DTIC ADA490450: Battery Power Efficiency of PPM and OOK in Wireless Sensor Networks

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BATTERYPOWEREFFICIENCYOFPPMANDOOKINWIRELESS SENSORNETWORKS
FengzhongQu∗, LiuqingYang† and AnanthramSwami‡
∗†Dept.ofECE,Univ.ofFlorida,P.O.Box116130,Gainesville,FL32611
‡ArmyResearchLab,2800PowderMillRoad,Adelphi,MD20783
Emails:∗[email protected],†[email protected],‡[email protected]
ABSTRACT also adopt a realistic empirically derived non-linear battery model
andtakeanalogcircuitpowerconsumptionintoconsideration.How-
Sensornodesinwirelesssensornetworks(WSNs)areoftenex-
ever,differentfrom[5],wheretheSERupperboundisconsidered,
pected to operate on batteries for a long period of time. Battery
theexactBERandcutoffrateareemployedhere.
power-ef(cid:191)ciencyisacriticalfactordictatingthelifetimeofWSNs.
In the following section, we will introduce the system model.
In this paper, we compare two pulse-based modulations, namely
InSection3, wewillspecifytwosystemdesigncriteria, BERand
pulse position modulation (PPM) and on-off keying (OOK), both
cutoffrate. InSection4,wewillgiveaclosed-formexpressionfor
ofwhicharesuitableforWSNsduetotheirlowcomplexitytrans-
thebattery poweref(cid:191)ciency ratio(de(cid:191)ned later). Then, resultsfor
ceivers. Thecomparisonisbasedonageneralmodelthatintegrates
bothdesigncriteriainsparseWSNsanddenseWSNswillbegiven
typicalWSNtransmissionandreceptionmoduleswithrealisticnon-
inSection5. Finally,weprovidenumericalresultsforouranalysis
linearbatterymodels. Weanalyzeandcomparethebatterypower-
inSection6andmakeconclusionremarksinSection7.
ef(cid:191)ciencyofPPMandOOKusingcoherentdetection,andwithbit
errorrate(BER)andcutoff ratecriteria. Ourresultsreveal thatin 2. SYSTEMMODEL
sparseWSNs,PPMismorebatterypower-ef(cid:191)cient.IndenseWSNs,
In this section, we will introduce the system model including the
OOKoutperformsPPM.Inaddition,thebatterypower-ef(cid:191)ciencyof
batterymodel,thepulse-basedmodulationsandthechannelmodel.
OOKincreasesastherequiredcutoffratedecreases.
IndexTerms— Battery,poweref(cid:191)ciency,WSN,PPM,OOK 2.1. Linearvs.Non-linearBatteryModels
With the battery output voltage being a constant V, the average
1. INTRODUCTION
power consumed by a system (e.g., a transmitter or a receiver) is
Battery power-ef(cid:191)ciency is a critical factor in wireless sensor net- determinedbythecurrentianditspdf(a.k.a.dischargecurrentpro-
works (WSNs) since sensor nodes are typically powered by non- (cid:191)le)f(i)asfollows: P = ImaxVif(i)di,,whereI andI
renewablebatteries[1].Amongtheexistingapproachesatthephys- Imin min max
aretheminimumandmaximumcurrents. Inanideallinearbattery
icallayertoimproveenergyef(cid:191)ciency,amajority(seee.g.,[2,3,4]) model, thebattery doesnot(cid:0)consume additionalpower; thatis, the
assumesthatthebatteriesareidealandlinear. Thisassumptionim-
power pumped out fromthe batteryisthesame asthe powercon-
pliesthattheenergyrequiredbyallthecomponentsisequaltothe
sumedbythesystem.Hence,theaverageactualpowerconsumption
batteryenergyconsumption. Infact,however, partofthebattery’s (AAPC)ofthebatteryisP =P.
0
capacity(storedenergy)maybewastedduringitsdischargeprocess,
This,however,isnotthecaseinpractice. Theadditionalpower
especiallywhenthedischargecurrentislarge. Thebatterymodels
lossassociatedwiththebatterydischargeprocesscanbecapturedby
extracted from experiments show that the actual battery discharge
thefollowingnonlinearmodel:
is a non-linear process [6, 7]. Compared to the conventional low
Imax Vi
powerbattery-drivensystemdesigns,usingthosenon-linearbattery P = ·f(i)·di, (1)
models has the potential to markedly improve the system lifetime 0 Imin μ(i)
(cid:2)
[9]. Thoughmostoftheseapproachesdealwithhardwareandsoft-
ware optimization of a single node [6, 10], or routing of energy- whereμ(i)∈[0.5,1]isthebatteryef(cid:191)ciencyfactor[6].Noticethat
constrainednetworks[8],realisticbatterymodelswererecentlyem- withμ(i)upperboundedby1,wehaveP0 ≥P.
ployedinthedesignofphysicallayerandevaluationofperformance In[6],twoexperiment-basedformulaswereprovidedtodescribe
forWSNs.In[5],thebatteryef(cid:191)cienciesofthepulsepositionmod- the relationship between the battery ef(cid:191)ciency factor μ(i) and the
ulation(PPM)andthefrequencyshiftkeying(FSK)havebeencom- dischargecurrenti:
paredundertheaveragesymbolerrorrate(SER)criterion. μ(i)=1−ωi and μ(i)=1−νi2 , (2)
In this paper, we compare the battery power-ef(cid:191)ciency of two
pulse-basedmodulations:PPMandon-offkeying(OOK).Insteadof whereωandνarebothpositiveconstants.Theseformulasshowthat
usingthenoncoherentreceiverin[5],weconsidercoherentreception thebatteryef(cid:191)ciencyfactorμ(i)isamonotonicallydecreasingfunc-
for both PPM and OOK. In addition to the error-performance ori- tionofi.Todistinguishdifferentscenarios,wewillusesuperscripts
entedbit-error-rate(BER)criterion,wealsoadopttherate-oriented oandptodenoteOOKandPPM;andsubscriptstandrtodenote
cutoffratecriterion. Withthebatterycriterion,wewillexploitthe quantitiesassociatedwithtransmitterandreceiver.
factthatthecutoffrateismaximizedbyoptimizingthetransmission Underthesamebandwidthef(cid:191)ciency(rate-bandwidthratio)and
probabilityof‘1’inOOK. BER/cutoff rate constraints, we will compare the average battery
ToensurefaircomparisonsbetweenM-aryPPMandbinaryOOK, powerconsumptionsforPPM(P0p)andOOK(P0o)intermsoftheir
anM-dependent duty-cycle factor isalsointroduced toequate the batterypoweref(cid:191)ciencyratio(BPER)de(cid:191)nedasfollows:
bandwidthef(cid:191)cienciesofthetwomodulationformats.Asin[5],we ρ:=10log(Pp/Po) . (3)
0 0
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1. REPORT DATE 3. DATES COVERED
2007 2. REPORT TYPE 00-00-2007 to 00-00-2007
4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER
Battery Power Efficiency of PPM and OOK in Wireless Sensor Networks
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Dept. of ECE,Univ. of Florida,P.O. Box 116130,Gainesville,FL,32611 REPORT NUMBER
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14. ABSTRACT

15. SUBJECT TERMS
16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF 18. NUMBER 19a. NAME OF
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Standard Form 298 (Rev. 8-98)
Prescribed by ANSI Std Z39-18
Withthisde(cid:191)nition, PPMismorebatterypower-ef(cid:191)cientifρ < 0 Withq =0.5,andwithcoherentdetectionforbothM-aryPPM
andOOKismorebatterypower-ef(cid:191)cientotherwise.Givenbatteries andOOK,wehaveestablishedthefollowingresultswithrespectto
withidenticalcapacityC ,theBPERcanbetranslatedintothera- therelationshipamongtherequiredtransmittedenergies.
0
tioofthebatterylifetimesoftwonodesemployingPPMandOOK: Lemma1: WithcoherentdetectionandequalBER,andwhenq =
s1i0delorgP(PTMbp/anTdboO)O=K−scρh.eTmoeesnwsuitrhetahefasiarmcoembapnadriwsoidnt,hweef(cid:191)wciiellnccoy.n- 0.5forOθO:K=,wEesph(Mave,d) = Edp(M) <1, ∀M ≤4. (7)
2.2. PPMandOOKModulations Eso(d) Edo
tFhoerpMul-saeryduPrPatMio,nt.heAscycmorbdoinlgpleyr,iothdeistraTnspsm=issMionTpbawnidtwhiTdpthbBeinigs Proof: TheBERof2-PPMisgivenbyPep = Q( Edp(2)/N0).
afoprprMox-iamryatPelPyM1/iTspB=ep M:=/TRBsppb.A=saloTrgsep2sBMult,≈thelobgMa2nMdwi,dwthheefr(cid:191)ecRiebpnciys EIctrboet(ah0se.en5s,afdos)lMlo=wisn0c.t5rheEaatsose(Edsdo,)s[i=nc.cfe.2PE(Pd5pM)(,2)(i6,s)aa]n.ndoInratchacodogdroidtniinaolgnlm,y(cid:0)E,obdpE(ubpMl(a2t,i,oddn)).dA=es-
the PPM data rate (bit/sec). OOK modulation, on the other hand, aresult,wehaveEsp(M,d)=log2MEbp(M,d)<Eso(d),∀M ≤4.
hasa(cid:191)xedcardinalityof2.Itsbandwidthef(cid:191)ciencyisthengivenby (cid:2)
Beo:= RBob = Tso1B ≈ TTspo ,whereRboistheOOKdatarate(bit/sec). Interestingly,for2-PPMandOOK,theBERcriterionisequiva-
Noticethat,inordertohavethesametransmissionbandwidth,PPM lenttotheaveragemutualinformationcriterion.Weassumeequiprob-
andOOKpulseshavethesamedurationofTp. ableOOK,q=1/2,sinceitmaximizesmutualinformation.
InordertoensureBeo=Bep,OOKsignalsneedtobeduty-cycled 3.2. CriterionII:CutoffRate
withfactor The cutoff rate R is the data rate below which the average BER
φ(M):=Tp/Tso=log2M/M. (4) ofrandomlyselectedcodesapproaches0whenthecodelengthap-
proaches in(cid:191)nity(seee.g., [11,14]). Weconsider adiscrete-input
Thus,fordifferentmodulationsizeM ofPPM,oneshouldusedif-
continuous-output(softdecision)channelmodel,whichiswellknown
ferentdutycycleφ(M)ofOOK.Clearly,φ(M) ≤ 0.5,wherethe
tooutperformaharddecisionchannel.Thenormalizedcutoffrateis
equalityholdsifandonlyifM =2.
M
2T.h3e.cChahnannenlemloMdeoldweleconsiderhereisaKth-powerpath-losschan- Rp=log2 1+(M −1)exp(−Edp(M)/2N0) /log2M, (8)
(cid:2) (cid:3)
nelwithadditivewhiteGaussiannoise(AWGN).Thechannelgain forM-aryPPM[14],and
factor G(d)depends on the transceiver distance dand is given by
[15,Chapter4] G(d)=Es/Ed=MldKG1, (5) Ro=−log2 q2+(1−q)2+2q(1−q)exp −4ENdo0 . (9)
(cid:2) (cid:4) (cid:5)(cid:3)
whereEsandEdarethetransmittedandreceivedenergypersymbol, for OOK [13]. Notice that, as Edo = Ebo(q,d)/q/G(d) [c.f. (6)],
MlisthelinkmarginandG1isthegainfactoratd=1,K ≥2. qav=era1g/e2einsenrgoytgpuearrbanitteEebod(qto,dm).axInimoitzheerthweocrudtso,ffforrataenRygoifvoernac(cid:191)uxtoefdf
3. SYSTEMDESIGNCRITERIA rate Ro, there exists an optimum q ∈ (0,0.5] that minimizes the
Basedonthebatteryandchannelmodels,andtheduty-cycledmod- averageenergyperbitEbo(q,d),assuggestedin[12,13].
ulations,wewillnextintroducethecomparisoncriteria.
4. NETWORKNODEAAPC
3.1. CriterionI:BER Noticethatboth thePPMand theduty-cycled OOKmay haveac-
In this case, the battery power ef(cid:191)ciencies of PPM and OOK will
tive and idle periods during the transmitting and receiving modes.
becompared under thesameBERrequirement. Speci(cid:191)cally, fora
Onlyduringtheactiveperiods,thetransmissionpowerandthecir-
prescribed BER value, we (cid:191)rst determine the required energy per
cuit power consumption are non-zero. As a result, the discharge
symbolatthereceiverforM-aryPPM,namelyEp(M),andthere-
d currentpdfsforbothmodulationsshouldhavethefollowingform:
quiredenergycorrespondingtosymbol‘1’atthereceiverforOOK,
namelyEdo. Withthechannelmodelin(5),therequiredtransmitted f(i)=C·δ(i−I)+(1−C)·δ(i), (10)
energypersymbolforM-aryPPMandOOKisgivenby:
whereC ∈(0,1]isamodulation-dependentconstant,I isthedis-
Esp(M,d)=Edp(M)G(d) and Eso(d)=EdoG(d). charge current during the active period and δ(·) is the Dirac delta
function.Thepdff(i)canbefullydescribedbyCandI.
Accordingly,theaveragetransmittedenergyperbitforM-aryPPM ForPPM,thetransmitteris‘on’overonepulsedurationTp,out
andOOKare,respectively: ofeachsymbol durationTsp = MTp. Asaresult, theconstantC
Ebp(M,d)= Elspo(gM2M,d) and Ebo(q,d)=q·Eso(d), (6) icnyc(l1e0d)yfioerldPiPngMCistoC=tpq=logM2(−M1.)/FMor.OOK,thetransmitterisduty-
TodetermineI in(10),oneneedstotakeintoaccountthetrans-
whereqistheprobabilitythatsymbol‘1’istransmitted. Theseen- missionpower(Ps)persymbolinordertosatisfythedesiredBER
ergiescanthenbeusedtoderivethedischargecurrentpro(cid:191)les,and or cutoff rate requirement, the circuit power consumption Pct, as
accordinglythebatterypoweref(cid:191)ciency.
wellasthepowerconsumptionsatthepowerampli(cid:191)er(PA)andthe
Remarksareduehereontheselectionofq forOOK.TheBER
DC/DCconverter. Infact,thelatterpowerconsumptionsdependon
issiggniavle-nto-bnyoiPseeora=tioQ(S(NRE)do,/b2uNti0s)i,nwdehpiecnhddeenpteonfdqs.oHnowtheeverer,cetrievaetd- αPs∈an(d0P,1c)t.aSnpdetchi(cid:191)ectarallnys,fdeerneoft(cid:191)incgienthceyloofssthceoeDf(cid:191)Cc/iDenCtocofnthveerPteAr aass
ingtheOOKtransceiv(cid:0)erpairasabinarysymmetricchannel(BSC) η∈(0,1),wehavethedischargecurrentduringtheactivetransmit-
withtransitionprobabilitiesP(0|1)=P(1|0)=Peo,wenoticethat tingperiodas[2,5]:
theaveragemutualinformationismaximizedwhenq=0.5.Hence,
thisvaluewillbeusedfortheBERcriterion. I =It=(Esβ+Pct)/(Vη) (11)
III ­ 526
forbothPPMandOOK,whereβ=(1+α)B.Hence,wehavethe Proof:FromLemma1,weknowthatEsp(M,d)<Eso(d),∀M ≤
transmitterAAPCsforPPMandOOKas[c.f.(1),(10)and(11)]: 4. Asaresult,wehaveItp(M,d) < Ito(d)[c.f. (11)]andaccord-
ingly rμ(M,d) < 1,∀M ≤ 4, since μ(I) is monotonically de-
P0pt = EMsp(ηMμ(,Idtp)(βM+,dP)c)t, P0ot =qlogM2M Esoη(μd()Iβto+(d)P)ct. (12) Lcreemasminag1wtihtahtrEebspp(eMct,tdo)I≤.IEnboa(d0d.i5ti,odn),,i∀tMisin≤di4c.atSeudbisntitthuetinpgrotohfesoef
into(16),wededucethatρ<0,∀M ≤4.
theFpourlsOeOduKra,twioennToptictoetchhaetctkhewrheectehievreorronnolytaneseigdnsatlohbaes‘boene’ndturarinnsg- 2EboF(o0r.5t,hde)a,c∀ceMpta>ble4B[E1R4,rCanhgapete(er.g5.].PAed<dit1io0n−a3ll)y,,Erbpμ((MM,,dd))<is
mitted. UnliketheOOKtransmittingmode,however,theOOKre- upperboundedby2asμ(i) ∈ [0.5,1]. These,togetherwith(16),
ceiverisalwaysactiveduringtheduty-cycleddurationTp=φ(M)Tso. provethe(cid:191)rstpartofProposition1.
Asaresult, theconstant C in(10)forOOKisCro = φ(M). For Toprovethesecondpart,wenoticethat ∂rμ = ∂rμ · ∂It,since
PtiPonMo,fatshtehpeuinlsfeo,rtmheatrieocnetirvaenrshmaisttteodciosnptiunrueolyuscloyncvheeycekdtbhyetrheecepiovseid- theonlyd-dependent terminrμ isIt. With∂dtheba∂ttIetrym∂dodels in
sfoigrenA,atlwtiehnehorarevdceeerCivtoiinnlgo(cm1a0toe)dfteho,erthPpePorsMeitiisaosnnoCotfrpath=PeA1tbr.auntsamloitwtednopiuslesea.mTphlie(cid:191)reer- (θ2)<, w1,e∀hMave≤∂∂4rItμp,as=sho(1−w−ωnω(1θin−ItpθL))2emmora1∂∂,rItμ∂∂prItμp=is(a−1l−2wωνaIθytp(sI(tp1n−)e2θg))2at.ivSei.ncIne
addition,astherequireddischargecurrentincreasesasdincreases,
(LNA)withnearlyconstantpowerconsumption.Noticethatthereis
wealsohave ∂It >0. Asaresult,∂ρ/∂d<0,whichimpliesthat
notransmissionpowereither.Thus,wehave ∂d
ρisamonotonicallydecreasingfunctionofd.(cid:2)
I =Ir =Pcr/(ηV), (13) Indense WSNswithsmalld, thecircuitpower consumptionis
comparabletothetransmitpowerandcannotbeneglected. Insuch
wherePcr isthecircuitpowerconsumptionatthereceiver. There- circumstances,weestablishthefollowingresults.
fore,wehavethebatteryAAPCsatthereceiveras[c.f.(1),(10)and Proposition2: WiththeBERcriterionandindenseWSNswhered
(13)]: issmallandthecircuitpowerconsumptioncannotbeneglected,the
P0pr = ημP(cIrr) and P0or = ημP(cIrr)logM2M. (14) follo1w.iFngorreMsul=ts2ho,lOdO: Kismorebatterypower-ef(cid:191)cientthanPPM.
Finally,supposethatthenodeoperatesinahalf-duplexcommu- 2. ForlargeM,OOKismorebatterypower-ef(cid:191)cientthanPPM
nicationmodewithaportionainthetransmittingmodeand(1−a) ifPcriscomparabletoPct.
inthereceivingmode. Combining (12), (14) andthede(cid:191)nitionof
BPER(3),wehave 3. OOKbecomeslessbatterypower-ef(cid:191)cientasdincreases.
ρ=10log(cid:0)(cid:3)Ebp((EMbo(,qd,)dβ)β++loqPg2PctMct)(cid:4)μμ((1I1Itotp))++PlPoc(cid:3)grc(cid:2)2rMM(cid:5), (15) 2siPtico(cid:3)Prnr.o1Ionft:haadWtdEihtbipeo(nn2,,Midt)fo==lloEw2,bos(wf0re.o5mh,adtvh)eeanplodrPgo2crotMμfs(2o=,fdL)ePm<ctm1aa.n1dSaunlPbodsgc(cid:2)t2rPiMtMruotpino=g-
(cid:2) (cid:6) theseinto(15),we(cid:191)ndthattheBPERρ>0(OOKmoreef(cid:191)cient)
wherePc(cid:3)r = (1a−μa()IPr)cr. forAMsM=2in.creases, Pc(cid:2)rM increaseswithfactor M ,whichdom-
5. BATTERYPOWEREFFICIENCYCOMPARISON inates the argumentloogf2tMhe logarithm function ilnog(21M5) when M is
In this section, we will compare the battery power ef(cid:191)ciencies of large,especiallyifPcriscomparabletoPct.Asaresult,theBPER
PPMandOOKusingtheBERandcutoffratecriteria. ρincreasesasM increasesandOOKbecomesmorebatterypower
ef(cid:191)cient.
5.1. BPERComparisonBasedonBER
As d increases, the transmitted energy becomes dominant and
ThedensityofWSNnodesdeterminestheaverageinter-sensordis-
tance d and thus the transmit power, which isproportional todK. renders OOKless poweref(cid:191)cient. Inthe extremecase, thecircuit
powercanbeignoredandthescenariosimpli(cid:191)estoasparseone.(cid:2)
Ontheotherhand,thecircuitpowerconsumptionremainsapproxi-
matelyconstantindependentofd.
InsparseWSNswithlarged,thecircuitpower consumptionis 5.2. BPERComparisonbasedonCutoffRate
much smaller than the transmit power and can be neglected; that As mentioned in Section 3, the cutoff rate Rp for PPM is maxi-
is, Pct = 0 and Pcr = 0. The BPER expression in (15) can be mizedwithequi-probableinputs,whileRo forOOKismaximized
simpli(cid:191)edto bychoosingdifferentq∈(0,0.5)valuesatdifferentRo.Exploiting
Ep(M,d) this,wehavethefollowingresults:
ρ=10log rμ(M,d)Eob(0.5,d) , (16) Proposition3: Withthecutoffratecriterion, thefollowingresults
b
(cid:7) (cid:8) hold:
wcahnebreeroμb(taMin,edd). := μ(Ito(d))/μ(Itp(M,d)). Thefollowingresults 1. WhenR→1,theresultsinPropositions1and2stillhold.
Proposition1: WiththeBERcriterionandinsparseWSNs,where 2. AsRdecreases,OOKbecomesmorebatterypower-ef(cid:191)cient.
dislargeandthecircuitpowerconsumptioncanbeneglected,the
followingresultshold: Proof: WhenR → 1, we have q → 0.5 and the required en-
1. PPMisalwaysmorebatterypoweref(cid:191)cientthanOOK∀M. ergy per bit for the optimized q approaches the one for q = 0.5
[12].Thus,itturnsouttobethesamesituationasfortheBERcrite-
2. The battery power-ef(cid:191)ciency advantage of PPM over OOK rion.AsRdecreases,qalsodecreases[12].Thisinturnreducesthe
increasesasdincreasesforM ≤4. circuitpowerconsumptionofOOK,andmakesOOKmorebattery
power-ef(cid:191)cientthanPPM(see(15)).(cid:2)
III ­ 527
10
M=2 10 M = 2, R = 0.99
8 M=4 M = 4, R = 0.99
M=8 8 M = 16, R = 0.99
6 M=16 M = 64, R = 0.99
M=32 6 M = 2, R = 0.1
4 M=64 M = 4, R = 0.1
B) 2 B) 4 M = 16, R = 0.1
d d M = 64, R = 0.1
ER ( 0 ER ( 2
P P
B B
(cid:237)2 0
(cid:237)4
(cid:237)2
(cid:237)6
(cid:237)4
(cid:237)8
(cid:237)6
0 20 40 60 80 100 120 140 160 0 50 100 150 200 250 300 350
d (m) d (m)
Fig.1.BPERvs.distancewithK =3,basedontheBERcriterion. Fig.2. BPERvs. distance with K = 3, based on the cutoff rate
Dashedcurves:sparseWSNassumption. criterion.
morebatterypower-ef(cid:191)cientinsparseWSNsorwithhighcutoffrate
Table1.Simulationparameters
requirement;whiletheduty-cycledOOKismoreef(cid:191)cientindense
Imax=10A Pcr =52.5mW G1 =27dB WSNsorwithlowcutoffraterequirement.
V =3.7V Pct=105.8mW Ml =40dB
8. REFERENCES
ω=0.05 BER=10−3 N /2=−171dBm/Hz
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7. CONCLUSIONS
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III ­ 528