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Research Article
Strong 𝑘-Barrier Coverage for One-Way Intruders
Detection in Wireless Sensor Networks
Junhai Luo and Shihua Zou
University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China
Correspondence should be addressed to Junhai Luo; junhai luo@uestc.edu.cn
Received January ; Revised April ; Accepted May
Academic Editor: Isaac Agudo
Copyright © J. Luo and S. Zou. is is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Intruders detection is one of the very important applications in Wireless Sensor Networks (WSNs). Sometimes detecting intruders
is not sucient; distinguishing whether an intruder is legal or illegal is necessary. Since -barrier coverage is widely used in detecting
intruders, a barrier construction algorithm is needed, which can not only detect an intruder but also judge an illegal intruder. An
intruder is dened as illegal if and only if it crosses straightly through the monitored region from the special side to another side.
On the contrary, it is a legal intruder. To detect an intruder and distinguish whether the intruder is legal or illegal, a strong -barrier
coverage algorithm is proposed. e strong -barrier coverage is a local barrier constructing algorithm and can detect any intruder
crossing the -barrier with a full probability. e strong -barrier coverage detects all intruders penetrating the annular region for
times. What is more, the proposed strong -barrier algorithm can provide a reliable judgement on whether an intruder is legal
or illegal, and the constructed -barrier coverage is dierent from the traditional one-way barrier coverage using binary barriers
that are intersected but not overlapped. Some simulation tests show that the proposed algorithm can construct strong -barrier
coverage very well.
1. Introduction
Wireless Sensor Networks (WSNs) have been studied for
years, which have many important applications for their
particular capabilities in monitoring environment, such as
in a battleeld or in an international border; all these
circumstances need a comprehensive monitoring. Barriers in
WSNs for intruders detection have been studied a lot, which
can assure that all intruders crossing a belt annular can be
detected. In some applications, only one direction crossing
the region is illegal. For example, people can leave a theater
without their movie tickets being detected, whereas they are
not allowed to see a movie without tickets. In the above
applications, it is not appropriate to use the traditional barrier
coverage models since they cannot distinguish the legal and
illegal intrusion behaviors.
In most previous works, researchers only considered
whether or not WSNs can form barrier coverage or whether
WSNs provide -barrier coverage. e theoretical basis of
designing barriers of WSNs is studied in []. In one barrier
coverage, intruders may cross the barrier from the gap with-
out being detected. Since one barrier coverage cannot meet
the requirements of intrusion detection in many applications,
high degree of coverage must be taken into account, and
the reasons of requiring -barrier rather than barrier are
discussed in []. A weekly -barrier coverage has been studied
in many literatures, such as []. For some applications of
WSNs, weekly -barrier coverage is not enough; thus the
strong -barrier coverage is needed, for example, a WSN with
a really high detecting probability. Detecting intruders with
highly probability relies on a strong barrier coverage.
In the study of barrier coverage, construction algorithms
for barrier have been researched much. Generally speaking,
there are two kinds of research directions, local barrier
construction and the global barrier construction algorithms.
ough global barrier coverage, such as the one in [],
which requires much fewer sensors than full coverage, is a
betting model of coverage for intrusion detection, it also has
limitations. en a local barrier coverage algorithm is studied
intensively in [–].
Hindawi Publishing Corporation
International Journal of Distributed Sensor Networks
Volume 2016, Article ID 3807824, 16 pages
http://dx.doi.org/10.1155/2016/3807824
International Journal of Distributed Sensor Networks
Our contributions in this paper are as follows:
() We nd that traditional one-barrier coverage model
is not suitable for some applications of WSNs in
intruders detection, especially in one-way intruders
detection.
() Comparing the previously binary barriers models, we
consider using a - (more than ) barrier model to
achieve the one-way intruders detection, which does
not need to satisfy the conditions in binary barrier
model.
() We propose a -barrier coverage algorithm, which
can easily construct barriers in monitored areas;
then we use the formed -barrier coverage model
to realize the goal of one-way intruders detection
without satisfying the limitations of binary barriers
coverage.
e remainder of the paper is organized as follows. Section
introducestherelatedwork.enthesystemmodel,thebar-
rier construction algorithm, and the barrier mending model
are presented in Section . Section shows an important
application of our model. e simulation results are presented
in Section . Finally, conclusion of this paper is presented in
Section .
2. Related Work
e authors in [] research the mathematical conditions of
building a weak barrier coverage in randomly deployment
WSNs and devise a centralized algorithm to determine
whether a region is -barrier covered. In literatures [–],
the authors study barrier coverage intensively. e authors
intheliterature[]supposethesituationofonebarrier,
and they study an energy-ecient border intrusion detection
algorithm, with measuring and guaranteeing the coverage
quality of WSNs.
In [], the authors introduce a weak -barrier coverage
problem by at least sensors in a belt region and propose
a simple algorithm to determine whether a belt region is
weakly -barrier covered. e strong barrier coverage of
WSNs is introduced in [], which is a model with a really
high probability to detect intruders. e authors in []
describe the worst- and best-case coverage calculation for
homogeneous isotropic of WSNs, in which they combine the
Voronoi diagram and graph search algorithm. In literatures
[, ], the authors present a fundamental geometric data
structure of the Voronoi diagram, which present us with a
preliminary knowledge of the Voronoi diagram. Sometimes it
is not sucient for weak -barrier coverage. In the literatures
[–], the strong barrier coverage has been researched
deeply. And the authors propose the minimum and maxi-
mum exposure path algorithms, respectively. e minimal
exposure path is thought to be the worst-case coverage of
WSNs, which is a weak barrier coverage. On the contrary, the
maximum exposure is best-case coverage of WSNs.
e authors in [–] consider that the sensors cannot
locally determine whether the sensor deployment provides
global barrier coverage. So the authors present a localized
sleep-wake-up algorithm for maximizing the network life-
time. Barriers in the above literatures are all presented in
one-dimensional space. In the literatures [, ], a -barrier
scheduling for the intruder detection in -dimensional space
isintroduced.eauthorsproposeadistributedscheme
whose target is providing low detection delay and low energy.
Considering that the detection delay and low energy at the
same time are a challenge, it is essential to consider them in
multidimensional space. Besides, a new concept of one-way
barrier coverage with wireless sensors has been introduced
in [–], and the authors propose the concept of one-
way barrier and establish a necessary condition for WSNs
to provide a one-way barrier coverage, which requires that
WSNs report illegal intruders but ignore the legal ones.
However, the two barriers, which are intersected but not
overlapped,arelimitedinbinarybarriers.
Motivatedbyworksoftheaboveliteratures,weproposeto
use -barrier coverage of WSNs to replace the previous binary
barriers to achieve the one-way detection while achieving
thesamegoalintheliteratures[–].Astrong-barrier
coverage algorithm is proposed, which is a local barrier
algorithm and can detect any intruders crossing the -barrier
with a full probability, assuring that all intruders penetrating
the annular region can be detected times. Furthermore, the
proposed -barrier model can make a reliable judgement on
whether an intruder is legal or illegal, which is dierent from
the traditional one-way barrier coverage. When compared
with the algorithm proposed in [] and another sensor
deployment, the number of sensors is much less.
3. System Model
3.1. Network Model. is paper assumes that sensors are
deployed in an annular region to detect intruders which
try to cross straightly through the monitored region and to
report the illegal intruders. An illegal intruder is an intruder
crossing through the monitored area from the special side to
the other side. If not, it is a legal intruder on opposite moving
direction. In this section, we give some basic denitions for
the annular region. e annular region is a special case of
a belt region whose two le and right boundaries coincide
with each other while its two upper and lower boundaries are
parallel, as shown in Figure . In addition, some denitions
about -barrier coverage are given. In Figure , we can see
that it is combined with two concentric rings, with the radius
of outer ring being 𝑂and inner ring being 𝐼,respectively.
e center of the area is marked as ,anditscoordinateis
known as (𝑂,𝑂).
e sensors are deployed following the Gaussian deploy-
ment, and the total number of sensors is . Each sensor
has an identical sensing radius 𝑠,andthecoveragemodel
of a sensor is called a disk model. When an intruder is in
the sensor’s sensing range, the intruders can be detected
with full probability. On the contrary, the intruders cannot
be detected. e disk model usually adopts the Voronoi
diagram to evaluate the detection possibility. In the literatures
[, ], the Voronoi diagram has been well studied. Besides,
thenumberofsensorsineachsingleringisdierent,and
International Journal of Distributed Sensor Networks
O
RI
RO
F : e initial wireless sensor network; sensors are distributed
as the Gaussian distribution.
the number of sensors deployed in each ring increases in
proportion to the circumference of each ring, which is shown
in (). e locations of sensors or their coordinates can be
obtained by GPS. Sensors can communicate with each other
while the distance between them is in the communication
radius 𝑐.𝑐≥2𝑠,where𝑠is the sensing radius of a sensor.
Denition 1 (annular belt region). A region bounded with
two up and down parallel curves and two overlapping right
and le boundary curves is called an annular belt region.
Denition 2 (barrier). A barrier is a sensor group with
sensing area overlap to form a belt coverage region starting
fromtheleboundarytotheright.eremightbemorethan
one barrier in belt region.
Denition 3 (-barrier coverage). A circular region is
referred to as -barrier coverage if and only if any intruders
crossing through the region can be detected times by the
WSNs.
Denition 4 (traditional -barrier coverage model). It is a
model with two barriers whose lower boundary of one barrier
and upper boundary of the other barrier overlap.
Denition 5 (global and local barriers). Global barrier means
that sensors can know a global knowledge of WSNs to build
a barrier; on the contrary, local barrier is dened as a barrier;
the constructing sensors of the barrier only know a local
background of WSNs.
Denition 6 (strong barrier coverage and weak barrier cover-
age). A weak barrier has at least one gas and a strong barrier
hasnogap,sothatnointruderscancrossthemonitored
area without being detected no matter what crossing paths
intruders would choose, but there is at least one safety path
A
BC O
k
RI
RO
.
.
.
1
F : e loop dividing gure, where the blue lines are the
dividing line, and the black lines are the two borders, and is preset
in our opinion, and ≥2.
that intruders could cross the monitored area without being
detected.
Denition 7 (alarm line). An alarm line is the bottom line
(or curve) of the innermost barrier, which will report an
alarm when an intruder crosses the alarm line from the other
barriers to the inner of region but does not report any alarm
whenever an intruder crosses the line from the inner region
to the outer region.
Denition 8 (one-way barrier coverage). A circular region
over which sensors are deployed is dened as one-way barrier
covered if and only if whenever an intruder crosses the
monitored region from the outer ring to the inner ring, and
at least one sensor reports an alarm; otherwise, there is not
any.
In this paper, we consider a belt region with its two
approximate vertical boundaries being overlapped, that is,
a circular region in Figure . e network model shown in
Figure describes the loop dividing, and the monitored area
is divided into equal concentric loops, which can be
expressed as
𝑤=𝑂−𝐼
,()
where is the required parameter predesigned. Assume that
all sensors know their local coordinates, and the coordinate
of the center point is known. Each sensor can communicate
with its neighbor sensors within its communication range.
Considering a sensor 𝑢,whosecoordinateis(𝑢,𝑢),aset
of its neighbor sensors is marked as () = {1,2,...,𝑡},
0<<. As shown in Figure , the blue rings represent
the inner and outer rings, and the black rings represent the
divided virtual rings.
3.2. Strong -Barrier Construction Algorithm. In this section,
we propose an algorithm to achieve -barrier coverage, which
needs much less sensors in building barriers. As mentioned
International Journal of Distributed Sensor Networks
the part of network model, the monitored area is a circular
area, which is divided into equal parts. In addition, the
way of building every barrier is identical in each part. e
construction of one barrier is introduced as follows, such as
the innermost circular loop, and others do the same.
ere are two steps in the barrier construction algorithm.
e rst step is to assign some basic information to sensors
and let them know the information of their neighbors’
locations. en the other step is to nd the remaining sensors
used in building a barrier.
3.2.1. Information Assignment. In this step, we divide the
into equalparts,and,ineverypart,abarrierisgoingto
be designed, as shown in Figure . Since the total number
of sensors is , we suppose that the number of sensors in
the innermost ring is , and the number of other circular
rings increases according to the circumference of each ring.
Suppose that circumference of the innermost ring is 𝑖,and
the circumference of adjacent outer ring is 𝑖+1,andtheradii
of sensors are 𝑖and 𝑖+1,respectively.entherelationship
oftheradiiisgivenby
𝑖+1 =𝑖+𝑤,()
where 𝑤is described in (). ese variables get the following
formulation:
𝑖
𝑖+1 =𝑖
𝑖+1 =2𝑖
2𝑖+1=𝑖
𝑖+1 ,()
where 𝑖and 𝑖+1 are the numbers of sensors deployed in two
adjacent circular rings deployed as the Gaussian distribution.
Moreover there is
1+2+⋅⋅⋅+𝑘=. ()
Previous sections have mentioned that the coordinates of sen-
sors are known, which are marked as ((1,1),...,(𝑛,𝑛)).
One of the limitations is the Euclidean distance between two
adjacent critical sensors; that is,
1,2=1−22+1−22.()
Anditmustsatisfythefollowingcondition:
1,2≤2𝑠,()
where 2𝑠is the critical condition for building an eective
barrier; the ultimate goal of our paper is to detect foreign
invaders. If (1,2)>2𝑠,therewillbeagapinthebarrier;
then it has to miss some invaders. 2𝑠≤
𝑐is to keep the
WSNs connecting and to ensure that adjacent sensors can
communicate with each other.
3.2.2. Barrier Construction Algorithm. e last step is specic
to constructing the barrier. Firstly, we randomly nd a
starting sensor and search the next satisfying sensor in turn.
In order to simplify the operation, we do the search along
the clockwise. Equation () describes the distance limitation
A1
rs
rs
dw
2rs
Nm+1
Nm
RiΔ𝜃 O
Nz
F : Graph of the next sensor in the maximum polar angle.
𝑠is the sensing radius of sensors, 𝑖is the innermost radius of the
circular ring, and is the same in each single circular rings.
of two adjoining sensors, but it cannot help us nd the
ideal candidate sensor. en at least one more condition is
really needed, which is the angular restriction. Noting that,
we consider the polar coordinates of sensors. e specic
expression of a sensor 𝑢is as follows:
𝑢=𝑢cos 𝑢
𝑢=𝑢sin 𝑢,()
where 𝑢is the polar radius and 𝑢is the polar angle. Since
the coordinate (𝑢,𝑢)of a sensor is known, the center point
is supposed as the pole, whose rectangular coordinate is
described as (𝑂,𝑂), and we can transform the rectangular
coordinate to the pole coordinate.
When nding the next sensor, it is not necessary to search
it in global scope because we have to construct strong
barriers, which has no gap between two adjoining sensors.
To satisfy the distance limitation, that is, (), it must be in the
polar angle interval, which is a constant value. As shown
in Figure , the maximum polar angle to nd the candidate
sensor is described in detail. ere are two tangent disks along
clockwise, whose centers are 𝑚and 𝑚+1,respectively.
Since radius of is big enough for the radii of sensors, the
length of arc between 𝑚and 𝑚+1 is as approximate as the
Euclidean distance 2𝑠.
In the triangle (𝑚𝑧),𝑧is the intersection of
the center line 𝑚𝑚+1 and circle 𝑚+1, and rectangular
coordinate is known as (𝑧,𝑧). = 4/()/𝑠is the
approximate maximum polar angle interval, which can be
obtained by using the Cosine theorem; that is,
cos = 2
𝑁𝑚𝑂+2
𝑁𝑧𝑂−2
𝑁𝑚𝑁𝑧
2𝑁𝑚𝑂𝑁𝑧𝑂.()
International Journal of Distributed Sensor Networks
en we can get as follows:
max =arccos 2
𝑁𝑚𝑂+2
𝑁𝑧𝑂−2
𝑁𝑚𝑁𝑧
2𝑁𝑚𝑂𝑁𝑧𝑂,()
where 𝑁𝑚𝑁𝑧=3
𝑠and 𝑁𝑚,𝑁2𝑂canbecalculatedby
using (), and in every circular ring is a constant value,
which is just dierent from the polar radius. Equation ()
is another condition to nd the next candidate. e angle
interval diagram is shown in Figure . en the remaining
sensors can be found to construct barriers in the same way
as before. At the same time, we will implement this method
in other rings. But while constructing the barrier, there may
be a situation that such a satisfying candidate sensor cannot
be found regardless of any eorts, so we have to dissolve this
barrier.
In our -barrier coverage algorithm, we can calculate
the minimal amount of nodes that can be used to create
a-barrier deployment. It is a variable changing with the
perimeter of ideal barriers and the sensing radius of sensor
nodes. Let us take min as the minimal amount of nodes, and
()is the radius of the ideal barriers, =1,2,...,; then the
formulaisasfollows:
min =⋅()
𝑠. ()
And the degree of redundancy of deployed nodes in each
circular is at least six times of the minimal amount of
nodes. When the degree is larger than six, our algorithm
can construct -barrier coverage more easily. e number of
sensors nodes deployed in each single circular rings is marked
as 𝑖,𝑖=6⋅min ,=1,2,...,. e six times is not literally
designed; it is achieved by many times of simulation.
e computational complexity of the proposed algorithm
is marked as (()),whichisrelativewith,and 𝑍.
is the maximal times of each searching in theory; 𝑍is the
actual searching number:
()= 𝑘
𝑚=1 1+52+33+𝑍
𝑝=1 6+𝑋
𝑞=𝑚+1 41+12+93+26+3⋅7+28+9. ()
1,2,3are variables satisfying some conditions. 1repre-
sents an identity matrix. 2represents a variable assignment.
3represents a constant assignment. 4represents a compari-
son. 5represents a multiplication. 6represents a addition. 7
represents a square root. 8means taking the absolute value.
e details of our -barrier are shown in Algorithm .
3.3. Barrier Mending Model
3.3.1. Energy Model. Aer running for a certain time, nodes
failure may be an unavoidable problem by running out of
energy or by some physical damage. In previous works, most
of them consider the remaining energy of an individual
sensor,whichcanbeagoodwaytodecidewhetherabarrier
needs to be mended. As one sensor fails, the barrier will
be destroyed. In this paper, we consider a strong -barrier
coverage, which should detect all intruders permeating the
monitored area almost being detected times. Once a hole
appears in a barrier, intruders may pass through the barrier
without being detected. Gap is the crack without any barrier
detecting an intruder’s incursion.
To maintain the monitoring quality, a barrier mend-
ing model is required. We can get the remaining energy
(described as 𝑟) of sensors as follows:
𝑟=𝑛𝑖
𝑖=1,𝑗=1,𝑖 ̸=𝑗𝑖−𝑅
𝑖+𝑇
𝑖⋅𝑅
𝑖𝑗 −𝑆⋅𝑖, ()
where 𝑅
𝑖and 𝑇
𝑖are energy for receiving and transmitting one
unit data, respectively; they all decline with the distance 𝑖𝑗
between two adjacent sensors and ,,=1,2,...,.And
is the parameters of signal decline. 𝑆is energy required
forsensingoneunitdata.𝑖is the initial energy reserve of
sensor𝑖.𝑖is the network lifetime of barrier𝑖;when()is
equal to zero, the network lifetime of barrier is achieving the
upper bound. We can get the distance of two neighboring
sensors by the GPS. We quote () from the literature [].
We can use () to calculate the lifetime of a single barrier.
Andthelifetimeofabarrierisrelatedtoboththenumberof
overlapping sensors (𝑖) in a barrier and the coverage ratio
(𝑖) of a barrier:
work time of barrier𝑖=𝑖⋅𝑖.
𝑖=the number of overlap sensor𝑖
the total number in barrier𝑖.
𝑖=a certain barrier coverage area
maximum coverage area .
()
en we can get relationship between network lifetime
andcoverageratio.Assumingthatistheworktimeof
network, we can get the relationship as follows:
𝑖=𝑖⋅𝑖
∑𝑘
𝑖=1 𝑖⋅𝑖⋅. ()
Once the remaining energy of a sensor is equal to zero,
it means that the sensor is dead. Two neighboring sensors
around the sensor in the same barrier can detect its failure.
e two neighboring sensors can transmit information to
each other. e previous sensor before the dead one in the
barrier has to nd another sensor to replace the dead one.
Atthesametime,thereplacementsensorconnectingwith
the latter sensor of the dead sensor in the barrier mending
International Journal of Distributed Sensor Networks
Require:𝑠=thesensingradiusofasensor;𝑐= the communication radius between two adjacent nodes; 𝑖=thenumber
of sensors deployed following the Gaussian deployment in the th circular ring; 𝑂=theouterradius;𝐼= the inner
radius; (𝑖,𝑗)= the Euclidean distance between sensor 𝑖and 𝑗;= the searching radius, which is a positive
discrete number; = the barrier number.
Ensure:1is the number of sensors deployed in rst circular ring according to the Gaussian distribution, set as
=(1,2,...,𝑚1)
while =1do
1is the starting sensor, its polar coordinates is
(1,1), 1=()cos 𝑚,
1=()sin 𝑚.=1,2,...,,()∼(()+/2,delta),𝑚=
𝑖∼(0,2), ()=+(−1)∗, =(𝑂−𝐼)/.
end while
repeat
search the next satisfying sensor, 𝑧∈
until ≤1,max (𝑧−1𝑧)≤2𝑠,max,
= 4
()/𝑠
if (𝑧𝑧+1)≥2𝑠,ormax≥4/()/𝑠then
break, fail to nd sensor 𝑧
end if
if max ≤4/()/𝑠, ≤1then
turn to next step
if 21≤2𝑠then
successfully nd the next sensor
end if
end if
go back to repeat to nd the next valid sensor;
while the number of sensors 𝑠in one barrier is equal to
the minimal number min =2()/2() do
if 𝑛min𝑛1≤2𝑠,then
succeed in building a barrier, break;
else 𝑛min𝑛1≥2𝑠, continue to nd the next valid senor, then
go back to step before two steps;
end if
end while
A : A strong k-barrier construction algorithm.
model must satisfy some requirements. In other words, the
new barrier can monitor one line of the eld and no intruders
can pass through the line without being detected. In other
words, the new barrier can monitor one line of the eld
andnointrudercanpassthroughthelinewithoutbeing
detected. ere are some limitations needing to be satised.
e limitations are the Euclidean distance between the dead
sensor and the replacement sensor and the distance between
the replacement sensor and the latter sensor. ese distances
all must be shorter than two times the sensing range, whereas
the Euclidean distance between the dead sensor and the latter
sensor should be shorter than the communication range 𝑐.
e mathematical expressions are N2N3≤(2
𝑠),N3N5≤
(2𝑠),N2N5≤𝑐,𝑐=2𝑠.AsshowninFigure,sensorsN,
N, N, N, N, and N belong to the same barrier, and these
sensors monitor one of the circular rings of the interested
area. Suppose that sensor N is dead, and both sensors N and
N can detect its failure. Since N is the previous sensor, it is
responsible for nding the replacement sensor N according
to the following rules. en N sends N a ag message, tells
N the remaining energy of N, and judges whether it should
ABON0
N1
N2
N3
N4
N5N9
N11
N12
k1
F : An example of barrier reconstruction.
wake up immediately or later. If yes, the sensor N sets the
ag = and sends it to senor N. If no, the sensor N sets
ag = , and it keeps sleeping. Aer N and N receive the
message ag = , they will know that the replacement sensor
will join the barrier to keep it working eectively. e new
barrier becomes N, N, N, N, N, and N.
International Journal of Distributed Sensor Networks
Since the remaining energy of each sensor can be cal-
culated according to (), there is 𝑟=
𝑖,whereis
a small mathematical variable less than , and it can be
calculated at every working time. change with the time
being spent on communication with the neighbor sensors is
worth discussion. As our barrier constructing algorithm is
a real-time communicating algorithm, the communication
time can really be ignored; then canbesetaszeroornearing
zero.
e procedure of nding a replacement sensor should
satisfy the following rules.
Rule 1. e previous sensor should select the replacement one
among the nearest neighborhoods in its ring, while they are
free to use.
Rule 2. If such a suitable sensor is not found, we can borrow
asuitablereplacementonetoformtheotherrings.
Rule 3. If no sensor can be found based on the above two
rules, the current barrier cannot be mended; then we release
the remaining sensors, which become redundant sensors and
arefreetohelpotherbarriersincasesomesensorsfail.
3.3.2. A Barrier Health System. e remaining energy of the
dying sensor𝑖is 𝑟𝑖; when it satises the condition that 𝑟𝑖=
⋅𝑖, its neighbor nodes need to search an alternative node
for it. is a least coecient of the initial energy reserve
of sensor𝑖, which is relative with the distance (𝑖𝑗) between
two neighbor nodes, and the speed of data transmission. e
Euclidean distance between two neighbors can be calculated
according to their coordinates, and the coordinates can be
obtained by GPRS.
Suppose that the speed of data transmission is equal,
marked as V. en the time of data transmission between the
dying node and its neighbor nodes is 𝑖𝑗.𝑖𝑗 =(
𝑖𝑗/V)𝑗𝑘 =
𝑗𝑘/V; they describe the time of date transmitting from two
neighboring nodes ,,and,.Andsensorrepresents the
dying sensor node:
min =𝑅
𝑖+𝑇
𝑖⋅𝑖𝑗 −𝑆⋅𝑖𝑗 +𝑗𝑘
𝑖.()
e remaining energy of the dying node is at least min
times the initial energy of sensor𝑖; its neighbor sensor nodes
need to nd its alternative node. Only, in this way, we may
ensure that the neighbors can nd an alternative node before
the dying node dies.
And an actual protocol that can be used to send the
alerts to the base station is in reference []. In [], nodes in
a cooperative node group will be considered as opponents
to each other; therefore, each node will maintain a -value
whichreectsthepayothatwouldhavebeenreceivedifthat
node selects one action and the other nodes jointly selected
the other action. Aer that, the node with the highest total
payo will be elected to forward the data packet to the next
cooperative node group towards the sink node.
Clockwise
Ak1
k2
kkO
s3
s1s2
̇
E
F : Application of one-way barrier in detecting dierent
intruders. s and s are the trajectories of crossing straight through
the monitored area and s is the trajectories of incompletely crossing
line.
4. Practical Application
is part presents the application of our WSNs in one-
way intruders detection. By using the barrier construction
algorithm proposed in this paper, a -barrier coverage can be
nally achieved as an ideal situation, as shown in Figure .
Sincethesensorsinournetworkaredistributedfollowing
the Gaussian distribution when =0,=1,wecan
construct the preset -barrier coverage very well by using
our algorithm. In the former section, it shows that the
barriers are almost constructed in the center of every circular
ring. Aer -barrier bridges being constructed perfectly, they
will be ultimately used in a practical application which is
called one-way barrier coverage. at is to say every single
intruder crossing straightly through the monitored area can
be detected to be legal or illegal.
Previous works using barriers to provide one-way barrier
coverage have been studied a lot. A new coverage model
called one-way barrier was rstly proposed in []. It proposed
the concept of neighboring barriers and designed dierent
protocols to provide one-way barrier coverage for dierent
sensor models based on neighboring barriers. In addition, a
one-way barrier coverage has been proposed in [], and the
single intruder has been considered in []. But when used to
detect multiple intruders, it is not so eective.
In this section, the model is used to detect the illegal
and legal intrusion. We also need to set an alarm line like
in [, , ]. But there is little dierent between the alarm
line in this paper and in literatures [, , ] because the
barriers in [, , ] are two neighboring barriers which
have a continuous overlapping region. ere are two special
barriers. However, in our WSNs, the above limitations are not
necessary conditions. is is an improvement we have made.
Our detection system is shown in Figure . In the monitored
International Journal of Distributed Sensor Networks
Intruder a
Intruder b
k1k2kkOA
Clockwise
.
.
.
(a) Invasion way of multiple intruders
Intruder a
Intruder b
k1k2kkO
O
A
Clockwise .
.
.
(b) Invasion way of multiple intruders
Intruder a
Intruder b
k1k2kkOA
Clockwise
.
.
.
(c) Invasion way of multiple intruders
F : ree kinds of invasion ways.
area, it has formed -barrier coverage being described by the
black rings with arrows. is situation is the ideal situation
and the direction of arrows is the direction of building
barriers. In fact, it does not matter how -barrier coverage
is constructed by using our algorithm; has to be more
than two. When isequaltotwo,ouralgorithmisjustthe
neighboring barriers proposed in [, , ]. at is to say, it is
a special situation of our model.
4.1. One Intruder. Obviously, WSNs with only one barrier
cannot furnish one-way barrier coverage. As mentioned
before, two barriers can provide one-direction barrier cov-
erage, but it must follows some special assumptions, such as
the limitations mentioned in literatures [–]. is paper
concentrates on using -barrier coverage to achieve the same
goal. Here we suppose that there is only one intruder crossing
the annual region. As shown in Figure , there are three
possible paths that one intruder may follow. For example, the
three red dotted lines with arrows are some possible invasion
paths of the intruders in Figure , described as s, s, and s,
respectively.
We assume that intruders penetrating straightly through
the circular monitored area from outside to inner region
are illegal intruders, which need to be detected. In practical
situation the circular monitoring area is like an isolation
belt, and only the intruders thoroughly penetrating the area
from outside to inside need to be broadcast, such as s.
On the contrary, intruders not thoroughly penetrating the
monitoring area or penetrating the area from the inside to
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outside are thought to be legal, like the paths s and s in
Figure . In order to distinguish the illegal intruders, we quote
the notion of alarm line in literature []. And the alarm line
in [] is a little dierent from to the one in this paper. An
alarmlinehereisalineorcurvealongthebeltwiththe
following property: the network reports an alarm whenever
an intruder crosses the alarm line from outside to inside, but
it does not report any alarm when an intruder crosses the
line from inside to outside. e bottom line of the innermost
barrier of WSNs is chosen as the alarm line.
Here we take -barrier as an example. When an intruder
thoroughly penetrates the monitoring area and enters into
the protected region, the intruder will be detected times
and will trigger the alarm line. It is illegal that the intruder is
detected times at rst and then triggers the alarm line. On
the contrary, it is legal. For example, the path s in Figure
is illegal, and the path s is legal, which will not report any
alarm. When the alarm is reported, we can easily distinguish
the illegal one. Since some intruders are not going to enter the
inner region of our monitored area, such as the path s shown
in Figure , an intruder enters into the monitoring area and is
detected several times being less than the maximum number
of barriers constructed in our model, but does not trigger the
alarm line; then the intruder is also thought to be legal. It is
obvious to see that our model can eectively detect the illegal
intruders, and it does not require two neighboring barriers,
and it can be used more widely. Above all, there are some
common situations most likely happened in our monitored
area.
4.2. Multiple Intruders. When considering more than one
intruderatthesametime,our-barrier coverage can provide
one-way barrier coverage if the intruders cross straight
through the region satisfying some constrains. AS shown
in Figures (a), (b), and (c), there are three possible
penetrating paths of intruders.
When intruders cross the circular area along the same
direction, such as in Figures (a) and (b), intruders and
either penetrate the circular rings from the outer boundary to
the inner boundary or from the inner boundary to the outer
boundary. In this case, intruders are detected −1times rst;
then they trigger the alarm line or trigger the alarm line rst;
then they will be detected −1times. Obviously, when there
are multiple intruders, we can detect the illegal intruders
depending on the order of triggering the alarm line rst or
being detected −1times rst. ere is no eect on each
intruder when intruders cross the circular rings with dierent
directions, as shown in Figure (c). ere exits a situation that
intruder triggersthealarmlinewhileintruderpenetrates
the circular rings and triggers the alarm line at the same; then
the detecting system may ignore the behavior of intruder .So
our -barrier coverage cannot detect multiple intruders well
under this circumstance.
5. Extended Application
In previous sections, we studied -barrier coverage of WSNs
in a circular area; here we are talking about its extended
application used in more generalized environment, for exam-
ple, with rectangular area. As seen in Figures (a) and (b),
the length is m, and width is m. In Figure (a), the
rectangular area has been divided into four width parts
equally, and sensors are deployed in the middle line of each
part following Gaussian deployment (=1,=+).
When sensors are deployed randomly in monitored area,
there are risks of sensors being deployed in some place with
high density; on the country, some places are with very few
sensors. Since the strong -barriers mean that no intruders
can penetrate the monitored area without being detected,
no gaps are allowed in barriers. To make sure of building
strong -barriers in WSNs with sensors randomly deployed,
we should deploy more than enough sensors in monitored
area.
e minimal amount of nodes in each barrier calculated
according to formula () is 5,5,5,5.Andwecanseein
Figure (b), which costs 6,6,6,6sensors in practical, our -
barriercoveragecanbeusedwellinrectangulararea,since
the error can be ignored in terms of the whole WSNs. Above
all, the proposed -barrier algorithm can not only be use in
a circular area, but also can be used in a more generalized
environment where the upper and lower boundaries are
parallel.
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6. Performance Evaluation
6.1. Simulation Methodology. e simulation results are
obtained in MATLAB. e objectives of the evaluation are
threefold: () testing the feasibility and eectiveness of our
algorithm in constructing -barrier coverage; () testing our
sensor network in detecting whether an intruder is legal or
illegal; and () studying the performance of our algorithm
under dierent system parameters, such as dierent sensing
radii of sensors, dierent barrier constructing models, and
dierent sensor distributions.
In the simulations, deploy nodes in an annular
region. e distribution of sensors follows the Gaussian
distribution and radius of the annual region ranges from
m to m. e sensing radii of all sensors are identical.
Intruders try to cross the region from one ring to the other
ring. Here the annular region is divided into four parts
with equal width. Without loss of generality, we assume that
the intruders’ always move from any of the two edges of
the annular region. We study dierent inuence of sensor
sensing radius in constructing our barriers. en we study the
impact of system parameters and intruders characteristics.
e sensing range is set as m and the communication range
issetasm.enumberofisassumedtobeinadvance.
Since the sensors are deployed as the Gaussian deployment,
the real value of may not exactly be . e number of sensors
in each part of the four annular regions is , , , ,
respectively, which are calculated according to the perimeter
of each ring.
6.2. Construction of the WSNs. To t e st the fe a s i b i l i t y and
eectiveness of our algorithm, Figure shows the initial
Gaussian deployment diagram, and we take =4.e
initial number of sensors is set as , , , from the
innermost circular ring to the outermost, respectively. e
sensors are almost deployed around the middle virtual line.
Here we take =0,=1.
Figure shows the simulation results of our algorithm.
We take s=8m, 𝑐=2
𝑠=16m, and =0,and
=1.Figure(a)showsthebarriersformedinthemodel
in Figure . We can see that there are four barriers in our
annular region. We do times in MATLAB, and we get four
barriers more than times. But there is also the situation
like in Figure (b) and there is only three barriers in our
monitored region, and the number of is smaller than the
preset value. But it just appears about times in the
times simulations. In Figures (a) and (b), the blue smooth
circular rings are our detected annular region and the red
dotted line is our generated barrier. Moreover, the points are
marked as sensors. In Figure , it is just shown the sensors
constructing barriers in each annular ring.
In the innermost circular ring of Figure (a), there is an
incomplete dotted line, which does not construct a complete
barrier, and the incomplete barrier is enlarged in Figure (b).
It shows that the barrier cannot nd a next suitable sensor
under our constraints. Such a barrier is not needed, then we
will dissolve it. And the sensors in the incomplete barrier can
go to sleep until they are waken up.
6.3. Impact of Sensing Radius. To e v aluate the i mp a c t o f s e n s -
ing radius on the performance of our barrier constructing
algorithm, we set the initial numbers of sensors as , , ,
from the innermost annular ring to the outermost one,
and sensors are deployed following the Gaussian deployment
in every annular ring. In addition, if we can build one barrier,
the number of sensors is enough. e sensing radii of sensors
are set to be m and m for each evaluation, respectively.
Dierent sensing radii are shown in Figure . In Figure ,
we can see that the larger the sensing radius is, the less the
sensorsareneededtobuildabarrierinthesamesituation.For
example, when 𝑠=8m,itneeds,,,sensorsinevery
barrier from the innermost to the outermost like Figure (c),
butitonlyneeds,,,sensors,when𝑠=10m. If we
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want to build a barrier to cover the same region, we would
better choose the sensors with larger sensing radius.
6.4. Comparison with Another Model. As the purpose of our
-barrier coverage in WSNs is to detect intruder invasion, we
can compare it with [], which uses a two-neighbor barrier
coverage to detect one-way intruders. We construct such a
two-neighbor barrier coverage using our -barrier coverage
algorithm. As shown in Figure (a), in Figure (b), it is
a -barrier coverage constructed by our -barrier coverage
algorithm, where =2. ey are dierent in nature. e
two neighboring barriers in Figure (a) are continuously
intersected but not anastomosed. But the -barrier coverage
in Figure (b) is separate. And the circular area is decided
into two width parts. e environment of these two situations
is the same. Sensor nodes are deployed following Gaussian
deployment in the middle line of each circular ring. When
the total number of sensor nodes deployed in the monitored
area is identical, we can see from Figure (c) that the number
of sensor nodes used in building two barriers between Figures
(a) and (b) is basically the same because the error is
negligible in terms of the whole WSNs. e comparison on
the number of sensor nodes used in building two barriers
between Figures (a) and (b) shows that our -barrier
algorithm can achieve a good performance when realizing the
same purpose.
6.5. Impact of Sensor Distribution. To evaluate the impact
of sensor distribution on the performance of our algorithm,
we adopt the Gaussian development model in Figure
and calculate the number of sensors needed to build a
barrier in Figure (a). Here we discuss another sensor
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(c) e comparison on the number of sensor nodes used in building
two barriers between (a) and (b)
F : Relevant comparison with our -barrier coverage.
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(c) e number of sensors for building barriers; the blue dotted one is
random deployment; the total number of sensors is ; the red dotted
one is Gaussian deployment; the total number of sensors is ; the radius
of each sensor is 𝑟𝑠=10m, no matter sensors are deployed by Gaussian
or random
F : Comparing our sensor distribution with random deployment.
distribution, which is the Uniform distribution, and com-
pare the sensor number used in building barriers with the
Gaussian deployment model. e reason why we choose
the Uniform distribution is that it is widely used in past
researches. e result is shown in Figures (a), (b), and
(c). Figure (a) shows the Uniform distribution generated
in MATLAB, and we can see that sensors are deployed
randomly and with no rules in the monitored region. To
compare the inuence of sensor distribution with Gaussian
distribution, the number of sensors distributed in ever y single
annularregionisthesameasthenumberinFigure.
Tobuildthebarriersbyusingthealgorithmproposed
in our paper, it is obvious that more sensors are required.
Figure (b) is a simulation result, and there are also four
barriers in the annular region. e sensing radius, the range
of our annular region, and the simulation times are the
same as the previous Figure . Comparing Figure (b) with
Figure (b), it is easy to see that it takes more sensors to
build barriers. In Figure (b), it shows barriers constructed
by using sensors with the Uniform distribution. Figure (c)
shows the contrast gure of the Gaussian distribution and
Uniform distribution, which plots the number of sensors
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F : e relationship between the percentage of nodes utilization and nodes redundancy.
in every barrier. In Figure , we can see more about the
relationship between randomly deployed sensor redundancy
and the number of strong -barrier coverage. Since sensors
are deployed following random deployment, it is more hard
to construct barriers than Gaussian deployment. In our -
barrier coverage algorithm, we can calculate the minimal
amountofnodesthatcanbeusedtobuilda-barrier
deployment according to formula ().
e degree of redundancy changes from six times to nine
times the minimal amount of sensor nodes in every barrier.
As can be seen in Figure , the higher the redundancy, the
lower the utilization rate of the nodes. It means that the
number of sensor nodes used in building barriers is inverse
to the nodes redundancy. When the degree is lower than six,
it is very dicult to complete -barrier coverage.
6.6. Impact of Delta Value (i.e., ). In this part, we evaluate
the impact of parameter on the performance of our
algorithm. As seen in simulations, varies from to . e
results are shown in Figures (a) and (b). Aer -time
simulations, we note that the number of sensors used in
building barriers is related to the delta value .Whenis
getting bigger, the performance is getting worse. And when
is big enough, the Gaussian distribution tends to be Uniform
distribution. In Figure (a), it is shown that there are almost
four overlapped lines, and when isequalto,,,,
respectively, the number of sensors used in building barriers
is nearly equal. As shown in Figure (b), the total number of
the sensors used to build the barriers is dierent. It is shown
that when =1, the performance is the best because the
number of sensors used in building -barrier coverage is the
least. In addition, when is smaller than , their performance
is similar to each other. erefore the bigger the is, the more
the total number of sensors is needed. For example, when
is more than , it is hard to get -barrier coverage, since
sensors are always developed outside the annular region, as
seen in Figure (c). At this time, the distribution of sensors
approximates the Uniform distribution adopted in Figure .
7. Conclusion
In this paper, we propose a barrier constructing algorithm in
WSNs for intruder detection, which constructs -barrier in a
circular area, and apply our algorithm in one-way intruders
detecting. When an intruder is detected times at rst, and it
is broadcasted at last, it is an illegal intruder. On the contrary,
if it is broadcasted at rst, then it will be detected at least one
time; it is a legal intruder. e goal of detecting whether an
intruder is legal or illegal is achieved well. On one hand, the
simulation results prove that our protocol can build -barrier
very well. On the other hand, the simulation results prove
that the total number of sensors used in building -barrier
is small. erefore the Gaussian distribution with low is a
good choice.
Competing Interests
e authors declare that they have no competing interests.
Acknowledgments
is work was supported in part by the Program for Science
and Technology Innovative Research Team for Young Schol-
ars in Sichuan Province, China (Grant no. TD),
National Natural Science Foundation of China (Grant no.
), the Fundamental Research Funds for the Cen-
tral Universities (Grant no. ZYGXX), the Overseas
Academic Training Funds, University of Electronic Sci-
ence and Technology of China (OATF, UESTC) (Grant no.
), and the Program for Science and Technology
Support in Sichuan Province (Grant nos. GZ and
GZ).
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Delta = 1
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(c) e Gaussian deployment of sensors with high delta (i.e., 𝜇=0,
delta =8), and the number of sensors deployed in the monitored region
isthesameasinFigure
F : Comparing with dierent delta (i.e., =0,delta).
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