ECE 4371, Fall, 2009OverviewSignal to Noise RatioSNRNoise in linear receiver using coherent detectionSlide 6Slide 7Noise in AM receiver using envelope detectionSlide 9Slide 10Slide 11Threshold EffectSystem Model and Noise ModelSignal after bandpass filterDiscriminator OutputNoise After DiscriminatorNoise After Discriminator cont.Slide 18SNR of FMSingle Tone FM SNRFM Threshold EffectExampleSlide 23FM Threshold Reduction (tracking filter)FM Preemphsis and DeemphasisSlide 26Slide 27Comparison of the noise performance of various CW modulation systems. Curve I: Full AM, m = 1. Curve II: DSB-SC, SSB. Curve III: FM, b = 2. Curve IV: FM, b = 5. (Curves III and IV include 13-dB pre-emphasis, de-emphasis improvement..)Slide 29ECE 4371, Fall, 2009Zhu HanDepartment of Electrical and Computer EngineeringClass 7Sep. 15th, 2009OverviewOverviewHomework HintSignal to Noise RatioAM with noise–Coherent decoder–Non-coherent decoderFM with noise–Analysis–Threshold effect–Preemphasis and deemphasisSignal to Noise RatioSignal to Noise RatioChannel model: additive white Gaussian noise (AWGN)Receiver model: a band-pass filer followed by an ideal demodulator Receiver modelIdealized characteristic of band-pass filtered noise.The baseband transmission model, assuming a message signal of bandwidth W, used for calculating the channel signal-to-noise ratio.The PSD of w(t) is denoted by20NSNRSNR(2.81) (SNR)(SNR)merit of Figureoutput at the noise ofpower averagesignal ddemodulate theofpower average)SNR(ratio noise-to-signaloutput The)( ofpower average)( ofpower average)SNR(ratio noise-to-signal channel The(2.80) )()()(ison demodulatifor signal filtered The(2.79) )2sin()()2cos()()(:tionrepresenta noise narrowbandin noise filtered TheCOOCtntstntstxt ftnt ftntncQcINoise in linear receiver using coherent detectionNoise in linear receiver using coherent detectionModel of DSB-SC receiver using coherent detectionfactor scalingdependent system:C(2.84) (baseband) 2 2(SNR)(2.83) )()()2cos()(022022DSBC,WNPACWNPACdffSPtmt fCAtsccWWMcc  detector.coherent by the rejected completely is )( 2. output.receiver at the additive are )( and )( 1. :indicates (2.86)(2.86) )(21)(21)(filter pass-Low componentsfrequency high )4sin()(21)4cos()()(21 )(21)(21 )2()cos()((2.85) )2sin()()2cos()()()2cos( )()()(tntntmtntmCAtyt ftnt ftntmCAtntmCAt ftxtvt ftnt ftntmt fCAtntstxQIIccQcIcIcccQcIcc59Noise in linear receiver using coherent detectionNoise in linear receiver using coherent detectionproblem! Serious bandwidth. and eperformancbetween off- tradeNo 2.SC-DSB ofmerit of figure same thehas SSBCoherent 1.(2.88) 1(SNR)(SNR)(2.87) 224)SNR(212)21(power ))(21( noise average The2Let 4power ))(21( signaloutput average TheSC-DSBCO022022SCDSBO,00222WNPACNWPACWNWNtnWBPACtmCAccITcc60Noise in linear receiver using coherent detectionNoise in linear receiver using coherent detectionNoise in AM receiver using envelope detectionNoise in AM receiver using envelope detectionModel of AM receiver )2cos()()2cos( (2.89) )2cos()(1)(t ftmkAt fAt ftmkAtscaccccac (2.91) )2sin()()2cos()()( )()()(:filter theofoutput At the(2.90) 2)1()SNR(022AMC,t ftnt ftntmkAAtntstxWNPkAcQcIaccacNoise in AM receiver using envelope detectionNoise in AM receiver using envelope detection(a) Phasor diagram for AM wave plus narrowband noise for the case of high carrier-to-noise ratio. (b) Phasor diagram for AM wave plus narrowband noise for the case of low carrier-to-noise ratio.  (2.92) )()()( )( of envelope)(21 22 ctntntmkAAtxtyQIac(2.95) 1(SNR)(SNR)(2.94) 2(SNR)1 2. 2 .1)()()()( )()( Assume22CO022AMO,02PkPkWNPkAkWNAtntmkAAtytntntmkAAaaAMacacIaccQIacc62Noise in AM receiver using envelope detectionNoise in AM receiver using envelope detectionWaste energy63Threshold EffectThreshold EffectOutput signal-to-noise ratio of an envelope detector for varying carrier-to-noise ratio.System Model and Noise ModelSystem Model and Noise ModelDiscriminator consists of a slope network and an envelope detector.Signal after bandpass filterSignal after bandpass filterThe incoming FM signal s(t) is defined byAt the bandpass filter outputDiscriminator OutputDiscriminator OutputNote that the envelope of x(t) is of no interest to us (limiter)  (2.141) )()( sin)( 21)( wheretttrdtd Atncd )138.2( )()(sin)()()()( BecausettAtrtttrAcc (2.139) )()(sin)()(20ttAtrdm kctfnoise additivemessage (2.140) )()( )(21)(2.40) (Fig isoutput tor discrimina ThetntmkdttdtvdfNoise After DiscriminatorNoise After Discriminator  (2.142) )(sin)(21)( ttrdtd Atncd (2.143) )(sin)()( have we, )( and )( of definition FromttrtnttrQ(2.144) )(21)(dttdn AtnQcd as )(simplify may Wesignal. message oft independen is )(then ),2 (0,over ddistributeuniformly is )()( AssumetntnttddThe quadrature appearsNoise After Discriminator cont.Noise After Discriminator cont.The average output signal power = kf2P Recall fjdtdTF2.nQ(t) nd(t)dtd Ac21)( fSQN)( fSdN(2.145) )()(22fSAffSQdNcNNoise After Discriminator cont.Noise After Discriminator cont.Assume that nQ(t) has ideal low-pass characteristic with bandwidth BT(2.146) 2 , )(220 TcNBfAfNfSd(2.147) , )( output receiver At the 2 If2200WfAfNfSWBcNTSNR of FMSNR of FMeffect quieting noise 1 (2.148) 32 )( ofpower Average2230 2200ccWWcAAWNdffANtn(2.149) 23)SNR(3022FM,WNPkAfcO(2.150) 2)SNR( isbandwidth messagein power noiseaverage the,2 is )( ofpower average The02FM,02WNAWNAtscCc(2.151) 3)SNR()SNR(22FMWPkfCO71Bandwidth effectSingle Tone FM SNRSingle Tone FM SNR )2sin(2cos)( t ffft fAtsmmcc 2.4) Example (from