通信原理英文版教学课件：class six-2FSK

26.1

IntroductionSinusoidalcarrier: orwhereA

－amplitude(V);f0

－frequency(Hz);

0=2f0

－angularfrequency(rad/s);

－initialphase(rad).Basicmodulationsystems:ASKFSKPSK3Vectorrepresentationandvectordiagram46.2

2ASK(Binaryamplitudeshiftkeying（二进制信号)6.2.1BasicprincipleExpression:

where0

＝2f0---istheangularfrequencyofcarrier

andA(t)isarectangularwaveform.

ModulationmethodsMultipliermethod:

envelopemaybenonrectangularSwitchingmethod:envelopemustberectangular5DemodulationmethodsEnvelopedetectionmethod

－carrierphaseinformationisnotused.Coherentdemodulationmethod－carrierphaseinformationisused.RemovenoiseRemovenoiseFlashDemo76.2.2PowerSpectralDensityAssumethegeneralexpressionofthe2ASKrandomsignalis

an

－binaryunipolarrandom

amplitude,itequalsto0or1

g(t)－symbolwaveform

T

－durationofthesymbol

thenthepowerspectraldensityofthe2ASKsignalcanbecalculatedas

式中，Ps(f)－powerspectraldensityofs(t)

PA(f)

－powerspectraldensityofA(t)

∴IfPA(f)hasbeenfound,thenPs(f)canbecalculatedbysubstitutingPA(f)intotheaboveequation.8FindPA(f):fromeq.(5.5-29):

wherefc

＝1/T

G1(f)－frequencyspectrumofg1(t) G2(f)－frequencyspectrumofg2(t)

∵Now,g1(t)=0,∴Theaboveequationbecomes

whereG(f)=G2(f)

Andifg2(t)isrectangularpulse,thenSowehaveSo9Find

Ps(f):fromtheaboveequation:

When

P=½,theaboveequationbecomesAndTherefore,wehaveFinally,weobtain10CurvesofPA(f)

andPs(f)(b)CurveofPs(f)(b)CurveofPA(f)Aftermodulation,thebandwidthistwiceofbasebandsignal.116.2.3SymbolErrorProbabilityAssumethesignalafterbandpassfilteringequalstowhere

∵n(t)isanarrowbandGaussianprocess,wehaveSubstitutingtheabovetwoequationsintoy(t),weobtain:

.12

Coherentdemodulation

Thevoltagex(t)atthesampling&decisionpointis

wherenc(t)－Gaussianprocess

∴When1istransmitted,theprobabilityofx(t)

is

When0istransmitted,theprobabilityofx(t)is13Let

h

be

thedecisionthreshold,thentheprobabilityofthewrongdecisionof0as1

isequaltowhere

Theprobabilityofwrongdecisionof0as1is14WhenP(1)=P(0),thetotalsymbolerrorprobabilityis

Whenhequalstheoptimumthresholdh*,Whenr>>1,

15Envelopedetection

∵Theoutputistheenvelopeofitsinputvoltage

y(t),wehave

Ifthedecisiontheresholdequalsh,anditisprescribedthatwhenV>h,thedecisionisreceived1,andwhenV

h,thedecisionisreceived0,thenitssymbolerrorprobabilitycanbefiguredout.Whenthesignaltonoiseratioislarge,thesymbolerrorprobabilityis:16

【Example

6.1】Fora2ASKsignaltransmissionsystem,assumethesymbolrateisRB=4.8106Baud,theamplitudeofthereceivedsignalA=1mV,thesingle-sidepowerspectraldensityoftheGaussiannoisen0=210-15W/Hz.Find:1）theoptimumsymbolerrorprobabilitywhenenvelopedecisionisused;2）theoptimumsymbolerrorprobabilitywhencoherentdemodulationisused.

17Solution:Thebandwidthofthebasebandrectangularpulsecanbeselectedas1/THz.Thebandwidthofthe2ASK

signalshouldbetwiceofit,i.e.,2/THz.Henceaccordingtothesignalrate,theoptimumbandwidthofthebandpassfilterinthereceivershouldbeselectedas:B2/T=2RB=9.6106Hz

Thereforethemeanpoweroftheoutputnoiseofthebandpassfilteris:

Henceitsoutputsignaltonoiseratiois:

∴（1）thesymbolerrorprobabilityfortheenvelopedetectionis

（2）thesymbolerrorprobabilityforthecoherentdemodulationis186.3

2FSK 6.3.1BasicPrincipleExpression:GenerationmethodsFrequencymodulationmethod:

phasecontinuousSwitchingmethod:

phasediscontinuous2FSKproductionFlashDemo20ReceptionmethodsCoherentreceiving:Noncoherentreceiving:Envelopedetection:EnvelopeDetectionDemo22Zero-crossingpointdetectionZero-CrossingPointDetectionFlashDemo24

6.3.2

PowerSpectralDensity

2FSKsignalcanberegardedasthesuperpositionoftwo2ASKsignalswithdifferentfrequencies:

where∵Powerspectraldensityof2ASKsignalis ∴

thepowerspectraldensityof2FSKsignalshouldbethesumofthepowerspectraldensitiesoftwo2ASKsignals:

6.3.2

PowerSpectralDensity

∵

Substitutingitintotheaboveequation,thepowerspectraldensityof2FSKsignalisobtainedas:26

Whentheprobabilitiesoftransmitting1andtransmitting0areequal,P=½,theaboveequationcanbereducedas:WhereG(f)isthefrequencyspectrumofbasebandpulseand

Sowehave

27

Ascanbeseenfromtheaboveequation,theforgoing4termsarethecontinuousspectrumpartandthelatter4termsarethediscretespectrumpart.Curves:Bandwidth:28

6.3.3MinimumFrequencySpace

Inprinciple,iftwosignalsareorthogonal,thentheycanbeseparatedcompletely.

Fornoncoherentreception:let2FSKsignalbe

forsatisfactionoforthogonalcondition,require:

i.e.,require

29

6.3.3MinimumFrequencySpace

Theintegratedresultoftheaboveequationis

Assumethefirstandthirdtermsequalzero,thentheaboveequationcanbereducedtoSince1

and0

arearbitraryconstants,itmustsimultaneouslyhave

Hencewehave

So

30

itequalwhenm=1,itgivestheminimumfrequencyspace1/T.Forcoherentreceiving,letthentheequationcanbereducedto

Hence,itisonlyrequiredthati.e.,theminimumfrequencyspaceequals1/2T

.316.3.4

SymbolErrorProbabilityAssumetheoutputvoltagewaveformofthefilterisSymbolErrorProbabilityofCoherentDemodulation

Whenthesymbol1istransmitted,thetworeceivedvoltagesafterpassingthetwobandpassfiltersis:Theyaremultipliedbythelocalcarrier,andthenlow-passfiltered.Hence,weobtain

andNormalvariablewith(A,n2)Normalvariablewith(0,

n2)33Duringdecision,once

V1<V0,thesymbolerrorwillbeoccurred.Thereforethesymbolerrorprobabilityis

Let

(A+n1c-n0c)=z,then

z

isalsoanormalrandomvariable,anditsmeanequalsA,itsvarianceis

Hence,wehave

where

—signaltonoiseratio

∵Pe0

andPe1

areequal,thetotalsymbolerrorprobabilityis:34SymbolErrorProbabilityofEnvelopeDetection

Whenthesymbol1istransmitted,thetwovoltagesatthesampling&decisiondeviceinputrespectivelyare

and

whereV1(t)－envelopeofthesignalinthepathoffrequencyf1;(generalizedRayleighdistribution) V0(t)－envelopeofthesignalinthepathoffrequencyf0;(Rayleighdistribution)35weobtainwhere —signaltonoiseratio

When0istransmitted,thesituationoferroroccurringisthesameasabove.So,thetotalsymbolerrorprobabilityis36Comparisonofsymbolerrorprobabilitiesofcoherentdetectionandenvelopedetection:Thereisnobigdifferencebetweenthemundertheconditionoflargesignaltonoiseratio.Inpracticalapplication,envelopedetectionismoreoftenused.

Comparisonofsymbolerrorprobabilitiesof2FSK

and2ASKsignals:Envelopedetection2ASK：

3dBdiference2FSK：Coherentdetection2ASK：

3dBdifference2FSK：37【Example6.2】Assumethereisa2FSKtransmissionsystem,itstransmissionbandwidthis2,400Hz;theapparentcarrierfrequenciesofthe2FSKsignalarerespectivelyf0=980Hz