Introduction to Digital Communications System

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1 Wireless Information Transmission System Lab. Introduction to Digital Communications System Institute of Communications Engineering National Sun Yat-sen University

2 Recommended Books Digital Communications / Fourth Edition (textbook) -- John G. Proakis, McGraw Hill Communication Systems / 4th Edition -- Simon Haykin, John Wiley & Sons, Inc. Digital Communications Fundamentals and Applications / 2nd Edition -- Bernard Sklar, Prentice Hall Principles of Communications / Fifth Edition -- Rodger E. Ziemer and William H. Tranter, John Wiley & Sons, Inc. Modern Digital and Analog Communication Systems -- B.P. Lathi, Holt, Rinehart and Winston, Inc. 2

3 Example of Communications System Local Loop Local Loop Local Loop Switch Transmission Equipment Central Office Switch Transmission Equipment Central Office Switch T1/E1 Facilities regenerator A/D Conversion (Digitization) T1/E1 Facilities regenerator A/D Conversion (Digitization) T1/E1 Facilities M U X SONET SDH Mobile Switching Center T1/E1 Facilities Base Station Transmission Equipment Central Office regenerator A/D Conversion (Digitization) Public Switched Telephone Network (PSTN) 3 Mobile Switching Center Base Station

4 Basic Digital Communication Nomenclature Textual Message: information comprised of a sequence of characters. Binary Digit (Bit): the fundamental information unit for all digital systems. Symbol (m i where i=1,2, M): for transmission of the bit stream; groups of k bits are combined to form new symbol from a finite set of M such symbols; M=2 k. Digital Waveform: voltage or current waveform representing a digital symbol. Data Rate: Symbol transmission is associated with a symbol duration T. Data rate R=k/T [bps]. Baud Rate: number of symbols transmitted per second [baud]. 4

5 Nomenclature Examples 5

6 Messages, Characters, and Symbols 6

7 Typical Digital Communications System From Other Sources Information Bits Source Bits Channel Bits Format Digital Input m i Digital Output mˆ i Source Encoding Encryption Channel Encoding Bit Stream Interleaving Multiplexing Modulation (t) s i Synchronization ˆ ( t) s i Frequency Spreading Digital Waveform Multiple Access TX RF PA C H A N N E L Format Source Decoding Decryption Channel Decoding Deinterleaving Demultiplexing Demodulation Frequency Despreading Multiple Access RX RF IF Information Sink Source Bits Optional Essential Channel Bits To Other Destinations 7

8 Wireless Information Transmission System Lab. Format Institute of Communications Engineering National Sun Yat-sen University

9 Typical Digital Communications System From Other Sources Information Bits Source Bits Channel Bits Format Digital Input m i Digital Output mˆ i Source Encoding Encryption Channel Encoding Bit Stream Interleaving Multiplexing Modulation (t) s i Synchronization ˆ ( t) s i Frequency Spreading Digital Waveform Multiple Access TX RF PA C H A N N E L Format Source Decoding Decryption Channel Decoding Deinterleaving Demultiplexing Demodulation Frequency Despreading Multiple Access RX RF IF Information Sink Source Bits Optional Essential Channel Bits To Other Destinations 9

10 Formatting and Baseband Transmission 10

11 Sampling Theorem 11

12 Sampling Theorem Sampling Theorem: A bandlimited signal having no spectral components above f m hertz can be determined uniquely by values sampled at uniform intervals of T s seconds, where 1 TS or sampling rate f S 2 f m 2 f m In sample-and-hold operation, a switch and storage mechanism form a sequence of samples of the continuous input waveform. The output of the sampling process is called pulse amplitude modulation (PAM). 12

13 Sampling Theorem 1 X S ( f ) = X ( f ) X δ ( f ) = X ( f nfs ) T 13 S n=

14 Spectra for Various Sampling Rates 14

15 Natural Sampling 15

16 Pulse Code Modulation (PCM) PCM is the name given to the class of baseband signals obtained from the quantized PAM signals by encoding each quantized sample into a digital word. The source information is sampled and quantized to one of L levels; then each quantized sample is digitally encoded into an l-bit (l=log 2 L) codeword. 16

17 Example of Constructing PCM Sequence 17

18 Uniform and Non-uniform Quantization 18

19 Statistical Distribution of Single-Talker Speech Amplitudes 50% of the time, speech voltage is less than ¼ RMS. Only 15% of the time, voltage exceeds RMS. Typical voice signal dynamic range is 40 db. 19

20 Problems with Linear Quantization Fact: Unacceptable S/N for small signals. Solution: Increasing quantization levels price is too high. Applying nonlinear quantization achieved by first distorting the original signal with a logarithmic compression characteristic and then using a uniform quantizer. At the receiver, an inverse compression characteristic, called expansion, is applied so that the overall transmission is not distorted. The processing pair is referred to as companding. 20

21 Implementation of Non-linear Quantizer 21

22 22 Companding Characteristics In North America: μ-law compression: In Europe: A-law compression: < + = + + = 0 for 1 0 for 1 sgn where sgn ) (1 log )] / ( [1 log max max x x x x x x y y e e μ μ < + + < + = 1 1 sgn log 1 )] / ( [ log sgn log 1 ) / ( max max max max max max x x A x A x x A y A x x x A x x A y y e e e

23 Compression Characteristics Standard values of μ is 255 and A is

24 Wireless Information Transmission System Lab. Source Coding Institute of Communications Engineering National Sun Yat-sen University

25 Typical Digital Communications System From Other Sources Information Bits Source Bits Channel Bits Format Digital Input m i Digital Output mˆ i Source Encoding Encryption Channel Encoding Bit Stream Interleaving Multiplexing Modulation (t) s i Synchronization ˆ ( t) s i Frequency Spreading Digital Waveform Multiple Access TX RF PA C H A N N E L Format Source Decoding Decryption Channel Decoding Deinterleaving Demultiplexing Demodulation Frequency Despreading Multiple Access RX RF IF Information Sink Source Bits Optional Essential Channel Bits To Other Destinations 25

26 Source Coding Source coding deals with the task of forming efficient descriptions of information sources. For discrete sources, the ability to form reduced data rate descriptions is related to the information content and the statistical correlation among the source symbols. For analog sources, the ability to form reduced data rate descriptions, subject to a fixed fidelity criterion I related to the amplitude distribution and the temporal correlation of the source waveforms. 26

27 Huffman Coding The Huffman code is source code whose average word length approaches the fundamental limit set by the entropy of a discrete memoryless source. The Huffman code is optimum in the sense that no other uniquely decodable set of code-words has smaller average code-word length for a given discrete memoryless source. 27

28 Huffman Encoding Algorithm 1. The source symbols are listed in order of decreasing probability. The two source symbols of lowest probability are assigned a 0 and a These two source symbols are regarded as being combined into a new source symbol with probability equal to the sum of the two original probabilities. The probability of the new symbol is placed in the list in accordance with its value. 3. The procedure is repeated until we are left with a final list of source statistics of only two for which a 0 and a 1 are assigned. 4. The code for each (original) source symbol is found by working backward and tracing the sequence of 0s and 1s assigned to that symbol as well as its successors. 28

29 Symbol S0 S1 S2 S3 S4 Symbol Example of Huffman Coding Probability Stage 1 Code Word Stage 2 Stage 3 Stage 4 S0 S1 S2 S3 S

30 Properties of Huffman Code Huffman encoding process is not unique. Code words for different Huffman encoding process can have different lengths. However, the average code-word length is the same. When a combined symbol is moved as high as possible, the resulting Huffman code has a significantly smaller variance than when it is moved as low as possible. Huffman code is a prefix code. A prefix code is defined as a code in which no code-word is the prefix of any other code-word. 30

31 Bit Compression Technologies for Voice Differential PCM (DPCM) Adaptive DPCM Delta Modulation (DM) Adaptive DM (ADM)... Speech Encoding 31

32 Differential PCM (DPCM) 32

33 Delta Modulation (DM) Delta modulation is a one-bit DPCM. Advantage: bit compression. Disadvantage: slope overload. 33

34 Speech Coding Objective Reduce the number of bits needed to be transmitted, therefore lowering the bandwidth required. 34

Displays long-term repetitive pattern corresponding to the duration of a pitch

35 Voiced Sound Speech Properties Arises in generation of vowels and latter portion of some consonants. Displays long-term repetitive pattern corresponding to the duration of a pitch interval Pulse-like waveform. Unvoiced Sound Arises in pronunciation of certain consonants such as s, f, p, j, x,, etc. Noise-like waveform. 35

36 Categories of Speech Encoding Waveform Encoding Treats voice as analog signal and does not use properties of speech: Source Model Coding or Vocoding Treats properties of speech to preserve word information Hybrid or parametric methods Combines waveform and vocoding 36

37 Linear Predictive Coder (LPC) 37

38 Multi-Pulse Linear Predictive Coder (MP-LPC) 38

39 Regular Pulse Excited Long Term Prediction Coder (RPE-LPT) 39

40 Code-Excited Linear Predictive (CELP) 40

41 Speech Coder Complexity 41

42 Speech Processing for GSM Composition of the 13 kbps signal: 36 bits for filter parameters every 20 ms. 9 bits for LTP every 5 ms. 47 bits for RPE every 5 ms. Thus, in a 20 ms (2080-bit block, or 260 sample) interval, we need a total of 36+9*20/5+47*20/5=260 bits. Data Rate = 260/(20 ms) = 13 kbps. 42

43 Speech Processing for IS-54 Composition of the 7.95 kbps signal: 43 bits for filter parameters every 20 ms. 7 bits for LTP every 5 ms. 88 bits for codebook every 20 ms. Thus, in a 20 ms (2080-bit block, or 260 samples) interval, we need a total of: 43+7*20/5+88=159 bits. Data Rate = 159/(20ms) = 7.95 kbps. 43

44 Wireless Information Transmission System Lab. Channel Coding Institute of Communications Engineering National Sun Yat-sen University

45 Typical Digital Communications System From Other Sources Information Bits Source Bits Channel Bits Format Digital Input m i Digital Output mˆ i Source Encoding Encryption Channel Encoding Bit Stream Interleaving Multiplexing Modulation (t) s i Synchronization ˆ ( t) s i Frequency Spreading Digital Waveform Multiple Access TX RF PA C H A N N E L Format Source Decoding Decryption Channel Decoding Deinterleaving Demultiplexing Demodulation Frequency Despreading Multiple Access RX RF IF Information Sink Source Bits Optional Essential Channel Bits To Other Destinations 45

46 Channel Coding Error detecting coding: Capability of detecting errors so that re-transmission or dropping can be done. Cyclic Redundancy Code (CRC) Error Correcting Coding: Capability of detecting and correcting errors. Block Codes: BCH codes, RS codes, etc. Convolutional codes. Turbo codes. Low Density Parity Check (LDPC) Code 46

47 CRC in WCDMA g CRC24 (D) = D 24 + D 23 + D 6 + D 5 + D + 1; g CRC16 (D) = D 16 + D 12 + D 5 + 1; g CRC12 (D) = D 12 + D 11 + D 3 + D 2 + D + 1; g CRC8 (D) = D 8 + D 7 + D 4 + D 3 + D

48 Channel Coding Adopted in WCDMA Type of TrCH BCH Coding scheme Coding rate PCH Convolutional 1/2 RACH coding CPCH, DCH, DSCH, FACH 1/3, 1/2 Turbo coding 1/3 No coding 48

49 Convolutional Coding in WCDMA Input D D D D D D D D (a) Rate 1/2 convolutional coder Output 0 G 0 = 561 (octal) Output 1 G 1 = 753 (octal) Input D D D D D D D D (b) Rate 1/3 convolutional coder Output 0 G 0 = 557 (octal) Output 1 G 1 = 663 (octal) Output 2 G 2 = 711 (octal) 49

50 Turbo Coder in WCDMA xk 1st constituent encoder zk Input xk D D D Input Turbo code internal interleaver Output 2nd constituent encoder z k Output x k D D D x k 50

51 Wireless Information Transmission System Lab. Interleaving Institute of Communications Engineering National Sun Yat-sen University

52 Typical Digital Communications System From Other Sources Information Bits Source Bits Channel Bits Format Digital Input m i Digital Output mˆ i Source Encoding Encryption Channel Encoding Bit Stream Interleaving Multiplexing Modulation (t) s i Synchronization ˆ ( t) s i Frequency Spreading Digital Waveform Multiple Access TX RF PA C H A N N E L Format Source Decoding Decryption Channel Decoding Deinterleaving Demultiplexing Demodulation Frequency Despreading Multiple Access RX RF IF Information Sink Source Bits Optional Essential Channel Bits To Other Destinations 52

53 Bursty Error in Fading Channel 53

54 Interleaving Mechanism (1/2) x x Write Clock Bit Interleaver j x n-bit Shift registers y y Read Clock Bit Stream before entering bit interleaver: x=(a 11 a 12 a 1n a 21 a 22 a 2n a j1 a j2 a jn ) 54

55 Interleaving Mechanism (2/2) y Conceptually, the WRITE clock places the bit stream x by the row while the REA clock takes the bit stream y by the column: a a... a 21 j1 a a a j Bit stream at the output of the bit interleaver: = ( a a a a a... a... a a... a ) j j 2 1n 2n a a a 1n 2n... jn jn 55

56 Burst Error Protection with Interleaver 56

57 Wireless Information Transmission System Lab. Modulation Institute of Communications Engineering National Sun Yat-sen University

58 Typical Digital Communications System From Other Sources Information Bits Source Bits Channel Bits Format Digital Input m i Digital Output mˆ i Source Encoding Encryption Channel Encoding Bit Stream Interleaving Multiplexing Modulation (t) s i Synchronization ˆ ( t) s i Frequency Spreading Digital Waveform Multiple Access TX RF PA C H A N N E L Format Source Decoding Decryption Channel Decoding Deinterleaving Demultiplexing Demodulation Frequency Despreading Multiple Access RX RF IF Information Sink Source Bits Optional Essential Channel Bits To Other Destinations 58

59 Modulation Digital Modulation: digital symbols are transformed into waveforms that are compatible with the characteristics of the channel. In baseband modulation, these waveforms are pulses. In bandpass modulation, the desired information signal modulates a sinusoid called a carrier. For radio transmission, the carrier is converted in an electromagnetic (EM) wave. 59

60 Digital Modulations Basic digital modulated signal: v(t) = A(t) cos (ωt + θ) Where A(t) = Amplitude; ω = Frequency; θ = Phase; 60

61 Basic Digital Modulations 61

62 Extended Modulated Signals M-FSK Example: 16-FSK Every 4 bits is encoded as: A cos( ω jt) j = 1,2,, 16 Gray Coding. 62

63 Gray Coding. Extended Modulated Signals M-PSK Example: 16-PSK Every 4 bits is encoded as: A sin( ω t+ θ ) j = 1, 2,,16 j Dotted lines are decision boundaries. 63

64 Extended Modulated Signals 16-QAM Every 4 bits is represented by one point in the signal constellation. Every point has its unique amplitude and phase. 64

65 Quadrature Phase Shift Keying (QPSK) 65

66 Spectrum of QPSK Signals sinπ ( f fc) T s sinπ ( f fc) T s PQPSK ( f ) = E b + π ( f fc) T π ( f fc) T

67 Offset QPSK (OQPSK) For QPSK, the occasional phase shift of πradians can cause the signal envelope to pass through zero for just an instant. The amplification of the zero-crossings brings back the filtered sidelobes since the fidelity of the signal at small voltage levels is lost in transmission. To prevent the regeneration of sidelobes and spectral widening, it is imperative that QPSK signals that use pulse shaping be amplified only using linear amplifiers, which are less efficient. A modified form of QPSK, called offset QPSK (OQPSK) or staggered QPSK is less susceptible to these deleterious effects and supports more efficient amplification. OQPSK ensures there are fewer baseband signal transitions. Spectrum of an OQPSK signal is identical to that of QPSK. 67

68 Offset QPSK (OQPSK) The time offset waveforms that are applied to the in-phase and quadrature arms of an OQPSK modulator. Notice that a halfsymbol offset is used. 68

69 π/4-dqpsk 69

70 Inter-Symbol Interference (ISI) 70

71 Inter Symbol Interference (ISI) Inter-Symbol Interference (ISI) arises because of imperfections in the overall frequency response of the system. When a short pulse of duration T b seconds is transmitted through a band-limited system, the frequency components constituting the input pulse are differentially attenuated and differentially delayed by the system. Consequently, the pulse appearing at the output of the system is dispersed over an interval longer than T b seconds, thereby resulting in intersymbol interference. Even in the absence of noise, imperfect filtering and system bandwidth constraints lead to ISI. 71

72 Nyquist Channels for Zero ISI The Nyquist channel is not physically realizable since it dictates a rectangular bandwidth characteristic and an infinite time delay. Detection process would be very sensitive to small timing errors. Solution: Raised Cosine Filter. 72

73 73 Raised Cosine Filter : Factor - Off Roll Bandwidth : Excess 2 1 for for 2 2 for 0 ) 2 4 ( cos 1 ) ( W W W r W W T W W f W f W W W W f W W W W f f H = = > < < < + = π

74 Raised Cosine Filter Characteristics 74

75 Raised Cosine Filter Characteristics 75

76 Equalization In practical systems, the frequency response of the channel is not known to allow for a receiver design that will compensate for the ISI. The filter for handling ISI at the receiver contains various parameters that are adjusted with the channel characteristics. The process of correcting the channel-induced distortion is called equalization. 76

77 Equalization 77

78 Introduction to RAKE Receiver Multiple versions of the transmitted signal are seen at the receiver through the propagation channels. Very low correlation between successive chips is in CDMA spreading codes. If these multi-path components are delayed in time by more than a chip duration, they appear like uncorrelated noise at a CDMA receiver. Equalization is NOT necessary Combine Coherently 78

79 Introduction to RAKE Receiver To utilize the advantages of diversity techniques, channel parameters are necessary to be estimated. Arrival time of each path, Amplitude, and Phase. Maximal Ratio Combiner (MRC): The combiner that achieves the best performance is one in which each output is multiplied by the corresponding complexvalued (conjugate) channel gain. The effect of this multiplication is to compensate for the phase shift in the channel and to weight the signal by a factor that is proportional to the signal strength. 79

80 Maximum Ratio Combining (MRC) MRC: G i =A i e -jq i Coherent Combining G 1 G 2 G L Channel Estimation Best Performance Receiver 80

81 Maximum Ratio Combining (MRC) Received Envelope: r = G r Total Noise Power: SNR: Since SNR L 2 rl = = 2 σ 2 n 81 L l l l= 1 σ L n = Gl σ n, l l= 1 2 l= 1 L l= σ n, l L 2 L rl Gl r l Glσ n, l l= 1 l= 1 σ nl, L L G l G l r = l 2

82 82 Maximum Ratio Combining (MRC) *, *, 1 1 2, 2 1 2, , 2, 1 1 2, 2, 2 1 SNRs from all Sum of Output SNR With equality hold : Inequality: Chebychev's l l l n l l n l L l l L l l n l L l l n l L l L l l n l l n l L L l L l l n l l n l L l l l r G r k G SNR r G r G SNR r G r G = = = = = = = = = = = = σ σ σ σ σ σ σ σ

83 Advantages of RAKE Receiver Consider a receiver with only one finger: Once the output of a single correlator is corrupted by fading, large bit error is expected. Consider a RAKE receiver If the output of a single correlator is corrupted by fading, the others may NOT be. Diversity is provided by combining the outputs Overcome fading Improve CDMA reception 83

Introduction to Digital Communications System

Introduction to Digital Communications System Recommended Books Digital Communications / Fourth Edition (textbook) -- John G. Proakis, McGraw Hill Communication Systems / 4th Edition -- Simon Haykin, John