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1
Secrecy Analysis of UAV-Based mmWave Relaying Networks
Xiaowei Pang, Mingqian Liu, Member, IEEE, Nan Zhao, Senior Member, IEEE, Yunfei Chen, Senior
Member, IEEE, Yonghui Li, Fellow, IEEE, and F. Richard Yu, Fellow, IEEE
Abstract—Employing unmanned aerial vehicles (UAVs) in
millimeter-wave (mmWave) networks as relays has emerged as
an appealing solution to assist remote or blocked communication
nodes. In this case, the network security becomes a great
challenge due to the presence of malicious eavesdroppers. In this
paper, we perform a secrecy analysis for a UAV-based mmWave
relaying network. We first investigate the relaying scheme without
jamming where the UAV decodes and forwards the information
from the source to the destination with malicious eavesdropping.
Furthermore, to enhance the secrecy performance, we propose
a cooperative jamming scheme via utilizing the destination and
an external UAV to cooperatively disrupt the eavesdroppers at
the two stages of relaying, respectively. Using the probability
of line-of-sight (LoS) between the UAV and ground nodes, the
three-dimensional (3D) antenna gain, and the Nakagami-m small-
scale fading model, the secrecy outage probability (SOP) of the
two schemes with and without jamming is analyzed. Closed-form
expressions for the SOP of the two schemes are obtained by
employing the Gauss-Chebyshev quadrature. Simulation results
are presented to validate the theoretical expressions of SOP and
to show the effectiveness of the proposed schemes.
Index Terms—Cooperative jamming, millimeter-wave, physical
layer security, relay, secrecy outage probability, unmanned aerial
vehicle
I. INTRODUCTION
Unmanned aerial vehicles (UAVs) have been deployed at an
astounding pace in wireless communication systems over the
past decade, thanks to their high mobility, on-demand deploy-
ment and enhanced line-of-sight (LoS) probability [1]. UAVs
have been extensively applied in multifarious scenarios for
different purposes, such as seamless coverage [2], relaying [3],
data gathering [4], and internet of things (IoT) applications [5].
On the standpoint of service provision, UAVs can be employed
as an aerial platform to enhance the communication quality of
existing terrestrial wireless systems [6]. Furthermore, UAVs
can also be integrated into cellular networks as aerial users to
Manuscript received August 27, 2020; revised December 29, 2020; accepted
March 03, 2021. The work was supported by the National Natural Science
Foundation of China (NSFC) under Grant 62071364 and 61871065. The
associate editor coordinating the review of this paper and approving it for
publication was J. Zhang. (Corresponding author: Mingqian Liu and Nan
Zhao.)
ensure ultra-reliable wireless links, as cellular-connected UAV
communication [7], [8].
As other communication devices, UAVs have to deal with
the growing data rate as well as the overcrowding spectrum. In
this regard, millimeter-wave (mmWave) communication offers
much wider bandwidth and is a promising technique to be
utilized in UAV networks to enable much higher capacity [9].
The short wavelength of mmWave allows massive antennas
to be packed on a small UAV so that beamforming can be
carefully designed to overcome the drawbacks of mmWave
such as severe path loss and blocking. Moreover, UAVs can
flexibly change their locations to avoid blockages and thus are
suitable for the mmWave transmission [10]. For example, a
novel channel tracking method based on the flight control was
proposed by Zhao et al. in [11], where the three-dimensional
(3D) geometry channel model was formulated as a function of
the UAV movement and the channel gain. A novel hardware-
efficient implementation for mmWave hybrid precoding was
proposed in [12], and hybrid precoding can also be employed
in mmWave UAV networks. Particularly, hybrid precoding was
jointly optimized with the UAV placement and power alloca-
tion in [13] to maximize the energy efficiency of mmWave
UAV networks.
An increasingly interesting application of UAVs is relaying
network, where UAVs act as relays to assist the transmission
between two terrestrial terminals without reliable direct links
due to obstacles or a long distance [14]. One of the challenges
for practical applications is to find the optimal location for a
static relay or the trajectory for a mobile relay. Particularly,
the optimum altitude of the UAV as a relaying station for
maximum reliability was investigated by Chen et al. in [15],
with both static and mobile UAVs considered. Moreover,
Chen et al. designed an algorithm to find the optimal UAV
position to establish the best wireless relay link in [16]. To
effectively minimize the decoding error probability subject to
the latency requirement for UAV-enabled relaying systems,
the UAV location and blocklength were jointly optimized in
[17]. and the UAV location and power allocation were jointly
optimized in [18], respectively. To achieve the full potential
of UAVs, the mobility of UAV was utilized by Zhang et al.
in [19], where the trajectory and transmit power are jointly
optimized to minimize the outage probability of the relay
network. Furthermore, Kong et al. in [20] proposed a novel
UAV-relaying method for mmWave communications, where
the UAV gradually adjusts its path to approach the optimal
location in an accurate and efficient way. In [21], Zhu et al.
jointly optimized the UAV position, analog beamforming, and
power control to maximize the achievable rate in a full-duplex
UAV relaying network. However, none of them has considered
the security aspect of UAV relaying networks.
2
Despite the advantages of UAV-enabled relaying networks,
the broadcast nature and the LoS of UAVs channels pose
great threats to the network security. Thus, it is important
to study physical layer security problem to provide secure
transmission by leveraging the imperfections of the commu-
nication medium [22]. Aiming at maximizing the secrecy
rate, Wang et al. proposed a mobile relaying scheme in a
four-node senario including a source, a destination, a UAV
relay, and an eavesdropper [23]. In [24], a joint precoding
scheme was proposed for UAV-aided networks to achieve
simultaneous wireless information and power transfer (SWIP-
T) while guaranteeing the secure transmission for passive
receivers. In [25], the secrecy performance of a mmWave
SWIPT UAV-based relaying system was analyzed, with both
amplify-and-forward (AF) and decode-and-forward (DF) pro-
tocols considered. Particularly, cooperative jamming has been
regarded as an effective enabler for secure communication
by imposing interference to eavesdroppers [26]. The resource
allocation and trajectory design were investigated by Li et
al. in [27] for secure UAV-enabled systems, where UAVs
can provide communications or serve as jammers. To ensure
energy-efficient secure UAV communication, the trajectory and
resource allocation were jointly optimized by Cai et al. in [28]
with the assistance of a multi-antenna jamming UAV. In [29],
Chen et al. proposed a new joint relay and jammer selection
scheme and maximized the secrecy rate via power allocation.
Employing UAVs as jammmers, the secrecy performance of
UAV-enabled mmWave networks was analyzed in [30] by Zhu
et al., with the practical constraints of UAV deployment and
unique propagation characteristics. However, none of them
has considered jointly employing the UAV and ground nodes
as jammers to disturb eavesdropping in mmWave UAV-based
relaying systems.
Motivated by these observations, we consider a UAV-based
mmWave relaying network in this paper, where a UAV is
employed to assist the communication between the ground
source and destination. We propose two UAV relaying schemes
with and without jamming, and analyze the secrecy perfor-
mance by deriving the secrecy outage probability (SOP). To
the best of our knowledge, this is the first work that utilizes
the destination and the UAV to cooperatively transmit jamming
signals in UAV-based mmWave relaying networks. The main
contributions of this paper are summarized as follows.
• A UAV-based mmWave relaying network is studied to
help forward confidential information from the ground
source to the destination in the presence of multiple
eavesdroppers that are assumed to be deployed according
to a homogeneous Poisson point process (HPPP) distri-
bution. We consider both the probabilities of LoS and
non-line-of-sight (NLoS) links when modeling mmWave
UAV-to-ground channels with Nakagami-m fading. In
addition, we employ the 3D antenna gain model to
characterize the mmWave directional transmission.
• We first investigate the secrecy performance of the
UAV-based mmWave relaying network without jamming,
where the transmission is divided into two time slots.
Specifically, the relaying UAV and eavesdroppers receive
the confidential information from the source in the first
time slot. In the second slot, the UAV forwards the mes-
sages to the destination in the presence of eavesdropping.
For a given secrecy rate threshold, the theoretical SOP of
the scheme is derived to evaluate the secrecy performance
by employing the Gauss-Chebyshev quadrature.
• To further guarantee the secure transmission, we develop
a cooperative jamming scheme exploiting the destination
and a jamming UAV to disturb the eavesdropping in the
two time slots, respectively. In contrast to the existing s-
tudies on UAV-based relaying networks without jamming
or only using UAVs as jammers, we not only employ a
jamming UAV but also exploit the destination to send
jamming signals at its spare time to promote the secure
performance. The theoretical SOP of the scheme with
cooperative jamming is derived by adopting a two-layer
Gauss-Chebyshev quadrature.
The remainder of this paper is organized as follows. In
Section II, the system model is introduced. The secrecy perfor-
mance of the UAV-based mmWave relaying networks without
and with cooperative jamming is investigated in Section III and
Section IV, respectively. In Section V, numerical results are
provided to validate the derived SOP performance, followed
by the conclusions in Section VI.
II. SYSTEM MODEL
Consider a UAV-based mmWave relaying network as illus-
trated in Fig. 1, where a UAV (U) is employed as a relay to
assist the transmission from the source (S) to the destination
(D). Note that there is no direct link between S and D due
to the severe path loss or blockage. Assume that the relaying
UAV works in half-duplex using the DF strategy. The total
transmission is divided into two time slots. In the first time
slot, S transmits signals to U in the first time slot, and in the
second time slot, U forwards the signals to D. Meanwhile,
multiple eavesdroppers on the ground intend to wiretap the
confidential information in both two slots. The distribution of
eavesdroppers is modeled as an HPPP Φ
E
with density λ
E
,
and we use E to denote the eavesdroppers with E ∈ Φ
E
.
Considering the small size of mmWave antennas, all the nodes
are assumed to be equipped with multiple antennas.
Two transmission schemes without and with cooperative
jamming are investigated in this paper. The scheme without
jamming includes the legitimate transmission from S to U
and from U to D with malicious eavesdropping, and its
transmission process can be referred to Fig. 1 by removing
the jamming links. For the scheme with cooperative jamming,
D is utilized to interfere the eavesdropping in the first time
slot by sending jamming signals
1
as shown in Fig. 1(a). In the
second time slot, an external UAV is employed as a jammer to
combat the eavesdropping as shown in Fig. 1(b). The relaying
UAV and jamming UAV are assumed to be deployed at the
same altitude H, while the vertical heights of terrestrial nodes
S, D, and E are negligible compared with H.
1
It is assumed that the antennas equipped at D can be used for either
transmitting or receiving signals at a specific time slot.
3
(a) First Time Slot
(b) Second Time Slot
Fig. 1. Illustration of the mmWave UAV-based relaying scheme with coop-
erative jamming. (a) Transmissions in the first time slot. (b) Transmissions in
the second time slot.
A. Channel Model
It is known that the air-to-ground channels can be LoS or
NLOS links due to the blockage effect [31]. According to [32],
the occurrence probability of LoS links is given as
P
L
(r) =
1
1 + A exp(−B(arctan(
H
r
) − A))
, (1)
where r denotes the horizontal distance between the UAV
and a ground node. A and B are constants relying on the
environment. Accordingly, the probability of NLoS links is
calculated as P
N
(r) = 1 − P
L
(r).
With the 3D distance of a LoS or NLoS link denoted by d,
the path loss model can be expressed as
L(d) =
β
L
d
−α
L
, LoS links,
β
N
d
−α
N
, NLoS links,
(2)
where α
L
and α
N
denote the path loss exponents for LoS
and NLoS links, respectively. β
L
and β
N
can be considered
as intercepts of the LOS and NLOS path loss formulas,
respectively.
In the following sections, we use d
ij
and r
ij
to denote the
3D distance and the horizontal distance between nodes i and
j, respectively, where i, j ∈ {S, D, E, U, J}. Without loss of
generality, we assume that each link experiences independent
Nakagami−m fading. Particularly, the small-scale fading pow-
er between the ith and jth nodes is denoted as h
ij
, which is
a Gamma random variable. We have h
ij
∼ Γ(N
L
, 1/N
L
) for
a LoS link and h
ij
∼ Γ(N
N
, 1/N
N
) for a NLoS link, where
N
L
and N
N
are integers and denote the Nakagami fading
parameters for LoS links and NLoS links, respectively.
B. 3D Antenna Gain
Assume that the relaying UAV (U) and jamming UAV (J)
are equipped with N
U
and N
J
antennas, respectively. For a
ground node g ∈ {S, D, E}, the number of antennas is denoted
as N
g
. Similar to [25], we adopt a 3D sectorized antenna mod-
el taking into account the directional mmWave transmission
and the UAV’s altitude. For each node j ∈ {S, D, E, U, J},
the main-lobe gain and side-lobe gain are expressed as G
j
M
with probability p
j
M
and G
j
m
with probability p
j
m
, respectively.
Thus, the directional antenna gain and the corresponding
probability can be written as [25]
G
a
i
=
G
a
M
, p
a
M
=
ψ
a
π
θ
a
π
G
a
m
, p
a
m
= 1 −
ψ
a
π
θ
a
π
, a ∈ {U, J}, (3)
G
g
i
=
G
g
M
, p
g
M
=
ψ
g
π
θ
g
π −θ
g
G
g
m
, p
g
m
= 1 −
ψ
g
π
θ
g
π −θ
g
, g ∈ {S, D, E}, (4)
where ψ
a
(ψ
g
) and θ
a
(θ
g
) denote the half-power beamwidth
in the azimuth and the elevation, respectively. Particularly, we
consider the worst case for the elevation angle at ground nodes
similar to [30], and accordingly the elevation angle of ground
nodes is uniformly distributed in the range of [θ
g
/2, π−θ
g
/2].
Assume perfect beam alignment for the legitimate links
between S (D) and U, and the misalignment caused by
UAV jittering is supposed to be well mitigated by existing
techniques [33]. Thus, the antenna gains from S to U and from
U to D can be given by G
SU
= G
S
M
G
U
M
and G
UD
= G
U
M
G
D
M
,
respectively. In contrast, the antenna gain of an eavesdropping
link (from U to E) or a jamming link (from J to E) can be
obtained as
G
aE
=
G
a
M
G
E
M
, p
1
= p
a
M
p
E
M
G
a
M
G
E
m
, p
2
= p
a
M
p
E
m
G
a
m
G
E
M
, p
3
= p
a
m
p
E
M
G
a
m
G
E
m
, p
4
= p
a
m
p
E
m
, a ∈ {U, J}. (5)
III. SECRECY ANALYSIS WITHOUT JAMMING
In this section, we analyze the secrecy performance of a
UAV-based relaying network without jamming. Using DF, the
signal-to-noise ratio (SNR) at the destination can be expressed
as
γ
D
=min
P
S
G
SU
L(d
SU
)h
SU
σ
2
U
,
P
U
G
UD
L(d
UD
)h
UD
σ
2
D
, (6)
where P
S
(P
U
) is the transmit power of S (U), and σ
2
U
(σ
2
D
) denotes the power of the additive white Gaussian noise
(AWGN) at U (D).
4
In addition, we suppose that the eavesdroppers are inde-
pendent and use the selection combining scheme to decode
the received signals from the source and the UAV. Thus, the
highest eavesdropping SNR among all the eavesdroppers can
be given as
γ
E
= max
max
E∈Φ
E
γ
SE
, max
E∈Φ
E
γ
UE
, (7)
where the SNR at each eavesdropper for decoding signals from
S and from U can be written as
γ
SE
=
P
S
G
SE
L(d
SE
)h
SE
σ
2
E
, (8)
γ
UE
=
P
U
G
UE
L(d
UE
)h
UE
σ
2
E
, (9)
and σ
2
E
is the noise power at eavesdroppers.
The achievable secrecy rate is
R
s
=
1
2
[log
2
(1 + γ
D
) − log
2
(1 + γ
E
)]
+
, (10)
where [x]
+
, max(x, 0). We set the threshold of secrecy rate
at the desired receiver D as R
th
, and thus, the secrecy outage
occurs when the secrecy rate is lower than R
th
. Specifically,
the secrecy outage probability of D can be derived as
P
sop
= P r {R
s
< R
th
}
= P r
1
2
log
2
(1 + γ
D
) −
1
2
log
2
(1 + γ
E
) < R
th
= P r
log
2
1 + γ
D
1 + γ
E
< 2R
th
= P r
1 + γ
E
> (1 + γ
D
)2
−2R
th
= 1 −
∞
0
F
γ
E
(1 + y)2
−2R
th
− 1
f
γ
D
(y)dy, (11)
where F
γ
E
(·) is the cumulative probability function (CDF) of
γ
E
and f
γ
D
(·) is the probability distribution function (PDF)
of γ
D
.
To derive the secrecy outage probability, the distributions
of the SNR at D as well as the highest eavesdropping SNR
at all the eavesdroppers are derived in Theorem 1.
Theorem 1: The CDF and PDF of γ
D
can be given as (12a)
and (12b) respectively at the top of the next page.
Proof: For the Gamma random variable h
ij
∼
Γ(N
i
, 1/N
i
), i ∈ {L, N}, the PDF and CDF of h
ij
can be
written as
f
h
(x) = N
N
i
i
x
N
i
−1
Γ(N
i
)
e
−N
i
x
, (13)
F
h
(x) = 1 −
N
i
−1
n=0
(N
i
x)
n
1
n!
e
−N
i
x
. (14)
Therefore, we can derive the CDF of γ
D
as
F
γ
D
(γ)=Pr
min(
P
S
G
SU
L(d
SU
)h
SU
σ
2
U
,
P
U
G
UD
L(d
UD
)h
UD
σ
2
D
)<γ
=1−Pr
P
S
G
SU
L(d
SU
)h
SU
σ
2
U
>γ
Pr
P
U
G
UD
L(d
UD
)h
UD
σ
2
D
>γ
=1−Pr
h
SU
>
σ
2
U
γ
P
S
G
SU
L(d
SU
)
Pr
h
UD
>
σ
2
D
γ
P
U
G
UD
L(d
UD
)
(a)
= 1−
i∈{L,N}
P
i
(r
SU
)
N
i
−1
n
1
=0
N
i
γσ
2
U
d
α
i
SU
P
S
G
SU
β
i
n
1
1
n
1
!
e
−
N
i
γσ
2
U
d
α
i
SU
P
S
G
S U
β
i
×
j∈{L,N }
P
j
(r
UD
)
N
j
−1
n
2
=0
N
j
γσ
2
D
d
α
j
UD
P
U
G
UD
β
j
n
2
1
n
2
!
e
−
N
j
γσ
2
D
d
α
j
UD
P
U
G
UD
β
j
= (12a). (15)
Step (a) is derived using the complementary cumulative dis-
tribution function (CCDF) of h
ij
by 1 − F
h
(x). Taking the
derivative of F
γ
D
(γ), we can easily obtain the PDF of γ
D
as
(12b).
The CDF of γ
E
can be expressed as
F
γ
E
(γ) = Pr
max
max
E∈Φ
E
γ
SE
, max
E∈Φ
E
γ
UE
< γ
= E
E∈Φ
E
Pr{γ
SE
< γ}
F
1
(γ)
E
E∈Φ
E
Pr{γ
UE
< γ}
F
2
(γ)
. (16)
Based on this, We will calculate F
γ
E
(γ) in Theorem 2 by
deriving F
1
(γ) and F
2
(γ) separately.
Theorem 2: The CDF of γ
E
can be given as (17) at the top
of the next page, where x
j
= cos(
2j−1
2J
π), v
j
=
R
U
2
(x
j
+ 1),
and J denotes the number of nodes in the Chebyshev-Gauss
approximation. In addition, R
U
is the maximum connection
distance in the horizontal plane between U and a specific
eavesdropper, and r
0
(R
0
) denotes the minimum (maximum)
connection distance between S and E.
Proof: First, define F
1
(γ) = E
E∈Φ
E
Pr{γ
SE
< γ}
.
Then, according to the generation function of the PPP [34],
we have
F
1
(γ) = exp
−2πλ
E
×
R
0
r
0
Pr{γ
SE
> γ}rdr
=exp
−2πλ
E
×
i∈{M,m}
p
E
i
R
0
r
0
Pr
h
SE
>
γσ
2
E
r
α
N
P
S
G
SE
β
N
rdr
. (18)
Particularly, the integral term in (18) can be calculated as
R
0
r
0
Pr
h
SE
>
γσ
2
E
r
α
N
P
S
G
SE
β
N
rdr
(b)
=
N
N
−1
n=0
R
0
r
0
N
N
γσ
2
E
r
α
N
P
S
G
SE
β
N
n
1
n!
e
−
N
N
γσ
2
E
r
α
N
P
S
G
S E
β
N
rdr (19)
(c)
=
N
N
−1
n=0
Γ
α
N
n+2
α
N
,
N
N
γσ
2
E
r
α
N
0
P
S
G
SE
β
N
−Γ
α
N
n+2
α
N
,
N
N
γσ
2
E
R
α
N
0
P
S
G
SE
β
N
n!α
N
N
N
γσ
2
E
P
S
G
SE
β
N
2
α
N
,
