Basic Radar Analysis

Basic Radar Analysis, Second Edition
	Contents
	Chapter 1 Radar Basics
		1.1 Introduction
		1.2 Radar Types
		1.3 Range Measurement
		1.4 Ambiguous Range
		1.5 Processing window and Instrumented Range
		1.6 Range-Rate Measurement: Doppler
		1.7 Decibels
		1.8 dB Arithmetic
		1.9 Complex Signal Notation
		1.10 Radar Block Diagram
		1.11 Exercises
		References
	Chapter 2 Radar Range Equation
		2.1 Introduction
		2.2 Basic Radar Range Equation
			2.2.1 Derivation of ES
				2.2.1.1 The Transmitter
				2.2.1.2 The Antenna
				2.2.1.3 Effective Isotropic Radiated Power
				2.2.1.4 Antenna Directivity
				2.2.1.5 The Target and Radar Cross Section
				2.2.1.6 Antenna Again
				2.2.1.7 Antenna Directivity Again
				2.2.1.8 Losses
			2.2.2 Derivation of EN
		2.3 A Power Approach to SNR
		2.4 Radar Range Equation Example
		2.5 Detection Range
		2.6 Search Radar Range Equation
		2.7 Search Radar Range Equation Example
		2.8 Radar Range Equation Summary
		2.9 Exercises
		References
		Appendix 2A: Derivation of Search Solid Angle Equation
	Chapter 3 Radar Cross Section
		3.1 Introduction
		3.2 RCS of Simple Shapes
		3.3 Swerling RCS Models
			3.3.1 Swerling Statistics
			3.3.2 Swerling Fluctuation Models
			3.3.3 Math Behind the Fluctuation Model
		3.4 Relation of Swerling Models to Actual Targets
		3.5 Simulating Swerling Targets
		3.6 Frequency Agility and SW2 or SW4 Targets
		3.7 Exercises
		References
	Chapter 4 Noise
		4.1 Introduction
		4.2 Noise in Resistive Networks
			4.2.1 Thevenin Equivalent Circuit of a Noisy Resistor
			4.2.2 Multiple Noisy Resistors
		4.3 Equivalent/Effective Noise Temperature for Active Devices
		4.4 Noise Figure
			4.4.1 Derivation of Noise Figure
			4.4.2 Attenuators
		4.5 Noise Figure of Cascaded Devices
		4.6 An Interesting Example
		4.7 Output Noise Energy When the Source Temperature Is Not T0
		4.8 A Note About Cascaded Devices and the Radar Range Equation
		4.9 Cascaded Attenuators
		4.10 Exercises
		References
	Chapter 5 Radar Losses
		5.1 Introduction
		5.2 Transmit Losses
		5.3 Antenna Losses
		5.4 Propagation Losses
		5.5 Receive Antenna and RF Losses
		5.6 Processor and Detection Losses
		5.7 Exercises
		References
		Appendix 5A: Waveguide Attenuation
		5A.1 Exercises
		Appendix 5B: Atmospheric and Rain Attenuation
		5B.1 Function tropatten.m
			5B.1.1 Compute International Civil Aviation Organization (ICAO) Standard Atmosphere 1964
			5B.1.2 Absorption Coefficient for Oxygen
			5B.1.3 Absorption Coefficient for Water Vapor
		5B.2 Function troprefract.m
		5B.3 Function troploss.m
		5B.4 Function rainAttn2way.m
	Chapter 6 Detection Theory
		6.1 Introduction
		6.2 Noise in Receivers
			6.2.1 IF Configuration
			6.2.2 Baseband Configuration
		6.3 Signal in Receivers
			6.3.1 Introduction and Background
			6.3.2 Signal Model for SW0/SW5 Targets
			6.3.3 Signal Model for SW1/SW2 Targets
			6.3.4 Signal Model for SW3/SW4 Targets
		6.4 Signal-Plus-Noise in Receivers
			6.4.1 General Formulation
			6.4.2 Signal-Plus-Noise Model for SW1/SW2 Targets
			6.4.3 Signal-Plus-Noise Model for SW0/SW5 Targets
			6.4.4 Signal-Plus-Noise Model for SW3/SW4 Targets
		6.5 Detection Probability
			6.5.1 Introduction
			6.5.2 Amplitude Detector Types
			6.5.3 Detection Logic
			6.5.4 Calculation of Pd and Pfa
				6.5.4.1 False Alarm Probability
				6.5.4.2 Detection Probability
					SW0/SW5 Target
					SW1/SW2 Target
					SW3/SW4 Target
			6.5.5  Behavior versus Target Type
		6.6 Determination of False Alarm Probability
			6.6.1 Pfa Computation Example
			6.6.2 Detection Contour Example
		6.7 Summary
		6.8 Exercises
		References
	Chapter 7 CFAR Processing
		7.1 Introduction
		7.2 Cell-Averaging CFAR
			7.2.1 Estimation of Interference Power
			7.2.2 CA-CFAR Analysis
			7.2.3 CA-CFAR Example
			7.2.4 CA-CFAR FIR Implementation
			7.2.5 CFAR Processing at the Edges of Instrumentation
		7.3 CA-CFAR with Greatest-of Selection
			7.3.1 GO-CFAR Example
		7.4 CA-CFAR with Smallest of Selection
			7.4.1 SO-CFAR Example
		7.5 Ordered Statistic CFAR
			7.5.1 OS-CFAR Example
		7.6 Minimum Selected CA-CFAR
			7.6.1 MSCA-CFAR Algorithm
			7.6.2 MSCA-CFAR Analysis
			7.6.3 MSCA-CFAR Example
		7.7 Summary
			7.7.1 CFAR Problems and Remedies
			7.7.2 CFAR Scale Factors
		7.8 Exercises
		References
		Appendix 7A: Maximum Likelihood Estimation
		Appendix 7B: Toeplitz Matrix and CFAR
	Chapter 8 Matched Filter
		8.1 Introduction
		8.2 Problem Definition
		8.3 Problem Solution
		8.4 Matched Filter Examples
			8.4.1 General Formulation
			8.4.2 Response for an Unmodulated Pulse
			8.4.3 Response for an LFM Pulse
		8.5 Summary
		8.6 Closing Comments
		8.7 Exercises
		References
	Chapter 9 Detection Probability Improvement Techniques
		9.1 Introduction
		9.2 Coherent Integration
			9.2.1 SNR Analysis
			9.2.2 Detection Analysis
		9.3 Noncoherent Integration
			9.3.1 Coherent and Noncoherent Integration Comparison
			9.3.2 Detection Example with Coherent and Noncoherent Integration
		9.4 Cumulative Detection Probability
			9.4.1 Cumulative Detection Probability Example
		9.5 m-of-n Detection
			9.5.1 m-of-n Detection Example for SW0/SW5, SW2 and SW4 Targets
			9.5.2 m-of-n and Noncoherent Comparison for SW1 and SW2 Targets
		9.6 Exercises
		Appendix 9A: Noise Autocorrelation at the Output of a Matched Filter
		Appendix 9B: Probability of Detecting SW1 and SW3 Targets on m Closely Spaced Pulses
			9B.1 Marcum Q Function
		Appendix 9C: Cumulative Detection Probability
	Chapter 10 Ambiguity Function
		10.1 Introduction
		10.2 Ambiguity Function Development
		10.3 Example 1: Unmodulated Pulse
		10.4 Example 2: LFM Pulse
		10.5 Numerical Techniques
		10.6 Ambiguity Function Generation Using the FFT
		10.7 Exercises
		References
	Chapter 11 Waveform Coding
		11.1 Introduction
		11.2 FM Waveforms
			11.2.1 LFM with Amplitude Weighting
			11.2.2 Nonlinear FM
				11.2.2.1 Fowle Example with Uniform Um(f )
				11.2.2.2 Fowle Example with Cosine on a Pedestal Um(f )
				11.2.2.3 NLFM Design Procedures
		11.3 Phase-coded Pulses
			11.3.1 Frank Polyphase Coding
			11.3.2 Barker-coded Waveforms
			11.3.3 PRN-coded Pulses
				11.3.3.1 Mismatched PRN Processing
		11.4 Step Frequency Waveforms
			11.4.1 Doppler Effects
		11.5 Costas Waveforms
			11.5.1 Costas Waveform Example
		11.6 Closing Comments
		11.7 Exercises
		References
		Appendix 11A: LFM and the sinc2(x) Function
	Chapter 12 Stretch Processing
		12.1 Introduction
		12.2 Stretch Processor Configuration
		12.3 Stretch Processor Operation
		12.4 Stretch Processor SNR
			12.4.1 Matched Filter
			12.4.2 Stretch Processor
		12.5 Practical Implementation Issues
			12.5.1 Stretch Processor Example
		12.6 Range-rate Effects
			12.6.1 Expanded Transmit and Receive Signal Models
			12.6.2 Stretch Processor Modification
			12.6.3 Slope Mismatch Effects
				12.6.3.1 Slope Mismatch Case 1: (hṘ = ( – no compensation
					Slope Mismatch Example 1
					Slope Mismatch Example 2
				12.6.3.2 Slope Mismatch Case 2: (hṘ = (r – Perfect Compensation
				12.6.3.3 Slope Mismatch Case 3: (hṘ = ( (1(2Ṙh/c)2 – Partial Compensation
			12.6.4 Range-rate Effects on Range Bias
				12.6.4.1 Case 1 – (hṘ = (
				12.6.4.2 Case 2: Imperfect Estimate of Ṙ
			12.6.5 Doppler Frequency Measurement Effects
			12.6.6 A Matched Filter Perspective
		12.7 Exercises
		References
	Chapter 13 Phased Array Antenna Basics
		13.1 Introduction
		13.2 Two-Element Array Antenna
			13.2.1 Transmit Perspective
			13.2.2 Receive Perspective
		13.3 N-Element Linear Array
		13.4 Directive Gain Pattern (Antenna Pattern)
		13.5  Beamwidth, Sidelobes, and Amplitude Weighting
		13.6 Steering
			13.6.1 Time-delay Steering
			13.6.2 Phase Steering
			13.6.3 Phase Shifters
		13.7 Element Pattern
		13.8 Array Factor Relation to the Discrete-time Fourier Transform
		13.9 Planar Arrays
			13.9.1 Weights for Beam Steering
			13.9.2 Array Shapes and Element Locations (Element Packing)
			13.9.3 Feeds
			13.9.4 Amplitude Weighting
			13.9.5 Computing Antenna Patterns for Planar Arrays
				13.9.5.1 Planar Arrays with Rectangular Packing
				13.9.5.2 Planar Arrays with Triangular Packing
			13.9.6 Directive Gain Pattern
			13.9.7 Grating Lobes
				13.9.7.1 Grating Lobes in Arrays with Rectangular Packing
				13.9.7.2 Grating Lobes in Arrays with Triangular Packing
		13.10 Polarization
		13.11 Reflector Antennas
		13.12 Other Antenna Parameters
		13.13 Exercises
		References
		Appendix 13A: An Equation for Taylor Weights
		Appendix 13B: Computation of Antenna Patterns
		13B.1 Linear Arrays
		13B.2 Planar Arrays
			13B.2.1 Rectangular Packing
			13B.2.2  Triangular Packing
	Chapter 14 AESA Basics and Related Topics
		14.1 Introduction
		14.2 T/R Module
		14.3 Time-delay Steering and Wideband Waveforms
			14.3.1 Subarray Size, Scan Angle, and Waveform Bandwidth
			14.3.2 Subarray Pattern Distortion Examples
			14.3.3 Array Beam Forming with TDUs
		14.4 Simultaneous Multiple Beams
			14.4.1 Overlapped Subarrays
			14.4.2 Nonuniform Subarray Sizes
			14.4.3 Transmit Array Considerations
		14.5 AESA Noise Figure
			14.5.1 T/R Module Noise Figure
			14.5.2 Subarray Gain and Noise Figure
			14.5.3 Array Gain and Noise Figure
			14.5.4 AESA Noise Figure Example
		14.6 Exercises
		References
		Appendix 14A: Derivation of the matched filter output for an AESA (Equation 14.10)
	Chapter 15 Signal Processors
		15.1 Introduction
		15.2 Signal Processor Structure
		References
	Chapter 16 Signal Processor Analysis
		16.1 Introduction
		16.2 Signal Model Generation
			16.2.1 Signal Model: Time Domain Analysis
			16.2.2 Signal Model: Frequency Domain Analysis
			16.2.3 Relation of PC and PS to the Radar Range Equation
		16.3 Signal Processor Analyses
			16.3.1 Background
		16.4 Exercises
		References
		Appendix 16A: Derivation Signal Processor Input Spectrum
		Appendix 16B: Proof that r(t) is Wide-Sense Cyclostationary
	Chapter 17 Clutter Model
		17.1 Introduction
		17.2 Ground Clutter Model
			17.2.1 Ground Clutter RCS Model
			17.2.2 Ground Clutter Spectrum Model
		17.3 Rain Clutter Model
			17.3.1 Rain Clutter RCS Model
			17.3.2 Rain Clutter Spectral Model
		17.4 Exercises
		References
	Chapter 18 Moving Target Indicator (MTI)
		18.1 Introduction
			18.1.1 MTI Response Normalization
		18.2 MTI Clutter Performance
			18.2.1 Clutter Attenuation
				18.2.1.1 Gaussian Spectrum
				18.2.1.2 Exponential Spectrum
			18.2.2 SCR Improvement
		18.3 Ground Clutter Example
		18.4 Rain Clutter Example
		18.5 Phase Noise
			18.5.1 Higher Order MTI Processors
			18.5.2 Staggered PRIs
			18.5.3 MTI Transients
		18.6 Exercises
		References
	Chapter 19 Digital Pulsed Doppler Processors
		19.1 Introduction
		19.2 Pulsed Doppler Clutter
		19.3 Signal Processor Configuration
		19.4 Digital Signal Processor Analysis Techniques
			19.4.1 Phase Noise and Range Correlation Effects
			19.4.2 ADC Considerations
		19.5 Summary and Rules of Thumb
		19.6 HPRF Pulsed Doppler Processor Example
		19.7 MPRF Pulsed Doppler Processor Example
		19.8 LPRF Pulsed Doppler Signal Processor Example
		19.9 Exercises
		References
		Appendix 19A: Derivation of
		Appendix 19B: FFT Frequency Response
	Chapter 20 Analog Pulsed Doppler Processors
		20.1 Introduction
		20.2 Analog Pulsed Doppler Signal Processor Example
		20.3 Exercises
		References
	Chapter 21 Chaff Analysis
		21.1 Introduction
		21.2 chaff analysis example
		21.3 Exercises
		References
	Chapter 22 Radar Receiver Basics
		22.1 Introduction
		22.2 Single-Conversion Superheterodyne Receiver
		22.3 Dual-Conversion Superheterodyne Receiver
		22.4 Receiver Noise
		22.5 The 1-dB Gain Compression Point
		22.6 Dynamic Range
			22.6.1 Sensitivity
				22.6.1.1 Tangential Sensitivity
			22.6.2 Minimum Detectable and Minimum Discernable Signal
			22.6.3 Intermodulation Distortion
			22.6.4 Required Dynamic Range
		22.7 Cascade Analysis
			22.7.1 Cascade Analysis Conventions
			22.7.2 Procedure
			22.7.3 Power Gain
			22.7.4 Noise Figure and Noise Temperature
			22.7.5 1-dB Compression Point
			22.7.6 Second-Order Intercept
			22.7.7 Third-Order Intercept
		22.8 Digital Receiver
			22.8.1 Bandpass Sampling
			22.8.2 Digital Down conversion
			22.8.3 Practical DDC
			22.8.4 CIC Filter Structure
				22.8.4.1 Basic Integrator
				22.8.4.2 Basic Comb Filter
				22.8.4.3 CIC Filter Frequency Response
				22.8.4.4 Example: CIC Decimation Filter
			22.8.5 Analog-to-Digital Converter
				22.8.5.1 Quantization
				22.8.5.2 Quantization Error
				22.8.5.3 Quantization Noise
				22.8.5.4 ADC Noise Figure
				22.8.5.5 Dither
		22.9 Receiver Configurations
		22.10 Exercises
		References
		Appendix 22A: Digital Down conversion Using Band-pass Sampling
	Chapter 23 Introduction to Synthetic ApertureRadar Signal Processing
		23.2 Background
			23.2.1 Linear Array Theory
			23.2.2 Transition to SAR Theory
		23.1 Introduction
		23.3 Development of SAR-Specific Equations
		23.4 Types of SAR
			23.4.1 Theoretical Limits for Strip Map SAR
			23.4.2 Effects of Imaged Area Width on Strip Map SAR Resolution
		23.5 SAR Signal Characterization
			23.5.1 Derivation of the SAR Signal
			23.5.2 Examination of the Phase of the SAR Signal
				23.5.2.1 Linear Phase, or Constant Frequency, Term
				23.5.2.2 Quadratic Phase, or LFM, Term
			23.5.3 Extracting the Cross-Range Information
		23.6 Practical Implementation
			23.6.1 A Discrete-Time Model
			23.6.2 Other Considerations
		23.7 An Algorithm for Creating a Cross-Range Image
		23.8 Example 1 - Generation of a Cross-range SAR Image
		23.9 Down-Range and Cross-Range Imaging
			23.9.1 Signal Definition
				23.9.1.1 Removal of the Carrier and Gross Doppler
				23.9.1.2 Single-Pulse Matched Filter
				23.9.1.3 Generation of the Sampled Signal
			23.9.2 Preliminary Processing Considerations
				23.9.2.1 Range Cell Migration Correction
				23.9.2.2 RCMC Algorithm
			23.9.3 Quadratic Phase Removal and Image Formation
		23.10 Algorithm for Creating a Cross- and Down-Range Image
		23.11 Example 2: Cross- and Down-range SAR Image
		23.12 An Image-Sharpening Refinement
		23.13 Closing Remarks
		23.14 Exercises
		References
	Chapter 24 Introduction to Space-Time Adaptive Processing
		24.1 Introduction
		24.2 Spatial Processing
			24.2.1 Signal Plus Noise
			24.2.2 Signal Plus Noise and Interference
			24.2.3 Example 1: Spatial Processing
		24.3 temporal processing
			24.3.1 Signal
			24.3.2 Noise
			24.3.3 Interference
			24.3.4 Doppler Processor
			24.3.5 Example 2: Temporal Processing
		24.4 Adaptivity Issues
		24.5 Space-Time Processing
			24.5.1 Example 3: Space-Time Processing
			24.5.2 Example 4: Airborne Radar Clutter Example
		24.6 Adaptivity Again
		24.7 Practical Considerations
		24.8 Exercises
		References
	Chapter 25 Sidelobe Cancellation
		25.1 Introduction
		25.2 Interference Canceller
		25.3 Interference Cancellation Algorithm
			25.3.1 Single Interference Signal
			25.3.2 Simple Canceler Example
			25.3.3 Multiple Interference Sources
		25.4 SLC Implementation Considerations
			25.4.1 Form of vm(t) and va(t)
			25.4.2 Properties of vs(t), vI(t), nm(t), and nan(t)
			25.4.3 Scaling of Powers
			25.4.4 Two Auxiliary Channel Open-Loop SLC Example
			25.4.5 Performance Measures
			25.4.6 Practical Implementation Considerations
			25.4.7 Two Auxiliary Channel Open-Loop SLC Example with SMI
		25.5 Howells-Applebaum Sidelobe Canceller
			25.5.1 Howells-Applebaum Implementation
			25.5.2 IF Implementation
			25.5.3 Single-Loop Howells-Applebaum SLC Example
			25.5.4 Two-Loop Howells-Applebaum SLC Example
		25.6 Sidelobe Blanker
		25.7 Exercises
		References
		Appendix 25A: Derivation of  (25.40)
	Chapter 26 Advances in Radar
		26.1 Introduction
		26.2 MIMO Radar
		26.3 Cognitive Radar
		26.4 Other Advancements in Radar Theory
		26.5 Hardware Advancements
		26.6 Conclusion
		References
	Appendix A Data Windowing Functions
	Acronyms and Abbreviations
	About the Authors
	Index