通信原理英文版课件：Ch3 Pulse Modulation

1、ReviewNoise in CW modulation systemsDefinitions of SNRsN0, (SNR)I, (SNR)C, (SNR)OFigure of merit = (SNR)O/(SNR)CDifferent modulation schemesDSB-SC, SSB: Coherent/linear detectionFull AM, FM: Nonlinear detection (threshold effect)1Review (Contd)Full AM, DSB, and SSBNo tradeoff is provided between ban

2、dwidth and noise performanceFigure of merit of DSB is 1, and that of full AM is less than 1/3FMCan trade bandwidth for improved performanceThreshold reduction (FMFB or PLL)Pre-emphasis and de-emphasisPLLFirst order and second order2Ch. 3 Pulse Modulation3.1 Introduction3.2 Sampling Process3.3 Pulse-

3、Amplitude Modulation3.4 Other Forms of Pulse Modulation3.5 Bandwidth-Noise Trade-off3.6 Quantization Process3.7 Pulse-Code Modulation3.8 Noise Considerations in PCM Systems3.9 Time-Division Multiplexing3.10 Digital Multiplexers3.11 Virtues, Limitations, and Modifications of PCM3.12 Delta Modulation3

4、.13 Linear Prediction3.14 Differential Pulse-Code Modulation3.15 Adaptive Differential Pulse-Code Modulation3.16 Computer Experiment: Adaptive Delta Modulation3.17 MPEG Audio Coding Standard3.18 Summary and Discussion33.1 IntroductionPulse modulation: some parameter of a pulse train is varied in acc

5、ordance with the message signalAnalog pulse modulationTransmission takes place in discrete timesE.g. amplitude, duration, or positionDigital pulse modulationDiscrete in both time and amplitudeA Basic ingredient of digital communications43.2 Sampling ProcessSampling processAnalog signal a sequence of

6、 samples that are usually spaced uniformly in timeSampling theoremHow to choose a proper sampling rate so that the sequence of samples uniquely defines the original analog signal5Sampling Process (Contd)Figure 3.1 The sampling process. (a) Analog signal. (b) Instantaneously sampled version of the an

7、alog signal.Ts: Sampling periodfs = 1/Ts: Sampling rateInstantaneous sampling and the ideal sampled signal6Sampling Process (Contd)7Sampling Process (Contd)Figure 3.2 Spectrum of (a) a strictly band-limited signal g(t), and (b) the sampled version of g(t) for a sampling period Ts = 1/2 W.8Sampling P

8、rocess (Contd)The sequence of samples g(n/2W) G(f) g(t)The discrete-time Fourier transform9Sampling Process (Contd)The interpolation formulaThe interpolation function10Sampling Process (Contd)The sampling theoremA band-limited signal of finite energy, which has no frequency components higher than W

9、Hertz, is completely described by specifying the values of the signal at instants of time separated by 1/2W seconds;A band-limited signal of finite energy, which has no frequency components higher than W Hertz, may be completely recovered from a knowledge of its samples taken at the rate of 2W sampl

10、es per second.Nyquist rateNyquist interval11Sampling Process (Contd)Figure 3.3 (a) Spectrum of a signal. (b) Spectrum of an undersampled version of the signal exhibiting the aliasing phenomenon.12Sampling Process (Contd)To combat the effects of aliasingUsing a low-pass anti-aliasing filter before sa

11、mplingAdopting a sampling rate slightly higher than the Nyquist rateMake the design of the reconstruction filter easier13Sampling Process (Contd)Figure 3.4 (a) Anti-alias filtered spectrum of an information-bearing signal. (b) Spectrum of instantaneously sampled version of the signal, assuming the u

12、se of a sampling rate greater than the Nyquist rate. (c) Magnitude response of reconstruction filter.143.3 Pulse-Amplitude ModulationPulse-amplitude modulation (PAM)The amplitudes of regularly spaced pulses are varied in proportion to the corresponding sample values of a continuous message signalSim

13、ilar to, but not the same as “natural sampling”Pulse shape is NOT necessary rectangularFigure 3.5 Flat-top samples, representing an analog signal.15PAM (Contd)Includes two operations “Sample and Hold”Instantaneous samplingHoldTo limit bandwidth of the modulated signal16PAM (Contd)Figure 3.6 (a) Rect

14、angular pulse h(t). (b) Spectrum H(f), made up of the magnitude |H(f)|, and phase argH(f).17PAM (Contd)Passing a low-pass filterAmplitude distortionT/2 delayAperture effect18PAM (Contd)Figure 3.7 System for recovering message signal m(t) from PAM signal s(t).When the duty cycle T/Ts 0.1, the equaliz

15、er is not necessary.193.4 Other Forms of Pulse ModulationPulse-duration modulation (PDM)Pulse-position modulation (PPM)Figure 3.8 Illustrating PDM and PAM. (a) Modulating wave. (b) Pulse carrier. (c) PDM wave. (d) PPM wave.20PPMPPM is more efficient than PDMWhen channel noise power is small compared

16、 to the peak pulse power, the figure of merit of PPM is proportional to (BT/W)2PPM has the threshold effectPPM is the optimum form of analog pulse modulation213.5 Bandwidth-Noise Trade-OffPPM and FM follow a square lowDigital pulse modulation can perform betterPulse-code modulation (PCM) is a basic

17、form of digital pulse modulationMessage signal coded binary pulses (discrete in both time and amplitude)Two processes to generate a binary PCM signal: Sampling and quantizationNoise performance follows an exponential law223.6 Quantization ProcessInfinite number of amplitude levels are usually not ne

18、cessaryDiscrete amplitude levels with sufficiently close spacing can make the distortion indistinguishableQuantization: the process of transforming the sample amplitude of a message signal into a discrete amplitude taken from a finite set of possible amplitudes.The quantization process is assumed me

19、moryless and instantaneous23Quantization Process (Contd)Figure 3.9 Description of a memoryless quantizer.Partition cellL: Total number of amplitude levelsmk: decision levels/decision thresholdsvk: representation levels/reconstruction levelsv = g(m): Quantizer characteristic24Quantization Process (Co

20、ntd)Figure 3.10 Two types of quantization: (a) midtread and (b) midrise.Uniform or nonuniformMidtread or midrise25Quantization NoiseQuantization noise: the difference between the input signal m and the output signal v.Figure 3.11 Illustration of the quantization process. (Adapted from Bennett, 1948,

21、 with permission of AT&T.)26Quantization Noise (Contd)M is zero mean, and the quantizer is assumed symmetric, so Q is also zero mean.The quantization error variableThe quantization step-size is27Quantization Noise (Contd)is the number of bits per sampleSince BT is proportional to R, (SNR)O increases

22、 exponentially with BT.Note: We are considering quantization noise.28Quantization Noise (Contd)Example: Sinusoidal modulating signal29Optimum Design of QuantizersFigure 3.12 Illustrating the partitioning of the dynamic range A m A of a message signal m(t) into a set of L cells.that minimize the aver

23、age distortionMean-square distortion:30Optimum Design of Quantizers (Contd)Solving the problem in an iterative manner (the Lloyd-Max quantizer)Optimizing the encoder for a given decoderThe nearest neighbor conditionOptimizing the decoder for a given encoderThe conditional mean requirementThe encoder

24、 is specified byand the decoder is specified by313.7 Pulse-Code ModulationFigure 3.13 The basic elements of a PCM system.ADC32Nonuniform QuantizerGiving more levels to weak signalsIs equivalent to passing the baseband signal through a compressor and then a uniform quantizerTwo commonly used compress

25、ors-lawA-lawExpander is used to restore the original signalA piecewise linear approximation is used33Nonuniform Quantizer (Contd)Figure 3.14 Compression laws. (a) m -law. (b) A-law.34EncodingEncoding: A process that translates the discrete set of sample values to a more appropriate form of signal.Ba

26、sic concepts:Code, symbol, code word, binary code, ternary codeLine codes:Unipolar NRZ, Polar NRZ, Uniploar RZ, Bipolar RZ, and split-phase (Manchester code)35Line CodesFigure 3.15 Line codes for the electrical representations of binary data. (a) Unipolar NRZ signaling. (b) Polar NRZ signaling. (c)

27、Unipolar RZ signaling. (d) Bipolar RZ signaling. (e) Split-phase or Manchester code.36Line Codes (Contd)Figure 3.16 Power spectra of line codes.37Differential EncodingFigure 3.17 (a) Original binary data. (b) Differentially encoded data, assuming reference bit 1. (c) Waveform of differentially encod

28、ed data using unipolar NRZ signaling.38RegenerationFigure 3.18 Block diagram of regenerative repeater.393.8 Noise Considerations in PCM SystemsTwo major sources of noiseChannel noise always presentQuantization noise signal dependentBit error rate (BER)Assuming all bits are of equal importanceSometim

29、es, bits need to be weighted differentlyShort enough spacing between regenerative repeaters large enough signal energy-to-noise density ratio (Eb/N0) channel noise is negligibleAt the above conditions, performance of a PCM system is limited by quantization noise.40Error ThresholdEb/N0Probability of

30、Error PeFor a Bit Rate of 10-5 b/s, This is about One Error Every4.3 dB10-210-3 Second8.410-410-1 Second10.610-610 Second12.010-820 minutes13.010-101 day14.010-123 monthsInfluence of Eb/N0 on the probability of errorAn error threshold occurs at about 11 dB, above which, Pe is negligible.In practice,

31、 an adequate margin is provided over the error threshold, so that the PCM system is robust to both channel noise and interference.413.9 Time-Division MultiplexingThe sampling process is a conservation of time, so time-division multiplexing (TDM) can be used to share a common communication channel am

32、ong multiple users.TDM introduces a bandwidth expansion with factor N, the number of usersSynchronization is essential for a TDM systemA TDM system is also highly sensitive to dispersion in the channel (requires equalization of both magnitude and phase)42TDM (Contd)Figure 3.19 Block diagram of TDM s

33、ystem.43Example: The T1 SystemThe T1 system is basic to the North American digital switching hierarchyCarries 24 voice channels, 1.544 Mbits/sSampling rate for each channel is 8 KHzQuantization8 bits/sample15-segment companding ( = 255)One synchronization bit per 248 bits443.10 Digital MultiplexersM

34、ultiplexing digital signals at different bit rates multimedia transmissionUsing a bit-by-bit interleaving procedureTwo major groupsLow bit rate multiplexingData streams from PC PSTNUsing modemsDigital hierarchyThe transmission part provided by telecommunication carriersStarts at 64 kb/s, accumulates

35、 to higher ratesBit rates varies from one country to another45Digital Multiplexers (Contd)Figure 3.20 Conceptual diagram of multiplexing-demultiplexing.46The US Digital HierarchyHaving 6 levelsBit stuffing is used to handle bit rate variationsA higher outgoing bit rateAn elastic storeA method to ide

36、ntify the stuff bitsDS064 kb/sDS11.544 Mb/s24 DS0DS26.312 Mb/s4 DS1DS344.736 Mb/s7 DS2DS4274.176 Mb/s6 DS3DS5560.160 Mb/s2 DS4473.11 Virtues, Limitations, and Modifications of PCMAdvantagesRobustness to channel noise and interferenceEfficient regeneration along the transmission pathEfficient exchang

37、e of bandwidth for SNR (following an exponential law)A uniform format for different baseband signals, easy of integrationComparative ease for dropping/reinserting a message source in a TDM systemSupporting encryption48Virtues, Limitations, and Modifications of PCM (Contd)Limitations and modification

38、sIncreased system complexityMay use very-large-scale integrated (VLSI) chipsMay use delta modulation with a simple quantizing strategyIncreased channel bandwidthMay use data compression techniques to reduce bandwidth, the cost is increased complexity493.12 Delta ModulationDelta Modulation (DM)Oversa

39、mpling with a rate much higher than the Nyquist rateThe correlation between adjacent samples is increased, so that a simple quantizing strategy may be usedOne bit per sample two quantization levels: staircase approximation50DM (Contd)Figure 3.22 Illustration of delta modulation.51DM (Contd)The origi

40、nal signalThe staircase approximation signalThe error signalThe quantized version of the error signal52The DM SystemFigure 3.23 DM system. (a) Transmitter; (b) Receiver.53Quantization Errors of DMFigure 3.24 Illustration of the two different forms of quantization error in delta modulation.is require

41、d.54Delta-Sigma ModulationFigure 3.25 Two equivalent versions of delta-sigma modulation system.553.13 Linear PredictionFigure 3.26 Block diagram of a linear prediction filter of order p.Prediction orderFinite-duration impulse response (FIR) discrete-time filter56Linear Prediction (Contd)Prediction e

42、rrorPerformance index (the mean-square error)Design objective: to choose the filter coefficients w1, w2, , wp, so that J is minimized.57Linear Prediction (Contd)Assuming x(t) is a sample function of a stationary process X(t) of zero mean, 2X is the variance of X(t) and RX(kTs) = RXk = Exnxn-k is the

43、 autocorrelation of X(t) for a lag of KTs, we have:Differentiating J with respect to wk, and setting the result to zero, we obtain:The Wiener-Hopf equations58Linear Prediction (Contd)The Wiener-Hopf equations in the matrix form:Assuming RX is nonsignular, the optimum solution isSince RX is Toeplitz,

44、 wo is uniquely defined by RXk, k = 0, 1, , p. Consequently, the minimum mean-square error is:59Linear Adaptive PredictionWhen RXk is not available, wk may be estimated in a “recursive” mannerUsing the method of steepest descentAdjusting the tap-weight in the direction opposite to the gradient vecto

45、r gk = J/wk, k = 1, 2, , pWith some simplifications, leading to the popular least-mean-square (LMS) algorithmSimple (computational complexity is linear with p) Stochastic (Walk around the optimal point, following a zig-zag path)60Linear Adaptive Prediction (Contd)Figure 3.27 Block diagram illustrating th