Frequency-Hopping Multicarrier
Direct-Sequence Code-Division Multiple
Access Systems
Lie-Liang Yang and Lajos Hanzo
Dept. of ECS, University of Southampton, SO17 1BJ, UK.
Tel: +44-703-593 125, Fax: +44-703-594 508
Email: [email protected] and [email protected]
http://www-mobile.ecs.soto n.ac .uk
Abstract| Against the back-cloth of the explosive
ex-pansion of the Internet and the continued dramatic
in-crease in demand for high-speed multimedia wireless
ser-vices, there is an urging demand for exible, broadband
transceivers.Aversatilebroadbandmultipleaccessscheme,
combining frequency-hopping (FH) with multicarrier
DS-CDMA(FH/MCDS-CDMA)isproposedandinvestigated.
The FH/MC DS-CDMA schemeis capableof meetingthe
requirementsoffuture mobilewireless systems, whilealso
ensuring compatibility with the existing 2nd- and
3rd-generationsystemsinthecontextofmultiratetransmission.
I. Introduction
Thereisarangeofactivitiesinvariouspartsoftheglobe
concerningthestandardization,researchanddevelopment
ofthethird-generation(3G)mobilesystemsknownas the
Universal Mobile TelecommunicationsSystem(UMTS) in
Europe, which was termed as the IMT-2000 system by
theInternationalTelecommunicationsUnion(ITU)[1],[2].
This is mainly due to the explosive growth of the
Inter-netandthecontinueddramaticincreasein demandforall
types of advanced multimedia wireless services including
voice and data. However, all the advanced services such
ashigh-resolutionmultimedia communications,which
de-mand data rate signicantly higher than 2Mb/s, are
un-likelytobesupportedbythe3Gsystems[3]. Consequently,
research continues in the context of techniques such as
broadbandaccessandhigh-exibilityterminals.
A potential candidate multiple access scheme meeting
these requirementshas beenproposedand investigatedin
[4] - [8]. The multiple-access scheme is constituted by
fre- quency-hopping (FH) based multicarrier DS-CDMA
(FH/MC DS-CDMA), where the entirebandwidth of
fu-ture systems can be divided into a number of sub-bands
and each sub-band canbe assignedasubcarrier.
Accord-ingto theprevalentservicerequirements,thesetof
legiti-Thiswork has been funded inthe frameworkof the ISTproject
IST-1999-12070 TRUST, which is partly funded by the European
Union. Theauthorswouldliketoacknowledge thecontributionsof
theircolleagues.
mate subcarrierscan be distributed to users in line with
their instantaneous information rate requirements. FH
techniques are employed foreach user, in order to evenly
occupythewholesystembandwidthand toeÆciently
uti-lize the available frequency resources. Specically, slow
FH, fast FH or adaptive FH techniques can be utilized
dependingonthesystem'sdesignandonthe
state-of-the-art. InFH/MCDS-CDMAsystemsthesub-bandsarenot
required to be of equal bandwidth. Hence existing
2nd-and 3rd-generation CDMA systemscan be supported
us-ing oneormoresubcarriers, consequentlysimplifying the
frequencyresourcemanagementandeÆcientlyutilizingthe
entire bandwidth available. This regime canalso remove
the rigid spectrum segmentation of existing `legacy'
sys-tems,whileensuringcompatibilitywithfutureBroadband
AccessNetworks(BAN)andun-licensedsystems.
Further-more, a number of sub-channels associated with variable
processinggainscanbeemployed,inordertosupport
var-iousservicesrequiringlow-toveryhigh-ratetransmissions,
forexampleforwirelessInternetaccess.
Inthistreatiseweinvestigatetheissueofmultirate
trans-missionin thecontextofFH/MCDS-CDMAsystemsand
study the achievable performance. Specically, the
sys-tem'sperformanceisevaluatedovertherangeofNak
agami-mmultipath fading channels,whichcloselymodelvarious
multipath channels, exhibiting Probability Density F
unc-tions(PDF)spanningtherangefromRayleighfading
chan-nels to non-fading Gaussian channels by varying a single
parameter, namely m, from one to innity [9]. Two
de-tection schemes are investigated in conjunction with the
receiverhaving perfect knowledgeorno knowledge of the
FH patterns employed. When the receiver invokes the
knowledgeoftheFHpatterns[5],thenconventional
hard-detectionoftenappliedin direct-sequence,slow
frequency-hopping CDMA (DS/SFH CDMA) systems is employed
forthesakeofsimplifyingthereceiver. Bycontrast,when
the receiver does nothave any knowledge concerning the
FH pattern used [4], then the proposed blind joint
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Serial P data Serial/ parallel converter and grouping Constant-weight codebook C(Q;U) Carrierselection Frequencysynthesizer Constellation Constellation Constellation mapping mapping mapping b0(t) b1(t) bU1(t) C0 C1 CU 1 Transmitted signal Spreading Multicarriermodulationd0 d1 dU 1 f1(t) f2(t) fU(t) 1 1 2
2 3 Q U
Fig.1. Transmitterdiagram ofthefrequency-hoppingmulticarrier
DS-CDMAsystemusingadaptivetransmission.
...
...
...
Rake Rake Rake combiner1 combiner2 combinerU Decision unit FHinformation Z1 Z2 ZU d0 d1 dU 1Channelstates(totransmitter)
received signal Carrierdemodulation Output data Parallel/ serial converter Frequencysynthesizer Carrierselection f 1 (t) f 2 (t) fU(t)
1 2 3 Q
Fig.2. Receiverblockdiagramofthefrequency-hoppingmulticarrier
DS-CDMAsystemusingconventionalRAKEreceiver.
accomplishbothdemodulationandFHpatternacquisition.
II. FH/MCDS-CDMA
ThetransmitterschematicoftheproposedFH/MC
DS-CDMA arrangement is depicted in Fig. 1. Each
subcar-rier of a user is assigned a pseudo-noise (PN) spreading
sequence (code). These PN sequences can be
simultane-ouslyassignedtoanumberofusers,providedthatonlyone
useractivates thesamePNsequence onthesame
subcar-rier. ThesePNsequencesproducenarrow-bandDS-CDMA
signals. In Fig. 1, C(Q;U) represents a constant-weight
codehavingU numberof`1'sand(Q U)numberof`0's.
Hence theweightof C(Q;U)isU. This code isreadfrom
a so-called constant-weight code book, which represents
thefrequency-hoppingpatterns. Theconstant-weightcode
C(Q;U) playstwodierent roles. Its rst roleis that its
weight-namelyU -determinesthenumberofsubcarriers
invoked, while itssecond function isthat the positionsof
theU numberofbinary`1'sdeterminestheselectionofaset
ofU numberofsubcarrierfrequenciesfromtheQoutputs
ofthefrequencysynthesizer. Furthermore,inthe
transmit-ter`side-information'reectingthechannel'sinstantaneous
qualitymightbeemployed,inordertocontrolits
transmis-sion andcodingmode,sothat the targetthroughputand
transmissionintegrityrequirementsaremet.
As shown in Fig. 1, the original bit stream having a
bitdurationofT
b
isrstserial-to-parallel(S-P)converted.
Then, these parallelbit streamsare groupedand mapped
to the potentially time-variant modulation constellations
ofthe U activesubcarriers. Let usassume thatthe
num-berofbitstransmitted byaFH/MCDS-CDMAsymbolis
b, and let us denote the symbol duration of the FH/MC
DS-CDMA signalby T
s
. Then, ifthe system is designed
forachievingahighprocessinggainandformitigatingthe
Inter-Symbol-Interference (ISI) in a constant-rate
trans-missionscheme,thesymboldurationcanbeextendedtoa
multiple ofthebitduration,i.e.,T
s =bT
b
. Bycontrast,if
thedesign aimsto support multiple transmission ratesor
channel-qualitymatchedvariableinformationrates,thena
constantbit duration of T
0 =T
s
canbe employed. Both
multirate and variable rate transmissions can be
imple-mentedbyemployingadierentnumberofsubcarriers
as-sociatedwithdierentmodulationconstellationsaswellas
dierentspreadinggains. As seenin Fig.1,after the
con-stellation mappingstage, each branch is DS spreadusing
the assigned PN sequence, and then this spread signalis
carrier modulated using one of the active subcarrier
fre-quencies derived from the constant-weight code C(Q;U).
Finally,allU activebranchsignalsare multiplexed,in
or-dertoformthetransmitted signal.
IntheFH/MCDS-CDMAreceiverofFig.2thereceived
signal associated with each active subcarrier is detected
usingfor exampleaRAKE combiner. Alternatively,
Mul-tiuser Detection (MUD) can be invoked, in order to
ap-proachthesingle-userbound. Incontrasttothe
transmit-terside,whereonlyU outofQsubcarriersaretransmitted
byauser,atthereceiverdierentdetectorstructuresmight
beimplementedbasedontheavailability[5]orlack [4]of
the FH pattern information. During the FH pattern
ac-quisitionstage,whichusuallyhappensatthebeginningof
transmissionorduringhand-over,tentativelyallQ
subcar-riers can be demodulated. The transmitted information
canbe detected and theFH patterns can be acquired
si-multaneouslybyusingblindjointdetectionalgorithms
ex-ploitingthecharacteristicsoftheconstant-weightcodes[4].
If however,the receiverhasthe explicit knowledge of the
FH patterns, then onlyU subcarriers haveto be
demod-ulated. However, if Fast Fourier Transform (FFT)
tech-niquesareemployedfordemodulation-asoftenisthecase
inmulticarrierCDMA orOFDMsystems,thenallQ
sub-carriersmightbedemodulated,wheretheinactive
subcar-riersonlyoutputnoise. Inthedecisionunit ofFig.2,these
`noise-output-only'branchescanbeeliminatedby
exploit-ingtheknowledgeoftheFHpatterns. Hence,thedecision
unitonlyoutputstheinformationtransmittedbytheactive
subcarriers. Finally,thedecisionunit'soutputinformation
is parallel-to-serialconverted in order to form theoutput
data.
At the receiver, the channel states associated with all
thesubchannelsmightbeestimatedorpredictedusing
pi-lot signals. This channelstateinformationcanbeutilized
forcoherentdemodulation. It canalsobefed backto the
transmitter ashighly protectedside-information, in order
toinvokearangeofadaptivetransmissionschemes
includ-ing power control and adaptive-rate transmission. Note
III. Multirate Transmission inFH/MCDS-CDMA
In future wirelesscommunicationsystemsawide range
ofinformationratesmustbeprovided,inordertosupport
dierent services, which demand dierent data rates and
dierent QoS. Hence, in this section a range of existing
andpossiblemultirateschemesaresummarized. Notethat
asystemmayemployacombinationofseveralofthe
mul-tirateschemeslistedbelow,in ordertoachievethedesired
datarate.
MultipleSpreadingCodes{Higherrateservicescan
besupportedinCDMAbasedsystemsbyassigninga
num-berofcodes.
VariableSpreadingFactors{Higherrateservicesare
supportedbyusinglowerspreadingfactorswithout
increas-ingthebandwidthrequired.
Variable RateFECCodes{Higherrateservicescan
besupported by assigninglesspowerful,higherrate FEC
codesassociatedwithreducedredundancy.
Dierent FEC Schemes { The range of coding
schemes might entaildierentclassesof FEC codes, code
structures, encoding/decoding schemes, puncturing
pat-terns,interleavingdepthsandpatterns,andsoon. Higher
rateservicescanbesupportedbycodingschemeshavinga
highercodingrate.
VariableConstellationSize{Higherrateservicescan
besupportedbytransmittingmulti-bitsymbolsassociated
withhigherconstellationsizes.
MultipleTimeSlots{Higherrateservicescanbe
sup-portedbyassigningacorrespondingnumberoftimeslots.
Multiple Bands { Higher rate services can be
sup-portedbyassigningahighernumberoffrequencybands.
Multiple Transmit Antennas { Employing multiple
transmit antennas based on space-time coding [10] is a
novel method of communicating over wireless channels,
whichwasalsoadoptedforthe3rd-generationmobile
wire-less systems. Multirate servicescan also be implemented
using multiple transmit antennas associated with certain
space-time codes. Typically, higher rate services can be
supported byahigher number oftransmit antennas
asso-ciatedwithappropriatespace-timecodes.
InthecontextoftheFH/MCDS-CDMAscheme,awide
range of multirate services can be supported by
combin-ingthevarious multirateschemesdiscussed above
accord-ing to the state-of-the-art. Furthermore, in the FH/MC
DS-CDMA system,asdiscussedpreviously,multirate
ser-vices canbe supported by activating dierent numberof
subcarriersassociatedwiththeconstant-weightcodes
hav-ing appropriate weights. This multirate scheme can be
viewed as a multiple band based arrangement. However,
theconstant-weightcodebasedFH patternshavearange
of attractive characteristics, which might be benecial in
thecontext oftheFH/MCDS-CDMAsystem. For
exam-ple, with the aid of blind joint soft-detection [4] the FH
patterns can also be acquired, while detecting the
trans-mitted information. In the remainder of this paper, we
investigatethe performance ofthe multirateFH/MC
DS-implementedbyusingdierentconstant-weightcodes.
IV. Detection of Multirate FH/MCDS-CDMA
Signals
Two detection schemes are investigated in conjunction
withthereceiverhavingperfectknowledgeornoknowledge
of the FH patterns employed. When the receiverinvokes
theexplicitknowledgeoftheFHpatterns[5],then
conven-tionalhard-detectionoftenapplied inDS/FHCDMA
sys-tems is employed for thesakeof simplifying thereceiver.
Basedonthehard-detectionscheme,theactivesubcarriers'
signalsaredetectedseparately,and eachactivesubcarrier
outputsonebit ofinformation,sinceBPSKmodulationis
assumed.
Bycontrast,whenthereceiverdoesnothaveany
knowl-edgeconcerningtheFHpatternused,thentheblindjoint
soft-detection techniques of [4] are used, in order to
si-multaneouslyaccomplishbothdatademodulationandFH
patternacquisition.Specically,in[4]asymbol-by-symbol
Maximum Likelihood Sequence Detection (MLSD)
algo-rithmhasbeenproposed. It wasshownthat,with theaid
oftheFHpatternsderivedfromagroupofconstant-weight
codeshavingagiven minimumdistance, the FHpatterns
canbesuccessfullyacquired,while simultaneously
detect-ingthetransmittedinformation.
V. Performance Results
In this section, the average BER performance of the
FH/MC DS-CDMA system is evaluated as a function of
the average received Signal-to-Noise Ratio (SNR) per bit
orasafunction ofthenumberof activeusersforthe
pro-posedsystem describedabove. Theperformanceis
evalu-ated overvarious multipath Nakagami-m fading channels
for the proposed FH/MC DS-CDMA system using slow
FH,whenseveralsymbolsaretransmittedduringeachFH
interval. The variables related to our investigations are
listedbelow,whilemoredetailsconcerningthesevariables
canbefoundin[4],[5].
N : NumberofchipsperbitbeforeSerial-to-Parallel
(S-P)conversionoftheFH/MCDS-CDMAsignal;
Q : Numberofsubcarriers;
U : Weightofconstant-weightcodes;
C(Q;U) : Constant-weightcodehavingalengthofQand
weightofU;
C(Q;U;d) : Constant-weightcode havingalength ofQ,
weightofU andminimumdistanceofd;
L : Numberofmultipathcomponents,ordiversityorder;
K : Numberofactiveusers;
m : FadingparameteroftheNakagamifadingchannels;
: Power-decayfactoroftheMultipathIntensityProle
(MIP),assuminganegativeexponentiallydecaying.
TheBERperformanceoftheconstant-weightcodebased
multirate FH/MC DS-CDMA systems using random FH
schemes is shown in Fig.3 and Fig.4 in termsof the
mul-tipath Nakagami-m fading channels having dierent
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Fig.3. BERversusSNRperbitperformancefortheconstant-weight
codebasedmultirateFH/MCDS-CDMAsystemoverboth
multi-pathRayleighfadingchannels(m=1)andmultipathNakagami
fadingchannels(m=3)forL=3uponvaryingthe numberof
dierentinformationratesprovided.Itisshownthatforagiven
valueofmtheBERincreases,asthenumberofinformationrates
providedincreases.
Fig.4. BERversusSNRperbitperformancefortheconstant-weight
codebasedmultirateFH/MCDS-CDMAsystemovermultipath
Nakagamifadingchannels(m=3)forL=3uponvaryingthe
numberofdierentinformationratesprovidedandthenumberof
activeusers,K.ItisshownthatforagivenvalueofK,theBER
increases,asthenumberofinformationratesprovidedincreases.
users (Fig.4). In Fig.3 we assumed m = 1
correspond-ingtomultipathRayleighfadingandm=3corresponding
tomultipathNakagamifading,whichalsocorrespondstoa
multipathRiceanfadingchannelassociatedwithK4:45.
InFig.3andFig.4,asingle-rate(1-rate)schemeiscreated
byemployingaweight-1constant-weightcodeC(8,1),while
a dual-rate (2-rate)system is supported by the
constant-weight codes C(8,1) and C(8,2). Similarly, a triple-rate
(3-rate)systemiscreatedusingC(8,1),C(8,2)andC(8,4),
and a quadruple-rate (4-rate) system is generated by the
codes C(8,1), C(8,2), C(8,4) and C(8,8). Let R
b
be the
informationrateprovidedbyasinglesubcarrier. Sincethe
symboldurationof themultirateFH/MCDS-CDMA
sys-tem was assumedto be aconstant, theinformation rates R
b , 2R
b , 4R
b
and 8R
b
, respectively. From the results of
Fig.3andFig.4weobservethat foragivenfading
param-eterminFig.3orforagivennumberofactiveusers,K in
Fig.4, thesystem's performance degrades, asthe number
ofinformationratessupportedincreases. Taking m=3in
Fig.3asanexample, thetransmitted energyperbitmust
beincreasedbyabout0.8dB,inorderthatthesystemcan
supporttheinformationratesofR
b
and2R
b
(dot),instead
ofthe soleinformationrate ofR
b
(diamond),while
main-tainingaBERof10 6
. Similarly,afurther 1.1dBor 4dB
transmitted energy perbit must be invested, in order to
upgradethesystemfromatwin-rateto triple-rateorfrom
triple-ratetoquadruple-rate,respectively. Notethat since
ahigherinformationraterequiresahighernumberof
sub-carriers, this results in the concomitant reduction of the
subcarrier-SNR. Hence, in order to maintain a constant
BER,thesubcarrier-SNRreductionmustbecompensated
by increasing the transmitted energy per bit. However,
due to the MAI-induced error oor, the associated SNR
losssometimescannotbe compensatedbysimply
increas-ing the transmitted power, as seen in Fig.3 for m =1 in
theBERrange of10 5
to 10 4
. Theresults ofFig.4also
show that as expected, the BER performance of FH/MC
DS-CDMA is degraded, when the numberof active users
increases.
Fig.5. BERversusSNRperbitperformanceoftheconstant-weight
codebased FH/MCDS-CDMA systemusingthe MLSD based
blindsoft-detection,undertheassumptionofconstantspreading
gain for multirate based systems. Under the multirate
trans-mission,similarBERperformancecanbeachievedbyinvoking
limitationsonthetransmittedFHcodes.
Inthe contextof theFH/MC DS-CDMAschemeusing
blind jointsoft-detection, since the receivermust acquire
theFHpatterns,while detectingthetransmitted
informa-tion,themostimportantperformancemeasureisthebit
er-rorprobabilityofdatadetectionandtheFHpattern
acqui-sition probability. Accordingly, in Fig.5a multirate
com-munication system was evaluated, under the assumption
that alltheinterferingusersemployedthesame
constant-weight code, namely C(32,16) and that the receiver had
Fig. 6. Acquisition success (AS) probability performance of the
constant-weightcodebasedFH/MCDS-CDMAsystemusingthe
MLSDbasedblindsoft-detection,undertheassumptionof
con-stant spreading gain for multirate based systems. If the SNR
perbitissuÆcientlyhigh,blindjointsoft-detectionscanacquire
theFHpatternsusedwithhighprobability,whiledetecting the
transmittedinformation.
Theconstant-weightcodesC(32,2,1),C(32,4,2),C(32,8,4),
C(32,14,8),C(32,16,16)andC(32,32)wereassumed,where
theconstant-weightcodeC(Q;U;d)were denedin terms
of their length, weights and minimum distance Q, U and
d, respectively. By observing the curves associated with
C(32,8,4), C(32,14,8), C(32,16,16) and C(32,32) we
con-clude that even though the systems transmit at dierent
rates,amoreorlesssimilarBERperformancecanbe
main-tained, when the channel quality is suÆciently high. By
contrast, the BER performance of the system using the
codesC(32,2,1)andC(32,4,2)wasinferiorwithrespectto
theothers',whichwasaconsequenceoftheirlowdistance.
Finally,inFig.6wecharacterizedtheAcquisitionSuccess
(AS) probability of the MLSD-based blind soft-detection
for the multirate transmission scenario, under the
as-sumptionthat alltheinterferingusersemployedthesame
constant-weight code, namelyC(32,16). Fromthe results
weobservethatif theSNR perbit issuÆcientlyhigh, all
thecurveswillreachanear-unityAS probability. This
al-lowsthereceivertoblindly acquire arestrictedset of FH
patterns exhibiting a minimum distance of d. These FH
patterns canbeusedbythetransmitter signallingthe
ac-tualFHpatternsusedforthetransmissionof`payload'
in-formationtothereceiver. Moreexplicitly,accordingtothe
above philosophy, a reduced set of constant-weight
code-wordshavingaminimumdistanceofdisusedforconveying
theside-informationconstitutedbytheFHpatternstobe
usedbythereceiverforpayloadinformationrecovery.
Dur-ingtheconsecutiveinformationtransmissionphasethena
randomlyselectedsetofFHpatternsfromthe Q
U
number
of FHcodes canbeused without imposing any minimum
distance limitations. In other words, following the blind
detection of the 'side-information' constituted by the FH
patterns used by the transmitter, successive
communica-tions can be based on the explicit knowledge of the FH
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