Radar Systems Analysis and Design Using MatLab

by admin in on June 5, 2019

Numerous books have been written on Radar Systems and Radar Applications. A limited set of these books provides companion software. There is need for a comprehensive reference book that can provide the reader with hands-on-like experience. The ideal radar book, in my opinion, should serve as a conclusive, detailed, and useful reference for working engineers as well as a textbook for students learning radar systems analysis and design. This book must assume few prerequisites and must stand on its own as a complete presentation of the subject. Examples and exercise problems must be included. User friendly software that demonstrates the theory needs to be included. This software should be reconfigurable to allow different users to vary the inputs in order to better analyze their relevant and unique requirements, and enhance understanding of the subject.

Radar Systems Analysis and Design Using MATLAB® concentrates on radar fundamentals, principles, and rigorous mathematical derivations. It also provides the user with a comprehensive set of MATLAB1 15.0 software that can be used for radar analysis and/or radar system design. All programs will accept user inputs or execute using the default set of parameters. This book will serve as a valuable reference to students and radar engineers in analyzing and understanding the many issues associated with radar systems analysis and design. It is written at the graduate level. Each chapter provides all the necessary mathematical and analytical coverage required for good understanding of radar theory.

Additionally, dedicated MATLAB functions/programs have been developed for each chapter to further enhance the understanding of the theory, and provide a source for establishing radar system design requirements. This
book includes over 1190 equations and over 230 illustrations and plots. There are over 200 examples and end-of-chapter problems. A solutions manual will be made available to professors using the book as a text. The philosophy behind Radar Systems Analysis and Design Using MATLAB is that radar systems should not be complicated to understand nor difficult to analyze and design.

All MATLAB programs and functions provided in this book can be downloaded from the CRC Press Web site (www.crcpress.com). For this purpose, create the following directory in your C-drive: C:\RSA. Copy all programs into this directory. The path tree should be as in Fig. F.1 in Appendix F. Users can execute a certain function/program GUI by typing: file_name_driver, where ile names are as indicated in Appendix F. The MATLAB functions and programs
developed in this book include all forms of the radar equation: pulse compression, stretch processing, matched filter, probability of detection calculations with all Swerling models, High Range Resolution (HRR), stepped frequency waveform analysis, ghk tracking filter, Kalman filter, phased array antennas, and many more.
The first part of Chapter 1 describes the most common terms used in radar systems, such as range, range resolution, Doppler frequency, and coherency.

The second part of this chapter develops the radar range equation in many of its forms. This presentation includes the low PRF, high PRF, search, bistatic radar, and radar equation with jamming. Radar losses are briefly addressed in this chapter. Chapter 2 discusses the Radar Cross Section (RCS). RCS dependency on aspect angle, frequency, and polarization are discussed. Target scattering matrix is developed. RCS formulas for many simple objects are presented. Complex object RCS is discussed, and target fluctuation models are
introduced. Continuous wave radars and pulsed radars are discussed in Chapter 3. The CW radar equation is derived in this chapter. Resolving range and Doppler ambiguities is also discussed in detail.

Chapter 4 is intended to provide an overview of the radar probability of detection calculations and related topics. Detection of fluctuating targets including Swerling I, II, III, and IV models is presented and analyzed. Coherent and non-coherent integrations are also introduced. Cumulative probability of detecting analysis is in this chapter. Chapter 5 reviews radar waveforms, including CW, pulsed, and LFM. High Range Resolution (HRR) waveforms and stepped frequency waveforms are also analyzed.

The concept of the matched filter, and the radar ambiguity function constitute the topics of Chapter 6. Detailed derivations of many major results are presented in this chapter, including the coherent pulse train ambiguity function. Pulse compression is in Chapter 7. Analog and digital pulse compressions are also discussed in detail. This includes fast convolution and stretch processors. Binary phase codes and frequency codes are discussed.

Chapter 8 presents the phenomenology of radar wave propagation. Topics like multipath, refraction, diffraction, divergence, and atmospheric attenuation are included. Chapter 9 contains the concepts of clutter and Moving Target Indicator (MTI). Surface and volume clutter are defined and the relevant radar equations are derived. Delay line cancelers implementation to mitigate the effects of clutter is analyzed.

Chapter 10 has a brief discussion of radar antennas. The discussion includes linear and planar phased arrays. Conventional beamforming is in this chapter. Chapter 11 discusses target tracking radar systems. The first part of this chapter covers the subject of single target tracking. Topics such as sequential lobing, conical scan, monopulse, and range tracking are discussed in detail. The second part of this chapter introduces multiple target tracking techniques.
Fixed gain tracking filters such as the and the filters are presented in detail. The concept of the Kalman filter is introduced. Special cases of the Kalman filter are analyzed in depth. Synthetic Aperture Radar (SAR) is the subject of Chapter 12. The topics of this chapter include: SAR signal processing, SAR design considerations, and the SAR radar equation. Arrays operated in sequential mode are discussed in this chapter. Chapter 13 presents an overview of signal processing. Finally, six appendices present discussion on the following: noise figure, decibel arithmetic, tables of the Fourier transform and Z-transform pairs, common probability density functions, and the MATLAB program and function name list.

Table of Contents

Chapter 1
Radar Fundamentals
1.1. Radar Classifications
1.2. Range
MATLAB Function “pulse_train.m”
1.3. Range Resolution
MATLAB Function “range_resolution.m”
1.4. Doppler Frequency
MATLAB Function “doppler_freq.m”
1.5. Coherence
1.6. The Radar Equation
MATLAB Function “radar_eq.m”
1.6.1. Low PRF Radar Equation
MATLAB Function “lprf_req.m”
1.6.2. High PRF Radar Equation
MATLAB Function “hprf_req.m”
1.6.3. Surveillance Radar Equation
MATLAB Function “power_aperture_eq.m”
1.6.4. Radar Equation with Jamming
Self-Screening Jammers (SSJ)
MATLAB Program “ssj_req.m”
Stand-Off Jammers (SOJ)
MATLAB Program “soj_req.m”
Range Reduction Factor
MATLAB Function “range_red_fac.m”
1.6.5. Bistatic Radar Equation
1.7. Radar Losses
1.7.1. Transmit and Receive Losses
1.7.2. Antenna Pattern Loss and Scan Loss
1.7.3. Atmospheric Loss
1.7.4. Collapsing Loss
1.7.5. Processing Losses
1.7.6. Other Losses
1.8. MATLAB Program and Function Listings
Chapter 2
Radar Cross Section (RCS)
2.1. RCS Definition
2.2. RCS Prediction Methods
2.3. RCS Dependency on Aspect Angle and Frequency
MATLAB Function “rcs_aspect.m”
MATLAB Function “rcs-frequency.m”
2.4. RCS Dependency on Polarization
2.4.1. Polarization
2.4.2. Target Scattering Matrix
2.5. RCS of Simple Objects
2.5.1. Sphere
2.5.2. Ellipsoid
MATLAB Function “rcs_ellipsoid.m”
2.5.3. Circular Flat Plate
MATLAB Function “rcs_circ_plate.m”
2.5.4. Truncated Cone (Frustum)
MATLAB Function “rcs_frustum.m”
2.5.5. Cylinder
MATLAB Function “rcs_cylinder.m”
2.5.6. Rectangular Flat Plate
MATLAB Function “rcs_rect_plate.m”
2.5.7. Triangular Flat Plate
MATLAB Function “rcs_isosceles.m”
2.6. RCS of Complex Objects
2.7. RCS Fluctuations and Statistical Models
2.7.1. RCS Statistical Models – Scintillation Models
Chi-Square of Degree 2m
Swerling I and II (Chi-Square of Degree 2)
Swerling III and IV (Chi-Square of Degree 4)
2.8. MATLAB Program/Function Listings
Chapter 3
Continuous Wave and Pulsed Radars
3.1. Functional Block Diagram
3.2. CW Radar Equation
3.3. Frequency Modulation
3.4. Linear FM (LFM) CW Radar
3.5. Multiple Frequency CW Radar
3.6. Pulsed Radar
3.7. Range and Doppler Ambiguities
3.8. Resolving Range Ambiguity
3.9. Resolving Doppler Ambiguity
3.10. MATLAB Program “range_calc.m”
Chapter 4
Radar Detection
4.1. Detection in the Presence of Noise
MATLAB Function “que_func.m”
4.2. Probability of False Alarm
4.3. Probability of Detection
MATLAB Function “marcumsq.m”
4.4. Pulse Integration
4.4.1. Coherent Integration
4.4.2. Non-Coherent Integration
MATLAB Function “improv_fac.m”
4.5. Detection of Fluctuating Targets
4.5.1. Detection Probability Density Function
4.5.2. Threshold Selection
MATLAB Function “incomplete_gamma.m”
MATLAB Function “threshold.m”
4.6. Probability of Detection Calculation
4.6.1. Detection of Swerling V Targets
MATLAB Function “pd_swerling5.m”
4.6.2. Detection of Swerling I Targets
MATLAB Function “pd_swerling1.m”
4.6.3. Detection of Swerling II Targets
MATLAB Function “pd_swerling2.m”
4.6.4. Detection of Swerling III Targets
MATLAB Function “pd_swerling3.m”
4.6.5. Detection of Swerling IV Targets
MATLAB Function “pd_swerling4.m”
4.7. Cumulative Probability of Detection
4.8. Solving the Radar Equation
4.9. Constant False Alarm Rate (CFAR)
4.9.1. Cell-Averaging CFAR (Single Pulse)
4.9.2. Cell-Averaging CFAR with
Non-Coherent Integration
4.10. MATLAB Function and Program Listings
Chapter 5
Radar Waveforms Analysis
5.1. Low Pass, Band Pass Signals and Quadrature
5.2. CW and Pulsed Waveforms
5.3. Linear Frequency Modulation Waveforms
5.4. High Range Resolution
5.5. Stepped Frequency Waveforms
5.5.1. Range Resolution and Range Ambiguity in SWF
MATLAB Function “hrr_profile.m”
5.5.2. Effect of Target Velocity
5.6. MATLAB Listings
Chapter 6
Matched Filter and the Radar Ambiguity
6.1. The Matched Filter SNR
6.2. The Replica
6.3. Matched Filter Response to LFM Waveforms
6.4. The Radar Ambiguity Function
6.5. Examples of the Ambiguity Function
6.5.1. Single Pulse Ambiguity Function
MATLAB Function “single_pulse_ambg.m”
6.5.2. LFM Ambiguity Function
MATLAB Function “lfm_ambg.m”
6.5.3. Coherent Pulse Train Ambiguity Function
MATLAB Function “train_ambg.m”
6.6. Ambiguity Diagram Contours
6.7. MATLAB Listings
Chapter 7
Pulse Compression
7.1. Time-Bandwidth Product
7.2. Radar Equation with Pulse Compression
7.3. Analog Pulse Compression
7.3.1. Correlation Processor
MATLAB Function “matched_filter.m”
7.3.2. Stretch Processor
MATLAB Function “stretch.m”
7.3.3. Distortion Due to Target Velocity
7.3.4. Range Doppler Coupling
7.4. Digital Pulse Compression
7.4.1. Frequency Coding (Costas Codes)
7.4.2. Binary Phase Codes
7.4.3. Frank Codes
7.4.4. Pseudo-Random (PRN) Codes
7.5. MATLAB Listings
Chapter 8
Radar Wave Propagation
8.1. Earth Atmosphere
8.2. Refraction
8.3. Ground Reflection
8.3.1. Smooth Surface Reflection Coefficient
MATLAB Function “ref_coef.m”
8.3.2. Divergence
8.3.3. Rough Surface Reflection
8.4. The Pattern Propagation Factor
8.4.1. Flat Earth
8.4.2. Spherical Earth
8.5. Diffraction
8.6. Atmospheric Attenuation
8.7. MATLAB Program “ref_coef.m”
Chapter 9
Clutter and Moving Target Indicator (MTI)
9.1. Clutter Definition
9.2. Surface Clutter
9.2.1. Radar Equation for Area Clutter
9.3. Volume Clutter
9.3.1. Radar Equation for Volume Clutter
9.4. Clutter Statistical Models
9.5. Clutter Spectrum
9.6. Moving Target Indicator (MTI)
9.7. Single Delay Line Canceler
MATLAB Function “single_canceler.m”
9.8. Double Delay Line Canceler
MATLAB Function “double_canceler.m”
9.9. Delay Lines with Feedback (Recursive Filters)
9.10. PRF Staggering
9.11. MTI Improvement Factor
9.12. Subclutter Visibility (SCV)
9.13. Delay Line Cancelers with Optimal Weights
9.14. MATLAB Program/Function Listings
Chapter 10
Radar Antennas
10.1. Directivity, Power Gain, and Effective Aperture
10.2. Near and Far Fields
10.3. Circular Dish Antenna Pattern
MATLAB Function “circ_aperture.m”
10.4. Array Antennas
10.4.1. Linear Array Antennas
MATLAB Function “linear_array.m”
10.5. Array Tapering
10.6. Computation of the Radiation Pattern via the DFT
10.7. Array Pattern for Rectangular Planar Array
MATLAB Function “rect_array.m”
10.8. Conventional Beamforming
10.9. MATLAB Programs and Functions
Chapter 11
Target Tracking
Part I: Single Target Tracking
11.1. Angle Tracking
11.1.1. Sequential Lobing
11.1.2. Conical Scan
11.2. Amplitude Comparison Monopulse
MATLAB Function “mono_pulse.m”
11.3. Phase Comparison Monopulse
11.4. Range Tracking
Part II: Multiple Target Tracking
11.5. Track-While-Scan (TWS)
11.6. State Variable Representation of an LTI System
11.7. The LTI System of Interest
11.8. Fixed-Gain Tracking Filters
11.8.1. The Filter
11.8.2. The Filter
MATLAB Function “ghk_tracker.m”
11.9. The Kalman Filter
11.9.1. The Singer -Kalman Filter
11.9.2. Relationship between Kalman and
MATLAB Function “kalman_filter.m”
11.10. MATLAB Programs and Functions
Chapter 12
Synthetic Aperture Radar
12.1. Introduction
12.2. Real Versus Synthetic Arrays
12.3. Side Looking SAR Geometry
12.4. SAR Design Considerations
12.5. SAR Radar Equation
12.6. SAR Signal Processing
12.7. Side Looking SAR Doppler Processing
12.8. SAR Imaging Using Doppler Processing
12.9. Range Walk
12.10. Case Study
12.11. Arrays in Sequential Mode Operation
12.11.1. Linear Arrays
12.11.2. Rectangular Arrays
12.12. MATLAB Programs
Chapter 13
Signal Processing
13.1. Signal and System Classifications
13.2. The Fourier Transform
13.3. The Fourier Series
13.4. Convolution and Correlation Integrals
13.5. Energy and Power Spectrum Densities
13.6. Random Variables
13.7. Multivariate Gaussian Distribution
13.8. Random Processes
13.9. Sampling Theorem
13.10. The Z-Transform
13.11. The Discrete Fourier Transform
13.12. Discrete Power Spectrum
13.13. Windowing Techniques

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