CS计算机代考程序代写 scheme matlab information theory AI algorithm Impact of Residual Hardware Impairment on the IoT Secrecy Performance of RIS-Assisted NOMA Networks

Impact of Residual Hardware Impairment on the IoT Secrecy Performance of RIS-Assisted NOMA Networks

Received February 12, 2021, accepted March 2, 2021, date of publication March 12, 2021, date of current version March 23, 2021.

Digital Object Identifier 10.1109/ACCESS.2021.3065760

Impact of Residual Hardware Impairment on the
IoT Secrecy Performance of RIS-Assisted
NOMA Networks
QIN CHEN 1, MEILING LI 1, XIAOXIA YANG1, RYAN ALTURKI 2,
MOHAMMAD DAHMAN ALSHEHRI 3, AND FAZLULLAH KHAN 4, (Senior Member, IEEE)
1School of Electronics Information Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, China
2Department of Information Science, College of Computer and Information Systems, Umm Al-Qura University, Makkah 24372, Saudi Arabia
3Department of Computer Science, College of Computers and Information Technology, Taif University, Taif 21944, Saudi Arabia
4Department of Computer Science, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan

Corresponding author: Meiling Li ( .cn)

This work was supported in part by the National Natural Science Foundation of China under Grant 62001320, in part by the Key Research
and Development Program of Shanxi under Grant 201903D121117, in part by the Scientific and Technological Innovation Programs of
Higher Education Institutions in Shanxi under Grant 201802090, in part by the Research Project Supported by Shanxi Scholarship Council
of China under Grant 2020-126, in part by the Graduate Education Innovation Project of Shanxi under Grant 2020SY419, and in part by
the Taif University Researchers Supporting Project under Grant TURSP-2020/126.

ABSTRACT Non-orthogonal multiple access (NOMA) technology is expected to effectively improve the
spectrum efficiency of fifth-generation and later wireless networks. As a new technology, reconfigurable
Intelligent surfaces (RIS) can achieve high spectral and energy efficiency with a low cost in wireless
networks. These are achieved by integrating a great quantity of low-cost passive reflective units (RUs) on
the plane. In this article, in order to meet the needs of high efficiency, low power consumption, and wide
coverage, we combine RIS-assisted NOMA technology with the internet of things (IoT). Because in the
actual wireless communication system, the residual hardware impairment (RHI) characteristics of the actual
transceiver equipment will have an important impact on system secrecy performance. Therefore, the study
will propose a single eavesdropper RIS-assisted downlink NOMA system with RHI (E-RHI-RIS-NOMA).
The study will also investigate the impact of RHI on the physical layer security (PLS) performance of the
system and the closed-form expression of the user’s secrecy outage probability (SOP) is derived. Finally,
the simulation results show that 1) the main factors affecting the SOP are the quantity of RUs in RIS,
the transmit SNR, and the target data rate, 2) it is proved that the hardware impairment of the transceiver
harms the system’s secrecy outage performance while the severity of the impact of RHI on the system
performance depends on the transmit SNR and target data rate. Moreover, RHI at different nodes has a
different influence on system secrecy performance. 3) the system performance of RIS relying on NOMA is
improved compared with orthogonal multiple access (OMA) and conventional NOMA.

INDEX TERMS Non-orthogonal multiple access, physical layer security, residual hardware impairment,
secrecy outage probability, reconfigurable intelligent surface, Internet of Things.

I. INTRODUCTION
Internet of Things (IoT) technology is getting a lot of
attention because of its huge potential to connect billions
of devices in numerous applications [1]. Driven by eco-
nomic and environmental concerns, and the scale of the
next-generation IoT system, the design of energy-efficient
high bandwidth wireless technology is becoming crucial [2].

The associate editor coordinating the review of this manuscript and

approving it for publication was Donghyun Kim .

Reconfigurable intelligent surfaces (RIS) are a revolutioniz-
ing technology in the field of wireless communication, which
can adjust the wireless environment to improve spectrum
and energy efficiency. It is considerd to be a extraordinary
prospect and valid green resolve scheme in the next wire-
less communication [3]–[5]. RIS are artificial surfaces of
electromagnetic materials controlled by integrated electronic
devices with unique wireless communication capabilities.
The intelligent radio environment is a kind of wireless net-
work that transforms wireless network environment into

VOLUME 9, 2021
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https://orcid.org/0000-0002-8604-5650
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Q. Chen et al.: Impact of RHI on the IoT Secrecy Performance of RIS-Assisted NOMA Networks

reconfigurable intelligent space, which is controlled by tele-
com operators and plays a positive role in information
transmission and processing [6]. Compared with current
technologies, RIS achieve deterministic and programmable
control of wireless environment behavior [7]. Most RIS
implementations compose two dimension (2D) metasur-
faces (MS) arrays.By tune-up the phase shift of each element
skillfully, the propagation characteristics of the signal can
be changed [8]. RIS can achieve lower energy consumption
compared with communication auxiliary technology similar
to amplifying and forwarding relays [5]. The RIS can be
easily embedded into the interior of buildings and onto the
surface of large vehicles not need to change the hardware and
software of the device, making IoT performance improve-
ments in connectivity, power, and coverage significantly less
costly [9], [10]. Meanwhile, RIS can achieve a large range of
coverage under low power consumption [1].

In the mass open heterogeneous access environment, IoT
security is seriously challenged [11]. In wireless networks
such as the IoT, communication security and secret protection
are very significant, because the electromagnetic transmis-
sion has the nature of broadcasting, which makes the commu-
nication of the IoT vulnerable to eavesdropping attacks [12].
Traditional security methods are mainly based on authentica-
tion and cryptography, which are implemented in the upper
layer of a wireless communication system but are relatively
independent of the physical layer. However, for the traditional
encryption technology, key management is difficult [13].
Physical layer security (PLS) technology from the perspec-
tive of information theory, makes use of the indeterminacy
and time-variability of the wireless channel to realize the
secure communication of encrypted link without key [14]
and developed a promising solution for secure IoT com-
munication. The PLS performance of downlink multi-user
orthogonal frequency division multiplexing (OFDM) and
uplink non-orthogonal multiple access (NOMA) IoT systems
is studied in [15] and [16] respectively. In [17], to enhance
the safety of the downlink multi-carrier IoT communica-
tion system with eavesdroppers, an effective PLS method
is proposed.

Driven by the uniqueness of RIS, some preliminary studies
have shown how to improve system secrecy performance
through RIS. Reference [18] considered a RIS-assisted Gaus-
sian multiple-input multiple-output (MIMO) eavesdropping
channel, and an optimization algorithm is proposed maxi-
mized the secrecy rate of the channel. However, [19] stud-
ied the PLS issues of two vehicle-mounted system models
using RIS-assisted transmission and [20] a single eaves-
dropping wireless communication system assisted by RIS
is studied. By jointly designing AP transmission waveform
and RIS reflection waveform, the confidentiality of legal
communication link is improved to the maximum. The RIS
propagate the incident electromagnetic wave to the target
receiver in the expected way by changing the attenuation
and scattering of the incident electromagnetic wave. Ref-
erence [21] proposed a multiple eavesdropper downlinks

multiple-input single-output (MISO) system to improve sys-
tem secrecy performance through RIS-assisted transmission.
NOMA technology has been considered a promising candi-
date for multiple access in future mobile networks because
of having high spectral efficiency, but also can guarantee
the fairness of users, and can obtain powerful connection
support [22], [23]. The core concept of NOMA is to use
superimposed coding (SC) technology at the transmitter and
successive interference cancellation (SIC) technology at the
receiver to serve multiple users on the same time-frequency
resource block [22]. NOMA enables IoT large-scale connec-
tion communication by increasing system throughput through
the simultaneous transmission of multiple signals on the
same resource block [24]. RIS provide a new method to
enhance the performance of NOMA systems that is to recon-
struct the wireless environment, which urges us to apply
RIS technology to the NOMA system [25]. The influence
of two distinct phase shift designs on the performance of
RIS-assisted NOMA system was investigated by [26]. In the
RIS-assisted NOMA system, [25] maximized the minimum
decoding signal-to-noise ratio (SINR) by considering both
the emission beam formation at BS and the phase shift at
the RIS. Reference [5] considered the MISO-NOMA system,
according to the characteristics of reflection amplitude and
phase shift, assuming that RIS reflection exists in both ideal
and non-ideal situations, a new algorithm is proposed to
obtain the maximum total rate of all users.

All the aforementioned works assumed that the ideal
situation of the transceiver. However, in actual communi-
cation systems, the transmitter and receiver hardware of
wireless nodes are affected by non-ideal (RHI, Residual
Hardware Impairment) characteristics frequently, such as I/Q
imbalance, amplifier amplitude nonlinearity, and phase noise
[27], [28]. Reference [29] investigated the effects of RHI
and channel estimation errors(CEEs) on the security and
reliability of multi-relay cooperative systems. References
[30] and [31] considered a NOMA system with RHI and
CEEs, and studied the outage probability of users under the
system. The spectrum and energy efficiency of RIS-aided
MISO system considering hardware impairment are analyzed
and revealed the adverse effects of hardware impairment
on system performance in [32]. Based on considering the
hardware impairment, the energy efficiency is analyzed in
the wireless communication system assisted by RIS [33].
According to the existing researchwork, the hardware impair-
ment has seriously affected the performance of the wireless
communication system with RIS-assisted transmission.

To the best of our knowledge, the secrecy performance of
RIS-assisted NOMA system with non-ideal (RHI) hardware
condition has not been investigated in the existing litera-
ture. Based on this motivation, this work investigates how
the security performance of RIS-assisted NOMA system is
affected by RHI. Specifically, the expressions of user secrecy
outage probability (SOP) under non-ideal (RHI) hardware
condition are derived, and the influence of user’s SOP on
system performance is analyzed. The numerical results show

42584 VOLUME 9, 2021

Q. Chen et al.: Impact of RHI on the IoT Secrecy Performance of RIS-Assisted NOMA Networks

that the severity of RHI’s impact on system performance is
closely related to the SNR, target data rate, and power allo-
cation coefficient, but it has nothing to do with the quantity
of reflection units (RUs) in RIS. In this case of high SNR and
high target data rate, RHI have amore significant influence on
the secrecy performance of the system, and when the power
allocation coefficient is taken at different values, the impact
on system security performance also varies. Simulation result
also shows RIS-assisted NOMA system compared with the
traditional NOMA system and improvement in the secrecy
performance, and the degree of performance improvement is
related to the number of RIS’s RUs. The key contributions of
this article are follow.
• We provide a RIS-assisted downlink NOMA system
with an eavesdropper. The model considers the impact
of RHI on system secrecy performance.

• The SOP expression of RIS-assisted NOMA system is
derived. These expressions can quantify the degradation
of secrecy performance caused by RHI. How RHI and
RIS’s RUs affect the secrecy performance of the NOMA
system is studied.

• Monte Carlo simulation studies the relationship between
the severity of RHI impact on system performance and
different parameters and provides useful insights into the
impact of RHI on the SOP of the NOMA system.

The rest of this article is arranged as below: Section II
describes the RIS-assisted NOMA system model, consid-
ering the influence of transceiver hardware imperfection.
Section III takes the SOP as the performance index to evaluate
the influence of the imperfect transceiver hardware on the per-
formance of the RIS-assisted NOMA system. In Section IV,
numerical results are given to prove the correctness of the
analysis. Ultimately, the Section V is the conclusion.

II. SYSTEM MODEL
As shown in Fig 1, a downlink E-RHI-RIS-NOMA system
is considered in this article, which consists of one base sta-
tion(BS), one RIS, which consists of N RUs, two legitimate
receivers (Dn, near the user, and Dm, far user), and one
eavesdropper(Eve). BS communicates with two legitimate
users at the same time and frequency through a RIS. Due to

FIGURE 1. E-RHI-RIS-NOMA system model.

long-distance or major obstacles, we presume that there is no
direct connection between the BS and the destination [34].
Furthermore, we assume that all nodes in the system have
only one antenna. The channel coefficients of the BS to i-th
RU, the i-th RU to destination Dκ (κ ∈ {n,m}) and the i-th
RU to Eve are denoted by hsi, gidκ and gie, respectively. And
all the channels follow independent Rayleigh fading.

In the first phase, BS sends a superimposed mixed signal
to RIS, assuming that the RF front end is not ideal, the trans-
mission signal at BS is

xS =

αnPSxn +


αmPSxm + µS (1)

where xn is the message of the n-th user (i.e.,Dn), E
[
|xn|

2
]
=

1, αn denotes the power allocation coefficient of the n-th user
and satisfying αn < αm and αn + αm = 1. In this article, we consider that each node in the system has RHI. The impact of RHI can be used as additional noise source to model [35]. Thus, µS denotes the distortion caused by hardware impair- ment at the BS, µs ∼ CN ( 0, ( ρtS )2 PS ) , ρtS stands for the BS’s error vector magnitudes (EVMs). According to the 3rd generation partnership project (3GPP) long term evolution advanced (LTE-A), the minimum and maximum hardware impairments are 0.08 and 0.175, respectively [36]. PS rep- resents the average transmitted power at the BS. In the second phase, RIS can play the part of repeater, for- warding information to the NOMA users. Therefore, the sig- nals received by legitimate users under the existence of RHI is given by yDκ = N∑ i=1 hsirigidκ ( xS + µDκ ) + nDκ (2) where κ ∈ {n,m}, ri = βi exp (jθi) is the response of the i-th RU, and the reflection coefficients of phase shift and amplitude of the i-th RU are represented by βi and θi respec- tively. Without losing generality, we presume that βi = 1. µDκ is the distortion caused by a hardware impairment at the legitimate user Dκ , µDκ ∼ CN ( 0, ( ρrDκ )2 PS ) , nDκ stands for the additive white Gaussian noise (AWGN) and nDκ ∼ CN ( 0, σ 2Dκ ) . To facilitate the analysis, we assume that σ 2Dκ = σ 2 D. On the other hand, when RIS-assisted transmitting infor- mation to the target user, the eavesdropper will intercept the corresponding information. Therefore, the signal received by the Eve can be given yE = N∑ i=1 hsirigie (xS + µE )+ nE (3) where µE represents the distortion caused by hardware impairment at the Eve, µE ∼ CN ( 0, ( ρrE )2 PS ) , nE repre- sents AWGN at the Eve, nE ∼ CN ( 0, σ 2E ) . We can achieve different phase shifts of RIS components independently by setting the corresponding set voltage with microcontroller [37]. We assume that RIS are completely VOLUME 9, 2021 42585 Q. Chen et al.: Impact of RHI on the IoT Secrecy Performance of RIS-Assisted NOMA Networks aware of the phase θi of BS → RIS channel hsi and the phase ψi of RIS → Dκ/Eve channel gid and gie, and choose the best phase shift, i.e. φi = − (θi + ψi) (4) ri can be further written as ri = exp (−j (θi + ψi)) (5) Next, by substituting (5) into (2) and (3), we can get [38] yDκ = Aκ ( xS + µDκ ) + nDκ (6) yE = Ae (xS + µE )+ nE (7) where Aκ = N∑ i=1 |hsi||gidκ |, Ae = N∑ i=1 |hsi| |gie|. Then by substituting (1) into (6) and (7), can be further expressed as yDκ = Aκ (√ αnPSxn + √ αmPSxm + µS + µDκ ) + nDκ = Aκ (√ αnPSxn + √ αmPSxm + µSDκ ) + nDκ (8) yE = Ae (√ αnPSxn + √ αmPSxm + µS + µE ) + nE = Ae (√ αnPSxn + √ αmPSxm + µSE ) + nE (9) where µSDκ and µSE represent the RHI’s aggregation dis- tortion in the link BS → Dκ and BS → Eve, respectively. µSDκ ∼ CN ( 0, ρ2SDκPs ) , ρ2SDκ = ( ρtS )2 + ( ρrDκ )2 , µSE ∼ CN ( 0, ρ2SEPs ) , ρ2SE = ( ρtS )2 + ( ρrE )2 . III. PERFORMANCE ANALYSIS In the E-RHI-RIS-NOMA system model shown in Fig. 1, the influence of transceiver hardware impairment on system performance is quantified. This section is structured as fol- lows: Section III-A gives the SIDNR. Section III-B analyzes the channel statistical characteristics, as the basis for the sub- sequent analysis of the secrecy outage performance. Finally, Section III-C provides the expressions of the SOP. A. SIDNR NOMA uses SIC receivers at the receiving end to realize multi-user detection (MUD). The basic principle of SIC is to gradually subtract the interference of users with the highest signal power, and operate in the order of signal power. Since in NOMA, users with poor channel state, larger power is allo- cated when transmitting information, so Dn first decodes the message of weakerDm. Consequently, the signal interference plus distortion noise ratio (SIDNR) for Dn to detect xm can be obtained from (8) γDn→Dm = αm|An| 2 |An| 2 ( αn + ρ 2 SDn ) + 1 ρS (10) where ρS = PS σ 2D average SNR of legal links, An = N∑ i=1 |hsi||gidn | is the equivalent BS − RIS − Dn channel. And then Dn subtracts the Dm signal from the received signal, the received SIDNR at Dn to detect its own message is given by γDn = αn|An| 2 |An| 2ρ2SDn + 1 ρS (11) WhenDm decode its ownmessage, the strongerDn’s signal xn will be treated as noise, and the SIDNR can be expressed as from (8) γDm = αm|Am| 2 |Am| 2 ( αn + ρ 2 SDm ) + 1 ρS (12) where Am = N∑ i=1 |hsi||gidm | is the equivalent BS−RIS − Dm channel. Similar to [39], we assume the worst case, that is the eavesdropper has strong detection capabilities, and can detect xn(or xm) without interference from xm (or xn). From (9), we can get the SIDNR when Eve intercepts information xn and xm, respectively. γEn = αn|Ae| 2 |Ae| 2ρ2SE + 1 ρE (13) γEm = αm|Ae| 2 |Ae| 2 ( αn + ρ 2 SE ) + 1 ρE (14) where ρE = PS σ 2E , Ae = N∑ i=1 |hsi| |gie| is the equivalent BS − RIS − Eve channel. B. CHANNEL STATISTICAL CHARACTERISTICS Based on the E-RHI-RIS-NOMA system model proposed in Fig 1, this section first analyzes the channel statistical characteristics of the composite variables involved in the article, as the basis for the subsequent analysis of the secrecy outage performance. Theorem 1: According to (11) and (12), the cumulative distribution function (CDF) of the γDn and γDm are displayed at the bottom of the next page. where γ (·, · ) and 0 (·) represent the lower incomplete Gamma function and Gamma function respectively. Proof: Please see Appendix A. Theorem 2: The probability density function (PDF) of the γEn and γEm are displayed at the bottom of the next page. Proof: Please see Appendix B. C. SECRECY OUTAGE PROBABILITY The SOP of the E-RHI-RIS-NOMA system is analyzed in this section. The secrecy outage event is defined as when the user’s secrecy rate is lower than a predeter- mined threshold, the secrecy outage happened. Cκ =⌈ log2 ( 1+ γDκ ) − log2 ( 1+ γEκ )⌉+ represents the achiev- able secrecy rate of .Therefore, the SOP expression can be 42586 VOLUME 9, 2021 Q. Chen et al.: Impact of RHI on the IoT Secrecy Performance of RIS-Assisted NOMA Networks formulated as SOPκ = Pr {Cκ < Rκ} = Pr { γDκ < 2 Rκ ( 1+ γEκ ) − 1 } = ∫ ∞ 0 FγDκ ( 2Rκ (1+ y)− 1 ) fγEκ (y) dy (19) where dxe+ = max {x, 0} [40], κ = {n,m} and Rκ is the target data rate of the user κ . In order to obtain the SOP of Dn and Dm respectively, we made the following analysis. 1) SOPn ANALYSIS Combining the discussion of FγDn (x) and fγEn (y) in Theo- rem 1 and Theorem 2, SOPn is given by SOPn = ∫ θ∗n 0 FγDn ( 2Rn (1+ y)− 1 ) fγEn (y) dy +] 1− FγEn ( θ ∗ n ) (20) where θ∗n=min ( αn ρ2SE , αn+ρ 2 SDn ( 1−2Rn ) 2Rnρ2SDn ) . Substituting (15) and (17) into (20), we can get the expression of SOP, finding the closed expres- sion is a challenging task. Nevertheless, the approx- imate expression can be obtained by utilizing the Gaussian-Chebyshev Quadrature theorem [41]. We let 31 (y) = FγDn ( 2Rn (1+ y)− 1 ) fγEn (y), (20) can be further approximated as SOPn ≈ V∑ v=1 θ∗n 2 π V √ 1− ϕ2v31 ( θ∗n 2 (1+ ϕv) ) + 1− FγEn ( θ ∗ n ) (21) where ϕv = cos ( 2v−1 2V π ) . 2) SOPm ANALYSIS Combining the discussion of FγDm (x) and fγEm (y) in Theo- rem 1 and Theorem 2, SOPm is given by SOPm = ∫ θ∗m 0 FγDm ( 2Rm (1+ y)− 1 ) fγEm (y) dy + 1− FγEm ( θ ∗ m ) (22) where θ∗m=min ( αm αn+ρ 2 SE , αm+ ( αn+ρ 2 SDm )( 1−2Rm ) 2Rm (αn+ρ2SDm ) ) . Similar to the analysis of SOPn, substituting (16) and (18) into (22), SOPm can be approximately expressed as SOPm ≈ V∑ v=1 θ∗m 2 π V √ 1− ϕ2v32 ( θ∗m 2 (1+ ϕv) ) + 1− FγEm ( θ ∗ m ) (23) where 32 (y2) = FγDm ( 2Rm (1+ y2)− 1 ) fγEm (y2). FγDn (x) =   γ ( π2 16−π2 N , 2π 16−π2 1√ αn−ρ 2 SDn x √ x ρS ) 0 ( π2 16−π2 N ) , x ≤ αn ρ2SDn 1, otherwise (15) FγDm (x) =   γ   π2 16−π2 N , 2π 16−π2 1√( αm− ( αn+ρ 2 SDm ) x ) xρS   0 ( π2 16−π2 N ) , x ≤ αm αn + ρ 2 SDm 1, otherwise (16) fγEn (y) =   αn ( 1√ αn−ρ 2 SE y ) π2 16−π2 N+2( 2π 16−π2 1 √ ρE ) π2 16−π2 N (√ y ) π2 16−π2 N−2 e − 2π 16−π2 1√ αn−ρ2SE y √ y ρE 20 ( π2 16−π2 N ) , y ≤ αn ρ2SE 0, otherwise (17) fγEn (y) =   αn ( 1√ αn−ρ 2 SE y ) π2 16−π2 N+2( 2π 16−π2 1 √ ρE ) π2 16−π2 N (√ y ) π2 16−π2 N−2 e − 2π 16−π2 1√ αn−ρ2SE y √ y ρE 20 ( π2 16−π2 N ) , y ≤ αn ρ2SE 0, otherwise (18) VOLUME 9, 2021 42587 Q. Chen et al.: Impact of RHI on the IoT Secrecy Performance of RIS-Assisted NOMA Networks IV. SIMULATION AND RESULTS In this section, the performance of E-RHI-RIS-NOMA sys- tem is analyzed and verified by building Matlab simulation platform and compare them with the traditional NOMA sys- tem without RIS-assisted. Assuming that the channels gain follow Rayleigh distribution, and how would the system per- formance be affected by the RHI level and the quantity of RUs in RIS are investigated. In this section, unless otherwise specified, we assume that the power allocation coefficients αn = 0.4, αm = 0.6, when αn 6= 0.4, αm = 1 − αn; The target data rates Rn and Rm of Dn and Dm are 0.1 bps/Hz and 0.05 bps/Hz, respectively. At the same time, assuming that all nodes are affected by RHI and ρts = ρ r Dn = ρrDm = ρrE = ρ. As can be seen from Fig. 2, the SOP curves in Monte Carlo are very consistent with the analytical results of the mathematical derivation, which proves the correctness of our derivation. Moreover, we can find that for NOMA users Dn andDm, the secrecy outage performance ofDn is significantly greater than that ofDm, and the performance gap between the two users becomes more obvious as the value of N increases. FIGURE 2. SOP of Dn and Dm. The secrecy outage performance of RIS-assisted NOMA for near user Dn by comparing three different cases is shown in Fig 3. We observe that with the increase of ρS , the secrecy performance of NOMA system is improved. Therefore, the secrecy performance can be improved by enhancing the transmit SNR. In addition, the secrecy performance of the system is closely related to the target data rate. When N is fixed, the higher the target data rate is, the higher the SOP is. Furthermore, when Rn is a fixed value, system security performance is improved with the increase of RUs. Fig. 4 describes the relationship between the SOP and the ρS at different target data rates and RHI levels when N = 3. As a benchmark, we simulated the SOP under ideal condi- tions, that is the situation where ρ = 0. Fig. 4 shows that with the increase of ρ, the user’s secrecy performance decreases. For example, when taking ρS = 1dB and Rn = 0.5bps/Hz, the value of ρ increases from 0 to 0.15, and the SOP increased FIGURE 3. SOP varies with ρS under different Rn and N, ρ = 0.1. FIGURE 4. SOP varies with ρS under different ρ and Rn, N = 3. from 5× 10−1 to 6× 10−1. Meanwhile, we observe that the influence of RHI on the security performance of the system increased with the increase of the target data rate. In Fig. 5, we can see the effect of RHI on the performance of secrecy outage when ρ and N are different. To compare the influence of RHI on the SOP, we draw the curve when ρ = 0 as a comparison. For the ideal situation, neither the transmitter nor the receiver will be affected by hardware impairments, and the best secrecy outage performance can be observed. As can be seen fromFig. 5, the presence of RHIwill notably reduce the performance of secrecy outage of the E- RHI-RIS-NOMA system. In particular, we observe that when N = 1, ρ increases from 0 to 0.15, to achieve the same SOP, the ρS should be increased by about 2dB. As shown in Fig. 5, the secrecy outage performance of user Dn shows a similar trend when we change values of N . Fig. 6 shows the variations of SOP for user Dn when RHI exists in different nodes. It can be seen that when RHI only 42588 VOLUME 9, 2021 Q. Chen et al.: Impact of RHI on the IoT Secrecy Performance of RIS-Assisted NOMA Networks FIGURE 5. SOP varies with ρS under different values of ρ and N , Rn = 0.1. FIGURE 6. SOP varies with ρS when RHI at different nodes and different N , Rn = 0.1. occurs in the destination node and eavesdropping node, it has a much bigger effect on the probability of secrecy outage, and the impact degree becomes more obvious with the increase of N . For example, taking N = 12, when the SOP is 1 × 10−2, there will be about 1dB performance improvement and 2dB performance loss under the cases of RHI existing only in the eavesdropper node and in the destination node compared with the ideal hardware case, respectively. In addition, it can also be seen that the joint RHI not only affects the legitimate users but also aggravates the performance of eavesdropping users. The total secrecy performance loss caused by this is slightly less than that of RHI only occurred in the destination node. As can be seen from Fig. 7, compared with RIS-assisted OMA and conventional NOMA systems, RIS-assisted NOMA system has more advantages in improving secrecy performance.With the increase of ρS , the performance advan- tage of RIS-assisted NOMA system is more obvious. And FIGURE 7. SOP of RIS-assisted NOMA contrasted with RIS-assisted OMA and conventional NOMA, ρ = 0.1. the higher the N value, the better the secrecy performance obtained for the RIS-assisted NOMA system. Therefore, the secrecy performance of the NOMA system can be effec- tively improved by deploying RIS reasonably. V. CONCLUSION In this article, the impacts of RHI on the secrecy outage per- formance under Rayleigh fading conditions of the proposed E-RHI-RIS-NOMA system model are investigated. In par- ticular, in order to evaluate the secrecy performance when the transceiver hardware is imperfection, an approximate closed-form expression for the probability of secrecy outage is derived. The simulation results show that the main factors affecting the SOP are the quantity of RUs in RIS, the transmit SNR, and the target data rate. Throughout simulations, it is proved that the secrecy outage performance of the system will be adversely affected by the hardware impairment of the transceiver, and the severity of the impact of RHI on the system performance depends on the transmit SNR, target data rate. Moreover, RHI at different nodes has a differ- ent influence on system secrecy performance. In addition, the simulation results show that compared to the RIS-assisted OMA system and the conventional NOMA system, the RIS- assisted NOMA system has greater advantage in terms of secrecy performance. This finding is helpful for the design of RIS in the actual system and satisfy a large number of connections. APPENDIX A PROOF OF THEOREM1 According to (10), we can get the cumulative distribution function (CDF) of γDn FγDn (x) = Pr { |An| 2 ( αn − ρ 2 SDn x ) ≤ x ρS } (A.1) VOLUME 9, 2021 42589 Q. Chen et al.: Impact of RHI on the IoT Secrecy Performance of RIS-Assisted NOMA Networks fγEn (y) =   αn ( 1√ αn−ρ 2 SEy ) π2 16−π2 N+2( 2π 16−π2 1 √ ρE ) π2 16−π2 N (√ y ) π2 16−π2 N−2 e − 2π 16−π2 1√ αn−ρ2SE y √ y ρE 20 ( π2 16−π2 N ) , y ≤ αn ρ2SE 0, otherwise (B.3) fγEm (y) =   αm ( 1√ αm− ( αn+ρ 2 SE ) y ) π2 16−π2 N+2( 2π 16−π2 1 √ ρE ) π2 16−π2 N (√ y ) π2 16−π2 N−2 e − 2π 16−π2 1√ αm−(αn+ρ2SE)y √ y ρE 20 ( π2 16−π2 N ) , y ≤ αm αn + ρ 2 SE 0, otherwise (B.4) for αn − ρ2SDnx ≥ 0, or equivalently x ≤ αn ρ2SDn : FγDn (x) = Pr  |An|2 ≤ x ρS ( αn − ρ 2 SDn x )   = Pr  An ≤ 1√( αn − ρ 2 SDn x ) √ x ρS   = FA1   1√( αn − ρ 2 SDn x ) √ x ρS   (A.2) FAn is the CDF of An, FAn (x) = γ (1+a, xb ) 0(1+a) , where a = k21 k2 − 1, b = k2k1 , with k1 = Nπ 2 and k2 = 4N ( 1− π 2 16 ) [34], the CDF of γDn can be written as FγDn (x) = γ ( π2 16−π2 N , 2π 16−π2 1√ αn−ρ 2 SDn x √ x ρS ) 0 ( π2 16−π2 N ) (A.3) According to (11), the CDF of γDm is defined as FγDm (x) = Pr { |Am| 2 ( αm − ( αn + ρ 2 SDm ) x ) ≤ x ρS } (A.4) Considering the condition of x ≤ αm αn+ρ 2 SDm , we have the same analysis process as (A.3), and we have the CDF of γDm as FγDm (x) = γ   π2 16−π2 N , 2π 16−π2 1√( αm− ( αn+ρ 2 SDm ) x )√ xρS   0 ( π2 16−π2 N ) (A.5) This completes the proof. APPENDIX B PROOF OF THEOREM2 In order to calculate the probability density functions (PDFs) of γEn and γEm , we need to obtain their CDF firstly. The anal- ysis process of the CDF is same as Appendix A. Therefore, according to (14) and (14), we recall the CDFs of γEn and γEm as below, and consider the conditions y ≤ αn ρ2SE and y ≤ αm αn+ρ 2 SE respectively FγEn (y) = γ ( π2 16−π2 N , 2π 16−π2 1√ αn−ρ 2 SEy √ y ρE ) 0 ( π2 16−π2 N ) (B.1) FγEm (y) = γ ( π2 16−π2 N , 2π 16−π2 1√( αm− ( αn+ρ 2 SE ) y )√ yρE ) 0 ( π2 16−π2 N ) (B.2) The PDFs of γEn and γEm are obtained by deriving (B.3) and (B.4) are displayed at the top of the page. REFERENCES [1] S. Arzykulov, G. Nauryzbayev, M. S. Hashmi, A. M. Eltawil, K. M. Rabie, and S. Seilov, ‘‘Hardware- and interference-limited cognitive IoT relaying NOMA networks with imperfect SIC over generalized non-homogeneous fading channels,’’ IEEE Access, vol. 8, pp. 72942–72956, Apr. 2020. [2] S. Buzzi, C.-L. I, T. E. Klein, H. V. Poor, C. Yang, and A. 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[41] A. Neumaier, Introduction to Numerical Analysis. Cambridge, U.K.: Cambridge Univ. Press, 1987. QIN CHEN is currently pursuing the master’s degree with the School of Electronics Information Engineering, Taiyuan University of Science and Technology (TYUST), China. Her main research interest includes the physical layer secrecy perfor- mance of non-orthogonal multiple access systems. MEILING LI received the M.S. and Ph.D. degrees in signal and information processing from the Beijing University of Posts and Telecommunica- tions, Beijing, in 2007 and 2012, respectively. She is currently a Professor with the School of Elec- tronics Information Engineering, Taiyuan Univer- sity of Science and Technology (TYUST), China. She is also a Visiting Research Scholar with the University of Warwick, U.K. Her research inter- ests include cognitive radio, cooperative com- munications, non-orthogonal multiple access, and physical layer security technology. VOLUME 9, 2021 42591 Q. Chen et al.: Impact of RHI on the IoT Secrecy Performance of RIS-Assisted NOMA Networks XIAOXIA YANG is currently pursuing themaster’s degree with the School of Electronics Information Engineering, Taiyuan University of Science and Technology (TYUST), China. Her main research interest includes the physical layer secrecy perfor- mance of wireless networks. RYAN ALTURKI received the Ph.D. degree from the University of Technology, Sydney, Australia. He is currently an Assistant Professor with the Department of Information Sciences, Col- lege of Computers and Information Systems, Umm Al-Qura University, Makkah, Saudi Ara- bia. His research interests include e-health, mobile technologies, the Internet of Things, and cyber security. MOHAMMAD DAHMAN ALSHEHRI received the Ph.D. degree in artificial intelligence of cyber- security for Internet of Things (IoT) from the University of Technology Sydney, Australia. He is currently an Assistant Professor with the Com- puter Science Department, Taif University, Saudi Arabia, and also a Visiting Professor with the School of Computer Science, University of Tech- nology Sydney (UTS), Australia. He developed six smart novel algorithms for the IoT to reinforce- ment cybersecurity with AI that can detect various behaviors of cyber-attacks and provide full secure and protection platform for the IoT from the most harmful cyber-attacks. Furthermore, he published several publications in high ranked international journals, top-tier conferences, and chapters of books. His current research interests include cybersecurity, artificial intelli- gence, the Internet of Things (IoT), and trust and reputation. He also received a number of international and national awards and prizes. FAZLULLAH KHAN (Senior Member, IEEE) received the Ph.D. degree in computer sci- ence from Abdul Wali Khan University Mardan, Pakistan. He is currently an Assistant Professor of computer science with Abdul Wali Khan Univer- sity Mardan. His research interests include secu- rity and privacy, the Internet of Things, machine learning, and artificial intelligence. Recently, he has been involved in latest developments in the field of the Internet of Vehicles security and privacy issues, software-defined networks, fog computing, and big data analytics. He has served more than ten conferences in leadership capacities, including the General Chair, the General Co-Chair, the Program Co-Chair, the Track Chair, and the Session Chair. His research has been published in IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGIES, IEEE ACCESS, Computer Networks (Elsevier), Future Generations Computer Systems (Elsevier), Journal of Network and Computer Applications (Elsevier), Computers and Electrical Engineering (Elsevier), andMobile Networks and Applications (Springer). He has served as the Guest Editor for IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS (JBHI) journal,Multimedia Technology and Applications (Springer),Mobile Networks and Applications (Springer), Inderscience Big data Analytics, and Neural Computing and Applications journal. 42592 VOLUME 9, 2021