ISSN 2315 4462 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[.]
Trang 1Fixed 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: dodinhthuan@iuh.edu.vn, tutrinhamber@gmail.com
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 h CN(0,1),g1 CN(0,1),g2 CN(0,1), 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
Trang 2classified 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
y h a Px a Px w (1)
where x x1, 2 are the normalized signal for D1, D2,
respectively It is assumed that 2 2
E x E x ,
1, 2
a a are power allocation factors To stipulate better
fairness between the users, we assume that a1a2
satisfying a1a21
Using AF scheme, the amplify gain is defined by
1
P h
(2)
In the second phase, the received signal at user D1 is
y Pg h a Px a Px w w (3)
where w w r, d are additive white Gaussian noise terms
with mean power 2 Similarly, the received signal at
user D2 is given by
y 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 x1 is given by
2
In which, we denote P2 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 x1 is given by
2
x
Then the received SINR at D2 to detect its own
information is given by
2
x
(7)
In case of imperfect SIC, we have
2
ipsic x
(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 i,i1, 2 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 2 1 2 2
A Outage Probability of D1
We first consider the outage probability for detecting
1
x at D1 can be expressed as
1 D x1, 1 Pr 1 1
OP OP (9)
Here, we denote Pr as probability function We first calculate each component of outage event as below
2
Pr
1
D x
a h g OP
(10)
2
h a a , we have OP D x1, 11, else
112 1
2 1
1
1 2
Pr
1
D x
a a
h
z
z dz
(11)
©2019 Journal of Communications 561
Trang 3Putting new variable as
Based on (11) we can find that:
1
1 2 1
1
1, 1
1 2 1
0
1
1 1
exp
D x
a a
z
z a a
a a
dt
(12)
It can be further manipulated as below
1
1, 1
2
0
2 1
exp
D x
OP
dt
(13)
Final step, it can be expressed the outage event as
below
2
1 exp
D x
OP
a a
B .Outage Probability of D2
1) Perfect SIC
Secondly, the outage probability for detecting x2 at D2
can be expressed as
2, 1 1 2, 2 2
Pr
(15)
Substituting (6) and (7) into (15), we have
2, 2 1 Pr 1, 2
D x
OP J J (16)
where
2 2
2
2
,
J
and
2 2
2 2
2 2 1
J
Exact analysis is
2
2 2 2
1
2
2 1
1
2 2
2
2
2 2
1 2
1
1,
1 Pr
1
1 Pr
1
D x
a h g OP
a h g
a
a
g
2
2 2
1
h
2
2 2 2
1
2
2 1
1
2 2
2
2
2 2
1 2
1
1,
1 Pr
1
1 Pr
1
D x
a h g OP
a h g
a
a
g
2
1
h
2 1
1
2 2
2
2
2 2
1
1,
1 Pr
1
1 Pr
1
a
a
g
2
2 2
1
1 Pr
1
h g
h
2
min a a,a
In the case of h2 1 0, it leads to following inequality h2 1 , the outage probability in this case can be calculated as OP D2, 2x 1
In the case of h2 1 0, the outage probability is given by
2, 2
1
0
0
1
1
4
D x
z
z
t
dt t
t dt t
(18) Similarly steps to achieve (11), it can be found outage probability in such as
D x OP
(19)
2) Imperfect SIC
2, 1 1 2, 2 2
Pr
ipsic
In this paper, we approximate the
2 2
2
2
1
x
a a
SNR regime when 2 1
1
2
2
2
2
2
1 Pr
1
ipsic
D x
a OP
a
©2019 Journal of Communications 562
Trang 42
2
2
2
2
1 Pr
Pr
1
ipsic
D x
a OP
a
(21)
Firstly, we consider the first item, if a a1 21we
obtain OP D ipsic2, 2x 1 , else a a1 21 we have
2 2
2
2
2 2 2
2 2
0
1 Pr
1 1
1 Pr
1
ipsic
D x
a
a h g OP
g
a h
t z
a z
(22)
In the first case of a2 h220 , it leads to
following equation h2 2 a2 , outage probability in
this case calculated as ipsic2, 2 1
D x
In the second case, as a2h220
2 2
1
2 2
2, 2
0
2
1
2
ipsic
D x
a
x z
a z
(23)
where
1 0
2
2
b
a b
a
y
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
2 exp
D x
OP
(25)
At high SNR, the outage probability at D2 will become
2
2, 2
2
2 exp
D x
OP
a
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
2
asym
OP R
R
(27)
The throughput at D2 will become
2
2
1 2
asym
OP R
R a
(28)
2 2
a a
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 a10.9,a20.1
Fig 2 Outage probability vs the transmit SNR Fig 2 plots the outage probability of considered scheme versus SNR for a simulation setting R11 bits/s/Hz, R2 1 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 R R1, 2 1, 2 bits/s/Hz,
R R1, 2 0.5,1.5bits/s/Hz for target rates Obviously
©2019 Journal of Communications 563
Trang 5in 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 R11 bits/s/Hz,R2 1bits/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 R10.5
bits/s/Hz, R2 2 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
2
2
2 2
1 exp
1
4 2
a
t
x
x a a
The intergal expression in (23) becomes
2
0
2
2 2
2
a a
©2019 Journal of Communications 564
Trang 6Now consider a following integration form
1 0
1 0
b
(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
2
2
a
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
REFERENCES
[1] Y Saito, et al., “Non-orthogonal multiple access (NOMA)
for cellular future radio access,” in Proc IEEE Veh Tech
Conf, Dresden, Germany, Jun 2013, pp 1-5
[2] S M R Islam, N Avazov, O A Dobre, et al,
“Power-domain non-orthogonal multiple access (NOMA) in 5G
systems: potentials and challenges,” IEEE
Communications Surveys Tutorials, no 99, p 1, Oct 2016
[3] D T Do and C B Le, “Application of NOMA in wireless
system with wireless power transfer scheme: Outage and
ergodic capacity performance analysis,” Sensors, vol 18,
no 10, 2018
[4] K T Nguyen, D T Do, X X Nguyen, N T Nguyen, and
D H Ha, “Wireless information and power transfer for full
duplex relaying networks: Performance analysis,” in Proc
Recent Advances in Electrical Engineering and Related
Sciences, HCMC, Vietnam, 2015, pp 53-62
[5] X X Nguyen and D T Do, “Maximum harvested energy
policy in full-duplex relaying networks with SWIPT,”
International Journal of Communication Systems (Wiley),
vol 30, no 17, 2017
[6] D T Do, H S Nguyen, M Voznak, and T S Nguyen,
“Wireless powered relaying networks under imperfect
channel state information: System performance and
optimal policy for instantaneous rate,” Radioengineering,
vol 26, no 3, pp 869-877, 2017
[7] X X Nguyen, D T Do, “Optimal power allocation and
throughput performance of full-duplex DF relaying
networks with wireless power transfer-aware channel,”
EURASIP Journal on Wireless Communications and
Networking, p 152, 2017
[8] D T Do, “Power switching protocol for two-way relaying
network under hardware impairments,” Radioengineering,
vol 24, no 3, 765-771, 2015
[9] Z Ding, P Fan, and H V Poor, “Impact of user pairing on
5G non-orthogonal multiple-access downlink
transmissions,” IEEE Trans Veh Technol., vol 65, no 8,
pp 6010–6023, Aug 2016
[10] S Shi, L Yang, and H Zhu, “Outage balancing in downlink nonorthogonal multiple access with statistical
channel state information,” IEEE Trans Wireless Commun., vol 15, no 7, pp 4718–4731, Jul 2016
[11] P Xu, Y Yuan, Z Ding, X Dai, and R Schober, “On the outage performance of non-orthogonal multiple access
with 1-bit feedback,” IEEE Trans Wireless Commun., vol
15, no 10, pp 6716–6730, Oct 2016
[12] P D Diamantoulakis, K N Pappi, Z Ding, and G K Karagiannidis, “Wireless-powered communications with
non-orthogonal multiple access,” IEEE Trans Wireless Commun., vol 15, no 12, pp 8422–8436, 2016
[13] M Ashraf, A Shahid, J W Jang, and K G Lee, “Energy harvesting non-orthogonal multiple access system with
multi-antenna relay and base station,” IEEE Access, vol 5,
2017
[14] Y Xu, C Shen, Z Ding, X Sun, S Yan, G Zhu, and Z Zhong, “Joint beamforming and power-splitting control in
downlink cooperative SWIPT NOMA systems,” IEEE Trans Signal Process., vol 65, no 18, pp 4874–4886,
2017
[15] A P Prudnikov, Y A Brychkov, and O I Marichev,
Integrals and Series, New York, NY, USA: Gordon and
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
©2019 Journal of Communications 565