,” arXiv, Feb. 2020.
[55] S. W. Ellingson, “Path loss in reconfigurable intelligent surface-enabled
channels,” ArXiV, Dec. 2019.
[56] W. Tang, M. Z. Chen, X. Chen, J. Y. Dai, Y. Han, M. D. Renzo,
Y. Zeng, S. Jin, Q. Cheng, and T. J. Cui, “Wireless communications with
reconfigurable intelligent surface: Path loss modeling and experimental
measurement,” ArXiV, Nov. 2019.
[57] R. Goody and Y. Yung, Atmospheric Radiation: Theoretical Basis. OUP
USA, 1995.
[58] L. S. Rothman, et al., “The HITRAN 2008 molecular spectroscopic
database,” J. Quant. Spectrosc. Radiat. Transfer, vol. 110, no. 9, pp.
533 – 572, Jun. 2009.
[59] D. Zwillinger, Standard mathematical tables and formulae. Boca Raton:
Chapman & Hall/CRC, 2003.
[60] S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther,
A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick,
C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless
sub-THz communication system with high data rate,” Nat. Photonics,
vol. 7, pp. 977 EP–, Oct. 2013.
[61] T. Nagatsuma, G. Ducournau, and C. C. Renaud, “Advances in terahertz
communications accelerated by photonics,” Nat. Photonics, vol. 10, pp.
371 EP –, May 2016.
[62] C. A. Balanis, Modern Antenna Handbook. New York, NY, USA:
Wiley-Interscience, 2008.
[63] W. Stutzman, Antenna theory and design. Hoboken, NJ: Wiley, 2013.
[64] V. S. Asadchy, M. Albooyeh, S. N. Tcvetkova, A. Diaz-Rubio, Y. Radi,
and S. A. Tretyakov, “Perfect control of reflection and refraction using
spatially dispersive metasurfaces,Physical Review B, vol. 94, no. 7,
Aug. 2016.
[65] R. Xu, H. Zhu, and J. Yuan, “Electric-field intrabody communication
channel modeling with finite-element method,” IEEE Trans. Biomed.
Eng., vol. 58, no. 3, pp. 705–712, mar 2011.
[66] R. Xu, W. C. Ng, H. Zhu, H. Shan, and J. Yuan, “Equation environment
coupling and interference on the electric-field intrabody communication
channel,” IEEE Trans. Biomed. Eng., vol. 59, no. 7, pp. 2051–2059, Jul.
2012.
[67] A. Shafie, N. Yang, and C. Han, “Multi-connectivity for indoor terahertz
communication with self and dynamic blockage,” in IEEE International
Conference on Communications (ICC), Dublin, Ireland, Jun. 2020.
[68] Z. Hossain and J. M. Jornet, “Hierarchical bandwidth modulation
for ultra-broadband terahertz communications,” in IEEE International
Conference on Communications (ICC), Shanghai, China, May 2019.
[69] C. Han and I. F. Akyildiz, “Distance-aware bandwidth-adaptive resource
allocation for wireless systems in the terahertz band,” IEEE Trans. THz
Sci. Technol., vol. 6, no. 4, pp. 541–553, Jul. 2016.
[70] J. J. Shynk, Probability, random variables, and random processes:
Theory and signal processing applications. Hoboken, New Jersey:
Wiley, 2013.
[71] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and
Products, 6th ed. New York: Academic, 2000.
Alexandros-Apostolos A. Boulogeorgos (S’11,
M’16, SM’19) was born in Trikala, Greece in 1988.
He received the Electrical and Computer Engineer-
ing (ECE) diploma degree and Ph.D. degree in
Wireless Communications from the Aristotle Uni-
versity of Thessaloniki (AUTh) in 2012 and 2016,
respectively.
From November 2012, he has been a member of
the wireless communications system group of AUTh,
working as a research assistant/project engineer in
various national and European communication and
networks projects. During 2017, he joined the information technologies
institute (ITI) at the Centre for Research & Technology Hellas (CERTH),
while, from November 2017, he has joined the Department of Digital Systems,
University of Piraeus, where he conducts research in the area of wireless
communications. Moreover, from October 2012 until September 2016, he
was a teaching assistant at the department of ECE of AUTh, whereas, from
February 2017, he serves as an adjunct professor at the Department of
ECE of the University of Western Macedonia and as an visiting lecturer
at the Department of Computer Science and Biomedical Informatics of the
University of Thessaly.
Dr. Boulogeorgos has authored and co-authored more than 60 technical
papers, which were published in scientific journals and presented at prestigious
international conferences. Furthermore, he is the holder of two (one national
and one European) patents. Likewise, he has been involved as member of
Technical Program Committees in several IEEE and non-IEEE conferences
and served as a reviewer in various IEEE journals and conferences. Dr.
Boulogeorgos was awarded with the “Distinction Scholarship Award” of
the Research Committee of AUTh for the year 2014 and was recognized
as an exemplary reviewer for IEEE Communication Letters for 2016 (top
3% of reviewers). Moreover, he was named a top peer reviewer (top 1% of
reviewers) in Cross-Field and Computer Science in the Global Peer Review
Awards 2019, which was presented by the Web of Science and Publons. His
current research interests span in the area of wireless communications and
networks with emphasis in high frequency communications, optical wireless
communications, as well as communications and digital signal processing
for biomedical applications. He is a Senior Member of the IEEE and a
member of the Technical Chamber of Greece. He is currently an Editor for
IEEE Communications Letters, and an Associate Editor for the Frontier In
Communications And Networks.
Angeliki Alexiou is a professor at the department
of Digital Systems, ICT School, University of Pi-
raeus. She received the Diploma in Electrical and
Computer Engineering from the National Technical
University of Athens in 1994 and the PhD in Elec-
trical Engineering from Imperial College of Science,
Technology and Medicine, University of London
in 2000. Since May 2009 she has been a faculty
member at the Department of Digital Systems, where
she conducts research and teaches undergraduate and
postgraduate courses in the area of Broadband Com-
munications and Advanced Wireless Technologies. Prior to this appointment
she was with Bell Laboratories, Wireless Research, Lucent Technologies,
(later Alcatel-Lucent, now NOKIA), in Swindon, UK, first as a member of
technical staff (January 1999-February 2006) and later as a Technical Manager
(March 2006-April 2009). Professor Alexiou is a co-recipient of Bell Labs
Presidents Gold Award in 2002 for contributions to Bell Labs Layered Space-
Time (BLAST) project and the Central Bell Labs Teamwork Award in 2004
for role model teamwork and technical achievements in the IST FITNESS
project. Professor Alexiou is the Chair of the Working Group on Radio
Communication Technologies and of the Working Group on High Frequencies
Radio Technologies of the Wireless World Research Forum. She is a member
of the IEEE and the Technical Chamber of Greece. Her current research
interests include radio interface for 5G systems and beyond, MIMO and high
frequencies (mmWave and THz wireless) technologies, cooperation, coordi-
nation and efficient resource management for Ultra Dense wireless networks
and machine-to-machine communications, ‘cell-less’ architectures based on
virtualization and extreme resources sharing and machine learning for wireless
systems. She is the project coordinator of the H2020 TERRANOVA project
(ict-terranova.eu) and the technical manager of H2020 ARIADNE project (ict-
ariadne.eu).
... Alternatively, due to the inherently discrete nature of the RIS elements, it is more natural to treat the RIS as a planar distribution of scatterers. The analysis can be simplified if the RIS elements are considered as point scatterers that bear the properties of conventional antennas, such as gain and directivity [28][29][30][31][32][33]. As with antennas, the local currents that induce radiation depend on the particular design of the RIS elements. ...
... By properly assigning the magnitude and phase of E t m,n , different RIS illumination conditions can be studied, e.g. illumination by plane waves, spherical waves [30][31][32][33] (see Appendix for details) or beams [34,35]. ...
... To find an equivalence between the MIMO and sheet model, the parameters in Eq.(4) and Eq.(28) must be such that, under the same illumination conditions, the received power is the same for all observation points. Often, it is assumed that R mn ≡ Γ mn and A U C ≡ l x l y [31,32]. As a result, the properties of the small radiating rectangles of the sheet model are associated with the properties of the MIMO elements via: ...
Preprint
Full-text available
A Reconfigurable Intelligent Surface (RIS) redirects and possibly modifies the properties of incident waves, with the aim to restore non-line-of-sight communication links. Composed of elementary scatterers, the RIS has been so far treated as a collection of point scatterers with properties similar to antennas in an equivalent massive MIMO communication link. Despite the discrete nature of the RIS, current design approaches often treat the RIS as a continuous radiating surface, which is subsequently discretized. Here we investigate the connection between the two approaches in an attempt to bridge the two seemingly opposite perspectives. We analytically find the factor that renders the two approaches equivalent and we demonstrate our findings with examples of RIS elements modeled as antennas with commonly used radiation patterns and properties consistent with antenna theory. The equivalence between the two theoretical approaches is analyzed with respect to design aspects of the RIS elements, such as gain and directivity, with the aim to provide insight into the observed discrepancies, the understanding of which is crucial for assessing the RIS efficiency.
... Inspired by this, a great amount of effort has been put on designing RIS that operate in the THz band [14]- [17] as well as theoretically characterizing the corresponding system performance [18]- [20]. In particular, in [14], a vanadium dioxide (VO 2 )-based multi-functional RIS was presented, while, in [15], a large-scale RIS that employs arrays of complementary metal-oxide-semiconductor (CMOS)-based chip tiles operating at 0.3 THz was reported. ...
... In [19], the authors assessed the joint impact of hardware imperfections and antenna misalignment on RIS-empowered indoor THz wireless systems. The coverage performance of RIS-empowered THz wireless systems was quantified in [20]. ...
... γ th γs 1, ξ 1 + 1, · · · , ξ L + 1 α 1 , · · · , α N , β 1 , · · · , β N , ξ 1 , · · · , ξ L , 0 , where γ th represents the SNR threshold. By applying (16) in (20), we get ...
Preprint
Full-text available
In this paper, we introduce a theoretical framework for analyzing the performance of multi-reconfigurable intelligence surface (RIS) empowered terahertz (THz) wireless systems subject to turbulence and stochastic beam misalignment. In more detail, we extract a closed-form expression for the outage probability that quantifies the joint impact of turbulence and misalignment as well as the effect of transceivers' hardware imperfections. Our results highlight the importance of accurately modeling both turbulence and misalignment when assessing the performance of multi-RIS-empowered THz wireless systems.
... Inspired by this, a great amount of effort has been put on designing RIS that operate in the THz band [14]- [17] as well as theoretically characterizing the corresponding system performance [18]- [20]. In particular, in [14], a vanadium dioxide (VO 2 )-based multi-functional RIS was presented, while, in [15], a large-scale RIS that employs arrays of complementary metal-oxide-semiconductor (CMOS)-based chip tiles operating at 0.3 THz was reported. ...
... In [19], the authors assessed the joint impact of hardware imperfections and antenna misalignment on RIS-empowered indoor THz wireless systems. The coverage performance of RIS-empowered THz wireless systems was quantified in [20]. ...
... γ th γs 1, ξ 1 + 1, · · · , ξ L + 1 α 1 , · · · , α N , β 1 , · · · , β N , ξ 1 , · · · , ξ L , 0 , where γ th represents the SNR threshold. By applying (16) in (20), we get ...
Conference Paper
Full-text available
In this paper, we introduce a theoretical framework for analyzing the performance of multi-reconfigurable intelligence surface (RIS) empowered terahertz (THz) wireless systems subject to turbulence and stochastic beam misalignment. In more detail, we extract a closed-form expression for the outage probability that quantifies the joint impact of turbulence and misalignment as well as the effect of transceivers' hardware imperfections. Our results highlight the importance of accurately modeling both turbulence and misalignment when assessing the performance of multi-RIS-empowered THz wireless systems.
... In terahertz wireless communication, the link is line-of-sight (LOS) dominant which may be blocked by random obstacles. To alleviate this adverse effect, reconfigurable intelligent surface (RIS) were introduced in terahertz wireless communication [4]- [6]. Through beam reflection, an indirect LOS link can be restored. ...
Preprint
Reconfigurable intelligent surface (RIS) can assist terahertz wireless communication to restore the fragile line-of-sight links and facilitate beam steering. Arbitrary reflection beam patterns are desired to meet diverse requirements in different applications. This paper establishes relationship between RIS beam pattern design with two-dimensional finite impulse response filter design and proposes a fast non-iterative algorithm to solve the problem. Simulations show that the proposed method outperforms baseline method. Hence, it represents a promising solution for fast and arbitrary beam pattern design in RIS-assisted terahertz wireless communication.
... In this section, we present numerical results to investigate the joint impacts of misalignment, multipath fading, channel conditions, and transceivers hardware imperfections on the outage and ergodic capacity performance of the RIS-aided THz communications. Following the practical parameters in [2], [19], [57]- [59], we set the parameters as follows: T = 27 • C, p = 101325 Pa, c = 3 × 10 8 m/s, w d /a = 6, G t = G r = 40 dBi, σ S = 0.01 m, and the number of Monte Carlo iterations is 10 6 . Figure 8 illustrates the outage probability performance versus the transmit power with d 2 = 20 m, N 0 = 0 dBW, L = 40, m ℓ,1 = 5, m ℓ,2 = 7, K ℓ,1 = 5, K ℓ,2 = 6, ∆ ℓ,1 = 0.6, ∆ ℓ,2 = 0.4, κ S = κ D = 0.1, and 2σ ℓ,1 (1 + K ℓ,1 ) = 2σ ℓ,2 (1 + K ℓ,2 ) = 20 dB (ℓ = 1, . . . ...
... By concentrating the transmission energy to radiate towards users, the receiving power and transmission coverage can be considerably improved. On the other hand, the RIS is equipped with a metamaterial surface of the integrated circuit, which can be programmed and customized to generate passive beamforming to control the reflection of the incident wave from the transmitting end to the target user and effectively bypass the barrier and increase the selection of transmission routes [223], [224]. ...
Preprint
TeraHertz (THz) band communications are envisioned as a key technology for 6G and Beyond. As a fundamental wireless infrastructure, THz communication can boost abundant promising applications. In 2014, our team published two comprehensive roadmaps for the development and progress of THz communication networks [1], [2], which helped the research community to start research on this subject afterwards. In particular, this topic became very important and appealing to the research community due to 6G wireless systems design and development in recent years. Many papers are getting published covering different aspects of wireless systems using the THz band. With this paper, our aim is looking back to the last decade and revisiting the old problems and pointing out what has been achieved in the research community so far. Furthermore, in this paper still to be investigated new research challenges for the THz band communication systems are presented by covering diverse subtopics such as from perspectives of devices, channel behavior, communication and networking problems, physical testbeds and demonstration systems. The key aspects presented in this paper will enable THz communications as a pillar of 6G and Beyond wireless systems in the next decade.
... In [59], a capacity evaluation of RIS-empowered sub-THz wireless systems was conducted. In [60], the authors assessed the joint impact of hardware imperfections and antenna misalignment on RISempowered indoor THz wireless systems, whereas the coverage performance of RIS-empowered THz wireless systems was quantified in [61]. In [62], the authors introduced a multi-RIS-empowered THz hybrid beamforming architecture and formulated the design problem of the digital and analog beamforming matrices, assuming that all the intermediate channels, between the transmitter and the receiver, experience neither fading nor misalignment. ...
Article
Full-text available
Reconfigurable intelligent surfaces (RISs) empowered high-frequency (HF) wireless systems are expected to become the supporting pillar for several reliability and data-rate hungry applications. Such systems are, however, sensitive to misalignment and atmospheric phenomena including turbulence. Most of the existing studies on the performance assessment of RIS-empowered wireless systems ignore the impact of the aforementioned phenomena. Motivated by this, the current contribution presents a theoretical framework for statistically characterizing cascaded composite turbulence and misalignment channels. More specifically, we present the probability density and cumulative distribution functions for the cascaded composite turbulence and misalignment channels. Building upon the derived analytical expressions and in order to demonstrate the applicability and importance of the extracted framework in different use case cases of interest, we present novel closed-form formulas that quantify the joint impact of turbulence and misalignment on the outage performance for two scenarios, namely cascaded multi-RIS-empowered free space optics (FSO) and terahertz (THz) wireless systems. For the aforementioned scenarios, the diversity order is extracted. In addition, we provide an insightful outage probability upper bound for a third scenario that considers parallel multi-RIS-empowered FSO systems. Our results highlight the importance of accurately modeling both turbulence and misalignment when assessing the performance of such systems.
Article
Full-text available
Information metasurfaces have become one of the research hotspots in the field of physics and information, because of the ability of manipulating electromagnetic waves. A series of research progress in the field of wireless communications based on information metasurfaces was introduced. Information metasurface can manipulate electromagnetic waves in real time and directly process digital coding information, and can further perceive, understand, even memorize, learn and recognize information, which makes it show great potential in the field of wireless communications. Firstly, the research progress of channel modeling was introduced and the channel improvement that information metasurfaces could achieve when they worked as a wireless relay. Secondly, the application of information metasurface in the new transmitter system was also introduced, which modulated the amplitude or phase of the carrier waves. Thus several simplified transmitter architectures could be realized. Thirdly, the realization of several new wireless communication systems using the information of the near field, far field and scattering field of the information metasurface was introduced. Finally, the future wireless communication based on information metasurface was summarized and prospected.
Preprint
In this paper, we study the performance of wideband terahertz (THz) communications assisted by an intelligent reflecting surface (IRS). Specifically, we first introduce a generalized channel model that is suitable for electrically large THz IRSs operating in the near-field. Unlike prior works, our channel model takes into account the spherical wavefront of the emitted electromagnetic waves and the spatial-wideband effect. We next show that conventional frequency-flat beamfocusing significantly reduces the power gain due to beam squint, and hence is highly suboptimal. More importantly, we analytically characterize this reduction when the spacing between adjacent reflecting elements is negligible, i.e., holographic reflecting surfaces. Numerical results corroborate our analysis and provide important insights into the design of future IRS-aided THz systems.
Article
Full-text available
Reconfigurable intelligent surfaces (RISs) comprised of tunable unit cells have recently drawn significant attention due to their superior capability in manipulating electromagnetic waves. In particular, RIS-assisted wireless communications have the great potential to achieve significant performance improvement and coverage enhancement in a cost-effective and energy-efficient manner, by properly programming the reflection coefficients of the unit cells of RISs. In this paper, free-space path loss models for RIS-assisted wireless communications are developed for different scenarios by studying the physics and electromagnetic nature of RISs. The proposed models, which are first validated through extensive simulation results, reveal the relationships between the free-space path loss of RIS-assisted wireless communications and the distances from the transmitter/receiver to the RIS, the size of the RIS, the near-field/far-field effects of the RIS, and the radiation patterns of antennas and unit cells. In addition, three fabricated RISs (metasurfaces) are utilized to further corroborate the theoretical findings through experimental measurements conducted in a microwave anechoic chamber. The measurement results match well with the modeling results, thus validating the proposed free-space path loss models for RIS, which may pave the way for further theoretical studies and practical applications in this field.
Article
Full-text available
Frequencies from 100 GHz to 3 THz are promising bands for the next generation of wireless communication systems because of the wide swaths of unused and unexplored spectrum. These frequencies also offer the potential for revolutionary applications that will be made possible by new thinking, and advances in devices, circuits, software, signal processing, and systems. This paper describes many of the technical challenges and opportunities for wireless communication and sensing applications above 100 GHz, and presents a number of promising discoveries, novel approaches, and recent results that will aid in the development and implementation of the sixth generation (6G) of wireless networks, and beyond. This paper shows recent regulatory and standard body rulings that are anticipating wireless products and services above 100 GHz and illustrates the viability of wireless cognition, hyper-accurate position location, sensing, and imaging. This paper also presents approaches and results that show how long distance mobile communications will be supported to above 800 GHz since the antenna gains are able to overcome air-induced attenuation, and present methods that reduce the computational complexity and simplify the signal processing used in adaptive antenna arrays, by exploiting the Special Theory of Relativity to create a cone of silence in over-sampled antenna arrays that improve performance for digital phased array antennas. Also, new results that give insights into power efficient beam steering algorithms, and new propagation and partition loss models above 100 GHz are given, and promising imaging, array processing, and position location results are presented. The implementation of spatial consistency at THz frequencies, an important component of channel modeling that considers minute changes and correlations over space, is also discussed. This paper offers the first in-depth look at the vast applications of THz wireless products and applications and provides approaches for how to reduce power and increase performance across several problem domains, giving early evidence that THz techniques are compelling and available for future wireless communications.
Article
Full-text available
The fifth generation (5G) mobile networks are envisaged to enable a plethora of breakthrough advancements in wireless technologies, providing support of a diverse set of services over a single platform. While the deployment of 5G systems is scaling up globally, it is time to look ahead for beyond 5G systems. This is mainly driven by the emerging societal trends, calling for fully automated systems and intelligent services supported by extended reality and haptics communications. To accommodate the stringent requirements of their prospective applications, which are data-driven and defined by extremely low-latency, ultra-reliable, fast and seamless wireless connectivity, research initiatives are currently focusing on a progressive roadmap towards the sixth generation (6G) networks, which are expected to bring transformative changes to this premise. In this article, we shed light on some of the major enabling technologies for 6G, which are expected to revolutionize the fundamental architectures of cellular networks and provide multiple homogeneous artificial intelligence-empowered services, including distributed communications, control, computing, sensing, and energy, from its core to its end nodes. In particular, the present paper aims to answer several 6G framework related questions: What are the driving forces for the development of 6G? How will the enabling technologies of 6G differ from those in 5G? What kind of applications and interactions will they support which would not be supported by 5G? We address these questions by presenting a comprehensive study of the 6G vision and outlining seven of its disruptive technologies, i.e., mmWave communications, terahertz communications, optical wireless communications, programmable metasurfaces, drone-based communications, backscatter communications and tactile internet, as well as their potential applications. Then, by leveraging the state-of-the-art literature surveyed for each technology, we discuss the associated requirements, key challenges, and open research problems. These discussions are thereafter used to open up the horizon for future research directions.
Conference Paper
Full-text available
We derive new expressions for the connection probability and the average ergodic capacity to evaluate the performance achieved by multi-connectivity (MC) in an indoor ultra-wideband terahertz (THz) communication system. In this system, the user is affected by both self-blockage and dynamic human blockers. We first build up a three-dimensional propagation channel in this system to characterize the impact of molecular absorption loss and the shrinking usable bandwidth nature of the ultra-wideband THz channel. We then carry out new performance analysis for two MC strategies: 1) Closest line-of-sight (LOS) access point (AP) MC (C-MC), and 2) Reactive MC (R-MC). With numerical results, we validate our analysis and show the considerable improvement achieved by both MC strategies in the connection probability. We further show that the C-MC and R-MC strategies provide significant and marginal capacity gain relative to the single connectivity strategy, respectively, and increasing the number of the user's associated APs imposes completely different affects on the capacity gain achieved by the C-MC and R-MC strategies. Additionally, we clarify that our analysis allows us to determine the optimal density of APs in order to maximize the capacity gain.
Conference Paper
Full-text available
The scarcity of spectrum resources in current wireless communication systems has sparked enormous research interest in the terahertz (THz) frequency band. This band is characterized by fundamentally different propagation properties resulting in different interference structures from what we have observed so far at lower frequencies. In this paper, we derive a new expression for the coverage probability of downlink transmission in THz communication systems within a three-dimensional (3D) environment. First, we establish a 3D propagation model which considers the molecular absorption loss, 3D directional antennas at both access points (APs) and user equipments (UEs), interference from nearby APs, and dynamic blockages caused by moving humans. Then, we develop a novel easy-to-use analytical framework based on the dominant interferer analysis to evaluate the coverage probability, the novelty of which lies in the incorporation of the instantaneous interference and the vertical height of THz devices. Our numerical results demonstrate the accuracy of our analysis and reveal that the coverage probability significantly decreases when the transmission distance increases. We also show the increasing blocker density and increasing AP density impose different impacts on the coverage performance when the UE-AP link of interest is in line-of-sight. We further show that the coverage performance improvement brought by increasing the antenna directivity at APs is higher than that brought by increasing the antenna directivity at UEs.
Article
Full-text available
This letter focuses on the secure transmission for an intelligent reflecting surface (IRS)-assisted millimeter-wave (mmWave) and terahertz (THz) systems, in which a base station (BS) communicates with its destination via an IRS, in the presence of a passive eavesdropper. To maximize the system secrecy rate, the transmit beamforming at the BS and the reflecting matrix at the IRS are jointly optimized with transmit power and discrete phase-shift constraints. It is first proved that the beamforming design is independent of the phase shift design under the rank-one channel assumption. The formulated non-convex problem is then converted into two subproblems, which are solved alternatively. Specifically, the closed-form solution of transmit beamforming at the BS is derived, and the semidefi-nite programming (SDP)-based method and element-wise block coordinate descent (BCD)-based method are proposed to design the reflecting matrix. The complexity of our proposed methods is analyzed theoretically. Simulation results reveal that the proposed IRS-assisted secure strategy can significantly boost the secrecy rate performance, regardless of eavesdropper's locations (near or blocking the confidential beam).