Best sum-throughput evaluation of cooperative downlink transmission nonorthogonal multiple access system

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 14, No. 1, February 2024, pp. 509~519
ISSN: 2088-8708, DOI: 10.11591/ijece.v14i1.pp509-519  509
Journal homepage: http://ijece.iaescore.com
Best sum-throughput evaluation of cooperative downlink
transmission nonorthogonal multiple access system
Ahmad Albdairat, Fayez Wanis Zaki, Mohammed Mahmoud Ashour
Department of Electronics and Communications Engineering, Faculty of Engineering, Mansoura University in Egypt, Mansoura, Egypt
Article Info ABSTRACT
Article history:
Received Feb 14, 2023
Revised Aug 4, 2023
Accepted Sep 6, 2023
In cooperative simultaneous wireless information and power transfer
(SWIPT) nonorthogonal multiple access (NOMA) downlink situations, the
current research investigates the total throughput of users in center and edge
of cell. We focus on creating ways to solve these problems because the fair
transmission rate of users located in cell edge and outage performance are
significant hurdles at NOMA schemes. To enhance the functionality of
cell-edge users, we examine a two-user NOMA scheme whereby the cell-
center user functions as a SWIPT relay using power splitting (PS) with a
multiple-input single-output. We calculated the probability of an outage for
both center and edge cell users, using closed-form approximation formulas
and evaluate the system efficacy. The usability of cell-edge users is
maximized by downlink transmission NOMA (CDT-NOMA) employing a
SWIPT relay that employs PS. The suggested approach calculates the ideal
value of the PS coefficient to optimize the sum throughput. Compared to the
noncooperative and single-input single-output NOMA systems, the best
SWIPT-NOMA system provides the cell-edge user with a significant
throughput gain. Applying SWIPT-based relaying transmission has no
impact on the framework’s overall throughput.
Keywords:
Cell-edge users
Decoding
Nonorthogonal multiple access
system
Probability
Sum-throughput analysis
Wireless communication
This is an open access article under the CC BY-SA license.
Corresponding Author:
Ahmad Albdairat
Department of Electronics and Communications Engineering, Faculty of Engineering, Mansoura
University in Egypt
Mansoura, Egypt
Email: ahmeddiab2785@yahoo.com
1. INTRODUCTION
To increase the system performance regarding the next gen of wireless network communication
technologies, nonorthogonal multiple access (NOMA) has recently appeared as a possible strategy [1]–[4].
The fundamental idea behind NOMA is that, unlike traditional orthogonal multiple access (OMA) systems,
There is user multiplexing in the power domain [1]. To illustrate, in a two-user NOMA system, a base station
(BS) converses with both users at once while one of them has a worse channel status and is typically placed
at the center of cell or close to the BS. Data signals from the two users are mounted at the BS with differing
power distributions, with a higher power allocation coefficient for cell-edge users compared to cell-center
users. The superposed signal is split at the receiver section using the successive interference cancellation
(SIC) methodology [2]. According to previous research [3], under certain conditions, NOMA can outperform
OMA and increase throughput by 34.2 at user of the cell edge. Cell center and edge users collaborate and
gain by being awarded greater bandwidth when NOMA is used; thus, the spectral efficiency can be greatly
increased [4].
According to the current literature, the functioning of NOMA poses the question of rate of data
fairness between users at the cell center and edge. The reality that users of cell-edge frequently experience

 ISSN: 2088-8708
Int J Elec & Comp Eng, Vol. 14, No. 1, February 2024: 509-519
510
lower rates than cell-center users makes user throughput fairness a crucial problem [5]. Furthermore, as
stated in a previous study [6], if the user of cell edge wants a maximum throughput similar to that of the user
of cell center, the power allocation coefficient of the user of cell center should be near to zero. A large
portion of the transmitted power is allotted to users of cell edge; thus, it might negatively affect the quality of
service of cell-center users. In addition, it could jeopardize the cell-edge users’ capacity to receive signals
reliably [7]. Therefore, solving the user throughput fairness problem while enhancing the cell-edge user’s
reception dependability is crucial in the NOMA context.
Using cooperative relaying transmissions is one way to approach this fairness problem while
ensuring the efficiency and dependability of the cell-edge user. Previous authors [8] presented a cooperative
NOMA transmitting technique wherein cell-center users (with improved channel characteristics) take
advantage of historical data already present in the NOMA scheme to increase the reception dependability of
cell-edge users (with weak connections to a BS). According to those results [8], cooperative NOMA
transmissions improve the outage probability (OP) compared with traditional OMA and noncooperative
NOMA systems. Zhang et al. [9] demonstrated how cooperative relaying transmissions, in which the cell-
center user serves as a relay, may greatly increase the sum rate of NOMA systems. However, a sizable
performance disparity still exists between cell-center and cell-edge users.
Another study [10] examined a two user NOMA system where the best user of cell center is chosen
to act as a relay to serve a cell-edge user operate better during outages. The problem of how cell-center users
equitably spend their energy is posed because they must analyze and transfer their data from the cell-edge
users, even if cooperative relaying transmissions are a acceptable approach to overcome the stated problems
in NOMA schemes. A novel wireless multiple access technique that is effective in terms of energy and
spectrum, the cooperative simultaneous wireless information and power transfer (SWIPT) NOMA protocol,
was presented [11] by merging cooperative NOMA and SWIPT. In particular, the study [11] revealed that, in
contrast to the traditional cooperative NOMA, the adoption of SWIPT allows the users of cell center to self-
power and has no impact on the benefits of variety for users of cell edge.
Time division multiple access and NOMA are wireless protocols used in the downlink scenario [12],
whereas in the uplink scenario, NOMA with timeshare is taken into account. Multiple-input, single-output
(MISO) system applications of NOMA have also been researched in the literature [13], [14]. Further, it was
investigated how the concept of quasi-degradation affected MISO-NOMA downlink communication [13].
A quality-of-service system model was also researched [14] while taking a two-user MISO-NOMA system
into account with two objective interference levels. Furthermore, An energy-saving and low-complexity
transmission technique for a BS with numerous antennas is called transmit antenna selection (TAS) [15],
[16]. Particularly, TAS systems might be a valuable compromise between the variety advantage and
installation expense [17]. Nguyen et al. [18] created user timetables and antenna selection methods to
increase the throughput of multiple-input multiple-output-NOMA networks, in which various selected
antennae split users into pairs. Networks with NOMA downlink energy harvesting (EH) multiple antennas
were examined using a TAS system [19]. A specialized EH amplify-and-forward relay facilitates the
transmission from the sender to receiver, where NOMA is conducted at the relay because the authors
expected direct linkages between a source and destination to be prohibited. In this study, a two-user
cooperative MISO-NOMA system is considered, in which a cell-center user serves as a relay to facilitate
communication from a BS to a cell-edge user. The proposed techniques increase energy efficiency for the
cell-center user while enhancing the cell-edge user’s performance. To achieve this, we provide cooperative
transmission networks where the BS uses TAS criteria, the user of cell center uses SWIPT and the decode-
and-forward relaying approach, and the cell-edge user uses selection merging. The following is a summary of
the paper’s key contributions. The full article follows the standard structure: introduction, system model,
outage performance analysis, performance analysis for the optimal sum throughput, numerical results and
discussion, and conclusions.
2. SYSTEM MODEL
In Figure 1, we take into account a CDT-NOMA downlink transmission which a BS, represented
with S, simultaneously interacts with a user of cell center (user 𝑋) and a cell-edge user (user 𝑌) using a
two-user NOMA scheme. Each user has a single antenna, whereas the BS has L antennae. We define ℎ𝐽𝐾 as
the channel fading coefficient from antenna j, 𝑗 = {1, . . . , 𝐿} to a user K, where 𝐾 ∈ {𝑋, 𝑌}, and Rayleigh
block flat fading is present in every wireless channel in the system, where a complicated independent
Gaussian random variable with zero mean and variance 𝜆𝑆,𝐿 can be used to model ℎ𝑗𝐾. Furthermore, we let
𝑛𝑎𝐾 and 𝑛𝑐𝐾 denote the downconverter at user 𝑇 and the additive white Gaussian noise at the receiving
antenna, respectively, with variance 𝜎𝑐𝐾
2
and zero mean 𝜎𝑎𝐾
2
. Thus, the channel gain |ℎ𝐴𝐵|2
, where 𝐴 ∈ {𝑗, 𝑋}

Int J Elec & Comp Eng ISSN: 2088-8708 
Best sum-throughput evaluation of cooperative downlink transmission nonorthogonal … (Ahmad Albdairat)
511
and 𝐵 ∈ {𝑋, 𝑌}, is an exponential random variable with probability density function 𝑓|ℎ𝐴𝐵|2(𝑧) =
1
𝜆𝐴𝐵
𝑒
−
𝑧
𝜆𝐴𝐵,
∀𝑧 ≥ 0; otherwise, 𝑧 < 0 and 𝑓|ℎ𝐴𝐵|2(𝑧) = 0, where 𝜆𝐴𝐵 indicates the mean of |ℎ𝐴𝐵|2
. Furthermore,
𝐸[|ℎ𝐴𝐵|2
] indicates the average gain of the channel equal to
𝑙
(𝑑𝐴𝐵/𝑑0)𝜖, where 𝑑𝐴𝐵 describes the separation
between two nodes, 𝜖 represents the path-loss exponent, the reference distance is specified by 𝑑0, and 𝑙 is the
average attenuation of the signal power at 𝑑0. Relay 𝑋 acts as a hybrid TS/PS EH relay in the presented
approach (see [20]–[24] and the references therein for additional information on hybrid TS/PS receivers).
Three subblocks of block time 𝑇 are separated. Relay 𝑁 initially harvests energy in the first subblock with an
𝛼𝑇 duration time, where 0 ≤ 𝛼 < 1 specifies the amount of block time used for EH. Relay 𝑁 concurrently
uses a portion of the received power denoted by 𝜌 for PS and a portion denoted by (1 − 𝜌) for EH. The
remaining portion (denoted by 0 ≤ 𝜌 < 1) is used for data decoding. Relay 𝑋 uses all captured energy to
execute its relaying activity in the final subblock with a (1 − 𝜌)𝑇/2 duration. Figure 2 displays the hybrid
TS/PS's timing structure for cooperative relaying communication.
Figure 1. System model
Figure 2. Timing framework of the hybrid TS/PS in cooperative relaying transmission
We assume the hybrid TS/PS SWIPT provides a thorough analysis and creates a generic analytical
model for SWIPT design. The hybrid receiver offers broad options for the design process. If TS or PS is not
required, then 𝛼 (or 𝜌) is set to zero. Given that TS and PS have equal status, it may not matter which phase
is completed first [22]. Furthermore, because the data decoding and relaying procedures are sequential,
considering TS first makes the temporal structure in Figure 2 more logical. The downlink case of the
proposed approach is performed in two stages: the EH and direct data transfer phases, which are required in
the first and second subblocks, and the cooperative relaying transfer phase, which is necessary for the third
subblock, following the period of the hybrid TS/PS EH protocol in Figure 2. The second and third subblocks
have identical lengths.
Furthermore, throughout the final subblock, or the cooperative relaying transfer phase, 𝑆 remains
silent while relay 𝑁 transmits to user 𝐹. The same frequency is used for direct and relaying communications.
Therefore, the cell-edge subscriber faces cochannel interference due to the continued broadcast by the BS if
relay 𝑋 continues to relay messages to user 𝑌. Therefore, the direct and relaying transmissions are
implemented in two distinct submodules to stop such cochannel interference. The literature has widely

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512
accepted using two independent subblocks, where a relay communicates to a sender while the BS is silent
(e.g., [25]–[30]).
2.1. First phase: energy harvesting
We assume that BS antenna 𝑗 transmits the data. Based on the NOMA concept, the purpose is to
send messages 𝑚𝑥 and 𝑚𝑦 for relay 𝑋 and user 𝑌, respectively, combined as √𝑃𝑋𝑚𝑋 + √𝑃𝑌𝑚𝑌 and
transmitted with antenna was chosen at the start of the 1’st subblock period, where 𝑃𝑋 and 𝑃𝑌 specify the
power allocation coefficients for relay 𝑋 and user 𝑌, respectively. Utilizing the NOMA concept, we presume
that |ℎ𝑗𝑋|2
> |ℎ𝑗𝑌|2
, 0 < 𝑃𝑋 < 𝑃𝑌, and 𝑃𝑋 + 𝑃𝑌 = 1.
2.1.1. Relay 𝑿
The observation that the antenna for user 𝑋 can be expressed as (1):
𝑦𝑗𝑋 = (√𝑃𝑋𝑃𝑆𝑚𝑥 + √𝑃𝑌𝑃𝑆𝑚𝑌)ℎ𝑗𝑋 + 𝑛𝑎𝑋, (1)
where ℎ𝑗𝑋 ∼ 𝐶𝑁(0, 𝜆𝑆𝑋) and 𝑛𝑎𝑋 ∼ 𝐶𝑁(0, 𝜎𝑎𝑋
2
). The overall harvested energy at relay 𝑋 connected to
antenna ii may be stated as follows using the hybrid TS/PS EH technique:
𝐸𝑗𝑋 = 𝜂𝑃𝑆|ℎ𝑗𝑋|2
𝛼𝑇 + 𝜂𝜌𝑃𝑆|ℎ𝑗𝑋|2
(1 − 𝛼)𝑇/2, (2)
where 𝜂 represents the efficiency of energy conversion scaled from 0 to 1, the channel gain between relay 𝑋
and antenna j represented by |ℎ𝑗𝑋|2
for data decoding (DD), The signal that was received at relay 𝑋 is
calculated as (3):
𝑦𝑗𝑋
𝐷𝐷
= √1 − 𝜌[(√𝑃𝑋𝑃𝑆𝑚𝑥 + √𝑃𝑌𝑃𝑆𝑚𝑌)ℎ𝑗𝑋 + 𝑛𝑎𝑋] + 𝑛𝑐𝑋, (3)
where 𝑛𝑐𝑋 ∼ 𝐶𝑁(0, 𝜎𝑐𝑋
2
). The SIC receiver at relay 𝑋 initially decodes 𝑚𝑌 based on the NOMA principle, the
next step deducts this fraction from the signal that arrives to get the intended information. (i.e., 𝑚𝑋) [31]. To
decode this, the received signal to interference plus noise ratio at relay 𝑋 is
𝛾𝑗𝑋
𝑚𝑌
=
(1−𝜌)𝑃𝑌𝑃𝑆|ℎ𝑗𝑋|2
(1−𝜌)𝑃𝑋𝑃𝑆|ℎ𝑗𝑋|2+(1−𝜌)𝜎𝑎𝑋
2 +𝜎𝑐𝑋
2 , (4)
When relay 𝑋 is used to decode 𝑚𝑋, the received signal-to-noise ratio (SNR) is represented as (5):
𝛾𝑗𝑋
𝑚𝑋
=
(1−𝜌)𝑃𝑌𝑃𝑆|ℎ𝑗𝑋|2
(1−𝜌)𝜎𝑎𝑋
2 +𝜎𝑐𝑋
2 . (5)
2.1.2. User 𝒀
User 𝑌 can execute EH or remain silent in the first subblock and only decode information in the
second subblock. Compared to relay 𝑋, user 𝑌 can decode the data signal because user 𝑌 has a greater
transmit power allocation; Consequently, interference from relay 𝑋’s data transmission might be regarded as
noise [32]. To decode 𝑚𝑌 using the received SNR at user 𝑌, the observed data may be represented as (6):
𝑦𝑗𝑌 = (√𝑃𝑋𝑃𝑆𝑚𝑥 + √𝑃𝑌𝑃𝑆𝑚𝑌)ℎ𝑗𝑌 + 𝑛𝑎𝑋 + 𝑛𝑐𝑋, (6)
where ℎ𝑗𝑌 ∼ 𝐶𝑁(0, 𝜆𝑆𝑌), 𝑛𝑎𝑌 ∼ 𝐶𝑁(0, 𝜎𝑎𝑌
2
), 𝑎𝑛𝑑𝑛𝑐𝑌 ∼ 𝐶𝑁(0, 𝜎𝑐𝑌
2
), and
𝛾𝑗𝑌 =
𝑃𝑌𝑃𝑆|ℎ𝑗𝑌|2
𝑃𝑋𝑃𝑆|ℎ𝑗𝑌|2+𝜎𝑎𝑌
2 +𝜎𝑐𝑌
2 . (7)
2.2. Second phase: direct data-decoded transmission
The following definition can be used to describe the transmit power of relay 𝑋 in the second phase,
assuming that the relaying mechanism is powered entirely by the energy captured during the initial phase, as
in [22], [23]. User 𝑌 uses the selection combining (SC) approach to merge two signals: the direct signal from
the BS and the relaying signal from relay 𝑋. Thus, the possible SNR for both signals received combined at
user 𝑌 can be written as (8):

513
𝑃𝑋 =
𝐸𝑗𝑋
(1−𝛼)𝑇/2
= 𝜂𝑃𝑆|ℎ𝑗𝑋|2
(
2𝛼
1−𝛼
+ 𝜌). (8)
The signal received by user F might be described as follows using the decode-and-forward relaying protocol:
𝑦𝑋𝑌 = (√𝑃𝑋ℎ𝑋𝑌𝑚
̂𝑌 + 𝑛𝑎𝑌 + 𝑛𝑐𝑌, (9)
where ℎ𝑋𝑌 ∼ 𝐶𝑁(0, 𝜆𝑋𝑌), and the re-encoded form of 𝑚𝑌 is represented by the symbol 𝑚
̂𝑌. The observed
SNR at user 𝑌 to detect 𝑚𝑌 sent by relay 𝑋 can be expressed from (8) and (9) as (10), (11)
𝛾𝑋𝑌 =
𝜂𝑃𝑆|ℎ𝑗𝑋|2|ℎ𝑗𝑌|2(
2𝛼
1−𝛼
+𝜌)
𝜎𝑎𝑌
2 +𝜎𝑐𝑌
2 , and (10)
𝛾𝑌
𝑆𝐶
= 𝑚𝑎𝑥{𝛾𝑗𝑌, 𝛾𝑋𝑌}. (11)
2.3. Proposed transmit antenna selection criteria
The suggested TAS technique is carried out by the signaling and channel state information (CSI)
assessment system prior to data transfer. We presume the necessary CSI for each scheme is available [33],
[34]. The ability of 𝑚𝑌 to be decoded at relay 𝑋 determines whether the cooperative relaying operation
succeeds. In light of this, the end-to-end SNR at user 𝑌 can be expressed in (12). This approach selects an
antenna from 𝐿 antennae to maximize the instantaneous transmission rate for user 𝑌. The outcome of the
scheme selection can be specified formally (14):
𝛾𝑌
𝑒2𝑒
= 𝑚𝑖𝑛{𝛾𝑗𝑋
𝑚𝑋
, 𝛾𝑌
𝑆𝐶
}. (12)
When user 𝑌 connects to antenna 𝑗, the instantaneous transmission rate is represented as (13)
𝑅𝑗𝑌 =
1−𝛼
2
𝑙𝑜𝑔2(1 + 𝛾𝑌
𝑒2𝑒
), where (13)
𝑗∗
= 𝑎𝑟𝑔𝑚𝑎𝑥
1≤𝑗≤𝐿
𝑚𝑖𝑛{𝛾𝑗𝑋
𝑚𝑌
, 𝑚𝑎𝑥{𝛾𝑗𝑌, 𝛾𝑋𝑌}}. (14)
3. OUTAGE PERFORMANCE ANALYSIS
The OP is a probability that the information rate will go under the required threshold rate for data
[35]. Assuming 𝑅𝑡ℎ,𝑋 and 𝑅𝑡ℎ,𝑌 indicate the desired data rates in bits/s/Hz for relay X and Y, respectively:
𝑎1 ≜
(1−𝜌)𝑃𝑌𝑃𝑆
2 +𝜎𝑐𝑋
2 , 𝑎2 ≜
(1−𝜌)𝑃𝑋𝑃𝑆
2 +𝜎𝑐𝑋
2 , 𝑏1 ≜
𝑃𝑌𝑃𝑆
𝜎𝑎𝑌
2 +𝜎𝑐𝑌
2 , 𝑏2 ≜
𝑃𝑋𝑃𝑆
𝜎𝑎𝑌
2 +𝜎𝑐𝑌
2 ,
𝑐 ≜ 𝜂𝑃𝑆(
2𝛼
1−𝛼
+ 𝜌)/(𝜎𝑎𝑌
2
+ 𝜎𝑐𝑌
2
), 𝜇𝑎 ≜
𝛾2
𝑎1−𝑎2𝛾2
, 𝜇𝑏 ≜
𝛾2
𝑏1−𝑏2𝛾2
, 𝑎𝑛𝑑 𝜃 ≜
𝑃𝑌
𝑃𝑋
.
Function 𝛺(𝜇, 𝑋, 𝜉) is described in (21). The suggested scheme’s OP for relay X and user Y can be
stated as:
3.1. Outage probability of relay 𝑿
When the SIC process is unable to correctly decode the message 𝑚𝑌 or when 𝑚𝑌 is correctly
decoded but 𝑚𝑋 is not, outage events happen at user 𝑁. Thus, the OP of relay 𝑋 may be written as (15)
𝑂𝑃𝑋 = 𝑃𝑟(𝛾𝑆𝑋
𝑚𝑌
< 𝛾2) + 𝑃𝑟(𝛾𝑆𝑋
𝑚𝑌
≥ 𝛾2, 𝛾𝑆𝑋
𝑚𝑋
), (15)
where 𝛾1 ≜ 22𝑅𝑡ℎ,𝑋−1
and 𝛾2 ≜ 22𝑅𝑡ℎ,𝑋−1
represent the corresponding thresholds of SNR for messages
successfully decoded 𝑚𝑋 and 𝑚𝑌. The OP of relay 𝑋 for the closed-form equation can be expressed as (16)
𝑂𝑃𝑋 = {1 − 𝑒
−
𝜇𝑎
𝜆𝑆𝑋 𝑖𝑓𝛾2 < 𝜃, 𝜇𝑎 ≥
𝛾
𝑎2
1 − 𝑒
−
𝛾1
𝜆𝑆𝑋𝑎2 𝑖𝑓𝛾2 < 𝜃, 𝜇𝑎 ≥
𝛾
𝑎2
1 𝑖𝑓𝛾2 ≥ 𝜃, ∀𝛾1. (16)
The OP of relay X may be written from (4), (5), and (12) as

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𝑂𝑃𝑋 = 𝑃𝑟(
𝑎1|ℎ𝑆𝑋|2
𝑎2|ℎ𝑆𝑋|2+1
< 𝛾2) + 𝑃𝑟(
𝑎1|ℎ𝑆𝑋|2
≥ 𝛾2, 𝑎2|ℎ𝑆𝑋|2
< 𝛾1). (17)
It is apparent that 𝑃𝑟(
𝑎1|ℎ𝑆𝑋|2
< 𝛾2) = 𝑃𝑟((𝑎1 − 𝑎2𝛾2)|ℎ𝑆𝑋|2
< 𝛾2 is equal to 1 if 𝛾2 ≥ 𝜃, where 𝜃 =
𝑎1
𝑎2
.
Therefore, the OP closed-form equation of relay 𝑋 may be obtained using specific algebraic methods using
certain algebraic operations to examine the relative connections between 𝛾1, 𝛾2, 𝑎𝑛𝑑 𝜃, as presented in (13).
3.2. Outage probability for user 𝒀
Message 𝑚𝑌 for user 𝑌 is decoded at user Y and in the SIC process at relay 𝑋, as observed in the
first phase of the system model. The SIC process connected to 𝑚𝑌 is already considered in the formulation of
𝛾𝑌
𝑒2𝑒
in (11). Consequently, the user Y's OP could be expressed as (18)
𝑂𝑃𝑌 = 𝑃𝑟(𝑚𝑖𝑛{𝛾𝑆𝑋
𝑚𝑌
, 𝑚𝑎𝑥{𝛾𝑆𝑌, 𝛾𝑋𝑌}} < 𝛾2), (18)
where the threshold of SNR for successfully message decoded 𝑚𝑌 is denoted by 𝛾2 ≜ 22𝑅𝑡ℎ,𝑌 − 1. The
following is an approximate closed form expression of user Y’s OP:
𝑂𝑃𝑌 = 1 − [1 − 𝑒
𝜇𝑏
𝜆𝑆𝑌] − 𝑒
−
𝜇𝑎
𝜆𝑆𝑋
−
𝜇𝑏
𝜆𝑆𝑌 × [𝑒
𝜇𝑏
𝜆𝑆𝑋 −
𝛾2
𝑐𝜆𝑆𝑌𝜆𝑆𝑋
𝛤 (0,
𝜇𝑎
𝜆𝑆𝑋
)] (19)
𝑂𝑃𝑌 =𝑃𝑟 𝑃𝑟 (𝑅𝑗𝑌 < 𝑅𝑡ℎ,𝑌) =𝑃𝑟 𝑃𝑟 (𝑚𝑎𝑥
1≤𝑗≤𝐿
{𝛾𝑗𝑋
𝑚𝑌
, {𝛾𝑗𝑌, 𝛾𝑋𝑌} } < 𝛾2) (20)
where the SNR threshold for successfully decoding message 𝑚𝑌 is represented by 𝑚𝑋, 𝛾 ≜ 22𝑅𝑡ℎ,𝑌/(1−𝛼)
.
4. PERFORMANCE ANALYSIS FOR THE OPTIMAL SUM THROUGHPUT
At this stage, we perform an optimum evaluation of the sum throughput, or 𝜏, of the NOMA
approaches explored for downlink case. We specifically offer a way to determine the optimal value of 𝜌,
indicated by 𝜌𝑜𝑝𝑡
, which maximizes the sum throughput of the network, which is possible to written as (21).
𝜏 = (1 − 𝑂𝑃𝑋)𝑅𝑡ℎ,𝑋 + (1 − 𝑂𝑃𝑌)𝑅𝑡ℎ,𝑌 = 𝑅𝑡ℎ,𝑋𝑒
−
𝜇𝑎
𝜆𝑆𝑋 + 𝑅𝑡ℎ,𝑌[𝑒
−
𝜇𝑎
𝜆𝑆𝑋
−
𝜇𝑏
𝜆𝑆𝑌 + (1 − 𝑒
−
𝜇𝑏
𝜆𝑆𝑌) ×
[𝑒
−
𝜇𝑎
𝜆𝑆𝑋 −
𝛾2
𝛾𝑆𝑋𝛾𝑋𝑌𝑐
𝛤(0,
𝜇𝑎
𝜆𝑆𝑋
)]]. (21)
We describe the issue under consideration as an unrestricted optimization problem, defined as (22)
𝑚𝑎𝑥
𝜌
𝜏 = 𝑓(𝜌), (22)
where 𝑓(𝜌): 𝑔(𝜌): (0,1) ⟶ 𝑅+
, and 𝑅+
stands for the collection of positive real numbers. To make the
analysis of 𝜏 as easy as possible to simplify 𝑔(𝜌), we assume that (1 − 𝜌)𝑛𝑎𝑋 ≈ 𝑛𝑎𝑋 because the noise
power that an antenna introduces is low. For notational simplicity, we let 𝛾𝑋 = 𝑃𝑆/(𝑛𝑎𝑋 + 𝑛𝑐𝑋) and
𝛾𝑌 = 𝑃𝑆/(𝑛𝑎𝑌 + 𝑛𝑐𝑌). Therefore, 𝑔(𝜌) can be represented as (23)
𝑔(𝜌) = 𝑔𝑗(𝜌) = 𝑟1𝑒
𝜈𝑖
1−𝜌 + 𝑟2𝑒
𝜅𝑎
1−𝜌
+𝜅𝑏
+ 𝑟2𝑒
𝜅𝑎
1−𝜌 +
𝑟2𝜅𝑐
𝜌
𝛤(0, −
𝜅𝑎
1−𝜌
), (23)
where j=1 if
𝛾2
𝑃𝑌−𝑃𝑋𝛾2
≥
𝛾1
𝑃𝑋
, j=2 where 𝑟1 = −𝑅𝑡ℎ,𝑋, 𝑟2 = −𝑅𝑡ℎ,𝑌, 𝜈1 = −
𝛾1
(𝑃𝑌−𝑃𝑋𝛾2)𝛾𝑋𝜆𝑆𝑋
, 𝜈2 = −
𝛾1
𝑃𝑋𝛾𝑋𝜆𝑆𝑋
,
𝜅𝑎 = −
𝛾2
(𝑃𝑌−𝑃𝑋𝛾2)𝛾𝑋𝜆𝑆𝑋
, 𝜅𝑏 = −
𝜇𝑏
𝜆𝑆𝑋
, 𝜅𝑐 = −
𝛾2
𝜆𝑆𝑋𝜆𝑋𝑌𝜂𝛾𝑌
,= 1 − 𝑒− 𝜇𝑏
𝜆𝑆𝑌
.
As observed, 𝑔(𝜌) has a very complex representation, making it difficult to perform an optimum
analysis on this function. We use the gradient descent approach [12] in this study to address the specified
issue. In particular, we propose the following simple yet effective technique for locating the ideal PS
coefficient. We write the optimal structure of this PS coefficient as 𝜌𝑜𝑝𝑡
. The goal is to create a minimizing
sequence: 𝜌0
, 𝜌1
, . . . 𝜌𝜅
, . . . ∈ domain g with 𝑔(𝜌𝜅
) ⟶ 𝑔(𝜌𝑜𝑝𝑡
) as 𝜅 ⟶ ∞, where,

515
𝜌𝜅+1
= 𝜌𝜅
+ 𝑡𝜅
𝛥𝜌𝜅
, (24)
where 𝜅 indicates the iteration number, 𝑡𝜅
denotes the step length, and 𝛥𝜌𝜅
represents a search direction step.
We selected a search vector which is the negative gradient of the function using the gradient
decrease approach 𝛥𝜌𝜅
= −𝛻𝑔𝜌𝜅
, resulting in 𝑔𝜌𝜅+1
< 𝑔𝜌𝜅
. Until the halting requirement is met, the
algorithm continues to execute (i.e., ||𝛻𝑔𝜌𝜅+1
||2 ≤ 𝜍, where 𝜍 identifies a stopping threshold and ||. ||2
implies 𝑙2 − 𝑛𝑜𝑟𝑚). In equation (19), the gradient of the desired function may be represented as in
technique 1, which provides more information about the proposed algorithm:
𝑔(𝜌) =
𝑟1𝜈𝑗𝑒
𝜈𝑗
1−𝜌
(1−𝜌)2 +
𝑟2𝜅𝑎𝑒
𝜅𝑎
1−𝜌
+𝜅𝑏
(1−𝜌)2 +
𝑟2𝜁𝜅𝑎𝑒
𝜅𝑎
1−𝜌
(1−𝜌)2 −
𝑟2𝜁𝜅𝑐𝑒
𝜅𝑎
1−𝜌
(1−𝜌)𝜌
−
𝑟2𝜅𝑐𝜁
𝜌2 𝛤(0, −
𝜅𝑎
1−𝜌
). (25)
The proposed technique allows for off-line optimization depending on the system characteristics obtained
through the estimate procedure for CSI (and in advance of the data transfer).
5. RESULTS AND DISCUSSION
This part presents the representative numerical results to check the designed evaluation and show
the reachable performance improvement of the ideal SWIPT-NOMA system in contrast to traditional OMA
or noncooperative NOMA systems and the PS-based SWIPT relay [36]. During the simulation setup,
considering that the source, N=X and F=Y users constitute a line network [37]–[40]. We also assumed the
following:
− The antenna noise power density is -100 dBm/Hz, and the bandwidth is 1 MHz,
− The information-processing noise power density is -90 dBm/Hz,
− The selected desired data rate is 1 bit/s/Hz, and user 𝑋 (𝑃𝑋) (power allocation coefficient) value is 0.1,
− User 𝑌’s power allocation coefficient is1-PX,
− S is located 10 meters away from user 𝑋,
− User 𝑌 and S are 3 meters apart,
− User 𝑋 and 𝑌 are separated by dSY-dSX,
− The path-loss exponent is 3,
− The path loss at the reference distance is -30 dB, and
− The EH process has a 0.70 energy conversion efficiency.
We define the OP’s of users 𝑁 and 𝐹 as a function of the transmit power PS (dB) and the PS
coefficient, respectively, of the source in Figures 3 and 4. These two figures illustrate a clear agreement
between the analytical and simulation results, demonstrating the accuracy of the established methodology.
Additionally, even in low SNR conditions, such as when PS is minimal, the approximate OP for user 𝐹
remains close to its actual value.
Figure 3. Outage probability for users 𝑁 and 𝐹, following the signal strength at the sender when ρ=0.3

 ISSN: 2088-8708
516
Figure 4. Outage probability for users 𝑁 and 𝐹 as a function of the power-splitting coefficient (PS=10 dB)
In traditional noncooperative NOMA systems, the cell-center user beats the cell-edge user, as
presented in Figures 3 and 4. We can still enhance the cell-edge user’s OP by applying a SWIPT-cooperative
relaying transfer. Therefore, the OP for user 𝑁 has decreased and is inferior to that for user 𝐹 for a specific
value of PS. The reality that user 𝑁 acts as an RF EH relay may be a factor. Specifically, some of the power
it receives is used to transmit information, lowering the received SNR of user 𝑁.
Figure 5 presents the outcome of the proposed methodology for locating the ideal PS coefficient. As
observed, the sum throughput is a curved function regarding the PS coefficient. Additionally, the objective
function’s relaxed value is quite close to its real value. We compared the performance of the traditional
OMA, noncooperative NOMA, and optimal SWIPT-NOMA systems in Figure 6. In the beginning considered
the combined throughput (bits/s/Hz) of the described three systems.
Figure 5. Advantage of the ideal value using the suggested technique when PS=10 dB
The benefit of NOMA with respect to throughput enhancement is confirmed by the fact that the
ideal SWIPT-NOMA and noncooperative NOMA systems produce a superior sum throughput compared with
the traditional OMA system. Unexpectedly, the possible sum throughputs of the noncooperative NOMA and
the best SWIPT-NOMA are comparable. Only one-half of a block period is spent using the NOMA
transmission when SWIPT-based relaying is used in the SWIPT-NOMA system. The BS transmits NOMA

517
data for the full block time in a noncooperative NOMA system. Due to the calculated values, we can
conclude that the sum throughput of the two-user NOMA system under consideration is not jeopardized by
the SWIPT-based relaying transmission by user 𝑁 to aid user 𝐹. In contrast, the throughput of user 𝐹 in the
best SWIPT-NOMA system is greater than that of the cell-edge user in the noncooperative NOMA system, as
illustrated in Figure 6. It implies that the throughput of cell-edge users in NOMA systems is increased using
cooperative relaying transmissions.
Figure 6. Comparisons of the OMA, noncooperative NOMA, and proposed NOMA systems for performance
6. CONCLUSION
This research investigated the OP and sum throughput of the cooperative PS-based SWIPT two-user
NOMA system. We applied the tight closed-form approximation expression for the OP of the cell-edge user
and the closed-form expression for the cell-center user. To discover the ideal PS coefficient value that
maximizes the sum throughput of the system under consideration, we suggested an approach employing the
gradient descent technique. According to the numerical findings, using a cooperative SWIPT relaying
transmission with an ideal PS coefficient can increase throughput for cell-edge users without endangering the
sum throughput of two-user NOMA systems. Thus, cooperative SWIPT relaying transmissions may be
considered a long-term fix for the problems of performance equity between cell-center and cell-edge users
and energy usage equity for cell-center users.
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BIOGRAPHIES OF AUTHORS
Ahmad Albdairat received the B.Eng. degree in communication engineering
from University of Mut’ah, Jordan, in 2007 and the M.S. degree in communication engineering
from University of Mut’ah, Jordan, in 2011. Currently, he is Jordanian Customs-Amman
Customs House Appraiser (Customs Valuation Officer) and Auditor. He can be contacted at
email: ahmeddiab2785@yahoo.com.
Fayez Wanis Zaki is a professor at the Faculty of Engineering, Mansoura
University. He received the B.Sc. in communication engineering from Menofia University
Egypt 1969, M.Sc. communication engineering from Helwan University Egypt 1975, and
Ph.D. from Liverpool University 1982. Worked as a demonstrator at Mansoura University,
Egypt from 1969, lecture assistant from 1975, a lecturer from 1982, associate prof. from 1988,
and prof. from 1994. Head of Electronics and Communication Engineering Department
Faculty of Engineering, Mansoura University from 2002 till 2005. He supervised several M.Sc.
and Ph.D. thesis. He has published several papers in refereed journals and international
conferences. He is now a member of the professorship promotion committee in Egypt. He can
be contacted at email: fwzaki2017@gmail.com.
Mohammed Mahmoud Ashour is an assistant professor at the Faculty of
Engineering Mansoura University, Egypt. He received B.Sc. from Mansoura University Egypt
in he received an M.Sc. degree from Mansoura University, Egypt in 1996. He receives a Ph.D.
degree from Mansoura University, Egypt 2005. Worked as lecturer assistant at Mansoura
University, Egypt from 1997, from 2005, an assistant professor. Fields of interest: network
modelling and security, wireless communication, and digital signal processing. He can be
contacted at email: mohmoh2@yahoo.com.

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