Radar Systems Analysis and Design Using MATLAB

Radar Systems Analysis and Design Using MATLAB
اسم المؤلف
Bassem R. Mahafza
التاريخ
7 مايو 2022
المشاهدات
62
التقييم
(لا توجد تقييمات)
Loading...

Radar Systems Analysis and Design Using MATLAB
Fourth Edition
Bassem R. Mahafza, Ph.D
President and CEO
Phased n Research, Inc.
Huntsville, Alabama, USA
Contents
Preface xvii
Author Bio xxi
Companion: MATLABM® Code – Disclaimer .xxiii
1 Radar Definitions and Nomenclature 1
1.1 Radar Systems Classifications and Bands .1
1.1.1 High Frequency (HF) and Very HF (VHF) Radars (A- and B-Bands) 2
1.1.2 Ultra High Frequency (UHF) Radars (C-Band) .2
1.1.3 L-Band Radars (D-Band) .4
1.1.4 S-Band Radars (E- and F-Bands) 4
1.1.5 C-Band Radar (G-Band) 4
1.1.6 X- and Ku-Band Radars (I- and J-Bands) 5
1.1.7 K- and Ka- Band Radars (J- and K-Bands) 5
1.1.8 Millimeter Wave (MMW) Radars (V- and W-Bands) .7
1.2 Radar Functional Block Diagram .7
1.3 Primary Radar Subsystems .8
1.4 Signal Classification 9
1.4.1 Signal Expansion Functions . 11
1.4.2 Fourier Series Expansion 12
1.4.2.1 Trigonometric Fourier Series 12
1.4.2.2 Complex Exponential Fourier Series . 13
1.4.3 Properties of the Fourier Series . 14
1.4.3.1 Addition and Subtraction 15
1.4.3.2 Multiplication 15
1.4.3.3 Average Power 15
1.4.4 Fourier Transform 16
1.5 Systems Classification 17
1.5.1 Linear and Nonlinear Systems 17
1.5.2 Time Invariant and Time Varying Systems . 18
1.5.3 Stable and Nonstable Systems 18
1.5.4 Causal and Noncausal Systems . 19
1.5.5 Convolution Integral . 19
1.6 Simplified View of the Radar Receiver Subsystem 19
1.6.1 Measuring Target Range .20
1.6.2 Unambiguous Range .22
1.6.3 Range Resolution . 24
1.6.4 Doppler Frequency 26
1.6.4.1 Doppler Frequency Extraction – Method I .26
1.6.4.2 Doppler Frequency Extraction – Method II 28
1.7 Coherence . 31
1.8 Decibel Arithmetic 32
Appendix 1.1: Fourier Transform Pairs and Properties Tables .35
Problems 35
Answers to Selected Problems . 37viii Contents
2 Basic Radar Waveforms and Antenna 39
2.1 Introduction .39
2.2 Common Radar Waveforms 39
2.2.1 Continuous Wave .39
2.2.2 Finite Duration Pulse 40
2.2.3 Periodic Pulses . 41
2.2.4 Finite Duration Pulse Train 42
2.3 Bandpass Signals .44
2.3.1 Analytic Signal (Pre-Envelope) 46
2.3.2 Pre-Envelope and Complex Envelope of Bandpass Signals 47
2.3.3 Linear Frequency Modulation Signal .49
2.4 Waveform Resolution .54
2.4.1 Range Resolution .54
2.4.2 Doppler Resolution 56
2.4.3 Combined Range and Doppler Resolution 57
2.5 Radar Antenna 58
2.5.1 Electromagnetic Waves (Radio Frequency Waves) .58
2.5.2 Antenna Radiated Power 59
2.5.3 Radiation Intensity 60
2.5.4 Radiation Pattern .60
2.5.4.1 Half-Power Beam Width . 62
2.5.4.2 Sidelobes 62
2.5.4.3 Beam Solid Angle . 62
2.5.4.4 Forward/Backward Ratio .63
2.5.4.5 Voltage Standing Wave Ratio .63
2.5.4.6 Antenna Bandwidth 63
2.5.5 Directivity .63
2.5.6 Antenna Gain .63
2.5.6.1 Effective Isotropic Radiated Power 64
2.5.7 Sidelobe Control .64
2.5.8 Antenna Effective Aperture .64
2.5.9 Antenna Near and Far Fields .66
2.5.10 Antenna Beam Shape Loss and Scan Loss . 67
2.5.10.1 Beam Shape Loss 67
2.5.10.2 Antenna Scan Loss . 67
2.5.10.3 Antenna U-V Space 69
2.5.11 Polarization . 70
Problems 78
Answers to Selected Problems .80
3 Radar Equation 81
Part I: Pulsed Radar
3.1 Radar Range Equation 81
3.1.1 Maximum Detection Range .85
3.2 Low PRF Radar Equation .89
3.3 High PRF Radar Equation . 91
3.4 Surveillance Radar Equation .93
3.4.1 Number of Beam Positions .97Contents ix
3.5 Blake Chart .98
3.6 Radar Equation with Jamming .98
3.6.1 Passive Jamming Techniques . 100
3.6.2 Radar Equation with Jamming 101
3.6.3 Self-Protection Jamming Radar Equation 103
Burn-Through Range . 105
3.6.4 Support Jamming Radar Equation 107
3.6.5 Range Reduction Factor 109
3.6.6 Noise (Denial) Jamming Techniques 110
3.6.6.1 Barrage Noise Jamming 110
3.6.6.2 Spot Noise and Sweep Spot Noise Jamming 111
3.6.6.3 Deceptive Jamming 112
3.6.7 Electronic Counter-Counter Measure Techniques 114
3.6.7.1 Receiver Protection Techniques . 114
3.6.7.2 Jamming Avoidance and Exploitation Techniques . 114
3.7 Bistatic Radar Equation 115
3.8 Radar Cross-Section . 117
3.8.1 RCS Prediction Methods . 119
3.9 Radar Losses 120
3.9.1 Transmit and Receive Losses . 120
3.9.2 Antenna Pattern Loss and Scan Loss 120
3.9.3 Atmospheric Loss 121
3.9.3.1 Atmospheric Absorption . 121
3.9.3.2 Atmospheric Attenuation Plots 123
3.9.4 Loss Due to Precipitation 126
3.9.5 Collapsing Loss 129
3.9.6 Processing Loss 130
3.9.6.1 Detector Approximation . 130
3.9.6.2 Constant False Alarm Rate Loss 130
3.9.6.3 Quantization Loss 130
3.9.6.4 Range Gate Straddle Loss . 130
3.9.6.5 Doppler Filter Straddle 132
Part II: Continuous Wave Radar
3.10 Overview of Continuous Wave Radars . 133
3.10.1 CW Radar Equation . 134
3.10.2 Frequency Modulation 135
3.10.3 Linear Frequency Modulated CW Radar . 139
3.10.4 Multiple Frequency CW Radar 141
3.11 MATLAB Program “range_calc.m” 142
Problems 144
Answers to Selected Problems . 147
4 Radar Wave Propagation . 149
4.1 Earth’s Impact on the Radar Equation . 149
4.2 Earth’s Atmosphere . 149
4.3 Atmospheric Models . 152
4.3.1 Index of Refraction in the Troposphere 152
4.3.2 Index of Refraction in the Ionosphere . 153x Contents
4.3.3 Mathematical Model for Computing Refraction . 155
4.3.4 Stratified Atmospheric Refraction Model 157
4.4 Four-thirds Earth Model 160
4.4.1 Target Height Equation . 161
4.5 Ground Reflection . 163
4.5.1 Smooth Surface Reflection Coefficient 163
4.5.2 Divergence 167
4.5.3 Rough Surface Reflection 168
4.5.4 Total Reflection Coefficient . 169
4.6 Pattern Propagation Factor 170
4.6.1 Flat Earth . 173
4.6.2 Spherical Earth . 174
4.7 Diffraction 177
Problems 183
Answers to Selected Problems . 183
5 Elements of Signal Processing of the Radar Receiver 185
5.1 Radar Receiver Block Diagram . 185
5.2 Correlation . 186
5.2.1 Correlation Coefficient 186
5.2.1.1 Energy Signals 186
5.2.1.2 Power Signals 189
5.2.2 Correlation Integral – Energy Signals . 189
5.2.3 Relationship between Convolution and Correlation Integrals . 190
5.2.4 Effect of Time Translation on the Correlation Function 191
5.2.5 Correlation Function Properties 191
5.2.5.1 Conjugate Symmetry . 192
5.2.5.2 Total Signal Energy 192
5.2.5.3 Total Area under the Autocorrelation Function 192
5.2.5.4 Maximum Value for the Autocorrelation Function . 193
5.2.5.5 Fourier Transform for the Correlation Function . 193
5.2.6 Correlation Integral – Power Signals 193
5.2.7 Energy and Power Spectrum Densities 194
5.2.8 Correlation Function for Periodic Signals 195
5.3 Discrete Time Systems and Signals 196
5.3.1 Sampling Theorem 197
5.3.1.1 Lowpass Sampling Theorem 197
5.3.1.2 Bandpass Sampling Theorem . 199
5.3.2 Z-Transform 200
5.3.3 Discrete Fourier Transform 201
5.3.3.1 Discrete Power Spectrum 202
5.3.4 Spectral Leakage and Fold-Over .203
5.3.4.1 Spectral Leakage .203
5.3.4.2 Spectral Fold-Over .205
5.3.5 Windowing Techniques 205
5.3.6 Decimation and Interpolation 209
5.3.6.1 Decimation 209
5.3.6.2 Interpolation 211
5.4 Radar Receiver Noise Figure . 211Contents xi
Appendix 5.1 Table of Z-Transform Pairs 215
Problems 217
Answers to Selected Problems . 219
6 Matched Filter . 221
6.1 Matched Filtering 221
6.1.1 Output Signal Power .222
6.1.2 Output Noise Power 223
6.1.3 Signal-to-Noise Ratio .223
6.1.4 Matched Filter Impulse Response .225
6.1.5 The Replica 225
6.1.6 Mean and Variance of the Matched Filter Output 226
6.2 General Formula for the Output of the Matched Filter .226
6.2.1 Stationary Target Case 227
6.2.2 Moving Target Case .228
6.3 Range and Doppler Uncertainty .230
6.3.1 Range Uncertainty .230
6.3.2 Doppler (Velocity) Uncertainty 233
6.3.3 Combined Range-Doppler Uncertainty .233
6.4 Target Parameter Estimation . 237
6.4.1 What Is an Estimator? . 237
6.4.2 Amplitude Estimation .238
6.4.3 Phase Estimation 239
Problems 239
Answers to Selected Problems . 240
7 Pulse Compression . 243
7.1 Time-Bandwidth Product 243
7.1.1 Radar Equation with Pulse Compression 244
7.1.2 Basic Principle of Pulse Compression . 245
7.2 Correlation Processor . 247
7.3 Stretch Processor . 251
7.4 Stepped Frequency Waveforms 259
7.4.1 Range Resolution and Range Ambiguity in SFW .263
7.5 Effect of Target Velocity on Pulse Compression .265
7.5.1 SFW Case 265
7.5.2 LFM Case 269
7.6 Range-Doppler Coupling in LFM .272
Problems 274
Answers to Selected Problems . 275
8 Radar Ambiguity Function .277
8.1 Ambiguity Function Definition 277
8.2 Effective Signal Bandwidth and Duration 279
8.3 Single Pulse Ambiguity Function 280
8.3.1 Time-Bandwidth Product . 281
8.3.2 Ambiguity Function 282xii Contents
8.4 LFM Ambiguity Function 283
8.4.1 Time-Bandwidth Product .284
8.4.2 Ambiguity Function 285
8.5 Coherent Pulse Train Ambiguity Function .288
8.5.1 Time-Bandwidth Product .288
8.5.2 Ambiguity Function 289
8.6 Pulse Train with LFM Ambiguity Function . 292
8.7 Stepped Frequency Waveform Ambiguity Function . 294
8.8 Nonlinear Frequency Modulation 295
8.8.1 Concept of Stationary Phase 296
8.8.2 Frequency-Modulated Waveform Spectrum Shaping 300
8.9 Ambiguity Diagram Contours 301
8.9.1 Range-Doppler Coupling in LFM Signals – Revisited .303
8.10 Discrete Code Signal Representation .304
8.10.1 Pulse-Train Codes 305
8.11 Phase Coding .309
8.11.1 Binary Phase Codes .309
Barker Code 310
Pseudo-Random Number Codes . 313
Linear Shift Register Generators 314
Maximal Length Sequence Characteristic Polynomial . 316
8.11.2 Polyphase Codes 317
Frank Codes 317
8.12 Frequency Codes . 318
8.13 MATLAB Ambiguity Plots for Discrete Coded Waveforms . 321
Problems 322
Answers to Selected Problems . 324
9 Radar Clutter . 325
9.1 Clutter Definition 325
9.2 Volume Clutter 325
9.2.1 Volume Cell . 326
9.2.2 Rain 326
9.2.3 Chaff 327
9.2.4 Radar Range Equation in Volume Clutter 328
9.2.5 Volume Clutter Spectra . 328
9.3 Area Clutter .330
9.3.1 Constant γ Model .330
9.3.2 Signal to Clutter, Airborne Radar 332
9.4 Clutter RCS, Ground-Based .333
9.4.1 Low PRF Case .333
9.4.2 High PRF Case .336
9.5 Amplitude Distribution .339
Problems 344
Answers to Selected Problems .346
10 Moving Target Indicator and Pulsed Doppler Radars 347
10.1 Area Clutter Spectrum .347
10.2 Concept of a Moving Target Indicator .348Contents xiii
10.2.1 Single Delay Line Canceler .350
10.2.2 Double Delay Line Canceler . 351
10.2.3 Delay Lines with Feedback (Recursive Filters) 353
10.3 PRF Staggering 354
10.4 MTI Improvement Factor . 357
10.4.1 Two-Pulse MTI Case 359
10.4.2 The General Case . 361
10.5 Subclutter Visibility 362
10.6 Delay Line Cancelers with Optimal Weights .363
10.7 Pulsed Doppler Radars 365
10.7.1 Pulse Doppler Radar Signal Processing . 367
10.8 Ambiguity Resolution 369
10.8.1 Range Ambiguity Resolution . 369
10.8.2 Doppler Ambiguity Resolution . 373
10.9 Phase Noise 376
Problems 381
Answers to Selected Problems .383
11 Random Variables and Random Processes .385
11.1 Random Variables .385
11.2 Multivariate Gaussian Random Vector 387
11.2.1 Complex Multivariate Gaussian Random Vector 390
11.3 Rayleigh Random Variables . 391
11.4 The Chi-Square Random Variables 392
11.4.1 Central Chi-Square Random Variable with N Degrees of Freedom 392
11.4.2 Non-Central Chi-Square Random Variable with N Degrees of
Freedom . 393
11.5 Random Processes 393
11.6 The Gaussian Random Process . 394
11.6.1 Lowpass Gaussian Random Processes . 395
11.6.2 Bandpass Gaussian Random Processes 396
11.6.3 The Envelope of a Bandpass Gaussian Process . 397
Problems 398
Answers to Selected Problems . 399
12 Target Detection – Single Pulse Case . 401
12.1 Single Pulse with Known Parameters 401
12.2 Single Pulse with Known Amplitude and Unknown Phase 404
12.2.1 Probability of False Alarm 408
12.2.2 Probability of Detection 409
Problems 412
Answers to Selected Problems . 413
13 Detection of Fluctuating Targets . 415
13.1 Pulse Integration . 415
13.1.1 Coherent Integration . 416
13.1.2 Noncoherent Integration . 417
13.1.3 Improvement Factor and Integration Loss . 418
13.2 Target Fluctuation: the Chi-Square Family of Targets 419xiv Contents
13.3 Probability of False Alarm Formulation for a Square Law Detector .420
13.3.1 Square Law Detection .422
13.4 Probability of Detection Calculation 424
13.4.1 Detection of Swerling 0 (Swerling V) Targets 425
13.4.2 Detection of Swerling I Targets 426
13.4.3 Detection of Swerling II Targets 427
13.4.4 Detection of Swerling III Targets .430
13.4.5 Detection of Swerling IV Targets .430
13.5 Computation of the Fluctuation Loss .433
13.6 Cumulative Probability of Detection .435
13.7 Constant False Alarm Rate 437
13.7.1 Cell-Averaging CFAR (Single Pulse) .437
13.7.2 Cell-Averaging CFAR with Noncoherent Integration 439
13.8 M-out-of-N Detection .441
13.9 Radar Equation-Revisited 443
13.9.1 Detection Range with Pulse Integration 443
Coherent Integration case: 445
Noncoherent Integration Case: 446
Appendix 13.1 Gamma Function .447
Incomplete Gamma Function 447
Problems 449
Answers to Selected Problems . 451
14 Radar Cross-Section .453
14.1 Radar Cross-Section Definition 453
14.2 RCS Dependency on Aspect Angle and Frequency .454
14.3 Target Scattering Matrix 458
14.4 RCS of Simple Objects 459
14.4.1 Sphere 460
14.4.2 Ellipsoid . 461
14.4.3 Circular Flat Plate 463
14.4.4 Truncated Cone (Frustum) .465
14.4.5 Cylinder .469
14.4.6 Rectangular Flat Plate . 470
14.4.7 Triangular Flat Plate 473
14.5 RCS of Complex Objects . 476
14.6 RCS Prediction Methods 477
14.6.1 Computational Electromagnetics 478
14.6.2 Finite Difference Time Domain Method 478
14.6.3 Finite Element Method 481
14.6.4 Integral Equations 482
14.6.5 Geometrical Optics 484
14.6.6 Physical Optics .484
14.6.6.1 Rectangular Plate .484
14.6.6.2 N-Sided Polygon .485
14.6.7 Edge Diffraction .486
14.7 Multiple Bounce 487
Problems 487
Answers to Selected Problems .489Contents xv
15 Phased Arrays 491
15.1 General Arrays 491
15.2 Linear Arrays . 493
15.2.1 Array Tapering . 497
15.2.2 Computation of the Radiation Pattern via the DFT 499
15.3 Planar Arrays .506
15.3.1 Rectangular Grid Arrays 506
15.3.2 Circular Grid Arrays .508
15.3.3 Concentric Grid Circular Arrays .509
15.3.4 Rectangular Grid with Circular Boundary Arrays 509
15.3.5 Hexagonal Grid Arrays . 510
15.4 Multiple Input Multiple Output (MIMO) – Linear Array .534
Problems 537
Answers to Selected Problems . 539
16 Adaptive Signal Processing 541
16.1 Nonadaptive Beamforming . 541
16.2 Adaptive Signal Processing Using Least Mean Square .545
16.3 The LMS Adaptive Array Processing .548
16.4 Sidelobe Cancelers 555
16.5 Space–time Adaptive Processing (STAP) . 559
16.5.1 Space–time Processing 559
16.5.2 Space–Time Adaptive Processing 561
Problems 565
17 Target Tracking . 567
Part I: Single Target Tracking
17.1 Angle Tracking 567
17.1.1 Sequential Lobing 568
17.1.2 Conical Scan . 569
17.2 Amplitude Comparison Monopulse 572
17.3 Phase Comparison Monopulse . 578
17.4 Range Tracking 581
Part II: Multiple Target Tracking
17.5 Track-While-Scan 582
17.6 State Variable Representation of an LTI System .584
17.7 The LTI System of Interest .588
17.8 Fixed-Gain Tracking Filters . 589
17.8.1 Notation: 589
17.8.2 The α β Filter . 592
17.8.3 The αβγ Filter 595
17.9 The Kalman Filter . 598
17.9.1 The Singer αβγ-Kalman Filter 607
17.9.2 Relationship between Kalman and αβγ Filters 609
MATLAB Function “kalman_filter.m” 610
17.10 MATLAB Kalman Filter Simulation . 610
Problems 620
Answers to Selected Problems . 621xvi Contents
18 Synthetic Aperture Radar . 623
18.1 Introduction . 623
18.1.1 Side Looking SAR Geometry . 624
18.2 SAR Design Considerations . 626
18.3 SAR Radar Equation . 631
18.4 SAR Signal Processing 632
18.5 Side Looking SAR Doppler Processing 632
18.6 SAR Imaging Using Doppler Processing .636
18.7 Range Walk 637
18.8 A Three-Dimensional SAR Imaging Technique .637
18.8.1 Background .638
18.8.2 DFTSQM Operation and Signal Processing .638
18.8.2.1 Linear Arrays 638
18.8.2.2 Rectangular Arrays 640
18.8.3 Geometry for DFTSQM SAR Imaging 641
18.8.4 Slant Range Equation 643
18.8.5 Signal Synthesis .645
18.8.6 Electronic Processing 646
18.8.7 Derivation of Eq. (18.71) .647
18.8.8 Non-Zero Taylor Series Coefficients for the kth Range Cell 649
Problems 651
Answers to Selected Problems . 652
Bibliography 653
Index .659xvii
Preface
Index
A
Active correlation, 251–259; see also Stretch
processing and pulse compression
Adaptive signal processing
adaptive arrays, 548–555
beamforming, 548 (see also Beamforming
LMS)
complex weights, 541, 550, 551–553, 558,
561–565
convergence parameter, 546–547
covariance matrix, 552, 553, 558, 565
SLC, 555–558
steering vector, 542, 543, 561
Ambiguity function
Barker code, 310–313
binary phase codes, 309–310
coherent pulse train, 288–292
coherent pulse train with LFM, 292–294
contour diagrams, 301–302
definition, 55, 277–279
Doppler ambiguity function, 56
ideal, 278, 279
LFM, 283–288
PRN, 313–314
properties, 277–278
pulse train code, 305–308
range ambiguity function, 55
single pulse, 280–283
stepped frequency, 294
Amplitude estimate, 238–239
Analytic signal, 46–49; see also Signals
Angle tracking, see Tracking
Antenna, 58–70
antenna loss, 67–69, 120
bandwidth, 63
beam solid angle, 62
definition, 58
directive pattern, 62, 81
directivity, 63
effective aperture, 54, 65, 82
effective isotropic radiated power (EIRP), 64
far field, 66–67
gain, 63, 65, 81, 82
half-power beam width, 62
isotropic pattern, 61, 82
near field, 66–67
number of beam positions, 94, 97–98
polarization, 60–62 (see also Polarization
radiation pattern)
scan loss, 67–70
sidelobe, 64
U-V space, 69–70
voltage standing ratio, 63
Arrays
circular arrays, 508
concentric grid circular arrays, 509
definition, 491
general array, 491–493
grating lobes – definition, 496
hexagonal grid, 510
linear array, 493–498
MIMO, 534–537
planar arrays, 506–516
radiation pattern via DFT computation,
499–501
rectangular arrays, 506–507
scan loss (see Antenna scan loss)
tapering, 497–498 (see also Windowing
techniques)
Atmosphere
atmospheric attenuation or loss, 121–129
atmospheric attenuation plots, 123–126
atmospheric models, 152–160
layers, 150
refraction, 151 (see also Index of refraction)
stratified, 157–160
Atmospheric absorption, 121–123
absorption due to oxygen, 122
absorption due to water vapor, 122
Attenuation
atmospheric attenuation (see Atmospheric
absorption)
clutter attenuation (see Clutter)
due to precipitation, 126–129
due to rain, 127
due to snow, 129
B
Backscatter coefficient statistical models
definition, 325, 330
surface clutter case, 330–333
volume clutter case, 328–330
Bandpass Gaussian process, 396, 397
Bandpass signals, 44–49; see also Signals660 Index
Barker code, 310–313
combined Barker codes, 310–312
Barrage jammers, see Jammers
Beamforming
conventional or nonadaptive beamforming,
541–544
STAP, 559–561
Binary detection, 441–443; see also M-out-of-N
detection
Binary phase codes, 309; see also Phase coding
Bistatic radar equation, 115–117
Blake chart, 98
Blind speed, 349, 356
Boltzmann’s constant, 83
Burn-through range, 105–107
C
Cancelers, see MTI
Chaff
as clutter, 327
passive jamming, 100
RCS, 101
Characteristic polynomial, 316
Chirp waveforms, 47–53, 249, 283–288; see also
Signals
down chirp, 49
up chirp, 49
Clutter
amplitude distribution, 339–344
area clutter, 330–333
attenuation, 357–360
backscatter coefficient, 325, 330 (see also
Backscatter coefficient statistical
models)
chaff, 327 (see also Chaff)
definition, 325
main beam clutter RCS, 333–336
rain clutter, 326–327
RCS high-PRF case, 337–338
RCS low-PRF case, 333–336
regions, 330, 331
sidelobe clutter RCS, 334, 335
signal to clutter ratio, 332–333
spectrum, 347–348
subclutter visibility, 362
surface height irregularity, 331
volume, 325–328
volume cell, 326
Codes
Barker, 310–313
binary phase codes, 309
combined Barker code, 310–312
Costas, 319
definition of discrete code signal, 304–305
Franks, 318
frequency codes, 318–321
polyphase codes, 317
PRN, 313–314 (see also Pseudo-random
number)
pulse train codes, 305–308
Coherence, 31–32
Coherent integration, see Pulse integration
Complementary error function, 403
Compressed pulse width, 244, 250
Compression gain, 244
Conical scan, see Tracking
Constant false alarm rate (CFAR), 437–441
cell averaging (single pulse), 437–438
cell-averaging CFAR (noncoherent
integration), 439–441
loss, 439, 440
Conventional beamforming, 541–544; see also
Beamforming
Convolution integral, 19, 190
Correlation integral
coefficient, 186–189
definition, 190
energy signals, 189
Fourier transform for the correlation
function, 193
periodic signals, 195–196
power signals, 193–194
properties, 191–193
Costas codes, see Codes; Frequency coding
Cross-over range
SOJ case, 108
SSJ case, 103
Cumulative probability of detection, 435–437
block diagram, 133
CW radar, 133–142
frequency modulation, 135–139
LFM, 139–141
modulation index, 135
multiple frequency CW radar, 141–142
radar equation, 142
CW waveforms, see Signals
D
Decibel arithmetic, 32–34
Decimation, 209–210
Delay line cancelers, see MTI
Detection
single pulse with known parameters,
403–412Index 661
single pulse with unknown phase, 404
table of single pulse probability of detection,
405
Detection of fluctuating targets, see Probability
of detection
Detection threshold, 403, 408, 421, 422
Diffraction, 177–182
Discrete coded waveforms, see Codes
Discrete Fourier transform, 201
Discrete power spectrum, 202–203
spectral fold-over, 188, 205
spectral leakage, 203–205
windowing techniques (see Windows)
Divergence, 167
Doppler definition, 26
Doppler beam sharpening, 623
Doppler frequency extraction methods,
26–29
Doppler resolution, 25, 56–57
Doppler scaling factor, 28
Doppler shift spectra, 29
Doppler uncertainty, 233
Duty factor, 22, 91
E
Effective aperture, 54, 65, 82
Effective bandwidth, 55
LFM signal, 284
single pulse, 282
Effective duration, 55
LFM signal, 285
single pulse, 282
Effective earth radius, 155, 156, 161, 174
Effective isotropic radiated power, 61
Electromagnetic waves, 58–59
polarization, 70–73
Electronic counter-counter measures (ECCM),
114–115
jamming avoidance techniques, 114–115
receiver protection techniques, 114
Electronic counter measures (ECM), 98–114
barrage noise jamming, 110
burn-through range, 105, 107
cross-over range, 103, 108
deceptive jamming, 112–113
DRFMs, 112
ECM taxonomy, 99–100
effective radiated power, 102
escort and self protection jamming, 103
noise denial jamming, 110
passive jamming techniques, 99 (see also
Chaff)
range reduction factor, 109–110
RGPO, 113
self-protection jamming, 103–107
spot-noise, 111
stand-off jamming, 107–108
sweep spot noise, 111
VPGO, 113
Energy spectrum density, 194–195
Euler’s phi function, 315
F
False alarm
false alarm number (see Number of false
alarm)
probability of false alarm, 40, 408, 421, 424,
439, 441
Far field, 67; see also Antennas FFT parameters
Finite difference time domain method (FDTD),
478–481
Finite element method, 481–482
Fixed gain tracking filters, 589–598
the αβ filter, 592–595
the αβγ filter, 595–598
filter equation, 589
gain matrix, 590
noise covariance matrix, 591
steady-state error, 591
transfer function, 594
variance reduction ratio, 593, 597
Footprint, 332, 625
Forth third earth, 160–161
Fourier series, 12–16
exponential, 13–14
properties, 14–16
trigonometric, 12–13
Fourier transform
definition, 16–17
pairs, 35
properties, 36
Frequency coding
Costas codes, 319
Frequency modulation
Fresnel integrals, 51
Fresnel spectrum, 51, 53
linear frequency modulated CW radar,
139–141
linear frequency modulation signal,
49–53
nonlinear frequency modulation,
295–301
Frustum, see RCS
Fundamental matrix, see State transition matrix662 Index
G
Gamma function, 421, 447
bandpass, 396
envelope, 397
Gaussian random process, 394–397
incomplete Gamma function, 447–448
lowpass, 395
Geometrical optics, 484
gh filter, see Fixed gain tracking filters, αβ filter
ghk filter, see Fixed gain tracking filters
Gram-Charlier series coefficients, 425, 427, 452
Grating lobes, 496
Ground reflection coefficient, 163–167
horizontal polarization, 164
total reflection coefficient, 168
vertical polarization, 163
H
Half cone angle, 467
Hamming, see Windows
Hanning, see Windows
Height equation, 161–162
I
Incomplete gamma function, 447–448
Index of refraction
definition, 150
in the ionosphere, 153–155
in the troposphere, 152–153
Integral equations, 482–483
Integration, see Pulse integration
Interpolation, 211
Ionosphere, 150, 153–155
J
Jacobian, 391, 406
Jammer power, 102
Jammers, see Electronic counter measures
(ECM)
K
Kalman filter, 598–619
advantages, 598, 606
equations, 606–607
relation to αβγ filter, 607
simulation, 610–619
Singer- αβγ Kalman filter, 607–609
structure, 606
L
LFM coefficient, 49
LFM waveforms, see Waveforms
Linear frequency modulation, 139–141
Linear Shift Register generators, 314–316
Linear system, 17
Linear time invariant system, 18
Lobe switching, see Tracking, sequential lobing
Losses, see Radar losses
Low pass waveforms, see Waveforms
M
Marcum’s Q-function, 410
Matched filter
definition, 221–222
general output formula, 226–229
impulse response, 225
output – moving target case, 228–229
output noise power, 223
output signal power, 222
output – stationary target case, 227–228
processor (see Pulse Compression)
replica, 225
SNR, 223, 224
MATLAB functions
absorption_range, 125
adaptive_array_lms, 555
ambiguity_code, 327
array, 520
atmo_absorp, 123
atmospheric_attn, 125
burn_through, 107
cicular_array, 508
circ_array, 514
clutter_rcs, 336
diffraction, 181
divergence, 168
doppler_freq, 31
double_cancler, 352
fluct, 433
ghk_tracker, 598
hprf_req, 92
improv_fac, 418
kalamn_filter, 610
lfm_ambg, 287
linear_array, 501
LMS, 547
lprf_req, 89
marcumsq, 412
matched_filter, 250
mono_pulse, 574Index 663
multipath, 176
pd_swerling1, 426
pd_swerling2, 428
pd_swerling3, 430
pd_swerling4, 432
pd_swerling5, 425
power_aperture, 95
pulse_train, 23
que-func, 408
radar_eq, 88
range_calc, 142
rcs_aspect, 455
rcs_circ_plate, 465
rcs_cylinder, 470
rcs_ellipsiod, 463
rcs_frequnecy, 456
rcs_frustum, 468
rcs_isoseles, 476
rcs_rect_plate, 463
rect_array, 512
ref_coef, 164
refraction, 160
single_cancler, 351
single-pulse-ambg, 282
sir_req, 106
ssj_req, 106
stretch, 258
surf_rough, 169
threshold, 422
train_ambg, 291
train_ambg_lfm, 294
Maximum detection range, 85–86
Maximum length sequences, 316
Mie
region, 462
series, 420
Minimum detectable signal, 85; see also
Maximum detection range
Monopulse, see Tracking
M-out-of-N detection, 441–443; see also Binary
detection
Moving target indicator (MTI)
delay line with feedback, 353–354
double delay line, 351–353
optimal weights, 363–365
single delay lines, 350–351
using multiple PRFS (see PRF staggering)
MTI improvement factor, 357–361
definition, 358
general case, 361
two-pulse MTI case, 359
Multipath
flat earth, 173–174
MATLAB program, 176
spherical earth, 174–177
Multivariate Gaussian random vector, 387–390
N
Near field, see Antennas
Noise
bandwidth, 83, 223
effective noise temperature, 83, 84
noise figure, 83, 213, 214
noise power, 83
Noncoherent integration, see Pulse integration
Nonlinear system, 17
Number of false alarm, 409
Nyquist sampling rate, 198
O
Orthogonal functions, 11
basis functions, 12
Orthonormal functions, 11
P
Pattern propagation factor, 149, 171
Phase
estimate, 239
spectrum shaping, 300–301
stationary, 296–300
Phase coding, 309–318
Barker code, 310–313
binary phase code, 309
pseudo random codes, 313–314
Phased arrays, see Arrays
N-sided polygon, 485
physical optics, 484
rectangular plate, 484
Phase Noise, 376–381
clutter attenuation, 380
definition, 376
formula, 378, 379
PSD, 376, 380
Phi function, see Euler’s phi function
Planck’s constant, 211
Polarization, 70–75
circular, 71
electric field, 71, 73
linear, 73
scattering matrix, 458–459
Power
ac-power, 194
average, 15, 16, 22664 Index
dc-power, 194
definition of, 10
total, 194
Power aperture product, 94
Power spectrum density, 196, 202
Precipitation, see Attenuation due to
precipitation
Pre-envelope, see Signals Prediction methods
of RCS
PRF staggering, 354–357
blind speeds, 349, 356
MTI response, 349
resolving Doppler ambiguities, 373–374
resolving range ambiguities, 369–373
Primitive root, 316
PRN codes, 313–314; see also Pseudo random
codes
Probability density functions, 385, 388, 395, 396,
402, 406, 407
joint, 386, 387, 391, 406
Probability of detection
cumulative, 435–437 (see also Cumulative
probability of detection)
fluctuation loss, 433–434
M-out-of-N detection, 441–443
single pulse with known parameters, 401–404
single pulse with unknown parameters,
404–408
square law detection, 422–424
Swerling I model, 426
Swerling II model, 427
Swerling III model, 430
Swerling IV model, 430
Swerling V model, 425
table of single pulse probability of detection,
405
Probability of false alarm, 403, 408, 421, 424,
438, 439, 441, 442
square law, 420–422
Propagation factor, 149, 170–177
flat earth, 173–174
spherical earth, 174–177
Pseudo random codes, 313–314
Pulse compression
basic principle, 245–247
correlation processor, 247–251
mismatch, 271
radar equation, 244
stepped frequency, 259–263
stretch processor, 251–259
time bandwidth product, 244
velocity distortion – LFM case, 269
velocity distortion – SFW case, 265
Pulsed Doppler radar, 365–369
block diagram, 336
high PRF, 335
low PRF, 335
medium PRF, 335
resolving Doppler ambiguity, 373–375
resolving range ambiguity, 369–373
Pulsed radar; see also Radar equation
Blake chart, 98
high-PRF, 91–92
low-PRF, 89–91
radar range equation, 81–88
surveillance, 93–97
Pulse energy, 10, 194
Pulse integration, 415–419
coherent integration, 416
improvement factor, 418
integration loss, 418
noncoherent integration, 417
Pulse repetition frequency (PRF), 21
Pulse repetition interval, 21
Q
Quadrature components, 45, 47
stepped frequency waveform, 262
Que-function, 410
R
Radar bands
C-band, 4
HF and VHF, 2
K-Band, 5
L-band, 4
MMW, 7
S-band, 4
UHF, 2
X-band, 5
Radar classifications, 1–7
Radar cross-section (RCS), 83, 117–119, 453–489
Radar equation
bistatic, 115–117
CW radar, 134
high PRF, 91
with jamming, 98, 101, 109
low PRF, 89
pulse compression, 244
surveillance (search), 93
synthetic aperture radar (SAR), 631
volume clutter, 328
Radar losses
antenna pattern, 120Index 665
atmospheric, 120–126
collapsing, 129
constant false alarm, 439
due to precipitation, 126–129
integration loss, 418
processing losses, 130–132
radar equation total loss, 85
scan, 67–69
Random processes, 394–398
Random variables
cdf, 385–387
characteristic function, 387
definition, 385
joint cdf, 386, 391
joint pdf, 354, 358
moments, 386
pdf definition, 385
Range
ambiguity, 22–24, 263, 369–373, 628
burn-through range (see Jammers)
definition, 20
maximum detection range, 85
profile in SFW, 262
resolution, 25, 245
unambiguous, 22, 628
uncertainty, 230–232
Range-Doppler coupling, 272–275, 303
Range reduction factor, 109–110
RCS fluctuation loss, 433–434
RCS of complex objects, 476
RCS of simple objects
circular flat plate, 463
cone, 465
cylinder, 469
dependency on aspect angle, 454–458
dependency on frequency, 454–458
dependency on polarization, 458
ellipsoid RCS, 461
N-sided polygon, 485
rectangular flat plate, 470, 484
sphere RCS, 460
triangular flat plate, 473
truncated cone (frustum), 465
Refraction, 152–160
Refractivity, 150
gradient, 150, 153
Repeater jammers, see Jammers
Replica, 225
Resolution
range, 25, 245, 630
Resolving Doppler ambiguity, 373
Resolving range ambiguity, 369
Rough surface reflection, 168
S
Sampling theorem, 197–200
bandpass sampling theorem, 199
lowpass sampling theorem, 197
Nyquist sampling rate, 198
Scan loss, see Array and Radar losses
Scattering matrix, see Target scattering
matrix
Schwartz inequality, 223
Self screening jammers, see Jammers
Signals
analytic definition of, 46
bandpass, 47
complex envelope, 47
continuous wave, 39
discrete, 196–211 (see also Discrete codes)
finite duration pulse, 40, 280
frequency modulation, 135–138
LFM, 47–53, 139, 249, 283–288
nonlinear FM, 295
periodic pulse train, 41, 288
pre-envelope, 47
SFW, 259–265, 294–295
Signals Prediction methods of RCS, 119
Signal-to-clutter-ratio, 333, 362
Signal-to-noise ratio (SNR)
matched filter, 223–225
SNR, 84, 85, 89, 91, 109, 244, 631
Snell’s law, 158
Space time adaptive processing, 559–565
spatial steering vector, 561
temporal steering vector, 561
Spectral fold-over, see Discrete Fourier
transform
Spectral leakage, see Discrete Fourier
transform
Stand off jammers, see Jammers
State transition matrix
definition, 585
LTI system, 588
properties, 585–586
State variable representation, 584–587
Stepped frequency waveforms (SFW), 259–265;
see also Waveforms
effect of target velocity, 265–267
frequency (Doppler) resolution, 264
quadrature components, 262
range profile, 263
range resolution, 263
unambiguous range, 264
Stratified atmosphere model, 157–160
Stretch processing, 251–259, see Active
correlation666 Index
Swerling targets, 425–434; see also Probability of
detection
Synthetic aperture radar (SAR)
azimuth resolution, 626, 627
coherent integration interval, 624
deramping, 634
design considerations, 626
Doppler history, 628
imaging, 636
maximum range, 625
minimum range, 625
PRF selection, 629, 630
radar equation, 631
range resolution, 626
range walk, 637
side looking, 624–626
signal processing, 632–635
SNR, 631
unambiguous range, 628
System classifications, 17–19
T
Target fluctuation, see Probability of detection
Target parameter estimation
amplitude, 38
definition, 237–238
phase, 239
Target scattering matrix, 458–459
Threshold, 403, 408, 421, 422
Time bandwidth product, see Pulse
compression
Time of false alarm, see False alarm time
Time on target, 94
Tracking
amplitude comparison monopulse, 572–578
angle tracking, 567–572
axis, 568–570
conical scan, 569–572
monopulse error, 578
phase comparison monopulse, 578–581
range tracking, 581–582
sequential lobing, 568
squint angle, 569, 571
sum beam, 573, 574
track-while-scan (TWS), 582
Troposphere, 150
U
Unambiguous range, see Range Uncertainty
combined range and Doppler, 233–237
uncertainty in Doppler, 233
uncertainty in range, 230–232
U-V space, 69–70
V
Van Vleck equation for atmospheric absorption
oxygen absorption equation, 121
water vapor absorption equation, 122
Velocity distortion in pulse compression
LFM case, 269–271
SFW case, 265–267
W
Waveforms
bandpass, 44–49
continuous wave, 39–40
discrete code, 304–308
effective bandwidth and duration, 55
energy, 10
finite duration pulse, 40–43, 280
finite duration pulse train, 42–44, 288–292
frequency modulation, 135–139
LFM, 139–141
LFM in CW radars, 139
multiple frequency CW, 141–142
power, 10
range and Doppler uncertainty, 233–237
stepped frequency, 265–267
Weibull distribution, 341
Windows, 205–209
array tapering, 497–499
Bartlet, 207, 498
common windows, 205–206
Hamming, 207, 498
Hanning, 207, 498
Kaiser, 207, 498
Z
Z-transform
definition, 200
pairs, 215–216

كلمة سر فك الضغط : books-world.net
The Unzip Password : books-world.net

تحميل

يجب عليك التسجيل في الموقع لكي تتمكن من التحميل
تسجيل | تسجيل الدخول

التعليقات

اترك تعليقاً