ECE 6640 Digital Communications

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1 ECE 6640 Digital Communication Dr. Bradley J. Bazuin Aitant Profeor Department of Electrical and Computer Engineering College of Engineering and Applied Science

2 Chapter 2 2. Formatting and Baeband Modulation. 1. Baeband Sytem. 2. Formatting Textual Data (Character Coding). 3. Meage, Character, and Symbol. 4. Formatting Analog Information. 5. Source of Corruption. 6. Pule Code Modulation. 7. Uniform and Nonuniform Quantization. 8. Baeband Modulation. 9. Correlative Coding. ECE

3 Sklar Communication Sytem Note and figure are baed on or taken from material in the coure textbook: ECE 6640 Bernard Sklar, Digital Communication, Fundamental and Application, 3 Prentice Hall PTR, Second Edition, 2001.

4 Signal Proceing Function ECE 6640 Note and figure are baed on or taken from material in the coure textbook: Bernard Sklar, Digital Communication, Fundamental and Application, Prentice Hall PTR, Second Edition,

5 Formatting Inure that the meage i compatible with digital proceing Tranmit formatting i where the ource information i tranlated into digital ymbol When data compreion i alo employed, the proce i called ource coding. (ee Chap. 13) ECE

6 Baeband Signaling Generation of the baeband waveform from the digital ymbol provide by formatting or ource coding. Thi could take the form of pule modulation or pule code modulation (PCM). The baeband ignal may be ent uing a wired connection or network to a receiver. applicable for wired application and wirele ECE

7 Formatting and Tranmiion Digital info. ource Textual info. Analog info. Sample Format Quantize Encode Pule modulate Tranmit ink Analog info. Textual info. Low-pa filter Format Decode Bit tream Pule waveform Demodulate/ Detect Channel Receive Digital info. ECE

8 Textual Data 5-bit coding Baudot: 32 character, alphabet plu 6 7-bit coding ASCII: American Standard Code for Information Interchange Originally deigned for telegraph; therefore, extra field 8-bit coding EBCDIC: Extended Binary Coded Decimal Interchange Code IBM ytem 16-bit coding Unicode Code may be ent erially with tart, parity and top bit Code may be tructured a word/ymbol ECE

9 Data Format for Aynchronou Data Communication Data i tranmitted character by character bit-erially. A character conit of one tart bit (0-level) 7 to 8 data bit (often, an ASCII character plu a parity bit) an optional parity bit one, or one and a half, or two top bit (1-level) leat ignificant bit i tranmitted firt mot ignificant bit i tranmitted lat ECE 6640 The tranmiion i a burt occurring at an unknown time but with known bit period. 9

The EIA-232E Electrical Specification ECE 6640 10 Electrical ignal on a pair

10 The EIA-232E Electrical Specification ECE Electrical ignal on a pair of wire ignal and ground. Negative logic often ued in phyical layer tranmiion.

11 Meage, Character and Symbol Meage i encoded into a equence of bit The bit tream may be a baedband ignal ASCII can generate a continuou bit tream if idle character are 1 Grouping of k-bit can be formed into ymbol M-ary ytem ue ymbol et where M=2^k For k=1, the bit rate and ymbol rate are the ame Defined waveform repreent each of the ymbol Therefore a meage baed bit tream can be repreented a a tring of Octal or Hex character in equence! ECE See Text Figure 2.5

12 A Review of Sampling Theorem We ue digital ignal proceing to tranmit and receive all form of communication. Digital communication inherently decribe bit value and ymbol value that conceptually exit for a defined period of time and then intantaneouly witch to another value. The tranmitted ignal can not phyically do thi! Tranmitted ignal mut exit at defined frequencie and within defined bandwidth limited bandwidth often tart at baeband. We may not dicu or imulate all the real world effect, even in thi cla. ECE

13 Analog to Digital Converion Sampling Sampling Theorem Nyquit rate f>=2*fmax Sample Rate Sample Period Impule Sampling Function x x t t n k 1 ECE T t x t x t x t t n T n x t xn T t n T n f T T 1 f w 2

14 Fourier Domain Replicated Spectra X X X X 1 T f f n f X n f Xf X f f X Xf ECE d f n f Xf 1 T 1 T k f n f Xf X k 1 T f Xf n f k d d

15 Fourier Domain Spectral replication at tep of f Appear a the convolution of the original pectrum by a comb waveform paced a f If the Nyquit rate i not maintained, the convolved element will overlap and become ditorted See Figure 2.6 on p. 64 (next lide) Note: Signal are not typically band limited; therefore, there will be ome aliaing whenever ampling i performed ECE

16 Sampling Spectral Replication: Perfect Impule Sampling ECE

17 Sampling Pule and Filter While Nyquit Theory and Impule Sampling i mathematically wonderful. Sampling rate above Nyquit are more practical (Fig. 2.7) 2.2 fmax for audio example (20 khz v kp CD rate) Impule mut be approximated by ignal with real duration and magnitude (Section Natural Sampling and Fig. 2.8) Sample by infinite equence of rect Math equivalent of convolving ampling impule with rect in time In frequency, convolve infinite replica with inc amp mod impule When thi ampling ignal i ued (mult. in time, conv. In freq.) you get Fig. 2.8 (next lide) X 1 T f c X f n f k ECE k

18 Sampling Spectral Replication: Non-ideal Rect Sampling ECE

19 Sample and Hold, Zero Order Hold Typical ADC ue a ample and hold prior to the ADC Sampling i typically an integration of the ignal for a fixed ampling period Hold i to inure the ADC ha a table ignal for a defined period of time (converion time) x t p t x t x t p t x t t n p T p t rect n t T ECE

20 ZOF Spectral Domain X p X p 1 f P f Xf n f T k The pectrum i haped by the inc function. 1 f T incf T Xf n f X p Note that if pectral analyi i being performed, an invere inc weighting hould be applied to correct the output. ECE T k f incf T Xf n f k

21 Filter and Aliaing If a ignal i under-ampled the output will have pectral content that i not deired. Engineering Nyquit 2.2 x fmax With digital pot filtering, ample at 4 x fmax (or 4.4) and then ue a half-band filter decimator (may be le expenive) If additional digital filtering will be employed, aliaed region of the pectrum may be digitally removed. Thi allow the tranition band to overlap and the topband to be placed nearer to the paband edge. ECE

22 Filter and Aliaing Uing a lightly higher ampling rate ECE

23 Filter Terminology BW PB SF BW SB BW BW SB PB Paband Frequencie where ignal i meant to pa Stopband Frequencie where ome defined level of attenuation i deired Tranition-band The tranition frequencie between the paband and the topband Filter Shape Factor The ratio of the topband bandwidth to the paband bandwidth See FilterNote and FIR_Filter_DSPNote or MRSP Chap 4 Nyquit/Raied Coine Filter ECE

24 Reducing the Sample Rate If additional digital filtering will be employed, aliaed region of the pectrum may be digitally removed. Thi allow the tranition band to overlap and the topband to be placed nearer to the paband edge. Dynamic Range ECE

25 Overampling Without Overampling High performance LPF Nyquit Sampling till include ome aliaed component With Overampling Lower performance LPF Aliaed component can be ignificantly reduced High performance digital filter likely to be employed Identical or imilar data rate can be achieved ECE

26 MATLAB Viualization Different ample rate Average power veru total power caling Frequency caling Filtered pule filter bandwidth All Chap2 cript StepRepone PuleTet1-3 ECE

27 2.5 Source of Corruption Quantization Noie Saturation Timing Jitter See Analog Device Radio Interymbol Interference (ISI) Symbol filter repone extend in time and overlap. A ymbol can be interfered with by other ymbol in time! ECE

28 Quantization Noie Round-off Error +/- one half of the LSB Uniform error ditribution about the quantized value Error mean 0 Error Variance q^2/12 Truncation Error 0 to +1 LSB Uniform error ditribution from one quantized value to the next Error mean 1/2 Error Variance q^2/12 2 q 12 ECE q 2 1 q 1 q e q 2 2 q 2 3 e 3 p e q 2 q 2 e 2 q 2 de de 1 q 3 q 24 q 24 3

29 Quantization Level The level defined for a typical L-level (2^k=L) ADC Quantized value rm V p q L 2 ECE

30 Quantized Peak SNR For an L level quantized ytem, letting power be the quare of one half the rm value of a maximum ine wave 2 q L rm Vp 2 2 The etimated ignal to noie ratio i SNR q q L 2 2 For 8-bit or 256 level 2 2 q 12 ECE q 2 L 8 SNR Nominally 6 db per bit q q SNR q 3 2 L rm 2 V 2 p dB

31 Interymbol Interference Web InterSymbol Interference (ISI) Nyquit ISI Criterion Inter Symbol Interference (ISI) and Raied coine filtering From C. Langton Complex to Real web ite Other clae (ECE6560 MRSP Chap. 4) A raied coine window/filter i a form of Nyquit filtering A combined tranmitting and receiving filter, each ue a quareroot raied coine filter. ECE

32 Interymbol Interference Matlab ISI Example Code The original 16-QAM data in real and imaginary The channel corrupted received data, no filtering The channel corrupted received data, SQRT RC Tx and RX filter 1 Eye Diagram for In-Phae Signal Amplitude Amplitude Time 1 Eye Diagram for Quadrature Signal Amplitude Amplitude Time ECE

33 2.6 Pule Code Modulation Ue the digital word/ymbol generated for each character or ADC value Note that the more information or accuracy per ymbol, a higher bit rate i required to maintain the ymbol rate. F demand a fixed, contant communication rate Text may be ent at any rate that i acceptable (non real-time) Thi can alo be referred to a Amplitude Shift Keying Note that ADC value if ent a pule would be called PAM or pule amplitude modulation ECE PAM may be dicrete or quantized

34 2.7 Uniform v. Non-uniform Quantization Uniform (linear) quantizing: No aumption about amplitude tatitic and correlation propertie of the input. Robut to mall change in input tatitic by not finely tuned to a pecific et of input parameter Simply implemented Non-uniform quantizing: Uing the input tatitic to tune quantizer parameter Larger SNR than uniform quantizing with ame number of level Non-uniform interval in the dynamic range with ame quantization noie variance ECE

35 Quantization Example ECE

36 Uniform v. Nonuniform (2) Application of linear quantizer: Signal proceing, graphic and diplay application, proce control application Application of non-uniform quantizer: Commonly ued for peech u-law in US, A-law in Europe ECE

37 Non-uniform Quantization When ome portion of the voltage range are not often ued, additional emphai can be given to thoe that are. μ-law algorithm (North America μ=255) A-law algorithm (Standard Value A=87.6) ECE

38 Non-uniform Quantization Matlab Example quantizing integer 0 to 255 Small value compreion, large value expanion 300 Reexpanion output output u-law A-Law Compreed input Re-expanded output Input to Output error ECE

39 Baeband Signaling Generation of the baeband waveform from the digital ymbol provide by formatting or ource coding. Thi could take the form of pule modulation or pule code modulation (PCM). The baeband ignal may be ent uing a wired connection or network to a receiver. Bit to bae band ymbol conideration. ECE

40 PCM Tranmiion Pule code modulation (PCM) i ued when a binary data tream i to be ent. In PCM the binary equence i ued to define logical ignal level for tranmiion. A logical level may map to bit (e.g. 0-High, 1-Low) A bit value may define whether a level change or not Mark : change whenever the bit i a one Space: change whenever the bit i a zero Period half-cycle can take on variou tructure baed on a bit value or the equence of bit See Figure 2.22 on p. 87 ECE

41 PCM Tranmiion ECE 6640 Figure 2.22 Variou PCM Waveform 41

42 PCM Common Waveform Type Mark (1 ) and Space (0 ) Non-return-to-zero (NRZ) Level, Mark, Space Return-to-zero (RZ) unipolar, bipolar, AMI (alternate mark inverion) Mancheter biphae level, biphae mark, biphae pace ECE

43 PCM Type NRZ Bipolar RZ Mancheter Biphae Mark Code AMI-Bipolar Encoding (Alternate Mark Inverion) ECE

44 PCM Type Selection Spectral characteritic (power pectral denity and bandwidth efficiency) Bit ynchronization capability Error detection capability Interference and noie immunity Implementation cot and complexity ECE

45 Spectral Attribute of PCM ECE

46 M-ary Pule-Modulation Waveform M-ary modulation i ued when ymbol data tream i to be ent M-ary waveform include: PAM: Pule-Amplitude Modulation PPM: Pule-Poition Modulation PDM: Pule-Duration Modulation or PWM: Pule-Width Modulation Multiple level can be tranmitted a one ymbol Other M-ary waveform QAM: Quadrature-Amplitude Modulation ECE

47 Correlative Code Web ite: Complex technology made real Complex communication technology made eay or Complex to Real by Charan Langton Tutorial 16 Partial Repone ignaling and Quadrature Partial Repone (QPR) modulation ECE

ECE 6640 Digital Communications

ECE 6640 Digital Communication Dr. Bradley J. Bazuin Aitant Profeor Department of Electrical and Computer Engineering College of Engineering and Applied Science Chapter. Formatting and Baeband Modulation.