Introduction to Digital Communications System

Transcription

1 Introduction to Digital Communications System

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 Format

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 T S 1 2 f m or sampling rate f 2 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). S f m 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 Source Coding

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

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 Channel Coding

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. 46

47 Linear Block Codes Encoder transforms block of k successive binary digits into longer block of n (n>k) binary digits. Called an (n,k) code. Redundancy = n-k; Code Rate = k/n; There are 2 k possible messages. There are 2 k possible code words corresponding to the messages. Code word (or code vector) is an n-tuple from the space V n of all n-tuple. Storing the 2 k code vector in a dictionary is prohibitive for large k. 47

48 Vector Spaces The set of all binary n-tuples, V n, is called a vector space over GF (2). GF: Galois Field. Two operations are defined: Addition: V + U = V1 + U1 + V2 + U V n + U n Scalar Multiplication: a V = av1 + av av n Example: Vector Space V (0101)+(1110)=(0+1, 1+1, 0+1, 1+0)=(1, 0, 1, 1) 1 (1010)=(1 1, 1 0, 1 1, 1 0)=(1, 0, 1, 0) 48

49 Subspaces A subset S of V n is a subspace if The all-zero vector is in S The sum of any two vectors in S is also in S. Example of S: V V V V = 0000 = 0101 = 1010 =

50 Reducing Encoding Complexity Key feature of linear block codes: the 2 k code vectors form a k-dimensional subspace of all n-tuples. Example: k = 3, 2 k = 8, n = 6, ( 6, 3 ) code Message Code Word A 3 - dimensiona l subspace of the vector space of all 6 - tuples. 50

51 1 2 Reducing Encoding Complexity It is possible to find a set of k linearly independent n- tuples v, v,..., v such that each n-tuple of the suspace k is a linear combination of v, v,..., v. 1 2 k Code word u = m1 v1 + m2v2 where m = 0 or 1 i i = 1,..., k m k v k 51

52 Generator Matrix v1 v11 v12 v1 n v 2 v21 v22 v 2n G = = = k n Generator Matrix v k vk1 vk2 vkn The 2 k code vectors can be described by a set of k linearly independent code vectors. Let m=[m 1, m 2,, m k ] be a message. Code word corresponding to message m is obtained by: v u = mg = [ m m m ] k 1 v v 2 k

53 Storage is greatly reduced. Generator Matrix The encoder needs to store the k rows of G instead of the 2 k code vectors of the code. For example: Let Then v G = v = and m= 2 v v1 = 1 v1+ 1 v2 + 0 v3 u = = [ 1 1 0] [ 1 1 0] v2 1 [ ] 1 [ ] 0 [ ] v = [ ] Code Vector for m= [ 110] 3

54 Systematic Code 54

55 Parity Check Matrix For each generator matrix G, there exists a parity check matrix H such that the rows of G are orthogonal to the rows of H. (u h=0) h1 h11 h12 h1 n h 2 h21 h22 h 2n H = = h ( n k) h( n k)1 h( n k)2 h( n k) n u = u, u,, u 1 2 n T uh = u1hi 1+ u2hi2 + + unhin = where i = 1, 2,, n k U is a code word generated by matrix G if and only if uh T =0 0 55

56 Parity Check Matrix and Syndrome In a systematic code with G=[P kxr I kxk ] H=[I rxr P T rxk ] u e r Received Code Error = + Vector Vector Vector Syndrome of r used for error detection and correction s = rh T Syndrome s = 0 0 If r is a code Otherwise vector 56

57 Example of Syndrome Test T H = [ In k P ] G = = H P Ik The 6-tuple is the code vector corresponding to the message T s = u H = = [ ] [ 0 0 0] Compute the syndrome for the non-code-vector T [ ] H [ 1 0 0] s = = 57

58 Weight and Distance of Binary Vectors Hamming Weight of a Vector: w(v) = Number of non-zero bits in the vector. Hamming Distance between 2 vectors: d(u,v) = Number of bits in which they differ. For example: u= v= d(u,v) = 5. d(u,v) =w(u+v) The Hamming Distance between 2 vectors is equal to the Hamming Weight of their vector sum. 58

59 Minimum Distance of a Linear Code The set of all code vectors of a linear code form a subspace of the n-tuple space. If u and v are 2 code vectors, then u+v must also be a code vector. Therefore, the distance d(u,v) between 2 code vectors equals the weight of a third code vector. d(u,v) =w(u+v)=w(w) Thus, the minimum distance of a linear code equals the minimum weight of its code vectors. A code with minimum distance d min can be shown to correct (d min -1)/2 erroneous bits and detect (d min -1) erroneous bits. 59

60 Example of Minimum Distance d min =3 60

61 Example of Error Correction and Detection Capability u v d min ( u, v) = 7 t max = d min 2 1 : Error Correcting Strength m max = d min 1 : Error Detecting Strength 61

62 Convolutional Code Structure 1 2 K k bits 1 2 k 1 2 k 1 2 k 1 2 n-1 n Output 62

63 Convolutional codes Convoltuional Code k = number of bits shifted into the encoder at one time k=1 is usually used!! n = number of encoder output bits corresponding to the k information bits r = k/n = code rate K = constraint length, encoder memory Each encoded bit is a function of the present input bits and their past ones. 63

64 Generator Sequence u r 0 r 1 r 2 v (1) (1) (1) (1) g0 = 1, g1 = 0, g 2 = 1, and g3 = 1. Generator Sequence: g (1) =( ) u r 0 r 1 r 2 r 3 v (2) (2) (2) (2) (2) g0 = 1, g1 = 1, g 2 = 1, g3 = 0, and g 4 = 1. Generator Sequence: g (2) =( ) 64

65 Convolutional Codes An Example (rate=1/2 with K=2) x 1 x 2 G 1 (x)=1+x 2 G 2 (x)=1+x 1 +x 2 0(00) Present Next Output 0(11) 00 1(11) (01) (00) 0(10) 1(10) (01) State Diagram 65

66 Trellis Diagram Representation 0(00) (00) 00 0(00) 00 0(00) 00 0(00) 0(00) 0(00) (11) 1(11) 1(11) 1(11) 1(11) 0(11) 0(11) 0(11) 0(11) 0(11) 1(00) 1(00) 1(00) 0(01) 0(01) 0(01) 0(01) 0(01) 1(10) 1(10) 1(10) 1(10) 0(10) 0(10) 0(10) 0(10) 1(01) 1(01) 1(01) Trellis termination: K tail bits with value 0 are usually added to the end of the code.

67 Encoding Process Input: Output: (00) 00 0(00) 00 0(00) 00 0(00) 00 0(00) 00 0(00) 00 0(00) 1(11) 1(11) 1(11) 1(11) 1(11) (11) 1(00) 01 0(11) 1(00) 01 0(11) 1(00) 01 0(11) 01 0(11) 0(01) 0(01) 10 1(10) 0(01) 0(01) 0(01) (10) 1(10) 1(10) 0(10) 11 1(01) 0(10) 11 1(01) 0(10) 11 1(01) 0(10) 11 67

68 Viterbi Decoding Algorithm Maximum Likelihood (ML) decoding rule received sequence r ML min(d,r)!! detected sequence d Viterbi Decoding Algorithm An efficient search algorithm Performing ML decoding rule. Reducing the computational complexity. 68

69 Basic concept Viterbi Decoding Algorithm Generate the code trellis at the decoder The decoder penetrates through the code trellis level by level in search for the transmitted code sequence At each level of the trellis, the decoder computes and compares the metrics of all the partial paths entering a node The decoder stores the partial path with the larger metric and eliminates all the other partial paths. The stored partial path is called the survivor. 69

70 Viterbi Decoding Process Output: Receive: (00) 0(00) 0(00) 0(00) 0(00) 0(00) 0(00) (11) 2 1(11) 1(11) 1(11) 1(11) (11) 1(00) 01 0(11) 1(00) 01 0(11) 1(00) 01 0(11) 01 0(11) 0(01) 0(01) 0(01) 0(01) 0(01) (10) (10) 1(10) 0(10) 1(10) 0(10) 1(10) 0(10) 11 1(01) 11 1(01) 11 1(01) 11 70

71 Viterbi Decoding Process Output: Receive: (00) 0(00) 0(00) 0(00) 0(00) 0(00) 0(00) (11) 2 1(11) 4 1(11) 1(11) 1(11) (11) 1(00) 01 0(11) 1(00) 01 0(11) 1(00) 01 0(11) 01 0(11) 0(01) 0(01) 0(01) 0(01) 0(01) (10) (10) 1(10) 0(10) 1(10) 0(10) 1(10) 0(10) (01) 11 1(01) (01) 11

72 Viterbi Decoding Process Output: Receive: (00) 0(00) 0(00) 0(00) 0(00) 0(00) 0(00) (11) 2 1(11) 4 1(11) 3 1(11) 1(11) (01) 1(10) (11) 1(00) 0(01) (10) 1(10) 2 1 0(11) 1(00) 0(01) 0(10) 1(10) 0(11) 1(00) 0(01) 0(10) 1(10) 0(11) 0(01) 0(11) 0(10) (01) (01) (01) 11

73 Viterbi Decoding Process Output: Receive: (00) 0(00) 0(00) 0(00) 0(00) 0(00) 0(00) (11) 2 1(11) 4 1(11) 3 1(11) 3 1(11) (01) 1(10) (11) 1(00) 0(01) (10) 1(10) 2 1 0(11) 1(00) 0(01) 0(10) 1(10) 2 3 0(11) 1(00) 0(01) 0(10) 1(10) 0(11) 0(01) 0(11) 0(10) (01) (01) (01) 11

74 Viterbi Decoding Process Output: Receive: (00) 0(00) 0(00) 0(00) 0(00) 0(00) 0(00) (11) 2 1(11) 4 1(11) 3 1(11) 3 1(11) (01) 1(10) (11) 1(00) 0(01) (10) 1(10) 2 1 0(11) 1(00) 0(01) 0(10) 1(10) 2 3 0(11) 1(00) 0(01) 0(10) 1(10) 3 3 0(11) 0(01) 0(11) 0(10) (01) (01) (01) 11 1

75 Viterbi Decoding Process Output: Receive: (00) 0(00) 0(00) 0(00) 0(00) 0(00) 0(00) (11) 2 1(11) 4 1(11) 3 1(11) 3 1(11) (01) 1(10) (11) 1(00) 0(01) (10) 1(10) 2 1 0(11) 1(00) 0(01) 0(10) 1(10) 2 3 0(11) 1(00) 0(01) 0(10) 1(10) 3 3 0(11) 0(01) 2 0(11) 0(10) (01) (01) (01) 11 1

76 Viterbi Decoding Process Output: Receive: (00) 0(00) 0(00) 0(00) 0(00) 0(00) 0(00) (11) 2 1(11) 4 1(11) 3 1(11) 3 1(11) (01) 1(10) (11) 1(00) 0(01) (10) 1(10) 2 1 0(11) 1(00) 0(01) 0(10) 1(10) 2 3 0(11) 1(00) 0(01) 0(10) 1(10) 3 3 0(11) 0(01) 2 0(11) 0(10) (01) (01) (01) 11 1

77 Viterbi Decoding Process Decision: Receive: (00) 0(00) 0(00) 0(00) 0(00) 0(00) 0(00) (11) 2 1(11) 4 1(11) 3 1(11) 3 1(11) (01) 1(10) (11) 1(00) 0(01) (10) 1(10) 2 1 0(11) 1(00) 0(01) 0(10) 1(10) 2 3 0(11) 1(00) 0(01) 0(10) 1(10) 3 3 0(11) 0(01) 2 0(11) 0(10) (01) (01) (01) 11 1

78 Channel Coding in GSM 78

79 Channel Coding in IS-54/136 79

80 Turbo Codes Basic Concepts Turbo coding uses parallel concatenation of two recursive systematic convolutional codes joined through an interleaver. Information bits are encoded block by block. Turbo codes uses iterative decoding techniques. Soft-output decoder is necessary for iterative decoding. Turbo codes can approach to Shannon limit. 80

81 Turbo Codes Encoder An Example X(t) Y(t) X(t) Interleaver Y (t) X'(t) When the switch is placed on the low position, the tail bits are feedback and the trellis will be terminated. 81

82 Turbo Codes Encoding Example A systematic convolutional encoder with memory 2 The dotted line is for termination code Test sequence: 1011 X 0 X D D 82

83 Turbo Codes Encoding Example X 0 =1 X 1 =

84 Turbo Codes Encoding Example X 0 =0 X 1 =

85 Turbo Codes Encoding Example X 0 =1 X 1 =

86 Turbo Codes Encoding Example X 0 =1 X 1 =

87 Turbo Codes Encoding Example 1 1 X 0 =0 X 1 =

88 Turbo Codes Encoding Example 0 1 X 0 =1 X 1 =

89 Turbo Codes Encoding Example 0 0 X 0 =0 X 1 =

90 Turbo Codes Encoding Example X D D X 1 Interleaver (X 0 ) D D X 2 Output sequence: X 0, X 1, X 2, X 0, X 1, X 2, X 0, X 1, X 2,... 90

91 Turbo Codes Encoding Example The second encoder input is the interleaved data

92 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

93 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 93

94 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) 94

95 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 95

96 Interleaving

97 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 97

98 Bursty Error in Fading Channel 98

99 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 ) 99

100 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 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 100

101 Burst Error Protection with Interleaver 101

102 Modulation

103 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 103

104 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. Why modulation? Antenna size should be comparable with wave length baseband transmission is not possible. Modulation may be used to separate the different signals using a single channel. 104

105 PCM Waveform Representations 105

106 PCM Waveform Representations PCM waveform is also called line codes. Digital baseband signals often use line codes to provide particular spectral characteristics of a pulse train. NRZ-L. NRZ-M. NRZ-S. Unipolar-RZ. Polar-RZ. Bi-φ-L. Bi-φ-M. Bi-φ-S. Dicode-NRZ. Dicode-RZ. Delay Mode. 4B3T. Multi-level. etc. 106

107 PCM Waveform : NRZ-L E 0 -E NRZ Level (or NRZ Change) One is represented by one level. Zero is represented by the other level. 107

108 PCM Waveform : NRZ-M E 0 -E NRZ Mark (Differential Encoding) One is represented by a change in level. Zero is represented by a no change in level. 108

109 PCM Waveform : NRZ-S E 0 -E NRZ Space (Differential Encoding) One is represented by a no change in level. Zero is represented by a change in level. 109

110 PCM Waveform : Unipolar-RZ E 0 -E Unipolar - RZ One is represented by a half-bit width pulse. Zero is represented by a no pulse condition. 110

111 PCM Waveform : Polar-RZ E 0 -E Polar - RZ One and Zero are represented by opposite level polar pulses that are one half-bit in width. 111

112 PCM Waveform : Bi-φ-L E 0 -E Bi-φ-L (Biphase Level or Split Phase Manchester o ) One is represented by a 10. Zero is represented by a

113 PCM Waveform : Bi-φ-M E 0 -E Bi-φ-M ( Biphase Mark or Manchester 1) A transition occurs at the beginning of every bit period. One is represented by a second transition one half bit period later. Zero is represented by no second transition. 113

114 PCM Waveform : Bi-φ-S E 0 -E Bi-φ-S ( Biphase Space) A transition occurs at the beginning of every bit period. One is represented by no second transition. Zero is represented by a second transition one-half bit period later. 114

115 PCM Waveform : Dicode - NRZ E 0 -E Dicode Non-Return-to-Zero A One to Zero or Zero to One changes polarity. Otherwise, a Zero is sent. 115

116 PCM Waveform : Dicode - RZ E 0 -E Dicode Return-to-Zero A One to Zero or Zero to One transition produces a half duration polarity change. Otherwise, a Zero is sent. 116

117 PCM Waveform : Delay Mode +E E Dicode Non-Return-to-Zero A One is represented by a transition at the midpoint of the bit interval. A Zero is represented by a no transition unless it is followed by another zero. In this case, a transition is placed at the end of bit period of the first zero. 117

118 PCM Waveform : 4B3T O-- 118

119 PCM Waveform : 4B3T Ternary words in the middle column are balanced in their DC content. Code words from the first and third columns are selected alternately to maintain DC balance. If more positive pulses than negative pulses have been transmitted, column 1 is selected. Notice that the all-zeros code word is not used. 119

120 PCM Waveform : Multilevel Transmission Multilevel transmission with 3 bits per signal interval. 120

121 Criteria for Selecting PCM Waveform DC component: eliminating the dc energy from the signal s power spectrum. Self-Clocking: Symbol or bit synchronization is required for any digital communication system. Error detection: some schemes provide error detection without introducing additional error-detection bits. Bandwidth compression: some schemes increase bandwidth utilization by allowing a reduction in required bandwidth for a given data rate. Noise immunity. Cost and complexity. 121

122 Spectral Densities of Various PCM Waveforms 122

123 Linear Modulation Techniques Digital modulation techniques may be broadly classified as linear and nonlinear. In linear modulation techniques, the amplitude of the transmitted signal, s(t), varies linearly with the modulating digital signal, m(t). Linear modulation techniques are bandwidth efficient, though they must be transmitted using linear RF amplifiers which have poor power efficiency. Using power efficient nonlinear amplifiers leads to the regeneration of filtered sidelobes which can cause severe adjacent channel interference, and results in the loss of all the spectral efficiency gained by linear modulation. Clever ways have been developed to get around these difficulties: QPSK, OQPSK, π/4-qpsk. 123

124 Digital Modulations Basic digital modulated signal: v(t) = A(t) cos (ωt + θ) Where A(t) = Amplitude; ω = Frequency; θ = Phase; 124

125 Basic Digital Modulations 125

126 Extended Modulated Signals M-FSK Example: 16-FSK Every 4 bits is encoded as: A cos( ω jt) j = 1,2,, 16 Gray Coding. 126

127 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. 127

128 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. 128

129 Binary Phase Shift Keying (BPSK) In BPSK, the phase of a constant amplitude carrier signal is switched between two values according to the two possible signals m 1 and m 2 corresponding to binary 1 and 0. Normally, the two phases are separated by 180 o. 2Eb sbpsk () t = m() t cos( 2 π fct+ θc ) 0 t Tb T = b () ( π ) { g t j f t } Re exp 2 BPSK 2Eb jθ sinπ ft c b gbpsk () t = m() t e P ()( f ) = 2E gbpsk t b Tb π ftb 2 2 E sinπ ( f fc) T b sinπ b ( f fc) T b PBPSK ( f ) = + 2 π ( f fc) T b π ( f fc) T b 129 c 2

130 Power Spectral Density (PSD) of a BPSK Signal. 130

131 BPSK Receiver BPSK uses coherent or synchronous demodulation, which requires that information about the phase and frequency of the carrier be available at the receiver. If a low level pilot carrier signal is transmitted along with the BPSK signal, then the carrier phase and frequency may be recovered at the receiver using a phase locked loop (PLL). If no pilot carrier is transmitted, a Costas loop or squaring loop may be used to synthesize the carrier phase and frequency from the received BPSK signal. 131

132 BPSK Receiver with Carrier Recovery Circuits 132

133 Operations of BPSK Receiver with Carrier Recovery Circuits The received signal is squared to generate a DC signal and an amplitude varying sinusoid at twice the carrier frequency. The DC signal is filtered out using a bandpass filter with center frequency tuned to 2f c. A frequency divider is used to recreate the waveform cos(2πf c t+θ). The output of the multiplier is applied to an integrate and dump circuit which forms the low pass filter segment of a BPSK detector. If the transmitter and receiver pulse shapes are matched, then the detection will be optimum. A bit synchronizer is used to facilitate sampling of the integrator output precisely at the end of each bit period. 133

134 Differential Phase Shift Keying (DPSK) Differential PSK is a noncoherent form of phase shift keying which avoids the need for a coherent reference signal at the receiver. dk = mk dk 1 134

135 Block Diagram of DPSK Receiver 135

136 Quadrature Phase Shift Keying (QPSK) 136

137 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

138 Block Diagram of a QPSK Transmitter 138

139 Block Diagram of a QPSK Receiver 139

140 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. 140

141 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. 141

142 π/4-dqpsk 142

143 Generic π/4-dqpsk Transmitter 143

144 π/4-dqpsk Baseband Differential Detector 144

145 Detection of Binary Signals in Gaussian Noise 145

146 Digital Demodulation Techniques Coherent detection: Exact replicas of the possible arriving signals are available at the receiver. This means that the receiver has exact knowledge of the carrier wave s phase reference, in which case we say the receiver is phase-locked to the transmitter. Coherent detection is performed by crosscorrelating the received signal with each one of the replicas, and then making a decision based on comparisons with preselected thresholds. Non-coherent detection: Knowledge of the carrier wave s phase is not required. The complexity of the receiver is thereby reduced but at the expense of an inferior error performance, compared to a coherent system. 146

147 Correlation Demodulator 147

148 Matched Filter Demodulator 148

149 Inter-Symbol Interference (ISI) 149

150 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. 150

151 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. 151

152 152 Raised Cosine Filter Factor: Roll- Off Excess Bandwidth: 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

153 Raised Cosine Filter Characteristics 153

154 Raised Cosine Filter Characteristics 154

155 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. 155

156 Equalization 156

157 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 157

158 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. 158

159 Maximum Ratio Combining (MRC) MRC: G i =A i e -jθ i Coherent Combining G 1 G 2 G L Channel Estimation Best Performance Receiver 159

160 Maximum Ratio Combining (MRC) Received Envelope: r = G r Total Noise Power: SNR: Since SNR L 2 rl = = 2 σ 2 n 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

161 161 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

162 Example of RAKE Receiver Structure 162

163 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 163