Broadcast Time Synchronization Algorithm for Wireless Sensor Networks Chaonong Xu 1)2)3), Lei Zhao 1)2), Yongjun Xu 1)2) and Xiaowei Li 1)2)

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1 Broadcast Tme Synchronzaton Algorthm for Wreless Sensor Networs Chaonong Xu )2)3), Le Zhao )2), Yongun Xu )2) and Xaowe L )2) ) Key Laboratory of Comuter Archtecture, Insttute of Comutng Technology Chnese Academy of Scences, Beng PR Chna, 8 2) Advanced Test Technology Lab, Insttute of Comutng Technolog Chnese Academy of Scences, Beng PR Chna, 8 3) Deartment of comuter scence, Hefe Unversty of Technology, Hefe PR Chna, 239 xu_chaonong@ct.ac.cn Abstract - We roosed a tme synchronzaton algorthm based on acet exchange mechansm for wreless sensor networs. A sngle-ho synchronzaton scheme was resented where ggybac technque and the least-squares lnear regresson technque were emloyed. Mult-ho synchronzaton scheme conssts of toology constructon algorthm, sngle-ho synchronzaton scheme and tme transformaton algorthm. Toology constructon algorthm constructs a breadth-frst sannng-tree. Sngle-ho synchronzaton scheme s emloyed on every sngle-ho area of the sannng-tree, and tme transformaton algorthm s to relate the tme of nodes n dfferent sngle-ho area. Smulaton results ndcate that n an 8-ho networ where every node has 8 neghbor nodes, the sngle ho synchronzaton error s about 6.86 mcroseconds on Mca2. Average synchronzaton error ncreases lnearly at the rate of 9.2 mcroseconds for one addtonal ho. To synchronze a mult-ho networ, 2n acets are needed n one synchronzaton cycle where n s the number of non-leaf node n the sannng tree. I. INTRODUCTION Recently, research nterest has been drawn towards wreless sensor networs (WSN). Tme synchronzaton [] s one of the basc servces of WSN. It can be used n many occasons such as tme-stamng sensor event, localzaton, energy-savng slee mode, data fuson and tme-dvson multlexng access to the shared wreless meda(tdma), etc. Many tme synchronzaton algorthms for WSN have been roosed over the ast few years [2][3][4][5][6][7]. They wll be dscussed n secton II. In ths aer, we resent BTS(broadcast tme synchronzaton) for wreless sensor networs. Based on acet exchange mechansm, t combnes the sender-recever synchronzaton scheme wth the recever-recever synchronzaton scheme. In sngle-ho networ, we conclude that ts synchronzaton error s the sum of two arts. One s the synchronzaton error caused by the sender-recever synchronzaton scheme, the other s the synchronzaton error caused by the recever-recever synchronzaton scheme. We mlement BTS and other two related algorthms on Smsync[8], a tme synchronzaton smulator whch smulates the tme character of Mca2 [9][]. The smulated results are also resented. We also extend BTS algorthm from sngle-ho to mult-ho networ. Mult-ho synchronzaton scheme conssts of three arts whch are the toology constructon algorthm, the sngle-ho synchronzaton algorthm and the tme transformaton algorthm whch s the most contrbuton of ths aer. The toology constructon algorthm constructs a breadth-frst sannng-tree. The sngle-ho synchronzaton algorthm s erformed n every sngle-ho area of the sannng-tree, and the tme transformaton algorthm s emloyed on the sannng-tree to relate the tme of nodes n dfferent sngle-ho area. BTS s ft for wreless sensor networs. Frst, only 2 acets are needed to synchronze a sngle-ho area n one synchronzaton cycle. So the energy consumton for tme synchronzaton s small. Second, BTS s a contnuous tme synchronzaton algorthm whch means that the local tme of node wll never be modfed. In many occasons such as energy-savng slee [], t s mortant to mae sure that the local tme of node s ndeendent wth the tme synchronzaton algorthm. Thrd, all algorthms n BTS are lghtweght n comlexty, even an eght-bt mcrocontroller wll suffce. The organzaton of ths aer s as follows: In secton II, we ntroduce the related wors. Secton III detals the BTS algorthm n a sngle-ho networ. Secton IV analyzes the synchronzaton error of BTS and some of ts features. Secton V exands BTS from sngle-ho to mult-ho networ. A toology constructon algorthm and a tme transformaton algorthm are also resented n ths secton. Secton VI resents the smulated results. The last secton s the conclusons of ths aer and future wors. II. RELATED WORKS Elson and Estrn roose RBS(reference broadcast synchronzaton) [3]. As shown by Fg., RBS s a tycal recever-recever synchronzaton algorthm [3], t excludes the tme uncertanty on sender. Fg. llustrates the crtcal ath of the sender-recever synchronzaton scheme and the receverrecever synchronzaton scheme. RBS(Reference Broadcast Synchronzaton) s a ar-wse synchronzaton algorthm n essence. So f all nodes n networ need to be synchronzed, ts energy consumton s tremendous. Furthermore, the reference node can not synchronze wth any other nodes. But the dea of recever-recever synchronzaton scheme s revolutonary. Many latter tme synchronzaton algorthms adot the dea. TPSN(Tmng-sync Protocol for Sensor Networs) [4] s a tycal sender-recever synchronzaton algorthm. It ndcates that synchronzaton error can be greatly decreased by stamng tme at MAC layer. HRTS(Herarchy Referencng Tme Synchronzaton Protocol) s not a ar-wse synchronzaton algorthm. Its synchronzaton scheme n sngle-ho networ s smlar to our BTS algorthm. So t wll be ntroduced n secton III.A. III. BTS IN SINGLE-HOP NETWORK

2 In ths secton, we ntroduce BTS algorthm n sngle-ho networ. Snce the synchronzaton scheme of BTS s derved from HRTS, we frst have an overvew of HRTS. Then we ntroduce ther dfference brefly. At last, BTS s ntroduced. Sender Recever Tme NIC Crtcal Path Sender Recever Recever2 Crtcal Path Fg.. Sender-recever and recever-recever synchronzaton Two terms have to be exlaned frstly, whch s the local tme and the estmated tme. Fg. 2 llustrates ther dfference. Counter ulse Local tme from other nodes Local tme Counter Local tme from other nodes Instantaneous Tme Synchronzaton Algorthm Contnuous Tme Synchronzaton Algorthm A. Contnuous synchronzaton Counter ulse Counter B. Instantaneous synchronzaton Fg. 2. Local tme and estmated tme The local tme s actually the value of tme counter whch ncreases wth counter ulse. If we loo tme synchronzaton algorthm as a system and the local tme as system nut, the estmated tme can be looed on as the system outut. Fg. 2.A llustrates ther relatonsh n contnuous tme synchronzaton algorthm. The estmated tme never nfluences the local tme. But for an nstantaneous tme synchronzaton algorthm as n the lower art of Fg. 2.B, at the begnnng of a synchronzaton cycle, the value of tme counter s relaced wth the estmated tme once the estmated tme s wored out by the nstantaneous tme synchronzaton algorthm. Snce then, the estmated tme s same to the local tme. Both of them wll ncrease wth counter ulse untl the next synchronzaton cycle. Its estmated tme s returned when a node s nqured about ts tme. So the duraton of synchronzaton cycle wll nfluence more heavly on nstantaneous tme synchronzaton algorthm than contnuous tme synchronzaton algorthm. A. HRTS n Sngle-ho Networ Fg. 3 llustrates the scheme of HRTS algorthm. When t s tme to synchronze, the tme reference node randomly aonts one of ts neghbours as the reler. Frst, t broadcasts a acet whch s referred as M, every of ts neghbours ncludng the reler records the arrval tme of M wth ther local tme and save t nto buffer. For examle, the reler records t as t2 and nodek records t as t2. Then, the reler wll return a acet to the tme reference node whch s referred as M2. In Fg. 3, t s the tme when M s ust transmtted, t4 s the tme when M2 s ust receved. Both of them are recorded NIC Estmated tme Estmated Tme = Local tme wth the local tme of the tme reference node. t2 s the tme when M s ust receved, t3 s the tme when M2 s ust transmtted. Both of them are recorded wth the local tme of the reler. t2 and t3 are contaned n M2 whch s send to the tme reference node by the reler. We assume that the roagaton delay of M and M2 are same and the tme offset between them s fxed durng the tme from t to t4. If we refer the roagaton delay of M as d, and the tme offset between the tme reference node and the reler s referred as d2. Snce the tme reference node has nown about the t, t2, t3 and t4 when t receves M2, so: Node The tme t t4 reference node The reler Node Node M M2 M3 t2 t2 t2 Fg. 3. Synchronzaton scheme of HRTS algorthm Tme t 2 = t+ d+ d2 t 4 = t3 + d d 2 d, d2 can be wored out as follows: d = ( t2 t + t4 t3) / 2 d 2 = ( t2 t + t3 t4) / 2 () If we refer the local tme of the tme reference node as T r, the local tme of the reler as T and the local tme of other nodes such as nodek as T. We can now that: T r = T - d2 (2) At last, the tme reference node broadcasts a message whch s referred as M3 wth t2 and d2 contaned n t. If we assume that all nodes receve M at the same tme, we can now that: T - T = t2 - t2 Combned wth equaton (2), t can be now that: T r = T + t2 - t2 - d2 (3) t2 - t2 - d2 s called comensated tme of nodek. NodeK can now adust ts local tme by addng comensated tme onto ts local tme. If K s equal to P, then t2 s same as t2, n that case, equaton (3) s equvalent to equaton (2). After adustment, the local tme of every node n the networ s equal to that of the tme reference node under assumton. We can thn that the whole networ s synchronzed at that nstant. B. BTS n Sngle-ho Networ In sngle-ho networ, BTS modfes HRTS n two asects. Frst, the t2 and d2 can be ggybaced n M of the next cycle. There are only two acets n one synchronzaton cycle. So when a node receves M, t not only records tme nformaton for ths cycle but also comutes the comensated tme for last cycle. Second, when the comensated tme s wored out, every node wll save t nto buffer nstead of adustng ts local tme mmedately. BTS then emloys the least-square lnear regresson technque to smooth the tter of synchronzaton error. So a lnear equaton whch descrbes the t3

3 tme relatonsh between tself and the tme reference node s setu. To descrbe the scheme of BTS n more formal language, we have some notatons: we refer the local tme of nodek as t ] [ when t sends M, [ t 2] when t receves M, [ t 3] when t sends M2, [ t 4] when t receves M2 n the th synchronzaton cycle. The cloc offset n the th synchronzaton cycle between nodek and the tme reference node s referred as[ d 2]. For convenence, we assume that the tme reference node s node. Stes n the th synchronzaton cycle are as follows: Ste: The tme reference node broadcasts M. It randomly aonts a neghbour node (assume t s nodek) as the reler for ths cycle, [ t2] and [ d 2] m of the (-) th synchronzaton cycle are also ggybaced n M (assume nodem s aonted as the reler n the (-) th synchronzaton cycle). At the same tme, the tme reference node records ts tme as [ t]. Ste 2: When one node(assume t s nodep) receves M, t records the arrval tme of M as [ t 2] wth ts local tme, t also comutes the comensated tme of the last cycle accordng to equaton (3), the value of the comensated tme s [ t 2] m [ t2] [ d2] m, for smlcty, we refer t as [ tc ]. Then the ont ( [ t 2], [ tc ] ) s saved nto ts buffer. The meanng of the ont s that when the local tme of nodep s [ t 2], t needs to add [ tc ] on ts local tme so as to synchronze wth the tme reference node. Ste 3: the nodek who s aonted as the reler for ths cycle sends M2 bac to the tme reference node wth [ t 2] and [ 3 contaned n t. t ] Ste 4: the tme reference node records the arrval tme of M2 as [ t 4]. It now wors out [ d 2] accordng to equaton (). When the nodep s nqured about the tme, ts estmated tme s returned. Stes are as follows: Ste : fnd the ont whose x-coordnate s the smallest n buffer. Notate the ont as ([ t 2],[ tc] ). Ste 2: construct a ont set {([ t 2] [ t2],[ tc ] [ tc] )} (for all n buffer) and do the least-squares lnear regresson on the constructed ont set. So lnear equaton y = x + b s constructed. We can now that b must be. Ste 3: f we refer the local tme of nodep as RT, then: = RT + ( RT [ t 2 ] ) + [ tc = ( + ) RT + [ tc ] [ t 2 ] ET ] = RT d = f RT ) P + ( (4) That s, nodep can estmate the local tme of node accordng to equaton (4). ET stands for the estmated value. Accordng to Fg. 2, t s also the estmated tme of nodep. We ont out here that ET may be unequal to the local tme of node n real crcumstance. Ther dfference s the synchronzaton error between nodep and node. We call and d as local sew and local offset of nodep resectvely. Equaton (4) means that the estmated tme of a node can be wored out based on ts local tme, local sew and local offset. Ths s the bass of the tme transformaton algorthm whch wll be dscussed latter. IV. ANALYSIS FOR BTS A. Error Analyss We now try to fnd what nfluences the synchronzaton error of BTS. For convenence, we assume that there are only three nodes n a sngle ho networ, ther ID number are, and 2 resectvely. We also assume that node s the tme reference node and the three nodes starts runnng at the same nstant and ther frequences are same at any nstant. So ther local tmes are comletely equal at any nstant. We now consder the nstant when M2 has ust been receved by node n th synchronzaton cycle. Assume that node s aonted as the reler n the cycle. It s obvous that the synchronzaton scheme between node and node s the sender-recever synchronzaton. It s same wth TPSN algorthm. There, the author declares that roagaton tme, receton tme are man erroneous factors. Of course, TPSN stams tme at MAC layer whle BTS does not, so the crtcal ath of BTS s from the alcaton layer of sender to that of recever. We refer the synchronzaton error caused by all comonents n the crtcal ath to beδ, (t can be ether ostve or negatve). So: RT = ET + δ (5), The synchronzaton scheme between node2 and node s the recever-recever synchronzaton. It s same wth RBS algorthm. There, the author declared that the receve tme on recever s man erroneous factor. We refer the synchronzaton error caused by t to be, 2 (t can be ether ostve or negatve). So: 2 ET = ET + (6),2 Accordng to equaton (5) and (6), So: 2 RT = ET + δ, + (7), 2 If e stands for the synchronzaton error between node2 and node, abs(x) s the functon whch gets bac the absolute value of the varable x, so: abs ( abs ( δ,) abs (,2 )) abs ( e) abs ( abs ( δ,) + abs (, 2 )) (8) From equaton (8), we can see that BTS s equvalent to RBS f δ, s zero. Furthermore, BTS s equvalent to TPSN f,2 s zero and tme-stamng at MAC layer. There exsts the nequalty between the reler and the non-reler n one synchronzaton cycle. For the reler, ts synchronzaton error s only nfluenced by the sender-recever synchronzaton scheme whle the synchronzaton error of the non-reler s nfluenced by both the sender-recever synchronzaton scheme and the recever-recever synchronzaton scheme. So n a sngle-ho networ, the average synchronzaton error wll ee ncreasng wth the number of node and ee aroachng a lmt whch t never reaches for ever. B. Other Analyss Both tme comlexty and sace comlexty of BTS algorthm are low. Both of them are O(n) where n s the sze of buffer. Furthermore, comutaton s no more than oeraton of

4 addton and multlcaton on nteger. Any 8-bt mcrocontroller suffces. The energy consumton of BTS s very low. Only 2 acets are transmtted for tme synchronzaton n each synchronzaton cycle. The oeraton of least-square lnear regresson wll not be done untl the node s nqured about ts tme. Snce the reler s randomly aonted n every cycle, the energy consumton wll be dstrbuted unformly n the networ. One fault of BTS s that the energy consumton of the tme reference node s tremendous. But n many alcatons, the sn node has suffcent energy suly. If the sn node s also the tme reference node, the fault can be overcome. Snce the synchronzaton error can not be decreased by the sze of buffer, buffer sze s not an mortant arameter. But t can smooth the tter of synchronzaton error n some degree. So f external envronment change fercely, the buffer sze should be set larger. In our exerment, t s set as 3. V. BTS IN MULTI-HOP NETWORK In ths secton, we extend BTS from sngle-ho to multho networ. Frst, a toology constructon algorthm s emloyed to construct a breadth-frst sannng-tree. Sngle-ho synchronzaton s erformed on every sngle-ho area n the sannng-tree. Second, a tme transformaton algorthm s ntroduced whch s emloyed to relate the tme of dfferent nodes whch belong to the dfferent sngle-ho area. A. Toology Constructon Algorthm It s obvous that the synchronzaton error of a node s hghly related to ts ho number to the tme reference node. So the am of the toology constructon algorthm s to construct a breadth-frst sannng-tree. Every node has a varable level to ndcate ts ho number to the tme reference node. Intally, ts value of the tme reference node s, and the value of other nodes are n+ where n s the number of node n networ. There s a feld named acet_level n M. When a node transmts M, t wll coy ts level nto the acet_level feld n M. When a node receves M, t wll test f the acet_level contaned n M s no less than the varable level. If yes, t wll gnore the message, otherwse, t wll udate ts level to be (acet_level+) and transmt another M. So, a tree herarchy toology s constructed wth the tme reference node as the root of the tree. B. Tme Transformaton Algorthm To clearly exlan the rncle of the tme transformaton algorthm, we tae an examle to descrbe ts dea. We tae Fg. 4 as examle. The sannng-tree s constructed by the toology constructon algorthm dscussed above. Assume that Node s the tme reference node. So: RT ET = (9) It s obvous that any node can drectly communcate wth ts son nodes n the sannng-tree. That s, a node and all of ts son nodes n the sannng-tree form a sngle-ho area. Based on t, we dvde the sannng-tree nto many sngle-ho areas where sngle-ho BTS algorthm can be drectly aled. Fg. 4 llustrates that there are 4 sngle-ho areas n the sannng-tree. Here, we focus on the tme of node, node, node2 and node3 to see how the tme transformaton algorthm wors. When we aly sngle-ho BTS algorthm on Area, node and node wll synchronze soon. If we don t consder synchronzaton error, we can now: ET = RT () Assume that s the local sew of node, d s the local offset of node. Accordng to (4), we can get the followng: ET = f ( RT) = d () By analogy, when we aly sngle-ho BTS algorthm on Area2 and Area4, we can get the followng: Area2 Area4 3 Fg. 4. A sannng-tree constructed by the toology constructon algorthm 2 RT ET = (2) 2 ET = f ( RT2 ) = 2 RT 2+ d 2 (3), 3 ET 2 = RT 2 (4) 3 ET 2 = f ( RT 3 ) = 3 RT 3+ d 3 (5) Accordng to (), (), we can get the followng: RT = d (6) Accordng to (), (), (2) and (3), we can get the followng: RT = 2 RT 2 + d 2 + d (7) Accordng to () to (5), we can get the followng: RT = 2 3 RT3 + 2 d 3 + d 2 + d (8) We recursvely defne and d as follows: = d = d + d = = = d = d (9) We have already referred to and as local sew and d local offset resectvely. Here, we refer to and d as global sew and global offset resectvely. Accordng to the recursve defnton, We now rewrte equaton (9),(6),(7) and (8) as follows: = RT + = RT d = d = RT + d + d = RT d = 2 RT2 + d 2 + d = 2 RT2 + d 2 + d = 2 RT2 d2 = 32 RT3 + 2d3 + d 2 + d = 32 RT3 + 2d3 d2 = 3 RT 3 + d 3 5 Area Area3 By analogy, for node, we can get the followng: RT = RT + d (2) So, f a node nows ts global sew, global offset, t can estmate the local tme of the tme reference node accordng to the local tme of ts own. Of course, global sew and global offset can be get recursvely. We now consder how to realze the algorthm. Every tme a node s about to send an M, t ggybacs ts global_sew and global_offset nto the M so that every of ts son nodes can construct ts own global_sew and global_offset based on equaton (9). The global_sew and global_offset of the tme reference node s and resectvely. We can see that the tme transformaton algorthm needs no any addtonal message. When a node s nqured about ts tme, t wors out

5 ts estmated tme of the tme reference node accordng to equaton (2) and returns t as results. VI. SIMULATION To test the erformance of BTS algorthm, we have develoed a tme synchronzaton smulator named Smsync. Secfc nformaton about Smsync can be got from [8]. In ths secton, we frst smulate BTS, RBS and HRTS algorthm n sngle-ho networ. Then, we smulate BTS algorthm n mult-ho networ. A. Smulaton n Sngle-ho Networ We frst realze BTS, RBS and HRTS n a sngle-ho networ on Smsync. 3 nodes named node, node and node2 are deloyed n a sngle-ho networ. Node s the tme reference node n BTS and HRTS. In RBS, node s the reference node. The synchronzaton cycle s set as seconds, the buffer sze s set as 3. For every algorthm, we smulate t for 5 mnutes. At the begnnng of every synchronzaton cycle, we nqure and record the tme of every node n sequence. At the end of smulaton, all these tme s exorted as a fle used for further analyss. So there are 3 tme tems for each node. For BTS and HRTS algorthm, based on the exorted fle, we wor out the dfference between node and node for every tme tem, the dfference between node2 and node for every tme tem s also wored out. The synchronzaton error s the mean of them. For RBS algorthm, we wor out the dfference between node and node2. The dfference s actually the synchronzaton error of RBS algorthm. The smulated results are lsted n Table I, there, µ s the mean of the synchronzaton error, σ s the standard devaton of the synchronzaton error. Ther unts are mcrosecond(µs).. s the number of messages used for tme synchronzaton n one synchronzaton cycle. N s the number of node n the networ. TABLE I SIMULATED RESULTS OF BTS, RBS AND HRTS Algorthm µ(unt: µs) σ(unt: µs) BTS RBS N(N-)+ HRTS Accordng to Table I, from the vew of synchronzaton error, RBS s the best, BTS taes the second lace and HRTS s the worst. The result s consstent wth our revous analyss. In secton IV, we have stated that the synchronzaton error of BTS must be larger than that of RBS. Furthermore, the synchronzaton scheme of BTS and HRTS are very ale, but HRTS s an nstantaneous synchronzaton algorthm whle BTS s a contnuous tme synchronzaton algorthm, so BTS wll not be nfluenced so heavly wth the duraton of synchronzaton cycle than HRTS. As to the message number n one synchronzaton cycle, RBS s the worst and BTS s the best. Based on the result, we can conclude that the ower consumton of BTS s the least. Table II s coed from [7], we can see that ts results of HRTS have great gas wth our smulated results, but ts results of RBS and ours are very ale. The reason s analyzed as follows: n [7], besdes a ublc wreless channel, every node has a secal wreless channel to drectly communcate wth the tme reference node. As n Fg. 3, the tme reference node broadcasts M and M3 usng the ublc channel so that all of ts neghbours can receve them, but the aonted reler reles to the tme reference node usng ts secal channel, so there s no wreless collson at all. But Smsync has already bult the wreless collson nto ts model. We have nown that wreless collson s the man cause of synchronzaton loss, so the results of HRTS from [7] must be better than our smulated results. As to the results of RBS, n [7], although every node has a secal channel, all messages have to be broadcasted usng the ublc channel, there must be some wreless collsons. So ts results of RBS and ours must be very ale. In a word, the results from [7] defend our results. TABLE II EXPERIMENT RESULTS FROM [7] Algorthm µ(unt: µs) σ(unt: µs) RBS HRTS B. Smulaton n Mult-ho Networ We also smulate the mult-ho BTS on Smsync. 2 nodes are deloyed alone a straght lne. Every node can only communcate wth ts last and next neghbour. The smulaton arameters and statstcal method are same to that of sngleho smulaton. We lst the detaled smulated results from ho to 8 hos n Table III. Fg. 5 llustrates the relaton between the mean of synchronzaton error and ho number. It also llustrates the relaton between the standard devaton of synchronzaton error and ho number. We can see that both the mean and the standard devaton of the synchronzaton error ncrease lnearly wth the ho number. Synchronzaton error ncreases at the rate of about 9.6 mcroseconds for one addtonal ho. TABLE III SIMULATED RESULTS OF MULTI-HOP BTS FOR LINEAR TOPOLOGY Ho number µ(unt: µs) σ(unt: µs) The lnear toology s not reresentatve. Snce every node has only one son node n ths toology, so n every sngle-ho area, the reler s fxed durng the smulaton. Accordng to, the synchronzaton error s only related to the sender-recever synchronzaton scheme and has no relaton wth the recever-recever synchronzaton scheme under ths toology. Another toology s smulated, the smulaton scenaro nvolves 8 nodes deloyed n a 9ⅹ9 grd n such way that each note can drectly communcated wth ts 8 neghbours. So t s a networ of 8 hos. The smulaton arameters and statstcal method are same to that of revous smulaton. We lst the detaled smulated results from ho to 8 hos n Table IV. Fg. 6 llustrates the relaton between the mean of synchronzaton error and ho number. It also llustrates the relaton between the standard devaton of synchronzaton

6 error and ho number. We can see that both the mean and the standard devaton of the synchronzaton error ncrease lnearly wth the ho number. Average synchronzaton error ncreases at the rate of about 9.2 mcroseconds for one addtonal ho. Accordng to Table IV, we can see that the synchronzaton error of BTS s about 6.86 mcroseconds n sngle-ho networ. Both Fg. 5 and Fg. 6 show that the mean and the standard devaton of the synchronzaton error ncrease lnearly wth the ho number. Comarng Table III wth Table IV, we can see that every tem n Table III s smaller than the corresondng tem n Table IV. Ths s caused by the nequalty between the reler and the nonreler n one synchronzaton cycle. For the lnear toology, every node s the reler. Synchronzaton Error(µs) Ho number Fg. 5. The relaton between synchronzaton error and ho number for lnear toology TABLE IV SIMULATED RESULTS OF MULTI-HOP BTS FOR NON-LINEAR TOPOLOGY Ho number µ(unt: µs) σ (unt: µs) Synchronzaton Error(µs) µ σ µ σ Ho number Fg. 6. The relaton between synchronzaton error and ho number for nonlnear toology VII. CONCLUSION AND FUTURE WORKS We have mlemented a lghtweght tme synchronzaton algorthm named BTS. Based on acet exchange mechansm, t combnes the sender-recever synchronzaton scheme wth the recever-recever synchronzaton scheme together. In sngle-ho networ, t emloys ggybac technque to reduce the number of acets necessary for tme synchronzaton. It buffers tme nformaton of acets and emloys the leastsquares lnear regresson technque on them to smooth tter of synchronzaton error. The sngle ho synchronzaton error s about 6.86 mcroseconds n an 8-ho networ where every node has 8 neghbour nodes. Average synchronzaton error ncreases at the rate of about 9.2 mcroseconds for one addtonal ho. In a sngle-ho networ, only 2 acets are transmtted n one synchronzaton cycle to synchronze all nodes. To synchronze a mult-ho networ n one synchronzaton cycle, 2n acets are transmtted where n s the number of sngle-ho cell n the sannng tree. n s also the number of non-leaf node n the sannng tree. It overcomes the demerts of both RBS and HRTS, and t s a retty trade-off between the synchronzaton recson and the energy consumton used for tme synchronzaton. We conclude that ts synchronzaton error s the sum of two arts. One art s caused by the sender-recever synchronzaton scheme. The other art s caused by the recever-recever synchronzaton scheme. To rove our conclusons, we mlement BTS and other two related algorthms on Smsync. The smulated result testfes our conclusons. To extent BTS from sngle-ho to mult-ho networ, we roose a tme transformaton algorthm. It needs no addtonal acets. We also fnd that both the mean and the standard devaton of a node s synchronzaton error ncrease lnearly wth ts ho number to the tme reference node. Our future wors are to realze BTS on Mca2, we beleve that n real envronment, some unexected henomena may occur when the networ s large enough. After all, to mantan the robustness and scalablty of BTS s an mortant tas. REFERENCES [] J. Elson and K. Römer, Wreless Sensor Networs: A New Regme for Tme Synchronzaton, ACM SIGCOMM Comuter Communcaton Revew, vol. 33, no., , Jan 23. [2] M. L. Schtu and C. Veerartthan, Smle, Accurate Tme Synchronzaton for Wreless Sensor Networs, n Proceedngs of IEEE Wreless Communcaton and Networng Conference (WCNC 23), New Orleans, LA, vol. 2,. 6-2, Mar 23. [3] J. Elson, L. Grod, and D. Estrn, Fne-Graned Tme Synchronzaton usng Reference Broadcasts, n Proceedngs of the ffth Symosum Oeraton System Desgn and Imlementaton (OSDI22), Boston, MA, , Dec 22. [4] S. Ganerwal, R. Kumar, and M. Srvastava, Tmng-Sync Protocol for Sensor Networs. n Proceedngs of the Frst ACM Conference on Embedded Networed Sensor Systems (SENSYS 23), Los Angeles, CA, ACM Press, , Nov 23 [5] J. V. Greunen and J. Rabaey, Lghtweght Tme Synchronzaton for Sensor Networs, n Proceedngs of the Second ACM Internatonal Worsho on Wreless Sensor Networs and Alcatons (WSNA 23), San Dego, CA,. -9, Set 23 [6] Mlos Marot, Branslav Kusy, Gyula Smon, and Aos Ledecz, The Floodng Tme Synchronzaton Protocol, n Proceedngs of the Second ACM Conference on Embedded Networed Sensor Systems (SenSys), Baltmore, MD, ACM Press, , Nov 24 [7] Hu Da, Rchard Han, TSync: A Lghtweght Bdrectonal Tme Synchronzaton Servce for Wreless Sensor Networs, ACM Moble Comutng and Communcatons Revew, vol. 8, no., , Jan 24 [8] Chaonong Xu, Le Zhao, Yongun Xu, Xaowe L, SmSync: An effectve Tme Synchronzaton Smulator for Sensor Networs, n Proceedngs of the Frst Internatonal Worsho on Sensor Networs and Alcatons (SNA 5), Beng, Chna,. 2-5, Oct.25. Avalable at: htt:// /subages/smsync.df. [9] Hll, J., and Culler, D, Mca: A Wreless Platform for Deely Embedded Networs, IEEE Mcro archve, vol. 22, no. 6,. 2-24, Nov 22 [] Mca2 and Mca2Dot: htt:// Networs. htm [] Fret Svraya and Bulent Yener, Tme Synchronzaton n Sensor Networs: A Survey, IEEE Networ vol. 8, no. 4,. 45-5, 24.