Digital Communication by simon haykins

7/22/2019 Digital Communication by simon haykins

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Scilab Code for

Digital Communication,

by Simon Haykin 1

Created byProf. R. Senthilkumar

Institute of Road and Transport Technologyrsenthil [email protected]

Cross-Checked byProf. Saravanan Vijayakumaran, IIT Bombay

[email protected]

23 August 2010

1Funded by a grant from the National Mission on Education through ICT,http://spoken-tutorial.org/NMEICT-Intro. This Text Book Companion andScilab codes written in it can be downlaoded from the website www.scilab.in


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Book Details

Authors: Simon Haykins

Title: Digital Communication

Publisher: Willey India

Edition: Wiley India Edition

Year: Reprint 2010

Place: Delhi

ISBN: 9788126508242

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Scilab numbering policy used in this document and the relation to theabove book.

Prb Problem (Unsolved problem)

Exa Example (Solved example)

Tab Table

ARC Additionally Required Code (Scilab Code that is not part of the abovebook but required to solve a particular Example)

AE Appendix to Example(Scilab Code that is an Appednix to a particularExample of the above book)

CF Code for Figure(Scilab code that is used for plotting the respective figureof the above book )

For example, Prb 4.56 means Problem 4.56 of the above book. Exa 3.51means solved example 3.51 of this book. Sec 2.3 means a scilab code whosetheory is explained in Section 2.3 of the book.

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Contents

List of Scilab Codes 4

1 Introduction 2

2 Fundamental Limit on Performance 5

3 Detection and Estimation 14

4 Sampling Process 27

5 Waveform Coding Techniques 31

6 Baseband Shaping for Data Transmission 39

7 Digital Modulation Techniques 59

8 Error-Control Coding 87

9 Spread-Spectrum Modulation 94

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List of Scilab Codes

CF 1.2 Digital Representation of Analog signal . . . . . . . . 2Exa 2.1 Entropy of Binary Memoryless source . . . . . . . . . 5Exa 2.2 Second order Extension of Discrete Memoryless Source 5Exa 2.3 Entropy, Average length, Variance of Huffman Encoding 7Exa 2.4 Entropy, Average length, Variance of Huffman Encoding 8Exa 2.5 Binary Symmetric Channel . . . . . . . . . . . . . . . 9Exa 2.6 Channel Capacity of a Binary Symmetric Channel . . 10Exa 2.7 Significance of the Channel Coding theorem . . . . . . 10Exa 3.1 Orthonormal basis for given set of signals . . . . . . . 14Exa 3.2 M ARY Signaling . . . . . . . . . . . . . . . . . . . . 16Exa 3.3 Matched Filter output for RF pulse . . . . . . . . . . 19Exa 3.4 Matched Filter output for Noise-like signal . . . . . . . 20Exa 3.6 Linear Predictor of Order one . . . . . . . . . . . . . . 22

CF 3.29 Implementation of LMS Adaptive Filter algorithm . . 24Exa 4.1 Bound on Aliasing error for Time-shifted sinc pulse . . 27Exa 4.3 Equalizier to compensate Aperture effect . . . . . . . . 28Exa 5.1 Average Transmitted Power for PCM . . . . . . . . . 31Exa 5.2 Comparision of M-ary PCM with ideal system (Channel

Capacity Theorem) . . . . . . . . . . . . . . . . . . . 31Exa 5.3 Signal-to-Quantization Noise Ratio of PCM . . . . . . 32Exa 5.5 Output Signal-to-Noise ratio for Sinusoidal Modulation 34CF 5.13a (a) u-Law companding . . . . . . . . . . . . . . . . . . 36CF 5.13b (b) A-law companding . . . . . . . . . . . . . . . . . . 36Exa 6.1 Bandwidth Requirements of the T1 carrier . . . . . . . 39

CF 6.1a (a) Nonreturn-to-zero unipolar format . . . . . . . . . 40CF 6.1b (b) Nonreturn-to-zero polar format . . . . . . . . . . . 40CF 6.1c (c) Nonreturn-to-zero bipolar format . . . . . . . . . . 42Exa 6.2 Duobinary Encoding . . . . . . . . . . . . . . . . . . . 44

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Exa 6.3 Generation of bipolar output for duobinary coder . . . 47

CF 6.4 Power Spectra of different binary data formats . . . . 48CF 6.6b (b) Ideal solution for zero ISI . . . . . . . . . . . . . . 49CF 6.7b (b) Practical solution: Raised Cosine . . . . . . . . . 51CF 6.9 Frequency response of duobinary conversion filter . . . 53CF 6.15 Frequency response of modified duobinary conversion

filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55Exa 7.1 QPSK Waveform . . . . . . . . . . . . . . . . . . . . . 59CF 7.1 Waveform of Different Digital Modulation techniques . 61Exa 7.2 MSK waveforms . . . . . . . . . . . . . . . . . . . . . 63CF 7.2 Signal Space diagram for coherent BPSK . . . . . . . 68Tab 7.3 Illustration the generation of DPSK signal . . . . . . . 70

CF 7.4 Signal Space diagram for coherent BFSK . . . . . . . 72CF 7.6 Signal space diagram for coherent QPSK waveform . . 74Tab 7.6 Bandwidth efficiency of M ary PSK signals . . . . . . 74Tab 7.7 Bandwidth efficiency of M ary FSK signals . . . . . . 76CF 7.29 Power Spectra of BPSK and BFSK signals . . . . . . . 77CF 7.30 Power Spectra of QPSK and MSK signals . . . . . . . 78CF 7.31 Power spectra of M-ary PSK signals . . . . . . . . . . 80CF 7.41 Matched Filter output of rectangular pulse . . . . . . 82Exa 8.1 Repetition Codes . . . . . . . . . . . . . . . . . . . . . 87Exa 8.2 Hamming Codes . . . . . . . . . . . . . . . . . . . . . 87

Exa 8.3 Hamming Codes Revisited . . . . . . . . . . . . . . . . 88Exa 8.4 Encoder for the (7,4) Cyclic Hamming Code . . . . . . 89Exa 8.5 Syndrome calculator for the(7,4) Cyclic Hamming Code 90Exa 8.6 Reed-Solomon Codes . . . . . . . . . . . . . . . . . . . 90Exa 8.7 Convolutional Encoding - Time domain approach . . . 91Exa 8.8 Convolutional Encoding Transform domain approach 92Exa 8.11 Fano metric for binary symmetric channel using convo-

lutional code . . . . . . . . . . . . . . . . . . . . . . . 93Exa 9.1 PN sequence generation . . . . . . . . . . . . . . . . . 94Exa 9.2 Maximum length sequence property . . . . . . . . . . 95Exa 9.3 Processing gain, PN sequence length, Jamming margin

in dB . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Exa 9.4Example9.5Slow and Fast Frequency hopping: FH/MFSK . . . . 100Fig 9.4Figure9.6Direct Sequence Spread Coherent BPSK . . . . . . . . 100ARC 1 Alaw . . . . . . . . . . . . . . . . . . . . . . . . . . . 103ARC 2 auto correlation . . . . . . . . . . . . . . . . . . . . . 106

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ARC 3 Convolutional Coding . . . . . . . . . . . . . . . . . . 107

ARC 4 Hamming Distance . . . . . . . . . . . . . . . . . . . . 108ARC 5 Hamming Encode . . . . . . . . . . . . . . . . . . . . 108ARC 5 invmulaw . . . . . . . . . . . . . . . . . . . . . . . . . 110ARC 6 PCM Encoding . . . . . . . . . . . . . . . . . . . . . . 110ARC 7 PCM Transmission . . . . . . . . . . . . . . . . . . . . 111ARC 8 sinc new . . . . . . . . . . . . . . . . . . . . . . . . . . 111ARC 9 uniform pcm . . . . . . . . . . . . . . . . . . . . . . . 112ARC 10 xor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

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List of Figures

1.1 Figure1.2a . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Figure1.2b . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.1 Example2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2 Example2.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3 Example2.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.1 Example3.1a . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.2 Example3.1b . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.3 Example3.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.4 Example3.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.5 Example3.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.6 Figure3.29 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.1 Example4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.2 Example4.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

5.1 Example5.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 335.2 Figure5.13a . . . . . . . . . . . . . . . . . . . . . . . . . . . 375.3 Figure5.13b . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

6.1 Figure6.1a . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416.2 Figure6.1b . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436.3 Figure6.1c . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456.4 Figure6.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

6.5 Figure6.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526.6 Figure6.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546.7 Figure6.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566.8 Figure6.15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

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7.1 Example7.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

7.2 Figure7.1a . . . . . . . . . . . . . . . . . . . . . . . . . . . . 647.3 Figure7.1b . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657.4 Figure7.1c . . . . . . . . . . . . . . . . . . . . . . . . . . . . 667.5 Example7.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 697.6 Figure7.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 707.7 Figure 7.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 737.8 Figure7.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 757.9 Figure7.12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 777.10 Figure7.29 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 797.11 Figure7.30 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 817.12 Figure7.31 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

7.13 Figure7.41a . . . . . . . . . . . . . . . . . . . . . . . . . . . 857.14 Figure7.41b . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

9.1 Example9.2a . . . . . . . . . . . . . . . . . . . . . . . . . . . 989.2 Example9.2b . . . . . . . . . . . . . . . . . . . . . . . . . . . 999.3 Figure9.6a . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1039.4 Figure9.6b . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1049.5 Figure10.12 . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

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Chapter 1

Introduction

Scilab code CF 1.2 Digital Representation of Analog signal

1 // C ap ti on : D i g i t a l R e p re s e nt a t i on o f Ana lo g s i g n a l2 // F i gu r e 1 . 2 : An al og t o D i g i t a l C on ve rs i on3 clear ;

4 close ;

5 clc ;

6 t = - 1: 0. 01 :1 ;

7 x = 2* sin ( ( % p i / 2 ) * t ) ;

8 d i g _d a t a = [ 0 , 1 ,0 , 0 , 0 , 0 , 1 , 0 ,0 , 0 , 0 , 0 , 0 , 0 ,1 , 1 , 0 , 1 , 0 ,1 ]

9 //10 figure

11 a = gca () ;

12 a . x _ l o c at i o n = o r i g i n ;13 a . y _ l o c at i o n = o r i g i n ;14 a . d a t a _ bo u n d s = [ - 2 , - 3 ;2 , 3 ]

15 plot ( t , x )

16 plot2d3 ( gnn ,0.5, sqrt ( 2 ) , - 9 )17 plot2d3 ( gnn ,-0.5,- sqrt ( 2 ) , - 9 )18 plot2d3 ( gnn ,1,2,-9)

19 plot2d3 ( gnn , - 1 , - 2 , - 9 )20 x l a b e l (

Time )21 y l a b e l (

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Figure 1.1: Figure1.2a

V o l t a g e )22 t i t l e ( Anal og Waveform )23 //24 figure

25 a = gca () ;

26 a . d a t a _ bo u n d s = [ 0 , 0 ;2 1 , 5 ] ;

27 plot2d2 ([1: length (dig_data)],dig_data ,5)

28 t i t l e ( D i g i t a l R e p r es e n t at i o n )

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Figure 1.2: Figure1.2b

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Chapter 2

Fundamental Limit on

Performance

Scilab code Exa 2.1 Entropy of Binary Memoryless source

1 / / C a pt i on : E nt ro py o f B i n ar y M em o ry le ss s o u r c e2 / / Exam ple 2 . 1 : E nt ro py o f B i n ar y M em o ry le ss S o u r ce3 / / p ag e 1 84 clear ;

5 close ;

6 clc ;

7 P o = 0 : 0. 0 1: 1 ;

8 H _P o = zeros (1 , length ( P o ) ) ;

9 for i = 2: length ( P o ) - 1

10 H _P o ( i) = - Po ( i ) *log2 ( P o ( i ) ) - ( 1 - P o ( i ) ) * log2 ( 1 - P o ( i

) ) ;

11 end

12 / / p l o t13 plot2d ( P o , H _ P o )

14 x l a b e l ( S ymb ol P r o b a b i l i t y , Po )15 y l a b e l ( H(Po) )

16 t i t l e ( E n tr o py f u n c t i o n H( Po ) )17 plot2d3 ( gnn ,0.5,1)

Scilab code Exa 2.2 Second order Extension of Discrete Memoryless Source

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Figure 2.1: Example2.1

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1 / / c a p t i o n : S ec on d o r d e r E x t en s i o n o f D i s c r e t e

M e mo r yl e ss S o u r c e2 / / Example 2 . 2 : E nt ro py o f D i s c r e t e M em or yl es s s o u r c e3 / / p ag e 1 94 clear ;

5 clc ;

6 P0 = 1/ 4; // p r o b a b i l i t y o f s o ur c e a l ph ab e t S07 P1 = 1/ 4; // p r o b a b i l i t y o f s o ur c e a l ph ab e t S18 P2 = 1/ 2; // p r o b a b i l i t y o f s o ur c e a l ph ab e t S29 H _R uo = P0 * log2 ( 1 / P 0 ) + P 1 * log2 ( 1 / P 1 ) + P 2 * log2 ( 1 / P 2 ) ;

10 disp ( E nt ro py o f D i s c r e t e M em o ry le ss S o u r ce )11 disp ( b i t s , H _ R u o )

12 // S ec on d o r d er E x te ns i on o f d i s c r e t e Me mo ry le sss o u r c e

13 P _ s ig m a = [ P 0 * P0 , P 0 * P 1 , P 0 * P2 , P 1 * P 0 , P 1 * P1 , P 1 * P 2 , P 2 * P0

, P 2 * P 1 , P 2 * P 2 ] ;

14 disp ( T ab le 2 . 1 A lp ha be t P a r t i c u l a r s o f Secondo r d e rE x te n si o n o f a D i s c r e t e Me mo ry le ss S ou rc e )

15 disp (

)16 disp ( S e qu e nc e o f S ym bo ls o f r u o2 : )17 disp (

S0 S0 S0 S1 S0 S2 S1 S0 S1 S1 S1 S2 S2 S0 S2 S1 S2 S2 )18 disp (P_s igma , P r o b a b i l i t y p ( s ig ma ) , i = 0 , 1 . . . . . 8 )19 disp (

)20 disp ( )21 H _ R u o_ S q u ar e = 0 ;

22 for i = 1: length ( P _ s i g m a )

23 H _ R uo _ S q ua r e = H _ R uo _ S q ua r e + P _ s i g ma ( i ) * log2 (1/

P _ s i g m a ( i ) ) ;

24 end25 disp ( b i t s , H _ R u o _ Sq u a r e , H( Ruo Square )= )26 disp ( H( R uo Sq uar e ) = 2H(Ruo ) )

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Scilab code Exa 2.3 Entropy,Average length, Variance of Huffman Encod-

ing

1 / / C a pt i on : E nt ro py , A ve ra ge l e n g t h , V a r i a n ce o f H uff man E nc odi ng

2 / / Example 2 . 3 : Huffman E nc od in g : C a l c u l a t i o n o f 3 / / ( a ) A ve ra g e c od eword l e n g th L 4 / / ( b ) E n tr o py H5 clear ;

6 clc ;

7 P0 = 0. 4; // p r o b a b i l i t y o f c ode wo rd 0 0 8 L0 = 2; / / l e n g t h o f c od ew or d S0

9 P1 = 0. 2; // p r o b a b i l i t y o f c ode wo rd 1 0 10 L1 = 2; / / l e n g t h o f c od ew or d S111 P2 = 0. 2; // p r o b i l i t y o f c od ewo rd 1 1 12 L2 = 2; / / l e n g t h o f c od ew or d S213 P3 = 0. 1; // p r o b i l i t y o f c od ewo rd 0 10 14 L3 = 3; / / l e n g t h o f c od ew or d S315 P 4 = 0. 1; // p r o b i l i t y o f co de wo rd 0 11 16 L4 = 3; / / l e n g t h o f c od ew or d S417 L = P 0 * L 0 + P1 * L 1 + P 2 * L2 + P 3 * L 3 + P 4 * L4 ;

18 H _R uo = P0 * log2 ( 1 / P 0 ) + P 1 * log2 ( 1 / P 1 ) + P 2 * log2 ( 1 / P 2 ) + P 3

* log2 ( 1 / P 3 ) + P 4 * log2 ( 1 / P 4 ) ;

19 disp ( b i t s ,L , A v e r ag e c o de w or d L e n g th L )20 disp ( b i t s , H _ R u o , E nt ro py o f Huffman c o d i ng r e s u l t

H )21 disp ( p e r c e n t , ( ( L - H _ R u o ) / H _ R u o ) * 1 0 0 , A v e r a ge c o d e

word l e n g t h L e x c e e ds t h e e n tr o p y H( Ruo ) by o n l y )

22 s i g ma _ 1 = P 0 * ( L0 - L ) ^ 2 + P 1 * ( L1 - L ) ^ 2 + P 2 * ( L2 - L ) ^ 2 + P 3 * ( L3

- L ) ^ 2 + P 4 * ( L 4 - L ) ^ 2 ;

23 disp (sig ma_1 , V a r i n a c e o f H uf fm an c o d e )

Scilab code Exa 2.4 Entropy, Average length, Variance of Huffman En-coding

1 / / C a pt i on : E nt ro py , A ve ra ge l e n g t h , V a r i a n ce o f H uff man E nc odi ng

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2 // Example2 . 4 : I l l u s t r a t i n g n on un i q ue ss o f t he

H uff man E nc odi ng3 // C a l c u l a t i o n o f ( a ) A ver ag e co de word l e ng t h L ( b) E n t ro p y H

4 clear ;

5 clc ;

6 P0 = 0. 4; // p r o b a b i l i t y o f c ode wo rd 1 7 L0 = 1; / / l e n g t h o f c od ew or d S08 P1 = 0. 2; // p r o b a b i l i t y o f c ode wo rd 0 1 9 L1 = 2; / / l e n g t h o f c od ew or d S1

10 P2 = 0. 2; // p r o b i l i t y o f c od ewo rd 0 00 11 L2 = 3; / / l e n g t h o f c od ew or d S2

12 P3 = 0. 1; // p r o b i l i t y o f c od ewo rd 0 01 0 13 L3 = 4; / / l e n g t h o f c od ew or d S314 P 4 = 0. 1; // p r o b i l i t y o f co de wo rd 0 01 1 15 L4 = 4; / / l e n g t h o f c od ew or d S416 L = P 0 * L 0 + P1 * L 1 + P 2 * L2 + P 3 * L 3 + P 4 * L4 ;

17 H _R uo = P0 * log2 ( 1 / P 0 ) + P 1 * log2 ( 1 / P 1 ) + P 2 * log2 ( 1 / P 2 ) + P 3

* log2 ( 1 / P 3 ) + P 4 * log2 ( 1 / P 4 ) ;

18 disp ( b i t s ,L , A v e r ag e c o de w or d L e n g th L )19 disp ( b i t s , H _ R u o , E nt ro py o f Huffman c o d i ng r e s u l t

H )20 s i g ma _ 2 = P 0 * ( L0 - L ) ^ 2 + P 1 * ( L1 - L ) ^ 2 + P 2 * ( L2 - L ) ^ 2 + P 3 * ( L3

- L ) ^ 2 + P 4 * ( L 4 - L ) ^ 2 ;

21 disp (sig ma_2 , V a r i n a c e o f H uf fm an c o d e )

Scilab code Exa 2.5 Binary Symmetric Channel

1 / / C a p t i o n : B i n a r y S y m me t ri c C h a nn e l2 / / E xa mp le 2 . 5 : B i n a r y S y mm et ri c C ha n ne l3 clear ;

4 clc ;

5 close ;

6 p = 0 . 4 ; // p r o b a b i l i t y o f c o r r e c t r e c e p t i o n7 pe = 1 -p ;// p r o b i l i t y o f e r r o r r e c e p t i o n ( i . e )

t r a n s i t i o n p r o b i l i t y8 disp (p , p r o b i l i t y o f 0 r e c e i v i n g i f a 0 i s s e n t =

p r o b i l i t y o f 1 r e c e i v i n g i f a 1 i s s en t= )

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9 disp ( T r a ns i t i o n p r o b i l i t y )

10 disp ( p e , p r o b i l i t y o f 0 r e c e i v i n g i f a 1 i s s en t =p r o b i l i t y o f 1 r e c e i v i n g i f a 0 i s s en t= )

Scilab code Exa 2.6 Channel Capacity of a Binary Symmetric Channel

1 / / C a pt i on : C ha nn el C a p a ci t y o f a B i n ar y S ym me tr icChannel

2 / / E xa mp le 2 . 6 : C h an n el C a p a c i t y o f B i n a r y S ym me tr iChannel

3 clear ;

4 close ;

5 clc ;6 p = 0 : 0. 0 1: 0 .5 ;

7 for i =1: length ( p )

8 if ( i ~ = 1 )

9 C (i ) = 1+ p (i ) *log2 ( p ( i ) ) + ( 1 - p ( i ) ) * log2 ( ( 1 - p ( i ) ) )

;

10 elseif ( i = = 1 )

11 C ( i ) = 1;

12 elseif ( i = = length ( p ) )

13 C ( i ) = 0 ;

14 end15 end

16 plot2d ( p , C , 5 )

17 x l a b e l ( T r a n s i t i o n P r o b i l i t y , p )18 y l a b e l ( C h an n el C a p ac i t y , C )19 t i t l e ( F ig ur e 2 . 10 V a r i a t io n o f c ha nn el c a p ac i t y o f

a b i n ar y s ym me tr ic c ha nn el w i th t r a n s i t i o np r o b i l i t y p )

Scilab code Exa 2.7 Significance of the Channel Coding theorem

1 / / C ap ti on : S i g n i f i c a n c e o f t h e C ha nn el C od in g t he or em2 // Example2 . 7 : S i g n i f i c a n c e o f t he c ha n ne l c o di n g

t he or e m3 // A ve r age P r o b i l i t y o f E rr or o f R e p et i t i o n Code

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4 clear ;

5 clc ;6 close ;

7 p = 10 ^ - 2;

8 p e_ 1 = p ; // A v er a ge P r o b i l i t y o f e r r o r f o r c o d e r a t er = 1

9 p e_ 3 = 3 * p ^2 *( 1 - p ) + p ^3 ; // p r o b i l i t y o f e r r o r f o r c o d er a t e r =1/3

10 p e _5 = 1 0* p ^ 3 * (1 - p ) ^ 2 + 5* p ^ 4 * (1 - p ) + p ^ 5 ; // e r r o r f o rc od e r a t e r =1/5

11 p e _7 = ( ( 7 *6 * 5 ) / ( 1 * 2* 3 ) ) * p ^ 4 *( 1 - p ) ^ 3 + ( 4 2 / 2) * p ^ 5 * (1 - p

) ^ 2 + 7 * p ^ 6 * ( 1 - p ) + p ^ 7 ; // e r r o r f o r c o de r a t e r =1/7

12 r = [ 1 , 1/ 3 , 1/ 5 , 1/ 7] ;13 p e = [ p e_ 1 , p e_ 3 , p e_ 5 , p e _7 ] ;

14 a = gca () ;

15 a . d a t a _ b o u n d s = [ 0 , 0 ; 1 , 0 . 0 1 ] ;

16 plot2d ( r , p e , 5 )

17 x l a b e l ( Code r a t e , r )18 y l a b e l ( A ver ag e P r o b a b i l i t y o f e r r or , Pe )19 t i t l e ( F i gu re 2 . 1 2 I l l u s t r a t i n g s i g n i f i c a n c e o f t h e

c h a n n e l c o d i n g t he or em )20 l e g e n d ( R e p e t i t i o n c o d es )21 xgrid (1)

22 disp ( T ab le 2 . 3 A v er a ge P r o b i l i t y o f E rr or f o rR e p e t i t i o n Code )

23 disp (

)24 disp (r , C o de R at e , r =1/ n , p e , A ve ra ge P r o b i l i t y o f

E r r o r , Pe )25 disp (

)

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Chapter 3

Detection and Estimation

Scilab code Exa 3.1 Orthonormal basis for given set of signals

1 // C ap ti on : Ort ho no rm al b a s i s f o r g i v en s e t o f s i g n a l s2 / / Example3 . 1 : F i nd i ng o r th o no r ma l b a s i s f o r t h e g i v e n

s i g n a l s3 // us in g GramS ch mi dt o r t h o g o n a l i z a t i o n p r oc e du r e4 clear ;

5 close ;

6 clc ;

7 T = 1;

8 t 1 = 0 : 0. 0 1: T / 3 ;9 t 2 = 0 : 0. 0 1: 2 * T /3 ;

10 t 3 = T / 3: 0. 01 : T ;

11 t 4 = 0 :0 .0 1: T ;

12 s1t = [0 , ones (1 , length ( t 1 ) - 2 ) , 0 ] ;

13 s2t = [0 , ones (1 , length ( t 2 ) - 2 ) , 0 ] ;

14 s3t = [0 , ones (1 , length ( t 3 ) - 2 ) , 0 ] ;

15 s4t = [0 , ones (1 , length ( t 4 ) - 2 ) , 0 ] ;

16 t 5 = 0 : 0. 0 1: T / 3 ;

17 p hi 1t = sqrt ( 3 / T ) * [ 0 , ones (1 , length ( t 5 ) - 2 ) , 0 ] ;

18 t 6 = T / 3 : 0 . 01 : 2 * T / 3 ;19 p hi 2t = sqrt ( 3 / T ) * [ 0 , ones (1 , length ( t 6 ) - 2 ) , 0 ] ;

20 t 7 = 2 * T /3 : 0. 0 1: T ;

21 p hi 3t = sqrt ( 3 / T ) * [ 0 , ones (1 , length ( t 7 ) - 2 ) , 0 ] ;

22 //

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23 figure

24 t i t l e ( F ig ur e3 . 4 ( a ) S et o f s i g n a l s t o beo r t h o n o r m a l i z e d )25 subplot ( 4 , 1 , 1 )

26 a = gca () ;

27 a . d a t a _ bo u n d s = [ 0 , 0 ;2 , 2 ] ;

28 plot2d2 ( t 1 , s 1 t , 5 )

29 x l a b e l ( t )30 y l a b e l ( s1 ( t ) )31 subplot ( 4 , 1 , 2 )

32 a = gca () ;

33 a . d a t a _ bo u n d s = [ 0 , 0 ;2 , 2 ] ;

34 plot2d2 ( t 2 , s 2 t , 5 )35 x l a b e l ( t )36 y l a b e l ( s2 ( t ) )37 subplot ( 4 , 1 , 3 )

38 a = gca () ;

39 a . d a t a _ bo u n d s = [ 0 , 0 ;2 , 2 ] ;

40 plot2d2 ( t 3 , s 3 t , 5 )

41 x l a b e l ( t )42 y l a b e l ( s3 ( t ) )43 subplot ( 4 , 1 , 4 )

44 a = gca () ;

45 a . d a t a _ bo u n d s = [ 0 , 0 ;2 , 2 ] ;

46 plot2d2 ( t 4 , s 4 t , 5 )

47 x l a b e l ( t )48 y l a b e l ( s4 ( t ) )49 //50 figure

51 t i t l e ( F i gu r e3 . 4 ( b ) The r e s u l t i n g s e t o f o rt ho no rm alf u n c t i o n s )

52 subplot ( 3 , 1 , 1 )

53 a = gca () ;

54 a . d a t a _ bo u n d s = [ 0 , 0 ;2 , 4 ] ;55 plot2d2 (t5, phi1t ,5)

56 x l a b e l ( t )57 y l a b e l ( phi 1 ( t ) )58 subplot ( 3 , 1 , 2 )

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Figure 3.1: Example3.1a

59 a = gca () ;

60 a . d a t a _ bo u n d s = [ 0 , 0 ;2 , 4 ] ;

61 plot2d2 (t6, phi2t ,5)

62 x l a b e l ( t )63 y l a b e l ( phi 2 ( t ) )64 subplot ( 3 , 1 , 3 )

65 a = gca () ;

66 a . d a t a _ bo u n d s = [ 0 , 0 ;2 , 4 ] ;

67 plot2d2 (t7, phi3t ,5)68 x l a b e l ( t )69 y l a b e l ( phi 3 ( t ) )

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Figure 3.2: Example3.1b

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Scilab code Exa 3.2 M ARY Signaling

1 // C apt i on :MARY S i g n a l i n g2 //E x ampl e 3 . 2 : MARY SIGNALING3 // S i gn a l c o n s t e l l a t i o n and R e p r e s e nt a t i o n o f d i b i t s4 clear ;

5 close ;

6 clc ;

7 a =1; / / a m p l i t u d e =18 T =1; / / Symbol d u r a t i o n i n s e c o n ds9 // Four m es sa ge p o i n t s

10 S i1 = [ ( - 3/ 2) * a * sqrt ( T ) , ( - 1 / 2 ) * a * sqrt ( T ) , ( 3 / 2 ) * a *

sqrt ( T ) , ( 1 / 2 ) * a * sqrt ( T ) ] ;11 a = gca () ;

12 a . d a t a _ bo u n d s = [ - 2 , - 0. 5; 2 , 0 .5 ]

13 plot2d ( S i 1 , [ 0 , 0 , 0 , 0 ] , - 1 0 )

14 x l a b e l ( phi 1 ( t ) )15 t i t l e ( F ig ur e 3 . 8 ( a ) S i gn a l c o n s t e l l a t i o n )16 xgrid (1)

17 disp ( F i gu r e 3 . 8 ( b ) . R e p re s e n ta t i o n o f t r a n s mi t t e dd i b i t s )

18 disp ( L o c . o f meg . p o i n t | ( 3/2) as qr t (T) | ( 1 / 2 ) a s q r t (

T) | ( 3 / 2 ) a s q r t ( T) | ( 1 / 2 ) a s q r t (T) )

19 disp (

)20 disp ( T r a ns m i tt e d d i b i t | 00 | 01

| 11 | 10 )21 disp ( )22 disp ( )23 disp ( F ig ur e 3 . 8 ( c ) . D e ci s i on i n t e r v a l s f o r

r e c e i v e d d i b i t s )24 disp ( R e ce i ve d d i b i t | 00 | 01

| 11 | 10 )25 disp (

)26 disp ( I n t e r v a l on p h i 1 ( t ) | x1 < a . s q rt (T) |a . s q r t (

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T)


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9 p hi t = sqrt ( 2 / T ) * cos ( 2 * % p i * f c * t 1 ) ;

10 h op t = p hi t ;11 p hi ot = convol ( p h i t , h o p t ) ;

12 p hi ot = p hi ot /max ( p h i o t ) ;

13 t 2 = 0 : 0. 0 1: 2 * T ;

14 subplot ( 2 , 1 , 1 )

15 a = gca () ;

16 a . x _ l o c at i o n = o r i g i n ;17 a . y _ l o c at i o n = o r i g i n ;18 a . d a t a _ bo u n d s = [ 0 , - 1 ; 1 , 1] ;

19 plot2d ( t 1 , p h i t ) ;

20 x l a b e l (

t )21 y l a b e l (

p h i ( t ) )22 t i t l e ( F i gu r e 3 . 1 3 ( a ) RF p u l s e i n pu t )23 subplot ( 2 , 1 , 2 )

24 a = gca () ;


28 plot2d ( t 2 , p h i o t ) ;

29 x l a b e l (

t )30 y l a b e l (

ph i0 ( t ) )31 t i t l e ( F i gu r e 3 . 1 3 ( b ) Matched F i l t e r o ut pu t )

Scilab code Exa 3.4 Matched Filter output for Noise-like signal

1 / / C a pt i on : Match ed F i l t e r o u tp u t f o r N o is e l i k es i g n a l

2 // Example3 . 4 : Matched F i l t e r o ut pu t f o r n o i s e l i k e

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i n p u t

3 clear ;4 close ;

5 clc ;

6 p h it = 0 .1 * rand ( 1 , 1 0 , uni f or m ) ;7 h op t = p hi t ;

8 p hi 0t = convol ( p h i t , h o p t ) ;

9 p hi 0t = p hi 0t /max ( p h i 0 t ) ;

10 subplot ( 2 , 1 , 1 )

11 a = gca () ;

12 a . x _ l o c at i o n = o r i g i n ;13 a . y _ l o c at i o n = o r i g i n ;

14 a . d a t a _ bo u n d s = [ 0 , - 1 ; 1 , 1] ;15 plot2d ([1: length ( p h i t ) ] , p h i t ) ;

16 x l a b e l (

t )17 y l a b e l (

p h i ( t ) )18 t i t l e ( F ig ur e 3 . 16 ( a ) N oi se L ik e i np ut s i g n a l )19 subplot ( 2 , 1 , 2 )

20 a = gca () ;


24 plot2d ([1: length ( p h i 0 t ) ] , p h i 0 t ) ;

25 x l a b e l (

t )26 y l a b e l (

ph i0 ( t ) )

27 t i t l e ( F i gu r e 3 . 1 6 ( b ) Matched F i l t e r o ut pu t )

Scilab code Exa 3.6 Linear Predictor of Order one

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1 / / C ap ti on : L i n e a r P r e d i c t o r o f O rd er o ne

2 // Example3 . 6 : LINEAR PREDICTION: Pr ed ic to r of OrderOne3 clear ;

4 close ;

5 clc ;

6 Rxx = [ 0. 6 1 0 .6 ];

7 h 01 = R xx ( 3 ) / Rx x ( 2) ; / / Rxx ( 2 ) = Rxx ( 0 ) , Rxx ( 3 ) =R x x ( 1)

8 s i gm a _E = R xx ( 2 ) - h 01 * R xx ( 3 ) ;

9 s i gm a _X = R xx ( 2 ) ;

10 disp (sig ma_E , P r e d i c t o r e r r o r v a r ia n c e )

11 disp (sig ma_X , P r e d i c t o r i n pu t v a r i a n c e )12 if ( s i gm a _X > s ig m a_ E )

13 disp ( The p r e d i c t o r e r r o r v a r i a n c e i s l e s s thant h e v a ri a nc e o f t he p r e d i c t o r i np ut )

14 end

Scilab code CF 3.29 Implementation of LMS Adaptive Filter algorithm

1 // Im pl em en ta ti on o f LMS ADAPTIVE FILTER2 // For n o i s e c a n c e l l a t i o n a p p l i c a t i o n3 clear ;

4 clc ;

5 close ;

6 o rd er = 1 8;

7 t = 0 : 0. 0 1 :1 ;

8 x = sin ( 2 * % p i * 5 * t ) ;

9 n oi se = rand (1 , length ( x ) ) ;

10 x _n = x + no is e ;

11 r e f_ n oi s e = n oi se * rand ( 1 0 ) ;

12 w = zeros (order ,1);

13 m u = 0 .0 1* ( sum ( x . ^ 2 ) / length ( x ) ) ;

14 N = length ( x ) ;15 for k = 1: 1 01 0

16 for i = 1 : N - o rd er - 1

17 b u ff e r = r e f _n o i se ( i : i + o r de r - 1) ;

18 d e s ir e d ( i ) = x _n ( i ) - b u f f er * w ;

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19 w = w + ( b u f fe r * m u * d e s i re d ( i ) ) ;

20 end21 end

22 subplot ( 4 , 1 , 1 )

23 plot2d ( t , x )

24 t i t l e ( O r i g n a l I n pu t S i g n a l )25 subplot ( 4 , 1 , 2 )

26 plot2d (t, noise ,2)

27 t i t l e ( r and om n o i s e )28 subplot ( 4 , 1 , 3 )

29 plot2d ( t , x _ n , 5 )

30 t i t l e ( S i g n a l +n o i s e )

31 subplot ( 4 , 1 , 4 )32 plot ( d e s i r e d )

33 t i t l e ( n o i s e r em ov ed s i g n a l )

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Figure 3.6: Figure3.29

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Chapter 4

Sampling Process

Scilab code Exa 4.1 Bound on Aliasing error for Time-shifted sinc pulse

1 / / C ap ti on : Bound on A l i a s i n g e r r o r f o r Times h i f t e ds i n c p u l s e

2 / / Exa mp le4 . 1 : Maximum bou nd on a l i a s i n g e r r o r f o rs i n c p u l s e

3 clc ;

4 close ;

5 t = - 1. 5 :0 . 01 : 2. 5;

6 g = 2 * s in c _n e w ( 2* t - 1) ;

7 disp (max ( g ) , A l i a s i n g e r r o r c an no t e xc ee d max | g ( t ) | )

8 f = - 1: 0. 01 :1 ;

9 G = [0 ,0 ,0 ,0 , ones (1 , length ( f ) ) , 0 , 0 , 0 , 0 ] ;

10 f 1 = - 1 . 04 : 0 .0 1 : 1. 0 4 ;

11 subplot ( 2 , 1 , 1 )

12 a = gca () ;

13 a . d a t a _ bo u n d s = [ - 3 , - 1 ;2 , 2 ];

14 a . x _ l o c at i o n = o r i g i n 15 a . y _ l o c at i o n = o r i g i n

16 plot2d ( t , g )17 x l a b e l ( t )18 y l a b e l ( g ( t ) )19 t i t l e ( F ig ur e 4 . 8 ( a ) S i n c p u l s e g ( t ) )20 subplot ( 2 , 1 , 2 )

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21 a = gca () ;

22 a . d a t a _ bo u n d s = [ - 2 , 0 ;2 , 2 ] ;

23 a . x _ l o c at i o n = o r i g i n 24 a . y _ l o c at i o n = o r i g i n 25 plot2d2 ( f 1 , G )

26 x l a b e l ( f )27 y l a b e l ( G( f ) )28 t i t l e ( F i g u re 4 . 8 ( b ) A mp li tu de s pe ct ru m |G( f ) | )

Scilab code Exa 4.3 Equalizier to compensate Aperture effect

1 / / C ap ti on : E q u a l i z e r t o c om pe ns at e A p er t ur e e f f e c t

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2 / / Exa mp le4 . 3 : E q u a l i z e r t o Co mp en sa te f o r a p e r t u r e

e f f e c t3 clc ;4 close ;

5 T _ Ts = 0 . 0 1 :0 . 0 1 :0 . 6 ;

6 / /E = 1 / ( s i n c n e w ( 0 . 5 T Ts ) ) ;7 E ( 1) = 1;

8 for i = 2: length ( T _ T s )

9 E ( i ) = ( ( %p i / 2) * T _ Ts ( i ) ) /( sin ( ( % p i / 2 ) * T _ T s ( i ) ) ) ;

10 end

11 a = gca () ;

12 a . d a t a _ bo u n d s = [ 0 , 0 . 8 ;0 . 8 , 1 . 2] ;

13 plot2d ( T _ T s , E , 5 )14 x l a b e l ( D uty c y c l e T/ Ts )15 y l a b e l ( 1 / s i n c ( 0 . 5 ( T/ Ts ) ) )16 t i t l e ( F i gu r e 4 . 1 6 N or ma li ze d e q u a l i z a t i o n ( t o

c o mpe n sa te f o r a p e rt u r e e f f e c t ) p l o t t ed v e rs u s T/Ts )

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Chapter 5

Waveform Coding Techniques

Scilab code Exa 5.1 Average Transmitted Power for PCM

1 / / C a p t i o n : A v e r ag e T r a n s m i t t e d P ow er f o r PCM2 / / E x am pl e5 . 1 : A v e r ag e T r a n s m i t t e d P ow er o f PCM3 / / P ag e 1 8 74 clear ;

5 clc ;

6 s i gm a _N = input ( E nt er t he n o i s e v a r i a n c e ) ;7 k = input ( E nt er t he s e p a r at i o n c o ns t an t f o r on o f f

s i g n a l i n g ) ;8 M = input ( E nt er t he number o f d i s c r e t e a mp li tu de

l e v e l s f o r NRZ p o l ar ) ;9 disp ( The a v e r ag e t r a n s m i t t e d p ower i s : )

10 P = ( k ^ 2 ) *( s i g m a _N ) * ( ( M ^ 2 ) - 1 ) / 1 2;

11 disp ( P )

12 / / R e s u l t13 // E n te r t he n o i s e v a r i a n c e 10614 // E nt e r t he s e p a r at i o n c o ns t a n t f o r ono f f s i g n a l i n g

715 // E nt e r t he number o f d i s c r e t e a mp li tu de l e v e l s f o r

NRZ p o l a r 216 // The a v er a ge t r a n sm i t t ed power i s : 0 . 0 00 0 1 22

Scilab code Exa 5.2 Comaprision of M-ary PCM with ideal system (Chan-nel Capacity Theorem)

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1 / / C a p t i o n : C o m pa r i so n o f Ma r y PCM w i th i d e a l s y st em

( C h a nn e l C a p a c i t y T he or em )2 / / E x am pl e5 . 2 : C o m pa r i so n o f Mary PCM system3 / / C h an n el C a p a c i t y t h eo r em4 clear ;

5 close ;

6 clc ;

7 P _ No B_ d B = [ - 2 0 :3 0] ; // I n pu t s i g n a l ton o i s e r a t i o P/NoB , d e c i b e l s

8 P _N oB = 1 0^ ( P _ No B _d B / 1 0) ;

9 k =7; // f o r Mar y PCM sys tem ;10 R b_ B = log2 ( 1 + ( 1 2 / k ^ 2 ) * P _ N o B ) ; // b an dwid th e f f i c i e n c y

i n b i t s / s e c / Hz11 C_B = log2 ( 1 + P _ N o B ) ; // i d e a l s ys te m a c c o rd i n g t o

Sha nnon s c h a n n e l c a p a c i t y t he or em12 / / p l o t13 a = gca () ;

14 a . d a t a _ bo u n d s = [ - 3 0 , 0 ; 40 , 1 0 ];

15 plot2d (P_NoB_dB ,C_B ,5)

16 plot2d (P _NoB_dB ,Rb_B ,5)

17 p o ly 1 = a . c h i l dr e n ( 1 ) . c h i l dr e n ( 1 ) ;

18 p o ly 1 . t h i c k ne s s = 2;

19 p ol y1 . l i n e_ s ty l e = 4 ;

20 x l a b e l ( I n pu t s i g n a l to n o i s e r a t i o P/NoB , d e c i b e l s )

21 y l a b e l ( B andwidth e f f i c i e n c y , Rb/B , b i t s p er s ec on dp er h e r t z )

22 t i t l e ( F i g u re 5 . 9 C om pa ri so n o f Ma r y PCM w i t h t h ei d e a l s sy te m )

23 l e g e n d ( [ I d e a l S ys te m , PCM ])

Scilab code Exa 5.3 Signal-to-Quantization Noise Ratio of PCM

1 / / C a p t i o n : S i g n a l toQ u a n t i z a t i o n N o i s e R a t io o f PCM2 / / E x am pl e5 . 3 : S i g n a l toQ ua n ti z a t i on n o i s e r a t i o3 / / C h a n n el B a nd wi d th B4 clear ;

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5 clc ;

6 n = input ( E nt er no . o f b i t s u se d t o e nc od e : )7 W = input ( E nt er t h e m es sa ge s i g n a l b an wi dt h i n Hz : )

8 B = n * W ;

9 disp (B , C ha nn el w id t h i n Hz : )10 SNRo = 6* n - 7.2;

11 disp ( S N R o , Output S i g n al t o n o i s e r a t i o i n dB : )12 // R es ul t 1 i f n = 8 b i t s13 // E nt e r no . o f b i t s u se d t o e nc od e : 814 // E n te r t he m es sa ge s i g n a l b an wi dt h i n Hz : 4 00 015 // C ha nnel w id th i n Hz : 3 2 0 0 0.

16 // Output S i gn a l t o n o i se r a t i o i n dB : 4 0 . 817 / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / /18 // R es ul t 2 i f n = 9 b i t s19 // E n te r no . o f b i t s u se d t o e nc od e : 920 // E n te r t he m es sa ge s i g n a l b an wi dt h i n Hz : 4 0 0021 / / Ch an ne l w id th i n Hz : 3 6 0 0 0 .22 // Output S i gn a l t o n o i se r a t i o i n dB : 4 6 . 823 / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / /24 // C on c l us i o n : c o mp ar in g r e s u l t 1 w i th r e s u l t 2 i f

number o f b i t s i n c r e as e d by 125

// c o r r es p o n d i ng o ut pu t s i g n a l t o n o i s e i n PCMi n c r e as e d by 6 dB .

Scilab code Exa 5.5 Output Signal-to-Noise ratio for Sinusoidal Modula-tion

1 / / E xa mp le 5 : D e l t a M o d u la t i o n t o a vo id s l o p eo v e r l o a d d i s t o r t i o n

2 / / maximum o u t p u t s i g n a l ton o i s e r a t i o f o rs i n u s o i d a l m od ul at io n

3 / / p ag e 2 07

4 clear ;5 clc ;

6 a0 = input ( E nt e r t he a mp li tu de o f s i n u s o i d a l s i g n a l: ) ;

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7 f0 = input ( E n t e r t he f re q u e n c y o f s i n u s o i d a l s i g n a l

i n Hz : ) ;8 fs = input ( E nt er t he s a mp li ng f r eq u e nc y i n s am pl esp e r s e c o n d s : ) ;

9 Ts = 1/ fs ; // S am pl in g i n t e r v a l10 d el ta = 2 * %p i * f0 * a 0 * Ts ; // S te p s i z e t o a vo id s l o pe

o v e r l o a d11 P ma x = ( a 0 ^2 ) / 2; / /maximum p e r m i s s i b l e o u t p u t p ow er12 s i gm a _Q = ( d e lt a ^ 2) / 3 ; // Q u an t iz a ti o n e r r o r o r n o i s e

v a r i a n c e13 W = f0 ;//Maximum mess age bandwidth14 N = W * Ts * s i gm a_ Q ; / / A ve ra ge o u tp ut n o i s e po wer

15 S NR o = P ma x / N; / / Maximum o u t p u t s i g n a l ton o i s er a t i o

16 S NR o_ dB = 1 0* log10 ( S N R o ) ;

17 disp (SNR o_dB , Maximum out pu t s i gn al ton o s i e i n dBf o r D e l t a M o du a lt i on : )

18 // R e s ul t 1 f o r f s = 8 000 H er tz19 // E nt e r t he a mp li tu de o f s i n u s o i d a l s i g n a l : 120 // E nt e r t h e f r e qu e n c y o f s i n u s o i d a l s i g n a l i n Hz

: 4 0 0 021 // E n te r t he s am pl in g f r eq u e nc y i n s am pl es p er

s e c o n d s : 8 0 0 022 //Maximum out pu t s i gn al ton o s i e i n dB f o r D el taM odual t i on : 5 . 1 7 1 7 8 4 9

23 /// / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / /

24 // R e s ul t 2 f o r f s = 1 600 0 H er tz25 // E nt e r t he a mp li tu de o f s i n u s o i d a l s i g n a l : 126 // E nt e r t h e f r e qu e n c y o f s i n u s o i d a l s i g n a l i n Hz

: 4 0 0 027 // E n te r t he s am pl in g f r eq u e nc y i n s am pl es p er

s e c o n d s : 1 6 0 0 028 //Maximum out pu t s i gn al ton o s i e i n dB f o r D el ta

M o d u a lt i o n : 3 . 8 5 9 1 1 529 //

/ / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / /

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30 // C o nc l us i on : c om pa ri ng r e s u l t 1 w it h r e s u l t 2 , i f t h e s a mp l in g f r e q u e n c y31 // i s d o ub le d t he s i g n a l t o n o i se i n c r e a s e d by 9 dB

Scilab code CF 5.13a (a) u-Law companding

1 / / C a p t i o n : uLaw companding2 / / F i g u r e 5 . 1 3 ( a ) M ulaw c o mp a nd i ng N o n l i n e a r

Q u a n t i z a t i o n3 // P l o tt i n g mulaw c h a r a c t e r i s t i c s f o r d i f f e r e n t4 / / V a lu e s o f mu5 clc ;

6 x = 0 :0 .0 1: 1; / / N o r ma l i ze d i n p u t7 m u = [ 0 , 5 , 25 5] ; // d i f f e r e n t v a l u e s o f mu8 for i = 1: length ( m u )

9 [ C x (i , :) , X m ax ( i ) ] = m ul aw ( x , mu ( i ) );

10 end

11 plot2d ( x / X m a x ( 1 ) , C x ( 1 , : ) , 2 )

12 plot2d ( x / X m a x ( 2 ) , C x ( 2 , : ) , 4 )

13 plot2d ( x / X m a x ( 3 ) , C x ( 3 , : ) , 6 )

14 xtitle ( C o m p r e s s i o n Law : uLaw companding ,

N o rm a l iz e d I n p u t | x | , N o r m a l i z e d O ut pu t | c ( x ) | );15 l e g e n d ( [ u =0 ] ,[ u=5 ] ,[ u=255 ])

Scilab code CF 5.13b (b) A-law companding

1 / / C a p t i o n : Al a w c o mp a n di n g2 / / F i g u r e 5 . 1 3 ( b ) Al a w c om pa nd in g , N o n l i n e a r

Q u a n t i z a t i o n3 / / P l o t t i n g Al aw c h a r a c t e r i s t i c s f o r d i f f e r e n t

4 // V a lu es o f A5 clc ;

6 x = 0 :0 .0 1: 1; / / N o r ma l i ze d i n p u t7 A = [ 1 , 2 , 87 .5 6] ; // d i f f e r e n t v a l u es o f A8 for i = 1: length ( A )

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37


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9 [ C x (i , :) , X m ax ( i ) ] = A la w ( x ,A ( i )) ;

10 end

11 plot2d ( x / X m a x ( 1 ) , C x ( 1 , : ) , 2 )

12 plot2d ( x / X m a x ( 2 ) , C x ( 2 , : ) , 4 )

13 plot2d ( x / X m a x ( 3 ) , C x ( 3 , : ) , 6 )

14 xtitle ( C o m p r e s s i o n Law : ALaw companding , N o rm a l iz e d I n p u t | x | , N o r m a l i z e d O ut pu t | c ( x ) | );

15 l e g e n d ( [ A =1 ] ,[ A=2 ] ,[ A=87.56 ])

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Chapter 6

Baseband Shaping for Data

Transmission

Scilab code Exa 6.1 Bandwidth Requirements of the T1 carrier

1 / / C a pt i on : B an dw id th R e qu i re m en t s o f t h e T1 c a r r i e r2 / / E xa mp le 6 . 1 : B an dw id th R e q u i r em e n t s o f t h e T1

C a r r i e r3 / / P ag e 2 5 14 clear ;

5 clc ;

6 Tb = input ( E nt er t he b i t d u r at i o n o f t he TDM s i g n a l: )

7 B o = 1 /( 2* T b ); / /minimum t r a n s m i s s i o n b an dw id th o f T1sy st e m

8 / / T r a ns m i s si o n b an dw id th f o r r a i s e d c o s i n e s pe ct ru mB

9 a lp ha = 1; // c o s i n e r o l l o f f f a c t o r10 f 1 = B o *( 1 - a lp ha ) ;

11 B = 2* Bo - f 1;

12 disp (B , T r an s mi s si o n ba ndwi dth f o r r a i s e d c o s i n e

s p ec t ru m i n Hz : )13 / / R e s u l t14 // E n te r t he b i t d u r at i o n o f t he TDM s i g n a l

: 0 . 6 4 7 1 0 615 / / T r a ns m i s si o n b an dw id th f o r r a i s e d c o s i n e s pe ct ru m

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i n H z : 1 5 4 5 5 9 5 . 1

Scilab code CF 6.1a (a) Nonreturn-to-zero unipolar format

1 // C apt i on : N onr et ur n toz e r o u n i p ol a r f or ma t2 / / F i g u re 6 . 1 ( a ) : D i s c r e t e PAM S i g n a l s G e n er a t io n3 // [ 1 ] . Un ip ol ar NRZ4 / / p ag e 2 355 clear ;

6 close ;

7 clc ;

8 x = [0 1 0 0 0 1 0 0 1 1];

9 bi n ar y _z e ro = [0 0 0 0 0 0 0 0 0 0];

10 bi na r y_ on e = [1 1 1 1 1 1 1 1 1 1];

11 L = length ( x ) ;

12 L1 = length ( b i n a r y _ z e r o ) ;

13 t o ta l _d u ra t io n = L * L ;

14 / / p l o t t i n g15 a = gca () ;

16 a . d a ta _ bo u nd s = [0 -2 ;L * L1 2 ];

17 for i =1: L

18 if ( x ( i ) = = 0 )

19 plot ( [ i * L - L + 1 : i * L ] , b i n a r y _ z e r o ) ;20 p o ly 1 = a . c h i l d re n ( 1 ) . c h i l d re n ( 1 ) ;

21 p o ly 1 . t h i c k n es s = 3 ;

22 else

23 plot ( [ i * L - L + 1 : i * L ] , b i n a r y _ o n e ) ;

24 p o ly 1 = a . c h i l d re n ( 1 ) . c h i l d re n ( 1 ) ;

25 p o ly 1 . t h i c k n es s = 3 ;

26 end

27 end

28 xgrid (1)

29 t i t l e ( U n i po l a r NRZ )

Scilab code CF 6.1b (b) Nonreturn-to-zero polar format

1 // C apt i on : N onr et ur n toz e r o p o l ar f or ma t

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2 / / F i g u re 6 . 1 ( b ) : D i s c r e t e PAM S i g n a l s G e n er a ti o n

3 // [ 2 ] . P ol a r NRZ4 / / p ag e 2 355 clear ;

6 close ;

7 clc ;

8 x = [0 1 0 0 0 1 0 0 1 1];

9 b in ar y_ ne ga ti ve = [ -1 -1 -1 -1 -1 -1 -1 -1 -1 -1];

10 b i na r y _ p os i t i v e = [1 1 1 1 1 1 1 1 1 1];

11 L = length ( x ) ;

12 L1 = length ( b i n a r y _ n e g a t i v e ) ;

13 t o ta l _d u ra t io n = L * L1 ;

14 / / p l o t t i n g15 a = gca () ;

16 a . d a ta _ bo u nd s = [0 -2 ;L * L1 2 ];

17 for i =1: L

18 if ( x ( i ) = = 0 )

19 plot ( [ i * L - L + 1 : i * L ] , b i n a r y _ n e g a t i v e ) ;


21 p o ly 1 . t h i c k n es s = 3 ;

22 else

23 plot ( [ i * L - L + 1 : i * L ] , b i n a r y _ p o s i t i v e ) ;


25 p o ly 1 . t h i c k n es s = 3 ;

26 end

27 end

28 xgrid (1)

29 t i t l e ( Po la r NRZ )

Scilab code CF 6.1c (c) Nonreturn-to-zero bipolar format

1 // C apt i on : N onr et ur n toz e r o b i p o l a r f or ma t

2 / / F i g u r e 6 . 1 ( c ) : D i s c r e t e PAM S i g n a l s G e n e r a ti o n3 // [ 3 ] . Bi P ol ar NRZ4 / / p ag e 2 355 clear ;

6 close ;

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7 clc ;

8 x = [0 1 1 0 0 1 0 0 1 1];9 b in ar y_ ne ga ti ve = [ -1 -1 -1 -1 -1 -1 -1 -1 -1 -1];

10 bi n ar y _z e ro = [0 0 0 0 0 0 0 0 0 0];

11 b i na r y _ p os i t i v e = [1 1 1 1 1 1 1 1 1 1];

12 L = length ( x ) ;

13 L1 = length ( b i n a r y _ n e g a t i v e ) ;

14 t o ta l _d u ra t io n = L * L1 ;

15 / / p l o t t i n g16 a = gca () ;

17 a . d a ta _ bo u nd s = [0 -2 ;L * L1 2 ];

18 for i =1: L

19 if ( x ( i ) = = 0 )20 plot ( [ i * L - L + 1 : i * L ] , b i n a r y _ z e r o ) ;


22 p o ly 1 . t h i c k n es s = 3 ;

23 elseif ( ( x ( i ) = = 1 ) & ( x ( i - 1 ) ~ = 1 ) )

24 plot ( [ i * L - L + 1 : i * L ] , b i n a r y _ p o s i t i v e ) ;


26 p o ly 1 . t h i c k n es s = 3 ;

27 else

28 plot ( [ i * L - L + 1 : i * L ] , b i n a r y _ n e g a t i v e ) ;


30 p o ly 1 . t h i c k n es s = 3 ;

31 end

32 end

33 xgrid (1)

34 t i t l e ( Bi P ol a r NRZ )

Scilab code Exa 6.2 Duobinary Encoding

1 / / C a p t i o n : D u o b i n ar y E n c o d i ng

2 / / Exa mp le6 . 2 : P r ec o de d D uo bi na ry c o d e r and d e c o d e r3 / / P ag e 2 5 64 clc ;

5 b = [ 0 ,0 , 1 , 0 ,1 , 1 , 0] ; / / i n p u t b i n a r y s e q u e n c e : p r e c o d e ri n p u t

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Figure 6.3: Figure6.1c

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6 a ( 1) = x or ( 1 , b (1 ) ) ;

7 if ( a ( 1 ) = = 1 )8 a _ vo lt s ( 1) = 1 ;

9 end

10 for k =2: length ( b )

11 a ( k ) = x or ( a (k - 1 ) ,b ( k )) ;

12 if ( a ( k ) = = 1 )

13 a _ v o l t s ( k ) = 1 ;

14 else

15 a _ v o l t s ( k ) = - 1 ;

16 end

17 end

18 a = a ;19 a _ v ol t s = a _ vo lt s ;

20 disp (a , P r ec o d er o ut p ut i n b i n a r y f or m : )21 disp (a_v olts , P r ec o de r o u tp ut i n v o l t s : )22 // D uo bi na ry c o de r o ut pu t i n v o l t s23 c ( 1) = 1 + a _v ol ts ( 1) ;

24 for k =2: length ( a )

25 c ( k ) = a _ vo l ts ( k - 1) + a _ vo l ts ( k ) ;

26 end

27 c = c ;

28 disp (c , D uo bi na ry c o d er o u tp u t i n v o l t s :

)

29 // D uo bi na ry d ec o de r o ut pu t by a p p l y in g d e c i s i o nr u l e

30 for k =1: length ( c )

31 if ( abs ( c ( k ) ) > 1 )

32 b_r (k ) = 0;

33 else

34 b _r ( k ) = 1;

35 end

36 end

37 b _r = b_r ;

38 disp ( b _ r , R e co ve re d o r i g i n a l s eq ue nc e a t d e t e c t o roupup t : )

39 / / R e s u l t40 / / P r ec o d er o u tp ut i n b i n a r y f or m :41 //

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42 // 1 . 1 . 0 . 0 . 1 . 0 . 0 .

43 //44 // P re co de r o ut pu t i n v o l t s :45 //46 // 1 . 1 . 1 . 1 . 1 . 1 . 1 .47 //48 // D uo bi na ry c o de r o ut pu t i n v o l t s :49 //50 // 2 . 2 . 0 . 2 . 0 . 0 . 2 .51 //52 // R ec ov er ed o r i g i n a l s e qu e nc e a t d e t e c t o r ou pupt :53 //

54 // 0 . 0 . 1 . 0 . 1 . 1 . 0 .

Scilab code Exa 6.3 Generation of bipolar output for duobinary coder

1 / / C ap ti on : G e ne r a ti o n o f b i p o l a r o ut p ut f o r d u ob i na r yc o d e r

2 // Example6 . 3 : O pe ra ti on o f C i r c u i t i n f i g u r e 6 . 1 33 // f o r g e n er a t i n g b i p o l a r f or ma t4 / / pa ge 2 56 and p ag e 2 575 / / R e f er T ab le 6 . 46 clc ;

7 x = [ 0 ,1 , 1 , 0 ,1 , 0 , 0 ,0 , 1 , 1] ; / / i n p u t b i n a r y s e q u e n c e :p r e co d e r i n pu t

8 y (1) = 1;

9 for k =2: length ( x ) + 1

10 y ( k ) = x or ( x (k - 1 ) ,y ( k -1 ) ) ;

11 end

12 y _ de l ay = y ( 1: $ - 1) ;

13 y = y ;

14 y _ d el a y = y _ de la y ;

15 disp (y , Modulo2 a d d er o u t pu t : )

16 disp (y_d elay , D e la y e l e m e n t o u t p u t : )17 for k = 1: length ( y _ d e l a y )

18 z ( k ) = y ( k +1 ) - y _d e la y ( k );

19 end

20 z = z ;

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21 disp (z , d i f f e r e n t i a l e n c o d e r b i p o l a r o u t p u t i n v o l t s

: )22 / / R e s u l t23 //Modulo 2 a d d er o u tp u t :24 // 1 . 1 . 0 . 1 . 1 . 0 . 0 . 0 .

0 . 1 . 0 .25 / / D el a y e l e m en t o u tp u t :26 // 1 . 1 . 0 . 1 . 1 . 0 . 0 . 0 .

0 . 1 .27 / / d i f f e r e n t i a l e n c o d e r b i p o l a r o u tp u t i n v o l t s :28 // 0 . 1 . 1 . 0 . 1 . 0 . 0 . 0 .

1 . 1 .

Scilab code CF 6.4 Power Spectra of different binary data formats

1 // C ap ti on : Power S p ec t ra o f d i f f e r e n t b i na r y d at af o r m a t s

2 // F ig ur e 6 . 4 : Power S p e ct a l D e n s i t i e s o f 3 / / D i f f e r e n t L i ne Co di ng T ec h ni q ue s4 / / [ 1 ] . NRZ P o l a r F or ma t [ 2 ] . NRZ B i p o l a r f o r m a t5 / / [ 3 ] . NRZ U n i p o l a r f o r m a t [ 4 ] . M a n ch e s t er f o r m a t6 / / P ag e 2 4 1

7 close ;8 clc ;

9 / / [ 1 ] . NRZ P o l a r f o r m a t10 a = input ( E n te r t h e A mp li tu de v a l u e : ) ;11 fb = input ( E nt er t he b i t r a t e : ) ;12 Tb = 1/ fb ; // b i t d u r a t i o n13 f = 0 : 1/ ( 10 0 * Tb ) : 2/ T b ;

14 for i = 1: length ( f )

15 S x x f _N R Z _ P ( i ) = ( a ^ 2 ) * T b *( s i n c _ n ew ( f ( i ) * T b ) ^ 2) ;

16 S x x f_ N R Z _B P ( i ) = ( a ^ 2 ) * Tb * ( ( s i n c _ ne w ( f ( i ) * T b ) ) ^ 2)

*(( sin ( % p i * f ( i ) * T b ) ) ^ 2 ) ;

17 if ( i = = 1 )18 S x x f _N R Z _U P ( i ) = ( a ^ 2 ) * ( Tb / 4 ) * ( ( s i n c _n e w ( f ( i ) * Tb

) ) ^ 2 ) + ( a ^ 2 ) / 4 ;

19 else

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20 S x x f _N R Z _U P ( i ) = ( a ^ 2 ) * ( Tb / 4 ) * ( ( s i n c _n e w ( f ( i ) * Tb

) ) ^ 2 ) ;21 end

22 S x x f _M a n c h ( i ) = ( a ^ 2 ) * T b *( s i n c _ n ew ( f ( i ) * T b / 2) ^ 2 ) * (

sin ( % p i * f ( i ) * T b / 2 ) ^ 2 ) ;

23 end

24 / / P l o t t i n g25 a = gca () ;

26 plot2d ( f , S x x f _ N R Z _ P )


28 p ol y1 . t h i ck n es s = 2 ; // t he t i c k n e s s o f a c ur ve .29 plot2d (f, Sxxf_NRZ_BP ,2)

30 p o ly 1 = a . c h i l dr e n ( 1 ) . c h i l dr e n ( 1 ) ;31 p ol y1 . t h i ck n es s = 2 ; // t he t i c k n e s s o f a c ur ve .32 plot2d (f, Sxxf_NRZ_UP ,5)


34 p ol y1 . t h i ck n es s = 2 ; // t he t i c k n e s s o f a c ur ve .35 plot2d (f, Sxxf_Manch ,9)


37 p ol y1 . t h i ck n es s = 2 ; // t he t i c k n e s s o f a c ur ve .38 x l a b e l ( fTb> )39 y l a b e l ( Sxx( f )> )40 t i t l e (

Power S p e c t r a l D e n s i t i e s o f D i f f e r e n t L in eC o d i n ig T e c hn i q ue s )41 xgrid (1)

42 l e g e n d ( [ NRZ Po la r Format , NRZ B i p o l a r f o r m a t , NRZU n i p o l a r f o r ma t , M a n c h e s t e r f o r m a t ]) ;

43 / / R e s u l t44 / / E n te r t h e A mp li tu de v a l u e : 145 // E nt e r t he b i t r a t e : 1

Scilab code CF 6.6b (b) Ideal solution for zero ISI

1 // C ap ti on : I d e a l s o l u t i o n f o r z e r o I S I2 // F ig ur e 6 . 6 ( b ) : I d e a l S o l u t i o n f o r I n te rs y m b ol

I n t e r f e r e n c e3 / / SINC p u l s e

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4 / / p ag e 2 49

5 rb = input ( E nt er t he b i t r a t e : ) ;6 Bo = rb /2;7 t = - 3 :1 / 1 00 : 3;

8 x = s i nc _ ne w ( 2* B o * t );

9 plot ( t , x )

10 x l a b e l ( t> ) ;11 y l a b e l ( p ( t )> ) ;12 t i t l e ( SINC P ul s e f o r z e r o I S I )13 xgrid (1)

14 / / R e s u l t15 // E nt e r t he b i t r a t e : 1

Scilab code CF 6.7b (b) Practical solution: Raised Cosine

1 // C ap ti on : P r a c t i c a l s o l u t i o n : R ai se d C os in e2 / / F i g u re 6 . 7 ( b ) : P r a c t i c a l S o l u t i o n f o r I n t e r sy m b o l

I n t e r f e r e n c e3 / / R a i s e d C o s i n e S p ec tr u m4 / / p ag e 2 505 close ;

6 clc ;

7 rb = input ( E nt er t he b i t r a t e : ) ;8 T b = 1/ r b ;

9 t = - 3 :1 / 1 00 : 3;

10 Bo = rb /2;

11 A l ph a = 0; // I n t i a l i z e d t o z er o12 x = t /T b;

13 for j = 1: 3

14 for i = 1: length ( t )

15 if ( ( j = = 3 ) & ( ( t ( i ) = = 0 . 5 ) | ( t ( i ) = = - 0 . 5 ) ) )

16 p ( j , i ) = s i n c_ n e w ( 2 * Bo * t ( i ) ) ;

17 else18 n um = s in c_ ne w ( 2* B o* t (i ) )* cos ( 2 * % p i * A l p h a *

B o * t ( i ) ) ;

19 d en = 1 - 1 6* ( A lp ha ^ 2 ) *( B o ^ 2) * ( t ( i) ^ 2) + 0 . 01 ;

20 p ( j , i ) = n um / d e n ;

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21 end

22 end23 A lp ha = A lp ha + 0 . 5;

24 end

25 a = gca () ;

26 plot2d ( t , p ( 1 , : ) )

27 plot2d ( t , p ( 2 , : ) )


29 p o l y 1 . f o r e g r o u n d = 2 ;

30 plot2d ( t , p ( 3 , : ) )


32 p o 1 y 2 . f o r e g r o u n d = 4 ;

33 p ol y2 . l i n e_ s ty l e = 3 ;34 x l a b e l ( t /Tb> ) ;35 y l a b e l ( p ( t )> ) ;36 t i t l e ( RAISED COSINE SPECTRUM P r a c t i c a l S o l u t i o n

f o r I S I )37 l e g e n d ( [ R O l l o f f F a c t o r =0 , R O l l o f f F a c t or = 0. 5 ,

R O l l o f f F a c t or =1 ])38 xgrid (1)

39 / / R e s u l t40 // E nt e r t he b i t r a t e : 1

Scilab code CF 6.9 Frequency response of duobinary conversion filter

1 / / C ap ti on : F re qu en cy r e s p o n s e o f d u ob i na r y c o n v e r s i o nf i l t e r

2 / / F i g u r e 6 . 9 : F r e qu e n cy R e s po n s e o f D u ob i na r yC on v e r s i on f i l t e r

3 / / ( a ) A m pl i tu d e R e s po n s e4 / / ( b ) P ha s e R e s po n s e5 / / P ag e 2 5 4

6 clear ;7 close ;

8 clc ;

9 rb = input ( E nt er t he b i t r a t e= ) ;10 T b = 1/ r b ; / / B i t d u r a t i o n

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11 f = - rb / 2 : 1/ 1 00 : r b / 2;

12 A m p l i tu d e _ Re s p o n se = abs (2* cos ( % p i * f . * T b ) ) ;13 P h a s e_ R e s po n s e = - ( %p i * f . * Tb ) ;

14 subplot ( 2 , 1 , 1 )

15 a = gca () ;

16 a . x _ l o c at i o n = o r i g i n ;17 a . y _ l o c at i o n = o r i g i n ;18 plot2d (f,Amplitude_Response ,2)


20 p ol y1 . t h i ck n es s = 2 ; // t he t i c k n e s s o f a c ur ve .21 x l a b e l ( F r e q u e n c y f > )22 y l a b e l ( | H( f ) | > )

23 t i t l e ( A mp li tu de R ep s on s e o f D uo bi na ry S i n g a l i n g )24 subplot ( 2 , 1 , 2 )

25 a = gca () ;

26 a . x _ l o c at i o n = o r i g i n ;27 a . y _ l o c at i o n = o r i g i n ;28 plot2d (f,Phase_Response ,5)


30 p ol y1 . t h i ck n es s = 2 ; // t he t i c k n e s s o f a c ur ve .31 x l a b e l (

F r e qu e n cy f > )32 y l a b e l (

)33 t i t l e ( P ha se R e ps o ns e o f D uo bi na ry S i n g a l i n g )34 / / R e s u l t35 // E n te r t he b i t r a t e =8

Scilab code CF 6.15 Frequency response of modified duobinary conver-sion filter

1 / / C a pt i on : F r eq u en c y r e s p o n s e o f m o d i f i e d d u o b in a r y

c o n v e r s i o n f i l t e r2 / / F i g u re 6 . 1 5 : F re qu en cy R es po ns e o f M o d if i e dd u o b in a r y c o n v e r s i o n f i l t e r

3 / / ( a ) A m pl i tu d e R e s po n s e4 / / ( b ) P ha s e R e s po n s e

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5 / / p ag e 2 59

6 clear ;7 close ;

8 clc ;

9 rb = input ( E nt er t he b i t r a t e= ) ;10 T b = 1/ r b ; / / B i t d u r a t i o n11 f = - rb / 2 : 1/ 1 00 : r b / 2;

12 A m p l i tu d e _ Re s p o n se = abs (2* sin ( 2 * % p i * f . * T b ) ) ;

13 P h a s e_ R e s po n s e = - (2 * % pi * f . * T b ) ;

14 subplot ( 2 , 1 , 1 )

15 a = gca () ;

16 a . x _ l o c at i o n = o r i g i n ;

17 a . y _ l o c at i o n = o r i g i n ;18 plot2d (f,Amplitude_Response ,2)


20 p ol y1 . t h i ck n es s = 2 ; // t he t i c k n e s s o f a c ur ve .21 x l a b e l ( F r e q u e n c y f > )22 y l a b e l ( | H( f ) | > )23 t i t l e ( A mp li tu de R ep s on s e o f M o d i f i e d D uo bi na ry

S i n g a l i n g )24 xgrid (1)

25 subplot ( 2 , 1 , 2 )

26 a = gca () ;

27 a . x _ l o c at i o n = o r i g i n ;28 a . y _ l o c at i o n = o r i g i n ;29 plot2d (f,Phase_Response ,5)


31 p ol y1 . t h i ck n es s = 2 ; // t he t i c k n e s s o f a c ur ve .32 x l a b e l (

F r e qu e n cy f > )33 y l a b e l (

)34 t i t l e ( P ha se R e ps o ns e o f M o d i f i e d D uo bi na ry

S i n g a l i n g )35 xgrid (1)

36 / / R e s u l t37 // E n te r t he b i t r a t e =8

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Chapter 7

Digital Modulation Techniques

Scilab code Exa 7.1 QPSK Waveform

1 / / C ap ti on : Waveforms o f D i f f e r e n t D i g i t a l M od ul at io nt e c h n i q u e s

2 / / Exa mp le7 . 1 S i g n a l S pa c e D ia gr am f o r c o h e r e n t QPSKs y s t e m

3 clear ;

4 clc ;

5 close ;

6 M =4;

7 i = 1 : M ;8 t = 0 :0 .0 01 :1 ;

9 for i = 1: M

10 s 1 (i , : ) = cos ( 2 * % p i * 2 * t ) * cos ( ( 2 * i - 1 ) * % p i / 4 ) ;

11 s2 (i , :) = - sin ( 2 * % p i * 2 * t ) * sin ( ( 2 * i - 1 ) * % p i / 4 ) ;

12 end

13 S 1 = [] ;

14 S 2 = [ ] ;

15 S = [];

16 I n p u t_ S e q ue n c e = [0 , 1 , 1 , 0 , 1 , 0 , 0 , 0 ];

17 m = [3 , 1 ,1 , 2] ;18 for i =1: length ( m )

19 S 1 = [ S1 s1 ( m( i ) ,:) ];

20 S 2 = [ S2 s2 ( m( i ) ,:) ];

21 end

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22 S = S 1 + S 2 ;

23 figure24 subplot ( 3 , 1 , 1 )

25 a = gca () ;

26 a . x _ l o c at i o n = o r i g i n ;27 plot ( S 1 )

28 t i t l e ( Bi nar y PSK w av e of Oddnumbered b i t s o f i n pu ts e q u e n c e )

29 subplot ( 3 , 1 , 2 )

30 a = gca () ;


33 t i t l e ( B i n a r y PSK w av e o f E vennumbered b i t s o f i n p u t s e q ue n c e )

34 subplot ( 3 , 1 , 3 )

35 a = gca () ;

36 a . x _ l o c at i o n = o r i g i n ;37 plot ( S )

38 t i t l e ( QPSK wav efo rm )39 //s i n ( ( 2 i 1) % p i / 4 ) %i ;40 / / a n n o t = d e c 2 b i n ( [ 0 : l e n g t h ( y ) 1] , lo g 2 (M) ) ;41 / / d i s p ( y , c o o r d i n a t e s o f m es sa ge p o i n ts )42

/ / d i s p ( a nn o t , d i b i t s v a l u e )43 / / f i g u r e ;44 //a =gc a ( ) ;45 / / a . d a t a b o u n d s = [ 1 , 1 ; 1 , 1 ] ;46 // a . x l o c a t i o n = o r i g i n ;47 // a . y l o c a t i o n = o r i g i n ;48 / / p l o t 2 d ( r e a l ( y ( 1 ) ) , i ma g ( y ( 1 ) ) , 2)49 / / p l o t 2 d ( r e a l ( y ( 2 ) ) , i ma g ( y ( 2 ) ) , 4)50 / / p l o t 2 d ( r e a l ( y ( 3 ) ) , i ma g ( y ( 3 ) ) , 5)51 / / p l o t 2 d ( r e a l ( y ( 4 ) ) , i ma g ( y ( 4 ) ) , 9)52 / / x l a b e l (

InPhase ) ;

53 / / y l a b e l (

Q uadr at ur e ) ;

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54 / / t i t l e ( C o n s t e l l a t i o n f o r QPSK )55 / / l e g e n d ( [ m es s ag e p o i n t 1 ( d i b i t 1 0 ) ; m e ss a ge

p o in t 2 ( d i b i t 0 0) ; m es sa ge p o in t 3 ( d i b i t 0 1) ; m es sa ge p o i n t 4 ( d i b i t 1 1) ] , 5 )

Scilab code CF 7.1 Waveform of Different Digital Modulation techniques

1 / / C ap ti on : Waveforms o f D i f f e r e n t D i g i t a l M od ul at io nt e c h n i q u e s2 / / F i g u r e 7 . 13 / / D i g i t a l M o du l at i on T e ch n i q ue s4 / / To P l o t t h e ASK , FSK a nd PSk W av ef or ms

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5 clear ;

6 clc ;7 close ;

8 f = input ( E nt er t h e A na lo g C a r r i e r F re qu en cy i n Hz ) ;

9 t = 0 :1 /5 12 :1 ;

10 x = sin ( 2 * % p i * f * t ) ;

11 I = input ( E nt er t he d i g i t a l b i n ar y d at a ) ;12 // Ge n e r a t i o n of ASK Wav ef or m13 X as k = [ ];

14 for n = 1: length ( I )

15 if ( ( I ( n ) = = 1 ) & ( n = = 1 ) )

16 X as k = [ x , X as k ] ;17 elseif ( ( I ( n ) = = 0 ) & ( n = = 1 ) )

18 Xask = [ zeros (1 , length ( x ) ) , X a s k ] ;

19 elseif ( ( I ( n ) = = 1 ) & ( n ~ = 1 ) )

20 X as k = [ X as k , x ] ;

21 elseif ( ( I ( n ) = = 0 ) & ( n ~ = 1 ) )

22 X as k = [ Xask , zeros (1 , length ( x ) ) ] ;

23 end

24 end

25 // Ge n e r a t i o n of FSK Wav ef or m26 X fs k = [ ];

27 x1 = sin ( 2 * % p i * f * t ) ;

28 x2 = sin ( 2 * % p i * ( 2 * f ) * t ) ;


30 if ( I ( n ) = = 1 )

31 X fs k = [ X fs k , x 2 ];

32 elseif ( I ( n ) ~ = 1 )

33 X fs k = [ X fs k , x 1 ];

34 end

35 end

36 // Ge n e r a t i o n of PSK Wav ef or m

37 X ps k = [ ];38 x1 = sin ( 2 * % p i * f * t ) ;

39 x2 = - sin ( 2 * % p i * f * t ) ;


41 if ( I ( n ) = = 1 )

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42 X ps k = [ X ps k , x 1 ];

43 elseif ( I ( n ) ~ = 1 )44 X ps k = [ X ps k , x 2 ];

45 end

46 end

47 figure

48 plot ( t , x )

49 xtitle ( A na lo g C a r r i e r S i g n a l f o r D i g i t a l M od ul at io n )

50 xgrid

51 figure

52 plot ( X a s k )

53 xtitle ( A m pl i tu d e S h i f t K ey i ng )54 xgrid

55 figure

56 plot ( X f s k )

57 xtitle ( F r eq u en c y S h i f t K ey in g )58 xgrid

59 figure

60 plot ( X p s k )

61 xtitle ( P ha se S h i f t K ey in g )62 xgrid

63//Example64 / / E nt er t h e A na lo g C a r r i e r F re qu en cy 2

65 / / E nt er t h e d i g i t a l b i n a r y d at a [ 0 , 1 , 1 , 0 , 1 , 0 , 0 , 1 ]

Scilab code Exa 7.2 MSK waveforms

1 / / C a pt i on : S i g n a l S pa c e d ia g ra m f o r c o h e r e n t BPSK2 / / E xa mp le 7 . 2 : S e q u e nc e a nd W av ef or ms f o r MSK s i g n a l3 // T abl e 7 . 2 s i g n a l s pa ce c h a r a c t e r i z a t i o n o f MSK4 clear

5 clc ;6 close ;

7 M =2;

8 T b = 1;

9 t 1 = - Tb : 0 . 01 : T b ;

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Figure 7.4: Figure7.1c

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10 t 2 = 0 : 0. 0 1: 2 * Tb ;

11 p hi 1 = cos ( 2 * % p i * t 1 ) . * cos ( ( % p i / ( 2 * T b ) ) * t 1 ) ;12 p hi 2 = sin ( 2 * % p i * t 2 ) . * sin ( ( % p i / ( 2 * T b ) ) * t 2 ) ;

13 t et a _0 = [ 0 , %p i ];

14 t e t a_ t b = [ % p i /2 , - % p i / 2 ] ;

15 S 1 = [ ] ;

16 S 2 = [ ] ;

17 for i = 1: M

18 s 1( i) = cos ( t e t a _ 0 ( i ) ) ;

19 s2 (i ) = - sin ( t e t a _ t b ( i ) ) ;

20 S 1 = [ S1 s1 ( i) * ph i1 ] ;

21 S 2 = [ S2 s2 ( 1) * p hi 2 ];

22 end23 for i = M : -1:1

24 S 1 = [ S1 s1 ( i) * ph i1 ] ;

25 S 2 = [ S2 s2 ( 2) * p hi 2 ];

26 end

27 I n p u t_ S e q ue n c e = [1 , 1 , 0 , 1 , 0 , 0 , 0 ];

28 S = [];

29 t = 0 :0 .0 1: 1;

30 S = [ S cos ( 0 ) * cos ( 2 * % p i * t ) - sin ( % p i / 2 ) * sin ( 2 * % p i * t ) ] ;

31 S = [ S cos ( 0 ) * cos ( 2 * % p i * t ) - sin ( % p i / 2 ) * sin ( 2 * % p i * t ) ] ;

32 S = [ S cos ( % p i ) * cos ( 2 * % p i * t ) - sin ( % p i / 2 ) * sin ( 2 * % p i * t )

];

33 S = [ S cos ( % p i ) * cos ( 2 * % p i * t ) - sin ( - % p i / 2 ) * sin ( 2 * % p i * t

) ];

34 S = [ S cos ( 0 ) * cos ( 2 * % p i * t ) - sin ( - % p i / 2 ) * sin ( 2 * % p i * t )

];


];


];

37 y = [ s 1 ( 1) , s 2 ( 1 ) ; s 1 ( 2) , s 2 ( 1 ) ; s 1 ( 2) , s 2 ( 2 ) ; s 1 ( 1) , s 2 ( 2 )

];38 disp (y , c o o r d i n a t e s o f m es sa ge p o i n t s )39 figure

40 subplot ( 3 , 1 , 1 )

41 a = gca () ;

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42 a . x _ l o c at i o n = o r i g i n ;

43 plot ( S 1 )44 t i t l e ( S c a l ed t im e f u n c ti o n s 1 ph i1 ( t ) )45 subplot ( 3 , 1 , 2 )

46 a = gca () ;


49 t i t l e ( S c a l ed t im e f u n c ti o n s 2 ph i2 ( t ) )50 subplot ( 3 , 1 , 3 )

51 a = gca () ;

52 a . x _ l o c at i o n = o r i g i n ;53 plot ( S )

54 t i t l e ( O bt ai n ed by a d d in g s 1 ph i1 ( t )+s2 p h i 2 ( t ) o n ab i t byb i t b a s i s )

Scilab code CF 7.2 Signal Space diagram for coherent BPSK

1 / / C a pt i on : S i g n a l S pa c e d ia g ra m f o r c o h e r e n t BPSK2 / / F i g u r e 7 . 2 S i g n a l S p ac e Di ag ra m f o r c o h e r e n t BPSK

s y s t e m3 clear

4 clc ;

5 close ;6 M =2;

7 i = 1 : M ;

8 y = cos ( 2 * % p i + ( i - 1 ) * % p i ) ;

9 a nn ot = d ec 2 bi n ( [ length ( y ) - 1 : - 1 : 0 ] , log2 ( M ) ) ;

10 disp (y , c o o r d i n a t e s o f m es sa ge p o i n t s )11 disp ( a n n o t , M es s ag e p o i n t s )12 figure ;

13 a = gca () ;

14 a . d a t a _ bo u n d s = [ - 2 , - 2; 2 , 2] ;

15 a . x _ l o c at i o n = o r i g i n ;16 a . y _ l o c at i o n = o r i g i n ;17 plot2d ( real ( y ( 1 ) ) , imag ( y ( 1 ) ) , - 9 )

18 plot2d ( real ( y ( 2 ) ) , imag ( y ( 2 ) ) , - 5 )

19 x l a b e l (

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InPhase ) ;20 y l a b e l (

Q uadr at ur e ) ;21 t i t l e ( C o n s t e l l a t i o n f o r BPSK )22 l e g e n d ( [ m es sa ge p o i n t 1 ( b i n a r y 1 ) ; m e ss a ge p o i n t

2 ( b i n a ry 0 ) ],5)

Scilab code Tab 7.3 Illustration the generation of DPSK signal

1 // C ap ti on : I l l u s t r a t i n g t he g e n e r a t i o n o f DPSK s i g n a l

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2 // T abl e7 . 3 G en er at io n o f D i f f e r e n t i a l Phase s h i f t

k ey in g s i g n a l3 clc ;4 b k = [ 1 ,0 , 0 , 1 ,0 , 0 , 1 ,1 ]; // i np ut d i g i t a l s eq ue nc e5 for i = 1: length ( b k )

6 if ( b k ( i ) = = 1 )

7 b k _n o t ( i ) = ~ 1;

8 else

9 b k _n o t ( i ) = 1 ;

10 end

11 end

12 d k_ 1 ( 1) = 1 & bk ( 1) ; // i n i t i a l va lu e o f d i f f e r e n t i a l

e n co d ed s e q u e n c e13 d k _ 1 _ n o t ( 1 ) = 0 & b k _ n o t ( 1 ) ;

14 d k ( 1) = x o r ( d k_ 1 ( 1 ) , d k _ 1_ n o t ( 1 ) ) / / f i r s t b i t o f d ps ke n c o d e r

15 for i=2: length ( b k )

16 d k_ 1 ( i) = d k (i - 1 ) ;

17 d k _1 _ no t ( i ) = ~ d k (i - 1 ) ;

18 d k ( i ) = x or ( ( d k _ 1 ( i ) & bk ( i ) ) , ( d k _ 1 _n o t ( i ) & b k _ no t ( i )

) ) ;

19 end

20 for i =1: length ( d k )

21 if ( d k ( i ) = = 1 )

22 d k _ r a d i a n s ( i ) = 0 ;

23 elseif ( d k ( i ) = = 0 )

24 d k _ r a d i a n s ( i ) = % p i ;

25 end

26 end

27 disp ( T ab le 7 . 3 I l l u s t r a t i n g t he G en er a ti o n o f DPSKS i g n a l )

28 disp (

)29 disp ( b k , ( bk) )30 b k _ no t = b k_ no t ;

31 disp ( b k _ n o t , ( bk no t ) )32 dk = dk ;

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33 disp ( d k , D i f f e r e n t i a l l y e n co de d s eq ue nc e ( dk ) )

34 d k _ ra d i an s = d k _r a di a ns ;35 disp (dk_radians , T ra n sm i tt ed p ha s e i n r a d i a n s )36 disp (

)

Scilab code CF 7.4 Signal Space diagram for coherent BFSK

1 / / C a pt i on : S i g n a l S pa c e d ia g ra m f o r c o h e r e n t BFSK2 / / F i g u r e 7 . 4 S i g n a l S p ac e Di ag ra m f o r c o h e r e n t BFSK

s y s t e m3 clear4 clc ;

5 close ;

6 M =2;

7 y = [ 1 ,0 ;0 , 1] ;

8 a n no t = d e c2 b i n ( [ M - 1: - 1 : 0] , log2 ( M ) ) ;

9 disp (y , c o o r d i n a t e s o f m es sa ge p o i n t s )10 disp ( a n n o t , M es s ag e p o i n t s )11 figure ;

12 a = gca () ;

13 a . d a t a _ bo u n d s = [ - 2 , - 2; 2 , 2] ;14 a . x _ l o c at i o n = o r i g i n ;15 a . y _ l o c at i o n = o r i g i n ;16 plot2d ( y ( 1 , 1 ) , y ( 1 , 2 ) , - 9 )

17 plot2d ( y ( 2 , 1 ) , y ( 2 , 2 ) , - 5 )

18 x l a b e l (

InPhase ) ;19 y l a b e l (

Q uadr at ur e ) ;

20 t i t l e ( C o n s t e l l a t i o n f o r BFSK )21 l e g e n d ( [ m es sa ge p o i n t 1 ( b i n a r y 1 ) ; m e ss a ge p o i n t

2 ( b i n a ry 0 ) ],5)

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Figure 7.7: Figure 7.4

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Scilab code CF 7.6 Signal space diagram for coherent QPSK waveform

1 / / C a pt i on : S i g n a l s p a c e d ia g ra m f o r c o h e r e n t QPSKwaveform

2 / / F i g u r e 7 . 6 S i g n a l S p ac e Di ag ra m f o r c o h e r e n t QPSKs y s t e m

3 clear

4 clc ;

5 close ;

6 M =4;

7 i = 1 : M ;

8 y = cos ( ( 2 * i - 1 ) * % p i / 4 ) - sin ( ( 2 * i - 1 ) * % p i / 4 ) * % i ;

9 a n no t = d e c2 b i n ( [ 0: M - 1 ] , log2 ( M ) ) ;10 disp (y , c o o r d i n a t e s o f m es sa ge p o i n t s )11 disp ( a n n o t , d i b i t s v al u e )12 figure ;

13 a = gca () ;

14 a . d a t a _ bo u n d s = [ - 1 , - 1; 1 , 1] ;

15 a . x _ l o c at i o n = o r i g i n ;16 a . y _ l o c at i o n = o r i g i n ;17 plot2d ( real ( y ( 1 ) ) , imag ( y ( 1 ) ) , - 2 )




21 x l a b e l ( In

Phase ) ;22 y l a b e l (

Q uadr at ur e ) ;23 t i t l e ( C o n s t e l l a t i o n f o r QPSK )24 l e g e n d ( [ m es sa ge p o i nt 1 ( d i b i t 1 0) ; m e ss a ge p o i n t

2 ( d i b i t 0 0) ; m es sa ge p o i nt 3 ( d i b i t 0 1) ;

m es sa ge p o i nt 4 ( d i b i t 1 1) ],5)

Scilab code Tab 7.6 Bndwidth efficiency of M ary PSK signals

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1 / / C ap ti on : Ba ndwid th e f f i c i e n c y o f Ma ry PSK s i g n a l s

2 // T ab le 7 . 6 : Bandwidth E f f i c i e n c y o f Mar y PSKs i g n a l s3 clear ;

4 clc ;

5 close ;

6 M = [ 2 , 4 ,8 , 1 6 ,3 2 , 64 ]; //Ma r y7 Ruo = log2 ( M ) . / 2 ; // Bandwidth e f f i c i e n c y i n b i t s / s /

Hz8 disp ( T ab le 7 . 7 Bandwidth E f f i c i e n c y o f Mar y PSK

s i g n a l s )9 disp (

)10 disp (M , M )11 disp (

)12 disp ( R u o , r i n b i t s / s /Hz )13 disp (

)

Scilab code Tab 7.7 Bandwidth efficiency of M ary FSK signals

1 / / C ap ti on : Ba ndwid th e f f i c i e n c y o f Ma ry FSK s i g n a l s2 // T ab le 7 . 7 : Bandwidth E f f i c i e n c y o f Mary FSK3 clear ;

4 clc ;

5 close ;

6 M = [ 2 , 4 ,8 , 1 6 ,3 2 , 64 ]; //Ma r y7 Ruo = 2* log2 ( M ) . / M ; // Bandwidth e f f i c i e n c y i n b i t s / s

/Hz

8 //M = M ;9 //Ruo = Ruo ;

10 disp ( T ab le 7 . 7 Bandwidth E f f i c i e n c y o f Mar y FSKs i g n a l s )

11 disp (

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)12 disp (M , M )13 disp (

)14 disp ( R u o , r i n b i t s / s /Hz )15 disp (

)

Scilab code CF 7.29 Power Spectra of BPSK and BFSK signals

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1 / / C a p t i o n : P ow er S p e c t r a o f BPSK a nd BFSK s i g n a l s

2 / / F i g u re 7 . 2 9 : C om pa ri so n o f Power S p e c t r a l D e n s i t i e so f BPSK3 // and BFSK4 clc ;

5 rb = input ( E nt er t he b i t r a t e= ) ;6 Eb = input ( E nt e r t he e ne rg y o f t he b i t= ) ;7 f = 0 : 1/ 1 00 : 8/ r b ;

8 Tb = 1/ rb ; / / B i t d u r a t i o n9 for i = 1: length ( f )

10 if ( f ( i ) = = ( 1 / ( 2 * T b ) ) )

11 S B _ F S K ( i ) = E b / ( 2 * T b ) ;

12 else13 S B_ F SK ( i ) = ( 8* E b * (cos ( % p i * f ( i ) * T b ) ^ 2 ) ) / ( ( % p i

^ 2 ) * ( ( ( 4 * ( T b ^ 2 ) * ( f ( i ) ^ 2 ) ) - 1 ) ^ 2 ) ) ;

14 end

15 S B _ P S K ( i ) = 2 * E b * ( s i n c _ n e w ( f ( i ) * T b ) ^ 2 ) ;

16 end

17 a = gca () ;

18 plot ( f * T b , S B _ F S K / ( 2 * E b ) )

19 plot ( f * T b , S B _ P S K / ( 2 * E b ) )


21 p ol y1 . f o r eg r ou n d = 6 ;

22 x l a b e l ( N o r m a l i z e d F r e q u e n cy > )23 y l a b e l ( N o r ma l i ze d Power S p e c t r a l D e ns i ty > )24 t i t l e ( PSK Vs FSK P ow er Sp e c t r a C ompar i son )25 l e g e n d ( [ F re q ue n cy S h i f t K ey in g , P ha se S h i f t K ey in g

])26 xgrid (1)

27 / / R e s u l t28 // E nt e r t h e b i t r a te i n b i t s p er s ec o nd : 229 // E n te r t he Energ y o f b i t : 1

Scilab code CF 7.30 Power Spectra of QPSK and MSK signals.

1 / / C a p t i o n : P ow er S p e c t r a o f QPSK a nd MSK s i g n a l s2 // F i g ur e 7 . 3 0 : C ompar i son of QPSK and MSK P ow er

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Spe c t r ums

3 / / c l e a r ;4 / / c l o s e ;5 // c l c ;6 rb = input ( E nt e r t he b i t r a t e i n b i t s p er s ec on d : )

;

7 Eb = input ( E nt er t h e E ne rg y o f b i t : ) ;8 f = 0 : 1/ ( 10 0 * rb ) : (4 / r b );

9 Tb = 1/ rb ; // b i t d u r at i o n i n s e co n d s10 for i = 1: length ( f )

11 if ( f ( i ) = = 0 . 5 )

12 S B_ MS K ( i ) = 4 * Eb * f ( i) ;

13 else14 S B _M S K ( i ) = ( 3 2* E b / ( % p i ^ 2) ) * ( cos ( 2 * % p i * T b * f ( i ) )

/ ( ( 4 * T b * f ( i ) ) ^ 2 - 1 ) ) ^ 2 ;

15 end

16 S B _ QP S K ( i ) = 4 * E b * s i nc _ n ew ( ( 2 * T b * f ( i ) ) ) ^2 ;

17 end

18 a = gca () ;

19 plot ( f * T b , S B _ M S K / ( 4 * E b ) ) ;

20 plot ( f * T b , S B _ Q P S K / ( 4 * E b ) ) ;


22 p ol y1 . f o r eg r ou n d = 3 ;

23 x l a b e l ( N o r m a l i z e d F r e q u e n cy > )24 y l a b e l ( N o r ma l i ze d Power S p e c t r a l D e ns i ty > )25 t i t l e ( QPSK Vs MSK Power Sp ec tr a Comparison )26 l e g e n d ( [ Minimum S h i f t K e y in g , QPSK ])27 xgrid (1)

28 / / R e s u l t29 // E nt e r t h e b i t r a te i n b i t s p er s ec o nd : 230 // E n te r t he Energ y o f b i t : 1

Scilab code CF 7.31 Power spectra of M-ary PSK signals

1 / / C a pt i on : Power s p e c t r a o f Ma r y PSK s i g n a l s2 / / F i g u re 7 . 3 1 C om pa ri so n o f Power S p e c t r a l D e n s i t i e s

o f Ma ry PSK s i g n a l s

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3 rb = input ( E nt er t he b i t r a t e= ) ;

4 Eb = input ( E nt e r t he e ne rg y o f t he b i t= ) ;5 f = 0 :1 /1 00 : rb ;6 Tb = 1/ rb ; / / B i t d u r a t i o n7 M = [ 2 ,4 , 8] ;

8 for j = 1: length ( M )

9 for i = 1 : length ( f )

10 S B _ P S K ( j , i ) = 2 * E b * ( s i n c _ n e w ( f ( i ) * T b * log2 ( M ( j ) ) )

^ 2 ) * log2 ( M ( j ) ) ;

11 end

12 end

13 a = gca () ;

14 plot2d ( f * T b , S B _ P S K ( 1 , : ) / ( 2 * E b ) )15 plot2d ( f * T b , S B _ P S K ( 2 , : ) / ( 2 * E b ) , 2 )

16 plot2d ( f * T b , S B _ P S K ( 3 , : ) / ( 2 * E b ) , 5 )

17 x l a b e l ( N o r m a l i z e d F r e q u e n cy > )18 y l a b e l ( N o r ma l i ze d Power S p e c t r a l D e ns i ty > )19 t i t l e ( P ower S p e c tr a o f Ma r y s i g n a l s f o r M =2 , 4 ,8 )20 l e g e n d ( [ M=2 , M=4 , M=8 ])21 xgrid (1)

22 / / R e s u l t23 // E nt e r t h e b i t r a te i n b i t s p er s ec o nd : 224

// E n te r t he Energ y o f b i t : 1

Scilab code CF 7.41 Matched Filter output of rectangular pulse

1 // C ap ti on : Matched F i l t e r o ut pu t o f r e c t a n g u l a r p u l s e2 / / F i g u r e 7 . 4 13 / / Ma tch ed F i l t e r Ou tp ut4 clear ;

5 clc ;

6 T =4;

7 a =2;8 t = 0 : T ;

9 g = 2* ones ( 1 , T + 1

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