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Principles of Modern Radar, Volume 1: Basic Principles

Chapter 1. Introduction and Radar Overview 1.1 Introduction 1.2 The Radar Concept 1.2.1 Subsystems introduced 1.3 The Physics of EM Waves 1.3.1 Wavelength, Frequency, Phase, and superposition (interference) 1.3.2 Intensity 1.3.3 Polarization 1.4 Interaction of EM Waves with Matter 1.4.1 Diffraction, and Antenna Diffraction 1.4.2 Attenuation 1.4.3 Refraction 1.4.4Reflection 1.5BasicRadarConfigurationsandWaveforms 1.5.1 Bistatic/Monostatic 1.5.2 CW/Pulsed 1.5.3 Coherent/Non-coherent 1.6 Noise, SNR, and Detection 1.7 Basic Radar Measurements 1.7.1 Target Position 1.7.2 Target Doppler 1.7.3 Polarization 1.7.4 Radar Resolution 1.8 Basic Radar Functions 1.8.1 Search 1.8.2 Track 1.8.3 Imaging 1.9 Radar Applications 1.9.1 Military Applications 1.9.2 Commercial Applications 1.10 Organization of This text 1.11 Further Reading 1.12 References 1.13 Problems Chapter 2. The Radar Range Equation 2.1 Introduction 2.2 Power Density at Distance R 2.3 Power Received From a Target 2.4 Receiver Thermal Noise 2.5 Signal-to-Noise Ratio and the Radar Range Equation 2.6 Multiple Pulse Effects 2.7 Summary of Losses 2.7.1 Transmit loss 2.7.2 Atmospheric Loss 2.7.3 Receive loss 2.7.4 Signal Processing Loss 2.8 Solving for other Variables 2.9 Decibel Form of the Radar Range Equation 2.10 The Average Power Form of the Radar Range Equation 2.11 Pulse Compression ­ Intrapulse Modulation 2.12 A Graphical Example 2.13 Extended Clutter as the Target 2.13.1 Surface clutter 2.13.2 Volume clutter 2.14 One-Way Link Equation 2.15 Search Form of the Radar Range Equation 2.16 Track Form of the Radar Range Equation 2.17 Some Implications of the Radar Range Equation 2.17.1 Average Power and Dwell Time 2.18 Further Reading 2.19 References 2.20 Problems Chapter 3. Radar Search and Overview of Detection in Interference 3.1 Introduction 3.2 Search Mode Fundamentals 3.2.1 Search Volume 3.2.2 Total Search Time 3.2.3 Electronically Scanned Antenna Issues 3.2.4 Search Regimens 3.2.4.1 Track-While-Scan 3.2.4.2 Search and Track 3.2.4.3 Hybrid Search and Track Systems 3.3 Overview of Detection Fundamentals 3.3.1 Overview of the Threshold Detection Concept 3.3.2 Probabilities of False Alarm and Detection 3.3.3 Noise PDF and False Alarms 3.3.3.1 Probability of False Alarm 3.3.3.2. False Alarm Rate 3.3.4. Signal Plus Noise PDF ­ Target Detection 3.3.5. Receiver Operating Curves 3.3.6. Fluctuating Targets 3.3.7. Interference Other Than Noise 3.3.8. Some Closed-Form Solutions 3.3.8.1ApproximateDetectionResultsforaNon-fluctuatingTarget 3.3.8.2 Swerling 1 Target Model 3.3.9Confirmationprocessing 3.3.10. Multiple Dwell Detection Principles ­ Cumulative PD 3.3.11. m out of n Detection Criterion 3.4 Further Reading 3.5 References Chapter 3.6 Problems Chapter 4. Propagation Effects and Mechanisms 4.1 Introduction 4.2 Propagation Factor 4.3 Propagation Paths and Regions 4.3.1 Monostatic and Bistatic Propagation 4.3.2 The Surface 4.3.3 The Atmosphere 4.4 Atmospheric Attenuation and Absorption 4.4.1 Clear Air Water Vapor 4.4.2 Rain 4.4.3 Fog 4.4.4 Snow and Hail 4.4.5 Dust 4.4.6 Smoke 4.5 Atmospheric Refraction 4.5.1 Standard Refraction 4.5.1.1 The Standard Atmosphere 4.5.1.2DefiningtheHorizon-theEffectiveModel 4.5.2 Anomalous Refraction 4.6 Turbulence 4.7 Exploiting the Ionosphere 4.8 Diffraction 4.9 Multipath 4.9.1 Propagation Paths and Superposition 4.9.2DescribingtheReflectingSurface 4.9.3TheMultipathReflectionCoefficient 4.9.3.1FresnelReflectionCoefficients 4.9.3.2 Divergence Factor 4.9.3.3 Roughness Factors 4.9.3.3.1 Specular Scattering 4.9.3.3.2 Diffuse Scattering 4.9.3.4 Angle Error 4.9.3.5ClassificationError 4.10 Skin Depth / Penetration ­ Transmitting Through Walls 4.11 Commercial Simulations 4.12 Summary and Further Reading 4.13 References Chapter 4.14 Problems 5. Characteristics of Clutter 5.1IntroductionandDefinitions 5.1.1 What is Clutter? 5.1.2 Comparison of Clutter and Noise 5.1.3BasicDefinitions 5.1.3.1ScatteringCoefficients 5.1.3.2 Clutter Polarization Scattering Matrix 5.2 General Charactistics of Clutter 5.2.1 Overview 5.2.2 Surface Clutter 5.2.2.1 General Dependencies 5.2.2.2 Average Value Data 5.2.2.2.1LandReflectivity

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5.2.2.2.2SeaReflectivity 5.2.2.3 Clutter Variability Properties 5.2.2.3.1 Land Clutter Variations 5.2.2.3.1.1 Temporal Variations 5.2.2.3.1.2 Spatial Variations 5.2.2.3.2 Sea Clutter Variation 5.2.2.3.2.1 Temporal Variations 5.2.2.3.2.2 Spatial Variations 5.2.3 Atmospheric Clutter 5.2.3.1 Average Value Data 5.2.3.1.1RainReflectivityAverageValues 5.2.3.1.2 Frozen Precipitation 5.2.3.2 Temporal Spectra 5.2.4 Millimeter Wave Clutter 5.3 Clutter Modeling 5.3.1 General Approaches for Estimating Detection Performance in Clutter 5.3.2 Clutter Models 5.3.2.1 Surface Clutter 5.3.2.2 Atmospheric Clutter Models 5.4 Concluding Remarks 5.4.1ReflectivitySummary 5.4.2 Clutter Effect on Detection 5.5 Recommended Reading 5.6 References 5.7 Problems Chapter 6. Target Reflectivity 6.1 Introduction 6.2BasicReflectionPhysics 6.2.1 Electromagnetic Wave Fundamentals 6.2.2 Electromagnetic Wave Polarization 6.2.3ElectromagneticWaveReflection 6.3RadarCrossSectionDefinition 6.3.1IEEERCSDefinition 6.3.2 Intuitive Derivation for Scattering Cross Section 6.3.3 Polarization Scattering Matrix 6.4 Three Scattering Regimes 6.4.1 Rayleigh Region Dipole Scattering 6.4.2 Resonant Region Scattering 6.4.3 High-Frequency Optics Region 6.5 High Frequency Scattering 6.5.1 Phase Addition 6.5.2 Specular Scattering 6.5.3 End Region Scattering 6.5.4 Edge Diffraction 6.5.5 Multiple Bounce Scattering 6.6 Examples 6.7 References 6.8 Further Reading 6.9 Problems Chapter 7. Target Fluctuation Models 7.1 Introduction 7.2 Radar Cross Section for Simple Targets 7.2.1 Basic Scatterers 7.2.2 Aspect Angle and Frequency Dependence of RCS 7.3 Radar Cross Section of Complex Targets 7.4 Statistical Characteristics of the RCS of Complex Targets 7.4. 1 RCS Distributions 7.4.2 RCS Correlation Properties 7.5 Target Fluctuation Models 7.5.1 Swerling Models 7.5.2 Extended Models of Target RCS Statistics 7.6 Doppler Spectrum of Fluctuating Targets 7.7 Further Reading 7.8 References 7.9 Problems Chapter 8. Doppler Phenomenology and Data Acquisition 8.1 Introduction 8.2 Doppler Shift 8.3 The Fourier Transform 8.4 Spectrum of a Pulsed Radar Signal 8.4.1 Spectrum of a Continuous Wave Signal 8.4.2 Spectrum of a Single Rectangular Pulse 8.4.3InfinitePulseTrain 8.4.4 Finite Pulse Train

8.4.5 Modulated Finite Pulse Train 8.4.6 Pulsed Waveform Spectrum with Moving Targets 8.4.7 Doppler Resolution 8.4.8 Receiver Bandwidth Effects 8.5 Why Multiple Pulses? 8.6 Pulsed Radar Data Acquisition 8.6.1 Video Detectors and Phase Shift 8.6.2 Coherent Detector 8.6.3 Pulsed Radar Data Matrix and Datacube 8.7 Doppler Signal Model 8.7.1 Measuring Doppler with Multiple Pulses 8.7.2 Coherent Pulses 8.8 Range-Doppler Spectrum for a Stationary Radar 8.8.1 Elements of the Doppler Spectrum 8.8.2 Range-Doppler Spectrum 8.9 Range-Doppler Spectrum for Moving Radar 8.9.1 Clutter Spreading 8.9.2 Clutter Spectrum Elements 8.9.3 Range-Doppler Clutter Distribution 8.9.4 Range and Velocity Ambiguity Effects 8.10 Further Reading 8.11 References 8.12 Problems Chapter 9. Radar Antennas 9.1 Introduction 9.2 Basic Antenna Concepts 9.2.1 The Isotropic Antenna 9.2.2 The Radiation Pattern 9.2.3 Beamwidth 9.2.4 Directivity and Gain 9.2.5 Sidelobes 9.3. Aperture Tapers 9.4 Effect of the Antenna on Radar Performance 9.5 Monopulse 9.6ReflectorAntennas 9.7 Phased Array Antennas 9.7.1 The Array Factor 9.7.2 Phase Shifters 9.7.3 Grating Lobes 9.7.4 Gain Loss 9.7.5 The Array Element 9.7.6 Wideband Phased Arrays 9.8 Array Architectures 9.8.1 Passive Array Architecture 9.8.2 Active Array Architecture 9.8.3 Subarray Architecture 9.9 Further Reading 9.10 References 9.11 Questions Chapter 10. Radar Transmitters 10.1 Introduction 10.2TransmitterConfigurations 10.3 Types of Power Sources 10.3.1 Oscillators 10.3.1.1 Gunn Diode Oscillators 10.3.1.2 IMPATT diode oscillators 10.3.1.3 Magnetron Oscillators 10.3.2Amplifiers 10.3.2.1CrossedFieldAmplifiers 10.3.2.2 Traveling-wave Tubes 10.3.2.3 Klystrons 10.3.2.4 Solid-state Transmit/Receive Modules 10.3.2.5 Microwave Power Modules 10.3.2.6 Summary of Microwave Source Power Levels 10.4 Modulators and Power Supplies 10.4.1 Line Type Modulators 10.4.2 Hard Tube Modulators 10.4.3 High Voltage Power Supplies 10.4.4 Power Supplies for Solid-State Phased Arrays 10.5 Transmitter Reliability 10.6 Transmitter Impacts on Spectral Purity 10.6.1 Time Varying Errors 10.6.2 Non-Time Varying Errors 10.7 Further Reading

©2009, SciTech Publishing · 911 Paverstone Drive, Suite B · Raleigh, NC 27615 · www.scitechpub.com · [email protected]

10.8 References 10.9 Problems Chapter 11. Radar Receivers 11.1 Introduction 11.2 Summary of Receiver Types 11.2.1 Crystal Video Receiver 11.2.2 Superregenerative Receivers 11.2.3 Homodyne Receivers 11.2.4 Superheterodyne Receivers 11.2.5 Digital Receivers 11.2.6 Instantaneous Frequency Measurement Receivers 11.2.7 Channelized Receivers 11.3 Major Receiver Functions 11.3.1 Receiver Protection 11.3.2 IF Preselection 11.3.3 Frequency Downconversion and Mixers 11.3.4 Selection of LO and IF Frequencies 11.4 Demodulation 11.4.1 Non-Coherent Demodulation 11.4.2 Coherent Demodultaion 11.4.3 Analog Coherent Detection Implementation & Mismatch Errors 11.5 Receiver Noise Power 11.6 Receiver Dynamic Range 11.6.1 Sensitivity Time Control 11.6.2 Gain Control 11.6.3 Coupling issues 11.7 Analog to Digital Data Conversion 11.7.1 Spurious Free Dynamic Range 11.7.2 Direct Digital Coherent Detection Implementation 11.7.2 Digital UP/DOWN Frequency Conversion 11.8 Further Reading 11.9 References 11.10 Problems Chapter 12. Radar Exciters 12.1 Introduction 12.2 Exciter-related Radar Performance Issues 12.2.1 Phase Noise Issues 12.2.2 Effect of Phase Noise on Clutter Reduction - MTI Processing 12.2.3 Effect of Phase Noise on Pulse-Doppler Processing 12.2.4 Effect of Phase Noise on Imaging 12.3 Exciter Design Considerations 12.3.1 Transmit Signal 12.3.2 Waveform Generation 12.3.2.1 Intra-pulse, Pseudorandom Biphase Modulation 12.3.2.2 Intra-pulse Linear Frequency Modulation (LFM) 12.3.2.3 Dwell-to-Dwell Frequency Change 12.4 Exciter Components 12.4.1 Stable Oscillators - Oscillator Technology 12.4.1.1 Crystal Reference Oscillator 12.4.1.2 Stable Local Oscillator 12.4.1.3 Phase-locked Oscillators for Stable Local Oscillators 12.4.1.4. Surface Acoustic Wave Oscillators 12.4.2 Synthesizers 12.4.3 Other devices 12.4.3.1 Assembly approaches 12.4.3.2 Mixers 12.4.3.3 Switches 12.4.3.4 Frequency Multipliers 12.4.3.5 Frequency Dividers 12.4.3.6Amplifiers 12.5 Timing and Control Circuits 12.6 Further Reading 12.7 References 12.8 Problems Chapter 13. The Radar Signal Processor 13.1 Introduction 13.2 Radar Processor Structure 13.3 Signal Processor Metrics 13.3.1 Hardware Metrics 13.3.2 Algorithm Metrics 13.4 Counting FLOPS: Estimating Algorithm Computational Requirements 13.4.1 General Approach 13.4.2Mode-SpecificFormulas

13.4.3ChoosingEfficientAlgorithms 13.5 Implementation Technology 13.5.1 Analog-to-Digital Conversion 13.5.2 Processor Technologies 13.5.3 COTS Technology and Modular Open Architectures 13.5.4TheInfluenceofMoore'sLaw 13.6 Fixed Point vs. Floating Point 13.7 Signal Processor Sizing 13.7.1 Considerations in Estimating Timing 13.7.2 Benchmarks 13.7.3 Software Tool Impacts 13.7.4 Data Rates 13.7.5 Onboard vs. Offboard Processing 13.8 Further Reading 13.9 References 13.10 Problems Chapter 14. Digital Signal Processing Fundamentals for Radar 14.1 Introduction 14.2 Sampling 14.2.1 The Nyquist Sampling Theorem 14.2.2 Sampling Non-Baseband Signals 14.2.3 Vector Representation of Sampled Signals 14.2.4 Data Collection and the Radar Datacube 14.3 Quantization 14.4 Fourier Analysis 14.4.1 The Discrete-Time Fourier Transform 14.4.2 Windowing 14.4.3 Spatial Frequency 14.4.4 The Discrete Fourier Transform (DFT) 14.4.5 Straddle Loss 14.4.6 The Fast Fourier Transform 14.4.7 Summary of Fourier Transform Relationships 14.5 The z Transform 14.6 Digital Filtering 14.6.1 Spectral Representations of LSI Systems 14.6.2 Digital Filter Characteristics and Design 14.6.2.1 FIR Filters 14.6.2.2 IIR Filters 14.6.2.3 Filter Design Comparison Example 14.6.3 Implementing Digital Filters 14.6.4 Shift-Varying and Nonlinear Systems 14.7 Random Signals 14.7.1 Probability Density Functions 14.7.2 Moments and Power Spectrum 14.7.3 White Noise 14.7.4 Time Averages 14.8 Integration 14.8.1 Coherent Integration 14.8.2 Noncoherent Integration 14.9 Correlation as a Signal Processing Operation 14.10 Matched Filters 14.11 Further Reading 14.12 References 14.13 Problems Chapter 15. Threshold Detection of Radar Targets 15.1 Introduction 15.2 Detection Strategies for Multiple Measurements 15.2.1 Dwells and Coherent Processing Intervals 15.2.2 Coherent, Noncoherent, and Binary Integration 15.2.3 Data Combination Strategies 15.3 Introduction to Optimal Detection 15.3.1 Hypothesis Testing and the Neyman-Pearson Criterion 15.3.2 The Likelihood Ratio Test 15.4 Statistical Models for Noise and Target RCS in Radar 15.4.1 Statistical Model of Noise 15.4.2 Statistical Models of Radar Cross Section for Targets 15.4.3 RCS Decorrelation Properties 15.4.4 Swerling Models 15.4.5 Extended Models of Target RCS Statistics 15.4.6 Statistics of Targets in Interference and the Detection Statistic 15.5 Threshold Detection of Radar Signals 15.5.1 Unknown Parameters 15.5.2TheOptimumDetectorforNonfluctuatingRadarSignals,N=1 15.5.3PerformancefortheNonfluctuatingSignalinGaussianNoise,N=1

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15.5.4OptimumDetectorforaNonfluctuatingTarget,N>1 15.5.5 Linear and Square-Law Detectors 15.5.6SquareLawDetectorPerformanceforaNonfluctuatingTarget,N>1 15.5.7Albersheim'sEquation 15.5.8 Fluctuating Targets 15.5.9 Frequency Agility 15.5.10Shnidman'sEquation 15.5.11 Detection in Clutter 15.5.12 Binary Integration 15.6 Further Reading 15.7 References 15.8 Problems Chapter 16. Constant False Alarm Rate Detectors 16.1 Introduction 16.2 Overview of Detection Theory 16.3 False Alarm Impact and Sensitivity 16.4 CFAR Detectors 16.4.1 Neyman-Pearson Detector 16.4.2. Basic CFAR Architecture 16.5 Cell Averaging CFAR 16.5.1 CA-CFAR Performance 16.5.1.1 Homogeneous Performance 16.5.1.2. CFAR Loss 16.5.2 CA-CFAR Performance in Heterogeneous Environments 16.5.2.1 Masking 16.5.2.2 Clutter Boundaries 16.6 Robust CFARs 16.6.1 Greatest-of CA-CFAR 16.6.2 Suppression of Mutual Target Masking 16.6.2.1. Smallest-of CA-CFAR 16.6.2.2. Trimmed Mean or Censored CFAR 16.6.2.3. Ordered Statistics CFAR 16.6.2.4. CS and OS-CFAR Numerical Example 16.6.3 Combining GO with CS or OS 16.7. Algorithm Comparison 16.8. Adaptive CFARs 16.9. Additional Comments 16.9.1 Non-Rayleigh Backgrounds 16.9.2 Clutter Map CFAR 16.10 Further Reading 16.11 References 16.12 Problems Chapter 17. Doppler Processing 17.1 Introduction 17.2 Review of Doppler Shift and Pulsed Radar Data 17.2.1 Doppler Shift 17.3 Pulsed Radar Doppler Data Acquisition and Characteristics 17.3.1 Review of Pulsed Radar Data Matrix and Doppler Signal Model 17.3.2 Generic Doppler Spectrum for a Single Range Bin 17.3.3 Review of Range and Velocity Aliasing and Coverage 17.4 Moving Target Indication 17.4.1 Pulse Cancellers 17.4.2 Blind Speeds and Staggered PRFs 17.4.3 MTI Figures of Merit 17.4.4 Limitations to MTI Performance 17.4.5 MTI from a Moving Platform 17.5 Pulse Doppler Processing 17.5.1 The Discrete Time Fourier Transform of a Constant-Velocity Target 17.5.2 Sampling the Doppler Spectrum and Straddle Loss 17.5.3 Signal-to-Noise Ratio in the Doppler Spectrum 17.5.4 Matched Filter and Filterbank Interpretations of Pulse Doppler Processing with the DFT 17.5.5 Fine Doppler Estimation 17.5.6 Modern Spectral Estimation in Pulse Doppler Processing 17.5.7 Metrics for Pulse Doppler Detection of Moving Targets 17.5.8 Dwell-to-Dwell Stagger 17.5.9 Blind Zones 17.5.10 PRF Regimes and Ambiguity Resolution 17.5.11 Transient Effects 17.6 Clutter Mapping and the Moving Target Detector 17.6.1 Clutter Mapping 17.7 Pulse Pair Processing

17.8 Further Reading 17.9 References 17.10 Problems Chapter 18. Radar Measurements 18.1 Introduction 18.2 Resolution, Accuracy, and Precision in Radar Measurements 18.2.1 Precision and Accuracy 18.2.2 Accuracy and Performance Considerations 18.3 Radar Signal Model 18.4 Parameter Estimation 18.4.1 Estimators 18.4.2 The Cramer-Rao Lower Bound 18.4.3 Precision and Resolution for the Gaussian Case 18.4.4 Signal and Target Variability 18.5 Range Measurements 18.5.1 Resolution and Sampling 18.5.2 Split-Gate Range Measurement Precision 18.6 Phase Measurements 18.7 Doppler and Range Rate Measurements 18.7.1 DFT Methods 18.7.2 DFT Interpolation Methods 18.7.3 Pulse-Pair Estimation 18.8 RCS Estimation 18.9 Angle Measurements 18.9.1 Angle Centroiding for Scanning Radars 18.9.2 Monopulse 18.9.2.1 Single Target 18.9.2.2 Multiple Unresolved Targets 18.10 Coordinate Systems 18.11 A Preview of Tracking 18.11.1The-Filter 18.11.2StateSpaceRepresentationofthe-Filter 18.12 Further Reading 18.13 References 18.14 Problems Chapter 19. Tracking Radar Targets 19.1 Introduction 19.2 Basics of Track Filtering 19.2.1 Parametric Estimation 19.2.1.1 Constant Velocity Filtering 19.2.1.2 Constant Acceleration Filtering 19.2.2 Stochastic State Estimation 19.2.2.1 Nearly Constant Velocity Filtering with Discrete White Noise Acceleration 19.2.2.2 Nearly Constant Velocity Tracking with LFM Waveforms 19.2.2.3 Nearly Constant Velocity Filtering with Continuous White Noise Acceleration 19.2.2.4 Nearly Constant Acceleration Filtering 19.2.2.5 Multiple Model Filtering for Highly Maneuvering Targets 19.3 Kinematic Motion Models 19.3.1 Nearly Constant Velocity Motion Motion 19.3.2 Nearly Constant Acceleration Motion Model 19.3.3 Singer Motion Model 19.3.4 Nearly Constant Speed Motion Model 19.4 Measurement Models 19.4.1 Measurements in Stabilized Coordinates 19.4.2 Measurements in Sine Space 19.4.3 Measurements with LFM Waveforms 19.4.4 Surveillance Radars with Measurements of Reduced Dimension 19.5 Radar Track Filtering 19.5.1 Nonlinear Least-Squares Estimation 19.5.2 Extended Kalman Filter 19.5.3 Converted Measurement Filter 19.6 Measurement-to-track Data Association 19.6.1 Measurement Validation and Gating 19.6.2 Nearest Neighbor Filter 19.6.3 Strongest Neighbor Filter 19.6.4 Probabilistic Data Association Filter (PDAF) 19.7 Performance Assessment of Tracking Algorithms 19.8 Further Reading 19.9 Problems Chapter 20. Fundamentals of Pulse Compression Waveforms 20.1 Introduction 20.2 Matched Filters 20.2.1 Relevance of SNR to Radar Performance

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20.2.2 Energy Form of the Radar Range Equation 20.2.3 The Form of the Matched Filter 20.2.4 Point Target Model 20.2.5 Match Filtered Response Proportional to Waveform Energy 20.2.6 Fourier Relationships and the Matched Filter 20.2.7 Derivation of the Matched Filter 20.2.8 The Radar Range Equation and Matched Filter Relationship 20.2.9. The Match Filtered Response for a Simple Pulse 20.2.10 Properties of the Match Filtered Response 20.3 Range Resolution 20.3.1ResolutionasDefinedbytheRayleighCriterion 20.3.2ResolutionDefinedinTermsofMainlobeWidth 20.3.3ResolutionDefinedinTermsofaSecondOrderMoment 20.3.4 The Relationship Between Bandwidth and Range Resolution 20.3.5 An Examination of Resolution Using 2 Point Targets 20.4 Straddle Loss 20.5 Pulse Compression Waveforms 20.5.1 Amplitude Modulation 20.5.2 Frequency Modulation 20.5.3 Phase Coded Waveforms 20.6 Pulse Compression Gain 20.7 Linear Frequency Modulated Waveforms 20.7.1 Time Domain Description of an LFM Waveform 20.7.2 Waveform Spectrum 20.7.3 Compressed Response Waveform Spectrum 20.7.4 Rayleigh Resolution 20.7.5 The Nominal Sidelobe Response 20.8 Matched Filter Implementations 20.8.1 Dispersive Filters 20.8.2. Digital Filters 20.9 Sidelobe Reduction in an LFM Waveform 20.9.1 Weighting and Time-Bandwidth Requirements 20.9.2 Straddle Loss Reduction 20.10 Ambiguity Functions 20.10.1 Ambiguity Function for a Simple Pulse 20.10.2 Ambiguity Function for an LFM Waveform 20.10.3 Range-Doppler Coupling 20.10.4 Spectral Interpretation of Range-Doppler Coupling 20.10.5 Dealing with Doppler Modulation in a Pulse Compression Waveform 20.10.6 The V-LFM 20.11 LFM Summary 20.12 Phase Coded Waveforms 20.12.1 The Structure and General Properties of Phase Coded Waveforms 20.12.2 Phase Codes Used in Radar 20.12.3 Phase Modulation 20.12.4 Equivalence Operations 20.12.5 Match Filtered Response of a Phase Code 20.12.6 Spectrum of a Phase Coded Waveform 20.12.7 Doppler Tolerance 20.13 Biphase Codes 20.13.1 Biphase Barker Codes 20.13.2 MPS codes 20.13.3 Maximal Length Sequences 20.13.4 Comparison of MLS and LFM Waveform Responses and Spectra 20.14 Polyphase Codes 20.14.1 Polyphase Barker Codes 20.14.2 Frank, P1, and P2 Codes 20.14.3 P3 & P4 Codes 20.15 Phase Code Summary 20.16 Further Reading 20.17 References 20.18 Problems Chapter 21. An Overview of Radar Imaging 21.1 Introduction 21.2 General Imaging Considerations 21.2.1 SAR as a Large Synthetic Antenna Aperture 21.2.2 SAR as Range-Doppler Imaging 21.2.3 SAR as a Signal Processing Exercise 21.3 Resolution Relationships and Sampling Requirements 21.3.1 Resolution Relationships 21.3.2 Synthetic Aperture Sampling Requirements 21.3.3 Miscellaneous Relationships 21.4 Data Collection 21.5 Image Formation

21.5.1 SAR Coordinate Systems 21.5.2 Linear Collection PSR 21.5.3 DBS Derivation 21.5.4 DBS Image Formation 21.5.5 DBS, Doppler, and the PSR 21.5.6 DBS Example 21.5.7 DBS Limitations 21.5.8 Matched Filter Imaging 21.5.9 Image Formation Survey 21.6 Image Phenomenology 21.6.1 No Return Areas 21.6.2 Shadowing 21.6.3 Foreshortening and Layover 21.6.4 Speckle 21.6.5 Man-Made Returns 21.6.6 Signal-to-Noise and Clutter-to-Noise Ratios 21.7 Summary 21.8 Further Reading 21.9 References 21.10 Problems

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