User Pairing Schemes for Capacity Maximization in Non-orthogonal Multiple Access Systems

Abstract

This paper addresses the issues related with conventional near–far user pairing in non-orthogonal multiple access. Performance effects of near–far pairing on regions with negligible channel gain differences between users are investigated. These regions occur when pairing is performed between cell center and cell edge users, thus leaving the cell mid users to be either paired with each other or kept unpaired. Pairing these mid users with each other causes successive interference cancelation (SIC) performance degradation resulting in capacity reduction for these users. On the other hand, leaving these mid users unpaired perfectly avoids the SIC issue but makes these users unable to benefit from the capacity gains provided by non-orthogonal multiple access. Therefore, two user pairing strategies have been proposed that can provide capacity gains to almost all the users by accommodating them in pairs, while avoiding or minimizing the mid users pairing problem.A generalized M-users pairing scheme is also proposed. Simulations have been performed to investigate the performance of proposed schemes for both perfect and imperfect SIC receiver scenarios in comparison with conventional pairing where the mid users are kept paired with each other. Simulation results show that proposed schemes achieve high capacity gains,especially when imperfect SIC is considered.

Full text

WIRELESS COMMUNICATIONS AND MOBILE COMPUTING
Wirel. Commun. Mob. Comput.
2016; 16:2884–2894
Published online 15 September 2016 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/wcm.2736
RESEARCH ARTICLE
User pairing schemes for capacity maximization in
non-orthogonal multiple access systems
Muhammad Basit Shahab, Mohammad Irfan, Md Fazlul Kader and Soo Young Shin*
Wireless and Emerging Network System Lab, Kumoh National Institute of Technology, Gumi, South Korea
ABSTRACT
This paper addresses the issues related with conventional near–far user pairing in non-orthogonal multiple access. Per-
formance effects of near–far pairing on regions with negligible channel gain differences between users are investigated.
These regions occur when pairing is performed between cell center and cell edge users, thus leaving the cell mid users to
be either paired with each other or kept unpaired. Pairing these mid users with each other causes successive interference
cancelation (SIC) performance degradation resulting in capacity reduction for these users. On the other hand, leaving these
mid users unpaired perfectly avoids the SIC issue but makes these users unable to benefit from the capacity gains provided
by non-orthogonal multiple access. Therefore, two user pairing strategies have been proposed that can provide capacity
gains to almost all the users by accommodating them in pairs, while avoiding or minimizing the mid users pairing problem.
A generalized M-users pairing scheme is also proposed. Simulations have been performed to investigate the performance
of proposed schemes for both perfect and imperfect SIC receiver scenarios in comparison with conventional pairing where
the mid users are kept paired with each other. Simulation results show that proposed schemes achieve high capacity gains,
especially when imperfect SIC is considered. Copyright © 2016 John Wiley & Sons, Ltd.
KEYWORDS
user pairing; capacity; non-orthogonal multiple access (NOMA); successive interference cancelation (SIC)
*Correspondence
Soo Young Shin, Wireless and Emerging Network System Lab, Kumoh National Institute of Technology, Gumi, South Korea.
E-mail: wdragon@kumoh.ac.kr
1. INTRODUCTION
The upswing and diversity in multimedia applications are
transforming the nature of wireless data traffic by demand-
ing high capacities and data rates. Furthermore, the expe-
ditiously developing Internet of Things is increasing the
volume of connected devices to an incredible extent. These
humongous static and mobile devices will soon surpass
the present number by a large magnitude. To fulfill the
incredibly high user data rates and system capacity require-
ments, future radio access is aiming towards the design and
implementation of 5G [1]. Among the key players in 5G,
non-orthogonal multiple access (NOMA) is being consid-
ered as one of the appealing candidates to achieve manifold
capacity gains because of its high spectral efficiency [2,3].
In NOMA, signals of multiple users are multiplexed in
the power domain, thus being able to use the same fre-
quency band. The multiplexed users are said to be in a
user pair. Impact of user pairing on the achievable sum
rates of NOMA has been carried out in [4]. It is shown
that users with more channel gain differences should be
paired to ensure that NOMA sum rates are not less than
conventional multiple access (MA) schemes. In [5], two
schemes, namely, NOMA with fixed power allocation and
cognitive inspired NOMA, are proposed to increase the
capacity gap between NOMA and MA. A user pairing
scheme based on the power requirements of users is given
in [6]. Proportional fairness based user pairing and power
allocation has been discussed in [7]. The works in [8–10]
also focus on the user fairness issue and power allocation
in NOMA.
Users in a cell are normally divided into three cate-
gories based on the channel quality indicator (CQI) values,
namely, high quality, medium quality, and low quality users
[11–15]. When we pair the high and low quality users with
each other for better capacity gains, users of medium qual-
ity are left unpaired. If these medium quality users are
paired with each other, the small channel gain difference
between these in-pair users causes successive interference
cancelation (SIC) performance degradation that results in
capacity decrease for these users [16–18]. On the other
hand, leaving these mid users unpaired perfectly avoids the
SIC imperfection issue but makes these users unable to
benefit from the capacity gains provided by NOMA. To the
2884 Copyright © 2016 John Wiley & Sons, Ltd.

M. B. Shahab
et al.
User pairing schemes in NOMA
best of our knowledge, user pairing schemes that consider
the mid users pairing problem have not been proposed in
the existing literature.
Moreover, in conventional near–far pairing, the capac-
ity gain achieved by low-gain users is more than that of
the high-gain users. This is because, for each user pair, the
targeted data rate of low-gain user must be satisfied first,
thus utilizing a high portion of power. The remaining less
power is then allocated to the high-gain user. Because of
this, the high-gain user cannot get enough benefit and has
less capacity gain. Therefore, the overall capacity gain of
the system decreases.
Principle contributions of this paper are summarized as
follows:
Firstly, we investigate the performance issues that
arise when conventional near–far user pairing is per-
formed. Region with negligible channel gain differ-
ence between in-pair users has been highlighted, and
the corresponding effects on different performance
metrics have been explored.
Secondly, two schemes for users pairing are proposed
by exploiting the trade-offs incorporated when pairing
is performed. A generalized M-users pairing scheme
is then developed, which divides cell users into multi-
ple groups, followed by one of the proposed schemes
for inter-group user pairing.
We analytically derive the exact ergodic sum capacity
of a two users pair considering the effects of per-
fect and imperfect SIC. The analytical results are later
verified through simulations.
Finally, we compare the achievable capacity of the
proposed techniques with conventional near–far pair-
ing by considering both perfect and imperfect SIC
receivers. Effect of increase in the number of paired
users is also investigated.
Rest of the paper is organized as follows. Section 2
explains the basic NOMA transmission protocol. Section 3
addresses the conventional near–far user pairing concept
and the related issues. Proposed user pairing schemes are
explained in Section 4. Mathematical analysis of the exact
ergodic sum capacity of a two users pair considering per-
fect and imperfect SIC is provided in Section 5. Simulation
results and discussions are carried out in Section 6. Finally,
Section 7 concludes the paper.
2. NON-ORTHOGONAL MULTIPLE
ACCESS
Consider a circular cellular region of radius Rwith the base
station (BS) at the center serving a total of Nusers. Sup-
pose Mrandomly distributed users out of Nare multiplexed
in the power domain. For any mth user at distance dmfrom
the BS, its channel gain is represented by jhmj2,where
hmDgm
p1Cdv
m
, with gmbeing the Rayleigh fading channel
gain and vrepresenting path loss factor [19]. Without loss
of generality, consider the channel gains to be arranged as
jh1j2jh2j2 jhMj2,wherejhMj2represents the cell
center user with highest gain. Let the user power allocation
factor be represented by a, and then, the powers allocated
to these users are in the order a1a2  aM.For
any mth user, the signal transmitted by the BS is pamPsm,
where smis the message signal for the mth user and P
is the total transmit power. So for Musers in a pair, the
cumulative signal sent by the BS is given by (1)
yD
M
X
mD1pamPsm.(1)
The signal received at the mth user can be written as
in (2)
rmDhm
M
X
mD1pamPsmCm,(2)
where mCN.0, 2/represents the complex additive
white Gaussian noise with mean zero and variance 2of
the mth user. Because users sharing the same band will
receive the signals of other users along with their own sig-
nals, interference becomes a problem. Thus, for all m>i,
the mth user will have to detect and remove the data of all
ith users using SIC. On the other hand, each ith user will
treat the signals of all mth users as noise. The total achiev-
able data rate of Mpaired users can be calculated using
(3)
Rpair D
M1
X
mD1
log2 1Camjhmj2
jhmj2PM
jDmC1ajC1
!
Clog21CaMjhMj2,
(3)
where represents the transmit signal to noise ratio (SNR)
per pair. For a cellular region with Nusers divided into
Luser pairs having Musers per pair, the total achievable
system capacity is given by (4)
RD
L
X
lD1
M1
X
mD1
log2 1Camjhmj2
jhmj2PM
jDmC1ajC1
l!
Clog21CaMjhMj2l,
(4)
where lis the transmit SNR between Musers of the lth
user pair. It is evident from (4) that the overall capacity
of downlink NOMA depends majorly on the channel gains
of users per pair and their allocated transmit powers. User
pairing in NOMA is explained in the next section.
3. USER PAIRING IN NOMA
To analyze conventional near–far pairing in NOMA, we
will restrict our discussion to the simplest case of two
users per pair. To maintain maximum channel gain dif-
ference between in-pair users, it is preferred to combine
users from the cell center (high CQI) and cell edge (low
Wirel. Commun. Mob. Comput.
2016; 16:2884–2894 © 2016 John Wiley & Sons, Ltd. 2885
DOI: 10.1002/wcm

User pairing schemes in NOMA M. B. Shahab
et al.
Figure 1. Conventional near–far user pairing in non-orthogonal
multiple access.
CQI) into pairs. The cell mid users (medium CQI) thus left
unpaired also need to be accommodated. If the cell mid
users are paired with each other, the channel gain differ-
ence between these in-pair users is very less. The scenario
has been depicted in Figure 1.
Considering inverse relation between channel gains and
allocated powers, the closeness in allocated powers of these
cell mid in-pair users leads to severe interference. The
probability that sum rates of these pairs are even less than
MA schemes is calculated in [4]. There are two reasons
for the capacity decrease in these cell mid pairs: increased
noise at low-gain users and SIC imperfections at high-
gain users. Both of these issues are due to the closeness in
channel gains and allocated powers [16,17].
Consider two paired users iand jhaving gains jhij2and
jhjj2,wherejhij2<jhjj2. The data rates Riand Rjachiev-
able by these users are given by log21Cjhij2a2
i
jhij2a2
jC1
and
log21Cjhjj2a2
j, respectively. For an orthogonal MA
technique, the supported data rates for iand jdenoted
by N
Riand N
Rjwill be equal to 1
2log21Cjhij2and
1
2log21Cjhjj2, respectively. Let Rtrepresent the tar-
geted capacity gain of NOMA compared with conven-
tional MA. The probability that capacity gain achieved
by NOMA is less than the targeted gain is given by
PRiCRjN
RiN
Rj<Rt. Difference between sum rates
of NOMA and MA RiCRjN
RiN
Rj, assuming very
high SNR, can be asymptotically expressed as (5)
lim
!1log2 1
a2
j!Clog2jhjj2a2
jlog2jhijjhjj,
Dlog2jhjjlog2jhij.
(5)
The probability P RiCRjN
RiN
Rj<Rtcan be
expressed as in (6)
Plog2jhjjlog2jhij<Rt!P jhjj2
jhij2<22Rt!.(6)
It is clear from (6) that NOMA can achieve its targeted data
rates if the ratio between channel gains of high-gain and
low-gain users is above a threshold. The probabilities that
individual capacities of in-pair users will be greater than
conventional MA are calculated in [4]. For users iand j,the
probabilities that their individual data rates will be higher
than conventional MA are shown in (7) and (8).
PRi>N
RiDP jhij2<12a2
j
a4
j!,(7)
PRj>N
RjDP jhjj2>12a2
j
a4
j!.(8)
These probabilities impose upper and lower bounds on
the channel gains of low-gain and high-gain users in a pair,
respectively. These probabilities will be high if the channel
gain difference between in-pair users is kept more than a
threshold. Therefore, if the cell mid users are paired with
each other, their individual and cumulative data rates can
be even less than MA.
Secondly, if cell mid users are still paired, their gain
difference can become negligible because of little mobil-
ity. This causes in-pair users interference to be very high,
requiring them to be un-paired and then re-paired with
some other users. This leads to continuous un-pairing and
re-pairing, thus increasing the computational complexity,
signaling overhead, and time delays at the transmitter.
Furthermore, when near–far users are paired, the power
allocated to low-gain user is very high compared with high-
gain user. Consider three users i,j,k, such that jhij2<
jhjj2<jhkj2. For the low-gain user i, capacity comparison
of user pairs .i,j/and .i,k/is given by (9)
log2 1Cjhij2aijk
jhij2akC1!>log2 1Cjhij2aijj
jhij2ajC1!,
(9)
given that aijk>aijjand ak<aj,whereaijkand aijjare
power factors allocated to the ith user when paired with
users kand j, respectively. According to (9), capacity of
low-gain user increases when paired with a more high-gain
user. On the other hand, for the high-gain user k, its capac-
ity gain decreases when paired with a more low-gain user
because of getting low power. This is shown in (10)
log21Cjhkj2akjj>log21Cjhkj2akji, (10)
given that akjj>akji.
It is clear from (9) that low-gain users want to get paired
with high-gain users. But from (10), it is evident that the
reverse is not true. So, a trade-off needs to be required for
pairing the users. It can be verified using (9) and (10) that
the overall effect of such a pairing will be a decrease in the
capacity gain of the pair. This is because when the power
of high-gain user is decreased by a proportion, its capacity
decreases by some factor. Contrary to this, when the power
of low gain is increased by the same proportion, its capacity
gain will be less than the capacity loss of high-gain user.
2886
Wirel. Commun. Mob. Comput.
2016; 16:2884–2894 © 2016 John Wiley & Sons, Ltd.
DOI: 10.1002/wcm

M. B. Shahab
et al.
User pairing schemes in NOMA
Although near–far pairing successfully achieves some
capacity gains for the cell edge users, but the issues that
arise for the middle and high-gain users are a big area
of concern. Following section explains the proposed user
pairing schemes.
4. PROPOSED PAIRING SCHEMES
Considering the highlighted points in Section 3, it is
evident that a user pairing scheme should embed two
considerations during pairing.
Overall sum of in-pair users channel gain differences
for all the pairs should be maximized.
The channel gain difference between any two in-pair
users should be greater than a threshold.
These two conditions are summarized as in (11)
max
8l,i,j
L
X
lD1jjhl,ij2jhl,jj2j,
subject to jjhl,ij2jhl,jj2j.
(11)
where jhl,ij2and jhl,jj2are gains of two users in the lth
pair and represents the minimum allowed channel gain
difference between any two in-pair users considering the
probabilities mentioned earlier in (7) and (8).
Any user pairing algorithm must satisfy the condition
mentioned in (11). Now, consider the case of two users
pairing. Let Q
hrepresent the median of channel gains of all
the users to be paired. Then, if pairing is performed in a
way that each pair contains one user with gain less than the
median and other user having gain greater than the median,
then the overall sum of in-pair users gain differences is
constant as expressed in (12)
L
X
lD1jhl,jj2jhl,ij2DK, (12)
where jhl,jj2>Q
hand jhl,ij2<Q
h. Considering the issues
related with conventional near–far pairing and condition
mentioned in (11) in the light of (12), two methodologies
for user pairing have been proposed.
4.1. Uniform channel gain difference
pairing
Uniform channel gain difference (UCGD) pairing focuses
on accommodating the cell mid users by maintain-
ing a relatively UCGD between in-pair users of all
pairs. Consider two users per pair case. Channel gains
of users present in the cell are divided into two
groups, followed by inter-group paring in such a way
that cell mid users are well accommodated. Con-
sider Nusers in a cellular area with sorted channel
gains jh1j2,jh2j2,ˇˇˇhN
2ˇˇˇ
2,ˇˇˇhN
2C1ˇˇˇ
2,ˇˇˇhN
2C2ˇˇˇ
2,,jhNj2.
Users channel gains are sorted such that jh1j2h2j2
jhNj2. Groups are made as shown in (13) and (14)
G1Dnjhij2:jhij2<Q
ho, (13)
G2Dnjhij2:jhij2>Q
ho. (14)
User gains jh1j2,jh2j2,ˇˇˇhN
2ˇˇˇ
2in group 1 are below
the median Q
h, while gains ˇˇˇhN
2C1ˇˇˇ
2,ˇˇˇhN
2C2ˇˇˇ
2,jhNj2in
group 2 are above it. Median is considered as a center point
because it equally divides users into two groups. Consider-
ing uniformly distributed even number of users in a cell, Q
h
will be an average of gains ˇˇˇhN
2ˇˇˇ
2and ˇˇˇhN
2C1ˇˇˇ
2as in (15)
Q
hDˇˇˇhN
2ˇˇˇ
2CˇˇˇhN
2C1ˇˇˇ
2
2. (15)
Two users (one from each group) can be paired if (16) is
satisfied.
jjhjj2jhij2j> 8i2G1,j2G2. (16)
For a user ifrom any group, the set Gjjiof users jfrom the
other group out of which any user can be paired with iis
given by (17)
GjjiDnjj.jjhjj2jhij2j>/
o. (17)
Consider the groups G1and G2defined above for two users
pairing. In the proposed UCGD pairing, for any user i2
G1, it is paired with a user j2G2using (18)
PairlD˚i,jji2G1,jDmin Gjji,81lL(18)
Conversely, for any user i2G2, it is paired with user j2
G1using (19)
PairlD˚i,jji2G2,jDmax Gjji,81lL(19)
It is obvious from (18) and (19) that UCGD pairing does
not focus on pairing the cell center and cell edge users with
each other. The technique actually finds users from the cell
mid that can be paired with either the cell center or cell
edge users. In this way, the proposed technique accommo-
dates these mid users by efficiently pairing them with cell
center and cell edge users, thereby allowing them to avail
high capacity gains provided by NOMA and still avoiding
or minimizing the SIC performance issue.
Consider a simplest case where large number of users
are uniformly distributed in a cell and are divided into two
groups according to (13) and (14). In this case, if there is
one to one correspondence between users from two groups,
Wirel. Commun. Mob. Comput.
2016; 16:2884–2894 © 2016 John Wiley & Sons, Ltd. 2887
DOI: 10.1002/wcm

User pairing schemes in NOMA M. B. Shahab
et al.
Figure 2. Uniform channel gain difference pairing.
the pairing mechanism can be expressed generally as in
(20).
PairlDjhij2,ˇˇˇhN
2Ciˇˇˇ
2,81i,lN
2(20)
This means that the minimum gain user of one group is
paired with minimum of the other group, followed by pair-
ing next minimum users of both groups and so on. This
process is continued until the highest gain users from both
groups are paired. This pairing scenario is summarized in
(20), which depicts the users which will be in each lth
pair. The final pairing results produced by UCGD pairing
scheme as per (20) are shown in (21):
0
B
B
B
@
Pair1
Pair2
.
.
.
PairL
1
C
C
C
AD
0
B
B
B
B
B
B
B
@
jh1j2,ˇˇˇhN
2C1ˇˇˇ
2
jh2j2,ˇˇˇhN
2C2ˇˇˇ
2
.
.
.
ˇˇˇhN
2ˇˇˇ
2,jhNj2
1
C
C
C
C
C
C
C
A
. (21)
From (21), it can be deduced that the average channel
gain difference between in-pair users follows a compara-
bly uniform behavior. Furthermore, when users in a cell
increase, the pairing scheme can more comfortably pair
users because of one to one correspondence between user
groups. After applying UCGD pairing, the scenario pre-
sented in Figure 1 can be expressed in Figure 2. This figure
can give a basic idea of the UCGD pairing scheme for
simple understanding.
Based on the conditions mentioned in (5)–(8), the capac-
ity comparisons in (9) and (10) and Figure 2, capacity
analysis of users from each category can be performed.
The major advantage of UCGD pairing is to accom-
modate cell mid users, causing a considerable capacity
increase for these users. This is because now they are nei-
ther paired with less gain difference users from their own
category nor left alone for using data with MA. Pairing mid
users with other category users reduces the interference at
the cell mid. This causes capacity increase in the cell mid,
especially for imperfect SIC receivers.
Low-gain users data rates for UCGD will be slightly
reduced if compared with conventional near–far pairing.
This is because they are now paired with cell mid users
instead of cell center, which require slightly more power
compared with the cell center users. Thus, a slight reduc-
tion in the power allocation for the cell edge users is
observed, reducing their data rates slightly.
Conversely, the data rates of high-gain users are higher
for UCGD as compared with conventional near–far. This is
because now the high-gain users are paired with cell mid
users instead of cell edge users, whose power requirement
is less than the cell edge users. This allows some increase
in the power allocation for high-gain users, thus increasing
their capacities.
4.2. Hybrid pairing
Hybrid user pairing scheme follows conventional near–far
pairing for the extreme end users with high channel gain
differences, but when the channel gain difference between
users start to decrease, it switches to the UCGD pairing.
This scheme continues to achieve the same data rates for
extreme low-gain and high-gain users as in conventional
pairing while still being able to minimize the mid users
issue by making some trade-offs.
Consider the sorted user channel gains jh1j2,jh2j2,
jhkj2ˇˇˇhN
2ˇˇˇ
2,ˇˇˇhN
2C1ˇˇˇ
2,ˇˇˇhN
2C2ˇˇˇ
2ˇˇˇhN
2Ckˇˇˇ
2,jhNj2,
where kindicates the point from where the pairing
schemes are switched. Users with channel gains less and
more than jhkj2and ˇˇˇhN
2Ckˇˇˇ
2respectively are paired using
conventional near–far pairing, while the rest using UCGD
pairing. Two users groups made according to (13) and (14)
are shown below in (22) and (23)
G1Djh1j2,jh2j2jhkj2,jhkC1j2ˇˇˇhN
2ˇˇˇ
2, (22)
G2DˇˇˇhN
2C1ˇˇˇ
2,ˇˇˇhN
2C2ˇˇˇ
2ˇˇˇhN
2Ckˇˇˇ
2jhNj2. (23)
For a user ifrom any group, the set of users jfrom the
other group that can be paired with iis same as defined in
(17). Considering the two groups G1andG2fortwousers
pairing, any user i2G1 can be paired with user j2G2
according to (24)
PairlDi,jjjDmax Gjji,81i<k
i,jjjDmin Gjji,8kiN
2
(24)
Conversely, for any user i2G2, it is paired with user j2
G1using (25)
PairlDi,jjjDmax Gjji,8N
2<i<N
2Ck
i,jjjDmin Gjji,8N
2CkiN(25)
Consider the case where large number of users are uni-
formly distributed in a cell and are divided into two groups
as defined in (22) and (23). In this case, for sorted users in
2888
Wirel. Commun. Mob. Comput.
2016; 16:2884–2894 © 2016 John Wiley & Sons, Ltd.
DOI: 10.1002/wcm

M. B. Shahab
et al.
User pairing schemes in NOMA
Figure 3. Hybrid pairing.
each group, the pairing scheme can be expressed generally
as in (26)
PairlD(jhij2,jhNC1ij2,81i,l<k
jhij2,ˇˇˇhN
2CikC1ˇˇˇ
2,8ki,lN
2
(26)
Pairing results of hybrid scheme are shown in (27)
0
B
B
B
B
B
B
B
B
B
B
B
B
B
@
Pair1
Pair2
.
.
.
Pairk1
Pairk
PairkC1
.
.
.
PairL
1
C
C
C
C
C
C
C
C
C
C
C
C
C
A
D
0
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
@
jh1j2,jhNj2
jh2j2,jhN1j2
.
.
.
jhk1j2,jhN.k2/j2
jhkj2,ˇˇˇhN
2C1ˇˇˇ
2
jhkC1j2,ˇˇˇhN
2C2ˇˇˇ
2
.
.
.
jhN
2j2,ˇˇˇhN
2CikC1ˇˇˇ
2
1
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
A
(27)
The result in (27) shows that initial pairs are made by join-
ing the end users, for example, jh1j2and jhNj2being the
lowest and highest gain users are paired, followed by pair-
ing the next lowest jh2j2and highest jhN1j2, and so on.
Once a specific point kis reached, then from this point
further, pairs are made using UCGD pairing scheme. The
scenario presented in Figure 1 can be expressed in Figure 3
after hybrid pairing is performed.
In comparison to Figure 1, it can be seen in Figure 3 that
to accommodate the two near users UE4and UE5, the two
immediate next users (UE3and UE6) will make a com-
promise. So, UE3will be paired with UE5,andUE
4will
be paired with UE6using UCGD pairing. Thus, if some X
number of users are very close to each other in the cen-
ter and cannot be paired, then X
2users from both sides will
accommodate them using UCGD pairing. Thus, the switch-
ing point kdepends upon the number of near gain users in
the center that cannot be paired.
This scheme achieves same capacities for extreme high
and low-gain users as in conventional pairing. Though
some of the high-gain and low-gain users that are not on
the extremes are used to accommodate cell mid users. For
these high-gain and low-gain users, the capacity analysis
is same as was carried out earlier for UCGD pairing. High
interference at the cell mid is still reduced here but with
some compromises from those high-gain and low-gain
users that are paired with them.
4.3. M-users UCGD pairing
We propose a generalized M-users pairing model by
extending the concepts of UCGD pairing, where Mrepre-
sents the number of users in each pair. Consider Nusers
in a cell with sorted channel gains. Let Mrepresent the
maximum number of users possible in a pair considering
the minimum channel gain difference requirement of the
in-pair users. We divide the cellular users into Ggroups,
where GDM. Because of a large number of users in a
cell, we assume that the number of users in each group is
the same.
For a user ifrom any group, it can be paired with a user
jfrom the immediate next higher gain group using (28)
PairlD˚i,jjjDmin Gjji. (28)
Similarly for a next high gain group, its user will be
selected for the pair according to (28) with respect to user
jand so on up till the highest gain group. Conversely, i
is paired with a user kfrom immediate previous low gain
group using (29)
PairlD˚i,kj,kDmax Gkji. (29)
For the next low gain group, its user will be selected for the
pair according to (29) with respect to user kandsoonup
till the lowest gain group.
Consider the simplest case where number of users in
each group are same and uniformly distributed. Let jhg,ij2
denote the ith user of the gth group. The set of M-users in a
pair is given by (30)
PairlDnjhg,ij2:81gGo, (30)
which means that the same indexed (corresponding) users
of all the groups are combined in a pair. For Gnumber of
groups, pairing results are summarized in (31)
0
B
B
B
@
Pair1
Pair2
.
.
.
PairL
1
C
C
C
AD0
B
B
B
@
jh1,1j2,jh2,1 j2,jhG,1j2
jh1,2j2,jh2,2 j2,jhG,2j2
.
.
.
jh1,Lj2,jh2,Lj2,jhG,Lj2
1
C
C
C
A
(31)
This is a generalized result for the UCGD based M-users
pairing with the assumption of same number of users in
all groups. Using the UCGD pairing to make a generalized
M-user pairing model provides a basis for pairing the max-
imum number of users in a pair by keeping the threshold
conditions satisfied. It provides an algorithmic level basis
for users pairing rather than random selection of users in
a pair. Channel gains of users in groups can be arranged
Wirel. Commun. Mob. Comput.
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DOI: 10.1002/wcm

User pairing schemes in NOMA M. B. Shahab
et al.
in the form of any data structure like sorted arrays or
trees, followed by inter-groups pairing. The pairing model
becomes more and more generic as the number of users in
a cell increase causing one to one correspondence between
users of all groups.
5. EXACT ERGODIC CAPACITY
ANALYSIS
This section provides a detailed mathematical analysis
in terms of exact ergodic capacity of two paired users
considering both perfect and imperfect SIC scenarios.
5.1. Perfect SIC
ConsideranearuserUE
1and far user UE2such that
jh1j2>jh2j2. Suppose they are paired with each other
over a common bandwidth B. Their power allocation fac-
tors are in the order a1<a2and a1Ca21. Assume
that the channel over each link is independent Rayleigh flat
fading with channel coefficients h1CN 0, 1Ddv
1
and h2CN 0, 2Ddv
2for the links BS!UE1and
BS!UE2, respectively, where drepresents the distance
and vis the path loss exponent. The achievable data rate of
UE1in the UE1-UE2pair is given by
C1DBlog21Cjh1j2a1. (32)
ThedatarateachievablebyUE
2can be derived as follows:
C2DBlog2.1Cmin.2,2!1//
DBlog2 1Cmin jh2j2a2
jh2j2a1C1,jh1j2a2
jh1j2a1C1!!
DBlog2 1Cmin jh2j2a2,jh1j2a2
min jh2j2a1,jh1j2a1C1!
DBnlog21Cmin jh1j2,jh2j2
log21Cmin jh1j2a1,jh2j2a1o,
(33)
where a2D1a1is used. The achievable sum rate C12
for the UE1-UE2pair is calculated by
C12 DC1CC2. (34)
Let X,min jh1j2,jh2j2,Y,min jh1j2,jh2j2a1,
and Z,jh1j2a1. The cumulative distribution functions
of X, Y, and Z can be represented as
FX.x/D1exp x
1exp x
2, (35)
FY.y/D1exp y
1a1exp y
2a1, (36)
FZ.z/D1exp z
1a1. (37)
The probability density functions (PDFs) of X, Y, and Z
are given as follows:
fX.x/D.bCc/exp..bCc/x/, (38)
fY.y/D.kCl/exp..kCl/y/, (39)
fZ.z/Dkexp.kz/, (40)
where bD1
1,cD1
2,kD1
1a1,andlD1
2a1.
Using the PDFs derived for X, Y, and Z, the ergodic capac-
ity for UE1and UE2can be calculated as follows. For UE1,
the ergodic capacity is given by
C1
erg DBk Z1
0
log2.1Cz/exp.kz/dz
DBEi..k// exp.k/
ln 2 ,
(41)
where Ei./represents the exponential integral function.
Similarly, the ergodic capacity for UE2can be written as
C2
erg DB.bCc/Z1
0
log2.1Cx/exp..bCc/x/dx
.kCl/Z1
0
log2.1Cy/exp..kCl/y/dy
DBEi..bCc// exp.bCc/
ln 2
CEi..kCl// exp.kCl/
ln 2 .
(42)
Therefore, the exact ergodic sum capacity for the UE1–
UE2pair can be calculated as
C12
erg DC1
erg CC2
erg. (43)
The result in (43) is for the case when perfect SIC is
considered at near user receiver.
5.2. Imperfect SIC
Normally, it is assumed that the near user can perfectly
decode and cancel the signal of far user. This is based
on the assumption of good pairing, so that the differences
between channel gains and power allocations of both users
are large enough for efficient detection (perfect SIC) of far
user’s signal at the near user. But for the bad pairing case,
when the difference in channel gains of both users is less,
the corresponding closeness in the power allocation of both
users causes confusion (interference) for the SIC process at
near user. In such scenario, the achievable data rate of UE1
in the UE1-UE2pair is given by
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User pairing schemes in NOMA
O
C1DBlog2 1Cjh1j2a1
1
C‡!
DBlog2 1Cjh1j2a1
1C‡ !,
(44)
where ‡represents the interference due to low-gain user’s
signal that may not be canceled perfectly. This interference
causes imperfections in the SIC process, which ultimately
degrades the achievable capacity. This interference can be
defined as a function of the channel gain difference of the
paired users or their allocated power factors difference. Let
O
Z,a1
1C‡ jh1j2; the cumulative distribution function of O
Z
can be written as follows:
FO
Z.Oz/D1exp .1C‡ / Oz
1a1. (45)
The PDFs of O
Zcan thus be written as follows:
fO
Z.Oz/DO
kexp O
kOz, (46)
where O
kD1C‡
1a1. The ergodic capacity for UE-1 can thus
be calculated as follows:
O
C1
erg DBZ1
0O
klog2.1COz/exp O
kOzdOz
DB
Ei O
kexp O
k
ln 2 .
(47)
For UE2, the ergodic capacity calculated for perfect SIC
can be used as it is because UE2does not perform SIC.
Therefore, the ergodic sum capacity for the UE1-UE2pair
considering imperfect SIC can be calculated as
O
C12
erg DO
C1
erg CC2
erg. (48)
6. SIMULATION RESULTS
Simulations are performed to evaluate the performance of
proposed pairing schemes compared with the conventional
near–far pairing. System overall capacity comparisons are
performed using both perfect and imperfect SIC cases.
In Figure 4, we present the analytical and simulation
results for ergodic sum capacity of two users per pair
case by considering perfect and imperfect SIC. The dis-
tance between BS and UE2is normalized to unity; that is,
d2D1. For the simplicity of presentation, BS, UE1,and
UE2are assumed to be collinear with d1D0.5. More-
over, we consider vD4, BD1 Hz, a1D0.1, and
a2D0.9. Here, varies from 0 to 45 dB. For the imperfect
SIC case, we assume ‡D25 dB to show the impact of
interference that will cause imperfections in the SIC pro-
cess. It is evident from Figure 4 that ergodic sum capacity
of the two user pair considering perfect SIC shows better
performance compared with the imperfect SIC case, par-
ticularly at high . It is also noted that, for the imperfect
Figure 4. Ergodic sum capacity analysis considering perfect and
imperfect successive interference cancelation (SIC).
SIC case, the ergodic sum capacity gradually increases up
to a certain . After that, the ergodic sum capacity remains
almost constant when exceeds that certain value because
of the interference terms in the denominator of (44). A per-
fect harmony between analytical and the simulation results
proves the legitimacy of our analysis.
Based on the analysis in Section 5 and the results shown
in Figure 4, we further perform the capacity compar-
isons for a system of 24 users in a cell where each pair
consists of two users. These capacity comparisons are per-
formed between orthogonal frequency-division multiple
access (OFDMA), conventional NOMA near–far pairing,
and proposed pairing schemes by considering perfect and
imperfect SIC as depicted in Figures 5 and 6, respectively.
Throughout the simulations, the abbreviations OFDMA
and OFDM are used interchangeably. Distribution of users
across the cell is uniform. For these two figures, we consid-
ered normalized channel gains between 0 and 1. Further,
we let BD1MHz;varies from 0 to 30 dB, and nor-
malized power per pair is 1; that is, a1Ca2D1. Within
a pair, fractional transmit power was used to define a1and
a2. So for two users with gains jh1j2and jh2j2in a pair,
a1Djh2j2
jh1j2Cjh2j2and a2D1a1. Thus, low-gain users get
high power and vice versa. Furthermore, for imperfect SIC,
we consider very small interference as an inverse relation
to the channel gain difference between users in a pair.
For the perfect SIC case, it can be seen in Figure 5 that
capacities of proposed pairing schemes are only slightly
better than the conventional pairing. This is because losses
due to SIC imperfections for cell mid pairs in conven-
tional near–far pairing have not been considered. But for
the imperfect SIC case in Figure 6, the difference in capac-
ities is evident from the graph. It can be seen that there is
very little capacity decrease for UCGD, some decrease for
hybrid pairing but great decrease for conventional scheme
in Figure 6 compared with Figure 5 even when a small
interference is considered.
Wirel. Commun. Mob. Comput.
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DOI: 10.1002/wcm

User pairing schemes in NOMA M. B. Shahab
et al.
Figure 5. Cell capacities versus transmit signal to noise ratios
(SNRs) (bandwidth D1MHz,users D24, perfect succes-
sive interference cancelation). UCGD, uniform channel gain
difference; OFDM, orthogonal frequency-division multiplexing.
Figure 6. Cell capacities versus transmit signal to noise ratios
(SNRs) (bandwidth D1 MHz, users in cell D24, imperfect suc-
cessive interference cancelation). UCGD, uniform channel gain
difference; OFDM, orthogonal frequency-division multiplexing.
The per user capacity comparison of all pairing schemes
has been performed in Figure 7 to analyze the interfer-
ence and SIC effect on individual user capacities. The same
parameters of Figures 5 and 6 are used here. Users on the
left and right sides on the x-axis of the graph have low and
high channel gains, respectively. Users in the center are cell
mid users with close channel gains. The capacity variations
of users in different regions follow the same reasoning as
described earlier throughout the work.
Furthermore, capacity analysis when the number of
users in a pair is increased is shown in Figures 8 and 9. The
Figure 7. User capacities (users D24, imperfect successive
interference cancelation (SIC)). UCGD, uniform channel gain
difference.
Figure 8. Cell capacities versus transmit signal to noise ratios
(SNRs) (bandwidth D1MHz,users D24, perfect succes-
sive interference cancelation). UCGD, uniform channel gain
difference; OFDM, orthogonal frequency-division multiplexing.
same parameters that were used in Figures 5 and 6 are used
here. The total number of users is still 24. The same total
power of the system is distributed equally among the pairs.
Within a pair with more than two users, similar formulas
are used to allocate the power as were used in Figures 5
and 6
It is clear from Figure 8 that as the number of users in a
pair increases, the overall capacity of the system increases
correspondingly. For the imperfect SIC case in Figure 9,
as the number of per pair users increases, the inter-user
channel gain difference becomes less. So, the impact of
high interference comes into play, thereby reducing the
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User pairing schemes in NOMA
Figure 9. Cell capacities versus transmit signal to noise ratios
(SNRs) (bandwidth D1MHz,users D24, imperfect suc-
cessive interference cancelation). UCGD, uniform channel gain
difference; OFDM, orthogonal frequency-division multiplexing.
overall capacity gain. If the capacities in Figure 8 are com-
pared with results of Figure 9, it is evident that as the
number of users in a pair are increased, the overall capacity
gain is reduced for the imperfect SIC case.
Moreover, as the number of users in a pair increases, the
end users suffer a lot. For example, in an M-user pair, the
highest gain user will have to perform SIC for the signals
of all M1 in-pair users, which raises questions on the
device computational power and the quality of SIC receiver
used. Similarly, the lowest gain user will treat the data of
all M1 in-pair high-gain users as noise. This will severely
affect the data rates of low-gain users. These aspects point
towards the need for an upper bound on the number of users
in a pair.
7. CONCLUSION
In this paper, effects of near–far user pairing on the per-
formance of cell center, mid, and edge users have been
investigated. It has been pointed out that as the near and far
users are paired in conventional near–far pairing, the cell
mid users are left unpaired. If these users are paired with
each other, the small difference in their channel gains and
allocated powers causes imperfections in the SIC, which
degrades their capacity ultimately. On the other hand, if
these users are left unpaired to be served with MA, the SIC
issue can be avoided, but these users cannot benefit from
the capacity gains provided by NOMA.
Therefore, two users pairing strategies are proposed that
can accommodate all the users in pairs in an intelligent
manner, so that the SIC imperfection issue can also be
avoided or minimized. It has been shown that the proposed
schemes give better capacity results compared with con-
ventional near–far pairing, especially when imperfect SIC
is considered. It is also shown that as the number of in-
pair users increases, the SIC imperfection effects increase
because of decreasing channel gain difference of in-pair
users. Furthermore, for a large number of users in a pair,
the highest gain users will have to decode and cancel the
signals of so many users through SIC, which will be chal-
lenging for the devices. Similarly, the lowest gain user will
face large amount of noise. This places upper bound on the
maximum number of users in a pair.
ACKNOWLEDGEMENTS
This research was supported by Basic Science Research
Program through the National Research Foundation of
Korea (NRF) funded by the Ministry of Education
(2015R1D1A1A01061075)
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AUTHORS’ BIOGRAPHIES
Muhammad Basit Shahab received
his BS in Electrical Engineering from
University of Engineering and Tech-
nology (UET) Lahore, Pakistan. His
MS in Electrical Engineering was
from University of Management and
Technology (UMT) Lahore, Pakistan.
Currently, he is working as graduate
research assistant at Wireless and Emerging Network Sys-
tem Lab, Kumoh National Institute of Technology, South
Korea. His main research areas are radio access technolo-
gies (RATs) for wireless communications, non orthogonal
multiple access (NOMA), ultra-dense cells, LTE/LTE-A,
and smart grids.
Mohammad Irfan received his BSc
degree in Electrical and Electronic
Engineering from Islamic University
of Technology, Dhaka, Bangladesh, in
2011. Currently, he is working as grad-
uate research assistant at wireless and
Embedded Networking System Lab,
while attending graduate school at
Kumoh National Institute of Technology, South Korea. His
main research area includes Orthogonal/Non-orthogonal
multiple access, MIMO, and new information carrying
domains for wireless communications.
Md Fazlul Kader was born in 1982.
He received his BSc and MSc in Com-
puter Science and Engineering (CSE)
from the Chittagong University of
Engineering and Technology (CUET),
Bangladesh, in 2005 and 2014, respec-
tively. Currently, he is working towards
a PhD at the WENS Lab., Kumoh
National Institute of Technology, South Korea. From
2007 onwards, he is a faculty member of the Depart-
ment of Applied Physics, Electronics, and Communication
Engineering, University of Chittagong, Bangladesh. His
major research interests include cognitive radio networks,
cooperative communications, MIMO, computer networks,
NOMA and spatial modulation.
Soo Young Shin received his BS, MS,
and PhD degrees in Electrical Engi-
neering and Computer Science from
Seoul National University, Korea in
1999, 2001, and 2006, respectively. He
was a visiting scholar in FUNLab at
University of Washington, US, from
July 2006 to June 2007. After 3 years
working in WiMAX design lab.of Samsung Electronics,
he is now assistant professor in School of Electronics in
Kumoh National Institute of Technology since September
2010. His research interests include wireless LAN, WPAN,
WBAN, wireless mesh network, sensor networks, coex-
istence among wireless networks, industrial and military
network, cognitive radio networks, and next generation
mobile wireless broadband networks.
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DOI: 10.1002/wcm