Outage Performance Analysis of Reconfigurable Intelligent Surfaces-Aided NOMA Under Presence of Hardware Impairment
Received November 3, 2020, accepted November 19, 2020, date of publication November 24, 2020,
date of current version December 8, 2020.
Digital Object Identifier 10.1109/ACCESS.2020.3039966
Outage Performance Analysis of Reconfigurable
Intelligent Surfaces-Aided NOMA Under
Presence of Hardware Impairment
ATLURI HEMANTH1, KAVETI UMAMAHESWARI1, ARJUN CHAKRAVARTHI POGAKU1,
DINH-THUAN DO1, (Senior Member, IEEE), AND BYUNG MOO LEE 2, (Senior Member, IEEE)
1Department of Computer Science and Information Engineering, College of Information and Electrical Engineering, Asia University, Taichung 41354, Taiwan
2Department of Intelligent Mechatronics Engineering and Convergence Engineering for Intelligent Drone, Sejong University, Seoul 05006, South Korea
Corresponding authors: Dinh-Thuan Do ( .tw) and Byung Moo Lee ( .kr)
This work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the
Korea Government (MSIT ) under Grant NRF-2020R1F1A1048470 and Grant NRF-2019R1A4A1023746.
ABSTRACT The future of wireless communications looks exciting with the potential new use cases and
challenging requirements of future 6th generation (6G) wireless networks. Since the traditional wireless
communications, the propagation medium has been perceived as a randomly behaving entity between the
transmitter and the receiver, which degrades the quality of the received signal due to the uncontrollable
interactions of the transmitted radio waves with the surrounding objects. The recent advent of reconfigurable
intelligent surfaces (RIS) in wireless communications enables, on the other hand, network operators to con-
trol the radio waves (the scattering, reflection, and refraction characteristics) to eliminate the negative effects
of natural wireless propagation. Recent results have revealed that non-orthogonal multiple access (NOMA)
benefits from RIS mechanism which can effectively provide effective transmissions. Motivated by the
potential of these emerging technologies, we study the impact of hardware impairment in RIS-aided NOMA
system in term of performance metrics. We then derive analytical expressions of outage probability and
throughput as main performance metrics. Simulations are conducted to validate the analytical expressions.
We find that the number of meta-surfaces in RIS, transmit power at the base station, power allocation factors
play important role to demonstrate improvement in system performance of RIS relying on NOMA compared
with orthogonal multiple access (OMA). Numerical results are presented to validate the effectiveness of the
proposed RIS-aided NOMA transmission strategies.
INDEX TERMS Reconfigurable intelligent surfaces, non-orthogonal multiple access, outage probability,
throughput.
I. INTRODUCTION
As a promising architecture to improve the energy and spec-
tral efficiency, intelligent reflecting surface (IRS) or so-called
as reconfigurable intelligent surface (RIS) are introduced
to intergrate to emerging wireless networks [1]–[3]. The
most advantage of RIS falls in its artificial planar pas-
sive radio array approach which exhibits high efficient in
term of cost-effective and energy consumption. In particu-
lar, by imposing an independent phase shift to the incident
signal, the IRS-adied cellular systems reconfigure each pas-
sive element in RIS to vary the channels between the base
The associate editor coordinating the review of this manuscript and
approving it for publication was Kezhi Wang.
station (BS) and mobile users constructively or destructively.
By jointly optimizing the active beamforming at the BS and
the passive beamforming at the IRS, IRS is considered as an
driver for improving the spectral and energy Efficiency for
IRS-aided wireless systems [4]–[11].
By optimizing the active beamforming at the transmit-
ter and the RIS, the authors in [12] and [13] presented
maximal received signal power for a multiple input single
output (MISO) strategy. Such technique is performed by
adjusting its phase shifters together with enabling active and
passive beamforming at the transmittter and RIS respectively.
In [14], the authors explored the RIS-aided offshore sys-
tem to provide high-speed data service and a cost-effective
coverage. In particular, to enhance the signal quality at the
212156 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ VOLUME 8, 2020
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A. Hemanth et al.: Outage Performance Analysis of Reconfigurable Intelligent Surfaces-Aided NOMA
vessels the shipborne RIS is replaced by offshore, and the
coastal base station is equipped with low-cost reconfig-
urable reflect-arrays (RRAs) without using the traditional
costly fully digital antenna arrays (FDAAs). In [15], the
multi-user RIS systemwas studied in downlink by employing
a multi-antenna base station (BS) which sends information
to various users to maximize benefits from the RIS reflect-
ing the incident signals. A wideband RIS-assisted single-
input multiple-output (SIMO) scheme is used in [16] to
employ orthogonal frequency division multiplexing (OFDM)
for communication systems, in which one can divide each
transmission frame into multiple sub-frames to execute chan-
nel estimation in same time with passive beamforming.
To deal with the growing demand for wireless access,
the fixed multiple access techniques satisfying orthogonal-
ity in time, code and frequency requirements correspond-
ing to time division multiple access (TDMA), code division
multiple access (CDMA), and frequency division multiple
access (FDMA). In order to overcome existing challenges
in the fifth generation (5G) of wireless systems, the con-
cept of non-orthogonal multiple access (NOMA) is explored
as new approach for multiple access which have recently
emerged with current wireless systems [17]–[24]. The advan-
tage of cooperative network [25] is included in NOMA
such as studies in [20], [21], [23], [24]. In power-domain
NOMA, each subcarrier is shared for multiple users and
allocating different power levels to the users is recognized
as way to achieve the diversity on that subcarrier. Following
the principle of NOMA, system can offer the difference in
channel gains among users. In the scenario of a two-user
NOMA, the user with higher channel gain (the first user)
is assigned with the lower power level compared to the
user with lower channel gain (the second user). Then, the
transmitter sends information of different users by super-
imposing signals. Despite significant advantages of NOMA
reported in [26], [27], several practical difficulties need be
tackled before NOMA can be effectively deployed. One
such challenge need be considered, i.e. the sensitivity of
NOMA to hardware impairments [28]. Another major chal-
lenge is resource management in multi-cell multiple-input
multiple-output NOMA (MIMO-NOMA) by high compu-
tational complexity, flexible clustering, and potential chan-
nel correlation [29]. Indeed, a typical NOMA transceiver
requires the high cost of MIMO implementation. Moreover,
the system performance of NOMA can be substantially lim-
ited when there are more than two users served in a cluster.
Clearly, these practical issues make it difficult to solely rely
on NOMA, particularly, when the massive connections and
larger coverage are required in emerging networks. In next
section, we will present potentials to integrate with NOMA
to improve system performance.
A. RELATED WORK
The integration of RIS to multiple access networks is
a cost-effective scheme for enlarging network cover-
age/connections and boosting spectrum/energy efficiency.
In [30], the authors presented theoretical performance com-
parison between RIS-assisted downlink communications
relying on NOMA and orthogonal multiple access (OMA).
They also considered the transmit power minimization prob-
lems under the discrete unit-modulus reflection constraint
on each RIS element. The RIS is deployed to construct a
strong combined channel gain at the cell-edge user. Further-
more, while RIS makes a smart radio environment by using
surfaces with capable of manipulating the propagation of
incident electromagnetic waves in a programmable manner
to actively alter the channel realization. By enabling both
NOMA and RIS in unique system, wireless channels could
be into a controllable system block that can be optimized to
enhance overall system performance, especially for system
with massive connections. Reference [31] investigated on
the usage of RIS ultra reliable and low latency communica-
tions (URLLC) system in uplink and proposed a compressive
sensing based RIS-based multiple user detection approach to
exhibit the sparsity and relativity characteristics of user sig-
nal in URLLC system. A combined-channel-strength (CCS)
based user ordering scheme is first proposed in [32]. They
further provided optimal value of the minimum decoding
signal-to-interference-plus-noise-ratio (SNDR) of all users
to optimize the rate performance and ensure user fairness.
In particular, they jointly optimized both the phase shifts
at the RIS and the power allocation at the base station.
In [33], they employed conventional spatial division multiple
access (SDMA) adopted at the base station to achieve orthog-
onal beams by enabling the spatial directions of the near
users’ channels. By aligning the cell-edge users’ effective
channel vectors with the predetermined spatial directions,
RIS-assisted NOMA is implemented to ensure that additional
cell-edge users served on these beams. However, a few paper
considered how RIS systems integrate with NOMA, and
references [30]–[33] motivate us to explore performance of
RIS-aided NOMA systems.
The main contributions of this paper are as follows
• Different from [34], [35], this paper presents a RIS-aided
NOMA system in downlink to achieve benefits from
NOMA to communicate simultaneously with their cor-
responding destinations via a RIS. It is assumed that the
RIS is in the form of a reflect-array comprisingN simple
and reconfigurable reflector elements, and controlled
by a communication oriented software. Unlike other
published work dealing with the calculation of symbol
error probability (SEP) [36], our work provides outage
performance evaluation of the RIS-aided NOMA system
in the presence of hardware impairments.
• The closed-form expressions of outage probability for
the RIS-aided NOMA system are derived. Since they are
formulated in terms of various system parameters, the
effect of each system parameter on the outage probabil-
ity can be numerically evaluated. For instance, the effect
of the number of metasurfaces in RIS on the outage
probability can be evaluated to how the system can
improve its performance in practice. It is demonstrated
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A. Hemanth et al.: Outage Performance Analysis of Reconfigurable Intelligent Surfaces-Aided NOMA
FIGURE 1. System model of RIS-aided NOMA.
in this work that the outage probability of the system
mainly relying on the number of metasurfaces in RIS.
• The derivations of asymptotic outage probabilities at
high transmit signal to noise ratio (SNR) for two users
are also provided as an important evaluation to design
such the RIS-aided NOMA system in practice. Fur-
thermore, compared with orthogonal multiple access
(OMA)-assisted RIS system, the considered system
exhibits more benefits and it becomes prominent can-
didate to implement for forthcoming networks.
The remainder of this paper is structured as follows.
In Section II, the system model of the the RIS-aided NOMA
is introduced under the presence of hardware impairment.
In Section III, the closed-form expressions of outage prob-
ability are derived for such system relying on decoding order
scheme in NOMA. Section IV gives simulation results and
corresponding performance analysis, followed by conclu-
sions and future directions in Section V.
II. SYSTEM MODEL
We consider the RIS-aided NOMA as depicted in Fig. 1,
in which the base station (S) intends to communicate with two
destinations. These users are classified as the far user (FU)
and near user (NU). To achieve simple design and low cost,
we assume that all nodes equipped a single-antenna while a
RIS consists of N meta-surfaces. We denote hi, giN and giF
as the baseband equivalent fading channels between S and
the i-th element in the RIS, channels from the i-th element
in the RIS to NU and FU as respectively. These channels
are assumed to be independent, identical, slowing varying,
flat. In this scenario, we consider their envelop of two links
related to FU and NU which follow Rayleigh distributions
with different scale parameters. The signal propagates from
the source to two kinds of users through the RIS, which aims
to enhance the signal quality at these destinations. In ideal
case, we assume that the RIS can achieve the channel state
information (CSI) of these users [34]. Luckily, the RIS can
use such CSI to maximize the received SNR at these destina-
tions.
In the context of NOMA, the base station send superimpose
signal containing signals s1, s2 which are targeted to user
NU and FU, respectively. To provide different quality of ser-
vice (QoS) for uses, higher power level a2 is assigned to user
FU, such allocation scheme must be satisfied a1 + a2 = 1.
We call Ps is transmit power at the base station. Following
principle of RIS, the received signal reflected by the RIS can
be formulated by
yNU =
N∑
i=1
hie
j8igiN
(√
a1Pss1 +
√
a2Pss2
)
+ w+ n, (1)
yFU =
N∑
i=1
hie
j8igiF
(√
a1Pss1 +
√
a2Pss2
)
+ w+ n, (2)
where 8i stands for the adjustable phase induced by the i-th
reflecting metasurface of the RIS, n is the additive white
Gaussian noise (AWGN) and variance equal N0, w is hard-
ware noise term, w ∈
(
0,
(
k2t + k
2
r
)
Ps
)
. In this case, we call
kt , kr are the distortion from the transmitter and receiver hard-
ware imperfections, and they can be modeled as a zero-mean
complex Gaussian process with variances |A|2k2t Ps, |A|
2k2r Ps
respectively.1
1It is noted that this model has been adopted in the literature by provid-
ing insights in several analytical and experimental such as [38]. In [39],
RIS-aided millimeter-wave (mmWave) systems is studied to address the
problems of the phase noise at RIS and the quantization error at base
stations. However, such impairments can be applied in other framework of
performance analysis.
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这里a1和a2可以看成是分配给NU和FU的传输功率效率/百分比
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硬件噪声
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硬件失真模型
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A. Hemanth et al.: Outage Performance Analysis of Reconfigurable Intelligent Surfaces-Aided NOMA
It is worth noting thatw is associated with hardware imper-
fection situations at transmitters and receivers. We denote
A =
N∑
i=1
|hi| |giN |, B =
N∑
i=1
|hi| |giF | for ease in further
computation.
At user NU, we consider FU’s signal as noise, and the
maximized signal to noise and distortion ratio (SNDR) to
detect signal s2 is given by [1]
9NU ,s2 =
|A|2a2Ps
|A|2
(
k2t + k
2
r
)
Ps + N0 + |A|2a1Ps
(3)
We can rewrite SNDR at user NU as below
9NU ,s2 =
|A|2a2ρs
|A|2
(
k2t + k
2
r
)
ρs + 1+ |A|2a1ρs
, (4)
where ρs =
Ps
N0
is so-called as signal to noise ratio (SNR) at
the base station.
It is noted that, we can rewrite (4) as
9NU ,s2 =
|A|2a2
|A|2
(
k2t + k
2
r
)
+
1
ρs
+ |A|2a1
(5)
By performing SIC at user NU, noise signal from user FU
is deleted, then we can compute SNDR to detect signal for
user NU as
9NU ,s1 =
|A|2a1Ps
|A|2
(
k2t + k
2
r
)
Ps + N0
(6)
Then, the SNDR at user NU can be rewritten by
9NU ,s1 =
|A|2a1ρs
|A|2
(
k2t + k
2
r
)
ρs + 1
. (7)
Similarly, we obtain SNDR at user NU to detect its own
signal as
9NU ,s1 =
|A|2a1
|A|2
(
k2t + k
2
r
)
+
1
ρs
. (8)
The user FU has different characteristic with NU, it does
not rely on SIC, we can obtain SNDR at user FU to detect its
own signal as
9FU ,s2 =
|B|2a2
|B|2
(
k2t + k
2
r
)
+
1
ρs
+ |B|2a1
(9)
Remark 1:We note that the SNDR in various expressions,
for example in (8), (9) imply that these users have the perfect
knowledge of channels hi, giN and giF . The channel state
information related to RIS, hi, giN and giF , are assumed to
be available via the channel estimation methods described in
[37]. The information about the predetermined beamforming
vectors is expected to be sent to from the RIS using a reli-
able control channel to the near and far users. Furthermore,
we note that the SNDR expressions contain the products
of the complex Gaussian distributed random variables, and
hence they are more complicated than that of conventional
NOMA.
III. PERFORMANCE ANALYSIS
In this section, based on the proposed approximations,
we derive new closed-form expressions for the outage proba-
bility, and throughput in delay-limited transmission mode for
the considered RIS-aided wireless systems.2
The considered RIS-aided NOMA system can classify
different users with corresponding required quality of ser-
vice (QoS) which is associated partly with locations of FU
and NU. In this case, outage probability is defined as ability
of SNDR 9NU ,s1 less than the predefined SNDR thresholds.
We denotePr(.) as outage probability. It can be formulated by
Pout = Pr (9 ≤ ρth) , (10)
where 9 and ρth are denoted as SNDR and SNDR threshold
respectively.
A. OUTAGE PROBABILITY AT USER NU
In this case, outage behavior at user NU occurs once user
NU cannot detect FU’signal and NU’s signal as well. We can
formulate such worse circumstance as below
Pout = Pr
(
9NU ,s1 ≤ ρth1, 9NU ,s2 ≤ ρth2
)
, (11)
where ρth1, ρth2 correspond to SNDR thresholds of users NU
and FU respectively. It is noted that ρth1 = 22R1 − 1, ρth2 =
22R2 − 1 with R1,R2 are target rates for NU, FU respectively.
We first compute outage probability for user NU when NU
cannot detect FU’s signal as below
When NU cannot detect FU’s signal, such outage event can
be addressed by
P0=Pr
(
|A|2a2
|A|2
(
k2t +k
2
r
)
+
1
ρs
+ |A|2a1
≤ ρth2
)
. (12)
Proposition 1: The closed-form expression of outage prob-
ability when NU cannot detect FU’s signal can be written
as (13), shown at the bottom of the next page.
Proof: See in Appendix A.
When NU cannot detect its own signal, such outage event
can be addressed by
P1 = Pr
(
|A|2a1
|A|2
(
k2t + k
2
r
)
+
1
ρs
≤ ρth1
)
(14)
Proposition 2: The closed-form expression of outage
probability when NU cannot detect its own signal and such
expression can be written as (15), shown at the bottom of the
next page.
Proof: See in Appendix B.
Next, we can achieve outage probability at user NU as
below
Pout,NU = P0 × P1. (16)
2The expressions of average bit error rate (BER), and ergodic capacity
are derived in [36] to provide extra performance metrics for the considered
RIS-aided wireless systems. Therefore, we do not intend to replicate these
metrics in this study
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SIC这里指的是串行干扰删除，基本原理是逐步减去最大信号功率用户的干扰，SIC 检测器在接收信号中对多个用户逐个进行数据判决，判决出一个用户就同时减去该用户信号造成的多址干扰（MAI），按照信号功率大小的顺序来进行操作，功率较大信号先进行操作。 这样一直进行循环操作，直至消除所有的多址干扰为止
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通信信道的中断概率是不支持给定信息速率的概率，因为信道容量可变。 中断概率定义为信息速率小于所需阈值信息速率的概率。 它是在指定时间段内发生中断的概率
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A. Hemanth et al.: Outage Performance Analysis of Reconfigurable Intelligent Surfaces-Aided NOMA
In following computations, the upper and lower incomplete
Gamma functions [ [40], eq. (8.350/2), (8.350/3)] are respec-
tively represented by γ (., .), while the Gamma function is
represented by 0(., .) [ [40], eq. (8.310)].
From (16), when 2 = max (ρth1, ρth2) and 2 ≤
1
k2t +k
2
r
, the closed-form expression of outage probability at
user NU is given as (17), shown in the middle of the
next page.
Remark 2: From (17), we observe that, for fixed data rates,
the outage probability decreases as N increases; thus, the
quality of service at user NU can be improved. Similarly, for
a given N , as we increase data rates, the outage probability
becomes worse.
B. OUTAGE PROBABILITY AT USER FU
The outage probability of user FU can be expressed by
Pout,FU = Pr
(
|B|2a2ρs
|B|2
(
k2t + k
2
r
)
ρs + 1+ |B|2a1ρs
≤ ρth2
)
.
(18)
Proposition 3: The closed-form expression of outage prob-
ability when FU cannot its own signal can be formulated as
(19), shown at the bottom of the next page.
Proof: Since the method of proof is similar with that of
Proposition 2, we do not consider it here.
C. DIVERSITY ORDER FOR NEAR USER
To provide insights of the obtained expression of outage
probability, we can compute the diversity order as
DNU = − lim
ρs→∞
log2
(
Pout,NU
)
log2 (ρs)
(20)
Then, we can simplify (20) as (21), shown at the bottom of
the next page.
Next, the diversity order of user NU is given by
DNU =
√
a1a2
256
N 2
4
. (22)
D. DIVERSITY ORDER FOR FAR USER
Similarly, we can calculate the diversity order for user FU as
DFU = − lim
ρs→∞
(
log2
(
Pout,FU
)
log2 (ρs)
)
. (23)
Then, we have diversity order for user FU as
DFU =
√
a2π2
a1(16− π2
N
4
. (24)
E. THROUGHPUT
In this scenario, we consider the throughput in delay-limited
transmission for RIS-aided NOMA system. As further per-
formance metric, the throughput of the whole system corre-
sponding the fixed bit rate R1, R2 for different demands of
services for users NU and FU, and such throughput can be
computed by
T = R1
(
1− Pout,NU
)
+ R2
(
1− Pout,FU
)
. (25)
IV. NUMERICAL RESULT
In this section, we investigate the performance of the
RIS-aided NOMA systems. We set level of hardware impair-
ments k2t = k
2
r = k = 0.1 except for specific cases.
For NOMA deployment, we set a1 = 0.3, a2 = 0.7.
All presented illustrations include average results over 106
independent channel realizations for the outage probability.
Although different QoS requirements for two users, we just
simulate same target rates for them, i.e. γth1 = γth2 = γth.
Fig. 2 shows the outage performance of RIS-aided NOMA
by comparing many cases of . In three cases of ρth at fixed
N = 10, it is shown that RIS-aided NOMA can improve
its performance at higher SNDR threshold ρth. Furthermore,
when we enhance transmit SNR at base station the received
signal at destinations can improve as well, as shown in Fig. 2,
very low value of outage probability can be achieved as
we can see with curves of outage probability. This can be
possibly explained by the fact that higher transmit SNR at
the base station leads to higher SDNR and hence the corre-
sponding outage probability can be enhanced. More impor-
tantly, RIS-aided NOMA shows outage performance in two
P0 =
γ
(
π2
16−π2
N , 2π
16−π2
√
a2
a1+
(
k2t +k
2
r
)
ρth2
√
ρth2
ρs
)
0
(
π2
16−π2
N
) , ρth2 ≤ 1k2t +k2r
1, otherwise
(13)
P0 =
γ
(
π2
16−π2
N , 2π
16−π2
√
a1
√
1+(k2t+k2r)ρth1
√
ρth1
ρs
)
0
(
π2
16−π2
N
) , ρth1 ≤ 1
k2t+k2r
1, otherwise
(15)
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A. Hemanth et al.: Outage Performance Analysis of Reconfigurable Intelligent Surfaces-Aided NOMA
FIGURE 2. Outage probability for case N = 10 (For near user).
methods of simulations, i.e. curves of outage probability in
Monte-Carlo match very tight with analytical results obtained
via mathematical derivations in (17). Here, we notice that the
outage performance of near user can be improved at higher
value of ρs although this user has hardware impairment.
Figure 3 demonstrates the outage probability of user NU
as a function of the transmission SNR ρs if we change values
of ρs and N . As a benchmark, the outage performance of
NOMA dual-hop relaying systems without RIS shows the
worst outage performance (case of N = 1). It is noted that
diversity order found in (20), and (22) which depends on
the number of RIS’s metasurfaces and not from the level
of hardware imperfections. Further more, power allocation
factor makes influence on outage performance.
FIGURE 3. Outage probability for different N and ρth (For near user).
Figure 4 illustrates the outage probability as a function
of the transmission SNR at the base station, for different
values of ρth and k , with fixed metasurfaces N = 5. We con-
sider perfect hardware impairment k = 0 as a benchmark,
the best outage performance can be observed for the ideal
case in which both the transmitter and receiver does not
experience the impact of hardware impairments. Moreover,
we observe that independently of ρs and k , degraded trends
on outage performance can be observed if we increase ρth.
It is worth noting that the importance of accurately mod-
eling the transmitter and receiver’s hardware imperfections
when evaluating the performance of RIS-assisted NOMA
systems. Moreover, we observe that the impact of hardware
P0 =
γ
(
π2
16−π2
N , 2π
16−π2
√
a1
√
1+(k2t+k2r)ρth1
√
ρth1
ρs
)
0
(
π2
16−π2
N
) × γ
(
π2
16−π2
N , 2π
16−π2
√
a2
√
a1+(k2t+k2r)ρth2
√
ρth2
ρs
)
0
(
π2
16−π2
N
)
(17)
P0 =
γ
(
π2
16−π2
N , 2π
16−π2
√
a2
√
a1+(k2t+k2r)ρth2
√
ρth2
ρs
)
0
(
π2
16−π2
N
) , ρth2 ≤ 1k2t+k2r
1, otherwise
(19)
DNU = − lim
ρs→∞
log2
γ
(
π2
16−π2
N , 2π
16−π2
√
a1√
1+(k2t+k2r)ρth1
√
ρth1
ρs
)
0
(
π2
16−π2
N
)
×
γ
(
π2
16−π2
N , 2π
16−π2
√
a2√
a1+(k2t+k2r)ρth2
√
ρth2
ρs
)
0
(
π2
16−π2
N
)
log2 (ρs)
(21)
VOLUME 8, 2020 212161
A. Hemanth et al.: Outage Performance Analysis of Reconfigurable Intelligent Surfaces-Aided NOMA
FIGURE 4. Outage probability vs ρs, for different values of ρth and k ,
assuming N = 5 (for near user).
FIGURE 5. Outage probability, for different values of N and K, for
ρth = 10dB (For near user).
imperfections becomes more severe when we increase ρth.
Similar trends of outage performance of user NU can be seen
when we change values of N as Fig. 5.
In Fig. 6, we can see variations of outage probability for
user FU. Similarly, case of N = 100 exhibits significant
improvement of outage performance for user FU. It can be
seen that big gap of outage probability when we change the
number of metasurfaces from N = 1 to N = 10. The reason
is that higher number of metasurfaces contributes to improve
SNDR, then the corresponding outage probability can be
enhanced. In other words, we observe that the impact of the
thresholds ρth on the RIS-assisted NOMA system would be
significant concern at two following scenarios (N = 10,
N = 100.
It can be concluded that outage probability of user FU
outperforms than that of user NU, as Fig. 7. The main reason
is that higher level of power is assigned to transmit signal
s2 for user FU. The performance gap among two users can be
seen clearly at case ofN = 1, but such gap becomes smaller at
FIGURE 6. Outage probability versus transmit SNR at base station for
user FU.
FIGURE 7. Comparison between outage behavior of NU and FU.
FIGURE 8. Throughput of the entire system.
case of N = 10. Other trends of curves of outage probability
can be seen similarly as previous figures.
Fig. 8 shows throughput performance of the consid-
ered system when we increase ρs. In this case, we set
212162 VOLUME 8, 2020
A. Hemanth et al.: Outage Performance Analysis of Reconfigurable Intelligent Surfaces-Aided NOMA
FIGURE 9. Comparison between RIS systems using NOMA and OMA.
R1 = R2 = 1 bps/Hz. That means our system can approach
to 2 at very high value of ρs. It can be explained that such
throughput depends on achieved outage probabilities in previ-
ous steps. It can be confirmed that our RIS system relying on
NOMA is better than that using OMA, as Fig. 9. This finding
benefits to design RIS in wireless systems to satisfy massive
connections.
V. CONCLUSION
In this paper, we have considered a generalized hardware
imperfections model in RIS systems at both transmitter and
receiver in the context of NOMA, which has been validated in
several prior works, in order to assess the impact of hardware
impairments on RIS-aided NOMA wireless systems. In par-
ticular, we derived simple closed-form expressions to evalua-
tion for outage performance and throughput in delay-limited
mode, which takes into account the level of transceivers hard-
ware imperfections. Through out simulations, the number of
meta-surfaces at the RIS, as well as the transmit SNR at the
base station and the SNDR threshold are determined as main
factors make influence on outage probability. Our results
manifested the detrimental impact of transceiver hardware
imperfections on the outage and throughput performance of
these systems. It can be concluded that main results are
relying on the importance of accurately modeling the level
of hardware impairments when evaluating the performance
of our considered systems as reported. In future, we consider
RIS systems for case of multiple users under the context of
NOMA scheme.
APPENDIX A
PROOF OF PROPOSITION 1
The expression of outage probability when the user NU can-
not detect user FU’s signal is given by
P0 = Pr
[
|A|2
(
a2 − ρth2
(
k2t +k
2
r
)
ρs
)
+a1 ≤ ρth2
]
(A.1)
We can rewrite (A.1) as
P0 = Pr
[
|A|2
(
a2 − ρth
(
k2t + k
2
r
))
+ a1 ≤
ρth2
ρs
]
(A.2)
Considering condition of ρth2 ≤
a2
k2t +k
2
r+a1
, we have new
expression as
P0 = Pr
[
|A|2 ≤
a2
a1 +
(
k2t + k
2
r
)
ρth2
ρth2
ρs
]
(A.3)
It is equivalent to
P0 = Pr
A ≤ √a2√
a1 +
(
k2t + k
2
r
)
ρth2
√
ρth2
ρs
(A.4)
We callF(X ) as the cumulative distribution function (CDF)
of variable X , then (A.4) is rewritten by
P0 = FA
A ≤ √a2√
a1 +
(
k2t + k
2
r
)
ρth
√
ρth2
ρs
(A.5)
By applying [ [41], eq. (8)], we have CDF as
FA (x) =
(
γ
(
a+ 1, xb
)
0 (1+ a)
)
, (A.6)
in which a = k
2
1
k2
− 1; b = k2k1 ; k1 =
Nπ
2 ; k2 = 4N
(
1− π
2
16
)
.
In our situation, we replace x =
√
a2√
a1+
(
k2t +k
2
r
)
ρth
√
ρth
ρs
to
(B.3), then such outage probability is given by
P0 =
γ
1+ k21
k22
− 1,
√
a2√
a1+(k
2
t +k
2
r )ρth
√
ρth2
ρs
k2
k1
0
(
k21
k2
− 1
)
+ 1
(A.7)
Now, we can achieve such outage probability as
P0 =
γ
(
Nπ
2
)2
(
4N
(
1− π
2
16
))2 ,
√
a2√
a1+(k
2
t +k
2
r )ρth
√
ρth2
ρs
4N
(
1− π
2
16
)
Nπ
2
0
( (
Nπ
2
)2
4N
(
1− π
2
16
)
)
(A.8)
This completes the proof.
APPENDIX B
PROOF OF PROPOSITION 2
We recall outage probability as below
P1 = Pr
[
|A|2a1 − ρth1
(
|A|2
(
k2t + k
2
r
)
ρs + 1
)]
≤ ρth1
(B.1)
It is noted that we can rewrite (B.1) as
P1 = Pr
[
|A|2
(
a1 − ρth1
(
k2t + k
2
r
))
+ 1 ≤
ρth1
ρs
]
(B.2)
VOLUME 8, 2020 212163
A. Hemanth et al.: Outage Performance Analysis of Reconfigurable Intelligent Surfaces-Aided NOMA
Considering condition of ρth1 ≤
a1
1+(k2t +k
2
r )
, we have new
expression as
P1 = Pr
[
|A|2 ≤
a1
1+
(
k2t + k
2
r
)
ρth1
ρth1
ρs
]
(B.3)
Similarly, P1 can be rewritten as
P1 = Pr
A ≤ √a1√
1+
(
k2t + k
2
r
)
ρth1
√
ρth1
ρs
(B.4)
Similarly, such outage probability is expressed by
P1 =
γ
(
Nπ
2
)2
(
4N
(
1− π
2
16
))2 ,
√
a1√
1+(k2t +k
2
r )ρth1
√
ρth1
ρs
4N
(
1− π
2
16
)
Nπ
2
0
( (
Nπ
2
)2
4N
(
1− π
2
16
)
)
(B.5)
This is end of the proof.
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ATLURI HEMANTH was born in Andhra Pradesh,
India, in 1997. He received the B.E degree in
electronics and communication engineering from
the Madanapalle Institute of Technology and Sci-
ence (MITS), Madanapalle, India, in 2018, and
the master’s degree from the Department of Com-
putational Microelectronics. He worked as a
Research Assistant with Asia University. His pre-
vious projects are with Nuvoton Technology Cor-
poration: Field-Plate Optimization of AlGaN/GaN
HEMTs, GaN HEMT Device Calibration by Physical TCAD, and LDMOS
1200VWITH linear P-Top Technology. He is currently working with Taiwan
Semiconductor Manufacturing Company (TSMC), where he is involved in
optimal permutation of power transmission line at high technology nano-fab
to decrease electromagnetic influence. He is also working as an Associate
Research Assistant with the Wireless Communication (WICOM) Lab that
is led by Dr. Dinh-Thuan Do, Asia University. His research interests include
the NOMA, backscatter systems, cognitive radio, compound semiconductors
device, reliability issues, and high-voltage applications of semiconductors.
KAVETI UMAMAHESWARI was born in Puliven-
dula, Andhra Pradesh, India. She received the
Bachelor of Technology degree from the Madana-
palle Institute of Technology and Science (MITS),
Madanapalle, India. She is currently pursuing the
master’s degree with computer science and infor-
mation engineering, Asia University, Taiwan. She
is also a member of the Wireless Communica-
tion (WICOM) Lab that is led by Dr. Dinh-Thuan
Do (Alex). Her research interests include NOMA,
communication systems, and reconfigurable intelligent surfaces (RIS).
ARJUN CHAKRAVARTHI POGAKU was born
in India. He received the B.S. degree from the
Madanapalle Institute of Technology and Science
(MITS), India. He is currently pursuing the mas-
ter’s degree with the Department of Computer
Science and Information Engineering, Asia Uni-
versity. He is also a member of the Wireless
Communication (Wi-Com) Lab, Asia University.
His research interests include telecommunication
engineering, wireless communications, and
satellite communications
DINH-THUAN DO (Senior Member, IEEE)
received the B.S., M.Eng., and Ph.D. degrees from
Vietnam National University–Ho Chi Minh City
(VNU-HCM), in 2003, 2007, and 2013, respec-
tively, all in communications engineering. Prior
to joining Ton Duc Thang University, he was a
Senior Engineer with the VinaPhone Mobile Net-
work from 2003 to 2009. He was a Visiting Ph.D.
Student with the Communications Engineering
Institute, National Tsing Hua University, Taiwan,
from 2009 to 2010. His publications include over 75 SCIE/SCI-indexed
journal articles, over 60 SCOPUS-indexed journal articles, and over 50 inter-
national conference articles. He is sole author in one textbook and one book
chapter. He was a recipient of the Golden Globe Award from the Vietnam
Ministry of Science and Technology (top ten excellent young scientists
nationwide), in 2015. He is currently serving as an Editor forComputer Com-
munications (Elservier) and KSII Transactions on Internet and Information
Systems. He is also serving as an Associate Editor for EURASIP Journal
on Wireless Communications and Networking (Springer) and Electronics.
He was a Lead Guest Editor of the Special Issue on Recent Advances for
5G: Emerging Scheme of NOMA in Cognitive Radio and Satellite Commu-
nications in Electronics, in 2019. He is also serving as a Guest Editor for the
Special Issue on Massive Sensors Data Fusion for Health-Care Informatics
in Annals of Telecommunications (Springer), in 2020, the Special Issue on
Power Domain Based Multiple Access Techniques in Sensor Networks in
International Journal of Distributed Sensor Networks (IJDSN), in 2020, and
the Special Issue on UAV-enabled B5G/6G Networks: Emerging Trends and
Challenges in Physical Communication (Elservier), in 2020.
BYUNG MOO LEE (Senior Member, IEEE)
received the Ph.D. degree in electrical and com-
puter engineering from the University of Califor-
nia at Irvine, Irvine, CA, USA, in 2006.
He had ten years of industry experience, includ-
ing research positions with the Samsung Electron-
ics Seoul Research and Development Center, the
Samsung Advanced Institute of Technology, and
the Korea Telecom Research and Development
Center. He is currently an Associate Professor with
the Department of Intelligent Mechatronics Engineering and Convergence
Engineering for Intelligent Drone, Sejong University, Seoul, South Korea.
During his industry experience, he participated in IEEE 802.16/11, Wi-Fi
Alliance, and 3GPP LTE standardizations and also participated in theMobile
VCE and Green Touch Research Consortiums, where he made numerous
contributions and filed a number of related patents. His research inter-
ests include the areas of wireless communications, signal processing, and
machine learning applications. He served as a Vice Chairman for the Wi-Fi
Alliance Display MTG from 2015 to 2016.
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