ECE 4371, Fall, 2014 Introduction to Telecommunication Engineering/Telecommunication LaboratoryOutlineReceiver StructureMatched FilterMatched filter examplePowerPoint PresentationSlide 7Slide 8Slide 9Slide 10Slide 11EqualizerZero-Forcing EqualizerTransversal Transversal Zero-Forcing EqualizerZero-Forcing Equalizer continueMMSE EqualizerAdaptive EqualizerDecision Feedback EqualizerDifferent types of equalizersTiming ExtractionExampleTiming/Synchronization Block DiagramTiming JitterECE 4371, Fall, 2014Introduction to Telecommunication Engineering/Telecommunication Laboratory Zhu HanDepartment of Electrical and Computer EngineeringClass 14Oct. 20th, 2014OutlineOutlineMatch FilterEqualizerTimingReceiver StructureReceiver StructureMatched filter: match source impulse and maximize SNR–grx to maximize the SNR at the sampling time/outputEqualizer: remove ISITiming –When to sample. Eye diagramDecision –d(i) is 0 or 1d(i)gTx(t)Noise na(t)?)()()(0iTniTriTr maxNSTi gRx(t)Figure 7.20Matched FilterMatched FilterInput signal s(t)+n(t)Maximize the sampled SNR=s(T0)/n(T0) at time T0Matched filter exampleMatched filter exampleReceived SNR is maximized at time T00Texample:transmit filterreceive filtert)()(0tgtTgRxTx0Tt)( tgTx0Tt)(tgTxMatched Filter: optimal receive filter for maximizedNS(matched)Matched Filter  (4.7) )(2 )()( (4.6) )(2)( is n(t) of )( PSD the, whiteis w(t)Since(4.5) )2exp()()()((4.4) )2exp()()()()( and )( of ransforms Fourier t thedenote )( and )(Let eperformanc optimal obtain to maximaze tohave Wepower signaloutput ousinstantane theis )( where (4.3) )()( as ratio noise-to-signal pulsepeak theDefine20220220222dffHNdffStnEfHNfSfSdf fTjfGfHTgdf ftjfGfHtgthtgfHfGTgtnETgNNNoooMatched Filter(4.10) )()( iff holds (4.9) inequality The )( )( . variablereal in functionscomplex are )( and )( where(4.9) )()()()(inequality sSchwarz' theRecallmaximum.a makes that )( find ),( Given(4.8) )(2)2exp()()(*21-22-212122212-21202xkxdxxdxxxxxdxxdxxdxxxfHfGdffHNdf fTjfGfH Matched FilterSince g(t)Matched Filter  ratio) PSDnoise energy to signal( waveformoft independen is which(4.20) 2)2()( (4.19) 2 )(2 )()( ispower noiseoutput average the(4.14) and (4.7) From(4.18) )( )( )2exp()()( (4.17) )2exp()( )2exp()()( )()()( , )( signal knowna Consider 0002max02202-20 orem)energy the sh'by Rayleig ( energy siganl2002*opt0NENEEkNkEENkdffGNk dffStnEkETgdffGkdf fTjfGTg fTjfGk fTjfGfkGfGfHfGtgNEProperties of Matched FiltersEqualizerEqualizerWhen the channel is not ideal, or when signaling is not Nyquist, There is ISI at the receiver side. In time domain, equalizer removes ISR. In frequency domain, equalizer flat the overall responses.In practice, we equalize the channel response using an equalizerZero-Forcing EqualizerThe overall response at the detector input must satisfy Nyquist’s criterion for no ISI:The noise variance at the output of the equalizer is:–If the channel has spectral nulls, there may be significant noise enhancement.Transversal Transversal Zero-Forcing EqualizerIf Ts<T, we have a fractionally-spaced equalizerFor no ISI, let:Zero-Forcing Equalizer continueZero-forcing equalizer, figure 7.22 and example 7.3Example: Consider a baud-rate sampled equalizer for a system for whichDesign a zero-forcing equalizer having 5 taps.MMSE EqualizerMMSE EqualizerIn the ISI channel model, we need to estimate data input sequence xk from the output sequence ykMinimize the mean square error.Adaptive EqualizerAdaptive EqualizerAdapt to channel changes; training sequenceDecision Feedback EqualizerDecision Feedback EqualizerTo use data decisions made on the basis of precursors to take care of postcursorsConsists of feedforward, feedback, and decision sections (nonlinear)DFE outperforms the linear equalizer when the channel has severe amplitude distortion or shape out off.Different types of equalizersDifferent types of equalizersZero-forcing equalizers ignore the additive noise and may significantly amplify noise for channels with spectral nullsMinimum-mean-square error (MMSE) equalizers minimize the mean-square error between the output of the equalizer and the transmitted symbol. They require knowledge of some auto and cross-correlation functions, which in practice can be estimated by transmitting a known signal over the channelAdaptive equalizers are needed for channels that are time-varyingBlind equalizers are needed when no preamble/training sequence is allowed, nonlinearDecision-feedback equalizers (DFE’s) use tentative symbol decisions to eliminate ISI, nonlinearUltimately, the optimum equalizer is a maximum-likelihood sequence estimator, nonlinearTiming ExtractionTiming ExtractionReceived digital signal needs to be sampled at precise instants. Otherwise, the SNR reduced. The reason, eye diagramThree general methods–Derivation from a primary or a secondary standard. GPS, atomic closkTower of base stationBackbone of Internet–Transmitting a separate synchronizing signal, (pilot clock, beacon)Satellite –Self-synchronization, where the timing information is extracted from the received signal itselfWirelessCable, FiberExampleExampleSelf Clocking, RZContain some clocking information. PLLTiming/Synchronization Block DiagramTiming/Synchronization Block DiagramAfter equalizer, rectifier and clipperTiming extractor to get the edge and then amplifierTrain the phase shifter which is usually PLLLimiter gets the square wave of the signalPulse generator gets the impulse responsesTiming JitterTiming JitterRandom forms of jitter: noise, interferences, and mistuning of the clock circuits.Pattern-dependent jitter results from clock mistuning and, amplitude-to-phase conversion in the clock circuit, and ISI,