research article a novel deployment scheme based on three...

Research ArticleA Novel Deployment Scheme Based on Three-DimensionalCoverage Model for Wireless Sensor Networks

Fu Xiao123 Yang Yang1 Ruchuan Wang123 and Lijuan Sun123

1 Nanjing University of Posts and Telecommunications Nanjing 210003 China2 Jiangsu High Technology Research Key Laboratory for Wireless Sensor Networks Nanjing 210003 China3 Key Lab of Broadband Wireless Communication and Sensor Network Technology Ministry of EducationNanjing 210003 China

Correspondence should be addressed to Fu Xiao xiaofnjupteducn

Received 4 May 2014 Accepted 4 June 2014 Published 17 June 2014

Academic Editor Shukui Zhang

Copyright copy 2014 Fu Xiao et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Coverage pattern and deployment strategy are directly related to the optimum allocation of limited resources for wireless sensornetworks such as energy of nodes communication bandwidth and computing power and quality improvement is largelydetermined by these for wireless sensor networks A three-dimensional coverage pattern and deployment scheme are proposed inthis paper Firstly by analyzing the regular polyhedron models in three-dimensional scene a coverage pattern based on cuboids isproposed and then relationship between coverage and sensor nodesrsquo radius is deduced also the minimum number of sensor nodesto maintain network arearsquos full coverage is calculated At last sensor nodes are deployed according to the coverage pattern after themonitor area is subdivided into finite 3D grid Experimental results show that compared with traditional random method sensornodes number is reduced effectively while coverage rate of monitor area is ensured using our coverage pattern and deterministicdeployment scheme

1 Introduction

With the development of wireless communication sensorand microelectromechanical system technology wide appli-cation prospect is exhibited forwireless sensor networks suchas in military environmental monitoring health medicinesmart home and other areas and it has shown a hugeadvantage especially in unmannedmonitoring or harsh envi-ronment thus wireless sensor networks act as an importantbasic perception network for internet of things (IOT) As oneof the basic problems in infrastructure widespread researchinterests have been attracted in coverage control and nodesrsquodeployment Research demonstrated that the deployment ofsensor nodes reflects the cost and the performance of wirelesssensor network by references [1 2] Reasonable deploymentcan obtain the optimum allocation of WSN resources thusthe perceived quality of the sensor network can be greatlyenhanced Given a sensor network the coverage problem

is a leading indicator to measure the effect of deploymentwhich reflects sensor nodersquos monitoring level in designatedsurveillance area [3] However most existing works on sensordeployment mainly concentrate on ideal two-dimensionalplanes Actually in real applications sensors are deployed onthree-dimensional environments

In this paper a three-dimensional coverage model andoptimum deployment scheme are proposed for wirelesssensor networks The rest of this paper is organized asfollows In Section 2 related works are introducedThe three-dimensional coverage problem in wireless sensor networkand optimum coverage pattern based on cuboids is proposedin Section 3 In Section 4 the relationship between coverageand sensor nodesrsquo radius is deduced and also the minimumnumber of sensor nodes tomaintain network arearsquos full cover-age is calculated Experimental results show the effectivenessof our method in Section 5 and conclusion is made inSection 6

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 846784 7 pageshttpdxdoiorg1011552014846784

2 The Scientific World Journal

2 Related Works

The deployment scheme is one of the most important prob-lems in wireless sensor networks which act as the funda-mental infrastructure for target monitor According to thedifferent methods of node deployment it can be divided intorandom deployment and deterministic deployment Deter-ministic deployment is characterized by calculating the pre-cise location of all sensor nodes and then placing each sensornode to obtain optimum connectivity and coverage by usingthe minimum number in monitoring area whose size andcharacteristic are known This deployment divides networkinto lattices and then sensor nodes are placed Dhillon andChakrabarty [4 5] proposed the maximum average coveragealgorithm and the maximum minimum coverage algorithmwhich are based on current node deployment sensor nodesare placed assignably in the grid through the use of optimizedstrategy to meet pointrsquos coverage requirements in each gridand ensure that the number of sensor nodes is minimizedwhile these node deployment schemes focus primarily on theideal 2D plane including the optimum deployment patternsbased on rules polygon [6]

In fact sensor nodes are in realistic three-dimensionalphysical world whose perception model and correspondingperception of the scene are 3D structure However traditionalsimplified 2D perception model and its cover-control algo-rithm are difficult to directly be applied in realistic 3D phys-ical environment [7 8] With the development of researchwork and the expanded demand for practical application3D sensor network attracts much attention such as acousticsensor network and atmospheric monitoring sensor networkwhich are based on 3D scene [9] Particularly in recentyears with the rise of underwater sensor network researchersstarted to think about the sensor nodesrsquo perception modeland its corresponding deployment method which is closer tothe realistic physics world Ammari and Das [10] presenteda distributed redeployment method for underwater sensornetwork by adjusting the position of nodes in the depthof the underwater to reduce the overlapping area so as toachieve maximum coverage of the network Alam and Haas[11] designed the Reuleaux tetrahedronmodel to characterize119896-coverage of a 3D field and investigated the correspondingminimum sensor spatial density considering the full cover-age problem and the connection problem of 3D field throughcalculating and comparing the common volume business ofpolyhydro Reference [12] concludes that when the ratio ofnodersquos communication radius to sensing radius is equal toor greater than a fixed value the cover effect of truncatedoctahedron is better than that of cube which is six-prismand rhombic dodecahedron Amac Guvensan and GokhanYavuz [13] analyzed and summarized the directional coveragemodels of wireless multimedia sensor networks and thoughtthat the sensing models of the sensor nodes for the three-dimensional space are the current hot spot Liu and Ma [14]studied the coverage problem of wireless sensor networks forrolling terrains and they derived the expected coverage ratiosunder the stochastic sensors deployment based on digitalelevation model (DEM) Topcuoglu et al [15 16] studiedpositioning and utilizing sensors on a 3D terrain however

AC

B

D

E

F

G

H

I

X

Z

Y

AAAAA

A998400

C998400

B998400

D998400

Figure 1 Coverage pattern Ω

these works are not suited to 3D environments such asatmospheric monitoring And Kong et al [17] studied thecomplex surface coverage problem in sensor networks

The most related work is Zhang et al [18] which stud-ied the problem of constructing low-connectivity and fullcoverage for three-dimensional sensor networks But theyspend much work on ensuring 119896-connectivity (119896 le 4) forthe whole network Our work is based on this while weput more emphasis on deterministic deployment for sensornetworks to ensure the three-dimensional space coverageThe Optimum coverage pattern and relationship betweencoverage and sensor nodesrsquo radius are deduced in this paperExperimental results show that compared with traditionalrandom method nodes number is reduced effectively whilecoverage rate of monitor area is ensured using our method

3 Three-Dimensional Coverage Problem inWireless Sensor Network

31 Problem Description In wireless sensor network weconsider that all sensors are of the same type and have sphere-shaped sensing field with radius 119903

119904 3D monitoring scene

coverage can be abstracted as the ball-coverage problemthat is covering a 3D space with several numbers of ballswith the same radium and each coverage area can beoverlapped and the requirement of completely coverage formonitoring area can be achieved finally Considering theaim of prolonging network lifetime optimization coverageproblem corresponds to a specific problem that maximumcovered a 3D space with least nodes

32 Definitions

Definition 1 (coverage pattern Ω) In three-dimensionalspace a coverage pattern Ω is defined as in Figure 1 where119860119861119862119863119860

1015840

1198611015840

1198621015840

1198631015840 is a cuboid with length width and height as

119909 119910 and 119911 and its volume is denoted by 119881 Plane 119864119865119866119867 islocated in the middle of cuboids 1198601198611198621198631198601015840119861101584011986210158401198631015840 That is to

The Scientific World Journal 3

say it is parallel to the bottom 119860119861119862119863 at 1199112 height and itscenter is point 119868

Nodes deployment scheme is as follows among five givenpoints 119864 119865 119866 119867 and 119868 a sensor node is placed at eachposition

Definition 2 (full coverage of coverage pattern Ω) Given acoverage pattern Ω and spheres with radius 119903 centering ateach point in five points119864119865119866119867 and 119868Ω is fully covered ifevery point in cuboid1198601198611198621198631198601015840119861101584011986210158401198631015840 can be covered at leastby one node

Definition 3 (covering density) The ratio of the total volumeof the five spheres with radius 119903 to the volume of cuboid119860119861119862119863119860

1015840

1198611015840

1198621015840

1198631015840 is called covering density of Ω which can

be denoted by 120590(119903 119881) as follows

120590 (119903 119881) =201205871199033

(3119881) (1)

Definition 4 (optimum coverage pattern Ω1015840) Given sensingrange 119903 a coverage pattern is called the optimum coveragepatternΩ1015840 if 120590(119903 119881) is minimum among all coverage patternswhich ensure the full coverage

4 Establishment of OptimumCoverage Pattern

From Definition 4 to obtain the optimum coverage pat-tern for each case the maximum volume of cuboid119860119861119862119863119860

1015840

1198611015840

1198621015840

1198631015840 which is denoted by 119881max should be

obtained as shown in (2) where 119909 119910 119911 are the lengths ofthree orthogonal edges in the cuboid as follows

119881max = 119909119910119911 (2)

119881max can be obtained by solving a nonlinear optimizationproblem under constraints generated from full coverage Asshown in Figure 1 compared with other planes parallel toplane119864119865119866119867 plane119860119861119862119863 andplane119860101584011986110158401198621015840119863 are the hardestto cover since the intersections of sensing spheres on theseplanes are smaller than those on other parallelograms Ifplanes 119860119861119862119863 and 119860101584011986110158401198621015840119863 are covered then any other par-allelograms parallel to plane 119864119865119866119867 in this coverage patternmust be covered According to the geometrical symmetrywe can map the full coverage of 3D cuboid to 2D rectangle119860119861119862119863 We suppose that the radius of sensor nodes is 119903

119904 then

the sensing range of nodes is a circular area with the radius 1199031015840119904

in plane 119860119861119862119863 As Figure 2 illustrated we can get

1199031015840

119904= radic1199032119904minus1199112

4 (3)

Theoptimum full coverage of rectangle119860119861119862119863 is obtainedif the intersections of five sensor nodesrsquo sensing sphere aresmallest in rectangle 119860119861119862119863 According to the relationship

A B

CD

r998400s

rsz

2

Figure 2 Coverage radius 1199031015840119904in plane 119860119861119862119863

A B

CD

N

J

M

x

y

(0 0)

Figure 3 Case 1 relationship between 119909 and 119910

between length 119909 width 119910 and sensing radius this problemcan be divided into the following three cases

Case 1 When 119909 gt 21199031015840119904 119910 gt 21199031015840

119904 as illustrated in Figure 3

Let point 119869 be the projection point of 119868 at rectangle119860119861119862119863Each sensing range of the sensor nodes at points 119864 119865 119866119867and 119868 is circular area with radius 1199031015840

119904centering at each point

in 119860 119861 119862 119863 and 119869 Assuming that 119860 is the origin point 119874at (0 0) 119861 at (119909 0) 119862 at (119909 119910) and 119863 at (119900 119910) then we canget coordinates of 119869 as (1199092 1199102) and |119860119872| = |119860119873| = 119903

1015840

119904is

known To ensure that the uncovered area in rectangle119860119861119862119863be covered by the circular area with radius 1199031015840

119904centered at 119869

which is not covered by the other four circular areas withradius 1199031015840

119904centering at 119860 119861 119862 119863 the following conditions

must be satisfied

|119869119872| le 1199031015840

119904

|119869119873| le 1199031015840

119904

(4)


AB

CD

N

JM

xy

(0 0)


That is

1199092

+ 1199102

minus 4119909radic1199032119904minus1199112

4le 0

1199092

+ 1199102


4le 0

119909 gt 2radic1199032119904minus1199112

4

119910 gt 2radic1199032119904minus1199112

4

119911 lt 2radic1199032119904minus1199112

4

(5)

Case 2 When 119909 gt 21199031015840119904 119910 le 21199031015840

119904 as seen in Figure 4

Similarly to ensure that rectangle119860119861119862119863 be fully coveredby five sensor nodes these following conditions should besatisfied

1199092

+ 1199102


4le 0

1199092

minus 1199102


4minus1199112

4le 0

119909 gt 2radic1199032119904minus1199112

4

119910 le 2radic1199032119904minus1199112

4

119911 lt 2radic1199032119904minus1199112

4

(6)

A x

N

JM

B

CD

y

(0 0)


Case 3 When 119909 le 21199031015840119904 119910 le 21199031015840


Similarly these following conditions should be satisfied toensure rectangle119860119861119862119863 be fully covered by five sensor nodes

1199092

minus 1199102


4minus1199112

4le 0

1199102

minus 1199092


4minus1199112

4le 0

119909 le 2radic1199032119904minus1199112

4

119910 le 2radic1199032119904minus1199112

4

119911 lt 2radic1199032119904minus1199112

4

(7)

Suppose themonitor environment is subdivided into cuboidswith length 119909 width 119910 height 119911 and volume 119881 and radius ofsensor nodes is 119903

119904 By solving formula (2) under constraint

as conditions (5) (6) and (7) we can obtain the optimumcoverage patternΩ1015840 as follows

119909 =2radic6119903119904

3

119910 =2radic6119903119904

3

119911 =2radic3119903119904

3

119881 =16radic3119903

3

119904

9

(8)


X

Z

Y

Figure 6 3D mesh dissections on the actual environment

5 Simulations and Analysis

Suppose that the actual environment is a 3D rectangular withlength 119871 width 119882 and height 119867 respectively The cuboidowns space division character and the real 3D physical envi-ronment can be subdivided into severalmeshes to achieve fullcoverage by adopting our optimal cuboid coverage patternTo facilitate analysis we ignore the region boundary in actualenvironment

51 3D Mesh Dissections on Actual Environment Based onstructure size of the optimum coverage pattern we subdi-vided the 3D rectangular into several small cuboids withlength equal to 2radic6119903

1199043 width equal to 2radic6119903

1199043 and height

equal to 2radic31199031199043 as shown in Figure 6 We considered each

little cuboid as an optimum coverage pattern and placedsensor nodes inΩ1015840 So the rectangular area is subdivided intocuboids as 1198601198611198621198631198601015840119861101584011986210158401198631015840 and sensor nodes are deployedin the corresponding vertexes 119860 119861 C 119863 1198601015840 1198611015840 1198621015840 1198631015840 andpoint 119868 Number 119873 of nodes to achieve full coverage of 3Dscene can be calculated as follows

119873 = ((lceil3119871

2radic6119903119904

rceil + 1) times (lceil3119882

2radic6119903119904

rceil + 1) + lceil3119871

2radic6119903119904

rceil)

times lceil119867

2radic31199031199043rceil

(9)

52 Performance Analysis We have conducted a series ofsimulation experiments in this given 3D monitor regionto compare the differences between random deploymentand deterministic deployment regarding required numberof sensor nodes For instance deploying the sensor nodesin a cube with edge length 1000m when 119903

119904= 30m we

need around 14645 nodes to achieve full coverage of sceneaccording to formula (5) We compare with random coveringalgorithm in the same area under the conditions of meetingthe same coverage The comparison results are shown inFigure 6 (meet 80 coverage in Figure 7(a) meet 90 cov-erage in Figure 7(b) and meet 100 coverage in Figure 7(c))We can see that the deterministic deployment pattern needssmaller number of nodes than the widely used random

Table 1The influence of initial nodes number on the scene coveragerate

Nodes number Random strategy Proposal strategy10000 6771 686011000 7116 754612000 7425 823213000 7700 891714000 7946 960315000 8165 10016000 8361 10017000 8537 100

deployment pattern under the conditions of meeting samecoverage

To validate the coverage influence of initial number ofnodes on actual environment between random deploymentand our deterministic deployment we deploy the sensornodes with 119903

119904= 30m in a cube with edge length of 1000m

and change the number of initial nodesThe results are shownin Table 1

Table 1 illustrates that our deterministic deployment canmake more coverage of actual area than random deploymentunder the condition of the same initial nodes As illustratedby Zhang et al [18] the constructing low-connectivity andfull coverage three-dimensional sensor networks had beenstudied Around 17200 nodes are needed to achieve 2-connectivity in a cube with edge length of 1000m and sensorcoverage radius equal to 30m which are the same as oursWhile in our scheme wemainly focused on coverage and lit-tle attention had been paid to connective in sensor networksno more than 15000 nodes are needed in our simulationresults Around 2200 nodes are reduced while coverage rateof monitor area is ensured using our method

6 Conclusion and Future Work

This paper mainly proposes a coverage pattern which isbased on cuboid structure through analyzing the coveragecharacteristics of 3D scene By deducing the required numberof sensor nodes for full coverage in 3D monitor spacetheoretically we get the deployment positions of sensor nodesbased on our coverage pattern after subdividing the finite3D grid triangulation of network area A series of simulationexperiments proves the availability of this deterministicdeployment scheme and significant number of sensor nodescan be saved using this proposed scheme

The results of this paper are carried out on the basisof 0-1 sphere sensing model and future research can becarried out following these directions (1) extending this0-1 sphere sensing model to probabilistic sphere sensingcoverage model (2) mobile sensor and 119896-coverage deploy-ment scheme Moreover connectivity problem is still anopen interesting problem in three-dimensional deploymentdomains


0 200 400 600 800 1000 1200 1400 1600 1800 20000

2

4

6

8

10

12

The length of the cube area (m)

The r

equi

red

num

ber o

f sen

sor n

odes

Meet the 80 coverage of the random coveringMeet the 80 coverage of our optimal covering

times104

(a) The condition of 80 coverage

0 500 1000 1500 20000

2

4

6

8

10

12

14

16

18


The r

equi

red

num

ber o

f sen

sor n

odes


times104

(b) The condition of 90 coverage

0 200 400 600 800 1000 1200 1400 1600 1800 2000The length of the cube area (m)

The r

equi

red

num

ber o

f sen

sor n

odes


times105

0

05

1

15

2

25

3

35

(c) The condition of 100 coverage

Figure 7 The condition of different coverage using our method and traditional random method

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research is supported by National Natural ScienceFoundation of China (nos 61373137 61373017 61170065 and61171053) Six Industries Talent Peaks Plan of Jiangsu (no2013-DZXX-014) Scientific Technological Support Project of

Jiangsu (no BE2012755) Scientific Research amp Industry Pro-motion Project for Higher Education Institutions (JHB2012-7) and Jiangsu Qinglan Project

References

[1] O E Onur C Ersoy H Delic and L Akarun ldquoSurveillancewireless sensor networks deployment quality analysisrdquo IEEENetwork vol 21 no 6 pp 48ndash53 2007

[2] S Kumar and D K Lobiyal ldquoSensing coverage predictionfor wireless sensor networks in shadowed and multipath


environmentrdquo The Scientific World Journal vol 2013 ArticleID 565419 11 pages 2013

[3] J Heidemann W Ye J Wills A Syed and Y Li ldquoResearchchallenges and applications for underwater sensor networkingrdquoin Proceedings of the IEEE Wireless Communications and Net-working Conference (WCNC rsquo06) pp 228ndash235 Las Vegas NevUSA April 2006

[4] S S Dhillon and K Chakrabarty ldquoSensor placement for gridcoverage under imprecise detectionsrdquo in Proceeding of theInternational Conference on Information Fusion pp 1581ndash1587Annapolis Md USA July 2002

[5] S S Dhillon and K Chakrabarty ldquoSensor placement foreffective coverage and surveillance in distributed sensor net-worksrdquo in Proceedings of the IEEEWireless Communications andNetworking Conference pp 1609ndash1614 New Orleans La USAMarch 2003

[6] X L Bai Z Q Yun D Xuan T H Lai and W Jia ldquoDeployingfour-connectivity and full-coverage wireless sensor networksrdquoin Proceedings of the 27th IEEE Communications Society Confer-ence on Computer Communications (INFOCOM rsquo08) pp 296ndash300 Phoenix Ariz USA April 2008

[7] H M Ammari and S K Das ldquoCritical density for coverageand connectivity in three-dimensional wireless sensor networksusing continuum percolationrdquo IEEE Transactions on Paralleland Distributed Systems vol 20 no 6 pp 872ndash885 2009

[8] D Pompili T Melodia and I F Akyildiz ldquoThree-dimensionaland two-dimensional deployment analysis for underwateracoustic sensor networksrdquo Ad Hoc Networks vol 7 no 4 pp778ndash790 2009

[9] K Akkaya and A Newell ldquoSelf-deployment of sensors formaximized coverage in underwater acoustic sensor networksrdquoComputer Communications vol 32 no 7 pp 1233ndash1244 2009

[10] H M Ammari and S K Das ldquoA study of k-coverage andmeasures of connectivity in 3D wireless sensor networksrdquo IEEETransactions on Computers vol 59 no 2 pp 243ndash257 2010

[11] S N Alam and Z J Haas ldquoCoverage and connectivity in three-dimensional networksrdquo in Proceedings of the ACM MobiCompp 346ndash357 Los Angeles Calif USA September 2006

[12] M K Watfa and S Commuri ldquoThe 3-dimensional wirelesssensor network coverage problemrdquo in Proceedings of the IEEEInternational Conference on Networking Sensing and Control(ICNSC 06) pp 856ndash861 Gainesville Fla USA May 2006

[13] M Amac Guvensan and A Gokhan Yavuz ldquoOn coverage issuesin directional sensor networks a surveyrdquo Ad Hoc Networks vol9 no 7 pp 1238ndash1255 2011

[14] L Liu and H Ma ldquoOn coverage of wireless sensor networks forrolling terrainsrdquo IEEE Transactions on Parallel and DistributedSystems vol 23 no 1 pp 118ndash125 2012

[15] H R Topcuoglu M Ermis and M Sifyan ldquoPositioning andutilizing sensors on a 3-D terrain part I-theory and modelingrdquoIEEE Transactions on Systems Man and Cybernetics C Applica-tions and Reviews vol 41 no 3 pp 376ndash382 2011

[16] H R Topcuoglu M Ermis and M Sifyan ldquoPositioning andutilizing sensors on a 3-D terrain part II-Solving with a hybridevolutionary algorithmrdquo IEEE Transactions on Systems Manand Cybernetics C Applications and Reviews vol 41 no 4 pp470ndash480 2011

[17] L Kong M Zhao X Liu Y Liu M Wu and W Shu ldquoSurfacecoverage in sensor networksrdquo IEEE Transaction on Parallel andDistributed Systems vol 25 no 1 pp 234ndash243 2014

[18] C Zhang X Bai J Teng D Xuan and W Jia ldquoConstructinglow-connectivity and full-coverage three dimensional sensornetworksrdquo IEEE Journal on Selected Areas in Communicationsvol 28 no 7 pp 984ndash993 2010

International Journal of

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Control Scienceand Engineering

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Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



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Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



2 Related Works

The deployment scheme is one of the most important prob-lems in wireless sensor networks which act as the funda-mental infrastructure for target monitor According to thedifferent methods of node deployment it can be divided intorandom deployment and deterministic deployment Deter-ministic deployment is characterized by calculating the pre-cise location of all sensor nodes and then placing each sensornode to obtain optimum connectivity and coverage by usingthe minimum number in monitoring area whose size andcharacteristic are known This deployment divides networkinto lattices and then sensor nodes are placed Dhillon andChakrabarty [4 5] proposed the maximum average coveragealgorithm and the maximum minimum coverage algorithmwhich are based on current node deployment sensor nodesare placed assignably in the grid through the use of optimizedstrategy to meet pointrsquos coverage requirements in each gridand ensure that the number of sensor nodes is minimizedwhile these node deployment schemes focus primarily on theideal 2D plane including the optimum deployment patternsbased on rules polygon [6]

In fact sensor nodes are in realistic three-dimensionalphysical world whose perception model and correspondingperception of the scene are 3D structure However traditionalsimplified 2D perception model and its cover-control algo-rithm are difficult to directly be applied in realistic 3D phys-ical environment [7 8] With the development of researchwork and the expanded demand for practical application3D sensor network attracts much attention such as acousticsensor network and atmospheric monitoring sensor networkwhich are based on 3D scene [9] Particularly in recentyears with the rise of underwater sensor network researchersstarted to think about the sensor nodesrsquo perception modeland its corresponding deployment method which is closer tothe realistic physics world Ammari and Das [10] presenteda distributed redeployment method for underwater sensornetwork by adjusting the position of nodes in the depthof the underwater to reduce the overlapping area so as toachieve maximum coverage of the network Alam and Haas[11] designed the Reuleaux tetrahedronmodel to characterize119896-coverage of a 3D field and investigated the correspondingminimum sensor spatial density considering the full cover-age problem and the connection problem of 3D field throughcalculating and comparing the common volume business ofpolyhydro Reference [12] concludes that when the ratio ofnodersquos communication radius to sensing radius is equal toor greater than a fixed value the cover effect of truncatedoctahedron is better than that of cube which is six-prismand rhombic dodecahedron Amac Guvensan and GokhanYavuz [13] analyzed and summarized the directional coveragemodels of wireless multimedia sensor networks and thoughtthat the sensing models of the sensor nodes for the three-dimensional space are the current hot spot Liu and Ma [14]studied the coverage problem of wireless sensor networks forrolling terrains and they derived the expected coverage ratiosunder the stochastic sensors deployment based on digitalelevation model (DEM) Topcuoglu et al [15 16] studiedpositioning and utilizing sensors on a 3D terrain however

AC

B

D

E

F

G

H

I

X

Z

Y

AAAAA

A998400

C998400

B998400

D998400

Figure 1 Coverage pattern Ω

these works are not suited to 3D environments such asatmospheric monitoring And Kong et al [17] studied thecomplex surface coverage problem in sensor networks

The most related work is Zhang et al [18] which stud-ied the problem of constructing low-connectivity and fullcoverage for three-dimensional sensor networks But theyspend much work on ensuring 119896-connectivity (119896 le 4) forthe whole network Our work is based on this while weput more emphasis on deterministic deployment for sensornetworks to ensure the three-dimensional space coverageThe Optimum coverage pattern and relationship betweencoverage and sensor nodesrsquo radius are deduced in this paperExperimental results show that compared with traditionalrandom method nodes number is reduced effectively whilecoverage rate of monitor area is ensured using our method

3 Three-Dimensional Coverage Problem inWireless Sensor Network

31 Problem Description In wireless sensor network weconsider that all sensors are of the same type and have sphere-shaped sensing field with radius 119903

119904 3D monitoring scene

coverage can be abstracted as the ball-coverage problemthat is covering a 3D space with several numbers of ballswith the same radium and each coverage area can beoverlapped and the requirement of completely coverage formonitoring area can be achieved finally Considering theaim of prolonging network lifetime optimization coverageproblem corresponds to a specific problem that maximumcovered a 3D space with least nodes

32 Definitions

Definition 1 (coverage pattern Ω) In three-dimensionalspace a coverage pattern Ω is defined as in Figure 1 where119860119861119862119863119860

1015840

1198611015840

1198621015840

1198631015840 is a cuboid with length width and height as

119909 119910 and 119911 and its volume is denoted by 119881 Plane 119864119865119866119867 islocated in the middle of cuboids 1198601198611198621198631198601015840119861101584011986210158401198631015840 That is to






1015840

1198611015840

1198621015840



120590 (119903 119881) =201205871199033

(3119881) (1)




1015840

1198611015840

1198621015840



119881max = 119909119910119911 (2)


119904 then



1199031015840

119904= radic1199032119904minus1199112

4 (3)


A B

CD

r998400s

rsz

2


A B

CD

N

J

M

x

y

(0 0)



Case 1 When 119909 gt 21199031015840119904 119910 gt 21199031015840





1015840

119904is





must be satisfied

|119869119872| le 1199031015840

119904

|119869119873| le 1199031015840

119904

(4)


AB

CD

N

JM

xy

(0 0)


That is

1199092

+ 1199102


4le 0

1199092

+ 1199102


4le 0

119909 gt 2radic1199032119904minus1199112

4

119910 gt 2radic1199032119904minus1199112

4

119911 lt 2radic1199032119904minus1199112

4

(5)

Case 2 When 119909 gt 21199031015840119904 119910 le 21199031015840



1199092

+ 1199102


4le 0

1199092

minus 1199102


4minus1199112

4le 0

119909 gt 2radic1199032119904minus1199112

4

119910 le 2radic1199032119904minus1199112

4

119911 lt 2radic1199032119904minus1199112

4

(6)

A x

N

JM

B

CD

y

(0 0)


Case 3 When 119909 le 21199031015840119904 119910 le 21199031015840



1199092

minus 1199102


4minus1199112

4le 0

1199102

minus 1199092


4minus1199112

4le 0

119909 le 2radic1199032119904minus1199112

4

119910 le 2radic1199032119904minus1199112

4

119911 lt 2radic1199032119904minus1199112

4

(7)




119909 =2radic6119903119904

3

119910 =2radic6119903119904

3

119911 =2radic3119903119904

3

119881 =16radic3119903

3

119904

9

(8)


X

Z

Y






1199043 and height



119873 = ((lceil3119871

2radic6119903119904


2radic6119903119904


2radic6119903119904

rceil)

times lceil119867


(9)


119904= 30m we













0 200 400 600 800 1000 1200 1400 1600 1800 20000

2

4

6

8

10

12


The r

equi

red

num

ber o

f sen

sor n

odes


times104


0 500 1000 1500 20000

2

4

6

8

10

12

14

16

18


The r

equi

red

num

ber o

f sen

sor n

odes


times104



The r

equi

red

num

ber o

f sen

sor n

odes


times105

0

05

1

15

2

25

3

35





Acknowledgments



References























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














1015840

1198611015840

1198621015840



120590 (119903 119881) =201205871199033

(3119881) (1)




1015840

1198611015840

1198621015840



119881max = 119909119910119911 (2)


119904 then



1199031015840

119904= radic1199032119904minus1199112

4 (3)


A B

CD

r998400s

rsz

2


A B

CD

N

J

M

x

y

(0 0)



Case 1 When 119909 gt 21199031015840119904 119910 gt 21199031015840





1015840

119904is





must be satisfied

|119869119872| le 1199031015840

119904

|119869119873| le 1199031015840

119904

(4)


AB

CD

N

JM

xy

(0 0)


That is

1199092

+ 1199102


4le 0

1199092

+ 1199102


4le 0

119909 gt 2radic1199032119904minus1199112

4

119910 gt 2radic1199032119904minus1199112

4

119911 lt 2radic1199032119904minus1199112

4

(5)

Case 2 When 119909 gt 21199031015840119904 119910 le 21199031015840



1199092

+ 1199102


4le 0

1199092

minus 1199102


4minus1199112

4le 0

119909 gt 2radic1199032119904minus1199112

4

119910 le 2radic1199032119904minus1199112

4

119911 lt 2radic1199032119904minus1199112

4

(6)

A x

N

JM

B

CD

y

(0 0)


Case 3 When 119909 le 21199031015840119904 119910 le 21199031015840



1199092

minus 1199102


4minus1199112

4le 0

1199102

minus 1199092


4minus1199112

4le 0

119909 le 2radic1199032119904minus1199112

4

119910 le 2radic1199032119904minus1199112

4

119911 lt 2radic1199032119904minus1199112

4

(7)




119909 =2radic6119903119904

3

119910 =2radic6119903119904

3

119911 =2radic3119903119904

3

119881 =16radic3119903

3

119904

9

(8)


X

Z

Y






1199043 and height



119873 = ((lceil3119871

2radic6119903119904


2radic6119903119904


2radic6119903119904

rceil)

times lceil119867


(9)


119904= 30m we













0 200 400 600 800 1000 1200 1400 1600 1800 20000

2

4

6

8

10

12


The r

equi

red

num

ber o

f sen

sor n

odes


times104


0 500 1000 1500 20000

2

4

6

8

10

12

14

16

18


The r

equi

red

num

ber o

f sen

sor n

odes


times104



The r

equi

red

num

ber o

f sen

sor n

odes


times105

0

05

1

15

2

25

3

35





Acknowledgments



References























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










AB

CD

N

JM

xy

(0 0)


That is

1199092

+ 1199102


4le 0

1199092

+ 1199102


4le 0

119909 gt 2radic1199032119904minus1199112

4

119910 gt 2radic1199032119904minus1199112

4

119911 lt 2radic1199032119904minus1199112

4

(5)

Case 2 When 119909 gt 21199031015840119904 119910 le 21199031015840



1199092

+ 1199102


4le 0

1199092

minus 1199102


4minus1199112

4le 0

119909 gt 2radic1199032119904minus1199112

4

119910 le 2radic1199032119904minus1199112

4

119911 lt 2radic1199032119904minus1199112

4

(6)

A x

N

JM

B

CD

y

(0 0)


Case 3 When 119909 le 21199031015840119904 119910 le 21199031015840



1199092

minus 1199102


4minus1199112

4le 0

1199102

minus 1199092


4minus1199112

4le 0

119909 le 2radic1199032119904minus1199112

4

119910 le 2radic1199032119904minus1199112

4

119911 lt 2radic1199032119904minus1199112

4

(7)




119909 =2radic6119903119904

3

119910 =2radic6119903119904

3

119911 =2radic3119903119904

3

119881 =16radic3119903

3

119904

9

(8)


X

Z

Y






1199043 and height



119873 = ((lceil3119871

2radic6119903119904


2radic6119903119904


2radic6119903119904

rceil)

times lceil119867


(9)


119904= 30m we













0 200 400 600 800 1000 1200 1400 1600 1800 20000

2

4

6

8

10

12


The r

equi

red

num

ber o

f sen

sor n

odes


times104


0 500 1000 1500 20000

2

4

6

8

10

12

14

16

18


The r

equi

red

num

ber o

f sen

sor n

odes


times104



The r

equi

red

num

ber o

f sen

sor n

odes


times105

0

05

1

15

2

25

3

35





Acknowledgments



References























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










X

Z

Y






1199043 and height



119873 = ((lceil3119871

2radic6119903119904


2radic6119903119904


2radic6119903119904

rceil)

times lceil119867


(9)


119904= 30m we













0 200 400 600 800 1000 1200 1400 1600 1800 20000

2

4

6

8

10

12


The r

equi

red

num

ber o

f sen

sor n

odes


times104


0 500 1000 1500 20000

2

4

6

8

10

12

14

16

18


The r

equi

red

num

ber o

f sen

sor n

odes


times104



The r

equi

red

num

ber o

f sen

sor n

odes


times105

0

05

1

15

2

25

3

35





Acknowledgments



References























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 200 400 600 800 1000 1200 1400 1600 1800 20000

2

4

6

8

10

12


The r

equi

red

num

ber o

f sen

sor n

odes


times104


0 500 1000 1500 20000

2

4

6

8

10

12

14

16

18


The r

equi

red

num

ber o

f sen

sor n

odes


times104



The r

equi

red

num

ber o

f sen

sor n

odes


times105

0

05

1

15

2

25

3

35





Acknowledgments



References























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article a novel deployment scheme based on three...

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