Handbook of Computer Simulation in Radio Engineering, Communications, and Radar

Sergey A. Leonov Alexander I. Leonov

Ы Artech House

Boston • London www. artechhouse. com

CONTENTS

PREFACE xix ACKNOWLEDGMENTS xxi

PARTI MATHEMATICAL MODELING IN RADIO ENGINEERING

Chapter 1 1.1 1.2

1.2.1 1.2.2

1.3 1.3.1 1.3.2 1.3.3 1.3.4

1.4 1.4.1 1.4.2 1.4.3

Chapter 2 Statistical synth

2.1 2.1.1 2.1.2

2.2 2.2.1 2.2.2

DETERMINISTIC MODELING Basic Definitions Mathematical Description of Signals Time-Domain Description Frequency-Domain Description Mathematical Description of Noise External Noise Intrinsic Noise Active Devices Noise Digital Circuits Noise Mathematical Description of Signal Processing Basic Models of Signal Processing Filters The Impulse Response The Transfer Function

STOCHASTIC MODELING esis of random functions

Random Events and Variables Statistical Description Simulation Algorithms Random Processes Statistical Description Simulation Algorithms

3 3 4 7

18 28 28 28 29 29 30 30 31 31

35

35 35 54 60 60 75

vii

viii Handbook of Computer Simulation

2.3 Random Fields 91 2.3.1 Statistical Description 91 2.3.2 Simulation Algorithms 95

Statistical analysis of random functions 2.4 Estimation of Random Function Parameters 98

2.4.1 Analysis of a Stationary Random Process 98 2.4.2 Analysis of a Nonstationary Random Process 102 2.4.3 Analysis of the Distribution Functions 103

2.5 The Random Processes and RF Circuits 104 2.5.1 Linear Circuits 104 2.5.2 Nonlinear Circuits 108 2.5.3 Random Narrowband Signal 111

Chapter 3 METHODS OF MODELING 115 3.1 Method of Carrier Frequency 115

3.1.1 Narrowband Signal Modeling 115 3.1.2 Modeling of Common Devices and Circuits 116 3.1.3 Simplified Algorithms 117

3.2 Method of Complex Envelope 118 3.2.1 Modeling of the Stationary Linear Circuits 118 3.2.2 Modeling of the Nonstationary Linear Circuits 122 3.2.3 Modeling of Inertialess Nonlinear Circuits 123 3.2.4 Modeling of Inertial-Type Nonlinear Circuits 127 3.2.5 Modeling of Common Devices and Circuits 131

3.3 Method of Statistical Equivalents 134 3.3.1 Method of Analytical Description 134 3.3.2 Method of Statistical Linearization 134 3.3.3 Method of Generation 140 3.3.4 Method of Filtration 141 3.3.5 Method of Information Parameter 144

3.4 Mathematical Description of Circuit Components 145 References 147 Selected Bibliography 148

PART 2 RADAR SYSTEM SIMULATION

Chapter 4 RADAR CROSS SECTION 153 4.1 Effective RCS 153

4.1.1 Description 153 4.1.2 Input Data 153 4.1.3 Model 153 4.1.4 Output Data 154 4.1.5 References 154 4.1.6 Examples 154

4.2 RCS Fluctuations 155 4.2.1 Description 155

Contents ix

4.2.2 4.2.3 4.2.4 4.2.5 4.2.6

4.3 4.3.1 4.3.2 4.3.3 4.3.4 4.3.5 4.3.6

4.4 4.4.1 4.4.2 4.4.3 4.4.4 4.4.5 4.4.6

4.5 4.5.1 4.5.2 4.5.3 4.5.4 4.5.5 4.5.6

4.6 4.6.1 4.6.2 4.6.3 4.6.4 4.6.5 4.6.6

4.7 4.7.1 4.7.2 4.7.3 4.7.4 4.7.5

Chapter 5 5.1

5.1.1 5.1.2 5.1.3 5.1.4

Input Data Model Output Data References Examples RCS of a Target for a Bistatic Radar Description Input Data Model Output Data References Examples RCS of Aircraft and Ships Description Input Data Model Output Data References Examples RCS of Antennas Description Input Data Model Output Data References Examples RCS of Birds and Insects Description Input Data Model Output Data References Examples RCS of Simple Shapes Description Input Data Model Output Data References

ANTENNAS AND PROPAGATION Antenna Patterns and Gain Description Input Data Model Output Data

155 155 156 156 156 158 158 158 158 159 159 159 160 160 160 160 160 161 161 162 162 162 162 162 162 162 163 163 163 163 163 163 163 164 164 164 166 170 170

171 171 171 171 172 173

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5.1.5 5.1.6

5.2 5.2.1 5.2.2 5.2.3 5.2.4 5.2.5 5.2.6

5.3 5.3.1 5.3.2 5.3.3 5.3.4 5.3.5

hapter 6 6.1

6.1.1 6.1.2 6.1.3 6.1.4 6.1.5 6.1.6

6.2 6.2.1 6.2.2 6.2.3 6.2.4 6.2.5 6.2.6

6.3 6.3.1 6.3.2 6.3.3 6.3.4 6.3.5 6.3.6

hapter 7 7.1

7.1.1 7.1.2 7.1.3 7.1.4 7.1.5

Reference Examples Phased-Array Patterns and Gain Description Input Data Model Output Data Reference Examples Pattern-Propagation Factor Description Input Data Model Output Data References

WAVEFORMS AND SIGNAL PROCESSING Pulsed Waveform Generation Description Input Data Model References Output Data Examples Digital Pulse Compression Description Input Data Model Output Data References Examples Frequency-Selective Filtering Description Input Data Model References Output Data Examples

DETECTION AND INTEGRATION Probability of Detection and False Alarm Description Input Data Model Output Data References

173 173 175 175 175 176 178 178 179 180 180 180 181 190 190

191 191 191 191 192 196 197 198 202 202 202 203 215 215 216 217 217 217 218 226 227 228

231 231 231 231 231 233 233

Contents xi

.2 7.2.1 7.2.2 7.2.3 7.2.4 7.2.5

.3 7.3.1 7.3.2 7.3.3 7.3.4 7.3.5

.4 7.4.1 7.4.2 7.4.3 7.4.4 7.4.5

8 .1 8.1.1 8.1.2 8.1.3 8.1.4 8.1.5

.2 8.2.1 8.2.2 8.2.3 8.2.4 8.2.5

.3 8.3.1 8.3.2 8.3.3 8.3.4 8.3.5

.4 8.4.1 8.4.2 8.4.3 8.4.4 8.4.5

i.5 8.5.1

Detectability Factor Description Input Data Model Output Data References Minimum Detectable Signal Description Input Data Model Output Data Reference M-out-of-N Integration Description Input Data Model Output Data References

LOSSES Atmospheric Attenuation Loss Description Input Data Model Output Data References Beamshape Loss Description Input Data Model Output Data Reference CFAR Loss Description Input Data Model Output Data References Fluctuation Loss Description Input Data Model Output Data References Integration Loss Description

234 234 234 234 236 236 237 237 237 237 237 237 238 238 238 238 239 239

241 241 241 241 242 248 248 249 249 249 249 251 251 252 252 252 253 254 254 255 255 255 255 256 256 257 257

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8.5.2 8.5.3 8.5.4 8.5.5

.6 8.6.1 8.6.2 8.6.3 8.6.4 8.6.5

.7 8.7.1 8.7.2 8.7.3 8.7.4 8.7.5

.8 8.8.1 8.8.2 8.8.3 8.8.4 8.8.5

.9 8.9.1 8.9.2 8.9.3 8.9.4 8.9.5 8.9.6

.10 8.10.1 8.10.2 8.10.3 8.10.4 8.10.5

.11 8.11.1 8.11.2 8.11.3 8.11.4 8.11.5

9 .1

9.1.1

Input Data Model Output Data References MTI Processing Loss Description Input Data Model Output Data References Propagation Loss Description Input Data Model Output Data Reference Quantization Loss Description Input Data Model Output Data Reference Straddling Losses Description Input Data Model Output Data Reference Examples Pulse Compression Weighting Loss Description Input Data Model Output Data Reference Clutter Distribution Loss Description Input Data Model Output Data References

MAXIMUM DETECTION RANGE Maximum Detection Range for a Generic Pulsed Radar Description

257 257 257 257 258 258 258 258 262 262 263 263 263 263 263 263 264 264 264 264 264 264 265 265 265 265 266 266 266 267 267 267 267 268 268 269 269 269 269 270 270

271

271 271

Contents xiii

9.1.2 9.1.3 9.1.4 9.1.5 9.1.6

9.2

9.2.1 9.2.2 9.2.3 9.2.4 9.2.5

9.3

9.3.1 9.3.2 9.3.3 9.3.4 9.3.5

9.4 9.4.1 9.4.2 9.4.3 9.4.4 9.4.5

9.5 9.5.1 9.5.2 9.5.3 9.5.4 9.5.5

9.6 9.6.1 9.6.2 9.6.3 9.6.4 9.6.5

9.7 9.7.1 9.7.2 9.7.3 9.7.4 9.7.5

9.8 9.8.1 9.8.2

Input Data Model Output Data References Examples Maximum Detection Range for a Generic Pulsed Radar in a Clutter Environment Description Input Data Model Output Data References Maximum Detection Range for a Generic Pulsed Radar in a Jamming Environment Description Input Data Model Output Data Reference Maximum Detection Range for an Altimeter Description Input Data Model Output Data Reference Maximum Detection Range for a Bistatic Radar Description Input Data Model Output Data Reference Maximum Detection Range for a Laser Radar Description Input Data Model Output Data Reference Maximum Detection Range for a Meteorological Radar Description Input Data Model Output Data Reference Maximum Detection Range for a Search Radar Description Input Data

271 272 274 274 274

275 275 275 277 282 282

283 283 283 284 289 289 290 290 290 290 292 292 293 293 293 293 295 295 296 296 296 296 297 297 298 298 298 299 300 300 301 301 301

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9.8.3 9.8.4 9.8.5

9.9 9.9.1 9.9.2 9.9.3 9.9.4 9.9.5

9.10

9.10.1 9.10.2 9.10.3 9.10.4 9.10.5

9.11 9.11.1 9.11.2 9.11.3 9.11.4 9.11.5

Chapter 10 10.1

10.1.1 10.1.2 10.1.3 10.1.4 10.1.5 10.1.6

10.2 10.2.1 10.2.2 10.2.3 10.2.4 10.2.5 10.2.6

10.3 10.3.1 10.3.2 10.3.3 10.3.4 10.3.5 10.3.6

10.4

Model Output Data Reference System Operating Range for a Secondary Radar Description Input Data Model Output Data Reference Maximum Detection Range for a Synthetic-Aperture Radar Description Input Data Model Output Data Reference Maximum Detection Range for a Tracking Radar Description Input Data Model Output Data References

MEASUREMENT ERRORS Angle Measurement Error Description Input Data Model Output Data References Examples Range Measurement Error Description Input Data Model Output Data References Examples Velocity Measurement Error Description Input Data Model Output Data References Examples Propagation Errors

301 302 302 303 303 303 304 306 306

307 307 307 307 308 308 309 309 309 310 311 311

313 313 313 313 314 316 316 317 318 318 318 319 320 320 321 322 322 322 323 324 324 325 326

Contents xv

10.3.6 10.4

10.4.1 10.4.2 10.4.3 10.4.4 10.4.5

10.5 10.5.1 10.5.2 10.5.3 10.5.4 10.5.5 10.5.6

Chapter 11 11.1

11.1.1 11.1.2 11.1.3 11.1.4 11.1.5 11.1.6

11.2 11.2.1 11.2.2 11.2.3 11.2.4 11.2.5 11.2.6

11.3 11.3.1 11.3.2 11.3.3 11.3.4 11.3.5

11.4 11.4.1 11.4.2 11.4.3 11.4.4 11.4.5

11.5 11.5.1 11.5.2 11.5.3

Examples Propagation Errors Description Input Data Model Output Data References Platform-Dependent Errors Description Input Data Model Output Data References Examples

NOISE AND INTERFERENCE IMMUNITY Noise and Interference Simulation Description Input Data Model Output Data Reference Examples Receiving System Noise Figure Description Input Data Model Output Data Reference Examples Signal-to-Interference Ratio Description Input Data Model Output Data Reference System Noise Temperature Description Input Data Model Output Data References MTI, Limitations to Performance Description Input Data Model

325 326 326 326 327 331 331 332 332 332 332 335 335 337

339 339 339 339 341 343 343 343 346 346 346 346 350 350 351 352 352 352 356 363 363 364 364 364 364 366 366 367 367 367 368

xvi Handbook of Computer Simulation

11.5.6 Examples 11.6 Subclutter Visibility

11.6.1 Description 11.6.2 Input Data 11.6.3 Model 11.6.4 Output Data 11.6.5 References

371 372 372 372 373 380 380

APPENDIXES

Appendix 1 Notations and Special Functions Used in the Handbook 383

Appendix 2 The Major Features of Delta Function 386 Appendix 3 Signal Models Based on Elementary Time-Domain

Functions 387 Appendix 4 The Decomposition Models of the Signals 389 Appendix 5 Basic Features of the Discrete Fourier Transform 391 Appendix 6 The Fast Fourier Transform Models 392 Appendix 7 Z-Transform of Some Common Functions 394 Appendix 8 Active Device Noise 395 Appendix 9 Recursive and Nonrecursive Filter Frequency Responses 397 Appendix 10 The Transfer Functions of a Pair of Cascaded Filters 398 Appendix 11 The Distribution Laws for the Discrete Random

Variables 399 Appendix 12 The Distribution Laws for the Continuous Random

Variables 402 Appendix 13 Integral Forms for Gaussian Distribution 414 Appendix 14 The Moments of Random Variables 416 Appendix 15 Moments of Discrete Random Variables 418 Appendix 16 Moments of Continuous Random Variables 419 Appendix 17 The Functional Transform of Random Variables 422 Appendix 18 Probability Density Function of Sum, Difference,

Product, and Quotient of Two Random Variables 425 Appendix 19 Simulation Algorithms for Common Distributions 427 Appendix 20 Basic Simulation Algorithms to Generate Random

Variables with Gaussian Distribution 429 Appendix 21 Simulation Algorithms Based on a Rigorous Solution

for the Reciprocal Functions 430 Appendix 22 Simulation Algorithms Derived by Means of Gamma

Distribution 432 Appendix 23 Common Correlation Functions and Spectra

of the Stationary Random Processes 434 Appendix 24 The Derivatives of the Random Process 435 Appendix 25 A Gaussian Random Process 436 Appendix 26 The Models of Common Pulses in Time and

Frequency Domains 438

Contents xvii

Appendix 27 The Spectral Densities for Common Pulsed Random Processes

Appendix 28 Probability Density Functions and Spectral Densities for Common Pulse Amplitude Distributions

Appendix 29 Spectral Densities for the Stationary Pulse Trains Appendix 30 Spectral Densities of the Stationary Pulse Trains

for Various Types of Modulation and Distribution of Pulse Parameters

Appendix 31 Simulation Algorithms Based on Recurrent Methods for the Stationary Processes with Common Correlation Functions

Appendix 32 Equations and Frequency Responses of the Formation Filter for the Stationary Processes with Common Correlation Functions

Appendix 33 Simulation Algorithm for a Three-Dimensional Gaussian Markovian Random Process

Appendix 34 Simulation Algorithms Based on the Discrete Models of Linear Systems (Formation Filters)

Appendix 35 Simulation Algorithms for the Vector Modulus and the Unit Vector

Appendix 36 Algorithms to Estimate Basic Parameters of a Stationary Ergodic Random Process

Appendix 37 Algorithms to Estimate the First Four Moments of a Nonstationary Random Process

Appendix 38 The Mathematical Expectations and Correlation Functions Based on Impulse Response Representation

Appendix 39 The Impulse and Frequency Responses for Common Linear Circuits

Appendix 40 The Normalized Correlation Functions and Spectral Densities at the Output of Common Linear Circuits

Appendix 41 The Characteristics of Nonlinear Circuits Appendix 42 Stochastic Parameters of the Sum of Random Noise

and Deterministic Signal Appendix 43 The Coefficients for Different Types of Modulation Appendix 44 Mathematical Models of Radio Devices at the Block

Diagram Level Appendix 45 Simplification of the Transfer Function Model Appendix 46 The Coefficients for Nonlinear Circuits Appendix 47 Mathematical Models for Common Devices

and Circuits Appendix 48 Statistical Linearization Coefficients Appendix 49 Mathematical Models of RCL

440

442 444

446

451

453

456

457

458

460

461

462

463

468 470

472 474

476 480 482

483 488 490

ABOUT THE AUTHORS 491

INDEX 493