A New Energy Efficient Data Gathering Approach in Wireless Sensor Networks

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1 Commuicatios ad Network, 0, 4, Published Olie February 0 ( A New Eergy Efficiet Data Gatherig Approach i Wireless Sesor Networks Jafar Amiri, Masoud Sabaei, Bahma Soltaiasab Departmet of Computer ad IT Egieerig, Professioal ad Techical Uiversity of Tabriz, Tabriz, Ira Departmet of Computer ad IT Egieerig, Amirkabir Uiversity of Techology, Tehra, Ira {Jafar_amiri85, Bahma_soltaiasab}@yahoo.com, sabaei@aut.ac.ir Received November 6, 00; revised October 30, 0; accepted November 5, 0 ABSTRACT Data gatherig i wireless sesor etworks is oe of the importat operatios i these etworks. These operatios require eergy cosumptio. Due to the limited eergy of odes, the eergy productivity should be cosidered as a key objective i desig of sesor etworks. Therefore the clusterig is a suitable method that used i eergy cosumptio maagemet. For this purpose may methods have bee proposed. Betwee these methods the LEACH algorithm has bee atted as a basic method. This algorithm uses distributed clusterig method for data gatherig ad aggregatio. The LEACH-C method that is the improvemet of LEACH, which performs the clusterig i cetralized mode. I this method, collectig the eergy level of iformatio of every ode directly i each period icreases the eergy cost. Also the pheomeo that is see by sesor odes cotiually chage over time. Thereby the iformatio received by odes is correlated. Sedig time correlated data i the etwork cause to eergy dissipatio. TINA method ad its improvemet have bee proposed i order to ot sedig correlated data. These approaches have reported errors. I this paper, the idea of ot sedig time correlated data of odes has bee cosidered by usig the time series fuctio. Also, a model to estimate the remaiig eergy of odes by the base statio has bee preseted. Fially, a method has bee proposed to aware the base statio from the umber of correlated data i each ode as the estimatio of eergy will be more precise. The proposed ideas have bee implemeted over the LEACH-C protocol. Evaluatio results showed that the proposed methods had a better performace i eergy cosumptio ad the lifetime of the etwork i compariso with similar methods. Keywords: Clusterig; Sesor Network; Data Correlatio; Time Series; Eergy Predictio. Itroductio Wireless sesor etworks are a class of wireless ad-hoc etworks. I these etworks, sesor odes collect data from physical eviromet ad after processig set to the base statio (BS ). Thus allow moitorig ad cotrol may types of physical parameters. Each sesor ode has limited eergy ad i most applicatios, replacig eergy sources are ot possible. So lifetime of sesor odes is highly depedet o eergy stored i their battery. Clusterig is a desigig method that used for maagemet of wireless sesor etworks. I this method, the etwork is divided ito several idepedet collectios that these collectios called cluster. So each cluster cotais a umber of sesor odes ad a cluster head ode. Member odes i a cluster sed their data to relative cluster head ode. Cluster head ode aggregates these data ad sed to the base statio. Therefore, clusterig i sesor etworks has advatages such as data aggregatio support [], data gatherig facilitatio [], orgaizig a suitable Base Statio. structure for scalable routig [3], ad efficiet propagatio of data i the etwork [4]. Data gatherig i wireless sesor etworks is a importat operatio i these etworks ad for this purpose may methods have bee proposed. The LEACH [5] protocol has bee cosidered as a hierarchical basic method. This method is suitable for moitorig applicatios. Each ode periodically seses the iformatio ad seds them. I this algorithm, the clusterig method has used for data gatherig ad aggregatio. The cluster ad cluster head selected radomly, therefore there is o assurace to select the exact improved umber ad uiform distributio of cluster head throughout the etwork. May improvemets i LEACH protocol have bee preseted. LEACH-C 3 method [6] is a example of these improvemets. I LEACH-C, the formig of clusters is doe usig a cetralized algorithm by the base statio i the startig of each period. Base Statio uses the received Low-eergy Adaptive Clusterig Hierarchy. 3 LEACH-Cetralized.

2 6 J. AMIRI ET AL. iformatio from odes for fidig the predetermied umber of cluster heads ad etwork cofiguratio withi the clusters. This iformatio cotais positio ad eergy of odes. Aother improvemet to this algorithm is the use of estimatio. Oe of these algorithms is LEACH- CE 4 [7]. I the proposed techique eergy level collected from all odes i two primary periods but ot collected i the other periods. Istead, the average eergy of iitial periods is used. Cosiderig that the eergy estimatio i this method is ot precise, this clusterig scheme is ot efficiet ad suitable. There is some proposed clusterig methods that ABCP [8] ad ABEE [9] ad HMM [0,] are samples of them. Each sesor ode is observer of a physical pheomeo. Also physical pheomeo such as temperature ad... cotiuously chage i time. So the iformatio provided by sesor odes is depedet o each other. Some algorithms that based o ot sedig of correlated data are cosidered. The TINA 5 [] algorithm is oe of them. I this algorithm the sesor ode compares the value of sampled data with previous data, if that be differet sed it ad otherwise goes to sleep mode. The proposed improvemet to this algorithm is that sesor ode decides to sed data with comparig the value of ew sample with last reported data [3]. These metioed algorithms due to error i report, is ot suitable. Therefore, a method proposed to icrease the accuracy of data reportig. For precise estimatio of odes eergy, the base statio must be aware of data time correlatio. So with existece of data time correlatio ad usig eergy estimatio of odes, a method suggested so that the base statio ca estimate odes eergy precisely. These methods avoid the overhead excess ad icrease the etwork lifetime. The remaiig of this article is orgaized as follows: I Sectio related works are reviewed. I Sectio 3 we itroduce correlated data algorithm with the eergy predictig techique ad the hybrid method. Aalysis of experimets with existig odes offered i Sectio 4, ad we fially i Sectio 5 summarize ad discuss the scheme. i LEACH is doe i two phases that these phases show i Figures ad 3: Setup phase is the stage of formig cluster ad cluster head. At this stage, cluster ad cluster head radomly selected. After formig the cluster, cluster head propagate TDMA 6 scheduler to specify the data trasfer time to member odes. The the steady-state phase started. I the steady-state phase, each member ode i cluster sed data to the cluster head oly i its time slot ad at the rest of time pieces for eergy coservatio goes to sleep mode. I this method, the cluster head cosumes more eergy for receivig, processig ad directly sedig this data to the BS ode. So for icreasig the life time of the etwork it is ecessary to replace role of cluster head betwee etwork odes. May improvemets over the LEACH method have bee provided that i these improvemets firstly, as far as possible the best clusterig ad cluster head selectio is doe, secodly possible as possible overhead of the protocol is to be reduced. LEACH- C method is a example of these improvemets... LEACH-C I LEACH-C, clusters formig i the begiig of every period are doe, usig the cetralized algorithm by the base statio. The base statio uses received iformatio from odes that icludes eergy ad ode status, uses Figure. A sesor etwork with clusterig.. Related Work.. LEACH Oe of the most famous hierarchical routig protocols Figure. Period of LEACH. based o clusterig, is the LEACH protocol. I this method, each cluster members sed their data to cluster head. The cluster head aggregate this data ad sed to the BS. So the commuicatio cost is reduced. Figure describes this cocept: The operatio of cluster formig ad data trasmissio 4 Figure 3. Details of period. LEACH-C-Estimate. 5 Temporal Coherecy-Aware i-network Aggregatio. 6 Time Divisio Multiple Access.

3 J. AMIRI ET AL. 63 this iformatio durig the setup phase for fidig predetermied umber of cluster heads ad etwork cofiguratio withi the clusters. Next classificatio of odes i the clusters is doe to miimize eergy cosumptio i order to trasfer their data to the related cluster head. Results show that LEACH-C overall performace is better tha LEACH because of the optimal formig of clusters by the base statio. I additio, the umber of cluster heads i each period of LEACH-C is equal to the expected optimal value. While i LEACH the umber of cluster heads varies i differet periods because of lack of global coordiatio. As i LEACH-C at the begiig of every period eergy of odes must be set to BS, therefore odes early discharged ad the etwork lifetime reduces. Aother improvemet o this algorithm is the use of eergy estimatio. The LEACH-CE method is a example of these methods..3. LEACH-CE I the LEACH-CE method, the eergy level of all odes collected oly i two primary periods ad ot be collected i other periods. Istead because of kowig iformatio about eergy level of odes, we ca calculate eergy cosumptio average for each ode by usig iformatio of two primary periods. This meas that reducig calculated eergy level from the eergy level of ode, causes predictig curret eergy level of ode. The problem of this algorithm is that firstly eergy estimatio is ot doe precisely ad secodly if odes have correlated data, while ot sedig correlated data meas that previous data is valid, so this pla of clusterig is ot suitable ad efficiet..4. TINA Pheomeo that observed by sesor odes, cotiu- ally chage i time. Therefore iformatio received by the odes is correlated o each other. These cases for physical pheomea that are cotiuous or repetitive, or i a applicatio that the accuracy is ot too importat, or i a etwork that ode desity i a regio is high, have see more. There are two types of data correlatio: ) spatial correlatio; ) Time correlatio. I the spatial correlatio, aggregatio is doe withi the etwork by cluster heads. This is oe of the proposed methods to reduce eergy cosumptio. So the odes that have correlated data sed them to cluster head ad cluster head after aggregatig these data sed to the base statio. This causes to prevet waste of eergy. This method has bee implemeted i LEACH protocol. But i the time correlatio, each ode ca have correlated data i successive times. Mohamed ad Sharaf proposed the TINA algorithm. The mai idea of TINA algorithm was that the sesor odes sed their data oly whe this data differ with previous data otherwise goes to sleep mode. This algorithm has a reportig error. There is a improvemet to this algorithm that preseted below..5. Improvemet of TINA I this method, the sesor ode decides to sed data by comparig the value of ewly sampled data with last reported data. However, sesor odes maitai last reported data. For better uderstadig, we describe this sectio with a example. Suppose that a give sesor ode that received data are.0, 0.95,.05, 0.95,.05 respectively. A threshold has bee cosidered that data chagig to this threshold is ot importat. The value of this threshold cosidered equal to 0%. First give data that is equal to.0 successfully set ad i the ext pe riod 0.95, will ot be set whe: 5% 0%.0 Otherwise that will be set. I the third stage.05 5% 0% that will ot set ad i the fourth 0.95 stage 5% 0% that will ot set. This me- thod is suitable whe pheomeo chages have ot a lot of swig or ay special evet i the etwork is doe. But as metioed previously most of pheomeo chage cotiuously with time. So most of data are i ascedig or descedig mode i the time slices. Or i a applicatio such as temperature for example i a certai time slot occurs a specific evet. So the proposed methods have errors ad are ot suitable. We offer a method to improve this algorithm ad prevet the waste of eergy. I additio, the problem of data time correlatio is ot cosidered i proposed protocols. Therefore, we will check the time correlatio of data i the proposed algorithms. 3. The Proposed Method 3.. Presetatio of Methods Three ideas are proposed here: ) the data time correlatio; ) Eergy estimatio model of odes ad 3) the hybrid method. I the data time correlatio algorithm, Time Series Forecastig method (TSF 7 ) used to decide sedig or ot sedig of data. The i time t i the begiig of each period, base statio sed percetage of error e(t) to all odes. First data sesed by ode ad set. Secod ad third ad fourth data set based o the improved TINA algorithm. The the ode rus time series fuctio to 7 Time Series Forecastig.

4 64 J. AMIRI ET AL. determie the value of predictio of tred lie model, to create tred model. I the ext times the sesed data compared with predicted value of tred model, if the differece betwee these two values exceeds a threshold value, data set to the give ode ad the ode recalculate predictio fuctio of tred model to update the tred lie. Otherwise, the sesor ode does ot sed the sesed data with this isurace that sesed data placed i accuracy rage of data. So oly some data have to be set that are very differet from the tred lie model. This help to prevet eergy loss. We call the ode eergy predictio model LEACH- CEC 8 ad describe as follow. For doig the best clusterig, that is eeded to kow eergy of the odes. The estimatio method is a method that has low cost ad is suitable. We also use the eergy estimatio method. For this, we divided LEACH-C protocol to three phases. Topology buildig phase, setup-state ad steady-state. I the first phase odes sed their positio to the BS. The BS creates etwork topology based o these positios. Oce the topology was formed i the base statio, base statio ode calculates the distace of odes to each other. The BS calculates the amout of eergy used i each ode i the setup-phase, usig a simple mathematical model. The deduct this amout from primary eergy ad calculates its remaiig eergy. Fially do the clusterig ad goes to the steady-state phase. I this phase for each ode, the data time correlated algorithm applied accordig to the followig method. BS ode should be iformed of data time correlatio i odes to estimate precisely eergy of them. Therefore cluster head create a table that cotaiig list of all members of the cluster. Cluster head registers every ode i to the table that have correlated data ad do ot set i certai times. I the ed of each period, cluster head seds this table with collected data to the base statio. This table cotais odes ID ad umber of times that these odes ot set data. Base statio uses this iformatio for clusterig decisios i cetralized methods. Ultimately that cause to eergy estimatio i cetralized methods is more carefully while the best clusterig is created ad the etwork lifetime icreases. So i total lifetime of the etwork, first phase has doe oce but setup ad steady-state phases doe as i LEACH-C. 3.. Process of Proposed Methods 3... Liear Predictio Method Usig Time Series Liear predictio method is a powerful techique to predict time series i a eviromet chagig with time. Suppose that you wat to cotact a idepedet variable x ad a depedet variable y to specify. If we assume that the true relatioship betwee these variables i a straight 8 LEACH-CE-Correlatio. lie ad the value observed for each value of y for every give x is a radom variable the we ca wrote: E y x a0 ax () where i this equatio a 0 is the width from the origi ad a is the slope of the lie that is uidetified fixed values. Observed value y ca be described with the followig equatio where the error ε created because of ot coformig real value to the amout of predicted value. y a0 ax () This patter is usually amed a simple liear regressio model. Because that has oly oe idepedet variable so that the x idepedet variables called predictio variable ad y called the respose variable. Predictio ad respose variables x ad y ca be time series i which case we have a time series regressio patter. There are several methods to estimate ukow parameters a, a 0 i Equatio () that ca be used. Oe method that a lot used is the least square error method i which the a 0, a estimates obtaied from miimizig sum of squares errors or remaiig s. Suppose we have observatios of (x, y ), (x, y ) (x, y ). A model that is based o these observatios is writte as follows: yi a0 a xi i, i,,, (3) Ad the total square error is as the follow: a, a y a a x i (4) 0 i 0 i So the total square error is simply the total squares of deviatios observed y i ad a a x 0 i. The estimated values of a 0 ad a that we call them a 0 ad a that achieved usig the least squares method by miimizig a, a toward ad a so we ca write: 0 a0 0 a 0 yi a0 axi i 0 a xi yi a0 axi i This system of equatios called least squares lie ormal equatios system that simplified as the followig: 0 a a x y i i i 0 i i i i i i i a x a x x y By solvig this system a 0 ad a estimates or o the other had ad a obtaied ad so: a0 i

5 J. AMIRI ET AL. 65 where i i i i i i i xi xi i i aˆ xi xyi y i xi i x y x y i x ad x i x aˆ y aˆ x 0 yi i liear regressio model is as follows: s s xy xx y. So the fitted simple yaˆ aˆ x 0 For each value of the predicted variable x we ca obtai correspodig value predicted respose from this equatio. The fitted values of ŷ i correspodig to observed values x ˆi for every i =,,, is the followig: y aˆ aˆ x i 0 The differece betwee ith give fitted value to a observed yi value called a residue so that: i eˆ y yˆ, i,,, (5) i i i If the fitted model regressio for data is appropriate, i this case remais do ot follow of appropriate form. There is o clear patter for the remais. This method stated by Equatio () that is a recursive method [9]: Liear predictio method is a powerful techique for predictig time series i a time-varyig eviromet. This method is expressed i Equatio (6) ad is a recursive method [9,0]: m y t T a y t a y t T a y t m T Estimated value at time t as a liear fuctio of previous values i the times t T, t T,, t mt has bee produced is obtaied. I Equatio () a, a,, a m are the liear predictio coefficiets, m is the model degree, T is the samplig time, y(t + T) is the ext observatio estimatio ad y(t), y(t T),, y(t mt) are the preset ad past observatios. The predictio error which is the differece betwee the predicted ad the real values (Equatio (7)) must be miimized. pridicted value Real value Error % *00% Real value I order to estimate the coefficiets of liear predictio model we use the least squares error method ad (6) (7) rewrite Equatio (6) with cosiderig modelig error i Equatio (8): a ytmtet y t a y t T a y t T m The error e(t) is geerated because of ot adoptig the liear predictio model to the real value. So to fid the coefficiets, a, a,, a m i Equatio (8) we use the sum least squares error ad set of liear fuctios. Preseted i Equatio (9). y t T y t y t T y t mt y t y t T y t m T yt mt y t k T y t mk T et a * a et T am et kt (8) (9) Y A E (0) Elemets i the matrix A are the coefficiets which ca be foud by least squares error method (): A T T Y () I Equatio (), φ T, is the traspose of the matrix φ, ad (φ T φ) is the iverse of matrix. I practice: If m is chose larger tha is required (i.e. over-estimatio of the model order), Equatio (), caot be solved for ay uique set of coefficiets, because of some colums i the matrix φ, are ot idepedet of each other. Hece φ T φ would be uique ad will ot have iverse. This meas that the system of equatios i Equatio (8) will have a ifiite umber of aswers for the coefficiets. Geometrically speakig, it is like fittig a ifiite umber of lies to a sigle poit which is ot the preferred case. If m is chose less tha the required value, the umber of idepedet equatios would be more tha the umber of ukow variables (a a m ). Such a system of equatios has to be solved for the best approximatio of coefficiets. The best approximatio for coefficiets (a a m ) is the use of the least squares error method. Obviously, that is how much precisio, the umber of the data set will icrease ad vice versa The Algorithm Used to Estimate the Eergy by Trasferrig Topology to the Base Statio As previously metioed, LEACH-C protocol divided to

6 66 J. AMIRI ET AL. three phases: topology buildig phase, setup-state ad steady-state ad this algorithm is proposed as followig. These three phases is called LEACH-CEC. a) Topology buildig phase ) Start of etwork. ) Base statio receives positio of all odes that cotai x ad y. 3) Base statio calculates distace of all odes with each other s usig the followig Formula (): d x x y y ab a b a b () 4) Ed of phase. b) Setup-state phase 5) If clusterig has chaged 5.) BS calculate eergy cosumptio per ode usig the Formulae (3) ad (4): ad E Tx l, d le l d : d d le l d : d d elec frissamp crossover 4 elec tworayamp crossover (3) ERx l le (4) elec Ad after computig, place the sum of two variables i t to the E i. 5.) Base statio calculates remaiig eergy (E R ) of each ode usig the Formula (5). E E E t R R i (5) 5.3) BS audit the iformatio received from CHs, if the odes ame with the umber of duplicate data is there, cosidered i terms of computig odes remaiig eergy. 5.4) If ER 0 the ode is dead. 5.5) Otherwise the ode is alive ad participates i Clusterig. 6) Clusterig is formed. E t i : The amout of cosumed eergy by ode i i time t. c) Steady-state phase(hybrid method) 7) If ode is a cluster head. 7.) Cluster head creates a table cotaiig ode ame ad the umber of correlated data. 7.) Cluster head collects data from the members of the cluster. 7.3) If the cluster head has ot received data from its member ode, registers ame of that ode i the table ad a uit to be added to the umber of correlated data. Cluster head seds the table with correlated data to the base statio. 8) Otherwise, that is a member ode. 8.) If the ode is i tur o the the ode rus correlated data algorithm i Figure 4. 8.) Otherwise goes to sleep mode.. Begi. For t = to m 3. Node read d t ; 4. If clusterig chage the 5. d t sed to CH or BS; 6. S = d t ; 7. Ed if 8. If (t = or 3 or 4) & ( st d t /d t > e) the 9. d t sed to CH or BS; 0. S = d t ;. Else. Node ot set & sleep; 3. Ed if 4. If (t > 4) the 5. Isert d t to Pt; //modelig widow 6. Calculate < a, a,, a m > est_ Coefficiet(); // estimate a, a,,a m based o the Modelig Widow 7. Calculate dpt based o the old a, a,...,a m ; 8. If dpt d t /d t > ucertaity the 9. Data sed to ch or bs; 0. Calculate < a, a,, a m > est_coefficiet(); //estimate ew m a, a,, a based o recet history values. Else. Sleep & wait util time goes oe step ahead; 3. Ed if 4. Ed if 5. Ed for 6. Ed Figure 4. Algorithm of ot sedig correlated data usig TSF. ETX amp l, d : Stregtheig the eergy to trasferrig bit data i distace d. friss amp : Radio eergy of amplifier. tworay amp : Radio eergy of amplifier. d: distace betwee receiver ad seder l: legth of data package. Table should be created by the cluster head i the steady-state phase. To explai this part, cosider a cluster with ode umbers, 3, 5, 6, 7, 4, ad 5 are chose. Assume that the ode 7 is cluster head ad the rest is member odes. If odes ad 5 respectively, each have ad correlated data, ode 7 as cluster head must create Table. This table must be dyamic ad at the ed of each period must be set with correlated data. 4. Simulatio ad Evaluatio of Methods 4.. Simulatio Eviromet Simulatios have bee doe o the Redhat9.0 Liux operatig system by usig NS etwork simulator. LEACH ad LEACH-C protocols Implemetatio are from the Uamp project at MIT Uiversity o NS. Simulatios have bee doe o the dimesios of m area with 00 sesor odes. The primary eergy of every Node is joule. Durig our simulatios we have chose some radom etwork topologies to obtai the mea results. Two modes for base statio locatio have bee cosidered. Oe positio i (50 ad 50) the exact

7 J. AMIRI ET AL. 67 Table. Iformatio of ode s correlated data i BS. Node ame Node Node5 Number of data correlated ceter of the etwork ad the latter is i positio (50 ad 00), which is ear the area uder moitorig. Each period of simulatio takes 0 secods log. Receivers ad trasmitters follow the model that their parameters are: E E E 8 8 elec 5.00 J bit, tx rx 5.00 J bit free-space-amp two-ray-amp.00 J bit/m,.30 J bit/m 5 4 Etx, E rx are Sed ad receive power eeded for each bit. Simulatios have doe usig LEACH, LEACH-C, LEACH-CE ad LEACH-CEC protocols. Simulatio assumptios: ) All odes are static ad have limited resources. ) Base statio has ot limited resources. 3) All odes at ay momet have data to sed. 4) All Nodes equipped with the locatio determiatio 4.. The Result of Simulatio I the NS simulator ad also LEACH ad LEACH-C protocols, data produced with the Uiform distributio. But i fact pheomeo that see by sesor odes are cotiuously chagig with time. Therefore, the iformatio received by the sesor odes is correlated. Therefore geerated data by the simulator must have a ormal distributio. Normal distributio Defiitio: we say a radom variable x is ormally distributed if its desity is as follows: ( x ) fxx fxx;, e (6) π where the parameters μ ad σ are ad σ > 0. Each distributio with the give desity fuctios as defied i relatio (6), called a ormal distributio. To show the parameters we have used μ ad σ symbols because we have kow that these are the mea ad variace parameters of distributio respectively. Figure 5 shows this cocept. For producig data by ormal distributio we assume μ = 0.8 ad σ =. I the metioed protocols data geerated i uiform distributio. So we have chaged the code of these protocols to ormal distributio. I additio, the actual amouts of eergy i each ode i all protocols of LEACH, LEACH-C, LEACH-CE ad LEACH-CEC i each period was calculated. I our first sceario where the base statio alog the etwork are located at the poit (50 ad 00). Before reviewig metioed protocols we first survey the data correlatio protocols. We will examie TINA, improvemet of TINA Protocols ad the idea proposed i cojuctio with data correlatio (TSF). The produced Data by a ode i the algorithms TINA, improvemet of TINA ad the proposed method (TSF) is reviewed. We took this result that the umber of data submissios i TSF method is less tha previous methods ad the accuracy is high. Figure 6 shows this cocept. We have ru each of desired protocols 0 times, so that resultig graphs are the average of results of the rus. The we calculated the mea of results ad by ruig data correlatio algorithms o them we extracted the followig results. We cocluded that the umber of set data i TSF method is less tha two other methods ad have a high accuracy. Error Percetage for correlated data i TSF method is equal to %. Diagram of Figure 6 describes this cocept. I a period i specified times we have geerated 0 times radom data ad we repeat it agai 0 times. The we calculated the average of them ad have ru the data correlatio algorithms over them ad extracted the followig Figure 5. Data geeratio model i a ode. Figure 6. Number of set data with correlated data.

8 68 J. AMIRI ET AL. results. I Figure 6 the average of correlated data umber i each period with 00 odes has show. Util the 300th time i each momet of sedig periods at least 6 data are correlated. From 300th to 400th time there is at least 5 correlated data. As is clear i the Figure 7 the umber of correlated data throws dow over time. Because of odes eergy level decrease over time ad the die. So the probability of existig correlated data will decrease The First Sceario I our first sceario where the base statio i poits (50 ad 00) is the etwork decided Figure 8 shows the amout of eergy cosumptio i each period. I Figure 8, we compared LEACH, LEACH-C, LEACH-CE ad the proposed LEACH-CEC protocols ad the we have cosidered the value of correlated data i discussed algo- Figure 7. Average umber of correlated data i each period. Figure 8. Total eergy cosumptio i the etwork topology.

9 J. AMIRI ET AL. 69 rithms. The we have obtaied the eergy cosumptios Value for each of protocols. We called them regularly LEACH-TSF, LEACH-C-TSF, LEACH-CE-TSF ad LEACH-CEC-TSF. Fially we compared them with each other. We ca see the LEACH-CEC-TSF method has better performace tha all of metioed methods. Figure 9 shows the umber of alive odes at differet times. I this Figure 9, 8 methods that metioed above are assessed by the umber of alive odes i each period. As i Figure 9, i the LEACH-CEC-TSF method the umber of alive odes is more tha all other methods. I Figure 9, i the cetralized protocols odes death time has bee started from 400, but i the distributed proto- cols death of odes has started from The Secod Sceario I the secod sceario the base statio s locatio chaged to the poit (50, 50). Figure 0 shows eergy cosumptio i each period. I this sceario first eergy estimatio of LEACH-CEC protocol has bee compared with the LEACH ad LEACH-C ad LEACH-CE protocols. Simulatios show that sice the base statio is located i the ceter of the etwork, so the eergy cosumptio is lower i compariso with the first sceario. Figure 9. Number of alive odes i each period. Figure 0. Total eergy cosumptio i the etwork topology.

10 70 J. AMIRI ET AL. Figure shows data correlatio i each of the LEACH ad LEACH-C ad LEACH-CE ad LEACH- CEC protocols. Simulatios show that data correlatio is ot depedet o the particular sceario. Number of live odes i each of the LEACH, LEACH-C, LEACH-CE ad LEACH-CEC protocols without data correlatio is compared i Figure. Applyig Data correlatio to the each of LEACH, LEACH-C, LEACH-CE ad LEACH-CEC protocols shows that live odes umber is further whe the base statio is located i the ceter of the etwork. This operatio has show i Figure 3. As see i the distributed protocol, death of odes started i time 0. But i LEACH, LEACH-C, LEACH- CE ad LEACH-CEC cetralized protocols death of odes started i time 360. As see the proposed methods have better performace tha the previously proposed techique preseted. Table shows the percetage of Figure. Compariso of eergy cosumptio values by applyig data correlatio. Figure. Comparig the umber of live odes.

11 J. AMIRI ET AL. 7 Figure 3. Number of live odes by applyig data correlatio. Table. Percetage of eergy improvemet protocols. LEACH-CEC-TSF LEACH-CE-TSF LEACH-C-TSF LEACH-TSF 8% 4.5% 4% 3.% Percetage of improvemet i first sceario 8.5% 4.8% 4.33% 3.3% Percetage of improvemet i secod sceario eergy improvemet by applyig TSF to each protocol. 5. Coclusios This article solves the problem of correlated data i all of discussed protocols i this paper. So the odes that have time correlated data ad sedig this data wastes their eergy ad thus etwork lifetime will decrease. By usig the algorithm of data time correlatio, the problem will be raised. Also we have elimiated periodic sedig of odes data i LEACH-C protocol. By usig eergy estimatio i LEACH-CEC method there is o eed for odes to sed their eergy level ad positio to the base statio. They oly have to sed their positio at the begiig of etwork to the base statio ad the base statio creates etwork topology ad usig a simple mathematical calculatio will calculate the eergy of odes. Totally we improved the lifetime of etwork by usig simulatio i LEACH, LEACH-C, LEACH-CE ad proposed LEACH-CEC protocols. Also we improved eergy cosumptio by usig estimatio methods. I the future works we will try to use classificatio of odes distaces scheme to estimate eergy of odes more precisely. REFERENCES [] S. Badyopadhyay ad E. Coyle, A Eergy Efficiet Hierarchical Clusterig Algorithm for Wireless Sesor Networks, Proceedigs of IEEE INFOCOM, Sa Fracisco, 30 March 003. [] M. Ali ad S. K. Ravula, Real-Time Support ad Eergy Efficiecy i Wireless Sesor Networks, School of Iformatio Sciece, Computer ad Electrical Egieerig Halmstad Uiversity, Halmstad, 008. [3] A. A. Abbasi ad M. Youis, A Survey o Clusterig Algorithms for Wireless Sesor Networks, Elsevier B.V, Amsterdam, 007. [4] M. Demirbas ad H. Ferhatosmaoglu, Peer-to-Peer Spatial Queries i Sesor Networks, Proceedig of 3rd IEEE Iteratioal Coferece o Peer-to-Peer Computig (pp 03), Liköpigs, August 003, pp [5] W. B. Heizelma, A. P. Chadrakasa ad H. Balakrisha, A Applicatio-Specific Protocol Architecture for Wireless Microsesor Networks, IEEE, Vol., No. 4, 00, pp [6] S. D. Murugaatha ad D. C. F. Ma, A Cetralized Eergy-Efficiet Routig Protocol for Wireless Sesor Networks, IEEE, Vol. 43, No. 3, 005, pp [7] W. B. Heizelma, A. P. Chadrakasa ad H. Balakrisha, Applicatio-Speci_c Protocol Architectures for Wireless Networks, IEEE Trasactios o Wireless Commuicatios, Vol., No. 4, 00, pp doi:0.09/twc [8] X. Wag, J.-J. Ma, S. Wag ad D.-W. Bi, Time Series Forecastig for Eergy-Efficiet Orgaizatio of Wireless Sesor Networks, MDPI, 0.

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