LATENCY-MINIMIZED DESIGN OF SECURE TRANSMISSIONS IN UA V-AIDED COMMUNICATIONS
Xiongwei Wu1,2, Qiang Li3, Yawei Lu2,4, H. Vincent Poor2, Victor C. M. Leung5,6and P . C. Ching1
1Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong SAR, China
2Department of Electrical Engineering, Princeton University, Princeton, USA
3School of Info. &Comm. Eng., University of Electronic Science and Technology of China, Chengdu, China
4Department of Electronic Engineering, Tsinghua University, Beijing, China
5College of Computer Science & Software Engineering, Shenzhen University, Shenzhen, China
6Department of Electrical & Computer Engineering, The University of British Columbia, Canada
ABSTRACT
Unmanned aerial vehicles (UA Vs) can be utilized as aerial base sta-
tions to provide communication service for remote mobile users due
to their high mobility and flexible deployment. However, the line-
of-sight (LoS) wireless links are vulnerable to be intercepted by the
eavesdropper (Eve), which presents a major challenge for UA V-aided
communications. In this paper, we propose a latency-minimized
transmission scheme for satisfying legitimate users’ (LUs’) content
requests securely against Eve. By leveraging physical-layer security
(PLS) techniques, we formulate a transmission latency minimization
problem by jointly optimizing the UA V trajectory and user associa-
tion. The resulting problem is a mixed-integer nonlinear program
(MINLP), which is known to be NP hard. Furthermore, the dimen-
sion of optimization variables is indeterminate, which again makes
our problem very challenging. To efficiently address this, we utilize
bisection to search for the minimum transmission delay and intro-
duce a variational penalty method to address the associated subprob-
lem via an inexact block coordinate descent approach. Moreover,
we present a characterization for the optimal solution. Simulation
results are provided to demonstrate the superior performance of the
proposed design.
Index Terms —Unmanned Aerial Vehicles, Physical-layer Se-
curity, Penalty Method, Latency
1. INTRODUCTION
Unmanned aerial vehicle (UA V)-aided communication has been
widely envisioned as a critical infrastructure for future Internet of
Things (IoT) networks [1, 2]. Different from conventional ground
base stations (BSs), UA Vs are capable of flexible movement, on-
demand deployment as well as high probability of line-of-sight
(LoS) wireless links [3]. Thus, it has many appealing applications,
e.g., serving as relays to provide ubiquitous communications for
remote mobile users, resuming Internet access for special areas,
aggregating or delivering content items in IoT applications [3–5].
However, due to the broadcast nature of line-of-slight (LoS)
wireless channels between UA Vs and legitimate users (LUs), con-
tent delivery is vulnerable to information leakage and likely to be
wiretapped by eavesdropper (Eve) [6]. In particular, UA Vs may
move around and get close to Eve when supporting content trans-
missions for LUs. This fact gives a new challenge to develop
This work was supported in part by the Global Scholarship Programme for Research
Excellence from CUHK, and in part by the U.S. National Science Foundation under
Grants CCF-0939370 and CCF-1513915.secure transmission designs for satisfying users’ demands. Some
preliminary works have been devoted to secure UA V-aided commu-
nications by leveraging physical-layer security (PLS). Specifically,
the research in [7] focused on improving the worst-case secrecy
rate among mobile users by generating a jamming signal in order to
confound Eves. The work in [6] studied secrecy energy efficiency
in multiple UA V-aided wireless networks by leveraging coopera-
tion. Moreover, covert communications for UA V-aided networks
was examined in [8], where the averaged covert transmission rate
was maximized by optimizing trajectory and transmission power.
Unfortunately, transmission latency for UA V-aided communications,
which is regarded as one of core concerns in future IoT networks [1],
has not been adequately studied so far. Only very few studies have
paid attention to this issue. Prior works in [9,10] proposed transmis-
sion designs to minimize latency of either data collection or content
downloads. None of the above latency-minimized studies takes into
account transmission security. Thus, secure transmission design
with a latency-minimized objective remains an open issue.
To bridge the research gap identified above, in this paper, we
develop a latency-minimized design for LUs while ensuring all re-
quested content is securely transmitted in the presence of an Eve.
Specifically, the UA V serves as an aerial base station to provide ser-
vice for LUs, which may be overheard by Eve. Taking advantage of
UA V movement and user association, we exploit the PLS technique
to generate degraded channels for Eve and thereby avoid information
leakage. Thus, a transmission latency minimization problem is for-
mulated by jointly optimizing the UA V trajectory and user associa-
tion strategy. The resulting problem is a mixed integer nonlinear pro-
gram, where the dimension of variables also needs to be optimized.
To deal with such a complicated problem, we introduce a bisec-
tion approach to efficiently find an optimized transmission latency
by addressing its corresponding subproblem with fixed transmission
latency in each iteration. Notably, instead of relaxing the binary
variables into continuous ones like most extant studies, a variational
penalty approach is proposed. Simulation results demonstrate signif-
icant advantages over the continuous relaxation method. Moreover,
the proposed design can effectively find a low-latency transmission
design through comparisons with baselines.
2. SYSTEM MODEL
As shown in Fig. 1, we consider a UA V-aided secure communica-
tions, where the UA V provides communication service for KLUs.
Specifically, each LU can request content items from the UA V byarXiv:2003.06564v1 [cs.IT] 14 Mar 2020 following certain content preference distribution (e.g., Zipf distri-
bution in [11]). Note that Eve is located around LUs, which can
wiretap information delivery between the UA V and LUs. Let K=
{1,2,···,K}be the set of indices of LUs. For ease of discussion,
each LU requires only one content each time; and all contents are
considered to be equal in size, each of which contains sbits. After
UAV
LU
Eve
Fig. 1 . An illustrative model for UA V-aided communications
users’ requests are revealed, the UA V is required to securely ferry
those contents to users with satisfactory quality of service. In this
paper, we focus on designing efficient secure transmission scheme
to minimize transmission delay.
Consider that UA V periodically flies over the area of inter-
est with period of T[6]. For ease of discussion, the contin-
uous time period is equally partitioned into discrete time slots
N={1,2,···,N}, withN=T/τ andτbeing the discrete
time interval. In general, τneeds to be sufficiently small so as to
ensure the position of UA V to be approximately static over each
time slot. Moreover, the UA V is assumed to fly at a fixed altitude
ofzin meters, which stands for the minimum altitude for avoiding
collision with ground obstacles. Subsequently, a two dimensional
Cartesian coordinate system is considered to measure the horizontal
coordinate of all nodes. Let R={r[n]|∀n∈N} be the UA V’s
trajectory, where r[n]∈R2denotes the horizontal coordinate of
the UA V at slot nmeasured in units of meters. The initial position
of UA V is denoted as r0. Regarding wireless links between the
UA V and LUs (or Eve) are assumed to be dominated by LoS; and
the Doppler impacts caused by UA V movement are able to be well
compensated [6]. Thus, the CSI between the UA V and LU kat slot
nis modeled as hk[n] =h0
(dk[n])2=h0
z2+/bardblr[n]−rk/bardbl2,wheredk[n]
denotes the distance between the UA V and LU k;rkdenotes the
coordinate of LU k; andh0stands for reference channel gain at 1
m [6, 12]. Similarly, the CSI between the UA V and Eve at slot nis
given byhe[n] =h0
z2+/bardblr[n]−re/bardbl2,whereredenotes the coordinates
of Eve [6, 12].
LetE=/bracketleftbig
ek[n]/bracketrightbig
∈ {0,1}K×Nbe user association strategy.
Specifically, if LU kis served by the UA V at slot n, we have ek[n] =
1, otherwise, ek[n] = 0 . To avoid interference when serving multi-
ple contents, the UA V is allowed to communicate at most one LU at
each slot, i.e.,/summationtext
k∈Kek[n]≤1,∀n.Consequently, the achievable
data rate for LU k∈K at slotnin bps is given by
Rk[n] =ek[n]log2/parenleftbigg
1+Ph0/σ2
(z2+/bar⌈blr[n]−rk/bar⌈bl2)/parenrightbigg
,∀n,k, (2)
wherePdenotes the transmission power; and σ2denotes the vari-
ance of additive Gaussian noise. Similarly, the achievable data rate
at slotnfor Eve wiretapping LU kis given by
Re,k[n] =ek[n]log2/parenleftbigg
1+Ph0/σ2
(z2+/bar⌈blr[n]−re/bar⌈bl2)/parenrightbigg
,∀n,k. (3)Accordingly, on the basis of PLS [13], we apply the Wyner’s wiretap
code and introduce redundant information to confound Eve. Thus,
the achievable average secrecy data rate for LU k∈K at slotnin the
presence of Eve is given by Rsec
k[n] = [Rk[n]−Re,k[n]]+,∀n,k,
where[·]+represents max{·,0}.
3. PROBLEM FORMULATION & PROPOSED DESIGN
Our objective is to minimize transmission delay (e.g., T=Nτ) for
all LUs while guaranteeing secure delivery. Thus, it is necessary to
jointly optimize UA V’s trajectory r, and user association E, which
leads to the following optimization problem:
P: min
R,E,NNτ (4a)
s.t. B0τ/summationtext
n∈NRsec
k[n]≥s,∀k, (4b)
/bar⌈blr[n+1]−r[n]/bar⌈bl2≤vmaxτ,∀n, (4c)
r[1] =r0,r[N] =r0, (4d)
/summationtext
k∈Kek[n]≤1,∀n, (4e)
ek[n]∈{0,1},∀k,∀n, (4f)
where constraint (4b) indicates the completion of content delivery,
andB0is the system bandwidth; and constraints (4c) and (4d) stand
for practical restrictions on UA V movements, with vmax being the
maximum speed of the UA V .
Although problemPis MINLP, we present the characterization
for an optimal solution N∗to problemP.
Proposition 1 There exists a unique optimal solution N∗satisfying
N∗≤
sK
B0τlog2(z2+ρ0)(z2+δe)
z2(z2+ρ0+δe)+/bar⌈blrK−r0/bar⌈bl+/summationtext
k∈Kδk
vmaxτ
,
(5)
whereρ0=Ph0
σ2;δe= max k/bar⌈blre−rk/bar⌈bl2;δk=/bar⌈blrk−rk−1/bar⌈bl,∀k∈
K; and⌈·⌉denotes the ceil operation; and the right-hand side of (5)
is also a feasible solution to P.
Proof: The proof of Proposition 1 is omitted due to the page limit.
It can be observed that the dimension of variables in problem
P(related to N) is not deterministic. To handle this difficulty, we
resort to bisection approach. By fixing N, problemPreduces to find
a feasible point to constraints (4b)–(4f). Subsequently, we consider
the following problem:
P(N) : max
R,E,λλ (6a)
s.t./summationtext
n∈NRsec
k[n]≥λ,∀k∈K, (6b)
(4c)−(4f). (6c)
Denote the optimal value for problem P(N)asλ∗. It is straightfor-
ward to see that if B0τλ∗≥s, an optimal solution to P(N)is a
feasible solution to the original P. Note that, to deal with secrecy
rate function in constraint (6b), we consider the following problem:
max
R,E,λλ (7a)
s.t.N/summationdisplay
n=1(Rk[n]−Re,k[n])≥λ,∀k∈K, (7b)
(4c)−(4f). (7c)
