Time Synchronization for Wireless Sensor Networks

Transcription

1 3 Tme Synchronzaton for Wrele Senor etwork Kyoung-Lae oh Texa A&M Unverty Yk-Chung Wu The Unverty of Hong Kong Khald Qaraqe Texa A&M Unverty Erchn Serpedn Texa A&M Unverty 3. Introducton Sgnal Model for Tme Synchronzaton Defnton of Clock Degn Conderaton Delay Component n Tmng Meage Delvery 3.3 Fundamental Approache to Tme Synchronzaton Sender-Recever Synchronzaton Recever- Only Synchronzaton Recever-Recever Synchronzaton 3.4 Extng Tme Synchronzaton Protocol Parwe Synchronzaton etwork-wde Synchronzaton 3.5 Adaptve Tme Synchronzaton for WS...40 Rate-Adaptve Tme Synchronzaton (RATS) RBS-Baed Adaptve Clock Synchronzaton Adaptve Multhop Tme Synchronzaton 3.6 Concluon Reference Introducton Wth the help of recent technologcal advance n mcro-electro-mechancal ytem (MEMS) and wrele communcaton, low-cot, low-power, and multfunctonal wrele enng devce have been developed. When thee devce are deployed over a wde geographcal regon, they can collect nformaton about the envronment and effcently collaborate to proce uch nformaton by formng a dtrbuted communcaton network, called the wrele enor network (WS). WS a pecal cae of wrele ad hoc network, and aume a multhop communcaton framework wth no common nfratructure, where the enor pontaneouly cooperate to delver nformaton by 009 by Taylor & Franc Group, LLC 373

2 374 Adaptve Sgnal Proceng n Wrele Communcaton forwardng packet from a ource to a detnaton. The feablty of WS keep growng rapdly, and WS have been regarded a fundamental nfratructure for future ubqutou communcaton due to a varety of promng potental applcaton: montorng the health tatu of human, anmal, plant, and envronment; control and ntrumentaton of ndutral machne and home applance; homeland ecurty; detecton of chemcal and bologcal threat and leak; etc. [, ]. Tme ynchronzaton a procedure for provdng a common noton of tme acro a dtrbuted ytem. It crucal for WS n performng a number of fundamental operaton, uch a: Data fuon: Data fuon a man operaton n all dtrbuted network for proceng and ntegratng n a meanngful way the collected data, and t requre ome or all node n the network to hare a common tmecale. Power management: Energy effcency a key degnng factor for WS nce enor are uually left unattended wthout any mantenance and battery replacement for ther lfetme after deployment. Mot energy-avng operaton trongly depend on tme ynchronzaton. For ntance, the duty cyclng (leep and wake-up mode control) help the node to ave huge energy reource by pendng mnmal power durng the leep mode. Thu, networkwde ynchronzaton eental for effcent duty cyclng, and t performance proportonal to the ynchronzaton accuracy. Tranmon chedulng: Many chedulng protocol requre tme ynchronzaton. For example, the Tme Dvon Multple Acce (TDMA) cheme, one of the mot popular communcaton cheme for dtrbuted network, only applcable to a ynchronzed network. Moreover, many localzaton, ecurty, and trackng protocol alo demand the node to tme tamp ther meage and enng event. Therefore, tme ynchronzaton appear a one of the mot mportant reearch challenge n the degn of energyeffcent WS. In general, ynchronzaton condered a crtcal problem for dtrbuted wrele ad hoc network due to t decentralzed nature and the tmng uncertante ntroduced by the mperfecton n hardware ocllator and meage delay n phycal and Medum Acce Control (MAC) layer. All thee uncertante caue the local clock of dfferent node to drft away from each other over the coure of a tme nterval. In the context of the Internet (a knd of dtrbuted network), tme ynchronzaton ha been thoroughly tuded and nvetgated. In the Internet, the etwork Tme Protocol (TP) [3] employed ubqutouly due to t dvere advantage, uch a calablty, robutne, and elf-confgurablty. Bede, TP doe not rely on GPS and a oftware-baed protocol. However, TP preent a number of challenge when appled to WS due to the unque nature of enor network: lmted power reource, wrele channel condton, and dynamc topology caued by moblty and falure. Therefore, dfferent type of ynchronzaton cheme have to be explctly degned for WS applcaton to cope wth thee challenge (ee alo the urvey n [4 9] for addtonal motvaton n th drecton). 009 by Taylor & Franc Group, LLC

3 Tme Synchronzaton for Wrele Senor etwork 375 Reearch work on tme ynchronzaton n the context of WS roughly began to appear n 00, where [5], for the frt tme, ponted out TP cannot be drectly appled to WS and decrbed ome mportant charactertc and degn prncple of tme ynchronzaton n WS. In the ame year and the next, two mportant tme ynchronzaton protocol for WS were reported: Tmng-ync Protocol for Senor etwork (TPS) [7] and Reference Broadcatng Synchronzaton (RBS) [8]. Thee two protocol et the tage for two fundamental approache of tme ynchronzaton n WS. After that, many extenon and generalzaton of TPS and RBS, and many dfferent ynchronzaton cheme baed on other dea, have been propoed n the lterature. otce that ymbol tmng ynchronzaton n the phycal layer, whch crtcal for accurate ymbol detecton at the recever, a dfferent problem and out of the cope of th chapter. The purpoe of th chapter threefold. Frt, th chapter ummarze the fundamental feature and theoretcal reult encountered n tme ynchronzaton of WS. Second, t repreent the urvey of extng tme ynchronzaton protocol for WS, focung manly on the gnal proceng apect, the mot recent development n th feld. Fnally, th chapter dcue the need for adaptve tme ynchronzaton cheme for WS, analyze the feature of the recently reported adaptve tme ynchronzaton protocol, and propoe everal reearch drecton for mprovng ther performance. The ret of th chapter organzed a follow. In ecton 3., the general clock model for tme ynchronzaton frt ntroduced and analyzed. Some mportant feature that have to be condered when degnng tme ynchronzaton protocol for WS are preented. Addtonally, varou delay component n tmng meage delvery are categorzed. Secton 3.3 preent three general and fundamentally dfferent tme ynchronzaton approache: ender-recever, recever-recever, and recever-only ynchronzaton. Thee bac approache are analyzed and compared to llutrate the common and dfferent charactertc n clock ynchronzaton of WS. Secton 3.4 categorze and urvey the extng ynchronzaton protocol and relate them to the reult preented n ecton 3.3. In ecton 3.5, reult concernng the mportance and effectvene of adaptve tme ynchronzaton cheme are preented, and the mot mportant adaptve ynchronzaton protocol are ntroduced a well. Fnally, ecton 3.6 ummarze and conclude th chapter. 3. Sgnal Model for Tme Synchronzaton 3.. Defnton of Clock Every ndvdual enor n a network ha t own clock. The counter n a enor ncreaed n accordance wth the zero-crong or the edge of the perodc output gnal of the local ocllator. When the counter reache a certan threhold value, an nterrupt created and delvered to the memory. The frequency of the ocllator and the threhold value determne the reoluton of the clock. Ideally, the clock of a enor node hould be confgured uch that C(t) t, where t tand for the deal or reference tme. However, due to the mperfecton of the clock ocllator, the clock functon of the th node modeled a 009 by Taylor & Franc Group, LLC

4 376 Adaptve Sgnal Proceng n Wrele Communcaton C () t θo+ θ t+ e, (3.) where the parameter θ o and θ are called clock offet (phae dfference) and clock kew (frequency dfference), repectvely, and e tand for random noe. Aumng the effect of random noe e neglgble, from (3.), the clock relatonhp between two node, ay node and node, can be repreented by C () t θ ( ) + θ ( ) C () t, o where θ o () and θ () are the relatve clock offet and kew between node and node, repectvely. Thu, θ o () 0 and θ () when the two clock are perfectly ynchronzed. Suppoe there are L node n the network, then the global network-wde ynchronzaton acheved when C (t) C j (t) for all, j,, L. Tme ynchronzaton n wrele enor network a complcated problem due to the followng reaon. Frt, every ngle ocllator ha unque clock parameter regardle of t type. For ntance, accordng to the data heet of a typcal crytal-quartz ocllator commonly ued n enor network, the frequency of a clock vare up to 40 ppm, whch mean clock of dfferent node can loe a much a 40 m n a econd. In other word, every ngle ocllator mght aume a dfferent kew parameter rangng from 0 to 0 ppm. otce that n general, the clock kew θ a tme-dependent random varable (RV) and there are two concept ued often n clock termnology regardng the nature of tme-dependent randomne preent n clock parameter. Thee concept are referred to a hort-term and long-term tablte, repectvely. For the ocllator currently ued n enor network, all thee parameter are almot contant for hort-term tme nterval [0]. Bede, the total power of the noe proce too mall to be effectve n hort tme pan []. Therefore, the parameter of a clock are aumed to be contant for the tme perod of nteret. A far a the long-term tablty concerned, the clock parameter are ubject to change due to envronmental or other external effect uch a temperature, atmopherc preure, voltage change, and hardware agng [0]. Hence, n general, the relatve clock offet keep changng wth tme, whch mean that the network ha to perform perodc tme reynchronzaton to adjut the clock parameter. 3.. Degn Conderaton Tme ynchronzaton for conventonal wred network ha been thoroughly tuded and a plethora of ynchronzaton protocol have been developed a urveyed n []. For wrele enor network, there are a number of unque and mportant factor to be condered when degnng tme ynchronzaton protocol a lted below. Energy conumpton: Energy conumpton momentou n wrele enor network due to ther lmted and generally nonrechargeable power reource. Hence, the degn of wrele enor network hould be ubjected to mantanng mnmal energy expendture n each enor node. Varou type of power 009 by Taylor & Franc Group, LLC

5 Tme Synchronzaton for Wrele Senor etwork 377 control procedure, uch a leep/wake-up mode and dynamc routng control, are commonly condered n th regard. Tme ynchronzaton one of the crtcal component contrbutng to energy conumpton due to the hghly energy conumng rado tranmon for achevng clock ynchronzaton. Indeed, the energy conumpton requred for tme ynchronzaton of a node approxmately 7% of the total energy pent by a node []. Potte and Kaer howed n [3] that the rado frequency (RF) energy requred to tranmt bt over 00 m (.e., 3 J) equvalent to the energy requred to execute 3 mllon ntructon. Therefore, developng effcent ynchronzaton algorthm repreent an deal mechanm for tradng computatonal energy for reduced (RF) communcaton energy. In the equel, energy effcency the man concern n degnng tme ynchronzaton protocol. Latency: Latency n meage delvery a fundamental factor when degnng communcaton network. For network baed on multhop tranmon lke wrele enor network, th even more crtcal becaue the uncertanty n meage delvery gnfcantly ncreae a the number of hop ncreae. Bede, the effect of channel varaton, moblty, and the ad hoc nature of wrele enor network make th problem more complex. Effcent localzaton and tme ynchronzaton protocol are neceary for reducng the latency error and jtter. Securty and relablty: etwork ecurty ha ganed huge attenton n recent year a the network become more acceble and vulnerable due to the development of ophtcated pyng technque and devce. Bede, unlke wred network, far more frequent meage loe occur n wrele network becaue of the tme-varyng nature of wrele channel. Therefore, a mechanm to cope wth meage loe and malcou attack n tme ynchronzaton wll be neceary for wrele enor network. etwork topology change: The performance of a tme ynchronzaton protocol cloely related to the network topology,.e., t vare wth the denty and dtrbuton of enor n the network. Therefore, any hft n the locaton or cale of enor ncur a network topology change, whch requre at t turn a new elfconfguraton. Moblty of the enor and battery tmeout are the man reaon for th change. Hence, for dynamc enor network, tme ynchronzaton protocol hould be able to adapt well to frequent network topology change. Scalablty: Scalablty another mportant factor n the degn of ynchronzaton protocol. The computatonal complexty of ynchronzaton algorthm become a crtcal problem a the number of enor become very large. Bede, many other crucal MAC operaton, uch a multhop routng and network confguraton, hghly depend on the network calablty a well Delay Component n Tmng Meage Delvery The man role of tme ynchronzaton n a dtrbuted network to enure a common tmecale for all the network node, and to provde the rght temporal coordnaton among all the node engaged n a collaboratve and dtrbuted nteracton wth the 009 by Taylor & Franc Group, LLC

6 378 Adaptve Sgnal Proceng n Wrele Communcaton phycal envronment. Tmng mmatch are manly from dfferent etup tme of node and tme varaton ntroduced by local ocllator runnng at dfferent frequence. Envronmental varaton, uch a temperature and agng, alo drve local clock ocllator to run unpredctably. All thee uncertante caue the local clock of dfferent node to drft away from each other over the coure of a tme nterval. Aume two node need to be ynchronzed. One of the node end t current tme to a neghborng node; f there abolutely no delay n the meage delvery, that neghborng node can mmedately know the dfference between t clock and t neghbor clock. Unfortunately, n a real wrele network, varou delay affect the meage delvery, makng tme ynchronzaton much more dffcult than t eem to be. In general, a ere of tmng meage tranmon requred to etmate the relatve tme offet among node. In ome ene, tme ynchronzaton n wrele enor network can be regarded a a proce of removng the nondetermntc delay durng tmng meage tranmon over wrele channel. There are a number of nondetermntc delay whle tranferrng meage between node. Kopetz and Ochenreter for the frt tme analyzed the tructure of meage delay and characterzed the delay component accordng to the proce of meage de lvery [4]. The delay component n meage delvery can be categorzed a follow:. Send tme: The tme pent n buldng the meage at the applcaton layer, ncludng other delay ntroduced by the operatng ytem when proceng the end requet. The end tme nondetermntc and can be up to hundred of mllecond dependng on the workload of the ytem.. Acce tme: The tme watng for acceng the channel after reachng the MAC layer. Th the mot gnfcant factor and hghly varable accordng to the pecfc MAC protocol. The acce tme nondetermntc and vare from mllecond up to econd dependng on the current network traffc. 3. Tranmon tme: The tme for tranmttng a meage at the phycal layer. Th delay can be etmated by the length of a meage and the peed of rado n the medum and n the order of ten of mllecond. 4. Propagaton tme: The actual tme for a meage to tranmt from the ender to the recever n a wrele channel. The propagaton tme determntc and le than µ, whch almot neglgble compared wth the other delay component. 5. Recepton tme: The tme requred for recevng a meage at the phycal layer, whch the ame a the tranmon tme. In ome cae, th delay ha been categorzed a a part of the receve tme, to be preented next. 6. Receve tme: Tme to contruct and end the receved meage to the applcaton layer at the recever. It a correpondng component of the end tme on the tranmtter de and can be vared due to the varable delay ntroduced by the operatng ytem. ote that the tme delay n meage tranmon alo dependent on other factor, uch a hardware platform, error correcton code, and modulaton cheme. The etmated tme delay dcued above n each component baed on the Mca platform [5]. More detaled analy can be found n [6]. 009 by Taylor & Franc Group, LLC

7 Tme Synchronzaton for Wrele Senor etwork Fundamental Approache to Tme Synchronzaton Tme ynchronzaton n wrele enor network can be acheved by tranferrng a group of tmng meage to the target enor. The tmng meage contan the nformaton about the tme tamp meaured by the tranmttng enor. There ext two well-known approache for tme ynchronzaton n wrele enor network, whch are categorzed a ender-recever ynchronzaton (SRS) and recever-recever ynchronzaton (RRS). SRS baed on the tradtonal model of two-way meage exchange between a par of node. For RRS, the node to be ynchronzed frt receve a beacon packet from a common ender, then compare ther recevng tme readng of the beacon packet to compute the relatve clock offet. Mot of the extng tme ynchronzaton protocol rely on one of thee two approache. For ntance, the etwork Tme Protocol (TP) [3] and the Tmng-ync Protocol for Senor etwork (TPS) [7] adopt SRS nce they depend on a ere of parwe ynchronzaton that aume two-way tmng meage exchange. otce alo that the Reference Broadcat Synchronzaton (RBS) protocol [8] rele on RRS nce t requre par of meage exchange among chldren node (except the reference) to compenate ther relatve clock offet. Recently, a new approach for tme ynchronzaton, called recever-only ynchronzaton (ROS), wa propoed. It am at mnmzng the number of requred tmng meage and energy conumpton durng ynchronzaton whle preervng a hgh level of accuracy [9]. Th approach can be ued to acheve network-wde ynchronzaton wth much le tmng meage than other well-known extng protocol uch a TPS and RBS. ext we wll preent and analyze each of thee ynchronzaton approache and llutrate how the general degn conderaton can be reolved n them. For all thee approache, we only preent the underlyng gnalng mechanm for performng parwe ynchronzaton,.e., ynchronzng a par of node, nce network-wde ynchronzaton can be mply acheved by performng a group of parwe ynchronzaton Sender-Recever Synchronzaton Th approach baed on the clacal two-way tmng meage exchange mechanm between two adjacent node. Conder a parent node P and one of t chldren node, node A, n Fgure 3.. The clock model for the two-way meage exchange depcted n Fgure 3., where θ (AP) o denote the clock offet between node A and node P and tmng meage are aumed to be exchanged multple () tme [4, 7]. Here, the tme tamp made durng the th meage exchange T (A), and T (A) 4, are meaured by the local clock of node A, and T (P), and T (P) 3, are meaured by the local clock of node P, repectvely. ode A tranmt a ynchronzaton packet, contanng the value of tme tamp T (A), to node P. ode P receve t at tme T (P), and tranmt an acknowledgment packet to node A at T (P) 3,. Th packet contan the value of tme tamp T (A),, T (P),, and T (P) 3,. Then, node A fnally receve the packet at T (A) 4,. A dcued before, packet delay can be characterzed nto everal dtnct component: end, acce, tranmon, propagaton, and receve tme. Thee delay component 009 by Taylor & Franc Group, LLC

8 380 Adaptve Sgnal Proceng n Wrele Communcaton Regon of parwe ync. (ode P and ode A) Recever-only ynchronzaton Sender Recever Synchronzaton (-Way Meage Exchange) B A P Parent node Fgure 3. Sender-recever ynchronzaton and recever-only ynchronzaton. ode P P T (P), T (P) 3, T (P), T (P) 3, T (P), T (P) 3, Clock offet ˆ(AP) o ode A ode B A B T (A), T (A) 4, T (B), T (P), T (A), T (A) 4, T (B), T (P), T (A), T (B), T (A) 4, T (P), ˆ(BP) o D D Fgure 3. Clock ynchronzaton model of SRS (node P and node A) and ROS (node B). are dvded nto two part: the fxed porton d and the varable porton X. The varable porton of delay depend on varou network parameter (e.g., network tatu, traffc, etc.) and etup, and therefore no ngle delay model can be found to ft for every cae. Thu far, everal probablty denty functon (PDF) model have been propoed for modelng random delay, the mot wdely deployed one beng Gauan, Gamma, exponental, and Webull PDF [0, ]. The Gauan delay model approprate f the delay are thought to be the addton of numerou ndependent random procee. In [8], the ch-quared tet howed that the varable porton of delay can be modeled a Gauan dtrbuted random varable (RV) wth 99.8% confdence. On the other hand, a ngle-erver M/M/ queue can fttngly repreent the cumulatve lnk delay for pontto-pont hypothetcal reference connecton, where the random delay are ndependently modeled a exponental RV []. Thu, we aume the random porton of delay are ether normal or exponentally dtrbuted RV. 009 by Taylor & Franc Group, LLC

9 Tme Synchronzaton for Wrele Senor etwork Clock Offet Etmaton Suppoe that the clock frequence of two node reman equal durng the ynchronzaton perod, and both X (AP) and X (PA) are normal dtrbuted RV wth mean μ and varance /. From Fgure 3., T (P), and T (A) 4, can be expreed a ( P) ( A) ( AP) ( AP) ( AP) T T + θ + d + X, (3.),, o ( A) ( P) ( PA) ( PA) ( PA) T T + θ + d + X, (3.3) 4, 3, o where θ (PA) o θ (AP) o, d (AP), and X (AP) denote the fxed and random porton of tmng delay n the meage tranmon from node A to node P, repectvely. By defnng the delay n uplnk U T (P), T (A), and downlnk V T (A) 4, T (P) 3,, the th delay obervaton correpondng to the th tmng meage exchange are gven by U θ (AP) o + d (AP) (AP) + X and V θ (PA) o + d (PA) + X (PA), repectvely. Then, the lkelhood functon baed on the obervaton {U } and {V } gven by ( AP) L( θ o, µ, ) ( π ) e ( AP) ( U d θ ( o AP) µ ) + ( ( PA) + θ ( o AP) V d µ ) where the number of meage exchange. Dfferentatng the log-lkelhood functon lead to ( AP) lnl( θo ) θ ( AP) o ( AP) ( AP) ( θo + d d PA ) ( ) U V., The fxed porton of delay are manly determned by the propagaton delay, and both up- and downlnk channel have the ame dtance. Thu, the fxed porton of delay d (AP) and d (PA) are aumed to be equal, and are denoted by d for the ret of th chapter. Indeed, the propagaton delay le than µ for range under 300 m, hence almot neglgble when compared to other domnant delay component whoe range are about hundred of mllecond [6]. The maxmum lkelhood etmate (MLE) of clock offet gven by [5] θˆ (AP) o argmax ( ) ln ( θ AP ) o ( ) θ U V L. o AP (3.4) Thu, node A can be ynchronzed to the parent node P by mply takng the dfference of the average delay obervaton U and V. For exponental random delay X (PA) and X (AP) wth the ame mean λ, the lkelhood functon baed on the obervaton {U } and {V } become 009 by Taylor & Franc Group, LLC

10 38 Adaptve Sgnal Proceng n Wrele Communcaton ( ) L( θ oap, λ) λ e U V d λ + I U θ ( AP) d, V + θ ( AP) d o 0 o 0, where I( ) tand for the ndcator functon (.e., I( ) whenever t nner condton hold, otherwe t equal to 0). In [3], Jeke proved that the maxmum lkelhood etmator of θ o (AP) ext when d unknown and exhbt the ame form a the etmator propoed n [4], namely, mnu mn θˆ (AP) V o. (3.5) otce from (3.4) and (3.5), t clear that f only one round of meage exchange performed ( ), the MLE of clock offet for both exponental and Gauan delay model become θˆ (AP) o (U V)/, whch exactly the ame clock offet etmator adopted n [7] Jont Clock Offet and Skew Etmaton The clock offet between two node generally keep ncreang due to the dfference of clock parameter of each ocllator. Thu, a model wth the ame clock frequency not uffcent for long-term ynchronzaton. Indeed, applyng the clock kew correcton mechanm ncreae the ynchronzaton accuracy and guarantee the long-term relablty of ynchronzaton. Fgure 3.3 how the effect of clock offet (θ o ) and kew (θ ) on tmng meage exchange between two node. Wthout lo of generalty, the reference tme T (A), et to be zero. Here, the tme tamp at node P n the th uplnk meage T (B), gven by ( P) ( A) ( AP) ( AP) ( A) ( T T + θ + θ ( T + d + X AP) ( AP),, o, ( + θ )( + + ) + θ ( AP ) o, ( AP) ( A) ( AP) T, d X ) + d + X (3.6) (AP) (A) where the term θ (T, + d + X (AP) ) due to the effect of clock kew. Smlarly, the tme tamp at node P n the th downlnk meage T (P) 3, take the equaton ( P) ( A) ( AP) ( AP) ( A) ( T T + θ + θ ( T d X PA) ( PA) 3, 4, o 4, ( + θ )( ) + θ ( AP ) o, ( AP) ( A) ( PA) T4, d X ) d X (3.7) (AP) (A) where the term θ (T 4, d X (PA) ) agan due to the effect of clock kew. For an eaer llutraton, we ntroduce the mplfed notaton θ θ (AP), θ o θ (AP) o, T, T (A),, T 4, T (A) 4,, T, T (P),, T 3, T (P) 3,, X X (AP), and Y X (PA) n th ecton, repectvely. Aumng {X } and {Y } are zero-mean ndependent Gauan dtrbuted RV wth varance /, then the jont PDF of X {X } and Y {Y } gven by 009 by Taylor & Franc Group, LLC

11 Tme Synchronzaton for Wrele Senor etwork 383 o : Clock offet (tme dfference) : Clock kew (frequency dfference) (AP) (A) (PA) (T d X ) 4, ode P ode A (AP) (A) (AP) (T + d + X ), (AP) o T (P) T (P), 3, T (P) T (P) 3,, T (A) T (A), 4, T (A) T (A), 4, (T (A) 0), Lnear clock kew model T (P) T (P) 3,, T (A) T (A), 4, d + X (AP) d + X (PA) T (A), T (P), T (P) 3, (AP) (A) (A) (T T ) 4,, T (A) 4, Fgure 3.3 Two-way tmng meage exchange model that aume clock offet and kew. f XY, ( xy, ) π T, + θo ( T, + d )( + θ T3, + ( T4, ) + + θo d ) ( + θ ) θ + θ e. Further aumng that the fxed porton of delay d known and θ /( + θ ), then the log-lkelhood functon (gnorng rrelevant addtve and multplcatve contant) for (θ o,θ ), baed on obervaton {T, }, {T, }, {T 3, }, and {T 4, }, gven by { }. ln L( θ o, θ ) θ ( θ o T ) + ( T + d),, + + θ ( θo T3, ) ( T4, d ) (3.8) It ha been hown n [5] that the value of θ o and θ that maxmze the above loglkelhood functon are gven, repectvely, by ˆ θ o ML ( T + T ) ( T + T ), 4,, 3,, 3,, ( T + T ) Q, 3, ( T + T ) ( T + T ) Q 4,, (3.9) ˆ θ ML ( T, + T4, ) ( T, + T3, ) Q + ( T, T3, ) + ( T, + T4, ) ( T, + T3, ) ( T, + T4, ) Q ( T + T ), 3, ( T + T ), 4,, (3.0) 009 by Taylor & Franc Group, LLC

12 384 Adaptve Sgnal Proceng n Wrele Communcaton where Q ( T, T, + T3, T4, + ( T, T3, ) d). ote that the jont MLE depend on the value of the fxed porton of delay d, whch aumed to be known n th ecton. Although etmatng d an achevable tak, we do not conder d another unknown (nuance) parameter due to the nherent hghly nonlnear and complex operaton requred for etmatng d. The Cramer-Rao lower bound (CRB) for the vector parameter θ [θ o, θ ] T can be derved from the Fher nformaton matrx I(θ) by takng t nvere. From (3.6), the econd-order dervatve of the log-lkelhood functon wth repect to θ o and θ are found a o θo lnl θ, θ, lnl θ, θ, θ 4 θ, o T, θ o ( ) + ( T θ ), 3, o o θo θ lnl θ, θ, θθ o θ T, +, θ, T T3 T 4,. Takng the negatve expectaton yeld lnl θ,, o θ E θo lnl θ, θ, o E θ,, E θθ o lnl θ θ o 4 θ, ( X+ T, + d ) + ( Y T4, + d ) E X, Y θ ( a ) ( T, + d) + ( T, d) + 4 θ E, θ θ T, T o 3, ( b ) T4 T +, X Y + T, + T4,, where (a) and (b) are due to X θ (T, θ o ) (T, + d) and Y θ (θ o T 3, ) + (T 4, d), and 009 by Taylor & Franc Group, LLC

13 Tme Synchronzaton for Wrele Senor etwork 385 T T, and T T 4 4, tand for the average of tme obervaton. Therefore, I θ θ θ θ ( ),, E L E ln o o,, ln ln L E θ θ θ θ o o L E L θ θ θθ θ o o o,,, ln, θ θ, θ T T T T,, + ( ) + ( ) + 4 θ T d T d. (3.) The CRB can be obtaned by takng the [,]th element of the nvere of the Fher nformaton matrx (.e., var (θˆ) [I (θ)] ), and the nvere I (θ) gven by I + 4 ( ) θ θ P P T T T T P T T T T P T T P T T θ, (3.) where P T d T d,, + ( ) + ( ) + 4. Conequently, the CRB of the jont clock offet and kew etmator are gven by var(ˆ ) ( ) θ θ o ML P P T T + + 4, (3.3) 009 by Taylor & Franc Group, LLC

14 386 Adaptve Sgnal Proceng n Wrele Communcaton ML θ θ var(ˆ θ ) θ P T + T 4 θ 4 + P T + T. (3.4) In fact, fndng the jont MLE of clock kew requre qute a number of computaton a n (3.0), and the fxed porton of delay d mut be known (or etmated), whch mght not be applcable for wrele enor network contng of low-end termnal. In practce, t requre an addtonal etmaton procedure, whch mght deterorate the robutne of the jont MLE. To overcome th lmtaton, a famly of robut and mple clock offet and kew etmator that do not requre pror knowledge of d have been propoed n [5] Recever-Only Synchronzaton Due to the power contrant, the communcaton range of a enor trctly lmted to a (rado-geometrcal) crcle whoe radu depend on the tranmon power (ee Fgure 3.). In th fgure, every node wthn the checked area (e.g., node B) can receve meage from both node P and node A. Suppoe that node P a parent (or reference) node, and node P and node A perform a parwe ynchronzaton ung two-way tmng meage exchange [7]. Then, all the node n the common coverage regon of node P and node A (checked regon) can receve a ere of ynchronzaton meage contanng the nformaton about the tme tamp of the parwe ynchronzaton. Ung th nformaton, node B can alo be ynchronzed to the parent node, node P, wth no extra tmng meage tranmon. Th approach called recever-only ynchronzaton (ROS). In general, all the enor node lyng wthn the checked area can be ynchronzed by only recevng tmng meage ung ROS. Here, node P and node A can be regarded a uper node nce they provde ynchronzaton beacon for all the node located n ther vcnty. In Fgure 3., conder an arbtrary node, ay node B, n the checked regon. Whle node P and node A exchange tme meage, node B can overhear thee tme meage. Hence, node B capable of obervng a et of tme readng ({T (B), } ) at t local clock when t receve packet from node A, a depcted n Fgure 3.. Bede, node B can alo receve the nformaton about a et of tme tamp {T (P), } obtaned by recevng the packet tranmtted by node P. Conderng the effect of both clock offet and kew, the recepton tme at node P n the th uplnk meage T (P), gven by ( P) ( A) ( AP) ( AP) ( A) T T + θ + θ ( T T ( A) ( AP) ( AP),, o,, ) + d + X, (3.5) where θ (AP) tand for the relatve clock kew between node A and node P. Lkewe, the recepton tme at node B n the th uplnk meage T (B), can be repreented by ( B) ( A) ( AB) ( AB) ( A) T T + θ + θ ( T T ( A) ( AB) ( AB),, o,, ) + d + X, (3.6) 009 by Taylor & Franc Group, LLC

15 Tme Synchronzaton for Wrele Senor etwork 387 where θ o (AB) and θ (AB) tand for the relatve clock offet and kew between node A and node B, and d (AB) and X (AB) denote the fxed and random porton of tmng delay n the meage tranmon from node A to node B, repectvely. Here, X (AB) aumed to be a normal dtrbuted RV wth mean μ and varance /. The lnear regreon technque can be appled to ynchronze node B and compenate the effect of the relatve clock kew between node P and node B. Subtractng (3.6) from (3.5) gve ( P) ( B) ( BP) ( BP) ( A) T T θ + θ ( T T ) + d d + X X. (3.7) ( A ) ( AP ) ( AB ) ( AP ) ( AB ),, o,, Snce d (AB) and d (AP) are fxed value and X (AB) and X (AP) are normal dtrbuted RV, the noe component can be defned by z[] μ + X (AP) X (AB), where μ d (AP) d (AB) and z[] ~ (μ, ). Let x[] T (P), T (B), μ and w[] z[] μ, then the et of oberved data can be wrtten n matrx notaton a follow: x Hθ+ w, where x [x[] x[] x[]] T, w [w[] w[] w[]] T, θ [θ o (BP) θ (BP) ] T, and T ( A) ( A) ( A) ( A),,,, H 0 T T T T. ote that the noe vector w ~ (0, I) and the matrx H the obervaton matrx whoe dmenon. From [6, theorem 3., p. 44], the mnmum varance unbaed (MVU) etmator for the relatve clock offet and kew gven by θˆ g(x), where g(x) atfe ln p( x; θ) I( θ)( g( x) θ ). (3.8) θ Snce the noe vector w zero mean and Gauan dtrbuted, from the reult n [6, p. 85], the dervatve of the log-lkelhood functon can be wrtten a T ln p( x; θ) H H [( H T H ) H T x θ], θ (3.9) where H T H aumed to be nvertble. Therefore, comparng (3.8) wth (3.9) yeld ˆ T T θ ( H H) H x, (3.0) T H H I( θ), (3.) 009 by Taylor & Franc Group, LLC

16 388 Adaptve Sgnal Proceng n Wrele Communcaton where I(θ) the Fher nformaton matrx. After ome mathematcal manpulaton, the jont clock offet and kew etmator can be expreed a [9] ˆ ˆ θ θ o (BP) (BP) D D D x D [] D x D x D [] [] x [], (3.) where D T, (A) T, (A). The Cramer-Rao lower bound (CRB) can be obtaned by nvertng the Fher nformaton matrx I(θ). From (3.), the Fher nformaton matrx gven by I( ) θ D D D. Then, nvertng I(θ) yeld I ( ) θ D D D D D. (3.3) Hence, from (3.3), the CRB for the relatve clock offet and kew become var o (BP) (ˆ ) θ D D D (3.4) and var (BP) (ˆ ) θ D D. (3.5) 009 by Taylor & Franc Group, LLC

17 Tme Synchronzaton for Wrele Senor etwork 389 otce further that the regularty condton for the CRB hold: E ln p( x; θ) E θ E E E ln p( x; θ) ( BP) θ o ln p( x; θ) ( ) θ BP ( BP ) ( BP ) xn [ ] θ D o θ BP BP xn [ ] ( ) θo ( ) θ D D Conequently, ung the reult n (3.), node B can be ynchronzed to node P. Lkewe, all the other node n the checked regon n Fgure 3. can be multaneouly ynchronzed to the parent node, node P, wthout any addtonal tmng meage tranmon, thu avng a gnfcant amount of energy. Bede, there no lo of ynchronzaton accuracy when compared wth other approache [9] Recever-Recever Synchronzaton Recever-recever ynchronzaton an approach to ynchronze a et of chldren node who receve the beacon meage from a common ender (a reference or parent node). Conder a parent (reference) node P and arbtrary node A and B, whch locate wthn the communcaton range of the parent node n Fgure 3.4. Suppoe, n Fgure 3.5 both node A and node B receve the th beacon from node P at tme ntant T (A) (B), and T, of ther local clock, repectvely. ode A and B record the arrval tme of the broadcat packet accordng to ther own tmecale and then exchange ther tme tamp. Suppoe Recever Recever ynchronzaton B A P Parent node Beacon Fgure 3.4 Recever-recever ynchronzaton. 009 by Taylor & Franc Group, LLC

18 390 Adaptve Sgnal Proceng n Wrele Communcaton Recever recever ynchronzaton (ode A and ode B) ode P P T, T, T, Clock offet ode A A (A) T, (B) T, (A) T, (A) T, (A) T, { (B) T } { (A) { (B)},j j T { (A) T } },j j,j j T,j j ˆ(AB) o ode B B (B) T, (B) T, (B) T, Fgure 3.5 Clock ynchronzaton model of RRS. X (PA) denote the nondetermntc delay component (random porton of delay) and d (PA) denote the determntc delay component (propagaton delay) from node P to node A; then T (A), can be wrtten a ( A) ( PA) ( PA) ( T, T, + d + X + PA ) ( PA) θo + θ ( T, T, ), (3.6) where T, the tranmon tme at the reference node, and θ o (PA) and θ (PA) are the clock offet and kew of node A wth repect to the reference node, repectvely. Smlarly, we can decompoe the arrval tme at node B a ( B) ( PB) ( PB) ( T, T, + d + X + PB ) ( PB) θo + θ ( T, T, ), (3.7) where d (PB), X (PB), θ o (PB), and θ (PB) tand for the propagaton (fxed) delay, random porton of delay, clock offet, and kew of node B wth repect to the reference node, repectvely. Subtractng (3.7) from (3.6), we obtan ( A) ( B) ( BA) ( BA) T T θ + θ ( T T ) + d,, o,, d + X X, (3.8) ( PA) ( PB) ( PA) ( PB) where θ (BA) o θ (PA) o θ (PB) o and θ (BA) θ (PA) θ (PB) are the relatve clock offet and kew between node A and node B at the tme they receve the th broadcat packet from the (PA) reference node, repectvely. Here, we aume thee random porton of delay X and X (PB) are normal dtrbuted RV wth mean μ and varance /. Indeed, (3.8) aume exactly the ame form a (3.7). Hence, the ame tep can be appled to derve the jont clock offet and kew etmator for ROS. More pecfcally, let the noe component z[] μ + X (BA), where μ d (PA) d (PB) and z[] ~ (μ, ). Let u alo defne x[] T (A), T (B), μ and w[] z[] μ. Ung mlar tep a n ROS, t traghtforward to how that the ame form of the jont clock offet and kew etmator (3.) can alo be 009 by Taylor & Franc Group, LLC

19 Tme Synchronzaton for Wrele Senor etwork 39 appled to RRS. Conequently, there no dfference between ROS and RRS wth regard to the accuracy of ynchronzaton nce the effect of random delay are the ame. Lkewe, the CRB for RRS can alo be obtaned ung a mlar procedure a n ROS. When there no relatve clock kew (θ (BA) 0), t traghtforward to how that the maxmum lkelhood etmator of the relatve clock offet θˆ (BA) o become ˆ (BA) ( A) ( B) θ o T, T,, (3.9) whch the equvalent to the etmator preented n [8]. The man beneft of th approach that all nondetermntc delay component on the tranmtter de (end tme and acce tme) are elmnated. Thu, a hgh degree of ynchronzaton accuracy can be acheved ung th approach. 3.4 Extng Tme Synchronzaton Protocol Thu far, a number of protocol have been uggeted to olve the problem of tme ynchronzaton n dtrbuted network. For general computer network, TP ha been adopted a the tandard tme ynchronzaton cheme of the Internet [3]. Although TP wa hown to perform well n computer network, t not drectly applcable to wrele enor network due to the unque challenge enor network face: lmted power reource, wrele channel condton, dynamc topology change, etc. (recall alo the degn conderaton preented n ecton 3..). TP enjoy unlmted (or rechargeable) energy reource and a relatvely tatc topology n computer network. However, thee are not avalable n enor network. Therefore, dfferent type of tme ynchronzaton protocol have been propoed to meet the degn requrement of wrele enor network []. Ideally, a tme ynchronzaton protocol hould be able to work optmally n term of all degn requrement of tme ynchronzaton, whch are energy effcency, calablty, precon, ecurty, relablty, and robutne to network dynamc. However, the complex nature of wrele enor network make t very dffcult to optmze the protocol wth repect to all thee requrement multaneouly. Due to the trade-off n atfyng thee requrement, each protocol degned to put dtnct emphae on dfferent requrement. Aumng varou crtera, tme ynchronzaton protocol can be categorzed nto dfferent clae: Mater-lave veru peer-to-peer Mater-lave: Where frt a tree-lke network herarchy arranged, and upon the completon of th arrangement only the connected node n the herarchy ynchronze wth each other. Peer-to-peer: Where any par of node n the network can ynchronze wth each other. 009 by Taylor & Franc Group, LLC

20 39 Adaptve Sgnal Proceng n Wrele Communcaton Clock correctng veru untethered clock Clock correctng: Where the clock functon n memory modfed after each run of the tme ynchronzaton proce. Untethered clock: Where every node mantan t own clock a t, and keep a tme-tranlaton table relatng t clock to other node clock. Thu, ntead of updatng t clock contantly, each node tranlate the tme nformaton n the data packet comng from other node to t own clock by ung the tme-tranlaton table. Synchronzaton approach Sender-recever: Where one of two node, whch are ynchronzng wth each other, end a tme-tamp meage whle the other one receve t. Recever-recever: Where a reference node tranmt ynchronzaton gnal and two ynchronzng node receve thee gnal and record the tme of recepton (tme tamp). Recever-only: Where a group of node can be multaneouly ynchronzed by only ltenng to the meage exchange of a par of node. Parwe ynchronzaton veru network-wde ynchronzaton Parwe ynchronzaton: Where the protocol are prmarly degned to ynchronze two node, although they uually can be extended to handle ynchronzaton of a group of node. etwork-wde ynchronzaton: Where the protocol are prmarly degned to ynchronze a large number of node n the network. Addtonal clafcaton can be found n [4]. In the followng, we wll ummarze the extng tme ynchronzaton protocol baed on the lat category Parwe Synchronzaton Tmng-Sync Protocol for Senor etwork (TPS) TPS [7] ue the two-way meage exchange mechanm, a dcued n the enderrecever ynchronzaton approach decrbed n ecton 3.3., to acheve the ynchronzaton between two node. Wth only one round of meage exchange, and wthout any tattcal model on the varable delay component X (AP) and X (PA) n (3.) and (3.3), a mple etmate for θ (AP) o propoed n [7] a ˆθ (AP) U V o, (3.30) where U T (P), T (A), and V T (A) 4, T (P) 3,. otce that n the orgnal form of TPS, t doe not etmate clock kew; therefore, frequent applcaton of TPS needed to keep the clock offet between two node under a certan lmt Maxmum Lkelhood Etmaton for Clock Offet Baed on Two-Way Meage Exchange Aume the clock offet θ (AP) o contant for round of meage exchange. If X (AP) and X (PA) n (3.) and (3.3) are exponentally dtrbuted wth the ame unknown mean λ, 009 by Taylor & Franc Group, LLC

21 Tme Synchronzaton for Wrele Senor etwork 393 and when d d (AP) d (PA) unknown, t proved n [3] that the ML etmator of θ o (AP) gven by ˆ mn θ (AP) o U mn V. (3.3) On the other hand, wth X (AP) and X (PA) n (3.) and (3.3) beng modeled a ndependent and normally dtrbuted RV wth the ame mean μ and varance /, the maxmum lkelhood (ML) etmate for θ o (AP) take the equaton (derved n ecton 3.3.) ˆθ o (AP) U V. (3.3) otce from (3.30) (3.3), t clear that f only one round of meage exchange performed, the TPS preented n (3.30) the ML etmator under both exponental and Gauan delay model Jont Clock Offet and Skew Etmaton Baed on Two-Way Meage Exchange When clock kew ext between two node, the clock offet between them wll ncreae lnearly, a hown n Fgure 3.3. In order to etablh long-term ynchronzaton, t more effcent to etmate jontly the clock offet and kew. In ecton 3.3., we derved the jont offet and kew ML etmator (ee equaton (3.9) and (3.0)), when the varable delay X (PA) and X (AP) are modeled a ndependent Gauan dtrbuted RV. When X (PA) and X (AP) are exponentally dtrbuted RV, the lkelhood functon for jont etmaton of the clock offet and kew very complcated. However, a oluton to th problem ha been recently reported n [7]. otce that the jont offet and kew ML etmator (equaton (3.9) and (3.0)) under Gauan delay aumpton are qute complcated. Bede, there no mple cloed-form oluton for the ML jont offet and kew etmaton when the delay are exponentally dtrbuted. For thee reaon, a famly of robut and mple clock offet and kew etmator, named maxmum lkelhood lke etmator (MLLE), ha been propoed n [5] Tny-Sync and Mn-Sync Tny-ync and Mn-ync [8] are two lghtweght clock ynchronzaton protocol that alo ue the two-way meage exchange. ode A and node P exchange meage jut lke n Fgure 3.3. The only dfference here that node P reple to node A mmedately after recevng the meage,.e., T (P), T (P) 3,. Aumng the clock between node A and node P are lnearly related, from (3.6) and (3.7) we have T θ ( P) ( AP), o ( AP) + θ ( A) ( AP) T + d + X,, 009 by Taylor & Franc Group, LLC

22 394 Adaptve Sgnal Proceng n Wrele Communcaton T θ ( P) ( AP), o ( AP) + θ ( A) ( PA) T d X. 4, Snce d, X (AP) (PA), and X θ (AP) o /( + θ (AP) ), we obtan are all nonnegatve, defnng θ /( + θ (AP) ) and θ o ( A) ( P) ( A) T θ T + θ T. (3.33),, o 4, (A) The 3-tuple of tme tamp (T,, T (P),, and T (A) 3, ) called a data pont. Wth meage exchange, the goal to fnd θ o and θ uch that they atfy (3.33) for. In general, th a lnear programmng problem and there are an nfnte number of oluton for th problem [9]. Although more tme tamp would generate tghter bound on θ o and θ, unfortunately, at the ame tme, the computatonal and torage requrement of the lnear programmng approach alo ncreae. Thu, uch an approach appear to be not utable for mplementaton n wrele enor node, whch have trctly lmted memory and computng reource. Tny-ync and Mn-ync tackle the problem a fndng the bet-ft lne that le between the bound et defned by the data pont. Baed on the obervaton that not all data pont are ueful, Tny-ync preerve only four contrant (the one that yeld the bet bound on the etmate) out of all data pont. Th reult n a very effcent algorthm. However, t hown by a counterexample [8] that th cheme doe not alway produce the optmal oluton nce ome data pont are condered uele and dcarded at a certan tme, a tep that actually mght provde a better bound f t properly condered wth another data pont that yet to come. Mn-ync an mproved veron of Tny-ync n the ene that t fnd the optmal oluton wth ncreaed complexty (but tll wth leer complexty than the lnear programmng approach). Mn-ync bacally ue an addtonal crteron to determne whether the data pont can be afely dcarded Reference Broadcat Synchronzaton (RBS) RBS [8] baed on the RRS approach dcued n ecton Let the tme tamp recorded at node A and node B for recevng the th (A) common packet be denoted a T, and T (B),, repectvely. The etmate of the clock offet between node A and node B propoed n [8] a ˆ (BA) ( A) ( B) θ o T, T,, (3.34) where tand for the total number of common packet receved by node A and node B. We have hown n ecton that the above etmator actually the ML etmator for the clock offet, aumng the random porton of the delay n meage delvere 009 by Taylor & Franc Group, LLC

23 Tme Synchronzaton for Wrele Senor etwork 395 are Gauan dtrbuted RV, and there no clock kew. When there a clock kew between node A and node B, leat-quare lnear regreon propoed n [8] to etmate the clock kew. The man advantage of RBS that by comparng the tme tamp of a common packet at two dfferent node, t remove the larget ource of nondetermntc error (end tme and acce tme) from the tranmon path. Thu, RBS provde a hgh degree of ynchronzaton accuracy. ote alo that RBS can be appled to commodty hardware and extng oftware n enor network a t doe not need acce to the low level of the operatng ytem Clock Offet and Skew Etmaton Baed on Broadcat Clock Under the ettng that a enor node oberve and ynchronze to a broadcat clock, [30] derve the ML etmator for clock offet and kew wth the broadcat meage delay beng modeled a unformly dtrbuted RV. It hown that the ML etmate n th cae generally not unque. Furthermore, the upport of the lkelhood functon not convex, whch leave out the poblty of takng the mean of all equally lkely oluton. Th motvated [30] to conder the lnear etmator for the clock offet and kew. Under the ame ettng, [3] derve the jont ML clock offet and kew etmator wth the aumpton that the broadcat meage delay are modeled a exponentally dtrbuted RV. It hown n [3] that a unque jont ML clock offet and kew etmate ext under certan condton, a oppoed to the cae of unformly dtrbuted delay. Furthermore, the Gbb ampler wa ntroduced n [3] to further enhance the performance of the jont ML etmator Floodng Tme Synchronzaton Protocol (FTSP) In [6], t argued that f one can tme-tamp the meage at the MAC layer, th mmedately elmnate three ource of delay uncertante: tranmt, acce, and receve tme. In th cae, the man delvery delay come from tranmon and recepton tme at the rado chp (ee ecton 3..3). Thee delay can be further decompoed nto:. Interrupt handlng tme, whch the delay between the rado chp rang and the mcrocontroller repondng to an nterrupt. Encodng tme, whch the tme t take for the rado chp to encode and tranform the meage nto a rado wave 3. Decodng tme, whch the tme for the rado chp at the recever to tranform the rado wave back nto bnary data 4. Byte algnment tme, whch the delay at the recever to ynchronze wth the byte boundary at the phycal layer FTSP [6] ue a ngle broadcated meage to etablh ynchronzaton pont between ender and recever, whle elmnatng the jtter of nterrupt handlng and encodng/decodng tme by utlzng multple MAC layer tme tamp on both the ender and recever de. Furthermore, the kew of the clock between ender and recever etmated ung multple meage and lnear regreon. 009 by Taylor & Franc Group, LLC

24 396 Adaptve Sgnal Proceng n Wrele Communcaton 3.4. etwork-wde Synchronzaton Untl th pont, we have only decrbed the tme ynchronzaton between two neghborng enor node. In th ecton, we wll dcu protocol for network-wde ynchronzaton Extenon of TPS In order to etablh a global tmecale for all the node n the enor feld baed on TPS, [7] propoe to create a herarchcal tructure (pannng tree) n the network (named level dcovery phae) before parwe ynchronzaton performed between adjacent level (named ynchronzaton phae). The level dcovery phae cont of the followng tep:. Select a root node ung an approprate leader electon algorthm and agn a 0 level to the root node.. The root node broadcat a level dcovery packet (LDP) contanng the dentty and level of the packet. 3. Every node that receve an LDP agn t level to a level greater (by one) than that of the receved packet and end a new level dcovery packet attachng t own level (once beng agned a level, a node neglect future packet requetng level dcovery to avod floodng congeton). 4. Repeat tep 3 untl every node n the network uccefully agn a level. After the pannng tree formed, the root node ntate the ynchronzaton phae by ynchronzng all the node n level. ext, the node n level ynchronze wth the node n level, and o on, untl all the node have been ynchronzed. otce that the ynchronzaton error of a node wth repect to the root node a nondecreang functon of the hop dtance becaue the random gnal error over each hop add up. A number of dfferent earchng algorthm can be condered n the contructon of the pannng tree. For ntance, Van Greunen and Rabaey uggeted ome prelmnary dea on contructng pannng tree wth low depth n order to mprove the accuracy of ynchronzaton [] Lghtweght Tme Synchronzaton (LTS) Alo baed on two-way meage exchange, [] propoe two network-wde ynchronzaton protocol. The frt one called centralzed multhop LTS, whch bacally the ame protocol a the extenon of TPS dcued above. The other one called dtrbuted multhop LTS. Th dtrbuted LTS algorthm move the reynchronzaton from the root node to the node that need reynchronzaton. When a node A determne that t need to be reynchronzed, t wll end a reynchronzaton requet to the root node. In order for node A to reynchronze, all node along the routng path from the root node to node A wll be ynchronzed n a parwe fahon Extenon of RBS The RBS protocol dcued n the above ubecton can only ynchronze a et of node that le wthn a ngle broadcat doman. In order to ynchronze a large enor network, 009 by Taylor & Franc Group, LLC

25 Tme Synchronzaton for Wrele Senor etwork 397 A P RBS baed on reference broadcat from P Gateway node B P RBS baed on reference broadcat from P C Fgure 3.6 Extenon of RBS to multhop. [8] propoe to ue gateway node for convertng tme tamp from one neghborhood tme bae to another. The dea llutrated n Fgure 3.6. ode P and P end out ynchronzaton beacon, and they create two overlappng neghborhood, where node B le n the overlappng area. Snce node A and node B le wthn the ame neghborhood, ther clock relatonhp (.e., clock offet and kew) can be etablhed from node P reference broadcat. Smlarly, the clock relatonhp between node B and node C can be etablhed from node P reference broadcat. Therefore, the clock relatonhp between node A and node C can be computed wth node B actng a a gateway Extenon of FTSP FTSP can be extended to network-wde ynchronzaton n a traghtforward manner. Frt, a root node, to whch the whole network beng ynchronzed, elected by the network. ode that are wthn the broadcat radu of the root node can receve tmetamped meage from the root node. They then etmate the offet and kew of ther own local clock, thu ynchronzng wth the root node. The newly ynchronzed node can then broadcat ynchronzaton meage to other node n the network. The advantage of th floodng proce that t begn wth the root node, and there no need to have a level herarchy, a oppoed to TPS Parwe Broadcat Synchronzaton Parwe broadcat ynchronzaton (PBS) employ both ender-recever and receveronly ynchronzaton approache to acheve network-wde ynchronzaton wth hgh energy effcency [9]. A dcued n ecton 3.3., n PBS a number of enor node can be ynchronzed by only overhearng tmng meage beng exchanged between par 009 by Taylor & Franc Group, LLC