Distributed Synchronization Technique for OFDMA-Based Wireless Mesh Networks Using a Bio-Inspired Algorithm

Transcription

1 Sensors 205, 5, ; do:0.3390/s Arcle OPEN ACCESS sensors ISSN Dsrbued Synchronzaon Technque or OFDMA-Based Wreless Mesh Neworks Usng a Bo-Inspred Algorhm M Jeong Km, Sung Joon Maeng and Yong Soo Cho * School o Elecrcal and Elecronc Engneerng, Chung-Ang Unversy, Seoul , Korea; E-Mals: kmmj@cau.ac.kr (M.J.K); aod0527@naver.com (S.J.M) * Auhor o whom correspondence should be addressed; E-Mal: yscho@cau.ac.kr; Tel.: ; Fax: Academc Edor: Leonhard M. Rendl Receved: June 205 / Acceped: 22 July 205 / Publshed: 28 July 205 Absrac: In hs paper, a dsrbued synchronzaon echnque based on a bo-nspred algorhm s proposed or an orhogonal requency dvson mulple access (OFDMA)-based wreless mesh nework (WMN) wh a me derence o arrval. The proposed me- and requency-synchronzaon echnque uses only he sgnals receved rom he neghbor nodes, by consderng he eec o he propagaon delay beween he nodes. I acheves a as synchronzaon wh a relavely low compuaonal complexy because s operaed n a dsrbued manner, no requrng any eedback channel or he compensaon o he propagaon delays. In addon, a sel-organzaon scheme ha can be eecvely used o consruc -hop neghbor nodes s proposed or an OFDMA-based WMN wh a large number o nodes. The perormance o he proposed echnque s evaluaed wh regard o he convergence propery and synchronzaon success probably usng a compuer smulaon. Keywords: wreless mesh nework; OFDMA; bo-nspred algorhm; dsrbued synchronzaon; me derence o arrval; me synchronzaon; requency synchronzaon. Inroducon Wreless mesh neworks (WMNs) based on orhogonal requency dvson mulple access (OFDMA) have been vewed wh consderable neres because hey can ncrease he daa raes and lexbly o resource allocaon whle avodng he nererence beween mulchannels []. OFDMA-based WMNs

2 Sensors 205, have been nvesgaed or varous applcaons, such as enerprse neworkng, wreless neworks or publc saey, and accal normaon and communcaon neworks [2]. One o he promnen challenges n dsrbued OFDMA-based WMNs s he synchronzaon beween nodes, parcularly when a global posonng sysem (GPS) sgnal s no avalable or a reerence mng. A rangng procedure beween he base saon and moble saon resolves he synchronzaon ssue n cenralzed neworks such as 3G, LTE, and WMAX sysems. However, because he nodes n a dsrbued WMN can drecly communcae wh each oher whou a cenral conroller, each node receves sgnals rom he neghbor nodes wh a me derence o arrval (TDoA), resulng n nersymbol nererence (ISI) and nercarrer nererence (ICI). Unlke cellular neworks, he nework opology n a dsrbued WMN can change requenly. In [3], closed-orm expressons or he average sgnal-o-nererence rao a he as Fourer ransorm (FFT) oupu n he presence o mng oses and carrer-requency oses (CFOs) among he users n an uplnk OFDMA are derved. Addonally, a parallel nererence canceller (PIC) s derved n order o mgae he eecs o he mng oses and CFOs by usng a mached ler deecor n he case o a bnary phase-sh keyng modulaon. In [4], a mulsage lnear PIC approach s proposed o mgae he eecs o muluser nererences due o CFOs n an uplnk OFDMA. In [5], an nererence-mgaon echnque based on he exenson o he cyclc prex (CP) and dynamc posonng o he FFT wndows s developed or OFDMA wreless ad-hoc neworks wh arbrary mng msalgnmens. In [6], a dsrbued clock-synchronzaon echnque usng he group neghborhood average s proposed or wreless sensor neworks. Here, he group averages o he ose and skew rae, measured a each sensor node, are used or he global synchronzaon. Ths echnque allows he sensor nework o quckly esablsh a consensus clock and manan a small devaon rom. Recenly, several dsrbued synchronzaon echnques were developed or OFDMA-based WMNs wh TDoAs. In [7], a mng-adjusmen echnque or mgang he nererence beween mulple nodes n an asynchronous OFDMA mesh nework usng a non-erave algorhm s proposed. In [8], a successve deecon echnque s proposed o mgae he eecs o he nererences caused by TDoAs n an OFDMA-based WMN. However, s compuaonal complexy and laency are relavely hgh, as lerng operaons or he orward and backward cancellaons n a rame are needed o remove he ISI and ICI caused by he TDoAs. In [9,0], a dsrbued me- and requency-synchronzaon echnque or OFDMA-based WMNs s proposed by updang he FFT sarng pons, ransmsson mes, and carrer requences accordng o he reques messages receved rom he neghbor nodes. Bo-nspred algorhms, whch explore he behavoral prncples o lvng organsms, have been successully appled n varous elds, ncludng communcaon neworks []. A prncple regardng he colonal movemen o lvng organsms suggess ha an enre organsm auonomously manans a paern o behavor whou he help o a cenral leader. Each ndvdual adaps s movemen o he local envronmen n a dsrbued manner, yeldng he synchronzaon o he enre colonal movemen [2 4]. The erm dsrbued mples ha he adjusmen o he ndvdual behavor s purely local wh smple rules and no conrolled by a sngle leader (or a ew leaders). In hs paper, dsrbued me- and requency-synchronzaon echnques based on a bo-nspred algorhm are proposed or nodes n an OFDMA-based WMN wh a TDoA. Updang ormulas or he dsrbued synchronzaon are proposed by consderng he propagaon delay beween he nodes, whch s

3 Sensors 205, essenal n real wreless communcaon channels. The proposed echnques, whch are based on a lockng algorhm, acheve dsrbued synchronzaon usng only he receved sgnals rom he neghbor nodes (whou requrng eedback channels) and a smple algorhm. Furhermore, a sel-organzaon scheme ha can eecvely consruc -hop neghbor nodes s proposed or an OFDMA-based WMN wh a large number o nodes. The paper s organzed as ollows: a prelmnary dscusson o an OFDMA-based WMN wh a TDoA and he lockng algorhm are presened n Secon 2. In Secon 3, a dsrbued me- and requency-synchronzaon echnque based on he lockng algorhm s proposed. The perormance o he proposed echnque s evaluaed usng compuer smulaons n Secon 4. Fnally, conclusons are drawn n Secon Prelmnares In hs paper, we consder an OFDMA-based WMN whou a cluser head. To avod co-channel nererence among he dsrbued nodes, we assume ha all he resources n he -hop neghbor nodes are allocaed orhogonally n he requency doman. We are prmarly concerned wh he nalzaon sage o he nework synchronzaon, whch occurs pror o he daa ransmsson. For he h node n an OFDMA-based WMN, he receved sgnal y () can be represened as: N K y ( ) = H [ k] X [ k]exp( j2 πkδ ( τ )) + z ( ) () j j j 0 k= 0 where H [ k ] s he channel ranser uncon beween he node and he neghbor node j, and X [ k ] j j s he OFDMA sgnal ransmed rom he -hop neghbor node j. N, Δ, K, j τ, and z () denoe he number o -hop neghbor nodes surroundng he node, subcarrer spacng, number o allocaed subcarrers, propagaon delay beween he nodes and j, and nose, respecvely. The arrval me o a sgnal ransmed rom a neghbor node, sampled wh a perod o T s, can be represened by consderng he propagaon delay beween he nodes, as ollows: ( n) = ( n) + τ, j =,, N j j j (2) where j ( n) denoes he arrval me o he sgnal rom he neghbor node j a he node, and ( n ) j denoes he ransmsson me o he node j n he n h samplng perod. Fgure shows an example o an OFDMA-based WMN conssng o hree mesh nodes wh deren propagaon delays. I Fgure s operaed as a cenralzed nework wheren Node s a conrol node, each clen node (Nodes 2 and 3) sends a rangng symbol o he conrol node (Node ) a he sar o he rangng process. Upon recevng he rangng symbol, he conrol node esmaes he round-rp propagaon delay usng he symbol mng ose (STO) esmaon echnque. Then, sends back o each clen node a rangng response ndcang he value o he mng advance (TA). Fnally, each clen node ransms a daa burs aer precompensang wh he TA normaon receved rom he conrol node. However, he synchronzaon beween he clen nodes (Nodes 2 and 3) canno be acheved n hs nework. Because each node n WMNs can drecly communcae wh oher nodes whou a cenral conroller, here can be ISI and ICI n he receved sgnal. I Fgure s operaed as a dsrbued WMN, any node can communcae drecly wh he neghbor nodes. For nsance, Node

4 Sensors 205, can receve sgnals smulaneously rom Nodes 2 and 3 n OFDMA-based WMNs. A Node, he TDoA o he sgnals rom Nodes 2 and 3 s gven as: TDoA( n) = ( 2 + τ2) ( 3 + τ3) (3) A TDoA may occur because o deren propagaon delays even when all he nodes n he WMN are synchronzed (dencal ransmsson mes). In an OFDMA-based WMN, such nererences caused by he neghbor nodes wh a TDoA resul n a loss o orhogonaly, sgncanly degradng he perormance even wh orhogonal resource allocaon. A smple echnque or mgang he nererences caused by he TDoA n an OFDMA-based WMN s o use an exended CP ha s larger han he sum o he maxmum TDoA and maxmum excess channel delay. However, hs decreases he specral ecency, as he exended CP should be nsered n every OFDM symbol or all nodes. Alhough he exended CP can be used or a large coverage, s always preerable ha he esmaed sarng pon o he OFDM symbol s precsely or slghly earler han he exac mng nsance. I he esmaed sarng pon o he OFDM symbol s beore he exac pon bu aer he end o he (lagged) channel response o he prevous OFDM symbol, he symbol does no overlap wh he prevous OFDM symbol and does no ncur any ISI due o he prevous symbol. In hs case, he phase ose caused by he STO can be easly compensaed by a sngle-ap requency-doman equalzer. However, he esmaed sarng pon o he OFDM symbol s oo much earler han he exac mng nsance (.e., he esmaed sarng pon o he OFDM symbol s pror o he end o he (lagged) channel response o he prevous OFDM symbol), he orhogonaly among he subcarrer componens s desroyed by he prevous symbol, yeldng ISI and ICI. Thereore, s always beer o synchronze he symbol mng as closely as possble wh he exac mng nsance or make slghly earler han he exac mng nsance. Fgure. Example o an OFDMA-based WMN ( N = 3 ). Bo-nspred algorhms such as an-colony, bee, and lockng algorhms have been appled o communcaon neworks owng o her useul characerscs. In parcular, hey are adapable o varous envronmenal condons, nherenly reslen o alure and damage, and able o perorm collaborave operaons based on a lmed se o rules. In hs paper, a lockng algorhm s used or

5 Sensors 205, me and requency synchronzaon n an OFDMA-based WMN wh a TDoA. The erm lockng represens he phenomenon whereby sel-propelled ndvduals are organzed no an ordered moon usng lmed envronmenal normaon and smple rules. In [4], F. Cucker and S. Smale provde a mahemacal model descrbng he evoluon o a lock. The Cucker-Smale model (C-S model) s gven as ollows: where () and () x and () d x () () = v > 0, =,, N (4) d d λ N v () ( () ())( () () = ψ ) j x j x v j = v (5) d N v are he locaon and velocy, respecvely, o he h agen. The varables N, λ, Ψ denoe he number o agens, couplng srengh (learnng acor), and communcaon-range uncon, respecvely. In he C-S model, each sel-propelled agen adjuss s velocy accordng o he veloces o s neghbors. As, he N agens exhb me-asympoc lockng phenomena. The veloces o he N agens converge o he average velocy or all he agens. 3. Dsrbued Tme- and Frequency-Synchronzaon Technques or an OFDMA-Based WMN The proposed me- and requency-synchronzaon echnques or an OFDMA-based WMN wh a TDoA are based on he C-S model, wheren each ndvdual locally adaps s movemen o he surroundng envronmen n a dsrbuve manner. I an ndvdual s nal velocy and poson are whn a ceran range, he convergence o he recursve algorhm s guaraneed accordng o he C-S model [3 5]. By consderng he agen and s velocy n he C-S model as a node and s ransmsson me n a WMN, a moded verson o he C-S model (moded C-S model) or dsrbued me-synchronzaon can be descrbed n a dscree-me doman as ollows: N λ ( n+ ) ( n) = ( ( n) ( n)) (6) j N In Equaons (4) and (5), s assumed ha he neghbors veloces can be deeced nsanly by observng he movemens o neghborng ndvduals. In real wreless communcaon channels, unlke he C-S model, here s always a propagaon delay beween nodes and j. Thereore, he ransmsson mes o he neghbor nodes n he moded C-S model should be changed o he arrval mes by consderng he propagaon delay beween he nodes. The ransmsson me o each node n a praccal WMN should be updaed usng he arrval me o he sgnal rom he neghbor node j a he node, as ollows: N λ ( n+ ) ( n) = ( ( n) ( n)) j N N λ λ = ( ( n) ( n)) + N j j N N τ (7) In Equaon (7), he error erm gven by he average o he propagaon delays s accumulaed n he dsrbued me-synchronzaon process. To use he moded C-S model n a praccal suaon, he esmaon and compensaon o he propagaon delays or all he neghbor nodes are needed; ha s,

6 Sensors 205, each node mus esmae he propagaon delays rom s neghbor nodes and reques TAs o s neghbor nodes hrough eedback channels. Ths precompensaon echnque has been appled n cenralzed cellular sysems by usng an nal rangng sgnal or perodc rangng sgnal. However, s nadequae or dsrbued WMNs wheren he mesh opology may requenly change. I also requres a large amoun o resources, such as me, bandwdh, and nework delay, because o he requen requess hrough he eedback channels. In hs paper, a dsrbued me-synchronzaon echnque or achevng as synchronzaon whou a eedback channel n an OFDMA-based WMN wh a TDoA s descrbed. Fgure 2 shows a lowchar o he proposed dsrbued me- and requency-synchronzaon echnques. The proposed synchronzaon echnques comprse hree seps: he me and requency updae (ransm mode), FFT wndow updae (receve mode), and sel-organzaon. In he me and requency updae, he ransmsson me and requency or each node are updaed usng he sgnals receved rom he neghbor nodes. The man ocus o he proposed echnque les n hs sep, where he bo-nspred algorhm s used o acheve he me and requency synchronzaon n a dsrbued manner. The ormulas or updang he ransmsson me and requency or he node are gven as: ( n + ) = c ( ) ( ) n + μ n Δ (8) ( n+ ) = c ( ) ( ) n + μ Δ n (9) Fgure 2. Flowchar o he proposed dsrbued synchronzaon echnque. In Equaons (8) and (9), each node updaes he nex ransm me ( n+ ) and requency ( n+ ) usng he arrval me j ( n) and requency ( n ) rom a neghbor node j. Parameers j ( c, c, μ, μ ) conrol he convergence speed and error accumulaon caused by he propagaon delays n he me and requency updae sep. Δ ( n) and Δ ( n) denoe he mng and requency correcon

7 Sensors 205, erms comprsng he average mng and requency errors, respecvely, beween he node and s neghbor nodes: N ( ) Δ n = ( ( ) ( )) α n n j j (0) N ( ) Δ n = ( ( ) ( )) α n n j j () The erm α j denoes he weghng acor beween he nodes and j, and s se as α =. j j The nal wegh α j s se as / N. Accordng o Equaons (0) and (), a eedback channel s no requred, because he arrval me and requency a each node can be esmaed usng only he receved sgnal. In he proposed echnque, s assumed ha each node perodcally ransms a preamble pror o he daa ransmsson. Then, he node can esmae he arrval me j ( n) and requency ( n ) j accordng o he preambles receved rom he neghbor nodes. The eec o he propagaon delay on he me-updang ormula s ndcaed by he ollowng equaon: N ( n+ ) = c ( n) + μ ( ( n) ( n)) j N N N = c ( n) + μ ( j( n) ( n)) + μ τj N N convenonal Flockngmodel error erm causedbypropagaondelay When here s no propagaon delay beween he nodes, he ormula wh he parameers c = μ = becomes he moded C-S model (dscree-me verson o C-S model). However, he convergence propery s no guaraneed or he C-S model when here s a propagaon delay. The approprae values o he synchronzaon parameers, c and μ, mus be deermned or he convergence o he updang ormula. To analyze he convergence propery o he proposed echnque, he ranser uncon o he updang ormula s expressed n he z-doman. I we regard he arrval me o he sgnal rom a neghbor node as he npu and he ransmsson me o he node as he oupu, he ranser uncon o he updang ormula or he node n Equaons (8) and (9) can be derved n he z-doman as: (2) μ H ( z) = z c + μ (3) Noe ha H ( z ) has a real pole a c μ. I hs pole les whn he un crcle n he z-plane, he proposed updang ormula are always asympocally sable. To reduce he accumulaed error erm N μ τ caused by he propagaon delays n he ransm-me updang sep o Equaon (2), μ j N should be seleced such ha μ < 0. Thus, n order o sasy he wo convergence condons or he me synchronzaon, c and μ should be seleced such ha: and < c μ < (4) I μ = c =, he proposed updang ormula operaes n a zero-pole condon ha exhbs he ases convergence speed. I μ =, he accumulaed error s mnmzed, yeldng he mnmal TDoA aer he convergence. The convergence condon or he requency synchronzaon can be derved n

8 Sensors 205, he same way as ha or he me synchronzaon. Unlke he me synchronzaon, he requency synchronzaon s no aeced by he propagaon delay n wreless channels. Thus, he convergence condon or he proposed requency-synchronzaon echnque s gven as: < c μ < (5) In he FFT wndow updae sep, he sarng pon o he FFT wndow s updaed wh he sgnals receved rom he neghbor nodes. The updang ormula or he FFT wndow poson o he node s gven as: ( ) FFT( n + ) = mn j ( n) + T, j CP (6) where T CP s he CP duraon. The sarng pon o he FFT wndow n he receve mode s deermned by he rs arrval me among he sgnals ransmed rom he neghbor node. When he maxmum TDoA s smaller han he CP duraon, he nererence caused by he deren sgnals arrval mes can be gnored by selecng he FFT wndow poson accordng o Equaon (6). By erang he updang ormulas o Equaons (8) and (0), he proposed me-synchronzaon echnque can acheve a global synchronzaon whou any addonal precompensaon procedures. Under he deal condons, he deren ransmsson mes o all he nodes converge o a common average value as n he C-S model. However, a TDoA may exs aer he convergence, especally when a -hop neghbor node s locaed ar away wh a large propagaon delay. The maxmum bound or he TDoA o each node aer he convergence s deermned by he derence beween he maxmum and mnmum propagaon delays, as ollows: 0 TDoA max( τ j) mn( τ j), j (7) I s possble o reach he maxmum bound o he TDoA n Equaon (5) when he ransmsson mes o all he nodes are synchronzed usng a GPS. In hs case, he arrval me rom a neghbor node s deermned only by he propagaon delay beween he nodes; hence, he maxmum bound o he TDoA s gven by he rgh-hand sde o Equaon (7). When a -hop neghbor node s locaed ar away, he maxmum TDoA aer he convergence may be larger han he CP duraon. In hs case, he WMN volaes he convergence condon (all TDoAs rom -hop neghbor nodes are whn he CP duraon), causng a loss o orhogonaly. The WMN can hen be reorganzed (sel-organzaon) by updang he weghs n Equaon (0) as ollows: α j( n) mn( j ( n)) j ( n) α j ( n+ ) = < max( j ( n)) + TCP ) (8) 0 oherwse The wegh beween he nodes and j s mananed he arrval me o he sgnal rom he node j alls whn he CP duraon. Oherwse, he wegh α s se as 0, mplyng ha he -hop lnk j beween he nodes and j s physcally dsconneced. In hs case, he -hop neghbor ls mus be recongured hrough a re-roung procedure so ha he dsconneced node can be suppored by s neghbor node. The perormance loss caused by dsconnecng he node s nsgncan because he lnk wh a large propagaon delay usually experences a sgncan pah loss. Table compares he

9 Sensors 205, proposed dsrbued synchronzaon echnque wh hree deren prevous echnques developed or OFDMA-based WMSs [7 0]. Table. Comparson o dsrbued synchronzaon echnques or OFDMA-based WMSs. Reerence [0] Reerence [9] Reerence [7] Proposed Ierave/non-erave Ierave Ierave Non-erave Ierave Consensus algorhm Yes Yes - - Flockng algorhm Yes Feedback channel Requred Requred Requred No requred Compuaonal complexy Medum Low Hgh Low 4. Smulaon Resuls In hs secon, he perormance o he proposed dsrbued me-synchronzaon echnque or an OFDMA-based WMN wh TDoAs s evaluaed by a smulaon. The parameers used or he smulaon are aken rom he proles n he IEEE 802.6e sandard (moble WMAX) [6,7]. RMa LoS s used or he channel model [8]. The locaons o he nodes are randomly chosen. The specc values o he parameers used n he smulaon are as ollows: (a) he sze o he FFT/IFFT( N ) s FFT 2048; (b) he CP lengh s 52; (c) he samplng perod ( T s ) s 0.29 us/sample; (d) he number o nodes n a WMN ( N ) s 3, 4, and 0; (e) he maxmum number o -hop nodes ( N ) s /( N ) ; and () he nal weghs ( α j ) are se as / N. A oal o 000 smulaon runs are conduced or all he scenaros n hs secon. Receved me Convergence curve (N=3) c =-, μ =-, Node c =-, μ =-, Node 2 c =, μ =, Node c =, μ =, Node 2 c =, μ = (Moded C-S model) 0 c =-, μ =- (Proposed) eraon (n) Fgure 3. Convergence curves o he moded C-S model and proposed me-synchronzaon echnque wh he propagaon delays ( [ τ, τ, τ ] = [394, 320, 330], [,, ] = [98, 52, 247] ). 2 3 Fgure 3 compares he perormance o he convenonal lockng model and proposed me-synchronzaon echnque when he propagaon delays are presen. In hs gure, he y-axs represens he arrval mes o he sgnals rom he neghbor Nodes and 2 a he Node 3 when N = 3.

10 Sensors 205, Here, [,, ] denoes he ransmsson mes o each node, and [ τ, τ, τ ] denoes he propagaon delays beween he nodes. As dscussed n Secon 3, he moded C-S model s he specal case o he proposed me-synchronzaon algorhm or c = μ =. Because he moded C-S model (convenonal lockng algorhm) does no sasy he second requremen ( μ < 0 ) or he convergence, he receved mes n hs gure do no converge, owng o he error accumulaon. On he oher hand, when he convergence condons are sased ( c =, μ = ), he TDoA aer he convergence s smaller han he CP duraon. Fgure 4 shows a convergence curve o he proposed requency-synchronzaon echnque when he propagaon delays are presen. Fgure 4a shows he case ( c =, μ = ) where he parameers c and μ sasy he condon. Fgure 4b shows he case ( c =, μ 0.0 = or c μ =.0 ) where he parameers c and μ do no sasy he condon. In hs gure, we observe ha he parameers sasyng he condon n Equaon (5) should be seleced or he convergence o he requency-synchronzaon echnque n Equaon (9). Fgure 5 shows a convergence curve o he proposed dsrbued me-synchronzaon echnque or N = 4. Here, he maxmum TDoA (596 samples) aer he convergence s larger han he CP duraon (52 samples). Because hs volaes he convergence condon, he sel-organzaon sep s appled, reducng he TDoA o 32 samples a compleon. (a) Convergence curve (N=3) c =-, μ =-, Node Frequency c =-, μ =-, Node 2 c =-, μ =-, Node 3 (b) Frequency c =-, μ =-0.0, Node c =-, μ =-0.0, Node 2 c =-, μ =-0.0, Node eraon (n) Fgure 4. Convergence curve o he proposed requency-synchronzaon echnque when he propagaon delays ([ τ, τ, τ ] = [394, 320, 330],[,, ] = [98, 52, 247] ) are presen Table 2 summarzes he synchronzaon success probably o he proposed echnque or N = 3, 4, and 0. Here, s assumed ha synchronzaon success s acheved when each node n a WMN s synchronzed no only wh he arge node bu also wh all he -hop neghbor nodes, wh TDoA beng smaller han he CP duraon. In Table 2, Beore dsrbued synchronzaon, Only dsrbued synchronzaon, and Synchronzaon and sel-organzaon reer o he synchronzaon success probables a he pons A, B, and C shown n Fgure 2, respecvely. Case I corresponds o he case

11 Sensors 205, where he node wh he larges TDoA s dsconneced. Case II corresponds o he case where all he -hop nodes no sasyng he convergence condon are dsconneced. Table 2. Synchronzaon success probably o he proposed echnque. Sep N = 3 N = 4 N = 0 Beore dsrbued synchronzaon 34% 27% 0% Only dsrbued synchronzaon 00% 99% 78% Synchronzaon and sel-organzaon Case I - 00% 88% Case II % In Table 2, we observe ha he synchronzaon success can be acheved wh only he dsrbued synchronzaon n mos cases when N s small (3 or 4). Fgure 5 ( N = 4 ) corresponds o he wors case (%), where he synchronzaon success canno be acheved wh only he dsrbued synchronzaon. As N ncreases, he synchronzaon success probably decreases because o he large number o neghbor nodes ha mus be synchronzed. For N = 0, he synchronzaon success probably obaned by only he dsrbued synchronzaon s 78%. The sel-organzaon sep mproves he success probably o 88 and 00% n Cases I and II, respecvely. The average number o dsconneced nodes n Case II s Convergence curve (N=4) Dsrbued synchronzaon sep Sel-organzaon sep 000 Receved me samples 32 samples Node 2 Node 3 Node eraon (n) Fgure 5. Convergence curve o he proposed synchronzaon echnque when he propagaon delays ( [ τ, τ, τ, τ, τ, τ ] = [95,342,952, 709,86, 769], [,,, ] = [50, 25, 500,0] ) are presen. To evaluae he perormance o he proposed synchronzaon echnque n mul-hop mesh neworks, a smulaon s perormed or he scenaro shown n Fgure 6. As shown n hs gure, he maxmum number o -hop neghbor nodes s hree. The locaons (propagaon delays) o he nodes are randomly chosen. Fgure 7 shows he convergence curves o he proposed synchronzaon algorhm n he mul-hop mesh nework.

12 Sensors 205, Fgure 6. Mul-hop nework opology used n he smulaon. 200 Convergence curve (N=6) 000 Receved me samples c =-, μ =-, Node c =-, μ =-, Node 2 c =-, μ =-, Node 4 Frequency eraon(n) (a) Convergence curve (N=6) c =-, μ =-, Node c =-, μ =-, Node 2 c =-, μ =-, Node 3 c =-, μ =-, Node 4 c =-, μ =-, Node 5 c =-, μ =-, Node eraon(n) (b) Fgure 7. Convergence curve o he proposed synchronzaon echnque n he mul-hop mesh nework ([ τ2, τ3, τ23, τ34, τ45, τ56, τ 46] = [432,832,048,68,28,296,49]). (a) Convergence curve o he proposed me-synchronzaon echnque (a Node 3); (b) Convergence curve o he proposed requency-synchronzaon echnque.

13 Sensors 205, Fgure 7a shows he convergence curves o he proposed me-synchronzaon algorhm when he propagaon delays are presen. Ths gure shows he convergence curves or -hop nodes, measured a Node 3. Here, we observe ha he maxmum TDoA beween he nodes aer he convergence s smaller han he CP lengh. Fgure 7b shows he convergence curves o he proposed requency-synchronzaon algorhm. In hs gure, he convergence curves or all he nodes are shown because he requency-synchronzaon algorhm s no aeced by he propagaon delays. Table 3 summarzes he synchronzaon success probably o he proposed echnque n he mul-hop mesh nework. Here, we observe ha he synchronzaon success probably obaned by he dsrbued synchronzaon only s 98.88%. Table 3. Synchronzaon success probably o he proposed echnque n he mul-hop mesh nework. Sep Node Node 2 Node 3 Node 4 Node 5 Node 6 Toal Only dsrbued synchronzaon 98.60% 98.60% 00% 98.70% 98.70% 98.70% 98.88% Synchronzaon & sel-organzaon 00% 00% 00% 00% 00% 00% 00% 5. Conclusons In hs paper, was shown ha he moded C-S model (dscree-me verson o he lockng algorhm) canno be drecly appled or dsrbued me-synchronzaon n an OFDMA-based WMN wh a TDoA, owng o he error-accumulaon eec. By consderng he propagaon delays beween he nodes, he proposed algorhm acheves me and requency synchronzaon n a dsrbued manner usng only he receved sgnals rom neghbor nodes. The proposed echnque was shown o acheve a as synchronzaon usng a smple algorhm because does no requre any precompensaon processes or he propagaon delays hrough eedback channels. The normaon obaned rom he sel-organzaon sep can be eecvely used o consruc -hop neghbor nodes n an OFDMA-based WMN, especally wh a large number o nodes. Acknowledgmens Ths research was suppored by he MSIP (Mnsry o Scence, ICT and Fuure Plannng), Korea, under he ITRC (Inormaon Technology Research Cener) suppor program (IITP-205-H ) supervsed by he IITP (Insue or Inormaon & communcaons Technology Promoon), and by Chung-Ang Unversy Excellen Suden Scholarshp. Auhor Conrbuons Km and Maeng developed he algorhm and smulaor or dsrbued synchronzaon n OFDMA-based WMNs wh a TDoA. Cho supervsed he projec. Conlcs o Ineres The auhors declare no conlc o neres.

14 Sensors 205, Reerences. Anouar, H.; Bonne, C.; Kalenberger, F.; Knopp, R. OpenArMesh An Expermenal Plaorm or Cooperave Mesh Neworks. In Proceedngs o he s COST200 Workshop MIMO Cooperave Communcaons, Trondhem, Norway, 3 4 June 2008; pp Akyldz, I.F.; Wang, X. A survey on wreless mesh neworks. IEEE Commun. Mag. 2005, 43, Raghunah, K.; Chockalngam, A. SIR analyss and nererence cancellaon n uplnk OFDMA wh large carrer requency and mng oses. IEEE Trans. Wrel. Commun. 2009, 8, Manohar, S.; Sreedhar, D.; Tka, V.; Chockalngam, A. Cancellaon o muluser nererence due o carrer requency oses n uplnk OFDMA. IEEE Trans. Wrel. Commun. 2007, 6, Hamd, K.A. Precse nererence analyss o OFDMA me asynchronous wreless ad-hoc nework. IEEE Trans. Wrel. Commun. 200, 9, Ln, L.; Ma, S.; Ma, M. A group neghborhood average clock synchronzaon proocol or wreless sensor neworks. Sensors 204, 4, Lee, S.G.; Ma, X. Tmng Adjusmen Technques o Mgae Inererence beween Mulple Nodes n OFDMA Mesh Neworks. In Proceedngs o he Inernaonal Conerence on Acouscs, Speech and Sgnal Processng, Prague, Czech Republc, May 20; pp Park, C.H.; Lee, M.A.; So, A.R.; Cho, Y.S. A bdreconal successve deecon echnque or asynchronous OFDMA-based wreless mesh neworks. IEEE Trans. Veh. Tech. 202, 6, Km, J.H.; Km, J.; Lm, K.J.; Kwon, D.S. Dsrbued Frequency Synchronzaon or Global Synchronzaon n Wreless Mesh Neworks. In Proceedngs o he Inernaonal Conerence on Wreless Communcaons, Kualar Lumpur, Malaysa, 8 0 Ocober 202; pp Km, J.; Km, J.H.; Lm, K.J. Dsrbued synchronzaon or OFDMA-based wreless mesh nework. ETRI J. 204, 36,.. Dressler, F.; Akan, O.B. A survey on bo-nspred neworkng. Compu. New. J. 200, 54, Hong, Y.W.; Scaglone, A. A scalable synchronzaon proocol or large scale sensor neworks and s applcaons. IEEE J. Sel. Areas Commun. 2005, 23, Reynolds, C.W. Seerng Behavors or Auonomous Characers. In Proceedngs o he Game Developers Conerence, San Jose, CA, USA, 5 9 March 999; pp Cucker, F.; Smale, S. Emergen Behavor n Flocks. IEEE Trans. Auom. Conrol 2007, 52, Ha, S.Y.; Lu, J.G. A smple proo o he Cucker-Smale lockng dynamcs and mean-eld lm. Commun. Mah. Sc. 2009, 7, IEEE Sandard or Local and Meropolan Area Neworks Par 6: Ar Inerace or Fxed Broadband Wreless Access Sysem; IEEE Sd ; The Insue o Elecrcal and Elecroncs Engneers Inc.: New York, NY, USA, 2004.

15 Sensors 205, Lee, K.D.; Leung, V.C.M. Far allocaon o subcarrer and power n an OFDMA wreless mesh nework. IEEE J. Sel. Areas Commun. 2006, 24, Gudelnes or he Evaluaon o Rado Transmsson Technologes or IMT-2000; Recommendaon ITU-R M.225; Inernaonal Telecommuncaon Unon: Geneva, Swzerland, by he auhors; lcensee MDPI, Basel, Swzerland. Ths arcle s an open access arcle dsrbued under he erms and condons o he Creave Commons Arbuon lcense (hp://creavecommons.org/lcenses/by/4.0/).