Enhancing Topology Control Algorithms in Wireless Sensor Network using Non-Isotropic Radio Models

Transcription

1 IJCSNS Iteratoal Joural of Computer Scece ad Network Securty, VOL.6 No.8B, August 6 5 Ehacg Topology Cotrol Algorthms Wreless Sesor Network usg No-Isotropc Rado Models Ma.Vctora Que ad Wo-Joo Hwag Departmet of Iformato ad Commucatos Egeerg, Ije Uversty, Gmhae, Gyeogam, South Korea Summary I realty, rado rage of ay wreless commucato devce does ot emulate a sotropc behavor or as modeled by theory. A sotropc atea s a hypothetcal lossless atea havg equal eergy beg radated or trasmtted all drectos. Alog wth wreless sesor etworks, ay wreless etwork suffered propagato complcatos cludg multpath propagato, shadowg ad path loss to ame a few whch are vtal factors to cosder a wreless evromet. Rado rregularty s ubqutous every wreless sesor etwork that t should be costtuted every protocol or algorthm desg. As per some other studes, rado propagato ca be evaluated by statstcal meas therefore, makg t a easer ad geeral way to characterze rado rregularty wthout beg depedet to ay specfc evromet. Furthermore, t could be very flexble varyg etwork codtos lke moblty. I ths paper, we develop both lear ad o-lear models to capture rado rregularty usg regresso aalyss o dstace ad receved sgal stregth. These models are assessed by mplemetg a smple mddleware to be added to topology cotrol algorthms. Key words: Rado Irregularty, No-sotropc Atea, Topology Cotrol, Regresso.. Itroducto The presece of rado rregularty wreless sesor etworks ad ts effect o etwork performace makes t a protocol desg varable whch caot be gored. Smplstc rado model assumes a perfect sphercal rado rage amog all odes the etwork. Studes show, that most of the proposed protocols developed before whch were based o sotropc rado rage model had gored ths pheomeo ad thus lead to flawed protocols. Smulato results whch utlzed a smplstc model may ot be vald the real world. Rado rregularty was prove to have a mpact o both the routg layer ad the MAC layer []. Former topology cotrol protocol desg oly accouts for power cosumpto o-rado rregularty evromet ad thus realty, performace suffers. Ths paper attempts to desg a mechasm for topology cotrol wth cosderato of rado rregularty. Ths study has two major objectves. Frst, to model rado rregularty statstcally based o dstace ad receved sgal stregth from a set of data gathered a expermet ad secod, to propose a soluto for topology cotrol algorthms. Rado rregularty evtably exsts wreless sesor etworks as vestgated by []. The paper explaed some otable causes of rado rregularty amely: o-sotropy, cotuous varato ad dfferece sedg power. From emprcal data gathered from MICA motes, they were able to establsh a Rado Irregularty Model (RIM). Furthermore, ther results showed that rado rregularty has a cosderable mpact o routg layer ad MAC layer protocols. They also proposed possble solutos for problems caused by rado rregularty. However, the suggested solutos were ot examed specfcally o performace parameters for localzato algorthms ad topology cotrol. The researchers [] vestgated a practcal realstc rado rage rregularty (RRI) model ad descrbed how t affected localzato algorthms sesor etworks. A costraed greedy forwardg rado propagato method s used to acheve localzato performace a realstc rado rage evromet. Surveyed causes of atteuato of rado rage are lmted ad evrometal depedet that makes the model dffcult to apply dfferet system codtos. There are umerous topology cotrol algorthms proposed whch largely depeds o coservg power ad varyg performace. A fault tolerat topology cotrol [3] uses hgher vertex coectvty whle makg use of the lttle power cosumpto the sleepg state to exted the lfetme of sesor etworks. As t mght be a good soluto coservg eergy, t was ot yet tested a hghly dyamc topology. O the other had, a effcet odemad topology cotrol [4] apples a specfc techque where ad whe the wreless ode eeds t. Ths s to mmze overhead o every ode at a gve tme. Asde from savg eergy, t keeps some other propertes lke: coectvty, power spaer, bouded-degree, localzed costructo ad guarateed packet delvery. Although, t has the ce propertes of a topology cotrol, t stll eeds full vestgato o moblty ad throughput. Aother scheme [5], categorzed eergy savg methods,.e. topology cotrol, to two types: actve subetwork ad short hops. They combed these two to create a two-level topology cotrol to further save eergy. Together wth [6], Correspodg Author Mauscrpt receved August 5, 6. Mauscrpt revsed August 5, 6.

2 6 IJCSNS Iteratoal Joural of Computer Scece ad Network Securty, VOL.6 No.8B, August 6 chage topology, eergy remag odes ad trasmsso rage determes the coordator selecto process amog odes. Smlarly, [7], ASCENT s formulated where certa odes rema actve as routers whle others are allowed to coserve eergy ther sleep state. The decso to become a actve router s based o ode coectvty ad observed data loss rates, provdg the etwork wth a opto to trade eergy cosumpto for coecto relablty. Although, there are a umber of topology algorthms curretly kow ths research feld, they however, are mssg a lk to varous real world scearos. Prevous studes show dscrepaces betwee expermetally observed to wdely used smulato models [8]. Aother mportat ssue whch ca be deduced from ther study s that oe must also take to accout the o-uform commucato qualty of etwork odes at all tmes. I [9], the researchers dd a comprehesve revew of commo assumptos beg doe ad hoc etwork smulatos. These are jumpstart studes brdgg the gap betwee real ad smulato models. Thus, these are the key pots whch motvated ths research. [] ad [] are some of the studes whch detfy real rado rage rregularty wreless sesor etworks. The rest of the paper s orgazed as follows. Secto descrbes the proposed model ad s further dvded to three subsectos. The frst subsecto llustrates the osotropc rado rage realty, the secod subsecto defes o-sotropc rado rage model usg lear regresso ad fally, the thrd subsecto defes a osotropc rado rage model usg o-lear regresso. I Secto 3, a way to ehace topology cotrol schemes wll be formulated. Fally, the cocluso wll be draw from the models ad soluto descrbed.. Proposed Model. No-Isotropc Rado Rage Model To show the exstece of o-sotropc property of wreless sesor etworks usg Chpco 43, the receved sgal stregth dbm s recorded dfferet drectos. Oe ode s assged as the fxed sedg ode that cotuously seds packets at costat sedg power ad mas powered whle aother ode s assged as the recevg ode that s beg moved aroud dfferet drectos. Both odes are at groud level ad have o physcal obstructos drectly betwee them as show Fg.. Fg. A smple expermet setup usg odes wth varyg drecto of the recevg ode. The output of the smple expermet above demostrates that whle chagg drectos at a certa dstace, the receved sgal stregth vares radomly, as show Fg.. We recorded observatos from 3cm. ad 6cm. dstace away from the sedg ode (mddle ode). The graph deotes that eve at a short dstace (3 cm. ad 6 cm. away from the sedg ode); the sgal stregth beg detected from dfferet drectos at the same dstace from the sedg ode vares at dfferet level. We repeat the same expermet, but ths tme varyg the dstace a sgle drecto, as show Fg. 3. Smlar from the frst expermet, the sedg ode (Node ) s mas powered whle the recevg ode (Node ) s beg moved away from the sedg ode ad s battery powered. After recordg the receved sgal stregth o the recevg ed, we were able to draw a scatterplot of the data, as show Fg. 4. Receved Sgal Stregth (dbm) Oretato (agle degrees) 6 cm. apart 3 cm. apart Fg. Receved sgal stregth from dfferet drectos.

3 IJCSNS Iteratoal Joural of Computer Scece ad Network Securty, VOL.6 No.8B, August 6 7 ad y-tercept s defed as: Receved Sgal Stregth Fg. 3 A expermet setup of two odes wth varyg dstace of the recevg ode (Node ) Dstace Fg. 4 A scatterplot of dstace vs. sgal stregth. The scatterplot llustrates a graph of the relatoshp betwee the dstace ad the receved sgal stregth betwee sedg ad recevg odes. From ths scatterplot, we ca derve a model usg lear or olear regresso. Regresso s a process of fdg a mathematcal model that best fts the data.. Lear Regresso The straght le model for the respose, that s, receved sgal stregth terms of dstace ca be wrtte as: y = β + β x ε, () + where y s the receved sgal stregth, x s the dstace, ε s estmato error ad β s are weghts. The ftted le of the determstc part of the equato s: y = β + β x. () The weghts β ad β correspods to y-tercept ad the slope of the ftted le, respectvely. Usg the least square method: The slope of the ftted le s defed as: xy β =, (3) xx Where xy = β = = y β x ; (4) x y x y, (5) = x ( x ), (6) xx = = y ( y ). (7) yy = xy, xx ad yy are the sum of squares error alog the correspodg axes. Also, x ad y are mea values of x ad y, respectvely. The least square le that would approxmate the data the scatterplot s: y = x. The resultg le that would approxmate the relatoshp betwee the receved sgal stregth ad dstace for the gve set of data s show Fg. 5. The least square le must satsfy: Where SE s the sum of errors ad for our case, we get: SE Σ [ y y ] =.6 Ths value s acceptable, sce we are tryg to mmze the value of the sum of error. The best ad deal approxmato s whe SE =, that s the pots le o a straght le ad that le s the best approxmate of the set of those pots. We also test the accuracy of the approxmato by Pearso product of momet coeffcet of correlato, r, where: r = SE = Σ [ y y = = = xx xy Ths meas that r s close to - ad a lear tred may exst betwee y ad x; that s receved sgal stregth s versely proportoal to dstace. The value r rages from - to. A value of shows that the lear equato descrbes the relatoshp perfectly ad postvely, wth all the pots lyg o the same le ad wth y creasg wth x. A value of - meas that the lear equato descrbes the relatoshp perfectly ad egatvely, wth all the pot lyg o the same le ad wth y decrease as x creases. Ths s smlar as what we have see our result. Lastly, a value of meas that the lear model s approprate ad thus there s o lear relatoshp yy ] = = (8)

4 8 IJCSNS Iteratoal Joural of Computer Scece ad Network Securty, VOL.6 No.8B, August 6 betwee the two varables (x ad y). Receved Sgal Stregth Dstace Fg. 5 A graph of the scatterplot wth supermposed least square le. A coveet way of measurg how well the least square le equato performs as a predctor of y s to compute the reducto the sum of squares of devatos that ca be attrbuted to x, expressed as a proporto of yy. Ths s through coeffcet of determato, gve by: E 689. r = = =.8996, (9) yy where the sum of square error (E) s gve by: E = Σ [ y y = ]. () The total sum of squares of devatos of the 4 samples of receved sgal stregth values about ther predcted values has bee reduced by 89.96%. That s, 89.96% of the sample varato of the receved sgal stregth ca be explaed by the least square le..3 No-Lear Regresso Smlarly, we could descrbe the scatterplot by olear regresso. Ths process s carred out repeatedly to mmze the value of the squared sum of dfferece betwee the data ad the ftted le, as defed by Eq. (). Therefore, we eed to maxmze the correlato dex or coeffcet of determato, r : Subject to: y = y = A + B log( + x ) = y By maxmzg, r ad varyg the values of A ad B, we would be able to produce a o-lear regresso betwee y ad x. Fg. 6 shows the o-lear regresso betwee receved sgal stregth ad dstace. Note that Eq. () has a ε term added to the determstc part of the equato. Ths term accouts for the error. We assumed that the ε has a mea of zero wth a estmated varace of: Receved Sgal Stregth s = E () Dstace Fg. 6 A graph of the scatterplot wth supermposed o-lear regresso curve. The square root of Eq. () s the estmated stadard devato, s. Table shows the estmated varace ad stadard devato or ε. The - s the degrees of freedom for error ad s deoted by umber of weghts subtracted from umber of samples. Table Estmated values for varace ad stadard devato for ε from Eq. (). We maxmze: r = = = [ y [ y y ] y] () Estmates for ε s s 4.6

5 IJCSNS Iteratoal Joural of Computer Scece ad Network Securty, VOL.6 No.8B, August Topology Cotrol The desg for topology cotrol cosders mmum power cosumpto but should stll mata the coectvty of the whole etwork. Lmted power s oe of the costrat ad characterstc of a wreless sesor etwork. The ablty of each ode to coserve eergy s a mportat aspect prologg the etwork lfetme. There are two sgfcat factors to cosder desgg a topology cotrol algorthm: ) the selecto of represetatve odes to form a etwork backboe ad ) the mateace of the etwork backboe. The frst oe volves desgg a set of crtera selectg whch ode would qualfy as a represetatve ode for a partcular group of odes ad that would jo other represetatve odes to form the etwork backboe. O the other had, the secod cosderato volves keepg the etwork fuctoal whle the role of beg a represetatve s dstrbuted amog other odes for a partcular tme. I the followg subsecto, we apply what we desged so far Geographc Adaptve Fdelty (GAF), as a example. 3. Geographc Adaptve Fdelty (GAF) GAF s a topology cotrol algorthm that dvdes the etwork to vrtual grds/cells ad assgs a sgle ode o each grd as the desgated router/leader that would stay awake for a gve tme. The odes the etwork perodcally wake up ad become the router to dstrbute the work load equally amog the odes. GAF has 3 states: sleep, dscovery ad actve states. Itally, the odes eter a dscovery state ad lstes for messages for other odes the grd, f aother ode s already desgated as the router all other odes the grd wll eter sleep state ad coserve eergy. Nodes the actve state partcpate routg ad the eter dscovery state after a specfed tme. The dmeso of the grd, r, GAF s dctated by trasmsso rage, R: R r 5 3. Modfed Bouded Dstace Forwardg For the purpose of mmzg problems caused by rado rregularty GAF, we may use Modfed Bouded Dstace Forwardg the etwork. Orgally, the dstace Bouded Dstace Forwardg, over whch a ode ca forward a message to a sgle hop, s restrcted. The modfed bouded dstace wll ow be dctated by half the rado rage of a sesor devce ad wth s or two stadard devato of ε for that specfc rado rage. We defe R = R/ ± ε, so that the ew equato s: R ' r. (3) 5 Therefore, resultg to a topology cotrol algorthm where the trasmsso rage s restrcted but also cosders the varace trasmsso rage. Fg. 7 shows the summary of the soluto for topology cotrol algorthms usg regresso. The frst step s to determe Mddleware Node awake? Node movg? yes start Set a coeffcet of determato lower boud, Rlower o o Add receved sgal stregth ad Dstace (va localzato methods) the data bak Topology Cotrol yes Solve by lear regresso Solve for coeffcet of determato, R yes Rlower < R Solve for ε o Use ε to determe the estmated trasmsso rage ad crtera for choosg the coordator ed Solve by No-Lear regresso Fg. 7 The summary of the mddleware mechasm corporated wth topology cotrol.

6 3 IJCSNS Iteratoal Joural of Computer Scece ad Network Securty, VOL.6 No.8B, August 6 how strct the coeffcet of determato should be or how much error s allowable the process. We leave ths choce to the topology cotrol desger, but we recommed that ths value should be close to. The followg steps are smlar as to what was descrbed the prevous sectos. Cosequetly, the amout of data to be stored the databak o each ode may create a bg overhead; therefore, t s madatory to have a lmt o how much data ca be stored. 4. CONCLUSION Ths paper attempts to mathematcally ad statstcally model rado rregularty usg lear ad o-lear regresso o a represetatve dataset of dstace ad receved sgal stregth. We test the approxmato by usg Pearso product of momet coeffcet of correlato ad coeffcet of determato to determe how well the regresso descrbes the relatoshp betwee two parameters. Fally, we gve a soluto o how to solve rado rregularty problem o topology algorthms (e.g. GAF) by addg a mddleware called Modfed Bouded Dstace Forwardg. Ackowledgmets Thak you to Dr. Le Cog Lo ad Ms. I-Yeup Kog for ther gudace. Refereces [] G. Zhou, T. He ad J. A. Stakovc, Impact of Rado Irregularty o Wreless Sesor Networks, Proceedgs of The Secod Iteratoal Coferece o Moble Systems, Applcatos, ad Servces (MobSys), Jue 4, pp [] S. Baz, Y. J, B. Q ad S.Wu, Realstc Rado Rage Irregularty Model ad Its Impact o Localzato for Wreless Sesor Networks, Proceedgs of 5 Iteratoal Coferece of Wreless Commucato, Networkg ad Moble Computg, September 5, pp [3] Y. Che ad S.H. So, A Fault Tolerat Topology Cotrol Wreless Sesor Networks, The 3rd ACS/IEEE Iteratoal Coferece o Computer Systems ad Applcatos, 5, p. 57. [4] Y. Wag, ad X. Sh, Effcet O-demad Topology Cotrol for Wreless Ad hoc Networks, Proceedgs of 4 th Iteratoal Coferece o Computer Commucatos ad Networks, 5, pp [5] B. Y, H. Sh ad Y. Shag, Two-Level Strategy for Topology Cotrol Wreless Sesor Networks, Proceedgs of th Iteratoal Coferece o Parallel ad Dstrbuted Systems, 5, vol., pp [6] B. Che, K. Jameso, H. Balakrsha ad R. Morrs, SPAN: A Eergy Effcet Coordato Algorthm for Topology Mateace Ad-Hoc Wreless Networks, Proceedgs of the IEEE Ifocom, July, pp [7] A. Cerpa ad D. Estr, ASCENT: Adaptve Self- Cofgurg sesor Networks Topologes, Proceedgs of Twety-Frst Aual Jot Coferece of the IEEE Computer ad Commucatos Socetes, Jue, vol. 3, pp [8] A. Cerpa, J.L. Wog, L. Kuag, L., M. Potkojak ad et al., Statstcal Model of Lossy Lks Wreless Sesors Networks, Fourth Iteratoal Symposum o Iformato Processg Sesor Networks, 5, pp [9] C.Kotz, C. Newport, R. Gray, J. Lu ad et al., Expermetal Evaluato of Wreless Smulato Assumptos, Proceedgs of the 7th ACM/IEEE Iteratoal Symposum o Modelg, Aalyss ad Smulato of Wreless ad Moble Systems (MSWM'4), October 4, pp Ma. Vctora Que receved her B.S. degree Computer Egeerg from Uversty of the Phlppes (Dlma, Quezo Cty, Phlppes) 3. She s ow takg her M.S. degree ad a afflate of Computer Networks Laboratory Ije Uversty (Gmhae, South Korea). Her research terest cludes computer ad sesor etworks. Wo Joo Hwag receved hs Ph.D Degree from Osaka Uversty Japa. He receved hs bachelor s degree ad M.S. degree Computer Egeerg from Pusa Natoal Uversty, Pusa, Republc of Korea, 998 ad. Hs research terests are sesor etworks ad ubqutous sesor etworks.