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Non-Orthogonal Multiple Access in Multi-UAV
Networks
Tianwei Hou∗, Yuanwei Liu†, Xin Sun∗, Zhengyu Song∗, and Yue Chen†
∗School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing, CN
†School of Electronic Engineering and Computer Science, Queen Mary University of London, London, UK
∗Email: 16111019@bjtu.edu.cn
Abstract—In this paper, the application of non-orthogonal
multiple access (NOMA) aided multiple unmanned aerial vehi-
cles (UAVs) wireless networks is investigated in the downlink
scenario. A new multiple UAVs framework, user-centric strategy
for providing emergency services in the rural area, is proposed by
utilizing a stochastic geometry model. In order to provide practical
insights for the proposed NOMA assisted UAV framework, an
imperfect successive interference cancelation (ipSIC) scenario
is taken into account. For the user-centric strategy, we derive
new exact expressions for the coverage probability. The derived
analytical results explicitly indicate that the ipSIC coefficient is a
dominant component in terms of coverage probability.
Index Terms—Non-orthogonal multiple access, stochastic geom-
etry, unmanned aerial vehicles.
I. INTRODUCTION
In the past decades, much research effort has been directed
towards developing remotely operated unmanned aerial vehi-
cles (UAVs), which stand as a potential candidate of aerial
base station (BS) to provide access services to wireless devices
located on the ground [1]. Due to the limited energy resources
on board of a UAV, achieving higher spectrum efficiency and
energy efficiency is of paramount importance to reap maximum
benefits from UAV based communication networks. To exploit
both the spectrum efficiency and energy efficiency in the next
generation wireless networks and beyond, especially in the
UAV communication networks, non-orthogonal multiple access
(NOMA) is considered to be a promising technique [2]. More
specifically, in contrast to the conventional OMA techniques,
NOMA is capable of exploiting the available resources more
efficiently by opportunistically capitalizing on the users specific
channel conditions on both single cell networks and cellular
networks [3].
Regarding the literature of UAV networks, early research
contributions have studied the performance of single UAV or
multiple UAVs networks. For mathematically tractable, the
distinctive channel characteristics for UAV networks were
investigated to demonstrate the channel propagation of UAV
networks in [4]. Jiang et al. [5] proposed a UAV assisted
ground-to-air network, where Rayleigh fading channel, which
is a well-known model in scattering environment, can be also
used to model the UAV channel characteristics in the case of
large elevation angles in the mixed-urban environment. Chetlur
et al. [6] proposed a downlink UAV network over Nakagami-
mfading channels, where UAVs are distributed in a finite 3-
D network. In order to improve the spectrum efficiency and
energy efficiency of UAV communications, new research on
UAV under emerging next generation network architectures is
needed.
In UAV-enabled wireless communications, the total UAV
energy is limited, which includes propulsion energy and com-
munication related energy [7]. Therefore, integrating UAVs and
NOMA into cellular networks is considered to be a promising
technique to significantly enhance the performance of terrestrial
users in the next generation wireless system and beyond, where
the energy efficiency and spectrum efficiency can be greatly
enhanced in downlink transmission to minimize communication
related energy [8]. A general introduction of UAV communi-
cations has been proposed by Liu et al. [9]. Some challenges
were concluded for future research directions. Zhao et al. [10]
proposed a UAV-assisted NOMA network, where UAV and
BS are cooperated to provide access services to ground users
simultaneously. Hou et al. [11] proposed a multiple-input
multiple-output (MIMO)-NOMA assisted UAV network, where
the closed-form expressions of outage performance and ergodic
rate were evaluated in the downlink scenario.
The previous contributions [9, 11] mainly consider NOMA
in single UAV cell or NOMA assisted uplink transmission, and
thus do not account for NOMA assisted downlink transmission
in UAV assisted cellular networks. The motivation of this paper
is that the proposed strategy is a promising solution for provid-
ing access services after disasters in the remote areas, where
all of terrestrial users located in the Voronoi cell can be served
by UAVs. In this paper, we consider a multi-cell set-up. We
propose a new NOMA assisted multi-UAV strategies, namely
user-centric strategy, and based on the proposed strategies, the
primary theoretical contributions can be summarized as follows:
1) We develop a potential association strategies to address
the impact of NOMA on the nearest user, namely user-centric
strategy, where stochastic geometry approaches are invoked to
model the locations of both UAVs and users. 2) We derive the
exact analytical expressions of a typical user in the NOMA
assisted user-centric strategy in terms of coverage probability.
3) Simulation results confirm our analysis, and illustrate that
by setting power allocation factors and targeted rate properly,
NOMA assisted multi-UAV frameworks has superior perfor-
mance over OMA assisted multi-UAV frameworks in terms of
coverage probability, which demonstrates the benefits of the
proposed strategies. Our analytical results also illustrate that
the coverage probability can be greatly enhanced by LoS links.
978-1-7281-1220-6/19/$31.00 ©2019 IEEE
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II. USER-CENTRIC ST RATE GY F OR EMERGENCY
COM MU NI CATI ON S
Focusing on downlink transmission scenarios, we consider
the user-centric strategy as shown in Fig. 1(a). In this article,
the UAV equipped with a single antenna communicates with
multiple users equipped with a single antenna each. For the
simplicity of theoretical analysis, as shown in Fig. 1(b), an
user is located at the original point in the user-centric strategy,
which becomes the typical user. Without loss of generality, we
consider that there is one user, namely fixed user, is already
connected to the UAV in the previous round of user association
process. For simplicity, we assume that the horizontal distances
between the fixed user and the connected UAV is rk, which can
be any arbitrary values, and the horizontal distance between the
typical user and the connected UAV is random, denoted by r.
In the user-centric strategy, we consider that two users, fixed
user and typical user, are paired to perform NOMA technique,
where paired NOMA users share the same frequency, time and
code resource blocks.
A. Channel Model
Consider the use of a composite channel model with two
parts, large-scale fading and small-scale fading. It is assumed
that the horizontal distance rand the height of the UAV hare
independent and identically distributed (i.i.d.). In this article,
large-scale fading represents the path loss between the UAV
and users. In order to better illustrate the LoS propagation
between the UAV and user, the small-scale fading is defined by
Nakagami-mfading, and the probability density function (PDF)
can be expressed as
f(x) = mmxm−1
Γ(m)e−mx,(1)
where mdenotes the fading parameter, and Γ(m)denotes
Gamma function.
In order to avoid infinite received power, it is assumed that
the height of the UAV is greater than 1m to simplify the ana-
lytical results. In downlink transmission, paired NOMA users
also detect interference from neighboring UAVs. Therefore, the
co-channel interference Ican be further expressed as follows:
I∆
=
j∈Ψ,dj>rt|gj|2Pud−αI
j,(2)
where Pudenotes the transmit power of the UAV, djand |gj|2
denote the distance and the small-scale fading between the user
and the j-th interfering UAV, αIdenotes the path loss exponent
between interfering UAV and the typical user.
Besides, in practical wireless communication systems, ob-
taining the channel state information (CSI) at the transmitter
or receiver is not a trivial problem, which requires the classic
pilot-based training process. Therefore, in order to provide
more engineering insights, it is assumed that the CSI of
UAVs is partly known at the typical user, where only distance
information between UAVs and the typical user is required.
B. SINR Analysis
For the user-centric strategy, since the distance of typical
user and its associated UAV is not pre-determined, focusing on
the typical user, there are two potential cases, namely far user
case and near user case, where 1) far user case, i.e., r > rk;
and 2) near user case, i.e., r < rk. We then turn our attention
on the SINR analysis of two potential cases. For the far user
case, where the serving distance of the typical user is greater
than that of the fixed user, the typical user treats the signal from
the fixed user as noise, and thus the SINR can be expressed as
SI N Rt,f =|ht|2r−α
tPuα2
v
σ2+|ht|2r−α
tPuα2
w+
j∈Ψ,dj>rt|gj|2Pud−αI
j
,
(3)
where rt=√h2+r2,αdenotes the path loss exponent
between the typical user and the connected UAV, and htdenotes
the channel coefficients for the typical user and its associated
UAV, σ2denotes the additive white Gaussian noise (AWGN)
power, α2
vand α2
wdenote the power allocation factors for the
far user and the near user, respectively. Note that α2
v+α2
w= 1
in NOMA communication.
For the near user case, when the typical user has smaller
serving distance to the UAV than that of the fixed user, the
SIC technique can be deployed at the typical user for decoding
the signal from the fixed user, and the SINR at the typical user
for the near user case can be expressed as
SI N Rt→f,n =|ht|2r−α
tPuα2
v
σ2+|ht|2r−α
tPuα2
w+
j∈Ψ,dj>rt|gj|2Pud−αI
j
.
(4)
Once the typical user decodes the information from the fixed
user successfully, the typical user can decode its own signal
with the SINR
SI N Rt,n =|ht|2r−α
tPuα2
w
σ2+β|ht|2r−α
tPuα2
v+
j∈Ψ,dj>rt|gj|2Pud−αI
j
,
(5)
where βdenotes the imperfect SIC coefficient. Since in practice
that SIC is not perfect, a fraction 0< β < 1is considered.
C. Coverage Probability of the User-centric Strategy
In the networks considered, we first focus on analyzing the
PDF of user distance distributions for paired NOMA users,
which will be used for both user-centric strategy and UAV-
centric strategy.
Lemma 1. The UAVs are distributed according to a HPPP with
density λ. It is assumed that the typical user is located at the
origin of the disc in the user-centric strategy, which is under
expectation over HPPP. The horizontal distance rbetween the
origin and UAVs, follows the distribution
fr(r) = 2πλre−π λr2, r ≥0.(6)
As such, the first step is to derive the Laplace transform of
interference for the typical user.
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Transmitting UAV
user
NOMA
Near user signal
detection
Far user
signal
detection
SIC of far
user signal
h
(a) Illustration of the system model.
-1000 -800 -600 -400 -200 0 200 400 600 800 1000
X coodinate(m)
-1000
-800
-600
-400
-200
0
200
400
600
800
1000
Y coodinate(m)
Users
UAVs
Typical user
Nearest UAV
(b) Top view of the user-centric strategy cellular net-
works.
Fig. 1: Illustration of NOMA assisted user-centric strategy model.
Lemma 2. For the user-centric strategy, and based on the
characteristic of stochastic geometry, the interference received
at both typical user and fixed user can be recognized as
the same. Therefore, the Laplace transform of interference
distribution for the paired NOMA users is given by
Lt(s) = e−2πλ
αI
mI
i=1 (mI
i)sPu
mIδI(−1)δI−iB−sPu
mIrαI
t
;i−δI,1−mI,
(7)
where δI=2
αI,mIdenotes the fading parameters between a
typical user and interfering UAVs, and B(; ) denotes incomplete
Beta function.
Proof: Please refer to Appendix A.
Then, we focus on the coverage behavior of the user-centric
strategy. The fixed power allocation strategy is deployed at
the UAV, where the power allocation factors α2
wand α2
vare
constant during transmission. It is assumed that the target
rates of the typical user and the fixed user are Rtand Rf,
respectively. Based on SINR analysis in (3), (4) and (5), the
coverage probability of the typical user can be expressed as
follows:
Pt(r) = Pt,n(r)P(r < rk) + Pt,f (r)P(r > rk)
= Pr (SI N Rt→f,n > εf, SI NRt,n > εt) Pr(r < rk)
+ Pr (SINRt,f > εt) Pr(r > rk),
(8)
where εt= 2Rt−1,εf= 2Rf−1,Pt,near(r)and Pt,f ar (r)
denote the coverage probability of the typical user for the near
user case and the far user case, respectively. P(r > rk)and
P(r < rk)denote the probability of far user case and near
user case, respectively. Therefore, the coverage probability of
the typical user for the near user case and far user case is given
in following two Lemmas.
Lemma 3. The coverage probability conditioned on the serving
distance of a typical user for the near user case in the user-
centric strategy is expressed in closed-form as
Pt,near(r) = rα(1−j)qj+(2+(α−αI)(i+a)−αb)qb+αn
t
×
m−1
n=0
n
p=0 n
p(−1)n
n!Λn
4Λn
5e−mMt∗σ2rα
t−Λ3r2+(α−αI)(i+a)
t,
(9)
where Mn
t=εt
Pu(α2
w−βεtα2
v),Mt→f=εf
Pu(α2
v−εfα2
w),
Mt∗=max {Mn
t, Mt→f},
Λ3=2πmλ
αI
∞
a=0
(mI)a
a!(i−δI+a)
mI
i=1 mI
iMt∗Pu
mIi+a
(−1)a,
Λn
4=p!
p
j=1
(−mMt∗σ2)j−1
k=0
(1−k)qj
qj!(j!)qj, and
Λn
5=(n−p)!
n−p
b=1
(−Λ3)
b−1
k=0
(δI−k)qb
qb!(b!)qb.
Proof: Please refer to Appendix B.
For the far user case, note that decoding will succeed if
the typical user can decode its own message by treating the
signal from the fixed user as noise. The coverage probability
conditioned on the serving distance of a typical user for the far
user case is calculated in the following Lemma.
Lemma 4. The coverage probability conditioned on the serving
distance of a typical user for the far user case in the user-centric
strategy is expressed in closed-form as
Pt,far(r) = rα(1−j)qj+(2+(α−αI)(i+a)−αb)qb+αn
t
×
m−1
n=0
n
p=0 n
p(−1)n
n!Λf
4Λf
5e−mMf
tσ2rα
t−Λf
3r2+(α−αI)(i+a)
t,
(10)
where Mf
t=εt
Pu(α2
v−εtα2
w),Λf
3=
2πmλ
αI
∞
a=0
(mI)a
a!(i−δI+a)
mI
i=1 mI
iMf
tPu
mIi+a
(−1)a,
Λf
4=p!
p
j=1
(−mMf
tσ2)j−1
k=0
(1−k)qj
qj!(j!)qj, and
Λf
5=(n−p)!
n−p
b=1
(−Λf
3)b−1
k=0
(δ−k)qb
qb!(b!)qb.
Proof: Similar to the procedure in Appendix B, we can
obtain the desired result in (10). The proof is complete.
Remark 1. Inappropriate power allocation such as, α2
v−
εtα2
w<0and α2
w−βεtα2
v<0, will lead to the coverage
probability always being zero.
Thus, the coverage probability of the typical user in the user-
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centric strategy can be calculated in the following Theorem.
Theorem 1. The exact expression of the coverage probability
for the typical user is expressed as
Pt=
rk
0
Pt,near(r)fr(r)dr +
∞
rk
Pt,far(r)fr(r)dr, (11)
where Pt,near(r)is given in (9),Pt,f ar (r)is given in (10), and
f(r)is given in (6).
III. NUM ER IC AL ST UD IE S
In this section, numerical results are provided to facilitate
the performance evaluation of NOMA assisted UAV cellular
networks. Monte Carlo simulations are conducted to verify
analytical results. The power allocation factors are α2
v= 0.6
for the far user and α2
w= 0.4for the near user. The path loss
exponent of interference links αIis set to 4, and the path loss
exponent of the desired transmission is 3. The height of the
UAV is fixed to 100 meters. The bandwidth of the downlink
transmission is set as BW = 300 kHz, and the power of
AWGN noise is set as σ2=−174 + 10log10(B W )dBm.
The UAV density λ=1
5002π. The horizontal distance of the
fixed user is 300m. The target rate of fixed users Rf= 0.5
BPCU.
A. User-centric strategy
First, we evaluate the coverage performance of downlink
NOMA users in the user-centric strategy. In Fig. 2(a), we can
see that, as the power of UAV increases, the coverage ceilings,
which are the maximum coverage probability for the proposed
networks, of both typical users and fixed NOMA users occur.
This is due to the fact that, as the higher power level of
interfering UAVs is deployed, the received SINR decreases
dramatically. It is observed that as imperfect SIC coefficient β
increases, the coverage probability of typical users decreases,
which indicates that the performance of NOMA assisted UAV
communication can be effectively improved by decreasing the
imperfect SIC coefficient.
Fig. 2(b) shows the coverage probability achieved by typical
users in both NLoS and LoS scenario. In order to better
illustrate the performance affected by the LoS transmission, the
NLoS case is also shown in the figure as a benchmark for com-
parison. In Fig. 2(b), we can see that higher fading parameter
mwould result in reduced outage probability for different UAV
power levels and different imperfect SIC coefficients. This is
because that the LoS link between the UAV and users provides
higher received power level.
Next, Fig. 3 plots the coverage probability of paired NOMA
users in the user-centric strategy versus target rate Rand power
allocation factor αv. It is observed that the coverage probability
is zero in the case of inappropriate target rates and power
allocation factors, which verifies the insights from Remark 1.
The coverage probability of typical users in OMA is also plot-
ted, which indicates that NOMA is capable for outperforming
OMA for the appropriate power allocation factors and target
rates of paired users. One can also observe that NOMA cannot
-60 -50 -40 -30 -20 -10 0
Pu(dBm)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Coverage probability
Typical user, β =0
Typical user, β =0.1
Typical user, β =0.3
Typical user, β =0.5
Fixed user, β =0
Fixed user, β =0.1
Fixed user, β =0.3
Fixed user, β =0.5
Simulation
α=3.5
α=3
(a) Coverage probability of user-centric NOMA versus transmit
power with different path loss exponent, where the fading
parameters m= 1 and mI= 1.
-60 -50 -40 -30 -20 -10 0
Pu(dBm)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Coverage probability
Typical user, NLoS, β =0
Typical user, NLoS, β =0.1
Typical user, NLoS, β =0.3
Typical user, NLoS, β =0.5
Typical user, LoS, β =0
Typical user, LoS, β =0.1
Typical user, LoS, β =0.3
Typical user, LoS, β =0.5
Simulation
(b) Coverage probability of user-centric NOMA versus transmit
power in both NLoS and LoS scenarios, where the fading
parameters m= 2 and mI= 1.
Fig. 2: Coverage probability of paired NOMA users versus the
power of UAV in the user-centric strategy, with target rate Rt=
1BPCU. The exact results of NOMA are calculated from (11).
Fig. 3: Coverage probability of typical users versus targeted
rate Rt=RBPCU, and power allocation factor. The transmit
power of UAVs is fixed to -30dBm. The fading parameters
m= 3 and mI= 2.
outperform OMA in the case of β= 0.15 for the user-centric
strategy. This indicates that hybrid NOMA/OMA assisted UAV
framework may be a good solution in the case of poor SIC qual-
ity. The UAV could intelligently choose the access techniques
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for improving the system coverage probability.
IV. CONCLUSIONS
We first proposed an overview on the an important new
paradigms in multi-UAV communications, which is applicable
for the case when all the users located in the Voronoi cell
are needed to be served by the UAV simultaneously. Then,
we focused on the performance evaluation of the proposed
frameworks. New analytical expressions for interference and
coverage probability were derived for characterizing the per-
formance in NOMA enhanced multi-UAV frameworks.
APP EN DI X A: PROO F OF LE MM A 2
By using the moment generating function (MGF) of Gamma
random variable |gj|, the Laplace transform of the interference
can be expressed as
Lt(s) = exp
−2πλ
∞
rt1−Ege−sPu|gj|2
mIrαIrdr
.
(A.1)
With the aid of Laplace transform for the Nakagami-
mdistribution with fading parameter mI, we can obtain
Egs|gj|2Pu
mIr−αI=1 + sPur−αI
mI−mI
. As such, by ap-
plying binomial expansion, and after some algebraic manipu-
lations, we have
Lt(s) = e−2πλ
αI
mI
i=1 (mI
i)sPu
mIδI(−1)δI−1
−sPu
rαI
tmI
0
ti−δI−1
(1−t)mIdt
,
(A.2)
where (a)is obtained by using t=−sPu
rαImI, and the proof is
complete.
APP EN DI X B: PROO F OF LE MM A 3
Then, we derive the coverage probability of the typical user
as
Pt,near (r) =
m−1
n=0
n
p=0 n
pe−mMt∗σ2rα
t−mMt∗σ2p
Λ1
×rαn
t(−1)n
n!EIΨ{exp (−mMt∗IΨrα
t)}(−mMtIΨ)n−p
Λ2
.
(B.1)
We then apply the Fa `
a di Bruno’s formula to solve the
derivative of p-th order as follows:
Λ1= exp −mMt∗σ2rα
tp!
×
p
j=1
−mMt∗σ2j−1
k=0
(1 −k)rα(1−j)
tqj
qj!(j!)qj,
(B.2)
where the sum qjis over all p-tuples of nonnegative integers
satisfying the constraint 1·q1+ 2 ·q2+· ·· +p·qp=p.
It is challenging to derive (n−p)-th order
derivation of incomplete Beta function directly. Thus,
the derived incomplete Beta function in (7) can
be transformed into B−sPu
mIrαI
t
;i−δI,1−mI=
−sPu
mIrαI
t(i−δI+a)∞
a=0
(mI)a
a!(i−δI+a), where (mI)adenotes
rising Pochhammer symbol, which can be calculated as
Γ(mI+a)
Γ(mI). Thus, the Laplace transform can be rewritten to
Lt(s) = exp −2πλ
αI
∞
a=0
(mI)a
a! (i−δI+a)
mI
i=1 mI
i
×sPu
mIi+a
(−1)ar−αI(i−δI+a)
t.
(B.3)
Then, by using Fa `
a di Bruno’s formula, Λ2can be trans-
formed into
Λ2= exp −Λ3r2+(α−αI)(i+a)
t(n−p)!
×
n−p
b=1
(−Λ3)
b−1
k=0
(δ−k)r2+(α−αI)(i+a)−αb
tqb
qb!(b!)qb,
(B.4)
where Λ3=2πλ
αI
∞
a=0
(mI)a
a!(i−δI+a)
mI
i=1 mI
iMt∗Pu
mIi+a
(−1)a,
and qbis over all (n−p)-tuples of nonnegative integers
satisfying the constraint 1·q1+2·q2+···+(n−p)·qb= (n−p).
Then, we can readily derive the desired results, and the proof
is complete.
ACK NOW LE DG ME NT
This work was supported by the Fundamental Research
Funds for the Central Universities under Grant 2019YJS008.
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