introduction of spread spectrum communications contents

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Navtech Seminars and GPS SupplySte 400, 6121 Lincolnia RdAlexandria VA 22312 USA

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Introduction to Spread-Spectrum CommunicationsBy Roger L. Peterson (Motorola), Rodger E. Ziemer (University of Co. at Colorado Springs), and David E.Borth (Motorola)Prentice Hall, 1995(Navtech order #2430)

Table of Contents

Preface ........................................................................................................XIIIAcknowledgments ...................................................................................................... XVIIPrologue ............................................................................................................ 1

Chapter 1 Basic Digital Communications Concepts ....................................................................... 61.1 Introduction ............................................................................................................ 61.2 Detection of binary signals in additive white Gaussian noise .......................................... 6

1.2.1 Coherent modulation schemes ........................................................................... 61.2.2 Noncoherent modulation schemes.................................................................... 12

1.3 Signal detection in geometric terms ............................................................................. 151.3.1 Gram-Schmidt procedure................................................................................. 151.3.2 Geometric view of signal detection .................................................................. 161.3.3 M-ary phase shift keying ................................................................................. 181.3.4 Coherent M-ary frequency shift keying ............................................................ 201.3.5 M-ary quadrature amplitude shift keying.......................................................... 211.3.6 Differentially coherent phase-shift keying........................................................ 221.3.7 Noncoherent M-ary FSK.................................................................................. 231.3.8 Hybrid modulation schemes............................................................................. 23

1.4 Comparison of modulation schemes............................................................................. 311.4.1 Bandwidth efficiency....................................................................................... 311.4.2 Power efficiency.............................................................................................. 32

1.5 Signaling through fading channels ............................................................................... 331.6 Summary .......................................................................................................... 41References .......................................................................................................... 41Problems .......................................................................................................... 43

Chapter 2: Introduction to Spread Spectrum Systems........................................................................ 472.1 Introduction .......................................................................................................... 472.2 Two communications problems ................................................................................... 48

2.2.1 Pulse-noise jamming ....................................................................................... 482.2.2 Low probability of detection............................................................................ 50

2.3 Direct sequence spread spectrum................................................................................. 642.4 Frequency hop spread spectrum................................................................................... 68

2.4.1 Coherent slow frequency hop spread spectrum................................................. 682.4.2 Noncoherent slow frequency hop spread spectrum........................................... 732.4.3 Noncoherent fast frequency hop spread spectrum............................................. 75

2.5 Hybrid direct sequence/frequency hop spread spectrum............................................... 752.6 Complex envelope representation of spread spectrum systems...................................... 782.7 Summary .......................................................................................................... 83References .......................................................................................................... 83Problems .......................................................................................................... 84

Chapter 3: Binary Shift Register Sequences for Spread Spectrum Systems........................................ 89

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3.1 Introduction .......................................................................................................... 893.2 Definitions, mathematical background and sequence generator fundamentals ............... 90

3.2.1 Definitions ...................................................................................................... 903.2.2 Finite field arithmetic ...................................................................................... 913.2.3 Sequence generator fundamentals .................................................................... 993.2.4 State machine representation of shift register generators..................................109

3.3 Maximal length sequences..........................................................................................1133.3.1 Properties of m-sequences...............................................................................1133.3.2 Power spectrum of m-sequences .....................................................................1153.3.3 Tables of polynomials yielding m-sequences...................................................1173.3.4 Partial autocorrelation properties of m-sequences ............................................1213.3.5 Power spectrum of c(t)c(t+H) ..........................................................................1253.3.6 Generation of specific delays of an m-sequence...............................................128

3.4 Gold codes .........................................................................................................1353.5 Nonlinear code generators ..........................................................................................1383.6 Summary .........................................................................................................142References .........................................................................................................143Problems .........................................................................................................144

Chapter 4: Code Tracking Loops.....................................................................................................1494.1 Introduction .........................................................................................................1494.2 Optimum tracking of wideband signals .......................................................................1504.3 Baseband delay lock tracking loop..............................................................................1534.4 Noncoherent delay lock tracking loop .........................................................................1644.5 Tau-dither noncoherent tracking loop..........................................................................1794.6 Double-dither noncoherent tracking loop ....................................................................1894.7 Noncoherent delay lock tracking loop with arbitrary data and

Spreading modulation.................................................................................................1924.8 Code tracking loops for frequency hop systems...........................................................2014.9 Summary .........................................................................................................213References .........................................................................................................215Problems .........................................................................................................216

Chapter 5: Initial Synchronization of the Receiver Spreading Code..................................................2215.1 Introduction .........................................................................................................2215.2 Problem definition and the optimum synchronizer ......................................................2235.3 Serial search synchronization techniques ....................................................................225

5.3.1 Calculation of the mean and variance of synchronization time.........................2255.3.2 Modified sweep strategies ..............................................................................2305.3.3 Continuous linear sweep of the uncertainty region ..........................................2335.3.4 Detection of a signal in additive white Gaussian noise.....................................240

5.4 Generalized analysis of average synchronization time .................................................2835.5 Synchronization using a matched filter .......................................................................2915.6 Synchronization by estimating the received spreading code.........................................3015.7 Tracking loop pull-in..................................................................................................3035.8 Summary .........................................................................................................308References .........................................................................................................311Problems .........................................................................................................315

Chapter 6: Performance of Spread Spectrum Systems in Jamming Environments.............................3196.1 Introduction .........................................................................................................319

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6.2 Spread spectrum communication system model ..........................................................3206.3 Performance of spread spectrum systems without coding ............................................326

6.3.1 Performance in AWGN or barrage noise jamming ..........................................3276.3.2 Performance in partial band jamming..............................................................3376.3.3 Performance in pulsed noise jamming.............................................................3506.3.4 Performance in single tone jamming ...............................................................3546.3.5 Performance in multiple tone jamming ...........................................................3686.3.6 Conclusions ...................................................................................................373

6.4 Summary .........................................................................................................374References .........................................................................................................375Problems .........................................................................................................378

Chapter 7: Performance of Spread Spectrum Systems with Forward Error Correction...................3817.1 Introduction .........................................................................................................3817.2 Elementary block coding concepts..............................................................................382

7.2.1 Basic concepts................................................................................................4037.2.2 Optimum decoding rule..................................................................................3857.2.3 Calculation of error probability.......................................................................391

7.3 Elementary convolutional coding concepts .................................................................4037.3.1 Basic concepts................................................................................................4037.3.2 Definition of a convolutional code ..................................................................4047.3.3 Decoding convolutional codes ........................................................................4087.3.4 Viterbi algorithm............................................................................................4137.3.5 Decoding and bit error probability ..................................................................427

7.3.6 Other topics 4297.4 Results for specific error correction codes...................................................................431

7.4.1 BCH codes.....................................................................................................4317.4.2 Reed-Solomon codes ......................................................................................4337.4.3 Maximum free distance convolutional codes...................................................4347.4.4 Repeat coding for the hard decision FH/MFSK channel..................................435

7.5 Interleaving .........................................................................................................4477.6 Coding bounds .........................................................................................................449

7.6.1 Error probability bounds using the channel parameter D..................................4497.6.2 Computational cutoff rate Ro..........................................................................453


Chapter 8: Introduction to Fading Channels.....................................................................................4608.1 Introduction .........................................................................................................4608.2 Statistical model of fading ..........................................................................................460

8.2.1 General fading channel model.........................................................................4628.2.2 WSSUS fading channels.................................................................................4678.2.3 Doubly spread channels..................................................................................4688.2.4 Time selective fading channels .......................................................................4718.2.5 Frequency selective fading channels ...............................................................4758.2.6 Nondispersive fading channels........................................................................480

8.3 Characterization of the mobile radio channel ..............................................................4828.3.1 time selective fading.......................................................................................4838.3.2 Frequency selective fading .............................................................................4868.3.3 Mobile radio path loss ....................................................................................488

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8.3.4 Shadowing .....................................................................................................4908.3.5 Coverage reliability ........................................................................................491

8.4 Requirement for diversity in fading channels ..............................................................4938.4.1 Diversity approaches ......................................................................................4978.4.2 Diversity combining methods .........................................................................5008.4.3 Performance of maximal ratio combining........................................................5028.4.4 Other diversity combining methods.................................................................5068.4.5 The Rake receiver...........................................................................................5078.4.6 Summary: The benefits of diversity.................................................................512


Chapter 9: Code Division Multiple Access Digital Cellular Systems................................................5209.1 Introduction .........................................................................................................5209.2 Cellular radio concept.................................................................................................520

9.2.1 Fundamentals of cellular radio systems...........................................................5219.2.2 Co-channel interference protection prediction .................................................5269.2.3 Cellular concept revisited ..............................................................................528

9.3 CDMA digital cellular systems...................................................................................5309.3.1 General aspects of CDMA digital cellular systems..........................................5359.3.2 Special aspects of CDMA digital cellular systems...........................................535

9.4 Specific examples of CDMA digital cellular systems..................................................5359.4.1 North American DS-CDM digital cellular system (IS-95)................................5369.4.2 Cooper and Nettleton DPSK-FHMA system...................................................5509.4.3 Bell Labs multilevel FSK frequency hop system.............................................5539.4.4 SFH900 system..............................................................................................5599.4.5 GSM-SFH digital cellular system...................................................................5619.4.6 Hybrid SFH TDMA/CDMA system for PCS applications...............................566


Chapter 10: Low Probability-of-Intercept Methods..........................................................................58410.1 Introduction .........................................................................................................58410.2 Nature of covert communications ...............................................................................58410.3 Energy detection in AWGN........................................................................................58610.4 Optimum intercept receivers for spread spectrum signals............................................591

10.4.1 Introduction ...................................................................................................59110.4.2 Optimum intercept receiver for direct sequence spread spectrum.....................59110.4.3 Intercept receivers for frequency hop spread spectrum....................................599

10.5 The OR/BMWD: Approximately optimum spread spectrum signal detector ................60210.6 Estimation of spread spectrum signal parameters ........................................................605References .........................................................................................................611Problems .........................................................................................................613

Appendix A: Summary of Phase-Locked Theory.............................................................................615A-1 Introduction .........................................................................................................615A-2 Phase-locked loop models and characteristics of operation ..........................................615

A-2.1 Synchronized mode: linear operation ..............................................................615A-2.2 Effects of noise...............................................................................................619

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A-2.3 Phase-locked loop tracking of oscillators with phase noise ..............................625A-2.4 Phase jitter plus noise effects ..........................................................................625A-2.5 Transient response..........................................................................................628A-2.6 Phase-locked loop acquisition.........................................................................631A-2.7 Effects of transport delay................................................................................635

A-3 Frequency Synthesis...................................................................................................636A-3.1 Introduction ...................................................................................................636A-3.2 Digital synthesizer..........................................................................................636A-3.3 Direct synthesis..............................................................................................638A-3.4 Phase-locked frequency synthesizers ..............................................................641

References .........................................................................................................643

Appendix B: Gaussian Probability Function ...................................................................................644Reference .........................................................................................................645

Appendix C: Power Spectral Densities for sequences of Random Binary Digitsand Random Tones ....................................................................................................646

Reference .........................................................................................................650

Appendix D: Calculation of the Power Spectrum of the Product of Two M-Sequences ....................651Reference .........................................................................................................659

Appendix E: Evaluation of Phase Discriminator Output Autocorrelation Functionsand Power Spectra......................................................................................................660

E-1 Noncoherent delay lock tacking loop ..........................................................................660E-2 Tau-dither noncoherent tracking loop..........................................................................665References .........................................................................................................671

Appendix F: Numerical Approximations for the Chi-Squared Probability Distributionand Marcum’s Q-Function..........................................................................................672

F-1 Introduction .........................................................................................................672F-2 Computation of the (Central) Chi-squared distribution ................................................672F-3 Generalized Marcum’s Q-Function .............................................................................676F-4 Noncentral Chi-squared distribution ...........................................................................678References .........................................................................................................681

Appendix G: Mathematical Tables ..................................................................................................682

Index .........................................................................................................689

introduction of spread spectrum communications contents

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