Secrecy Performance of the UAV Enabled Cognitive Relay Network

Abstract

Unmanned aerial vehicles (UAVs) have been recently applied to improve physical-layer security in wireless
communication networks. This work considers a cognitive relay
network where UAV is used as a mobile relay to bridge the
communication from a secondary transmitter to a secondary
receiver. Our purpose is to maximize the secrecy rate under
certain UAV trajectory and power constraints by designing a
joint optimization algorithm. Solving the optimization problem
is computationally challenging as the utility functions are nonconcave and constraints are non-convex. Thus, an efficient
iterative convex approximation algorithm based on a successive
optimization approach is introduced to address the proposed nonconvex optimization problems. The computer simulations show
that our algorithm can achieve a rapid coverage rate and the
UAV trajectory is optimized successfully. Results in this study
demonstrate that the proposed design outperforms conventional
schemes.

Full text

Secrecy Performance of the UAV enabled Cognitive
Relay Network
Dinh Chi-Nguyen1, Pubudu N. Pathirana1, Ming Ding2, Aruna Seneviratne3
1School of Engineering, Deakin University, Waurn Ponds, VIC 3216, Australia {cdnguyen, pubudu.pathirana@deakin.edu.au}
2Data61, CSIRO, Australia {ming.ding@data61.csiro.au}
3School of Electrical Engineering and Telecommunications, UNSW, NSW, Australia {a.seneviratne@unsw.edu.au}
Abstract—Unmanned aerial vehicles (UAVs) have been re-
cently applied to improve physical-layer security in wireless
communication networks. This work considers a cognitive relay
network where UAV is used as a mobile relay to bridge the
communication from a secondary transmitter to a secondary
receiver. Our purpose is to maximize the secrecy rate under
certain UAV trajectory and power constraints by designing a
joint optimization algorithm. Solving the optimization problem
is computationally challenging as the utility functions are non-
concave and constraints are non-convex. Thus, an efficient
iterative convex approximation algorithm based on a successive
optimization approach is introduced to address the proposed non-
convex optimization problems. The computer simulations show
that our algorithm can achieve a rapid coverage rate and the
UAV trajectory is optimized successfully. Results in this study
demonstrate that the proposed design outperforms conventional
schemes.
Index Terms—UAV, optimization, security, cognitive relay
I. INTRODUCTION
Physical layer security techniques have been applied widely
in secrecy enhancement of communication systems. Coopera-
tive relaying has been exploited as a highly effective technique
to improve wireless physical-layer security [1]. However, most
of the existing relaying schemes rely on static relays or fixed
stations, and such traditional systems can be expensive and
have low secrecy network performance. Thanks to UAVs’
mobility and flexibility, a new paradigm using UAVs enabled
relaying techniques has become a promising solution. The use
of UAVs as mobile relays leads to dynamic models, which
adapts perfectly with various communication environment,
aiming at maximizing secrecy network throughput [2]. The
authors in this work employed the UAV to optimize the source
power allocation and secrecy capacity in the ground wire-
tap channel, while the work [3] focused on the problems of
UAV trajectory design and the source power allocations for
maximizing the secrecy rate of the relay network. Note that the
above studies addressed their iterative optimization problems
through the block coordinate descent algorithm, which can
result in high iteration complexity.
Recently, UAVs have also been considered in cognitive
relay systems. The work [4] employed UAVs to increase
the cognitive radio gain of data link between the primary
user and the secondary user in the network system where a
system of primary base stations was designed through the same
unmanned aerial vehicle (UAV) relay. Moreover, authors in
the study [5] exploited the UAVs mobile capability based on
the trajectory design to enhance the cognitive communication
performance. However, the deployment of UAVs for cognitive
relay networks to improve secrecy network throughput has not
been considered.
In this paper, we introduce a novel secure framework for
the cognitive relaying network by employing the UAV’s high
mobility. The system consists of a secondary transmitter (S),
a secondary receiver (D), a primary user (P) and an eaves-
dropper (E), all with a single antenna. The UAV operates as a
mobile relay to bridge the communication from the secondary
transmitter to the secondary receiver. Specially, the proposed
strategy solves the joint optimization of the transmit power and
UAV trajectory via the successive approximation method in
order to maximize the secrecy rate for the secondary network.
The rest of this paper is organized as follows. The Section
II will introduce the system model and problem formulation
of UAV based cognitive relay network. In Section III, a novel
iterative algorithm using the successive convex optimization
method is proposed for trajectory optimization and power
allocations problems. Simulation results will be presented to
demonstrate the secrecy performance of the proposed algo-
rithms in Section IV. Finally, our conclusions are drawn in
Section V.
II. SYSTEM MODEL AND PROBLEM FORMULATION
In this section, we present the system model and problem
formulation considered in our paper.
A. System Model
We consider an UAV enabled cognitive relay network where
a secondary transmitter (S) sends information to a secondary
receiver (D) in the presence of a primary user (P) that operates
over the same frequency band and an eavesdropper (E). The
UAV is assumed to have a large buffer and operate as a mobile
relay to receive data from the secondary transmitter and re-
transmit it to the secondary receiver based on the decode-
and-forward (DF) relaying strategy as shown in Fig.1. The
proposed network includes ground nodes whose locations are
assumed to be known and such locations are represented by
three-dimensional (3D) Cartesian coordinates. Specifically, S,
D and P on the ground have coordinates (0,0,0),(D, 0,0)

Fig. 1. System model of UAV enabled cognitive relay system
and (xu, yu,0), respectively. The eavesdropper also has a fixed
location of (xe, ye,0). It is assumed that UAV operates at a
fixed altitude hfor a finite time period T. The duration of
UAV’s operation is Ntime slot, which can be divided into
nsmall slots. Therefore, the dynamic coordinate of the UAV
relay can be defined as (x[n], y[n], h), where x[n]and y[n]
denote the UAV’s x- and y-coordinates with a time index
n, respectively. Also, it is assumed that the initial and final
coordinates of UAV are pre-determined as (x0, y0, h)and
(xF, yF, h), respectively.
Let denote Vmax(m/s)as the maximum speed of UAV in
each time slot whose length is specified as τ=T
N(s), we can
calculate the maximum distance that the UAV can fly within
in a single time slot as Lmax =Vmaxτ. Thus, the mobility
constraint can be formulated as
(x[n+ 1] −x[n])2+ (y[n+ 1] −y[n])2≤L2
max,
n= 0, ..., N −1,
{x[0], y[0]}={x0, y0},{x[N], y[N]}={xF, yF}.
(1)
Next, we also assume that the legitimate link between the
UAV and ground nodes and the eavesdropping link between
the UAV and the eavesdropper are line-of sight (LoS) channels.
Thus, the LoS channel power gain from UAV to the ground
node in time slot n follows the free-space path loss model,
given by [6]: gUG =β0
d2
UG
, where β0denotes the channel
power gain at the reference distance d0= 1m, and dUG is
the distance from the UAV to the ground node in the time
slot n. Therefore, we can calculate the channel gains of the
secondary transmitter-UAV link, the UAV-secondary receiver
link, the UAV-eavesdropper link as
gRS =β0
dRS2=β0
x[n]2+y[n]2+h2,(2a)
gRD =β0
d2
RD
=β0
(D−x[n])2+y[n]2+h2,(2b)
gRE =β0
d2
RE
=β0
(xe−x[n])2+ (ye−y[n])2+h2.(2c)
We denote ps[n]and pr[n]as the transmit power of the
secondary transmitter and UAV in time slot n, respectively. In
practice, the transmit power is constrained by average power,
denoted by ¯
P. Also, at the (n)th time slot, UAV can only
forward data after receiving from secondary transmitter at the
(n−1)th time slot. Following these conditions, the transmit
power constraints can be formulated as
1
N−1
N−1
X
k=1
ps[k]≤¯
Ps,(3a)
1
N
N
X
k=2
pr[k]≤¯
Pr,(3b)
ps[k]≥0, k = 1, ..., N −1; pr[k]≥0, k = 2, ..., N, (3c)
ps[N] = pr[1] = 0.(3d)
In the absence of the eavesdropper, the achievable rate from
the UAV to the ground node in bits/second/Hertz (bps/Hz)
in time slot n can be defined as
RUG [n] = log2(1 + gU G [n]pr[n]
σ2)
=log2(1 + β0pr[n]
σ2d2
UG
) = log2(1 + γ0pr[n]
d2
UG
),
(4)
where σ2is the additive white Gaussian noise (AWGN) power
at the receiver and γ0=β0/σ2is the reference signal-to-noise
ratio (SNR).
It is assumed that processing delay at the relay is one slot, we
have the information causality constraints [3]
n
X
k=2
RD[k]≤
n−1
X
k=1
RR[k], n = 2, ..., N, (5a)
n
X
k=2
RE[k]≤
n−1
X
k=1
RR[k], n = 2, ..., N, (5b)
RS[N] = RR[1] = 0,(5c)
where RD[n], RR[n]and RE[n]denote the optimal data rates
of the secondary receiver, relay and eavesdropper at slot n,
respectively. Besides, we also consider the interference link
from UAV to primary user. At a certain time slot n, the
interference power on UAV-primary user channel is
Pu=pr[n]gRU [n] = β0pr[n]
(x[n]−xu)2+ (y[n]−yu)2+h2.
(6)
Further, the average interference temperature (IT) constraint
at the primary user also needs to be considered to protect
communications. Applying the result from [7], interference
power at the primary user should be limited below a IT
threshold, denoted by  > 0. Thus we have
N
X
n=1
β0pr[n]
(x[n]−xu)2+ (y[n]−yu)2+h2≤. (7)
Now we start to calculate the achievable rate on the main
channel and eavesdropping channel to determine the achiev-
able secrecy rate of the secondary system. The achievable rate

from the UAV to the secondary receiver in bits/second/Hertz
(bps/Hz)in time slot n can be expressed from (4) as
RRD =log2(1 + γ0pr[n]
d2
RD
)
=log2(1 + γ0
(D−x[n])2+y[n]2+h2).
(8)
Similarly, the achievable rate from the UAV to the eavesdrop-
per in bps/Hz in time slot n is given by
RRE =log2(1 + γ0pr[n]
d2
RE
) =
log2(1 + γ0
(xe−x[n])2+ (ye−y[n])2+h2).
(9)
From (8) and (9), the average secrecy rate achievable for the
secondary system in bps/Hz over the total Ntime slots is
given by
Rs{ps[n], pr[n], x[n]n, y[n]}=1
N
N
X
n=1
(RRD −RRE ).(10)
B. Problem Formulation
In this work, our objective is to maximize the secrecy
rate of the secondary network communication system, by
jointly optimizing the UAV trajectory {x[n], y[n]}and the
transmit power allocation {ps[n], pr[n]}, subject to the UAV
mobility constraints in (1), transmit power constraints in (3),
information causality constraints in (5) and IT constraints in
(7). Therefore, the optimization problem can be formulated as
below
P1 : max
pr[n],x[n],y[n]
1
N
N
X
n=1
(RRD −RRE )
s.t. (1),(3),(5),(7).
Note that problem (P1) is a non-convex optimization
problem, as the objective function is non-concave and con-
straint (3) is non-convex with respect to {x[n], y[n]}and
{ps[n], pr[n]}. Therefore, it is challenging to solve the pro-
posed problem. In the next section, we propose an efficient
iterative strategy based on a successive approximation method,
which achieves a fast coverage rate for the designed algorithm.
III. PROP OS ED OPTIMIZATION ALGORITHM
In this section, an efficient optimization algorithm is
presented to solve the problem (P1). Unlike previ-
ous studies [3,5], which partitioned optimization variables
{x[n], y[n], ps[n], pr[n]}into two blocks by the block coordi-
nate descent method, we introduce a single-block optimization
solution through using the successive approximation method.
The merits of proposed design consist of reducing significantly
iterative computation cost and achieving a fast coverage rate
for the optimization algorithm. The detailed design is given as
below. Problem P1can be rewritten as
P2 : max
pr[n],ps[n],x[n],y[n]
1
N
N
X
n=1
(RRD −RRE )
s.t.
n
X
i=2
log2(1 + γ0pr[n]
d2
RD
)≤
n−1
X
i=1
log2(1 + γ0ps[n]
d2
RS
), n = 2, ..., N,
(11a)
n
X
i=2
log2(1 + γ0pr[n]
d2
RE
)≤
n−1
X
i=1
log2(1 + γ0ps[n]
d2
RS
), n = 2, ..., N,
(11b)
N
X
n=1
β0pr[n]
(x[n]−xu)2+ (y[n]−yu)2+h2≤, (11c)
(x[n+ 1] −x[n])2+ (y[n+ 1] −y[n])2<=L2
max,(11d)
1
N−1
N−1
X
n=1
ps[n]≤¯
Ps,1
N
N
X
n=2
pr[n]≤¯
Pr,(11e)
ps[n]≥0, n = 1, ..., N −1, pr[n]≥0, n = 2, ..., N . (11f)
Note that solving the problem (P2) is challenging due to
the non-concavity of the objective function and non-convexity
of constraints (11a),(11b)and (11c). This motivates us to
develop a successive convex approximation algorithm. To that
end, we propose to use the following inequalities whose proof
results have been provided in [8] in the domain {x > 0, y >
0, k > 0}
ln(1 + 1
xy )≥ln(1 + 1
xkyk)+ xkyk
xkyk+ 1(2 −x
xk−y
yk),(12)
ln(1+ x
y)≤ln(1+ xk
yk)+( 1
1 + xk
yk
)[1
2(x2
xk+xk)1
y−xk
yk].(13)
Firstly, the objective function need to be approximated by
finding the concave lower bound for RRD and convex upper
bound for RRE over the feasible set. Let replace (D−x[n])2+
y[n]2+h2≤drd and denote x=1
γ0pr, y =drd , using (12)
we can find a concave lower bound at the local point {pk
r, dk
rd}
RRD ≥RRDlb =log2(e)ln(1 + γ0pk
r
dk
rd
) +
log2(e)γ0pk
r
dk
rd +γ0pk
r
(2 −pk
r
pr
−drd
dk
rd
).
(14)
Similarly, by replacing (E−x[n])2+ (S−y[n])2+h2≥dre
and let denote x=γ0pr, y =dre , we can also find an upper
bound of RRE at the feasible point {pk
r, dre}based on (13)
RRE ≤RREup =log2(e)ln(1 + γ0pk
r
dk
re
)
log2(e)dk
re
dk
re +γ0pk
r
[1
2dre
(γ0p2
r
pk
r
+γ0pk
r)−γ0pk
r
dk
re
].
(15)
In the next step, we develop approximation solutions for non-
convex constraints (11a),(11b)and (11c). By introducing the

slack variable drd1≤(x[n]−D)2+y[n]2+h2, the upper bound
for RRD at the feasible point {pk
r, drd1}can be expressed as
RRD ≤RRDup =log2(e)ln(1 + γ0pk
r
dk
rd1
) +
log2(e)dk
rd1
dk
rd1+γ0pk
r
[1
2drd1
(γ0p2
r
pk
r
+γ0pk
r)−γ0pk
r
dk
rd1
].
(16)
At the feasible point {pk
s, drs}, the right hand side of con-
straints (11a),(11b)can also be equivalently expressed as
RRS ≥RRSlb =log2(e)ln(1 + γ0pk
s
dk
rs
) +
log2(e)γ0pk
s
dk
rs +γ0pk
s
(2 −pk
s
ps
−drs
dk
rs
),
(17)
where drs ≥x[n]2+y[n]2+h2is the slack variable
introduced to simplify the problem. Note that the constraints
dre[n]≤(E−x[n])2+ (S−y[n])2+h2and dr d1[n]≤
(x[n]−D)2+y[n]2+h2are non-convex with respect to
{x[n], y[n]}variables. Following the first order Taylor expan-
sion of quadratic function respect to two variables x > 0
and y > 0:f(x, y)≥f(xk, y k) + Ofx(xk, yk)(x−xk) +
Ofy(xk, yk)(y−yk), we can find the convex upper bound for
the above constraints at any local point {x[n]k, y[n]k}
dre[n]≤(x[n]k−E)2+ (y[n]k−S)2+h2+
2(x[n]k−E)(x[n]−x[n]k) + 2(y[n]k−S)(y[n]−y[n]k),
(18)
drd1[n]≤(x[n]k−D)2+ (y[n]k)2+h2+
2(x[n]k−D)(x[n]−x[n]k)+2y[n]k(y[n]−y[n]k).(19)
Finally, (11c)can be equivalently replaced by
N
X
n=1
β0pr[n]
dru[n]≤, (20)
by introducing a new slack variable dru[n]≤(x[n]−xu)2+
(y[n]−yu)2+h2. Analogously, by using the first order Taylor
expansion of quadratic function with two variables x[n]and
y[n], we have
dru[n]≤(xk[n]−xu)2+ (yk[n]−yu)2+h2+
2(xk[n]−xu)(x[n]−xk[n]) + 2(yk[n]−yu)(y[n]−yk[n]).
(21)
From results (14) −(21), (P2) can be reformulated as a more
tractable problem
P3 : max
pr[n],ps[n],drd[n],dr e [n],
drd1[n],dru [n],x[n],y[n]
1
N
N
X
n=1
(RRDlb −RREup )
s.t.
n
X
i=2
RRDup ≤
n−1
X
i=1
RRSlb ,(22a)
n
X
i=2
RREup ≤
n−1
X
i=1
RRSlb ,(22b)
drs ≥x[n]2+y[n]2+h2, n = 1, ..., N , (22c)
drd ≥(D−x[n])2+y[n]2+h2, n = 1, ..., N , (22d)
(18) −(21) satisfied, (22e)
(11d)−(11f)satisfied. (22f)
Note that from inner approximated objective function and
constraints, the objective value of problem (P3) must be equal
or lower than that of problem (P2). Also, the solution to
problem (P3) must be a feasible solution to problem (P2) [2].
It is easy to see that the approximate problem (P3) is convex
and the feasible region is convex, thus it can be solved
effectively by convex solvers to find the optimal solution
through employing the iterative algorithm. The path-following
method is described in the Algorithm 1, which is guaranteed
to converge to its locally optimal solution.
Algorithm 1: Optimal UAV trajectory and power allocation
Initialization: Set k= 0 and initiate the feasible point
x[n]k, y[n]k, pr[n]k, ps[n]k
1: repeat
2: Solve (22) to obtain the optimal solutions:
x[n]∗, y[n]∗, pr[n]∗, ps[n]∗, drd [n]∗, dre[n]∗, drd1[n]∗, dru[n]∗
3: Update: x[n]k+1 := x[n]∗, y[n]k+1 :=
y[n]∗, pr[n]k+1 := pr[n]∗, ps[n]k+1 := ps[n]∗, drd[n]k+1 :=
drd[n]∗, dr e[n]k+1 := dre [n]∗, drd1[n]k+1 :=
drd1[n]∗, dru [n]k+1 := dru[n]∗.
4: Set k:= k+ 1
5: until Convergence
IV. NUMERICAL RES ULT S
This section will demonstrate the performance of the pro-
posed algorithm via simulations. MOSEK [9], the state-of-
the-art convex solver, is employed in the Matlab environment
using the YALMIP toolbox [10]. A cognitive network whose
communication bandwidth per link is 20MHz and carrier fre-
quency is 5GHz. The receiver noise power is set to σ2=−104
dBm. The channel power gain at the reference distance at
d0= 1mis assumed to be 1. The IT threshold is set at 10−3.
The average transmit power at UAV and secondary transmitter
are ¯
Pr=¯
Ps= 30dBm. The UAV is assumed to fly at an
altitude H= 100mwith a speed V= 50m/s during a period
T= 100s. The number of time slots used in simulation is
N= 100. The distance between secondary transmitter Sand
secondary receiver Dis set to D= 2000m, while the primary
user Uis at coordinate (3000,3000,0). The Eavesdropper E
are located at three different locations, namely (500,300,0),
(1000,300,0),(1500,300,0), respectively.

Fig. 2. UAV trajectories under different Eavesdropper’s locations
The Algorithm 1 is employed to optimize the UAV trajec-
tory. The initial and final coordinates of UAV are assumed at
(0, 0, 0) and (2000, 0, 0), respectively. As shown in Fig.2,
the UAV trajectories are adjusted in an adaptive manner cor-
responding to the change of Eavesdropper’s location, aiming
at staying away from the eavesdropper in order to improve
the transmitter-UAV and UAV-receiver links and impair the
Eavesdropper-UAV link. Also, the UAV always follows a
downward curved path to bridge the communication from
transmitter to receiver. The optimal UAV trajectory is achieved
after several iterations.
Fig.3 illustrates the secrecy rate (bps/Hz)versus the num-
ber of iterations. We demonstrate the performance of our
design by comparing with other two schemes. Case 1: only
UAV’s trajectory optimization is considered, while UAV is
kept at a static position (0, D/2, 0) and Case 2: only power
allocation is optimized. The illustrated results demonstrate the
superior performances of the proposed joint optimization algo-
rithm. Clearly, the designed scheme achieves a stable secrecy
throughput gain after six iterations, while the conventional
model with static relay shows its limitation in improving
secrecy network performance. The results confirm that the
optimization of both trajectory and power allocation improves
significantly the secrecy rate of the considered cognitive relay
network, which exhibits the advantage of our algorithm.
Fig. 3. Secrecy rates versus iterations
V. CONCLUSIONS
In this paper, we propose a new secure scheme for the
UAV enabled cognitive relay network by developing a joint
optimization algorithm to achieve an optimal secrecy rate.
Unfortunately, the optimization problem is highly non-convex,
which is very difficult to be solved effectively. Therefore, our
work presents a novel single-block optimization solution by
using the successive approximation method with respect to
both trajectory and power variables. Our simulation results
demonstrate the superiority of our joint optimization algorithm
in secrecy throughput enhancement in comparison with the
traditional benchmarks.
ACKNOWLEDGMENT
This work was supported by CSIRO Data61, Australia.
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