Spread Spectrum Systems for GNSS and Wireless Communications

Jack K. Holmes

ARTECH H O U S E BOSTON|LONDON artechhouse.com

Contents

Chapter 1 An Introduction to Spread Spectrum Systems 1 1.0 Introduction 1 1.1 A Very Brief History of Spread Spectrum Communications 2 1.2 A Digital Spread Spectrum Communication Systems Model 3 1.3 Narrowband Signals 4

1.3.1 Narrowband Process Via the Complex Envelope 4 1.3.2 Narrowband Signals Through Narrowband Systems 5 1.3.3 Complex Envelope Characterization for Direct Sequence and

Frequency-Hopping Signals 7 1.4 Direct Sequence Spread Spectrum Systems 8

1.4.1 Direct Sequence Spreading with Binary Phase Shift Keying (BPSK) 8 1.4.2 Quadriphase Direct Sequence Spread Spectrum Systems 23 1.4.3 Minimum Shift Keying (MSK) 28

1.5 Frequency-Hopped Spread Spectrum Systems 30 1.5.1 Noncoherent Slow Frequency-Hopped Systems with MFSK Data

Modulation 33 1.5.2 Noncoherent Fast Frequency-Hopped Systems with MFSK Data

Modulation 34 1.5.3 Noncoherent Slow Frequency-Hopped Systems with DPSK Data

Modulation 36 1.5.4 Noncoherent Slow Frequency-Hopped Signals with BPSK Data

Modulation 39 1.6 Hybrid Spread Spectrum Systems 40

1.6.1 Hybrid DS with Slow Frequency Hopping with BPSK Data 40 1.6.2 Hybrid OQPSK DS with SFH with BPSK Data 41

1.7 Time Hopping Spread Spectrum Signals 42 1.8 An Introduction to OFDM 44

1.8.1 OFDM Communication System Implemented Via the FFT 45 1.8.2 OFDM Intersymbol Interference Reduction Techniques 46 1.8.3 OFDM Power Spectral Density 46

1.9 An Introduction to Ultrawideband Communications 47 1.9.1 A Brief Early History of UWB Communications 47 1.9.2 Description of UWB Signals 48 1.9.3 Regulatory Constraints and Spectral Masks for Various UWB

Applications 53 1.9.4 Impact of the Transmit Antenna on the Transmitted Signal 53 1.9.5 The Advantages and the Disadvantages of Impulse Versus

Multicarrier UWB 56 1.9.6 Advantages of UWB Systems 56 1.9.7 Applications of UWB 56

1.10 The Near-Far Problem 5 7 1.11 Low Probability oflnterception 57 1.12 Summary 58 References 58 Problems 60

vn

VIII Spread Spectrum Systems for GNSS and Wireless Communications

Chapter 2 Binary Shift Register Codes for Spread Spectrum Systems 63 2.0 Introduction 63 2.1 Finite Field Arithmetic 63

2.1.1 Polynomial Arithmetic 65 2.2 Shift Register Sequences 66

2.2.1 Equivalence of the Fibonacci and Galois Formsofa Linear SRG 70 2.3 Mathematical Characterization of SRGs 72

2.3.1 The Shift Register Matrix 72 2.3.2 The Characteristic Equation and Characteristic Polynomial 73

2.4 The Generating Function 75 2.5 The Correlation Function of Sequences 78

2.5.1 Periodic Correlation Functions for Sequences 81 2.5.2 Aperiodic Correlation Functions for Sequences 83

2.6 Codes for Spread Spectrum Multiple Access Applications 84 2.6.1 Binary Maximal Length Sequences 84 2.6.2 Gold Codes 94 2.6.3 Gold-Like Sequences and Dual BCH Sequences 103 2.6.4 Kasami Sequences 104 2.6.5 Bent Sequences 106 2.6.6 Comparisonof CDMA Code Performance 106

2.7 Sequences with Good Aperiodic Correlation 107 2.7.1 Barker and Williard Sequences 108 2.7.2 Neuman-Hofman Sequences 109 2.7.3 Partial Period Correlation for m-Sequences 109 2.7.4 Frequency-Hopping Multiple Access Code Generators 111

2.8 Summary 114 References 114 Problems 116

Chapter 3 Jamming Performance of Uncoded Spread Spectrum Systems 121 3.0 Introduction 121 3.1 Jammer Types 123 3.2 Bit Error Rate Performance in Broadband Noise Jamming 125

3.2.1 DS/PSK in Broadband Noise Jamming 125 3.2.2 SFH/DPSK in Broadband Noise Jamming 129 3.2.3 SFH/PSK in Broadband Noise Jamming 132 3.2.4 SFH/MFSK in Broadband Noise Jamming 133 3.2.5 FFH/BFSK in Broadband Noise Jamming 137 3.2.6 Hybrid DS-SFH SS Modulation in Broadband Noise Jamming 138

3.3 BER Performance in Partial Band Noise Jamming 140 3.3.1 DS/PSK in Partial Band Noise Jamming 140 3.3.2 SFH/DPSK Systems in Partial Band Noise Jamming 144 3.3.3 SFH/PSK BER in Partial Band Noise Jamming 146 3.3.4 SFH/MFSK in Partial Band Noise Jamming 148 3.3.5 FFH/MFSK in Partial Band Noise Jamming 151 3.3.6 Hybrid DS-SFH/MFSK in Partial Band Noise Jamming 154 3.3.7 Hybrid DS-SFH/DPSK in Partial Band Noise Jamming 157

3.4 Bit Error Rate Performance in Pulsed Jamming 157 3.4.1 Bit Error Rate Performance for DS/PSK in Pulsed Jamming 157 3.4.2 Performance of SFH/MFSK in Pulsed Jamming 159 3.4.3 Performance of SFH/DPSK in Pulsed Jamming 160 3.4.4 Performance of Hybrid DS-SFH/MFSK in Pulsed Jamming 160

Contents ix

3.4.5 Performance of Hybrid DS-SFH/DPSK in Pulsed Jamming 161 3.5 Bit Error Rate Performance in Tone Jamming 161

3.5.1 Bit Error Rate Performance for DS(BPSK)/BPSK in Tone Jamming 161

3.5.2 Bit Error Rate Performance for DS(QPSK)/BPSK in Tone Jamming 165

3.5.3 Bit Error Rate Performance for DS(MSK)/BPSK in Tone Jamming 168

3.6 Multitone Jamming Bit Error Rate Performance 173 3.6.1 Multitone Jamming Bit Error Rate Performance for SFH/MSK 173 3.6.2 Multitone Jamming Bit Error Rate Performance for SFH/DPSK 175

3.7 Degradation Due to Interference or Jamming in DS Systems 178 3.7.1 Equivalent Noise Spectral Density for DS(BPSK)/BPSK Systems 179 3.7.2 Carrier to Equivalent Noise Spectral Density Ratio for

DS(BPSK)/BPSK 181 3.7.3 Equivalent Noise Spectral Density Degradation for

DS(BPSK)/BPSK Systems 183 3.7.4 Degradation to NRZ Signals Due to Narrowband Jammers for

DS(BPSK)/BPSK Signals 185 3.8 Summary 186 References 186 Problems 187

Chapter 4 Jamming Performance of Coded Spread Spectrum Systems 191 4.0 Introduction 191 4.1 Interleaver Structures for Coded Systems 192

4.1.1 Block Periodic Interleaving 192 4.1.2 Convolutional Interleaving 194

4.2 Linear Block Coding 195 4.2.1 Linear Block Coding Concepts 195 4.2.2 Rule for Optimum Decoding with No Jammer Side Information 208 4.2.3 Rule for Optimum Decoding with Jammer Side Information 211 4.2.4 Computationofthe Block Coded Word and Bit Error Rate 213

4.3 Convolutional Codes 224 4.3.1 Convolutional Code Encoder Characterization 224 4.3.2 The Transfer Function of a Convolutional Code and the Free

Distance 228 4.3.3 Decoding of Convolutional Codes 230 4.3.4 The Viterbi Algorithm 232 4.3.5 Error Probabilities for Viterbi Decoding of Convolutional Codes 238 4.3.6 Sequential Decoding of Convolutional Codes 242 4.3.7 Threshold Decoding of Convolutional Codes 242 4.3.8 Nonbinary Convolutional Codes 243

4.4 Iteratively Decoded Codes 243 4.4.1 Turbo Codes 244 4.4.2 A Serial Concatenated Convolutional Code 249 4.4.3 Serial Concatenated Block Codes 251 4.4.4 Parallel Concatenated Block Codes 251 4.4.5 Low-Density Parity Check Codes 252

4.5 Selected Results for Some Error Correction Codes 253 4.5.1 Böse, Chaudhuri, and Hocquenghem Codes 253 4.5.2 Reed-Solomon Codes 255 4.5.3 Convolutional Codes with Maximum Free Distance 257

x Spread Spectrum Systems for GNSS and Wireless Communications

4.5.4 Hard- and Soft-Decision FFH/MFSK with Repeat Coding BER Performance 259

4.6 Shannon's Capacity Theorem, the Channel Coding Theorem, and BW Efficiency 266

4.6.1 Shannon's Capacity Theorem 267 4.6.2 Channel Coding Theorem 267 4.6.3 Bandwidth Efficiency 267

4.7 Application ofError Control Coding 268 4.8 Summary 269 References 269 Selected Bibliography 272 Problems 272

Chapter 5 Carrier Tracking Loops and Frequency Synthesizers 275 5.0 Introduction 275 5.1 Tracking of Residual Carrier Signals 275 5.2 PLL for Tracking a Residual Carrier Component 276

5.2.1 The Likelihood Function for Phase Estimation 276 5.2.2 The Maximum-Likelihood Estimation of Carrier Phase 277 5.2.3 Long Loops and Short Loops 278 5.2.4 The Stochastic Differential Equationof Operation 279 5.2.5 The Linear Model of the PLL with Noise 281 5.2.6 The Various Loop Filter Types 283 5.2.7 Transient Response of a Second-Order Loop 286 5.2.8 Steady State Tracking Error When the Phase Error Is Small 287 5.2.9 The Variance of the Linearized PLL Phase Error Due to Thermal

Noise 290 5.2.10 Frequency Response of the Active Filter Second-Order PLL 292 5.2.11 Phase Noise Effects of the Total Phase Error in the PLL 293 5.2.12 Nonlinear PLL Results 297

5.3 Frequency Synthesizers 299 5.3.1 Digital Frequency Synthesis 299 5.3.2 Direct Frequency Synthesis 301 5.3.3 Indirect Frequency Synthesis 303 5.3.4 Indirect Frequency Synthesis Transfer Functions 304

5.4 Tracking of BPSK Signals 306 5.4.1 Tracking a BPSK Signal with a Squaring Loop 306 5.4.2 Tracking a BPSK Signal with an Integrate-and-Dump Costas

Loop 310 5.4.3 Tracking a BPSK Signal with a Passive Arm Filter Costas Loop 314 5.4.4 Steady State Tracking Error for the Costas and Squaring Loops 315 5.4.5 Costas Loop with Hard-Limited In-Phase Arm Processing 315 5.4.6 Improved Frequency Acquisition of a Passive Filter Costas

Loop 315 5.4.7 Lock Detectors for Costas and Squaring Loops 317 5.4.8 False Lock in Costas Loops 318 5.4.9 Decision-Directed Feedback Loops 326

5.5 Multiphase Tracking Loops 330 5.5.1 The JV-th Power Loop 330 5.5.2 The N-Phase Costas Loop 331 5.5.3 Demod-Remod Quadriphase Tracking Loop 331 5.5.4 Modified Four-Phase Costas Loop-SQPSK Modulation 3 31

5.6 Frequency Locked Loops 341

Contents XI

5.6.1 The Cross Product FLL 341 5.7 Summary 342

References 343 Problems 345

Chapter 6 Code Acquisition in Direct Sequence Receivers 349 6.0 Introduction 349 6.1 The Acquisition Problem 354 6.2 Active Search Acquisition (Sliding Correlator) 354

6.2.1 Mean Acquisition Time Model for an Active Search System 355 6.2.2 Analysis of the Active Search System 356 6.2.3 Single Dwell Mean Acquisition Time Formula with Doppler 361 6.2.4 Mean Acquisition Time for the Double Dwell Time Search 362 6.2.5 Active Acquisition System Structures Used for Acquisition for

BPSK, QPSK, OQPSK, and MSK 364 6.3 Acquisition Probability Versus Time for Active Correlation 368 6.4 Parallel Methods of Active Code Acquisition 371

6.4.1 Active Search Mean Acquisition Time with Parallel Processing 372 6.5 Active Code Search Utilizing the FFT 375

6.5.1 Signal Modeling for BPSK Code Acquisition Utilizing the FFT 375 6.5.2 Model for the Correlator Output Out of the FFT 380 6.5.3 Evaluation of the FFT Enhanced Acquisition System Output

Variance for an Arbitrary Gaussian Noise Process 382 6.5.4 BPSK Code Modulation Evaluation of PD and PFA for Arbitrary

Noise 384 6.5.5 Gaussian Approximation of the Detection Probability for BPSK 386 6.5.6 Losses Between Bins in a Zero Padded FFT 387 6.5.7 The Frequency Search Range and Total Frequency Losses Using

an FFT 388 6.5.8 The Correlator Bins of the FFT Are Uncorrelated 389 6.5.9 BPSK Code Modulation y in a Matched Spectral Jammer 390 6.5.10 BPSK Code Modulation y in a Narrowband Jammer 391 6.5.11 Balanced QPSK and Balanced OQPSK Acquisition Performance 394 6.5.12 A Gaussian Approximation for PD for Balanced QPSK and

Balanced OQPSK 398 6.6 An Optimum Sweep Search Technique for Active Acquisition 400 6.7 Sequential Detection 403

6.7.1 Sequential Probability Ratio Test 404 6.7.2 Sequential Detection for DS Acquisition with BPSK Data

Modulation 404 6.7.3 A Sequential Detection Implementation 407 6.7.4 Acquisition Time ofa Sequential Detector 409 6.7.5 The Tong Detector 412

6.8 Transform Methods Used in Code Acquisition 415 6.9 Code Acquisition Using a Passive Matched Filter 417

6.9.1 The Matched Filter 417 6.9.2 Optimum Time of ArrivalEstimator 419 6.9.3 Digital Passive Matched Filter Introduction 420 6.9.4 DPMF Acquisition Model 421 6.9.5 Digital Matched Filter Acquisition Time Model 422 6.9.6 Signal Model for DPMF 424 6.9.7 Noise Variance Equation for a Gaussian Random Process Model

ofa Jammer 426

xii Spread Spectrum Systems for GNSS and Wireless Communications

6.9.8 Variance Evaluation of an MSJ 426 6.9.9 Correlation Signal Voltage Loss 427 6.9.10 Combining Coherent Segments of the DMF with the FFT 428 6.9.11 Detection and False Alarm Probability Densities for the NRZ

Code Case 430 6.9.12 The Acquisition Probability 433 6.9.13 Mean Acquisition Time Calculation 436

6.10 Serial Active Search for Acquisition of FH/MFSK Signals 439 6.10.1 Serial Active Search for Acquisition of FFH/MFSK Signals 439 6.10.2 Detection and False Alarm Probabilities for FFH/MFSK Serial

Active Search 444 6.10.3 Detection and False Alarm Probabilities for SFH/MFSK Serial

Active Search 447 6.10.4 Acquisition Time Calculations for FFH/MFSK and SFH/MFSK 450

6.11 Summary 451 References 452 Selected Bibliography 454 Problems 455 Appendix 6A Signal Flow Graphs and Discrete Time Invariant Markov Processes 458

Chapter 7 Direct Sequence Code-Tracking Loops 473 7.0 Introduction 473 7.1 Basis for the Early-Late Gate Code-Tracking Loop 473

7.1.1 Maximum-Likelihood Estimate Formulation 474 7.1.2 Maximum-Likelihood Estimate of the PN Code Timing 475

7.2 Full-Time Code-Tracking Loops 477 7.2.1 Baseband Early-Late Gate Code-Tracking Loop with NRZ

Symbols 478 7.2.2 Noncoherent Early-Late Gate I-Q Code-Tracking Loop 483 7.2.3 Noncoherent Early-Late Gate RF Implemented Code-Tracking

Loop 492 7.2.4 Noncoherent I-Q Dot Product Code-Tracking Loop with

Passive Arm Filters 493 7.2.5 Noncoherent I-Q Dot Product Code-Tracking Loop with

Active Arm Filters 501 7.3 Early-Late Gate Noncoherent I-Q Code-Tracking with Filtering and

Interference 502 7.3.1 Signal Model for the Noncoherent I-Q Early-Late Gate Code-

Tracking Loop with Channel Filtering 502 7.3.2 Signal and Noise Terms in the Noncoherent I-Q Early-Late Gate

Code Loop with Channel Filtering 505 7.3.3 Signal Terms in the Noncoherent I-Q Early-Late Gate Code

Loop with Channel Filtering 507 7.3.4 Closed-Loop Operation of the Noncoherent I-Q Early-Late

Gate Code Loop with Channel Filtering 513 7.3.5 Noncoherent I-Q Early-Late Gate Code-Tracking Loop with Channel

Filtering of N(t) a t /= 0 516 7.3.6 Noncoherent Early-Late Gate I-Q Code Loop Tracking Error

Variance with Channel Filtering 519 7.3.7 Noncoherent Early-Late Gate Code I-Q Tracking Error

Variance with Thermal Noise and Without Channel Filtering 521

Contents Xlll

7.3.8 Noncoherent Early-Late Gate I-Q Code-Tracking Error Variance with Channel Filtering in White Gaussian Noise with NRZ Symbols 522

7.3.9 Noncoherent Early-Late Gate I-Q Code-Tracking Performance with Narrowband Gaussian Interference Plus White Gaussian Noise with NRZ Symbols and No Channel Filtering 523

7.4 Time-Shared Noncoherent Code-Tracking Loops 527 7.5 Performance of a Noncoherent RF Implemented Time Gated Early-Late Gate

Bandpass Code-Tracking Loop 536 7.6 Steady State Error of Code-Tracking Loops Without Noise 542

7.6.1 First-Order Noncoherent I-Q Early-Late Gate Code-Tracking Loop 542 7.6.2 Second-Order Ideal Noncoherent I-Q Early-Late Gate

Code-Tracking Loop 544 7.7 Early-Late Gate Noncoherent I-Q Code-Tracking Loop Pull-In Without Noise 545 7.8 Multipath Effects 548

7.8.1 Multipath Effects on Filtered Noncoherent Code-Tracking Loops 548 7.8.2 Multipath Effects on Baseband Coherent I-Q Code-Tracking Loops 554 7.8.3 The Multipath Error Plots Are the Same for Coherent and

Noncoherent Code-Tracking Loops 555 7.9 Mean Time to Lose Lock for a First-Order Early-Late Gate RF Code-Tracking

Loop 556 7.9.1 Model for the Analysis of the Mean Slip Time Performance of the

Early-Late Gate Code-Tracking Loop with RF Implementation 558 7.9.2 Mean Slip Time Comparison of Theory and Simulation for the

Early-Late Gate Code-Tracking Loop with RF Implementation 559 7.10 Wideband Jamming Effects on Tracking and Mean Time to Lose Lock for

the Early-Late Gate Code-Tracking Loop with RF Implementation 560 7.11 Cramer-Rao Bound on Code-Tracking Error 562 7.12 Phase Rotation and Heterodyning for Receiver Use 565

7.12.1 Heterodyning the Signal to Near Baseband 565 7.12.2 Phase Rotation or Single Sideband Translation 566

7.13 Pulsing and Blanking in a Baseband Early-Late Code-Tracking Loop 568 7.13.1 Baseband Signal and Code Loop Model for a Baseband

Early-Late Gate I-Q Code-Tracking Loop with Pulsing 569 7.13.2 Füll Correlation in the Coherent Baseband I-Q Code-Tracking

Loop When the Signal Is Pulsed 570 7.13.3 Synchronous Blanking of the Noise When the Signal Is Pulsed Off 574

7.14 Summary 577 References 577 Selected Bibliography 579 Problems 579 Appendix 7A Mean Time to Lose Lock for a First-Order Early-Late Gate Code-

Tracking Loop with Either Bandpass Arm Filters or Baseband Arm Filters 582

Chapter 8 Tracking of Frequency-Hopped Signals 591 8.0 Introduction 591 8.1 Dataless Frequency-Hopped Time Tracking Loop Model 591

8.1.1 Loop Model for the Frequency-Hopping Loop Without Data 597 8.1.2 Evaluation of the Spectral Density of the Noise Terms 598 8.1.3 Closed Loop Tracking Loop Performance 600

8.2 Frequency-Hopping Tracking with BPSK and DPSK Data Modulation 601 8.3 Summary 602 References 602

XIV Spread Spectrum Systems for GNSS and Wireless Communications

Problem 602

Chapter 9 Multiple Access Methods for Digital Wireless Cellular Communications 603 9.0 Introduction 603 9.1 Brief History of Cellular Systems 603 9.2 Cellular Communications 604

9.2.1 Cellular System Architecture 604 9.2.2 Mobile Cells 604 9.2.3 Mobile Clusters 605 9.2.4 Frequency Reuse in a Cellular System 605 9.2.5 Cell Splitting 606 9.2.6 Handoff 606 9.2.7 More on Cell Structure 607 9.2.8 Assignment Strategies for Channelization 609

9.3 Multiple Access Techniques for Wireless Communications 609 9.3.1 A Brief Introduction to Multiple Access 610 9.3.2 Frequency Division Multiple Access 611

9.4 Time Division Multiple Access 612 9.4.1 The EfficiencyofTDMA Systems 613 9.4.2 TheNumber of Available Channels in aTDMA System 614

9.5 Spread Spectrum Multiple Access 615 9.5.1 Frequency-Hopped Multiple Access 615 9.5.2 Code Division Multiple Access 615 9.5.3 Hybrid Techniques for Spread Spectrum Signals 617

9.6 Space Division Multiple Access 619 9.7 The Capacityof Cellular CDMA ofa Single Cell 619 9.8 Packet Radio Access Techniques 624

9.8.1 ALOHA Channel 624 9.8.2 The Slotted ALOHA Channel 626

9.9 Carrier Sense Multiple Access Protocols 629 9.9.1 1-Persistent CSMA 629 9.9.2 Nonpersistent CSMA 630 9.9.3 p-Persistent CSMA 630 9.9.4 Conceptual Comparison of the Multiple Access Methods 630

9.10 Multiuser Detection Concepts 631 9.10.1 The Matched Filter for CDMA Signals 632 9.10.2 Conventional Single User Detector in the Synchronous Case 635 9.10.3 Decorrelating Detector 636 9.10.4 Minimum Mean Square Error Estimator 639 9.10.5 Additional Types of Multiuser Detector Systems 642 9.10.6 Successive Interference Cancellation 642 9.10.7 Multistage Interference Cancellation 643 9.10.8 Bit Error Rate Performance Estimates of the Detectors 644

9.11 An Example of a CDMA System: cdma2000 646 9.11.1 cdma2000 Layering Structure Overview 648 9.11.2 Forward Link and Reverse Link Channels Overview 648 9.11.3 Physical Layer of cdma2000 649 9.11.4 Forward Link Physical Channels 650 9.11.5 cdma2000 Reverse Physical Channels 661 9.11.6 Data Services in cdma2000 668

9.12 WCDMA 668 9.12.1 WCDMA Radio Frequency Protocol Architecture 668 9.12.2 WCDMA Channels 669

Contents xv

9.12.3 WCDMA Physical Layer 669 9.12.4 WCDMA Channel Coding 672 9.12.5 WCDMA Power Control 673 9.12.6 WCDMA Random Access 674 9.12.7 WCDMA Initial Cell Search 674 9.12.8 WCDMA Handover 674 9.12.9 WCDMA Packet Data Services 674

9.13 Summary 676 References 676 Problems 678

Chapter 10 An Introduction to Fading Channels 679 10.0 Introduction 679 10.1 An Introduction to Radio Propagation 679 10.2 Outdoor Models for Large-Scale Effects 680

10.2.1 Free Space Path Loss Model 680 10.2.2 Received Signal Power and the Electric Field Strength 682 10.2.3 Plane Earth Propagation Path Loss Model 683 10.2.4 Egli's Path Loss Model 684 10.2.5 Okumura-Hata Path Loss Model 685 10.2.6 COST-231 Hata Path Loss Model 685 10.2.7 ECC-33 Path Loss Model 686 10.2.8 Microcell Propagation Models 687

10.3 Large-Scale Effects for Indoor Models 689 10.3.1 Log-Normal Path Loss Model for Indoors 689 10.3.2 Floor Attenuation Factor Path Loss Model 690

10.4 Small-Scale Effects Multipath Fading 691 10.4.1 Rayleigh and Rician Fading Models 693 10.4.2 Small-Scale Fading Types 695 10.4.3 Multipath Time Delay Spread Fading 695 10.4.4 Fading Effects of Multipath Doppler Spread 698

10.5 Characterization of Wideband Channels 700 10.5.1 Deterministic Models 700 10.5.2 Stochastic Time-Variant Linear Channels 703 10.5.3 The Wide-Sense Stationary Channels 706 10.5.4 The Uncorrelated Scattering Channel 708 10.5.5 The Wide-Sense Stationary Uncorrelated Scattering Channel 709

10.6 The Effects of a Rayleigh Fading Channel on the Bit Error Rate 711 10.6.1 The Effects of a Rayleigh Fading Channel on the BPSK Bit Error

Rate 711 10.6.2 The Effects of a Rayleigh Fading Channel on the DPSK Bit Error

Rate 713 10.6.3 The Effects of a Rayleigh Fading Channel on Noncoherent

Orthogonal BFSK Bit Error Rate 714 10.6.4 Nakagami Fading Channel Model 714

10.7 Mitigation Methods for Multipath Effects 715 10.7.1 Diversity for Multipath Improvement 716 10.7.2 Combining Methods for Fading Mitigation 716

10.8 Equalization for Multipath Improvement 723 10.8.1 Baseband Transversal Symbol Rate Equalizer 723 10.8.2 Baseband Adaptive Equalization 726 10.8.3 Baseband Decision Feedback Equalizers 730

10.9 Diversity Techniques for Multipath Improvement 732

xvi Spread Spectrum Systems for GNSS and Wireless Communications

10.9.1 Multipath Performance Improvement Via Diversity Techniques for Binary Channels 732

10.10 The RAKE Receiver 739 10.10.1 The Tapped Delay Line Channel Model for a Frequency Selective

Slowly Fading Channel 739 10.10.2 The RAKE Receiver 740 10.10.3 Performance ofthe RAKE Receiver 742

10.11 Binary Coded Chernoff BER Bounds for Fading Channels 743 10.11.1 Chernoff Bound for Binary Linear Block Codes 743 10.11.2 Coded Orthogonal FSK Signal Model for Fading Channels 745 10.11.3 BER of Soft-Decision Decoding and FSK Modulation with

Linear Binary Block Codes over Rayleigh Fading Channels 746 10.11.4 BER of Hard-Decision Decoding and FSK Modulation with

Linear Binary Block Codes over Rayleigh Fading Channels 748 10.11.5 Chernoff Bounds for the BER of Convolutional Codes over

Rayleigh Fading Channels with Soft and Hard Decisions and Binary FSK Modulation 750

10.12 Smart Antenna Systems for Wireless Systems 752 10.12.1 Smart Antenna Systems 752 10.12.2 Adaptive Array Smart Antennas 752 10.12.3 Adaptive Array Spatial Processing 757 10.12.4 Forming Smart Antennas with Switched Beams 757 10.12.5 MIMO Systems 758

10.13 Summary 759 References 760 Problems 762

Chapter 11 Low Probability of Detection Systems 765 11.0 Introduction 765 11.1 Low Probability of Intercept (LPI) 766

11.1.1 Covert Communications 766 11.1.2 The LPI Scenario 766 11.1.3 Brief Signal Propagation Summary 768

11.2 An Introduction to Radiometrie Detectors 769 11.2.1 The Radiometer 770 11.2.2 Limitations ofthe Radiometer Performance Results 772 11.2.3 Low-Pass Filter Radiometer 775 11.2.4 The Correlation Radiometer 777 11.2.5 Relationship ofthe Output SNR and the Deflection 779 11.2.6 The Optimum Detector for Frequency-Hopped Waveforms 780 11.2.7 The Filter Bank Combiner 781

11.3 Spectrum Analyzers 784 11.3.1 Narrowband Signal Spectrum Analyzer Performance 786 11.3.2 Wideband Signal Spectrum Analyzer Performance 787

11.4 Second-Order Cyclostationary Feature Detection 788 11.4.1 Cyclostationary Processes 788 11.4.2 The Baseband and Carrier Cyclostationarity 788 11.4.3 BPSK Through a Filter and Squarer Circuit 789 11.4.4 Balanced QPSK Through a Filter and Squarer Circuit 796 11.4.5 Balanced OQPSK Through a Filter and Squarer Circuit 797 11.4.6 MSK Through a Filter and Squarer Circuit 798 11.4.7 Frequency-Hopped Signals with MFSK Through a Filter and

Squarer Circuit 800

Contents xvu

11.4.8 Slow Frequency-Hopped Signals with DPSK Data Modulation Through a Filter and Squarer Circuit 802

11.4.9 Delay and Multiply Chip Rate Detectors with Balanced QPSK 804 11.5 Performance of a Chip Rate Detector for BPSK 806 11.6 Frequency Estimation of an Unmodulated Tone with a Limiter

Discriminator 810 11.7 Summary 812 References 813 Selected Bibliography 814 Problems 814 Appendix 11A Samples from a Bandpass Filtered Gaussian Random Process 816

Chapter 12 Lock Detector Theory and Absorbing Markov Chains 819 12.0 Introduction 819 12.1 Absorbing Markov Chains 819 12.2 The Fundamental Matrix 822 12.3 Mean and Variance of the Number of Times a Process Is in a Transient

State 823 12.4 Mean and Variance of the Number of Times a Process Is in a Transient

State—General Case 827 12.5 The Probability of Starting in a Transient State and Ending in a Persistent

State 832 12.6 Lock Detector Performance 834 12.7 Lock Detector System Models 838

12.7.1 Residual Carrier Loop Lock Detector Block Diagram Model 838 12.7.2 Suppressed Carrier Lock Detector 840 12.7.3 PN Code Acquisition Lock Detector 841 12.7.4 A Frequency-Hopping Lock Detector for SFH/DPSK 841

12.8 Summary 843 References 843 Selected Bibliography 843 Problems 843

About the Author 847

Index 849