Content uploaded by Wali Ullah Khan
Author content
All content in this area was uploaded by Wali Ullah Khan on Jun 28, 2019
Content may be subject to copyright.
Efficient Power Allocation for Multi-Cell Uplink
NOMA Network
Wali Ullah Khan1, Furqan Jameel2, Tapani Ristaniemi2, Basem M. Elhalawany3, Ju Liu1
1School of Information Science and Engineering, Shandong University, Qingdao 266237, China.
2Faculty of Information Technology, University of Jyvaskyla, FI-40014 Jyvaskyla, Finland.
3Benha University, Egypt.
Abstract—Digital technologies are rapidly shaping the modern
concepts of urbanization. It is a key element of developing
practical smart cities of the future. In fact, they are the catalyst
for the increasing networking of all areas of life in a smart city.
Recent development in the domain of communication technolo-
gies has opened new avenues to realize the concept of smart
cities. One of such communication technology is non-orthogonal
multiple access (NOMA) for future cellular communications. This
article, therefore, focuses on the interference management of
uplink cellular NOMA systems. Specifically, we propose a power
optimization technique for NOMA to improve the sum-rate in a
multi-cell environment. We also consider Nakagami-m faded links
to analyze the applicability of our proposed scheme under various
channel conditions. The simulation results show that the proposed
NOMA approach outperforms conventional orthogonal multiple
access (OMA) technique in the multi-cell uplink scenario.
Index Terms—Nakagami-m, Non-orthogonal multiple access
(NOMA), Multi-cell, Power optimization, Smart city
I. INTRODUCTION
Wireless communication is rapidly shaping the future of
expanded connectivity of billions of devices. The future smart
cities are mainly driven by the seamless connectivity of
wireless devices. Digital infrastructure and mobility solutions
are some of the key indicators of future smart cities [1],
[2]. Another focal point is a modernization of legacy cellular
infrastructure. Due to this reason, a key element of many smart
city approaches is the central role of information and commu-
nication technologies (ICT) [3]. The ICT plays a key role in the
concepts for future urban development. But a smart city is not
a technological entity. It is rather a social-economic-technical
structure. The city planners and technology companies are not
so enthusiastic about the possibility of social exchange, but
rather dream of a fully automated and fully connected city. In
this context, a key element is the communication infrastructure
that is able to satisfy the demands of the users [4]. In this
direction, it becomes necessary to avoid orthogonal utilization
of resources and move towards non-orthogonality. Therefore,
it is anticipated that non-orthogonal multiple access (NOMA)
is going to be one of the key enablers of future cellular
technologies [5], [6].
NOMA works by accommodating multiple users on the
same frequency/ time resource by assigning different power
levels to them. Some of the key techniques used at the
transmitter and receiver ends are the superposition coding
(SC), and successive interference cancellation (SIC), respec-
tively. The SC is one of the fundamental building blocks
of information encoding techniques of communication theory.
The objective of SC is to transmit information simultaneously
at the same time to several nodes by a single transmitter. In
[7], [8], Bergmans, and Gallager theoretically demonstrated
the capability of SC to approach the capacity of both Gaussian
broadcast channel and general channel. Later, the SC technique
was applied to other communication channels including the
multiple access, relay, interference, and wiretap channels. The
experimental performance of SC technique was first investi-
gated by Vanka et al. [9] in software-defined network. On the
other hand, SIC is a well known physical layer decoding tech-
nique, that allows a receiver to decode different user packets
simultaneously coming from the transmitter [10]. According
to the principle of SIC technique, a pair of users multiplexed
on the same spectrum resource will schedule according to
their channel strength. The user with good channel condition
will apply SIC, decode the signal of the user with weak
channel quality, remove it and then decode its own signal.
The weak user does not apply SIC and decode the signal with
the interfering signal of the strong user [11].
There are several advantages of exploiting non-
orthogonality of frequency and time resources. In particular,
NOMA in power domain multiplexing is capable of
accommodating multiple users with different types of quality
of service (QoS) requests over the same spectrum/time
resource [3], [6]. Therefore, power-domain NOMA is a
key candidate technology for the Internet of Thing (IoT)
which connects a large number of nodes. By exploiting
the power domain for user multiplexing, NOMA is able to
accommodate more users to cope with network overload.
Unlike orthogonal multiple access (OMA) where users are
served over exclusively allocated spectrum resources, NOMA
can utilize the bandwidth more efficiently by accommodating
multiple users over the same spectrum/time resource [12].
Besides this, unlike conventional OMA system with grant-
based transmission where each user first needs to send the
scheduling request for a grant to the base station which causes
a high transmission delay and signaling cost, NOMA does
not need scheduling [13]. Therefore, the transmission delay
and signaling overhead are reduced drastically in NOMA
systems.
Although NOMA techniques are very useful for multiplex-
ing signals, interference among users belonging to different
cells can degrade the decoding performance. Different group-
978-1-7281-1217-6/19/$31.00 ©2019 IEEE
ing strategies have been proposed to address the increased
interference [14]–[16]. For instance, the authors of [14] pro-
posed an interference mitigation strategy by selecting two
users with high channel-gain difference which has been proved
to improve the NOMA system sum rate considerable. The
same scenario was extended for the case when a number of
users are required to be assigned to the same group [15]. In
a similar manner, Liang et al. in [16] proposed to optimize
the capacity of a NOMA with the help of matching theory
algorithm. Game theocratic approaches have also gained much
prominence to reduce the effect of interference in NOMA [17],
[18]. In this domain, a suboptimal strategy for half-duplex
cognitive NOMA systems was proposed by the authors of [17].
Similarly, a matching game was proposed by Di et al. in [18]
to connect users and mitigate the interference. This approach
not only maximized the total sum rate but also improved the
user fairness of NOMA systems.
However, there still exist many challenges in terms of
interference mitigation that obstruct the widespread adoption
of NOMA techniques. Firstly, most of the studies consider
only single cell scenario where the base station (BS) em-
ploys NOMA techniques to distribute resources among users.
Second, fewer studies exist in NOMA that takes into ac-
count channel variations and the effect of interference beyond
conventional Rayleigh faded channels. Finally, to the best of
our knowledge, there is a gap in the literature for studying
interference mitigation for uplink NOMA scenarios, where
most of the literature concentrate on downlink scenarios. To
fill this glaring gap in NOMA literature, we aim to develop
a comprehensive case study of uplink NOMA system that
optimizes the power allocation to manage interference in a
multi-cell environment. To understand the impact of channel
variations in uplink NOMA, we have considered Nakagami-
m faded wireless links across all cells. The studies show
significant improvement in NOMA gain for the proposed
power allocation scheme.
The remainder of the paper is organized as follows. Section
II provides an overview of the system model and problem
formulation. Section III discusses the proposed power opti-
mization scheme. In Section IV, we present simulation results
along with their discussion. Finally, Section V provides some
concluding remarks and future research directions.
II. SY ST EM MO DE L AN D PROB LE M FORMULATION
We consider an uplink NOMA-based transmission as shown
in Fig. 11, which consists of Mcells, where BS ={BSm|m=
1,2,3, ...M }, constitute a network under co-channel tech-
nique. In each cell, a BS is located at the center and intends
to communicate with Ndifferent NOMA users (NUs), where
NU ={NUn|n= 1,2,3, ...N }. We assume that all nodes
of the network including BSs and NUs are equipped with
a single antenna. In the network, each BS has complete
knowledge of its serving NUs. We consider full spectrum
1In figure 1, the interference between cell of BS2and cell of BSMis due to
co-channel deployment. The co-channel interference also exists among other
cells but all are omitted for the sake of clarity.
BS-1
BS-3
BS-2
BS-M
Desired signal
Co-channel interference
Base station NOMA user
Fig. 1. Uplink transmission of multi-cell NOMA network
reuse such that each cell share the same spectrum resource and
causes interference to other cells of the network. The channels
between BSs and NUs undergo Nakagami fading. Without loss
of generality, we sort the channel to co-channel interference
plus noise ratios (CCINRs) of NUs associated with BSmas
h1,m
ICC
1,m +σ2≤ ·· · ≤ hn,m
ICC
n,m +σ2≤ ·· · ≤ hN,M
ICC
N,M +σ2,(1)
where hn,m is the channel gain of NUnat BSm,σ2is the
variance of additive white Gaussian noise (AWGN), and ICC
n,m
is the co-channel interference from other cells to BSmas
ICC
n,m =
M
m′=1,m′̸=m
hn′,m′
m
N
n′=1,n′̸=n
χn′,m′pn′,m′+σ2(2)
To facilitate the uplink NOMA transmission, BSmapply SIC
to detect and decode multiple NUs signals. Let sn,m is a
transmitted signal of NUnto BSm, thereby the received signal
of NUnat BSmcan be expressed as
zn,m =hn,mχn,m √pn,msn,m
desired signal
+ ¯
ω
noise
+hn,m
N
n′=1,n′̸=n
χn′,m√pn′,m sn′,m
interference of NUs
+
M
m′=1,m′̸=m
hn′,m′
mN
n′=1
χn′,m′√pn′,m′sn′,m′
co-channel interference
,
(3)
where hn,m is defined in (1), χn,m = 1 shows the NUn
association with BSm,2pn,m is the NUntransmit power, and
¯ωis the zero mean AWGN, respectively. According to the
2The users association to the BSs play an important role in enhancing
performance of the network, however, is beyond the scope of this work.
CCINRs order expressed in (1), the transmit power of NUs in
BSmshould satisfy as
p1,m >·· · > pn,m >··· > pN,M .(4)
Following (3), the received signal to interference plus noise
ratio (SINR) of NUnat BSmis given by
τn,m =χn,mpn,m |hn,m|2
INU
n,m +ICC
n,m +σ2,(5)
where INU
n,m is the interference of NUs after SIC process, and
can be expressed as
INU
n,m =|hn,m|2
N
n′=1,n′̸=n
χn′,mpn′,m .(6)
We aim to minimize the co-channel interference and max-
imize the sum rate while guaranteeing the QoS of NUs in
different cell. This can be obtained by solving the power
optimization problem. Mathematically, the problem can be
formulated as
max
pn,m M
m=1
N
n=1
Rn,m = log2(1 + τn,m)(7a)
s.t.
M
m=1
Rn,m ≥¯
Rmin,∀n, (7b)
M
m=1
χi,npn,m ≤Pm,∀n, (7c)
pn,m ≥0,∀n, m. (7d)
where ¯
Rmin and Pmrepresent the minimum rate threshold
for QoS and total battery power, respectively. Equation (7a) is
the objective function of sum rate maximization. Constraint
in (7b) guarantees the QoS of NUs in each cell, while
constraints in (7c) and (7d) together limit the user transmit
power, respectively.
III. PROP OS ED POWER OPTIMIZATION SCH EM E
The objective of the optimization problem (7) is to mitigate
the co-channel interference and maximize the sum rate of the
system through optimal allocation of user transmit power at
the uplink transmission of different cells. Due to co-channel
interference, the optimization problem becomes non-convex
which is hard to solve through traditional convex optimization
scheme. Thus we provide a tractable suboptimal scheme where
KKT conditions are satisfied. To do so, first we derive the
Lagrangian function of optimization problem (7) as
L(p, ϕ, ψ) =
M
m=1
N
n=1
Rn,m +
N
n=1
ϕnM
m=1
Rn,m −¯
Rmin
+
N
n=1
ψnPm−
M
n=1
pn,m,(8)
where ϕnand ψare the Lagrange multipliers. Applying KKT
conditions as
∂L(.)
∂pn,m
=∂
∂pn,m M
m=1
N
n=1
Rn,m +
N
n=1
ϕnM
m=1
Rn,m
−¯
Rmin+
N
n=1
ψnPm−
M
n=1
pn,m,(9)
∂L(.)
∂pn,m
=∂
∂pn,m M
m=1
N
n=1
Rm,n −
M
m=1
ϕn−
N
n=1
Rn,m
−ψn,(10)
∂L(.)
∂pn,m
=∂
∂pn,m (1 + ϕn) log2(1 + τn,m ) +
N
i<n
(1 + ϕi)
×log2(1 + τi,m) +
M
m′=1,m′̸=m
N
n′=1
(1 + ϕ′
n)
×log2(1 + τn′,m′)−ψn,(11)
∂L(.)
∂pn,m
= (1 + ϕn)1
ln2(1 + τn,m)×∂
∂pn,m
(1 + τn,m)
+
N
i=1,i̸=n
(1 + ϕi)1
ln2(1 + τn,m)×∂
∂pn,m
(1 + τi,m)
+
M
m′=1,m′̸=m
N
n′=1
(1 + ϕn′)1
ln2(1 + τn,m)
×∂
∂pn,m
(1 + τn′,m′)−ψn,(12)
∂L(.)
∂pn,m
=(1 + ϕn)1
ln2(1 + pn,m|hn,m |2
INU
n,m+ICC
n,m+sigma2)×∂
∂pn,m
×1 + pn,m |hn,m|2
INU
n,m +ICC
n,m +σ2+
N
i=1,i̸=n
(1 + ϕi)
×1
ln2(1 + τn,m)×∂
∂pn,m
(1 + τi,m)
+
M
m′=1,m′̸=m
N
n′=1
(1 + ϕn′)1
ln2(1 + τn,m)
×∂
∂pn,m
(1 + τn′,m′)−ψn,(13)
After simplification, we obtain
∂L(.)
∂pn,m
=(1 + ϕn)λn,m
ln2(1 + pn,mλn,m )
−γNU
n,m −γCC
n,m −ψn= 0,(14)
where λnis the channel to interference plus noise ratio of
NUnassociated with BSm, and can be given by
λn,m =χn,m|hn,m |2
INU
n,m +ICC
n,m +σ2,(15)
while γNU and γCC are the interference of NUs after SIC
process and co-channel interference causes by other cells, both
are expressed as
γNU
n,m =
M
i<n
(1 + ϕi)τi,m|hi,m |2
ln2(1 + τi,m)(INU
i,m +ICC
i,m +σ2),
(16)
γCC
n,m =
M
m′=1,m′̸=m
N
n′=1 (1 + ϕn′)τn′,m′|hn,m
m|2
ln2(1 + τn′,m′)(INU
n′,m′+ICC
n′,m′+σ2).
(17)
For detailed derivation proof of (14), please refer to Appendix
of [19]. The allocated power of NUnassociated with BSmcan
be obtained from (14) as
p∗
n,m =(1 + ϕn)
γNU
n,m +γCC
n,m +ψn−1
λn,m +
,(18)
where (α)+=max(0, α)and Lagrange multipliers can be
obtained and iteratively updated by subgradient technique as
ϕn(x+ 1) = ϕn(x)−δ(x)×M
m=1
N
n=1
Rn,m −¯
Rmin+
,
(19)
ψn(x+1) = ψn(x)−δ(x)×Pm−
M
m=1
N
n=1
pn,m+
.(20)
where xindex iteration number, and δ≥0is the step size.
First, Lagrange multipliers ϕnand ψnare updated using p∗
n,m
obtained from (18). Then, optimal ϕnand ψnare used to
calculate the optimal pn,m. The iteration process can be ended
on convergence.
Assuming the active number of NUs associated with each
BS on the same spectrum resource is N. Then, the complexity
of the solving problem (7) employing the proposed scheme
in xiteration is O(N2). If the number of total iterations
required for convergence of the proposed scheme is K, and
the number of total BSs in the network is M, thereby the
overall complexity of our proposed multi-cell model becomes
O(KM N2).
IV. SIM UL ATION RESULTS
In this section, we provide simulation results of the proposed
power optimization technique. Unless mentioned otherwise,
the initial user power is 3 W for each user, the number of
active user in each cell is 3 and the number of cells varies
from 1−7.
Figure 2 shows the sum rate of the network against the
increasing number of cells. It can be seen that the increase
in the number of cells in the environment generally results
in improving the sum rate. It is mainly due to the fact that
the capability of accommodating new users also increases
with an increase in the number of cells. To provide a fair
comparison, we applied the proposed optimization scheme
to both NOMA and OMA users. We noted that the power
optimization strategy for NOMA outperforms the conventional
OMA technique even for a single cell. Moreover, as the
number of cells increases, the separation between OMA and
1234567
Number of cells in the network
0
5
10
15
20
25
Sum rate of the network (b/s/Hz)
Proposed NOMA
Conventional OMA
Fig. 2. Number of cells in the network versus sum rate of the network. The
user transmit power is 3 W, number of active user in each cell is 3, and
number of cells varies from 1-7.
1 1.5 2 2.5 3 3.5 4
Per user transmit power
0
5
10
15
20
25
Sum rate of the network (b/s/Hz)
Proposed NOMA
Conventional OMA
Fig. 3. Available user transmit power versus sum rate of the network. The
number of cell is 7, number of active user in each cell is 3, and power values
for each user varies from 1-4 W.
NOMA grows. This indicates the effectiveness of our proposed
strategy to manage interference as the number of cells grows.
Specifically, when the total number of cells grow up to 7,
the OMA technique only achieves a sum-rate of 8 bit/sec/Hz,
whereas, the sum-rate of proposed NOMA scheme becomes
more than double by achieving 17 bit/sec/Hz.
Figure 3 shows the sum-rate as a function of per-user
transmit power. One can observe that the sum-rate of the
network increases with an increase in the transmit power of
the user. However, similar to the last figure, as the transmit
power of the individual user increases, the separation between
OMA and proposed NOMA technique increases considerably.
This also shows that the proposed NOMA technique is more
flexible in managing interference against the increase in per-
user power.
To highlight the impact of channel variations, we plot sum-
rate of the network against different values of Nakagami-m
1 1.5 2 2.5 3 3.5 4
Per user transmit power
5
10
15
20
25
Sum rate of the network (b/s/Hz)
Proposed NOMA, m=1
Conventional OMA, m=1
Proposed NOMA, m=2
Conventional OMA, m=2
Proposed NOMA, m=3
Conventional OMA, m=3
Fig. 4. Sum-rate of the network against different values of Nakagami-m
parameter. The number of cell is 7, number of active user in each cell is 3,
and power values for each user varies from 1-4 W.
parameter in Figure 4. Note that similar to the last figure,
an increase in transmit power of the user brings a significant
increase in sum-rate of the proposed NOMA user. As the value
of Nakagami-m parameter increases, the fading conditions be-
come less severe which improves the sum-rate of the network.
In this case, the proposed NOMA scheme outperforms the
OMA scheme across all values of m. However, as the transmit
power per user increases the different curves of Nakagami-m
parameter start to converge for both OMA and NOMA. This
convergence of curves of different values of m, suggests that
the impact of Nakagami-m parameter reduces at higher values
of per-user transmit power.
V. CONCLUSION
In this paper, we have proposed a power optimization
techniques for multi-cell uplink NOMA systems. Moreover,
we analyzed the performance of our proposed scheme un-
der Nakagami-m fading. It has been shown that the pro-
posed NOMA technique outperforms the conventional OMA
technique in terms of sum-rate. We have also provided the
complexity analysis of the proposed uplink NOMA scheme
which shows a fairly lightweight nature of our multi-cell power
optimization scheme. These results can provide much-needed
design insights for NOMA-aided cellular networks in smart
cities.
Although the results provided in this article are suitable for
optimizing the power and managing the interference, they are
not enough to improve the spectral efficiency. To achieve this
objective, we aim to employ multi-objective optimization for
the NOMA systems. Thus, our next focus is on exploring joint
spectral and power optimization techniques for uplink NOMA
systems. This interesting problem will be addressed in future
studies.
ACK NOW LE DG ME NT
This work is partially supported by the National Key R & D
Plan (2017YFC0803403), the National Natural Science Foun-
dation of China (61371188) and the Fundamental Research
Funds of Shandong University (2018GN051).
REF ER EN CE S
[1] T. Han, X. Ge, L. Wang, K. S. Kwak, Y. Han, and X. Liu, “5G con-
verged cell-less communications in smart cities,” IEEE Communications
Magazine, vol. 55, no. 3, pp. 44–50, 2017.
[2] M. S. Ali, E. Hossain, and D. I. Kim, “LTE/LTE-A random access for
massive machine-type communications in smart cities,” IEEE Commu-
nications Magazine, vol. 55, no. 1, pp. 76–83, 2017.
[3] M. Shirvanimoghaddam, M. Dohler, and S. J. Johnson, “Massive non-
orthogonal multiple access for cellular IoT: Potentials and limitations,”
IEEE Communications Magazine, vol. 55, no. 9, pp. 55–61, 2017.
[4] J. Montalban, P. Scopelliti, M. Fadda, E. Iradier, C. Desogus,
P. Angueira, M. Murroni, and G. Araniti, “Multimedia multicast ser-
vices in 5G networks: Subgrouping and non-orthogonal multiple access
techniques,” IEEE Communications Magazine, vol. 56, no. 3, pp. 91–95,
2018.
[5] G. Wunder, P. Jung, M. Kasparick, T. Wild, F. Schaich, Y. Chen,
S. Ten Brink, I. Gaspar, N. Michailow, A. Festag et al., “5GNOW: non-
orthogonal, asynchronous waveforms for future mobile applications,”
IEEE Communications Magazine, vol. 52, no. 2, pp. 97–105, 2014.
[6] F. Jameel, S. Wyne, S. J. Nawaz, Z. Chang, and T. Ristaniemi, “Outage
Analysis of Relay-Aided Non-Orthogonal Multiple Access with Partial
Relay Selection,” in 2018 IEEE Globecom Workshops (GC Wkshps),
Dec 2018, pp. 1–6.
[7] P. Bergmans, “Random coding theorem for broadcast channels with de-
graded components,” IEEE Transactions on Information Theory, vol. 19,
no. 2, pp. 197–207, 1973.
[8] R. G. Gallager, “Capacity and coding for degraded broadcast channels,”
Problemy Peredachi Informatsii, vol. 10, no. 3, pp. 3–14, 1974.
[9] S. Vanka, S. Srinivasa, Z. Gong, P. Vizi, K. Stamatiou, and M. Haenggi,
“Superposition coding strategies: Design and experimental evaluation,”
IEEE Transactions on Wireless Communications, vol. 11, no. 7, pp.
2628–2639, 2012.
[10] S. Sen, N. Santhapuri, R. R. Choudhury, and S. Nelakuditi, “Succes-
sive interference cancellation: A back-of-the-envelope perspective,” in
Proceedings of the 9th ACM SIGCOMM Workshop on Hot Topics in
Networks. ACM, 2010, p. 17.
[11] N. I. Miridakis and D. D. Vergados, “A survey on the successive
interference cancellation performance for single-antenna and multiple-
antenna OFDM systems,” IEEE Communications Surveys & Tutorials,
vol. 15, no. 1, pp. 312–335, 2013.
[12] Y. Saito, Y. Kishiyama, A. Benjebbour, T. Nakamura, A. Li, and
K. Higuchi, “Non-orthogonal multiple access (NOMA) for cellular
future radio access,” in Vehicular Technology Conference (VTC Spring),
2013 IEEE 77th. IEEE, 2013, pp. 1–5.
[13] L. Dai, B. Wang, Y. Yuan, S. Han, I. Chih-Lin, and Z. Wang, “Non-
orthogonal multiple access for 5G: solutions, challenges, opportunities,
and future research trends,” IEEE Communications Magazine, vol. 53,
no. 9, pp. 74–81, 2015.
[14] Z. Ding, P. Fan, and H. V. Poor, “Impact of User Pairing on 5G
Nonorthogonal Multiple-Access Downlink Transmissions,” IEEE Trans.
Vehicular Technology, vol. 65, no. 8, pp. 6010–6023, 2016.
[15] M. S. Ali, H. Tabassum, and E. Hossain, “Dynamic user clustering
and power allocation for uplink and downlink non-orthogonal multiple
access (NOMA) systems,” IEEE Access, vol. 4, pp. 6325–6343, 2016.
[16] W. Liang, Z. Ding, Y. Li, and L. Song, “User pairing for downlink non-
orthogonal multiple access networks using matching algorithm,” IEEE
Transactions on Communications, vol. 65, no. 12, pp. 5319–5332, 2017.
[17] W. Xu, X. Li, C.-H. Lee, M. Pan, and Z. Feng, “Joint Sensing Duration
Adaptation, User Matching, and Power Allocation for Cognitive OFDM-
NOMA Systems,” IEEE Transactions on Wireless Communications,
vol. 17, no. 2, pp. 1269–1282, 2018.
[18] B. Di, L. Song, and Y. Li, “Sub-channel assignment, power allocation,
and user scheduling for non-orthogonal multiple access networks,” IEEE
Transactions on Wireless Communications, vol. 15, no. 11, pp. 7686–
7698, 2016.
[19] W. U. Khan, Z. Yu, S. Yu, G. A. S. Sidhu, and J. Liu, “Efficient
power allocation in downlink multi-cell multi-user NOMA networks,”
IET Communications, vol. 13, no. 4, pp. 396–402, 2019.
