Content uploaded by Wali Ullah Khan
Author content
All content in this area was uploaded by Wali Ullah Khan on Oct 12, 2019
Content may be subject to copyright.
applied
sciences
Article
Joint User Pairing, Channel Assignment and Power
Allocation in NOMA based CR Systems
Zain Ali 1, Yanyi Rao 2,* , Wali Ullah Khan 3and Guftaar Ahmad Sardar Sidhu 1,*
1Department of Electrical and Computer Engineering, COMSATS University Islamabad,
Islamabad 44000, Pakistan; zainalihanan1@gmail.com
2School of Computer Science and Educational Software, Guangzhou University, Guangzhou 510006, China
3School of Information Science and Engineering, Shandong University, Qingdao 266237, China;
waliullahkhan30@gmail.com
*Correspondence: yanyirao0824@163.com (Y.R.); guftaarahmad@comsats.edu.pk (G.A.S.S.)
Received: 22 August 2019; Accepted: 2 October 2019; Published: 12 October 2019
Abstract:
The fifth generation (5G) wireless communication systems promise to provide massive
connectivity over the limited available spectrum. Various new transmission paradigms such as
non-orthogonal multiple access (NOMA) and cognitive radio (CR) have emerged as potential 5G
enabling technologies. These techniques offer high spectral efficiency by allowing multiple users to
communicate on the same frequency channel, simultaneously. A combination of both techniques
may further enhance the performance of the system. This work aims to maximize the achievable
rate of a multi-user multi-channel NOMA based CR system. We propose an efficient user pairing,
channel assignment and power optimization technique for the secondary users while the performance
of primary users is guaranteed through interference temperature limits. The results show that, at
small values of the power budget or high interference threshold, optimizing channel allocation
and user pairing proves to be more beneficial than optimal power allocation to the user pairs.
The proposed joint optimization technique provides promising results for all values of the power
budget, interference threshold and rate requirement of the communicating users.
Keywords:
non-orthogonal multiple access; underlay communication; cooperative communication;
cognitive radio
1. Introduction
Orthogonal multiple access (OMA) techniques have proven their efficiency in the fourth
generation (4G) of communication systems [
1
,
2
]. However, the high spectral efficiency requirements
of the fifth generation (5G) of communication systems call for better technologies. Recently,
non-orthogonal multiple access (NOMA) [
3
] has come forward and been shown to outperform OMA [
4
].
Some common techniques of NOMA include index modulation [
5
,
6
], code division [
7
], and power
domain [
8
]. The power domain NOMA is considered to be the backbone of the 5G communication
networks because of least computational complexity and excellent performance. Hence, this paper
focuses on power domain type of NOMA. In NOMA, the signals of different users are transmitted
simultaneously on the same channel with different power levels. Then, on reception successive
interference cancellation (SIC) is employed to remove the interference where possible. In NOMA,
each channel is shared by multiple users. Thus, the spectrum efficiency of NOMA systems is very
high [
9
]. In multi user NOMA systems the complexity and delay because of SIC increases rapidly with
the number of users sharing a channel. Hence, in a practical scenario, it becomes more beneficial to
consider a combination of NOMA and OMA where the available spectrum is divided into multiple
channels and each channel is shared by multiple users in a NOMA fashion. Similarly, the cognitive
Appl. Sci. 2019,9, 4282; doi:10.3390/app9204282 www.mdpi.com/journal/applsci
Appl. Sci. 2019,9, 4282 2 of 17
radio (CR) also offers high spectral efficiency. The CR employs the idea of spectrum reuse to offer
high spectral efficiency. In CR, the licensed primary users (PUs) and unlicensed secondary users
(SUs) communicate on the same channel, simultaneously. However, the SUs are required to keep the
transmission power at a low level so that the PUs would not face harmful interference [10].
Optimization of resource allocation can significantly enhance the performance of a communication
systems [
11
]. The problem of optimizing resource allocation in CR and NOMA systems have been
considered multiple times in the literature. The authors of [
12
] optimized power allocation to
minimize the energy consumption in a NOMA system. In [
13
], the authors allocated power in
a NOMA system to guarantee the minimum quality of service (QoS) requirement of every user.
The authors of [
14
] proposed a technique for energy efficiency maximization in NOMA systems.
In [
15
], the authors studied power allocation in NOMA systems to maximize the secrecy rate of
communicating users. The problem of maximizing sum rate in a NOMA system was considered
by [
16
]. However, the work considered just two user NOMA case and did not guarantee the rate
requirement of the users. Considering the problem of achieving fairness in NOMA systems, the authors
of [
17
] proposed a sequential quadratic programming based solution. For CR systems, the authors
of [
18
] optimized power loading for maximizing the energy efficiency of the communication system.
In [
19
], the authors optimized power allocation to enhance the security of a CR system with a secondary
receiver and one eves dropper. The authors of [
12
–
17
] considered single channel communication that
cannot be directly mapped to multi channel systems. In NOMA, the delay of SIC increases with the
number of users, hence, it is not feasible for all the users in the systems to communicate on a single
channel. Thus, the solutions provided in [
12
–
17
] lack practical application. A CR system is expected to
accommodate multiple SUs. However, in [
18
,
19
], the authors considered single SU. Some works in the
literature [
20
,
21
] have also consider multi user CR systems however did not consider the optimization
of power allocation.
Joint optimization of power and channel allocation can further enhance the performance of the
systems. The authors of [
22
] optimized power and channel allocation in NOMA systems to minimize
the power consumption of the network. [
23
] considered multi user NOMA system for energy efficiency
maximization. The problem of sum rate maximization in in multi user NOMA systems was considered
by [
24
]. On the other hand, considering CR systems, the authors of [
25
] optimized power loading and
channel allocation for achieving fairness among the SUs. [
26
] considered optimization of resource
allocation for energy efficiency maximization in CR systems. The problem of maximizing the sum rate
in a CR system was solved in [
27
]. Integration of the NOMA into cognitive radio systems can result in
further improvement in the network’s performance.
Some works in the literature have also considered resource allocation for NOMA based CR
systems. The authors of [
28
] optimized power allocation to maximize the number of of admitted SUs in
the system. [
29
] discussed sum rate maximization in a NOMA based CR system. The works reported in
the literature have many deficiencies. The NOMA problems considered in [
12
,
14
–
16
,
22
,
24
,
28
] ignored
the required minimum gap in received power for SIC. Similarly, the frameworks proposed in [
16
,
18
,
19
,
24
,
27
] did not consider the rate requirements of the communicating nodes. Some works [
23
,
24
,
26
,
28
]
did not transform the problem to a convex form so the optimality of the solution cannot be guaranteed.
Similar to the systems in [
12
–
19
], the NOMA based CR system considered in [
29
] consists of a single
channel and the solution technique cannot be mapped to a multi channel scenario. In this work, we aim
to maximize the sum rate in a multi user NOMA based underlay CR system. The main contribution of
this work are listed below:
•
A problem is formulated to maximize sum rate of a multi user NOMA based underlay CR system.
•
Unlike previous works, the resource allocation is optimized while accounting for the rate
requirement of each user and NOMA constraint of sufficient gap in received power for SIC. Further,
the constraints of power budget and interference temperature are also taken into consideration.
•
The original non convex optimization problem is transformed into a convex form and the closed
form expressions for optimal power allocation are derived.
Appl. Sci. 2019,9, 4282 3 of 17
•An efficient technique for the user pairing and channel allocation is proposed.
•Simulation results thoroughly discuss the performance of the proposed technique.
The remainder of the paper is organized as follows. The system model and problem formulation
is presented in Section 2. Section 3provides the proposed solution technique. The simulation results
are discussed in Section 4. Finally, the work is concluded in Section 5.
2. System Model and Problem Formulation
We consider a cooperative NOMA CR system where a secondary transmitter (ST) communicates
with
W
number of secondary receivers (SRs) in the presence of primary receivers (PRs), as shown in
Figure 1. The available spectrum is divided into
W/
2 channels and each channel is shared by two
NOMA users. (The hardware complexity and delay due to SIC increase with the number of users per
channel. Thus, the proposed system model considers two users per channel [
30
].) Without loss of
generality, we consider the
W
users are sorted in descending order of their channel gains and divided
into two sets of equal size. The set containing first
W
2
users with larger values of channel gains is
called the set of strong users and is represented as
A
. Similarly, the users in the second set are called
weak users because they have weak channel conditions compared to the nodes in the set of strong
users; the set of weak user is denoted as
B
. On each channel, a strong user is paired with a weak user.
Then, on reception the strong user employs SIC to decode its signal without any interference from
the weak user, whereas the weak user faces interference because of the strong users signal. The gains
of the
c
th channel from ST to
n
th strong user and
i
th weak user are represented as
|hn,c|2
and
|hi,c|2
,
respectively. The channel gain from ST to the PRs at the
c
th channel is denoted as
|fc|
. To facilitate the
mathematical formulation of the problem, a binary variable xn,i,cis introduced such that:
xn,i,c=
1, when nth strong user is paired with ith weak user and are allocated cth channel,
∀n∈ A,i∈ B
0, otherwise,
PR
ST
|hn,c|2
|hi,c|2
|fc|2
ith weak user
nth strong user
Figure 1. Considered system model.
We aim to maximize the sum rate of the NOMA system subject to the interference temperature of
the primary network, QoS guarantee of each user, limited battery power at the BS and sufficient gap in
the received powers for SIC. The problem can be mathematically written as:
Appl. Sci. 2019,9, 4282 4 of 17
P1:
max
xn,i,c,Pn,i,c,Sn,i,c
W/2
∑
n=1
W/2
∑
i=1
W/2
∑
c=1
xn,i,c log2 1+Pn,i,c|hn,c|2
σ2!+log2 1+Sn,i,c|hi,c|2
Pn,i,c|hi,c|2+σ2!!,∀n∈ A,i∈ B,(1)
s.t.
W/2
∑
n=1
W/2
∑
i=1
xn,i,c(Sn,i,c|hn,c|2−Pn,i,c|hn,c|2)≥ψ,∀c,n∈ A,i∈ B,(2)
W/2
∑
n=1
W/2
∑
i=1
xn,i,c(Pn,i,c+Sn,i,c)|fc|2≤Ith ,∀c,n∈ A,i∈ B,(3)
W/2
∑
n=1
W/2
∑
i=1
W/2
∑
c=1
xn,i,c(Pn,i,c+Sn,i,c)≤PT,∀n∈ A,i∈ B,(4)
W/2
∑
i=1
W/2
∑
c=1
xn,i,clog2 1+Pn,i,c|hn,c|2
σ2!≥RT,∀n,n∈ A,i∈ B,(5)
W/2
∑
n=1
W/2
∑
c=1
xn,i,clog2 1+Sn,i,c|hi,c|2
Pn,i,c|hi,c|2+σ2!≥RT,∀i,n∈ A,i∈ B,(6)
W/2
∑
n=1
W/2
∑
c=1
xn,i,c=1, ∀i,n∈ A,i∈ B,(7)
W/2
∑
i=1
W/2
∑
c=1
xn,i,c=1, ∀n,n∈ A,i∈ B,(8)
W/2
∑
n=1
W/2
∑
i=1
xn,i,c=1, ∀c,n∈ A,i∈ B.(9)
The objective of the problem is given in Equation (1) where
σ2
denotes the variance of additive
white Gaussian noise (AWGN),
Pn,i,c
is the power allocated for the signal of
n
th strong user paired
with
i
th weak user at
c
th channel and
Sn,i,c
represents the power of the
i
th weak user paired with
n
th
strong user at the
c
th channel. The first term in the objective represents the rate of the strong user and
the second term is the rate of the weak user paired with the corresponding strong user. For SIC, a
sufficient gap in the received powers of the signals of the strong user and weak user is required and is
ensured by Equation (2). To protect the PRs from harmful interference, we have Equation (3) where
Ith
represents the interference threshold. The constraint in Equation (4) guarantees that the power
allocation at the ST follows the power budget where
PT
is the available power at the ST. The minimum
rate requirement (
RT
) of each user is ensured by Equations (5) and (6). The constraint in Equation (7)
guarantees that each weak user pairs with one and only one strong user and is allocated one channel.
It is also required that every strong user must pair with only one weak user and communication on a
single channel, this demand is mathematically written as in Equation (8). Finally, Equation (9) makes
sure that each channel accommodate only one user pair.
3. Proposed Solution
The problem in
P1
is complex, non-convex and is very hard to solve for optimal solution because
of high inter-dependency and inseparable
Sn,i,c
. To make the problem more tractable, we propose
to allocated power in two steps. First, to distribute the available power in all user pairs and then
distribute the power among the users in the pair. The power allocated to the user pair consisting of
n
th
strong user and
i
th weak user at
c
th channel is denoted as
Qn,i,c
. Then, the fractions of
Qn,i,c
allocated
for the signal of strong user is denoted as
αn,i,c
, and
(
1
−αn,i,c)
represents the fraction allocated to
the weak user. Thus, the transmit powers are given by
Pn,i,c=αn,i,cQn,i,c
and
Sn,i,c= (
1
−αn,i,c)Qn,i,c
.
After this, the transformed problem is given as:
Appl. Sci. 2019,9, 4282 5 of 17
P2:
max
xn,i,c,Qn,i,c,αn,i,c
W/2
∑
n=1
W/2
∑
i=1
W/2
∑
c=1
xn,i,c log2
1+αn,i,cQn,i,c|hn,c|2
σ2!+log2
1+(1−αn,i,c)Qn,i,c|hi,c|2
αn,i,cQn,i,c|hi,c|2+σ2!!,∀n∈ A,i∈ B,(10)
s.t.
W/2
∑
n=1
W/2
∑
i=1
xn,i,c((1−αn,i,c)Qn,i,c|hn,c|2−αn,i,cQn,i,c|hn,c|2)≥ψ,∀c,n∈ A,i∈ B,(11)
W/2
∑
n=1
W/2
∑
i=1
xn,i,cQn,i,c|fc|2≤Ith ∀c,n∈ A,i∈ B,(12)
W/2
∑
n=1
W/2
∑
i=1
W/2
∑
c=1
xn,i,cQn,i,c≤PT,∀n∈ A,i∈ B,(13)
W/2
∑
i=1
W/2
∑
c=1
xn,i,clog2 1+αn,i,cQn,i,c|hn,c|2
σ2!≥RT,∀n,n∈ A,i∈ B,(14)
W/2
∑
n=1
W/2
∑
c=1
xn,i,clog2 1+(1−αn,i,c)Qn,i,c|hi,c|2
αn,i,cQn,i,c|hi,c|2+σ2!≥RT,∀i,n∈ A,i∈ B,(15)
0≤αn,i,c≤1, ∀c,n∈ A,i∈ B.(16)
The problem in
P2
is still non-convex because of Equations (10) and (15). To convert the problem
in convex form, we substitute
βn,i,c=αn,i,cQn,i,c
, which makes the objective a convex function in
βn,i,c
and
Qn,i,c
(a discussion on the convexity of
P2
and
P3
is given in Appendix A). In addition, to transform
the problem into a standard minimization problem, we multiply the objective by
−
1. The problem
after transformation is:
P3:
min
xn,i,c,Qn,i,c,βn,i,c
W/2
∑
n=1
W/2
∑
i=1
W/2
∑
c=1
−xn,i,c log2 1+βn,i,c|hn,c|2
σ2!+log2 1+(Qn,i,c−βn,i,c)|hi,c|2
βn,i,c|hi,c|2+σ2!!,∀n∈ A,i∈ B,(17)
s.t.
W/2
∑
n=1
W/2
∑
i=1
xn,i,c((Qn,i,c−βn,i,c)|hn,c|2−βn,i,c|hn,c|2)≥ψ,∀c,n∈ A,i∈ B,(18)
W/2
∑
n=1
W/2
∑
i=1
xn,i,cQn,i,c|fc|2≤Ith ∀c,n∈ A,i∈ B,(19)
W/2
∑
n=1
W/2
∑
i=1
W/2
∑
c=1
xn,i,cQn,i,c≤PT,∀n∈ A,i∈ B,(20)
W/2
∑
i=1
W/2
∑
c=1
xn,i,clog2 1+βn,i,c|hn,c|2
σ2!≥RT,∀n,n∈ A,i∈ B,(21)
W/2
∑
n=1
W/2
∑
c=1
xn,i,clog2 1+(Qn,i,c−βn,i,c)|hi,c|2
βn,i,c|hi,c|2+σ2!≥RT,∀i,n∈ A,i∈ B, (22)
βn,i,c≥0, ∀n∈ A,i∈ B. (23)
Although we have converted the objective of
P3
to a convex form, the problem is still non-convex
because of the constraint in Equation (22). We take advantage of the fact that Equation (22) is
equivalent to:
log2 1+
W/2
∑
n=1
W/2
∑
c=1
xn,i,c (Qn,i,c−βn,i,c)|hi,c|2
βn,i,c|hi,c|2+σ2!!≥RT,∀i,n∈ A,i∈ B, (24)
Appl. Sci. 2019,9, 4282 6 of 17
then we can transform Equation (24) into a linear function as:
W/2
∑
n=1
W/2
∑
c=1
xn,i,c((Qn,i,c−βn,i,c)|hi,c|2−(2RT−1)βn,i,c|hi,c|2)≥(2RT−1)σ2,∀i,n∈ A,i∈ B, (25)
Note that, if this technique were applied for transformation of Equation (15), it would result in
a non-convex function because
αn,i,cQn,i,c
makes the function non-convex. Similarly, we transform
Equation (21) to a linear function to reduce the computational complexity. After the conversion, the
constraint in Equation (21) is given by:
W/2
∑
i=1
W/2
∑
c=1
xn,i,cβn,i,c|hn,c|2≥(2RT−1)σ2,∀n,n∈ A,i∈ B, (26)
For the given value of
xn,i,c
, the problem is now convex. Hence, optimal solution can be obtained
by employing duality theory [31]. The dual problem is given below:
max
λi,µc,η,τn,θi
D(λi,µc,η,τn,θi), (27)
s.t. λi≥0, µc≥0, η≥0, τn≥0, θi≥0, ∀n∈ A,i∈ B.
The
D(λi
,
µc
,
η
,
τn
,
θi)
in Equation (28) is called the dual function and
λi
,
µc
,
η
,
τn
,
θi
are the dual
variables. The dual function is given as:
D(λi,µc,η,τn,θi) = min
Qn,i,c,βn,i,c
L(λi,µc,η,τn,θi,Qn,i,c,βn,i,c),∀n∈ A,i∈ B, (28)
where L(λi,µc,η,τn,θi,Qn,i,c,βn,i,c)is the Lagrangian of the problem and is written as:
L=−
W/2
∑
n=1
W/2
∑
i=1
W/2
∑
c=1
xn,i,clog2 1+βn,i,c|hn,c|2
σ2!+log2 1+(Qn,i,c−βn,i,c)|hi,c|2
βn,i,c|hi,c|2+σ2!+
W/2
∑
c=1
λi
(ψ−
W/2
∑
n=1
W/2
∑
i=1
xn,i,c(Qn,i,c|hn,c|2−2βn,i,c|hn,c|2)) +
W/2
∑
c=1
µc(
W/2
∑
n=1
W/2
∑
i=1
xn,i,cQn,i,c|fc|2−Ith)+
η(
W/2
∑
n=1
W/2
∑
i=1
W/2
∑
c=1
xn,i,cQn,i,c−PT) +
W/2
∑
n=1
τn((2RT−1)σ2−(
W/2
∑
i=1
W/2
∑
c=1
xn,i,cβn,i,c|hn,c|2)) + θi
((2RT−1)σ2−(
W/2
∑
n=1
W/2
∑
c=1
xn,i,c((Qn,i,c−βn,i,c)|hi,c|2−(2RT−1)βn,i,c|hi,c|2))),∀n∈ A,i∈ B. (29)
Simplifying Equation (29), we get:
L=
W/2
∑
n=1
W/2
∑
i=1
W/2
∑
c=1
xn,i,c −log2 1+βn,i,c|hn,c|2
σ2!−log2 1+(Qn,i,c−βn,i,c)|hi,c|2
βn,i,c|hi,c|2+σ2!−λi
(Qn,i,c|hn,c|2−2βn,i,c|hn,c|2) + µc(Qn,i,c|fc|2) + ηQn,i,c−τn(βn,i,c|hn,c|2)−θi((Qn,i,c−
βn,i,c)|hi,c|2−(2RT−1)βn,i,c|hi,c|2)!+
W/2
∑
i=1
λiψ−
W/2
∑
c=1
µcIth −ηPT+
W/2
∑
n=1
τn(2RT−1)σ2
+
W/2
∑
i=1
θi(2RT−1)σ2,∀n∈ A,i∈ B. (30)
Appl. Sci. 2019,9, 4282 7 of 17
Note that
∑W/2
i=1λiψ−∑W/2
c=1µcIth −ηPT+∑W/2
n=1τn(
2
RT−
1
)σ2+∑W/2
i=1θi(
2
RT−
1
)σ2
are constants,
thus can be ignored. The problem can be decomposed into following W3
8sub-problems:
min
βn,i,c,Qn,i,c −log2 1+βn,i,c|hn,c|2
σ2!−log2 1+(Qn,i,c−βn,i,c)|hi,c|2
βn,i,c|hi,c|2+σ2!−λi
(Qn,i,c|hn,c|2−2βn,i,c|hn,c|2) + µc(Qn,i,c|fc|2) + η(Qn,i,c)−τn(βn,i,c|hn,c|2)−θi
((Qn,i,c−βn,i,c)|hi,c|2−(2RT−1)βn,i,c|hi,c|2)!,∀n∈ A,i∈ B. (31)
As the problem is convex, we can apply Karush–Kuhn–Tucker (KKT):
−|hn,c|2
σ2+βn,i,c|hn,c|2−
−(σ2+βn,i,c|hi,c|2)−(Qn,i,c−βn,i,c)|hi,c|4
(σ2+βn,i,c|hi,c|2)2
(σ2+βn,i,c|hi,c|2) + (Qn,i,c−βn,i,c)|hi,c|2
σ2+βn,i,c|hi,c|2
+2λi|hn,c|2−τn|hn,c|2+θi|hi,c|2
+θi(2RT−1)|hi,c|2=0. (32)
Simplifying Equation (32), we get:
−|hn,c|2
σ2+βn,i,c|hn,c|2+|hi,c|2
βn,i,c|hi,c|2+σ2+2λi|hn,c|2−τn|hn,c|2+θi|hi,c|2+θi(2RT−1)|hi,c|2=0. (33)
Then, optimal value of βn,i,cis obtained as given below:
β∗
n,i,c= (−(|hi,c|2+|hn,c|2)σ2(|hn,c|2(2λi−τn) + 2RT|hi,c|2θi)±pΛn,i,c
(2|hi,c|2|hn,c|2(|hn,c|2(2λi−τn) + 2RT|hi,c|2θi)) !+
,∀n∈ A,i∈ B, (34)
where (v)∗=max(v, 0), and the value of Λn,i,cis given by:
Λn,i,c= ((−|hi,c|2+|hn,c|2)σ2(|hn,c|2(2λi−τn) + 2RT|hi,c|2θi)(|hn,c|2(|hn,c|2σ2(2λi−τn)+
|hi,c|2(4−2λiσ2+σ2τn)) + 2RT|hi,c|2(−|hi,c|2+|hn,c|2)σ2θi))),∀n∈ A,i∈ B,
Similarly, the value of Qn,i,cis derived as:
Q∗
n,i,c= −σ2
|hi,c|2+1
−|hn,c|2λi+η− |hi,c|2θi+|fc|2µc!+
,∀n∈ A,i∈ B. (35)
As now we have β∗
n,i,cand Q∗
n,i,c, we can calculate α∗as:
α∗
n,i,c=β∗
n,i,c
Q∗
n,i,c
,∀n∈ A,i∈ B. (36)
With this, the optimal values of Pn,i,cand Sn,i,care given by:
P∗
n,i,c=α∗
n,i,cQ∗
n,i,c,∀n∈ A,i∈ B. (37)
S∗
n,i,c= (1−α∗
n,i,c)Q∗
n,i,c,∀n∈ A,i∈ B. (38)
Appl. Sci. 2019,9, 4282 8 of 17
Until this point, we have ignored
xn,i,c
; now, the solution of following problem yields the solution
of xn,i,c:
min
xn,i,c
W/2
∑
n=1
W/2
∑
i=1
W/2
∑
c=1
Ψn,i,c, (39)
where
Ψn,i,c= −log2 1+β∗
n,i,c|hn,c|2
σ2!−log2 1+(Q∗
n,i,c−β∗
n,i,c)|hi,c|2
β∗
n,i,c|hi,c|2+σ2!−λi(Qn,i,c|hn,c|2
−2β∗
n,i,c|hn,c|2) + µc(Q∗
n,i,c|fc|2) + ηQ∗
n,i,c−τn(β∗
n,i,c|hn,c|2)−θi((Q∗
n,i,c−β∗
n,i,c)|hi,c|2−
(2RT−1)β∗
n,i,c|hi,c|2)!,∀n∈ A,i∈ B.
To solve the problem, we propose the technique provided in Algorithm 1.
Algorithm 1 User pairing and channel allocation.
1. Initialize x=zero W
2,W
2,W
2
2. Pair An
with
B(W/2)+1−n
,
∀n=
1, 2, 3...
W
2
, where
An
represents the
n
th user in the set of strong
users sorted in descending order of channel gains and
Bz
denotes the
z
th user in the sorted set of
all the weak users. Then, the nth user pair is given as ξn.
3. Set PAn=PBn=PT
W,∀n=1, 2, 3, ... W
2.
4. Calculate
the rate of each user pair (
ξn
) for every channel as
ϑξn,c=log2
1
+PAn|hAn,c|2
σ2!+
log2 1+PBW+1−n|hBW+1−n,c|2
PAn|hBW+1−n,c|2+σ2!.
5. Find lsuch that ϑξn,l== max(ϑξn,c)∀c=1, 2, 3... W
2.
6. Set xξn,l=1.
7. Remove user pair ξnand channel lfrom the search.
8. Repeat steps 2–7, W
2−1 times.
9. Return x∗
n,i,c.
We know that a user with better channel conditions requires less power to achieve the required
rate as compared to the user with bad channel conditions. Thus, if the very weak user is paired with
a very strong user, the strong user would only require a little power to satisfy its rate, thus leaving large
amount of available energy for the weak user. In this scheme, we pair the users such that the strongest
user is paired with the weakest user. In Step 1, we initialize a three-dimensional matrix
x
having size
W
2
in all dimensions. Then, in Step 2, we pair the users together such that the strongest user is paired
with the weakest user, the second strongest user is paired with the second weakest and so on. In Step 3,
to find the channel allocation, we first decide the available power equally among all the users. In Step
4, we calculate the rate of each user pair. Then, in Steps 5 and 6, we find the channels for which each
respective pair provides maximum rate and assign that channel to the user pair, respectively. The user
pair that has been allocated a channel is removed from the allocation process along with the allocated
Appl. Sci. 2019,9, 4282 9 of 17
channel. As there are
W
2
user pairs and channels, Steps 2–7 are repeated
W
2−
1 times because the last
user pair is automatically assigned the last remaining channel.
Now, it remains to solve the dual problem. We employ sub-gradient method [
32
] to solve the
problem for dual variables; the dual variable updates in the uth iteration are given by:
λu
i=λu−1
i+δ ψ−
W/2
∑
n=1
W/2
∑
i=1
xn,i,c(Qn,i,c|hn,c|2−2βn,i,c|hn,c|2)!,∀n∈ A,i∈ B,
µu
c=µu−1
c+δ W/2
∑
n=1
W/2
∑
i=1
xn,i,cQn,i,c|fc|2−Ith!,∀n∈ A,i∈ B,
ηu=ηu−1+δ W/2
∑
n=1
W/2
∑
i=1
W/2
∑
c=1
xn,i,cQn,i,c−PT!,∀n∈ A,i∈ B,
τu
n=τu−1
n+δ (2RT−1)σ2−
W/2
∑
i=1
W/2
∑
c=1
xn,i,cβn,i,c|hn,c|2!,∀n∈ A,i∈ B,
θu
i=θu−1
i+δ (2RT−1)σ2−
W/2
∑
n=1
W/2
∑
c=1
xn,i,c((Qn,i,c−βn,i,c)|hi,c|2−(2RT−1)βn,i,c|hi,c|2)
!,∀n∈ A,i∈ B,
where δis the step size.
4. Simulation Results
In this section, we demonstrate the performance of the proposed scheme. The comparison of the
following techniques is presented:
•Opt:
This refers to the joint power, user pairing and channel allocation technique presented in
Section 3.
•Fix-Qn,i,c:
In this case, we allocate equal amount of power to each user pair while keeping in
account the interference constraint. Then, we optimize
αn,i,c
and
xn,i,c
as proposed in Section 3.
The power allocation to the pairs in this case is given by:
Qn,i,c=min PT
W/2 ,Ith
|fc|2,∀c,∀n∈ A,i∈ B.
•Random-xn,i,c:
In this technique, a user from the set of strong users is paired with a weak user at
random, and then this pair is allocated a channel randomly. While the pairing and allocation is
random, we keep in account that a strong user must only pair with one weak user and vice versa.
Similarly, each channel is allocated to just one user pair and, further, a user pair cannot be assigned
more than one channel.
For the simulations, we considered Rayleigh fading channels and the values of
W
,
σ2
,
PT
,
ψ
,
RT
,
and Ith
were taken to be 10, 0.01, 10 W, 0.1 W and 1 b/s/hz and 1 W, respectively,
until specified otherwise.
The effect of
PT
on the sum rate of all the schemes is shown in Figure 2. It can be seen that an
increase in
PT
generally results in increasing the sum rate for all the schemes. However, after a certain
point, the positive impact of increase in
PT
on the rate reduces. This is because at this point the
interference generated by user pairs with better channels have reached
Ith
. Thus, no more power is
allocated to these pairs and the extra power is assigned to comparatively bad users. It can be seen
that in Opt when
PT≥
13 the sum rate does not change at all. At this point, the interference of
all user pairs has become equal to
Ith
. Hence, when
PT
increases, the power allocated to the users
remains unchanged. A similar trend can be seen in the case of Random-
xn,i,c
. The figure shows that
Opt outperforms all the other schemes. When
PT
is increased the interference generated by a user
Appl. Sci. 2019,9, 4282 10 of 17
pair may become equal to
Ith
. With further increases the interference of more and more user pairs
become equal to the threshold. Hence, no more power can be allocated for the transmissions of these
users. In the case of
Opt
and
Random −xn,i,c
, when the interference of pairs that offer higher rates
become equal to the threshold the remaining power is allocated to the users with comparatively bad
channel gains. However, Fix-
Qn,i,c
is incapable of distributing the remaining power to the other user
pairs. Thus, an increase in
PT
is more beneficent for
Opt
and Random-
xn,i,c
as compared to Fix-
Qn,i,c
.
Thus, for
PT<
6.5, the sum rate provided by Fix-
Qn,i,c
is greater than Random-
xn,i,c
. When
PT>
6.5,
the Fix-Qn,i,cprovides worst performance.
4 5 6 7 8 9 10 11 12 13 14
PT(Watts)
22
23
24
25
26
27
28
29
Sum Rate (b/s/Hz)
Opt
Fix-Qn,i,c
Random-xn,i,c
Figure 2. Impact of PTon sum rate for 3 different techniques.
The impact on the power consumption of each scheme for changing
PT
is presented in Figure 3.
The transmission power of each scheme increase with
PT
until the interference generated by each user
pair becomes equal to
Ith
. After this point, an increase in
PT
has no effect. The power consumption
of Opt at this point is equal to Random-
xn,i,c
. However, Figure 2shows that the sum rate provided
by Opt is greater than these schemes. Thus, it could be concluded that Opt is more efficient than
Random-
xn,i,c
. In the case of Fix-
Qn,i,c
, when
PT≤
5.5, the scheme takes advantage of full power
available. For
PT>
5.5, the interference of some pairs become equal to
Ith
. In this situation, all the
other schemes allocate the extra power to other user pairs and so are capable of taking advantage of
the increase in
PT
. However, in the case of Fix-
xn,i,c
, this extra power is not allocated to any other user
pair, thus resulting in poor performance as compared to the other schemes.
The interference of each user pair in each scheme is compared in Figure 4. In all the cases where
Qn,i,c
is optimized, when the interference of a user pair reaches threshold an increase in the slope
of some other pair’s curve is observed. This shows that the power allocated to this user pair has
increased because the extra power is now being allocated to this pair. However, in the case of Fix-
Qn,i,c
,
the interference of each pair increases at a constant rate with
PT
. This is because in this scheme the extra
power is wasted and each pair just gets its own equal share from the increased vale of power budget.
Appl. Sci. 2019,9, 4282 11 of 17
4 5 6 7 8 9 10 11 12 13 14
PT(Watts)
4
6
8
10
12
14
Total power consumption (Watts)
Opt
Fix-Qn,i,c
Random-xn,i,c
Figure 3. PTVS power consumption of all the considered techniques.
4 5 6 7 8 9 10 11 12 13 14
PT(Watts)
0
0.2
0.4
0.6
0.8
1
Interference of each pair (Watts)
Opt
Fix-Qn,i,c
Random-xn,i,c
Figure 4. Effect of increasing PTon the interference generated by each user pair in the system.
Figure 5shows the impact of
Ith
on the sum rate. Initially, an increase in
Ith
results in increasing
the sum rate of each scheme. At these points, the transmit power of the users are upper bounded by
Ith
. Thus, when
Ith
increase, the transmit power of each pair also increases. This results in enhancing
the sum rate. After a certain point, an increase in
Ith
has no impact on the sum rate. At these points,
each scheme is already transmitting with full available power. Hence, no more power is available
for transmission. It can be seen that Opt out performs all the other schemes. For
Ith <
1.5, the worst
performance is provided by Fix-
Qn,i,c
because the power allocation to user pairs is bounded by
Ith
and
the scheme cannot reallocated the extra power to the pairs that generate less interference. However,
when
Ith >
1.5 the Fix-
Qn,i,c
performs better than Random-
xn,i,c
. At larger values of
Ith
, the power
allocation of less user pairs is bounded by
Ith
so Fix-
Qn,i,c
can take advantage of the available power
and so the sum rate of Fix-Qn,i,cat these points surpasses Random-xn,i,c.
Appl. Sci. 2019,9, 4282 12 of 17
0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
Ith (Watts)
24.5
25
25.5
26
26.5
27
27.5
28
28.5
29
Sum Rate (b/s/Hz)
Opt
Fix-Qn,i,o
Random-xn,i,o
Figure 5. A comparison of sum rate offered by each scheme for increasing PT.
The sum rate of each scheme also depends on
RT
, as shown in Figure 6. To make the impact of
RT
more prominent, we considered
Ith =
2
W
, so that the power allocation is not bounded by interference.
For small values, increasing
RT
has no impact on the sum rate because the rate of each user is already
greater than
RT
. However, after a certain point when
RT
is further increased the sum rate decreases
as a result. This is because at these points to satisfy the rate constraint the power allocation of the
weak users is increased. The same amount of power results in larger value of rate for a user with good
channel condition as compared to a user with low value of channel gain, thus, when power allocated
to a user with better channel conditions is reduced and is allocated to the user with poor channel,
the sum rate decreases. Further, the Opt offers larger values of sum rate compared to all other schemes
for each
RT
. The Random-
xn,i,c
has the worst performance because in random pairing if two users
with poor channel conditions are paired together. This pair would require a large amount of power
to meet
RT
. Thus, less power would be available for the user pairs that can offer high rates. Hence,
with an increase in RTthe rate of Random-xn,i,cis affected more as compared to the other schemes.
1.4 1.6 1.8 2 2.2 2.4 2.6
RT(b/s/Hz)
26.5
27
27.5
28
28.5
29
Sum Rate (b/s/Hz)
Opt
Fix-Qn,i,c
Random-xn,i,c
Figure 6. Impact of increasing RTon the sum rate of the techniques.
The convergence behavior of all the dual variables is presented in Figure 7. It can be seen that all
the dual variables converge within a reasonable number of iterations.
Appl. Sci. 2019,9, 4282 13 of 17
0 500 1000 1500 2000 2500 3000 3500 4000
Iterations
0
0.5
1
1.5
2
2.5
3
Values of dual variables
Figure 7. Convergence of dual variables.
5. Conclusions
In this study, we considered the problem of maximizing the sum rate of the secondary users
in a NOMA based CR system. The constraints of power budget, interference temperature, QoS
requirement of each user and NOMA power gap were taken into account. For the solution, we
first transformed the non-convex optimization problem into a convex form. We proposed a dual
decomposition based solution for power allocation. An efficient algorithm for user pairing and channel
allocation was also designed. The simulations compared the performance of the proposed scheme
with two scenarios. In the first case, the power allocated to each user pair was optimized for random
user pairing and channel allocation (Random-
xn,i,c
). In the second scenario, fix amount of power
was allocated to each pair where the user pairing and channel allocation was carried out as in the
proposed Opt scheme. In both cases, the allocated power to a pair was distributed among the user as
in Opt. The results show that at small values of available power or high interference threshold the
advantages of intelligent user pairing and channel allocation surpass optimal power allocation to the
pairs. However, at low interference threshold or high power budget the optimal power allocation to
each pair provides better performance. In addition, as the rate requirement of users in the system
increases the gap in the rates offered by Fix-
Qn,i,c
and Random-
xn,i,c
also increases. At higher values of
RT
, Fix-
Qn,i,c
provides much better performance as compared to Random-
xn,i,c
. The results show that
the proposed Opt scheme offers more rate as compared to the other cases. In future works, we will
incorporate some intelligent algorithms [
33
,
34
] into the considered system, in order to enhance the
system performance.
Author Contributions:
Z.A., and G.A.S.S., contributed to the conception and development of the analytical model
of the study. Z.A., G.A.S.S., W.U.K. and Y.R., contributed to the acquisition of simulation results. All authors read
and approved the final manuscript.
Funding: This research received no external funding.
Conflicts of Interest: The authors declare no conflict of interest.
Abbreviations
The abbreviations used in this manuscript are listed below:
ST Secondary transmitter
CR Cognitive radio
SR Secondary receiver
PR Primary receiver
SIC Successive interference cancellation
Appl. Sci. 2019,9, 4282 14 of 17
Appendix A
If a problem has convex or concave objective function and all the constraints are convex or
linear, then the problem is called a convex problem. Here, we discuss the convexity of
P2
and
P3
.
For a multi-variable function, if all the eigenvalues of the Hessian matrix are negative, the function is
called concave, and, if the eignvalues are positive, the function is convex. However, if some eigenvalues
are positive and other are negative, the function is non-convex.
Appendix A.1. Convexity of P2
To check whether the objective function of
P2
is convex in
αn,i,c
and
Qn,i,c
, we calculate the Hessian
matrix as given below:
H="Ω1Ω2
Ω3Ω4#
where
Ω1=(|hi,c|2− |hn,c|2)Q2
n,i,cσ2(2αn,i,c|hi,c|2|hn,c|2Qn,i,c+ (|hi,c|2+|hn,c|2)σ2)
(αn,i,c|hn,c|2Qn,i,c+σ2)2(αn,i,c|hi,c|2Qn,i,c+σ2)2
Ω2=Ω3=(|hi,c|2− |hn,c|2)σ2(α2
n,i,c|hi,c|2|hn,c|2Q2
n,i,c−σ4)
(αn,i,c|hn,c|2Qn,i,c+σ2)2(αn,i,c|hi,c|2Qn,i,c+σ2)2
Ω4=−α2
n,i,c|hn,c|4
(αn,i,c|hn,c|2Qn,i,c+σ2)2+|hi,c|4 α2
n,i,c
(αn,i,c|hi,c|2Qn,i,c+σ2)2−1
(hi,cQn,i,c+σ2)2!.
For eigenvalues, we need to transform the Hessian into triangular matrix. Then, the values in the
diagonal are the eigenvalues. Performing matrix operations, we transform
H
into upper-triangular
matrix as:
H="Ω1Ω2
0Ω5#
where
Ω5=κ
Q2
n,i,c(αn,i,c|hn,c|2Qn,i,c+σ2)(|hi,c|2Qn,i,c+σ2)2Q2
n,i,c(αn,i,c|hi,c|2Qn,i,c+σ2),
the value of κis given by:
κ=−2α3
n,i,c|hi,c|8|hn,c|4Q5
n,i,c−2|hi,c|6Q2
n,i,cσ6−2|hi,c|2(|hi,c|2− |hn,c|2)Qn,i,cσ8+ (−|hi,c|2+|hn,c|2)σ10
+α2
n,i,c(−6|hi,c|6|hn,c|4Q4
n,i,cσ2+6|hi,c|6|hn,c|2Q3
n,i,cσ4−6|hi,c|4|hn,c|4Q3
n,i,cσ4+3|hi,c|4|hn,c|2Q2
n,i,cσ6−
3|hi,c|2|hn,c|4Q2
n,i,cσ6) + αn,i,c(−4|hi,c|6|hn,c|2Q3
n,i,cσ4−2|hi,c|4|hn,c|4Q3
n,mkσ4+2|hi,c|6Q2
n,i,cσ6−2|hi,c|2
|hn,c|4Q2
n,i,cσ6+|hi,c|2(|hi,c|2− |hn,c|2)Qn,i,cσ8+ (|hi,c|2− |hn,c|2)|hn,c|2Qn,i,cσ8),
with
Ω1
and
Ω5
the eigenvalues. It can be seen that
Ω1
will always be negative as
|hn,c|2>|hi,c|2
.
However, the sign of
Ω5
depends on the values of
Qn,i,c
and
αn,i,c
. As,
Qn,i,c
and
αn,i,c
are optimization
variables and will change values during optimization, this may result in positive value of
Ω5
. Hence,
the function is non-convex. Similarly, the eigenvalues of Equation (15) are
|hi,c|4Q2
n,i,c
(αn,i,c|hi,c|2Qn,i,c+σ2)2
and
σ2(2(−1+αn,i,c)|hi,c|4Q2
n,i,c+ (−2+αn,i,c)|hi,c|2Qn,i,cσ2−σ4)
(|hi,c|2Qn,i,c+σ2)2Q2
n,i,c(αn,i,c|hi,c|2Qn,i,c+σ2)
. As
α≤
1, it can be concluded that one
eigenvalue is positive and other is negative. The function in Equation (15) is non-convex.
Appl. Sci. 2019,9, 4282 15 of 17
Appendix A.2. Convexity of P3
The hessian of the objective of P3 is:
H="Φ1Φ2
Φ3Φ4#
where
Φ1=(|hn,c|2− |hi,c|2)σ2(2βn,i,c|hi,c|2|hn,c|2+ (|hi,c|2+|hn,c|2)σ2)
(βn,i,c|hi,c|2+σ2)2(βn,i,c|hn,c|2+σ2)2,
Φ2=Φ3=0,
Φ4=|hi,c|4
(|hi,c|2Qn,i,c+σ2)2
As
|hn,c|2>|hi,c|2
, it can be concluded that
Φ1
and
Φ4
will always be positive and thus the
objective function is convex. The Hessian of Equation (22) is given below; as one eigenvalue is positive
and other is negative, the function is non convex.
H=
|hi,c|4
(|hi,c|2βn,i,c+σ2)20
0−|hi,c|4
(|hi,c|2Qn,i,c+σ2)2
References
1.
Xie, H.; Gao, F.; Zhang, S.; Jin, S. A unified transmission strategy for TDD/FDD massive MIMO systems
with spatial basis expansion model. IEEE Trans. Veh. Technol. 2016,66, 3170–3184. [CrossRef]
2.
Xie, H.; Gao, F.; Jin, S.; Fang, J.; Liang, Y. Channel estimation for TDD/FDD massive MIMO systems with
channel covariance computing. IEEE Trans. Wirel. Commun. 2018,17, 4206–4218. [CrossRef]
3.
Wang, Z.Y.; Yu, H.Y.; Wang, D.M. Channel and Bit Adaptive Power Control Strategy for Uplink NOMA VLC
Systems. Appl. Sci. 2019,9, 220. [CrossRef]
4.
Marcano, A.S.; Christiansen, H.L. Performance of non-orthogonal multiple access (NOMA) in mm-wave
wireless communications for 5G networks. In Proceedings of the International Conference on Computing,
Networking and Communications (ICNC), Santa Clara, CA, USA, 26–29 January 2017; pp. 969–974.
5.
Althunibat, S.; Mesleh, R.; Qaraqe, K. Quadrature index modulation based multiple access scheme for 5G
and beyond. IEEE Commun. Lett. 2019. [CrossRef]
6.
Althunibat, S.; Mesleh, R.; Rahman, T.F. A novel uplink multiple access technique based on index-modulation
concept. IEEE Trans. Commun. 2019,67, 4848–4855. [CrossRef]
7.
Wu, Y.; Attang, E.; Atkin, G.E. Low complexity NOMA system with combined constellations. IEEE Wirel.
Commun. Lett. 2019. [CrossRef]
8.
Ali, A.; Baig, A.; Awan, G.M.; Khan, W.U.; Ali, Z.; Sidhu, G.S. Efficient resource management for sum
capacity maximization in 5G NOMA systems. Appl. Syst. Innov. 2019,2, 27. [CrossRef]
9.
Fang, F.; Cheng, J.; Ding, Z. Joint energy efficient subchannel and power optimization for a downlink NOMA
heterogeneous network. IEEE Trans. Veh. Technol. 2019,68, 1351–1364. [CrossRef]
10.
Liu, M.; Song, T.; Hu, J.; Yang, J.; Gui, G. Deep learning-inspired message passing algorithm for efficient
resource allocation in cognitive radio networks. IEEE Trans. Veh. Technol. 2019,68, 641–653. [CrossRef]
11.
Gao, Y.; Xiao, Y.; Wu, M.; Xiao, M. Energy efficient power allocation with demand side coordination for
OFDMA downlink transmissions. IEEE Trans. Wirel. Commun. 2019,18, 2141–2155. [CrossRef]
Appl. Sci. 2019,9, 4282 16 of 17
12.
Cui, J.; Ding, Z.; Fan, P. A novel power allocation scheme under outage constraints in NOMA systems.
IEEE Signal Process. Lett. 2016,23, 1226–1230. [CrossRef]
13.
Yang, Z.; Ding, Z.; Fan, P.; Dhahir, N.A. A general power allocation scheme to guarantee quality of service in
down–link and uplink NOMA systems. IEEE Trans. Wirel. Commun. 2016,15, 7244–7257. [CrossRef]
14.
Zhang, Y.; Wang, H.M.; Zheng, T.X.; Yang, Q. Energy-efficient transmission design in non-orthogonal
multiple access. IEEE Trans. Veh. Technol. 2017,66, 2852–2857. [CrossRef]
15.
Feng, Y.; Yan, S.; Yang, Z.; Yang, N.; Yuan, J. Beamforming design and power allocation for secure
transmission with NOMA. IEEE Trans. Wirel. Commun. 2019,18, 2639–2651. [CrossRef]
16.
Choi, J. Power allocation for max-sum rate and max-min rate proportional fairness in NOMA. IEEE Commun.
Lett. 2016,20, 2055–2058. [CrossRef]
17.
Ali, Z.; Sidhu, G.A.S.; Waqas, M.; Gao, F. On fair power optimization in nonorthogonal multiple access
multiuser networks. Emerg. Telecommun. Technol. 2018,29, 3540. [CrossRef]
18.
Zhou, F.; Beaulieu, N.C.; Li, Z.; Si, J.; Qi, P. Energy-efficient optimal power allocation for fading cognitive
radio channels: Ergodic capacity, outage capacity, and minimum-rate capacity. IEEE Trans. Wirel. Commun.
2015,15, 2741–2755. [CrossRef]
19.
Quach, T.X.; Tran, H.; Uhlemann, E.; Kaddoum, G.; Tran, Q.A. Power allocation policy and performance
analysis of secure and reliable communication in cognitive radio networks. Wirel. Netw.
2019
,25, 1477–1489.
[CrossRef]
20.
Yin, C.; Palacios, E.G.; Vo, N.S.; Duong, T.Q. Cognitive heterogeneous networks with multiple primary users
and unreliable backhaul connections. IEEE Access 2018,7, 3644–3655. [CrossRef]
21.
Zhang, J.; Nguyen, N.P.; Zhang, J.; Palacios, E.G.; Le, N.P. Impact of primary networks on the performance
of energy harvesting cognitive radio networks. IET Commun. 2016,10, 2559–2566. [CrossRef]
22.
Wei, Z.; Ng, D.W.K.; Yuan, J.; Wang, H.M.; Jin, S. Optimal resource allocation for power-efficient MC-NOMA
with imperfect channel state information. IEEE Trans. Commun. 2017,65, 3944–3961. [CrossRef]
23.
Wei, Z.; Ng, D.W.K.; Yuan, J. Power-efficient resource allocation for MC-NOMA with statistical channel state
information. In Proceedings of the IEEE Global Communications Conference (GLOBECOM), Washington,
DC, USA, 4–8 December 2016; pp. 1–6.
24.
Lei, L.; Yuan, D.; Ho, C.K.; Sun, S.J. Power and channel allocation for non-orthogonal multiple access in 5G
systems: Tractability and computation. IEEE Trans. Wirel. Commun. 2016,15, 8580–8594. [CrossRef]
25.
Ali, Z.; Sidhu, G.A.S.; Waqas, M.; Gao, F.; Jin, S. Achieving energy fairness in multiuser uplink CR
transmission. In Proceedings of the IEEE Wireless Communications and Networking Conference, Doha,
Qatar, 3–6 April 2016; pp. 1–6.
26.
Wang, S.; Shi, W. ; Wang, C. Energy-efficient resource management in OFDM-based cognitive radio networks
under channel uncertainty. IEEE Trans. Commun. 2015,63, 3092–3102. [CrossRef]
27.
Pao, W.C.; Chen, Y.F.; Chuang, S.Y. Efficient power allocation schemes for OFDM-based cognitive radio
systems. AEU Int. J. Electron. Commun. 2011,65, 1054–1060. [CrossRef]
28.
Zeng, M.; Tsiropoulos, G.I.; Dobre, O.A.; Ahmed, M.H. Power allocation for cognitive radio networks
employing non-orthogonal multiple access. In Proceedings of the IEEE Global Communications Conference
(GLOBECOM), Washington, DC USA, 4–8 December 2016.
29.
Zabetian, N.; Baghani, M.; Mohammadi, A. Rate optimization in NOMA cognitive radio networks.
In Proceedings of the International Symposium on Telecommunications (IST), Tehran, Iran, 27–28 September
2016; pp. 62–65.
30.
Saito, Y.; Kishiyama, Y.; Benjebbour, A.; Nakamura, T.; Li, A.; Higuchi, K. Non-orthogonal multiple access
(NOMA) for cellular future radio access. In Proceedings of the Vehicular Technology Conference (VTC
Spring), Dresden, Germany, 2–5 June 2013.
31. Boyd, S.; Vandenberghe, L. Convex Optimization; Cambridge University Press: Cambridge, UK, 2004.
32.
Boyd, S.; Mutapcic, A. Subgradient Methods Notes for EE364; Winter 2006-07; Standford University: Stanford,
CA, USA, 2006.
Appl. Sci. 2019,9, 4282 17 of 17
33.
Xia, J. Intelligent Secure Communication for Internet of Things with Statistical Channel State Information of
Attacker. IEEE Access 2019,PP, 1–10. [CrossRef]
34.
Liu, G. Deep Learning Based Channel Prediction for Edge Computing Networks Towards Intelligent
Connected Vehicles. IEEE Access 2019,7, 114487–114495. [CrossRef]
c
2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons Attribution
(CC BY) license (http://creativecommons.org/licenses/by/4.0/).
