Secrecy Performance of RIS Aided NOMA Networks

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Secrecy Performance of RIS Aided NOMA
Networks
Yingjie Pei∗, Xinwei Yue∗, Wenqiang Yi†, Yuanwei Liu†, Xuehua Li∗and Zhiguo Ding‡
∗Beijing Information Science and Technology University, Beijing, China
†Queen Mary University of London, London, UK
‡University of Manchester, Manchester, UK
Abstract—Reconfigurable intelligent surface (RIS) has been
regarded as a promising technology since it has ability to create
the favorable channel conditions. This paper investigates the
secrecy performance of RIS aided non-orthogonal multiple access
(NOMA) networks, where the internal eavesdropping scenario
is taken into consideration. More specifically, novel closed-form
and asymptotic expressions of secrecy outage probability for
the k-th user are derived. According to the analytical results,
the secrecy diversity orders at users are acquired in the high
signal-to-noise ratio region. Simulation results show that the
applying of RIS in NOMA networks can remarkably improve
the performance of secrecy outage behaviour and secrecy system
throughput compared to RIS aided orthogonal multiple access
networks.
I. INTRODUCTION
As one of pivotal technologies for the next generation
communication networks, non-orthogonal multiple access (NO-
MA) has attracted extensive attention due to its remarkable
spectral efficiency and superiority for massive connectivity
compared to orthogonal multiple access (OMA) [1–3]. The
authors of [4] investigated the performance of NOMA networks
in terms of outage probability and ergodic rate. The cooperative
NOMA scheme was survey in [5], where the nearby user
with better channel conditions was regarded as the relaying.
To ensure the secure transmission in NOMA networks. The
authors of [6] evaluated the secrecy performance of large-
scale downlink NOMA networks with the presence of an
eavesdropper (Eve). In addition, the superimposed signal is
transmitted simultaneously to all users in NOMA networks,
which makes it possible for users with poor channel condition
to wiretap others’ information as internal Eves [7]. Triggered
by this, the authors of [8] researched the secrecy performance
of unified NOMA framework by taking into account stochastic
geometry under external and internal eavesdropping scenarios.
Additionally, the secure communications of cooperative NOMA
networks was revealed in [9], where the secrecy throughput was
improved greatly.
Reconfigurable intelligent surface (RIS) has been widely
considered an effective approach to improve the reliability
of wireless communication networks [10–12]. Compared with
traditional active relaying, the authors of [13] highlighted the
achievable rate of RIS-enhanced networks. In [14], the ergodic
capacity of RIS aided single-input single-output system were
analyzed in detail. For further exploration, researchers have
dived into surveying the integrate of RIS to NOMA networks
[15–17]. The coherent phase shifting and random phase shifting
of RIS-NOMA were proposed in [18], which achieves the
tradeoff between complexity and reliability. In [19], the on-
off control scheme is proposed in NOMA networks to simply
reconfigure phase shifting elements at RIS. The ergodic rate
of RIS-NOMA for multiple users were evaluated in-depth
with imperfect/perfect successive interference cancellation in
[20], where the 1-bit scheme was utilized at RIS. Further,
the authors of [21] analyzed the required power and outage
performance by introducing continuous/discrete phase shifting
in RIS-NOMA networks with multiple antennas. In [22], the
authors synthetically investigated uplink and downlink RIS-
NOMA scenarios, where the closed-form expression of outage
probability for the cell-edge user was derived. The authors of
[23] proposed a multiple RISs-assisted NOMA scheme and
each RIS was assumed to serve a targeted user precisely.
RIS is able to be explored for ensuring the secure com-
munication of wireless networks and have been blended with
physical layer security. A RIS aided secure wireless transmis-
sion system was considered in [24], where the secrecy rate
was maximized to protect the privacy of users. In [25], the
authors evaluated secrecy performance of RIS aided multiple-
input single-output system by designing phase shift and beam-
forming. To further explore the secrecy performance of RIS-
NOMA networks, the authors of [26] focused on defending
eavesdropping by employing artificial noise. In [27] deployed
RIS to achieve higher channel gains and protect users from
vicious external Eves in NOMA networks. On this basis, further
investigation was processed in [28] to analyze the negative
effect caused by external/internal Eve on the secrecy outage
probability (SOP) as well as effective secrecy throughput of
RIS-NOMA. In [29], RIS was introduced to achieve reli-
able communication for two dead zone NOMA users with a
single/multiple-antenna base station (BS). To better understand
the benefits brought by multiple RISs, a secure NOMA trans-
mission scheme with distributed RISs was proposed in [30],
where transmitting power and phase shifters were optimized
jointly for maximal secrecy rate.
The previously mentioned theoretical literature has laid a sol-
id foundation for the comprehension of RIS-NOMA networks.
With regard to urban secure communication, the authors of [8]
highlighted the secrecy outage behaviour in an unified NOMA
network without utilizing RIS. Additionally, the authors of
[28] analyzed the secure performance of RIS-NOMA networks,

where only two users are taken into account. Inspired by the
treatises above, we specifically investigate secrecy performance
of RIS-NOMA networks, where the superimposed wireless sig-
nals are delivered from BS to multiple non-orthogonal users via
the assistance of RIS in the presence of Eves. More specifically,
the internal eavesdropping scenario is fully discussed. The on-
off control is selected to design the phase shifts of RIS because
of the finite resolution of practical IRS phase shifters.
II. SYSTEM MO DE L
A. System Descriptions
Considering a RIS-aided NOMA secure communication s-
cenario, where a base station transmits the superposed signals
to Kusers via the assistance of a RIS. For the purpose of
intuitive analysis, we assume that each node in the system is
equipped with single antenna. The RIS is mounted with M
reconfigurable reflecting elements, which can be controlled by
a programmable logic device. The complex channel coefficient
from the BS to RIS and from the RIS to k-th user are
represented by hbr ∈CM×1,hrk ∈CM×1, respectively.
Given that obstacles can scatter a great deal of radio signals
in practical urban district scenarios, all wireless links from
BS to RIS and to users are supposed to be Rayleigh fading
channels. The direct links between BS and users experience
severe attenuation, and thus the communication can be only
established through the RIS. Without loss of generality, the
cascade channel gains of BS-RIS and-users are ordered as
hH
r1Θhbr
26·· · 6hH
rk Θhbr 
26·· · 6hH
rK Θhbr 
2,
where Θ=βdiag ejθ1, ejθ2..., ejθM∈CM×Mrepresents the
reflecting parameters matrix of RIS, β∈[0,1] and θm∈[0,2π)
are the reflecting amplitude parameter and the phase shift of
the m-th reflecting element, respectively.
B. Signal Model
In RIS-NOMA communication networks, the signal streams
of users are broadcast to each user by using the superposition
coding scheme. Hence the received signal at the k-th user is
shown as
yk=hH
rk Θhbr
K

i=1 aiPsxi+nk,(1)
where xiis supposed to be unity power signal for the i-th
user, i.e., E{|xi|2}= 1. The Psis the normalized transmission
power at BS. To ensure user fairness, aidenotes the power
allocation factor of the i-th user, which meets the relationship
a1>·· · >ak>·· · >aKwith
K

i=1
ai= 1.hbr =
h1
br ·· ·hm
br ···hM
br H, where hm
br ∼ CN (0, Nbr)denotes the
complex channel coefficient between BS and the m-th reflecting
element of RIS. The hrk =h1
rk ···hm
rk ···hM
rk H, where
hm
rk ∼ CN (0, Nrk )denotes the complex channel coefficient
between the m-th reflecting element of RIS and the k-th user.
The nkdenotes the additive white Gaussian noise (AWGN)
with mean power parameter NU. The αis path loss exponent.
dbr and drk denote the distance between BS and RIS, between
RIS and the k-th user, respectively.
According to the NOMA principle, the received signal-to-
interference-plus-noise ratio (SINR) for the k-th user to detect
the g-th user information (k>g) can be given by
γk→g=ρhH
rk Θhbr
2ag
ρhH
rk Θhbr
2νg+ 1,(2)
where νg=K
i=g+1 ai,ρ=Ps
NUdenotes the transmit SNR of
channels between the BS and legitimate users.
After striking out the previous (K-1) users’ messages with
SIC, the received SINR for the K-th user to detect its own
information can be shown as
γK=ρhH
rK Θhbr 
2aK.(3)
The broadcast characteristics are capable of increasing the
susceptibility to potential eavesdropping during the propagation
of wireless signals. In the case of internal eavesdropping
scenario, the most distant user, i.e., user 1, is regarded as
an internal Eve since it has the worst channel condition.
As a result, the received signal at internal Eve is given by
yIE =hH
r1Θhbr
K

i=1
√aiPsxi+ne, where nerepresents the
AWGN of internal Eve with mean power parameter NE. In
this case, the SINR for internal Eve to detect the k-th user
information (1 <k<K) is given as follows
γIE →k=hH
r1Θhbr
2akρe
ρehH
r1Θhbr
2νk+ 1,(4)
where νk=K
i=k+1 ai,ρe=Ps
NErepresents the transmit SNR
of eavesdropping channel from BS to internal Eve.
Similarly, the SINR for internal Eve to decode the K-th user’s
information can be given by
γIE →K=hH
r1Θhbr
2aKρe.(5)
C. RIS-NOMA with On-off Control
As revealed in the aforementioned analysis, choosing an
appropriate phase shift design is pivotal to evaluating the secure
performance of RIS-NOMA networks. Hence, a typical type of
phase shift design, i.e., on-off control, is considered in this
paper, where each diagonal element of RIS is regarded as
1 (on) or 0 (off) [19, 20]. More specifically, suppose that M
=PQ, where Pand Qare both positive integers. We define
V=IP⊗1Q∈CM×Pand the p-th column of Vis denoted
by vp, where Iµdenotes a µ×µidentity matrix, 1µdenotes a
µ×1all-ones column vector and ⊗means Kronecker product.
As a result, the the cascaded Rayleigh channels hH
rk Θhbr
can be defined as Hk,hH
rk Θhbr =vH
pDrk hbr with
k= 1,2,·· · , K, where Dr k is diagonal matrices with its
diagonal elements composed from hH
rk .
With the design of on-off control, equation (2) and (3) can
be rewritten as
˜γk→g=ρ|Hk|2ag
ρ|Hk|2νg+ 1,(6)

and
˜γK=ρ|HK|2aK,(7)
respectively. For the sake of facilitating subsequent analysis,
several channel statistical formulas are derived in the following.
Lemma 1. Under the condition of on-off control, the CDF of
SINR for the k-th user to decode the g-th user’s information (1
6g6k) can be given by
F˜γk→g(x)≈κ
K−k

l=0 K−k
l(−1)l
k+l1−2
Γ (Q)
×xλ−1
(ag−νgx)
Q
2
KQxλ−1
(ag−νgx)k+l
,
(8)
where κ=K!
(K−k)!(k−1)! ,λ=ρNbrNr k,KQ(x)denotes
the modified Bessel function of the second kind and Γ (Q)
represents the gamma function with parameter Q.
Proof: See Appendix A.
Lemma 2. After striking out the previous K-1 users messages,
the CDF of SINR for the K-th user to decode its own informa-
tion can be given by
F˜γK(x)≈κ
K−k

l=0 K−k
l(−1)l
k+l
×1−2
Γ (Q)x
λaKQ
2
KQ2x
λaKk+l
.
(9)
III. SEC RE CY PERFORMANCE EVALUATIO N
In this section, the SOP is selected as a crucial metric to
evaluate the security performance of RIS-NOMA networks with
the existence of internal Eves. In order to trace the approximate
security features, secrecy diversity order is obtained in the high
SNR region according to the analytic outcomes.
A. Statistical Models for Wiretap Channels
Considering on-off control, the cascaded internal eavesdrop-
ping channels can be transformed into the following
˜γIE →k=|H1|2akρe
ρe|H1|2νkx+ 1,(10)
and
˜γIE →K=|H1|2aKρe,(11)
respectively.
Lemma 3. Under the condition of on-off control, the PDF of
SINR for the internal Eve to decode the k-th users information
is given by (12), shown at the top of next page, where p(x) =
x
(ak−νkx)ρeNbrNr1.
B. Secrecy Outage Probability
In this subsection, the closed-form and asymptotic SOP
expressions for users are obtained. We suppose that the most
distant user is regarded as the internal Eve and tends to wiretap
other users’ information. The secrecy rate for the k-th user
(k= 2,3,·· · , K) can be expressed as
CIE
k= [log2(1 + ˜γk)−log2(1 + ˜γIE →k)]+.(13)
Hence, the secrecy outage event occurs when the secrecy rate
CIE
kis less than the target secrecy rate RIE
kand the SOP
expression for the k-th user is given as follows
PIE
out,k (Rk) = P˜γk<2RIE
k(1 + ˜γI E→k)−1
=∞
0
f˜γI E→k(x)F˜γk2RIE
k(1 + x)−1dx.
(14)
Theorem 1. Under the condition of on-off control, the closed-
form expression of SOP for the internal Eve to decode infor-
mation of the k-th user is shown as,
PIE
out,k =κ
K−k

l=0 K−k
l(−1)l
k+l
×1−2
Γ (Q){u(ς)}Q
2KQ2u(ς)k+l
,(15)
where u(ς) = ςλ−1
ak−ςνkand ς= 2RI E
k1 + QNbrNr1akρe
ρeQNbrNr1νk+1 −1.
C. Secrecy Diversity Order
To gain more insights, the asymptotic performance in the
high SNR region of SOP is investigated. The secrecy diversity
order is expressed as follows
div =−lim
ρ→∞
log [Pasy
out (ρ)]
log ρ,(16)
where Pasy
out (ρ)denotes the asymptotic SOP with factor ρ. The
asymptotic behaviors for users in internal wiretap scenarios is
analyzed in the following.
Corollary 1. Under the condition of internal eavesdropping,
the asymptotic SOPs of the k-th user at the high SNR regime
for Q= 1 and Q>2 are expressed as
PIE
asy,k RIE
k=κ
k1−1
Γ (Q){1 + u(ς) ln [u(ς)]}k
,(17)
and
PIE
asy,k RIE
k=κ
kς
(Q−1) (ak−νkς)λk
,(18)
respectively.
Proof: According to [19], in the cases of Q= 1 and Q>
2,KQ(x)can be rewritten approximately as
KQ(x)≈1
x+x
2ln x
2,(19)

f˜γIE→k(x)≈κ
K−k

l=0 K−k
l(−1)l{1−2
Γ (Q)[p(x)]Q
2KQ2p(x)}k+l−1
×ak[p(x)]Q−1
Γ (Q) (ak−νkx)xp(x){KQ−12p(x)+KQ+1 2p(x)} − QKQ2p(x).(12)
and
KQ(x)≈1
2(Q−1)!
(x/2)Q−(Q−2)!
(x/2)Q−2.(20)
By substituting (15) into (19) and (20), we can obtain (17) and
(18), respectively, and the proof is completed.
Remark 1. Upon plugging (17) and (18) into (16), we see that
the secrecy diversity order becomes k which is associated with
channel ordering.
D. System Secrecy Outage Probability
In order to characterize the holistic secrecy performance
of RIS-NOMA networks, the system SOP can be defined as
follows
PIE
sys = 1 −
K

k=1 1−PIE
out,k,(21)
where PIE
out,k can be obtained from (15).
E. Delay-Limited Transmission
Given the delay-limited transmission mode, the superposed
messages are transmitted at a constant rate, which is limited
to the SOP on account of the malicious attack from Eve.
Therefore, the secrecy system throughput of RIS-NOMA net-
works under delay-limited transmission mode can be defined
as follows
RIE
T=
K

k=1 1−PIE
out,kRI E
k,(22)
where Pout,k can be acquired from (15).
TABLE I: The table of Monte Carlo simulation parameters
Average SNR of Eve ρe= 10 dB
The power allocation coefficient for users
a1= 0.6
a2= 0.3
a3= 0.1
The target secrecy rates for users RIE
k= 0.04 BPCU
k∈ {1,2,3}
The distance from BS to RIS dbr = 3 m
The distance from RIS to users
dr1= 6 m
dr2= 4 m
dr3= 2 m
IV. NUMERICAL RES ULT S
In this section, numerical results are provided to substantiate
the accuracy of theoretical expressions derived in the afore-
mentioned sections. For sake of notational simplicity, Monte
Carlo simulation parameters involved are summarized in Table
I, where BPCU is an abbreviation for bit per channel use,
and the number of Monte Carlo repetitions is 106. The path
loss exponent αis set to 2. Suppose that K= 3 and the
variances of complex channel fading coefficients are repre-
sented as Nbr =d−α
br and Nrk =d−α
rk , respectively. Without
loss of the generality, the secure performance of RIS-NOMA
and conventional OMA transmission schemes are considered
benchmarks for comparison purposes.
Fig. 1 plots the SOP versus transmitting SNR in internal
eavesdropping scenario, where M= 16 and RIE
1=RIE
2=
RIE
3= 0.04 BPCU. The analysis curves demonstrated can be
acquired by (15). Additionally, asymptotes of SOP converge
in the high SNR region based on (17) and (18), which also
confirms the correctness of derivation. It can be seen that
user 3 has a lower outage probability compared with user 2.
This is due to the fact that user 3 is equipped with higher
quality channel conditions, which gives it a greater advantage
in anti-eavesdropping. Furthermore, we can also observe that
the secrecy outage behaviours of users are becoming worse
since the setup of on-off control varies from P= 2, Q= 8 to
P=Q= 4. The reason is that a smaller value of Qmeans
fewer elements at RIS are set to 1 (on) for arbitrary vpand the
channel gains for users are degraded because of the reduction
of working elements.
Fig. 2 plots the system SOP versus power allocation with
fixed transmitting SNR under internal eavesdropping scenarios,
where ρ= 10 dB, M= 16, P= 2, Q= 8 and RIE
1=RIE
2=
0.04 BPCU. Note that we consider a pair of users (K= 2) in
RIS-NOMA networks while the power allocation coefficients
for user 1 and user 2 are set as a1=aTand a2= 1 −aT,
where aTpresents the power offset parameter ranging from
0 to 1, i.e., aT∈[0,1]. It can be seen from this figure that
as the value of aTincreases, the secrecy outage behaviours
of RIS-NOMA networks become worse seriously. This can be
explained that user 1 with poor channel conditions is regarded
as an internal Eve, and allocating more power to user 1 can
inevitably strengthen its eavesdropping ability while weakening
the received signal quality of another user, thus reducing the
system SOP.
Fig. 3 plots the secrecy system throughput versus SNR in
delay-limited transmission mode under internal eavesdropping
case, where ρe= 10 dB, M= 16, P= 2 and Q= 8.

-10 0 10 20 30 40
SNR (dB)
10-6
10-4
10-2
100
Secrecy outage probability
Simulation
Asymptotic
RIS-OMA
User2-Exact analysis
User3-Exact analysis
P = 2, Q = 8
P = 4, Q = 4
Fig. 1: SOP versus transmit SNR under internal eavesdropping
scenario, with M= 16, P= 2, Q= 8, ρe= 10 dB, RIE
1=
RIE
2=RIE
3= 0.04 and RIE
OM A = 0.12 BPCU.
Fig. 2: System SOP versus power allocation with fixed trans-
mitting SNR under internal eavesdropping scenario, where ρe
= 10 dB, RIE
1=RIE
2= 0.04 BPCU, M= 16, P= 2 and Q=
8.
The analysis curves of secrecy system throughput for RIS-
NOMA are plotted according to (15). As can be observed from
the figure, the improvement of secrecy system throughput is
achieved by increasing the target secrecy rate. This is because
that larger amounts of data stream can be transmitted with
a higher default value of target secrecy rate as long as no
secrecy outage occurs in RIS-NOMA networks. Considering
the secrecy outage behaviors are becoming worse when larger
target secrecy rate is applied in RIS-NOMA networks [28],
there exists a tradeoff to balance the performance of SOP and
secrecy system throughput.
0 10 20 30 40 50
SNR (dB)
0
0.1
0.2
0.3
0.4
0.5
Secrecy system throughput
Asymptotic
RIS-OMA
SST-IE-pSIC
R1
IE=0.08, R2
IE=0.17, R3
IE=0.25 BPCU
R1
IE=0.08, R2
IE=0.08, R3
IE=0.15 BPCU
Fig. 3: Secrecy system throughput versus transmitting SNR for
RIS-NOMA under internal eavesdropping case, where ρe= 10
dB and M= 16.
V. CONCLUSION
In this paper, the secrecy performance of RIS-NOMA net-
works were investigated with on-off control. New closed-form
and asymptotic expressions of SOP for the k-th user were
derived in RIS-NOMA networks. On this basis, the secrecy
diversity order of the k-th user was acquired which can be
determined by the channel ordering. Referring to the analytical
results, it was shown that the RIS-NOMA networks can obtain
a superior secrecy outage behavior compared with RIS-OMA.
Furthermore, the expressions of secrecy system throughput
in delay-limited transmission mode were derived. The results
showed that the throughput performance of RIS-NOMA is
much greater than that of RIS-OMA communication schemes.
APPENDIX A: PROO F OF LE MM A 1
The SINR for the k-th user to decode the g-th user’s
information is shown as ˜γk→g=ρ|Hk|2ag
ρ|Hk|2νg+1 . Hence, the CDF
of ˜γk→gis given by
F˜γk→g(x) = P(˜γk→g< x)
=Pρ|Hk|2ag
ρ|Hk|2νg+ 1 < x
=F|Hk|2x
(ag−νgx)ρ,(A.1)
The PDF of the cascaded channels from BS to RIS and to users
can be expressed as follows [31]
f|Hk|2(z) = 2zQ−1
2
Γ (Q)√NbrNr kQ+1 KQ−12z
NbrNr k .
(A.2)

Applying integration operation and some simple manipulations
to (A.2), it can be rewritten as
F|Hk|2(z) = 4
Γ (Q)z
NbrNr k Q+1
2
×1
0
yQKQ−12z
NbrNr k
ydy. (A.3)
According to [32, Eq. (6.561.8)], F|Hk|2(z)can be further
rewritten as
F|Hk|2(z) = 1 −2
Γ (Q)z
NbrNr k Q
2
KQ2z
NbrNr k .
(A.4)
Considering hH
r1Θhbr
26·· · 6hH
rk Θhbr 
26·· · 6
hH
rK Θhbr 
2, the CDF of cascaded channel with order is given
by [33, 34]
FORD
|Hk|2(z) = κ
K−k

l=0 K−k
l(−1)l
k+l
×1−2
Γ (Q)z
NbrNr k Q
2
KQ2z
NbrNr k k+l
.
(A.5)
By substituting (A.5) into (A.1), we obtain (8) and the proof
is completed.
REF ER EN CE S
[1] L. Dai, B. Wang, Y. Yuan, S. Han, I. Chih-lin, and Z. Wang, “Non-
orthogonal multiple access for 5G: solutions, challenges, opportunities,
and future research trends,” IEEE Commun. Mag., vol. 53, no. 9, pp.
74–81, Sep. 2015.
[2] Y. Liu, Z. Qin, M. Elkashlan, Z. Ding, A. Nallanathan, and L. Hanzo,
“Nonorthogonal multiple access for 5G and beyond,” Proc. IEEE, vol.
105, no. 12, pp. 2347–2381, Dec. 2017.
[3] X. You, C.-X. Wang, J. Huang, X. Gao, Z. Zhang, M. Wang, Y. Huang,
C. Zhang, Y. Jiang, J. Wang et al., “Towards 6G wireless communication
networks: Vision, enabling technologies, and new paradigm shifts,” SCI
CHINA INFORM SCI, vol. 64, no. 1, pp. 1–74, 2021.
[4] Z. Ding, Z. Yang, P. Fan, and H. V. Poor, “On the performance of non-
orthogonal multiple access in 5G systems with randomly deployed users,”
IEEE Signal Process. Lett., vol. 21, no. 12, pp. 1501–1505, Dec. 2014.
[5] X. Yue, Y. Liu, S. Kang, A. Nallanathan, and Z. Ding, “Exploiting
full/half-duplex user relaying in NOMA systems,” IEEE Trans. Commun.,
vol. 66, no. 2, pp. 560–575, Feb. 2018.
[6] 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.
[7] Z. Ding, Z. Zhao, M. Peng, and H. V. Poor, “On the spectral efficiency and
security enhancements of NOMA assisted multicast-unicast streaming,”
IEEE Trans. Commun., vol. 65, no. 7, pp. 3151–3163, Jul. 2017.
[8] X. Yue, Y. Liu, Y. Yao, X. Li, R. Liu, and A. Nallanathan, “Secure
communications in a unified non-orthogonal multiple access framework,”
IEEE Trans. Wireless Commun., vol. 19, no. 3, pp. 2163–2178, Mar. 2020.
[9] B. Su, W. Yu, H. Liu, A. Chorti, and H. V. Poor, “Secure transmission
design for cooperative NOMA in the presence of internal eavesdropping,”
IEEE Wireless Commun. Lett., to appear in 2022.
[10] Q. Wu and R. Zhang, “Intelligent reflecting surface enhanced wireless
network via joint active and passive beamforming,” IEEE Trans. Wireless
Commun., vol. 18, no. 11, pp. 5394–5409, Nov. 2019.
[11] ——, “Towards smart and reconfigurable environment: Intelligent reflect-
ing surface aided wireless network,” IEEE Commun. Mag., vol. 58, no. 1,
pp. 106–112, Jan. 2020.
[12] Q. Wu, S. Zhang, B. Zheng, C. You, and R. Zhang, “Intelligent reflecting
surface-aided wireless communications: A tutorial,” IEEE Trans. Com-
mun., vol. 69, no. 5, pp. 3313–3351, May 2021.
[13] Y. Yang, B. Zheng, S. Zhang, and R. Zhang, “Intelligent reflecting surface
meets OFDM: Protocol design and rate maximization,” IEEE Trans.
Commun., vol. 68, no. 7, pp. 4522–4535, Jul. 2020.
[14] T. Van Chien, L. T. Tu, S. Chatzinotas, and B. Ottersten, “Coverage
probability and ergodic capacity of intelligent reflecting surface-enhanced
communication systems,” IEEE Commun. Lett., vol. 25, no. 1, pp. 69–73,
2021.
[15] B. Zheng, Q. Wu, and R. Zhang, “Intelligent reflecting surface-assisted
multiple access with user pairing: NOMA or OMA?” IEEE Commun.
Lett., vol. 24, no. 4, pp. 753–757, Apr. 2020.
[16] J. Zuo, Y. Liu, Z. Qin, and N. Al-Dhahir, “Resource allocation in
intelligent reflecting surface assisted NOMA systems,” IEEE Trans.
Commun., vol. 68, no. 11, pp. 7170–7183, Nov. 2020.
[17] Y. Guo, Z. Qin, Y. Liu, and N. Al-Dhahir, “Intelligent reflecting surface
aided multiple access over fading channels,” IEEE Trans. Commun.,
vol. 69, no. 3, pp. 2015–2027, Mar. 2021.
[18] Z. Ding, R. Schober, and H. V. Poor, “On the impact of phase shifting
designs on IRS-NOMA,” IEEE Wireless Commun. Lett., vol. 9, no. 10,
pp. 1596–1600, Oct. 2020.
[19] Z. Ding and H. Vincent Poor, “A simple design of IRS-NOMA transmis-
sion,” IEEE Commun. Lett., vol. 24, no. 5, pp. 1119–1123, May 2020.
[20] X. Yue and Y. Liu, “Performance analysis of intelligent reflecting surface
assisted NOMA networks,” IEEE Trans. Wireless Commun., vol. 21, no. 4,
pp. 2623–2636, Apr. 2022.
[21] Z. Sun and Y. Jing, “On the performance of multi-antenna IRS-assisted
NOMA networks with continuous and discrete IRS phase shifting,” IEEE
Trans. Wireless Commun., To appear in 2022.
[22] Y. Cheng, K. H. Li, Y. Liu, K. C. Teh, and H. Vincent Poor, “Downlink
and uplink intelligent reflecting surface aided networks: NOMA and
OMA,” IEEE Trans. Wireless Commun., vol. 20, no. 6, pp. 3988–4000,
Jun. 2021.
[23] Y. Cheng, K. H. Li, Y. Liu, K. C. Teh, and G. K. Karagiannidis, “Non-
orthogonal multiple access (NOMA) with multiple intelligent reflecting
surfaces,” IEEE Trans. Wireless Commun., vol. 20, no. 11, pp. 7184–7195,
Nov. 2021.
[24] M. Cui, G. Zhang, and R. Zhang, “Secure wireless communication via
intelligent reflecting surface,” IEEE Wireless Commun. Lett., vol. 8, no. 5,
pp. 1410–1414, Oct. 2019.
[25] X. Yu, D. Xu, and R. Schober, “Enabling secure wireless communications
via intelligent reflecting surfaces,” in IEEE Proc. of Global Commun.
Conf. (GLOBECOM), Dec. 2019, pp. 1–6.
[26] Z. Zhang, L. Lv, Q. Wu, H. Deng, and J. Chen, “Robust and secure com-
munications in intelligent reflecting surface assisted NOMA networks,”
IEEE Commun. Lett., vol. 25, no. 3, pp. 739–743, Mar. 2021.
[27] L. Yang, J. Yang, W. Xie, M. O. Hasna, T. Tsiftsis, and M. D. Renzo,
“Secrecy performance analysis of RIS-aided wireless communication
systems,” IEEE Trans. Veh. Technol., vol. 69, no. 10, pp. 12 296–12 300,
Oct. 2020.
[28] C. Gong, X. Yue, X. Wang, X. Dai, R. Zou, and M. Essaaidi, “Intelligent
reflecting surface aided secure communications for NOMA networks,”
IEEE Trans. Veh. Technol., vol. 71, no. 3, pp. 2761–2773, Mar. 2022.
[29] Z. Zhang, J. Chen, Q. Wu, Y. Liu, L. Lv, and X. Su, “Securing
NOMA networks by exploiting intelligent reflecting surface,” IEEE Trans.
Commun., vol. 70, no. 2, pp. 1096–1111, Feb. 2022.
[30] Z. Zhang, C. Zhang, C. Jiang, F. Jia, J. Ge, and F. Gong, “Improving
physical layer security for reconfigurable intelligent surface aided NOMA
6G networks,” IEEE Trans. Veh. Technol., vol. 70, no. 5, pp. 4451–4463,
May 2021.
[31] H. Liu, H. Ding, L. Xiang, J. Yuan, and L. Zheng, “Outage and BER
performance analysis of cascade channel in relay networks,” vol. 34, pp.
23–30, Aug. 2014.
[32] I. Gradˇ
stejn and I. M. Ryˇ
zik, “Table of integrals, series, and products,
6th ed,” 2000.
[33] H. A. David and H. N. Nagaraja, Order statistics. John Wiley & Sons,
2004.
[34] F. Fang, Y. Xu, Q.-V. Pham, and Z. Ding, “Energy-efficient design of irs-
noma networks,” IEEE Trans. Veh. Technol., vol. 69, no. 11, pp. 14 088–
14 092, Nov. 2020.