Power Allocation for Downlink NOMA Heterogeneous Networks

Abstract

Non-Orthogonal Multiple Access (NOMA) and Heterogeneous Network (HetNet) are two significant and promising enabling techniques to further improve overall system performance for next-generation mobile communication systems. In this study, we develop a novel NOMA HetNet through applying NOMA technique to both macrocell and small-cell of conventional HetNet, which improves the spectral efficiency whereas results in a more complex interference environment. To tackle this complicated interference problem and maximize the overall throughput of this NOMA HetNet, meanwhile ensure the desired quality of service (QoS) of each user, we mathematically formulate a power allocation problem which proves to be an NP-hard problem. Then, to deal with this optimization problem, we propose a users scheduling scheme and an iterative distributed power control algorithm. The simulation results demonstrate that compared with the conventional orthogonal multiple access (OMA) HetNet systems and single-tier NOMA networks, the combination of OMA technique and HetNet with the proposed algorithm can greatly improve the system performance in terms of spectral efficiency and outage performance.

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Date of publication xxxx 00, 0000, date of current version xxxx 00, 0000.
Digital Object Identifier 10.1109/ACCESS.2017.DOI
Power Allocation for Downlink NOMA
Heterogeneous Networks
DADONG NI1, (Student Member, IEEE), LI HAO1,(MEMBER, IEEE), QUANG THANH TRAN1 2,
AND XIAOMIN QIAN1
1Key Lab of Information Coding and Transmission, Southwest Jiaotong University, Chengdu, China.
2Faculty of Electrical and Electronic Engineering of University of Transport and Communications, Hanoi, Vietnam.
Corresponding author: Dadong Ni (e-mail: dadongni@hotmail.com).
This work was supported by the National Natural Science Foundation of China (NSFC) Project (No.61271245).
ABSTRACT Non-Orthogonal Multiple Access (NOMA) and Heterogeneous Network (HetNet) are two
significant and promising enabling techniques to further improve overall system performance for next-
generation mobile communication systems. In this study, we develop a novel NOMA HetNet through
applying NOMA technique to both macrocell and small-cell of conventional HetNet, which improves the
spectral efficiency whereas results in a more complex interference environment. To tackle this complicated
interference problem and maximize the overall throughput of this NOMA HetNet, meanwhile ensure the
desired quality of service (QoS) of each user, we mathematically formulate a power allocation problem
which proves to be an NP-hard problem. Then, to deal with this optimization problem, we propose a users
scheduling scheme and an iterative distributed power control algorithm. The simulation results demonstrate
that compared with the conventional orthogonal multiple access (OMA) HetNet systems and single-tier
NOMA networks, the combination of OMA technique and HetNet with the proposed algorithm can greatly
improve the system performance in terms of spectral efficiency and outage performance.
INDEX TERMS Non-orthogonal multiple access, heterogeneous networks, user scheduling scheme,
distributed power allocation algorithm.
I. INTRODUCTION
WITH the explosive growth of smart devices and rapid
arising of various media services, the deep longings
for extremely higher aggregate data rate, better coverage and
higher spectral efficiency (SE) increase and become more
intensive [1]. To cope with these issues, the technologies of
HetNet and NOMA, which exploit respectively spatial diver-
sity and multi-user diversity, are enabling and attract much
attention. Consisting of various base stations with vastly dif-
ferent transmit power and coverage area, the basic framework
of a heterogeneous network was provided in the provisions of
the fourth generation (4G) mobile system long ago [2]–[6].
On the other hand, as a promising technique for future radio
access(FRA), NOMA was proposed by NTT DOCOMO [7]
to enable multiple users to share the identical radio resource
at the same time, which should be distinguished through
different power levels [7]–[10]. To successfully retrieve the
desired information from the overlapped signals, successive
interference cancelation (SIC) technique is utilized at the
receivers in NOMA networks [7].
Due to the scarcity of spectrum resource, the co-
channel deployment scenario between macrocell and small-
cell prefers to be employed [5]. While in HetNet the co-
channel deployment of small and macro-cells can improve
the spectral efficiency, the unavoidable cross-tire interfer-
ence would occur. Thus, the authors in [4], [11], [12] dis-
cussed diverse advanced interference mitigation and resource
management approaches for orthogonal-frequency-division
multiple-access (OFDMA) HetNet. The work in [13] present-
ed some cooperative distributed radio resource management
algorithms for the scene of hyper-dense small-cell deploy-
ment. To eliminate the cross-tier interference of downlink
OFDMA HetNet, a dynamic power allocation scheme was
proposed in [14], in which the transmit power of each
small-cell base station (BS) was controlled dynamically upon
the feedback from macro-tier. To optimize the sum rate
and energy efficiency of small-tier simultaneously, a multi-
objective optimization problem was formulated in [15] to
jointly allocate the subchannel and power in the uplink and
downlink of a two-tier OFDMA HetNet. In [16], a throughput
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D. Ni et al.: Power Allocation for Downlink NOMA Heterogeneous Networks
FIGURE 1. The architecture of NOMA HetNet.
maximization problem of OFDMA HetNet was studied under
the QoS and per-tier minimum sum-rate constraints.
In general, it is unlikely to constantly improve the spectral
efficiency only through the orthogonal multiple access tech-
nique. As a result, NOMA technique dramatically attracts
the attention of the academic community. The basic concepts
of uplink and downlink NOMA networks were exploited in
[7], [17], and various challenges for NOMA networks in-
volving power allocation and user scheduling were discussed
in [17]. Power allocation therein plays a significant role
in enhancing the system performance of NOMA networks
since the signals of multiple users are superposed under
certain power partitions, and thereby attracts a lot of research
attention. For instance, the closed-form formulae of outage
probability and ergodic sum-rate were derived for two-user
static power allocation NOMA system in [18]. The authors
in [19] analyzed the drawbacks of fixed power allocation
in NOMA network and proposed a general two-user power
allocation scheme. On the other hand, the influence of power
allocation on fairness performance of NOMA network was
investigated in [20], and the power allocation algorithms for
two users NOMA networks were investigated under sum rate
maximization and proportional fairness criteria in [21]. To
further improve the system performance, the work in [22]
proposed a MIMO collaborative communication scheme with
NOMA technique to accommodate two users in each stream
and designed a novel precoder to suppress the inter-stream
interference of MIMO-NOMA multicell networks.
Since the most transmit power are consumed by the cell-
edge users who always experience the worst channel con-
ditions according to NOMA protocol, it will hinder the
performance improvement of NOMA networks. To deal with
this problem, the authors in [23] firstly proposed a strategy
that combines HetNet and NOMA, and indicated that this
cooperative scheme could enhance the spectral efficiency. In
[24], the energy efficiency optimization scheme of NOMA
HetNet was investigated, in which only small-cells employed
NOMA technique, meanwhile the cellular network utilized
MIMO technique. Similarly, in [25], the resource allocation
problem was focused in which macrocell networks employed
OMA protocol and small-cells served two users on single
subcarrier through NOMA principle without taking the us-
er QoS constraints into account. Instead, to make full use
of the advantage of NOMA technique, as shown in Fig.1,
we develop a NOMA heterogeneous network, where the
NOMA protocol is applied to both macrocells and small
cells. As a result, the interference environment becomes more
complicated due to the multi-user interference and cross-
tier interference. Therefore, the existing interference man-
agement approaches are not applicable, and more advanced
interference management is required to further improve the
system performance of this NOMA HetNet.
In this paper, we formulate a resource allocation problem
to maximize the sum-rate of NOMA HetNet under the con-
straints of total transmit power and users QoS requirement,
which proves to be NP-hard. As depicted in [7], the optimal
decoding order of SIC is along with the ascending sequence
of channel gain normalized by the inter-cell interference and
noise power. It means that the user decode order in NOMA
HetNet is closely intertwined with the power allocation in
each cell which increases the difficulty greatly of solving
the resource allocation problem. Consequently, to solve the
resource allocation problem in NOMA HetNet, we first pro-
pose a user scheduling scheme to determine the maximum
users set subjected to the systems service capability, then
upon which we develop an iterative distributed power con-
trol algorithm to obtain the total transmit power of each
cell. The simulation results demonstrate that the proposed
NOMA HetNet can provide greater improvement in spectral
efficiency (SE) and lower outage performance compared with
conventional OMA HetNet and single-tier NOMA network.
The remainder of this paper is organized as follows. In
Section II, we introduce the NOMA HetNet system model.
Section III formulates a power allocation problem and pro-
vides the solution of this optimization problem. The numer-
ical results and analysis are presented in Section V. Finally,
the conclusions are given in Section VI.
II. SYSTEM MODEL
As shown in Fig.1, we consider a downlink NOMA hetero-
geneous network, involving one macro base station (MBS)
located at the center of the macrocell and one overlaid small
BS (SBS) deployed at the edge of the macrocell. For notation
convenience, we use BS-ito denote the two BSs, where i= 1
stands for MBS and i= 2 for SBS. There are U1macrocell
users (MUE) distributed randomly in the macrocell and U2
small-cell users (SUE) distributed randomly in small-cell,
respectively. Let Ui,{1,2,· · · , Ui}be the set of users
connected with BS-i. All the devices and BSs are assumed
to equip with single antenna scenario.
In this paper, BSs are supposed to deliver the superposed
signals to their own users via NOMA principle. Accordingly,
each user receives not only the desired signals from its serv-
ing BS, but also interfering signals from the cross-tier BS. We
assume that the users are capable of utilizing SIC technique
to retrieve its desired signals. Let UE-(i, k)represent the kth
user in Uiand BS-j, j 6=ibe the interfering BS. Hence, the
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D. Ni et al.: Power Allocation for Downlink NOMA Heterogeneous Networks
received signal at UE-(i, k)is
yi,k =
Ui
X
n=1 pρi,nPihi,i,k +
Uj
X
m=1 pρj,mPjhj,i,k +ni,k ,
i= 1,2and i 6=j,
(1)
where hj,i,k denotes the channel fading coefficient between
BS-jand UE-(i, k)which accounts for both large- and small-
scale channel fading, Pirepresents the total power consump-
tion of BS-i,ρi,n is the power allocation fraction for UE-
(i, n), and ni,k ∼ CN (0, σ 2)stands for the corresponding
additive white Gaussian noise (AWGN) with noise variance
σ2.
As described in [7], the optimal decode order is in the as-
cending order of normalized channel gain which is represent-
ed as the channel gain-to-the noise and inter-cell interference
power ratio. Thereby, the normalized channel gain of UE-
(i, k)is formulated as:
gi,k =|hi,i,k|2
P
n∈Uj
ρj,nPj|hj,i,k |2+σ2.(2)
For simplicity, let gi,1≥gi,2≥ · · · ≥ gi,Ui. According to
SIC protocol, UE-{i, k}can decode the signals from the user
set {UE-(i, k + 1),UE-(i, k + 1), . . . , UE-(i, Ui)}succes-
sively. By subtracting these signals from the received signals,
UE-{i, k}finally obtains its desired signals through treating
the signals of the remaining users as noise. Therefore, the
received signal to interference plus noise ratio (SINR) of UE-
(i, k)is given by [7]
γi,k =ρi,kPigi,k
k−1
P
u=1
ρi,uPigi,k + 1
.(3)
Denote Ri,k =Wlog2(1 + γi,k)as the data rate of
UE-(i, k), where Wrepresents the total bandwidth. The
achievable sum rate of this NOMA HetNet system is
C=X
i∈{1,2}X
k∈Ui
Ri,k.(4)
On the other hand, to perform efficient SIC, the decoded
signals should be accurately distinguished with the remaining
undetectable signals as shown in the expression below,

ρi,k0−
k0−1
X
u=k+1
ρi,u
gi,kPi≥Pdif f ,∀k∈ {2,· · · , Ui},
(5)
where Pdiff stands for the required minimum power differ-
ence between the decoded and undetectable signals. Follow-
ing this representation, a necessary condition for the power
allocation in each cell was introduced in [26] as
ρi,k −
k−1
X
u=1
ρi,u!Pigi,k−1≥Pdif f , i ∈{1,2}, k∈ Ui/{1},
(6)
which will be considered in the following resource man-
agement for NOMA HetNet to guarantee the system perfor-
mance.
III. POWER ALLOCATION FOR DOWNLINK NOMA
HETNET
In the previous section, the system model of NOMA HetNet
has been presented, from which we can observe that the
interference environment becomes more complicated due to
the multi-user interference and cross-tier interference. Thus,
an advanced resource management is called for to mitigate
the interference and ensure the system performance improve-
ment, which is the focus of this section.
A. PROBLEM FORMULATION
Denoting the power allocation vector in cell ias
ρi={ρi,1, ρi,2,· · · , ρi,Ui},i= 1,2, to maximize the sum
rate, the power allocation problem for NOMA HetNet is
mathematically formulated as
(P1) max
ρ1,ρ2


C=X
i∈{1,2}X
k∈Ui
Ri,k


(7)
subject to
X
k∈Ui
ρi,k ≤1, i ∈ {1,2},(C7.1)
ρi,k ≥0, i ∈ {1,2}, k ∈ Ui,(C7.2)
ρi,k −
k−1
X
u=1
ρi,u!Pigi,k−1≥Pdif f , i ∈{1,2}, k∈ Ui/{1},
(C7.3)
Ri,k ≥Rth
i,k, i ∈ {1,2}, k ∈ Ui,(C7.4)
where Rth
i,k represents the data rate requirement of UE-(i, k).
Then (C7.1) denotes the total power constraint for each BS,
(C7.2) ensures that the power allocation for each user is
nonnegative, (C7.3) guarantees the effective SIC as discussed
in Section II, and (C7.4) supports the data rate requirement of
every user.
As shown in (2) and (3), the increased transmit power
of BS-iis beneficial for the sum rate of cell iwhile does
harm to that of cell j. Thus, it is difficult to distinguish
the convexity of above optimization problem (7), and the
optimization problem (7) is a NP-hard problem. To deal with
this situation, we replace (C7.4) by following linear form
ρi,kPigi,k −Ith
i,k k−1
X
u=1
ρi,uPigi,k + 1!≥0,(8)
where Ith
i,k = 2Rth
i,k/W −1represents the desired minimum
SINR for UE-(i, k).
Theorem I: As the global optimization of previous opti-
mization problem (7) is achieved, for any given user k∈
{2,3,· · · , Ui}, at least one of the two inequalities (C7.3) and
(8) is an equation.
Proof: See Appendix A
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D. Ni et al.: Power Allocation for Downlink NOMA Heterogeneous Networks
An necessary condition for the global optimization of (7)
is provided by Theorem I. Some insights into the power al-
location for user k, k ∈ {2,3,· · · , Ui}are also obtained. We
suppose that the total power consumption of BS-i, i ∈ {1,2}
is ˜
Piwhere ˜
Pi≤Pi. Thus, we can rewrite aforementioned
optimization problem (P1) as:
(P2) max
ρ1,ρ2


C=X
i∈{1,2}X
k∈Ui
Ri,k


(9)
subject to
X
k∈Ui
ρi,k = 1, i ∈ {1,2},(C9.1)
ρi,k ≥0, i ∈ {1,2}, k ∈ Ui,(C9.2)
ρi,k −
k−1
X
u=1
ρi,u!˜
Pigi,k−1≥Pdif f , i∈{1,2}, k ∈Ui/{1},
(C9.3)
ρi,k ˜
Pigi,k ≥Ith
i,k k−1
X
u=1
ρi,u ˜
Pigi,k + 1!, i ∈ {1,2}, k ∈ Ui,
(C9.4)
˜
Pi≤Pi, i ∈ {1,2}.(C9.5)
Obviously, above optimization problem (P2) is equiva-
lent to the original optimization problem (P1). Once ˜
Piis
confirmed, the optimal decoding order in each cell can be
determined as well. Note that the decoding order in cell i
should be updated in real time as the consumption power of
BS-j, j 6=ichanges, which greatly increases the difficulty of
solving the optimization problem (P2). However, the optimal
power allocations for all users except the last decoding user
are given in following theorem.
Theorem II: With the fixed ˜
Pi, i ∈ {1,2}, to guarantee
the QoS demand of user k, k ∈ {2,3,· · · , Ui}, the optimal
power allocation for user kis
ρi,k =1
2

Pdiff
˜
Pigi,k−1
+ 1 −
Ui
X
j=k+1
ρi,j 
,(10)
if and only if
Ith
i,k ≤ Pdiff
˜
Pigi,k−1+ 1 −
Ui
P
u=k+1
ρi,u!
2
˜
Pigi,k−1+ 1 −
Ui
P
u=k+1
ρi,u −Pdiff
˜
Pigi,k !;(11)
Otherwise,
ρi,k =Ith
i,k
1 + Ith
i,k 
1−
Ui
X
j=k+1
ρi,j +1
˜
Pigi,k 
.(12)
Proof: See Appendix B.
Based on Theorem II, with known total power consump-
tion of all BSs, the power allocation in cell ican be calculated
by
ρi,k =























"1
2 Pdiff
˜
Pigi,k−1+ 1 −
|Ui|
P
j=k+1
ρi,j !#+
, k ∈Φ,
"Ith
i,k
1+Ith
i,k 1−
|Ui|
P
j=k+1
ρi,j +1
˜
Pigi,k !#+
, k ∈Φ0,
"1−
|Ui|
P
j=2
ρi,j #+
, k = 1,
(13)
where [•]+= max{0,•}.Φdenotes the set of user conform-
ing to (11) and Φ0is the complementary set of Φ.
B. USER SCHEDULING SCHEME
Note that the user with better channel condition has a higher
priority over the user with worse channel condition, due
to the fact that the user with better channel condition can
contribute more capacity in NOMA HetNet but only con-
sumes less power. However, as we can see in (13), the
power allocation for all users are estimated in the inverse
order of their normalized channel gain. To guarantee the
QoS requirement of users with better channel condition, the
maximum connection capability of each cell would like to be
determined firstly with the known transmit power of each BS.
Thus, in this section, we propose a user scheduling scheme
to determine the connection capability of NOMA HetNet
with fixed maximum transmit power of each BS. The pro-
posed user scheduling scheme is described detailedly as
following:
1) Initialization: The maximum transmit power of BSs are
set to be ˜
Pi=Pi, i ∈ {1,2}, respectively. Denote
Ui, i ∈ {1,2}the set of users in cell i.
2) Main loop (iteration):
Step 1. With fixed ˜
Piand Ui, i ∈ {1,2}, the decoding
order in each cell is confirmed firstly, and then the
power allocation ρi, i ∈ {1,2}can be estimated
through the formulation (13). Afterward, ρi, i ∈
{1,2}should be validated as follows.
Step 2. If the constraints of all users in each cell can be
met, break out of the loop. If the constraints of
some users with higher priority are not met in
every cell, the user in this NOMA HetNet system
with worst channel condition should be eliminat-
ed, and then go to Step 1.
Step 3. If the constraints of some users with higher priority
are not fulfilled only in cell t, we should identify
whether the constraints of all users in cell tcan be
satisfied by controlling the transmit power of BS-
t0, t06=t. The needed minimum transmit power
of BS t0,Pmin
t0, can be evaluated by following
Theorem III with fixed transmit power ˜
Pt. Let
˜
Pt0=Pmin
t0and recalculate the power allocation
ρi, i ∈ {1,2}. If the constraints of some users in
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D. Ni et al.: Power Allocation for Downlink NOMA Heterogeneous Networks
cell tcannot be satisfied as usual, the user in cell
twith worst channel condition should be eliminat-
ed, and then go to Step 1; Otherwise, break out of
the loop.
3) Output: The connection capability of each cell is ob-
tained and return Ui, i ∈ {1,2}.
Theorem III: With the given transmit power of BS-j,
˜
Pjand fixed serving users of BS-i,Ui, i 6=j, the needed
minimum transmit power of BS-iis calculated by Pmin
i=
PUi
k=1 pmin
i,k , where









pmin
i,1=Ith
i,1
gi,1
pmin
i,k = max(Ith
i,k k−1
X
u=1
pmin
i,u +1
gi,k!,Pdif f
gi,k−1
+
k−1
X
u=1
pmin
i,u ),k 6= 1
.
(14)
Proof: See Appendix C.
C. ITERATIVE DISTRIBUTED POWER ALLOCATION
Once the users set is determined, the aforementioned opti-
mization problem (P2) can be cast as:
(P3) max
˜
P1,˜
P2

X
i∈{1,2}X
k∈Ui
Ri,k


(15)
subject to
X
k∈Ui
ρi,k = 1, i ∈ {1,2},(C15.1)
ρi,k >0, i ∈ {1,2}, k ∈ Ui,(C15.2)
Pi≤Pi, i ∈ {1,2},(C15.3)
where ρican be estimated according to (13).
Obviously, (P3) also has the same optimal solution as (P1),
but greatly reduces the dimension of optimization problems.
Fixed the transmit power of one BS, the suboptimal transmit
power of another BS with the potential of being a global
optimum can be obtained through Fibonacci method, which
is depicted in Algorithm 1. The computational complexity
of Algorithm 1 is O(ln(/L)/ln(2/3)) where is the arith-
metic precision and Lis the length of the feasible region of
the variable.
Finally, the suboptimal total power consumption for each
BS can be estimated alternately by utilizing the Algorithm 1
until the algorithm converges.
IV. NUMERICAL RESULTS AND DISCUSSIONS
In this section, we demonstrate the system performance
of downlink NOMA HetNet with the proposed resource
management scheme through Monte Carlo simulations. We
consider a two-tier cellular network involving one small-cell
deployed at the edge of the macrocell, where the NOMA
principle is employed in both macrocell and small-cell, and
the users are distributed randomly. We suppose that each user
can perfectly retrieve their intended information by using
Algorithm 1 Obtain optimal transmit Piwith fixed Pj
Input: Pmax
i, Pj,  > 0;
1: Calculate Pmin
iaccording to Theorem III;
2: while |Pmax
i−Pmin
i| ≤ do
3: Let P0
i=Pmin
i+Pmax
i−Pmin
i
3,P00
i=Pmin
i+
2(Pmax
i−Pmin
i)
3;
4: Estimate {ρ0
i,ρ0
j}and {ρ00
i,ρ00
j};
5: Calculate C0(ρ0
i,ρ0
j)and C00(ρ00
i,ρ00
j);
6: if C0< C00 then
7: Pmin
i=P0
i.
8: else
9: Pmax
i=P00
i.
10: end if
11: end while
12: return Pi=Pmax
i+Pmin
i
2.
0 2 4 6 8 10 12 14 16 18 20
The number of iterations
12
14
16
18
20
22
24
achievable data rate (Mbps)
macrocell
smallcell
FIGURE 2. Convergence of the proposed Algorithm 1.
the technique of SIC. The modified Hata urban propagation
model [27] is adopted here and some significant simulation
parameters are provided in Table I.
TABLE 1. system parameters
Noise power spectrum density -174dBm/Hz
Noise figure 9dB
Number of sub-channel 8
Bandwidth of sub-channel 180kHz
Radius of macrocell 250m
Radius of small-cell 30m
Transmit power of CBS {PC}20W
Transmit power of SBS {PS}10dBm ∼30dBm
The performance of the proposed NOMA HetNet is com-
pared with that of one-tier NOMA system (termed as NOMA
system) as well as conventional OMA HetNet [28]. To ensure
a fair comparison, the bandwidth and total power consump-
tion in three systems are identical, i.e. all spectral resource
is utilized to multiplex the users in NOMA HetNet and one-
tier NOMA system, and the transmit power of BS in one-tier
NOMA network is set to be the sum power of all base station
in a heterogeneous network.
VOLUME 4, 2016 5

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D. Ni et al.: Power Allocation for Downlink NOMA Heterogeneous Networks
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
data rate requirement (Mbit/s)
10-4
10-2
100
outage probability
(a)
NOMA HetNet
OMA HetNet
NOMA system
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
data rate requirement (Mbit/s)
15
20
25
30
spectral efficiency (bit/s/Hz)
(b)
NOMA HetNet
OMA HetNet
NOMA system
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
data rate requirement (Mbit/s)
10-2
100
outage probability
(c)
macrocells in NOMA HetNet
smallcells in NOMA HetNet
macrocells in OMA HetNet
smallcells in OMA HetNet
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
data rate requirement (Mbit/s)
10
12
14
16
spectral efficiency (bit/s/Hz)
(d)
macrocells in NOMA HetNet
smallcells in NOMA HetNet
macrocells in OMA HetNet
smallcells in OMA HetNet
FIGURE 3. Illustration of the outage probability and spectral efficiency as
P1= 20W, P2= 0.1W,U1= 5 and U2= 3. (a) and (b) respectively
illustrate the influence of varying data rate requirements on the overall
performance of three systems in term of outage probability and spectral
efficiency; (c) and (d) detailedly explore the outage performance and spectral
efficiency for different cell in heterogeneous network versus the data rate
requirement of users, respectively.
Fig.2 illustrates the convergence performance of the pro-
posed Algorithm 1, where the numbers of users distributed in
macrocell and small-cell are set to be 5and 3, respectively.
We assume the data rate requirement of each user is 2Mbit/s,
and the maximum transmit power of MBS and SBS are set to
be 20W and 1W. It can be seen that our proposed Algorithm
1 can converges quickly with finite iterations.
Fig.3 depicts the curves of the outage probability and
spectral efficiency (SE) versus user data rate requirement.
It clearly points out that NOMA HetNet outperforms one-
tier NOMA as well as OMA HetNet from Fig.3(a) and
Fig.3(b) in terms of both outage performance and spectral
efficiency. The main reason is that NOMA HetNet combines
the advantages of NOMA technique and heterogeneous net-
works, which can not only improve the spectral efficiency
by using non-orthogonal access manner, but also reduce
the outage probability by offloading overfull users to the
small cell. Compared with one-tier NOMA network, OMA
HetNet system improves the spectral efficiency by shortening
10 12 14 16 18 20 22 24 26 28 30
transmit power of SBS (dBm)
10-2
outage probability
(a)
NOMA HetNet
OMA HetNet
NOMA system
10 12 14 16 18 20 22 24 26 28 30
transmit power of SBS (dBm)
15
20
25
30
spectral efficiency (bit/s/Hz)
(b)
NOMA HetNet
OMA HetNet
NOMA system
10 12 14 16 18 20 22 24 26 28 30
transmit power of SBS (dBm)
10-5
outage probability
(c)
MUE in NOMA HetNet
SUE in NOMA HetNet
MUE in OMA HetNet
SUE in OMA HetNet
10 12 14 16 18 20 22 24 26 28 30
transmit power of SBS (dBm)
6
8
10
12
14
16
spectral efficiency (bit/s/Hz)
(d)
macrocell in NOMA HetNet
smallcell in NOMA HetNet
macrocell in OMA HetNet
smallcell in OMA HetNet
FIGURE 4. As P1= 20dB,U1= 5,U2= 3 and Rth = 2Mbit/s, (a) and (b)
respectively explore the influence of varying transmit power of SBS on the
overall performance in term of outage probability and spectral efficiency; (c)
and (d) detailedly show the curves of outage probability and spectral efficiency
for different cell versus transmit power of SBS, respectively.
the distance between transmitter and receivers, but at the
cost of worse outage performance due to the introduction
of inter-tier interference. Besides, as shown in Fig.3(c), the
outage performances of MUE and SUE decline gradually
with the increase of data rate requirement for both NOMA
HetNet and OMA HetNet. While the outage performance
of MUE in NOMA HetNet always outperforms that in O-
MA one, the outage performance of SUE behaves worse
in NOMA as 0.856Mbit/s ≤Rth ≤2Mbit/s because OMA
can provide adequate resources in this region. Further, as
shown in Fig.3(d), NOMA HetNet acquires much higher
SE compared with OMA both for macrocell and small-
cell. Note that for the macrocell, the SE remains unchanged
as Rth <1.5Mbit/s and deteriorates significantly when
Rth >1.5Mbit/s, which makes sense since some users have
to be abandoned as the data rate user data rate requirement is
higher due to the limited radio resources.
With the increase of the transmit power of SBS, the system
performance of one-tier NOMA network is almost unchange
as illustrated in Fig.4(a) and Fig.4(b), since the transmit
power of SBS is extremely small compared with that of
6VOLUME 4, 2016

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI
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D. Ni et al.: Power Allocation for Downlink NOMA Heterogeneous Networks
2345678
the number of macrocell users
10-2
outage probability
(a)
NOMA HetNet
OMA HetNet
NOMA system
2345678
the number of smallcell users
10-2
outage probability
(b)
NOMA HetNet
OMA HetNet
NOMA system
2345678
the number of macrocell users
10-2
outage probability
(c)
macrocells in NOMA HetNet
smallcells in NOMA HetNet
macrocells in OMA HetNet
smallcells in OMA HetNet
2345678
the number of smallcell users
10-2
outage probability
(d)
macrocells in NOMA HetNet
smallcells in NOMA HetNet
macrocells in OMA HetNet
smallcells in OMA HetNet
FIGURE 5. Outage probability comparison of three systems with varying
number of users as P1= 20W, P2= 0.1Wand Rth = 2Mbit/s. (a) and (c)
reveal the influence of varying number of macrocell users on the outage
probability with U2= 3; (b) and (d) show the curves of outage probability
versus the varying number of small users with U1= 5.
MBS. The influences of the increasing transmit power of
SBS on heterogeneous networks are represented detailedly
in Fig.4(c) and Fig.4(d). As illustrated in Fig.4(c), the outage
probability of MUE increases gradually with the growing
SBS transmit power in both systems, while NOMA HetNet
performs much better than OMA HetNet. Meanwhile, the
outage performance of SUE improves with the increase of
SBS transmit power in both NOMA and OMA HetNet.
Obviously, the slope of the curve of SUE in OMA HetNet
is greater than that of MUE in OMA HetNet, which can
provide a perfect explanation of the cause of saturation point
in Fig.4(a). Besides, the outage performance of SUE in OMA
HetNet outperforms that in NOMA HetNet when the SBS
transmit power is greater than 20dBm. In particular, as shown
in Fig.4(d), the SE of small-cell in OMA HetNet is also
superior to that of NOMA HetNet as P2≥28dBm, which
means that the influence of SBS transmit power on SE of
NOMA HetNet exerts less due to the fact that more wide
bandwidth is utilized in NOMA HetNet.
The outage probability comparison of three systems with
the varying user number is depicted in Fig.5. It is easy to
2345678
the number of macrocell users
15
20
25
spectral efficiency (bit/s/Hz)
(a)
NOMA HetNet
OMA HetNet
NOMA system
2345678
the number of smallcell users
20
25
30
spectral efficiency (bit/s/Hz)
(b)
NOMA HetNet
OMA HetNet
NOMA system
2345678
the number of macrocell users
10
12
14
16
18
spectral efficiency (bit/s/Hz)
(c)
macrocells in NOMA HetNet
smallcells in NOMA HetNet
macrocells in OMA HetNet
smallcells in OMA HetNet
2345678
the number of smallcell users
10
12
14
16
spectral efficiency (bit/s/Hz)
(d)
macrocells in NOMA HetNet
smallcells in NOMA HetNet
macrocells in OMA HetNet
smallcells in OMA HetNet
FIGURE 6. Spectral efficiency comparison with varying number of users as
P1= 20W, P2= 0.1Wand Rth = 2Mbit/s. (a) and (c) illustrate the spectral
efficiency versus varying number of macrocell users as U2= 3; (b) and (d)
represent the curves of spectral efficiency with the varying number of smallcell
users as U1= 5.
observe that with the increasing number of MUEs or SUEs,
the outage performances of three systems gradually decline
as illustrated in Fig.5(a) and Fig.5(b). In particular, as shown
in Fig.5(c) and Fig.5(d), the outage performances of both
MUE and SUE decline gradually as NOMA scenario is
employed since more power would be consumed to support
the growing number of users but bring about serious inter-tier
interference. Further, while NOMA HetNet always performs
better than OMA HetNet in terms of the MUE outage perfor-
mance as shown in Fig.5(c), its outage performance of small-
cell user can only surpass that of OMA when the number
of MUE is less than 4due to the multi-user interference.
In Fig.5(d) where U1= 5, with the growing SUE number,
the outage probability of SUE increases sharply and that
of MUE declines slightly in OMA HetNet. However, for
NOMA HetNet, the outage performances of both MUE and
SUE decrease slightly as the SUE number increases, and
the outage performance of SUE in NOMA HetNet cannot
outperform OMA one until U2≥3.
Fig.6 shows the spectral efficiency with varying number
of users. As shown in Fig.6(a) and Fig.6(b), the spectral
VOLUME 4, 2016 7

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D. Ni et al.: Power Allocation for Downlink NOMA Heterogeneous Networks
5 6 7 8 9 10 11 12 13 14 15
number of subchannel
10-4
10-3
10-2
10-1
100
outage probability
MUE in NOMA HetNet
SUE in NOMA HetNet
MUE in OMA HetNet
SUE in OMA HetNet
(a)
5 6 7 8 9 10 11 12 13 14 15
number of subchannel
9
10
11
12
13
14
15
16
17
spectral efficiency (bit/s/Hz)
macrocell in NOMA HetNet
smallcell in NOMA HetNet
macrocell in OMA HetNet
smallcell in OMA HetNet
(b)
FIGURE 7. Illustration of the outage probability and spectral efficiency with
varying number of sub-channel as P1= 20W, P2= 0.1W,U1= 5 and
U2= 3 and Rth = 2Mbit/s. (a) outage probability versus varying number of
sub-channel; (b) spectral efficiency versus varying number of sub-channel.
efficiency of one-tier NOMA network increases gradually
with the increasing number of MUEs, but declines with the
increasing number of SUEs. The essential reason is that the
edge users (smallcell users) always require more transmit
power but produce less data rate, instead the inner users
(macrocell users) consume less transmit power but can bring
more data rate. Besides, from Fig.6(c) and Fig.6(d), we can
see that in OMA HetNet, with the increase of the user number
in one cell, its SE would fluctuate while that of the other
cell would remain constant. The main reason is that the users
with worse channel condition are interrupted sequentially due
to the restriction of transmit power and spectrum resource.
In general, the NOMA HetNet possesses a greater spectral
efficiency compared with OMA HetNet because NOMA
principle could make full use of the spectrum resource.
The outage performance and SE versus varying sub-
channel number are depicted in Fig.7. Because all sub-
channels are utilized to accommodate multiple users, the
available bandwidth in NOMA HetNet linearly increases
with the growth of sub-channel number. As we can see from
Fig.7(a), with the increasing number of sub-channels, the
outage performances of MUE and SUE in both NOMA and
OMA HetNet can be improved. Specifically, as the number
of sub-channel is greater than 8, the outage performance of
SUE in OMA HetNet surpasses that of NOMA HetNet. As
shown in Fig.7(b), regardless of which transmission principle
is adopt in heterogeneous network, the spectral efficiency of
small-cell gradually increases with the growing number of
sub-channels. However, the influence of sub-channel number
on the spectral efficiency of macrocell in NOMA HetNet
is extremely finite which brings about a slight reduction in
spectral efficiency of macrocell with the increasing number
of sub-channels. Similarly, the curve of spectral efficiency of
macrocell in OMA HetNet declines firstly to a saddle point,
and then gradually increases. The main reason is that as the
number of sub-channels is more, the interference experienced
by each sub-channel becomes smaller so that the spectral
efficiency of macrocell will be improved gradually with the
increasing number of sub-channels.
V. CONCLUSIONS
By exploiting spatial diversity and multi-user diversity re-
spectively, heterogeneous networks and NOMA technique
are two essential strategies to enhance the spectral efficien-
cy and improve the overall system performance for next-
generation wireless communication networks. In this paper,
we develop a novel heterogeneous network in which NO-
MA technology is employed at macrocell and small-cell. To
mitigate the more complicated interference and maximize
the overall throughput of this NOMA HetNet subjected to
the constraints of the user QoS demand and total transmit
power of BSs, we formulate a power allocation problem
which proves to be an NP-hard problem. To deal with this
optimization problem, we propose a user scheduling scheme
and iterative power control algorithm to capture a suboptimal
solution. Simulation results demonstrate that compared with
conventional OMA HetNet and one-tier NOMA network, the
system performance of NOMA HetNet with the proposed
radio resource management scheme performs much better in
terms of outage performance and spectral efficiency.
.
APPENDIX A VERIFICATIONS OF THEOREM I
The Theorem I will be demonstrated by contradiction. First-
ly, we assume ρ0
i={ρ0
i,1, ρ0
i,2,· · · , ρ0
i,Ui}is the optimal
solution of optimization problem (P1) and the following
strict inequalities exist for UE-(i, k).
ρ0
i,k −
k−1
X
u=1
ρ0
i,u!Pigi,k−1> Pdif f ,(16)
and
ρ0
i,kPigi,k −Ith
i,k k−1
X
u=1
ρ0
i,uPigi,k + 1!>0.(17)
8VOLUME 4, 2016

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D. Ni et al.: Power Allocation for Downlink NOMA Heterogeneous Networks
Hence, the sum rate of users from UE-(i, 1) to UE-(i, k)
can be formulated as
Tk(ρ0
i) =
k
X
m=1
Ri,m
= log21 + ρ0
i,1Pigi,1
+log2 1 + ρ0
i,2Pigi,2
ρ0
i,1Pigi,2+ 1!+· · ·
+ log2



1 + ρ0
i,kPigi,k
k−1
P
u=1
ρ0
i,j Pigi,k + 1




= log2 ρ0
i,1Pigi,1+1
ρ0
i,1Pigi,2+1!+log2"ρ0
i,1+ρ0
i,2
Pigi,2+1
ρ0
i,1+ρ0
i,2
Pigi,3+1#+
· · · + log2



k−1
P
u=1
ρ0
i,j Pigi,k−1+ 1
k−1
P
u=1
ρ0
i,j Pigi,k + 1




+ log2" k
X
u=1
ρ0
i,j !Pigi,k + 1#.
(18)
Let ρ00
i={ρ0
i,1,· · · , ρ0
i,k−2, ρ00
i,k−1, ρ00
i,k, ρ0
i,k+1,· · · , ρ0
i,Ui}
be a feasible solution of optimization problem (P1) where
ρ00
i,k =ρ0
i,k −∆, ρ00
i,k−1=ρ0
i,k−1+ ∆ which makes at least
one equality of (C7.3) and (8) hold.
Then we can get the increment of sum rate as
Tk(ρ00
i)−Tk(ρ0
i)=log2











k−1
P
j=1
ρ0
i,j +∆!Pigi,k−1+ 1
k−1
P
j=1
ρ0
i,j +∆!Pigi,k +1











−log2











k−1
P
j=1
ρ0
i,j !Pigi,k−1+ 1
k−1
P
j=1
ρ0
i,j !Pigi,k + 1











= log2λ+ ∆Pigi,k−1
λ+ ∆Pigi,k ,
(19)
where λ= [Pk−1
j=1 ρ0
i,j Pigi,k−1+ 1][Pk−1
j=1 ρ0
i,j Pigi,k + 1]
+∆Pigi,k−1Pk−1
j=1 ρ0
i,j Pigi,k. Due to ∆Pigi,k−1>∆Pigi,k,
we can get
Tk(ρ00
i)−Tk(ρ0
i)>0.(20)
Additionally, since the total transmit power of BS iis un-
change, it would not affect the performance of another cell
j, j 6=i. Therefore we can see that the achievable throughput
Tk(ρ0
i)is not maximum, which is contradictory with the
original assumption. Then the Theorem I is proved.
APPENDIX B VERIFICATIONS OF THEOREM II
According to Theorem I, for any user k, k ∈ {2,3,· · · , Ui},
at least one equality holds between the two inequalities
(C9.3) and (8). If the inequality (C9.3) is equation, i.e.,
ρi,k −
k−1
X
u=1
ρi,u!Pigi,k−1=Pdif f .(21)
After some algebraic operations, the power allocation ρ(1)
i,k
is expressed as:
ρ(1)
i,k =1
2 Pdiff
˜
Pigi,k−1
+ 1 −
Ui
X
u=k+1
ρi,u!.(22)
Similarly, as the inequality (8) is equation, the power
allocation ρ(2)
i,k is given by:
ρ(2)
i,k =Ith
i,k
1 + Ith
i,k 1−
Ui
X
u=k+1
ρi,u +1
˜
Pigi,k !.(23)
Due to the constraints (C9.3) and (8) should be satis-
fied simultaneously, the optimal power allocation for user
k, k ∈ {2,3,· · · , Ui}is ρ∗
i,k = max{ρ(1)
i,k , ρ(2)
i,k }. Therefore,
if ρ∗
i,k =ρ(1)
i,k , we can get
Ith
i,k
1+ Ith
i,k 1−
Ui
X
u=k+1
ρi,u +1
˜
Pigi,k
!≤1
2 Pdiff
˜
Pigi,k−1
+1 −
Ui
X
u=k+1
ρi,u
!.
(24)
After some algebraic operations, above inequality (24) can
be further simplified to
Ith
i,k ≤ Pdiff
Pigi,k−1+ 1 −
Ui
P
u=k+1
ρi,u!
2
Pigi,k−1+ 1 −
Ui
P
u=k+1
ρi,u −Pdiff
Pigi,k !.(25)
Thus, we can get that ρ∗
i,k =ρ(1)
i,k if and only if the
inequality (25) holds, otherwise ρ∗
i,k =ρ(2)
i,k .
APPENDIX C VERIFICATIONS OF THEOREM III
The users with better channel condition should be satisfied
firstly since they have the higher priority. Therefore, to fulfill
the SINR requirement of UE-(i, 1) with fixed transmit power
Pj, j 6=i, the minimum power allocation pmin
i,1is given by:
pmin
i,1=Ith
i,1
gi,1
.(26)
However, for the user k, k ∈ {2,3,· · · , Ui}, at least one
equality holds between the two inequalities (C9.3) and (8)
according to Theorem I. If the inequality (C9.3) is equation,
i.e.,
pi,k −
k−1
X
u=1
pi,u!gi,k−1=Pdif f .(27)
VOLUME 4, 2016 9

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI
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D. Ni et al.: Power Allocation for Downlink NOMA Heterogeneous Networks
After some algebraic operations, the minimum power allo-
cation for UE-(i, k),p0
i,k, is expressed as:
p0
i,k =Pdiff
gi,k−1
+
k−1
X
u=1
pmin
i,u .(28)
Similarly, as the inequality (8) is an equation, the minimum
power allocation p00
i,k is given by:
p00
i,k =Ith
i,k k−1
X
u=1
pmin
i,u +1
gi,k!.(29)
Since the constraints (C9.3) and (8) should be satisfied si-
multaneously, the minimum power allocation for user k, k ∈
{2,3,· · · , Ui}is pmin
i,k = max{p0
i,k, p00
i,k}. Therefore, the
minimum power allocation for each user can be successively
calculated along with the ascending order of normalized
channel condition for user set Ui.
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DADONG NI received the B.S. degree in Elec-
tronic and Information Engineering from In-
formation Engineering University of the PLA,
Zhengzhou, China, in 2010, and M.S. degree in
Information and Communication Systems from
Southwest Jiaotong University, Chengdu, China,
in 2013. He is currently pursuing the Ph.D. degree
in Information and Communication Systems at the
key Lab of Information Coding and Transmission,
Southwest Jiaotong University, Chengdu, China.
His research interests include non-orthogonal multiple access, heteroge-
neous networks and radio resource management.
10 VOLUME 4, 2016

2169-3536 (c) 2018 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEE permission. See
http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI
10.1109/ACCESS.2018.2835568, IEEE Access
D. Ni et al.: Power Allocation for Downlink NOMA Heterogeneous Networks
LI HAO received the B.S., M.S. and Ph.D. degree
from Tianjin University, University of Electronic
Science and Technology of China and Southwest
Jiaotong University, China, in 1993, 1996 and
2003, respectively. From 2005 to now, she works
in Southwest Jiaotong University, Chengdu, Chi-
na. She is currently a professor of the School of
Information Science and Technology, Southwest
Jiaotong University, and serves as a director of
Dean’s Office of Southwest Jiaotong University.
She served as the chair of IEEE Chengdu Section. Her research interests
include 5G technologies, communication and information systems, wireless
transmission and high-mobility communication.
QUANG THANH TRAN received the B.S. and
M.S. degree in telecommunication engineering
from University of Transport and Communication-
s, Hanoi, Vietnam, in 2005 and 2009, respectively,
and the M.S. degree in Information and Commu-
nication Systems from Southwest Jiaotong Uni-
versity, Chengdu, China, in 2012. From 2005 to
now, he is a Lecturer with the Faculty of Electrical
and Electronic Engineering of University of Trans-
port and Communications, Hanoi, Vietnam. He is
currently pursuing the Ph.D. degree in Information and Communication
Systems at the key Lab of Information Coding and Transmission, Southwest
Jiaotong University, Chengdu, China. His research interests include wireless
traffic prediction, high mobility wireless communication design.
XIAOMIN QIAN received the B.S. degree in Elec-
tronic and Information Engineering from the PLA
Information Engineering University, Zhengzhou,
China, in 2009. She is currently pursuing the Ph.D.
degree in Communication and Information System
with the Key Laboratory of Information Coding
and Transmission, Southwest Jiaotong University,
Chengdu, China. Her research interests include
wireless communication theory, with particular
focus on cognitive radio, spectrum sensing and
access and vehicular networks.
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