Considering a dual-hop energy-harvesting (EH) non-orthogonal multiple access (NOMA) relaying system, this paper consider novel relaying protocols based on time power switching-based relaying (TPSR) architecture for amplify-and-forward modes. We introduce novel system model relaying network with impacts of energy harvesting fractions and derive analytical expressions for outage probability for the information transmission link. It confirmed that right selection of power allocation for NOMA to obtain optimal performance. Theoretical results show that, in comparison with the conventional solutions, the proposed model can achieve optimal throughput efficiency for sufficiently small threshold SNR with condition of controlling time switching fractions and power splitting fractions appropriately in TPSR protocol. We also explore impacts of transmission distances in each hop, transmission rate, the other key parameters of TPSR to outage performance for different channel models. Simulation results are presented to corroborate the proposed methodology.

1. TELKOMNIKA, Vol.16, No.5, October 2018, pp. 1907~1917
ISSN: 1693-6930, accredited First Grade by Kemenristekdikti, Decree No: 21/E/KPT/2018
DOI: 10.12928/TELKOMNIKA.v16i5.9385  1907
Received March 23, 2018; Revised June 22, 2018; Accepted July 19, 2018
Exploiting Outage Performance of Wireless Powered
NOMA
Dinh-Thuan Do*, Le Chi Bao
Faculty of Electronics Technology, Industrial University of Ho Chi Minh City, Vietnam
12 Nguyen Van Bao, Go Vap Dist., Ho Chi Minh City, Vietnam
*Corresponding author, e-mail: dodinhthuan@iuh.edu.vn; baole.iuh@gmail.com
Abstract
Considering a dual-hop energy-harvesting (EH) non-orthogonal multiple access (NOMA) relaying
system, this paper consider novel relaying protocols based on time power switching-based relaying
(TPSR) architecture for amplify-and-forward modes. We introduce novel system model relaying network
with impacts of energy harvesting fractions and derive analytical expressions for outage probability for the
information transmission link. It confirmed that right selection of power allocation for NOMA to obtain
optimal performance. Theoretical results show that, in comparison with the conventional solutions, the
proposed model can achieve optimal throughput efficiency for sufficiently small threshold SNR with
condition of controlling time switching fractions and power splitting fractions appropriately in TPSR
protocol. We also explore impacts of transmission distances in each hop, transmission rate, the other key
parameters of TPSR to outage performance for different channel models. Simulation results are presented
to corroborate the proposed methodology.
Keywords: non-orthogonal multiple access, energy harvesting, outage probability
Copyright © 2018 Universitas Ahmad Dahlan. All rights reserved.
1. Introduction
Together with the rapid growth of services and applications in wireless, the demand for
increasing power consumption in wireless terminals has dramatically enlarged. Motivated from
advantages of various energy harvesting (EH) architectures, relaying network has now been
proposed to improve the overall system energy efficiency through considering information
transmission and energy-transmission cooperation. The popular energy resources in EH
including solar and wind that is intermittent under impacts the environmental alteration, radio
frequency (RF) signal is considered as a new viable source which can be applied in wireless
power transfer (WPT) [1]. Nevertheless, regarding relay nodes using batteries to power,
including mobile devices, because of the short battery lifespan. Besides that, some negative
impacts may result from the use of extra energy so it may prevent batteries from performing any
relaying. In [2]-[7], the authors have put forward energy harvesting in relaying networks.
For instance, assuming a stationary and ergodic process in terms of energy scavenged by the
relay, by taking energy-constrained and energy-unconstrained relays into account, the symbol
error rate was obtained. In this case, from any source the energy could be harvested. The work
in [3] focused on two harvest-and-forward protocols relying on either power splitting or time
switching, where the relay receives information signal from the source and uses the harvested
energy to amplify and forward source signal to the destination.
The authors in [4] the wireless energy can be harvested by relays and by
interference [5] and the total harvested energy was then allocated for transmissions of signals to
different destinations and system performance can be examined in these scenarios. The
practical insight into this study is the superior allocation of the total harvested energy among all
transmissions. Likewise, by using tools from stochastic geometry, the relaying performance was
analyzed under the impact of random locations of relays, where energy from the source node is
scavenged by the relays. Joint power splitting and antenna selection scheme were taken into
consideration in [7], where multiple antennas are provided for the relay to carry out energy
harvesting process at the source node, therefore, the best portion of power splitting and the best
antenna can be chosen that help optimize the achievable rate.

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Consider as a favorable applicant for the fifth generation (5G) wireless networks, non-
orthogonal multiple access (NOMA) has been deployed since NOMA can be straightforwardly
joint with relaying networks, small cells, device-to-device, cognitive radio networks. At the base
station (BS), signals are superimposed as key idea of NOMA in which users’ signal with
different power allocation coefficients, and better channel condition together with assigned
successive interference cancellation (SIC) to eliminate the other users’ signals before
distinguishing its own signal [8]. Alternately, a special case of the information theoretic concept,
namely superposition coding, is similar with the concept of NOMA. Furthermore, user fairness is
considered as key feature of NOMA. As compared to conventional water-filling power
distribution, worse channel condition is assigned for NOMA with higher power compared with
those in case of better channel conditions, trade-off between system throughput and user
fairness are improved. As a result, to an increase in spectral efficiency for all users in NOMA
where shares the same time slot, frequency and spreading code.
The existing advanced schemes such as multiple-input multiple-output (MIMO) can be
included in NOMA as an attractive property in research about NOMA [9]. In different system
model, NOMA is studied in cooperative relaying networks (CRS) [10], heterogeneous
system [11], and device-to-device (D2D) networks with full-duplex scheme [12]. In other trend,
the cooperative NOMA (C-NOMA) together with CRS as investigation in [13] in which spatially
multiplexed scheme to serve a single user, while the other papers [9], [11] concentrated on
scheme related to a group of users. Outage performance of several relaying networks can be
explored in [14-16].
Motivated by these discussions, in this paper we propose and analyse a relaying
system with WPT under collecting energy from an external energy resource. Our results show
that the TPSR factor and the transmission power at the relay should be jointly designed to
achieve an optimal throughput efficiency, and that optimizing the TPSR factor alone is
inadequate as performed in the literature. The main contributions of this paper can be shown as:
a. The new architecture related to EH (namely EH-NOMA protocol) is investigated and the
impact of energy-aware fractions on system performance are studied. Such system model
is design as combination of the two traditional EH receivers TSR and PSR in one unique
protocol.
b. We derive some analytical expressions of cumulative distributation function (CDF) of
signal-to-interference-plus-noise ratio (SINR) and then outage proability is derived for
delay-limited transmission (DLT) scheme with considerations of power allocation in EH-
NOMA protocol applied at the relay.
c. Next, Monte Carlo simulations are presented the outage performance to corroborate our
analysis and the impact of some significant parameters on proposed protocol in EH
assisted networks are investigated.
The remainder of this paper is organized as follows: Section 2 presents the system model
and TPSR protocol is investigated. In section 3, we derive the analytical expressions of outage
probability and throughput in delay-limited transmission. Section 4 examines the simulation
results. Finally, Section 5 completes with conclusion remarks for the paper and reviews the
important results.
2. System Model
We consider cooperative AF relaying network, where the source  S communicates
with two destinations  1, 2D D through an intermediate relay  R . The link between the source
and the destination is unreliable or unavailable, so the transmission can only happen
successfully with the aid of the wireless powered relay. In particular, the relay node deployed in
this paper is characterized as energy-constrained. Furthermore, each node is furnished with a
single antenna, and half-duplex mode using amplify-and-forward (AF) strategy is deployed in
the relay.
The relay acquires two independent data symbols during two time epochs, 1x from S
directly and 2x through the relay, whereas the EH-NOMA delivers a single data symbol.
This paper uses time power based relaying energy harvesting (TPSR) protocol [2-3].
In particular, during the first phase S broadcasts a superposition-coded signal 1 1 2 2a x a x to the

3. TELKOMNIKA ISSN: 1693-6930 
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relay (i.e., R) and the destination D, where SP represents the total transmit power of the source
S, and 1 2,a a symbolizes the power allocation quantity for symbol 1 2,x x respectively. It can be
supposed that D is the NOMA-far user from the viewpoint of the relay, and therefore, 1 2a a to
satisfy condition 1 2 1a a  . The channel gains between the nodes are modeled as
 ~ 0,S SRh CN and  ~ 0,D RDh CN , assumed that all channels follow flat fading Rayleigh
distribution.
Source
(S)
Destination
(D1)
Relay
(R)
PS
hS
d1 d2
hD1
Energy harvesting
Information Processing
Destination
(D2)
hD2
Figure 1. System model of EH-NOMA
During the first phase, the received signals at the relay is given by
     1 1 2 2
1
1
1 1 ,A C
R S S R Rm
y P h a x a x n n
d
       (1)
where  2
0, A
A
R nRn CN  stands for antenna noise,  2
0, C
C
R nRn CN  is complex additive white
Gaussian noise (AWGN) at relay due to signal RF converting to base band siganl. Using
Amplify-and-Forward (AF) scheme, the relay will be amplified with factor G as given by
   
2
2 2
1
1
.
1 1S S
nA nCm
G
P h
d
   

   
(2)
After signal processing at relay, in the second phase the relay amplifies the received
signal to forward to destination with power as RP , this power depends on harvested power in
first phase. In such model, role of D1 and D2 is similar, we only consider on performance of D1.
The received signal at destination D1 denoted as Dy given by:
2
G
,R D A C
D R D Dm
P h
y y n n
d
   (3)

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where  2
0, A
A
D nDn CN  and  2
0, C
C
D nDn CN  are respectively white Gaussian noise (AWGN)
at destination and converting operation to base band from RF signal at destination D1. Plugging
Ry and G from (1) and (2) into (2.26), Dy can be expressed as
 1 1 2 2 1
2 22 2
2 1 2 1 2
(1 )
,
(1 ) (1 )
m
R S S D R D R
D D
m m m m m
S S nR S S nR
P P h h a x a x P d h n
y n
P h d d P h d d d

   
 
  
   
(4)
We denote  1 A C
R R Rn n n @ and A C
D D Dn n n@ as overall noise AWGN at the relay and
destination. Therefore,  2 2 2
1 A CnR nR nR    @ is total variance noise AWGN at relay in TPSR.
The harvested energy for signal processing at relay in energy harvesting phase denoted as
TPSR
hE re-used in next signal processing  1 ,T and hence the transmit power at relay can be
computed as
   
2
11 1
TPSR
S Sh
R m
P hE
P
T d


 
 
  
   
(5)
By replacing RP from (5) into (4). As a result, the received signal at destination Dy can be
given by:
   
 
 
 
2
2
2 2
1 2 2 1
2
2 1
2 2
2 2 1
1
1 (1 )
1 (1 )
m
S S S S D S
D
m m m m
S S nR
Signal part
m m
S S D R
D
m m m
S S nR
Noise part
P h d P h h x
y
d d P h d d
P h d d h n
n
d P h d d
  
  
 
  


  
 
  
(6)
3. Outage performance Analysis
We first determine the signal to noise ratio (SNR), and then we perform outage
probability. Such outage event is evaluated as probabily to the following rate less than the
pre-defiend threshold rate  Pr RD thI I
 2
1
log 1 ,
2
RD DI SNR  (7)
In which SNR is computed by
2
2
{| | }
.
{| | }
D
Signal part
SNR
Noise part



(8)
At destination D1, the device first decode noise term of D2’s signal and then applying SIC to
detect its own signal. As a result, it can be obtained specific SNR for detect D2’s signal as

5. TELKOMNIKA ISSN: 1693-6930 
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 
    
 
2 2 2
1 2
1, 2 2 2 2
2 2 22 2 2 1
1 1 1 1 1 2 2
1
.
1
1 1 1
S S D
D x m
m m m nR nD
S S D D nR nD
S S
P h h a
SNR
d
P h h a d h d d
P h
 
  
      



     
(9)
We need find simple form of (9) for next calculation. The reason for simplify above expression is
that small component can be eliminated, i.e.
  2 2 2
1
2
1
0
m
nR nD
S S
d
P h
  
 at high SNR. As a result, at
high SNR, the received SNR for symbols 2x at the destination D1 in approximate value can be
given as
 
    
2 2 2
1 2
1, 2 2 2 22 2 2
1 1 1 1 1 2
1
.
1 1 1
S S D
D x m m m
S S D D nR nD
P h h a
SNR
P h h a d h d d
 
      


    
(10)
Then, D1 perform SIC to detect 1x signal with the received SNR given by
 
  
2 2 2
1 1
1, 1 2 2 2
1 1 1 2
1
.
1 1
S S D
D x m m m
D nR nD
P h h a
SNR
d h d d
 
    


  
(11)
Similarly, after SIC operation at destination D2, the receiving SNR for detecting 2x given by
 
  
2 2 2
2 2
2, 2 2 2 2
1 2 1 2
1
.
1 1
S S D
D x m m m
D nR nD
P h h a
SNR
d h d d
 
    


  
(12)
It can be shown that the probability for each SNR, for example the receiving SNR for detecting
2x at D2 corresponding with probability given by
 
 
  
  
 
2 2 2
2 2
2, 2 0 02 2 2
2 1 1 2
2
2 1 2 0
2 2 2
1 0
1
Pr
1 1
1 1
.
1
S S D
D x m m m
D nR nD
m m
nD
D m
S S nR
P h h a
SNR SNR Pr SNR
h d d d
d d SNR
Pr h
P h d SNR
 
    
  
   
 
   
    
  
  
   
(13)
The following theorem provides an exact expression for the outage probability achieved by the
two-stage AF relay in the proposed EH-NOMA. More importantly, the overall outage probability
for such EH-NOMA with the proposed TPSR relaying scheme is given by
 
     
1, 2 2 1, 1 1 2, 2 2
1, 2 2 1, 1 1 2, 2 2
Pr , ,
Pr Pr Pr
EH NOMA D x D x D x
D x D x D x
OP SNR SNR SNR
SNR SNR SNR
  
  
    
    (14)
To perform above outage event, it must be calculated separated probability components. For
simplicity, we assume that 2
1 2 0 2 1R
SNR     at the fixed rate R . In special case high SNR,
it can be shown the closed-form expression of remaining outage probability can be shown
respectively as:

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 
 
  
  
 
2 2 2
1 1
1, 1 0 02 2 2
1 1 1 2
2
2 1 2 0
1 2 2
2 1 0
1
Pr
1 1
1 1
.
1
S S D
D x m m m
D nR nD
m m
nD
D m
S S nR
P h h a
SNR SNR Pr SNR
h d d d
d d SNR
Pr h
a P h d SNR
 
    
  
   
 
   
    
  
  
   
(15)
and
 
 
    
1, 2 0
2 2 2
1 2
02 2 22 2 2
1 1 1 1 2
Pr
1
1 1 1
D x
S S D
m m m
D nR S S D nD
SNR SNR
P h h a
Pr SNR
h d P h h a d d
 
      

 
  
      
(16)
Lemma 1: We denote 2
1 0 ,m
nRd      2
1 2 0(1 ) 1 m m
nDd d       and  1 .SP    The
outage expression can be given by:
 
  
2 2
02 2 2
1 1 2
2
2
1
1 1
.
S S DTPSR
out m m m
D nR nD
D
S
P h h
OP Pr
h d d d
Pr h
h
 

    

 
 
  
    
 
  
  
(17)
And it can be solved by
 0
0
1
1
Pr 1 exp exp
4 4
1 exp ,
SR SR SR RD
SR SR RD SR RD
SNR d
K

  
 
   
  
  


   
        
      
  
              

(18)
where 1 ( )K  is first order Bessel function.
Proof: See in appendix. Applying Lemma 1, it can be obtained several outage event as below
 1, 1 0
1 10
1
1 1 1
1
Pr 1 exp exp
4 4
1 exp ,
D x
SR SR SR RD
SR SR RD SR RD
SNR d
K

  
 
   
  
  


   
        
      
  
              

(19)
where 2
1 0 ,m
nRd SNR     2
1 2 0(1 ) 1 m m
nDd d SNR      ,   2
1 1
1 .S
P a   
 1, 2 0
2 2 20
1
2 2 2
1
Pr 1 exp exp
4 4
1 exp ,
D x
SR SR SR RD
SR SR RD SR RD
SNR SNR d
K

  

   
  
  


   
        
      
  
              

(20)
where    2 2
2 2 0 11 .SP a SNR a    

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 2, 2 0
3 3 30
1
3 3 3
1
Pr 1 exp exp
4 4
1 exp ,
D x
SR SR SR RD
SR SR RD SR RD
SNR SNR d
K

  

   
  
  


   
        
      
  
              

(21)
where   2
3 2
1 .S
P a   
4. Numerical Results
Unless otherwise stated, we set the source transmission rate, R=3 (bits/sec/Hz) in the
delay limited transmission mode, energy harvesting efficiency, 1  , source transmission
power, Ps=1 Joules/sec and path loss exponent 3m  (which corresponds to an urban cellular
network environment). The distances 1 2,d d are normalized to unit value. For simplicity, similar
noise variances at the relay and the destination nodes are assumed, i.e., different kinds of noise
variance is set as 2
0.01  . The mean values, ,SR RD  of the exponential random variables
2 2
,S Dh h , respectively, are set to 1.
Figure 2 plot the outage probability for cooperative NOMA with different power
allocation factors for AF relaying, where energy harvesting fractions contribute to change outage
performance shown as different curves. Observing the Figure 2, one can conclude that
compared among three cases of EH-NOMA with two-stage maxmin relaying, the proposed
scheme with higher time–aware energy harvesting allocation for energy harvesting can realize
better outage performance as fixed power–aware energy harvesting factor. Furthermore,
Figure 2 manifest that EH-NOMA can remarkably enhance the outage performance at high
transmit power at source SP . More importantly, the analytical curves match very well with Monte-
Carlo results.
Figure 2. Outage performance versus transmit power at source at fixed power-aware energy
harvesting
Figure 3 plot the outage probability for cooperative NOMA in case of fixed time-aware
energy harvesting factor is set and varying power–aware energy harvesting factor in TPSR
protocol. As can be seen clearly that the proposed scheme with higher power-aware energy
harvesting allocation for energy harvesting can realize better outage performance due to more
energy for signal processing. Similarly, Figure 3 confirmed that that EH-NOMA can provide the
best outage performance as reasonable chosen of SP .

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1914
Figure 3. Outage performance versus transmit power at source at fixed time-aware energy
harvesting
As can be seen in Figure 4, it shows the optimal throughput versus changing variance
noise term in EH- NOMA in case of changing transmit power at source. It is noted that
throughput can be shown as 0(1 ) (1 )Eh NOMAOP R   corresponding fixed rate 0R . As can be
seen clearly that the proposed scheme with higher transmit power ( 3 ( / )SP J s can realize
better throughput performance due to more energy for signal processing. It is noted that noise
term contributes to lower throughput, especially at high noise -20 to -10dB.
Figure 4. Outage throughput versus noise as varying transmit power at source
In Figure 5, we compare the outage performance for EH-NOMA with OMA scheme by
using different users’ target rates and different numbers of relays. It can be observed from
Figure 5 that OMA relaying schemes can achieve better outage performance than the NOMA
scheme. Furthermore, we can also see that the outage performance of NOMA is enhanced
significantly with high transmit power at source. In addition, Figure 5 also demonstrates that
energy harvesting remain operation of relay where has signal processing and outage

9. TELKOMNIKA ISSN: 1693-6930 
Exploiting Outage Performance of Wireless Powered…. (Dinh-Thuan Do)
1915
performance at acceptable as reasonable selection of related parameters as in simulation
result.
Figure 5. Compare the outage performance for EH-NOMA with OMA scheme by using different
users’ target rates and different numbers of relays.
5. Conclusion
In this paper, we have proposed AF relay schemes for EH-NOMA. With regard to EH-
NOMA relaying schemes, we have derived asymptotic analytical expressions for outage
probability. The proposed cooperative NOMA schemes not only achieve reasonable
performance but also yield better outage performance than OMA at specific scenarios. In
addition, compared to different power allocation fractions, the proposed NOMA relay schemes
can further improve the outage probability compared to OMA.
Appendix
PROOF OF LEMMA 1:
It is required that
2
0.Sh   Therefore,
TPSR
outP can be given in two cases below:
In case of
2
Sh   then:
2
2
.TPSR
out D
S
P Pr h
h

 
 
  
  
(A1)
In case of
2
Sh   then:
2
2
1.TPSR
out D
S
P Pr h
h

 
 
   
  
(A2)
Therefore,
TPSR
outP can be formulated as

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TELKOMNIKA Vol. 16, No. 5, October 2018: 1907-1917
1916
 
2
2
2 2
/
2
0
2
/
/
0 /
( )
( )
( ) 1 exp ( ) ,
S
S
S S
TPSR
out D h
D h
h h
RD
P Pr h f d
Pr h f d
f d f d
x
 
 
 
 

 
 

 
 

   
 


 
   
 
   
   
          


 
(A3)
where SR and RD are respectively average gain of channels
2
Sh and
2
,Dh
 2
1 SR
SRSh
f e 
  
 is (PDF) of random variables
2
,Sh
 2
2
( ) 1 RD
DDhF Pr h e 
   
    stands for (CPF) of random variable
2
.Dh As a
result,
TPSR
outP can be expressed as
 /
1
1 exp .TPSR
out
SR SR RD
P d
 
 

 

  
    
     
 (A4)
We change to new variable .    As a result, outage probability can be computed
completely. This complete the proof.
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