Comparative performance of forwarding protocols based on detection probability and search angle in a Multi-hop CDMA wireless sensor networks

Transcription

1 Intrnational Journal o Snsors and Snsor Ntworks 014; (): 14-5 Publishd onlin Jun 30, 014 ( doi: /j.ijssn Comparativ prormanc o orwarding protocols basd on dtction probability and sarch angl in a Multi-hop CDMA wirlss snsor ntworks Uma Datta 1, Sumit Kundu 1 Elctronics & Instrumntation Dpt., CSIR-CMERI, Durgapur, India Dpt. o ECE, National Institut o Tchnology Durgapur, Durgapur, India addrss: uma_datta58@yahoo.in (U. Datta), sumitkundu@yahoo.com (S. Kundu) To cit this articl: Uma Datta, Sumit Kundu. Comparativ Prormanc o Forwarding Protocols Basd on Dtction Probability and Sarch Angl in a Multi-hop CDMA Wirlss Snsor Ntworks. Intrnational Journal o Snsors and Snsor Ntworks. Vol., No., 014, pp doi: /j.ijssn Abstract: Enrgy consrvation is on o th most important issus in wirlss ad hoc and snsor ntworks, whr nods ar likly to rly on limitd battry powr. Many nw algorithms hav bn proposd or th problm o routing data in snsor ntworks. In this papr, w propos a nw orwarding tchniqu whr nods ar placd in a random ashion maintaining a minimum distanc btwn any two nods and study its prormanc on a multi-hop CDMA wirlss snsor ntwork (WSN). a nw routing protocol whr slction o intrmdiat nod is basd on a mtric combining dtction probability and maximum orwarding distanc towards th sink is proposd to rduc rtransmissions in a wirlss channl impaird by path loss and shadow ading. W provid a dtail dscription o th routing schm basd on th proposd concpt and rport on its nrgy and latncy prormanc using nd-to-nd btwn sourc and inal dstination. Prormanc o this schm is compard with an xisting sarch angl basd protocol, calld narst nighbor basd orwarding, whr an intrmdiat nod in th rout slcts th narst nod within a sctor angl, considrd as sarch angl, towards th dirction o th dstination as th nxt hop. Litim o ntwork in both cass is compard. Furthr, all paramtrs ar stimatd by incorporating rror control schm as applicabl to WSN and compard with simpl schm. A solution or packt siz optimization is introducd such that th ct o multi hop routing by varying dirnt paramtrs ar capturd. Optimization solution is ormalizd by using dirnt objctiv unctions, i.., packt throughput, nrgy icincy, and rsourc utilization. Kywords: Multi-op Communication, Forwarding Protocol, Sarch Angl, Rout Divrsity, Packt Siz Optimization, Nod Litim 1. Introduction In wirlss snsor ntworks nrgy consrvation is on o th ky tchnical challngs. It is ncssary to dvis ntworking schms which mak judicious us o limitd nrgy rsourcs without compromising th ntwork connctivity and th ability to dlivr data rliably to th intndd dstination. Many nw algorithms hav bn proposd or th problm o routing data in snsor ntworks. Almost all o th routing protocols can b classiid as data-cntric, hirarchical or location-basd although thr ar w distinct ons basd on ntwork low or QoS awarnss [1]. Data-cntric protocols ar qurybasd and dpnd on th naming o dsird data, which hlps in liminating many rdundant transmissions. irarchical protocols aim at clustring th nods so that clustr hads can do som aggrgation and rduction o data in ordr to sav nrgy. Location-basd protocols utiliz th position inormation to rlay th data to th dsird rgions rathr than th whol ntwork. Th last catgory includs routing approachs that ar basd on gnral ntwork-low modling and protocols that striv or mting som QoS rquirmnts along with th routing unction. Svral routing protocols ar dscribd in th litratur, basd on location inormation o snsor / rlay nods [, 3, 4, 5]. A routing schm whr ach intrmdiat nod in a multi-hop rout slcts th narst nod within a sctor o angl ( θ) toward th dirction o th dstination as th nxt hop, is considrd in []. owvr, nod isolation may occur in cas o low sarch

2 15 Uma Datta, Sumit Kundu: Comparativ Prormanc o Forwarding Protocols Basd on Dtction Probability and Sarch Angl in a Multi-hop CDMA Wirlss Snsor Ntworks angl in such schm. Gographic inormation-basd orwarding (GIF) is an icint schm or inding th appropriat rlay nod or nxt hop utilizing th location inormation whil avoiding a larg numbr o control packts during rout discovry. Th routing schm whr slction o nxt rlay nod is basd on maximum advancd distanc, to minimiz th numbr o hops rom th sourc to th dstination nod, is dscribd in [3], ignoring th unrliability o wirlss channl. Consquntly, prormanc may dgrad substantially ovr a bad channl and consums mor nrgy or succssul rcption o a packt du to incras in numbr o rtransmissions. An ctiv approach or th rduction o unncssary rtransmission du to propagation impairmnt is to choos th nxt hop rlay nod that is in good channl condition. An icint advancmnt mtric (EAM) is proposd in [4], considring th orwarding distanc and th probability o succssul packt transmission in a wirlss channl situation within a spciid rgion, dind by ( R, φ/ ) to ( R, φ/ ), as shown in Fig.1. owvr, in a wirlss channl impaird by path loss and shadow ading, a nw routing protocol whr slction o intrmdiat nod is basd on a mtric combining dtction probability ollowing [6], and maximum orwarding distanc towards th inal dstination may provid anothr solution whr rduction o unncssary rtransmission du to propagation impairmnt may b possibl. Figur 1. Scnario o a sourc nod and th potntial rlay nods in Channl Awar Gographic Inormd Forwarding (CAGIF) protocol [4]. Givn that th snsors hav limitd nrgy, bur spac, and othr rsourcs, dirnt MAC protocols ar bing dvlopd by svral rsarchrs. To handl a larg numbr o nods, whr a numbr o nods simultanously and asynchronously accss a channl, CDMA is a good choic as a MAC protocol [7, 8, 9]. CDMA has bn widly usd in cllular ntworks whr powr control is rquird to combat th nar-ar problm. As WSN ar opratd without any cntral inrastructur and all nods ar battry opratd with simpl transcivrs, it is diicult to achiv prct powr control. CDMA has bn advocatd or WSN in [7, 8], whr distribution o intrrnc powr in randomly distributd nods is discussd. BER and nrgy consumption in CDMA WSN multi-hop communication with ixd hop lngth is studid in [10] using ininit automatic rpat rqust () with CRC. Abov analyss o multi hop communication do not includ any routing topology or th slction o nighboring nods until it rachs th dstination. Framwork as proposd in [, 3, 4], whr th positions o th nods ar random, ar mor ralistic snsor ntwork scnarios. In this papr, considring random placmnt o nods, w ar proposing on nw routing protocol whr slction o intrmdiat nod is basd on a mtric combining probability o dtction o nighbors considring a maximum orwarding rang in shadowd nvironmnt [6] and maximum advancd distanc towards th inal dstination. W ar analyzing th prormancs o CDMA basd WSNs using th proposd routing protocol and compar with th routing protocol as proposd in [] considring th sam wirlss channl nvironmnt. and orward rror corrction (FEC) ar th ky rror control stratgis in wirlss snsor ntworks. ybrid () schm, incorporating both rtransmission and FEC, is anothr approach to minimiz nrgy[11,1]. Propr combination o and FEC using dirnt rtransmission stratgis nds invstigation or minimization o nrgy. For xampl, hop by hop rror dtction and corrction schm using rror control cod rsults in highr nrgy consumption at vry nod, spcially du to signiicant nrgy consumption or dcoding which rducs ntwork li tim in turn. owvr, i dcoding is considrd only at th sink which is not nrgy constraind, powr consumptions at intrmdiat nods may b rducd signiicantly. This tchniqu may b invstigatd in dsigning an icint wirlss snsor ntwork. Furthr, th dtrmination o optimal packt siz is important paramtrs or nrgy constraind and dlay snsitiv WSN. A cross layr solution or packt siz optimization is prsntd in [13], whr cross layr cts o multi hop routing, th broadcast natur o wirlss channl using carrir sns mchanism, and th cts o rror control tchniqus ar capturd. Such analysis may b xtndd in contxt o dsigning an icint CDMA basd multi hop WSN. In th prsnt papr, our contributions ar as ollows: 1. A nw orwarding protocol in a random WSN, kping a minimum distanc btwn any two nods as in [8], is proposd and simulatd on MATLAB; which capturs prslctd probability o dtction and maximum orwarding distanc towards th inal dstination and, considring path loss and log normal shadow ading.. W apply this protocol on a CDMA basd WSN or prormanc valuation. An analytical ramwork has bn dvlopd to modl th MAI and NI at ach hop to valuat link BERs ollowd by avrag rout BER btwn th sink and th sourc. 3. An appropriat modl has bn usd to valuat th nrgy consumption and dlay or succssul dlivry o a packt rom a sourc nod to sink in multi hop using ndto-nd and typ I (-I) schm using BC coding, whr dcoding is don only at sink. 4. Furthr, multi-hop prormanc is also analyzd or

3 Intrnational Journal o Snsors and Snsor Ntworks 014; (): th modl whr slction o nxt hop nighboring nod is basd on th narst nod within a sctor o angl (θ) towards th dirction o th dstination as proposd in [] considring sam wirlss channl condition having sam rrnc distanc btwn sourc and dstination as in th proposd protocol. 5. Impact o dirnt ntwork paramtrs lik nod dnsity, sarch angl, probability o dtction on nrgy consumption, dlay ar analyzd and compard using th schms. 6. Ntwork litim, which is dind as th tim to th irst nod ailur in th path [], is valuatd in ach cas and compard. 7. Packt siz optimization is ormalizd by using thr dirnt objctiv unctions, i.., packt throughput, nrgy icincy, and rsourc utilization. Th rmaindr o th papr is organizd as ollows: Th systm modl or th xisting sarch angl basd and th proposd protocol is prsntd in sction. Sction 3 prsnts our analytical approach to valuat th nd-to-nd BER, nrgy consumption, dlay, and nod/ntwork litim. Cross layr solution or packt optimization is discussd in sction 4. Rsults basd on our dvlopd ram work ar prsntd in Sction 5. Finally w conclud in Sction 6.. Ntwork Modl and Problm Dscription In this sction, w dscrib th wirlss snsor ntwork modl using two orwarding protocols and th basic assumptions considrd in th papr. A. Routing Protocol Basd on Sarch Angl W considr a routing schm ollowing [], whr ach intrmdiat nod in a multi-hop rout slcts th narst nod within a sctor o angl 'θ' towards th dirction o th dstination as th nxt hop as shown in Fig.. Lt W b a random variabl dnoting th distanc to th narst nighbor (as indicatd by r R in arlir chaptrs) in a two dimnsional Poisson nod distribution. Y -Y -Y Figur 3. Ntwork with random distribution o snsor nods. ( θ) W F ( w) = 1 = 1 = 0 w > Y ρ s θ( w r0) / 0 othrwis. Y r w Y Th numbr o hops dpnds on th nod dnsity o th ntwork, sarch angl 'θ' and distanc btwn th sourc and dstination. In our analysis w considr an avrag numbr o hops to valuat th prormanc o WSN. Th avrag numbr o hops on a rout dpnds on th valu o sarch angl (θ) and is stimatd as [Panichpapiboon, 006; Panichpapiboon, 004]: (1) Z n rand = () E[ W cosς] whr Z is th avrag lngth o th rrnc path btwn a sourc and dstination nod. r E [ W cosς] is th avrag projctd hop lngth and Z can b rprsntd by Z = Y [ + ln(1 + )] (3) 3 In our analysis, w assum that ach hop dviats with rspct to th rrnc path, by an angl ς, whr ς is uniormly distributd in th intrval btwn ( θ /, θ/ ) as shown in Fig.1. Following [], avrag projctd hop lngth E[ W cos ς] is xprssd by: Figur. Multi-hop rout btwn th sourc and th dstination in a random topology ollowing narst nighbor basd routing protocol []. For a ixd nod spatial dnsity with larg 'N', th CDF o th distanc to th narst nighbor within a sctor angl o 'θ' in a torus, as xprssd in [] is appropriatly modiid in contxt o our ntwork scnario, as shown in Fig.3 whr w incorporat a minimum distanc ( r 0 ) paramtr as: E[ Wcosς] = E[ W] E[cosς] (4) For larg ntwork ara, ollowing [14], it can b shown that in our cas, E[ W] π /(ρs θ) + r0, and E [cosς] (/ θ) sin( θ / ) Thus, w obtain th avrag numbr o hops as: n rand Y [ + ln(1 + )] = 3 (5) ( π /(ρsθ) + r0) (/ θ) sin( θ / )

4 17 Uma Datta, Sumit Kundu: Comparativ Prormanc o Forwarding Protocols Basd on Dtction Probability and Sarch Angl in a Multi-hop CDMA Wirlss Snsor Ntworks B. Forwarding Protocol Basd on Probability o Dtction: W propos an algorithm or th slction o nxt hop nighbors as intrmdiat nods or th multi-hop path btwn sourc nod and th inal dstination i.. sink nod. W considr a ntwork architctur as shown in Fig., whr nods ar randomly distributd kping minimum distanc btwn any two nods, qual to r 0. W ar ocusing on a circular rgion o radius Z, as statd by (3), to kp th rrnc distanc btwn th sourc and sink almost sam (qual to Z ) in both cass, i.. th proposd schm and narst nighbor basd schm, or prormanc comparison. Sink is considrd to b at th cntr and sourcs ar at th priphry. Othr nods ar considrd only as intrmdiat rlay nods. Channl conditions, i.. path loss and shadowing ar assumd to b ixd at a particular lvl throughout th ntwork. Th proposd algorithm o th routing protocol, considring path loss and shadowing in th wirlss channl, is simulatd on MATLAB platorm through ollowing stps: i) Locations o all nods ar assumd to b known. Nod at th cntr is considrd as sink and nods at th priphry rgion ar considrd as sourcs. Othr nods ar considrd only as intrmdiat rlay nods. Onc a sourc nod has a packt to snd, slction o intrmdiat rlay nods to snd th packt rom sourc to th dstination i.. th sink is govrnd by th ollowing stps: ii) Channl conditions, i.. path loss ( β ), and shadowing ( σ ) ar assumd to b ixd at a particular lvl. Considring a maximum orwarding distanc and standard dviation o shadowing, avrag snsing distanc, R, is valuatd using Tabl I as in [Tsai, 008]. Nxt, ollowing [Tsai, 008], probability o dtction o all othr nods in th ntwork rom th dsignatd sourc nod is stimatd as: P dt 10 R ( r ( i, n) ) Q( ) R 10 β log ( r ( i, n)/ R) = (6) σ whr r R ( i, n) is th distanc btwn th transmittr and th n-th nod or i -th hop. Initially or th sourc nod, i =1. iii) Amongst all nods, th rlaying nod, i.. th rcivr or th prsnt hop, is slctd as th on who simultanously satisis th ollowing conditions: aving probability o dtction gratr than or qual to a prslctd valu, ( P dt ) sl, i.. P dt ( rr( i, n) ) >= ( Pdt) sl at that channl condition, closst to th dstination, i.. th sink, and towards th sink. iv) Th slctd rlay nod o th prsnt hop will bcom th transmittr or th nxt hop. Th rlay nod or th nxt hop, i.. i =, is ound ollowing sam approachs o stps (ii) and (iii). This is rpatd until th packt rachs th inal dstination through multi-hop transmission. v) All hop distancs or th slctd rlay nods, i.. ( i, m), whr m is th slctd nod in i -th hop ar r R calculatd rom known locations, with i =1,, ----, or numbr o hops. Slction o intrmdiat nods basd on MATLAB simulation is shown in Fig dstination sourc Figur 4. Possibl multi-hop rout btwn sourc and dstination in a random topology ollowing th proposd protocol. C. MAC Protocol and Transmission Schm r w considr CDMA-basd MAC protocol. In this prsnt work w assum two routing protocols sparatly, whr a nod can idntiy its intndd nighbor, govrnd by th routing protocols as dscribd abov, nsurs th data low rom sourc to sink in multihop. For xampl in Fig.5, dstination nod, i.. sink, D is rciving inormation rom th sourc nods S, S1, S, S3 tc., via multi-hop communication using digital rlays, as mployd in any rgnrativ systms. Rlays rgnrat th rcivd signal and thn transmit th sam with powr control to th nxt hop. As w ar considring a CDMA snsor ntwork, any nod can transmit to its narst nxt nighbor nod at any tim, so that sourc inormation inally rachs at th dstination D. At a particular instant, considring two protocols sparatly, w assum that nods (,h,i), (d,,h,i), (j,k,l), (a,b,c) ar usd as intrmdiat nods to rout th inormation rom sourc nods S, S1, S,S3 rspctivly to th sink, i.. th dstination D. r w considr that ach transcivr is having a rciv thrshold P r. Each transmittr adjusts its transmission powr so as to achiv a givn lvl o rcivd powr ( P r ) at its intndd rcivr. Accordingly th transmit powr dpnds upon th distanc btwn th transmittr and th rcivr pair ( r R (i) ), and th statistics o shadowing. Svral concurrnt nods thos ar snding thir inormation to any intrmdiat rlay nod on th path,.g. h within th ara πr R would caus MAI at h. Th concurrnt transmittd signal powr gnratd by th sourc/rlay nods situatd within th intrrnc rang r I ( r I = rr) o h, which ar snding inormation to thir rspctiv dstination nod, might b snsd by h. This would caus NI to h. During propagation o signal rom sourc to sink via dirnt nods, th dsird signal at ach rcivr nod is accompanid with MAI and NI. W obtain th intrrnc powr distribution at ach rcivr nod ollowing assumptions and dinitions [8, 10]:

5 Intrnational Journal o Snsors and Snsor Ntworks 014; (): c ρsπ rr = (10) whr ρ S is th nod dnsity, r I is th intrrnc distanc qual to rr. Activity actors dtrmin th numbr o activ nods at any instant in th two layrs contributing MAI and NI, which ar ractions o c 1 and cas givn in (9) and (10) Estimation o Avrag Rout BER, Enrgy Consumption and Latncy Figur 5. Signal low at a particular instant in multi-hop communication 3. Analysis o Rout BER, Enrgy Consumption, Dlay, and Litim W assum an avrag numbr o hops btwn a sourc nod and th dstination nod, or sink, i.. = n rand, as dtrmind by (5). Channl conditions ar assumd to b sam or all th hops rom sourc to sink Estimation o Intrrnc Powr Following [10], th man valu o th collctd intrrnc powr η rom an intrring nod (i.. d is transmitting signal to it s intndd rcivr ) to any dsird rcivr (i.. h): η = η. σsdh m + Sdh. η can b ound out as in [8] as: whr σsd m + Sd. σrd m + Rd α+ α+ α α 4PR ( rr r0 )( ri r0 ) = γp α α R ( α 4) r r ( r r )( r r ) I I R (7) η = (8) m S d, 0 m R d ar th man and standard dviation o shadowing ( S d 0 0 σ S d, σr d ar th ) and pc ( R ) d rspctivly or an arbitrary path d. Furthr α is th path loss xponnt < α < 6 and m, σ ar th man and standard dviation o shadowing o th path d dh btwn th nods d and h. S dh S dh 3.. Numbr o Potntial Intrring Nighbors Undr th Poisson approximation, or vry larg numbr o nods ( N ) and vry small ara o intrrnc rgion compard to th total ara (A), th xpctd numbrs o nods within th rciving and intrrnc rang o th rcivr ar [8] c I R = π(r -r ) (9) 1 ρs With dirct squnc BPSK o sprading bandwidth BW, and or constant rcivd signal powr lvls with powr control rror, ollowing [10, 16], th man probability o rror at any hop can b approximatd by: P = Q = Q E b = Q χ R PR Rb = φ R BW P R PR R I BW ψ ( ) Q b (11) W stimat avrag BER or ach hop individually as ach hop, having avrag distanc o rrior i -th hop, will hav dirnt numbr o intrrrs. Nxt w stimat th avrag rout BER considring an avrag numbr o = nrand hops. Th rout BER or hops, without any rror corrction mchanism applid at th intrmdiat rlay nods, is xprssd by th rlation [14], whr ( i) ( P ) = 1 1 P (1) (i) i = 1 P is th man probability o rror at i -th hop. Furthr n bits/packt is considrd in orward transmission o inormation and nb bits/packt or NACK /ACK with an assumption o instantanous rror r rcption o NACK/ACK. Assuming prct rror dtction o a CRC cod and ininit rtransmissions, and -I mchanisms ar usd or rror corrction. In th prsnt schms, th packt is chckd only at dstination (D) or rror control; rtransmissions o th packt ar rqustd to sourc (S), with a NACK coming back rom D to S via th sam multi-hop path till th packt is rcivd corrctly. Considring th sink is not an nrgy constraind nod, two schms o rror control ar proposd: Schm I: Error control is basd on simpl, i.. th packt rom sourc consists o n bits mssag including CRC, and ovrhad ( β bits) is transmittd and is chckd at sink only or corrctnss. It snds a rtransmission rqust to th sourc or an ntirly nw rtransmission in cas o rcipt o rronous packt. Schm II: Error control is basd on hybrid typ I

6 19 Uma Datta, Sumit Kundu: Comparativ Prormanc o Forwarding Protocols Basd on Dtction Probability and Sarch Angl in a Multi-hop CDMA Wirlss Snsor Ntworks (-I), whr th packt rom sourc consisting o l BC bits including n bits mssag, and ncoding bits or on bit rror corrction capability using BC coding is transmittd. At sink, th packt is dcodd. It discards rronous packts (whn rrors rmain atr BC dcoding), snds a rtransmission rqust to th sourc or an ntirly nw rtransmission. Rtransmissions tak plac at th sam cod rat until th packt is corrctly dcodd. Schm I Avrag nd-to-nd packt rror lvl or hops is n ( P ) = 1 (1 ( P ) ) (13) whr ( P ) is givn in (1). Lt succssul dlivry o a packt rom sourc to dstination is occurrd at n th numbr o rtransmissions. Avrag numbr o rtransmissions or succssul dlivry o a packt [17]: ( 1 ( ) ( N ) = 1/ ) (14) P Th nrgy E b rquird to communicat on bit o inormation rom sourc to sink through -hop communication i.. nd-to-nd dlivry [18]: b i= 1 ti r E = ( P + P )/ R (15) whr Rb is th data rat, P ti is th man o transmittd powr or i-th hop o lngth r Ri, and is rprsntd by [10]: P ti = P R r α Ri σ S m + d S d m. b Rd R d σ + (16) W hav includd th nrgy consumption du to start-up transints o transcivrs whil calculating th nrgy consumption or data communication. It is obsrvd that start-up nrgy consumd in th transmittr / rcivr varis approximatly rom 10 micro Joul to 45 micro Joul [19], [0]. Assuming avrag start-up nrgy rom slp mod to ithr transmit/rciv mod is qual to 10 micro Joul, th nrgy consumd pr packt rom sourc to sink, i.. singl loop transmission o inormation rom sourc to sink via hops, with ACK/NACK rom sink to sourc via multi-hop is: ( E 3 pkt ) b b b. = E n + E n (17) W assum that ach nod will b wak up, ithr in transmit or rciv mod, rom slp stat and will rmain in th activ stat, without going to slp stat, until th inormation is rcivd corrctly at sink. Sinc on th avrag, ach packt rquirs ( N) numbr o rtransmissions rom sourc to dstination or succssul dlivry, avrag nrgy consumd by a packt through multi-hop communication o hops is: E 3 av b b b. = ( N).( E n + E n ) (18) Enrgy consumd only by th mssag in singl transmission, i.. th ctiv nrgy E 3 ti r b. i= 1 = (( ( P + P ) ( n β ))/ R (19) whr β is th numbr o ovrhad bits. Avrag packt dlay or succssul transmission o packt is obtaind as [1]: av D = ( N). n / R (0) Now w dscrib th schm incorporating -I using BC coding. Schm II Th packt rror rat (PER) or th schm as in [11] is: ( PER l BC I = ) BC ( + n t l = 1 i ) i= 0 BC. (( P ) i b ).(1 ( P l i ) ) (1) is th total numbr o bits to b transmittd and is th sum o lngth o ram chck squnc, and n bits as dscribd abov. Avrag numbr o rtransmissions or succssul rcption o a packt [17]: ( N) BC = 1/(1 ( PER I ) BC) () In th prsnt cas, w assum ngligibl nrgy or BC ncoding at sourc nod, and nrgy consumd at sink is ignord sinc th sink is not an nrgy constraind nod. With ths assumptions, th nrgy consumd pr packt by th sourc and rlay nods in singl loop transmission o inormation via hops including start up nrgy o ach nod, with ACK/NACK via multi-hop is: ( E 3 pkt ) BC b BC b b. = E l + E n (3) whr E b is xprssd in (15). Avrag nrgy rquird or succssul dlivry o packt E BC 3 av BC b BC b b. = ( N).( E l + E n ) (4) Avrag packt dlay or succssul transmission o packt is obtaind as [1]: 3.4. Ntwork Litim bch av D = ( N). l / R (5) BC BC r, ollowing [], w considr th tim to th irst nod ailur as th ntwork litim (i.., a worst-cas approach). W assum that vry nod has an initial init b

7 Intrnational Journal o Snsors and Snsor Ntworks 014; (): battry nrgy dnotd by E batt and packts ar transmittd with avrag rat λt without quuing. Th avrag nrgy dpltd pr scond du to transmission and rcption is simply λ E, whr E = E is t packt packt av/ th avrag nrgy consumd pr nod whil dlivring a packt succssully rom sourc to sink in ach schm. Finally, th total tim it taks to compltly xhaust th initial battry nrgy o any nod can b writtn as: τ = E λ E ) (6) batt /( t packt This simpl analysis dos not tak into account th nrgy consumd whn a nod is procssing packts. Thus, th litim o a nod will b shortr than what is prdictd by our analysis. 4. Packt Siz Optimization Following [13], optimization ramwork basd on ndto-nd prormanc mtrics using ininit btwn sourc and sink, as dscribd in schm I, is ormulatd. Optimization solution is ormulatd by using thr dirnt objctiv unctions, which highlight dirnt aspct o communication in WSN and can b slctd according to th rquirmnts. Th two objctiv unctions ar dind as [13]: 1. Packt throughput: This unction considrs th nd-tond packt succss rat and th avrag dlay or succssul rcption o a packt o payload l ( n β) through multi hop communication. d = pktput ( 1 ( P ) ) D U = ( n β ) / (7) Maximizing this unction, by stting d ( U pktput ) = 0, dl pktput rsults in optimal packt siz L opt that achiv high packt throughput or a particular orwarding protocol and pktput channl condition. Atr simpliication, L opt is xprssd by: L pktput opt = 4β β ln1 ( ( P ) ) av d β (8). Rsourc utilization: This unction considrs both nrgy consumption and dlay or succssul rcption o a packt, and is xprssd by: rs av av d ( 1 ( P ) U = E D / l ) (9) whr l ( n β) is th mssag lngth. Minimizing this d = d unction, by stting ( Urs) = 0, rsults in optimal dl d rs packt siz ( L opt ), that balancs th trado btwn nrgy consumption and latncy, spcially usul or dlay rs snsitiv WSN. Atr simpliication, L opt is obtaind as: L rs opt = 4β β + ln1 ( ( P ) ) β (30) Enrgy icincy is anothr objctiv unction, which may b considrd or optimization. Considring succssul rcption o a packt rom sourc to sink, nrgy icincy is xprssd by: av ξ = E / E (31) Maximizing this unction rsults in optimal packt siz, that achivs high nrgy icincy. owvr, considring startup nrgy, closd orm solution o optimizd packt lngth using nrgy icincy ξ is not straight orward to obtain. W valuat it with th hlp o simulation undr such startup nrgy includd cas. 5. Rsults Sam channl condition and avrag rrnc distanc btwn sourc and sink ar considrd or both schms. Paramtrs usd in prsnt analysis, basd on smi-analytic mthod, ar givn in Tabl 1. Paramtr Tabl 1. Paramtrs usd in th analysis. Valu Valu o Y 100 m Min. distanc btwn two nods ( r 0 ) 1 m Procssing Gain ( pg ) 18 Constant rciv powr ( P R ) 1.0x mw Path loss paramtr ( α ) 3 Transmission rat (R b) 0.0kbps NACK/ACK (n b) bits Standard dviation o pc (σ R) 1dB Standard dviation o Shadowing (σ s) 3 db Band width 5 Mz Ovrhad ( β ) 8 bits Start up nrgy/nod Maximum orwarding distanc 10micro Joul 30 m Man o all shadowing and pc componnts ar considrd to b zro. W assum that 50% o total nods within rciving distanc ( r Ri ) o sink ar activ or MAI whil 5% o nods btwn rciving and intrring distanc o sink ar activ or NI. For othr intrmdiat rlay nods, 5% o total nods within r Ri ar activ or MAI whil sam prcntag o nods btwn r Ri and r Ii ar activ or NI at any instant. All paramtrs at ach hop ar calculatd considring distanc btwn two conscutiv nods as rrimtr, whr rris ar calculatd

8 1 Uma Datta, Sumit Kundu: Comparativ Prormanc o Forwarding Protocols Basd on Dtction Probability and Sarch Angl in a Multi-hop CDMA Wirlss Snsor Ntworks by using (1) and (5) or sarch angl basd protocol. Th procdur adoptd or th valuation o link BER, ollowd by rout BER and avrag rout BER or th stimation o dirnt QoS paramtrs, using th two orwarding protocols, ar dscribd blow: (A): Forwarding protocol basd on sarch angl with narst nighbor: 1. Avrag numbr o hops btwn sourc and dstination nrand is calculatd by using (5) or a particular sarch angl ( θ), and rrnc distanc as xprssd by (3), considring Y=100m.. Avrag hop distancs ( r Ri ) ar stimatd using (1), by gnrating n rand numbr o random variabls. 3. Link BER at ach hop is valuatd using (11), ollowd by rout BER or that θ using (1). Enrgy consumption at ach link or transr o ixd lngth inormation or a singl ralization o sourc to dstination path is stimatd. 4. Avrag rout BER and rout nrgy consumption or snding a ixd lngth inormation rom sourc and rciving at sink through multi hop or a particular θ is obtaind by computing arithmtic avrag o larg numbr o ralizations o rout BER and rout nrgy consumption. 5. Avrag dlay or snding inormation rom sourc to sink, nod litim, and objctiv unctions, lik packt throughput, nrgy icincy, and rsourc utilization ar valuatd by using th valu o avrag rout BER and avrag rout nrgy consumption using nd to nd. 6. Paramtrs lik nod litim, dlay or succssul rcption o inormation rom sourc to sink ar also stimatd using nd to nd -I using BC coding. (B): Forwarding protocol basd on probability o dtction with maximum advancmnt: Sam channl condition and avrag rrnc distanc btwn sourc and sink as prvious protocol ar considrd. Undr th proposd protocol, all link distancs i.. rris ar stimatd atr slction o intrmdiat rlay nods by th dvlopd algorithm as dscribd in sction. Nxt th QoS paramtrs,.g. nod litim, dlay ar valuatd by similar mthod as in schm A. Fig.6 compars th variation o avrag rout BER with nod dnsitis undr two dirnt protocols. Impact o sarch angls (θ ) o narst nighbor basd protocol, and probabilitis o dtction with maximum snsing distanc o 30m on proposd protocol ar shown considring dirnt corrlation amongst intrrrs only. In cas o narst nighbor basd protocol, incras in nod dnsity or sarch angl improvs th link BER as dscribd arlir. This in turn rsults in rduction in avrag rout BER with nod dnsity or θ (curvs i and iii). In cas o channl snsitiv orwarding protocol, highr probability o dtction rducs distanc o nxt hop nighbor or a ixd channl condition, which rsults in improvd link BER ollowd by lowr rout BER (curvs v and vi). With incras in nod dnsity, kping probability o dtction ixd at a lvl, numbr o intrrrs incrass, which in turn incrass th avrag rout BER. Thus th proposd channl snsitiv orwarding protocol may outprorm th othr in som cass and choic o sarch angl plays an important rol. Incras in corrlation amongst intrrrs rsults in incras in link BER ollowd by incras in avrag rout BER undr both th protocols (curv ii, iii and curv iv, vi). Figur 6. Variation o avrag rout BER with nod dnsity and corrlation amongst intrrrs undr two dirnt orwarding protocols. Following th dinition o ntwork litim as dind arlir, avrag nrgy consumd by ach nod or succssul transmission o a packt dirctly govrns th ntwork litim. Fig.7 compars th variation o avrag nrgy consumd by ach participating rlay nod or succssul transmission o a typical packt o lngth 63 bits with nod dnsitis undr svral valus o sarch angl ( θ), probability o dtction or two dirnt orwarding protocols. In cas o narst nighbor basd orwarding protocol, with incras in nod dnsity as wll as incras in sarch angl, link distanc dcrass, thus transmit powr at ach nod dcrass which lads to th dcras in avrag nrgy consumd by ach nod or succssul transmission o a packt (curv i, ii; Fig.7) ollowd by incras in nod litim with incras in sarch angl or nod dnsity as shown in (curv iii, iv; Fig.8). In cas o channl snsitiv orwarding protocol, or a ixd channl condition o shadowing and path loss, variation o link distanc is insigniicant with incras in nod dnsity, as it is dictatd by th probability o dtction. Thus variation o avrag nrgy consumption pr nod and subsquntly variation o nod litim with nod dnsity is insigniicant (curv iii, iv o Fig.7 and curv i, ii o Fig.8). igh dtction probability ( P dt ) rducs th link distancs. At lowr valu o dtction probability ( P dt 0. 8), link distanc incrass which causs highr transmit nrgy at ach nod and signiicant incras in numbr o rtransmissions at highr nod dnsitis. Consquntly, avrag nrgy consumption pr nod incrass and avrag nod litim dcrass with incras in nod dnsity (curv iii, iv o Fig.7 and curv i, ii o Fig.8 rspctivly).

9 Intrnational Journal o Snsors and Snsor Ntworks 014; (): 14-5 Figur 7. Variation o avrag nrgy consumption/nod or succssul transmission o packt with nod dnsity undr two dirnt orwarding protocols. Figur 8. Variation o avrag nod litim with nod dnsity or two dirnt orwarding protocols undr EE transmission. Fig.9 compars th variation o nd to nd (EE) dlay/latncy with nod dnsitis undr two orwarding protocols or succssul transmission o a packt o lngth 63 bits using. Using narst nighbor basd orwarding protocol, avrag rout BER improvs with incras in nod dnsity as wll as incras in sarch angl. Thus avrag dlay o th ntwork dcrass with incras in θ or nod dnsity du to rduction in numbr o rtransmissions (curvs i, iv) undr such protocol. owvr, in cas o channl snsitiv protocol, with incras in nod dnsity at a ixd probability o dtction, as wll as dcras in probability o dtction kping nod dnsity ixd; numbr o intrrrs incrass, which incrass dlay (curvs ii, iii) du to incrasd numbr o rtransmissions. Figur 9. Variation o avrag rout dlay with nod dnsity or two dirnt orwarding protocols. Fig.10 dpicts and compars th variation o packt throughput ( U pktput ), as drivd in (8) using nd to nd, with packt lngths undr two dirnt orwarding protocols or a ixd nod dnsity 0.016/m. At low packt lngth rgion, low packt throughput is du to ovrhad, which is comparabl with th packt lngth. At high packt lngth rgion, packt throughput dcrass du to dgradation in PER. This dcras is signiicant in cas o low sarch angl, i.. 0 dgr, (curv vi) or low probability o dtction, i.. P dt 0. 6, (curv v). It is du to highr numbr o intrrrs, associatd with highr hop lngth which occurs undr th two cass as mntiond abov, i.. low θ, as wll as low P dt. With incras in sarch angl or dtction probability, rout PER or a ixd packt lngth improvs du to improvd rout BER. Subsquntly, dlay or succssul dlivry o packt dcrass and packt throughput incrass as in Fig.10. Th optimizd packt lngths ( pktput L opt ), as obsrvd rom th curvs, or dirnt sarch angls and dtction probabilitis, match approximatly with thos obtaind dirctly by using (8), as shown in tabl. Figur 10. Variation o packt throughput rom sourc to sink with packt lngths or two dirnt orwarding protocols.

10 3 Uma Datta, Sumit Kundu: Comparativ Prormanc o Forwarding Protocols Basd on Dtction Probability and Sarch Angl in a Multi-hop CDMA Wirlss Snsor Ntworks Tabl. Optimizd packt lngth using packt throughput or dirnt sarch angls, probabilitis o dtction; nod dnsity 0.016/m Routing protocol basd on sarch angl Routing protocol basd on probability o dtction Sarch angl Dtction prob. >=0.99 >=0.8 Optimizd packt lngth (bits/pkt) Optimizd packt lngth (bits/pkt) Fig.11 shows th variation o rsourc utilization ( U rs), as in (30), with packt lngth undr two dirnt orwarding protocols or a ixd nod dnsity 0.016/m, considring start up nrgy at ach nod. At low packt lngth rgion, U rsis signiicantly high du to rasonabl siz o ovrhad, which is comparabl with th mssag lngth. At high packt lngth rgion, du to incras in numbr o rtransmission, Ursincrass slowly. In cas o low sarch angl, th rat o incras is apprciably high (curv i) du to high link distanc and associatd high BER. It is obsrvd that thr xists an optimum packt lngth, dpnding on th ntwork condition, which yilds minimum rsourc utilization byond which rsourc utilization incrass du to signiicant incras in rout PER. Th optimizd packt lngths ( L rs opt ), as obsrvd rom th curvs via smi-analytic approach match with thos obtaind numrically by using (30), as shown in tabl 3. Figur 11. Variation o rsourc utilization with packt lngths or two dirnt orwarding protocols. Tabl 3. Optimizd packt lngth using rsourc utilization or dirnt sarch angls, probabilitis o dtction; nod dnsity 0.016/m Routing protocol basd on sarch angl Routing protocol basd on probability o dtction Sarch angl Dtction prob. >=0.99 >=0.8 Optimizd packt lngth (bits/pkt) Optimizd packt lngth (bits/pkt) Fig. 1 dpicts th variation o nrgy icincy, as xprssd in (31), with packt lngth or a ixd nod dnsity 0.016/m, undr svral valus o sarch angl and dtction probability using th two orwarding protocols. With high sarch angl or high P dt, insigniicant dcras in nrgy icincy with packt lngth is obsrvd (curv i and ii). It is du to th lssr nrgy consumption or communication as compard with th nrgy consumption in cas o highr hop lngth associatd with lowr P dt and lowr sarch angl (curv iii, iv). Figur 1. Variation o nrgy icincy with packt lngths or two dirnt orwarding protocols. Fig.13 compars th variation o nod litim with nod dnsitis or svral valus o sarch angls ( θ ) and dtction probability using th two orwarding protocols. Cass with and without incorporating rror control and corrction schms using BC coding (63, 57, 1) at sourc and sink ar considrd. With EE, th mssag lngth is 57 bits. Using channl snsitiv protocol, and considring P dt 0. 99, it is sn that thr is no signiicant dirnc in litim o ach sourc/ rlay nods o th snsor ntwork systm undr with rspct to th schm using BC (curv i, ii). It is du to insigniicant dirnc in numbr o rtransmissions or link distancs associatd with P dt Using narst nighbor basd orwarding protocol, at low sarch angl,.g. 40 dgr, whr link distanc is comparativly high, litim is highr using -I with BC coding as compard with only ininit rom sink to sourc (curv v, vi), in spit o transmission o xtra bits atr ncoding. This is mainly du to signiicant rduction in PER, which subsquntly rsults in signiicantly lss numbr o rtransmissions as compard with th schm without rror corrcting capability at sink. Considring narst nighbor basd protocol, with incras in nod dnsitis or (θ), avrag hop distanc dcrass. In this cas incorporation o rror corrction capability is not signiicant as compard to only (curv iii, iv).

11 Intrnational Journal o Snsors and Snsor Ntworks 014; (): Conclusions Figur 13. Variation o avrag litim with nod dnsitis or dirnt rror control schms undr two orwarding protocols. Fig.14 compars th variation o avrag rout dlay with nod dnsitis undr two dirnt orwarding protocols. Cass basd on ininit o 57 bit packt and a BC (63,57,1) codd packt basd -I ar considrd or both th orwarding protocols. In cas o channl awar protocol with P dt 0. 99, outprorms th othr schm at low nod dnsity, i.. low intrrnc rgion. owvr at high nod dnsity rgion, BC coding shows bttr prormanc. It is sn that using narst nighbor basd orwarding protocol with sarch angls 40 dgr, whr avrag hop distanc is high, BC coding outprorms schm ovr all nod dnsitis. Furthr, with incras in sarch angl ( θ) as wll as nod dnsity, avrag rout BER improvs undr narst nod basd routing. In this condition, incorporation o -I at sink may lad to incras in dlay du to transmission o xtra ovrhad (curv iii and iv). In this papr, using a smi-analytical modl, th nd-tond prormanc in trms o avrag Rout BER, avrag nod litim, dlay in succssul rcption o packtizd data rom sourc to sink via multi hop is stimatd using a nw channl awar orwarding protocol, whr slction o intrmdiat rlay nods or multi hop opration is basd on th probability o dtction combind with maximum advancd distanc with rspct to th dstination. Th prormanc is compard with th narst nighbor basd orwarding protocol, whr intrmdiat rlay nods is slctd as th narst nod within a sctor o angl ( θ ) towards th dirction o dstination. Variation o nrgy consumption/nod and nod/ntwork litim with nod dnsity is lowr in cas o channl awar protocol than narst nighbor basd protocol. Packt throughput, nrgy icincy, and rsourc utilization mtric ar also compard or th two protocols. Optimum packt lngth which yilds bst packt throughput, nrgy icincy, and rsourc utilization ar indicatd undr two protocols. Bst packt throughput is obtaind with lowr link distanc. Bst rsourc utilization within a rang o packt lngth is obsrvd with narst nighbor basd protocol with high sarch angl and channl awar basd protocol with high probability o dtction, i.. with lowr link distanc. Considring start up nrgy, high nrgy icincy is obsrvd at low packt lngth rgion, whr packt rror rat is minimum, which rsults dcras in avrag numbr o rtransmissions ollowd by lowr avrag nrgy consumption or succssul transmission o packt. Incorporation o -I btwn sourc and sink provid bttr prormanc in trms o incrasd litim and minimum dlay in succssul transmission o packtizd data. Prormanc using narst nighbor basd protocol with low sarch angl,.g. 00, dgrads signiicantly. This study will b usul in slcting icint orwarding protocol, which is an important stp in dsigning nrgy icint along with dlay critical CDMA WSN. Rrncs [1] Akkaya K., and Younis M., A Survy on Routing Protocols or Wirlss Snsor Ntworks, Journal on Ad oc Ntworks, Elsvir publication, vol.3, issu 3, May 005, pp [] Panichpapiboon, S., Frrari, G., Tonguz, O.K., Optimal Transmit Powr in Wirlss Snsor Ntwork, IEEE Transactions on Mobil Computing, Vol.5, No. 10, Octobr 006, pp Figur 14. Variation o avrag dlay or succssul transmission o a packt with nod dnsitis or dirnt rror control schms undr two orwarding protocols. [3] Zorzi and R. Rao, Gographic random orwarding (GRaF) or ad hoc and snsor ntworks: Multihop prormanc, IEEE Trans. Mobil Comput., vol., no. 4, pp , Oct. Dc. 003.

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