Fixed Power Allocation for Outage Performance Analysis on ...

Fixed Power Allocation for Outage Performance Analysis

on AF-assisted Cooperative NOMA

Dinh-Thuan Do and Tu-Trinh T. Nguyen Faculty of Electronics Technology, Industrial University of Ho Chi Minh City, Vietnam

Email: [email protected], [email protected]

Abstract—In this paper, new radio access scheme that

combining relaying protocol and Non-orthogonal Multiple

access (NOMA) system is introduced. In particular, different

scenarios for fixed power allocation scheme are investigated. In

addition, the outage probability of both weak and strong user is

derived and provided in closed-form expressions. Such outage

is studied in high SNR scenario and comparison performance

between these NOMA scenarios is presented. Numerical

simulations are offered to clarify the outage performance of the

considered scheme if varying several parameters in the existing

schemes, and to verify the derived formula. Index Terms—Cooperative non-orthogonal multiple access,

outage probability, AF

I. INTRODUCTION

As one favorable technology in future fifth-generation

(5G) wireless networks, non-orthogonal multiple access

(NOMA) has been proposed to increase spectral

efficiency [1]. By permitting multiple users served in the

same time, frequency or code domain, spectral efficiency

and user fairness are improved in NOMA compared with

Orthogonal Multiple Access (OMA). In NOMA, the

transmitter superposes multiple users’ messages and the

receivers deploys successive interference cancellation

(SIC) to distinct the mixture signals in the power domain

[2]. In [3], the system performance regarding outage

probability (OP) and ergodic capacity were studied in

typical dual-hop NOMA transmission.

The fixed relaying and adaptive relaying schemes have

been suggested to implement cooperative communication.

The full-duplex and relaying network are investigated in

[4], [5]. Recently, in relaying networks, two well- known

cooperative relaying protocols are studied, namely

Amplify Forward (AF) and decode forward (DF) [6, 7].

By AF protocols, received signal from the source is

amplified to forward to the destination, while the received

signal in DF protocols need be first decoded, then re-

encoded to forward to the destination. The author in [8]

presented hardware impairment as important impact on

system performance of such relaying scheme.

The relaying scheme as consideration can be deployed

together with NOMA. Formerly, superposition coding is

proposed in wireless network and currently it is named as

NOMA. Such scheme improves the throughput of a

broadcast/multicast system and efficient broadcasting is

Manuscript received November 12, 2018; revised June 3, 2019.

doi:10.12720/jcm.14.7.560-565

achieved. Additionally, the influence of user coupling on

the performance in NOMA is investigated [9], in which

both the fixed power distribution assisted NOMA (F-

NOMA) and cognitive radio assisted NOMA (CR-

NOMA) systems were considered in term of the outage

performance. Furthermore, the outage balancing among

users was investigated by deploying user grouping and

decoding order selection [10]. In particular, the optimal

decoding order and power distribution in closed-form

formula for downlink NOMA were performed. In [11],

only feed back one bit of its channel state information

(CSI) to a base station (BS) is considered in term of

outage behavior of each NOMA user in downlink NOMA.

As advantage of such model as providing higher fairness

for multiple users, it lead to NOMA with better

performance as comparison with conventional

opportunistic one-bit feedback. In order to increase the

specific data rate, the wireless powered communication

networks (WPCN) scheme is deployed with NOMA

uplink system in [12]. By using the harvested energy in

the first time slot, the strong users in NOMA can be

forward signal to the weak users’ messages in the second

time slot in case of using half-duplex (HD) scheme [13].

The maximising the data rate in the strong user with

guaranteeing the QoS of the weak user is considered as in

[14] to solve tackle of SWIPT NOMA system related to

half-duplex case.

Motivated by above analysis in [9], this paper presents

a fixed power allocation scheme to show outage

performance of separated users in the NOMA scheme in

case of deployment of AF scheme.

II. SYSTEM MODEL

We consider a downlink cooperative NOMA scenario

consisting of one base station denoted as BS, one relay R

and two users (i.e., the nearby user D2 and distant user

D1). The Amplify-and –Forward (AF) protocol is

employed at each relay and only one relay is selected to

assist BS conveying the information to the NOMA users

in each time slot. All wireless channels in the scenario

considered are assumed to be independent non-selective

block Rayleigh fading and are disturbed by additive white

Gaussian noise with mean power 2 . The wireless

channel 1 2(0,1), (0,1), (0,1),h CN g CN g CN denote

the complex channel coefficient of BS-R, R-D1, R-D2,

respectively. In principle of NOMA, two users are

©2019 Journal of Communications 560

Journal of Communications Vol. 14, No. 7, July 2019

classified into the nearby user and distant user by their

quality of service (QoS) not sorted by their channel

conditions. In this case, we assume transmit power at

relay and the BS is the same.

R

BS

D1

D2

Cell-center

Cell-edge

Fig. 1. System model of AF-NOMA

Based on the aforementioned assumptions, the

observation at the relay R is given by

1 1 2 2R ry h a Px a Px w (1)

where 1 2,x x are the normalized signal for D1, D2,

respectively. It is assumed that 2 2

1 2 1E x E x ,

1 2,a a are power allocation factors. To stipulate better

fairness between the users, we assume that 1 2a a

satisfying 1 2 1a a .

Using AF scheme, the amplify gain is defined by

2 2

1

P h

(2)

In the second phase, the received signal at user D1 is

1 1 1 1 2 2D r dy Pg h a Px a Px w w

(3)

where ,r dw w are additive white Gaussian noise terms

with mean power 2 . Similarly, the received signal at

user D2 is given by

2 2 1 1 2 2 2D r dy Pg a Px a Px h Pg w w (4)

To evaluate system performance, we first consider the

received signal to interference plus noise ratio (SINR) at

D1 to detect 1x is given by

2 22

1 1

1 2 2 2 22

2 1 1 1

a h g

a h g h g

(5)

In which, we denote 2P as signal to noise ratio

(SNR) at the BS.

By considering in SIC is also invoked by D2 and the

received SINR at D2 to detect 1x is given by

2 22

1 2

2, 1 2 2 2 22

2 2 2 1x

a h g

a h g h g

(6)

Then the received SINR at D2 to detect its own

information is given by

2 22

2 2

2, 2 2 2

2 1x

a h g

h g

(7)

In case of imperfect SIC, we have

2 22

2 2

2, 2 2 2 22

2 1

ipsic

x

a h g

f h g

(8)

Remark 1: With regard to optimize of power

allocation can be studied to obtain better performance as

further work considered in our next papers. However,

such computation of power allocation needs more

complexity in signal processing as overhead information

of power allocation must be known to control power

associated with each users.

III. OUTAGE PERFORMANCE ANALYSIS

In this section, we performs analysis on the

performance of AF-NOMA scheme in terms of outage

probability for several signal processing cases. To make

its convenient in analysis, this paper presents exact

expressions for the outage probability. In order to reduce

the computation complexity, a tight lower bound for the

outage probability is provided in the high-SNR regime to

better understand the behavior of the network.

In general, an outage event occurs at the strong or the

weak user when the user fails to decode its own signal. In

this section, we denote the threshold SNR as , 1,2i i .

Based on the rate requirements of the users, we can

choose different target rate values for R1 and R2, and we

will demonstrate how the R1 and R2 affect the outage

performance in the numerical result section. For sake of

brevity, we denote 1 22 2

1 22 1, 2 1R R .

A. Outage Probability of D1

We first consider the outage probability for detecting

1x at D1 can be expressed as

1 1, 1 1 1PrD xOP OP (9)

Here, we denote Pr . as probability function. We

first calculate each component of outage event as below

2 22

1 1

1, 1 12 2 2 22

1 2 1

Pr1

D x

a h gOP

h g a h g

(10)

In the event of 2

1 2 1 1 0h a a , i.e.

2

1 1 2 1h a a , we have 1, 1 1D xOP , else

1

1 2 1

2

1

1, 1 1 2

1 2 1 1

1

1 2 1 1

12

Pr

11 exp

D x

a a

hOP g

h a a

zz dz

z a a

(11)



Putting new variable as

1

1 2 1 1

1 2 1

tt

z a a za a

Based on (11) we can find that:

1

1 2 1

1

1, 1

1 2 1 1

1 2 1

1 1 1 1

1 2 1 1 2 10

11 exp

11

exp

D x

a a

zOP z dz

z a a

a a

t tdt

t a a t a a

(12)

It can be further manipulated as below

1

1, 1

1 2 1 1 2 1

2

1 1 1 2 1

1 2 1 1 2 10

211 exp

exp

D xOPa a a a

a a tdt

t a a a a

(13)

Final step, it can be expressed the outage event as

below

1

1, 1 1 1 1

1 2 1

21 expD xOP

a a

(14)

where

1 1 1 2 1

1 22

1 2 1

2a a

a a

B. .Outage Probability of D2

1) Perfect SIC

Secondly, the outage probability for detecting x2 at D2

can be expressed as

2 2, 2 2, 1 1 2, 2 2

2, 1 1 2, 2 2

Pr

1 Pr ,

D x x x

x x

OP OP or

(15)

Substituting (6) and (7) into (15), we have

2, 2 1 21 Pr ,D xOP J J (16)

where

22

1 2

1 12 22

2 2

2

,2 2

1

a h gJ

h g a h g

and

22

2 2

2 22

2

2

21

a h gJ

h g

.

Exact analysis is

2 22

2 2

2, 2 22 2

2

22

1 2

12 22

2 2

2 2 2 221

2 2 2

1

2 2 2 222

2 2

2

2 2 221 2

2 2

1 2

2

2

1 Pr ,1

2

2 21

1,

1 Pr

1

min ,1 Pr

1

D x

a h gOP

h g

a h g

h g a h g

aa h g h g

ah g h g

a aa h g h

g

2 2 2 22

2 2

2

2

2 2

1 Pr 1

11 Pr

1

h g h g

hg

h

2 22

2 2

2, 2 22 2

2

22

1 2

12 22

2 2

2 2 2 221

2 2 2

1

2 2 2 222

2 2

2

2 2 221 2

2 2

1 2

2

2

1 Pr ,1

2

2 21

1,

1 Pr

1

min ,1 Pr

1

D x

a h gOP

h g

a h g

h g a h g

aa h g h g

ah g h g

a aa h g h

g

2 2 2 22

2 2

2

2

2 2

1 Pr 1

11 Pr

1

h g h g

hg

h

12 22

2 2

2 2 2 221

2 2 2

1

2 2 2 222

2 2

2

2 2 221 2

2 2

1 2

2

2

2 21

1,

1 Pr

1

min ,1 Pr

1

h g a h g

aa h g h g

ah g h g

a aa h g h

g

2 2 2 22

2 2

2

2

2 2

1 Pr 1

11 Pr

1

h g h g

hg

h

(17)

where 1 2

2

1 2

min ,a a

a

.

In the case of 2

1 0h , it leads to following

inequality 2

1h , the outage probability in this case

can be calculated as 2, 2 1D xOP .

In the case of 2

1 0h , the outage probability is

given by

2, 2

1

0

0

11 exp

1

1 1 1 1 11 exp 1

1 2 4 11 exp exp 1 .

4

D x

zOP z dz

z

tdt

t

tdt

t

(18)

Similarly steps to achieve (11), it can be found outage

probability in such as

2, 2 2

1 2

2 1 11 2exp 1

1 12 1

D xOP

(19)

2) Imperfect SIC

2, 2 2, 1 1 2, 2 2

2, 1 1 2, 2 2

Pr

1 Pr ,

ipsic ipsic

D x x x

ipsic

x x

OP or

(20)

In this paper, we approximate the

22

1 2

2, 1 1 22 22

2 2

2

2 21

x

a h ga a

h g a h g

in high

SNR regime when 2 1 .

1

2, 2 1

2

2 22

2 2

22 2 22

2

1 Pr

Pr .1

ipsic

D x

aOP

a

a h g

f h g



1

2, 2 1

2

2 22

2 2

22 2 22

2

1 Pr

Pr1

ipsic

D x

aOP

a

a h g

f h g

(21)

Firstly, we consider the first item, if 1 2 1a a we

obtain 2, 2 1ipsic

D xOP , else 1 2 1a a we have

2

2

2 22

2 2

2, 2 22 2 22

2

2 22

22

2 2

2 2

2

2

2 20

1 Pr1

11 Pr

11 exp exp .

ipsic

D x

a

a h gOP

f h g

f hg

a h

t zt z dzdt

a z

(22)

In the first case of 2

2 2 0a h , it leads to

following equation 2

2 2h a , outage probability in

this case calculated as 2, 2 1ipsic

D xOP .

In the second case, as 2

2 2 0a h

2

2

1

2

2

2, 2

2 20

2 2 2 2

2

2 2 22

11 exp exp

21 exp , 1

ipsic

D x

a

x zOP x z dz dx

a z

a a aa

(23)

where

1

0

2, 2exp exp 1,

2

2 exp

b

aba b a a

a

yy y dy

a

(24)

Proof: see in Appendix

C. Asymtotic Analysis

And the lower bounds of the outage probability in

(14)and (19) are shown to be tight bounds in the medium-

and high-SNR regimes.

At high SNR, the outage probability at D1 will become

1

1, 1

1 2 1

2expD xOP

a a

(25)

At high SNR, the outage probability at D2 will become

2

2, 2

2

2expD xOP

a

(26)

To further evaluation of system, we consider the

throughput in delay-limited mode. In particular, the

throughput mainly depends on the outage probability.

The throughput at D1 will become

1 1

1

1 1 1

1 2 1

1

2exp ,

asym OP R

Ra a

(27)

where

1 1 1 2 1

1 22

1 2 1

2a a

a a

.

The throughput at D2 will become

2 2

2

2 1 2

2

1

2exp ,

asym OP R

Ra

(28)

where 2 2

2 2

22

2 1aa

.

IV. NUMERICAL RESULTS

In this section, the outage performance of the downlink

AF-NOMA network under Rayleigh fading channel is

evaluated via numerical examples to validate derived

formula. Moreover, the fixed power allocation is applied

in order to further evaluation of such NOMA. Without

loss of generality, we assume the distance in each link of

two-hop relaying NOMA is normalized to unity. In the

following simulations, we set the fixed power allocation

factors for NOMA users as 1 20.9, 0.1a a

Fig. 2. Outage probability vs. the transmit SNR

Fig. 2 plots the outage probability of considered

scheme versus SNR for a simulation setting1 1R

bits/s/Hz, 2 1R bits/s/Hz. It can be seen that the exact

analytical results and simulation results are matched very

well. In particular, it shown that as the system SNR

increases, the outage probability decreases. Another

important observation is that the outage probability for

User D1 of NOMA outperforms for User D2. Note that

the results related to such outage performance resulted

from power allocation for each user in NOMA.

In Fig. 3, the outage probability versus system SNR is

presented in different threshold SNR parameters. In this

case, our parameters are 1 2, 1,2R R bits/s/Hz,

1 2, 0.5,1.5R R bits/s/Hz for target rates. Obviously



in this case, the outage probability curves match exactly

with the Monte Carlo simulation results. One can observe

that adjusting the target rates of NOMA users will affect

the outage behaviors of considered scheme. As the value

of target rates increases, the outage performance will

becomes worse. It is worth noting that the setting of

reasonable threshold SNR or target rate for NOMA users

is prerequisite based on the specific application

requirements of different scenarios.

Fig. 3. Outage probability vs. the transmit SNR with different threshold SNR

Fig. 4 plots system outage probability versus SNR in

high SNR mode. It can be observed that the analytical

results meet with that in high SNR case. In Fig. 4, the

outage performance comparison in high SNR regime, in

which we setup 1 1R bits/s/Hz,

2 1R bits/s/Hz. This

illustration indicates that our derived expressions are tight

result for evaluation in related NOMA networks.

Fig. 4. Outage performance comparison in high SNR regime

Fig. 5 plots system throughput versus SNR in delay-

limited transmission mode. Here, we set 1 0.5R

bits/s/Hz, 2 2R bits/s/Hz. Furthermore, the AF-based

NOMA scheme for D1 outperform D2 in terms of system

throughput. This phenomenon indicates that it is of

significance to consider the impact of power allocation

for such scheme when designing practical cooperative

NOMA systems.

Fig. 5. Throughput performance vs. the transmit SNR

V. CONCLUSIONS

This paper presented a novel downlink cooperative

communication system that combines NOMA with AF

relaying techniques in analytical model for outage

analysis. The proposed scheme in term of outage

performance is considered under impacts of various

parameters in cooperative NOMA systems. Furthermore,

impact of the transmit SNR of the source node in

cooperative relaying NOMA on the throughput is

performed via simulation and acceptable threshold can be

shown to the system evaluation. The superior

performance of the proposed schemes was demonstrated

by the numerical results. As a future work, it will be

interesting to investigate the user fairness problem only

with relative locations of the users as in group. More

importantly, the outage probability of both strong and

weak users in the system is derived and verified by

comparing numerical simulations and analytical

simulation.

APPENDIX (PROOF OF PROPOSITION 1)

In (23), we can express in following formula

2

2

2

2

1

2 2

22 2 2

2 2 2 20

22 2 2

2

2 22

22 2

1 2

22

1exp

2 41exp exp 1

4

22exp 1

2 1 ,

a

x zx z dz

a z

tx dt

a a t a a

xa aa

xaa

(A.1)

The intergal expression in (23) becomes

22 2 2

2

2 220

22 2

1 2

22

22 exp exp 1

2 1

x xa aa

x dxaa



Now consider a following integration form

1

0

1

0

, 2 exp 2

2exp 2 exp

b

a b x ax b ax b dx

b yy y dy

a a

(A.2)

The integral formula in can be obtained by using [15,

vol. 4, eq. (1.1.2.3)] and re-expressed as. The first term in

(23) can be fulfilled by applying [15, vol. 4, eq. (3.16.2.4)]

1

0

4 exp

2 4 4 4exp 1,

4 4 4

2exp 1,

2

a x a x x dx

a a aa

aa a

(A.3)

The second term in (A.2) is difficult for producing

closed-form because of the Bessel function and

exponential function. This is end of proof.

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[15] A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev,

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Breach, 1992.

Dinh-Thuan DO received the B.S.

degree, M.Eng. degree, and Ph.D. degree

from Viet Nam National University

(VNU-HCMC) in 2003, 2007, and 2013

respetively, all in Communications

Engineering. He was a visiting Ph.D.

student with Communications

Engineering Institute, National Tsing

Hua University, Taiwan from 2009 to 2010. Prior to joining Ton

Duc Thang University, he was senior engineer at the VinaPhone

Mobile Network from 2003 to 2009. Dr. Thuan was recipient of

Golden Globe Award from Vietnam Ministry of Science and

Technology in 2015. His research interest includes signal

processing in wireless communications network, cooperative

communications, full-duplex transmission and energy

harvesting. His publications include 25 + SCI/SCIE journals

and 50+ conference papers. He also serves as Associate Editor

of Bulletin of Electrical Engineering and Informatics journal

(SCOPUS).

Tu-Trinh T. Nguyen received the

B.Sc. degree in Electrical-

Electronics Engineering from

Industrial University of Ho Chi

Minh City, Vietnam (2018). She is

working at WICOM lab. Her

research interest includes signal

processing in wireless communications network, NOMA,

relaying networks.



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