Secrecy_Analysis_of_ABCom-Based_Intelligent_Transportation_Systems_With_Jamming.pdf

2880 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 25, NO. 3, MARCH 2024
Secrecy Analysis of ABCom-Based Intelligent
Transportation Systems With Jamming
Shaobo Jia , Rong Wang, Yao Xu , Yi Lou , Member, IEEE, Di Zhang , Senior Member, IEEE,
and Takuro Sato, Life Fellow, IEEE
Abstract— Employing ambient backscatter communication
(AmBC) technology in Intelligent Transportation Systems (ITS)
has emerged as an appealing solution to boost the awareness of
crosswalks. However, the AmBC-based ITS is expected to face
serious security threats due to the presence of malicious eaves-
droppers. In this paper, we investigate the secure multi-antenna
transmission in an AmBC-based ITS coexisting with a passive
eavesdropper with jamming. Specifically, a cooperative jammer
is placed in the system to deliberately disrupt the eavesdropper
without affecting the legitimate receiver. In order to characterize
the performance of the proposed scheme, new approximate
closed-form expressions of secrecy outage probability (SOP) are
derived by adopting the Gauss-Chebyshev quadrature. Addition-
ally, the asymptotic behavior of SOP at the high signal-to-noise
ratio (SNR) regime is also studied to provide more insights into
the system design. We also derive the asymptotic SOP, when
the number of transmit antennas tends to infinity. Monte Carlo
simulations are provided to demonstrate the validity of our
analytical results and to show that 1) the secrecy performance
can be significantly improved by allocating part of the transmit
power to perform cooperative jamming and 2) the optimal power
allocation factor is related to the total transmit power.
Index Terms— Intelligent transportation system, ambient
backscatter communication, physical layer security, cooperative
jamming, secrecy outage probability.
Manuscript received 31 December 2022; revised 10 February 2023;
accepted 24 February 2023. Date of publication 6 March 2023; date of
current version 18 April 2024. This work was supported in part by the
Henan Provincial Key Science and Technology Research Projects under Grant
222102210097 and Grant 212102210175, in part by the Henan Provincial
Postdoctoral Research Projects under Grant 22120005, in part by the National
Science Foundation of China (NSFC) under 62001423 and Grant 62101152,
in part by the Joint Funds of NSFC under Grant U22A2001, in part by
the Henan Key Laboratory of Network Cryptography Technology under
Grant LNCT2021-A06, in part by the Natural Science Foundation of Jiangsu
Province under Grant BK20220438, and in part by the Natural Science
Foundation of the Higher Education Institutions of Jiangsu Province under
Grant 22KJB510033. The Associate Editor for this article was S. Mumtaz.
(Corresponding author: Di Zhang.)
Shaobo Jia and Rong Wang are with the School of Electrical and Informa-
tion Engineering, Zhengzhou University, Zhengzhou 450001, China (e-mail:
ieshaobojia@zzu.edu.cn; wangrong3190@163.com).
Yao Xu is with the College of Electronic and Information Engineering,
Nanjing University of Information Science and Technology, Nanjing 210044,
China (e-mail: yaoxu@nuist.edu.cn).
Yi Lou is with the College of Information Science and Engineering,
Harbin Institute of Technology at Weihai, Weihai 264209, China (e-mail:
louyi@ieee.org).
Di Zhang is with the School of Electrical and Information Engineering,
Zhengzhou University, Zhengzhou 450001, China, and also with the Commu-
nication and Intelligent System Laboratory, School of Electrical Engineering,
Korea University, Seoul 02841, South Korea (e-mail: dr.di.zhang@ieee.org).
Takuro Sato is with the School of Fundamental Science and Engineering,
Waseda University, Tokyo 169-8555, Japan (e-mail: t-sato@waseda.jp).
Digital Object Identifier 10.1109/TITS.2023.3250427
I. INTRODUCTION
RECENTLY, empowered by the upcoming technolo-
gies such as 6G communications [1], [2], artificial
intelligence [3], big data, and other technologies, Intelli-
gent Transportation System (ITS) will significantly enhance
the robustness of wireless connectivity, enable data shar-
ing between humans and vehicles, and develop reliable
autonomous driving applications, which are considered to
be an inevitable trend in the future development of the
transportation system. Moreover, the safety of the vulnerable
traffic participants, i.e., pedestrians, cyclists, and motorcyclists,
should be of uppermost priority in the ITS [4]. To reduce
traffic-related fatalities, one appealing solution is to develop
active collision prevention systems with emergency braking
and crash reduction functions on autonomous vehicles by
carrying out timely information interaction between traffic
participants and vehicles.
The Internet of Vehicles (IoV) integrates billions of smart
devices into ITS [5], which makes it difficult, or even
impossible, to perform maintenance on the batteries of these
devices frequently. To facilitate the development of such
devices, the reliance on the batteries should be reduced or
even eliminated. In order to mitigate this challenge, ambient
backscatter communication (AmBC) can solve such problems
with ultra-low power consumption [6], [7]. In AmBC systems,
the backscatter devices utilize the existing radio-frequency
(RF) resources to transfer data among ITS entries, such as
vehicles, infrastructure Road Side Units (RSUs), and the cloud
in the IoV network [8], [9]. Therefore, AmBC can prolong the
lifetime of vehicle sensors and RSUs by reflecting the signals
that need to be transmitted, such as emergency messages,
with the help of the ubiquitous RF signals in the environment
towards intended vehicles without exploiting any oscillatory
circuity.
Despite the advantages of AmBC-based ITS, the exposed
nature of wireless channels and the widespread deployment
of tags pose great threats to network security. To mitigate
the related risks, physical layer security (PLS) that enhances
communication security from the inner by exploring the
inherent physical characteristics of physical communication
channels, which does not rely on eliminating the risks from
cryptographic analysis of attackers, is envisioned as a promis-
ing solution [10]. In the area of PLS, the pioneering work
of Wyner [11] defined the fundamental notion of secrecy
1558-0016 © 2023 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See https://www.ieee.org/publications/rights/index.html for more information.
Authorized licensed use limited to: Motilal Nehru National Institute of Technology. Downloaded on July 20,2024 at 14:14:26 UTC from IEEE Xplore. Restrictions apply.

JIA et al.: SECRECY ANALYSIS OF ABCom-BASED INTELLIGENT TRANSPORTATION SYSTEMS WITH JAMMING 2881
capacity as the difference between the main channel and the
wiretap channel, and it was proved that perfect secrecy could
be ensured when the condition of the wiretap channel is
worse than that of the main channel. Since then, a wealth
of relevant research has achieved significant success in the
security of conventional wireless communication systems [12],
[13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23].
This conception of applying artificial noise (AN) to enhance
the secure transmission was first introduced in [17], and further
studied in [18], [19], [20], [21], [22], and [23].
A. Related Works
Recently, significant work has been done on the PLS of
backscatter communication systems using AN. For instance,
the work in [24] investigated the security of backscatter
communication systems based on a single-reader single-tag
model by injecting AN to the conventional continuous wave
(CW) signal, while ignoring the Gaussian noise at the eaves-
dropper. In [25], AN-assisted-scheme was studied for secure
backscatter relaying communications. However, both systems
in [24] and [25] were considered free-space path loss channel
models, ignoring the effect of small-scale fading in real
channels. In [26], the work of [24] was extended to a more
general multiple-input multiple-output (MIMO) case, and the
energy supply power and the precoding matrix of the injected
AN were jointly optimized for secrecy rate maximization.
Different from [24], [25], and [26], Yang et al. in [27] avoided
using AN directly, but used only one randomized CW signal
at the reader to enhance security. The results showed that the
system performance in terms of secrecy rate could be greatly
improved by introducing a small variance into the CW signal.
By enhancing the backscattered signal at the intended
reader, tag selection has served as an effective way for security
enhancement in multi-tag AmBC systems [28], [29], [30],
[31]. In [28], considering the correlation between the forward
and backscatter links, an optimal tag selection scheme was
proposed for secure multi-tag backscatter communication sys-
tems. Moreover, exact and asymptotic closed-form expressions
for the SOP were derived to evaluate the secrecy performance.
In [29], a realistic scenario in which both the reader and
eavesdropper are in motion was explored in a multi-tag AmBC
system, and the influence of their movements on the system’s
secrecy performance was examined by deriving an analytical
expression of SOP. However, in [28] and [29], the fixed
reflection coefficient (RC) was considered, ignoring the power
consumed by tags. In [30], considering a practical non-linear
energy harvesting model, an adaptive power RC scheme was
proposed to maximize the power of the backscattered signal
under the energy-causality constraint of the tags. Additionally,
the optimal tag was selected for maximizing the secrecy
capacity. Based on the results in [30], the authors in [31]
further proposed a novel tag selection scheme to maximize
the ergodic security capacity and SOP simultaneously.
Analyzing system performance from the perspective of
reliability and security is also a common means of PLS [32],
[33], [34], [35]. In [32], a source-noise-assisted secure trans-
mission scheme was investigated in AmBC-assisted vehicles
and pedestrians networks by injecting AN into the RF source.
Closed-form expressions of outage probability (OP) and inter-
cept probability (IP) were derived to characterize the secrecy
performance. To go a step further, the OP and IP were
investigated in cognitive AmBC networks in [33]. To address a
more practical case, the authors in [34] conduct the reliability
and security analysis in ambient backscatter non-orthogonal
multiple access (NOMA) systems by taking the in-phase and
quadrature-phase imbalance into consideration. Extensions of
the system model in [34] to the spectrum sharing environments
were presented in [35], in which the exact and asymptotic
expressions for the OP and IP were derived.
B. Motivation and Contributions
Cooperative jamming (CJ) is an extension of the idea of AN,
which adds a cooperative node in the original communication
network to emit AN, targeting to cover up confidential infor-
mation in the presence of malicious eavesdroppers. There are
a wealth of works on PLS combined with CJ, e.g., [36],
[37], [38], and references therein. However, employing CJ
for security enhancement in AmBC systems is still in its
infancy. In related works [32], [39], source-noise-assisted
secure transmission schemes were investigated in AmBC sys-
tems. Additionally, the trade-off between security and relia-
bility were analyzed. Nevertheless, these works have not yet
addressed the secrecy outage performance analysis, which
is a key performance metric in PLS studies when lacking
the eavesdropper’s channel state information (CSI). As far
as we know, there is currently no literature considering the
use of CJ as a security enhancement scheme for AmBC
networks. Motivated by this observation, this paper studies the
secure transmission of a multi-antenna AmBC-based ITS by
utilizing CJ.
The main contributions of this work are summarized as
follows:
• We provide a novel cooperative jamming scheme for
security enhancement in AmBC-based ITS in the pres-
ence of passive eavesdropping. Different from existing
works in [32], in which the reader is forced to share
the injected AN with the RF source. In our scheme,
a cooperative jammer is placed in the system to emit AN
aiming to confound the eavesdropper without impairing
the channel quality of the legitimate receiver.
• We derive novel closed-form expressions of SOP by
employing the Gauss-Chebyshev quadrature. In order
to obtain further insights, we also present closed-form
expressions of asymptotic SOPs for the cases of high SNR
and large antenna arrays.
• Monte Carlo simulations are performed to verify the
derived expressions. It is shown that allocating part of the
power to perform cooperative jamming is an effective way
to improve the secrecy performance of the considered
system when the transmit power is relatively high. More-
over, the optimal power allocation factor for minimizing
the SOP is closely related to the total transmission power.

Fig. 1. System model for the considered AmBC-based ITS.
C. Organization and Notations
The rest of this paper is organized as follows. Section II
presents the system model. In Section III, exact and asymp-
totic SOPs for the proposed secure transmission scheme with
jamming are investigated. Numerical results are provided in
Section IV, which is followed by our conclusions in Section V.
In this paper, we denote the expectation operation by
E[·]. CN µ, σ2

denotes the Gaussian random variable with
mean µ and variance σ2. | · | denotes the absolute value
of a complex-valued scalar and Pr (·) denotes the probabil-
ity. K
k

= K!
(K−k)!k! is the binomial coefficient. FX (·) and
fX (·) denote the cumulative distribution function (CDF) and
the probability density function (PDF), respectively. 0(α) =
R ∞
0 xα−1 exp (−x)dx denotes the Gamma function. Ei (x) =
R x
−∞
eρ
ρ dρ is the exponential integral function. K1 (·) is the
first order modified Bessel function of the second kind.
II. SYSTEM MODEL
We consider an AmBC-based ITS as illustrated in Fig. 1,
including a radio frequency (RF) source (S), a reader R,
a cooperative jammer (J), a backscatter tag (T), and a pas-
sive eavesdropper (Eve). In the considered AmBC system,
S which can be the Road Side Unit (RSU) intends to transmit
confidential information to R. Specifically, R can be the
autonomous vehicle that requires emergency braking in front
of the crosswalk. In order to boost the awareness of R,
T installed near the crosswalk uses the backscatter technology
to modulate pedestrian information onto the RF signal and
send it to R. Therefore, R receives two types of signals: direct
link signal from S and the backscatter link signal from T. In the
meanwhile, Eve tries to overhear both two transmissions for
interception purposes. In order to further improve communica-
tion security, J is introduced into the system to emit AN aiming
to impair Eve’s channel. It is assumed that S is equipped with
Nt antennas, J is equipped with Nj antennas, and other nodes
are equipped with a single antenna.
As depicted in Fig. 1, hsr , hst , gtr , hse, gte and hje are
channel fading coefficients of the links of S R, S T, T R, S Eve,
T Eve and J Eve, respectively. All wireless links are assumed
to be independent Rayleigh fading, where the channel gains
are modeled as zero-mean complex Gaussian random variables
(RVs). Without loss of generality, we assume that each entry
of hi follows CN

0, 1
λi

, where i ∈ {sr, st, se, je}, and gj
follows CN

0, 1
λj

, where j ∈ {tr, te}.
Considering a passive eavesdropper, we assume that the
prior information of Eve except for the statistical information
is unavailable for all the nodes in the network. We highlight
that the statistical information is just used for facilitating our
performance analysis, not for our secure transmission design.
Notably, this assumption has been widely used in existing
works concerning on PLS, e.g., [18], [20], [37], and reference
therein.
In the AmBC-ITS, S transmits an information-bearing signal
x with E[|x|2] = 1. Simultaneously, T backscatters it to R
with its own message c, where E[|c|2] = 1. Accordingly, the
transmit signal of S is
st =
p
φPw1x, (1)
where P is the total transmit power consumed at S and J,
φ ∈ (0, 1] is the power allocation factor which represents
the fraction of transmit power allocated to S. Since hse is
not known to S, we choose the precoding vector of the
information-bearing signal x as w1 = hsr
∥hsr ∥ to maximize
the channel capacity of the direct link. In order to eliminate
the additional interference generated by J to R and T while
interfering with Eve, J adopts the zero-forcing beamforming
scheme, i.e., the conditions hjr sj = 0 and hjt sj = 0 are
satisfied. Therefore, the transmit signal of T can be designed
as
sj =
p
(1 − φ)PW2z, (2)
where W2 ∈ CNj ×(Nj −2) is the precoding matrix of the
jamming signal which lies in the null space of hjr and hjt . z
is an (Nj − 2) × 1 AN vector. Since J does not know hje, the
transmit power is distributed equally to each entry of z. That
is, all the entries of z are independently identically distributed
(i.i.d) complex RVs obeying CN

0, 1
Nj −2

.
Consequently, the received signal at R and E can be respec-
tively written as
yR =
p
φP
hH
sr
∥hsr ∥
hsr x +
p
βφP
hH
sr
∥hsr ∥
hst gtr xc + nr , (3a)
yE =
p
φP
hH
sr
∥hsr ∥
hsex +
p
(1 − φ)PWH
2 hjez
+
p
βφP
hH
sr
∥hsr ∥
hst gtexc + ne, (3b)
where β is the reflection coefficient, and nr ne ∼ CN 0, σ2

denote the additive white Gaussian noise (AWGN) at R and
E, respectively.
Similar to existing works [32], [38], [40], we consider the
ideal CSI assumption. R or Eve decodes the received signal
utilizing successive interference cancellation (SIC). R or Eve
first decodes the signal x of S and then decodes the signal
c of T. When decoding signal x, signal c will be treated as
interference. According to (3), we can obtain the signal-to-
interference-plus-noise ratios (SINRs) for R and Eve to detect

x as
γR,x =
φP∥hsr ∥2
βφP9st |gtr |2
+ σ2
, (4a)
γE,x =
φP9se
(1−φ)P
Nj −2 WH
2 hje
2
+ βφP9st |gte|2
+ σ2
, (4b)
respectively, where we have defined 9st ≜
hH
sr
∥hsr ∥ hst
2
and
9se ≜
hH
sr
∥hsr ∥ hse
2
for ease of notation.
The signal c is hidden in the signal yR. After R or Eve
successfully decodes x, using SIC, it can be subtracted from
yR. Thus, the SINR to decode c at R and Eve can be
respectively expressed by
γR,c =
βφP9st |gtr |2
σ2
, (5a)
γE,c =
βφP9st |gte|2
(1−φ)P
Nj −2 WH
2 hje
2
+ σ2
. (5b)
The instantaneous secrecy capacity can be expressed as
CS = [CR − CE ]+
=

log2 (1 + γR) − log2 (1 + γE )
+
. (6)
where [x]+ ≜ max(0, x). The SOP which is defined as the
probability that the instantaneous secrecy capacity falls below
a target secrecy rate RS (RS 0). Hence, the SOP can be
mathematically derived as
Pout = Pr(CS Rs). (7)
III. SECRECY OUTAGE PERFORMANCE ANALYSIS
In this section, we analyze the secrecy performance of the
considered system in terms of SOP. Moreover, the asymptotic
expression and diversity order of SOP in the high SNR regime
are also derived.
A. Secrecy Outage Probability for R Decodes Signal x
Substituting (4) into (7), the SOP for the S-R link can be
determined as
Pout,x = Pr γR,x εγE,x + ε − 1

= Pr
φγ ∥hsr ∥2
βφγ 9st |gtr |2
+ 1

εφγ 9se
(1−φ)γ
Nj −2 WH
2 hje
2
+ βφγ 9st |gte|2
+ 1
+ ε − 1

 ,
(8)
where we have defined ε ≜ 2RS,x for ease of notation, and
RS,x stands for the threshold of the target data rate of x.
Observing (8), we find that there are a series of RVs
involved in deriving Px
out . Therefore, it is intractable to obtain
the exact closed-form expression. To deal with this trouble-
some problem, we employ a two-layer Gaussian-Chebyshev
quadrature to obtain a new approximate closed-form expres-
sion of SOP. Then, we have the following theorem.
Theorem 1: Under the considered system, the SOP for the
S-R link is approximated as
Pout,x ≈
π4λst
16H L
L
X
l=1
q
1 − v2
l sec2
(sl)
H
X
h=1
q
1 − v2
h
× sec2
(sh) FγR,x (ε tan (sl) + ε − 1, tan (sh))
× fγE ,x (tan (sl) , tan (sh)) exp (−λst tan (sh)) , (9)
where
FγR,x (x, 9st ) = 1 − λtr
Nt −1
X
k=0
λk
sr xk
k!(φγ )k
k
X
t=0

k
t

(β9st φγ )t
× exp

−
λsr x
φγ

× (λsr xβ9st + λtr )−1−t
0 (1 + t) , (10a)
fγE ,x (x, 9st ) =
λteλseβ9st exp

−λsex
φγ

(ψx + 1)2−Nj
(λte + λseβ9st x)2
+
λse(1−φ)λte
φλje
exp

−λsex
φγ

(ψx + 1)1−Nj
λte + λseβ9st x
+
λseλte
φγ exp

− x
φγ λse

(ψx + 1)2−Nj
λte + λseβ9st x
,
(10b)
with ψ ≜ λse(1−φ)
(Nj −2)φλje
, vl = cos

(2l−1)π
2L

, sl =
π
4 (vl + 1) , vh = cos

(2h−1)π
2H

, sh = π
4 (vh + 1), L and H
are the parameters to trade off complexity and accuracy.
Proof: See Appendix A.
Corollary 1: At a high SNR regime, i.e., P
σ2 → ∞,
the asymptotic SOP for R decoding x in the considered
AmBC-ITS can be approximated as
P∞
out,x ≈ 1 + λtr
Nt −1
X
k=0
λk
sr
π2
4L
L
X
l=1
q
1 − v2
k sec2
(sk)F4 (sk)
×
λsr (−1 − k) sk
k
(λsr sk + λtr )2+k
+
ksk−1
k
(λsr sk + λtr )1+k
!
, (11)
where F4 (x) is shown as (12), at the bottom of the next page.
with a = λse(1−φ)x
λjeεφ(Nj −2)β
, b = 1 − λse(1−φ)
λjeεφ(Nj −2) (ε − 1), c =
−λsex+ελte
λseβ(ε−1) , d = ε
λseβ(ε−1) , e = x
β(ε−1) , vk = cos

(2l−1)π
2L

,
sk = 8
2 (vk + 1).
Proof: See Appendix B.
Remark 1: The results derived in (11) shows that the
expression of SOP is independent of the total transmit power P
as it goes to infinity. This signifies that there is a performance
floor when P is sufficiently large.
B. Secrecy Outage Probability for R Decodes Signal c
Substituting (5) into (7), the SOP for the S-T-R link can be
determined as
Pout,c
= Pr γR,c εγE,c + εc − 1


= Pr

βφγ 9st |gtr |2

εβφγ 9st |gte|2
(1−φ)γ
Nj −2 WH
2 hje
2
+ 1
+ ε − 1


=
Z ∞
0
Z ∞
0
Z ∞
0
F|gtr |2

 εz
(1−φ)γ
Nj −2 w + 1
+
ε − 1
βφγ x


× f|gte|2 (z) f9st (x) f WH
2 hje
2 (w) dzdxdw, (13)
where εc ≜ 2RS,c with RS,c standing for the threshold of target
date rata of c. Since 9st , |gtr |2
and |gte|2
are independently
and exponentially distributed RVs with variances 1
λst
, 1
λtr
, 1
λte
.
Then, we have theorem 2.
Theorem 2: Under the considered system, the SOP for the
S-T-R link is given by (14), as shown at the bottom of the
page, where 11 = 2
q
λst λtr (εc−1)
βφγ , 12 = (Nj −2)λjeλtr εc
(1−φ)γ λte
, 13 =

λtr εc
λte
+ 1

λje(Nj −2)
(1−φ)γ .
Proof: See Appendix C.
Remark 2: Upon using (9) and (14), we can readily obtain
the SOP for the scheme without jamming by setting φ = 1.
Corollary 2: At a high SNR regime, i.e.γ = P
σ2 → ∞, the
asymptotic result of SOP for the S-T-R link of the considered
AmBC-ITS can be expressed as (15) according to (14) by
using 0(s,x)
xs → −1
s , when x → 0.
P∞
out,c =
(
1 − 11K1 (11) ×

1 − 12 exp(13)
Nj −3

, φ ̸= 1
1 − λte
λtr ε+λte
, φ = 1
.
(15)
C. Large Antenna Array Analysis
In this subsection, we investigate the system’s asymptotic
behavior when S and J are equipped with large antenna arrays.
It is noted that for the exact SOP derived in (9) and (11),
as the number of antennas increases, the number of summa-
tions in the equations will increase rapidly, which imposes
an excessive complexity. Motivated by this, we seek good
approximations for the SOP associated with large antenna
arrays. With the aid of the theorem of large values, we have
the following approximations [18], [19], lim
Nt →∞
∥hsr ∥2
= Nt
λsr
,
lim
Nj →∞
WH
2 hje
2
=
Nj −2
λje
.
1) Asymptotic SOP for R decoding x: The following theo-
rem gives the asymptotic SOP for R decoding x.
Theorem 3: Under the considered system, as Nt and Nj
go to infinity, the asymptotic SOP for the S-R link can be
approximated as (16), shown at the bottom of the page, where
vr = cos

(2r−1)π
2R

, sr = π
4 (vt + 1), vt = cos

(2t−1)π
2T

,
st = T
2 (vt + 1), δ = λse
φγ

(1−φ)γ
λje
+ 1

, ϑ = φγ Nt
λsr ε − ε−1
ε . R
and T are the parameters to trade off complexity and accuracy.
Proof: See Appendix D.
2) Asymptotic SOP for R decoding c: The following theorem
gives the asymptotic SOP for R decoding x.
Theorem 4: Under the considered system, as Nt and Nj go
to infinity, the asymptotic SOP for the S-T-R link is given by
P
Nt ,Nj →∞
out,c = 1 −
λte
λtr εcλje
(1−φ)γ +λje
+ λte
11K1 (11) . (17)
Proof: See Appendix E.
Remark 3: The results derived in (17) show that the expres-
sion of SOP P
Nt ,Nj →∞
out,c is independent of the number of
antennas in our large antenna array analysis.This signifies that
the SOP for decoding c is hardly affected by Nt or Nj .
IV. NUMERICAL RESULTS
In this section, our numerical results are presented to
characterize the secrecy outage performance of AmBC-based
ITS. Without special instructions, the simulation parameters
used in this section are summarized in Table I. Especially,
the channel coefficients are randomly generated as Rayleigh
F4 (x) = 1 − exp(−λst e) +
λst
bNj −2
Nj −2
X
p=0

Nt − 2
p

−
a
b
p
d
p
X
h=1
(−1)h−1
−a
b + c
h
a
b
h−p
exp

aλst
b

Ei

1 − k + p,
aλst
b

−
a
b
+ e
h−p
exp

aλst
b

Ei
h
1 − h + p,
a
b
+ e

λst
i
+
1
−c + a
b
p exp (cλst ) (0 [0, cλst ] − 0 [0, (c + e) λst ])
!
.
(12)
Pout,c =
(
1 − 11K1 (11) × (1 − 12 exp (13) × 1
Nj −3
3 0 Nj − 3, 13

, φ ̸= 1
1 − λte11 K1(11)
λtr ε+λte
, φ = 1
. (14)
PNt →∞
out,x ≈ −
λteλst
λseβϑ
exp (−δϑ) exp(
λteλst
λseβϑ
)Ei(−
λteλst
λseβϑ
) +
λst π3ϑ
8RT
R
X
r=1
T
X
t=1
q
1 − v2
t
q
1 − v2
r exp

λtr
tan(sr )βφγ

sec2
(sr )
× exp

−λtr Nt
λsr β tan(sr )(εst + ε − 1)

exp(−λst tan(sr ))

λseβ tan(sr ) exp(−δst )λte
(λseβ tan(sr )st + λte)2
+
δ exp(−δst )λte
λseβ tan(sr )st + λte

. (16)

TABLE I
SIMULATION PARAMETERS
Fig. 2. The SOP versus P under two different schemes.
fading in each trial. As benchmarks, the secure transmission
schemes without jamming are also evaluated in Fig. 2 and
Fig. 3, which can be viewed as a special case of the proposed
jamming scheme when φ = 1. In this case, S only uses
beamforming for transmitting the desired signals. Specifically,
we label it as “without jamming” in these two figures. From
all these figures, it is shown that the analytical results are an
excellent match with the simulation results, which validates
the accuracy of our derivations.
Fig. 2 depicts the SOP versus the total transmit power
P under two different schemes. The curves represent the
approximate analytical SOP for decoding signals x and c
derived in (9) and (14), respectively. The asymptotic analytical
SOP for decoding signals x and c are derived in (11) and (15),
respectively. Fig. 2 confirms the close agreement between the
simulation and analytical results. For the proposed jamming
scheme, it is seen that the reduced SOP can be achieved
by increasing the total transmit power. This is because more
power can be allocated to the jamming signal to confuse
Eve as P increases. A specific observation is that a floor
effect for the proposed jamming scheme for decoding x starts
to appear when P = 25 dBm. This is because R suffers
from the interference from T, and the interference at R is
increased for a large P value. However, for R decoding x,
the interference from S can be canceled by adopting SIC, thus
Fig. 3. The SOP versus P under two different schemes with different λst .
the SOP always decreases as P increases. This phenomenon
is also confirmed by the insights in Remark 1. To illustrate
the effect of jamming on the secrecy outage probability, the
curves without jamming are also evaluated in the figure.
To be specific, the secrecy outage performance of the jamming
scheme significantly outperforms the one without jamming
when P ≥ −8 dBm. Moreover, the performance gap enlarges
as P increases, this confirms the superiority of the jamming
scheme. It can be observed from Fig. 2 that the asymptotic
curves tightly approximate the analytical curves in the high
SNR region, which confirms the correctness of our analysis.
In Fig. 3, we investigate the effect of β on the SOP with
different λst . We can observe that as expected, the SOP for R
decoding x (Pout,x ) increases as β increases, since R suffers
from more interference from the T for a larger β. On the
contrary, the SOP for R decoding c (Pout,c) decreases as β
increases. This behavior is due to the fact that T can be more
efficient in backscattering its own signal c to R for a larger β
value, leading to an enhanced S-T-R link. Another option for
enhancing the S-T-R link is to decrease λst , since it improves
the channel quality of the S-T link. A smaller λst results in
more power being employed to backscatter c, thus the SOP
for decoding x can be decreased. By contrast, the SOP for
decoding c can be increased. Additionally, the secrecy outage
performance of the proposed jamming scheme significantly
outperforms the scheme without jamming in the whole range
of β, which again indicates that allocating part of the power to
perform cooperative jamming is an efficient way to achieve a
secrecy performance improvement when higher transmit power
is available. Therefore, we will focus on evaluating the secrecy
performance of the AmBC-based ITS with jamming in the
following.
In Fig. 4, we illustrate the effect of φ on the SOP with
different λst and β. Again, we can observe that the S-T-
R link can be enhanced by increasing β or decreasing λst ,
thereby leading to an increased SOP for decoding x, or a
reduced SOP for decoding c. Thus, there exists a trade-off
between Px
out and Pc
out , and appropriate β should be designed

Fig. 4. The SOP versus φ with different λst and β.
Fig. 5. The SOP versus P with different target secrecy rates for decoding
x and c.
to satisfy diverse security requirements in practical AmBC-
based ITS. Another observation is that the SOP is not a
monotonic function of φ. This phenomenon indicates that it
is of salient significance to optimize φ, which depends on
the system parameters. In most cases, we should resort to
an exhaustive search method to obtain the optimal φ. It is
worth pointing out that adaptive power allocation design is
capable of improving the secrecy performance of the scenarios
considered [20], but this is beyond the scope of this paper.
Fig. 5 plots the SOP versus φ under different target secrecy
rates for decoding x and c. We can observe that as expected,
both the SOP for decoding x and c increase as the target
secrecy rates (RS,x and Rs,c) increase, which means that the
appropriate target secrecy rates need to be selected to improve
the secrecy performance of the systems. It is worth noting that
the optimal φ increases as the target secrecy rates increase.
This behavior indicates that more power should be allocated
to the information signal to support a larger target secrecy rate.
Fig. 6. The SOP for decoding x versus P and φ with Nt = N j = 15 and
λje = 10.
Fig. 7. The SOP versus Nt with different P.
Fig. 6 plots the SOP for decoding x versus P and φ.
It is observed that the SOP decreases as P increases with
a relatively small φ, which is in coincidence with Fig. 2.
Another special observation is that when the φ exceeds 0.7, the
SOP first decreases then increases as P increases, which is in
contrast to the traditional trend. This behavior can be explained
as follows. Both R and Eve suffer from the interference arising
from the T as inferred from (4). Accordingly, the SNRs at both
R and Eve increase as P increases and eventually converge to
different constants when P is large enough. However, when
the φ is relatively large or the channel quality of the jamming
link is bad, the interference arising from the jammer has little
impact on the SNR at Eve, then the SNR at R hits the ceiling
prior to Eve. As a result, there is a trade-off between P and the
SOP. It is worth noting that the power allocation factor φ also
affects the optimal SOP associated with different values of
P. For instance, when the transmit power is relatively low,
i.e., P ≤ −2.5 dBm, more power should be allocated to
the information-bearing signal to support the target secrecy
rate RS,x . By contrast, more power should be allocated to
the jamming signal to aiming to lower the SOP when P
−2.5 dBm.

Fig. 8. Large analysis for the SOP for decoding x versus Nt with
λse = 0.3 and RS,x = 2 bit/s/Hz.
Fig. 7 examines the effects of Nt on the SOP with different
P. It is observed that the SOP decreases as Nt increases.
This behavior is due to the plausible fact that ∥hsr ∥2
and
WH
2 hje
2
in (4) follow Gamma distributions with parameters

Nt , 1
λsr

and

Nj − 2, 1
λje

, which results in a higher SNR at
R for decoding x benefiting from the improved multi-antenna
diversity gain. However, 9st and |gtr |2
in (5) stays almost
the same. Therefore, there is little performance gain for R
decoding c with increased Nt
Fig. 8 investigates the impact of large antenna arrays on
the SOP for R decoding x parameterized by different P.
The dashed curves represent the large Nt analytical SOP,
corresponding to the results derived in (16). It is observed
that as Nt increases, the approximation used in our analysis
approaches the exact SOP. This phenomenon indicates that
when Nt is a sufficiently large number, the asymptotic SOP
derived converges to the exact values, which relaxes the
computation of the exact SOP.
V. CONCLUSION
In this paper, the secrecy performance of applying coop-
erative jamming in AmBC-ITS was examined. Specifically,
a cooperative jammer was placed in the system to deliber-
ately disrupt the eavesdropper without affecting the legitimate
receiver. New approximate closed-form expressions of SOP
were derived by adopting the Gauss-Chebyshev quadrature for
characterizing the system’s secrecy performance. Additionally,
asymptotic SOPs for the cases of high SNR and large antenna
arrays were also derived, respectively. Numerical simulations
were presented to verify the correctness of the derived expres-
sions and the superiority of the proposed jamming scheme.
It was concluded that allocating part of the power to perform
cooperative jamming is an effective way to achieve secrecy
performance improvement when the transmit power is rel-
atively high. Furthermore, optimizing the power allocation
factor between the information signal and jamming signal can
further improve the secrecy performance of the considered
system, which is our future research direction.
APPENDIX
A. Proof of Theorem 1
Proof: According to (8), Px
out can be further derived as
Pout,x =
Z ∞
0
Z ∞
0
FγR,x (εx + ε − 1, w)
× fγE,x (x, w) f9st (w) dxdw. (18)
As shown in (18), to obtain the closed-form expression of
SOP, we should characterize the CDF of γR,x and PDF of
γE,x . Mathematically, the CDF of γR,x is expressed as
FγR,x (x, 9st ) = Pr γR,x ≤ x

=
Z ∞
0
F∥hsr ∥2

xβ Ay +
x
φγ

f|gtr |2 (y) dy,
(19)
Since ∥hsr ∥2
follows a Gamma distribution with parameters

Nt , 1
λsr

, the CDF of ∥hsr ∥2
is expressed as
F∥hsr ∥2 (x) = 1 −
Nt −1
X
k=0
(λsr )k
xk
k!
exp (−λsr x) . (20)
Substituting (20) into (19) and using [41, eq. (3.351.3)],
we can readily obtain the CDF of γR,x as (10a).
According to (4b), we can obtain that CDF of γE,x as
FγE,x (x, 9st )
= Pr γE,x ≤ x

=
Z ∞
0
Z ∞
0
F9se
(1 − φ)x
Nj − 2

φ
y + βx9st z +
x
φγ
!
× f WH
2 hje
2 (y) f|gte|2 (z) dydz. (21)
Similarly, the positive RV WH
2 hje
2
follows a Gamma
distribution with parameters

Nj − 2, 1
λje

, the PDF of
WH
2 hje
2
is given by
f
WH hje
2 (y) =
λ
Nj −2
je yNj −3 exp −λje y

0 Nj − 2
. (22)
Resorting to [18], we know that 9se is an exponentially
distributed RV. Therefore, the PDF of 9se is f9se (x) =
λse exp (−λsex). Substituting (22) and f9se (x) into (21) and
utilizing [41, eq. (3.351.3)], we have
FγE ,x (x, 9st )
= 1 − exp

−
λsex
φγ

λ
Nj −2
je
0 Nj − 2

×
λte
λseβx9st + λte
Z ∞
0
exp −λje (ψx + 1) y

yNj −3
dy
= 1 − exp

−
λsex
φγ

(ψx + 1)2−Nj
λte
λseβx9st + λte
. (23)
Taking the derivation of γE,x w.r.t. x, we can readily obtain
the PDF of γE,x as (10b).

Similarly, 9st is an exponentially distributed RV. Substitut-
ing the obtained (10) and the PDF of 9st into (18), we have
Pout,x =
Z ∞
0
Z ∞
0
FγR,x (εx + ε − 1, w)
× fγE,x (x, w) λst exp (−λst w) dxdw. (24)
However, due to the high complexity of FγR,x (x, w) and
fγE,x (x, w), it is obvious that Px
out is rather cumbersome to
be solved directly in a closed form. Therefore, adopting the
variable substitution x = tan θ and x = tan ϕ, Px
out can be
reformulated as
Pout,x = sec2
(θ)sec2
(ϕ)
Z π
2
0
Z π
2
0
FγR,x (ε tan θ + ε − 1, tan ϕ)
× fγE,x (tan θ, w) λst exp (−λst tan ϕ) dθdϕ. (25)
By employing a two-layer Gaussian-Chebyshev quadrature
successively, the asymptotic result of SOP for the S-R link
can be finally attained as (9).
This completes the proof of Theorem 1.
B. Proof of Corollary 1
Proof: When γ = P
σ2 → ∞, (4) can be rewritten as
γ ∞
R,x =
∥hsr ∥2
β9st |gtr |2
,
γ ∞
E,x =
φ9se
(1−φ)
Nj −2 WH
2 hje
2
+ βφ9st |gte|2
. (26)
Substituting (26) into (7), the asymptotic SOP is derive as
P∞
out,x = Pr




1 + ∥hsr ∥2
β9st |gtr |2
1 + εφ9se
(1−φ)
N j −2 WH
2 hje
2
+βφ9st |gte|2
ε




= Pr(∥hsr ∥2
4|gtr |2
)
=
Z ∞
0
Z ∞
0
F∥hsr ∥2 (4x) f|gtr |2 (x) f4 (y) dxdy, (27)
where we have defined
4 ≜ β9st

 εφ9se
(1−φ)
Nj −2 WH
2 hje
2
+ βφ9st |gte|2
+ ε − 1


From (27), we know that to derive the closed-form expres-
sion of Px,∞
out , we should first characterize the PDF of the
positive RV 4. Mathematically, the CDF of 4 is expressed as
(28), shown at the bottom of the page, where we have defined
Z ≜ WH
2 hje
2
Substituting (22) and the PDF of 9st into 41 in (28), after
some algebraic manipulations, 41 can be further derived as
(29), shown at the bottom of the page, where (a) follows by
using [41, eq. (3.351.3)].
Utilizing the binomial theorem, 41 can be expressed as
41 = 1 +
λte
bNj −2

1 −
a
b
a
b + v
Nj −2
d
v + c
F4 (x) = Pr

9st
x
β (ε − 1)
, 9se

x
β9st
− (ε − 1)
(1−φ)
Nj −2 Z + βφ9st |gte|2
εφ


=
Z x
β(ε−1)
0
Z ∞
0
Z ∞
0
F9se



x
βv
− (ε − 1)
(1−φ)
Nj −2 z + βφvu
εφ

 fZ (z) dz f|gte|2 (u) du
| {z }
41
f9st (v) dv, (28)
41 = 1 −
λ
Nj −2
je
0 Nj − 2

Z ∞
0
Z ∞
0
exp

−λse

x
βv
− (ε − 1)
(1−φ)
Nj −2 z + βφvu
εφ

 zNj −3
exp −λjez

dz
× λte exp (−λteu) du
= 1 −
λteλ
Nj −2
je
0 Nj − 2

Z ∞
0
exp

−λse
εφ

x
βv
− (ε − 1)

(1 − φ)
Nj − 2
z

zNj −3
exp −λjez

dz
×
Z ∞
0
exp

−λseβφvu
εφ

x
βv
− (ε − 1)

exp (−λteu) du
(a)
= 1 −
λteε
λsex − λseβ (ε − 1) v + ελte
×
λse(1 − φ)
εφλje Nj − 2

x
βv
− (ε − 1)

+ 1
!2−Nj
= 1 + λte
a
v
+ b
2−Nj d
v + c
. (29)

= 1 +
dλte
bNj −2
Nt −2
X
p=0

Nj − 2
p

−
a
b

p
1
v + a
b
p
1
v + c
| {z }
42
.
(30)
Utilizing [eq.(2.102)], 42 can be represented as
42 =
p
X
h=1
(−1)h−1
−a
b + c
h
1
v + a
b
p−h+1
+
1
(−c+ a
b )p
v + c
. (31)
Substituting (31) into (30), we can obtain 41. Substituting
the obtained 41 into (28), F4 (x) can be furher derived as
F4 (x) =
Z e
0

1 +
λted
bNj −2
Nj −2
X
p=0

Nj − 2
p

−
a
b
p
×


p
X
h=1
(−1)h−1
−a
b + c
h
1
v + a
b
p−h+1
+
1
(−c+ a
b )p
v + c




× λst exp (−λst v) dv. (32)
Utilizing [41, eq. (3.462.17)], the CDF of 4 can be finally
attained as (12).
Substituting (20) into (27), P∞
out,x can be written as
P∞
out,x =
Z ∞
0
Z ∞
0

1 −
Nt −1
X
k=0
λk
sr (yx)k
k!
exp (−λsr yx)


× λsr exp (−λtr x) f4(y)dxdy
=
Z ∞
0
1 − λtr
N−1
X
k=0
λk
sr (y)k
(λsr y + λtr )1+k
!!
f4(y)dy.
(33)
Using integration by parts, P∞
out,x can be reformulated as
P∞
out,x
= 1 + λtr
Nt −1
X
k=0
λk
sr
×
Z ∞
0
F4 (x)

λsr (−1 − k) xk
(λsr x + λtr )2+k
+
kxk−1
(λsr x + λtr )1+k

dx.
(34)
Using the variable substitution x = tan θ, and employing
the Gaussian-Chebyshev quadrature successively, Px
out can be
finally given by (11).
This completes the proof of corollary 1.
C. Proof of Theorem 2
Proof:
Substituting the CDF of |gtr |2
and the PDF of |gte|2
into
(13), Pout,c can be further derived as
Pout,c =
Z ∞
0
Z ∞
0

1 − exp

−λtr (εc − 1)
βφγ x

×
λte
λtr εc
(1−φ)γ
N j −2 w+1
+ λte

× f9st (x) f WH
2 hje
2 (w) dxdw.
(35)
Then substituting the PDF of 9st into (35) and utilizing
[28, eq. (3.324.1)], we have
Pout,c
= 1 −
Z ∞
0
λst λte
λtr εc
(1−φ)γ
N j −2 w+1
+ λte
×
Z ∞
0
exp

−λtr (εc − 1)
βφγ x
− λst x

f WH
2 hje
2 (w)dxdw
= 1 −
Z ∞
0
λte11K1 (11)
λtr εc
(1−φ)γ
N j −2 w+1
+ λte
f WH
2 hje
2 (w) dw. (36)
Substituting (22) into (44), after some algebraic manipula-
tions, we have
Pout.c = 1 −
λ
Nj −2
je 11K1 (11)
0 Nj − 2

×
Z ∞
0
λte
λtr εc
(1−φ)γ
N j −2 w+1
+ λte
| {z }
K
wNj −3
exp −λjew

dw.
(37)
Subsequently, it is ready to obtain that K in (37) can be
re-expressed as
K =
λte(1−φ)γ
Nj −2 w + λte + λtr εc − λtr εc
λte(1−φ)γ
Nj −2 w + λte + λtr εc
= 1 −
λtr εc
λte(1−φ)γ
Nj −2 w + λte + λtr εc
= 1 −
Nj − 2

λtr εc
λte (1 − φ) γ
1
w + (Nj −2)(λte+λtr εc)
λte(1−φ)γ
. (38)
Substituting (38) into (37) and utilizing [28, eq. (3.383.10)],
Pout,c can be finally given by (14).
D. Proof of Theorem 3
Proof: Substituting lim
Nt →∞
∥hsr ∥2
= Nt
λsr
,
lim
Nj →∞
WH hje
2
=
Nj −2
λje
into (4), the corresponding
SNR for R decoding x
γ̃R,x =
φγ Nt
βφγ 9st |gtr |2
+ 1

λsr
,
γ̃E,x =
φγ 9se
(1−φ)γ
λje
+ βφγ 9st |gte|2
+ 1
. (39)
Similarly as we derive Px
out , the SOP for R decoding x when
Nt → ∞ can be derived as
PNt →∞
out,x =
Z ∞
0
Z ∞
0
Fγ̃R,x (εx + ε − 1, w)
× fγ̃E,x (x, w) f9st (w) dxdw. (40)

Under a given 9st , the CDF of γ̃R,x is readily derived as
Fγ̃R,x
(x, 9st ) = Pr(γ̃R,x x)
= 1 − F|gtr |2

φγ Nt
xλsr βφγ 9st
−
1
βφγ 9st

=
(
1, x φγ Nt
λsr
exp

−λtr Nt
λsr β9st x + λtr
9st βφγ

, x ≤ φγ Nt
λsr
.
(41)
Subsequently, the CDF of γ̃E,x is derived as
Fγ̃E,x (x, 9st )
= Pr(γ̃E,x x)
=
Z ∞
0
F9se

xβ9st z +
x
φγ

(1 − φ)γ
λje
+ 1

f|gte|2 (z) dz
= 1 −
λte exp (−ax)
λseβ9st x + λte
. (42)
Taking the first order of (42), we can obtain the PDF of
γ̃E,x as
fγ̃E,x
(x, 9st ) =
λseβ9st exp(−δx)λte
(λseβ9st x + λte)2
+
δ exp(−δx)λte
λseβ9st x + λte
.
(43)
Substituting (41) into (40), PNt →∞
out,x can be further derived
as
PNt →∞
out,x
=
Z ∞
0
Z ∞
ϑ
fγ̃E,x
(x, w)dx f9st (w)dw
| {z }
I1
+
Z ∞
0
Z ϑ
0
Fγ̃R,x
(εx + ε − 1, w) fγ̃E,x
(x, w)dx f9st (w)dw
| {z }
I2
.
(44)
Substituting (43) into I1 and using (42), after some alge-
braic manipulations, we have
I1 = λteλst exp (−aϑ)
Z ∞
0
exp(−λst w)dw
λseβϑw + λte
(b)
= −
λteλst
λseβϑ
exp (−aϑ) exp(
λteλst
λseβϑ
)Ei(−
λteλst
λseβϑ
), (45)
where (b) follows by using [41, eq. (3.352.4)].
Substituting (42) and (43) into I2, we have
I2 = λst
Z ∞
0
Z ϑ
0
exp

−λtr Nt
λsr βw(εx + ε − 1)
+
λtr
wβφγ

×

λseβw exp(−δx)λte
(λseβwx + λte)2
+
δ exp(−δx)λte
λseβwx + λte

× exp(−λst w)dxdw. (46)
However, due to the complex integrals involved in (46), it is
obvious that I2 is rather cumbersome to be solved directly in a
closed form. Similarly, as we derive Pout,x , using the variable
substitution w = tan ψ and employing a two-layer Gaussian-
Chebyshev quadrature successively, the asymptotic result of
I2 can be finally attained as
I2 ≈
π3ϑλst
8RT
R
X
r=1
q
1 − v2
r sec2
(sr )
T
X
t=1
q
1 − v2
t
× Fγ̃R,x
(εst + ε − 1, tan(sr )) fγ̃E,x
(st , tan(sr ))
× exp(−λst tan(sr )). (47)
Substituting (45) and (47) into (44), PNt →∞
out,x can be finally
given by (16).
E. Proof of Theorem 4
Proof: Substituting lim
Nj →∞
WH
2 hje
2
=
Nj −2
λje
into (5a),
the corresponding SNR for E decoding c is
γ Nt →∞
E,c ≈
βφγ
hH
sr
∥hsr ∥ fst
2
|gte|2
(1−φ)γ
λje
+ 1
. (48)
Substituting (48) and (5b) into (7), we have
PNt →∞
out,c
= Pr

γR,c εcγ Nt →∞
E,c + εc − 1

= Pr

βφγ 9st |gtr |2

εcβφγ 9st |gte|2
(1−φ)γ
λje
+ 1
+ εc − 1


= λteλst
Z ∞
0
Z ∞
0
F|gtr |2

εcxλje
(1 − φ)γ + λje
+
εc − 1
βφγ y

× exp (−λtex) exp (−λst y) dxdy
= 1 −
λst λte
λtr εcλje
(1−φ)γ +λje
+ λte
×
Z ∞
0
exp

−λtr (εc − 1)
βφγ x
− λst x

dx. (49)
Using [41, eq. (3.324.1)], PNt →∞
out,c is finally given by (17).
REFERENCES
[1] U. M. Malik, M. A. Javed, S. Zeadally, and S. U. Islam, “Energy-
efficient fog computing for 6G-enabled massive IoT: Recent trends
and future opportunities,” IEEE Internet Things J., vol. 9, no. 16,
pp. 14572–14594, Aug. 2022.
[2] K. M. S. Huq, S. Mumtaz, J. Rodriguez, P. Marques, B. Okyere, and
V. Frascolla, “Enhanced C-RAN using D2D network,” IEEE Commun.
Mag., vol. 55, no. 3, pp. 100–107, Mar. 2017.
[3] R. S. Peres, X. Jia, J. Lee, K. Sun, A. W. Colombo, and J. Barata,
“Industrial artificial intelligence in industry 4.0—Systematic review,
challenges and outlook,” IEEE Access, vol. 8, pp. 220121–220139, 2020.
[4] Y. Liu, M. Xiao, S. Chen, F. Bai, J. Pan, and D. Zhang, “An intelligent
edge-chain-enabled access control mechanism for IoV,” IEEE Internet
Things J., vol. 8, no. 15, pp. 12231–12241, Aug. 2021.
[5] D. Zhang, Y. Liu, L. Dai, A. K. Bashir, A. Nallanathan, and B. Shim,
“Performance analysis of FD-NOMA-based decentralized V2X sys-
tems,” IEEE Trans. Commun., vol. 67, no. 7, pp. 5024–5036, Jul. 2019.
[6] X. Lu, D. Niyato, H. Jiang, D. I. Kim, Y. Xiao, and Z. Han, “Ambient
backscatter assisted wireless powered communications,” IEEE Wireless
Commun., vol. 25, no. 2, pp. 170–177, Apr. 2018.

[7] R. Long, H. Guo, L. Zhang, and Y.-C. Liang, “Full-duplex backscatter
communications in symbiotic radio systems,” IEEE Access, vol. 7,
pp. 21597–21608, 2019.
[8] N. Van Huynh, D. T. Hoang, X. Lu, D. Niyato, P. Wang, and D. I. Kim,
“Ambient backscatter communications: A contemporary survey,” IEEE
Commun. Surveys Tuts., vol. 20, no. 4, pp. 2889–2922, 4th Quart., 2018.
[9] S. A. Busari et al., “Generalized hybrid beamforming for vehicular
connectivity using THz massive MIMO,” IEEE Trans. Veh. Technol.,
vol. 68, no. 9, pp. 8372–8383, Sep. 2019.
[10] Y. Wu, A. Khisti, C. Xiao, G. Caire, K.-K. Wong, and X. Gao,
“A survey of physical layer security techniques for 5G wireless networks
and challenges ahead,” IEEE J. Sel. Areas Commun., vol. 36, no. 4,
pp. 679–695, Apr. 2018.
[11] A. D. Wyner, “The wire-tap channel,” Bell Syst. Tech. J., vol. 54, no. 8,
pp. 1355–1387, Jan. 1975.
[12] P. K. Gopala, L. Lai, and H. El Gamal, “On the secrecy capacity of fad-
ing channels,” IEEE Trans. Inf. Theory, vol. 54, no. 10, pp. 4687–4698,
Oct. 2008.
[13] M. Bloch and J. Barros, Physical Layer Security: From Information
Theory to Security Engineering. Cambridge, U.K.: Cambridge Univ.
Press, 2011.
[14] F. Oggier and B. Hassibi, “The secrecy capacity of the MIMO wiretap
channel,” IEEE Trans. Inf. Theory, vol. 57, no. 8, pp. 4961–4972,
Aug. 2011.
[15] D. Wang et al., “Cooperative hybrid nonorthogonal multiple access-
based mobile-edge computing in cognitive radio networks,” IEEE Trans.
Cogn. Commun. Netw., vol. 8, no. 2, pp. 1104–1117, Jun. 2022.
[16] D. Wang, T. He, F. Zhou, J. Cheng, R. Zhang, and Q. Wu, “Outage-
driven link selection for secure buffer-aided networks,” Sci. China Inf.
Sci., vol. 65, no. 8, pp. 1–16, Aug. 2022.
[17] R. Negi and S. Goel, “Secret communication using artificial noise,” in
Proc. IEEE 62nd Veh. Technol. Conf., Dallas, TX, USA, Sep. 2005,
pp. 1906–1910.
[18] X. Zhou and M. R. McKay, “Secure transmission with artificial noise
over fading channels: Achievable rate and optimal power allocation,”
IEEE Trans. Veh. Technol., vol. 59, no. 8, pp. 3831–3842, Oct. 2010.
[19] Y. Liu, Z. Qin, M. Elkashlan, Y. Gao, and L. Hanzo, “Enhancing
the physical layer security of non-orthogonal multiple access in large-
scale networks,” IEEE Trans. Wireless Commun., vol. 16, no. 3,
pp. 1656–1672, Mar. 2017.
[20] S. Jia, J. Zhang, S. Chen, W. Hao, and W. Xu, “Secure multiantenna
transmission with an unknown eavesdropper: Power allocation and
secrecy outage analysis,” IEEE Trans. Inf. Forensics Security, vol. 17,
pp. 2906–2919, 2022.
[21] S. Jia, J. Zhang, D. Zhang, W. Hao, and F. Gao, “Power allocation
and outage analysis for secure MISO cognitive radio networks with an
unknown eavesdropper,” IEEE Trans. Veh. Technol., vol. 69, no. 12,
pp. 16294–16298, Dec. 2020.
[22] H.-M. Wang, T. Zheng, and X.-G. Xia, “Secure MISO wiretap channels
with multiantenna passive eavesdropper: Artificial noise vs. artificial fast
fading,” IEEE Trans. Wireless Commun., vol. 14, no. 1, pp. 94–106,
Jan. 2015.
[23] H.-M. Wang, C. Wang, D. W. K. Ng, M. H. Lee, and J. Xiao, “Artificial
noise assisted secure transmission for distributed antenna systems,” IEEE
Trans. Signal Process., vol. 64, no. 15, pp. 4050–4064, Aug. 2016.
[24] W. Saad, X. Zhou, Z. Han, and H. V. Poor, “On the physical layer secu-
rity of backscatter wireless systems,” IEEE Trans. Wireless Commun.,
vol. 13, no. 6, pp. 3442–3451, Jun. 2014.
[25] H. Song, Y. Gao, N. Sha, Q. Zhou, and F. Yao, “A distinctive method to
improve the security capacity of backscatter wireless system,” in Proc.
IEEE 2nd Adv. Inf. Technol., Electron. Autom. Control Conf. (IAEAC),
Chongqing, China, Mar. 2017, pp. 272–276.
[26] Q. Yang, H.-M. Wang, Y. Zhang, and Z. Han, “Physical layer security in
MIMO backscatter wireless systems,” IEEE Trans. Wireless Commun.,
vol. 15, no. 11, pp. 7547–7560, Nov. 2016.
[27] Q. Yang, H.-M. Wang, Q. Yin, and A. L. Swindlehurst, “Exploiting
randomized continuous wave in secure backscatter communications,”
IEEE Internet Things J., vol. 7, no. 4, pp. 3389–3403, Apr. 2020.
[28] Y. Zhang, F. Gao, L. Fan, X. Lei, and G. K. Karagiannidis, “Secure com-
munications for multi-tag backscatter systems,” IEEE Wireless Commun.
Lett., vol. 8, no. 4, pp. 1146–1149, Aug. 2019.
[29] T. S. Muratkar, A. Bhurane, P. K. Sharma, and A. Kothari, “Physical
layer security analysis in ambient backscatter communication with
node mobility and imperfect channel estimation,” IEEE Commun. Lett.,
vol. 26, no. 1, pp. 27–30, Jan. 2022.
[30] Y. Liu, Y. Ye, and R. Q. Hu, “Secrecy outage probability in backscatter
communication systems with tag selection,” IEEE Wireless Commun.
Lett., vol. 10, no. 10, pp. 2190–2194, Oct. 2021.
[31] Z. Liu, Y. Ye, X. Chu, and H. Sun, “Secrecy performance of backscatter
communications with multiple self-powered tags,” IEEE Commun. Lett.,
vol. 26, no. 12, pp. 2875–2879, Dec. 2022.
[32] M. Li, X. Yang, F. Khan, M. A. Jan, W. Chen, and Z. Han, “Improving
physical layer security in vehicles and pedestrians networks with ambient
backscatter communication,” IEEE Trans. Intell. Transp. Syst., vol. 23,
no. 7, pp. 9380–9390, Jul. 2022.
[33] X. Li et al., “Physical layer security of cognitive ambient backscatter
communications for green Internet-of-Things,” IEEE Trans. Green Com-
mun. Netw., vol. 5, no. 3, pp. 1066–1076, Sep. 2021.
[34] X. Li, M. Zhao, Y. Liu, L. Li, Z. Ding, and A. Nallanathan, “Secrecy
analysis of ambient backscatter NOMA systems under I/Q imbalance,”
IEEE Trans. Veh. Technol., vol. 69, no. 10, pp. 12286–12290, Oct. 2020.
[35] X. Li et al., “Cognitive AmBC-NOMA IoV-MTS networks with IQI:
Reliability and security analysis,” IEEE Trans. Intell. Transp. Syst.,
vol. 24, no. 2, pp. 2596–2607, Feb. 2023.
[36] G. Chen, Y. Gong, P. Xiao, and J. A. Chambers, “Physical layer network
security in the full-duplex relay system,” IEEE Trans. Inf. Forensics
Security, vol. 10, no. 3, pp. 574–583, Mar. 2015.
[37] S. Jia, J. Zhang, H. Zhao, and R. Zhang, “Relay selection for improved
security in cognitive relay networks with jamming,” IEEE Wireless
Commun. Lett., vol. 6, no. 5, pp. 662–665, Oct. 2017.
[38] X. Pang, M. Liu, N. Zhao, Y. Chen, Y. Li, and F. R. Yu, “Secrecy anal-
ysis of UAV-based mmWave relaying networks,” IEEE Trans. Wireless
Commun., vol. 20, no. 8, pp. 4990–5002, Aug. 2021.
[39] X. Li et al., “Hardware impaired ambient backscatter NOMA sys-
tems: Reliability and security,” IEEE Trans. Commun., vol. 69, no. 4,
pp. 2723–2736, Apr. 2021.
[40] S. Mumtaz, K. M. S. Huq, A. Radwan, J. Rodriguez, and R. L. Aguiar,
“Energy efficient interference-aware resource allocation in LTE-
D2D communication,” in Proc. IEEE ICC, Sydney, NSW, Australia,
Jun. 2014, pp. 282–287.
[41] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and
Products. New York, NY, USA: Academic, 2014.
Shaobo Jia received the B.S. and M.S. degrees from
the School of Underwater Acoustic Engineering,
Harbin Engineering University, China, in 2011 and
2014, respectively, and the Ph.D. degree from the
Communication Research Centre, Harbin Institute of
Technology, China, in 2019. He is currently a Lec-
turer with the School of Information Engineering,
Zhengzhou University, China. His research inter-
ests include physical layer security, cognitive radio
networks, ambient backscatter communications, and
IRS communications.
Rong Wang received the B.S. degree from the
School of Electrical and Information Engineer-
ing, Chongqing University of Technology, China,
in 2021. She is currently pursuing the M.S. degree
with the School of Electrical and Information Engi-
neering, Zhengzhou University, China. Her main
research interests include physical layer security,
cognitive radio networks, and ambient backscatter
communication.

Yao Xu received the B.E. and Ph.D. degrees in
information and communication engineering from
the Harbin Institute of Technology, Harbin, China,
in 2016 and 2021, respectively. From 2019 to 2020,
he was a Visiting Student with the Department of
Electrical and Computer Engineering, The Univer-
sity of British Columbia, Vancouver, BC, Canada.
He is currently a Lecturer with the School of Elec-
tronic and Information Engineering, Nanjing Uni-
versity of Information Science and Technology. His
research interests include non-orthogonal multiple
access, orthogonal time frequency space modulation, and cooperative com-
munication networks.
Yi Lou (Member, IEEE) received the B.S. degree
in communication engineering from Jilin University,
Jilin, China, in 2009, and the M.S. and Ph.D. degrees
in communication engineering from the Harbin Insti-
tute of Technology, Harbin, China, in 2013 and
2017, respectively. He was a Visiting Student at
The University of British Columbia, Kelowna, BC,
Canada, in 2016. From 2018 to 2022, he was an
Associate Professor with Harbin Engineering Uni-
versity. Since 2022, he has been an Associate Pro-
fessor with the College of Information Science and
Engineering, Harbin Institute of Technology at Weihai, Weihai. His research
interests include underwater communications and cooperative communica-
tions. He received the Best Poster Award from ACM WUWNet in 2021.
Di Zhang (Senior Member, IEEE) received the
Ph.D. degree (Hons.) in electrical engineering from
Waseda University, Tokyo, Japan, in 2017. He was
a Visiting Student with National Chung Hsing Uni-
versity, Taichung, Taiwan, in 2012, and a Senior
Researcher with Seoul National University, Seoul,
South Korea, from 2017 to 2018. He is currently
an Associate Professor with Zhengzhou University,
Zhengzhou, China, and a Visiting Scholar with
Korea University, Seoul. He has participated in
many international collaboration projects in wireless
communications and networking co-funded by the EU FP-7, EU Horizon
2020, Japanese Shoumushou, NICT, and Korea National Research Foundation
(NRF). His research interests include wireless communications, signal pro-
cessing, and wireless networking, especially the short packet communications
and its various applications. He was a TPC Member of various IEEE flagship
conferences, such as IEEE International Conference on Communications
(ICC), IEEE Wireless Communications and Networking Conference (WCNC),
IEEE Vehicular Technology Conference (VTC), and IEEE Consumer Com-
munications and Networking Conference (CCNC). He was a recipient of the
ITU Young Author Award in 2019 and the IEEE Outstanding Leadership
Award in 2019. He was the Chair of IEEE flagship conferences, such as
IEEE ICC and IEEE WCNC. He is an Editor of IEEE ACCESS and IET
Quantum Communication and an Area Editor of the KSII Transactions on
Internet and Information Systems. He was the Guest Editor of the IEEE
WIRELESS COMMUNICATIONS, IEEE Network, IEEE ACCESS, and IEICE
Transactions on Internet and Information Systems.
Takuro Sato (Life Fellow, IEEE) received the
Ph.D. degree in electronics engineering from Niigata
University, Niigata, Japan, in 1993. Since 1995,
he has been a Professor with the Niigata Insti-
tute of Technology, where his research focused on
code division multiple access (CDMA), orthogo-
nal frequency-division multiplexing, and personal
communication systems. In 2004, he joined Waseda
University, Tokyo, as a Professor. He has been
involved in the research on pulse code modula-
tion transmission equipment development, mobile
communications, data transmission, and digital signal processing. He has
developed the wideband CDMA system for personal communication system
and joined the PCS Standardization Committee in the USA and Japan. His
contributions are mainly in high-speed cellular modem technologies and their
international standardizations. He has authored 11 books and more than
200 articles. His current research interests include next-generation mobile
communications, wireless communications, and their global standardizations.
He is a fellow of IEICE and JSST. He is an Academician of the Engineering
Academy of Japan.

Secrecy_Analysis_of_ABCom-Based_Intelligent_Transportation_Systems_With_Jamming.pdf

More Related Content

Similar to Secrecy_Analysis_of_ABCom-Based_Intelligent_Transportation_Systems_With_Jamming.pdf (20)

Recently uploaded (20)

Secrecy_Analysis_of_ABCom-Based_Intelligent_Transportation_Systems_With_Jamming.pdf