Handbook of Radar Signal Analysis (Advances in Applied Mathematics)

Cover
Half Title
Series  Page
Title Page
Copyright Page
Table of Contents
Preface
Editors
Contributors
Acknowledgments
Chapter 1: Signals and Systems - Refresher
	1.1. Signal Classification
	1.2. Signal Expansion Functions
		1.2.1. Fourier Series Expansion
			Trigonometric Fourier Series
			Complex Exponential Fourier Series
		1.2.2. Properties of the Fourier Series
			Addition and Subtraction
			Multiplication
			Average Power
	1.3. Fourier Transform
		1.3.1. Fourier Transform Pairs and Properties Tables
	1.4. Systems Classification
		1.4.1. Linear and Nonlinear Systems
		1.4.2. Time Invariant and Time Varying Systems
		1.4.3. Stable and Nonstable Systems
		1.4.4. Causal and Noncausal Systems
	1.5. Spectra of Common Radar Signals
		1.5.1. Continuous Wave Signal
		1.5.2. Finite Duration Pulse Signal
		1.5.3. Periodic Pulse Signal
		1.5.4. Finite Duration Pulse Train Signal
	1.6. Convolution Integral
	1.7. Correlation
		1.7.1. Correlation Coefficient
			Energy Signals
			Power Signals
		1.7.2. Correlation Integral Energy Signals
		1.7.3. Relationship between Convolution and Correlation Integrals
		1.7.4. Effect of Time Translation on the Correlation Function
		1.7.5. Correlation Function Properties
			Conjugate Symmetry
			Total Signal Energy
			Total Area under the Autocorrelation Function
			Maximum Value for the Autocorrelation Function
			Fourier Transform for the Correlation Function
		1.7.6. Correlation Integral Power Signals
		1.7.7. Energy and Power Spectrum Densities
		1.7.8. Correlation Function for Periodic Signals
	1.8. Bandpass Signals
		1.8.1. Analytic Signal (Pre-Envelope)
		1.8.2. Pre-Envelope and Complex Envelope of Bandpass Signals
		1.8.3. Spectrum for a Linear Frequency Modulation Signal
	1.9. Discrete Time Systems and Signals
		1.9.1. Sampling Theorem
			Lowpass Sampling Theorem
			Bandpass Sampling Theorem
	1.10. Z-Transform
	1.11. Discrete Fourier Transform
		1.11.1. Discrete Power Spectrum
		1.11.2. Spectral Leakage and Fold-Over
			Spectral Leakage
			Spectral Fold-Over
		1.11.3. Windowing Techniques
			Interpolation
		1.11.4. Decimation and Interpolation
			Decimation
			Interpolation
	1.12. Random Variables and Random Processes
		1.12.1. Random Variables
		1.12.2. Multivariate Gaussian Random Vector
		1.12.3. Complex Multivariate Gaussian Random Vector
		1.12.4. Rayleigh Random Variables
		1.12.5. The Chi-Square Random Variables
			Central Chi-Square Random Variable with N Degrees of Freedom
			Noncentral Chi-Square Random Variable with N Degrees of Freedom
		1.12.6. Random Processes
		1.12.7. Gaussian Random Process
		1.12.8. Lowpass Gaussian Random Processes
		1.12.9. Bandpass Gaussian Random Processes
		1.12.10. Envelope of a Bandpass Gaussian Process
Chapter 2: Radar Systems Basics
	2.1. Radar Block Diagram
	2.2. Radar Specific Terms
		2.2.1. Range
		2.2.2. Unambiguous Range
		2.2.3. Range Resolution
		2.2.4. Doppler Frequency
			Doppler Frequency Extraction - Method I
			Doppler Frequency Extraction - Method II
	2.3. Radar Systems Classifications and Bands
		2.3.1. High Frequency and Very HF Radars (Aand B-Bands)
		2.3.2. Ultra High Frequency Radars (C-Band)
		2.3.3. L-Band Radars (D-Band)
		2.3.4. S-Band Radars (E- and F-Bands)
		2.3.5. C-Band Radar (G-Band)
		2.3.6. X- and Ku-Band Radars (I- and J-Bands)
		2.3.7. K- and Ka- Band Radars (J- and K-Bands)
		2.3.8. Millimeter Wave Radars (V- and W-Bands)
	2.4. Decibel Arithmetic
	2.5. Electromagnetic Waves (RF Waves)
		2.5.1. Polarization
	2.6. Coherence
	2.7. Radar Antenna
		2.7.1. Antenna Directivity and Gain
		2.7.2. Antenna Power Radiation Pattern
		2.7.3. Near and Far Fields
		2.7.4. Beam Shape Loss and Scan Loss
			Beam Shape Loss
			Antenna Scan Loss
		2.7.5. Number of Beam Positions
	2.8. Radar Cross-Section
		2.8.1. RCS Prediction Methods
	2.9. Radar Measurement Errors
Chapter 3: Radar Equation
	3.1. Radar Range Equation
		3.1.1. Maximum Detection Range
		3.1.2. Blake Chart
		3.1.3. Low Pulse Repetition Frequency Radar Equation
		3.1.4. High PRF Radar Equation
		3.1.5. Surveillance Radar Equation
	3.2. Bistatic Radar Equation
	3.3. Radar Losses
		3.3.1. Transmit and Receive Losses
		3.3.2. Antenna Pattern Loss and Scan Loss
		3.3.3. Atmospheric Loss
			Atmospheric Absorption
			Atmospheric Attenuation Plots
			Attenuation Due to Precipitation
		3.3.4. Collapsing Loss
		3.3.5. Processing Loss
			Detector Approximation
			Constant False Alarm Rate Loss
			Quantization Loss
			Range Gate Straddle Loss
			Doppler Filter Straddle Loss
			Other Losses
	3.4. Noise Figure
	3.5. Continuous Wave Radars
		3.5.1. CW Radar Equation
		3.5.2. Frequency Modulation
		3.5.3. Linear Frequency Modulated CW Radar
		3.5.4. Multiple Frequency CW Radar
Chapter 4: Radar Propagation Medium
	4.1. Earth’s Impact on the Radar Equation
	4.2. Earth’s Atmosphere
	4.3. Atmospheric Models
		4.3.1. Index of Refraction in the Troposphere
		4.3.2. Index of Refraction in the Ionosphere
		4.3.3. Mathematical Model for Computing Refraction
		4.3.4. Stratified Atmospheric Refraction Model
	4.4. Four-Third Earth Model
		4.4.1. Target Height Equation
	4.5. Ground Reflection
		4.5.1. Smooth Surface Reflection Coefficient
		4.5.2. Divergence
		4.5.3. Rough Surface Reflection
		4.5.4. Total Reflection Coefficient
	4.6. Pattern Propagation Factor
		4.6.1. Flat Earth
		4.6.2. Spherical Earth
	4.7. Diffraction
Chapter 5: Radar Electronic Warfare Techniques
	5.1. Electronic Warfare Classes
	5.2. Passive Jamming Techniques
	5.3. Radar Equation with Jamming
		5.3.1. Self-Protection Jamming Radar Equation
			Burn-Through Range
		5.3.2. Support Jamming Radar Equation
		5.3.3. Range Reduction Factor
	5.4. Noise (Denial) Jamming Techniques
		5.4.1. Barrage Noise Jamming
		5.4.2. Spot Noise and Sweep Spot Noise Jamming
	5.5. Deceptive Jamming
	5.6. Electronic Counter-Counter Measure Techniques
		5.6.1. Receiver Protection Techniques
		5.6.2. Jamming Avoidance and Exploitation Techniques
	5.7. Case Studies
		5.7.1. Hypothetical Victim-Radar Parameters
		5.7.2. Self-Screening Jamming Case
		5.7.3. Support Jamming Case
Chapter 6: Matched Filter Receiver
	6.1. Matched Filtering
		6.1.1. Matched Filter Impulse Response
		6.1.2. The Replica
		6.1.3. Mean and Variance of the Matched Filter output
	6.2. General Formula for the Output of the Matched Filter
		6.2.1. Stationary Target Case
		6.2.2. Moving Target Case
	6.3. Waveform Resolution
		6.3.1. Range Resolution
		6.3.2. Doppler Resolution
		6.3.3. Combined Range and Doppler Resolution
	6.4. Range and Doppler Uncertainty
		6.4.1. Range Uncertainty
		6.4.2. Doppler (Velocity) Uncertainty
	6.5. Combined Range-Doppler Uncertainty
	6.6. Target Parameter Estimation
		6.6.1. What Is an Estimator?
		6.6.2. Amplitude Estimation
		6.6.3. Phase Estimation
	6.7. Pulse Compression
		6.7.1. Time-Bandwidth Product
		6.7.2. Radar Equation with Pulse Compression
		6.7.3. Basic Principle of Pulse Compression
		6.7.4. Correlation Processor
		6.7.5. Stretch Processor
		6.7.6. Stepped Frequency Waveforms
			Range Resolution and Range Ambiguity in SFW
		6.7.7. Effect of Target Velocity on Pulse Compression
			SFW Case
			LFM Case
			Range-Doppler Coupling in LFM
Chapter 7: Radar Ambiguity Function
	7.1. Ambiguity Function Definition
	7.2. Effective Signal Bandwidth and Duration
	7.3. Single Pulse Ambiguity Function
		7.3.1. Time-Bandwidth Product
		7.3.2. Ambiguity Function
	7.4. LFM Ambiguity Function
		7.4.1. Time-Bandwidth Product
		7.4.2. Ambiguity Function
	7.5. Coherent Pulse Train Ambiguity Function
		7.5.1. Time-Bandwidth Product
		7.5.2. Ambiguity Function
	7.6. Pulse Train with LFM Ambiguity Function
	7.7. Stepped Frequency Waveform Ambiguity Function
	7.8. Nonlinear Frequency Modulation
		7.8.1. Concept of Stationary Phase
		7.8.2. Frequency Modulated Waveform Spectrum Shaping
	7.9. Ambiguity Diagram Contours
		7.9.1. Range-Doppler Coupling in LFM Signals - Revisited
	7.10. Discrete Code Signal Representation
		7.10.1. Pulse-Train Codes
	7.11. Phase Coding
		7.11.1. Binary Phase Codes
			Barker Code
			Pseudo-Random Number Codes
			Linear Shift Register Generators
			Maximal Length Sequence Characteristic Polynomial
		7.11.2. Polyphase Codes
			Frank Codes
	7.12. Frequency Codes
Chapter 8: Target Detection
	Part I: Single Pulse Detection
		8.1. Single Pulse with Known Parameters
		8.2. Single Pulse with Known Amplitude and Unknown Phase
			8.2.1. Probability of False Alarm
			8.2.2. Probability of Detection
	Part II: Detection of Fluctuating Targets
		8.3. Pulse Integration
			8.3.1. Coherent Integration
			8.3.2. Noncoherent Integration
			8.3.3. Improvement Factor and Integration Loss
			8.3.4. Probability of False Alarm Formulation for a Square Law Detector
			8.3.5. Square Law Detection
		8.4. Probability of Detection Calculation
			8.4.1. Detection of Swerling 0 (Swerling V) Targets
			8.4.2. Detection of Swerling I Targets
			8.4.3. Detection of Swerling II Targets
			8.4.4. Detection of Swerling III Targets
			8.4.5. Detection of Swerling IV Targets
		8.5. Cumulative Probability of Detection
		8.6. Constant False Alarm Rate
			8.6.1. Cell-Averaging CFAR (Single Pulse)
			8.6.2. Cell-Averaging CFAR with Noncoherent Integration
		8.7. M-out-of-N Detection
		8.8. Radar Equation-Revisited
		8.9. Gamma Function
			8.9.1. Incomplete Gamma Function
Chapter 9: Radar Signal Processing in Clutter
	9.1. Introduction
	9.2. Clutter Definition
	9.3. Volume Clutter
		Volume Cell
		Rain
		Chaff
		9.3.1. Radar Range Equation in Volume Clutter
		9.3.2. Volume Clutter Spectra
	9.4. Area Clutter
		9.4.1. Constant Y Model
		9.4.2. Signal to Clutter, Airborne Radar
	9.5. Clutter RCS, Ground-Based
		9.5.1. Low PRF Case
		9.5.2. High PRF Case
	9.6. Amplitude Distribution
	9.7. Area Clutter Spectrum
	9.8. Doppler Processing
		9.8.1. Range and Doppler Processing
		9.8.2. Range and Doppler Ambiguity
		9.8.3. Generalized Spectrum for Ground and Airborne Systems
	9.9. Moving Target Indicator
		9.9.1. Two Pulse Canceler
		9.9.2. Three Pulse Canceler
		9.9.3. The N+1 Pulse Canceler
		9.9.4. Recursive MTI Filter
		9.9.5. Blind Speeds and PRF Staggering
		9.9.6. MTI Figures of Merit
	9.10. Pulse Doppler Processing
		9.10.1. Discrete Time Fourier Transform
		9.10.2. Discrete Fourier Transform
		9.10.3. Windowing
	9.11. Ambiguity Resolution
		9.11.1. Range Ambiguity Resolution
		9.11.2. Doppler Ambiguity Resolution
		9.11.3. Pulse Pair Processing
	9.12. Limitations of Doppler Processing
	Appendix 9-A: Fill Pulses in Pulse Doppler Radars
		9.A.1. Range and Doppler Ambiguities
		9.A.2. Overview of Fill Pulses
		9.A.3. Pulse Doppler Waveform with Fill Pulses
		9.A.4. Recovery of Fill Pulses
		9.A.5. Doppler Filtering Fill Pulses
		9.A.6. Caveats and Extension
Chapter 10: Radar Tracking
	10.1. Introduction
	10.2. Basic Concepts
		10.2.1. Tracking Architecture
		10.2.2. State Space Representation
	10.3. Measurements
		10.3.1. Angle Measurements
			Sequential Lobing
			Amplitude Comparison Monopulse
			Phase Comparison Monopulse
			Range Tracking and Measurements
			Measurement Accuracy
	10.4. Filtering
		10.4.1. Least Squares
		10.4.2. Recursive Least Squares
		10.4.3. Kalman Filter
		10.4.4. Extended Kalman Filter
	10.5. Derivation of Recursive Least Squares
	10.6. Data Association
		10.6.1. Gating
			Global Nearest Neighbor
			Joint Probabilistic Data Association
			Multiple Hypothesis Tracker
	10.7. Tracking Maneuvering Targets
		10.7.1. Field Parameter Filters
		10.7.2. Dynamic Parameter Filters
		10.7.3. Multiple Model Filters
Chapter 11: Canonical and Finite Difference Time Domain Methods for RCS Computation
	11.1. Radar Cross-Section Definition
	11.2. RCS Dependency on Aspect Angle and Frequency
	11.3. Target Scattering Matrix
	11.4. Scattering off Basic Canonical Objects
		11.4.1. Cylinder
		11.4.2. Dielectric-Capped Wedge
			Far Scattered Field
			Plane Wave Excitation
			Special Cases
			Sample Numerical Results
		11.4.3. Spheres
		11.4.4. Ellipsoids
	11.5. RCS Approximations of Simple Objects
		11.5.1. Finite Length Cylinder
		11.5.2. Circular Flat Plate
		11.5.3. Rectangular Flat Plate
		11.5.4. Triangular Flat Plate
		11.5.5. Truncated Cone (Frustum)
	11.6. RCS Using Computational Electromagnetics
		11.6.1. The Standard Finite Difference Time Domain Method
	11.7. RCS Using the FDTD Method
		11.7.1. RCS of a Sphere
		11.7.2. RCS of Complex Objects
Chapter 12: Integral and Physical Optics Methods for RCS Computation
	12.1. Introduction
	12.2. Radiation and Scattering
		12.2.1. Maxwell’s Equations
		12.2.2. Boundary Conditions
		12.2.3. Formulations for Radiation
		12.2.4. Near and Far Fields
			Three-Dimensional Far Field
		12.2.5. Formulations for Scattering
			Surface Equivalent
			Surface Integral Equations
	12.3. Numerical Methods
		12.3.1. Method of Moments
			MoM For 3-D Surfaces of Arbitrary Shape
			Fast Multipole Method
			Adaptive Cross-Approximation
		12.3.2. Physical Optics
		12.3.3. Physical Theory of Diffraction
		12.3.4. Shooting and Bouncing Rays
		12.3.5. Scattering Centers
			Scattering Center Definition
			Extraction
			Scattering Center Models
	12.4. RCS Data Products
	12.5. Scattering Coordinate System
		12.5.1. Target Geometry Coordinate System
		12.5.2. Spherical Coordinates
			Sampling on the Sphere
			Vertical and Horizontal Polarizations
		12.5.3. Aspect and Roll Coordinates
		12.5.4. Measurement Coordinate System
	12.6. Examples
		12.6.1. Bodies of Revolution
			Frustum
			Cone-Sphere
			Monoconic Reentry Vehicle
		12.6.2. Complex Three-Dimensional Objects
			Trihedral Corner Reflector
			Business Jet
Chapter 13: Antennas for Radar Applications
	13.1. Antenna Types
	13.2. Antenna Basic Parameters
		13.2.1. Radiation Pattern
			Half-Power Beamwidth
			Beam Solid Angle
			Sidelobe
			Forward / Backward Ratio
			Voltage Standing Wave Ratio
			Antenna Bandwidth
		13.2.2. Antenna Radiated Power
		13.2.3. Radiation Intensity
		13.2.4. Directivity
		13.2.5. Antenna Gain
		13.2.6. Antenna Effective Aperture
	13.3. General Antenna Arrays
	13.4. Linear Arrays
	13.5. Array Tapering
	13.6. Planar Arrays
		13.6.1. Rectangular Grid Arrays
		13.6.2. Circular Grid Arrays
		13.6.3. Concentric Grid Circular Arrays
		13.6.4. Recursive Circular 2-D Arrays
		13.6.5. Rectangular Grid with Circular Boundary Arrays
	13.7. Three-Dimensional Arrays
		13.7.1. Rectangular Parallelepiped 3-D Array
		13.7.2. Spherical 3-D Arrays
		13.7.3. Arbitrary Arrays
	13.8. Array Feeding and Beamforming Networks
		13.8.1. General Forms of Array Feeding Networks
		13.8.2. Wideband Operation of Feeding Networks
		13.8.3. Array Beamforming Networks
		13.8.4. Power-Divider Beamforming Networks
		13.8.5. Butler and Blass Matrix
		13.8.6. Rotman Lens
		13.8.7. Design Considerations for Beamforming Networks
		13.8.8. Feeding and Beamforming Networks for Two-Dimensional Arrays
Chapter 14: Synthetic Aperture Radar
	14.1. Basic Strip-Map Synthetic Aperture Radar Concept
		14.1.1. Down Range Resolution
		14.1.2. Cross-Range Resolution
		14.1.3. Pulse Repetition Frequency Considerations
	14.2. SAR Image Formation
		14.2.1. Image Formation Processing Steps
		14.2.2. Motion Compensation
		14.2.3. Image Formation
		14.2.4. Auto-Focus Techniques
	14.3. Image Quality Considerations
	14.4. Spotlight SAR
		14.4.1. Motion through Resolution Cells
		14.4.2. Polar Format Algorithm
		14.4.3. Interferometric Synthetic Aperture Radar
	14.5. Inverse Synthetic Aperture Radar
Chapter 15: Wideband Radar Applications
	15.1. Introduction
	15.2. Band Versus Bandwidth
		15.2.1. Various Bandwidths
		15.2.2. Narrow Band, Medium Band and Wideband
	15.3. Wideband Radar Applications
		15.3.1. Foliage Penetrating Synthetic Array Radar
		15.3.2. Automotive Blind Spot Warning and Collision Avoidance
		15.3.3. Space Object Identification
		15.3.4. Ground Perimeter Surveillance
		15.3.5. Pavement Profiling and Inspection
		15.3.6. Wall-Penetrating Radar for Detecting People
		15.3.7. Noninvasive Construction Scanning
		15.3.8. Industrial Robot Control
		15.3.9. Compact Radar Range
		15.3.10. Airport Security Imaging and Detection
		15.3.11. Application Conclusions
Chapter 16: Modern Digital Array Antennas for Radar Applications
	16.1. Introduction
	16.2. Introduction to Digital Arrays
	16.3. Comparison of Array Antenna Architectures by Example
	16.4. Other Digital Array Advantages
	16.5. Extreme Data Rate Demands in Digital Arrays
	16.6. Digital Down-Conversion and Digital Up-Conversion
	16.7. Array Factor versus Huygens-Fresnel Principle
	16.8. Simultaneous Receive Beams
	16.9. Array Scanning Effects to Antenna Pattern
	16.10. Noise Figure and Third Order Intercept in AESA
	16.11. Concluding Remarks
Bibliography
Index