Outage probability analysis of EH NOMA system network over Rayleigh fading channel using selection combining at the receiver

Bulletin of Electrical Engineering and Informatics
Vol. 9, No. 1, February 2020,pp. 256~264
ISSN: 2302-9285,DOI: 10.11591/eei.v9i1.1651  256
Journal homepage: http://beei.org
Outage probability analysis of EH NOMA system network over
Rayleigh fading channel using selection combining
at the receiver
Phu Tran Tin1, Minh Tran2, Tran Thanh Trang3
1
Faculty of Electronics Technology, Industrial University of Ho Chi Minh City, Vietnam
2
Optoelectronics Research Group, Faculty of Electrical and Electronics Engineering,
Ton Duc Thang University, Vietnam
3
National Key Laboratory of Digital Control and System Engineering, Vietnam
Article Info ABSTRACT
Article history:
Received Jun 4, 2019
Revised Sep 26, 2019
Accepted Nov 10, 2019
Non-orthogonal multiple access (NOMA) with advantages such as superior
spectral efficiency has been considered as a promising multiple access
technique for the fifth-generation (5G) mobile networks. In this research,
we propose energy harvesting (EH) NOMA system relaying network over
Rayleigh fading channel using selection combining at the receiver.
Firstly, we investigate the system performance in terms of the closed-form
expression of the outage probability (OP). Here we compare the OP of two
destination users of the proposed system. Finally, all the results is convinced
by the Monte Carlo simulation. From the results, we can confirm that all
the analytical and simulation results are the same in connection with
the primary system parameters.
Keywords:
Energy harvesting (EH)
Monte carlo
Outage probability (OP)
Power beacon
Relaying network This is an open access article under the CC BY-SA license.
Corresponding Author:
Minh Tran,
Optoelectronics Research Group,
Faculty of Electrical and Electronics Engineering,
Ton Duc Thang University, Ho Chi Minh City, Vietnam.
Email: tranhoangquangminh@tdtu.edu.vn
1. INTRODUCTION
Non-orthogonal multiple access (NOMA) with advantages such as superior spectral efficiency has
been considered as a promising multiple access technique for the fifth-generation (5G) mobile
networks [1-6]. In comparison with the traditional water-filling power allocation strategy, NOMA can
transfermore power to the users in the worse channelconditions. It leads to a better trade-off between system
throughput and user fairness. From the previous researches, authors investigated the impact of user pairing o n
downlink NOMA systems as in [7], the authors in [8] have considered the power allocation with the max-min
fairness criterion of the model system. An uplink NOMA scheme with joint power and subcarrier allocations
hasbeen proposed and investigated in [9]. In [10], a cooperation-based NOMA scheme for coordinated direct
and relay transmissions is studied. Furthermore, a diversity-oriented detection mechanism forthe cooperative
relaying system using NOMA is considered by authors in [11]. The performance of transmit antenna
selection for NOMA assisted multiple-input-multiple-output (MIMO) relay networks is presented in [12].
Then inspired by user collaboration,a cooperative NOMA transmission scheme is presented in [13].
In this research, we propose energy harvesting (EH) NOMA network system over the Rayleigh
fading channel using selection combining at the receiver. In the first stage, we investigate and derive

Bulletin of Electr Eng & Inf ISSN: 2302-9285 
Outage probability analysisof eh noma system network over rayleigh fading channel… (Phu Tran Tin)
257
the closed-form expression of the outage probability (OP) of the model system by Monte Carlo simulation.
Then the comparison of the OP of two destination users is investigated in connection with the primary system
parameters. Finally, all the results are convinced by the Monte Carlo simulation. From the results, we can
convince that all the analytical and simulation results are the same in connection with the primary system
parameters.The main contributions of this research are listed as:
- The EH NOMA network system over the Rayleigh fading channel using selection combining
at the receiver is proposed.
- The closed-form expression of the system OP is investigated and derived.
- The comparison of the OP of two destination users is investigated.
- All the results are convinced by the Monte Carlo simulation.
2. SYSTEM MODEL
The EH NOMA network system over the Rayleigh fading channel using selection combining
at the receiver is drawn in Figure 1. In this system model, we denote Source is S, Relay is R, D1 and D2
are two Destination nodes. We assume that all links between them (i.e., S-to-D1,2, S-to-R, and R-to-D1,2)
are available. The Rayleigh fading channel coefficients of S-to-D1,2, S-to-R, and R-to-D1,2 links are denoted
as hSD1,2, hSR, and hRD1,2, respectively as shown in Figure 1. The energy harvesting and information
processing (IT) are illustrated in Figure 2. In this protocol, the transmission block time T, which consists
of three-time slots. In the first-time slot αT (α is the time switching factor, 0<α<1), the relay harvests energy
from the source node S. In the second interval time (1-α)T/2, the source S transfers the information to
R and D1,2 at the same time. Finally, the relay node R transfers the information to the destination nodes
D1,2 in the remaining time slot (1-α)T/2.
EH
IT
S R
D1
1
Rd
h
SR
h
D2
2
Sd
h
1
Sd
h
2
Rd
h
IT
RàD1,D2
IT
SàR, D1, D2
αT (1-α)T/2
T
EH at R
(1-α)T/2
Figure 1. System model Figure 2. The time switching protocol
Energy harvesting phase
In the first slot time αT, we formulate the received signal as:
r sr s s r
y h P x n
= + (1)
The received energy can be computed as:
2
r sr s
E T h P

= (2)
Where 0 1

  is the energy conversion efficiency.
The average transmit power at the R node can be calculated as:
( )
2
1 / 2
s
r sr s
E
P h P
T


= =
−
(3)
Where we denote
2
1



=
−
.

 ISSN: 2302-9285
Bulletin of Electr Eng & Inf, Vol. 9, No. 1, February 2020 : 256 – 264
258
Information transmission
In the second slot time, S transmits the superposed signal 1 1 2 2
s s
a P x a P x
+ to relay, D1 and D2
according to the NOMA scheme [1]. a1, a2 are the power allocation coefficients for D1 and D2, where we
assume 1 2 2 1
1,
a a a a
+ =  , x1 and x2 are the transmit signal for D1 and D2, respectively. Hence, the received
signal at the R node, D1 and D2 can be expressed as respectively [14].
( )
1 1 2 2
r sr s s r
y h a P x a P x n
= + + (4)
( )
1 1 1
1 1 2 2
D sd s s d
y h a P x a P x n
= + + (5)
( )
2 2 2
1 1 2 2
D sd s s d
y h a P x a P x n
= + + (6)
Where 1 2
,
d d
n n are the additive white Gaussian noise (AWGN) at theD1 and D2 with zero-mean and variance
N0, respectively. From (6), we separate the received signal at the D2 into two parts included signal and noise
part for D2 to detect x1.
2 2 2 2
2 2 1 1
D sd s sd s d
signal noise
y h a P x h a P x n
= + + (7)
Hence, the received signal to interference and noise ratio (SINR) for D2 to detect x1 is given as:
 
 
2 2
2
2 2
2 2
2
2 2
2 2
2
1 0 1 1
sd s sd
sd
sd s sd
signal h a P h a
noise h a P N h a




= = =
 + +
(8)
Where
0
s
P
N
 = is the transmit signal to noise ratio (SNR).
From (5), SIC is first used for D1 by detecting and decoding the information of D2.
Hence, the received signal at the D1 can be rewritten as:
1 1 1 1
2 2 1 1
D sd s sd s d
signal noise
y h a P x h a P x n
= + + (9)
Then, the received SINR at D1 is given by:
1
21
1
2
2
2
1 1
sd
sd
sd
h a
h a



=
+
(10)
After the far user message is decoded, D1 can decode its own information with the SINR
asfollowing
1 1
2
1
sd sd
h a
 
= (11)
During the third slot time, the relaying node will amplify the received signal and forward to D1 and
D2 with the amplifying factor 2
0
r r
r s sr
x P
y P h N
 = =
+
. The received signals at the D1 and D2
are expressed as,respectively.

259
1 1 1 1 1
rd rd r rd rd r rd
y h x n h y n

= + = + (12)
Substituting (4) into (12)
( )
1 1 1
1 1 2 2
rd rd sr s s r rd
y h h a P x a P x n n
  
= + + +
 
(13)
And
( )
2 2 2 2 2
2 2 2
1 1 2 2
rd rd r rd rd r rd
rd sr s s rd r rd
y h x n h y n
h h a P x a P x h n n

 
= + = +
= + + +
(14)
Where 1 2
,
rd rd
n n was denoted the AWGN at D1 and D2, respectively. From (14), the received SINR for D2
to detect x2 is given as:
 
 
2
2
2 2
2
2 2
2
2 2
2 2 2
1 1/
sr rd
rd
sr rd rd
signal h h a
noise h h a h


 

= =
 + +
(15)
Using the fact thatN0<<Pr,hence, (15) can be rewritten as:
2
2
2 2
2
2 2
2
2
2
2 2
2 2
1
2
2
2
2 2
2
1
1/
1/
sr rd
rd
sr rd rd
sr rd
sr rd rd
h h a
h h a h
h h a
h h a h


 

 
=
+ +

+ +
(16)
The received SINR when D1 first detect D2’s information is given by:
1
21
1 1
2
2
2
2 2
2
1 1/
sr rd
rd
sr rd rd
h h a
h h a h


 

+ +
(17)
Applying SIC operation,the received SINR for D1 is given by:
1
1
1
2
2
1
2
1/
sr rd
rd
rd
h h a
h




+
(18)
3. SYSTEM PERFORMANCE ANALYSIS
The outage probability (OP) of the destination node D2 can be given by:
( )
( ) ( )
2 2 2
2 2
1
02
02 02
Pr max ,
Pr Pr
D sd rd
sd rd
OP   
   
 
= 
 
=  
(19)
Where 2
2
02 2 1
R
 = − with R2 being the target rate at the D2. From (8), we have:

 ISSN: 2302-9285
260
( )
 
( )
 
2
2
2
2
2
2
2
02 02
2
1
2
2 02 1 02
02
2 02 1
2 02 1
2 02 1
Pr Pr
1
Pr
1 exp ,
1,
sd
sd
sd
sd
sd
h a
h a
h a a
if a a
a a
if a a

  

  
 

 

 
 
 = 
 
+
 
= − 
  
− − 
  
 
= −
  



(20)
Where 2
sd
 is the mean of the random variable (RV) 2
2
sd
h . From (16), we can calculate the second
probability of (19)
( )
( )
 
2
2
2 2
1 1
2
02
2
2
2
02
2 2
2
1
1 2 2
02
1 2 1 2
02
2 1 2 02 1 1 02
02
1 2 1
1 2 02 1 1 02
0
02
Pr
Pr
1/
Pr
1/
Pr
Pr
1 exp
rd
sr rd
sr rd rd
rd
sr
h h a
h h a h
a
a
a a
f d f d
a a

 

 


 
 

   

      


  
      
 




 
 
=  =
 
+ +
 
 
 =
 
+ +
 
 
− −  =
 
 
 
+  =
 
 
− −
 
− −
 
  1 1
1 2 02 1 1 02
exp( )
sr d
a a

  
     

 
−
 
 
− −
 

(21)
Where we denote
2
2
2
02
1 2
2 02 1
, ,
sr rd
h h
a a

  
  
= = =
−
, sr
 and 2
rd
 are the mean of RV 2
2
2
,
sr rd
h h , respectively.
By changing a variable 02
1 2 02 1 1 02 1
02
( )
x
x a a
 
      

+
= − −  = , (21) can be rewritten as:
( ) ( )
2
2
02
02
02
02
0
exp
Pr 1
exp exp
sr sr
rd
rd sr x
dx
x
   
 

   
 

−
 = −
   
− −
   
 
 

(22)
Apply eq (3.324,1) of [15], (22) can be reformulated as:
( ) ( )
2
2 2
02
1
Pr 1 2exp
2
rd sr
sr rd sr rd
K
   
     
 
 = − −
 
 
 
 
 
(23)
Where ( )
v
K • is the modified Bessel function of the second kind and vth order. Substituting (20) and (23) into
(19), finally, we can obtain:
( )
 
( )
2 2
2 2
1
1
1 exp
1 2exp 2
D sd
sr rd sr rd
sr
OP
K
 
     
 
 
= − −
 
 
 
 
− −  
 
 
 
 
 
(24)

261
Hence, the outage probability (OP) of the destination D1 can be given by:
( )
( )
( )
( )
1 21 1
21 1
21 1
21 1
1
02 01
02 01
02 01
02 01 1 2
Pr ,
Pr ,
1 Pr ,
1 Pr ,
D sd sd
rd rd
sd sd
rd rd
OP
P P
   
   
   
   
=  
  
 
= −   
 
 
−   = 
 
(25)
Where ( )
21 1
1 02 01
1 Pr ,
sd sd
P    
 
= −  
 
, ( )
21 1
2 02 01
1 Pr ,
rd rd
P    
 
= −  
 
. And 1
2
01 2 1
R
 = − with R1 being the target
rate at the D1 From (10) and (11), P1 can be calculated as:
( )
1
1
1
1 1
1
1 1
2
2
2
1 02 1 01
2
1
2 2
02 01
2 02 1 1
2
02 01
2 02 1 1
2
1 Pr ,
1
1 Pr ,
1 Pr max ,
Pr 1 exp
sd
sd
sd
sd sd
sd
sd sd
h a
P h a
h a
h h
a a a
h
a a a
h

  

 
   
 
   

 
 
 
 
= −  
 
 
+
 
 
 
 
= −  
 
−
 
 
 
 
= − 
 
 
−
 
 
 
 
=   = − − 
 
 
(26)
Where 1
sd
 is the mean of RV 1
2
sd
h and 02 01
2 02 1 1
max ,
a a a
 
   
 
 =  
−
 
. From (17) and (18), P2 can be
calculated as:
( ) ( )
1
1 1
1
1
1 3
1
2
2
2
2 2
2
1
2 2
2
1
02 01
2
3 1
1
3 1
1
3 1
1
1 1 3 3
/
1/
1 Pr
,
1/
/
1 Pr ,
/
Pr ,
/
1 Pr ,
1
1 1
sr rd
sr rd rd
sr rd
rd
h h a
h h a h
P
h h a
h
A
A
A
B
B
B
f d f d
 



 

 


 


 


 

   
 


−
 
 
 
+ +
 
= −  
 
  
 
+
 
 
= −  
 
−
 
 
  
 
−
 
 

= −   
 
−
 
= −
= −
 
( )
( )
( )
3 1
1
1 1
1
1 1
1
/
/
1 exp exp
rd
sr sr
F f d
d
 

 

 
   





 
 

−
 
 
−
 
 
 

 
= − − −
 
−
 
 


(27)

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262
Where
( )
1
2
2
1 3
02 01
2 02 1 1
, ,
, , max ,
sr rd
h h
A B A B
a a a
 
 
   
= =
= =  =
−
. And 1
,
sr rd
  are the mean of RV
2
sr
h , 1
2
rd
h ,
respectively changing variable 1
y 
= −, (27) can be rewritten as:
( )
( )
1
1
2
0
0
1 exp exp
1 exp exp
rd
sr sr
rd
sr sr sr
P y dy
y
y dy
y

 


  




 
= − − − +
 
   
 

 
= − −  − −
 
 


(28)
Apply equation (3.324,1)of [table of integral], (22) can be reformulated as:
( ) 1 1
2 1
1 2exp 2
sr rd sr rd
sr
P K
   

 
 
 
 
= − −   
 
 
(29)
where ( )
v
K • is the modified Bessel function of the second kind and vth order. Substituting (26) and (29)
into (25), finally, the outage probability of D1 can be claimed as:
( )
( )
1 1
1 1
1
1
1 exp
1 2exp 2
D sd
sr rd sr rd
sr
OP
K

   

 
 
= − − 
 
 
 
 
 
 
− −   
 
 
 
 
(30)
4. NUMERICAL RESULTS AND DISCUSSION
In this section, we investigate the OP of the model system using Monte Carlo simulation in
connection with the primary system parameters [16-26]. In Figure 3, the effect of a2 on the system OP
is plotted with the primary system parameters as η=0.8, R1=R2=0.25, 0.5 bps/Hz, α=0.5. From the results,
we can see that the OP of the destination D1 significantly decreases with the rising of a2. However, the OP
of the D2 decreases when a2 increases from 0.55 to 0.7 and after that has a massive increase with
the remaining values of a2. In the same way, the system OP versus α is drawn in Figure 4. In this simulation,
we set η=0.8, R1=R2=0.5 bps/Hz, PS/N0=0.5, and a2=0.7, 0.9. As shown in Figure 4, we can state that the OP
of the model system has a slight decrease when α varies from 0 to 1. In both Figures 3 and 4, the simulation
and analyticalresults are the same with all values of α and a2.
Figure 3. OP versus a2 Figure 4. OP versus α

263
Furthermore, we investigate the effect of η and ψ on the OP of the model system as plotted in
Figures 5 and 6. In these Figures, we set the primary parameters as a2=0.7, 0.9, R1=R2=0.5 bps/Hz,
PS/N0=0.5. From Figures 5 and 6, it can be observed that the system OP has a slight decrease when η varies
from 0 to 1 and the system OP crucially decreases with the rising of ψ from 0 to 25. In all two Figures,
the analytical and simulation results agree well with each other. On another hand, the comparison
of the system OP of two destination nodes is demonstrated in all Figures. From the results, we can state that
the system OP of the destination node D2 is better than the destination node D1.
Figure 5. OP versus η Figure 6. OP versus ψ
5. CONCLUSION
In this research, we propose EH NOMA network system over the Rayleigh fading channel using
selection combining at the receiver. The closed-form expression of the OP of the model system by Monte
Carlo simulation is derived. Moreover, the comparison of the OP of two destination users is investigated in
connection with the primary system parameters. From the results, we can see that all the analytical
and simulation results are the same with the primary system parameters using Monte Carlo simulation.
These results can be provided a novel recommendation for improving the performance of the EH NOMA
communication network system.
ACKNOWLEDGEMENTS
This research was supported by National Key Laboratory of Digital Control and System
Engineering (DCSELAB), HCMUT, VNU-HCM, Vietnam.
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