Nonorthogonal multiple access (NOMA) where all users share the entire time and frequency resource has paid attention as one of the key technologies to enhance the spectral efficiency and the total throughput. Nevertheless, as the number of users and SIC error increase, the interuser interference and the residual interference due to the SIC error also increase, resulting in performance degradation. In order to mitigate the performance degradation, we propose groupingbased NOMA system. In the proposed scheme, all users are divided into two groups based on the distance between the BS and each user, where one utilizes the first half of the bandwidth and the other utilizes the rest in the orthogonal manner. On the other hand, users in each group share the spectrum in the nonorthogonal manner. Grouping users can reduce both the interuser interference and residual interference due to the SIC error, so it can outperform conventional NOMA system, especially in case that the number of users and the SIC error increase. Based on that, we also present the hybrid operation of the conventional and the proposed NOMA systems. In numerical results, the total throughput of the proposed NOMA systems is compared with that of the conventional NOMA systems with regard to the number of users and SIC error. It is confirmed that the proposed NOMA system outperforms the conventional NOMA system as the number of users and the SIC error increase.
1. INTRODUCTION
Recently, according to the increasing of smart phones, wireless internet applications and multimedia services, mobile network traffic has been explosively increasing
[1]
. This trend will be expected to be mobile traffic volume 1000 times larger than today’s by 2020
[2]
. In this reason, the importance and research of 5G system to drastically enhance the capacity, compared with 4G system including long term evolution – advanced (LTEA) have paid attention.
In order to cope with the explosive increase in data traffic and enhance the system capacity in 5G, 1000fold capacity enhancement has become one of the most important issues in the
3^{rd} generation partnership project (3GPP) workshop on release 12 and onwards
on June 2012
[3]
. In this workshop, various core technologies for higher spectral efficiency under massive small cell environment have been introduced.
In particular, nonorthogonal multiple access (NOMA) scheme has been proposed as one of several promising technologies that can improve capacity in 5G systems
[4]

[9]
. In NOMA, all users share limited resources (time and frequency) by using superposition coding. Because the communication resources in NOMA are shared by all the users, the sum capacity can be enhanced, compared with orthogonal multiple access (OMA) such as orthogonal frequency division multiple access (OFDMA). However, interuser interference due to resource sharing occurs, resulting in performance degradation. For this, a successive interference cancellation (SIC) scheme is required in the receiver.
SIC performance is dependent on the transmission power of each user in downlink (DL) NOMA systems. In
[10]
, the authors proposed the optimal power allocation scheme to maximize edgeuser throughput under the condition that total user throughput in NOMA is the same as that in OMA. In
[11]
, the authors proposed a power allocation method based on proportional fairness scheduling and in
[12]
, a suboptimal power allocation method to reduce complexity was proposed.
In these previous works, SIC is assumed to be perfectly performed without SIC error. However, in practical systems, SIC error does occur, resulting in performance degradation
[13]
. Furthermore, even though SIC is perfectly performed, residual interference exists, which is not removed by SIC because its transmission power is lower than that of the desired signal. Therefore, as the number of the total users increases, total capacity is degraded by the residual interference.
In this paper, a new NOMA scheme based on user grouping is proposed in order to mitigate performance degradation due to the interuser interference as well as SIC error. In the proposed groupingbased NOMA scheme, all the users do not share all spectrum resource. Instead, all the users are divided into two groups based on the distance between the base station (BS) and each user. Each group utilizes the half of the total frequency resource in the orthogonal method, respectively. On the other hand, users in each group share the half of the total frequency resource in the nonorthogonal method. We analyze the performance of the groupingbased NOMA, which depends on the number of users, the SIC error and the total transmission power. We compare the performance of the groupingbased NOMA with the conventional NOMA and present the condition that the groupingbased NOMA outperforms the conventional NOMA with respect to the number of users, the SIC error and the transmission power. In simulation results, we compare the performance between them according to the number of users, the SIC error and the transmission power.
The remainder of this paper is organized as follows: Section 2 describes the system model of the general NOMA. In Section 3, a new NOMA scheme is proposed and the performance of the proposed scheme is analyzed. The numerical and simulation results are presented in Section 4 and also concluding remarks are given in Section 5.
2. CONVENTIONAL NOMA SYSTEM
The conventional DL NOMA system is depicted in
Fig. 1
. It consists of one BS and K users. For simplicity, the kth user (
k
∈ {1, 2, ⋯
K
}) assumed to be located at the kth distant position from the BS. The BS transmits a signal for the kth user over the total bandwidth which is denoted as
W
,
x_{k}
, with the transmission power,
P_{k}
. Then, the transmission signal over
W
bandwidth,
x
, can be written as:
Conventional DL NOMA System Model
In the receiver of the kth user, the received signal can be written as:
In (2), the channel,
h_{k}
, is denoted as the combination of the frequency domain complex channel coefficient and path loss between the BS and the kth user and is modeled as complex Gaussian distributed reflecting the path loss due to the distance between the BS and the kth user.
n_{k}
denotes complex additive white Gaussian noise (AWGN) in the receiver of the kth user where mean and variance are zero and
respectively. In addition,
P_{k}
is the transmission power of the kth user. In DL NOMA system, the higher power is allocated to the user with the larger channel gain
[14]
. In other words, if 
h
_{1}

^{2}
>
h
_{2}

^{2}
> ⋯ >
h_{K}

^{2}
, the allocated power is as follows:
p
_{1}
<
p
_{1}
⋯ <
p_{K}
. As for the user with larger channel gain (i.e., the distance between the BS and the user is shorter), SIC can be accurately performed, so SIC is performed, with allocating lower power. On the other hand, as for the user with smaller channel gain (i.e., the distance between the BS and the user is longer), the received signal power is also smaller, so it is hard to perform SIC. In this case, the desired signal is directly detected without SIC, with allocating higher power. It is noted that there exists interuser interference which is not removed by SIC, after performing SIC in the receiver of the kth user.
Therefore, after receiving the signal,
y_{k}
, at the kth user, all the signals from
x
_{k}
_{+1}
to
x_{K}
are successively detected and extracted from
y
_{k}
by SIC. In this case, the received signal to interference plus noise ratio (SINR) of the kth user can be expressed as
where
I_{e}
denotes the interuser interference from the signals from
x
_{1}
to
x
_{k}
_{1}
, which is not removed after SIC and can be expressed as
I_{r}
denotes the residual interference occurring due to SIC error and can be expressed as
where
is the detected signal for SIC.
From (3)(5), the rate of the kth user,
R_{k}
, can be easily obtained as
Also, the sum rate,
R
, is
3. THE PROPOSED NOMA SYSTEM
 3.1 Groupingbased NOMA Scheme
As shown in (4)(5), as the number of users and SIC error increase,
I_{e}
and
I_{r}
drastically increase. Therefore, the SINR and throughput of the kth user can be. In this case, sharing the entire frequency resource by all the users cannot guarantee the performance enhancement, compared with OMA systems.
To mitigate the performance degradation due to the number of users and the SIC error, we propose a groupingbased NOMA scheme. First, all the users are sorted according to the distance between the BS and each of them as shown in
Fig. 1
. Then, all users are divided into two groups: in Group 1, the users with the odd index are included and the others are included in Group 2 as follows:
where
s
_{1}
and
s
_{2}
are denoted as Group 1 and Group 2, respectively. Users in
s
_{1}
share the first half of the bandwidth and users in
s
_{2}
share the rest. It is noted that
s
_{1}
and
s
_{2}
exclusively utilizes bandwidth in the orthogonal manner. In the groupingbased NOMA, each user utilizes the half of the entire bandwidth compared with the conventional NOMA, so the throughput could be reduced. However,
I_{e}
and
I_{r}
can be also reduced, so the total throughput can outperform that of the conventional NOMA as the number of users and the SIC error increase.
 3.2 Power Allocation Method
As mentioned above, the optimal and suboptimal power allocation methods have been already proposed
[7]

[9]
and any of them can be applied in the proposed NOMA system. However, in
[7]

[9]
, the main target is to guarantee fairness, whereas we focus on enhancing the total throughput compared the conventional NOMA in this paper. Furthermore, the previous power allocation schemes have high complexity. In this reason, we consider a simple power allocation method in this paper.
The transmission power of the kth user in Group i (i = 1 or 2),
P
_{i}
_{,}
_{k}
, is presented as
[14]
In (10), the transmission power of the kth user is inversely proportional the channel gain. That is, in each group, the lowest power is allocated to the user closest to the BS and the highest power is allocated to the user farthest from the BS. In order to use the total transmission power of the proposed NOMA scheme equal to that of the conventional NOMA for fairness, the transmission power of the kth user is normalized by the sum of all the channel gains.
 3.3 SINR and Throughput Performance
After users in each group perform SIC, the SINR of the jth
user in Group i (i = 1 or 2) can be written as:
where
I_{i}
_{,}
_{e}
and
I_{i}
_{,}
_{r}
are the interuser interference and the residual interference due to the SIC error, respectively, and can be expressed as follows:
In (12) and (13), it is noted that the number of interferers consisting of (12) and (13) is smaller than that of conventional NOMA system, because all users are divided into two groups. Therefore, both
I_{i}
_{,}
_{e}
and
I_{i}
_{,}
_{r}
are reduced, which can mitigate the performance degradation.
I_{i}
_{,}
_{e}
is the net power of users not participating in SIC in the receiver of the jth user in Group i, so it always occurs and causes performance degradation. On the other hand,
I_{i}
_{,}
_{r}
depends on the SIC performance. In perfect SIC,
is always the same as
so
I_{i}
_{,}
_{r}
= 0. In other words, there is no residual interference. However, in case of imperfect SIC, the probability of
occurs and
I_{i}
_{,}
_{r}
≠ 0.
then
E
[ ] means the expectation operator. As for an excellent SIC performance such as iterative SIC and turbo SIC, the value of
σ
^{2}
is small. On the other hand, as for poor SIC performance such as linear SIC, the value of
σ
^{2}
increases.
The throughput of the jth user in Group i,
R_{i}
_{,}
_{j}
, is
Compared with (6),
is multiplied to the prelog term because each user utilizes the half of the entire bandwidth in the groupingbased NOMA.
Based on (14), the total throughput,
R
, can be obtained
 3.4 Hybrid Operation of Conventional and Groupingbased NOMA Systems
In (14), each user of the groupingbased NOMA utilizes the half of the entire bandwidth, so
is multiplied to the prelog term. It could cause the performance degradation. If the number of users is small and
I_{i}
_{,}
_{r}
is also small due to small
σ
^{2}
, the throughput loss due to interuser interference and the residual interference is not dominant. In this case, the performance of the groupingbased NOMA is worse than that of the conventional NOMA. On the other hand, if the number of users is large and
I_{i}
_{,}
_{r}
is high due to large
σ
^{2}
, the throughput will be severely degraded due to interuser interference and the residual interference. In this case, by reducing the number of the interferers via the groupingbased NOMA, the throughput degradation can be mitigated.
Therefore, the total throughput can be enhanced through a hybrid operation of conventional and groupingbased NOMA systems according to the interference power. That is, the groupingbased NOMA system operates if
E
[
R_{i}
_{,}
_{j}
] >
E
[
R_{k}
]. On the other hand, if
E
[
R_{i}
_{,}
_{j}
] <
E
[
R_{k}
], the conventional NOMA system operates. As a result, the total throughput can be enhanced.
4. SIMULATION RESULTS
In this section, we compare sum rates OMA and conventional NOMA systems with the proposed groupingbased NOMA system according to the values of the total transmission power, the number of the total users and the residual interference power. Parameters that we consider for simulation is shown in
Table 1
.
Simulation Parameters
Fig. 2
shows the sum rate comparison of OMA, NOMA and groupingbased NOMA systems when the total transmission power is 33dBm, which means relay or small cell network. The sum rate of OMA is constant, irrespective of the number of the total users. In
Fig. 2
, GNOMA denotes groupingbased NOMA. OMA users exclusively utilizes bandwidth, so bandwidth per user is reduced, as the number of the total users increase. As a result, the sum rate is constant. On the other hand, in case of perfect SIC, sum rates of NOMA and groupingbased NOMA increases, as the number of the total users increases. It is because both systems can enhance the spectral efficiency due to sharing the frequency resource, as the number of the total users increases.
Sum rate comparison of OMA, NOMA and groupingbased NOMA when the total power is 33dBm.
However, in case of imperfect SIC, sum rates of both system do not increase even though the number of users increases, because the residual interference due to imperfect SIC also increases, resulting in performance degradation. In NOMA, if the error variance,
σ
^{2}
, is bigger than 10
^{5}
, the sum rate of NOMA is less than that of OMA.
In case of perfect SIC, NOMA outperforms groupingbased NOMA when the number of the total users are small. Because residual interference does not exist, NOMA where all users share all resource can guarantee the higher spectral efficiency. However, if the number of users is more than 15, groupingbased NOMA outperforms NOMA, because interuser interference increases. By splitting SINR degradation due to interuser interference into two groups, groupingbased NOMA shows the higher spectral efficiency. This tendency is more obvious as the SIC error increases.
When SIC error exists, the residual interference causes the drastic reduction of NOMA performance. However, by splitting residual interference power due to the SIC error into two groups, groupingbased NOMA can mitigate the performance degradation. In case of
σ
^{2}
= 10
^{6}
, when the number of users is more than just 6, groupingbased NOMA shows better performance. In case of
σ
^{2}
, the sum rate of OMA is higher than that of NOMA, which means NOMA cannot be applied, whereas groupingbased NOMA still outperforms OMA as well as NOMA.
Fig. 3
shows the sum rate comparison of OMA, NOMA and groupingbased NOMA systems when the total transmission power is 40dBm, which means macro cell network. The higher total transmission enables higher received signal power, compared with
Fig. 2
, so the region where NOMA outperforms groupingbased NOMA is wider. In case of perfect SIC, until the number of users increases up to 40, the sum rate of NOMA is better than that of groupingbased NOMA. Under the environment with no the residual interference, even though interuser interference increases, the received SINR is still better than that of groupingbased NOMA due to higher total transmission power. Therefore, NOMA outperforms groupingbased NOMA in perfect SIC.
Sum rate comparison of OMA, NOMA and groupingbased NOMA when the total power is 40dBm.
However, once the residual interference due to imperfect SIC exists, groupingbased NOMA is better than NOMA. In case of
σ
^{2}
= 10
^{6}
, when the number of users is more than 6, groupingbased NOMA outperforms NOMA. It is because the residual interference drastically increases as the number of users increases in spite of higher transmission power. Therefore, under the environment with the residual interference due to SIC error, groupingbased NOMA can mitigate the performance degradation and guarantee higher performance than NOMA.
Based on
Fig. 2
and
3
, due to the transmission power, the number of users and the value of
σ
^{2}
a hybrid operation of conventional NOMA and the groupingbased NOMA systems enables to maintain the best performance.
5. CONCLUSIONS
In this paper, we propose the groupingbased NOMA system, where all users are divided into two groups based on the distance. As the number of users is more, the SIC error is bigger and the transmission power is less, the total interference drastically increases in conventional NOMA, resulting in performance degradation. The proposed groupingbased NOMA system can mitigate the throughput loss by splitting the total interference into two groups at the cost of spectral efficiency. Because each user in the groupingbased NOMA utilizes the half of the entire bandwidth, the proposed scheme could show worse performance than the conventional NOMA in case of small number of users, high transmission power and the small SIC error. However, in the practical and general environment where many users try to share the resource with the small transmission power when SIC error exists, the groupingbased NOMA outperforms the conventional NOMA system.
Acknowledgements
The research was supported by a grant from the Academic Research Program of Korea National University of Transportation in 2014.
BIO
Sungmook Lim
He received the B.S. and Ph.D. degrees in Electrical and Electronic Engineering at Yonsei University, Seoul, Korea in 2005 and 2012, respectively. From September 2012 to March 2014, he was a Postdoctoral Fellow at Yonsei University where his research interents were in 5G wireless communications. Since March 2014, he joined the Department of Electronics Engineering at Korea National University of Transportation as an Assistant Professor. His current research interests include the field of 5G wireless communications focusing on multicarrier and multiantenna systems, cooperative relaying, and ITS.
Kyunbyoung Ko
He (corresponding author) received the B.S., M.S., and Ph.D. degrees in Electrical and Electronic Engineering at Yonsei University, Seoul, Korea in 1997, 1999, and 2004, respectively. From March 2004 to February 2007, he was a senior engineer in Samsung Electronics, Suwon, Korea where he developed Mobile WiMAX systems for broadband wireless services. Since March 2007, he joined the Department of Control and Instrumentation Engineering at Korea National University of Transportation as an Associate Professor. His current research interests include the field of wireless communications focusing on multicarrier and multiantenna systems, cooperative relaying, and ITS.
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