Coverage Analysis of mmWave Networks With Cooperative NOMA Systems

Abstract

In this letter, a cooperative non-orthogonal multiple access (NOMA) method is utilized in millimeter wave (mmWave) communications to active non-line-of-sight (NLOS) users, where NOMA users are modeled with the aid of Poisson point process (PPP) and all users are severed by a central base station (BS). Closed-form expressions for outage probabilities of paired NOMA users are derived to characterize the performance of the proposed networks. Our numerical results show that the proposed system outperforms the traditional mmWave networks using non-cooperative NOMA. Index Terms-Cooperative non-orthogonal multiple access, stochastic geometry, millimeter wave communications.

Full text

1
Coverage Analysis of MmWave Networks With
Cooperative NOMA Systems
Huailong Shen, Wenqiang Yi, Zhijin Qin, Yuanwei Liu, Fei Li, and Arumugam Nallanathan
Abstract—In this letter, a cooperative non-orthogonal mul-
tiple access (NOMA) method is utilized in millimeter wave
(mmWave) communications to active non-line-of-sight (NLOS)
users, where NOMA users are modeled with the aid of Poisson
point process (PPP) and all users are severed by a central base
station (BS). Closed-form expressions for outage probabilities of
paired NOMA users are derived to characterize the performance
of the proposed networks. Our numerical results show that the
proposed system outperforms the traditional mmWave networks
using non-cooperative NOMA.
Index Terms—Cooperative non-orthogonal multiple access,
stochastic geometry, millimeter wave communications.
I. INT ROD UC TI ON
Millimeter-Wave (mmWave) is a promising technique in
the fifth-generation (5G) network owing to the large available
bandwidth [1]. For dense networks with massive users, the
severe propagation path loss and low penetration capability
of mmWave signals require the help of new multiple access
technologies [2]. One promising method to further enhance
the spectrum efficiency is introducing non-orthogonal multiple
access (NOMA) into mmWave systems [2]. Another problem
for mmWave communications is the high outage probability
for non-line-of-sight (NLOS) users due to the quasi-optical
property [3, 4]. Most existing studies ignore the performance
of NLOS users [2, 5]. However, network designers would not
give up NLOS users just because these users have weak
channel gain.
Cooperative NOMA is to let NOMA users with good
channel conditions act as relays to assist NOMA users with
weak channel conditions [6]. In this letter, we use cooperative
NOMA to active NLOS users in mmWave communications.
The main motivation is that the data rate at NLOS users is hard
to satisfy the required quality of services and hence additional
transmission can be obtained from the better performing line-
of-sight (LOS) users. For example, in a Poisson point process
(PPP) based spatial model [7], when the signal noise is −40
dBm and the transmit power of base stations (BSs) equals to
20 W, the probability that one BS successfully sends messages
to its nearest LOS user is five times larger than that for the
nearest NLOS user. This gain can be used to serve NLOS
users. Compared with traditional relay techniques, the selected
NLOS user has one more signal from LOS users at the relaying
time slot.
The main contributions of this letter are summarized as
follows: Firstly, we propose a cooperative NOMA method to
H. Shen, F. Li are with Nanjing University of Posts and Telecommunica-
tions, Nanjing, China. (email:{1217012422, lifei}@njupt.edu.cn)
W. Yi, Z. Qin, Y. Liu, A. Nallanathan are with Queen Mary Univer-
sity of London, London E1 4NS, U.K. (email: {w.yi, z.qin, yuanwei.liu,
a.nallanathan}@qmul.ac.uk).
active mmWave-enabled NLOS users. By using this method,
the coverage performance of NLOS users has a huge improve-
ment. Secondly, we propose two user selection schemes from
the perspective of user performance enhancement and user
selection fairness. Lastly, we derive a closed-form expression
of outage probabilities for two paired NOMA users.
II. SYSTEM MO DE L
In this letter, we consider a downlink mmWave-NOMA
dense network where one BS located at the origin S= (0,0)
serves massive single-antenna users that are located in the cell
center1. The coverage of this BS is a circle with a radius
R. BSs with massive antennas are able to generate multiple
orthogonal beams in the angle domain, which is known as
beam division multiple access (BDMA) techniques [8]. To
simplify the analysis, a sectored antenna model [7] is applied
as shown in Fig. 1 and each beam has a constant antenna
gain. Since there is no interference between beams, this letter
focuses on a typical beam with antenna gain M. Users are
modeled according to a PPP Φwith the density λ. Due to the
large user density, there exists more than one user in the typical
beam. Based on this spatial model, the path loss gain L(rk)
of user klocated at k′∈Φis LX(rk) = CXr−αX
k, where
rkis the communication distance between the user kand the
BS, CXis the intercept and αXis the path loss exponent.
X ∈ {N, L}represent NLOS and LOS links, respectively.
Due to the quasi-optical property of mmWave signals, the
impact of obstacles is greater than that of path loss and small-
scale fading in most mmWave communications [2]. Based on
this property, we consider a LOS-NLOS pairing strategy. User
A is randomly selected from the NLOS user group and user B
is the nearest LOS user to BS or randomly selected from the
LOS user group. The locations of user A and user B are A′
and B′, respectively. The decode-and-forward (DF) approach
is implemented at user B. Two cooperative NOMA stages [9]
are described below.
A. Stage 1: Direct Transmission
During the first stage, the BS broadcasts one message
pAsA+pBsBto user A and user B based on NOMA schemes,
where pkis the power allocation coefficient, skis the desired
message of user k, and k∈ {A, B}.
We assume that |pA|2>|pB|2with |pA|2+|pB|2= 1.
User A decodes its own message directly, and the signal-to-
1This paper focuses on enhancing NLOS users in mmWave communication
via cooperative NOMA technique. A basic single cell is applied as a
preliminary analysis. For other network structures, our future work will study
the impact of inter-cell interference.

2
interference-plus-noise ratio (SINR) of user A is given by
SINRA=PSM|hA|2|pA|2LN(rA)
PSM|hA|2|pB|2LN(rA) + σ2,(1)
where hkmodels the small scale Nakagami fading [7] from
the BS to user kand |hk|2is a normalized Gamma random
variable. PSis the transmit power of the BS and σ2is thermal
noise.
When performing NOMA, user B carries out the successive
interference cancellation (SIC). It first decodes the message of
user A, then subtracts this message from the received signal
to detect its own message. As a result, the received SINR at
user B to detect its partner’s information is given by
SINRA
B=PSM|hB|2|pA|2LL(rB)
PSM|hB|2|pB|2LL(rB) + σ2.(2)
If the decoding is successful, the received signal-to-noise
ratio (SNR) at user B to detect its own information is
SNRB=PSM|hB|2|pB|2LL(rB)
σ2.(3)
B. Stage 2: Cooperative Transmission
We assume NOMA user pairs use orthogonal frequencies
and hence no inter-pair interference exists. During this stage,
user B retransmit the decoded messages sAto user A. Under
this situation, the received information at user A is
y2
A=PtLL(rA,B)sAhA,B +σ2,(4)
where Ptis the transmit power of user B, hA,B is the
independent Nakagami fading between user A and user B.
The rA,B is the distance from user B to user A, it can be
calculated by rA,B =r2
A+r2
B−2rArBcos(θ), and θis the
angle ∠A′SB′. Due to the high directional beamforming, we
assume θis small. Therefore, we can approximate the distance
between user A and user B as rA,B ≈ |rA−rB|and the path
between user A and B can be a LOS or NLOS link, which
respectively represent the upper bound and the lower bound
of our system.
Then the received SNR for user A to decode sAthat is
retransmitted from user B can be expressed as
SNRA
A→B=PtLL(rA,B)|hA,B|2
σ2.(5)
At the end of this stage, user A uses maximal-ratio combin-
ing (MRC) to combine the signals from the BS and user B [9].
Adding the SNR of the stage 2and the SINR of the stage 1
together, the received SINR of user A is
SINRMRC = SINRA+ SNRA
A→B
=PSM|hA|2|pA|2LN(rA)
PSM|hA|2|pB|2LN(rA) + σ2+PtLL(rA,B)|hA,B|2
σ2.
III. PERFORMANCE EVALUATI ON
In this section, we characterize the outage performance
depending on the distance distributions of user A and user B.
The cumulative density function (CDF) of the distance from
the BS to a random selected user A is
FN(r) = ϑ
0r
0(1 −p(t))tdtdθ
BNϑR2/2=2r
0(1 −p(t))tdt
BNR2,(6)
Fig. 1: A system diagram for the considered cooperative
mmWave-NOMA scenario. The paired user A and user B are
located in the considered beam region with the beam gain M.
where BN=2∫R
0(1−p(t))tdt
R2,ϑis the beam angel, p(rk)is the
LOS probability function of the user k. Based on the rectangle
Boolean scheme in [7], p(rk) = e−βrkand βis a parameter
related to the average size and the density of the blockages.
The probability density function (PDF) of the distance from
the BS to user A is given by
fN(r) = dFN(r)
dr =2
BNR2(1 −p(r)) r. (7)
On the one side, since the nearest LOS user has the best
channel condition, it has the largest performance gain to
provide additional transmission to other NLOS users. On the
other side, randomly selecting a LOS user helps to ensure the
fairness of user selection and avoid overloading at the same
user. Therefore, for user B, we consider two choices: 1) the
nearest LOS user and 2) random LOS user.
1) The CDF of the distance from the BS to the nearest LOS
user B can be expressed as follows
FLNL(x) = 1 −Pr[ΦLOS ∩O (0, x) = ∅]
= 1 −exp −ϑλ x
0
tp (t)dt,(8)
where ΦLOS is the thining PPP of LOS points, O (0, x)is
the circle of BS with a radius r. The probability that the BS
has at least one LOS user is BNL=FLNL(R). The PDF of
the distance from the BS to the nearest LOS user B is
fLNL(x) = ϑλxp(x)e−ϑλ ∫x
0rp(r)dr
BNL
.(9)
2) The CDF of the distance from the BS to a random
selected user B is as follows
FLR(r) = ϑ
0r
0p(t)tdtdθ
BLϑR2/2=2r
0p(t)tdt
BLR2,(10)
where BL=2∫R
0p(t)tdt
R2. The PDF of the distance from the
BS to a random selected user B can be expressed as
fLR(r) = 2p(r)r
BLR2.(11)
1) Outage Probability of User B: There may be an outage
of user B for two reasons under NOMA protocols. The first

3
is that user B fails to decode sA. The second is that sA
can be decoded successfully by user B but the decoding of
sBis failed. After that, user B’s outage probabilities can be
calculated as follows:
PB= Pr SINRA
B< τA] + Pr[SINRA
B> τA,SNRB< τB,
(12)
where τA= 22RA−1and τB= 22RB−1with Rkbeing the
target rate at user k. To ensure the implementation of NOMA
protocols, we hold the condition that |pA|2−|pB|2τA>0[9].
Theorem 1. The outage probability of user B PBis given by
PB≃FrB(FY(rB),0, R),(13)
where
FY(rB) = G NLrαL
Bmax (εA, εB)
CL
, NLfLS(rB),(14)
Fy(f(y), a, b) = π(b−a)
2n
n

i=1
f(xi+ 1) (b−a)
2+a
×1−x2
i1/2(15)
and NXis the parameter of the Nakagami small scale
fading. G(x, y)is the lower incomplete gamma function.
εA=τAσ2
PSM(|pA|2−τA|pB|2)and εB=τBσ2
PSM|pB|2,S∈ {NL, R}
represent the nearest LOS user B and random selected user
B, respectively. The xi= cos 2i−1
2nπindicates the Gauss-
Chebyshev node and the subscript yof Fy(f(y), a, b)is the
independent variable of the function f(y). The value of nis
to balance the precision and complexity [9]. The equality of
equation (13) can be created only if n→ ∞.
Proof: Let X=|hA|2LN(rA),Y=|hB|2LL(rB),Z=
|hA,B|2LX(rA,B), equation (12) is changed to
PB= Pr(Y < εA) + Pr(Y > εA, Y < εB).(16)
When εA< εB, we have PB= Pr(Y < εB). When εA≥
εB, we have PB= Pr(Y < εA). Based on the PDF of the
gamma variable |hB|2,PBis given by
PB= Pr (Y < max (εA, εB)) = R
0FY(rB)drB.(17)
With the aid of Gaussian-Chebyshev quadrature, which
is defined as b
af(y)dy ≃Fy(f(y), a, b). We obtain this
theorem.
Remark 1. Note that Mhas a negative correlation with the
lower incomplete gamma function in (14). We find outage
probabilities of user B decrease with the increase of the beam
gain M.
2) Outage Probability of User A: Under cooperative NOMA
protocols, outage encountered by user A happens in two
circumstances. The first is when user B decodes sAbut fails
to support the targeted rate at user A. The second is when the
decoding of sAis failed at both user A and user B. On this
basis, outage probabilities of user A is as follows:
PA= Pr(SINRMRC < τA,SINRA
B> τA)
+ Pr(SINRA< τA,SINRA
B< τA),(18)
Theorem 2. By utilizing MRC, the outage probability of
user A can be expressed as
PA≃FrB(FrA(Fx(F1(x, rA, rB),0, εA),0, R),0, R)
+ FrB(FL(rB),0, R) FrA(FN(rA),0, R),(19)
where
F1(x, rA, rB) = (1 − FY(rB))fX(x)fN(rA)GNX
× |rA−rB|αXτA−PSMx|pA|2
PSMx|pB|2+σ2σ2
PtCX
, NXfLS(rB),
(20)
fX(x) = xNN−1
Γ(NN)NNrαN
A
CNNN
e−NNrαN
Ax
CN,(21)
FX(rk) = GNXεkrαX
k
CX
, NXfX(rk),(22)
and Γ(x)is the gamma function.
Proof: With the aid of the proof in Theorem 1, equation
(18) can be expressed as
PA= Pr Z < τA−PSM x|pA|2
PSMx|pB|2+σ2σ2
Pt
, X < εA, Y > εA
  
Ξ1
+ Pr (X < εA) Pr(Y < εA)
  
Ξ2
,(23)
Based on the PDF of X,Y, and Z, we obtain that
Ξ1=
R

0
R

0
εA

0F1(x, rA, rB)dxdrAdrB,(24)
Ξ2=R
0FN(rA)drAR
0FY(rB)drB.(25)
With the aid of Gaussian-Chebyshev quadrature, we have this
theorem.
Assumption 1: In mmWave communications, the received
power from NLOS paths is negligible [2]. We assume user A
obtains information only from user B via LOS transmission.
Based on Assumption 1, we are able to ignore the NLOS
part before ”+” in (12). After that, the received SINR of user
A can be obtained as:
SINRMRC =PtLL(rA,B)|hA,B |2
σ2.(26)
Corollary 1. Based on Assumption 1, we can simplify Ξ1as

Ξ1≃FrBFrAGNLτAσ2|rA−rB|αL
PtCL
, NLfL(rB)
×(1 − FY(rB))fN(rA),0, R,0, R.(27)
Proof: Due to ignoring the NLOS part, the simplified Ξ1
can be derived via 
Ξ1= Pr Z < τAσ2
Pt, Y > εA.
Corollary 1 can by used in Theorem 2 to simply the outage
probability of user A PA.

4
IV. NUMERICAL RES ULT S
Numerical results are provided in this section to evaluate the
outage performance of the considered networks. The reference
distance is d0= 1 m, which means CL=CN. We assume
the average LOS range of the network 1/β =RL/√2m.
The LOS disc range is RL= 80 m, the density of users is
λ= 1/(r2
cπ)=1/(52π)m−2. The path loss law for LOS is
αL= 2,NL= 3. The path loss law for NLOS is αN= 4,
NN= 2. The carrier frequency is fm= 28 GHz, |pA|2= 0.6,
|pB|2= 0.4, bandwidth per resource block is B= 100MHz,
and PS= 20W, Pt= 4W.
-55 -50 -45 -40 -35 -30 -25 -20 -15
Noise Power in dB
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Outage Probability for User B
Theorem 1,Random,M=80
Theorem 1,Random,M=100
Theorem 1,Random,M=120
Cooperative OMA,Nearest,M=100
Theorem 1,Nearest,M=80
Theorem 1,Nearest,M=100
Theorem 1,Nearest,M=120
Non-cooperative,Nearest,M=100
Simulation
Fig. 2: Outage probability of user B with different Mversus
noise.
-95 -90 -85 -80 -75 -70 -65 -60 -55
Noise Power in dB
0
0.2
0.4
0.6
0.8
1
1.2
Outage Probability for User A
Theorem 2, Nearest-NLOS
Non-cooperative NOMA, Nearest-LOS
Corollary 1, Random-NLOS
Cooperative OMA, Nearest-LOS
Non-angel-simplification, Nearest-LOS
Corollary 1, Nearest-LOS
Theorem 2-Nearest-LOS
Corollary 1, Random-LOS
Simulation
Fig. 3: Outage probability of user A versus noise and the com-
parison of outage probability with non-cooperative NOMA.
12345678910
SINR threshold of user A 10-3
10-7
10-6
10-5
10-4
10-3
10-2
10-1
Outage Probability for User A
Corollary 1, Random-LOS, Pt=4w
Corollary 1, Random-LOS, Pt=8w
Corollary 1, Random-LOS, Pt=12w
Corollary 1, Random-LOS, Pt=16w
Fig. 4: Outage probability of user A with different transmit
power of user B versus SINR thresholds of user A.
Fig. 2 plots the outage probability of user B versus noise. S-
ince theoretical results match simulations perfectly, this figure
validates the accuracy of the proposed analytical expressions.
Moreover, Fig. 2 demonstrates that the outage probability of
user B decreases with the increase of Mas discussed in
Remark 1. Fig. 2 also shows that the random selected user
B always obtains a higher outage probability than the nearest
LOS user B. Compared with the cooperative OMA scheme,
the proposed cooperative NOMA scheme with the nearest LOS
user performs better.
Fig. 3 plots the outage probability of user A versus noise
for both non-cooperative NOMA and cooperative NOMA. The
figure demonstrates the outage probability of NLOS users
with cooperative NOMA is significantly lower than that of
NLOS users with non-cooperative NOMA. The reason is that
cooperative NOMA in the high SINR region ensures reliable
reception for the NLOS users. This phenomenon shows that
applying cooperative NOMA in mmWave communications is
helpful and essential. Fig. 3 shows that when the path between
users A and B is a LOS path, the outage probability of user
A is much lower than when the path between users A and
B is a NLOS path. Although the performance is not good in
the case of the NLOS path between users, it performs very
well in the case of the LOS path between users, so we can
consider adopting our protocol in the case of the LOS path
between users in the future. Fig. 3 also illustrates that our
simplification of the distance between users is reasonable.
Fig. 4 plots the outage probability of user A with different
transmit power of user B versus SINR thresholds of user A.
This figure demonstrates that the outage probability of user A
decreases as the transmit power of user B increases. This is
owing to the high transmit power at user B contributes to the
reliable reception at user A.
V. CONCLUSION
In this letter, we have proposed a cooperative mmWave-
NOMA method to enhance the performance of blocked users.
A spatial model based on stochastic geometry has been
provided to analyze outage probabilities. The analytical and
numerical results have demonstrated that the proposed co-
operative NOMA system outperforms the traditional non-
cooperative NOMA system in mmWave communications. For
actual BDMA impact and multiple beam user pairing for
sparse networks, we will study them in future work.
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