通信原理英文版課件：Ch4 Baseband Pulse Transmission

1、Ch. 4 Baseband Pulse Transmission4.1 Introduction4.2 Matched filter4.3 Error rate due to noise4.4 Intersymbol interference4.5 Nyquists criterion for distortionless baseband binary transmission4.6 Correlative-level coding4.7 Baseband M-ary PAM transmission4.8 Digital subscriber lines4.9 Optimum linea

2、r receiver4.10 Adaptive equalization4.11 Computer experiments: Eye patterns4.12 Summary and discussion14.1 IntroductionThe problem of transmission digital data over baseband channelDo not concern source of the digital dataThe typical channel is dispersive, which leads to intersymbol interference (IS

3、I)Pulse shaping is adopted to correct ISIAdditive channel noiseOptimal detection of signals under AWGN is achieved by matched filter24.2 Matched FilterThe problem: the pulse shape is known, what is the optimal receiver in AWGN channel?Figure 4.1 Linear receiver.The answer: maximizing the peak pulse

4、signal-to-noise ratioThe output signal power at time TThe average output noise power3Matched Filter (Contd)4Matched Filter (Contd)The Schwarzs inequalityThe equality holds if, and only ifwhere k is an arbitrary constant.5Matched Filter (Contd)With the Schwarzs inequality, we haveso thatwhen6Matched

5、Filter (Contd)The impulse response of the optimum filter, the matched filter, is a time-reversed and delayed version of the input signal g(t).7Properties of Matched FiltersThe peak pulse signal-to-noise ratio of a matched filter depends only on the signal energy-to-noise spectral density ratio.Since

6、we haveThe Rayleighs energy theorem8Properties of Matched Filters (Contd)We also haveSoThe signal energy-to-noise spectral density ratio.E: the signal energy, unit: JoulesN0/2: the noise spectral density, unit: watts/Hertz is dimensionless.9Example: Matched Filter for Rectangular PulseFigure 4.2(a)

7、Rectangular pulse. (b) Matched filter output. (c) Integrator output.10Example: Matched Filter for Rectangular Pulse (Contd)Figure 4.3 Integrate-and-dump circuit.For the special case of a rectangular pulse, the matched filter may be implemented using an integrate-and-dump circuit.114.3 Error Rate Due

8、 to NoiseFigure 4.4 Receiver for baseband transmission of binary-encoded PCM wave using polar NRZ signaling.Binary PCM systemPolar NRZ signalingAWGN with zero mean and PSD N0/212Error Rate Due to Noise (Contd)Suppose symbol 0 was sent13Error Rate Due to Noise (Contd)the complementary error functionF

9、or large positive values of u,14Error Rate Due to Noise (Contd)Figure 4.5 Noise analysis of PCM system. (a) Probability density function of random variable Y at matched filter output when 0 is transmitted. (b) Probability density function of Y when 1 is transmitted.15Error Rate Due to Noise (Contd)S

10、imilarly, when symbol 1 was sent16Error Rate Due to Noise (Contd)The average probability of symbol errorUsing Leibnizs rule, differentiating Pe with respect to , and setting the result to zero, we obtain:17Error Rate Due to Noise (Contd)For the special case of p0 = p1 = 1/2, the optimal threshold is

11、 opt = 0, andFigure 4.6 Probability of error in a PCM receiver.Following an exponential law184.4 Intersymbol Interference (ISI)Figure 4.7 Baseband binary data transmission system.Using discrete PAM as an example discrete pulse modulation schemeStudying binary modulation first, then generalizing to M

12、-ary case19ISI (Contd)p(t) is normalized by setting p(0) = 1.Transmission delay is set to zero in this equation.20ISI (Contd)Sampling y(t) at ti = iTb, we getThe desired termThe ISIThe noise term214.5 Nyquists Criterion for Distortionless Baseband TransmissionThe problem: Designing the transmit and

13、receive filters g(t) and c(t), to achieve perfect reception in the absence of noise, that is,In the above case, we have (noise is ignored):22Nyquists Criterion (Contd)The Nyquists criterion23Ideal Nyquist ChannelThe Nyquists criterionThe overall system bandwidth, also called the Nyquist banwidthThe

14、ideal Nyquist channelThe Nyquist rate24Ideal Nyquist Channel (Contd)Figure 4.8 (a) Ideal magnitude response. (b) Ideal basic pulse shape.Having zeros at t = Tb, 2Tb, 25Ideal Nyquist Channel (Contd)Figure 4.9 A series of sinc pulses corresponding to the sequence 1011010.26Ideal Nyquist Channel (Contd

15、)Practical difficulties of the ideal Nyquist channelUnrealizable magnitude characteristic of P(f)Has a slow rate of decay of p(t) (p(t) decreases as 1/|t| for large |t|)27Ideal Nyquist Channel (Contd)The effect of timing errorThe ISI caused by timing error t, possible to diverge28Raised Cosine Spect

16、rumThe rolloff factorThe transmission bandwidth29Raised Cosine Spectrum (Contd)Figure 4.10 Responses for different rolloff factors. (a) Frequency response. (b) Time response.30Raised Cosine Spectrum (Contd)Ensures zero crossings1/|t|2 decreasing from large |t|ISI from timing error decreases as is in

17、creased from zero to unity.31Raised Cosine Spectrum (Contd) = 1, the full-cosine rolloff characteristicAt t = Tb/2 = 1/4W, p(t) = 0.5, that is, the pulse width measured at half amplitude is Tb;There are zero crossing at t = nTb/2, n = 2, 3, Channel bandwidth is 2W324.6 Correlative-Level CodingAlso c

18、alled partial-response signalingIntroducing ISI to achieve the maximum signaling rate of 2W symbols/s in a bandwidth of W HzThe implementation is realizable and perturbation-tolerant33Duobinary Signaling(Class I Partial Response)Figure 4.11 Duobinary signaling scheme.ak = 1ck = ak + ak-1 = 0 or 234D

19、uobinary Signaling (Contd)Decaying with 1/|t|235Duobinary Signaling (Contd)Figure 4.12 Frequency response of the duobinary conversion filter. (a) Magnitude response. (b) Phase response.36Duobinary Signaling (Contd)Figure 4.13 Impulse response of the duobinary conversion filter.hI(t) has two distingu

20、ishable values at the sampling instants37Duobinary Signaling (Contd)Detection:Decision feedbackDrawbacks: error propagation, which can be avoided by precoding.Figure 4.14 A precoded duobinary scheme.38Duobinary Signaling (Contd)Figure 4.15 Detector for recovering original binary sequence from the pr

21、ecoded duobinary coder output.39Example 4.3 Duobinary Coding with PrecodingBinary sequence bk0010110Precoded sequence dk11100100Two-level sequence ak+1+1+1-1-1+1-1-1Duobinary coder output ck+2+20-200-2Binary sequence obtained by applying Eq.4.760010110Table 4.1 Illustrating Example 4.3 on duobinary

22、coding40Modified Duobinary Signaling (Class IV Partial Response)Figure 4.16 Modified duobinary signaling scheme.41Modified Duobinary Signaling (Contd)Decaying with 1/|t|242Modified Duobinary Signaling (Contd)Figure 4.17 Frequency response of the modified duobinary conversion filter. (a) Magnitude re

23、sponse. (b) Phase response.43Modified Duobinary Signaling (Contd)Figure 4.18 Impulse response of the modified duobinary conversion filter.hI(t) has three distinguishable values at the sampling instants44Generalized Form of Correlative-Level Coding (Partial-Response Signaling)Figure 4.19 Generalized

24、correlative coding scheme.Partial-response signaling requires a larger SNR.454.7 Baseband M-ary PAM TransmissionThe symbol durationThe bit durationThe number of symbols in the constellation46M-ary PAM (Contd)Figure 4.20 Output of a quaternary system. (a) Waveform. (b) Representation of the 4 possibl

25、e dibits, based on Gray encoding.Gray encoding474.8 Digital Subscriber LinesA digital subscriber line (DSL) provides connection between end user and central office (that is, the local loop)Figure 4.21 Block diagram depicting the operational environment of digital subscriber lines.48DSL (Contd)DSL tr

26、ansmits digital data over twisted pairsDSL provides full-duplex transmissionTime compression multiplexingSimple to implementRequiring a higher data rateEcho-cancellation modeNeed hybrid and echo cancellerDo not require a higher data rateIs commonly used49DSL (Contd)Figure 4.22 Full-duplex operation

27、using (a) time compression multiplexing, and (b) echo-cancellation.50DSL (Contd)Impairments during transmission (the echo-cancellation mode)Echo: leakage from transmitter to receiver at the same endIntersymbol interference (ISI)Crosstalk: interference from adjacent twisted pairs in a cableNear-end c

28、rosstalk (NEXT)Far-end crosstalk (FEXT)51DSL (Contd)Figure 4.24 (a) Near-end crosstalk (NEXT). (b) Far-end crosstalk (FEXT).52DSL (Contd)Figure 4.25 Model of twisted-pair channel.53Line Code for DSLsDesirable features of signal transmitting over DSLsNo DC componentPSD should be low at high frequenci

29、es, since at high frequencies:Transmission attenuation becomes severeCrosstalk increases dramatically54Line Code for DSLs (Contd)Potential candidatesManchester codeModified duobinary codeBipolar code2B1Q codeTwo bits is encoded into one 4-level symbolHaving best performance55Asymmetric Digital Subsc

30、riber Lines (ADSLs)ADSL supports three services in a frequency division wayDownstream data transmissionUp to 9 Mb/sUpstream data transmissionUp to 1 Mb/sPlain old telephone service (POTS)A splitter and bidirectional filter are used for the FDMSupports high data rate applications, such as video-on-de

31、mand (VOD)56ADSLs (Contd)Figure 4.26 (a) Illustrating the different band allocations for an FDM-based ADSL system. (b) Block diagram of splitter performing the function of multiplexer or demultiplexer. Note: both filters in the splitter are bidirectional filters.574.9 Optimum Linear ReceiverThe prob

32、lem is designing of optimum receiver for a linear channel with both ISI and additive noiseTwo main solutionsZero-forcing equalizerSimple to implementPoor performance with low SNRMinimum-mean square error (MMSE) equalizer58MMSE Equalizer59MMSE Equalizer (Contd)The mean-square error is defined as:Diff

33、erentiating J with respect to c(t), and setting the result to zero, we have:60MMSE Equalizer (Contd)The MMSE equalizer61MMSE Equalizer (Contd)A MMSE equalizer is the cascade connection of two componentsA matched filter q(-t)A transversal (tapped-delay-line) equalizerRequiring infinite number of taps

34、In practice, using sufficient number of tapsWhen the tap delay is Tb, the equalizer is named “synchronous”62MMSE Equalizer (Contd)Figure 4.27 Optimum linear receiver consisting of the cascade connection of matched filter and transversal equalizer.63Practical ConsiderationsIn practice, the channel is

35、 time varyingUsing adaptive receiver to realize the full transmission capabilityAdaptive implementation of both the matched filter and the equalizer in a combined mannerSynchronous equalizer and fractionally spaced equalizer (FSE)644.10 Adaptive EqualizerFigure 4.28 Block diagram of adaptive equaliz

36、er.65Adaptive Equalizer (Contd)Two operation modes of the adaptive equalizerTraining modeA known training sequence is used to adjust equalizer tapsThe pseudo noise (PN) sequence is usually used as training sequenceDecision-directed mode (tracking mode)The mode for normal data transmissionEqualizer taps are adjusted by previous decisions66LMS A