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INDIAN JOURNAL OF SCIENCE AND TECHNOLOGY
RESEARCH ARTICLE
OPEN ACCESS
Received: 16-02-2024
Accepted: 01-04-2024
Published: 19-04-2024
Citation: Anwar H, Abass AAA,
Kadhim R (2024) Performance of
Relaying System with NOMA over
Symmetric
α
-Stable Noise Channels.
Indian Journal of Science and
Technology 17(17): 1745-1754. https
://doi.org/10.17485/IJST/v17i17.432
∗Corresponding author.
huda@utq.edu.iq
Funding: None
Competing Interests: None
Copyright: © 2024 Anwar et al. This
is an open access article distributed
under the terms of the Creative
Commons Attribution License, which
permits unrestricted use,
distribution, and reproduction in
any medium, provided the original
author and source are credited.
Published By Indian Society for
Education and Environment (iSee)
ISSN
Print: 0974-6846
Electronic: 0974-5645
Performance of Relaying System with
NOMA over Symmetric
α
-Stable Noise
Channels
Huda Anwar1∗, Ahmed A Alabdel Abass1, Rawaa Kadhim1
1Department of Electrical and Electronic Engineering, University of Thi-Qar, Iraq
Abstract
Objectives: This paper investigates the performance of a candidate 5G
transmission system technique that is Non-Orthogonal Multiple Access (NOMA)
over
α
-stable channels. This type of channel gets more attention in the
research community because of its ability to model new IoT scenarios.
However, there is a research gap in applying this type of channel to different
wireless communications scenarios. In this work, we envision a scenario where
users employ NOMA communications in the presence of an obstacle. As
our mathematical analysis and simulation results show, there is a significant
difference in performance when considering
α
-stable channels. Methods: To
characterize the performance of the proposed noise channel, performance
metrics such as outage probability and achievable rate are discussed. More
particularly, we derive expressions for both outage probability and achievable
rate for three NOMA users, considering the near user as a relay. In this paper,
we consider additive symmetric
α
-stable noise channels with alpha
α
∈(1, 2).
We present expressions for achievable rate and outage probability for each
user (near, middle, and far) and investigate its behavior for different values
of alpha (
α
). Findings: Based on the simulation results, it is shown that the
high achievable rate observed for low alpha values while reduced as alpha is
increased. Also, due to the influence of alpha, the outage probability is highly
affected by
α
for small rate thresholds (Ro). In an envisioned scenario of three
users with only one user forwarding the transmission to the other two, our
results show that the near and middle users’ outage probability decreases
as alpha
α
increases. Novelty: Despite this extensive study of the NOMA on
individual channels, transmission under
α
-stable channel is not considered to
the best of the authors’ knowledge.
Keywords: NOMA; relaying; Cooperative Non-Orthogonal Multiple Access;
Symmetric
α
-Stable Noise Channels; Achievable rate
1 Introduction
e rapid growth of mobile internet devices is immense and will supplementary increase
over the next few decades, which will certainly pose a massive trac demand for
persistent communications(1). e h generation (5G) mobile communication
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networks have raised concerns due to their ability to support diverse applications and communication needs. As cellular
communication improves, the number of mobile users continues to grow(2)on a daily basis, resulting in robust trac. Mobile
users in 5G are estimated to be 100 times more than in 4G. e 5G network faces high demand; one of the future solutions is
the use of Nonorthogonal multiple access (NOMA).
Radio access technologies for cellular mobile communications are typically characterized by multiple access schemes, e.g.,
frequency division multiple access (FDMA), time division multiple access (TDMA), and code division multiple access (CDMA),
where signals are transmitted at dierent frequency, time, and codes. However, NOMA is a promising radio access strategy for
5G wireless networks due to its considerable spectral eciency and capacity to service a large number of users(3). e key
characteristic behind NOMA is that multiuser signals are superimposed at the base station (BS) with dierent power allocation
coecients but at the same frequency/time/code at the transmitter side. On the receiver side, successive interference cancellation
(SIC) is applied to the user with a better channel condition, in order to remove the other users’ signals before detecting its own
signal(4).
Cooperative communications schemes have received a considerable recommendation for 5G implementation due to their
ability to oer many advantages, such as minimizing fading, while addressing the problem of implementing more antennas on
small communications terminals, such as spatial diversity(5). On the other hand, the combination of NOMA with cooperative
relaying has been considered recently to improve reliability and system capacity(6) . Meaning that users with better channel
conditions need to decode the messages for the others, and therefore these users can be used as relays to improve the reception
reliability for the users with poor connections to the base station. e key advantage of exploiting cooperative communications
in NOMA is that it can enhance system performance, including eciency and reliability, which are both key challenges in
wireless communication.For instance, the authors in(2)suggested a relay-to-relay (R2R) scheme to provide a greater sum rate
because it employs a relay based on the power available to it. ey consider a total of 500 users at any given moment, with random
arrivals and departures. e user’s arrival and departure processes are random using a Poisson distribution. e performance of
NOMA-based cooperative relay transmission CRS over Rician-shadowed fading channels has been analyzed in(5)and provided
specic analytical formulations for achievable rates. Furthermore, in(7)authors studied a cooperative relaying system with
NOMA (CRS-NOMA) system’s performance over
κ
−
µ
fading channels, namely outage probability and achievable rate as
performance metrics. Analytical formulas for outage probability and average achievable rates were developed for two symbols.
In(3), the authors have considered a performance of a bidirectional relaying system that utilizes non-orthogonal multiple access
BR-NOMA in terms of ergodic sum capacity, outage probability, and outage sum capacity. Analytical equations for ESC, OP,
and OSC are oered for optimal information exchange under perfect and imperfect consecutive interference cancellation. In(8)
the author’s study examines the performance of a cooperative relaying full duplex Non Orthogonal Multiple Access (CR-FD-
NOMA) system in downlink and uplink scenarios over Nakagami-m fading distribution by deriving an approximated closed
form BER expression of both the users in downlink and uplink systems.
In wireless networks controlled by the
α
-
µ
generalized fading model, the author’s (9)examines the average achievable rate
and outage probability of a cooperative relaying system (CRS) based on NOMA (CRS-NOMA). e average achievable rate is
represented in closed form using Meijer’s G-function and the extended generalized bivariate Fox’s H-function (EGBFHF), and
the outage probability is denoted using the lower incomplete Gamma function.
e performance of a two-user downlink NOMA network has been considered by assuming perfect and imperfect channel
state information (CSI) in (10). ey derived a closed-form expression for the outage probability over
η
−
µ
fading channels. e
outage performance of two cooperative relaying scenarios of the cooperative NOMA system over Nakagami-m fading channels
has been investigated in(11,12). Furthermore, in (13)the authors used relay nodes with NOMA To improve system performance
in addition to beamforming. e system performance is demonstrated through closed-form expression of outage probability
(OP) and ergodic rate (ER) over Rayleigh fading channels.
In an eort to rise the transmission reliability for the sixth generation (6G) cognitive Internet of ings network, some
academics have recently taken cooperative relaying protocols into consideration in their research, as in(14)where achievable
rates of the cognitive IoT system with amplify-and-forward (AF) and decode-and-forward (DF) relaying modes are maximized.
However, in underwater, wireless communications(15), signal and image processing(16), and molecular communications(17),
impulsive noise can arise; impulsive cannot be held using Gaussian models. A key class of these models are the symmetric
α
-
stable distributions, which can be viewed as generalizations of zero-mean Gaussian models (
α
= 2) and preserve stability for
independent random variables. is approach leads to the additive symmetric
α
-stable noise channel. Interestingly, among the
exploited distributions, the
α
-stable distribution could most precisely t the actual deployment of legacy base stations (BSs),
which is also consistent with the trac distribution in broadband and cellular networks(18). Despite this extensive study of the
NOMA on individual channels, it remains
α
-stable. ere is no study on
α
-stable noise channel, to the best of the authors’
knowledge. e rest of this paper is organized as follows: Section II introduces the proposed system model. Simulation results
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Anwar et al. / Indian Journal of Science and Technology 2024;17(17):1745–1754
and discussions are presented in the III Section. Our conclusions are outlined in Section IV.
2 Methodology
In this section, we study the performance of an envisioned scenario of cooperative NOMA over alpha stable noise channel. We
provide an expression for the outage probability and the achievable rate for each user. We adopt the system model proposed
in(19). In this system model, a downlink cooperative NOMA network system with the source represented by the base station
(BS), and three users: the near user (Dn), the middle user (Dm), and the far user (D f). Assuming the near user has very good
channel conditions with the base station, assume that each node in the system has a single antenna (the base station and each
user has one antenna). Also, consider the model with a xed power allocation has a power control circuit in the base station
to divide the transmit power among the three users and give the signals a power weight. Unlike Gaussian models, the
α
-stable
distribution is used which characterized by heavy tails, which accounts for a high probability of large amplitude noise(20).
Evaluating system performance under Additive Symmetric
α
-Stable Noise fading channel is rather challenging. In order to
derive the exact expression of the achievable rate, we propose an analytical method using incomplete Gamma function.
e
α
-stable random variables are heavy-tailed probability density functions. e probability density function of an
α
-
stable random variable is parameterized by four parameters(21): the exponent 0 <
α
≤2; the scale parameter
γ
∈R+; the skew
parameter
β
∈[−1, 1]; and the shi parameter
δ
∈R. As such, a common notation for a general
α
-stable distributed random
variable is N′∼S
α
(
γ
,
β
,
δ
). In the case
β
=
δ
= 0, the random variable N is a symmetric
α
-stable random variable denoted
by N ∼S
α
(
γ
, 0, 0)(22). Specically, we consider the case where there are users located at the cell edge or out of coverage, in
that case their signal can be relayed by a relay to improve the reliability for those users(23). is scenario is depicted in Figure 1
below.
Fig 1. e envisioned scenario
Assume that the power allocation vector is w={wn,wm,wf}, for system in Figure 1the achievable rate according to(19),
Rn
coop =1
2log2(1+|hsn |2P
twn
σ
2)(1)
Rm
coop =1
2log2(1+|hsn |2P
twm
σ
2)(2)
Rf
coop =1
2log2(1+|hsn |2P
twf
|hsn|2P
tWm+
σ
2)(3)
Where:
hsn : e fading coecient between the BS and the near user Dn.
hnm : e fading coecient between the near user Dnand the middle user Dm.
hn f : e fading coecient between the near user Dnand the far user D f.
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Wn: power allocation coecient for near user
Wm: power allocation coecient for middle user
Wf: power allocation coecient for far user
σ
2: the variance of the AWGN.
P
t: transmitted power
In the next section we provide mathematical expression of the achievable for the
α
-stable noise channel model for each user.
2.1 Achievable Rate
In Equation (4) the achievable rate of the near user under symmetric
α
-stable noise channel is presented, the near user (relay)
will send the signals to both the middle and far users through a special channel between the relay and the middle user and
another one between the relay and the farthest user. Assume that the power allocation vector is w={wn,wm,wf}, then the rate
equations for the users can be written as shown in Equations (4), (5) and (6).
Rn
coop =1
α
log2(1+|hsn |
α
c
α
n
γα
N
)(4)
Rm
coop =1
α
log2(1+|hnm |
α
c
α
m
γα
N
)(5)
Rf
coop =1
α
log2(1+
hn f
α
c
α
f
hn f
α
c
α
m+
γα
N
)(6)
Where:
cn=wnP
t(7)
cm=wmP
t(8)
cf=wfP
t(9)
•hsn : e fading coecient between the BS and the Dn.
•hnm : e fading coecient between the Dnand the Dm.
•hn f : e fading coecient between the Dnand the D f.
•
γ
N: symmetric
α
-stable noise channel.
2.2 Outage probability
e outage probability dened as the probability that the received SNR falls below a given threshold(22)is expressed
mathematically as follows:
P
out =Pr(C≤Ro)(10)
Next we provide the outage probabiltiy expression in Claim 1.
Claim 1: For the scenario shown in Figure 1with the communications links follow
α
-stable distribution where 0 <
α
≤2,
then the outage probability expression for the three users is given by:
1.For the near user:Pn
out ∼
=1−exp [−
λ
(
2(
α
Rn
0)−1
SNR
α
n
)
2
α
](11)
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2.For the midd le user:Pm
out ∼
=1−exp [−
λ
((2
α
Rm
0)−1
SNR
α
m
)
2
α
](12)
3.For t he far user:Pf
out ∼
=1−exp [−
λ
y
γα
N
(1−yc
α
m)
2
α
]i f
β
f
β
m
>((2
α
Rf
o)−1)
1
α
(13)
Proof:
Outage probability for the near user:
Starting by the denition of the outage probability,
Pn
out =PrRn≤Rn
O≤Pr1
α
log2(1+(hsn |
α
c
α
n
γα
N≤Rn
0
Using the approximation F2
g(x) = 1−e−
λ
x, and let c
α
n
γα
N=SNR
α
n,
en, 1
α
log2(1+|hsn |
α
SNR
α
n)≤Rn
0⇒log2(1+|hsn |
α
SNR
α
n)≤
α
Rn
o
=1+|hsn|
α
SNR
α
n≤2
α
Rn
0=⇒|hsn|
α
≤2(
α
Rn
0)−1
SNR
α
n
=⇒Pn
out =Pr
|hsn|
α
≤(2(
α
Rn
0)−1
SNR
α
n
)
1
α
=1−exp [−
λ
(2(
α
Rn
0)−1
SNR
α
n
)
2
α
=⇒Pn
out ∼
=1−exp [−
λ
(2(
α
Rn
0)−1
SNR
α
n
)
2
α
(11)
Outage probability for the middle user:
Pm
out =PrRm≤Rm
O≤Pr(1
α
log21+|hnm |
α
c
α
m
γα
N≤Rm
0.Using the approximation F2
g(x) = 1−e−
λ
xand letting c
α
m
γα
N
=SNR
α
m,
=⇒1
α
log2(1+|hnm |
α
SNR
α
m≤Rm
0=⇒log2(1+|hnm |
α
SNR
α
m)≤
α
Rm
0=⇒1+|hnm|
α
SNR
α
m≤2
α
Rm
0. As a result,
|hnm|
α
≤(2
α
Rm
0)−1
SNR
α
m=⇒Pm
out =Pr(|hnm|
α
≤((2
α
Rm
0)−1
SNR
α
m)
1
α
= 1-exp [-
λ
((2
α
Rm
0)−1
SNR
α
m)
2
α
=⇒Pm
out ∼
=1−exp [−
λ
((2
α
Rm
0)−1
SNR
α
m
)
2
α
(12)
Outage probability for the Far user:
Pf
out ≤PrRf
coop ≤Rf
O≤Pr(1
α
log2(1+|hn f |
α
c
α
f
|hn f |
α
c
α
m+
γα
N
≤Rf
O)
=⇒1+ |hn f |
α
c
α
f
|hn f |
α
c
α
m+
γα
N
≤2
α
Rf
O=⇒|hn f |
α
c
α
f
|hn f |
α
c
α
m+
γα
N
≤2
α
Rf
O−1
Let
hn f
α
=x
α
,y=(2
α
Rf
O)−1
c
α
f, then,
x
α
≤y(x
α
c
α
m+
γα
N)=yx
α
c
α
m+y
γα
N
=⇒x
α
−yx
α
c
α
m≤y
γα
N
=⇒x
α
(1−yc
α
m)≤y
γα
N
Assume 1−yc
α
m>0=⇒yc
α
m<1=⇒(2
α
Rf
O)−1
c
α
f
c
α
m<1
=⇒cf
cm
α
>(2
α
Rf
O)−1=⇒cf
cm
>( (2
α
Rf
O)−1)
1
α
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=⇒
β
fP
t
β
mP
t
>( (2
α
Rf
O)−1)
1
α
=⇒
β
f
β
m
>( (2
α
Rf
O)−1)
1
α
=⇒x≤(y
γα
N
(1−yc
α
m))
1
α
=⇒
hn f
≤(y
γα
N
(1−yc
α
m))
1
α
=⇒Pf
out ≤Pr [
hn f
≤y
γα
N
(1−yc
α
m)1
α
]
=⇒Pf
out ∼
=1−exp [−
λ
y
γα
N
(1−yc
α
m)
2
α
](13)
which proves Claim 1.
Table 1below provides a description for the used notations.
Table 1. Description for the Notation
Notation Description
γα
NSymmetric
α
-stable noise channel
α
Characteristic exponent
β
Skew parameter
δ
Shi parameter
SNR
α
nand SNR
α
mSignal to noise ratio for near (n refer to near user) and middle (m refer to middle
user) user under eect of alpha channel
c
α
n,c
α
mand c
α
fSignal power for near, middle and far user under eect of alpha channel. (n refer
to near user, m refer for middle user and f refer to far user)
wn,wmand wfpower allocation vector for near user, middle user and far user.
In the next section we show the performance of the system according to our derived equations. However, these equations,
Equations (1), (2), (3), (4), (5) and (6), show that the classical assumption of Gaussian channel does not hold and the value of
α
directly aects the performance.
3 Result and discussion
In this section, we use outage probability and achievable rate of system as metrics to verify the performance of the cooperative
NOMA system over symmetric alpha stable noise channel. MATLAB is used to simulate the model.
As seen from Figure 2the achievable rate for both near and middle user are similar. e near user sends the signals to both
the middle and far users through a special channel between the relay and the middle user and another one between the relay
and the farthest user.
From the simulation, one can perceive that the achievable rate changes as
α
it changes from 0.75 to 1.1. For example, at 20
dBm, the achievable rates for near, middle, and far users are = 46 bps/Hz, = 47 bps/Hz, and = 1.7 bps/Hz for
α
equal to 0.75.
At 20 dBm and
α
equal to 1.1, the achievable rates for three users are = 27 bps/Hz, 28 bps/Hz, and 1.16 bps/Hz. Also, results
show that by increasing the transmitted power, an improvement in data rates for the middle user can be achieved, with a value
ranging from 22 bps/Hz to 50 bps/Hz. As
α
increases to 2, it results in a signicant decrease in the achievable rates for all users
compared to the scenario where
α
is 0.75.
In the next part of the simulation we consider the outage probability with dierent cn
γ
Nvalues. e simulated curves are based
on Monte-Carlo simulations over 1000 realizations of the fading channel. Figure 3presents the outage probability for the near
user for dierent values of R0and
α
when cn
γ
Nequals to 1 and 3. As seen from Figure 3for we observe that for small R0the
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Fig 2. e achievable rate performance of near, middel and far users for
α
=0.75,1.1and 2
outage probability is highly inuenced by
α
. As cn
γ
Nincreased to 6 and 10 in Figure 4the outage probability is highly inuenced
by
α
for high R0values.
In Figures 5and 6, for the middle user, the user with the lowest power allocation still suers from changing the value of
α
more than the other users. However, the far user in Figures 7and 8shows interesting behavior because there seems to be a
point below R0≈0.425 where the value of
α
= 2 gives a better outage probability performance for the far user, where the knote
appears in the far user curve at a higher value of R0≈0.64 , also an interesting knote for R0≈0.67. is shows that increasing cn
γ
N
beyond certain limits does not aect the outage probability in a senseable way. As a result, increasing the cn
γ
Nis more benecial
to the far user since this is combined with higher power allocation for that user.
Fig 3. e outage probability for near user for varying R0and
α
, ( cn
γ
N= 1 and cn
γ
N= 3) and
λ
= 1
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Fig 4. e outage probability for near user for varying R0and
α
, ( cn
γ
N= 6 and cn
γ
N= 10) and
λ
= 1
Fig 5. e outage probability for middle user for varying R0and
α
, ( cn
γ
N= 1 and cn
γ
N= 3) and
λ
= 1
Fig 6. e outage probability for middle user for varying R0and
α
, ( cn
γ
N= 6 and cn
γ
N= 10) and
λ
= 1
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Fig 7. Plot of the outage probability for far user for varying R0and
α
, ( cn
γ
N= 1 and cn
γ
N= 3) and
λ
= 1
Fig 8. Plot of the outage probability for far user for varying R0and
α
, ( cn
γ
N= 6 and cn
γ
N= 10 ) and
λ
= 1
4 Conclusion
is paper has investigated user relaying in cooperative NOMA system under symmetric
α
-stable noise channel with three
users. We obtained formulas for the three users’ outage probabilities. e outage probability is greatly impacted by the inuence
of
α
, with this aect being more pronounced for lower values of
α
. Furthermore, we have demonstrated that as
α
increases,
the outage probability for near and middle users rises as well. e simulation ndings demonstrated that, in the case of the
Gaussian distribution model, large achievable rates are shown for low
α
values and decrease as alpha approaches 2. Based
on the analytical results, it was shown that achievable rate of middle user was superior to far user in low
α
due to channel’s
strength. In conclusion, accounting for
α
-stable noise in simulation models for NOMA systems is essential for a more accurate
representation of real-world communication channels. e unique statistical properties of
α
-stable noise introduce challenges
that impact interference, system capacity, and the robustness of NOMA schemes, all of which collectively aect the achievable
rates in the simulated environment. Interestingly, our simulation results have shown that increasing the signal to noise ratio
aects the far user outage probability more than other users and there is some knote in the outage probability curve where
α
=
2 is better than the lower values for medium to high signal to noise ratio values.
References
1) Van-Dinh Nguyen, Duong TQ, Vien QT. Emerging Techniques and Applications for 5G Networks and Beyond. Mobile Networks and Applications.
https://www.indjst.org/ 1753
Anwar et al. / Indian Journal of Science and Technology 2024;17(17):1745–1754
2020;25:1984–1986. Available from: https://doi.org/10.1007/s11036-020-01547- x.
2) Balyan V. Cooperative relay to relay communication using NOMA for energy ecient wireless communication. Telecommunication Systems.
2021;77(2):271–281. Available from: https://dx.doi.org/10.1007/s11235-021-00756- 3.
3) Kader MF, Uddin MB, Sarker MAL, Shin SY. Bidirectional relaying using non-orthogonal multiple access. Physical Communication. 2019;33:266–274.
Available from: https://dx.doi.org/10.1016/j.phycom.2019.01.014.
4) Wang Z, Peng Z, Pei Y, Wang H. Performance Analysis of Cooperative NOMA Systems with Incremental Relaying. Wireless Communications and Mobile
Computing. 2020;2020:1–15. Available from: https://dx.doi.org/10.1155/2020/4915638.
5) Panić SR, Khotnenok S. NOMA cooperative relaying systems over Rician-Shadowed fading channels. Bulletin of Natural Sciences Research. 2022;12(2):31–
35. Available from: https://dx.doi.org/10.5937/bnsr12-40124.
6) Zhang X, Lv N. Performance Analysis of Anti-Interference Cooperative NOMA System for Aviation Data Links. Electronics. 2023;12(10):1–13. Available
from: https://dx.doi.org/10.3390/electronics12102182.
7) Khatalin S, Miqdadi H. On the Performance of Cooperative Relaying Systems with NOMA in Fading Environment. Wireless Communications and Mobile
Computing. 2022;2022:1–15. Available from: https://doi.org/10.1155/2022/1319687.
8) Sashiganth M, iruvengadam SJ, Kumar DS. BER analysis of full duplex NOMA downlink and uplink co-operative user relayingsystems over Nakagami-
m fading environment. Physical Communication. 2020;38:100963. Available from: https://dx.doi.org/10.1016/j.phycom.2019.100963.
9) Kumar V, Cardi B, Flanagan MF. Performance Analysis of NOMA-Based Cooperative Relaying in alpha-µ Fading Channels. In: ICC 2019 -
2019 IEEE International Conference on Communications (ICC). IEEE. 2019. Available from: https://doi.org/10.1109/ICC.2019.8761527.
10) Hữu TQ, Ong MD. Performance Analysis of NOMA Over n-m Fading Channels with imperfect SIC. EAI Endorsed Transactions on Industrial Networks
and Intelligent Systems. 2023;10(1):1–9. Available from: https://dx.doi.org/10.4108/eetinis.v10i1.2833.
11) Gong X, Yue X, Liu F. Performance Analysis of Cooperative NOMA Networks with Imperfect CSI over Nakagami-m Fading Channels. Sensors.
2020;20(2):1–18. Available from: https://dx.doi.org/10.3390/s20020424.
12) Nguyen TTH, Tran XN. Performance of Cooperative NOMA System with a Full-Duplex Relay over Nakagami-m Fading Channels. In: 2019 3rd
International Conference on Recent Advances in Signal Processing, Telecommunications & Computing (SigTelCom). IEEE. 2019. Available from:
https://doi.org/10.1109/SIGTELCOM.2019.8696186.
13) Hieu TC, Cuong NL, Hoang TM, Quan DT, Hiep PT. On Outage Probability and Ergodic Rate of Downlink Multi-User Relay Systems with Combination
of NOMA, SWIPT, and Beamforming. Sensors. 2020;20(17):1–23. Available from: https://dx.doi.org/10.3390/s20174737.
14) Lu W, Si P, Huang G, Han H, Qian L, Zhao N, et al. SWIPT Cooperative Spectrum Sharing for 6G-Enabled Cognitive IoT Network. IEEE Internet of
ings Journal. 2021;8(20):15070–15080. Available from: https://dx.doi.org/10.1109/jiot.2020.3026730.
15) Hägglund K. Symmetric alpha-Stable Adapted Demodulation and Parameter Estimation. 2018. Available from: https://www.diva-portal.org/smash/get/
diva2:1244671/FULLTEXT01.pdf.
16) Ghahfarokhi MAB, Ghahfarokhi PB. Applications of stable distributions in time series analysis, computer sciences and nancial markets. World
Academy of Science, Engineering and Technology. 2009;49:1027–1031. Available from: https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&
doi=be824f0aeca52caa603aa1cb14581513cee2a643.
17) Farsad N, Guo W, Chae CB, Eckford A. Stable Distributions as Noise Models for Molecular Communication. In: 2015 IEEE Global Communications
Conference (GLOBECOM). IEEE. 2015. Available from: https://doi.org/10.1109/GLOCOM.2015.7417583.
18) Zhou Y, Li R, Zhao Z, Zhou X, Zhang H. On the
α
-Stable Distribution of Base Stations in Cellular Networks. IEEE Communications Letters.
2015;19(10):1750–1753. Available from: https://doi.org/10.1109/LCOMM.2015.2468718.
19) Msayer HS, Swadi HL, AlSabbagh HM. Enhancement Spectral and Energy Eciencies for Cooperative NOMA Networks. Iraqi Journal for Electrical and
Electronic Engineering. 2023;19(1):57–61. Available from: https://dx.doi.org/10.37917/ijeee.19.1.7.
20) De Freitas M, Egan M, Clavier L, Savard A, Gorce JM. Power Control in Parallel Symmetric
α
-Stable Noise Channels. In: 2019 IEEE 20th International
Workshop on Signal Processing Advances in Wireless Communications (SPAWC). IEEE. 2019. Available from: https://doi.org/10.1109/SPAWC.2019.
8815443.
21) Qi T, Wang J, Peng Q, Li X, Chen X. Channel Capacity and Bounds In Mixed Gaussian-Impulsive Noise. . Available from: https://doi.org/10.48550/arXiv.
2311.08804.
22) De Freitas M, Egan M, Clavier L. Achievable Rates of Additive Symmetric
α
-Stable Noise Channels. . Available from: https://www.gretsi.fr/data/colloque/
pdf/2017_lopesdefreitas286.pdf.
23) Ding Z, Peng M, Poor HV. Cooperative Non-Orthogonal Multiple Access in 5G Systems. IEEE Communications Letters. 2015;19(8):1462–1465. Available
from: https://dx.doi.org/10.1109/lcomm.2015.2441064.
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