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Radar Systems

Analysis and Design

Using

MATLAB

Library of Congress Cataloging-in-Publication Data

Mahafza, Bassem R. Radar systems & analysis and design using Matlab p. cm. Includes bibliographical references and index. ISBN 1-58488-182-8 (alk. paper)

1. Radar. 2. System analysis—Data processing. 3. MATLAB. I. Title.

TK6575 .M27 2000 521.38484—dc21 00- CIP

This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use.

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No claim to original U.S. Government works International Standard Book Number 1-58488-182- Library of Congress Card Number 00- Printed in the United States of America 4 5 6 7 8 9 0 Printed on acid-free paper

Preface

Numerous books have been written on Radar Systems and Radar Applica- tions. 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 presen- tation of the subject. Examples and exercise problems must be included. User friendly software that demonstrates the theory needs to be included. This soft- ware 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 pro-

vides the user with a comprehensive set of MATLAB 1 5.0 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 under- standing the many issues associated with radar systems analysis and design. It is written at the graduate level. Each chapter provides all the necessary mathe- matical and analytical coverage required for good understanding of radar the- ory. 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 sys- tems should not be complicated to understand nor difficult to analyze and design.

All MATLAB programs and functions provided in this book can be down- loaded 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

1. All MATLAB functions and programs provided in this book were developed using MATLAB 5.0 - R11 with the Signal Processing Toolbox, on a PC with Windows 98 operating system.

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 Kal- man 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 arith- metic, tables of the Fourier transform and Z-transform pairs, common proba- bility density functions, and the MATLAB program and function name list.

MATLAB is a registered trademark of The MathWorks, Inc. For product information, please contact: The MathWorks, Inc. 3 Apple Hill Drive Natick, MA 01760-2098 USA Tel: 508-647- Fax: 508-647- E-mail: info@mathworks.com Web: www.mathworks.com

Bassem R. Mahafza Huntsville, Alabama January, 2000

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Acknowledgment

I would like to acknowledge the following for help, encouragement, and support during the preparation of this book. First, I thank God for giving me the endurance and perseverance to complete this work. I could not have com- pleted this work without the continuous support of my wife and four sons. The support and encouragement of all my family members and friends are appreci- ated. Special thanks to Dr. Andrew Ventre, Dr. Michael Dorsett, Mr. Edward Shamsi, and Mr. Skip Tornquist for reviewing and correcting different parts of the manuscript. Finally, I would like to thank Mr. Frank J. Collazo, the man- agement, and the family of professionals at COLSA Corporation for their support.

Table of Contents

Preface

Acknowledgment

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 Problems

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 Problems

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 Problems

Chapter 5

Radar Waveforms Analysis

5.1. Low Pass, Band Pass Signals and Quadrature Components 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 Problems

Chapter 6

Matched Filter and the Radar Ambiguity

Function

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 Problems

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 Problems

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” Problems

Chapter 9

Clutter and Moving Target Indicator (MTI)

9.1. Clutter Definition 9.2. Surface Clutter 9.2.1. Radar Equation for Area Clutter

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 Filters MATLAB Function “kalman_filter.m” 11.10. MATLAB Programs and Functions Problems

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 Problems

Chapter 13

Signal Processing

13.1. Signal and System Classifications

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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 Problems

Appendix A

Noise Figure

Appendix B

Decibel Arithmetic

Appendix C

Fourier Transform Table

Appendix D

Some Common Probability Densities

Chi-Square with N degrees of freedom Exponential Gaussian Laplace Log-Normal Rayleigh Uniform Weibull

Appendix E

Z - Transform Table

Appendix F

MATLAB Program and Function Name List

Bibliography

Continuous Wave (CW) or Pulsed Radars (PR). CW radars are those that con- tinuously emit electromagnetic energy, and use separate transmit and receive antennas. Unmodulated CW radars can accurately measure target radial veloc- ity (Doppler shift) and angular position. Target range information cannot be extracted without utilizing some form of modulation. The primary use of unmodulated CW radars is in target velocity search and track, and in missile guidance. Pulsed radars use a train of pulsed waveforms (mainly with modula- tion). In this category, radar systems can be classified on the basis of the Pulse Repetition Frequency (PRF), as low PRF, medium PRF, and high PRF radars. Low PRF radars are primarily used for ranging where target velocity (Doppler shift) is not of interest. High PRF radars are mainly used to measure target velocity. Continuous wave as well as pulsed radars can measure both target range and radial velocity by utilizing different modulation schemes.

Table 1.1 has the radar classifications based on the operating frequency.

High Frequency (HF) radars utilize the electromagnetic waves’ reflection off the ionosphere to detect targets beyond the horizon. Some examples include the United States Over The Horizon Backscatter (U.S. OTH/B) radar which operates in the frequency range of , the U.S. Navy Relocatable Over The Horizon Radar (ROTHR), see Fig. 1.1, and the Russian Woodpecker radar. Very High Frequency (VHF) and Ultra High Frequency (UHF) bands are used for very long range Early Warning Radars (EWR). Some examples include the Ballistic Missile Early Warning System (BMEWS) search and track monopulse radar which operates at (Fig. 1.2), the Perimeter and Acquisition Radar (PAR) which is a very long range multifunction phased

TABLE 1.1. Radar frequency bands.

Letter designation Frequency (GHz)

New band designation (GHz) HF 0.003 - 0.03 A VHF 0.03 - 0.3 A<0.25; B>0. UHF 0.3 - 1.0 B<0.5; C>0. L-band 1.0 - 2.0 D S-band 2.0 - 4.0 E<3.0; F>3. C-band 4.0 - 8.0 G<6.0; H>6. X-band 8.0 - 12.5 I<10.0; J>10. Ku-band 12.5 - 18.0 J K-band 18.0 - 26.5 J<20.0; K>20. Ka-band 26.5 - 40.0 K MMW Normally >34.0 L<60.0; M>60.

5 – 28 MHZ

245 MHz

array radar, and the early warning PAVE PAWS multifunction UHF phased array radar. Because of the very large wavelength and the sensitivity require- ments for very long range measurements, large apertures are needed in such radar systems.

Figure 1.1. U. S. Navy Over The Horizon Radar. Photograph obtained via the Internet.

Figure 1.2. Fylingdales BMEWS - United Kingdom. Photograph obtained via the Internet.