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1、东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件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
2、.7 Baseband M-ary PAM transmission4.8 Digital subscriber lines4.9 Optimum linear receiver4.10 Adaptive equalization4.11 Computer experiments: Eye patterns4.12 Summary and discussion1东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件4.1 IntroductionThe problem of transmis
3、sion digital data over baseband channelDo not concern source of the digital dataThe typical channel is dispersive, which leads to intersymbol interference (ISI)Pulse shaping is adopted to correct ISIAdditive channel noiseOptimal detection of signals under AWGN is achieved by matched filter2东南大学移动通信国
4、家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件4.2 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 signal-to-noise ratioThe output signal power at time TThe avera
5、ge output noise power3东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Matched Filter (Contd)4东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Matched Filter (Contd)The Schwarzs inequalityThe equality holds if, and only ifwhere k is an arbi
6、trary constant.5东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Matched Filter (Contd)With the Schwarzs inequality, we haveso thatwhen6东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Matched Filter (Contd)The impulse response of the optim
7、um filter, the matched filter, is a time-reversed and delayed version of the input signal g(t).7东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Properties of Matched FiltersThe peak pulse signal-to-noise ratio of a matched filter depends only on the signal energy-to-no
8、ise spectral density ratio.Sincewe haveThe Rayleighs energy theorem8东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Properties of Matched Filters (Contd)We also haveSoThe signal energy-to-noise spectral density ratio.E: the signal energy, unit: JoulesN0/2: the noise sp
9、ectral density, unit: watts/Hertz is dimensionless.9东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Example: Matched Filter for Rectangular PulseFigure 4.2(a) Rectangular pulse. (b) Matched filter output. (c) Integrator output.10东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communicati
10、on Systems)”Communication Systems)”课件课件Example: 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.11东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication System
11、s)”Communication Systems)”课件课件4.3 Error Rate Due 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 N0/212东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)
12、”课件课件Error Rate Due to Noise (Contd)Suppose symbol 0 was sent13东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Error Rate Due to Noise (Contd)the complementary error functionFor large positive values of u,14东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communicat
13、ion Systems)”课件课件Error 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.15东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Syst
14、ems)”Communication Systems)”课件课件Error Rate Due to Noise (Contd)Similarly, when symbol 1 was sent16东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Error Rate Due to Noise (Contd)The average probability of symbol errorUsing Leibnizs rule, differentiating Pe with respect
15、to , and setting the result to zero, we obtain:17东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Error Rate Due to Noise (Contd)For the special case of p0 = p1 = 1/2, the optimal threshold is opt = 0, andFigure 4.6 Probability of error in a PCM receiver.Following an ex
16、ponential law18东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件4.4 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
17、M-ary case19东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件ISI (Contd)p(t) is normalized by setting p(0) = 1.Transmission delay is set to zero in this equation.20东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件ISI (Contd)Sampling y(t) at
18、 ti = iTb, we getThe desired termThe ISIThe noise term21东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件4.5 Nyquists Criterion for Distortionless Baseband TransmissionThe problem: Designing the transmit and receive filters g(t) and c(t), to achieve perfect reception in
19、 the absence of noise, that is,In the above case, we have (noise is ignored):22东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Nyquists Criterion (Contd)The Nyquists criterion23东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Ideal Nyquist
20、 ChannelThe Nyquists criterionThe overall system bandwidth, also called the Nyquist banwidthThe ideal Nyquist channelThe Nyquist rate24东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Ideal Nyquist Channel (Contd)Figure 4.8 (a) Ideal magnitude response. (b) Ideal basic
21、pulse shape.Having zeros at t = Tb, 2Tb, 25东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Ideal Nyquist Channel (Contd)Figure 4.9 A series of sinc pulses corresponding to the sequence 1011010.26东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)
22、”课件课件Ideal Nyquist Channel (Contd)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|)27东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Ideal Nyquist Cha
23、nnel (Contd)The effect of timing errorThe ISI caused by timing error t, possible to diverge28东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Raised Cosine SpectrumThe rolloff factorThe transmission bandwidth29东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communic
24、ation Systems)”课件课件Raised Cosine Spectrum (Contd)Figure 4.10 Responses for different rolloff factors. (a) Frequency response. (b) Time response.30东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Raised Cosine Spectrum (Contd)Ensures zero crossings1/|t|2 decreasing from
25、large |t|ISI from timing error decreases as is increased from zero to unity.31东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Raised 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
26、half amplitude is Tb;There are zero crossing at t = nTb/2, n = 2, 3, Channel bandwidth is 2W32东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件4.6 Correlative-Level CodingAlso called partial-response signalingIntroducing ISI to achieve the maximum signaling rate of 2W s
27、ymbols/s in a bandwidth of W HzThe implementation is realizable and perturbation-tolerant33东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Duobinary Signaling(Class I Partial Response)Figure 4.11 Duobinary signaling scheme.ak = 1ck = ak + ak-1 = 0 or 234东南大学移动通信国家重点实验室
28、“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Duobinary Signaling (Contd)Decaying with 1/|t|235东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Duobinary Signaling (Contd)Figure 4.12 Frequency response of the duobinary conversion filter. (a) Magnitude
29、response. (b) Phase response.36东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Duobinary Signaling (Contd)Figure 4.13 Impulse response of the duobinary conversion filter.hI(t) has two distinguishable values at the sampling instants37东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communi
30、cation Systems)”Communication Systems)”课件课件Duobinary Signaling (Contd)Detection:Decision feedbackDrawbacks: error propagation, which can be avoided by precoding.Figure 4.14 A precoded duobinary scheme.38东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Duobinary Signalin
31、g (Contd)Figure 4.15 Detector for recovering original binary sequence from the precoded duobinary coder output.39东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Example 4.3 Duobinary Coding with PrecodingBinary sequence bk0010110Precoded sequence dk11100100Two-level se
32、quence 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 coding40东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Modified Duobinary Signaling (Class IV Partial Respon
33、se)Figure 4.16 Modified duobinary signaling scheme.41东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Modified Duobinary Signaling (Contd)Decaying with 1/|t|242东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Modified Duobinary Signaling (C
34、ontd)Figure 4.17 Frequency response of the modified duobinary conversion filter. (a) Magnitude response. (b) Phase response.43东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Modified Duobinary Signaling (Contd)Figure 4.18 Impulse response of the modified duobinary conv
35、ersion filter.hI(t) has three distinguishable values at the sampling instants44东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Generalized Form of Correlative-Level Coding (Partial-Response Signaling)Figure 4.19 Generalized correlative coding scheme.Partial-response si
36、gnaling requires a larger SNR.45东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件4.7 Baseband M-ary PAM TransmissionThe symbol durationThe bit durationThe number of symbols in the constellation46东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”
37、课件课件M-ary PAM (Contd)Figure 4.20 Output of a quaternary system. (a) Waveform. (b) Representation of the 4 possible dibits, based on Gray encoding.Gray encoding47东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件4.8 Digital Subscriber LinesA digital subscriber line (DSL)
38、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.48东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件DSL (Contd)DSL transmits digital data over twi
39、sted 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 used49东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)
40、”课件课件DSL (Contd)Figure 4.22 Full-duplex operation using (a) time compression multiplexing, and (b) echo-cancellation.50东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件DSL (Contd)Impairments during transmission (the echo-cancellation mode)Echo: leakage from transmitter
41、to receiver at the same endIntersymbol interference (ISI)Crosstalk: interference from adjacent twisted pairs in a cableNear-end crosstalk (NEXT)Far-end crosstalk (FEXT)51东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件DSL (Contd)Figure 4.24 (a) Near-end crosstalk (NEXT
42、). (b) Far-end crosstalk (FEXT).52东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件DSL (Contd)Figure 4.25 Model of twisted-pair channel.53东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Line Code for DSLsDesirable features of signal transm
43、itting over DSLsNo DC componentPSD should be low at high frequencies, since at high frequencies:Transmission attenuation becomes severeCrosstalk increases dramatically54东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Line Code for DSLs (Contd)Potential candidatesManche
44、ster codeModified duobinary codeBipolar code2B1Q codeTwo bits is encoded into one 4-level symbolHaving best performance55东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Asymmetric Digital Subscriber Lines (ADSLs)ADSL supports three services in a frequency division wayD
45、ownstream 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-demand (VOD)56东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communicatio
46、n Systems)”课件课件ADSLs (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.57东南大学移动通信国家重点实验室“ “通信系统通信系统( (Com
47、munication Systems)”Communication Systems)”课件课件4.9 Optimum Linear ReceiverThe problem 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) equaliz
48、er58东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件MMSE Equalizer59东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件MMSE Equalizer (Contd)The mean-square error is defined as:Differentiating J with respect to c(t), and setting the result t
49、o zero, we have:60东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件MMSE Equalizer (Contd)The MMSE equalizer61东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件MMSE Equalizer (Contd)A MMSE equalizer is the cascade connection of two components
50、A matched filter q(-t)A transversal (tapped-delay-line) equalizerRequiring infinite number of tapsIn practice, using sufficient number of tapsWhen the tap delay is Tb, the equalizer is named “synchronous”62东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件MMSE Equalizer
51、(Contd)Figure 4.27 Optimum linear receiver consisting of the cascade connection of matched filter and transversal equalizer.63东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Practical ConsiderationsIn practice, the channel is time varyingUsing adaptive receiver to real
52、ize the full transmission capabilityAdaptive implementation of both the matched filter and the equalizer in a combined mannerSynchronous equalizer and fractionally spaced equalizer (FSE)64东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件4.10 Adaptive EqualizerFigure 4.2
53、8 Block diagram of adaptive equalizer.65东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Adaptive Equalizer (Contd)Two operation modes of the adaptive equalizerTraining modeA known training sequence is used to adjust equalizer tapsThe pseudo noise (PN) sequence is usual
54、ly used as training sequenceDecision-directed mode (tracking mode)The mode for normal data transmissionEqualizer taps are adjusted by previous decisions66东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件LMS Algorithm67东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”
55、Communication Systems)”课件课件LMS Algorithm (Contd)Figure 4.29 Signal-flow graph representation of the LMS algorithm involving the kth tap weight.LMS algorithm is a feedback system, and therefore is possible to diverge.When the step-size parameter is small, after a large number of iterations, LMS algor
56、ithm is roughly similar to the steep-descent algorithm.68东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Operation of the EqualizerFigure 4.30 Illustrating the two operating modes of an adaptive equalizer: For the training mode, the switch is in position 1; and for the
57、 tracking mode, it is moved to position 2.69东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件Decision-Feedback Equalization (DFE)Figure 4.31 Impulse response of a discrete-time channel, depicting the precursors and postcursors. 70东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communicati
58、on Systems)”Communication Systems)”课件课件DFE (Contd)Figure 4.32 Block diagram of decision-feedback equalizer.The feedback section subtracts out the ISI produced by previously detected symbols from the estimates of future samples.71东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Syste
59、ms)”课件课件DEF (Contd)When the frequency response of a linear channel has severe amplitude distortion or relatively sharp amplitude cutoff, the DFE offers a significant improvementDFE suffers from error propagationDecision errors tend to occur in bursts72东南大学移动通信国家重点实验室“ “通信系统通信系统( (Communication Systems)”Communication Systems)”课件课件4.11 Computer Experiments:Eye PatternsFigure 4.33 Interpretation of the eye pattern.73
