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Turk J Elec Eng & Comp Sci
() : –
T¨
UB˙
ITAK
doi:10.3906/elk-10.3906/elk-2005-155
On the Outage Performance of SWIPT-NOMA-CRS with imperfect SIC and CSI
Ferdi KARA1
1Wireless Communication Technologies Laboratory (WCTLab), Department of Electrical and Electronics, Faculty of Engineering,
Zonguldak Bulent Ecevit University, Zonguldak, Turkey,
ORCID iD: https://orcid.org/0000-0001-8038-2747
Received: .202 Accepted/Published Online: .202 Final Version: ..202
Abstract: In this paper, a non-orthogonal multiple access based cooperative relaying system (NOMA-CRS) is considered
to increase spectral efficiency. Besides, the simultaneous wireless information and power transfer (SWIPT) is proposed
for the relay in NOMA-CRS. In SWIPT-NOMA-CRS, three different energy harvesting (EH) protocols, power sharing
(PS), time sharing (TS) and ideal protocols are implemented. The outage performances of the SWIPT-NOMA-CRS
are studied for all three EH protocols. In the analysis, to represent practical/reasonable scenarios, imperfect successive
interference canceler (SIC) and imperfect channel state information (CSI) are taken into consideration. The derived
outage probability (OP) expressions are validated via computer simulations. Besides, the OP for the benchmark scheme,
NOMA-CRS without EH, is also derived under imperfect SIC and CSI. Based on extensive simulations, it is revealed
that the SWIPT-NOMA-CRS outperforms NOMA-CRS without EH. Finally, the effects of all parameters on the outage
performance of the SWIPT-NOMA-CRS are discussed and for the given scenarios, the optimum PS factor, TS factor
and power allocation coefficients are demonstrated.
Key words: simultaneous wireless information and power transfer, non-orthogonal multiple access, cooperative relaying
systems, outage analysis, imperfect SIC, channel estimation errors
1. Introduction
The new era of the wireless communications is beyond the personal communication and it has now many
different applications such as Internet of Things (IoT) networks, vehicular communication etc. Hence, the
future wireless networks (5G and beyond) are to meet challenging requirements such as very high spectral
efficiency, ultra wide coverage and low energy consumption [1]. To this end, the future networks will have the
interplay between physical layer techniques such as non-orthogonal multiple access (NOMA) [2], cooperative
relaying system (CRS) [3] and wireless power transfer [4].
The main idea of the NOMA is to allow multiple users sharing the same resource block. NOMA has gen-
erally divided into two groups as code-domain (CD)-NOMA and power-domain (PD)-NOMA. In CD-NOMA,
the users share the same resource block with sparse codes, so it is mostly called sparse code multiple access
(SCMA) whereas in PD-NOMA, the users are multiplexed with different power allocation (PA) coefficients.
Compared to orthogonal multiple access schemes, the main advantage of the NOMA schemes is the spectral
efficiency since all users are allocated in the same resource block whereas the main disadvantage is the error
Correspondence: f.kara@beun.edu.tr
This work is licensed under a Creative Commons Attribution 4.0 International License.
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performance decay due to the inter-user-interference (IUI) [2]. Thanks to its potential, NOMA1has been imple-
mented in other physical layer techniques such as cooperative communication [5], visible light communication
[6] and index modulation [7].
CRS schemes have been studied for two decades because they provide a remarkable performance gain
in device-to-device communications. However, due to the cooperative phase, the spectral efficiency of the
CRS schemes decreases. To alleviate this performance loss, NOMA-based CRS is proposed in [8] where the
source implements NOMA in the first phase to increase spectral efficiency and it is proved that NOMA-CRS is
superior to conventional CRS. Therefore, NOMA-CRS has attracted recent attention from both academia and
industry [8–16]. In those works, NOMA-CRS has been investigated in terms of capacity, outage probability
(OP) and error probability. Ergodic capacity of the NOMA-CRS is analyzed over Rayleigh [8] and Rician [9]
fading channels. Then, two different NOMA-CRS schemes have been considered in [10] and OP expression is
derived over Rayleigh fading channels. The error performance of the NOMA-CRS is investigated in [11] and a
machine learning aided power optimization is proposed to minimize bit error rate. Then, two more NOMA-CRS
schemes are proposed in [12,13], and capacity/outage performances are investigated. Moreover, NOMA-CRS
schemes have been considered when multiple relays are available. NOMA-based diamond relaying, as a subset
of the NOMA-CRS with two relays, is analyzed in [14] and [15] in terms of capacity and error performances,
respectively. Contrary to [8–15], NOMA-CRS is investigated in [16] when an amplify-forward relay is used
rather than a decode-forward relay. However, the aforementioned studies assume that the relay node has its
own independent (infinite) energy source to help the device-to-device communication. It is neither feasible
nor fair for the relay which consumes its energy/battery for a communication where its own symbol is not
transmitted. Furthermore, those studies mostly assume perfect successive interference canceler (SIC) at the
relay (except for [11,15]) and perfect channel state information (CSI) at all nodes (except for [10]). These are
also not practical assumptions and should be relaxed.
On the other hand, simultaneous wireless information and power transfer (SWIPT) is very promising to
increase energy efficiency [4]. SWIPT is proved to be practical and it can support nodes with limited energy [17].
To this end, SWIPT has attracted tremendous attention [18,19]. Besides, since it is easily applicable, SWIPT
integration into all other physical layer techniques has also taken remarkable consideration [20–29]. Specifically,
the relay node can harvest its energy to re-transmit the symbols of the source, thus SWIPT-cooperative NOMA
schemes have been analyzed in terms of capacity, outage and error performances [20–23]. SWIPT usage with
NOMA has also been investigated in many studies. However, to the best of the author’s knowledge, the SWIPT
integration into NOMA-CRS has not been studied well although other NOMA-involved systems have been
analyzed with SWIPT [24–27]. Only two studies in the literature consider NOMA-CRS with SWIPT. In [28],
the authors consider a CRS where the source transmits two symbols in two time slots and in the second phase,
an energy harvesting relay re-transmits the symbol of the first phase. The considered model in [28] is different
from the conventional NOMA-CRS schemes [8–16] since a power allocation is not implemented. Nevertheless,
it is called as SWIPT-CRS deploying NOMA since an SIC should be performed at the destination due to the
second phase. The authors provide outage probability analysis for the considered model. Then, in [29], the
author’s preliminary work, a NOMA-CRS with SWIPT is considered and only the achievable rate is analyzed.
However, these two studies assume perfect SIC at the relay/destination and perfect CSI at all nodes. Thus,
these assumptions should be relaxed and the analysis should be further extended for practical scenarios.
1This paper deals with PD-NOMA, thus NOMA is used for PD-NOMA after this point.
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Figure 1. The illustration of SWIPT-NOMA-CRS
Based on above discussions, in this paper, the NOMA-CRS with SWIPT is proposed where the relay
harvests its energy from radio frequency (RF) waves to transmit symbols. In SWIPT integration, three different
energy harvesting (EH) protocols, power sharing (PS), time sharing (TS) and ideal protocols, are implemented.
All non-practical assumptions are relaxed, to this end, the OP expressions for all EH protocols are derived with
imperfect SIC and CSI. Besides, the OP for the benchmark, NOMA-CRS without EH, is also derived. It is
revealed that the SWIPT-NOMA-CRS outperforms NOMA-CRS without EH. Then, the effects of EH factors
and PA coefficient are discussed for the outage performance of the SWIPT-NOMA-CRS.
The rest of the paper is organized as follows. In Section 2, the SWIPT-NOMA-CRS is introduced where
all EH protocols and power transfers are defined. The information transferring in SWIPT-NOMA-CRS and the
related signal-to-interference plus noise (SINR) definitions are also given in this section. Then, in Section 3, the
theoretical analysis of OP is performed. In Section 4, the analysis is validated via computer simulations and
performance comparisons are presented. Finally, Section 5 discusses the results and concludes the paper.
2. System Model
A NOMA-based relaying system is considered for a device-to-device communication where a source (S), a
decode-forward (DF) relay (R) and a destination (D) are located. All nodes are assumed to be equipped with
single antenna. The channel fading coefficient between each node follows C N (0,Ωk), k ={sr, sd, rd}where
Ωkdenotes the large-scale path loss component. The imperfect channel state information (CSI) is considered
and the estimated channel at each node is given by ˆ
hk=hk+where =CN (0, κ) which is an appropriate
model for the practical channel estimation techniques. The DF relay operates in half duplex mode. Thus,
the total communication is completed in two phases. In order to alleviate inefficiency of the CRS, NOMA is
implemented at the source so that the spectral efficiency is increased. Besides, it is assumed that the relay
do not have independent energy source and it harvests its energy from the RF signal in the first phase to
transmit symbols in the second phase. Therefore, the source implements a SWIPT so that the system is called
SWIPT-NOMA-CRS. The illustration of the SWIPT-NOMA-CRS is given in Figure 1.
2.1. Transmit Power and Energy Harvesting
In the energy-constrained networks, a node can harvest energy from the RF signals so that it can use it to
transmit symbols. In the EH, the RF signals are converted to Direct Current (DC) power via energy receiver
(called rectenna) [18]. This rectenna can be placed on the same circuit with a transceiver, hence the SWIPT
becomes possible. According to internal characteristics (due to the diode ) of the rectenna, the EH protocols are
categorized in two groups : 1) linear EH 2) non-linear EH. In this paper, the linear EH protocols are considered
where the received RF waves are converted a DC power with a energy conversion coefficient.
As explained above, the relay node harvests its energy from the RF signal transmitted by the source. In
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this paper, within the linear EH models, three different EH protocols (i.e., PS, TS and ideal protocols) [23] are
implemented. Time schedules for all three EH protocols are shown in Figure2. In Figure2, the time schedule of
the benchmark is also given where no EH is implemented and the total energy is shared among the source and
relay.
2.1.1. Benchmark (No EH)
As considered in the literature, if the relay has no ability to harvest energy, it has its own energy source, and
the total consumed energy/power is the sum of the energy/power consumed by the source and the relay. As
shown in Figure 2(a), the source and the relay consume their energy within T/2seconds. Thus, for fairness,
considering the total energy consumption during Tseconds, the transmit powers of both source and relay are
given as
Ps=Pr=PT.(1)
where Psand and Prare the transmit powers of the source and relay. PTis the total consumed power during
the whole communication (Tseconds).
2.1.2. Power Sharing (PS) Protocol
As shown in Figure 2(b), in the PS protocol, the communication times from source-to-relay (S-R) and from
relay-to-destination (R-D) are equal and cover half of the total Tduration. Thus, by considering the total
consumed energy during Tseconds, the transmit power of the source within T/2seconds is equal to
Ps= 2PT.(2)
The relay harvests its energy during the first T/2seconds, hence the harvested energy in PS protocol is given
as
EH=ηρPs
ˆ
hsr
2(T/2),(3)
where ηis the energy conversion coefficient and it is given as 0 < η < 1. In (3), ρis the PS factor as
represented in Figure 2(b). It is noteworthy that the energy is harvested according to the estimated channel
ˆ
hsr . The harvested energy is consumed by the relay to transmit symbols between R-D within the remained T/2
seconds. Therefore, the transmit power of the relay in PS protocol is obtained as
Pr=ηρPs
ˆ
hsr
2.(4)
2.1.3. Time Sharing (TS) Protocol
As shown in Figure 2(c), in TS protocol, the source transmits power for EH in the first ξT seconds and then,
it transmits information (data) in the next (1 −ξ)T/2second. Thus, the total consumed energy by the source
in TS mode is given by Ps(1 + ξ)T/2. For fairness, regarding the total consumed energy in Tseconds with total
power PT, the source power in TS protocol is obtained as
Ps=2PT
(1 + ξ),(5)
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Figure 2. Time schedules for a) Benchmark (No EH) b) EH with PS protocol c) EH with TS protocol d) EH with ideal
protocol
where ξis the TS factor as given in Figure 2(c). The harvested energy from this source power within ξT
seconds is given as
EH=ηPsˆ
hsr(ξ T ).(6)
Since this harvested energy at the relay is consumed within the remained (1 −ξ)/2seconds, the transmit power
of the relay in TS protocol is derived as
Pr= 2ηξ
(1 −ξ)Psˆ
hsr.(7)
2.1.4. Ideal Protocol
In the ideal protocol, as shown in Figure 2(d), the source transmits power during T/2seconds. Thus, again by
considering the total consumed power within Tseconds, the transmit power of the source, in ideal protocol, is
given as
Ps= 2PT.(8)
During the first T/2seconds, the relay harvests energy from the RF wave between S-R, thus the harvested
energy is given as
EH=ηPs
ˆ
hsr
2(T/2).(9)
It is noteworthy that the energy and data transfers are achieved with the same power Ps, in the ideal
protocol whereas the transmit power of the source is allocated by ρfor energy and data transfers in the PS
protocol. This is the main difference between the PS and ideal protocols.
Then, this harvested energy is consumed by the relay to transmit symbols between R-D link within T/2
seconds. Therefore, the transmit power of the relay, in ideal protocol, is obtained as
Pr=ηPs
ˆ
hsr
2.(10)
2.2. Information Transfer
As explained above and shown in Figure 1, the information transfer is completed in two phases. In the first
phase, the source implements NOMA for the consecutive two symbols of the destination to increase spectral
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efficiency and broadcasts this superposition coded symbol to both relay and destination. Thus, the received
signals by both nodes are given as
yk=ppPs√αx1+p(1 −α)x2hk+nk, k =sr, sd, (11)
where αis the PA coefficient (i.e., α < 0.5 ) among the symbols. nkis the additive white Gaussian noise
(AWGN) and follows CN (0, σ2) . It is hereby noted that the hkin (11) is the actual channel fading coefficient
between nodes and it is estimated as ˆ
hk=hk+at the receiving nodes as explained above. Besides, it is
noteworthy that the transmit power of the source changes according to the used EH protocol as explained in
detail in the previous subsection (see eq. (1), (4), (7) and (10)). Thus, the pcoefficient denotes the ratio how
much the source power is allocated for the information transfer. According to the EH protocol, it is given as
p=(1−ρ, in PS protocol,
1,in TS, ideal protocols and in no EH.(12)
In the first phase, according to the received signal ysd ,x2symbols are detected with a conventional detector
(e.g., maximum likelihood (ML)) at the destination by pretending x1symbols as a noise. At the same time,
the relay implements a successive interference canceler (SIC) to detect x1symbols. In the SIC process, the
relay firstly detects x2symbols with a ML detector, then it subtracts these estimated x2symbols from the
received signal ysd . Finally, it implements one more ML detector to detect x1symbols based on the remained
signal after subtraction. In the second phase, the relay re-transmits the detected x1symbols to the destination.
Hence, the received signal in the second phase is given as
yrd =pPrˆx1hrd +nrd ,(13)
where ˆx1is the detected symbol at the relay after SIC. It is worth noting that Pris the transmit power of the
relay and changes according to the EH protocol since it is harvested from the source-relay link in the first phase
(or it has its own energy in no EH benchmark) (see eq. (1), (4), (7) and (10)). Besides, the channel fading
coefficient hrd is estimated as ˆ
hrd at the destination. Lastly, the destination detects x1symbols based on yr d .
2.3. Received Signal-to-Interference plus Noise Ratios (SINRs)
As given in (11), the source transmits superposition-coded NOMA symbols in the first phase, thus an interference
occurs. Both relay and destination detect x2symbols firstly by pretending x1symbols as noise. Therefore, by
considering imperfect CSI at the nodes, the received SINRs for the x2symbols at the nodes are given as
SI N R(sr)
x2=(1 −α)pPsˆγsr
αpPsˆγsr +pPsκ+σ2,
SI N R(sd)
x2=(1 −α)pPsˆγsd
αpPsˆγsd +pPsκ+σ2.
(14)
where ˆγk,|ˆ
hk|2is defined and it follows exponential distribution with the parameter ˆ
Ωk= Ωk−κ. In (14),
the first terms in the denominators define the interference due to the x1symbols (NOMA signalling) whereas
the second and the third terms are the effects of the imperfect CSI and the AWGN, respectively.
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On the other hand, the relay implements SIC to detect x1symbols in the first phase, thus, by also
considering imperfect SIC, the received SINR for the x1symbols at the relay is given as
SI N R(sr)
x1=αpPsˆγsr
(1 −α)pPs|g|2+pPsκ+σ2,(15)
where the first term in the denominator denotes the imperfect SIC effect where gfollows CN (0, δΩsr ) . 0 < δ < 1
is defined where δ= 0 and δ= 1 denote perfect SIC and no SIC cases, respectively. Just like (14), in (15), the
second and the third terms of the denominator are the effects of the imperfect CSI and the AWGN, respectively.
In (14) and (15), the transmit power of the source is given in (1), (2), (5) and (8) according to the EH protocol.
Lastly, the received SINR in the second phase is given as
SI N R(rd)
ˆx1=Prˆγrd
Prκ+σ2.(16)
It is important to note that Prin (16) will include the ˆγsr random variable if any of EH protocols is implemented
(see (4), (7) and (10)). It can be given as independent from ˆγsr only if no EH is implemented (1).
3. Outage Probability (OP) Analysis
The outage event for a communication system is defined as the probability of the achievable rate being below
the target rate (QoS). To this end, the outage probability for the symbols in SWIPT-NOMA-CRS is given by
Pi(out) = P(Ri<´
Ri), i = 1,2,(17)
where Riand ´
Ridenote the achievable rate and the target rate of xi, i = 1,2 symbols. Hence, as firstly,
the achievable rates of the symbols should be defined. Since a cooperative communication is considered, the
achievable rate of x1symbols is limited by the weakest link [30]. Thus, according to the Shannon Theory [31],
the achievable rate of x1symbols is given as
R1=ζB log21 + min{SI N R(sr)
x1, SI NR(rd)
ˆx1},(18)
where B=1/Tthe bandwidth. In (18), ζexists since the total communication is handled in two phases.
According to the time schedules of EH protocols in Figure 2 and Section 2.1, it is defined as
ζ=(1−ξ
2,in TS protocol
1
2,in PS and ideal protocols and in no EH (19)
On the other hand, although cooperative communication is not considered for the x2symbols, to guarantee SIC
operation, the achievable rate at the relay for x2symbols should not also cause outage. Thus, the achievable
rate of x2symbols is also given as [8]
R2=ζB log21 + min{SI N R(sr)
x2, SI NR(sd)
x2}.(20)
Firstly, to obtain P2(out), by substituting (14) into (20) then into (17), the OP2is defined as
P2(out) = Pmin (1 −α)pPsˆγsr
αpPsˆγsr +pPsκ+σ2,(1 −α)pPsˆγsd
αpPsˆγsd +pPsκ+σ2< φ2,(21)
2In the following OP analysis, Bis removed for notation simplicity since it is equal in all scenarios and does not affect the
analysis.
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KARA/Turk J Elec Eng & Comp Sci
where φi= 2 ´
Ri/ζ−1, i = 1,2. The probability of P(Z < z) is represented by FZ(z) which is called the
cumulative distribution function (CDF) of Z. If Z= min{X, Y }is defined and in case X and Y are statistically
independent, the CDF of the Z is given by FZ(z)=FX(z) + FY(z)−FX(z)FY(z) [32] where FX() and FY()
are the CDFs of Xand Yrandom variables, respectively. Recalling ˆγsr and ˆγsd are statistically independent,
X,(1−α)pPsˆγsr
αpPsˆγsr +pPsκ+σ2,Y,(1−α)pPsˆγsd
αpPsˆγsd+pPsκ+σ2and/or ˆγsr ,X(pPsκ+σ2)
(1−(1+X)α)pPs, ˆγsd ,Y(pPsκ+σ2)
(1−(1+Y)α)pPsare defined.
Therefore, the OP of x2symbols is given as
P2(out) = FX(φ2) + FY(φ2)−FX(φ2)FY(φ2) = Fˆγsr (A1) + Fˆγsd (A1)−Fˆγsr (A1)Fˆγsd (A1),(22)
where A1,φ2(pPsκ+σ2)
(1−(1+φ2)α)pPsis defined for representation/notation simplicity. As defined in (14), ˆγk=|ˆ
hk|2
follows exponential distribution, hence the CDF of the ˆγkis Fˆγk(.)=1−exp (−ˆγk/ˆ
Ωk) where ˆ
Ωk= Ωk−κis
defined. Thus, the OP of the x1symbols is derived as
P2(out) = 1−exp −A1
ˆ
Ωsr +1−exp −A1
ˆ
Ωsd −1−exp −A1
ˆ
Ωsr 1−exp −A1
ˆ
Ωsd .(23)
Likewise in the analysis of x2symbols, the OP of the x1symbols is obtained, by substituting (15) and (16)
into (18) then into (17), as
P1(out) = Pmin αpPsˆγsr
(1 −α)pPs|g|2+pPsκ+σ2,Prˆγrd
Prκ+σ2< φ1.(24)
Recalling Pris a function of Psand ¯γsr based on the EH, the OP of the x1symbols is rewritten as
P1(out) = Pmin αpPsˆγsr
(1 −α)pPs|g|2+pPsκ+σ2,ΥPsˆγsr ˆγrd
ΥPsˆγsrκ+σ2< φ1(25)
where Υ is the power transformation coefficient from the power of the source in that EH protocol and according
to section 2.1, it is given as
Υ =
ηρ, in PS protocol,
2ηξ
1−ξ,in TS protocol,
η, in ideal protocol.
(26)
In (25), since both SINRs include ˆγsr they are statistically correlated. Besides, the second SINR includes
the same random variable on both nominator and denominator, thus the joint CDF is very hard to obtain.
Nevertheless, without loss of generality, to derive a very tight approximate expression, the rule of independent
random variables given in (22) is applied. The OP of the x1symbols is obtained as
P1(out)∼
=Fˆγsr (A2) + Fˆγsr ,ˆγrd (φ1)−Fˆγsr (A2)Fˆγsr ,ˆγr d (φ1),(27)
where A2,φ1((1−α)pPsδˆ
Ωsr+pPsκ+σ2)
αpPsis defined for notation simplicity. Fˆγsr ,ˆγrd is the joint CDF for the second
SINR term in (25). Since the ˆγsr is exponentially distributed, the first term in (27) can be easily obtained as
Fˆγsr (A2)=1−exp −A2
ˆ
Ωsr .(28)
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KARA/Turk J Elec Eng & Comp Sci
The second term in (27) is obtained as
Fˆγsr ,ˆγrd (φ1) =
φ1
ZZ
0
ΥPsˆγsr ˆγrd
ΥPsˆγsrκ+σ2dˆγsrdˆγrd,=
∞
Z
0
1
ˆ
Ωrd
exp (−ˆγrd/ˆ
Ωrd)
∞
Z
φ1σ2
(ˆγr d−φ1κ)ΥPs
1
ˆ
Ωsr
exp (−ˆγsr/ˆ
Ωsr)dˆγsr dˆγr d,
= 1 −
∞
Z
0
1
ˆ
Ωrd
exp −ˆγrd
ˆ
Ωrd −φ1σ2
(ˆγrd −φ1κ) ΥPsˆ
Ωsr !dˆγrd.
(29)
Since the exponential expression includes a complex polynomial in (29), to the best of the author’s knowledge,
it has no closed-form solution. Nevertheless, it can be easily computed by numerical tools such as MATLAB,
MAPPLE, MATHEMATICA. By substituting (28) and (29), the OP of x1symbols is derived.
Since both symbols are transmitted to the same destination in NOMA-CRS, the system is considered to
be in outage in case any of the symbols being in outage. Therefore, the OP of the SWIPT-NOMA-CRS is equal
to the union outage probabilities of the symbols and it is given by
PSW I P T −NOMA−CRS (out) = P1(out)∪P2(out) = P1(out) + P2(out)−P1(out)P2(out).(30)
It is derived by substituting (23) and (27) into (30).
3.1. Benchmark Analysis (NOMA-CRS without EH)
As explained in the system model, the first phases in SWIPT-NOMA-CRS and NOMA-CRS without EH are
the same. The only difference is the power of the source. Therefore, the OP of x2symbols in NOMA-CRS
without EH is also equal to (23).
On the other hand, since no EH is implemented, the relay will have its own energy thereby the SINR
between R-D will be independent from the first phase (do not include ˆγsr anymore). Therefore, by using (24)
and considering that ˆγsr and ˆγrd are statistically independent, the OP of x1symbols is obtained, by repeating
steps between (21)-(23), as
P1(out) = 1−exp −A2
ˆ
Ωsr +1−exp −A3
ˆ
Ωrd −1−exp −A2
ˆ
Ωsr 1−exp −A3
ˆ
Ωrd (31)
where A3,φ1(Prκ+σ2)
Pr. Lastly, the overall OP of the NOMA-CRS without EH is derived by substituting (23)
and (31) into (30).
4. Numerical Results
In this section, the derived OP expressions of the SWIPT-NOMA-CRS are validated for all EH protocol and
without EH (benchmark). In the following figures, the lines denote the theoretical curves whereas the markers
represent computer simulations. Besides, unless the figures are presented with respect to one of the parameters,
the simulation parameters are given in Table. Moreover, in the figures, the curves with the same parameters
(e.g., κ,α) are noted with dashed circles.
In Figure 3 and Figure 4, the outage performances of x1symbols are presented for perfect SIC ( δ= 0)
and imperfect SIC ( δ= 0.001 ) cases, respectively. In both figures, the results are given for two different PA
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KARA/Turk J Elec Eng & Comp Sci
Table 1. Simulation parameters
Parameter Value Parameter Value
Ωk, k =sr, sd, rd [10,2,10] Time sharing factor (ξ) 0.2
Imperfect CSI factor (κ) 0 (perfect CSI), 0.01 Imperfect SIC factor (δ) 0 (perfect SIC), 0.001
Power allocation (α) 0.1 and 0.2 Bandwidth (B) 1 MHz
Energy conversation coefficient (η) 0.95 Target Rates ( ´
Ri, i = 1,2) [500Kbps, 100Kbps]
Power sharing factor (ρ) 0.2
coefficient and for both perfect CSI and imperfect CSI cases. Firstly, it is noteworthy that the derived OP
expressions match well with simulations for all EH protocols which proves that the analysis is very tight.
Besides, the derived OP for without EH protocol is perfectly-matched with simulations. In both figures,
the OP of x1symbols have better performances in all SWIPT-NOMA-CRS schemes (the EH protocols are
implemented) rather than NOMA-CRS without EH (benchmark). For instance, according to the EH protocol,
the SWIPT-NOMA-CRS schemes achieve the same outage performance with ∼2.5dB to 4 dB less power
than NOMA-CRS without EH. This is very promising for energy efficiency. However, with the increase of SIC
uncertainties, the advantage of the TS protocol can be diminished in high SNR region. This is explained as
follows. The transmit power of the source is higher in SWIPT-NOMA-CRS (with EH protocols). Therefore,
the effect of imperfect SIC becomes greater in the first phase in SWIPT-NOMA-CRS since the imperfect SIC
effect depends on the source power given in (15). In addition to this, in TS protocol, since the power transfer
and information transfer are achieved by time division duplex, the information transfer is implemented with
a lower duration and this increases φiin TS protocol due to the ζ(see (19) and below (21)). However, one
can easily see that the probability of the imperfect SIC becomes very low in SWIPT-NOMA-CRS when an
actual modulator/detector is implemented since, with the increase of the transmit power, the error probability
decreases significantly. Then, in Figure 5, the outage performance of x2symbols are presented for two different
PA and CSI conditions. As seen from the figures, the derived OP expressions match perfectly with simulations
for all EH and without EH protocols. The SWIPT-NOMA-CRS is again superior to NOMA-CRS in terms of
outage performances of x2symbols in all scenarios. Indeed, this performance gain is more than the one of x1
symbols. The SWIPT-NOMA-CRS can provide ∼3dB to 5 dB energy efficiency.
Since the validations of the derived OP expressions for both symbols are presented in Figure 3-Figure 5
and the overall outage probability of the SWIPT-NOMA-CRS is defined as the union of the OPs of the symbols
(30), in the following figures, only the OP of the SWIPT-NOMA-CRS (union OP of the symbols) is presented.
In order to investigate the effect of the imperfect SIC, in Figure 6, the OP of the SWIPT-NOMA-CRS is given
with respect to imperfect SIC effect ( δ). In Figure 6, the total transmit SNR is assumed to be 30dB . As seen
in the previous figures, with the increase of the imperfect SIC effect, the gap between performances becomes
lower. Nevertheless, as expected from the previous results, the PS and ideal protocols in SWIPT-NOMA-CRS
still outperforms NOMA-CRS without EH even a bit whereas the TS protocol performs worse with higher
imperfect SIC effects. Besides, if the imperfect SIC effect becomes too high (e.g. δ≥ −5dB ), all considered
scenarios are always in outage. In Figure 6(a) and Figure 6(b), one can see that the imperfect CSI does not have
too much effect on the outage performance when imperfect SIC is higher, since the performance is dominated
by the imperfect SIC. This is also seen in comparisons of PA coefficients. Since the imperfect SIC causes
worse performance of x1symbols and it pulls down the overall performance of SWIPT-NOMA-CRS, the better
performance is achieved by increasing the allocated power to x1symbols (e.g., α= 0.2 ).
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KARA/Turk J Elec Eng & Comp Sci
0 5 10 15 20 25 30 35 40
Total SNR (PT/2) (dB)
10-5
10-4
10-3
10-2
10-1
100
Outage Probability
NOMA-CRS, without EH (Benchmark)
SWIPT-NOMA-CRS,PS protocol
SWIPT-NOMA-CRS,TS protocol
SWIPT-NOMA-CRS,ideal protocol
0 5 10 15 20 25 30 35 40
Total SNR (PT/2) (dB)
10-5
10-4
10-3
10-2
10-1
100
Outage Probability
NOMA-CRS, without EH (Benchmark)
SWIPT-NOMA-CRS,PS protocol
SWIPT-NOMA-CRS,TS protocol
SWIPT-NOMA-CRS,ideal protocol
19.8 19.9 20 20.1 20.2
0.009
0.01
0.011
0.012
0.013
19.8 19.9 20 20.1 20.2
0.015
0.02
0.025
=0.01
=0.01
Lines: Theoretical
Markers: Simulations
Lines: Theoretical
Markers: Simulations
=0
(perfect CSI) =0
(perfect CSI)
a) b)
Figure 3. Outage Performance of x1symbols with perfect SIC ( δ= 0 ) a) PA α= 0.1 b) PA α= 0.2 .
0 5 10 15 20 25 30 35 40
Total SNR (PT/2) (dB)
10-3
10-2
10-1
100
Outage Probability
NOMA-CRS, without EH (Benchmark)
SWIPT-NOMA-CRS,PS protocol
SWIPT-NOMA-CRS,TS protocol
SWIPT-NOMA-CRS,ideal protocol
0 5 10 15 20 25 30 35 40
Total SNR (PT/2) (dB)
10-3
10-2
10-1
100
Outage Probability
NOMA-CRS, without EH (Benchmark)
SWIPT-NOMA-CRS,PS protocol
SWIPT-NOMA-CRS,TS protocol
SWIPT-NOMA-CRS,ideal protocol
Lines: Theoretical
Markers: Simulations
=0.01
=0
(perfect CSI)
=0.01
=0
(perfect CSI)
a) b)
Lines: Theoretical
Markers: Simulations
Figure 4. Outage Performance of x1symbols with imperfect SIC ( δ= 0.001 )a) PA α= 0.1 b) PA α= 0.2 .
In order to reveal the effect of EH protocol and PA parameters, in Figure 7, the OP of the SWIPT-NOMA-
CRS is presented with respect to these parameters. In Figure 7, δ= 0 , κ= 0 and the total SNR is 30 dB .
In Figure 7(a) and Figure 7(b), the PA coefficient is α= 0.2 . In Figure 7(a), OP of the SWIPT-NOMA-CRS
is given in PS protocol with the change of PS factor (ρ). To compare, the performances of the ideal protocol
in SWIPT-NOMA-CRS and of the NOMA-CRS without EH are also presented. One can easily see that the
PS factor (ρ) has a dominant effect on the OP and according to chosen ρ. The SWIPT-NOMA-CRS with PS
protocol can achieve similar performance to ideal protocol or it can have worse performance than NOMA-CRS
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KARA/Turk J Elec Eng & Comp Sci
0 5 10 15 20 25 30 35 40
Total SNR (PT/2) (dB)
10-6
10-5
10-4
10-3
10-2
10-1
Outage Probability
NOMA-CRS, without EH (Benchmark)
SWIPT-NOMA-CRS,PS protocol
SWIPT-NOMA-CRS,TS protocol
SWIPT-NOMA-CRS,ideal protocol
0 5 10 15 20 25 30 35 40
Total SNR (PT/2) (dB)
10-6
10-5
10-4
10-3
10-2
10-1
Outage Probability
NOMA-CRS, without EH (Benchmark)
SWIPT-NOMA-CRS,PS protocol
SWIPT-NOMA-CRS,TS protocol
SWIPT-NOMA-CRS,ideal protocol
24.8 24.9 25 25.1 25.2
1
1.2
1.4
10-3
24.8 24.9 25 25.1 25.2
1.2
1.4
1.6
1.8 10-3
=0.01
=0.01
=0
(perfect CSI) =0
(perfect CSI)
a) b)
Lines: Theoretical
Markers: Simulations
Lines: Theoretical
Markers: Simulations
Figure 5. Outage Performance of x2symbols a) PA α= 0.1 b) PA α= 0.2 .
-30 -25 -20 -15 -10 -5
imperfect SIC effect ( ) (dB)
10-2
10-1
Outage Probability
NOMA-CRS, without EH (Benchmark)
SWIPT-NOMA-CRS,PS protocol
SWIPT-NOMA-CRS,TS protocol
SWIPT-NOMA-CRS,ideal protocol
-30 -25 -20 -15 -10 -5 0
imperfect SIC effect ( ) (dB)
10-2
10-1
100
Outage Probability
NOMA-CRS, without EH (Benchmark)
SWIPT-NOMA-CRS,PS protocol
SWIPT-NOMA-CRS,TS protocol
SWIPT-NOMA-CRS,ideal protocol
-15.05 -15 -14.95
0.123
0.124
0.125
0.126
0.127
-15.05 -15 -14.95
0.116
0.118
0.12
0.122
=0.1
=0.2
=0.1
=0.2
Lines: Theoretical
Markers: Simulations
Lines: Theoretical
Markers: Simulations
b)
a)
Figure 6. Outage Performance of the SWIPT-NOMA-CRS with respect to imperfect SIC effect ( δ) a) κ= 0 (perfect
CSI) b) κ= 0.01 (imperfect CSI).
without EH. To this end, considering the performance gain over NOMA-CRS without EH, the optimum PS
factor (ρ∗) can be given as 0.25 for the given conditions. Likewise, the OP of the SWIPT-NOMA-CRS in TS
protocol is given in Figure 7(b) with respect to TS factor (ξ). Based on provided comparisons in Figure 7(b),
the SWIPT-NOMA-CRS can outperform NOMA-CRS without EH when only 0.05 ≤ξ≤0.25 which is a very
short range compared to the PS protocol. Then, the OPs of all EH and without EH protocol are presented with
respect to PA coefficient (α) in Figure 7(c). In Figure 7(c), the PS and TS factors are chosen as ρ= 0.25 and
ξ= 0.15 according to the obtained values from Figure 7(a) and Figure 7(b). As can be seen from Figure 7(c),
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KARA/Turk J Elec Eng & Comp Sci
0 0.2 0.4 0.6 0.8 1
PS factor ( )
10-3
10-2
Outage Probability
NOMA-CRS, without EH (Benchmark)
SWIPT-NOMA-CRS,PS protocol
SWIPT-NOMA-CRS,ideal protocol
0 0.2 0.4 0.6 0.8 1
TS factor ( )
10-4
10-3
10-2
10-1
100
Outage Probability
NOMA-CRS, without EH (Benchmark)
SWIPT-NOMA-CRS,TS protocol
SWIPT-NOMA-CRS,ideal protocol
0 0.1 0.2 0.3 0.4 0.5
PA coefficient ( )
10-4
10-3
Outage Probability
NOMA-CRS, without EH (Benchmark)
SWIPT-NOMA-CRS,PS protocol
SWIPT-NOMA-CRS,TS protocol
SWIPT-NOMA-CRS,ideal protocol
Lines: Theoretical
Markers: Simulations
Lines: Theoretical
Markers: Simulations Lines: Theoretical
Markers: Simulations
c)
a) b)
Figure 7. Outage Performance of the SWIPT-NOMA-CRS with respect to EH factor and PA coefficient a) in PS
protocol vs. PS factor ( ρ) b) in TS protocol vs. TS factor ( ξ) c) in all protocols vs. PA coefficient (α)
with the use of optimal EH factor values, SWIPT-NOMA-CRS always outperforms NOMA-CRS without EH
regardless of PA coefficient which is very promising for energy efficiency. With the increase of α, the outage
performances for all cases becomes better. Nevertheless, this increase is floored after α∼0.35. To this end, for
the considered scenario, the optimum PA coefficient can be given as α∗= 0.35.
Lastly, to investigate the effects of the target rates (QoS requirements) on the outage performance, in
Figure 8, the OPs of the SWIPT-NOMA-CRS are given with respect to ´
R1and ´
R2. In Figure 8, the total
transmit SNR is 30dB . The PS factor, TS factor and PA coefficient are set to ρ= 0.25 , ξ= 0.15 and α= 0.35
according to discussion on Figure 7. As expected, if one of the target rates is increased, all scenarios have worse
outage performance. The best outage performance is achieved when lower rates are required as QoS. On the
other hand, if too strict QoS requirements (too high target rates) are demanded, SWIPT-NOMA-CRS with
TS protocol may be in always outage. Based on provided comparisons, it is clear that SWIPT-NOMA-CRS
outperforms NOMA-CRS without EH for any QoS requirement.
5. Conclusion
In this paper, the SWIPT-NOMA-CRS is proposed where the relay node harvests its energy from the RF signal
between source and relay. In the SWIPT-NOMA-CRS, three different EH protocol (e.g., PS, TS and ideal
protocols) are implemented. The closed-form OP expressions are derived for all EH protocols under imperfect
SIC and CSI. The derivations are validated via simulations. The proposed SWIPT-NOMA-CRS outperforms
conventional NOMA-CRS without EH significantly and it can reduce the energy consumption up to ∼5dB for
the same OP target which is very promising for the energy-constraint networks (e.g., IoT). Based on simulations,
as expected, the ideal protocol has the best performance. On the other hand, the PS protocol is superior to the
TS protocol. Moreover, the effects of the EH and PA parameters on the OP are discussed and it is revealed
that the PS protocol is more flexible than the TS protocol. The PS protocols outperforms the conventional
NOMA-CRS without EH within a very large PS factor range whereas it is a very small TS factor range in the
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KARA/Turk J Elec Eng & Comp Sci
Figure 8. Outage Performance of the SWIPT-NOMA-CRS with respect to target rates ( ´
R1,´
R2) a) NOMA-CRS
without EH (benchmark) b) PS protocol ( ρ= 0.25 ) c) TS protocol (ξ= 0.15 ) d) ideal protocol.
TS protocol. To this end, the optimum parameters are represented for the minimum OP in given scenarios.
Finally, as future works, the energy efficiency of other NOMA schemes can be increased thanks to the SWIPT
integration and the analysis of imperfect SIC and CSI can be extended for these systems.
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