Content uploaded by Wen Wang
Author content
All content in this area was uploaded by Wen Wang on Nov 16, 2021
Content may be subject to copyright.
1
Secrecy Performance Analysis of IRS-Aided
UAV Relay System
Wen Wang, Hui Tian, and Wanli Ni
Abstract
In this letter, we study the secrecy performance of an intelligent reflecting surface (IRS)-aided
unmanned aerial vehicle (UAV) relay communication system in the presence of multiple ground eaves-
droppers (Eves). Specifically, a UAV equipped with an IRS is deployed as a passive relay to forward the
signals transmitted from the base station to users. By modeling the distribution of Eves with stochastic
geometry theory and taking the estimation errors into account, we extract the novel expressions for the
statistical characterizations of the signal-to-noise ratio, for both legitimate receiver and Eves. For com-
pleteness, different eavesdropping channels are investigated, namely, the cooperative and independent
Eve cases. The secrecy outage probability (SOP) is analytically evaluated to unveil the impact of the
number of reflecting elements and the location of UAV on SOP performance. Finally, numerical results
corroborate the theoretical analysis.
Index Terms
Intelligent reflecting surface, secrecy outage probability, UAV relay communications.
I. INTRODUCTION
Due to their flexible deployment and on-demand mobility, unmanned aerial vehicles (UAVs)
are anticipated to provide ubiquitous wireless service in the fifth generation and beyond networks
[1]. Nevertheless, the broadcast nature and dominating line-of-sight (LoS) channels make the
confidentiality of UAV-enabled communications vulnerable to security threats. In this regard,
physical layer security (PLS), which can exploit the randomness characteristics of wireless
channels, becomes a key complementary security mechanism [2]. However, the conventional
PLS approaches rely on more complex hardware and protocols, such as jamming signal [3],
The authors are with the State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and
Telecommunications, Beijing 100876, China (e-mail: {wen.wang, tianhui, charleswall}@bupt.edu.cn).
2
relay selection [4] and so on. The energy consumption and complexity of these implementations
pose great challenges to the effectiveness of PLS in real scenarios. This motivates us to develop
a novel effective security communication system.
Benefiting from their peculiar property of modifying the propagation environment and en-
hancing the communication quality, intelligent reflecting surfaces (IRSs) have been widely in-
vestigated as an extremely effective supplement for the PLS technology [5]. Generally, IRSs are
comprised of abundant low-cost passive reflecting elements. By adaptively adjusting the phase
shift of each IRS element, the signals from different paths can be coherently combined at the
legitimate receiver (Bob) to enhance the desired signal power, or destructively at the eaves-
droppers (Eves) to avoid information leakage [6]. Furthermore, different from the conventional
amplify and forward (AF) relay, IRSs do not require complex signal processing operations, thus
the energy consumption can be reduced significantly. These impressive capabilities allow IRSs
to smartly reconfigure a propagation environment for UAV-enabled communications with low
energy consumption, while UAV can provide more degrees of freedom to IRSs’ orientation and
location deployment, thanks to its high mobility. Accordingly, the interplay between UAV and
IRSs fully reaps their individual benefits, which can be further exploited to improve the secrecy
performance of wireless communication.
Enlightened by the potentials of integrating IRSs into UAV-enabled networks, the design of
UAV-mounted IRS (UAV-IRS) relay systems has attracted increasing attention [7]–[10]. From an
optimization point of view, the authors in [7] maximized the transmission capacity for a UAV-
IRS assisted millimeter wave network by jointly designing the IRS’s beamforming and UAV’s
location. Likewise, a flying IRS was leveraged for the signal-to-noise ratio (SNR) maximization
in [8]. On the other hand, there are several works that verify the superiority of UAV-IRS relay
in communication improvements by different statistical characterizations, such as capacity and
outage probability analysis [9], [10]. However, regarding the secure performance, the existing
theoretical analysis focus on terrestrial IRS scenarios, and the research on the synergy of IRS
and UAV technologies remains an open issue. Specifically, [11] provided analytical expressions
for the secrecy outage probability (SOP) of an IRS-assisted terrestrial system in the presence of
an Eve, while the authors in [12] and [13] extended the analysis to systems with multiple Eves.
Such an IRS architecture is difficult to find appropriate places for installation due to practical
factors like site rent and impact of urban landscape. This ground-based design is also limited in
performance, since IRSs deployed on the buildings can at most serve terminals located in the half
3
Obstacle
IRS
e
r
Bob
Ă
Eve
Eve
Ă
Ă
Ă
Eve
BS
Fig. 1: System model of IRS-aided UAV relay system.
space [8]. Besides, these studies restricted to single-input settings and overlooked the randomness
of the distribution of Eves in reality. Furthermore, to simplify analysis, the derivations in [11]–
[13] are based on the assumption that all links follow Rayleigh channels. Thus these derived
results can not be directly applied to the UAV-enabled systems which are dominated by LoS
paths.
Motivated by the aforementioned background, we investigate the secrecy performance of a
UAV-IRS relay assisted multiple-input single-output (MISO) system over Rician fading channels.
Specifically, the contributions of this paper are summarized as follows: 1) We consider an
integrated UAV-IRS relay communication system, where a UAV-IRS relay in the sky is deployed
to assist the secure transmission from the base station (BS) to Bob, in the presence of multiple
Eves; 2) After statistically characterizing the received SNRs of Bob and Eves, we extract the
novel expressions of the SOP for non-colluding and colluding Eve cases; 3) We conduct the
asymptotic analysis to reveal some insights for system operation. Specifically, in the special
case with an Eve, employing large-scale IRS, and deploying the UAV close to Bob, while far
away from Eve, are quite beneficial for SOP improvements; 4) Numerical results verify the
accuracy of analytical results and the superiority of the proposed UAV-IRS relay system.
4
II. SY ST EM MO DE L
Consider an IRS-assisted downlink wireless communication system, where one UAV equipped
one IRS serves as a passive relay to assist the communication from one ground BS to Bob in
the presence of a random number of Eves, as shown in Fig. 1. Due to the obstacle of high
buildings, there is no direct channel between the BS and users. Bob and Eves are located at
the ground, while the spatial distribution of Eves follows a homogeneous two-dimensional (2D)
PPP Φewith density λe. Specifically, the secrecy guard zone technique is introduced to protect
the transmission. It is assumed that the UAV can physically detect suspicious Eves within the
secrecy guard zone [2]. This region is modeled as a disk on the ground, with a radius recentered
at the UAV’s horizontal projection. Accordingly, the UAV-IRS relay assists the communication
only when there is no Eve inside the region.
We assume that the BS is equipped with Nantennas, while all users are single antenna. The
IRS consists of M=Mx×Mzreflective elements, forming a Mx×Mzuniform rectangular array.
Then the transmit and receive array response vectors of the BS-UAV link can be respectively
given by [14]
at=1, e−j2πdt
λsin ξtcos ψt, . . . , e−j2(N−1)πdt
λsin ξtcos ψtT,(1a)
ar=1, e−j2πdrx
λsin ξrcos ψr, . . . , e−j2(Mx−1)πdrx
λsin ξrcos ψrT
⊗1, e−j2πdrz
λsin ξrsin ψr, . . . , e−j2(Mz−1)πdrz
λsin ξrsin ψrT,(1b)
where dt,drxand drzare respectively the antenna separation at the BS, at the IRS of x-dimension
and z-dimension, λis the carrier wavelength, and ⊗denotes the Kronecker product. Moreover,
ξtand ψtare the vertical and horizontal angle-of-departures from BS to IRS, while ξrand ψr
are the vertical and horizontal angle-of-arrivals from BS to IRS, respectively.
Since UAVs are usually at altitudes high enough to establish LoS links with ground devices,
and also experience small-scale fading due to the rich scattering, all communication links can
be modeled by the Rician channel [15]. Therefore, the channel between the BS and UAV can
be given by
Ha=ph0d−α1
a
| {z }
path loss sβ1
β1+ 1H+r1
β1+ 1 e
H!
| {z }
array response and small−scale fading
,(2)
where h0is the reference distance channel power gain, dais the distance between the BS and
UAV, α1≥2is the path-loss exponent and β1is the Rician factor. Here, the deterministic LoS
5
component H=e−j2πda
λar⊗aT
tand the non-LoS (NLoS) component e
H∼ CN(0,I)[14]. By
applying the channel estimation method based on the Maximum-Margin Matrix Factorization
[16], we assume that the perfect channel state information (CSI) of the BS-IRS and IRS-Bob
links can be obtained. However, since Eves are not currently scheduled users, the CSI from the
IRS to Eves is only partially available. Accordingly, the channel of the UAV-Bob and UAV-Eve
kcan be respectively modeled as
hH
b=qh0d−α2
b sβ2
β2+ 1gb+r1
β2+ 1e
g!,(3a)
hH
k=qh0d−α2
k sβ2
β2+ 1gk+r1
β2+ 1e
g+rτ2
1−τ2e!,(3b)
where dband dkare the distances of UAV-Bob, UAV-Eve klinks, α2and β2are the path loss
exponent and Rician factor, respectively. The generation process of the LoS components gb=
[gb1, gb2, . . . , gbM ]and gk= [gk1, gk2, . . . , gkM ], is similar to that of H.e
g= [eg1,eg2,...,egM]∼
CN(0,I),τ∈[0,1] and e= [e1, e2, . . . , eM]∼ CN(0,I)denote the NLoS component, imper-
fectness of hH
kand CSI error vector [6], respectively.
Thus, the received signal at Bob or Eve kis given by
yi=hH
iΘHawx+ni, i ∈ {b, k},(4)
where Θ=diag(φ1, φ2, . . . , φM)is the diagonal matrix for the IRS, with φm=ejθm, and
θm∈[0,2π)denoting the phase shift of the m-th element. Let pwdenote the transmit power,
then the precoding vector w=√pwf. Similar to [17], in order to provide a general framework,
it is assumed that the transmit beamformer obeys f= [f1, f2, . . . , fN]T=1
N[1,1,...,1]T.
III. CHANNEL STATISTICS
A. Main Channel Statistics
By introducing a new vector θ= [φ1, φ2, . . . , φM]H, invoking the equation hΘb =θHdiag(h)b
and defining eγb=pwh2
0d−α1
ad−α2
b
(β1+1)(β2+1)N0, the received SNR at Bob can be given by
γb=|hH
bΘHaw|2
N0
=eγb(pβ2gb+e
g)Θ(pβ1H+e
H)f2(5a)
=eγbθHb2=eγb
M
X
m=1 |bm|ej(θm+θbm)2(5b)
(a)
=eγb
M
X
m=1 |bm|2,(5c)
6
where (a)follows that we adjust the phase shift of IRS based on θm=−θbm. Let Hmn and
e
Hmn denote the n-th element in the m-th row of Hand e
H, respectively, then we have
b=diag(pβ2gb+e
g)(pβ1H+e
H)f= [b1, b2, . . . , bM]T
= [|b1|ejθb1,|b2|ejθb2,...,|bM|ejθbM ]T,(6a)
bm=XN
n=1(pβ1β2gbmHmn +pβ1Hmnegm
+pβ2gbm e
Hmn +egme
Hmn)fn.(6b)
Proposition 1: The cumulative distribution function (CDF) of γbcan be expressed as
Fγb(x)=1−Q1/2(λb/σb,√x/σb),(7)
where the non-centrality parameter λb=peγbu,σb=peγbeσband Qν(a, b)denotes the general-
ized Marcum Q-function.
Proof: The existence of the product of complex Gaussian random variables (RVs), egme
Hmn,
makes the exact distribution of bmtoo complicated to be used for further derivation. For
tractability, Gamma approximation is adopted to tackle it [18]. Accordingly, bmand |bm|become
Gamma distributed RVs with shape and scale parameters as κ=β1β2
β1+β2+1 ,ϑ=β1+β2+1
√β1β2.
Furthermore, based on the central limit theorem (CLT), for a sufficiently large number of
units, i.e., M1,PM
m=1 |bm|can be approximated as a Gaussian distributed RV with mean
u=Mκϑ =M√β1β2and variance eσ2
b=Mκϑ2=M(β1+β2+ 1) [11]. Thus, γbturns out to
be a non-central chi-square RV, with its CDF obtained as (7), which completes the proof.
B. Eavesdropping Channel Statistics
Potential eavesdroppers in real scenarios are either cooperative or independent. For complete-
ness, we introduce the SNR analysis frameworks for these two cases, respectively.
•Cooperative eavesdroppers (Case 1): In this case, all ground eavesdroppers are assumed
to be collusive. Therefore, from the perspective of eavesdropping, the optimal eavesdropping
technique is to apply maximum ratio combination to the signals received by the eavesdroppers
before detection [19].
Accordingly, the effective eavesdropping SNR is the sum of the received SNRs at Eves, which
is, γe1=Pk∈Φe,rk≥reγk, where rkis the horizontal distance between the UAV and Eve k, and γk
7
denotes the SNR of Eve k. Similar to γb, by defining eγk=pwh2
0d−α1
ad−α2
k
(β1+1)(β2+1)N0,γkcan be formulated
as
γk=|hkΘHaw|2
N0
=eγk(pβ2gk+e
g+αe)Θ(pβ1H+e
H)f2(8a)
=eγkθHk2=eγk
M
X
m=1 |ekm|ej(θm+θk m)2,(8b)
where α=qτ2(β2+1)
1−τ2and k=diag(√β2gk+e
g+αe)(√β1H+e
H)f= [|ek1|ejθk1,|ek2|ejθk2, ..., |ekM|ejθkM ]T.
Once again, by applying the CLT, we readily obtain
XM
m=1 |ekm|ej(θm+φk m)∼ CN(u, eσ2
k),(9)
where u=M√β1β2,eσ2
k=M(α2(β1+ 1) + β1+β2+ 1). Thus, γkbecomes a non-central
chi-square RV with two degrees of freedom and the non-centrality parameter λk=peγku.
Proposition 2: The moment-generating function (MGF) of the cooperative homogeneous PPP
distributed eavesdroppers can be derived as
Mγe1(s) = exp n2πλeZ∞
de
yαexp A1
yα2+B1−yα2−B1
yα2+B1
ydyo,(10)
where A1=λ2
kdα2
ks,B1=−2σ2
kdα2
ksand de=pr2
e+H2, with Hdenoting the deployment
height of the UAV.1
Proof: Let Mγk(s)denote the MGF of γk, then for the colluding Eves, the MGF of γe1can
be calculated by
Mγe1(s) = EΦehY
k∈Φe,rk≥re
Mγk(s)i.(11)
As such, by applying the probability generating functional for the 2D PPP [20], the MGF of
γe1can be rewritten as
Mγe1(s) = exp n−λeZR21−E(esγk)rdro(12a)
= exp n−2πλeZ∞
re1−Mγk(s)rdro.(12b)
Note that γkfollows the non-central chi-square distribution, thus Mγk(s) = expλ2
ks
1−2σ2
ks/(1 −2σ2
ks),
where σ2
k=1
2eγkeσ2
k. By substituting Mγk(s)into (12b), we arrive at (10).
1It is worth mentioning that the deployment height Hcan be different values as long as it follows the UAV commercial flying
rules.
8
Corollary 1: If the LoS links from UAV to Eves are blocked, ie., the LoS components are
negligible (β2→0), the UAV-Eves links convert to Rayleigh channels. As such, γkfollows the
exponential distribution with parameter ˆ
λk=M
4eγk(β1+ 1)(1 + τ2
1−τ2). Then the MGF of γkcan
be given by Mγk=1
1−sˆ
λk
. Furthermore, the MGF of γe1in (10) can be simplified as
ˆ
Mγe1(s) = exp n2πλeA2
εα2dεα2
e2F11, ε;ε+ 1; A2
dα2
eo,(13)
where A2=ˆ
λkdα2
ks,ε= 1 −2
α2, and 2F1(a, b;c;z)is the Gaussian hypergeometric function.
•Independent eavesdroppers (Case 2): In this case, to protect their eavesdropping activities,
we assume that eavesdroppers can be modeled as a set of independent and identical uniformly
distributed points without cooperation together. Under this assumption, the one that can obtain
the greatest SNR is the most detrimental Eve, and its probability density function (PDF) is given
in the following proposition.
Proposition 3: The PDF of the independent homogeneous PPP distributed eavesdroppers
can be derived as
fγe2(x) = Fγe2(x)×(−µA3x−µ−1+B3C3Qα2
i=1 ai
Qα2
i=1 bi
×α2Fα2"a1+ 1, . . . , ai+ 1, . . . , aα2+ 1
b1+ 1, . . . , bi+ 1, . . . , bα2+ 1 ;C3x#),(14)
where A3=−r2
eΓ(µ)D3
α2(−C3)µ,B3=1
2r2
eD3,D3=2πλe
1−2exp( λ2
k
(1−)σ2
k
),C3=−rα2
e
σ2
kdα2
k
,µ=2
α2, with Γ(·)de-
noting the Gamma function. ai=i+1
α2,bi=i+2
α2,∀i∈ {1,2, . . . , α2}, and pFqha1, . . . , ap
b1, . . . , bq
;ci
is the Generalized hypergeometric series.
Proof: Since the RV γkobeys the non-central chi-square distribution with parameter λk, its
CDF can be expressed as
Fγk(x)=1−Q1(λk/σk,√x/σk).(15)
Assuming that {x1, x2, . . . , xN}are N(N > 1) independent variables, then according to the
probability theory, we have Fz(z) = Pr{max{x1, x2, . . . , xN} ≤ z}. On the basis, taking the
9
independent eavesdropping channels and Eves’ PPP distribution into account, the CDF of γe2
can be derived as
Fγe2(x) = EΦeY
k∈Φe,rk≥re
Fγk(x)(16a)
= exp −λeZR2
(1 −Fγk)rdr(16b)
(a)
≈exp −2πλe
1−2Z∞
re
exp −x
σ2
kexp λ2
k
(1 −)σ2
krdr(16c)
= exp nA3x−µ+B3α2Fα2a1, . . . , ai, . . . , aα2
b1, . . . , bi, . . . , bα2
;C3xo,(16d)
where (a)is obtained by utilizing the approximation of the Marcum Q-function given in [21],
with ∈(0,1
2)denting the Chernoff parameter. Finally, taking the derivative of (16d), the PDF
of γe2can be obtained as (14).
Corollary 2: As for the Rayleigh channel, the CDF of γkin (15) can be expressed as
Fγk(x) = 1 −e−x
ˆ
λk. Accordingly, the CDF of γe2in (16d) can be derived as
ˆ
Fγe2(x) = exp −A4x−µΓ(µ, B4x),(17)
where A4=µπλeˆ
λµ
kd2
k,B4=dα2
e
ˆ
λkdα2
k
, and Γ(·,·)corresponds to the upper incomplete Gamma
function. Similarly, further derivation yields the PDF of γe2in Case 2 as
ˆ
fγe2(x) = A4exp −A4Γ(µ, B4x)
xµBµ
4e−B4x
x+µΓ(µ, B4x)
xµ+1 .(18)
IV. SECRECY PERFORMANCE ANALYSIS
A. Secrecy Outage Probability Analysis
The SOP is defined as the probability that the instantaneous secrecy rate falls below a threshold
secrecy rate Rth(Rth >0) [2]. Hence, let ω= 2Rth , the SOP can be expressed as
P= Prnlog2(1 + γb)−log2(1 + γe)< Rtho(19a)
=Z∞
0
Fγb(ω−1 + ωx)fγe(x)dx. (19b)
•Cooperative eavesdroppers (Case 1): Notice that due to the involvement of the generalized
Marcum Q-function with the fractional-order in (7), it is difficult to obtain the exact SOP
10
expression. To tackle this issue, by utilizing the inequality Q1/2(a, b)≤Q1(a, b)[21], we can
approximate (7) as
Fγb(x)≥1−e−qX∞
n=0
qn
n!Xn
k=0
e−x
2σ2
b
k!(x
2σ2
b
)k,(20)
where q=λ2
b
2σ2
b
. By substituting (20) and (10) into (19b), the SOP of Case 1 can be approximately
calculated by
Pco = 1 −e−qX∞
n=0
qn
n!Xn
k=0
1
k!Eγe1[e−zzk],(21)
where z=ω−1+ωx
2σ2
b
. Furthermore, by leveraging the equivalent transformation E[zkesz] = dk
dskE[esz] =
M(k)
z(s), the property of MGF Mz(s) = exp ((ω−1)s
2σ2
b
)Mγe1(ωs
2σ2
b
), and denoting s=−1, the closed-
form expression of SOP can be derived as
Pco = 1 −e−qX∞
n=0
qn
n!Xn
k=0
1
k!M(k)
z(−1).(22)
•Independent eavesdroppers (Case 2): Substituting (7) and (14) into (19b), the SOP of
Case 2 can be obtained as:
Pin =Z∞
0
Fγe2(x)n−µA3x−µ−1+B3C3Qα2
i=1 ai
Qα2
i=1 bi
×α2Fα2ha1+ 1, . . . , ai+ 1, . . . , aα2+ 1
b1+ 1, . . . , bi+ 1, . . . , bα2+ 1 ;C3xio
×1−Q1/2(λb/σb,√ω−1 + ωx/σb)dx. (23a)
B. Asymptotic Secrecy Outage Probability Analysis
Although (22) and (23a) show the SOP of the proposed system in the presence of multiple
Eves, the tricky involvement of higher-order derivatives and integrals makes these expressions
too complex to provide insights. Notice that the key difficulty in deriving a tractable SOP is the
double randomness of Eves’ spatial distribution and channel information, under which it is quiet
difficult to simplify the eavesdropping channel statistics. To facilitate the derivation and obtain
further insights into the system’s operation, we analyze the asymptotic behavior of the SOP in
the case of single Eve.
11
Assuming that the average SNR of the UAV-IRS relay obeys ¯γ=pwh2
0
dα1
aN0→ ∞, and utilizing
the approximation of the non-central chi-square distribution in [22], we obtain the following
approximate equalities
Fγb(x)≈1
2h1 + erfx−MA5σ2
b
2(MA5)1/4σ2
bi,(24a)
fγe(x)≈1
2√π(2MA6)1/4σ2
k
exp −(x−2MA6σ2
k)2
4√2MA6σ4
k,(24b)
where A5=β1β2
β1+β2+1 ,A6=β1β2
α2(β1+1)+(β1+β2+1) , and erf(·)denotes the error function. Upon
substituting (24a) and (24b) into (19b), and after some further mathematical manipulations, the
asymptotic SOP can be obtained as
P=√2s3C5
2v1×n−1−erf(pB5
v2
v1
) + 2 erfpB5(v2
v1
+s1v1)o
×exp n−B5s2
1+ 2√2s2
2−(v2
v1
)2o+ exp(−B5v3),(25a)
where B5=1
4M3
2,C5=1
ωt ,t=
eγk
eγb=d2
b
d2
k∈(0,1),s1=A
3
4
5,s2=A
3
4
6,s3= (A6
A5)3
4,v1=
q1+2√2s2
3C2
5,v2= 2√2s2s3C5−s1, and v3= 2√2(C5−1)2s2
2.
Corollary 3: In scenarios where the LoS links from UAV to the ground users are blocked
and there is only rich scattering, (3a) and (3b) turn out to be Rayleigh channels. Accordingly,
by defining B6=√Mπ and C6=1−τ2
ωt , the asymptotic SOP can be simplified as follows:
ˆ
P=pπB6C6−1−erf(pB6C6−1
2B
3
2
6) + 2 erf(pB6C6)
×exp(B6C2
6−B2
6C6) + exp(−B2
6C6).(26a)
Furthermore, by respectively taking the derivative of Pin (25a) and ˆ
Pin (26a) w.r.t Mand
t, we can readily obtain
P0(M)<0, P 0(t)>0,ˆ
P0(M)<0,ˆ
P0(t)>0.(27)
From (27), we have P→0when M→ ∞ or t→0. These properties indicate that whether
the LoS or NLoS components are dominate in our proposed system, employing the large-scale
IRS, and deploying the UAV close to Bob, but away from Eve, have quite positive impacts on
the SOP performance.
12
-10 -8 -6 -4 -2 0
10
-4
10
-3
10
-2
10
-1
10
0
Analysis (Cooperative eavesdroppers case)
Simulation (Cooperative eavesdroppers case)
Analysis (Independent eavesdroppers case)
Simulation (Independent eavesdroppers case)
M=20,30,40
SOP
M=20,30,40
g
(dB)
Fig. 2: SOP versus ¯γ(H= 30 m, λe= 10−4,re= 8 m, Rth = 10−4bits/s/Hz, dab = 0).
0 2 4 6 8 10
0.00
0.05
0.85
0.90
0.95
1.00
SOP
Simul., (Co.,), Simul., (In.,),
Anal., (Co., H=40m, w/o IRS), Anal., (In., H=40m, w/o IRS),
Anal., (Co., H=30m, w/o IRS), Anal., (In., H=30m, w/o IRS),
Anal., (Co., H=40m, M=20), Anal., (In., H=40m, M=20),
Anal., (Co., H=30m, M=20), Anal., (In., H=30m, M=20).
d
ab
(m)
Fig. 3: SOP versus dab (λe= 10−4,¯γ= 8 dB, re= 8 m, Rth = 10−4bits/s/Hz).
V. SIMULATION RESU LTS
This section is focused on validating the theoretical analysis through Monte Carlo simulations
and reporting the proposed integrated UAV-IRS relay system performance. Specifically, we denote
dab as the horizontal distance of the UAV-Bob link. Besides, other parameters are set as β1= 3
dB, β2= 10 dB, α1= 2.2,α2= 3,dt
λ=dr
λ= 0.5,N= 5 and τ= 0.5.
13
0 2 4 6 8 10
10
-7
10
-6
10
-5
10
-4
10
-3
10
-2
6.6×10
-1
6.8×10
-1
7×10
-1
7.2×10
-1
7.4×10
-1
SOP
Simul., (Co.,), Simul., (In.,) ,
Anal., (Co., R
th
=10
-3
,
l
e
=10
-4
), Anal., (In., R
th
=10
-3
,
l
e
=10
-4
),
Anal., (Co., R
th
=10
-4
,
l
e
=10
-4
), Anal., (In., R
th
=10
-4
,
l
e
=10
-4
),
Anal., (Co., R
th
=10
-3
,
l
e
=10
-5
), Anal., (In., R
th
=10
-3
,
l
e
=10
-5
),
Anal., (Co., R
th
=10
-4
,
l
e
=10
-5
), Anal., (In., R
th
=10
-4
,
l
e
=10
-5
)
r
e
(m)
Fig. 4: SOP versus re(H= 30 m, M= 30,¯γ= 8 dB, dab = 0).
Fig. 2 shows the SOP versus the average SNR of the UAV-IRS relay, ¯γ, of Case 1 and Case
2, where different number of IRS elements Mare considered. Note that compared with Case
2,Case 1 has a greater risk of information leakage. However, the SOP is a decreasing function
in ¯γin both cases. This indicates that breaking Eves’ mutual connection and increasing ¯γcan
effectively enhance the secrecy performance. As found in SOP analysis, we can also observe
that the SOP decreases as Mincreases. This is due to the fact that, the large-scale IRS can
provide a stronger cascaded channel for legitimate signal reception but substantially deteriorate
the information reception at Eves. Moreover, it is worth mentioning that the simulation and
analytical results are in good agreement, which verifies the presented theoretical framework.
Fig. 3 characterizes the SOP versus dab for various height Hunder two different schemes:
with IRS (‘M=20’) and the AF scheme without IRS (‘w/o IRS’) [4], of Case 1 and Case 2. As
expected, a general trend is that the SOP of all schemes increases with the growth of dab. The
reason is that, increasing the horizontal distance between the UAV-IRS relay and Bob reduces
the received signal at Bob, while the signal at Eves are less affected, thus resulting in poor
secrecy performance. This phenomenon is also confirmed by the insights given in the asymptotic
SOP analysis. Another observation is that, a lower SOP is reached with a smaller Hvalue. This
behavior is caused by the fact that, as Hdecreases, the increase of LoS legitimate channel power
gains is more significant than that of eavesdropping channels. These results show that deploying
14
the UAV directly above the legitimate receiver and reducing the deployment height as much
as possible within the allowable range are quite beneficial to SOP improvements. In addition,
it is evident that our proposed IRS-assisted system obviously outperforms the corresponding
AF-relaying one in terms of the SOP, which demonstrates IRSs’ advantages in improving the
secrecy performance of wireless communication.
Fig. 4 shows the SOP versus refor different Rth and λe, of Case 1 and Case 2. We can
observe that the SOP decreases with the increase of the UAV’s effective detection radius, re,
which verifies the importance of the secrecy guard zone technique in the secrecy performance
enhancement. Another option for enhancing the PLS is to reduce the eavesdroppers’ density
λe. This behavior is due to the fact that, a lower λeresults in less eavesdroppers, thus greatly
reducing the diversity gain of information eavesdropping. Specifically, it is worth noting that a
lower λealso reduces the gap between Case 1 and Case 2. Since a higher threshold secrecy rate
means the communication system requires a larger channel secrecy rate, we can also observe
that the systems with a lower Rth perform better than the one with a larger Rth.
VI. CONCLUSION
In this paper, we have analyzed the secrecy performance of a UAV-IRS relay MISO system.
Specifically, a practical wireless environment was considered, where estimated channels on
the IRS were subject to estimation errors, and the distribution of Eves was modeled based
on the stochastic geometry. The SOP expressions were derived for characterizing the secrecy
performance in both cooperative and independent Eve cases, and validated through simulations.
Finally, simulation results were provided to demonstrate the derived results.
REFERENCES
[1] M. Mozaffari, W. Saad, M. Bennis, Y. -H. Nam, and M. Debbah, “A tutorial on UAVs for wireless networks: Applications,
challenges, and open problems,” IEEE Commun. Surveys Tuts., vol. 21, no. 3, pp. 2234-2360, 3rd Quart., 2019.
[2] Y. Liu, Z. Qin, and M. Elkashlan et al, “Enhancing the physical layer security of non-orthogonal multiple access in
large-scale networks,” IEEE Trans. Commun., vol. 16, no. 3, pp. 1656-1672, Mar. 2017.
[3] J. Kang, J. Yang, and J. Ha et al, “Joint design of optimal precoding and cooperative jamming for multiuser secure
broadcast systems,”IEEE Trans. Veh. Technol., vol. 66, no. 11, pp. 10551-10556, Nov. 2017.
[4] H. Wang, Y. Zhang, and X. Zhang et al, “Secrecy and covert communications against UAV surveillance via multi-hop
networks,” IEEE Trans. Commun., vol. 68, no. 1, pp. 389-401, Jan. 2020.
[5] Q. Wu, and R. Zhang, “Towards smart and reconfigurable environment: Intelligent reflecting surface aided wireless
network,” IEEE Commun. Mag., vol. 58, no. 1, pp. 106–112, Jan. 2020.
15
[6] S. Hong, C. Pan, and H. Ren, “Robust transmission design for intelligent reflecting surface-aided secure communication
systems with imperfect cascaded CSI,” IEEE Trans. Wireless Commun., vol. 20, no. 4, pp. 2487-2501, Apr. 2021.
[7] Q. Zhang, W. Saad, and M. Bennis, “Reflections in the sky: Millimeter wave communication with UAV-carried intelligent
reflectors.” in Proc. IEEE GLOBECOM, Waikoloa, Dec. 2019, pp. 1-6.
[8] H. Lu, Y. Zeng, and S. Jin et al, “Aerial intelligent reflecting surface: Joint placement and passive beamforming design
with 3D beam flattening,” IEEE Trans. Wireless Commun., 2021, early access, doi: 10.1109/TWC.2021.3056154.
[9] M. Al-Jarrah, E. Alsusa, and A. Al-Dweik et al, “Capacity analysis of IRS-based UAV communications with imperfect
phase compensation,” IEEE Wireless Commun. Lett., 2021, early access, doi: 10.1109/LWC.2021.3071059.
[10] T. Shafique, H. Tabassum, and E. Hossain, “Optimization of wireless relaying with flexible UAV-borne reflecting surfaces,”
IEEE Trans. Commun., vol. 69, no. 1, pp. 309-325, Jan. 2021.
[11] L. Yang, J. Yang, and W. Xie et al, “Secrecy performance analysis of RIS-aided wireless communication systems,” IEEE
Trans. Veh. Technol., vol. 69, no. 10, pp. 12296-12300, Oct. 2020.
[12] I. Trigui, W. Ajib, and W.-P. Zhu, “Secrecy outage probability and average rate of RIS-aided communications using
quantized phases,” IEEE Commun. Lett., 2021, early access, doi: 10.1109/LCOMM.2021.3057850.
[13] P. Xu, G. Chen, and G. Pan et al, “Ergodic secrecy rate of RIS-assisted communication systems in the presence of discrete
phase shifts and multiple eavesdroppers,” IEEE Wireless Commun. Lett., vol. 10, no. 3, pp. 629-633, Mar. 2021.
[14] M. Hua, L. Yang, and Q. Wu et al, “UAV-assisted intelligent reflecting surface symbiotic radio system,” IEEE Trans.
Wireless Commun., 2021, early access, doi: 10.1109/TWC.2021.3070014.
[15] C. You, and R. Zhang, “3D trajectory optimization in rician fading for UAV-enabled data harvesting,” IEEE Trans. Wireless
Commun., vol. 18, no. 6, pp. 3192-3207, Jun. 2019.
[16] E. Shtaiwi, H. Zhang, and S. Vishwanath et al, “Channel estimation approach for IRS assisted MIMO systems,” IEEE
Trans. Cognit. Commun. Netw., vol. 7, no. 2, pp. 452-465, Jun. 2021.
[17] T. Hou, Y. Liu, and Z. Song et al, “MIMO-NOMA networks relying on reconfigurable intelligent surface: A signal
cancellation-based design,” IEEE Trans. Commun., vol. 68, no. 11, pp. 6932-6944, Nov. 2020.
[18] H. Wu, X. Tao, and N. Zhang et al, “Cooperative UAV cluster-assisted terrestrial cellular networks for ubiquitous coverage,”
IEEE J. Sel. Area Commun., vol. 36, no. 9, pp. 2045-2058, Sept. 2018.
[19] G. Geraci, S. Singh, and J. G. Andrews et al, “Secrecy rates in broadcast channels with confidential messages and external
eavesdroppers,” IEEE Trans. Wireless Commun., vol. 13, no. 5, pp. 2931-2943, May. 2014.
[20] S. N. Chiu, D. Stoyan, and W. S. Kendall et al,Stochastic Geometry and Its Applications. San Francisco, CA, USA: Wiley,
Aug. 2013.
[21] D. A. Shnidman, “See also “Note on “Calculation of the probability of detection and the generalized Marcum Q-function”,”
IEEE Inform. Theory, vol. 37, pp. 1233, Jul. 1991.
[22] N. L. Johnson, S. Kotz, and N. Balakrishnan, Continuous Univariate Distributions, vol. 1. New York, NY, USA: Wiley,
1994.
