Physical Layer Security in RIS-assisted Networks in Fisher-Snedecor Composite Fading

Abstract

In this study, we investigate the physical layer security (PLS) of a reconfigurable intelligent surface (RIS) enabled system over generalized fading channels. The RIS concept is becoming an essential technology for the achievement of smart radio environments, where large number of passive, miniature cells, are designed to influence incident signal. Key benefits have been demonstrated for RIS-assisted PLS purposes, due
to the flexibility of simultaneously enhancing or suppressing signal beams to different users. Due to the potential of such RIS-assisted systems as reported in the literature, we study a system with a RIS-based access point for transmission, at the source node. The system is modelled with reference to a receiver transmitter pair in the presence of an eavesdropper. The Fisher-Snedecor model is adopted to analyse the composite fading and shadowing channel. Expressions are derived for the average secrecy capacity and secrecy outage probability of the network. The derived expressions can be adopted for the PLS analysis of RIS-assisted networks for several common distributions such as Rayleigh, Nakagami-m and the one-sided Gaussian distributions. The results were validated using Monte-Carlo simulations. The results indicate the clear secrecy benefit of employing a RIS enabled access point for various fading and shadowing conditions.

Full text

Physical Layer Security in RIS-assisted Networks in
Fisher-Snedecor Composite Fading
Abubakar Makarfi1,Khaled Rabie1, Omprakash Kaiwartya2, Osamah Badarneh3, Galymzhan Nauryzbayev4, Rupak Kharel1
1Faculty of Science and Engineering, Manchester Metropolitan University, UK
2School of Science and Technology, Nottingham Trent University, UK
3Electrical and Communication Engineering Department, German-Jordanian University, Jordan
4School of Engineering and Digital Sciences, Nazarbayev University, Kazakhstan
Emails:{a.makarfi, r.kharel, k.rabie}@mmu.ac.uk; omprakash.kaiwartya@ntu.ac.uk; Osamah.Badarneh@gju.edu.jo;
galymzhan.nauryzbayev@nu.edu.kz.
Abstract—In this study, we investigate the physical layer secu-
rity (PLS) of a reconfigurable intelligent surface (RIS) enabled
system over generalized fading channels. The RIS concept is
becoming an essential technology for the achievement of smart
radio environments, where large number of passive, miniature
cells, are designed to influence incident signal. Key benefits
have been demonstrated for RIS-assisted PLS purposes, due
to the flexibility of simultaneously enhancing or suppressing
signal beams to different users. Due to the potential of such
RIS-assisted systems as reported in the literature, we study a
system with a RIS-based access point for transmission, at the
source node. The system is modelled with reference to a receiver
transmitter pair in the presence of an eavesdropper. The Fisher-
Snedecor model is adopted to analyse the composite fading and
shadowing channel. Expressions are derived for the average
secrecy capacity and secrecy outage probability of the network.
The derived expressions can be adopted for the PLS analysis of
RIS-assisted networks for several common distributions such as
Rayleigh, Nakagami-m and the one-sided Gaussian distributions.
The results were validated using Monte-Carlo simulations. The
results indicate the clear secrecy benefit of employing a RIS-
enabled access point for various fading and shadowing conditions.
Index Terms—Fisher-Snedecor fading channels, physical layer
security, reconfigurable intelligent surfaces, secrecy capacity,
secrecy outage probability.
I. INT ROD UC TI ON
Recent research trends in wireless communications have
shifted towards beyond 5G capabilities, with an ambition of
ultra-high data rate transmissions up to 1 Tbps per user. This
will be possible through the efficient utilization of the extended
spectrum in the terahertz (THz) band (0.1 – 10 THz). A
consequence of this ambitious objective is the requirement for
new paradigms for transceiver architecture and computing. A
potential enabling technology in realising THz communication
is reconfigurable intelligent surfaces (RISs), also known as
reflector-arrays or intelligent walls.
The RIS concept a technology envisaged as an integral
part of next generation beyond 5G and 6G networks. The
aim is to enable a controllable smart radio environment, with
This work is a direct result of research on the European Regional Develop-
ment Fund (ERDF) Greater Manchester Cyber Foundry, which is part funded
by the ERDF.
improved coverage, spectrum efficiency and signal quality
[1], [2]. RISs have thus been defined as man-made surfaces
of electromagnetic materials that are electronically controlled
with integrated electronics and have unique wireless commu-
nication capabilities [3]. RIS-based transmission schemes have
several key features, such as full-band response, nearly passive
with dedicated energy sources, easy deployability on different
surfaces like buildings, vehicles or indoor spaces, as well as
being nearly unaffected by receiver noise [3], [4].
Several configurations have been investigated, because RISs
have the flexibility to be deployed in several shapes, locations
and sizes, from tens to hundreds of cells [3]. Also, existing
RIS-related literature have shown that while most RIS-enabled
applications are designed with the RIS as a reflector [3],
[5], some research have studied the RIS as a transmitter (or
access point) [3], [4] or RIS as a signal receiver [6]. These
configurations enable several benefits such as signal-to-noise
ratio (SNR) maximisation, improved spectral efficiency and
beamforming optimisation as discussed extensively in [3],
[4], [7]–[13]. Benefits have also been demonstrated for RIS-
assisted physical layer security (PLS) [14]–[18] purposes.
The main attraction of RIS-assisted PLS technologies is due
to the flexibility of simultaneously enhancing or suppressing
signal beams to different users [5]. It is worth noting that,
through PLS we can accomplish secure key-less transmission
by exploiting the fundamental features of the radio environ-
ment, such as noise, fading and interference. PLS in wireless
communication networks has remained an issue of importance,
more so due to the increasing shift towards inter-connected
systems. PLS has been widely studied for various network
types as reported in [19]–[24], as well as for RIS-assisted PLS
for wireless applications [5].
Inspired by the promising potential of RIS-based tech-
nologies for PLS in wireless communication networks, this
paper is therefore dedicated to studying the PLS of RIS-
enabled networks over composite fading. The Fisher-Snedecor
Fcomposite fading model was selected for the composite
analysis, because it provides accurate modeling and character-
ization of the simultaneous occurrence of multipath fading and
shadowing. Moreover, the Fisher-Snedecor Fmodel, while
being more mathematically tractable, encompasses numerous
2020 12th International Symposium on Communication Systems, Networks and Digital Signal Processing
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fading distributions of interest to wireless communications.
Special cases include the Nakagami-m(ms→ ∞), Rayleigh
(ms→ ∞, m = 1) and one-sided Gaussian distribution
(ms→ ∞, m =1
/2). Thus, a key motivation for this study.
The network model assumes a transmitter-receiver pair in the
presence of an eavesdropper. The performance of the proposed
system is evaluated in terms of the average secrecy capacity
(ASC) and the secrecy outage probability (SOP).
From the aforementioned, the main contributions of this
paper is as follows. The PLS of a RIS-assisted system is
analyzed over composite fading and shadowing. The Fisher-
Snedecor model is employed. A reference source node em-
ploys a RIS-based access point (AP) for transmission. This
allows for the derivation of expressions for the ASC and SOP
of the system. To the best of our knowledge, this is the first
analysis of PLS of a RIS-based network over composite fading
and shadowing. Closed-form expressions are derived and the
accuracy of the analysis verified with Monte Carlo simulations.
The results indicate the versatility of the derived expressions
in analysing the effects of fading and shadowing, as well as
other parameters in the network.
The paper is organised as follows. In Section II, the system
model under investigation is described. Thereafter, in Section
III, we derive expressions for efficient computation of the
ASC and SOP of the system. Lastly, in Sections IV and
V, the results are presented and main conclusions outlined,
respectively.
II. SY ST EM MO DE L
We consider a network of IoT nodes, as illustrated in Fig.
1. Each transmitter-receiver pair consists of a source node
(S) and a legitimate destination node (D) for the transmitted
information. We assume a classic Wyner’s wiretap model in
our analysis [25], such that Ssends confidential information to
D, while a passive eavesdropper1node (E) attempts to receive
and decode the confidential information. It is assumed that S
uses a RIS-based AP for trasnmission, as shown in the block
diagram. The RIS configuration allows transmission from S
without RF processing through direct wired connections (such
as with optic fibre). The system further assumes a smart AP
with full channel state information (CSI) at RIS. The RIS-
induced phases can be adjusted to maximise the received SNR
through appropriate phase cancellations and proper alignment
of reflected signals from the intelligent surface.
For a RIS consisting of Nelements, the received signal at
Dand Ecan respectively be represented as
yD="N
X
n=1
hD,ne−j φn#x+wD,(1)
yE="N
X
n=1
hE,n e−jφn#x+wE,(2)
where xrepresents the transmitted signal by Swith power
Ps, while the terms wDand wEare the respective additive
white Gaussian noise (AWGN) at Dand E. The term φnis
1We define a passive node as one that only receives the signal, but makes
no active attempt to disrupt. For e.g. through jamming.
Figure 1: Illustration of the system model with two legitimate nodes (S
and D) and one eavesdropper E.
Figure 2: RIS configured as an AP for transmission.
the reconfigurable phase induced by the nth reflector of the
RIS, which through phase matching, the SNR of the received
signals can be maximised2.
The terms hi,n =qgi,nr−β
i, i ∈ {D, E}, are the coeffi-
cients of the channel links from S, with distances ri, path-loss
exponent βand channel gain gi,n, modelled as independently
distributed Fisher-Snedecor FRVs with the following PDF
and CDF respectively [26]
f(gn)=Υng−1
nG1,1
1,1Λngn
1−msn
mn, msn>1,(3)
and
Fgn(v)=ΥnG1,2
2,2Λnv
1−msn,1
mn,0,(4)
where n∈ {1,2, . . . , N },Υn=1
Γ(mn)Γ(msn)and Λn=
mn
(msn−1)¯gn. The terms Gs,t
u,v [·]is the Meijer’s G-function [27,
Eq. (8.3.1.1)], Γ (z) = ´∞
0tz−1e−tdt is the gamma function
[28, Eq. (8.310)]and ¯gn=E[gn]is the mean of g. The
notation E[·]is the expectation operator. The terms mnand
msnare the fading and shadowing parameters of the n-th path,
respectively.
From (1) and (2), the SNRs at Dand Eare
γD=PN
n=1 Ps|hD,n |2
N0
,(5)
and
γE=PN
n=1 Ps|hE,n |2
N0
,(6)
where N0is the power spectral density of the AWGN, assumed
to be equal at both links.
2Phase cancellation methods in RIS are discussed in [4]. For brevity, details
are not reproduced here.
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III. PER FO RM AN CE ANA LYSIS
In this section, we derive analytical expressions for the ASC
and SOP of the system.
A. Average Secrecy Capacity
Here we derive expressions for the ASC of the system. The
achievable ASC is given by [29]
Cs=(CD−CE, γD> γE,
0, γD< γE,(7)
where CD=E[log2(1 + γD)] and CE=E[log2(1 + γE)]
are the average capacities of the main and eavesdropping links,
respectively. The terms γDand γDare given in (5) and (6),
while E[·]is the expectation operator.
First, we compute the average capacity at D, given by
CD=E[log2(1 + γD)]
=
∞
ˆ
0
log2 1 + Psr−β
d
N0
gD!f(gD)dgD,(8)
where gD=PN
n=1 gd,n. As can be observed, the RV gD
is a sum of independent Fisher-Snedecor Fdistributed RVs,
therefore, from (3) and [30, Eq. (7)], the PDF is given by
f(g) = 1
gB (N m, Nms)gm
NmsN m
×2F1N(m+ms), N m;Nm;−gm
Nms,(9)
where 2F1(α;β;γ;z)is the Gauss hypergeometric function
[28, Eq. (9.111)] and B(., .)is the Beta function [28, Eq.
(8.384.1)]. To proceed, we express the PDF (9) in a more
tractable form.
Using the relation B(x, y) = Γ(x)Γ(y)
Γ(x+y)[28, Eq. (8.384.1)]
and 2F1(α;β;γ;−z) = Γ(γ)z
Γ(α)Γ(β)G1,2
2,2 z
−α, −β
−1,−γ![28, Eq.
(9.34.7)] with some algebraic manipulations, the PDF in (9)
can be rewritten as
f(g) = gNm
Γ (Nm) Γ (Nms)m
NmsN m+1
×G1,2
2,2 gm
Nms
−N(m+ms),−Nm
−1,−Nm !.(10)
With the appropriate change of variables and representing
the logarithmic function in terms of the Meijer G-function with
the aid of [31, Eq. (11)], i.e.,
ln (1 + z) = G1,2
2,2hz
1,1
1,0i,(11)
we can re-express (8) as
CD=Λd
ln (2)
∞
ˆ
0
(ξdgD)NmdG1,2
2,2ηdgD
1,1
1,0
×G1,2
2,2 ξdgD
−N(md+ms,d),−Nmd
−1,−Nmd!dgD
(a)
=Λd
ln (2)
∞
ˆ
0
G1,2
2,2ηdgD
1,1
1,0
×G1,2
2,2 ξdgD
−Nms,d,0
Nmd−1,0!dgD,(12)
where (a)was obtained using [28, Eq. (9.31.5)]. Also, ξd=
md
Nms,d,ηd=Psr−β
d
N0and Λd=ξd
Γ(Nmd)Γ(N ms,d).
The integral in (12) can be evaluated using [28, Eq.
(7.811.1)], to obtain the average capacity as3
CD=Λd
ξdln (2) G3,3
4,4ηd
ξd
1−Nmd,0,1,1
Nms,d,0,1,0.(13)
Using analysis similar to the derivation of (13), the average
capacity of the eavesdropper link can be represented as
CE=Λe
ξeln (2) G3,3
4,4ηe
ξe
1−Nme,0,1,1
Nms,e,0,1,0,(14)
where ηe=Psr−β
e
N0,ηe=Psr−β
e
N0and Λe=ξe
Γ(Nme)Γ(N ms,e).
From (7), (13) and (14), the ASC can be represented as
Cs=1
ln (2) Λd
ξd
G3,3
4,4ηd
ξd
1−Nmd,0,1,1
Nms,d,0,1,0
−Λe
ξe
G3,3
4,4ηe
ξe
1−Nme,0,1,1
Nms,e,0,1,0.(15)
B. Secrecy Outage Probability
In this section, we derive analytical expressions for the SOP
in Fisher-Snedecor Fcomposite fading. The SOP is defined
as the probability that the secrecy capacity falls below a target
secrecy rate [32]. This can be represented as
Po=Pr [Cs< Rs],(16)
where Rsis the pre-determined target secrecy rate. From (7)
and (16), we obtain
Po=Pr log21 + γD
1 + γE< Rs
=Pr 1 + γD
1 + γE
<2Rs
(a)
≈Pr [γD< νγE]
'Pr [gD< νrgE],(17)
where gD=PN
n=1 gd,n,gE=PN
n=1 ge,n,νr= 2Rsrβ
dr−β
e,
while γDand γEare defined in (5) and (6) respectively. The
3Given the Meijer G-function Gs,t
u,v [x| · ], then the solution in (13) con-
verges if the first G-function in the integrand is subject to the constraint
|arg x|<s+t−1
2u−1
2vπ[28, Eq. (7.811.1)].
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line (a)in (17) follows from the approximation, 1+x
1+y'x
y
[21].4
Thus, the average SOP can be defined as
Po=
∞
ˆ
0
νrgE
ˆ
0
f(gD)f(gE)dgDdgE
=
∞
ˆ
0
FD(νrgE)f(gE)dgE,(18)
where f(gE)is the PDF of gE, defined in (10) and FD(.)is
the CDF of gD, which follows the distribution of the sum of
independent Fisher-Snedecor Fdistributed RVs. This can be
evaluated using [30, Eq. (9)] as
FD(νrgE) = Γ (Nmd+Nms,d)
Γ (1 + Nmd) Γ (Nms,d)νrgEmd
Nms,dN md
×2F1N(md+ms,d), N md; 1 + N md;−νrgEmd
Nms,d,
(19)
where it is worth noting that (19) converges if |νrgEmd
Nms,d|<1.
Using [28, Eq. (8.384.1)] and [28, Eq. (9.34.7)] with similar
algebraic manipulations to the derivation of (10), the CDF can
be rewritten as
FD(νrgE) = Λd
ξd
G1,2
2,2 νrgEξd
1−Nms,d,1
Nmd,0!,(20)
where ξd=md
Nms,dand Λd=ξd
Γ(Nmd)Γ(N ms,d).
From (10), (18) and (20), we can express the average SOP
as
Po=ΛdΛe
ξd
∞
ˆ
0
(ξegE)NmeG1,2
2,2 νrgEξd
1−Nms,d,1
Nmd,0!
×G1,2
2,2 ξegE
−N(me+ms,e),−Nme
−1,−Nme!dgE
(b)
=ΛdΛe
ξd
∞
ˆ
0
G1,2
2,2 νrgEξd
1−Nms,d,1
Nmd,0!
×G1,2
2,2 ξegE
−Nms,e,0
Nme−1,0!dgE,
(c)
=ΛdΛe
νrξdξd
G3,3
4,4ξe
νrξd
−Nmd,−Nms,e,0,0
Nms,d−1,−1, N me−1,0,
(21)
where (b)was obtained using [28, Eq. (9.31.5)] and (c)was
obtained with the aid of [28, Eq. (7.811.1)].
After further simplication with the help of [28, Eq. (9.31.1)]
and [28, Eq. (9.31.5)], we can re-write the average SOP as5
4This approximation is commonly used in the literature for such analysis
(see [21], [23] and the references therein). The approximation becomes more
accurate as x and y become larger, and is justified because the SNR for a
RIS-enabled system is maximised.
5The solution in (21) holds subject to similar constraints imposed in (13).
12345678910
Source Transmit Power, Ps
1.52
1.54
1.56
1.58
1.6
1.62
1.64
1.66
1.68
Average Secrecy Capacity
Simulation
N = 8, md = 1.5 (analytical)
N = 8, md = 5.5 (analytical)
N = 16, md = 1.5 (analytical)
N = 16, , md = 5.5 (analytical)
Figure 3: Impact of RIS-to-Dlink fading severity mdon ASC versus
source transmit power Ps, for different number of RIS cells N.
12345678910
Source Transmit Power, Ps
1.5
1.52
1.54
1.56
1.58
1.6
1.62
1.64
1.66
1.68
Average Secrecy Capacity
Simulation
N = 8, me = 1.5 (analytical)
N = 8, me = 5.5 (analytical)
N = 16, me = 1.5 (analytical)
N = 16, , me = 5.5 (analytical)
Figure 4: Impact of RIS-to-Elink fading severity meon ASC versus
source transmit power Ps, for different number of RIS cells N.
Po=ΛdΛe
ξdξe
G3,2
3,3ξe
νrξd
1−Nmd,1−Nms,e,1
Nms,d,0, N me.(22)
IV. NUM ER IC AL RE SU LTS AND DISCUSSIONS
This section discusses results of mathematical analysis from
earlier expressions derived in the paper, by studying the
effects of key system parameters. Monte Carlo simulations
are conducted on MATLAB to validate the mathematical
analysis. Unless otherwise stated, we have assumed source
power Ps= 10 W, RIS-to-Enormalized distance rE= 1 m,
RIS-to-Ddistance rD= 0.75rEand pathloss exponent β= 4
to represent a lossy environment, given the high attenuation
in higher THz frequencies [33]6.
The impact of the multipath fading parameters mdand meof
the main legitimate channel and eavesdropper’s channel on the
6Path-loss at lower LTE bands (900 MHz, 1800MHz) at a distance of 1
Km, could be experienced in 1 m for the THz spectrum.
2020 12th International Symposium on Communication Systems, Networks and Digital Signal Processing
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ASC performance is illustrated in Figs. 3 and 4, respectively. It
can be observed that the ASC improves when Psincreases for
all parameters, however, the number of RIS cells is not directly
proportional to the ASC performance when Psincreases,
because the SNR is already maximized. This means that within
the regions investigated, the fading parameters have greater
effect. In Fig. 3, we can observe that for fixed number of cells
and shadowing severity, the ASC improves as mdincreases.
This is because lower mddepicts a higher fading severity,
which in turn means that the number of multipath clusters
arriving at Dincreases, and thus, the received SNR increases.
On the other hand, in Fig. 4, we observe that the ASC increases
as the fading severity of the eavesdropper’s link increasess (i.e
fading parameter is reduced). This means that mdand megive
counter effects, though mdhas a much more positive effect on
the ASC as demonstrated by the higher secrecy rates in Fig.
3.
In Fig. 5, we study the impact of shadowing on the SOP,
where we consider two values for the shadowing parameter
of the RIS-to-Dlink i.e. ms,d= 1 (severe) and ms,d= 10
(light). It can be noted that, there is a higher probability of
outage when Nis lower, due to the lower SNR received at D.
Furthermore, for a given number of RIS cells, a more severe
shadowing effect results in a higher SOP, because of the lower
SNR received at D. Similar performance can be demonstrated
when the impact of shadowing on the eavesdropper’s link is
analyzed, although not presented for the sake of brevity.
V. CO NC LU SI ON S
In this paper, we investigated the PLS performance of a
RIS-based network over Fisher-Snedecor Fcomposite fading
and shadowing channels. Particularly, exact expressions were
derived for the ASC and SOP of the system. The results
highlight the effect of varying the severity of multipath fading
and shadowing on the secrecy performance of the system.
Specifically, the results have shown that increasing the severity
of the multipath fading in the legitimate link or the shadowing
of the eavesdropper’s link improve the secrecy performance.
REF ER EN CE S
[1] 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 J. Wireless Commun.
Netw., vol. 2019, no. 1, p. 129, May 2019. [Online]. Available:
https://doi.org/10.1186/s13638-019-1438-9
[2] C. Liaskos, S. Nie, A. Tsioliaridou, A. Pitsillides, S. Ioannidis, and
I. Akyildiz, “A new wireless communication paradigm through software-
controlled metasurfaces,” IEEE Commun. Mag., vol. 56, no. 9, pp. 162–
169, Sep. 2018.
[3] E. Basar, M. D. Renzo, J. D. Rosny, M. Debbah, M.-S. Alouini, and
R. Zhang, “Wireless communications through reconfigurable intelligent
surfaces,” IEEE Access, vol. 7, pp. 116 753–116 773, 2019.
[4] E. Basar, “Transmission Through Large Intelligent Surfaces: A New
Frontier in Wireless Communications,” in 2019 European Conf. Netw.
Commun. (EuCNC), Jun. 2019, pp. 112–117.
[5] S. Gong, X. Lu, D. T. Hoang, D. Niyato, L. Shu, D. I. Kim,
and Y.-C. Liang, “Towards smart radio environment for wire-
less communications via intelligent reflecting surfaces: A compre-
hensive survey,” arXiv:1912.07794, Dec. 2019. [online]. Available:
https://arxiv.org/abs/1912.07794.
0 0.5 1 1.5
Secrecy capacity threshold, R s
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Secrecy outage probability
Simulation
N = 8, msd = 1 (analytical)
N = 8, msd = 10 (analytical)
N = 16, msd = 1 (analytical)
N = 16, , msd = 10 (analytical)
Figure 5: Impact of RIS-to-Dlink shadowing severity ms,don SOP
versus secrecy capacity threshold, Rs, for different number of RIS cells
N.
[6] 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,” ArXiv, vol. abs/1810.05667, 2018.
[7] L. Subrt and P. Pechac, “Controlling propagation environments using
intelligent walls,” in 6th European Conf. Antennas Propag. (EUCAP),
Mar. 2012, pp. 1–5.
[8] S. Hu, F. Rusek, and O. Edfors, “Beyond Massive MIMO: The Potential
of Data Transmission With Large Intelligent Surfaces,” IEEE Trans. Sig.
Process., vol. 66, no. 10, pp. 2746–2758, May 2018.
[9] Q. Wu and R. Zhang, “Beamforming optimization for intelligent re-
flecting surface with discrete phase shifts,” in IEEE Int. Conf. Acoust.,
Speech and Sig. Process. (ICASSP), May 2019, pp. 7830–7833.
[10] ——, “Intelligent reflecting surface enhanced wireless network: Joint
active and passive beamforming design,” in IEEE Global Commun. Conf.
(GLOBECOM), Dec. 2018, pp. 1–6.
[11] X. Tan, Z. Sun, J. M. Jornet, and D. Pados, “Increasing indoor spectrum
sharing capacity using smart reflect-array,” in IEEE Int. Conf. Commun.
(ICC), May 2016, pp. 1–6.
[12] C. Huang, A. Zappone, M. Debbah, and C. Yuen, “Achievable Rate
Maximization by Passive Intelligent Mirrors,” in IEEE Int. Conf. Acoust.
Speech Sig. Process. (ICASSP), Apr. 2018, pp. 3714–3718.
[13] A. U. Makarfi, K. M. Rabie, O. Kaiwartya, O. S. Badarneh, X. Li, and
R. Kharel, “Reconfigurable intelligent surface enabled IoT networks in
generalized fading channels,” arXiv:1912.06250, Dec. 2019. [online].
Available: https://arxiv.org/abs/1912.06250.
[14] M. Cui, G. Zhang, and R. Zhang, “Secure wireless communication via
intelligent reflecting surface,” IEEE Wireless Commun. Lett., pp. 1–1,
2019.
[15] J. Chen, Y.-C. Liang, Y. Pei, and H. Guo, “Intelligent Reflecting Surface:
A Programmable Wireless Environment for Physical Layer Security,”
IEEE Access, vol. 7, pp. 82 599–82 612, 2019.
[16] X. Yu, D. Xu, and R. Schober, “Enabling secure wireless communica-
tions via intelligent reflecting surfaces,” in IEEE Global Commun. Conf.
(GLOBECOM), Dec 2019, pp. 1– 6.
[17] Z. Chu, W. Hao, P. Xiao, and J. Shi, “Intelligent reflecting surface aided
multi-antenna secure transmission,” IEEE Wireless Commun. Lett., pp.
1–1, 2019, Early Access.
[18] H. Shen, W. Xu, S. Gong, Z. He, and C. Zhao, “Secrecy rate
maximization for intelligent reflecting surface assisted multi-antenna
communications,” IEEE Commun. Lett., vol. 23, no. 9, pp. 1488–1492,
Sep. 2019.
[19] Y. Ai, M. Cheffena, A. Mathur, and H. Lei, “On Physical Layer Security
of Double Rayleigh Fading Channels for Vehicular Communications,”
IEEE Wireless Commun. Lett., vol. 7, no. 6, pp. 1038–1041, Dec. 2018.
[20] A. U. Makarfi, R. Kharel, K. M. Rabie, O. Kaiwartya, and G. Nau-
ryzbayev, “Physical Layer Security in Vehicular Communication Net-
2020 12th International Symposium on Communication Systems, Networks and Digital Signal Processing
(CSNDSP)

works in the Presence of Interference,” in IEEE Global Commun. Conf.
(GLOBECOM), Dec. 2019, pp. 1–6.
[21] A. Pandey and S. Yadav, “Physical Layer Security in Cooperative AF
Relaying Networks With Direct Links Over Mixed Rayleigh and Double-
Rayleigh Fading Channels,” IEEE Trans. Veh. Tech., vol. 67, no. 11, pp.
10 615–10 630, Nov. 2018.
[22] L. Xu, X. Yu, H. Wang, X. Dong, Y. Liu, W. Lin, X. Wang, and J. Wang,
“Physical layer security performance of mobile vehicular networks,”
Mobile Netw. Appl., pp. 1–7, Apr. 2019.
[23] A. Pandey and S. Yadav, “Performance evaluation of amplify and
forward relaying cooperative vehicular networks under physical layer
security,” Trans. Emerging Telecommun. Technol., vol. 29, no. 12, p.
e3534, Oct. 2018.
[24] A. U. Makarfi, K. M. Rabie, O. Kaiwartya, X. Li, and R. Kharel,
“Physical Layer Security in Vehicular Networks with Reconfigurable
Intelligent Surfaces,” in accepted for IEEE Veh. Technol. Conf. (VTC),
Spring 2020, pp. 1–6.
[25] H. Lei, I. S. Ansari, G. Pan, B. Alomair, and M. Alouini, “Secrecy
Capacity Analysis Over α-µFading Channels,” IEEE Commun. Lett.,
vol. 21, no. 6, pp. 1445–1448, Jun. 2017.
[26] S. K. Yoo, S. L. Cotton, P. C. Sofotasios, M. Matthaiou, M. Valkama,
and G. K. Karagiannidis, “The Fisher–Snedecor F distribution: A simple
and accurate composite fading model,” IEEE Commun. Lett., vol. 21,
no. 7, pp. 1661–1664, Jul. 2017.
[27] A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integrals, and
Series: More Special Functions, Gordon and Breach Sci. Publ., New
York, 1990, vol. 3.
[28] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and
Products. Califonia: Academic Press, 7th ed., 2007.
[29] M. Bloch, J. Barros, M. R. D. Rodrigues, and S. W. McLaughlin, “Wire-
less information-theoretic security,” IEEE Trans. Inf. Theory, vol. 54,
no. 6, pp. 2515–2534, Jun. 2008.
[30] O. S. Badarneh, D. B. da Costa, P. C. Sofotasios, S. Muhaidat, and S. L.
Cotton, “On the sum of fisher-snedecor F variates and its application to
maximal-ratio combining,” 2019.
[31] V. S. Adamchik and O. I. Marichev, “The algorithm for calculating
integrals of hypergeometric type functions and its realization in reduce
systems,” in Proc. Int. Conf. on Symbolic and Algebraic Comput., 1990,
pp. 212–224.
[32] A. Salem, K. A. Hamdi, and E. Alsusa, “Physical Layer Security
Over Correlated Log-Normal Cooperative Power Line Communication
Channels,” IEEE Access, vol. 5, pp. 13909–13 921, 2017.
[33] R. Singh and D. Sicker, “Beyond 5G: THz Spectrum Futures and
Implications for Wireless Communication,” in 30th European Conf. of
the Int. Telecommun. Society (ITS), Jun. 2019, pp. 1–30.
2020 12th International Symposium on Communication Systems, Networks and Digital Signal Processing
(CSNDSP)