Intercept Behavior Analysis of Industrial Wireless Sensor Networks in the Presence of Eavesdropping Attack

0.22 MB·English

by  Yulong Zou

IEEETRANSACTIONSONINDUSTRIALINFORMATICS(ACCEPTEDTOAPPEAR) 1
Intercept Behavior Analysis of Industrial Wireless
Sensor Networks in the Presence of Eavesdropping
Attack
Yulong Zou, Senior Member, IEEE, and Gongpu Wang
5 Abstract—This paper studies the intercept behavior of an WIRELESS sensor networks (WSNs) were initially mo-
1 industrial wireless sensor network (WSN) consisting of a sink tivated by the military for battlefield surveillance [1],
0 node and multiple sensors in the presence of an eavesdropping and now are further developed for various industrial applica-
2 attacker, where the sensors transmit their sensed information to
tionssuchasthe assemblyline monitoringand manufacturing
thesinknodethroughwirelesslinks.Duetothebroadcastnature
n of radio wave propagation, the wireless transmission from the automation for the sake of improving the factory efficiency,
a sensorstothesinkcanbereadilyoverheardbytheeavesdropper reliability, and productivity [2], [3], which are referred to as
J
for interception purposes. In an information-theoretic sense, the theindustrialWSNs[4]-[6].Inindustrialapplications,thereal-
1 secrecy capacity of the wireless transmission is the difference
time communications among the spatially distributed sensors
3 between the channel capacity of the main link (from sensor to
should satisfy strict security and reliability requirements [7].
sink)andthatofthewiretaplink(fromsensortoeavesdropper).

] If the secrecy capacity becomes non-positive due to the wireless The failure of ensuring the security and reliability of the
T
fadingeffect,thesensor’sdatatransmissioncouldbesuccessfully sensed information transmissions may cause an outage of the
I intercepted by the eavesdropper and an intercept event occurs productionline, a damageof the factory machine,or eventhe
.
s in this case. However, in industrial environments, the presence
loss of workers’ lives. Moreover, in industrial environments,
c of machinery obstacles, metallic frictions and engine vibrations
[ the machinery obstacles, metallic frictions, engine vibrations
makes the wireless fading fluctuate drastically, resulting in the

degradationofthesecrecycapacity.Asaconsequence,anoptimal and equipment noise are hostile to the radio propagation
1
sensorschedulingschemeisproposedinthispapertoprotectthe and certainly adversely affect the performance of wireless
v
6 legitimatewirelesstransmissionagainsttheeavesdroppingattack, transmissions.
where a sensor with the highest secrecy capacity is scheduled to
1 In industrial WSNs, due to the broadcast nature of radio
transmit its sensed information to the sink. Closed-form expres-
1 propagation, the wireless medium is open to be accessed by
sionsoftheprobabilityofoccurrenceofaninterceptevent(called
0
intercept probability) are derived for the conventional round- both authorized and unauthorized users, leading WSNs to be
0
robin scheduling and the proposed optimal scheduling schemes. morevulnerabletotheeavesdroppingattackthanwiredsensor
.
2 Also, an asymptotic intercept probability analysis is conducted networks, where communicating nodes are physically con-
0 to provide an insight into the impact of the sensor scheduling
nected with wire cables and a node without being connected
5 on the wireless security. Numerical results demonstrate that the
is unable to access for illegal activities. To be specific, as
1 proposedsensorschedulingschemeoutperformstheconventional
: round-robin scheduling in terms of the intercept probability. long as an eavesdropper hides in the industrial WSNs, the
v
legitimate wireless transmissions among the sensors can be
i Index Terms—Intercept behavior, industrial wireless sensor
X readily overheard by the eavesdropper, which may decode
networks, sensor scheduling, intercept probability, Nakagami
r fading. its tapped transmissions and violate the confidentiality of the
a
sensors’ information communications [8]. Therefore, it is of
importance to investigate the protection of industrial WSNs
I. INTRODUCTION
against the eavesdropping attack.
Traditionally, the cryptographic techniques were exploited
to protect the wireless communications against eavesdrop-
Manuscript received July 14, 2014; revised December 14, 2014; accepted ping, which typically rely on secret keys and can prevent
January30,2015.Paperno.TII-14-0732. an eavesdropper with limited computational capability from
Copyright (c) 2009 IEEE. Personal use of this material is permitted.
intercepting the data transmission between wireless sensors.
However, permission to use this material for any other purposes must be
obtained [email protected]. However,an eavesdropperwithunlimitedcomputingpoweris
This work was partially supported by the Priority Academic Program stillabletocracktheencrypteddatacommunicationswiththe
Development of Jiangsu Higher Education Institutions, the National Natural
aidofexhaustivekeysearch(knownasthebrute-forceattack)
Science Foundation of China (Grant Nos. 61302104 and 61401223), the
Scientific Research FoundationofNanjingUniversity ofPostsandTelecom- [9], [10]. Moreover,the secret key distribution and agreement
munications (Grant No.NY214001), andthe Natural Science Foundation of between the wireless sensors exhibit numerousvulnerabilities
JiangsuProvince (GrantNo.BK20140887).
and further increase the security risk. To this end, physical-
Y. Zou (corresponding author) is with the School of Telecommunications
andInformationEngineering,NanjingUniversityofPostsandTelecommuni- layersecurity is emergingasa promisingparadigmfor secure
cations, Nanjing, Jiangsu210003,China(e-mail: [email protected]). communications by exploiting the physical characteristics of
G. Wang (corresponding author) is with the School of Computer and
wireless channels, which can effectively protect the confi-
Information Technology, Beijing Jiaotong University, Beijing, China (email:
[email protected]). dentialityof communicationagainstthe eavesdroppingattack,
IEEETRANSACTIONSONINDUSTRIALINFORMATICS(ACCEPTEDTOAPPEAR) 2
even with unlimited computational power [11]. channel, instead of a simpler Rayleigh fading model used in
Thephysical-layersecurityworkwaspioneeredbyShannon [20].
in[12]andextendedbyWynerin[13],whereaninformation- The sensor scheduling to be studied in this paper exhibits
theoreticframeworkwasestablishedbydevelopingachievable some advantages over the conventional relay selection [15],
secrecy rates for a classical wiretap channel model consisting [16] and the artificial noise methods [17]-[19] in terms of
of one source, one destination and an eavesdropper. In [14], reducing the system implementation complexity and saving
the so-called secrecy capacity was shown as the difference the power resource. Specifically, in [15] and [16], additional
between the channel capacity of the main link from source networknodeswereintroducedandemployedforrelayingthe
to destination and that of the wiretap link from source to transmissions between the source and destination, which are
eavesdropper. If the secrecy capacity becomes non-positive refereed to as relay nodes. Given multiple relay nodes avail-
(i.e., the channel capacity of the main link becomes less able, the authorsof [15]and [16]investigatedthe relay selec-
than that of the wiretap link), the eavesdropper will succeed tion for wireless security enhancement, where the relay node
in intercepting the source message and an intercept event is that can achieve the highest secrecy against eavesdropping
considered to occur in this case [15], [16]. This implies that is chosen as the “best” relay to assist the source-destination
increasing the secrecy capacity can effectively decrease the transmissions.Althoughtherelayselectionstudiedin[15]and
probability that the eavesdropper successfully intercepts the [16] improvesthe wireless physical-layersecurity, it relies on
source message. However, the secrecy capacity of wireless additional relay nodes and requires complex synchronization
transmission is severely limited due to the wireless fading among spatially distributed relays, resulting in extra system
effect.Moreover,thepresenceofmachineryobstacles,metallic complexity. In addition, the artificial noise methods were
frictions and engine vibrations in industrial environments devisedin[17]-[19]toimprovewirelesssecuritybygenerating
makes the wireless fading fluctuate drastically, resulting in a a sophisticatedly-designed artificial noise for confusing the
further degradation of the secrecy capacity. eavesdropperonlywithoutaffectingthelegitimatedestination.
To overcome this limitation, considerable research efforts This, however, costs additional energy resources for the ar-
have been devoted to improving the secrecy capacity of the tificial noise generation, compared to the sensor scheduling,
wireless transmission through the artificial noise generation whereasensorwiththehighestsecrecyagainsteavesdropping
[17]-[19].The artificial noise aided security approachesallow is scheduled for data transmission without consuming any
the legitimate transmitters to generate a specifically designed additionalenergyresources.Sincewirelesssensorsareusually
interfering signal (called artificial noise) such that only the powered with limited batteries, the energy becomes one of
eavesdropper is adversely affected by the artificial noise, the mostpreciousresourcesin industrialWSNs, which makes
while the intended receiver remains unaffected. This leads the sensor scheduling more attractive than the conventional
to a degradation of the wiretap link in terms of the channel artificial noise methods from the energy saving perspective.
capacity without affecting the channel capacity of the main Themaincontributionsofthispaperaresummarizedasfol-
link, resulting in an increased secrecy capacity. In [17] and lows. First, an optimal sensor scheduling scheme is proposed
[18], the authors considered the use of multiple antennas for for protecting the industrial wireless transmission against
generating the artificial noise and showed that the number of the eavesdropping attack, where a sensor with the highest
antennasatthelegitimatetransmittershouldbemorethanthat secrecy capacity is selected to transmit its sensed informa-
atthelegitimatereceiverforthesakeofensuringthatthemain tion to the sink. The conventional round-robin scheduling is
link is unaffectedby the artificial noise. Additionally,in [19], also considered as a benchmark.Second, closed-form expres-
Goeckelinvestigatedtheemploymentofcooperativerelaysfor sions of the intercept probability for the conventional round-
the artificial noise generation and demonstrated a significant robin scheduling and the proposed optimal sensor scheduling
security improvementin terms of the secrecy capacity. schemesarederivedinNakagamifadingenvironments.Third,
Itispointedoutthatalthoughtheartificialnoiseapproaches an asymptotic intercept probability analysis is conducted and
in [17]-[19] can effectively enhance the wireless secrecy ca- thediversityorderoftheproposedschedulingschemeisshown
pacity,additionalpowerresourcesareconsumedforgenerating asthesumofNakagamishapingfactorsofthemainlinksfrom
the artificial noise to confuse the eavesdropper. To this end, the sensors to the sink. Finally, numerical results show the
Zou et al. proposed the multiuser scheduling scheme in [20] advantageof the proposedsensor scheduling scheme overthe
forimprovingthewirelessphysical-layersecuritywithoutany conventionalround-robinscheduling in terms of the intercept
additional power cost and showed the security improvement probability.
of cognitive radio networks in terms of the secrecy capacity Theremainderofthispaperisorganizedasfollows.Section
andinterceptprobability.Inthispaper,we examinethesensor IIpresentsthesystemmodelofanindustrialWSNinthepres-
schedulinginanindustrialWSNconsistingofasinknodeand ence of eavesdropping attack and describes the conventional
multiple sensors in the presence of an eavesdropper,differing round-robinschedulingaswellastheproposedoptimalsensor
from the multiuser scheduling for cognitive radio networks scheduling schemes. Next, in Section III, the closed-form
as studied [20]. More specifically, in industrial WSNs, the intercept probability expressions of the conventional round-
wireless channel is complicated due to the machinery obsta- robin scheduling and proposed optimal scheduling schemes
cles, metallic frictions and engine vibrations. This motivates are derived in Nakagami fading environments. In Section IV,
us to consider the use of a complex fading model (i.e., we present the asymptotic intercept probability analysis, fol-
Nakagami model) for characterizing the industrial wireless lowedbySectionV, wherethe numericalinterceptprobability
IEEETRANSACTIONSONINDUSTRIALINFORMATICS(ACCEPTEDTOAPPEAR) 3
assume that the CSIs of both the main channel and wiretap
s
1
main link channelareavailable,whichisanassumptioncommonlyused
wiretap link in the physical-layer security literature (e.g., [14]-[20]).
s
2
B. Conventional Round-Robin Scheduling
Obstacle .. Eavesdropper (e) For comparison purposes, let us first examine the con-
Sink .
ventional round-robin scheduling as a benchmark, where N
Obstacle
sensors take turns in accessing a given channel and thus each
s
N
Sensors sensor has an equal chance to transmit its sensed data to
the sink. Without any loss of generality, we consider that s
Fig.1. AnindustrialWSNconsistingofasinkandNsensorsinthepresence is scheduled to transmit its signal x (E(|x |2) = 1) withi
ofaneavesdropper (e). i i
power P and rate R , where R is specified to the maximum
i i i
achievablerate(alsoknownasthechannelcapacity)froms to
i
comparison between the conventional and proposed sensor thesink,whichguaranteesthattheergodiccapacityisachieved
schedulingschemesarepresented.Finally,SectionVIprovides by the legitimate transmission.
some concluding remarks. It needs to be pointed out that the sensed information xi
could be different types of data for different sensors. For
example, the N sensors of Fig. 1 may be used to detect
II. SENSOR SCHEDULING IN INDUSTRIAL WSNS
and monitor different aspects of an industrial plant environ-
A. System Model ment, including the machine motion, temperature, moisture,
pressure, and so on. The sensor data may also be obtained
As shown in Fig. 1, we consider an industrial WSN con-
by exploiting the collaboration between multiple sensors for
sisting of a sink node and N sensors in the presence of
distributed state estimation [23]-[25]. Although the sensors
an eavesdropper, where all nodes are assumed with single
may generate different types of data, their data streams are
antenna and the solid and dash lines represent the main link
assumed with the same priority in accessing the wireless
and wiretap link, respectively. Notice that the eavesdropper
channel for transmission in this paper. However, in practice,
of Fig. 1 could be either an illegitimate user or a legitimate
differentdatatypesmayhavedifferentqualityofservice(QoS)
userwhoisinterestedintappingotherusers’datainformation.
requirements. For example, some sensors may have time-
For notational convenience, N sensors are denoted by S =
critical data with a strict real-time requirement, which should
{s |i=1,2,··· ,N}. As illustrated in Fig. 1, the presence of
i
be assigned with a higher priority in accessing the wireless
machinery obstacles, metallic frictions and engine vibrations
channel than the others. It is of interest to consider different
in industrial environments is hostile to the radio propagation,
QoS requirements for different sensor data, which is out of
whichmakesthewirelessfadingfluctuatedrastically.We thus
the scope of this paper and regarded as future work.
considertheuse of Nakagamifadingmodelforcharacterizing
Thus, we can express the received signal at sink as
both the main channel and wiretap channel. It is pointed out
that the Nakagami model is more complex than other fading
y = P h x +n , (1)
s i is i s
models (e.g., Rayleigh fading, etc.), which is widely used in
p
literature [21], [22]. where his is a fading coefficient of the main channel from
In the industrial WSN of Fig. 1, N sensors communicate si to the sink and ns represents the zero-mean additive white
withthesinkusinganorthogonalmultipleaccessmethodsuch Gaussiannoise(AWGN)withvarianceN0.UsingtheShannon
as the time division multiple access (TDMA) and orthogonal capacity formula [12] and (1), we can obtain the channel
frequencydivision multiple access (OFDMA). When a sensor capacity of main link from si to sink as
(e.g., si) is scheduled to transmit its data to the sink over |h |2P
is i
a channel (e.g., a time slot in TDMA or an OFDM sub- Cs(i)=log2(cid:18)1+ N0 (cid:19), (2)
carrier in OFDMA), the eavesdropper attempts to intercept
the information transmitted from s . Traditionally, given an where i ∈ S. Meanwhile, due to the open nature of wireless
i
orthogonal channel, a node with the highest data throughput medium,the eavesdroppercan overhearthe signaltransmitted
is typically selected among N sensors to access the given from si and attempts to decode xi from its overheard signal.
channel and to communicate with the sink, which aims at Following the physical-layer security literature [11]-[20], the
maximizingthe transmissioncapacity withoutconsideringthe eavesdropper is assumed to have the perfect knowledge of
eavesdropping attack. By contrast, this paper is focused on legitimate transmissions from si to sink, includingthe coding
improvingthe wireless physical-layer security with the aid of and modulation scheme, encryption algorithm and secret key,
sensor scheduling. In order to effectively defend against the except that the source signal xi is confidential. Hence, the
eavesdropping attack, the sensor scheduling should take into signal overheard at eavesdropper e is given by
account the channel state information (CSI) of both the main
y = P h x +n , (3)
e i ie i e
channel and wiretap channel, differing from the traditional
p
scheduling method, where only the CSI of main channel is whereh isafadingcoefficientofthewiretapchannelfroms
ie i
consideredfor the throughputmaximization.Inthis paper,we to the eavesdropper and n represents the zero-mean AWGN
e
IEEETRANSACTIONSONINDUSTRIALINFORMATICS(ACCEPTEDTOAPPEAR) 4
with variance N0. Using (3), we can similarly obtain the III. EXACT INTERCEPTPROBABILITY ANALYSIS OVER
channel capacity of wiretap link from si to eavesdropper e NAKAGAMI FADING CHANNELS
as
|h |2P In this section, we analyze the intercept probability of the
ie i
C (i)=log 1+ . (4)
e 2(cid:18) N0 (cid:19) conventionalround-robinschedulingandtheproposedoptimal
sensor scheduling schemes over Nakagami fading channels.
As discussed in [13] and [14], the secrecy capacity is shown
as the difference between the channel capacity of main link
and that of wiretap link. Therefore, in the presence of eaves-
A. Round-Robin Scheduling
droppingattack, the secrecy capacity of wireless transmission
from s to sink can be obtained as As shown in [15]-[17],when the secrecy capacity becomes
i
non-positive (i.e., the channel capacity of the main link be-
C (i)=C (i)−C (i), (5)
secrecy s e comeslessthanthatofthewiretaplink),theeavesdropperwill
where C (i) and C (i) are given by (2) and (4), respectively. succeed in decoding and intercepting the source message and
s e
an intercept event is considered to occur in this case. Hence,
giventhats is scheduledto transmitto the sink, theintercept
C. Proposed Optimal Sensor Scheduling i
probability of s -to-sink transmission is obtained from (5) as
i
This subsection presents an optimal sensor scheduling
scheme to maximize the secrecy capacity of the legitimate Pi =Pr[C (i)<0]=Pr[C (i)<C (i)]. (9)
int secrecy s e
transmission. Naturally, a sensor with the highest secrecy
capacity should be chosen and scheduled to transmit its data Substituting (2) and (4) into (9) yields
to the sink. Hence, from (5), the optimal sensor scheduling
criterion is given by Piint =Pr |his|2 <|hie|2 , (10)
(cid:0) (cid:1)
Optimal User=argmaxCsecrecy(i) where |h |2 and |h |2 are Gamma distributed random vari-
i∈S is ie
=argmax1+ |hiNs|02Pi, (6) a|hbilee|s2waritehinredseppeecntidveenPtDofFesaschhoowthneirna(n8d).dNeontoitnigngthXatis|h=is||2haisn|d2
i∈S 1+ |hie|2Pi and X =|h |2, we obtain
N0 ie ie
whereS representsthesetofN sensors.Itisobservedfrom(6) Pi =Pr(X <X )
thatthechannelstateinformation(CSI)(i.e.,|h |2 and|h |2) int is ie
is ie
of each sensor is required for determiningthe optimal sensor, = f (x )f (x )dx dx
which can be obtained by using classic channel estimation ZZ Xie ie Xis is ie is (11)
xis<xie
methods [26]-[28]. More specifically, each sensor may first ∞ m
i
etrsatnimsmatietsitthseoewstnimCatSeIdCthSroIutoghthechsainnkn.elAfetsetrimcoaltlieocntinagndallthtehne =Z0 Γ(mi,σi2sxie)fXie(xie)dxie,
sensors’CSI,thesinkcanreadilydeterminetheoptimalsensor wheref (x )isgivenby(8)andΓ(m , mix )denotesthe
and notify the whole network. Thus, in the presence of an lower inXcoiempileete gamma function as givienσi2bsyie
eavesdropper,the secrecy capacity of legitimate transmissions
relying on the proposed sensor scheduling scheme can be Γ(m , mix )= σmi2sixie 1 xmi−1exp(−x)dx.
obtained from (6) as i σi2s ie Z0 Γ(mi)
1+ |his|2Pi Onecanobservefrom(11)thattheinterceptprobabilityofthe
Cspercorpeocsyed =mi∈aSxlog21+ |hiNe|02Pi. (7) si-to-sinktransmissionisindependentofthetransmitpowerPi
 N0  andnoisevarianceN0,whichimpliesthatincreasingthetrans-
It is pointed outthat the wireless link between any two nodes mitpowercannotimprovethewirelessphysical-layersecurity.
of Fig. 1 is modeled as the Nakagami fading channel. Thus, Thisalsomotivatesustoexplorenewapproaches(e.g.,sensor
|h |and|h |areNakagamidistributedrandomvariableswith scheduling) for improving the wireless security against the
is ie
respectiveshapefactorsm andk ,which,inturn,leadstothe eavesdropping attack. In the round-robin scheduling scheme,
i i
factthat|h |2 and|h |2 areGammadistributed,i.e.,|h |2 ∼ N sensors take turns in transmitting to the sink and thus the
is ie is
Γ(m ,σi2s) and |h |2 ∼ Γ(k ,σi2e), where σ2 and σ2 are interceptprobabilityoftheround-robinschedulingisthemean
i mi ie i ki is ie
expected values of |h |2 and |h |2, respectively. Denoting of N sensors’ intercept probabilities, yielding
is ie
X =|h |2 and X =|h |2, we can obtain the probability
is is ie ie N
density functions (PDFs) of Xis and Xie as Pround = 1 Pi , (12)
int N int
f (x )= 1 (mi)mixmi−1exp(−mixis) Xi=1
Xis is Γ(m ) σ2 is σ2
i is is (8) where N is the number of sensors and Pi is given by (11).
1 k k x int
f (x )= ( i )kixki−1exp(− i ie), It is noted that numerical intercept probability results of the
Xie ie Γ(k ) σ2 ie σ2
i ie ie round-robin scheduling scheme can be readily determined by
where Γ(·) denotes Gamma function. using (12).
IEEETRANSACTIONSONINDUSTRIALINFORMATICS(ACCEPTEDTOAPPEAR) 5
B. Optimal Sensor Scheduling as MER λ →∞. Following [15], the diversity gain of the
me
conventionalround-robin scheduling scheme is expressed as
Thissubsectionderivesanexactinterceptprobabilityofthe
proposed optimal sensor scheduling scheme over Nakagami
log(Pround)
fadingchannels.Asaforementioned,anintercepteventoccurs d =− lim int , (15)
round
whenthesecrecycapacitybecomesnon-positive.Hence,using λme→∞ log(λme)
(7), we obtain the intercept probability of proposed sensor where Pround is given by (12). We first rewrite Pi from (11)
int int
scheduling scheme as as
Pipnrtoposed =Pr Cspercorpeocsyed <0 Piint =Pr(Xis <Xie)
(cid:0) 1(cid:1)+ |his|2Pi Xis Xie (16)
=Prmi∈aSxlog21+ |hiNe|02Pi<0 (13) =Pr(cid:18) σe2 < σe2 (cid:19),
=Pr(cid:20)mi∈aSx(cid:18)NN00++||hhiies||22PPNii0(cid:19)<1(cid:21),  Dwehneoretiσnge2 >Yis0=isthXσeie2sr,efYeireen=ceXcσhie2ea,nnαeilsg=ainσσoim22sftahnedwαirieeta=pliσσni2e2ek,.
we readily obtain the PDFs of Y and Y from (8) as
is ie
where S denotes the set of N sensors. Noting that for
different sensors i ∈ S, random variables |his|2 and |hie|2 f (y )= 1 ( mi )miymi−1exp(− miyis )
are independent of each other, we can simplify (13) as given Yis is Γ(m ) α λ is α λ
i is me is me
(17)
by 1 k k y
f (y )= ( i )kiyki−1exp(− i ie).
Yie ie Γ(k ) α ie α
Pproposed = N Pr N0+|his|2Pi <1 i ie ie
int iY=1 (cid:18)N0+|hie|2Pi (cid:19) λUsing→th∞e ,PwDeFsobotfainYi(s18a)ndatYthiee gtoivpeonfbthye(f1o7l)loawnidngleptatigneg,
me
= N Pr |his|2 <|hie|2 (14) wanhderleetteixnpg(λ−αmisi→λymise∞),=w1e fcoarnλfmureth→er r∞ewirsiteusPedi. Uassing (18)
iY=1 (cid:0) (cid:1) me int
N ζ(m ,k ,α ) m mi 1 mi
= Pi , Pi = i i ie i · , (19)
int int m Γ(m ) (cid:18)α (cid:19) (cid:18)λ (cid:19)
iY=1 i i is me
wherePiint isgivenby(11).Sofar,wehavederivedtheclosed- where ζ(mi,ki,αie) is given by
forminterceptprobabilityexpressionsofboththeconventional
∞ 1 k ki
round-robin scheduling and the proposed optimal schedul- ζ(m ,k ,α )= ( i ) ymi+ki−1
ing schemes in Nakagami fading environments. It is worth i i ie Z0 Γ(ki) αie ie
mentioningthat althoughthe interceptprobabilityexpressions kiyie
×exp(− )dy .
ie
given by (12) and (14) can be used to conduct numerical α
ie
performance evaluation, it fails to provide an insight into the
Combining (12) and (19) yields
impact of the number of sensors on the intercept probability.
Therefore, the following section presents an asymptotic in- 1 N ζ(m ,k ,α ) m mi
tercept probability analysis to characterize the diversity order Pround = i i ie i
int N m Γ(m ) (cid:18)α (cid:19)
performance. Xi=1 i i is
1 mi−mi∈iSnmi (20)
×
IV. ASYMPTOTIC INTERCEPTPROBABILITY ANALYSIS OF (cid:18)λme(cid:19)
SENSORSCHEDULING 1 mi∈iSnmi
· .
Inthissection,weanalyzetheasymptoticinterceptprobabil- (cid:18)λ (cid:19)
me
ityofboththeconventionalround-robinandproposedoptimal
Substituting (20) into (15) gives
scheduling schemes.
d =minm , (21)
round i
A. Conventional Round-Robin Scheduling i∈S
Let us first consider the conventional round-robin schedul- which showsthat the interceptprobabilityof the conventional
ing as baseline.For notationalconvenience,the averagechan- round-robin scheduling decreases exponentially with minmi
i∈S
nel gains of the main link and wiretap link (i.e., σ2 and σ2) as λ → ∞, where m is the Nakagami shaping factor
is ie me i
are represented by σ2 =α σ2 and σ2 =α σ2, where σ2 of the channel from sensor s to sink. In other words, the
is is m ie ie e m i
andσ2 arecalledthe referencechannelgainsofthe mainlink diversitygainoftheround-robinschedulingwithN sensorsis
e
andthewiretaplink,respectively.Moreover,letλ represent determinedbythesensor with thesmallest Nakagamishaping
me
the ratio of σ2 to σ2, i.e., λ = σ2 /σ2, which is referred factor. This also means that upon increasing the number of
m e me m e
to as the main-to-eavesdropper ratio (MER) throughout this sensors, the wireless security of the conventionalround-robin
paper. We will examine the asymptotic intercept probability scheduling scheme would not improve, and even degrades.
IEEETRANSACTIONSONINDUSTRIALINFORMATICS(ACCEPTEDTOAPPEAR) 6
∞ 1 k k y yie 1 m m y
Pi = ( i )kiyki−1exp(− i ie)dy ( i )miymi−1exp(− i is )dy
int Z0 Γ(ki) αie ie αie ieZ0 Γ(mi) αisλme is αisλme is
∞ 1 k k y yie 1 m
= ( i )kiyki−1exp(− i ie)dy ( i )miymi−1dy (18)
Z0 Γ(ki) αie ie αie ieZ0 Γ(mi) αisλme is is
∞ 1 k m k y
= ( i )ki( i )miymi+ki−1exp(− i ie)dy .
Z0 miΓ(ki)Γ(mi) αie αisλme ie αie ie
B. Proposed Optimal Sensor Scheduling
100
Inthissubsection,weanalyzethediversitygainofproposed
optimal sensor scheduling through an asymptotic intercept 10−1
probability analysis for λ → ∞. Similarly to (15), the
me
dbiyversity gaindporofpposreodp=os−edλsmeleinm→so∞r slochgloe(gPd(uipnλlrtiomnpoges)esdc)h,eme is gi(v2e2n) Intercept probability111000−−−432
where Pround is given by (14). Substituting (19) into (14), we
have int 10−5 RRoouunndd−−rroobbiinn sscchheedduulliinngg ww.. NN==24
Proposed scheduling w. N=2
Proposed scheduling w. N=4
N ζ(m ,k ,α ) m mi 10−6
Pipnrtoposed = (cid:20) miΓ(im )ie (cid:18)α i(cid:19) (cid:21) −5 0 MER5 (dB) 10 15
iY=1 i i is
(23)
N Fig. 2. Intercept probability versus MER λme of the conventional round-
1 iP=1mi robin scheduling and the proposed optimal scheduling schemes fordifferent
·(cid:18)λ (cid:19) , numberofsensorswithmi=ki=1.5andαis=αie=1.
me
for λ →∞. Substituting Pround from (23) into (22) gives
me int
link are specified to m = k = 1.5, unless otherwise
N i i
stated. Additionally, the fading coefficients |h |2 and |h |2
d = m , (24) is ie
proposed i
are assumed to be independent and identically distributed
Xi=1
(i.i.d.) random variables, leading to α =α =1.
is ie
which shows that for λ → ∞, the intercept probability of
me Fig. 2 shows the intercept probability of the round-robin
proposed optimal sensor scheduling scheme decreases expo-
scheduling and the optimal scheduling schemes by plotting
nentially with N m , i.e., the diversity order of N m
i=1 i i=1 i (12) and (14) as a function of MER for different number of
is achieved byPthe proposed scheduling scheme. POne can
sensors N. As shown in Fig. 2, as the number of sensors
also observe from (24) that the diversity order of proposed
increases from N = 2 to N = 4, the intercept probability
sensor scheduling scheme is the sum of Nakagami shaping
performance of the conventional round-robin scheduling re-
factors m of the main links from N sensors to sink. Thus,
i mains the same, showing that no security benefit is achieved
as the number of sensors N increases, the diversity order of
by the round-robin scheduling with an increasing number of
proposed sensor scheduling scheme increases accordingly. In
sensors. By contrast, upon increasing the number of sensors
otherwords,increasingthenumberofsensorscansignificantly
from N = 2 to N = 4, the intercept probability of the
decrease the intercept probability of the proposed scheduling
proposed optimal scheduling scheme decreases significantly.
scheme.Bycontrast,thenumberofsensorsevenhasanegative
Inaddition,Fig.2alsoshowsthatforboththecasesofN =2
impactonthesecurityperformanceoftheconventionalround-
and N = 4, the proposed optimal sensor scheduling scheme
robin scheduling, as implied from (21). This further confirms
strictlyoutperformstheround-robinschedulingintermsofthe
the advantage of the proposed optimal scheduling over the
intercept probability.
round-robin scheduling.
In Fig. 3, we show the intercept probability versus MER
λ oftheround-robinschedulingandtheoptimalscheduling
me
V. NUMERICAL RESULTSAND DISCUSSIONS schemes for different Nakagami shaping factors. One can see
In this section, we present numerical results on the inter- fromFig.3thatastheNakagamishapingfactorsincreasefrom
cept probability of the conventional round-robin scheduling mi = ki = 1 to mi = ki = 2, the intercept probabilities of
and the proposed optimal sensor scheduling schemes. To be both the round-robin scheduling and the optimal scheduling
specific, the numerical intercept probabilityresults of the two schemesdecreasesignificantly.Fig.3alsoshowsthatforboth
schedulingschemesare obtainedthroughusing (12)and (14). mi = ki = 1 and mi = ki = 2, the intercept probability
The wireless link between any two network nodes in Fig. performanceoftheproposedoptimalschedulingisbetterthan
1 is modeled by the Nakagami fading channel, where the that of the round-robin scheduling.
Nakagami shaping factors of both the main link and wiretap Fig.4illustratestheinterceptprobabilityversusthenumber
IEEETRANSACTIONSONINDUSTRIALINFORMATICS(ACCEPTEDTOAPPEAR) 7
100 100
10−2 10−2
Intercept probability1100−−64 Intercept probability1100−−64
Round−robin scheduling w. m=k=1
i i
10−8 Round−robin scheduling w. mi=ki=2 10−8 Round−robin scheduling w. N=2
Proposed scheduling w. m=k=1 Round−robin scheduling w. N=4
i i Proposed scheduling w. N=2
Proposed scheduling w. mi=ki=2 Proposed scheduling w. N=4
10−10 10−10
0 5 10 15 20 −5 0 5 10 15 20 25
MER (dB) MER (dB)
Fig. 3. Intercept probability versus MER λme of the conventional round- Fig.5. Comparisonbetweentheexactandasymptoticinterceptprobabilities
robin scheduling andthe proposed optimal scheduling schemes fordifferent oftheround-robin scheduling andtheproposed optimalscheduling schemes
Nakagamishapingfactors withN =3andαis=αie=1. fordifferent numberofsensorswithmi=ki=1.5andαis=αie=1.
100 with each other in high MER region, implying the tightness
of asymptotic intercept probability analysis for λ → ∞.
me
10−2 As shown in Fig. 5, the slopes of intercept probability curves
of proposed optimal scheduling become much steeper, as the
Intercept probability1100−−64 dTinneuhtcmeirsrebcameespreetsaopnfarsotsbtehmnaabsutoiclrwihstyitfNhaosftaeipnnrrcoirsnpepcoaersseeeedasdsiafonsrpgotmλinmmuaNemlb→sec=rheo∞d2fu,ltsioecnnogNsnosfircrsh=m,eitmnh4gee.
Round−robin scheduling w. λ =3 the advantage of exploiting the optimal sensor scheduling for
me
10−8 Round−robin scheduling w. λme=5 defending against the eavesdropping attack.
Proposed scheduling w. λ =3
me
Proposed scheduling w. λ =5
me
10−10 VI. CONCLUSION AND FUTURE WORK
2 4 6 8 10 12 14
The number of sensors (N)
In this paper, we investigated the use of sensor scheduling
Fig. 4. Intercept probability versus the number of sensors N of the to improve the physical-layer security of industrial WSNs
conventional round-robin scheduling and the proposed optimal scheduling against the eavesdropping attack and proposed an optimal
schemesfordifferentMERvalueswithmi=ki=1.5andαis=αie=1. sensor scheduling scheme, aiming at maximizing the secrecy
capacity of wireless transmissions from sensors to the sink.
We also considered the conventional round-robin scheduling
of sensors of the conventional round-robin scheduling and as a benchmark. We derived exact closed-form expressions
the proposed optimal scheduling schemes for different MER of the intercept probability for both the conventional round-
values. It can be observed from Fig. 4 that for both the cases robinschedulingandtheproposedoptimalschedulingschemes
of λme = 3 and λme = 5, the intercept probability of the in Nakagami fading environments. An asymptotic intercept
conventionalround-robinscheduling keeps unchanged, as the probability analysis was also presented to characterize the
number of sensors increases. By contrast, with an increasing diversity gains of the round-robinscheduling and the optimal
numberofsensors,theinterceptprobabilityperformanceofthe sensor scheduling schemes. Numerical results demonstrated
optimalschedulingschemeissignificantlyimproved,showing that the proposed optimal scheduling scheme performs better
the security advantage of the proposed scheduling approach than the conventional round-robin scheduling in terms of the
over the conventionalround-robin scheduling. intercept probability. In addition, upon increasing the number
Fig. 5showsthecomparisonbetweenthe exactandasymp- of sensors, the intercept probability of the proposed optimal
totic intercept probabilities of the round-robinscheduling and sensorschedulingschemesignificantlydecreases,showingthe
theproposedoptimalschedulingschemesfordifferentnumber physical-layer security enhancement of industrial WSNs.
of sensors N. One can see from Fig. 5 that the intercept In the present paper, we only examined the single-antenna
probability of the round-robin scheduling corresponding to case, where each network node is equipped with the single
N = 2 is the same as that corresponding to N = 4, antenna.Itisofhighinteresttoextendtheresultsofthispaper
further showing that no security benefit is achieved by the to a generalscenario with multiple antennasfor each network
round-robinscheduling as the number of sensors increases. It node. Also, we have not considered the QoS requirement in
is also observed from Fig. 5 that for both the round-robin the sensor scheduling,where allthe sensors are assumedwith
scheduling and proposed optimal scheduling schemes, the the same priority and scheduled for data transmissions solely
exact and asymptotic intercept probability results match well based on their channel state information without considering
IEEETRANSACTIONSONINDUSTRIALINFORMATICS(ACCEPTEDTOAPPEAR) 8
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