RADIAL BASIS FUNCTION DECISION FEEDBACK EQUALISERASSISTED
BURST-BY-BURST ADAPTIVE MODULATION
M. S. Yee, L. Hanzo
Dept. ofElectr. andComp. Sc., Univ. ofSouthampton, SO171BJ, UK.
Tel: +44-703-593 125,Fax: +44-703-594508
Email:[email protected], http://www-mobile.ecs.sot on.a c.u k
ABSTRACT
The performance of radial basis function decision
feedback equalised burst-by-burst adaptive
modu-lation ispresentedfor transmissionoverdispersive
wideband mobile channels. Radial Basis Function
(RBF)networkbasedchannelequalisershaveaclose
relationship with Bayesianschemes. The RBF
de-cisionfeedback equaliser (RBFDFE) iscapable of
estimating the 'short term bit error rate' of the
received data burst and this estimate is used as
the modem mode switching criterion in order to
switchbetweendierentmodulationschemes. This
schemeis shown to give asignicant improvement
intermsofmeanbit errorrate(BER)andbits per
symbol(BPS)performancecomparedtothatofthe
individual xedmodulation schemes.
1. BACKGROUND
Burst-by-burst Adaptive Quadrature Amplitude
Modula-tion(AQAM) schemes employ ahigher-order modulation
scheme,whenthechannelqualityisfavourable,inorderto
increasethethroughputandconversely,amorerobustlower
ordermodulation schemeis utilized toimprovethe mean
BERperformance, whenthe channel envelopeencounters
adeepfade. Theprinciples of AQAM schemewere
sum-marizedforexamplebyWong[1 ]et al. In thispaper, we
presentanovel adaptivemodemschemefortransmissions
over wideband mobile channels, which employs a Radial
BasisFunction (RBF)based channel equaliser with
deci-sionfeedback,inordertomitigatetheeectsofthe
disper-sive widebandchannel. Chen, McLaughlin, Mulgrewand
Grant[2 ]proposedarangeofso-calledRBFnetworkbased
channelequalisers, whichare potentially capableof
error-freely detectingthe received signalling symbols even in a
scenario,wherethephasorsbecomelinearlynon-separable
duetothe inter-symbol interference (ISI)inicted bythe
channel. Inthissituationconventionalequaliserswouldbe
unabletoremovetheeectsofISIandhencewouldexhibit
aresidualBER.Additionally,Chenetal.[3]introduced
de-cisionfeedbackintheirRBF-basedequaliser,inorderto
re-duceitscomputationalcomplexity.TheRBFdecision
feed-back equaliser (RBFDFE) wasthenextended to
higher-orderQAM schemes, which wereinvestigated in[5 ]. The
Thenancialsupportofthefollowingorganisationsis
grate-fullyacknowledged: MotorolaECID,Swindon, UK;European
Community, Brussels,Belgium; Engineering and Physical
Sci-encesResearchCouncil,Swindon,UK;MobileVirtualCentreof
Excellence,UK.
reader is referred to the above references forbackground
reading.
2. SYSTEMOVERVIEW
ThestructureofthejointAQAMandRBFnetworkbased
equalisationschemeisportrayedinFigure1. Thereceiver
rstextractsthemodulationmodeusedinitsreceiveddata
burst. Atthesametimethecorruptedreceiveddataburst
is equalised, the BER of the transmitted burst is
calcu-latedattheoutputof theRBFDFEanditisusedasthe
AQAMmodemmodeswitchingcriterioninorderto
deter-minethemodemmodetobeusedduringthenext
transmis-sionburst. Thisregimeassumes aTimeDivision Duplex
(TDD)arrangement,wheretheuplink(UL) channel
qual-ityisestimatedonthebasisoftheDownlink(DL)channel
quality.
Modulation
Mode
Switch
Switching
Threshold
Look-up Table
Modulation
Level
Estimator
Modulation
Mode of Data
Burst
Short Term
Probability of
Bit Error of the
Data Burst
Equalised
Data
DFE
RBF
Data
Transmitter
Noise
Channel
Receiver
Figure1: Systemschematicof thejoint adaptive
modula-tionandRBFequaliserscheme
2.1. Switching Criterion
TheM-QAMRBFequaliserof[5]consistsofMRBF
net-worksthatprovidetheconditionalprobabilitydensity
func-tionofeachlegitimateQAMsymbol,Ii;i=1;:::;M,ifthe
channelimpulseresponse(CIR)isknown. Furthermore,the
centers oftheRBFnetworkare assignedthevaluesofthe
channelstates. TheoutputsoftheRBFnetworksaregiven
by[2 ,3,5]:
i
(v k
) =
ns X
j=1 w
j '
j (v
k );
'j(vk) = exp( kvk cjk
2 =2
2 );
i=1;:::;M (1)
where is the RBF width, wj are the RBF weights, cj
are the RBFcenters andns isthe numberof the hidden
probability ofeachlegitimate M-QAMsymbol, &i(k);i=
1;:::; M can be evaluated from the conditional density
function,iofEquation1asfollows:
&i(k) = P(I
k
=Iijv k
)
=
i (v
k )P(I
k
=I
i )
P(vk)
: (2)
Therefore{fromthea-posterioriprobabilitiesofsymbols{
wecanobtainthea-posterioriprobabilitiesofthebits
rep-resentingthe QAMsymbols. The a-posterioriprobability
oftheithbitoftheQAMsymbolsbeing0,forexample,is
thesumofthea-posterioriprobabilitiesofthesymbolswith
theirithbitbeing0.Therefore,theprobabilityofbiterror
associatedwiththedecisionthattheithbithasthevalue
(either0or1)exhibitingthemaximuma-posteriori
proba-bility,~& i bit
(k),isgivenbyP i b
(k)=1 &~ i bit
(k). Giventhe
probabilityofbiterror,P i b
(k),fortheithbitofanAQAM
symbol,theaverage probabilityofbiterrorfor adetected
AQAMsymbolatsignallinginstantkisgivenby
P b
(k)= P
BPS-1 i=0
P i b
(k)
BPS
; (3)
whereBPSisthenumberofbitsperAQAMsymboland
theoverallprobabilityofbiterrorforthedetectorisgiven
byP bit
=EfP
b (k)g.
For our joint AQAMand RBF DFE scheme, we are
unable to employ the true average probability of bit
er-ror P bit
as the modemmodeswitching criterion, since a
promptburst-by-burstbasedmodemmodeselectionis
re-quired. Henceweinvokedtheestimatedshort term
prob-ability of bit error or BER, P
bit,short-term
, which was
estimatedby averaging P b
(k) of Equation 3 over a single
transmissionburstaccordingto:
P
bit,short-term =
P F n=1
Pb(n)
F
; (4)
whereFisthenumberofAQAMsymbolsperframe. Thus,
wecouldestimatethechannelqualityonaframe-by-frame
basis,basedontheestimatedP
bit,short-term value.
The estimated short-term BER perceived by the
re-ceiveriscomparedtoasetofswitchingBERvalues
corre-spondingto thevariouslegitimatemodulationmodesand
themodulationmodeisselectedfor thenexttransmission
burstassumingreciprocityoftheuplinkanddownlink. This
impliesthatthesimilarityoftheshort-termBERof
consec-utiveULandDLdataburstscanbeexploited,inorderto
setthenextmodulationmode. Themodulationmodes
uti-lizedinoursystemareBPSK,4-QAM,16-QAM,64-QAM
andnotransmission(NOTX).
Therefore,themodulationmodeisswitchedaccording
totheestimatedshort-termBER,P
bit,short-term ,as
fol-lows:
Mod.
Mode =
8 > > > > > <
> > > > > :
NOTX ifP
bit,short-term
P
M 2
BPSK ifP
M 2
>P
bit,short-term
P
M 4
4QAM ifP
M 4
>P
bit,short-term
P
M 16
16QAM ifP
M 16
>P
bit,short-term
P
M 64
64QAM ifP
M 64
>P
bit,short-term ,
(5)
whereP M i
;i=2;4;16;64aretheswitchingBERthresholds
correspondingtothevariousM-QAMmodes.
3. SIMULATIONRESULTS
3.1. Assumptions
In our simulations the following assumptions were
stipu-lated:
1. Perfectchannelimpulseresponseestimationor
chan-nel state estimation was used at the receiver. The
RBFs'centerswere assignedthevaluesofthe
chan-nelstates[5 ].
2. The channel impulse response is time-invariant for
the duration of the transmission burst, but varies
fromburstto burst,whichcorrespondstoassuming
thatthechannelisslowlyvarying.
3. Weassumedfurthermorethatthereceiverhad
per-fect,ieerror-freeknowledgeofthemodulationmode
usedinitsreceivedtransmissionburst.
4. The RBF DFE used in the system neglected error
propagationduetoerroneousdecisionfeedback,which
inpracticaltermsimpliedanegligiblylowprobability
ofsymbolerrors,hencefeedingthecorrectsymbolto
theRBFsubsetcenterselectionprocess[5].
3.2. Simulation Model and BER-motivated Mode
Switching
Inourexperimentspseudo-randomsymbolswere
transmit-tedinaxed-lengthburst. Thesimulationparametersare
listedinTable1,notingthatweanalysedthejointAQAM
and RBF equaliser scheme over a two-path equal-weight
Rayleighfadingchannel. Thewidebandfadingchannelwas
frame-invariant.TheRBFDFEusedinoursimulationshad
afeedforwardorderofm=2,feedbackorderofn=1and
decisiondelayof=1. Wewillanalysetheperformanceof
thejointAQAM/RBF DFEfor two systems, ahigher
in-tegrityscheme,havingatargetBERof10 4
,whichcanbe
renderederror-freebyerrorcorrectioncodingandhencewe
referredtothisarrangementasadatatransmissionscheme;
thelowerintegrityschemewas designedformaintaininga
BERof10 2
,whichisadequateforspeechtransmission
es-peciallyinconjunctionwithFEC.ThetargetBPSvaluesof
theseschemeswere3and4.5bitspersymbol,respectively.
No.ofdatasymbolsperburst 144
No.oftrainingsymbolsperburst 27
TransmissionFrequency 1.9GHz
TransmissionRate 2.6MBd
VehicularSpeed 30mph
NormalisedDopplerFrequency 3:310
5
Channelweights 0:707+0:707z
1
Table1: Simulationparameters
The BER switching thresholds corresponding to
M-QAM,P
M i
;i=2;4;16;64,can beobtainedbyestimating
theBERdegradation/improvement,whenthemodulation
mode is switched from M-QAM to a higher/lower
num-ber of modulationlevels. In this experiment, we obtain
thisBER degradation/improvement measurefromthe
es-timatedshort-termBER ofeverymodulationmodeused,
underthesameinstantaneouschannelconditions. Figure2
10
-16
10
-15
10
-14
10
-13
10
-12
10
-11
10
-10
10
-9
10
-8
10
-7
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
Estimated Short-term BER of 4 QAM
10
-5
2
5
10
-4
2
5
10
-3
2
5
10
-2
2
5
10
-1
2
5
10
0
Estimated
Short-term
BER
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64 QAM
16 QAM
.
BPSK
64 QAM
16 QAM
4 QAM
BPSK
NO TX
Target BER bound
P
64
4
P
16
4
P
4
4
P
2
4
Figure2:Theestimatedshort-termBERforallthepossible
modulationmodesthatcanbeinvoked,assumingthatthe
currentmodeis4-QAM{versustheestimatedshort-term
BERof 4-QAMfor thetwo-pathRayleighfading channel
ofTable1.
modulationmodesthatcanbeinvoked,assumingthatthe
current modeis 4-QAM, versus the estimated short-term
BERof4-QAMunderthesameinstantaneouschannel
con-ditions. The short-term BERs of the modulation modes
areobtainedonaburst-by-burstbasisfromEquation4. In
ordertoobtainthetargetBERof10 2
,Figure2
demon-strateshoweachswitchingBERthresholdP 4 i
isobtained.
Forexample, if the estimated short-term BERof the
re-ceived4QAMtransmissionburstisbelowP 4 16
=10 12
,the
modulationmodecanbeswitchedto16-QAMforthenext
transmission burst, since theshort-term BERof this
16-QAMtransmissionburstisexpectedtobebelowthetarget
BERof10
2
.The4QAMerrorprobabilityofP 4 16
=10 12
used inthisexampleforswitchingto16QAMappears
ex-tremely conservative, but it is justied by the large
un-certaintyassociated with the estimation of the BER due
to the Rayleigh-fadedimpulse response taps. This
man-ifests itself also in the rather spread nature of the BER
estimatesinFigure2. Afeasible technique formitigating
thisphenomenonisemployingthefade-trackingschemeof
Figure11.2inReference[6 ].
UsingthemethoddemonstratedbyFigure2,the
switch-ing BER thresholdswere obtained for thetarget BERof
10 2
and 10 4
,as listed inTable 2 and Table 3,
respec-tively in the context of all possible combinations of the
modetransitions. Notethat theextremelylowvaluesfor
P 4 16
=110
45
andP
16 64
=110
50
inTable3were
ob-tainedbyextrapolatingthecurvessimilartoFigure2but
for16-QAMand64-QAM,respectively,inordertoachieve
thetargetBERof10 4
.
3.3. RBF/AQAMPerformanceComparisonwith
ConstituentFixedModulationSchemes
The performance of the joint AQAM/RBFDFE is
com-paredwiththatoftheconstituentxedmodulationschemes
in Figure 3. The BER and BPS performance was
eval-uated for two dierentadaptive modulation schemes. In
the rstscheme, the transmitteralwaystransmitteddata
withouttransmissionblockingordisabling. Bycontrast,in
P M 2 P M 4 P M 16 P M 64
NOTX 910
3
510
5
0:0 0:0
BPSK 110
2
510
5
0:0 0:0
4-QAM 610
2
110
2
110
12 0:0
16-QAM 210
1
110
1
110
2
110
8
64-QAM 310
1
210
1
910
2
110
2
Table 2: The switching BERthresholds P M i
of the joint
adaptivemodulationandRBFDFE schemefor thetarget
BERof 10
2
overthetwo-pathRayleighfadingchannelof
Table1. P M 2 P M 4 P M 16 P M 64
NOTX 910
5
110
15
0:0 0:0
BPSK 110
4
110
15
0:0 0:0
4QAM 1:510
2
110
4
110
45
0:0
16QAM 1:210
1
510
2
110
4
110
50
64QAM 2:210
1
1:510 1
310
2
110
4
Table 3: The switching BERthresholds P M i
of the joint
adaptivemodulationandRBFDFE schemefor thetarget
BERof 10
4
overthetwo-pathRayleighfadingchannelof
Table1.
the second scheme, dummydata was transmitted,
when-everthe estimatedshort-termBERofthereceivedBPSK
transmissionburstwashigherthanthetargetBER,a
sce-nario, which wereferedtoastransmission blocking. The
transmissionofdummydataduringblockingallowedusto
keepmonitoringthe BER,inordertodeterminewhento
commencetransmissionandinwhichmodemmode.
WewillcommencebyanalysingFigure3(a),wherethe
joint AQAM/RBF DFE scheme was designed for speech
transmision, i.e. for a BER of 10 2
. For the adaptive
scheme, which did notincorporate transmission blocking,
the performancewith adaptive modulation was better or
equivalenttotheperformanceofBPSKintermsofthemean
BERandmeanBPSfortheSNRrangebetween0dBand
8dB. Atthe channelSNRof 8dB, eventhough themean
BERperformanceisequivalentfortheBPSKmodeofthe
adaptiveschemeandforthexed-modeBPSKscheme,the
meanBPSfortheadaptiveschemeimprovedbyafactorof
1.35,resultinginameanBPSof1.35. IntheSNRrangeof
8dBto15dB,theadaptiveschemeoutperformedthe4QAM
scheme in terms of its mean BER performance. At the
channelSNRof15dB,themeanBERsofbothschemesare
equivalent,althoughthemeanBPSoftheadaptivescheme
is approximately 2.6, resulting in a substantial
improve-ment,whencomparedto4QAM.Theadaptiveschemethat
utilizedtransmissionblockingachievedameanBERbelow
10 2
.AstheSNRimproved,theperformanceofthe
adap-tiveschemesbothwithandwithouttransmissionblocking
converged,sincetheprobabilityofencounteringhigh
short-termBERsreduced. ThemeanBERandmeanBPS
per-formance of both adaptive schemes converged to that of
64QAMfor highSNRs, where 64QAMbecamethe
domi-nantmodulationmode.
Similartrendswereobservedfordata-quality
transmis-sion,i.e. for the10 4
However,wenotethatfortheSNRrangebetween8dBto
17dB,themeanBERoftheadaptiveschemewithout
trans-missionblockingwasbetter,thanthatofBPSK.This
phe-nomenonwasalsoobservedinthewidebandjointAQAM
andDFEschemeof[1 ],whichcanbeexplainedasfollows.
ThemeanBERofthesystemistheratioofthetotal
num-ber of biterrors tothe totalnumberof bits transmitted.
ThemeanBERwill decreasewithadecreasingnumberof
biterrorsandwith anincreasingnumberofthe totalbits
transmittedinthedataburst. Foraxednumberof
sym-bolstransmitted,thenumberoftotalbitstransmittedina
databurstisconstantfortheBPSKscheme,whileforthe
adaptiveschemethetotalnumberofbitstransmittedina
databurstincreased,whenahigher-ordermodulationmode
wasused. However,whenahigher-ordermodulationmode
wasusedfortransmission,theprobabilityoferroneousbits
increased. Ifthe relativebits per symbolincrementupon
usingAQAMishigherthantherelativebiterrorratio
in-crement,thenthemeanBERofthe adaptiveschemewill
beimproved.ConsequentlytheadaptivemeanBERcanbe
lowerthanthatofBPSK.
Insummary,the joint adaptivemodulation and RBF
DFEschemehasitsadvantages,whencomparedtothe
indi-vidualxedmodulationschemesintermsofmeanBERand
meanBPSperformance.Notehoweverthatthetarget
per-formanceforspeechanddatatransmissionintermsof the
meanBPS(4.5and3,respectively)canonlybeachievedfor
theadaptiveschemewithandwithouttransmission
block-ing, ifthe channel SNR isabove about 22dB. Thus, the
advantageof using anadaptiveschemewith transmission
blocking isthatthe performanceof the joint AQAM and
RBFDFEschemecanbe'tuned'toacertainrequiredmean
BERperformance. Furthermore,duetothemodemmode
switchingtheassociatedbiterrorsexhibitalessburstyerror
distributionthanthatofxedmodems,whichrendersthe
AQAMschememoreamenabletochannelcoding,resulting
inhigherchannelcodinggains. However,thedisadvantage
is that the utilization of transmission blocking results in
transmissionlatency-anissuewhichwasaddressedin
ref-erence[7 ].
3.4. ComparisonwithUpperBound Performance
In this section, wecompare the performance of the joint
AQAM/RBFDFE withitsupperboundperformanceand
derivetheBERswitchingthresholds, P M i
;i =2;4;16;64.
Inderivingtheupperboundperformanceofthejoint
adap-tive modulation and RBF based equalisation scheme, in
addition tothe assumptionslistedin Section3.1, wealso
assumethattheshort-termBERestimateP
bit,short-term
isknownpriortotransmissionforallthemodulationmodes
used inthe system. We also assumethat given the
esti-matedP
bit,short-term
foraparticularmodulationmode,
thetransmitterhasperfectknowledgeofthecorresponding
short-termprobabilityofbiterrorfortheothermodulation
modes usedinthe systemunder thesame channel
condi-tions.
Inourexperimentspseudo-randomsymbolswere
trans-mitted in a xed-length burst for all modulation modes
overtheframe-invariantwidebandchannel. Thereceiver
re-ceivedeachdata bursthavingdierentmodulation modes
and equalised each oneof them independently. The
esti-matedshort-termBERforeachmodulationmodewas
ob-0
5
10
15
20
25
30
35
40
SNR (dB)
10
-7
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
BER
0
5
10
15
20
25
30
35
40
0
1
2
3
4
5
6
BPS
64 QAM BER
16 QAM BER
4 QAM BER
BPSK BER
without TX blocking
TX blocking
- BER :
AQAM RBF DFE
without TX blocking
TX blocking
- BPS :
AQAM RBF DFE
(a)SpeechTransmission
0
5
10
15
20
25
30
35
40
SNR (dB)
10
-7
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
BER
0
5
10
15
20
25
30
35
40
0
1
2
3
4
5
6
BPS
64 QAM BER
16 QAM BER
4 QAM BER
BPSK BER
without TX blocking
TX blocking
- BER :
AQAM RBF DFE
without TX blocking
TX blocking
- BPS :
AQAM RBF DFE
(b)DataTransmission
Figure 3: The BER and BPS performance of the joint
AQAM/RBFDFE,showingalsotheBERperformanceof
theconstituentxedmodulationschemes,namelyBPSK,
4-QAM,16-QAMand64-QAM,overthetwo-path
Rayleigh-fadingchannelofTable1.Themodemmodeswitching
lev-elsusedforthe jointAQAM/RBFDFE schemearelisted
inTable2.
tained. Thehighest-ordermodulationmode,M
that
pro-videdashort-termBERP M
bit,short-term
,whichwasbelow
thetargetBERP
bit,target ,when:
M
=max
(
M=2;4;16;64;
suchthatP M
bit,short-term
P
bit,target g
;
(6)
waschosentobetheactualmodulationmodethatwasused
bythetransmitteranditsreceivedequalisedframewasused
fortheactualBERcalculationofthesystem.
Figure 4(a) shows the BERand BPS performance of
the joint AQAM/RBF DFE scheme designed for
speech-transmissionwiththeswitchingthresholdsgiveninTable2
{whenusingthecurrentreceivedframe'sBERestimate,in
transmis-0
5
10
15
20
25
30
35
40
SNR (dB)
10
-7
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
BER
0
5
10
15
20
25
30
35
40
0
1
2
3
4
5
6
BPS
without TX blocking
TX blocking
without TX blocking - upper bound
TX blocking - upper bound
BER :
without TX blocking
TX blocking
without TX blocking - upper bound
TX blocking - upper bound
BPS :
(a)SpeechTransmission
0
5
10
15
20
25
30
35
40
SNR (dB)
10
-7
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
BER
0
5
10
15
20
25
30
35
40
0
1
2
3
4
5
6
BPS
without TX blocking
TX blocking
without TX blocking - upper bound
TX blocking - upper bound
BER :
without TX blocking
TX blocking
without TX blocking - upper bound
TX blocking - upper bound
BPS :
(b)DataTransmission
Figure 4: The BER and BPS performance of the joint
AQAM/RBFDFEschemeusing the current BER
es-timate in order toestimate thenext burst's
trans-mission mode, and its upperbound performance, using
theparameterslistedinTable1. Themodemmode
switch-inglevelsusedfor thejointAQAM/RBFDFEschemeare
listed inTable 2 andTable 3 for speech-transmission and
data-transmission,respectively.
sion burst{ in contrast toitsupperbound performance.
Theperformancecomparisonshowsthatthereislittle
per-formance degradation, when the current received burst's
short-termBERestimateisusedtocontrolthemodulation
modeof thenext transmissionburstbasedonthe
switch-ingparametersofTable2fortheAQAMschemedesigned
for speech transmission. Since the channel of Table 1 is
slowlyvarying,the performanceof thejointAQAM/RBF
DFEschemebasedontheswitchingparametersofTable2
iscomparabletoitsupperboundperformance.
Figure4(b)showstheBERandBPSperformanceofthe
jointAQAM/RBFDFEschemedesignedfor
data-transmis-sionwiththeswitchingthresholdsgiveninTable3in
com-parison to its upper bound performance. The
degrada-tion withrespecttothe upperbound performanceof the
AQAM/RBFDFE schemedesignedfor data-transmission
is more signicant compared to the adaptive scheme
de-signedfor speech-transmission,asseeninFigure4(a)and
Figure4(b). NotethatforthelowBERswitching
thresh-oldsofP 4 16
(=110 45
)andP 16 64
(=110
50
)inTable3,
whichwereusedintheadaptiveschemeforthetargetBER
of 10 4
,the RBFDFE isunable toprovidea high
accu-racyBERestimate. AstheSNRimproves, thefrequency
of encountering the switchingthresholds P 4 16
and P
16 64
in-creasesandthustheperformancedegradationcomparedto
theupperboundincreases.
4. CONCLUSIONS
TheRBFDFEwasshowntoprovidean'on-line'BER
es-timationofthereceiveddataburst,whichwasusedasthe
modemmodeswitchingcriterionfortheadaptive
modula-tionscheme. Oursimulationresults showedthatthe
pro-posedRBF DFE-assisted burst-by-burstadaptivemodem
outperformed the individualconstituentxed modulation
modes interms of meanBERand BPS performance. A
methodtoobtaintheswitchingBERthresholdsofthejoint
AQAM/RBFDFEschemewasproposedandwasshownto
providelittleperformancedegradationincomparisontothe
associatedupperboundperformance.
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