Blind Soft Detection Assisted Frequency Hopping Multicarrier DS CDMA Systems

BLIND SOFT-DETECTION ASSISTED FREQUENCY-HOPPING

MULTICARRIER DS-CDMA SYSTEMS

Lie-Liang Yang and Lajos Hanzo

Dept. ofECS, University ofSouthampton,SO171BJ, UK.

Tel: +44-703-593125, Fax: +44-703-594508

Email: lh@ecs.soton.ac.uk, http://www-mobile.ecs.so ton. ac. uk

ABSTRACT

Aslow frequency hopping, multicarrier direct-seq-uence,code-division multiple-access(SFH/MC DS-CDMA)schemeisproposedandinvestigated,which hasthepotentialofprovidinga jointframeworkfor 2nd-generationnarrow-bandCDMA,3rd-generation wideband CDMA and high-rate broadband access networks. Blindsoft-detectionoftheSFH/MC DS-CDMAsignalsisinvestigated,assumingthatthe re-ceiverhasnoknowledgeoftheassociated frequency-hopping(FH)patternsinvoked. The system's per-formance is evaluated over therange of Nakagami multipath fading channels. The results show that the blind soft-detection not only achieves the re-quired bit error rate performance, but it is also capable of blindly acquiring the FH patterns em-ployed. Thisassiststhemobileinaccessingthe net-workwithouttheknowledgeoftheFHpatternsor duringsofthand-over.

1. INTRODUCTION

Withtheemergenceofbroadbandwirelessaccessnetworks (BRAN) requiring bandwidths substantially higher than that of the 3rd generation systems [1 ] it is of increasing signicance tocreate aBRAN framework, which is back-wardscompatiblewith2ndand3rdgenerationschemes. An attractivecandidate schemecapableofachievingthese re-quirementsisconstitutedbytheproposedfrequency-hopping (FH)basedmulticarrierDS-CDMA (FH/MC DS-CDMA) arrangement, where no rigid spectral segmentation is re-quiredfortheco-existenceofvariouswirelesssystems. Specif-ically,theentirebandwidth canbedividedintoanumber ofsub-bandsandeachsub-bandcanbeassigneda subcar-rier. Asubcarriercoulddeliveranarrow-bandIS-95type serviceor-similarlytotheemergingmulti-carrierassisted cdma2000 system - it could invoke a number of carriers, whileemployingavarietyofdierentspreadingfactors.

FHcan be invoked for each user, in order to occupy thewholesystem'sbandwidthandtoeÆcientlyutilize the system's frequency resources. Various slow and fast FH schemesoradaptiveFHtechniques canbesupported, de-pendingonthestate-of-the-art. InFH/MCDS-CDMA

sys-Thenancialsupportofthefollowingorganisationsis grate-fullyacknowledged:EPSRC,UK,theComissionoftheEuropean Communities,Brussels,BelgiumandMotorolaECID,Swindon, UKandtheVirtualCentreofExcellence(VCE)inMobile Com-munications.

temsthesub-bandsarenotrequired tobe ofequal band-width. Hence existing 2nd- and 3rd- generation CDMA systems can besupported using one or more subcarriers, consequently simplifying the frequency resource manage-ment andeÆciently utilizing the entire bandwidth avail-able. Furthermore,theproposedsystemconceptlendsitself tounlicensedoperation,erradicatingtheineÆcientspectral segmentationofdierentco-existingsystems.

InthistreatiseweproposeaFH/MCDS-CDMAsystem employing slow FHand binary modulation. The system operates in a multipathfading environment, and a max-imum ratio combining (MRC) assisted RAKE receiver is used. Thesystem's performance isinvestigated over var-ious Nakagami-mmultipathfading channels,describinga varietyofprobabilitydensityfunctions(pdf)rangingfrom aRayleighfading channeltoanon-fadingGaussian chan-nelbyvaryingasingleparameter, namelym,fromoneto innity [2]. We assumethatthemobilestation(MS) has noknowledgeofthefrequency-hopping(FH)patterns em-ployed,sinceitisabouttoattemptitsinitialaccesstothe system.HencetheMShastoinfertheFHpatternemployed bythebasestation(BS) blindly. Wewillshowthatblind soft-detectionusingmaximumlikelihooddetection(MLD) -whichisconsideredtobetheoptimumscheme-canbe uti-lized,inordertosimultaneously accomplishboth informa-tiondetection andFHpatternacquisition. Following this initialblindFHpatternacquisitiontheMSreceivestheFH patterncodefromtheBSandmayproceedtothe informa-tion reception phase by exploiting theexplicit knowledge oftheFHpattern. However,theproposedblind-detection solutionscanbeappliedbyboththeBSandMS.

2. SFH/MCDS-CDMASYSTEM

2.1. TransmitterModel

Thetransmitter schematic alongwith themultipleaccess channelisshown inFig.1. There areK usersinthe sys-temandeachsubcarrierofeachuserisassignedarandom spreading sequence. In the schematic C(Q;U

k

) denotes a constant-weight code assigned to user k, which has Uk numberofbinary`1's,indicatingtheactivatedFHcarriers. Hencetheweight ofC(Q;Uk)isUk. Thiscode isselected fromtheconstant-weightcodebookoftheschematic,which describestheFHpatterns. Thereare

Q U

k

=Q!=U k

!(Q Uk)!numberofpossiblesuchweight-Uksequencesandthe constant-weight code C(Q;Uk) describes theFH patterns employed. Specically, C(Q;Uk) determinesthepositions oftheU

k

Channel

data

S-P

Carrier selection

Constant

weight

code

book

Frequency

synthesizer

1

2

1

2

d0 d1 dUk1 C (k ) 0 C (k ) 1 C (k ) Uk1 C(Q;Uk) cos (2f (k ) 0 t+' (k ) 0 ) cos (2f (k ) 1 t+' (k ) 1 ) cos (2f (k ) Uk1 t+' (k ) Uk1 ) Uk P P h (k ) h (j) h (K) sk(t) sj(t) sK(t) n(t) r(t)

Figure 1: Transmitter andchannel block diagram of the frequency-hoppingmulticarrierDS-CDMAsystems.

ofasetof U k

numberofactiveFHsubcarrierfrequencies fromtheQoutputsofthefrequencysynthesizer.

The originalbit stream having abit durationof T b

is rstserial-to-parallel(S-P)converted,asseeninthe schema-tic, yieldingUk parallel streams. The assignment of bits totheactivated subcarriers is controlled bythe constant-weightcodeC(Q;U

k

). Dependingonthespecicaimsofthe systemdesign, we canassign every U

k

-thbit tothesame subcarrier and in this parallel system thebit-duration is henceextended to T = UkTb. This assists in mitigating theinter-symbol-interference(ISI)inahigh-bitrate trans-mission scheme. Alternatively, the proposed parallel sys-temcan beused tomaintain T =T

b

in eachsubchannel, hence assisting in high-rate or variable-rate transmission upon employing a dierent number of subcarriers, as we willhighlight duringour furtherdiscourse. Theoretically, Qnumberof dierentinformation rates can be generated bychanging theweightof thecode C(Q;U

k

). As seenin Fig.1,thedirect-sequence(DS)spread,transmittedsignal ofthekthusercanbeformulatedas:

sk(t)= U k 1 X u k =0 p 2Pd (k ) u k (t)c (k ) u k

(t)cos 2f (k ) u

k t+'

(k ) u

k

; (1)

whereP denotesthetransmittedpowerper carrier,while U

k

is the weight of the constant-weight FH code of the kthuser. Furthermore,

n d (k ) u k (t) o , n c (k ) u k (t) o , n f (k ) u k o and n ' (k ) u k o

denotethecurrentdatastream'swaveforms,theDS spreadingwaveforms,thesubcarrierfrequencyset andthe phaseanglesintroducedinthecarriermodulationprocess, respectively. LetTcbethechipdurationoftheDS spread-ingwaveformsandN=T

b

=Tc.Thentheprocessinggainof N

P =T=T

c

equalstoU k

N orN,dependingon thechoice ofthebit duration,as discussedpreviously. Furthermore, weassumethattheFHintervalisTh,andthatthenumber ofdatabits,N

b =T

h

=T,transmittedperhopisapositive integer,whichisstrictlylargerthan1,implyingslowFH.

2.2. NakagamiChannelModel

Weconsideredafrequency-selectivemultipathchannel[3 ], whosecomplexlow-passimpulseresponseforsubcarrieru

k ofuserkisgivenby:

h (k ) u k (t)= Lp 1 X lp=0 (k ) u k ;lp e j (k ) u k ;lp

Æ(t lpTc); (2)

where lpTc is the relative delay of thelp-th path of user kwithrespecttothemainpath,thephases

n (k ) u k ;lp o are independent identically distributed(iid) randomvariables uniformlydistributedintheinterval(0;2),whilsttheL

p tapweights n (k ) u k ;l p o

areindependentNakagami-mrandom variableswithapdfof[4 ]:

p( (k ) u

k ;lp

)=M( (k ) u k ;lp ;m; (k ) u k ;lp );

M(R ;m;)= 2m m R 2m 1 (m) m e ( m=)R 2 ; (3)

where () represents thegamma function, and m is the Nakagami-m fading parameter, which is dened as m = E 2 [( (k ) u k ;l p ) 2 ]=Var[( (k ) u k ;l p ) 2

]. Theparameter (k ) u k ;l p isthe secondmomentof

(k ) u k ;lp ,i.e (k ) u k ;lp =E[( (k ) u k ;lp ) 2

]. We as-sumeanegativeexponentiallydecayingmultipathintensity prole(MIP)distributiongivenby:

(k ) u k ;lp = (k ) u k ;0 e lp

; 0: (4)

where (k ) u

k ;0

istheaveragesignalstrengthcorrespondingto therstresolvablepathandistherateofaveragepower decay.

2.3. ReceiverModel

BPF

BPF

BPF

MRC

MRC

MRC

0

0

0

...

Decision

unit

...

(L l 1)Tc (L l 1)Tc (L l 1)Tc

(L 1)Tc (L 1)Tc (L 1)Tc L 1 L 1 L 1 l l l Z0 Z1 ZQ1

nT+(L 1)Tc;n=1;2;::: ^ d0 ^ d1 ^ du 1 r(t)

Figure2: Receiverblockdiagramofthefrequency-hopping multicarrierDS-CDMAsystems.

Weassumethattherstuseristheuser-of-interestand considerthe conventional matched lterbased RAKE re-ceiverwithMRCofdiversityorderofL,asshowninFig.2. Incontrasttothetransmitterside,whereonlyU

k

outofQ subcarriersaretransmittedbytheuserk,atthereceiverall Qsubcarriersarealwaystentativelydemodulated.The in-formationbitstransmittedoverthedierentsubcarriersare blindsoft-detectedjointlyusingtheMLDapproach. Con-sequently,fromthepointofviewofthereceiver,each sub-carriercanbe viewedas anon-o typesignallingscheme. Whenasubcarrierisactivelyusedforsignallingandhence itisin theon-state,theMRCoutputsamplesgive+1 or -1 information, otherwise, while passive andhence in the o-state,theMRCstageoutputsnoise.

3. BLINDSOFT-DETECTION OFSFH/MC

DS-CDMASIGNALS

3.1. Statistics of theMRC outputs

sub-bandsassociatedwiththeQnumberofsubcarriers,and areassumedtohaveachievedtimesynchronizationwiththe correspondinginitialpathofthesubcarriersofthereference signal. Ifweassumethatperfectestimatesofthechannel tapweightsareavailable,thenafterappropriatelydelaying theindividualmatchedlteroutputs,inorderto synchro-nizetheLnumberofpathsignalsusedbytheRAKE com-biner,theqthMRCoutputsampledatt=nT+(L 1)T

c inordertodetectthenthsymbolcanbeexpressedas:

Z q

[n]=D q

[n]+I q

[n]: (5)

Assuming thatZq[n] is an independentGaussian dis-tributedvariable,ieinvokingtheGaussianapproximation forthemultipathandmultiple-accessinterference,thenthe meanvalueofZ

q

[n]canbeexpressedas:

Dq[n]= r

P 2

Tdq(n) L 1 X

l=0

2 q;l

; (6)

where d q

(n)isthenthbit transmittedon subcarrier qby thereferenceuseranddq(n) 2f+1; 1;0gwith`0' repre-senting theo-state. Forsimplicity,weassumethatthere exists nospectraloverlapbetween thespectralmain-lobes oftwoadjacentsubcarriers[5 ],andinterferenceisinicted only,whenaninterferinguseractivatesthesamesubcarrier, asthereferenceuser,encounteringaso-calledhit[6 ]. Con-sequently,assumingthatthereexistsK

h ,(0K

h

K 1)

numberofinterferingsignals,allofwhichactivatetheq-th subcarrierduringthenthsymbol'stransmissionofthe ref-erencesignal,thevarianceofZq[n]canbeexpressedas:

2

= PT

2 2

" q(L

p

;) 1

2N p

+ K

h q(L

p ;) 3N

p

+

20E b N

0

1 #

0

L 1 X

l=0

2 q;l

; (7)

where E b

= PT istheaverage transmittedenergy-per-bit andq(L

p

;)=(1 e Lp

)=(1 e

),if6=0,otherwise, q(L

p ;)=L

p

,if=0.

3.2. Symbol-by-Symbol Maximum Likelihood De-tection

Assuming that thereceiver is aware ofthe weight of the transmittedconstant-weightcode,butnotofthepositions ofthebinary`1's,thereceiverhastodetectnotonlythe po-sitionsofthe`1's,whichindicatethesubcarriersused,but alsotheantipodalbinarymodulatedinformationconveyed bytheactivatedsubcarriers. Letusexpressthenthinput data inthe vectorial form ofDi = fdi;0;di;1;:::;di;Q 1g, where0iM 1representstheconstant-weightcode set ofweight U andM is the number of weight-U codes included in thisset. Thenaset of QMRCsamplesZ = fZ1;Z2;:::;ZQ 1ginFig.2-whichwerefer tohereas a receivedsymbolorvector-areinputtothe`decisionunit' invokingaMLD,whichisbasedonthecomputationofthe probabilitiesdenedas:

p(ZjD i

)= 1 (2

2 )

Q=2

exp 0

B @

P Q 1 q=0

Zq

p P

2 Tdi;q

P L 1 l=1

2 l

2

2 2

1

C A ;

i=0;1;:::;M 1; (8)

where we assume that the subcarriers received over the samemultipathrayundergothesame fadingattenuation. Thedecisioncriterionisbasedonselectingthesignal corre-spondingtothemaximumofthesetofprobabilitiesf p(ZjD

i )g. The complexityof theMLD for areceived symbol or vectorisdeterminedbyboththelength andtheweightof theconstant-weight code invoked. The average detection complexityorder(O)canbeexpressedasO 3

Q =Q

. Ap-parently,thiscomplexityisexcessive,renderingthe associ-ated detectioncomplexityimpractically high,when evalu-atingEq.(8)forallpossiblecodewords,ifthevalueofQis high. Hence weimposesomelimitations ontheminimum distanceofthecodesintheconstant-weightcode-book rep-resentingtheFHpatterns, inorderto simplifythe detec-tion. Thisreducesthesizeoftheset.

Let C(Q;2v;U) represent a constant-weight code set having acode length ofQ andweight ofU, asdiscussed previously.Furthermore,lettheminimumdistancebetween anypairofcodesfromC(Q;2v;U)be2v,wherevisan inte-gerlargerthanzero. Then,thiscodeconstitutesaspecic, reduced-size subset of the constant-weight code C(Q;U), where the number of codewords was M =

Q U

. By con-trast,letA(Q;2v;U)representthenumberofcodewordsof theconstant-weightcodeC(Q;2v;U). Then,iftheFH pat-ternsaredeterminednowbyalltheA(Q;2v;U)codewords, thedetectioncomplexitywillbereducedfromO(3

Q =Q)to O(A(Q;2v;U)2

U ).

4. PERFORMANCEOF THEBLIND

SOFT-DETECTION

AsshownforexampleinFig.3,fortheSFH/MCDS-CDMA system usingaconstant-weight code C(Q;2v;U) in order toactivatethesubcarriersandusingareceiverwithoutthe explicit knowledge of the FH pattern - except for know-ingthenumberoftheactivesubcarriers-wehaveto con-siderthosecodes, whichhaveidentical`1' positionsinthe FHcode, correspondingto identicalactivated subcarriers. However,potentiallydierentdatasymbolsareconveyedon theseactivesubcarriers. Werefertotheseasintra-setcodes or intra-codes, forshort. Explicitly,theaboveintra-codes arederivedfromagivenconstant-weightcodeandactivate thesamesubcarriers. Bycontrast,theso-calledinter-codes arederivedfromdierentconstant-weightcodeshavingthe samenumberof`1'FHcodepositions,butactivatedierent subcarriers.

Figure 3: Example of intra-codes and inter-codes of a constant-weight code C(10;4;5) for an SFH/MC DS-CDMAsystemusing10subcarriers.

Itcanbeshownthattheaverageprobabilitiesof intra-codeerrorandinter-codeerror foragivennumberofhits, K

h

,canbeapproximatedas:

P intra

(K h

; s

)(U 1)P(K h

; s

); (9)

Pinter(Kh;s)2 v

[A(Q;2v;U) 1]P

Kh; v

s 2

; (10)

whereinEq.(9)andEq.(10)wehave:

P(K h

;)= r

1+

(1+) ms

(m s

+ 1 2 ) 2

p

(m

s +1)

2

F 1

1;m

s +

1 2

;m s

+1; 1 1+

; (11)

=

s 2ms

=

q(L;2) 2mq(L;) ;

=

q(Lp;) 1 2N

p +

K h

q(Lp;) 3N

p +

20E

b N

0

1

1 ; (12)

and ()istheGammafunctiondenedas (z)= R

1 0

e t

t z 1

dt, z>0,

2 F

1

(a;b;;c;z)isthehypergeometricfunctiondened as[4 ]:

2F1(a;b;;c;z)= 1 X

k =0 (a)

k (b)

k z

k

(c)kk!

; (13)

and(a)k=a(a+1)(a+k 1); (a)0=1.

Theaveragebit errorprobabilityforaSFHbased sys-temcanbeexpressedas[6 ]:

Pb= K 1 X

K h

=0

K 1

Kh

P K

h h

(1 Ph) K 1 K

h

P(Kh;s); (14)

where0 Kh K 1andPh istheprobabilityofahit fromaninterferingsignal,whichcanbeexpressedas:

P h

= Q 1 U

k 1

Q U

k

=

U k Q

; (15)

ifweassumethattheFHpatternofthekthinterferinguser isdeterminedrandomlyby aconstant-weight codechosen fromthesetof

Q U

k

codes. TheprobabilityofP(K h

;s)inEq.(14)denotesthe con-ditionalbit error probability,given thatK

h

hitsoccurred

fromtheotherK 1interferingusers,which-accordingto Eq.(9)andEq.(10)anduponomittingthedetailed deriva-tions-canbeexpressedas:

P(K h

; s

)=

U 1

U P(K

h ;

s )

+ 2

v

[ A(Q;2v;U) 1] 2

P

K h

; vs

2

: (16)

5. NUMERICALRESULTS

In thissection,theaverage BERperformanceisevaluated asafunctionoftheaveragesignal-to-noiseratio(SNR)per bit,whichisobtainedbycomputing

b

= (1 e

Lp )

1 e

0 E

b N0

=q(Lp;)

0

E b N0

; (17)

forallsystemsdescribedabove.

Fig.4showstheBERperformanceoftheproposedSFH /MCDS-CDMAsystemwithrespecttothemultipath fad-ingparametersm=0:5; 1;2; 5; 10; 50.Therangeofother parameters used is explicitly stated in the corresponding gures. TheNakagamiparametermrepresentsthe dier-ent fadingenvironments,rangingfromtheworst-case one-sidedGaussianfadingtoRayleigh,andnallytothemost favourablenon-fadingcase. Theparametersusedareshown inthegure. Asexpected,foragivenSNRperbit,theBER decreasesuponincreasingthevalueofm,whichimpliesthat thechannelfadingbecomeslesssevere. Thesystem perfor-mance iscriticallyaectedbytheparameterm,iebythe communicationenvironmentencountered.

In Fig.5 we evaluated the intra-code word error rate (WER)accordingtoEq.(9)andtheinter-codeWERfrom Eq.(10), aswellastheirsumforourSFH/MCDS-CDMA systemusingblindsoft-detection. Fromtheresultswe con-cludedthatthetotalWERwastypicallydominatedbyone ofits contributing factors. Namely,forverylowSNRper bitvaluesitwasdominatedbytheWERoftheinter-code decisions,whileformoderatetohighSNRsperbit,bythe WERoftheintra-codeerrors. Sincetheinter-codeWERof Eq.(10)isafunctionofv,hence,fromEq.(9)andEq.(10) weinferthat,ifv>2,thetotalWERwillbedominatedby Eq.(9),providedthattheSNRperbit issuÆcientlyhigh. This property suggeststhat for v > 2 error-control tech-niques can be introduced, in order to correct the intra-code errors by increasing the minimumdistance between theintra-codes,andhencetodecreasetheintra-codeWER ofEq.(9),andconsequentlytodecrease thetotal WERof theblindsoft-detectionscheme.

Fig.6comparedtheperformanceofblindsoft-detection to that of hard-detection, which benetted from the ex-plicit knowledge of theFH patterns employed. Dierent Nakagamifading parameters, namelym = 1; 2; 10 were used,wheretheBERofhard-detectionwasintroducedasa benchmarker. TheresultsshowthatforasuÆcientlyhigh SNRperbitandasuÆcientlygoodchannelstate,theBER performanceofblindsoft-detectionwassuperiortothatof thehard-detection.AswediscussedinthecontextofFig.5, iferror-controlisintroducedforintra-codeerror-correction, then an improved BER performance can be achieved by blindsoft-detection.

InFig.7amulti-ratecommunicationsystemwas charac-terisedusingaconstantprocessinggainofN

p

Letthe rate ofeach transmittedsubcarrierbe Rb. Then thepractical rates supportedbythesystem mightbeR

b , 2R

b , 4R

b , 8R

b , 16R

b

, or 32R b

, since theconstant-weight codesC(32,2,1),..., C(32,32) as shown inthe gurewere assumed. Duetothehighminimumdistanceofthecodes C(32,8,4), C(32,14,8), C(32,16,16), and C(32,32), we ob-serve that even though thesystems transmit at dierent rates,amoreorlesssimilarBERperformancecanbe main-tained,whenthechannelqualityissuÆcientlyhigh- assum-ing appropriate constant-weight codes. By contrast, the BERperformanceofthesystemusingtheconstant-weight codesofC(32,2,1)andC(32,4,2)wasinferiorwithrespect totheothers',duetotheirrelativelylowminimumdistance.

Figure4: BERversusSNRperbitperformanceupon vary-ingthefadingparametermintherangeof

1 2

to50 employ-ingtheconstant-weightcodeC(16,12,8), Lp=3resolvable paths,diversityorderL=3,K=50users,bit-durationto chip-durationratioN=127andMIPdecayfactor=0.

6. REFERENCES

[1] E.Dahlman,B.Gudmundson,M.NilssonandJ.Skold, \UMTSandIMT-2000basedonwidebandCDMA," IEEECommun.Mag.,Vol.36,No.9,pp.70-80,Sept. 1998.

[2] N.Nakagami,\Them-distribution,ageneralformula forintensitydistributionofrapidfading,"inStatistical MethodsinRadioWave Propagation,W.G.Homan, ed.Oxford,England:Pergamon,1960.

[3] J. G. Proakis, Digital Communications, 3rd ed. New York: McGraw-Hill,1995.

[4] T. Eng and L. B. Milstein, \Coherent DS-CDMA performance in Nakagami multipath fading," IEEE Trans. on Commun., Vol. 43, No. 2/3/4, pp. 1134-1143,Feb./Mar./Apr.1995.

[5] S.KondoandL.B.Milstein,\Performanceof multicar-rierDSCDMAsystems,"IEEETrans.on Commun., Vol.44,No.2,pp.238-246,Feb.1996.

[6] T. Vlachos and E. Geraniotis, \Performance study of hybrid spread-spectrum random-access communi-cations," IEEE Trans. on Commun., Vol. 39, No. 6, pp.975-985,June1991.

Figure 5: WERversus SNRperbit performance ofblind soft-detectionuponvaryingthediversityorderL.

Figure 6: BER versus SNRper bit performance compari-son between hard-detectionandblind soft-detectionupon varyingthefadingparameterm.