Multilevel/AES-LDPCC-CPFSK with Channel Equalization over WSSUS Multipath Environment.

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ContentslistsavailableatScienceDirect

International

Journal

of

Electronics

and

Communications

(AEÜ)

j o ur na l ho m e p a g e :w w w . e l s e v i e r . d e / a e u e

Multilevel/AES-LDPCC-CPFSK

with

channel

equalization

over

WSSUS

multipath

environment

Hakan

Cam

a

_,

_Osman

_N.

_Ucan

b

_,

_Volkan

_Ozduran

c,∗ a_Turkish_Air_Force_Academy,₃₄₁₄₉_Yesilyurt,_Istanbul,_Turkey

b_Istanbul_Aydin_University,_Faculty_of_Engineering_and_{Architecture,}_Department_of_Electrical_and_Electronics_Engineering,_Florya,_{Kucukcekmece,}_Istanbul,_Turkey c_Istanbul_University,_Faculty_of_Engineering,_Department_of_Electrical_and_Electronics_Engineering,₃₄₃₂₀_Avcilar,_Istanbul,_Turkey

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received13December2010 Accepted24March2011 Keywords:

AdvancedEncryptionStandard Lowdensityparitycheckcodes ContinuousPhaseFrequencyShiftKeying WSSUS

Channelequalization

a

b

s

t

r

a

c

t

Inthispaper,inordertoensuresecureandrobustcommunication,anewtypeofdataencryptionand errorcorrectionmechanismcalledMultilevel/AdvancedEncryptionStandard-LowDensityParityCheck Coded-ContinuousPhaseFrequencyShiftKeying(Multilevel/AES-LDPCC-CPFSK)iscarriedout.Here,we havechosenAESfordataencryption,LDPCcodesforerrorcorrectionandCPFSKformodulation.We haveevaluatederrorperformanceofthisschemeoverWide-SenseStationaryUncorrelatedScattering (WSSUS)multipathchannelswithchannelequalization.Wehavesimulated5-levelAES,2-levelLDPCfor 4CPFSKand16CPFSKoverWSSUSchannelsmodeledbyCooperationintheﬁeldofScience&Technology, Project#207(COST207).Wehaveconcludedthatourproposedstructurehaspromisingresultscompared toTurboCodesforallSNRvaluesinWSSUSchannels.

1. Introduction

Encryptionanderrorcorrectionmechanismsarerequiredfor secureandrobustcommunication.AESalgorithmisasymmetric blockcipherprovidingsecuresensitiveinformation.128,192or 256bitsofdatablockscanbeprocessedbyAESusingkeylengths of128,196and256bits.Itisbasedonroundfunctionswhichare ByteSubstitution,RowShifting,ColumnMixingandKeyAddition [1–3].LDPCcodesarewellknownerrorcorrectioncodes,providing lowencoderanddecodercomplexity[4].Manyauthorshave inves-tigatedLDPCcodes;ZyablovandPinkster[5],Margulis[6],Tanner [7],MacKayandNeal[8],Wiberg[9].Thesestudieshavedeﬁned thebasicprinciplesofLDPCcodes.Therealsocanbefoundmany studiesinliteraturewhichhaveexpandedtherangeofLDPCcode usagebyHaleyetal.[10],Cuietal.[11],Lubyetal.[12],Johnson [13],BingandJun[14],Abematsuetal.[15],NikandFekri[16].

Bandwidthefﬁciencyisoneofthemainperformancecriteria inmultipathchannels.CPFSK,aspecialkindofContinuousPhase Modulation(CPM)[17],providesagoodbandwidthefﬁciencyand biterrorperformance withits additionalmemoryunit. Various studieshavebeeninvestigatedaboutthedifferentaspectsofCPFSK bythefollowingauthors;Osman[18],Sakamotoetal.[19],Altay [20],ChengandLu[21].ContinuousPhaseEncoder(CPE)and Mem-oryless Mapper (MM) are two components of CPFSK. CPEis a

∗ Correspondingauthor.Tel.:+905358415755. E-mailaddress:volkan@istanbul.edu.tr(V.Ozduran).

convolutionalencoder.Itproducescodewordsequencesthatare mappedontowaveformsbyMM,whichcreatescontinuousphase signals.CPEprovidesnotonlypowerefﬁciencybutalsophase con-tinuity.

WSSUSisabasicmultipathchannelmodeltodescribethefading dispersivechannels.Ithastwomainparametersforcharacterizing offadingandmultipatheffects,whicharepropagationdelayand Dopplershift[8].WSSUSchannelscanbemodeledasin Coopera-tionintheﬁeldofScience&Technology,Project#207(COST207) withstandardproﬁlessuchasTypicalUrban(TU),BadUrban(BU) andHillyTerrain(HT).SinceCOST207isaseverefadingchannel, variouschannelequalizerssuchasLeastMeanSquares(LMS)and RecursiveLeastSquares(RLS)areemployed.

Inthispaper,anewjointscheme,“Multilevel/Advanced Encryp-tionStandard-LowDensityParityCheckCoded-ContinuousPhase FrequencyShiftKeying(ML/AES-LDPCC-CPFSK)”issimulatedover WSSUS multipath environment with channel equalization. The basic idea of using multilevel encryption and encoding is to partition information bits into several levels and encrypt and encode each level separately by AEScipher and LDPCencoder. Inthisapproach,“ML/AEScipher”encryptsinformationbits,then “ML/LDPCencoder”[22]encodestheseparallelbits,afterthat,the codedbitsareturnedintoserialtoparallelaccordingtothetype of modulation. CPEencodes thelast level of thesebits to pro-videphasecontinuity,then,MMmapsthecodedbitsintoM-ary CPFSKsignalsandthesesignalsaresenttochannel.CPFSK demod-ulator demodulatesthenoisysignalsatthereceiver side.Then, “Signalconstellationandprobabilitycalculationblock”processes 1434-8411/$–seefrontmatter © 2011 Elsevier GmbH. All rights reserved.

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thesesignals,and oneandzeroprobabilitiesofreceivedsignals areevaluated.Ineverylevel“LDPCdecoder” decodesthese sig-nalsandinputbitsareestimatedfromthesebits.Finally,“ML/AES decryptionblock”decryptsthesebitstreams.

Organizationofthispaperis asfollows:In Section2,abrief overviewofAESalgorithmisgiven.ThenLDPCcodesandCPFSK modulationaredescribedinSections3and4,respectively. ML/AES-LDPCC-CPFSKsystemsareinvestigatedinSection5.Finally,error performanceoftheproposedschemeisdiscussedinSection6. 2. AdvancedEncryptionStandard

AES is known worldwide as Rijndael symmetric-key block cipherwhichdesignedbyJoanDaemenandVincentRijmen.The blocksizeofAESis128bits,andthekeylengthscanbe128,192or 256bits[3].Thekeysizedeterminesthenumberofroundstobe performed.Forinstance,forthekeysizeof128,192and256bits, thenumberofroundsare10,12and14,respectively.

Inourproposedscheme,weusetheversionofRijndaelthathas a128-bitkey,operateson128-bitplaintextsandhas10rounds. Multipleof128bits(5×128bits)arefedintoAESEncryptionblock. TheinputlevelofML/LDPCblockdeterminestheinputlevelofAES. Itisbothpossibletooperateonlongsizedatablocksandprovide bandwidth-efﬁcienttransmissionatthesametimewithmultilevel inputs.

3. LowDensityParityCheckCodes

LDPCcodesarethemembersofbinarylinearblockcodesfamily. Thesecodescanbedescribedasverysparseparitycheckmatrix H,whichcontainsmanyzerosandonlyfewones.Itispossibleto representaLDPCcodeasagraph,namelybipartitegraph,whose node-setcanbepartitionedintotwonon-emptysetsVandCand everyedgeconnectsanodeinVwithanodeinC.Thevariableand checknodescorrespondtothecolumnsandrowsofparitycheck matrixHandrepresentabitsymbolinthecodewordsandaparity equationofcode,respectively.Anedgebetweeneachvariablenode andchecknodecanberepresentedbya“1”incorrespondingrow andcolumnintheparity-checkmatrix.Inthispaperonlyregular LDPCcodesareinvestigated.InregularLDPCcodes,everycolumnof Hcontainsjamountof“1”andeveryrowofHisﬁlledwithkamount of“1”,whichjandkdenotevariablenodedegreeandchecknode degree,respectively.TherearetwokindsofLDPCcodes:regularand irregular[23].HereregularLDPCcodesareinvestigated.Inregular LDPCcodesallrowsandcolumnsoftheparitycheckmatrixHhas thesamedegreewhichcorrespondstothenumberof“1”bitsin theserowsandcolumns.Allvariablenodeshavedegreejandall checknodeshavedegreekinabipartitegraphofregularLDPCcode. Thebipartitegraphofaregular(3,4)LDPCcodeisdepictedinFig.1 andthecorrespondingparitycheckmatrixofthiscodeisdescribed asanexample. H=

⎡

⎢

⎣

0 0 1 0 0 1 1 1 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 0 0 1 0 0 0 1 1 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 1 1 0 0 0 0 0 1 1 0 0

⎤

⎥

⎦

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LDPCcodes canberepresented withtwo parameters:(n,k), wherencorrespondstoinformationbitsandkcorrespondsto

code-Variable Node

Check Node

Fig.1.Bipartitegraphrepresentationofregular(3,4)LDPCcode.

words.ALDPCcodewithaparitycheckmatrixH,whichhasn−k rowsandkcolumns,encodeskinformationbitsintoncodewords. CodewordsofthisLDPCcodesatisfythefollowingrelation:

HxT=0 (2)

whereH,xandTreferstoparitycheckmatrix,codewordand trans-poseoperation,respectively.TheparitycheckmatrixHofanLDPC codecanbedeﬁnedas:

H=[Hp|Hu] (3)

whereHpisparitybitssubmatrixandHuisinformationbits

sub-matrix.Likewisecodewordscanbedeﬁnedas:

X=[Xp|Xu] (4)

wherexpisasetofparitybitsandxuisasetofinformationbits.

Thefollowingrelationcanbedeﬁned:

b=HuXuT (5)

Withthisequality,encodingofabinarysystematic(n,k)LDPCcode becomesequivalenttosolvingthefollowingequation:

b=HpXpT (6)

Fromthisequationthefollowingrelationcanbedeﬁned:

XpT=H−1p b (7)

3.2. DecodingofLDPCcodes

LDPC codes can be decoded by Message Passing Algorithm (MPA),which iterativelyupdates the probabilitiesof bitnodes.

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Someauthorshavecalleddifferentnamesforthisalgorithmlike Sum Product Algorithm (SPA) or Belief Propagation Algorithm (BPA)atthesametime.Atthispoint,sometermsandformulations whichweusedinMPAaredeﬁnedasfollows:

yi:setofreceivedsignal

ci:setofbitnode

b:0,1

qij(b):theprobabilityofmessagetobepassedfrombitnodecito

thechecknodefj

rji(b):theprobabilityofmessagetobepassedfromchecknodefj

tothebitnodeci

Rj=setofcolumnlocationsofthe1sinthejthrow

Rj/i: setofcolumnlocationsof1sinthejthrow,excludingthe

variablenodei

Cj=setofrowlocationsofthe1sintheithcolumn

Ci/j:setofrowlocationsof1sintheithcolumn,excludingthecheck

nodej

Kij:constantvalues

Qi(b):posteriorprobabilityofthecodebitci

pi=prob(ci=1|yi)

DecodingprocessofLDPCCodescanbeexplainedstepbystep inthefollowingsection.

Step1:Initialization

Allbitnodessendtheirqij(0)andqij(1)messages.Sincenoother

informationisavailableatthisstep,theprobabilitiesofmessages (qij(0)andqij(1))canbecomputedusingEqs.(8)and(9).

q_ij(0)₌1₋p_i₌prob(c_i₌0_|y_i)₌ 1 1+e−2yi/2 (8) qij(1)=pi=prob(ci=1|yi)= 1 1₊e2yi/2 (9) Step2:Paritynodeupdates(ﬁrsthalfrounditeration)

Thechecknodescalculatetheirrji(0)andrji(1)response

mes-sagesaccordingtoEqs.(10)and(11). rji(0)= 1 2+ 1 2

i_∈Rj/i (1−2qij(1)) (10) rji(1)=1−rji(0) (11)

Step3:Bitnodeupdates(secondhalfrounditeration)

The bitnodes update theirresponse messages to thecheck nodes.So,theprobabilitiesofmessages(qij(0)andqij(1))canbe

updatedusingEqs.(12)and(13). qij(0)=Kij(1−pi)

j∈Ci/j rji(0) (12) qij(1)=Kijpi

j_∈Ci/j rji(1)) (13)

whereconstantskijareselectedtoensureqij(0)+qij(1)=1

Step4:Softdecision

AllthebitnodescalculatetheQi(0)andQi(1)posterior

proba-bilitiesofthecodebitciusingEqs.(14)and(15).

Qi(0)=Ki(1−pi)

j∈Ci rij(0) (14) Qi(1)=Kipi

j∈Ci rij(1) (15)

whereconstantskiareselectedtoensureQi(0)+Qi(1)=1

Step5:Harddecision

Finally,allthebitnodesupdatetheircurrentestimationci of

theirvariableci bycalculatingtheprobabilitiesfor0 and1

andvotingforthebiggeroneasinEq.(16). ˆci=

1 Qi(1)> 1 2 0 other (16)

Step6:If ˆcHT₌₀_or_the_number_of_iterations_reaches_the_maximum

limit,thenthealgorithmterminates,otherwiseitreturnstostep2. 4. ContinuousPhaseFrequencyShiftKeying

CPFSKisaspecialkindofCPM[23],whichhasanM-dimensional form.Atthispointsometermsandformulationswhichareusedin CPFSKaredeﬁnedasfollows:

(t,Y):tilted-phaserepresentationofCPM

Y:inputsequenceofM-arysymbols,Yi∈{0,1,2,...,M−1}.

h: modulationindex h=J/P,where Jand Parerelativelyprime integers

T:channelsymbolperiod q(t):phaseresponsefunction L:integer

g(t):frequencypulse s(t):transmittedsignal

f1:asymmetriccarrierfrequencywheref1=fc−h(M−1)/2T

fc:carrierfrequency

Es:energyperchannelsymbol

0:initialcarrierphase

Tilted-phaserepresentationofCPMwasderivedbyRimoldiin [17],withtheinformation-bearingphasegivenby

(t,Y )=4h

∞

i=0

Yiq(t−iT ) (17)

Here,Jisgenerallychosenas1andPiscalculatedas2tothepower ofthenumberofmemoriesinCPE.Modulationindexcanbe com-putedfromtheequationofh=1/P.Thephaseresponsefunction q(t)isacontinuousandmonotonicallyincreasingfunctionsubject tothefollowinginequalities:

q(t)=

0 t_≤0

1/2 t≥LT (18)

Thephaseresponseiscanbedescribedasin

q(t)=

t

−∞

g()d (19)

Transmittedsignals(t)canbecomputedfromthefollowing equa-tion:

s(t,Y )=

2Es

T cos(2f1t+(t,Y )+0) (20) wheref1Tisassumedasanintegerforsimpliﬁcationwhenusing

theequivalentrepresentationoftheCPMwaveform. 5. Wide-SenseStationaryUncorrelatedScattering enviromentandequalization

Indigitalcommunicationsystemsmultipathfadingisthemost importantfactorforsystemperformance.Duetovariousobjects surrounding,scattering,diffractionandreﬂectioncausethe multi-pathfadingwhichhasfrequencyandtimedispersivenature.Since

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Fig.2.GeneralMultilevel/AES-LDPCC-CPFSKscheme.

changingcharacteristicsofchannelduetothemovementofthe mobilestationitcanbeassumedasatime-variantandmultipath fadingchannel and this channel canbe described as statistical WSSUS channel. Thischannel model canbe characterizedby a twodimensionalscatteringfunctionwhichhastwoparameters; Dopplerfrequencyduetothemobilemovementandechodelay duetomultipatheffects.Fadingstatisticsofthischannelmodelare assumedtobeconstantforashorttimeinterval.Sincesevere trans-missionconditionsofWSSUSchannelsandtheaddednoise,signals arecorruptedandneedtoberegeneratedbyusingchannel equaliz-ers.Undersevereconditionsreceiversrequirethecharacteristicsof atransmissionchannelforchannelidentiﬁcation.Butthese charac-teristicsarenotalwaysavailableandchannel’sequivalentimpulse responsehastobeestimated.Itisimpossibletoestimate infor-mationbitswithoutchannelequalization.Thuschannelequalizer blockisnecessaryforallschemesinWSSUSchannelsfor perfor-manceimprovement.

6. Proposedscheme

InFig.2,blockdiagramofdesignedjointML/AES-LDPCC-CPFSK modelisdepicted.Ascanbeseenfromthis ﬁgure,thereexists a “ML/AESEncryption block”for theencryption of messagebit sequences.Multilevelinputstothisblockaremultipleof128bits (M×128bits)andaredependentontheinputlevelof“ML/LDPC block”[22].Aftertheencryptionblock,thereisaLDPCencoderat everylevelofthesystemmodelandaCPEwhichisserially con-nectedtotheLDPCencoderatthelastlevel.Encodedmessagebit sequenceisconvertedfromserialtolog2Mparallelbranchinthe

multilevelschemeaccordingtothetypeofM-aryCPFSK modula-tion.Then,eachLDPCencoderprocessestheinformationsequence simultaneously.Thelevelof“ML/LDPCblock”determinesthelevel of“ML/AESEncryptionblock”(i.e.2,3and4levelsofLDPC,the lev-elsofAESare5,7and10,respectively).TheoutputofthelastLDPC encoderisrunthroughtheCPE.CPEisusedtoshapethemodulated signal’sspectrumforphasecontinuity.Finally,allencoderoutputs andCPEoutputaremappedtoCPFSKsignalsbyamemoryless map-peraccordingtopartitioningrule.Inthepartitioningrule,signal setisdividedintotwosubsetsbytheMSBofSerialtoParallel(S/P) converteroutput.Iftheﬁrstoutputz11is0,thentheﬁrstsubset

ischosen,ifz11is1,thenthesecondsubsetischosen.Thesecond

outputz12bitdividesthesubsetsintotwogroupsasthesimilar

way.Thispartitioningprocesscontinuesuntilthelastpartitioning level.Thesesignalsarerunthroughthechannel.Noiseisadded accordingtothechannelmodel.ChannelEqualizerblockprocesses thesecorruptedandnoiseaddedsignalsequence.Atthereceiver sideofthecommunicationchannel,“CPFSKdemodulator” demod-ulatesthecorruptednoisysignals.Then“Signalconstellationand probabilitycalculationblock”processesthesesignalstoevaluate oneand zero probabilitiesof receivedsignals.After that“LDPC decoder”decodesthesesignalsandinputbitsareestimatedfrom decodedbitsineverypartitioninglevel.Finally,thesebitstreams aregonethroughthe“ML/AESdecryptionprocess”andestimated bitsequencescanbedecrypted.Forabetterbiterrorperformance, someofthemessagebitsequenceswhichwillbeknownbyreceiver blockasinpilotsymbolcommunication[24],canbeusedinthelast levelofAEStoestimatechannelparameters.

In Fig. 3, the partitioning mechanism for 4CPFSK system is depictedinorder toexplainthepartitioning of ML/AES-LDPCC-CPFSK. In theﬁrst partitioninglevel z1 deﬁneswhich subset is

chosen.Ifz1=0,thenﬁrstsubset{s0,s1,s4,s5}ischosen,ifz1=1,

thenthesecondsubset{s2,s3,s6,s7}ischosen.Atthesecond

par-titioninglevel,ifweassumethattheﬁrstsubsetischoseninﬁrst partitioninglevel,z2z3bitsspecifywhichsignalwillbetransmitted

tothechannel.Similarly,intheﬁrstpartitioninglevel,ifthesecond subsetischosen,z2z3bitsspecifywhichsignalwillbetransmitted

tothechannel.Table1summarizesthisprocess.

ItcanbeseenfromFig.3thatinitialandendingphaseof trans-mittedsignalwilltake(0,)valuesifmodulationindexhofan LDPCC-4CPFSKsystemischosenas1/2.Input–outputdataand sig-nalconstellationsforthissystemaresummarizedinTable1.Here,

Table1

Input–outputandsignalconstellationfor4CPFSK.

z1issystematicbit,z2andz3arethebitsencodedbyCPE.Here,z2

helpstoshowusatwhichphasethesignalwillstartatthenext

codinginterval.Iftheinitialphase(n)is“0”and“z2”is0,the

end-ingphaseoftheinstantsignalandthestartingangleofthenext

signalphase(n+1)is“0”,ifn=0andz2=1,n+1=,ifn=1and

z2=0,n+1=,ifn=1andz2=1,n+1is0.Iftheinitialphaseis“0”,

thenthesignalispositive,iftheinitialphaseis“1”,thenthesignal

isnegative.Onlyiftheseconditionsaremetiscontinuitygranted.

AccordingtoFig.3andTable1,thetransmittedsignalsatthephase

transitionsareasfollows:from0phaseto0phase,s0,s2;from0

phasetophase,s1,s3;fromphaseto0phase,s5,s7andfrom

phasetophase,s4,s6.

Messagepassingalgorithmisusedfordecodingatthereceiver sideofLDPCcodes.Oneandzeroprobabilitiesofreceivedsignal areusedinthisalgorithm.Foreverydecodinginterval,these prob-abilitiesareﬁrstlyevaluatedforallparallelinputbranchsequences

accordingtopartitioningrule.Atthispoint,sometermsand formu-lationsaredeﬁnedasfollows:

rk:receivedsignal

L:partitioninglevel

si:transmittedM-aryCPFSKsignal

Pj_i:probabilitywhereidenotes0or1

Oneandzeroprobabilitiesofreceivedsignalarecomputedfrom thefollowingequations:

PL 0= 1 M

_M−1

i=0 1 (rk−s2i)2

(21) PL 1= 1 M

_M−1

i=0 1 (rk−s2i+1)2

(22)

ThenreceivedsignalismappedtoonedimensionalBPSKsignalas canbedescribedinbelow.

L=1− 2·P L 0 PL 0+PL1 (23) InFig.3,itcanbeshownthatineverypartitioninglevel proba-bilitycomputationsandmappingareexecutedaccordingtosignal set.TheseprobabilitiesarecalculatedasinEqs.(24)–(27)for par-titioninglevel1and2.

P₀1=1₄

₃

i=0 1 (rk−s2i)2

(24) P1 1= 1 4

₃

i=0 1 (rk−s2i+1)2

(25) P2 0= 1 4

₁

i=0 1 (rk−si)2 + 1 (rk−si+4)2

(26) P₁2=1₄

₁

i=0 1 (rk−si+2)2 + 1 (rk−si+6)2

(27)

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Fig.5.FivelevelAEStwolevelLDPCC-16CPFSKscheme.

Theseoneandzeroprobabilitiesofreceivedsignalareevaluated andthen ˆciisestimatedfromEqs.(9)–(13)foreverypartitioning

level.

Partitioningmechanismfor16CPFSKsystemhasthesame prop-ertyasin4CPFSK.

6.1. Five-levelAEStwo-levelLDPCcoded4CPFSK

In Fig. 4, ﬁve-level AES two-level LDPC coded 4CPFSK sys-temmodelisdepicted.Firstofall“5-levelAESEncryptionblock” encrypts5parallelmessagebitsequenceswhicharemultipleof 5×128bitsandthus5×128bitslonginputdatacanbeprocessed simultaneously.Five-levelinputs aredependentonthenumber oftwo-levelLDPC.Aftertheencryptionprocess,two-levelLDPC encoderencodestheseencryptedparallelbitsequences.Atthis stage, LSB bits are encoded by CPEfor phase continuity. Then memorylessmapper mapsthesecodedbitsinto4CPFSKsignals. ThesesignalsaresenttotheWSSUSmultipathchannel.Noiseis addedaccordingtothechannel model.ChannelEqualizerblock processesthesecorruptedandnoiseaddedsignalsequence.Atthe receiversideofthecommunicationchannel,“CPFSKdemodulator” demodulatesthenoisycorruptedsignals.“Signalconstellationand probabilitycalculationblock”is thenprocessedthesesignals in everyleveltoevaluateoneandzeroprobabilitiesofreceived sig-nals.Afterthat“LDPCdecoder”decodesthesesignalsandsoinput bitsequencesareestimatedfromdecodedbitsinevery partition-inglevel.Intheﬁnalstep,“5-levelAESdecryptionprocess”decrypts theseestimatedbitsequences.

6.2. Five-levelAEStwo-levelLDPCcoded16CPFSK

InFig.5,ﬁve-levelAEStwo-levelLDPCcoded16CPFSKsystem modelisdepicted.Inthisscheme“AESEncryptionblock”and“LDPC Encoderblock”worklikein“Five-levelAEStwo-levelLDPCcoded 4CPFSK”asdescribedinSection6.1.Thenencodedbitsareturned intoserialtoparallelwithtwobranchesforeachoutputof“LDPC Encoderblock”.Here,LSBbitsareencodedbyCPEagainforphase continuity.Thenmemorylessmappermapsthesecodedbitsinto 16CPFSKsignals.ThesesignalsaresenttotheWSSUSmultipath channel.Noiseisaddedaccordingtothechannelmodel.Channel Equalizerblock processesthesecorruptedand noiseadded sig-nalsequence.Atthereceiversideofthecommunicationchannel,

“CPFSKdemodulatorblock”,“Signalconstellationandprobability calculationblock”,“LDPCdecoderblock”and“5-levelAES decryp-tion block” work like in “Five-level AES two-level LDPC coded 4CPFSK”.Finally,estimatedbitsequencescanbedecrypted. 7. Performanceanalysisanddiscussion

Here, we investigate multilevel AES encryption, multilevel LDPCcoded CPFSK structures and join theseschemes as “Mul-tilevel/AdvancedEncryptionStandard-LowDensityParityCheck Coded-ContinuousPhaseFrequencyShiftKeying (ML/AES-LDPCC-CPFSK)”. Thus a real communication environment is achieved employingbothdataencryptionandchannelencoding.Westudy ontwodifferentmodulationtechniques;“FivelevelAEStwolevel LDPCC-4CPFSK”and“FivelevelAEStwolevelLDPCC-16CPFSK”over WSSUSchannelswithRLS,LMSequalization.Weuseregular(3,4) LDPCcodeswithablocklengthof302bits,andmaximum100 iter-ations.TheBitErrorRatio(BER)versusSignaltoNoiseRatio(SNR) curvesoftheproposedsystemsareobtainedforBU,TUandHT typesofCOST207(Figs.6–8).Inoursimulationweuseseventeen

-5 -4 -3 -2 -1 0 1 2 10-4 10-3 10-2 10-1 100 Eb/No (dB) BER

Five-level AES two-level LDPC coded 4CPFSK&16CPFSK over BU type of COST207

4CPFSK RLS 4CPFSK LMS 16CPFSK RLS 16CPFSK LMS

Fig.6. Performanceof ﬁve-levelAES two-levelLDPCcoded 4CPFSK&16CPFSK schemeoverBUtypeofCOST207channel.

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-5 -4 -3 -2 -1 0 1 2 10-4 10-3 10-2 10-1 100 Eb/No (dB) BER

Five-level AES two-level LDPC coded 4CPFSK&16CPFSK over TU type of COST207

Fig.7. Performanceof ﬁve-levelAES two-levelLDPCcoded 4CPFSK&16CPFSK schemeoverTUtypeofCOST207channel.

channelcoefﬁcientsforBU,TUandHTascanbeseenfromTable2. Weassumethevelocityofthemobileradiocommunication ter-minalas100km/h.ThecarrierfrequencyofCOST207channelis takenas950MHz.ThemaximumDopplerShiftistakenas88Hzand minimumDopplerperiodischosenas11.4ms.Finally,thesymbol periodisassumedas3.7␮s.

Althoughidealdataencryptionisassumedinmostoftherelated comparedmodels[18,20,23,24]weincludedataencryptionblock. WehavesimulatedourschemesforvariousSNRvaluesoverWSSUS channelmodels.AsitcanbeseenfromTables3and4,FivelevelAES twolevelLDPCC-4CPFSK&16CPFSKsystemsshowhigherBER per-formanceinallSNRvaluesover2Level-TurboCodes4PhaseShift Keying(2L-TC4PSK)[24]forTU,BU,HTtypeofCOST207withRLS, LMS.Thus,bothhighercodinggainandreductioninthenumberof CPFSKlevelsareachieved.

-4 -2 0 2 4 6 8 10-4 10-3 10-2 10-1 100 Eb/No (dB) BER

Five-level AES two-level LDPC coded 4CPFSK&16CPFSK over HT type of COST207

Fig.8. Performance ofﬁve-levelAES two-levelLDPC coded 4CPFSK&16CPFSK schemeoverHTtypeofCOST207channel.

Table2

ChannelcoefﬁcientsofBU,TUandHTtypesofCOST207.

BU TU HT

−0.0484−0.2943i −0.1651+0.5534i −1.0607+0.2118i −0.0000−0.4282i −0.0506+0.7480i −1.3775−0.0015i 0.0447−0.5339i 0.0849+0.9113i −1.5213−0.1868i 0.0815−0.6063i 0.2169+1.0292i −1.4957−0.3254i 0.1064−0.6414i 0.3215+1.0907i −1.3252−0.4056i 0.1162−0.6368i 0.3778+1.0881i −1.0507−0.4232i 0.1090− 0.5919i 0.3702+1.0178i −0.7242− 0.3814i 0.0839−0.5077i 0.2910+0.8806i 0.4014−0.2902i 0.0418−0.3872i 0.1403+0.6815i −0.1342−0.1641i −0.0152−0.2351i −0.0733+0.4294i 0.0356−0.0203i −0.0835−0.0577i −0.3338+0.1373i 0.0820+0.1237i −0.1582+0.1375i −0.6196−0.1790i −0.0021+0.2523i −0.2335+0.3418i −0.9057−0.5011i −0.2047+0.3541i −0.3030+0.5460i −1.1663−0.8090i −0.4962+0.4224i −0.3599+0.7407i −1.3771−1.0820i −0.8341+0.4562i −0.3978+0.9165i −1.5177−1.3001i −1.1686+0.4600i −0.4108+1.0649i −1.5736−1.4452i −1.4497+0.4420i

Table3

ComparisonofBER-SNR(indB)valuesof2L-TC4PSK[24]andﬁvelevelAEStwolevelLDPCC-4CPFSKa_for_TU,_BU,_HT_type_of_COST207_with_RLS,_LMS.

TU BU HT

RLS LMS RLS LMS RLS LMS

BER [24] a _Gain _[24] a _Gain _[24] a _Gain _[24] a _Gain _[24] a _Gain _[24] a _Gain

1.00E−01 2 −2 4 0 −2 2 3 −2 5 4 −2 6 5 −2 7 7 −2 9 1.00E−02 3 0 3 4 0 4 5 0 5 6 0 6 7 1.8 5.2 9 1.8 7.2 1.00E−03 4 1.2 2.8 5 1.2 3.8 6 1.2 4.8 7 1.2 5.8 9 4.4 4.6 10 3.4 6.6 1.00E−04 5 2 3 6 1.6 4.4 7 1.6 5.4 8 1.6 6.4 10 8 2 11 4 7 1.00E−05 7 8 1.9 6.1 8 9 1.8 7.2 12 12 4.4 7.6 [24]:2L-TC4PSK.

a_Five_level_AES_two_level_{LDPCC-4CPFSK.}

Table4

ComparisonofBER-SNR(indB)valuesof2L-TC4PSK[24]andﬁvelevelAEStwolevelLDPCC-16CPFSKa_for_TU,_BU,_HT_type_of_COST207_with_RLS,_LMS.

TU BU HT

RLS LMS RLS LMS RLS LMS

BER [24] a _Gain _[24] a _Gain _[24] a _Gain _[24] a _Gain _[24] a _Gain _[24] a _Gain

1.00E−01 2 −5 7 0 −5 5 3 −5 8 4 −5 9 5 −5 10 7 −5 12 1.00E−02 3 −3 6 4 −2 6 5 −3 8 6 −3 9 7 −3 10 9 −2 11 1.00E−03 4 −2 6 5 −1.3 6.3 6 −2 8 7 −1.5 8.5 9 −2 11 10 −0.5 10.5 1.00E−04 5 −1.85 6.85 6 −1.2 7.2 7 −1.85 8.85 8 −1.3 9.3 10 −1.85 11.85 11 −0.2 11.2 1.00E−05 7 −1.8 8.8 8 −1 9 8 −1.8 9.8 9 −1.2 10.2 12 −1.8 13.8 12 0 12 [24]:2L-TC4PSK.

(8)

Asitcanbeseenfromsimulationresults,ML/AES-LDPCC-CPFSK schemeshavebettererrorperformancethan2L-TC4PSK[24] mod-els.

8. Conclusion

Inthispaper,wepresentanewjointencryptionanderror cor-rectionstructuretoensuresecureandrobustcommunicationin WSSUSchannelswithoutadditionalcomplexity.Forthispurpose, weintroduceMultilevel/AdvancedEncryptionStandard-Low Den-sityParityCheckCoded-ContinuousPhaseFrequencyShiftKeying andweevaluateerrorperformanceoverWSSUSchannelsforTU,BU andHTtypeofCOST207withRLS,LMSequalization.Itisshownthat ourproposedsystemprovidessecure,reliabledatatransmission withhigherrorcapability,bandwidthefﬁciencyandreductionof transmissionpowerusage.Thus,oursystemhasimportantpower andbandwidthadvantagesandisverysuitableforlowpowerand bandlimitedapplications.

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