spread spectrum communications handbook; Marvin K. Simon

CONTENTS Preface xv Preface to First Edition xvi PART 1 INTRODUCTION TO SPREADSPECTRUM COMMUNICATIONS Chapter 1 A SpreadSpectrum Overview 3 1.1 A Basis for a Jamming Game 3 1.2 Energy Allocation Strategies 6 1.3 SpreadSpectrum System Configurations and Components 9 1.4 Energy Gain Calculations for Typical Systems 17 1.5 The Advantages of Spectrum Spreading 20 1.5.1 Low Probability of Intercept (LPI) 20 1.5.2 Independent Interference Rejection and MultipleAccess Operation 25 1.5.3 HighResolution TimeofArrival (TOA) Measurements 29 1.6 Design Issues 37 1.7 References 38 1.7.1 Books on Communication Theory 38 1.7.2 Books on Resolution and Ambiguity Functions 39 1.7.3 Recent Books and Proceedings on SpreadSpectrum Communications 39 1.7.4 SpreadSpectrum Tutorials and General Interest Papers 39 Chapter 2 The Historical Origins of SpreadSpectrum Communications 41 2.1 Emerging Concepts 42 2.1.1 Radar Innovations 42 2.1.2 Developments in Communication Theory 45 2.1.3 Correlator Mechanization 47 2.1.4 Protected Communications 48 2.1.5 Remote Control and Missile Guidance 58 http:jntu.blog.com http:jntu.blog.com2.2 Early SpreadSpectrum Systems 65 2.2.1 WHYN 65 2.2.2 A Note on CYTAC 71 2.2.3 HushUp 71 2.2.4 BLADES 73 2.2.5 Noise Wheels 78 2.2.6 The Hartwell Connection 84 2.2.7 NOMAC 87 2.2.8 F9CARake 90 2.2.9 A Note on PPM 100 2.2.10 CODORAC 100 2.2.11 MSequence Genesis 106 2.2.12 ANARC50 Development at Magnavox 108 2.3 Branches on the SS Tree 111 2.3.1 SpreadSpectrum Radar 111 2.3.2 Other Early SpreadSpectrum Communication Systems 112 2.3.3 SpreadSpectrum Developments Outside the United States 121 2.4 A Viewpoint 123 2.5 References 125 Chapter 3 Basic Concepts and System Models 137 3.1 Design Approach for AntiJam Systems 137 3.2 Models and Fundamental Parameters 139 3.3 Jammer Waveforms 141 3.3.1 Broadband and PartialBand Noise Jammers 141 3.3.2 CW and Multitone Jammers 143 3.3.3 Pulse Jammer 143 3.3.4 Arbitrary Jammer Power Distributions 143 3.3.5 RepeatBack Jammers 144 3.4 Uncoded DirectSequence Spread Binary PhaseShiftKeying 144 3.4.1 Constant Power Broadband Noise Jammer 147 3.4.2 Pulse Jammer 150 3.5 Coded DirectSequence Spread Binary PhaseShiftKeying 153 3.5.1 Interleaver and Deinterleaver 158 3.5.2 Unknown Channel State 159 3.5.2.1 Soft Decision Decoder 160 3.5.2.2 Hard Decision Decoder 162 3.5.3 Known Channel State 165 3.5.3.1 Soft Decision Decoder 166 3.5.3.2 Hard Decision Decoder 168 3.6 Uncoded FrequencyHopped Binary FrequencyShiftKeying 169 iv http:jntu.blog.com Contents http:jntu.blog.com3.6.1 Constant Power Broadband Noise Jammer 172 3.6.2 PartialBand Noise Jammer 174 3.6.3 Multitone Jammer 176 3.7 Coded FrequencyHopped Binary FrequencyShiftKeying 178 3.8 InterleaverHop Rate Tradeoff 180 3.9 Receiver Noise Floor 180 3.10 Discussion 183 3.11 References 183 Appendix 3A: Interleaving and Deinterleaving 184 Chapter 4 General Analysis of AntiJam Communication Systems 189 4.1 System Model 190 4.2 Coded Bit Error Rate Bound 194 4.3 Cutoff Rates 196 4.4 Conventional Coherent BPSK 198 4.5 DSBPSK and Pulse Jamming 204 4.6 Translation of Coded Error Bounds 205 4.7 Conventional NonCoherent MFSK 208 4.7.1 Uncoded 208 4.7.2 Coded 213 4.8 FHMFSK and PartialBand Jamming 217 4.9 Diversity for FHMFSK 227 4.10 Concatenation of Codes 235 4.10.1 Binary Super Channel 235 4.10.2 Mary Super Channel 238 4.10.3 ReedSolomon Outer Codes 238 4.11 Summary of Bit Error Bounds 246 4.11.1 DSBPSK with Pulse Jamming 246 4.11.2 FHMFSK with PartialBand Noise Jamming 247 4.11.3 Coding Functions 249 4.12 References 249 Appendix 4A: Chernoff Bound 250 Appendix 4B: Factor of OneHalf in Error Bounds 251 Appendix 4C: ReedSolomon Code Performance 260 Chapter 5 Pseudonoise Generators 264 5.1 The StorageGeneration Problem 264 5.2 Linear Recursions 271 5.2.1 Fibonacci Generators 271 5.2.2 Formal Power Series and Characteristic Polynomials 273 5.2.3 Galois Generators 275 5.2.4 State Space Viewpoint 278 5.2.5 Determination of Linear Recursions from Sequence Segments 280 Contents http:jntu.blog.com v http:jntu.blog.com5.3 MemoryEfficient Linear Generators 281 5.3.1 Partial Fraction Decompositions 281 5.3.2 Maximization of Period for a Fixed Memory Size 283 5.3.3 Repeated Factors in the Characteristic Polynomial 284 5.3.4 MSequences 285 5.4 Statistical Properties of MSequences 286 5.4.1 Event Counts 287 5.4.2 The ShiftandAdd Property 288 5.4.3 Hamming Distance Properties of Derived RealInteger Sequences 289 5.4.4 Correlation Properties of Derived Complex RootsofUnity Sequences 291 5.5 Galois Field Connections 297 5.5.1 Extension Field Construction 297 5.5.2 The LFSR as a Galois Field Multiplier 298 5.5.3 Determining the Period of Memory Cell Outputs 299 5.5.4 The Trace Representation of MSequences 301 5.5.5 A Correlation Computation 304 5.5.6 Decimations of Sequences 305 5.6 NonLinear FeedForward Logic 307 5.6.1 A Powersofa Representation Theorem 307 5.6.2 Key’s Bound on Linear Span 311 5.6.3 Difference Set Designs 315 5.6.4 GMW Sequences 317 5.7 DirectSequence MultipleAccess Designs 326 5.7.1 A Design Criterion 326 5.7.2 Welch’s Inner Product Bound 327 5.7.3 Crosscorrelation of Binary MSequences 329 5.7.4 Linear Designs 334 5.7.5 A TransformDomain Design Philosophy 340 5.7.6 Bent Sequences 344 5.8 FrequencyHopping MultipleAccess Designs 352 5.8.1 Design Criteria 352 5.8.2 A Bound on Hamming Distance 353 5.8.3 An FHMA Design Employing an MSequence Generator 354 5.8.4 ReedSolomon Sequences 355 5.9 A Look at the Literature 360 5.10 References 362 Appendix 5A: Finite Field Arithmetic 367 Appendix 5B: Factorizations of 2n—1 and Selected Primitive Polynomials 398 vi http:jntu.blog.com Contents http:jntu.blog.comPART 2 CLASSICAL SPREADSPECTRUM COMMUNICATIONS Chapter 1 Coherent Direct Sequence Systems 405 1.1 DirectSequence Spread Coherent Binary PhaseShift Keying 407 1.2 Uncoded Bit Error Probability for Arbitrary Jammer Waveforms 409 1.2.1 Chernoff Bound 410 1.2.2 Gaussian Assumptions 411 1.3 Uncoded Bit Error Probability for Specific Jammer Waveforms 412 1.3.1 CW Jammer 414 1.3.2 Random Jammer 416 1.4 Pulse Jamming 418 1.4.1 Arbitrary Time Distribution 418 1.4.2 Worst Case Jammer 420 1.5 Standard Codes and Cutoff Rates 422 1.5.1 The Additive White Gaussian Noise Channel 422 1.5.2 Jamming Channels 424 1.6 Slow Frequency NonSelective Fading Channels 428 1.6.1 Continuous Jammer with No Coding 428 1.6.2 Continuous Jammer with Coding—No Fading Estimate 430 1.6.3 Continuous Jammer with Coding—Fading Estimate 436 1.6.4 Pulse Jammer with No Coding 441 1.7 Slow Fading Multipath Channels 442 1.8 Other Coding Metrics for Pulse Jamming 453 1.9 Discussion 460 1.10 References 462 Chapter 2 NonCoherent FrequencyHopped Systems 464 2.1 Broadband Noise Jamming 471 2.2 Worst Case Jamming 475 2.2.1 PartialBand Noise Jamming 475 2.2.2 Multitone Jamming 480 2.2.2.1 Random Jamming Tone Phase 483 2.2.2.2 Band Multitone Jamming 484 2.2.2.3 Independent Multitone Jamming 493 2.3 Coding Countermeasures 497 2.3.1 Time Diversity 497 2.3.1.1 PartialBand Noise Jamming 500 2.3.1.2 Band Multitone Jamming 512 2.3.1.3 Independent Multitone Jamming 535 Contents http:jntu.blog.com vii http:jntu.blog.com2.3.1.4 Time Diversity Overview 540 2.3.2 Coding Without Diversity 546 2.3.2.1 Convolutional Codes 547 2.3.2.2 ReedSolomon Codes 562 2.3.2.3 Concatenated Codes 565 2.3.3 Coding With Diversity 567 2.3.3.1 Optimum Code Rates 593 2.4 Slow Fading Uniform Channels 600 2.4.1 Broadband Jamming—No Diversity 602 2.4.2 Broadband Jamming—Diversity and Coding 604 2.4.3 PartialBand Jamming 612 2.5 Worst Noise Jammer Distribution—Slow Fading Uniform Channel 615 2.5.1 Uncoded 615 2.5.2 Diversity and Coding 619 2.6 Worst Noise Jammer Distribution—Slow Fading Nonuniform Channel 622 2.6.1 Uncoded 623 2.6.2 Diversity and Coding 626 2.7 Other Coding Metrics 630 2.7.1 Energy Quantizer 633 2.7.2 Hard Decision with One Bit Quality Measure 636 2.7.3 List Metric 641 2.7.4 Metrics for Binary Codes 652 2.8 References 660 Appendix 2A: Justification of Factor of 12 for FHMFSK Signals with Diversity in PartialBand Noise 662 Appendix 2B: Combinatorial Computation for n
1 Band Multitone Jamming 664 PART 3 OTHER FREQUENCYHOPPED SYSTEMS Chapter 1 Coherent Modulation Techniques 669 1.1 Performance of FHQPSK in the Presence of PartialBand Multitone Jamming 670 1.2 Performance of FHQASK in the Presence of PartialBand Multitone Jamming 680 1.3 Performance of FHQPSK in the Presence of PartialBand Noise Jamming 687 1.4 Performance of FHQASK in the Presence of PartialBand Noise Jamming 690 1.5 Performance of FHPNQPSK in the Presence of PartialBand Multitone Jamming 693 1.6 Performance of FHPNQASK in the Presence of PartialBand Multitone Jamming 698 viii http:jntu.blog.com Contents http:jntu.blog.com1.7 Performance of FHQPR in the Presence of PartialBand Multitone Jamming 699 1.8 Performance of FHQPR in the Presence of PartialBand Multitone Jamming 710 1.9 Summary and Conclusions 713 1.10 References 713 Chapter 2 Differentially Coherent Modulation Techniques 715 2.1 Performance of FHMDPSK in the Presence of PartialBand Multitone Jamming 716 2.1.1 Evaluation of Q2pnm 719 2.2 Performance of FHMDPSK in the Presence of PartialBand Noise Jamming 728 2.3 Performance of DQASK in the Presence of Additive White Gaussian Noise 731 2.3.1 Characterization of the Transmitted Signal 31 2.3.2 Receiver Characterization and Performance 732 2.4 Performance of FHDQASK in the Presence of PartialBand Multitone Jamming 739 2.5 Performance of FHDQASK in the Presence of PartialBand Noise Jamming 748 2.6 References 749 PART 4 SYNCHRONIZATION OF SPREADSPECTRUM SYSTEMS Chapter 1 Pseudonoise Acquisition in Direct Sequence Receivers 753 1.1 Historical Survey 753 1.2 The Single Dwell Serial PN Acquisition System 765 1.2.1 Markov Chain Acquisition Model 767 1.2.2 Single Dwell Acquisition Time Performance in the Absence of Code Doppler 770 1.2.3 Single Dwell Acquisition Time Performance in the Presence of Code Doppler and Doppler Rate 777 1.2.4 Evaluation of Detection Probability PD and False Alarm Probability PFA in Terms of PN Acquisition System Parameters 781 1.2.5 Effective Probability of Detection and Timing Misalignment 785 1.2.6 Modulation Distortion Effects 786 1.2.7 Reduction in Noise Spectral Density Caused by PN Despreading 786 1.2.8 Code Doppler and Its Derivative 787 1.2.9 Probability of Acquisition for the Single Dwell System 789 Contents http:jntu.blog.com ix http:jntu.blog.com1.3 The Multiple Dwell Serial PN Acquisition System 794 1.3.1 Markov Chain Acquisition Model 798 1.3.2 Multiple Dwell Acquisition Time Performance 801 1.4 A Unified Approach to Serial Search Acquisition with Fixed Dwell Times 811 1.4.1 The Flow Graph Technique 811 1.5 Rapid Acquisition Using Matched Filter Techniques 817 1.5.1 Markov Chain Acquisition Model and Acquisition Time Performance 824 1.5.2 Evaluation of Detection and False Alarm Probabilities for Correlation and Coincidence Detectors 827 1.5.2.1 Exact Results 829 1.5.2.2 Approximate Results 831 1.5.2.3 Acquisition Time Performance 833 1.6 PN Sync Search Procedures and Sweep Strategies for a NonUniformly Distributed Signal Location 834 1.6.1 An Example—Single Dwell Serial Acquisition with an Optimized Expanding Window Search 838 1.6.2 Application of the Circular State Diagram Approach 843 1.7 PN Synchronization Using Sequential Detection 860 1.7.1 A Brief Review of Sequential Hypothesis Testing as Applied to the NonCoherent Detection of a Sine Wave in Gaussian Noise 864 1.7.2 The Biased SquareLaw Sequential Detector 867 1.7.3 Probability of False Alarm and Average Test Duration in the Absence of Signal 868 1.7.4 Simulation Results 877 1.8 SearchLock Strategies 885 1.8.1 Mean and Variance of the Acquisition Time 887 1.8.1.1 Evaluation of Probability Lock 890 1.8.1.2 Evaluation of Mean Dwell Time 891 1.8.2 Another SearchLock Strategy 896 1.9 Further Discussion 898 1.10 References 899 Chapter 2 Pseudonoise Tracking in Direct Sequence Receivers 903 2.1 The DelayLocked Loop 904 2.1.1 Mathematical Loop Model and Equation of Operation 904 2.1.2 Statistical Characterization of the Equivalent Additive Noise 909 2.1.3 Linear Analysis of DLL Tracking Performance 911 2.2 The TauDither Loop 915 x http:jntu.blog.com Contents http:jntu.blog.com2.2.1 Mathematical Loop Model and equation of Operation 916 2.2.2 Statistical Characterization of the Equivalent Additive Noise 920 2.2.3 Linear Analysis of TDL Tracking Performance 922 2.3 Acquisition (Transient) Behavior of the DLL and TDL 928 2.4 Mean Time to LossofLock for the DLL and TDL 933 2.5 The Double Dither Loop 935 2.6 The Product of Sum and Difference DLL 937 2.7 The Modified Code Tracking Loop 941 2.8 The Complex Sums Loop (A PhaseSensing DLL) 948 2.9 Quadriphase PN Tracking 949 2.10 Further Discussion 952 2.11 References 956 Chapter 3 Time and Frequency Synchronization of FrequencyHopped Receivers 958 3.1 FH Acquisition Techniques 959 3.1.1 Serial Search Techniques with Active Correlation 959 3.1.2 Serial Search Techniques with Passive Correlation 983 3.1.3 Other FH Acquisition Techniques 985 3.2 Time Synchronization of NonCoherent FHMFSK Systems 989 3.2.1 The Case of FullBand Noise jamming 992 3.2.1.1 Signal Model and Spectral Computations 992 3.2.1.2 Results of Large Nh 997 3.2.2 The Case of PartialBand Noise Jamming 999 3.2.2.1 Results of Large Nh 1000 3.2.3 The Effects of Time Synchronization Error on FHMFSK Error Probability Performance 1001 3.2.3.1 Conditional Error Probability Performance—No Diversity 1002 3.2.3.2 Conditional Error Probability Performance—mDiversity with NonCoherent Combining 1006 3.2.3.3 Average Error Probability Performance in the Presence of Time Synchronization Error Estimation 1009 3.3 Frequency Synchronization of NonCoherent FHMFSK Systems 1011 3.3.1 The Case of FullBand Noise Jamming 1013 3.3.1.1 Signal Model and Spectral Computations 1013 3.3.2 The Case of PartialBand Noise Jamming 1017 3.3.3 The Effects of Frequency Synchronization Error on FHMFSK Error Probability Performance 1017 Contents http:jntu.blog.com xi http:jntu.blog.com3.3.3.1 Average Error Probability Performance in the Presence of Frequency Synchronization Error Estimation 1022 3.4 References Appendix 3A: To Prove That a Frequency Estimator Based upon Adjacent Spectral Estimates Taken at Integer Multiples of 1T Cannot be Unbiased 1026 PART 5 SPECIAL TOPICS Chapter 1 Low Probability of Intercept Communications 1033 1.1 Signal Modulation Forms 1035 1.2 Interception Detectors 1036 1.2.1 Ideal and Realizable Detectors 1037 1.2.1.1 Detectability Criteria 1037 1.2.1.2 Maximum or Bounding Performance of Fundamental Detector Types 1037 (1) Wideband Energy Detector (Radiometer) 1038 (2) Optimum Multichannel FH PulseMatched Energy Detector 1040 (3) Filter Bank Combiner (FBC) Detector 1045 (4) Partialband Filter Bank Combiner (PBFBC) 1050 1.2.1.3 Signal Structures and Modulation Considerations 1055 1.2.2 Nonidealistic Detector Performance 1059 1.2.2.1 The Problem of Time Synchronization 1059 (1) Wideband Detector with Overlapping I Ds Each of Duration Equal to That of the Message 1059 (2) Wideband Detector with Single (Nonoverlapping) I D of Duration Equal to Half of the Message Duration 1063 (3) Wideband Detector with a Continuous Integration PostDetection RC Filter 1064 (4) Filter Bank Combiner with Overlapping I Ds Each of Hop Interval Duration 1066 1.2.2.2 The Problem of Frequency Synchronization 1070 (1) Doppler Effects 1070 (2) Performance of the FBC with Frequency Error 1070 xii http:jntu.blog.com Contents http:jntu.blog.com1.2.3 Detector Implementation 1074 1.2.3.1 Basic Configurations 1074 (1) Wideband SingleChannel Detectors 1074 (2) Channelized Detectors 1076 1.2.3.2 Other Possible Feature Detector Configurations 1077 1.3 Performance and Strategies Assessment 1083 1.3.1 Communicator Modulation and Intercept Detectors 1083 1.3.2 AntiJam Measures 1087 1.3.3 Optimum LPI ModulationCoding Conditions 1089 1.4 Further Discussion 1089 1.5 References 1092 Appendix 1A: Conditions for Viable Multichannel Detector Performance 1093 Chapter 2 Multiple Access 1096 2.1 Networks 1099 2.1.1 Decentralized (PointtoPoint) Networks 1099 2.1.2 Centralized (MultipointtoPoint) Networks 1103 2.2 Summary of Multiple Access Techniques 1105 2.3 SpreadSpectrum Multiple Access with DSBPSK Waveforms 1110 2.3.1 PointtoPoint 1110 2.3.2 Conventional MultipointtoPoint 1113 2.3.3 Optimum MultipointtoPoint 1116 2.4 SpreadSpectrum Multiple Access with FHMFSK Waveforms 1123 2.4.1 PointtoPoint 1124 2.4.2 Conventional MultipointtoPoint 1136 2.4.3 Optimum MultipointtoPoint 1142 2.5 Discussion 1148 2.6 References 1148 Chapter 3 Commercial Applications 1158 3.1 Key Events in the Commercial Market 1160 3.2 The United States FCC Part 15 Rules 1160 3.2.1 Indoor Applications 1161 3.2.2 Outdoor Applications 1162 3.2.3 Direct Sequence Versus Frequency Hopping 1162 3.2.3.1 Conversion of Narrowband Radios 1163 3.2.3.2 Cost of Development and Products 1163 3.2.3.3 Performance 1163 3.2.4 Multipath and Diversity 1165 3.2.5 Results of The Part 15 Rule 1166 Contents http:jntu.blog.com xiii http:jntu.blog.com3.3 The Digital Cellular CDMA Standard 1169 3.3.1 Overview of the CDMA Digital Cellular System (IS95) 1170 3.3.2 Comparison of IS95, IS54, and GSM 1172 3.4 A New Paradigm for Designing Radio Networks 1173 3.5 The Potential Capacity of Direct Sequence Spread Spectrum CDMA in HighDensity Networks 1176 3.5.1 Data Versus Voice Applications 1179 3.5.2 Power Control 1179 3.5.3 Time Synchronization and Orthogonal Codes 1179 3.5.4 The Outbound Channel 1180 3.5.5 Frequency Reuse and Antenna Sectorization 1181 3.5.6 Narrowbeam and Delayline Antennas 1181 3.6 Spread Spectrum CDMA for PCSPCN 1182 3.6.1 Binary Orthogonal Codes 1183 3.6.2 SCDMA Equivalent to BitLevel TDMA 1183 3.6.3 A HighDensity Voice PCS System 1186 3.6.3.1 BitError Probabilities 1188 3.6.3.2 Computer Simulations 1191 3.6.3.3 Other System Issues 1192 3.6.3.4 Comparison with DECT 1193 3.7 Higher Capacity Optional Receivers 1194 3.8 Summary 1195 3.9 References 1196 Appendix 3A: Multipath and Diversity 1198 Appendix 3B: Error Bounds for InterferenceLimited Channels 1208 Index 1215 xiv http:jntu.blog.com Contents http:jntu.blog.comxv PREFACE In the nine years since the publication of the first edition of Spread Spectrum Communications, the world’s political situation has changed considerably. The U.S. Department of Defense has reduced its support for the development of new communication systems as well as their acquisition. One might question the need for a second edition of a book written about robust techniques for antijamming (AJ) and lowprobabilityofintercept (LPI) communications. However, while it is already painfully clear that the close of the Cold War has not ended warfare, the past decade has also ushered in a new era of mobile communications. The qualities that make spreadspectrum techniques useful in military communications—fine timeresolution, low powerdensity, privacy, and a high immunity to interference—are also extremely desirable in today’s mobile communications systems. Encouraged by enlightened FCC actions, spreadspectrum technology is being transferred from the Department of Defense to the arena of commercial mobile cellular communications. The emerging markets for spreadspectrum systems have the potential to dwarf those of the past. Are the design techniques for military communication systems truly applicable to the commercial environment? Does yesteryear’s jammer have anything to teach us about managing multipleuser noise in a spreadspectrum multipleaccess radio network? The answer—an unqualified “yes”—is attested to by the successes of companies that are penetrating the commercial marketplace with spreadspectrum products. This revised edition contains new material on the emerging commercial applications of spreadspectrum techniques as well as minor modifications to the book’s original fourteen chapters. We believe that since it is based on sound engineering principles and is not bound to a particular implementation technology, it will retain its usefulness for the foreseeable future. Marvin K. Simon Jim K. Omura Robert A. Scholtz Barry K. Levitt http:jntu.blog.com http:jntu.blog.comPREFACE TO FIRST EDITION Not more than a decade ago, the discipline of spreadspectrum (SS) communications was primarily cloaked in secrecy. Indeed, most of the information available on the subject at that time could be found only in documents of a classified nature. Today the picture is noticeably changed.The open literature abounds with publications on SS communications, special issues of the IEEE Transactions on Communications have been devoted to the subject, and the formation of an annual conference on military communications, MILCOM, now offers a public forum for presentation of unclassified (as well as classified) papers dealing with SS applications in military systems. On a less formal note, many tutorial and survey papers have recently appeared in the open literature, and presentations on a similar level have taken place at major communications conferences. Finally, as further evidence we cite the publication of several books dealing either with SS communications directly or as part of the more general electronic countermeasures (ECM) and electronic countercounter measures (ECCM) problem. References to all these forms of public documentation are given in Section 1.7 of Chapter 1, Part 1. The reasons for this proliferation can be traced to many sources. While it is undoubtedly true that the primary application of SS communications still lies in the development of enemy jamresistant communication systems for the military, largely within the confines of classified programs, the emergence of other applications, in which both the military and civilian sectors are involved, as playing a role of everincreasing importance. For example, to minimize mutual interference, the flux density of transmissions from radio transmitters must often be maintained at acceptably low radiation levels. A convenient way to meet these requirements is to spread the power spectrum of the signal before transmission and despread it after reception—the nonhostile equivalent of the military lowprobabilityofintercept (LPI) signal design. Another instance in which SS techniques are particularly useful in a nonantijam application is in multipleaccess communications in which many users share a single communication channel.The assignment of a unique SS sequence to each user allows him or her to transmit simultaneously over the common channel with a minimum of mutual interference, simplifying the network control requirements. xvi http:jntu.blog.com http:jntu.blog.comExtremely accurate positioning can be computed by using signals from several satellites in synchronous and asynchronous orbits. Satellites transmitting pseudorandom noise sequences modulated onto the transmitted carrier signal provide the means for accomplishing the required range and distance determination at any point on the earth. Finally, SS techniques can improve the reliability of transmission in frequencyselective fading and multipath environments. Spreading the bandwidth of the transmitted signal over a wide range of frequencies reduces its vulnerability to interference and often provides some diversity gain at the receiver. At the heart of all these potential applications lies the increasing use of digital forms of modulation for transmitting information, driven by the tremendous advances made over the last decade in microelectronics. This trend no doubt will continue, and thus it should not be surprising that more and more applications for spreadspectrum techniques will continue to surface. Indeed, the stateoftheart is advancing so rapidly (e.g., witness the recent improvements in frequency synthesizers boosting frequency hop rates from the Khopssec to the Mhopssec ranges over SS bandwidths in excess of a GHz) that today’s primarily theoretical concepts will be realized tomorrow. Unclassified research and developments in spreadspectrum communications have arrived at a point of maturity necessary to justify a textbook on SS communications that goes far beyond the level of those available on today’s market. Such is the purpose of Spread Spectrum Communications. Contained within the fourteen chapters of its three volumes is an indepth treatment of SS communications that should appeal to the specialist already familiar with the subject as well as the neophyte with little or no background in the area. The book is organized into five parts, within which the various chapters are for the most part selfcontained. The exception is Chapter 3, Part 1, which deals with basic concepts and system models and serves as a basis for many of the other chapters that follow. As would be expected, the more traditional portions of the subject are treated in the first two parts, while the latter three parts deal with more specialized aspects. The authors envision that an introductory onesemester course in SS communications taught at a graduate level in a university might cover all or parts of Chapters 1, 3, 4, 5 of Part 1, Chapters 1 and 2 of Part 2, and Chapters 1 and 2 of Part 4. In composing the technical material presented in Spread Spectrum Communications, the authors have intentionally avoided referring by name to specific modern SS systems that employ techniques such as those discussed in many of the chapters. Such a choice was motivated by the desire to offer a unified approach to the subject that stresses fundamental principles rather than specific applications. Nevertheless, the reader should feel confident that the broad experience of the four authors ensures that the material is practical as well as academically inspiring. In writing a book of this magnitude, we acknowledge many whose efforts should not go unnoticed. Credit is due to Paul Green for originally suggesting Preface to First Edition http:jntu.blog.com xvii http:jntu.blog.comthe research that uncovered the material in Chapter 2, Part 1, and to Bob Price for the tireless sleuthing which led to much of the remarkable information presented there. Chapter 5, Part 1 benefited significantly from the comments of Lloyd Welch, whose innovative research is responsible for some of the elegant sequence designs presented there. Per Kullstam helped clarify the material on DSBPSK analysis in Chapter 1, Part 2. Paul Crepeau contributed substantially to the work on list detectors. Last but by no means least, the authors would like to thank James Springett, Gaylord Huth, and Richard Iwasaki for their contributions to much of the material presented in Chapter 4, Part 5. Several colleagues of the authors have aided in the production of a useful book by virtue of critical reading andor proofing. In this regard, the efforts of Paul Crepeau, Larry Hatch,Vijay Kumar, Sang Moon,WeiChung Peng, and Reginaldo Polazzo, Jr. are greatly appreciated. It is often said that a book cannot be judged by its cover. The authors of Spread Spectrum Communications are proud to take exception to this commonly quoted cliche. For the permission to use the historically significant noisewheel cover design (see Chapter 2, Part 1, Section 2.2.5), we gratefully acknowledge the International Telephone and Telegraph Corp. Marvin K. Simon Jim K. Omura Robert A. Scholtz Barry K. Levitt xviii http:jntu.blog.com Preface to First Edition http:jntu.blog.comPart 1 INTRODUCTION TO SPREADSPECTRUM COMMUNICATION http:jntu.blog.com http:jntu.blog.comhttp:jntu.blog.com http:jntu.blog.comChapter 1 A SPREADSPECTRUM OVERVIEW Over thirty years have passed since the terms spreadspectrum (SS) and noise modulation and correlation (NOMAC) were first used to describe a class of signaling techniques possessing several desirable attributes for communication and navigation applications, especially in an interference environment. What are these techniques? How are they classified? What are those useful properties? How well do they work? Preliminary answers are forthcoming in this introductory chapter. We will motivate the study of spreadspectrum systems by analyzing a simple game, played on a finitedimensional signal space by a communications system and a jammer, in which the signaltointerference energy ratio in the communication receiver’s data detection circuitry serves as a payoff function. The reader is hereby forewarned that signaltointerference ratio calculations alone cannot illustrate many effects which, in subtle ways, degrade more realistic performance ratios, e.g., biterrorrate in coded digital SS systems. However, the tutorial value of the following simple energy calculations soon will be evident. 1.1 A BASIS FOR A JAMMING GAME The following abstract scenario will be used to illustrate the need for spectrum spreading in a jamming environment, to determine fundamental design characteristics, and to quantify one measure of SS system performance. Consider a synchronous digital communication complex in which the communicator has K transmitters available with which to convey information to a cooperating communicator who possesses K matching receivers (see Figure 1.1).Assume for simplicity that the communication signal space has been “divided equally” among the K transmitters. Hence, with a bandwidth W ss available for communicating an information symbol in a Ts second interval (0, Ts), the resultant transmittedsignal function space of dimension approximately 2TsWss is divided so that each transmitter has a 3 http:jntu.blog.com http:jntu.blog.comDdimensional subspace, D
2TsWssK, in which to synthesize its output signal. Denote an orthonormal basis for the total signal space by ck(t), k
1, 2, . . . , 2TsWss, i.e., (1.1) where the basis functions may be complex valued, and ( ) denotes conjugation. Then the signal emitted by the kth transmitter is of the form (1.2) where (1.3) and {aj} is a datadependent set of coefficients.We will refer to the above as an orthogonal communication system complex of multiplicity K. Of course, real systems generally radiate real signals.The reader may wish to view mk(t) as the modulation on the radiated signal Re{mk(t) exp (jvct u)}. Without loss of generality, we can dispense with the shift to RF during this initial discussion. In a simplified jamming situation, the signal zi(t) observed at the ith receiver in the receiving complex might be (1.4) where ni(t) represents internally generated noise in the ith receiver, J(t) is an externally generated jamming signal, and the Kterm sum represents the total output signal of the transmitter complex. One signal processing zi 1t2
a K k
1 mk 1t2 J1t2 ni1t2. Nk
5j: 1k  12D 6 j  kD6 mk1t2
a jHNk aj cj 1t2,
Ts 0 cj1t2c k 1t2 dt
e 1, 0, j j
 k k 4 A SpreadSpectrum Overview Figure 1.1. The scenario for a game between a jammer and a communication system complex. http:jntu.blog.com http:jntu.blog.comstrategy for the ith receiver is to project the received signal onto the set of basis functions for the ith transmitter’s signal space, thereby calculating

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SPREAD SPECTRUM COMMUNICATIONS HANDBOOK

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COMMUNICATIONS

1.3 Spread-Spectrum System Configurations and Components 9

1.5.2 Independent Interference Rejection and

1.7.2 Books on Resolution and Ambiguity Functions 391.7.3 Recent Books and Proceedings on Spread-Spectrum

2.2 Early Spread-Spectrum Systems 65

2.3.2 Other Early Spread-Spectrum

2.3.3 Spread-Spectrum Developments Outside

3.4 Uncoded Direct-Sequence Spread Binary Phase-Shift-Keying 144

3.5 Coded Direct-Sequence Spread Binary Phase-Shift-Keying 153

3.6 Uncoded Frequency-Hopped Binary

3.6.1 Constant Power Broadband Noise Jammer 172

3.7 Coded Frequency-Hopped Binary Frequency-Shift-Keying 178

Chapter 4 General Analysis of Anti-Jam Communication Systems 189

5.2.2 Formal Power Series and Characteristic Polynomials 273

5.2.5 Determination of Linear Recursions from

5.3 Memory-Efficient Linear Generators 281

5.3.2 Maximization of Period for a Fixed Memory Size 2835.3.3 Repeated Factors in the Characteristic Polynomial 284

5.4.3 Hamming Distance Properties of Derived

5.4.4 Correlation Properties of Derived Complex

5.5.3 Determining the Period of Memory Cell Outputs 299

5.7.3 Cross-correlation of Binary M-Sequences 329

5.8.3 An FHMA Design Employing an M-Sequence

Appendix 5B: Factorizations of 2n—1 and Selected

PART 2 CLASSICAL SPREAD-SPECTRUM

COMMUNICATIONS

1.1 Direct-Sequence Spread Coherent Binary Phase-Shift

1.6.2 Continuous Jammer with Coding—No Fading

1.6.3 Continuous Jammer with Coding—Fading

2.3.1.4 Time Diversity Overview 540

2.5 Worst Noise Jammer Distribution—Slow Fading

2.6 Worst Noise Jammer Distribution—Slow Fading

Appendix 2A: Justification of Factor of 1/2 for FH/MFSK Signals

Appendix 2B: Combinatorial Computation for n
1 Band

1.1 Performance of FH/QPSK in the Presence of

1.2 Performance of FH/QASK in the Presence of

1.3 Performance of FH/QPSK in the Presence of

1.4 Performance of FH/QASK in the Presence of

1.5 Performance of FH/PN/QPSK in the Presence of

1.6 Performance of FH/PN/QASK in the Presence of

1.7 Performance of FH/QPR in the Presence of

1.8 Performance of FH/QPR in the Presence of

Chapter 2 Differentially Coherent Modulation Techniques 715

2.1 Performance of FH/MDPSK in the Presence of

2.2 Performance of FH/MDPSK in the Presence of

2.3 Performance of DQASK in the Presence of Additive

2.4 Performance of FH/DQASK in the Presence of

2.5 Performance of FH/DQASK in the Presence of

SYSTEMS Chapter 1 Pseudonoise Acquisition in Direct Sequence Receivers 753

1.2.2 Single Dwell Acquisition Time Performance in the

1.2.3 Single Dwell Acquisition Time Performance in the

1.2.4 Evaluation of Detection Probability P Dand False

Alarm Probability P FAin Terms of PN Acquisition

1.2.5 Effective Probability of Detection and Timing

1.2.7 Reduction in Noise Spectral Density Caused by

1.2.9 Probability of Acquisition for the Single

1.3 The Multiple Dwell Serial PN Acquisition System 794

1.3.2 Multiple Dwell Acquisition Time Performance 8011.4 A Unified Approach to Serial Search Acquisition with

1.5 Rapid Acquisition Using Matched Filter Techniques 8171.5.1 Markov Chain Acquisition Model and Acquisition

1.6 PN Sync Search Procedures and Sweep Strategies for a

1.6.1 An Example—Single Dwell Serial Acquisition with

1.6.2 Application of the Circular State Diagram

1.7.1 A Brief Review of Sequential Hypothesis Testing

as Applied to the Non-Coherent Detection of

1.7.3 Probability of False Alarm and Average Test

Chapter 2 Pseudonoise Tracking in Direct Sequence Receivers 903

2.1.1 Mathematical Loop Model and Equation of

2.1.2 Statistical Characterization of the Equivalent

2.1.3 Linear Analysis of DLL Tracking Performance 911

2.2.1 Mathematical Loop Model and equation of

3.2 Time Synchronization of Non-Coherent FH/MFSK

3.2.1.1 Signal Model and Spectral Computations 992

3.2.3 The Effects of Time Synchronization Error on

3.2.3.1 Conditional Error Probability

3.2.3.2 Conditional Error Probability

Performance—m-Diversity with

3.2.3.3 Average Error Probability Performance

in the Presence of Time Synchronization

3.3 Frequency Synchronization of Non-Coherent FH/MFSK

3.3.1.1 Signal Model and Spectral Computations 1013

3.3.3 The Effects of Frequency Synchronization Error on FH/MFSK Error Probability Performance 1017

3.3.3.1 Average Error Probability Performance

in the Presence of Frequency

3.4 References

Appendix 3A: To Prove That a Frequency Estimator Based

upon Adjacent Spectral Estimates Taken at

Integer Multiples of 1/T Cannot be Unbiased 1026

Chapter 1 Low Probability of Intercept Communications 1033

1.2.1.2 Maximum or Bounding Performance of

(1) Wideband Energy Detector

(2) Optimum Multichannel FH

(3) Filter Bank Combiner (FBC) Detector 1045(4) Partial-band Filter Bank Combiner

1.2.1.3 Signal Structures and Modulation

1.2.2.1 The Problem of Time Synchronization 1059

(1) Wideband Detector with Overlapping

I & Ds Each of Duration Equal to

(2) Wideband Detector with Single (Non-overlapping) I & D of Duration Equal to Half of the

1.3.1 Communicator Modulation and Intercept

2.1.2 Centralized (Multipoint-to-Point) Networks 1103

2.3 Spread-Spectrum Multiple Access with DS/BPSK

3.3 The Digital Cellular CDMA Standard 11693.3.1 Overview of the CDMA Digital Cellular

3.5 The Potential Capacity of Direct Sequence Spread

Appendix 3B: Error Bounds for Interference-Limited Channels 1208

However, while it is already painfully clear that the close of the Cold Warhas not ended warfare, the past decade has also ushered in a new era ofmobile communications The qualities that make spread-spectrum tech-niques useful in military communications—fine time-resolution, low power-density, privacy, and a high immunity to interference—are also extremelydesirable in today’s mobile communications systems Encouraged by enlight-ened FCC actions, spread-spectrum technology is being transferred from theDepartment of Defense to the arena of commercial mobile cellular com-munications The emerging markets for spread-spectrum systems have thepotential to dwarf those of the past.

Are the design techniques for military communication systems trulyapplicable to the commercial environment? Does yesteryear’s jammer haveanything to teach us about managing multiple-user noise in a spread-spec-trum multiple-access radio network? The answer—an unqualified “yes”—isattested to by the successes of companies that are penetrating the commer-cial marketplace with spread-spectrum products

This revised edition contains new material on the emerging commercialapplications of spread-spectrum techniques as well as minor modifications

to the book’s original fourteen chapters We believe that since it is based onsound engineering principles and is not bound to a particular implementa-tion technology, it will retain its usefulness for the foreseeable future

Marvin K Simon Jim K Omura Robert A Scholtz Barry K Levitt

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PREFACE TO FIRST EDITION

Not more than a decade ago, the discipline of spread-spectrum (SS) munications was primarily cloaked in secrecy Indeed, most of the informa-tion available on the subject at that time could be found only in documents

com-of a classified nature

Today the picture is noticeably changed The open literature abounds with

publications on SS communications, special issues of the IEEE Transactions

on Communications have been devoted to the subject, and the formation of

an annual conference on military communications, MILCOM, now offers apublic forum for presentation of unclassified (as well as classified) papersdealing with SS applications in military systems On a less formal note, manytutorial and survey papers have recently appeared in the open literature, andpresentations on a similar level have taken place at major communicationsconferences Finally, as further evidence we cite the publication of severalbooks dealing either with SS communications directly or as part of the moregeneral electronic countermeasures (ECM) and electronic counter-countermeasures (ECCM) problem References to all these forms of public docu-mentation are given in Section 1.7 of Chapter 1, Part 1

The reasons for this proliferation can be traced to many sources While it

is undoubtedly true that the primary application of SS communications stilllies in the development of enemy jam-resistant communication systems forthe military, largely within the confines of classified programs, the emergence

of other applications, in which both the military and civilian sectors areinvolved, as playing a role of ever-increasing importance For example, tominimize mutual interference, the flux density of transmissions from radiotransmitters must often be maintained at acceptably low radiation levels Aconvenient way to meet these requirements is to spread the power spectrum

of the signal before transmission and despread it after reception—the hostile equivalent of the military low-probability-of-intercept (LPI) signaldesign

Another instance in which SS techniques are particularly useful in a anti-jam application is in multiple-access communications in which manyusers share a single communication channel The assignment of a unique SSsequence to each user allows him or her to transmit simultaneously over thecommon channel with a minimum of mutual interference, simplifying thenetwork control requirements

non-http://jntu.blog.com

Extremely accurate positioning can be computed by using signals fromseveral satellites in synchronous and asynchronous orbits Satellites trans-mitting pseudorandom noise sequences modulated onto the transmitted car-rier signal provide the means for accomplishing the required range anddistance determination at any point on the earth.

Finally, SS techniques can improve the reliability of transmission in quency-selective fading and multipath environments Spreading the band-width of the transmitted signal over a wide range of frequencies reduces itsvulnerability to interference and often provides some diversity gain at thereceiver

fre-At the heart of all these potential applications lies the increasing use ofdigital forms of modulation for transmitting information, driven by thetremendous advances made over the last decade in microelectronics Thistrend no doubt will continue, and thus it should not be surprising that moreand more applications for spread-spectrum techniques will continue to sur-face Indeed, the state-of-the-art is advancing so rapidly (e.g., witness therecent improvements in frequency synthesizers boosting frequency hoprates from the Khops/sec to the Mhops/sec ranges over SS bandwidths inexcess of a GHz) that today’s primarily theoretical concepts will be realizedtomorrow

Unclassified research and developments in spread-spectrum tions have arrived at a point of maturity necessary to justify a textbook on

communica-SS communications that goes far beyond the level of those available on

today’s market Such is the purpose of Spread Spectrum Communications.

Contained within the fourteen chapters of its three volumes is an in-depthtreatment of SS communications that should appeal to the specialist alreadyfamiliar with the subject as well as the neophyte with little or no background

in the area The book is organized into five parts, within which the variouschapters are for the most part self-contained The exception is Chapter 3,Part 1, which deals with basic concepts and system models and serves as abasis for many of the other chapters that follow As would be expected, themore traditional portions of the subject are treated in the first two parts,while the latter three parts deal with more specialized aspects The authorsenvision that an introductory one-semester course in SS communicationstaught at a graduate level in a university might cover all or parts of Chapters

1, 3, 4, 5 of Part 1, Chapters 1 and 2 of Part 2, and Chapters 1 and 2 of Part 4

In composing the technical material presented in Spread Spectrum Communications, the authors have intentionally avoided referring by name

to specific modern SS systems that employ techniques such as those cussed in many of the chapters Such a choice was motivated by the desire

dis-to offer a unified approach dis-to the subject that stresses fundamental ples rather than specific applications Nevertheless, the reader should feelconfident that the broad experience of the four authors ensures that thematerial is practical as well as academically inspiring

princi-In writing a book of this magnitude, we acknowledge many whose effortsshould not go unnoticed Credit is due to Paul Green for originally suggesting

the research that uncovered the material in Chapter 2, Part 1, and to BobPrice for the tireless sleuthing which led to much of the remarkable infor-mation presented there Chapter 5, Part 1 benefited significantly from thecomments of Lloyd Welch, whose innovative research is responsible for some

of the elegant sequence designs presented there Per Kullstam helped ify the material on DS/BPSK analysis in Chapter 1, Part 2 Paul Crepeau con-tributed substantially to the work on list detectors Last but by no meansleast, the authors would like to thank James Springett, Gaylord Huth, andRichard Iwasaki for their contributions to much of the material presented

clar-in Chapter 4, Part 5

Several colleagues of the authors have aided in the production of a ful book by virtue of critical reading and/or proofing In this regard, theefforts of Paul Crepeau, Larry Hatch, Vijay Kumar, Sang Moon, Wei-ChungPeng, and Reginaldo Polazzo, Jr are greatly appreciated

use-It is often said that a book cannot be judged by its cover The authors of

Spread Spectrum Communications are proud to take exception to this

com-monly quoted cliche For the permission to use the historically significantnoise-wheel cover design (see Chapter 2, Part 1, Section 2.2.5), we gratefullyacknowledge the International Telephone and Telegraph Corp

Marvin K Simon Jim K Omura Robert A Scholtz Barry K Levitt

Part 1

INTRODUCTION TO SPREAD-SPECTRUM COMMUNICATION

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Chapter 1

A SPREAD-SPECTRUM OVERVIEW

Over thirty years have passed since the terms spread-spectrum (SS) andnoise modulation and correlation (NOMAC) were first used to describe aclass of signaling techniques possessing several desirable attributes for com-munication and navigation applications, especially in an interference envi-ronment What are these techniques? How are they classified? What arethose useful properties? How well do they work? Preliminary answers areforthcoming in this introductory chapter

We will motivate the study of spread-spectrum systems by analyzing a ple game, played on a finite-dimensional signal space by a communicationssystem and a jammer, in which the signal-to-interference energy ratio in thecommunication receiver’s data detection circuitry serves as a payoff func-tion The reader is hereby forewarned that signal-to-interference ratio cal-culations alone cannot illustrate many effects which, in subtle ways, degrademore realistic performance ratios, e.g., bit-error-rate in coded digital SS sys-tems However, the tutorial value of the following simple energy calculationssoon will be evident

sim-1.1 A BASIS FOR A JAMMING GAME

The following abstract scenario will be used to illustrate the need for trum spreading in a jamming environment, to determine fundamentaldesign characteristics, and to quantify one measure of SS system perfor-mance Consider a synchronous digital communication complex in which

spec-the communicator has K transmitters available with which to convey mation to a cooperating communicator who possesses K matching receivers

infor-(see Figure 1.1) Assume for simplicity that the communication signal space

has been “divided equally” among the K transmitters Hence, with a width W ss available for communicating an information symbol in a T ssec-

band-ond interval (0, T s), the resultant transmitted-signal function space of

dimension approximately 2T s W ssis divided so that each transmitter has a

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D-dimensional subspace, D
2T s W ss /K, in which to synthesize its output

signal Denote an orthonormal basis for the total signal space by ck (t), k

1, 2, , 2T s W ss, i.e.,

(1.1)where the basis functions may be complex valued, and ( )* denotes conju-

gation Then the signal emitted by the k-th transmitter is of the form

(1.2)where

(1.3)

and {a j} is a data-dependent set of coefficients We will refer to the above as

an orthogonal communication system complex of multiplicity K.

Of course, real systems generally radiate real signals The reader may wish

to view m k (t) as the modulation on the radiated signal Re{m k (t) exp (jv c tu)} Without loss of generality, we can dispense with the shift to RF duringthis initial discussion

In a simplified jamming situation, the signal z i (t) observed at the i-th

receiver in the receiving complex might be

(1.4)

where n i (t) represents internally generated noise in the i-th receiver, J(t) is

an externally generated jamming signal, and the K-term sum represents the

total output signal of the transmitter complex One signal processing

strategy for the i-th receiver is to project the received signal onto the set of basis functions for the i-th transmitter’s signal space, thereby calculating

(1.5)

In the absence of jamming and receiver noise, the properties of the

ortho-normal basis insure that z j
a j , and thus, the i-th receiver correctly

discov-ers the data dependent set of coefficients {aj}, used by the i-th

where J0(t) represents that portion of the jamming signal orthogonal to all

of the 2T s W ssbasis functions used in producing the composite signal The

receiver noise component n 0i (t) likewise is orthogonal to all possible

trans-mitted signals These representations indicate that, in general, the projection

(1.5) of z i (t) onto c j (t) in the i-th receiver produces

(1.8)

The everpresent thermal noise random variable n ij, assumed complex

Gaussian, independent, and identically distributed for different values of i and/or j, represents the relatively benign receiver perturbations in the absence of jamming The jamming signal coefficients J jare less easily clas-sified, and from the jammer’s point of view, hopefully are unpredictable bythe receiver

The total energy E J in the jamminig signal J(t) over the time interval (0, T s) is given by

(1.9)

Obviously, the energy term involviong J9(t) serves no useful jamming

pur-pose, and henceforth, will be assumed zero (In keeping with this tive aspect of communication system design, we also assume that the jammerhas full knowledge of timing and of the set {cj (t)} of basis functions.) The sum in (1.9) can be partitioned into K parts, the i-th part representing the energy E Ji used to jam the i-th receiver Thus,

zi1t2 c*j1t2 dt for all j H Ni

A similar partition holds for the total transmitted signal energy E s, namely

(1.11)

E Si being the energy used by the i-th transmitter The additive partitions

(1.10), (1.11) are a direct result of the orthogonality requirement placed onthe signals produced by the transmitter complex

The above signal representations and calculations have been made underthe assumption that the channel is ideal, causing no attenuation, delay, ordistortion in conveying the composite transmitted signal to the receiver com-plex, and that synchronous clocks are available at the transmitter and

receiver for determining the time interval (0, T s) of operation Hence, tant considerations have been suppressed in this initial discussion, so that

impor-we may focus on one major issue facing both the communication systemdesigner and the jammer designer, namely their allocations of transmitter

energy and jammer energy over the K orthogonal communication links.

1.2 ENERGY ALLOCATION STRATEGIES

Within the framework of an orthogonal communication system complex of

multiplicity K, let’s consider the communicator and jammer to use the lowing strategies for allocating their available energies, E S and E Jrespec-

fol-tively, to the K links.

Communicators’ strategy: Randomly select K S links, K S  K, for equal energy allocations, each receiving E S /K Sunits The remaining links are notutilized

Jammer’s strategy: Randomly select K Jreceivers for equal doses of

jam-ming energy, each receiving E J /K Junits The remaining channels are notjammed

The quantity K S is referred to as the diversity factor of the communication system complex When K Sexceeds unity, the receiver must employ a diver-

sity combining algorithm to convert the outputs of the K Schosen links into

a single output for the system user The performance measure to beemployed here, in determining the effectiveness of these strategies, will notdepend on specifying a particular diversity combining algorithm

The randomness required of these strategies should be interpreted asmeaning that the corresponding adversary has no logical method for pre-dicting the choice of strategy, and must consider all strategies equally likely.Furthermore, random selection of communication links by the transmittershould not affect communication quality since all available links are assumed

to have equal attributes (Examples of link collections with non-uniformattributes will be considered in Part 2, Chapter 2.)

The receiving complex, having knowledge of the strategy selected for

communication, will collect all E S units of transmitted energy in the K S

receivers remaining in operation However, the amount of jamming energy

collected by those same K Sreceivers is a random variable whose value is determined by which of the jamming strategies is selected (denotes a binomial coefficient) Under the equally likely strategy assump-

tion, the probability that the jammer strategy will include exactly N of the

K Sreceivers in use, is given by

(1.12)

where

(1.13)(1.14)Using (1.12)—(1.14), it is possible to compute the expected total effective jam-

ming energy E Jeff sensed by the K Sreceivers, namely

(1.15)

E being the expected value operator Despite the complicated form of

Pr(N), it can be verified that

(1.16)and hence, that

(1.17)More generally, it can be verified that when the communicators use the strat-egy described above, (1.17) is the average total effective jamming energy forany arbitrary distribution of jamming energy

This idealized situation leads one to conclude, based on (1.17), that thereceiver can minimize the jammer’s effectiveness energy-wise by not using

diversity, i.e., by using K S
1 Furthermore, the multiplicity K of the

orthogonal communication system complex should be made as large as

pos-sible to reduce E Jeff, i.e., the complex should be designed to use all of the

available bandwidth The energy-optimal communication strategy (K S
1)

using a single one of the K available communication links, is called a pure spread-spectrum strategy This strategy, with its accompanying threat to use

any of K orthogonal links, increases the total signal-to-jamming ratio from

E S /E J at each receiving antenna’s terminals to KE S /E Jat the output of the

designated receiver, and therefore qualifies as an anti-jam (AJ) modulation

technique

The improvement E J /E Jeff in signal-to-jamming ratio will be called the

energy gain EG of the signalling strategy played on the orthogonal

com-munication system complex

(1.18)

Hence, the energy gain for a pure SS strategy is the multiplicity factor of thecomplex In this fundamental form (1.18), the energy gain is the ratio of the

signal space dimension 2T s W ssperceived by the jammer for potential

com-munication use to the total dimension K S D of the K S links’ D-dimensional signal spaces which the receiver must observe For a fixed T s W ssproduct, thisdefinition of energy gain makes no distinction between diversity and SS

strategies using the same signal space dimension K S D The reader may

rec-ognize the fact that the quantity called the multiplicity factor, or energy gain

in this chapter, is sometimes referred to as the processing gain of the SS tem This nomenclature is by no means universally accepted, and we will

sys-instead identify the term processing gain PG with the ratio W ss /R b , where R b

is the data rate in bits/second It is easily verified from (1.18) that

process-ing gain and energy gain are identical when R b
K S D/2T s, e.g., for binary

orthogonal signalling (D
2) with no diversity (K S
1)

Two key assumptions were made in showing that the pure SS strategy isbest: (1) The channel is ideal and propagates all signals equally well, and (2)the proper performance measure is the total effective jamming energy Ifeither of the above assumptions is not acceptable, then the jammer’s strat-egy may influence the performance measure, and the optimum diversity fac-

tor K Smay be greater than one Indeed, in later chapters it is shown that theuse of bit-error rate (BER) as a performance measure implies that the opti-mum diversity factor can exceed unity

Let’s summarize the requirements characteristic of a digital trum communication system in a jamming environment:

spread-spec-1 The bandwidth (or equivalently the link’s signal-space dimension D)

required to transmit the data in the absence of jamming is much less than

the bandwidth W ss(or equivalently the system’s signal space dimension

2T s W ss) available for use

2 The receiver uses inner product operations (or their equivalent) to

con-fine its operation to the link’s D-dimensional signal space, to

demodu-late the signal, and thereby to reject orthogonal jamming waveformcomponents

3 The waveforms used for communication are randomly or domly selected, and equally likely to be anywhere in the available band-

width (or equivalently, anywhere in the system’s 2T s W ssdimensional nal space).

sig-The term pseudorandom is used specifically to mean random in appearance

but reproducible by deterministic means

We will now review a sampling of the wide variety of communication tem designs which possess SS characteristics

sys-1.3 SPREAD-SPECTRUM SYSTEM CONFIGURATIONS

AND COMPONENTS

A pure spread-spectrum strategy, employing only a single link at any time,can be mechanized more efficiently than the system with potential diversity

factor K, shown in Figure 1.1 In an SS system, the K transmitter-receiver

pairs of Figure 1.1 are replaced by a single wideband communication linkhaving the capability to synthetize and detect all of the waveforms poten-tially generated by the orthogonal communication system complex.The pure

SS strategy of randomly selecting a link for communication is replaced with

an equivalent approach, namely, selecting a D-dimensional subspace for waveform synthesis out of the system’s 2T s W ss-dimensional signal space Thisrandom selection process must be independently repeated each time a sym-bol is transmitted Independent selections are necessary to avoid exposingthe communication link to the threat that the jammer will predict the sig-nal set to be used, will confine his jamming energy to that set, and hence,will reduce the apparent multiplicity and energy gain to unity

Three system configurations are shown in Figure 1.2, which illustratebasic techniques that the designer may use to insure that transmitter andreceiver operate synchronously with the same apparently random set ofsignals The portions of the SS system which are charged with the respon-sibility of maintaining the unpredictable nature of the transmission are

double-boxed in Figure 1.2 The modus operandi of these systems is as

follows:

1 Transmitted reference (TR) systems accomplish SS operation by mitting two versions of a wideband, unpredictable carrier, one (x(t)) modulated by data and the other (r(t)) unmodulated (Figure 1.2(a)).

trans-These signals, being separately recovered by the receiver (e.g., one may

be displaced in frequency from the other), are the inputs to a tion detector which recovers the data modulation The wideband carrier

correla-in a TR-SS system may be a truly random, wideband noise source,unknown by transmitter and receiver until the instant it is generated foruse in communication

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2 Stored reference (SR) systems require independent generation at

trans-mitter and receiver of pseudorandom wideband waveforms which areidentical in their essential characteristics (Figure 1.2(b)) The receiver’s

SS waveform generator is adjusted automatically to keep its output inclose synchronism with the arriving SS waveform Data detection, then,

is accomplished by cross-correlation The waveform generators are tialized prior to use by setting certain parameters in the generating algo-rithm, thereby denying the jammer knowledge of the waveform set beingused (even if the jammer has succeeded in determining the generator’sstructure)

ini-3 Matched filter (MF) systems generate a wideband transmitted signal by

pulsing a filter having a long, wideband, pseudorandomly controlledimpulse response (Figure 1.2(c)) Signal detection at the receiveremploys an identically pseudorandom, synchronously controlled,matched filter which performs the correlation computation Matched fil-ter systems differ from SR systems primarily in the manner in which theinner-product detection process is mechanized, and hence, have exter-nally observed properties similar to those of SR systems

Certainly, a pure TR system has several fundamental weaknesses including:(1) The system is easily spoofed since a jammer can in principle transmit apair of waveforms which are accepted by the receiver, (2) relatively poor per-formance occurs at low signal levels because noise and interference are pre-sent on both signals which are cross-correlated in the receiver, (3) the data

is easily determined by any listener who has access to both transmitted nals, and (4) the TR system’s two channels may require extra bandwidth andmay be difficult to match Some of the problems associated with TR systemsmay be mitigated by randomly changing parameters of one of the commu-nication links (e.g., by protecting one of the TR wideband links with an SR-like technique) Historical examples of SR-protected TR systems will begiven in the next chapter

sig-Spread-spectrum waveform generators for SR systems employing the lowing general modulation formats have been built The output of an SS

fol-waveform generator is given the generic name c(t) and is a (possibly

com-plex-valued) baseband representation of the SS waveform

1 Recorded modulation: The waveform w(t) of duration T pis recorded, and

if necessary, extended periodically to give

has the form

(1.20)

In all likelihood, the complex baseband signal c(t) never physically

appears in the transmitter or receiver Instead, the pseudorandomly

gen-erated sequence {f n} of frequency shifts will drive a frequency

synthe-sizer to produce a real-valued IF or RF carrier-modulated version of c(t).

The sequence {fn} of random phases is a by-product of the modulationprocess

3 Time hopping (TH): Assuming that the pulse waveform p(t) has tion at most T s /M T, a typical time hopping waveform might be

dura-(1.21)

In this example, time has been segmented into T ssecond intervals, witheach interval containing a single pulse pseudorandomly located at one

of M Tlocations within the interval

4 Direct sequence (DS) modulation: Spread-spectrum designers call the

waveform

(1.22)

direct sequence modulation Here, the output sequence {c n} of a random number generator is linearly modulated onto a sequence of

pseudo-pulses, each pulse having a duration T c called the chip time.

5 Hybrid modulations: Each of the above techniques possesses certain

advantages and disadvantages, depending on the system design tives (AJ protection is just one facet of the design problem) Potentially,

objec-a blend of modulobjec-ation techniques mobjec-ay provide better performobjec-ance objec-atthe cost of some complexity For example, the choice

(1.23)may capture the advantages of the individual wideband waveforms

c (i) (t) and mitigate their individual disadvantages.

Three schemes seem to be prevalent for combining the data signal d(t) with the SS modulation waveform c(t) to produce the transmitted SS signal x(t).

1 Multiplicative modulation: Used in many modern systems, the

transmit-ted signal for multiplicative modulation is of the form

(1.24)Mechanization simplicity usually suggests certain combinations of dataand SS formats, e.g., binary phase-shift-keyed (BPSK) data on a DS sig-

nal, or multiple frequency-shift-keyed (MFSK) data on a FH signal.Thesemodulation schemes are the ones of primary interest in this book.

2 Delay modulation: Suggested for use in several early systems, and a

nat-ural for mechanization with TH-SS modulation, this technique transmitsthe signal

(1.25)

3 Independent (switching) modulation: Techniques (1) and (2) are

sus-ceptible to a jamming strategy in which the jammer forwards the mitted signal to the receiver with no significant additional delay (a severegeometric constraint on the location of the jammer with respect to thetransmitter and receiver), but with modified modulation This repeaterstrategy, which if implementable, clearly reduces the multiplicity factor

trans-K of the SS system to unity, can be nullified by using a transmitted

sig-nal of the form

modu-lation The cost of independent data modulation is a clearly increased

hardware complexity.

The data demodulation process in a digital SS system must compute innerproducts in the process of demodulation That is, the receiver must mecha-nize calculations of the form

(1.27)

where in general m T (t) and m R (t) represent complex baseband signals and (m T , m R) is their inner product However, one or both of these complex base-band signals usually appears in modulated form as a real IF or RF signal

(1.28)The inner product (1.27) can be recovered from the modulated signal(s) inseveral ways, as illustrated in Figure 1.3 For example, the receiver can first

demodulate the signal x T (t) to recover the real and imaginary parts of m T (t)

and then proceed with straightforward correlation or matched filteringoperations using baseband signals On the other hand, as indicated in Figures1.3(c) and 1.3(d), there are alternative ways to compute the inner product,

which do not require that both signals be shifted to baseband first.

In all cases, the heart of the SS receiver is its synchronization circuitry, andthe heartbeats are the clock pulses which control almost all steps in forming

14 A Spread-Spectrum Overview

Figure 1.3. Examples of correlation-computing block diagrams.The dashed portions

of the diagrams can be eliminated when the modulations m T (t) and m R (t) are real

and, in addition, the local oscillator is phase-coherent, i.e., fe 0 Solid line processing

is often called the “in-phase” channel, while the dashed line processing is called the

“quadrature” channel.

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Spread-Spectrum System Configurations and Components 15

Figure 1.3. Continued.

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the desired inner product Recovery of Re{(m T , m R )} and Im{(m T , m R)}requires three levels of synchronization.

1 Correlation interval synchronization: Correlators require pulses to

indi-cate when the interval of integration is to begin and when it is to end

In the bandpass correlator of Figure 1.3(d), interval sync not only vides the timing for the sampling operation, but also initializes the nar-rowband filter’s state to zero at the beginning of each correlationinterval Typically, in DS systems these signals correspond to the datasymbol clock pulses In FH systems in which the data symbol timeexceeds the hop time, the interval sync pulses must indicate the dura-tion of a single frequency, since correlation operations spanning randomphase transitions are not generally useful

pro-2 SS generator synchronization: Timing signals are required to control the

epoch of the system’s SS waveform generator’s output and the rate atwhich that output is produced Direct sequence systems employ a clock

ticking at the chip rate 1/T cfor this purpose, while FH systems have a

similar clock operating at the hopping rate 1/T h

3 Carrier synchronization: Ideal reduction of the SS signal to baseband in

the receiver is possible if a local oscillator (or oscillator network) is able whose output is in frequency and phase synchronism with thereceived signal’s carrier (i.e., fe
0 in Figure 1.3) The above level ofcarrier sync is often available in DS systems, but usually only frequencysynchronism is attained in FH systems

avail-In some SS systems, the above synchronization signals are derived from asingle clock; in others, the carrier local oscillator is independent of the clocksignals which control its modulation Automatic control circuitry generally

is included to align the receiver’s clocks for proper demodulation of theincoming signal, although some systems have been built in which ultrastableclocks are initially aligned and then are allowed to drift in a free-runningmode until communication is concluded Proper operation of the correlationcomputing circuits generally requires control of the symbol clock epoch to

within a small fraction of the correlation interval’s duration T Similarly, it

is necessary to adjust the SS generator clock’s ticks to within a small tion of the reciprocal of the SS modulation’s short-term bandwidth, i.e., thebandwidth of the energy spectrum of the SS reference waveform within acorrelation interval Section 1.5.3 will indicate that the SS generator clock

frac-error for DS and FH systems must be a small fraction of T c and T h, tively, to maintain correlator operation at nearly maximum output signal lev-els, as required

respec-Frequency synchronous operation of correlation detectors requires thatthe phase drift between the incoming carrier (excluding SS modulation) andthe receiver’s local oscillator, over a correlation interval, be a fraction ofradian, i.e., the quantity fein Figure 1.3 may be assumed nearly constant dur-ing the correlation computation (Phase synchronism of the local oscillatorrequires, in addition, that febe near zero.) The bandpass correlator is a fre-

16 http://jntu.blog.com A Spread-Spectrum Overview

quency synchronous device requiring that the input to its narrowband filter

be centered in its passband to an error tolerance of a fraction of the rocal of the correlation time

recip-Output threshold crossing techniques, similar to those used in radar tion, are an alternative to MF output sampling in Figure 1.3(b), and may havehigher tolerance to synchronization errors than SR/DS systems However,any realized tolerance to synchronization errors implies a potential weak-ness to repeater jamming

detec-1.4 ENERGY GAIN CALCULATIONS FOR TYPICAL SYSTEMS

The following examples illustrate the energy gain calculation for basic SSsystems In each case, the SS system is viewed (in the terminology of Section1.2) as replacing an orthogonal communication system complex, and its mul-

tiplicity factor K determined, thereby evaluating the energy gain of the

sys-tem via (1.18)

Example 1.1. Let’s examine a SS system using binary (1) DS spreadingmodulation as in (1.22), multiplicative data modulation (1.24), and single-channel phase-synchronous detection (solid line portion of Figure 1.3(a))

over the data symbol duration T s of N c chip times, i.e., T s
N c T c Hence, thepseudorandom quantities which are known to the receiver, but unknown tothe jammer, are the DS pulse modulation sequence and the car-rier phase fT The inner product of two such waveforms with differentpseudorandom variables and data modulations is given by

(1.29)

For any particular choice of and fT, and regardless of the

val-ues of the data modulation d and d , constants over (0, T s), the two signalsare orthogonal if either T T
p/2 or is orthogonal to

Since the set of real N c -tuples forms an N c-dimensional space (and furthermore an orthogonal basis of vectors with 1 entries can be

found when N c is a multiple of 4), and since carrier phase differences of

, p c¿Nc43c1, p cNc4

Re5dc1t2ej1v c tf T 26Re5d¿c¿1t2ej 1v c tf¿ T 26dt

c1, c2, p cNc

Energy Gain Calculations for Typical Systemshttp://jntu.blog.com 17

magnitude p/2 cause orthogonality, the jammer is forced to view his form selection problem as being defined for an orthogonal communication

wave-system complex with multiplicity factor K given by

(1.30)

Example 1.2. Suppose that two independently hopped SS waveforms,

c(0)(t) and c(1)(t), of the form (1.20) are employed in a switching modulation scheme as in (1.26) to transmit binary data The data symbols’ duration T s spans M Dhop times Frequency-synchronous correlation computations in thereceiver are then carried out over individual hop times, and the correlator’s

sync clock produces a pulse every T hseconds The signal parameters, known

to the receiver but not to the jammer, are th two pseudorandom hopping

possible data symbols Two similar FH waveforms have inner product

(1.31)Orthogonality between two such waveforms is guaranteed, regardless of thevalues of the phases and data symbols (d, d), provided that

(1.32)

where k is any non-zero integer, for all d, d in {0, 1} We assume that twosuch orthogonal frequency waveforms are used by the communication sys-

tem as f 0n and f 1n , with a different pair for each n, 1  n  M D

If the transmitter and receiver are capable of producing and observing M F distinct orthogonal tones (assume M Fis even for convenience), it is clear thatduring each hop the jammer mmust contemplate combatting a pure SS strat-

egy on an orthogonal communication system complex of multiplicity M F/2.Therefore, during each hop time a single link in the orthogonal system com-plex requires four dedicated orthonormal basis functions (e.g., sines and

cosines at two distinct frequencies), and uses 4M D such functions over M D

hops By the same reasoning the number of basis functions available to the

entire complex is 2M F M D, and hence, the energy gain of (1.18) is given by

Example 1.3. One possible hybrid SS communication system employs TH,

FH, and DS modulations to produce the wideband waveform

(1.34)

in which p(t) is a unit-amplitude rectangular pulse of chip time duration T c

A total of N cpulses, modulated by the sequence are concatenated

to produce a DS waveform of duration T h, which in turn is frequency-hopped

to one of M F frequencies and time-hopped to one of M Ttime intervals within

the symbol time T s Hence,

(1.35)

Modulation by the n-th M-ary data symbol d nis accomplished by switching

the DS modulation to the d n -th of M orthogonal vectors

Two such hybrid SS signals have inner product given by

(1.36)Here dz is the Kronecker delta function, which is one if z
0 and is zerootherwise Orthogonality of these waveforms can be achieved, regardless of

the data values (d, d) and random phase values , if one or more ofthe following conditions holds:

observe the signal in a 2M-dimensional space whose basis over the interval (0, T s ) consists of Re{c (d) (t) exp(j2pf c t)} evaluated for each of the M values

of d, with the random hop phase f0set at 0 and at p/2 The jammer,

how-ever, must choose his waveform to jam a signal space of dimension 2N c M F M T,

whose basis consists of the sines and cosines of N c orthogonal DS tions hopped over M F orthogonal tones and M T disjoint time intervals

modula-Therefore, the nominal energy gain EG of this system is

1.5 THE ADVANTAGES OF SPECTRUM SPREADING

We have seen the advantages of making a jammer counteract an ensemble

of orthogonal communication systems The bandwidth increase which mustaccompany this SS strategy has further advantages which we will outlinehere

1.51 Low Probability of Intercept (LPI)

Spectrum spreading complicates the signal detection problem for a veillance receiver in two ways: (1) a larger frequency band must be moni-tored, and (2) the power density of the signal to be detected is lowered inthe spectrum-spreading process The signal may have further desirableattributes based in part on LPI, such as low probability of position fix (LPPF)which includes both intercept and direction finding (DFing) in its evalua-tion, or low probability of signal exploitation (LPSE) which may appendadditional effects, e.g., source identification

sur-For now let’s simply evaluate the power spectral density (PSD) of an SSsignal to determine its general properties Consider a signal of the form

(1.41)

where m T (t) represents the total modulation as a result of data and

spectrum-spreading effects, and fTis a random phase variable uniformly distributed

on (p, p) The PSD S x (f) of the waveform x(t) is defined as

Here F2Tis the time-limited Fourier transform

(1.43)

and hence, E { 0F2 T { x ( t ) }02} is the average energy spectral density of a 2T

second signal segment Conversion of this energy density to a power

den-sity is accomplished by division by 2T, and S x (f) then is simply the ing form as T becomes large Averaging over the random phase f Tleads

limit-to the relation

(1.44)

where S m (f) is the PSD of the modulation m T (t) We will now evaluate S m (f) for two basic SS modulation designs.

1 DS/BPSK modulation: The waveform corresponding to a DS signal

antipodally modulated by binary data is

(1.45)

in which the data value has the opportunity to change every N c

chip times (:xK denotes the integer part of x), and p(t) is a pulse shape which

is non-zero only in the interval (0, T c ) The calculation of S m (f) is simplified

by letting the limit parameter T grow in multiples of the symbol time N c T c.Hence,

(1.46)

By converting the sum index n in (1.45) to kN c  m where k ranges from

K to K  1 and m ranges between 0 and N c 1, it is possible to showthat

(1.47)

where P(f) is the Fourier transform of the chip pulse p(t) Inserting this

transform into (1.46) and ensemble averaging over the data sequence

{d k) which we assume to be composed of independent binary randomvariables, each equally likely to be 1 or 1, gives