通信原理英文版教學課件：class six-2ASK

26.1

IntroductionSinusoidalcarrier: orwhereA

－amplitude(V);f0

－frequency(Hz);

0=2f0

－angularfrequency(rad/s);

－initialphase(rad).Basicmodulationsystems:ASKFSKPSK3Vectorrepresentationandvectordiagram46.2

2ASK6.2.1BasicprincipleExpression:

where0

＝2f0---istheangularfrequencyofcarrier

andA(t)isarectangularwaveform.

ModulationmethodsMultipliermethod:

envelopemaybenonrectangularSwitchingmethod:envelopemustberectangular5DemodulationmethodsEnvelopedetectionmethod

－carrierphaseinformationisnotused.Coherentdemodulationmethod－carrierphaseinformationisused.RemovenoiseRemovenoise66.2.2PowerSpectralDensityAssumethegeneralexpressionofthe2ASKrandomsignalis

wherean

－binaryunipolarrandom

amplitude

g(t)－symbolwaveform

T

－durationofthesymbol

thenthepowerspectraldensityofthe2ASKsignalcanbecalculatedas

式中，Ps(f)－powerspectraldensityofs(t)

PA(f)

－powerspectraldensityofA(t)

∴IfPA(f)hasbeenfound,thenPs(f)canbecalculatedbysubstitutingPA(f)intotheaboveequation.7FindPA(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)

Now,thesymbolwaveformofthebasebandsignalisarectangularpulse,soitisknownG(nfc)=0forall

integersofn

0.ThereforetheaboveequationbecomesSowehave8Find

Ps(f):fromtheaboveequation:

When

P=?,theaboveequationbecomeswhereTherefore,wehaveFinally,weobtain9CurvesofPA(f)

andPs(f)(b)CurveofPs(f)(b)CurveofPA(f)106.2.3SymbolErrorProbabilityAssumethesignalafterbandpassfilteringequalstowhere

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

.11

Coherentdemodulation

Thevoltagex(t)atthesampling&decisionpointis

wherenc(t)－Gaussianprocess

∴When1istransmitted,theprobabilityofx(t)

is

When0istransmitted,theprobabilityofx(t)is12Let

h

be

thedecisionthreshold,thentheprobabilityofthewrongdecisionof0as1

isequaltowhere

Theprobabilityofwrongdecisionof0as1is13WhenP(1)=P(0),thetotalsymbolerrorprobabilityis

Whenhequalstheoptimumthresholdh*,Whenr>>1,

14Envelopedetection

∵Theoutputistheenvelopeofitsinputvoltage

y(t),wehave

Ifthedecisiontheresholdequalsh,anditisprescribedthatwhenV>h,thedecisionisreceived1,andwhenV

h,thedecisionisreceived0,thenitssymbolerrorprobabilitycanbefiguredout.Whenthesignaltonoiseratioislarge,thesymbolerrorprobabilityis:15

【Example

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

16Solution:Thebandwidthofthebasebandrectangularpulsecanbeselectedas1/THz.Thebandwidthofthe2ASK

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

Thereforethemeanpoweroftheoutputnoiseoftheband