To: My wife and four sons; Wayne and shirley; 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 o 2004 by Chapman hall/CRCCRC Press LLC reface 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 calcula tions. It is intended to serve as an engineering reference for radar engineers working in the field of radar systems. The MATLaBRl code provided in this book is designed to provide the user with hands-on experience in radar sys tems, 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, sev eral 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 dis- cussed, 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 engi neers 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 opera tions and design philosophy. Additionally, Part I includes several mini design case studies pertinent to different chapters in order to help enhance understand- ing of radar design in the context of the material presented in different chap ters 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 math Works, Inc. For product infor mation, please contact: The Math Works, Inc., 3 Apple Hill Drive, Natick, MA 01760-2098Usa.Webwww.mathworks.com o 2004 by Chapman hall/CRCCRC Press LLC 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 devel- oped and made available All MATLAB programs and functions provided in this book can be down- loadedfromtheCrcPressWebsite(www.crcpress.com).Forthispurpose followthisprocedure1)fromyourWebbrowsertypehttp://www.crc press. com,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 down loaded from The Math Works Web site by following these steps: 1)from your Webbrowsertype:http:/mathworks.com/matlabcentrallfileexchange/",2) place the curser on"Companion Software for Books"and click on"Communi cations". 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 I 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 over- view of the radar probability of detection calculations and related topics Detection of fluctuating targets including Swerling I, Il, Ill, and Iv models is presented and analyzed. Coherent and non-coherent integration are also intro duced. 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 ana- lyzed. Chapter 4 presents in detail the principles associated with the radar ambiguity function. This includes the ambiguity function for single pulse, Lin ear 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 (MTD. 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 o 2004 by Chapman hall/CRCCRC Press LLC 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 chap ter covers the subject of single target tracking. Topics such as sequential lob ing, 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 aB and the aBy filters are presented in detail. The concept of the Kalman filter is introduced Special cases of the Kal man 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 Its an overview of Electronic Counter Measures(ECM) techniques. Top ics 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 depen dency on aspect angle, frequency, and polarization is discussed. The target scattering matrix is developed. RCs formulas for many simple objects are pre sented. 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 consid erations, and the Sar radar equation. Finally Chapter 13 presents an overview of signal processin 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 Bassemr. mahafza Huntsville. alabama July. 2003 Atef z. elsherbeni Oxford, Mississippi July. 2003 o 2004 by Chapman hall/CRCCRC Press LLC 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 o 2004 by Chapman hall/CRCCRC Press LLC Table of contents Preface Acknowledgment PARTT Chapter I Introduction to radar basics 1. 1. Radar Classifications 1. 2. Range 1.3. Range resolution 1. 4. Doppler Frequency 1.5. The Radar equation 1.5. 1. Radar Reference range 1.6. Search(Surveillance) 1.6. 1. Mini Design Case Study 1.1 1.7. Pulse Integration 1.7. 1 Coherent Integration 1.7.2. Non-Coherent Integration 1.7.3. Detection Range with Pulse Integration 1.7.4. Mini Design Case Study 1. 2 1. 8. Radar Losses 1. 8.1. Transmit and Receive losses 1.8.2. Antenna Pattern Loss and Scan loss 1.8.3. Atmospheric Loss 1. 8.4. Collapsing Loss 1.8.5. Processing Losses 1.8.6. Other losses 1.9. " MyRadar"Design Case Study-Visit 1 o 2004 by Chapman hall/CRCCRC Press LLC 1.9.1 Authors and publisher disclaimer 1.9.2. Problem Statement 1.9.3. A Design 1.9.4. A Design Alternative 1.10. MATLAB Program and Function Listings Listing1.1. Function‘ radar eg. m” Listing 1. 2. Program fig1 12 m Listing 1.3. Program/13.m Listing 1. 4. Program"ref snr.m Listing1.5. Function‘ power aperture.m” Listing 1.6. Program fig/ 16.m Listing 1. 8. Program "figI 19 m".m Listing 1. 7. Program" l I Listing 1.9. Program fig/ 21.m Listing 1. 10. Function "pulse integration. m Listing l 11 Program "myradarvisit/1.m Listing 1. 12. Program fig1 27 Appendix la Pulsed radar 1A. 1. Introduction 1A. 2. Range and doppler ambiguities 1A.3. Resolving range ambiguity IA. 4. Resolving Doppler Ambiguity ppendix IB Noise Figure 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 2.4.1. Coherent Integration 2.4.2. Non-Coherent Integration 2.4.3. Mini design Case Study 2 2.5. Detection of Fluctuating Targets 2.5.1. Threshold Selection o 2004 by Chapman hall/CRCCRC Press LLC 2.6. Probability of Detection Calculation 2.6. 1. Detection of Swerling V Targets 2.6.2. Detection of Swerling I Targets 2.6.3. Detection of Swerling II Targets 2.6.4. Detection of Swerling III Targets 2.6.5. Detection of Swerling IV Targets 2.7. The Radar Equation Revisited 2. 8. Cumulative probability of detection 2.8. 1. Mini Design Case Study 2.2 2.9. Constant False Alarm Rate(CFAR) 2.9.1. Cell-Averaging CFAR (Single Pulse) 2.9.2. Cell-Averaging CFAR with Non-Coherent Integra 2.10. MvRadar Design Case study - Visit 2 2.10.1. Problem Statement 2. 10.2. A Design 2. 10.2.1. Single Pulse(per Frame) Design Option 2. 2. Non-Coherent Integration Design Option 2.11. MATLAB Program and Function Listings Listing 2. 1. Program fig2 2m Listing 2. 2. FI gue func.m Listing 2.3. Program fig2 3m Listing 2.4. Function "marcumsgm Listing 2.5. Program " prob snr.m Listing 2.6. Program fig2 6a.m Listing 2. 7. Function"i g prov fac Listing 2. 8 Program fig2 6b Listing 2.9. Function incomplete gammam Listing 2.10. Function factor m Listing 2. 1l. Program ig2 7m Listing 2. 12. Function threshold Listing 2. 13. Program fig2 8m Listing 2. 14. FI d swerling 5 Listing 2. 15. Pr fig2 9 Listing 2.16. Function "pd swerling.m Listing 2. 17. Program fig 10m isting 2. 18. Program "fig2 labm Listing2.19. Function‘ pd swerling2.m” Listing2.20. Program‘fg212.m” Listing 2.21. Function "pd swerling 3 m Listing 2.22. Program"fig2 13m Listing 2.23 Function "pd swerling.m Listing 2. 24. Program " fig2 14m o 2004 by Chapman hall/CRCCRC Press LLC