Simulations for Radar Systems Design

Transcription

1 Simulations for Radar Systems Design Bassem R. Mahafza, Ph.D. Decibel Research, Inc. Huntsville, Alabama Atef Z. Elsherbeni Professor Electrical Engineering Department The University of Mississippi Oxford, Mississippi CHAPMAN & HALL/CRC A CRC Press Company Boca Raton London New York Washington, D.C.

2 Library of Congress Cataloging-in-Publication Data Mahafza, Bassem R. MATLAB simulations for radar systems design / Bassem R. Mahafza, Atef Z. Elsherbeni p. cm. Includes bibliographical references and index. ISBN (alk. paper) 1. Radar Computer simulation. 2. Radar Equipment and supplies Design and construction Data processing. 3. MATLAB. I. Elsherbeni, Atef Z. II. Title TK6585.M dc 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. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage or retrieval system, without prior permission in writing from the publisher. The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from CRC Press LLC for such copying. Direct all inquiries to CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation, without intent to infringe. Visit the CRC Press Web site at No claim to original U.S. Government works International Standard Book Number Library of Congress Catalog Number Printed in the United States of America Printed on acid-free paper

3 To: My wife and four sons; Wayne and Shirley; and in the memory of my parents Bassem R. Mahafza To: My wife and children; my mother; and in the memory of my father Atef Z. Elsherbeni

4 Preface The emphasis of MATLAB Simulations for Radar Systems Design is on radar systems design. However, a strong presentation of the theory is provided so that the reader will be equipped with the necessary background to perform radar systems analysis. The organization of this book is intended to teach a conceptual design process of radars and related trade-off analysis and calculations. It is intended to serve as an engineering reference for radar engineers working in the field of radar systems. The MATLAB 1 code provided in this book is designed to provide the user with hands-on experience in radar systems, analysis and design. A radar design case study is introduced in Chapter 1 and carried throughout the text, where the authors view of how to design this radar is detailed and analyzed. Trade off analyses and calculations are performed. Additionally, several mini design case studies are scattered throughout the book. MATLAB Simulations for Radar Systems Design is divided into two parts: Part I provides a comprehensive description of radar systems, analyses and design. A design case study, which is carried throughout the text, is introduced in Chapter 1. In each chapter the authors view of how to design the case-study radar is presented based on the theory covered up to that point in the book. As the material coverage progresses through the book, and new theory is discussed, the design case-study requirements are changed and/or updated, and of course the design level of complexity is also increased. This design process is supported by a comprehensive set of MATLAB 6 simulations developed for this purpose. This part will serve as a valuable tool to students and radar engineers in helping them understand radar systems, design process. This includes 1) learning how to go about selecting different radar parameters to meet the design requirements; 2) performing detailed trade-off analysis in the context of radar sizing, modes of operations, frequency selection, waveforms and signal processing; 3) establishing and developing loss and error budgets associated with the design; and 4) generating an in-depth understanding of radar operations and design philosophy. Additionally, Part I includes several mini design case studies pertinent to different chapters in order to help enhance understanding of radar design in the context of the material presented in different chapters. Part II includes few chapters that cover specialized radar topics, some of which is authored and/or coauthored by other experts in the field. The material 1. MATLAB is a registered trademark of the The MathWorks, Inc. For product information, please contact: The MathWorks, Inc., 3 Apple Hill Drive, Natick, MA USA. Web:

5 included in Part II is intended to further enhance the understanding of radar system analysis by providing detailed and comprehensive coverage of these radar related topics. For this purpose, MATLAB 6 code has also been developed and made available. All MATLAB programs and functions provided in this book can be downloaded from the CRC Press Web site ( For this purpose, follow this procedure: 1) from your Web browser type 2) click on Electronic Products, 3) click on Download & Updates, and finally 4) follow instructions of how to download a certain set of code off that Web page. Furthermore, this MATLAB code can also be downloaded from The MathWorks Web site by following these steps: 1) from your Web browser type: 2) place the curser on Companion Software for Books and click on Communications. 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, clutter calculations, radar ambiguity functions, ECM, chaff, and many more. Chapter 1 describes the most common terms used in radar systems, such as range, range resolution, and Doppler frequency. This chapter develops the radar range equation. Finally, a radar design case study entitled MyRadar Design Case Study is introduced. Chapter 2 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 integration are also introduced. Cumulative probability of detection analysis is in this chapter. Visit 2 of the design case study MyRadar is introduced. Chapter 3 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 (MF) is introduced and analyzed. Chapter 4 presents in detail the principles associated with the radar ambiguity function. This includes the ambiguity function for single pulse, Linear Frequency Modulated pulses, train of unmodulated pulses, Barker codes, and PRN codes. Pulse compression is introduced in Chapter 5. Both the MF and the stretch processors are analyzed. Chapter 6 contains treatment of the concepts of clutter. This includes both surface and volume clutter. Chapter 7 presents clutter mitigation using Moving Target Indicator (MTI). Delay line cancelers implementation to mitigate the effects of clutter is analyzed. Chapter 8 presents detailed analysis of Phased Arrays. Linear arrays are investigated and detailed and MATLAB code is developed to calculate and plot

6 the associated array patterns. Planar arrays, with various grid configurations, are also presented. Chapter 9 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 αβ and the αβγ filters are presented in detail. The concept of the Kalman filter is introduced. Special cases of the Kalman filter are analyzed in depth. Chapter 10 is coauthored with Mr. J. Michael Madewell from the US Army Space and Missile Defense Command, in Huntsville, Alabama. This chapter presents an overview of Electronic Counter Measures (ECM) techniques. Topics such as self screening and stand off jammers are presented. Radar chaff is also analyzed and a chaff mitigation technique for Ballistic Missile Defense (BMD) is introduced. Chapter 11 is concerned with the Radar Cross Section (RCS). RCS dependency on aspect angle, frequency, and polarization is discussed. The target scattering matrix is developed. RCS formulas for many simple objects are presented. Complex object RCS is discussed, and target fluctuation models are introduced. Chapter 12 is coauthored with Dr. Brian Smith from the US Army Aviation and Missile Command (AMCOM), Redstone Arsenal in Alabama. This chapter presents the topic of Tactical Synthetic Aperture Radar (SAR). The topics of this chapter include: SAR signal processing, SAR design considerations, and the SAR radar equation. Finally Chapter 13 presents an overview of signal processing. Using the material presented in this book and the MATLAB code designed by the authors by any entity or person is strictly at will. The authors and the publisher are neither liable nor responsible for any material or non-material losses, loss of wages, personal or property damages of any kind, or for any other type of damages of any and all types that may be incurred by using this book. Bassem R. Mahafza Huntsville, Alabama July, 2003 Atef Z. Elsherbeni Oxford, Mississippi July, 2003

7 Acknowledgment The authors first would like to thank God for giving us the endurance and perseverance to complete this work. Many thanks are due to our families who have given up and sacrificed many hours in order to allow us to complete this book. The authors would like to also thank all of our colleagues and friends for their support during the preparation of this book. Special thanks are due to Brian Smith, James Michael Madewell, Patrick Barker, David Hall, Mohamed Al-Sharkawy, and Matthew Inman who have coauthored and/or reviewed some of the material in this reference book.

8 Table of Contents Preface Acknowledgment PART I Chapter 1 Introduction to Radar Basics 1.1. Radar Classifications 1.2. Range 1.3. Range Resolution 1.4. Doppler Frequency 1.5. The Radar Equation Radar Reference Range 1.6. Search (Surveillance) Mini Design Case Study Pulse Integration Coherent Integration Non-Coherent Integration Detection Range with Pulse Integration Mini Design Case Study Radar Losses Transmit and Receive Losses Antenna Pattern Loss and Scan Loss Atmospheric Loss Collapsing Loss Processing Losses Other Losses 1.9. MyRadar Design Case Study - Visit 1

9 1.9.1 Authors and Publisher Disclaimer Problem Statement A Design A Design Alternative MATLAB Program and Function Listings Listing 1.1. Function radar_eq.m Listing 1.2. Program fig1_12.m Listing 1.3. Program fig1_13.m Listing 1.4. Program ref_snr.m Listing 1.5. Function power_aperture.m Listing 1.6. Program fig1_16.m Listing 1.7. Program casestudy1_1.m Listing 1.8. Program fig1_19.m Listing 1.9. Program fig1_21.m Listing Function pulse_integration.m Listing Program myradarvisit1_1.m Listing Program fig1_27.m Appendix 1A Pulsed Radar Appendix 1B Noise Figure 1A.1. Introduction 1A.2. Range and Doppler Ambiguities 1A.3. Resolving Range Ambiguity 1A.4. Resolving Doppler Ambiguity Chapter 2 Radar Detection 2.1. Detection in the Presence of Noise 2.2. Probability of False Alarm 2.3. Probability of Detection 2.4. Pulse Integration Coherent Integration Non-Coherent Integration Mini Design Case Study Detection of Fluctuating Targets Threshold Selection

10 2.6. Probability of Detection Calculation Detection of Swerling V Targets Detection of Swerling I Targets Detection of Swerling II Targets Detection of Swerling III Targets Detection of Swerling IV Targets 2.7. The Radar Equation Revisited 2.8. Cumulative Probability of Detection Mini Design Case Study Constant False Alarm Rate (CFAR) Cell-Averaging CFAR (Single Pulse) Cell-Averaging CFAR with Non-Coherent Integration MyRadar Design Case Study - Visit Problem Statement A Design Single Pulse (per Frame) Design Option Non-Coherent Integration Design Option MATLAB Program and Function Listings Listing 2.1. Program fig2_2.m Listing 2.2. Function que_func.m Listing 2.3. Program fig2_3.m Listing 2.4. Function marcumsq.m Listing 2.5. Program prob_snr1.m Listing 2.6. Program fig2_6a.m Listing 2.7. Function improv_fac.m Listing 2.8 Program fig2_6b.m Listing 2.9. Function incomplete_gamma.m Listing Function factor.m Listing Program fig2_7.m Listing Function threshold.m Listing Program fig2_8.m Listing Function pd_swerling5.m Listing Program fig2_9.m Listing Function pd_swerling1.m Listing Program fig2_10.m Listing Program fig2_11ab.m Listing Function pd_swerling2.m Listing Program fig2_12.m Listing Function pd_swerling3.m Listing Program fig2_13.m Listing 2.23 Function pd_swerling4.m Listing Program fig2_14.m

11 Listing Function fluct_loss.m Listing Program fig2_16.m Listing Program myradar_visit2_1.m Listing Program myradar_visit2_2.m Listing Program fig2_21.m Chapter 3 Radar Waveforms 3.1. Low Pass, Band Pass Signals and Quadrature Components 3.2. The Analytic Signal 3.3. CW and Pulsed Waveforms 3.4. Linear Frequency Modulation Waveforms 3.5. High Range Resolution 3.6. Stepped Frequency Waveforms Range Resolution and Range Ambiguity in SWF Effect of Target Velocity 3.7. The Matched Filter 3.8. The Replica 3.9. Matched Filter Response to LFM Waveforms Waveform Resolution and Ambiguity Range Resolution Doppler Resolution Combined Range and Doppler Resolution Myradar Design Case Study - Visit Problem Statement A Design MATLAB Program and Function Listings Listing 3.1. Program fig3_7.m Listing 3.2. Program fig3_8.m Listing 3.3. Function hrr_profile.m Listing 3.4. Program fig3_17.m Chapter 4 The Radar Ambiguity Function 4.1. Introduction 4.2. Examples of the Ambiguity Function Single Pulse Ambiguity Function LFM Ambiguity Function

12 Coherent Pulse Train Ambiguity Function 4.3. Ambiguity Diagram Contours 4.4. Digital Coded Waveforms Frequency Coding (Costas Codes) Binary Phase Codes Pseudo-Random (PRN) Codes 4.5. MyRadar Design Case Study - Visit Problem Statement A Design 4.6. MATLAB Program and Function Listings Listing 4.1. Function single_pulse_ambg.m Listing 4.2. Program fig4_2.m Listing 4.3. Program fig4_4.m Listing 4.4. Function lfm_ambg.m Listing 4.5. Program fig4_5.m Listing 4.6. Program fig4_6.m Listing 4.7. Function train_ambg.m Listing 4.8. Program fig4_8.m Listing 4.9. Function barker_ambg.m Listing Function prn_ambg.m Listing Program myradar_visit4.m Chapter 5 Pulse Compression 5.1. Time-Bandwidth Product 5.2. Radar Equation with Pulse Compression 5.3. LFM Pulse Compression Correlation Processor Stretch Processor Distortion Due to Target Velocity 5.4. MyRadar Design Case Study - Visit Problem Statement A Design 5.5. MATLAB Program and Function Listings Listing 5.1. Program fig5_3.m Listing 5.2. Function matched_filter.m Listing 5.3. Function power_integer_2.m Listing 5.4. Function stretch.m Listing 5.5. Program fig5_14.m

13 Chapter 6 Surface and Volume Clutter 6.1. Clutter Definition 6.2. Surface Clutter Radar Equation for Area Clutter - Airborne Radar Radar Equation for Area Clutter - Ground Based Radar 6.3. Volume Clutter Radar Equation for Volume Clutter 6.4. Clutter Statistical Models 6.5. MyRadar Design Case Study - Visit Problem Statement A Design 6.6. MATLAB Program and Function Listings Listing 6.1. Function clutter_rcs.m Listing 6.2. Program myradar_visit6.m Chapter 7 Moving Target Indicator (MTI) and Clutter Mitigation 7.1. Clutter Spectrum 7.2. Moving Target Indicator (MTI) 7.3. Single Delay Line Canceler 7.4. Double Delay Line Canceler 7.5. Delay Lines with Feedback (Recursive Filters) 7.6. PRF Staggering 7.7. MTI Improvement Factor Two-Pulse MTI Case The General Case 7.8. MyRadar Design Case Study - Visit Problem Statement A Design 7.9. MATLAB Program and Function Listings Listing 7.1. Function single_canceler.m Listing 7.2. Function double_canceler.m Listing 7.3. Program fig7_9.m Listing 7.4. Program fig7_10.m Listing 7.5. Program fig7_11.m Listing 7.4. Program myradar_visit7.m

14 Chapter 8 Phased Arrays 8.1. Directivity, Power Gain, and Effective Aperture 8.2. Near and Far Fields 8.3. General Arrays 8.4. Linear Arrays Array Tapering Computation of the Radiation Pattern via the DFT 8.5. Planar Arrays 8.6. Array Scan Loss 8.7. MyRadar Design Case Study - Visit Problem Statement A Design 8.8. MATLAB Program and Function Listings Listing 8.1. Program fig8_5.m Listing 8.2. Program fig8_7.m Listing 8.3. Function linear_array.m Listing 8.4. Program circular_array.m Listing 8.5. Function rect_array.m Listing 8.6. Function circ_array.m Listing 8.7. Function rec_to_circ.m Listing 8.8. Program fig8_53.m Chapter 9 Target Tracking Single Target Tracking 9.1. Angle Tracking Sequential Lobing Conical Scan 9.2. Amplitude Comparison Monopulse 9.3. Phase Comparison Monopulse 9.4. Range Tracking Multiple Target Tracking 9.5. Track-While-Scan (TWS) 9.6. State Variable Representation of an LTI System 9.7. The LTI System of Interest 9.8. Fixed-Gain Tracking Filters The αβ Filter The αβγ Filter

15 9.9. The Kalman Filter The Singer αβγ-kalman Filter Relationship between Kalman and αβγ Filters MyRadar Design Case Study - Visit Problem Statement A Design MATLAB Program and Function Listings Listing 9.1. Function mono_pulse.m Listing 9.2. Function ghk_tracker.m Listing 9.3. Program fig9_21.m Listing 9.4. Function kalman_filter.m Listing 9.5. Program fig9_28.m Listing 9.6. Function maketraj.m Listing 9.7. Function addnoise.m Listing 9.8. Function kalfilt.m PART II Chapter 10 Electronic Countermeasures (ECM) Introduction Jammers Self-Screening Jammers (SSJ) Stand-Off Jammers (SOJ) Range Reduction Factor Chaff Multiple MTI Chaff Mitigation Technique MATLAB Program and Function Listings Listing Function ssj_req.m Listing Function sir.m Listing Function burn_thru.m Listing Function soj_req.m Listing Function range_red_factor.m Listing Program fig8_10.m Chapter 11 Radar Cross Section (RCS) RCS Definition RCS Prediction Methods Dependency on Aspect Angle and Frequency

16 11.4. RCS Dependency on Polarization Polarization Target Scattering Matrix 11.5 RCS of Simple Objects Sphere Ellipsoid Circular Flat Plate Truncated Cone (Frustum) Cylinder Rectangular Flat Plate Triangular Flat Plate Scattering From a Dielectric-Capped Wedge Far Scattered Field Plane Wave Excitation Special Cases RCS of Complex Objects RCS Fluctuations and Statistical Models RCS Statistical Models - Scintillation Models MATLAB Program and Function Listings Listing Function rcs_aspect.m Listing Function rcs_frequency.m Listing Program example11_1.m Listing Program rcs_sphere.m Listing Function rcs_ellipsoid.m Listing Program fig11_18a.m Listing Function rcs_circ_plate.m Listing Function rcs_frustum.m Listing Function rcs_cylinder.m Listing Function rcs_rect_plate.m Listing Function rcs_isosceles.m Listing Program Capped_WedgeTM.m Listing Function DielCappedWedgeTM Fields_LS.m Listing Function DielCappedWedgeTMFields_PW.m Listing Function polardb.m Listing Function dbesselj.m Listing Function dbessely.m Listing Function dbesselh.m Listing Program rcs_cylinder_complex.m Listing Program Swerling_models.m

17 Chapter 12 High Resolution Tactical Synthetic Aperture Radar (TSAR) Introduction Side Looking SAR Geometry SAR Design Considerations SAR Radar Equation SAR Signal Processing Side Looking SAR Doppler Processing SAR Imaging Using Doppler Processing Range Walk A Three-Dimensional SAR Imaging Technique Background DFTSQM Operation and Signal Processing Geometry for DFTSQM SAR Imaging Slant Range Equation Signal Synthesis Electronic Processing Derivation of Eq. (12.71) Non-Zero Taylor Series Coefficients for the k th Range Cell MATLAB Programs and Functions Listing Program fig12_12-13.m Chapter 13 Signal Processing Signal and System Classifications The Fourier Transform The Fourier Series Convolution and Correlation Integrals Energy and Power Spectrum Densities Random Variables Multivariate Gaussian Distribution Random Processes Sampling Theorem The Z-Transform The Discrete Fourier Transform Discrete Power Spectrum Windowing Techniques MATLAB Programs Listing Program figs13.m

18 Appendix 13A Fourier Transform Table Appendix 13B Some Common Probability Densities Appendix 13C Z - Transform Table Chapter 14 MATLAB Program and Function Name List Bibliography