Radar systems analysis and design using MATLAB

Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
Preface
Author Bio
Companion: MATLAB® Code - Disclaimer
Chapter 1 Radar Definitions and Nomenclature
	1.1 Radar Systems Classifications and Bands
		1.1.1 High Frequency (HF) and Very HF (VHF) Radars (A- and B-Bands)
		1.1.2 Ultra High Frequency (UHF) Radars (C-Band)
		1.1.3 L-Band Radars (D-Band)
		1.1.4 S-Band Radars (E- and F-Bands)
		1.1.5 C-Band Radar (G-Band)
		1.1.6 X- and Ku-Band Radars (I- and J-Bands)
		1.1.7 K- and Ka- Band Radars (J- and K-Bands)
		1.1.8 Millimeter Wave (MMW) Radars (V- and W-Bands)
	1.2 Radar Functional Block Diagram
	1.3 Primary Radar Subsystems
	1.4 Signal Classification
		1.4.1 Signal Expansion Functions
		1.4.2 Fourier Series Expansion
			1.4.2.1 Trigonometric Fourier Series
			1.4.2.2 Complex Exponential Fourier Series
		1.4.3 Properties of the Fourier Series
			1.4.3.1 Addition and Subtraction
			1.4.3.2 Multiplication
			1.4.3.3 Average Power
		1.4.4 Fourier Transform
	1.5 Systems Classification
		1.5.1 Linear and Nonlinear Systems
		1.5.2 Time Invariant and Time Varying Systems
		1.5.3 Stable and Nonstable Systems
		1.5.4 Causal and Noncausal Systems
		1.5.5 Convolution Integral
	1.6 Simplified View of the Radar Receiver Subsystem
		1.6.1 Measuring Target Range
		1.6.2 Unambiguous Range
		1.6.3 Range Resolution
		1.6.4 Doppler Frequency
			1.6.4.1 Doppler Frequency Extraction – Method I
			1.6.4.2 Doppler Frequency Extraction – Method II
	1.7 Coherence
	1.8 Decibel Arithmetic
	Appendix 1.1: Fourier Transform Pairs and Properties Tables
	Problems
	Answers to Selected Problems
Chapter 2 Basic Radar Waveforms and Antenna
	2.1 Introduction
	2.2 Common Radar Waveforms
		2.2.1 Continuous Wave
		2.2.2 Finite Duration Pulse
		2.2.3 Periodic Pulses
		2.2.4 Finite Duration Pulse Train
	2.3 Bandpass Signals
		2.3.1 Analytic Signal (Pre-Envelope)
		2.3.2 Pre-Envelope and Complex Envelope of Bandpass Signals
		2.3.3 Linear Frequency Modulation Signal
	2.4 Waveform Resolution
		2.4.1 Range Resolution
		2.4.2 Doppler Resolution
		2.4.3 Combined Range and Doppler Resolution
	2.5 Radar Antenna
		2.5.1 Electromagnetic Waves (Radio Frequency Waves)
		2.5.2 Antenna Radiated Power
		2.5.3 Radiation Intensity
		2.5.4 Radiation Pattern
			2.5.4.1 Half-Power Beam Width
			2.5.4.2 Sidelobes
			2.5.4.3 Beam Solid Angle
			2.5.4.4 Forward/Backward Ratio
			2.5.4.5 Voltage Standing Wave Ratio
			2.5.4.6 Antenna Bandwidth
		2.5.5 Directivity
		2.5.6 Antenna Gain
			2.5.6.1 Effective Isotropic Radiated Power
		2.5.7 Sidelobe Control
		2.5.8 Antenna Effective Aperture
		2.5.9 Antenna Near and Far Fields
		2.5.10 Antenna Beam Shape Loss and Scan Loss
			2.5.10.1 Beam Shape Loss
			2.5.10.2 Antenna Scan Loss
			2.5.10.3 Antenna U-V Space
		2.5.11 Polarization
	Problems
	Answers to Selected Problems
Chapter 3 Radar Equation
	Part I: Pulsed Radar
	3.1 Radar Range Equation
		3.1.1 Maximum Detection Range
	3.2 Low PRF Radar Equation
	3.3 High PRF Radar Equation
	3.4 Surveillance Radar Equation
		3.4.1 Number of Beam Positions
	3.5 Blake Chart
	3.6 Radar Equation with Jamming
		3.6.1 Passive Jamming Techniques
		3.6.2 Radar Equation with Jamming
		3.6.3 Self-Protection Jamming Radar Equation
			Burn-Through Range
		3.6.4 Support Jamming Radar Equation
		3.6.5 Range Reduction Factor
		3.6.6 Noise (Denial) Jamming Techniques
			3.6.6.1 Barrage Noise Jamming
			3.6.6.2 Spot Noise and Sweep Spot Noise Jamming
			3.6.6.3 Deceptive Jamming
		3.6.7 Electronic Counter-Counter Measure Techniques
			3.6.7.1 Receiver Protection Techniques
			3.6.7.2 Jamming Avoidance and Exploitation Techniques
	3.7 Bistatic Radar Equation
	3.8 Radar Cross-Section
		3.8.1 RCS Prediction Methods
	3.9 Radar Losses
		3.9.1 Transmit and Receive Losses
		3.9.2 Antenna Pattern Loss and Scan Loss
		3.9.3 Atmospheric Loss
			3.9.3.1 Atmospheric Absorption
			3.9.3.2 Atmospheric Attenuation Plots
		3.9.4 Loss Due to Precipitation
		3.9.5 Collapsing Loss
		3.9.6 Processing Loss
			3.9.6.1 Detector Approximation
			3.9.6.2 Constant False Alarm Rate Loss
			3.9.6.3 Quantization Loss
			3.9.6.4 Range Gate Straddle Loss
			3.9.6.5 Doppler Filter Straddle
	Part II: Continuous Wave Radar
	3.10 Overview of Continuous Wave Radars
		3.10.1 CW Radar Equation
		3.10.2 Frequency Modulation
		3.10.3 Linear Frequency Modulated CW Radar
		3.10.4 Multiple Frequency CW Radar
	3.11 MATLAB Program “range_calc.m”
	Problems
	Answers to Selected Problems
Chapter 4 Radar Wave Propagation
	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-thirds 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
	Problems
	Answers to Selected Problems
Chapter 5 Elements of Signal Processing of the Radar Receiver
	5.1 Radar Receiver Block Diagram
	5.2 Correlation
		5.2.1 Correlation Coefficient
			5.2.1.1 Energy Signals
			5.2.1.2 Power Signals
		5.2.2 Correlation Integral – Energy Signals
		5.2.3 Relationship between Convolution and Correlation Integrals
		5.2.4 Effect of Time Translation on the Correlation Function
		5.2.5 Correlation Function Properties
			5.2.5.1 Conjugate Symmetry
			5.2.5.2 Total Signal Energy
			5.2.5.3 Total Area under the Autocorrelation Function
			5.2.5.4 Maximum Value for the Autocorrelation Function
			5.2.5.5 Fourier Transform for the Correlation Function
		5.2.6 Correlation Integral – Power Signals
		5.2.7 Energy and Power Spectrum Densities
		5.2.8 Correlation Function for Periodic Signals
	5.3 Discrete Time Systems and Signals
		5.3.1 Sampling Theorem
			5.3.1.1 Lowpass Sampling Theorem
			5.3.1.2 Bandpass Sampling Theorem
		5.3.2 Z-Transform
		5.3.3 Discrete Fourier Transform
			5.3.3.1 Discrete Power Spectrum
		5.3.4 Spectral Leakage and Fold-Over
			5.3.4.1 Spectral Leakage
			5.3.4.2 Spectral Fold-Over
		5.3.5 Windowing Techniques
		5.3.6 Decimation and Interpolation
			5.3.6.1 Decimation
			5.3.6.2 Interpolation
	5.4 Radar Receiver Noise Figure
	Appendix 5.1 Table of Z-Transform Pairs
	Problems
	Answers to Selected Problems
Chapter 6 Matched Filter
	6.1 Matched Filtering
		6.1.1 Output Signal Power
		6.1.2 Output Noise Power
		6.1.3 Signal-to-Noise Ratio
		6.1.4 Matched Filter Impulse Response
		6.1.5 The Replica
		6.1.6 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 Range and Doppler Uncertainty
		6.3.1 Range Uncertainty
		6.3.2 Doppler (Velocity) Uncertainty
		6.3.3 Combined Range-Doppler Uncertainty
	6.4 Target Parameter Estimation
		6.4.1 What Is an Estimator?
		6.4.2 Amplitude Estimation
		6.4.3 Phase Estimation
	Problems
	Answers to Selected Problems
Chapter 7 Pulse Compression
	7.1 Time-Bandwidth Product
		7.1.1 Radar Equation with Pulse Compression
		7.1.2 Basic Principle of Pulse Compression
	7.2 Correlation Processor
	7.3 Stretch Processor
	7.4 Stepped Frequency Waveforms
		7.4.1 Range Resolution and Range Ambiguity in SFW
	7.5 Effect of Target Velocity on Pulse Compression
		7.5.1 SFW Case
		7.5.2 LFM Case
	7.6 Range-Doppler Coupling in LFM
	Problems
	Answers to Selected Problems
Chapter 8 Radar Ambiguity Function
	8.1 Ambiguity Function Definition
	8.2 Effective Signal Bandwidth and Duration
	8.3 Single Pulse Ambiguity Function
		8.3.1 Time-Bandwidth Product
		8.3.2 Ambiguity Function
	8.4 LFM Ambiguity Function
		8.4.1 Time-Bandwidth Product
		8.4.2 Ambiguity Function
	8.5 Coherent Pulse Train Ambiguity Function
		8.5.1 Time-Bandwidth Product
		8.5.2 Ambiguity Function
	8.6 Pulse Train with LFM Ambiguity Function
	8.7 Stepped Frequency Waveform Ambiguity Function
	8.8 Nonlinear Frequency Modulation
		8.8.1 Concept of Stationary Phase
		8.8.2 Frequency-Modulated Waveform Spectrum Shaping
	8.9 Ambiguity Diagram Contours
		8.9.1 Range-Doppler Coupling in LFM Signals – Revisited
	8.10 Discrete Code Signal Representation
		8.10.1 Pulse-Train Codes
	8.11 Phase Coding
		8.11.1 Binary Phase Codes
			Barker Code
			Pseudo-Random Number Codes
			Linear Shift Register Generators
			Maximal Length Sequence Characteristic Polynomial
		8.11.2 Polyphase Codes
			Frank Codes
	8.12 Frequency Codes
	8.13 MATLAB Ambiguity Plots for Discrete Coded Waveforms
	Problems
	Answers to Selected Problems.
Chapter 9 Radar Clutter
	9.1 Clutter Definition
	9.2 Volume Clutter
		9.2.1 Volume Cell
		9.2.2 Rain
		9.2.3 Chaff
		9.2.4 Radar Range Equation in Volume Clutter
		9.2.5 Volume Clutter Spectra
	9.3 Area Clutter
		9.3.1 Constant γ Model
		9.3.2 Signal to Clutter, Airborne Radar
	9.4 Clutter RCS, Ground-Based
		9.4.1 Low PRF Case
		9.4.2 High PRF Case
	9.5 Amplitude Distribution
	Problems
	Answers to Selected Problems
Chapter 10 Moving Target Indicator and Pulsed Doppler Radars
	10.1 Area Clutter Spectrum
	10.2 Concept of a Moving Target Indicator
		10.2.1 Single Delay Line Canceler
		10.2.2 Double Delay Line Canceler
		10.2.3 Delay Lines with Feedback (Recursive Filters)
	10.3 PRF Staggering
	10.4 MTI Improvement Factor
		10.4.1 Two-Pulse MTI Case
		10.4.2 The General Case
	10.5 Subclutter Visibility
	10.6 Delay Line Cancelers with Optimal Weights
	10.7 Pulsed Doppler Radars
		10.7.1 Pulse Doppler Radar Signal Processing
	10.8 Ambiguity Resolution
		10.8.1 Range Ambiguity Resolution
		10.8.2 Doppler Ambiguity Resolution
	10.9 Phase Noise
	Problems
	Answers to Selected Problems
Chapter 11 Random Variables and Random Processes
	11.1 Random Variables
	11.2 Multivariate Gaussian Random Vector
		11.2.1 Complex Multivariate Gaussian Random Vector
	11.3 Rayleigh Random Variables
	11.4 The Chi-Square Random Variables
		11.4.1 Central Chi-Square Random Variable with N Degrees of Freedom
		11.4.2 Non-Central Chi-Square Random Variable with N Degrees of Freedom
	11.5 Random Processes
	11.6 The Gaussian Random Process
		11.6.1 Lowpass Gaussian Random Processes
		11.6.2 Bandpass Gaussian Random Processes
		11.6.3 The Envelope of a Bandpass Gaussian Process
	Problems
	Answers to Selected Problems
Chapter 12 Target Detection – Single Pulse Case
	12.1 Single Pulse with Known Parameters
	12.2 Single Pulse with Known Amplitude and Unknown Phase
		12.2.1 Probability of False Alarm
		12.2.2 Probability of Detection
	Problems
	Answers to Selected Problems
Chapter 13 Detection of Fluctuating Targets
	13.1 Pulse Integration
		13.1.1 Coherent Integration
		13.1.2 Noncoherent Integration
		13.1.3 Improvement Factor and Integration Loss
	13.2 Target Fluctuation: the Chi-Square Family of Targets
	13.3 Probability of False Alarm Formulation for a Square Law Detector
		13.3.1 Square Law Detection
	13.4 Probability of Detection Calculation
		13.4.1 Detection of Swerling 0 (Swerling V) Targets
		13.4.2 Detection of Swerling I Targets
		13.4.3 Detection of Swerling II Targets
		13.4.4 Detection of Swerling III Targets
		13.4.5 Detection of Swerling IV Targets
	13.5 Computation of the Fluctuation Loss
	13.6 Cumulative Probability of Detection
	13.7 Constant False Alarm Rate
		13.7.1 Cell-Averaging CFAR (Single Pulse)
		13.7.2 Cell-Averaging CFAR with Noncoherent Integration
	13.8 M-out-of-N Detection
	13.9 Radar Equation-Revisited
		13.9.1 Detection Range with Pulse Integration
			Coherent Integration case:
			Noncoherent Integration Case:
	Appendix 13.1 Gamma Function
		Incomplete Gamma Function
	Problems
	Answers to Selected Problems
Chapter 14 Radar Cross-Section
	14.1 Radar Cross-Section Definition
	14.2 RCS Dependency on Aspect Angle and Frequency
	14.3 Target Scattering Matrix
	14.4 RCS of Simple Objects
		14.4.1 Sphere
		14.4.2 Ellipsoid
		14.4.3 Circular Flat Plate
		14.4.4 Truncated Cone (Frustum)
		14.4.5 Cylinder
		14.4.6 Rectangular Flat Plate
		14.4.7 Triangular Flat Plate
	14.5 RCS of Complex Objects
	14.6 RCS Prediction Methods
		14.6.1 Computational Electromagnetics
		14.6.2 Finite Difference Time Domain Method
		14.6.3 Finite Element Method
		14.6.4 Integral Equations
		14.6.5 Geometrical Optics
		14.6.6 Physical Optics
			14.6.6.1 Rectangular Plate
			14.6.6.2 N-Sided Polygon
		14.6.7 Edge Diffraction
	14.7 Multiple Bounce
	Problems
	Answers to Selected Problems
Chapter 15 Phased Arrays
	15.1 General Arrays
	15.2 Linear Arrays
		15.2.1 Array Tapering
		15.2.2 Computation of the Radiation Pattern via the DFT
	15.3 Planar Arrays
		15.3.1 Rectangular Grid Arrays
		15.3.2 Circular Grid Arrays
		15.3.3 Concentric Grid Circular Arrays
		15.3.4 Rectangular Grid with Circular Boundary Arrays
		15.3.5 Hexagonal Grid Arrays
	15.4 Multiple Input Multiple Output (MIMO) – Linear Array
	Problems
	Answers to Selected Problems
Chapter 16 Adaptive Signal Processing
	16.1 Nonadaptive Beamforming
	16.2 Adaptive Signal Processing Using Least Mean Square
	16.3 The LMS Adaptive Array Processing
	16.4 Sidelobe Cancelers
	16.5 Space–time Adaptive Processing (STAP)
		16.5.1 Space–time Processing
		16.5.2 Space–Time Adaptive Processing
	Problems
Chapter 17 Target Tracking
	Part I: Single Target Tracking
	17.1 Angle Tracking
		17.1.1 Sequential Lobing
		17.1.2 Conical Scan
	17.2 Amplitude Comparison Monopulse
	17.3 Phase Comparison Monopulse
	17.4 Range Tracking
	Part II: Multiple Target Tracking
	17.5 Track-While-Scan
	17.6 State Variable Representation of an LTI System
	17.7 The LTI System of Interest
	17.8 Fixed-Gain Tracking Filters
		17.8.1 Notation:
		17.8.2 The α β Filter
		17.8.3 The αβγ Filter
	17.9 The Kalman Filter
		17.9.1 The Singer αβγ-Kalman Filter
		17.9.2 Relationship between Kalman and αβγ Filters
			MATLAB Function “kalman_filter.m”
	17.10 MATLAB Kalman Filter Simulation
	Problems
	Answers to Selected Problems
Chapter 18 Synthetic Aperture Radar
	18.1 Introduction
		18.1.1 Side Looking SAR Geometry
	18.2 SAR Design Considerations
	18.3 SAR Radar Equation
	18.4 SAR Signal Processing
	18.5 Side Looking SAR Doppler Processing
	18.6 SAR Imaging Using Doppler Processing
	18.7 Range Walk
	18.8 A Three-Dimensional SAR Imaging Technique
		18.8.1 Background
		18.8.2 DFTSQM Operation and Signal Processing
			18.8.2.1 Linear Arrays
			18.8.2.2 Rectangular Arrays
		18.8.3 Geometry for DFTSQM SAR Imaging
		18.8.4 Slant Range Equation
		18.8.5 Signal Synthesis
		18.8.6 Electronic Processing
		18.8.7 Derivation of Eq. (18.71)
		18.8.8 Non-Zero Taylor Series Coefficients for the kth Range Cell
	Problems
	Answers to Selected Problems
Bibliography
Index