Radar Handbook, Third Edition

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ABOUT THE EDITOR IN CHIEF Merrill Skolnik was Superintendent of the Radar Division at the U.S. Naval Research Laboratory for over 30 years. Before that he was involved in advances in radar while at the MIT Lincoln Laboratory, the Institute for Defense Analyses, and the Research Division of Electronic Communications, Inc. He is the author of the popular McGraw-Hill textbook Introduction to Radar Systems, now in its third edition, the editor of Radar Applications, as well as being a former editor of the Proceedings of the IEEE. He earned the Doctor of Engineering Degree from The Johns Hopkins University, where he also received the B.E and M.S.E degrees in electrical engineering. He is a member of the U.S. National Academy of Engineering, a Fellow of the IEEE, and the first recipient of the IEEE Dennis J. Picard Medal for Radar Technologies and Applications.

iii

RADAR HANDBOOK Merrill I. Skolnik Editor in Chief Third Edition

New York Chicago San Francisco Lisbon London Madrid Mexico City Milan New Delhi San Juan Seoul Singapore Sydney Toronto

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Cataloging-in-Publication Data is on file with the Library of Congress McGraw-Hill books are available at special quantity discounts to use as premiums and sales promotions, or for use in corporate training programs. To contact a representative, please visit the Contact Us pages at www.mhprofessional.com. Radar Handbook, Third Edition Copyright © 2008 by The McGraw-Hill Companies. All rights reserved. Printed in the United States of America. Except as permitted under the Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of publisher. 1 2 3 4 5 6 7 8 9 0 DOC DOC 0 1 9 8 ISBN 978-0-07-148547-0 MHID 0-07-148547-3 Sponsoring Editor Wendy Rinaldi Editorial Supervisor Janet Walden Project Editor LeeAnn Pickrell Acquisitions Coordinator Mandy Canales Copy Editor LeeAnn Pickrell Proofreader Susie Elkind Production Supervisor Jean Bodeaux Composition International Typesetting & Composition Illustration International Typesetting & Composition Art Director, Cover Jeff Weeks Cover Designer Mary McKeon Information has been obtained by McGraw-Hill from sources believed to be reliable. However, because of the possibility of human or mechanical error by our sources, McGraw-Hill, or others, McGraw-Hill does not guarantee the accuracy, adequacy, or completeness of any information and is not responsible for any errors or omissions or the results obtained from the use of such information.

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CONTENTS Contributors Preface Chapter 1 An Introduction and Overview of Radar Merrill Skolnik 1.1 Radar in Brief /

xiii xv 1.1 1.1

1.2 Types of Radars /

1.5

1.3 Information Available from a Radar /

1.7

1.4 The Radar Equation /

1.10

1.5 Radar Frequency Letter-band Nomenclature /

1.13

1.6 Effect of Operating Frequency on Radar /

1.14

1.7 Radar Nomenclature /

1.18

1.8 Some Past Advances in Radar /

1.19

1.9 Applications of Radar /

1.20

1.10 Conceptual Radar System Design /

1.22

Chapter 2 MTI Radar William W. Shrader and Vilhelm Gregers-Hansen 2.1 Preface /

2.1 2.1

2.2 Introduction to MTI Radar /

2.2

2.3 Clutter Filter Response to Moving Targets /

2.9

2.4 Clutter Characteristics /

2.10

2.5 Definitions /

2.19

2.6 Improvement Factor Calculations /

2.23

2.7 Optimum Design of Clutter Filters /

2.25

2.8 MTI Clutter Filter Design /

2.33

2.9 MTI Filter Design for Weather Radars /

2.46

2.10 Clutter Filter Bank Design /

2.52

2.11 Performance Degradation Caused by Receiver Limiting /

2.59

2.12 Radar System Stability Requirements /

2.65

2.13 Dynamic Range and A/D Conversion Considerations /

2.78

2.14 Adaptive MTI /

2.80

2.15 Radar Clutter Maps /

2.83

2.16 Sensitivity-velocity Control (SVC) /

2.87

2.17 Considerations Applicable to MTI Radar Systems /

2.91

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Chapter 3 Airborne MTI James K. Day and Fred M. Staudaher 3.1 Systems Using Airborne MTI Techniques /

3.1 3.1

3.2 Coverage Considerations /

3.2

3.3 Airborne MTI Performance Drivers /

3.3

3.4 Platform Motion and Altitude Effects on MTI Performance /

3.3

3.5 Platform-motion Compensation Abeam /

3.10

3.6 Scanning-motion Compensation /

3.14

3.7 Simultaneous Platform Motion and Scan Compensation /

3.18

3.8 Platform-motion Compensation, Forward Direction /

3.21

3.9 Space-time Adaptive Motion Compensation /

3.23

3.10 Effect of Multiple Spectra /

3.31

3.11 Example AMTI Radar System /

3.32

Chapter 4 Pulse Doppler Radar John P. Stralka and William G. Fedarko 4.1 Characteristics and Applications /

4.1 4.1

4.2 Pulse Doppler Clutter /

4.14

4.3 Dynamic-range and Stability Requirements /

4.24

4.4 Range and Doppler Ambiguity Resoluton /

4.31

4.5 Mode and Waveform Design /

4.35

4.6 Range Performance /

4.39

List of Abbreviations /

4.48

Chapter 5 Multifunctional Radar Systems for Fighter Aircraft David Lynch, Jr. and Carlo Kopp 5.1 Introduction /

5.1 5.1

5.2 Typical Missions and Modes /

5.10

5.3 A-A Mode Descriptions & Waveforms /

5.16

5.4 A-S Mode Descriptions & Waveforms /

5.28

Chapter 6 Radar Receivers Michael E. Yeomans 6.1 The Configuration of a Radar Receiver /

6.1 6.1

6.2 Noise and Dynamic-range Considerations /

6.4

6.3 Bandwidth Considerations /

6.9

6.4 Receiver Front End /

6.10

6.5 Local Oscillators /

6.14

6.6 Gain Control /

6.22

6.7 Filtering /

6.24

6.8 Limiters /

6.29

6.9 I/Q Demodulators /

6.31

6.10 Analog-to-Digital Converters /

6.35

6.11 Digital Receivers /

6.40

6.12 Diplex Operation /

6.46

6.13 Waveform Generation and Upconversion /

6.47

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Chapter 7 Automatic Detection, Tracking, and Sensor Integration W. G. Bath and G. V.Trunk 7.1 Introduction /

7.1 7.1

7.2 Automatic Detection /

7.1

7.3 Automatic Tracking /

7.22

7.4 Networked Radars /

7.46

7.5 Unlike-sensor Integration /

7.49

Chapter 8 Pulse Compression Radar Michael R. Ducoff and Byron W. Tietjen 8.1 Introduction / 8.2 Pulse Compression Waveform Types /

8.1 8.1 8.2

8.3 Factors Affecting Choice of Pulse Compression Systems /

8.26

8.4 Pulse Compression Implementation and Radar System Examples /

8.28

Appendix / Chapter 9 Tracking Radar Dean D. Howard 9.1 Introduction / 9.2 Monopulse (Simultaneous Lobing) /

8.36 9.1 9.1 9.3

9.3 Scanning and Lobing /

9.16

9.4 Servosystems for Tracking Radar /

9.17

9.5 Target Acquisition and Range Tracking /

9.20

9.6 Special Monopulse Techniques /

9.24

9.7 Sources of Error /

9.26

9.8 Target-caused Errors (Target Noise) /

9.26

9.9 Other External Causes of Error /

9.37

9.10 Internal Sources of Error /

9.42

9.11 Summary of Sources of Error /

9.43

9.12 Error Reduction Techniques /

9.46

Chapter 10 The Radar Transmitter Thomas A. Weil and Merrill Skolnik 10.1 Introduction /

10.1

10.2 Linear-beam Amplifiers /

10.1 10.4

10.3 Magnetron /

10.14

10.4 Crossed-field Amplifiers /

10.16

10.5 Gyrotrons /

10.17

10.6 Transmitter Spectrum Control /

10.19

10.7 Grid-controlled Tubes /

10.21

10.8 Modulators /

10.23

10.9 Which RF Power Source to Use? /

10.25

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Chapter 11 Solid id-State Transmitters Michael T. Borkowski 11.1 Introduction /

11.1 11.1

11.2 Advantages of Solid State /

11.1

11.3 Solid-state Devices /

11.5

11.4 Designing for the Solid-state Bottle Transmitter /

11.17

11.5 Designing for the Solid-state Phased Array Transmitter /

11.24

11.6 Solid-state System Examples /

11.37

Chapter 12 Reflector Antennas Michael E. Cooley and Daniel Davis 12.1 Introduction /

12.1 12.7

12.2 Basic Principles and Parameters /

12.3

12.3 Reflector Antenna Architectures /

12.16

12.4 Reflector Feeds /

12.25

12.5 Reflector Antenna Analysis /

12.37

12.6 Mechanical Design Considerations /

12.35

Acknowledgments / Chapter 13 Phased Array Radar Antennas Joe Frank and John D. Richards 13.1 Introduction / 13.2 Array Theory /

12.47 13.1 13.7 13.9

13.3 Planar Arrays and Beam Steering /

13.15

13.4 Aperture Matching and Mutual Coupling /

13.20

13.5 Low-sidelobe Phased Arrays /

13.28

13.6 Quantization Effects /

13.34

13.7 Bandwidth of Phased Arrays /

13.38

13.8 Feed Networks (Beamformers) /

13.46

13.9 Phase Shifters /

13.57

13.10 Solid-state Modules /

13.53

13.11 Multiple Simultaneous Receive Beams /

13.54

13.12 Digital Beamforming /

13.56

13.13 Radiation Pattern Nulling /

13.57

13.14 Calibration of Active Phased Array Antennas /

13.60

13.15 Phased Array Systems /

13.62

Chapter 14 Radar Cross Section Eugene F. Knott 14.1 Introduction /

14.1 14.1

14.2 The Concept of Echo Power /

14.4

14.3 RCS Prediction Techniques /

14.16

14.4 RCS Measurement Techniques /

14.27

14.5 Radar Echo Suppression /

14.36

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Chapter 15 Sea Clutter Lewis B. Wetzel 15.1 Introduction /

15.1 15.1

15.2 The Sea Surface /

15.3

15.3 Empirical Behavior of Sea Clutter /

15.7

15.4 Theories and Models of Sea Clutter /

15.27

15.5 Summary and Conclusions /

15.37

Chapter 16 Ground Echo Richard K. Moore 16.1 Introduction /

16.1 16.1

16.2 Parameters Affecting Ground Return /

16.4

16.3 Theoretical Models and Their Limitations /

16.7

16.4 Fading of Ground Echoes /

16.12

16.5 Measurement Techniques for Ground Return /

16.19

16.6 General Models for Scattering Coefficient (Clutter Models) /

16.29

16.7 Scattering Coefficient Data /

16.35

16.8 Polarimetry /

16.46

16.9 Scattering Coefficient Data Near Grazing /

16.52

16.10 Imaging Radar Interpretation /

16.55

Chapter 17 Synthetic Aperture Radar Roger Sullivan 17.1 Basic Principle of SAR /

17.1 17.1

17.2 Early History of SAR /

17.2

17.3 Types of SAR /

17.2

17.4 SAR Resolution /

17.6

17.5 Key Aspects of SAR /

17.10

17.6 SAR Image Quality /

17.16

17.7 Summary of Key SAR Equations /

17.21

17.8 Special SAR Applications /

17.22

Chapter 18 Space-Based Remote Sensing Radars R. Keith Raney 18.1 Perspective / 18.2 Synthetic Aperture Radar (SAR) /

18.1 18.1 18.5

18.3 Altimeters /

18.29

18.4 Planetary Radars /

18.43

18.5 Scatterometers /

18.53

18.6 Radar Sounders /

18.59

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Chapter 19 Meteorological Radar R. Jeffrey Keeler and Robert J. Serafin 19.1 Introduction /

19.1 19.1

19.2 The Radar Equation for Meteorological Targets /

19.3

19.3 Design Considerations /

19.6

19.4 Signal Processing /

19.19

19.5 Operational Applications /

19.25

19.6 Research Applications /

19.33

Chapter 20 HF Over-the-Horizon Radar James M. Headrick and Stuart J. Anderson 20.1 Introduction /

20.1

20.2 The Radar Equation /

20.5

20.3 Factors Influencing Skywave Radar Design /

20.7

20.4 The Ionosphere and Radiowave Propagation /

20.13

20.5 Waveforms for HF Radar /

20.21

20.6 The Transmitting System /

20.23

20.7 Radar Cross Section /

20.26

20.8 Clutter: Echoes from the Environment /

20.29

20.9 Noise, Interference, and Spectrum Occupancy /

20.40

20.10 The Receiving System /

20.45

20.11 Signal Processing and Tracking /

20.49

20.12 Radar Resource Management /

20.54

20.13 Radar Performance Modeling /

20.55

Appendix: HF Surface Wave Radar /

20.70

Chapter 21 Ground Penetrating Radar David Daniels 21.1 Introduction / 21.2 Physics of Propagation in Materials /

20.1

21.1 21.1 21.6

21.3 Modeling /

21.13

21.4 Properties of Materials /

21.18

21.5 GPR Systems /

21.20

21.6 Modulation Techniques /

21.21

21.7 Antennas /

21.24

21.8 Signal and Image Processing /

21.30

21.9 Applications /

21.35

21.10 Licensing /

21.39

Chapter 22 Civil Marine Radar Andy Norris 22.1 Introduction /

22.1 22.1

22.2 The Challenges /

22.3

22.3 International Standards /

22.7

22.4 Technology /

22.10

22.5 Target Tracking /

22.17

xi

22.6 User Interface /

22.19

22.7 Integration with AIS /

22.23

22.8 Radar Beacons /

22.25

22.9 Validation Testing /

22.28

22.10 Vessel Tracking Services /

22.29

Appendix The Early Days of CMR /

22.31

List of Maritime Radar-related Abbreviations /

22.33

Acknowledgments /

22.34

Chapter 23 Bistatic Radar Nicholas J. Willis 23.1 Concept and Definitions /

23.1 23.1

23.2 Coordinate Systems /

23.3

23.3 Bistatic Radar Equation /

23.4

23.4 Applications /

23.9

23.5 Bistatic Doppler /

23.14

23.6 Target Location /

23.17

23.7 Target Cross Section /

23.19

23.8 Surface Clutter /

23.22

23.9 Unique Problems and Requirements /

23.26

Chapter 24 Electronic Counter-Countermeasures Alfonso Farina 24.1 Introduction /

24.1 24.1

24.2 Terminology /

24.2

24.3 Electronic Warfare Support Measures /

24.2

24.4 Electronic Countermeasures /

24.5

24.5 Objectives and Taxonomy of ECCM Techniques /

24.8

24.6 Antenna-related ECCM /

24.10

24.7 Transmitter-related ECCM /

24.31

24.8 Receiver-related ECCM /

24.32

24.9 Signal-processing-related ECCM /

24.33

24.10 Operational-deployment Techniques /

24.36

24.11 Application of ECCM Techniques /

24.37

24.12 ECCM and ECM Efficacy /

24.54

Acronym List /

24.56

Acknowledgments /

24.58

Chapter 25 Radar Digital Signal Processing James J. Alter and Jeffrey O. Coleman 25.1 Introduction /

25.1 25.1

25.2 Receive Channel Processing /

25.2

25.3 Transmit Channel Processing /

25.20

25.4 DSP Tools /

25.22

25.5 Design Considerations /

25.34

25.6 Summary /

25.37

Acknowledgments /

25.38

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Chapter 26 The Propagation Factor, Fp, in the Radar Equation Wayne L. Patterson 26.1 Introduction /

26.1 26.1

26.2 The Earth’s Atmosphere /

26.2

26.3 Refraction /

26.3

26.4 Standard Propagation /

26.4

26.5 Anomalous Propagation /

26.6

26.6 Propagation Modeling /

26.13

26.7 EM System Assessment Programs /

26.18

26.8 AREPS Radar System Assessment Model /

26.23

26.9 AREPS Radar Displays /

26.25

Index

1.1

xiii

CONTRIBUTORS James J. Alter Naval Research Laboratory (CHAPTER 25) Stuart J. Anderson Australian Defense Science and Technology Organisation (CHAPTER 20) W. G. Bath The Johns Hopkins University Applied Physics Laboratory (CHAPTER 7) Michael T. Borkowski Raytheon Company (CHAPTER 11) Jeffrey O. Coleman Naval Research Laboratory (CHAPTER 25) Michael E. Cooley Northrop Grumman, Electronic Systems (CHAPTER 12) David Daniels ERA Technology (CHAPTER 21) Daniel Davis Northrop Grumman Corporation (CHAPTER 12) James K. Day Lockheed Martin Corporation (CHAPTER 3) Michael R. Ducoff Lockheed Martin Corporation (CHAPTER 8) Alfonso Farina SELEX Sistemi Integrati (CHAPTER 24) William G. Fedarko Northrop Grumman Corporation (CHAPTER 4) Joe Frank The Johns Hopkins University Applied Physics Laboratory (CHAPTER 13) Vilhelm Gregers-Hansen Naval Research Laboratory (CHAPTER 2) James M. Headrick Naval Research Laboratory, retired (CHAPTER 20) Dean D. Howard Consultant to ITT Industries, Inc. (CHAPTER 9) R. Jeffrey Keeler National Center for Atmospheric Research (CHAPTER 19) Eugene F. Knott Tomorrow’s Research (CHAPTER 14) Carlo Kopp Monash University (CHAPTER 5) David Lynch, Jr. DL Sciences, Inc. (CHAPTER 5) Richard K. Moore The University of Kansas (CHAPTER 16) Andy Norris Consultant in Navigation Systems (CHAPTER 22) Wayne L. Patterson Space and Naval Warfare Systems Center (CHAPTER 26) Keith Raney The Johns Hopkins University Applied Physics Laboratory (CHAPTER 18) John D. Richards The Johns Hopkins University Applied Physics Laboratory (CHAPTER 13) Robert J. Serafin National Center for Atmospheric Research (CHAPTER 19) William W. Shrader Shrader Associates (CHAPTER 2) Merrill Skolnik (CHAPTERS 1 and 10) Fred M. Staudaher Naval Research Laboratory, retired (CHAPTER 3)

xiv

John P. Stralka Northrop Grumman Corporation (CHAPTER 4) Roger Sullivan Institute for Defense Analyses (CHAPTER 17) Byron W. Tietjen Lockheed Martin Corporation (CHAPTER 8) G. V. Trunk The Johns Hopkins University Applied Physics Laboratory (CHAPTER 7) Thomas A. Weil (CHAPTER 10) Lewis B. Wetzel Naval Research Laboratory, retired (CHAPTER 15) Nicholas J. Willis Technology Service Corporation, retired (CHAPTER 23) Michael E. Yeomans Raytheon Company (CHAPTER 6)

xv

PREFACE Radar is an important example of an electrical engineering system. In university engineering courses, the emphasis usually is on the basic tools of the electrical engineer such as circuit design, signals, solid state, digital processing, electronic devices, electromagnetics, automatic control, microwaves, and so forth. But in the real world of electrical engineering practice, these are only the techniques, piece parts, or subsystems that make up some type of system employed for a useful purpose. In addition to radar and other sensor systems, electrical engineering systems include communications, control, energy, information, industrial, military, navigation, entertainment, medical, and others. These are what the practice of electrical engineering is all about. Without them there would be little need for electrical engineers. However, the practicing engineer who is involved in producing a new type of electrical engineering system often has to depend on acquiring knowledge that was not usually covered in his or her engineering courses. The radar engineer, for example, has to understand the major components and subsystems that make up a radar, as well as how they fit together. The Radar Handbook attempts to help in this task. In addition to the radar system designer, it is hoped that those who are responsible for procuring new radar systems, those who utilize radars, those who maintain radar systems, and those who manage the engineers who do the above, also will find the Radar Handbook to be of help in fulfilling such tasks. The third edition of the Radar Handbook is evidence that the development and application of radar for both civilian and military purposes continue to grow in both utility and in improved technology. Some of the many advances in radar since the previous edition include the following: - The extensive use of digital methods for improved signal processing, data processing, decision making, flexible radar control, and multifunction radar - Doppler weather radar - Ground moving target indication, or GMTI - An extensive experimental database describing low-angle land clutter, as obtained by MIT Lincoln Laboratory, that replaced the previously widely used clutter model that dated back to World War II - The realization that microwave sea echo at low grazing angles is due chiefly to what are called “sea spikes” - The active-aperture phased array radar system using solid-state modules, also called active electronically scanned arrays (AESA), which is attractive for some multifunction radar applications that need to manage both power and spatial coverage - Planetary exploration with radar - Computer-based methods for predicting radar propagation performance in realistic environments

xvi

- Operational use of HF over-the-horizon radar - Improved methods for detecting moving targets in clutter, including space-time adaptive processing - Operational use of inverse synthetic aperture radar for target recognition - Interferometric synthetic aperture radar, or InSAR, to obtain the height of a resolved scatterer or to detect moving ground targets as well as provide a SAR image of a scene - High precision space-based altimeters, with accuracy of a few centimeters, to measure the Earth’s geoid - Ultrawideband radar for ground penetrating and similar applications - Improved high power, wide bandwidth klystron power sources based on clustered cavity resonators, as well as the multiple-beam klystron - The appearance of wide bandgap semiconductors that allow better performance because of high power and high operating temperatures - The availability of high-power millimeter-wave generators based on the gyroklystron - Nonlinear FM pulse compression with low sidelobe levels - The replacement, by the computer, of the operator as information extractor and decision maker The above are not listed in any particular order, nor should they be considered a complete enumeration of radar developments since the appearance of the previous edition. There were also some radar topics in previous editions of the Radar Handbook that are of lesser interest and so were not included in this edition. The chapter authors, who are experts in their particular field, were told to consider the reader of their chapter as being knowledgeable in the general subject of radar and even an expert in some other particular area of radar, but not necessarily knowledgeable about the subject of the particular chapter the author was writing. It should be expected that with a book in print as long as the Radar Handbook has been, not all chapter authors from the previous editions would be available to do the third edition. Many of the previous authors have retired or are no longer with us. Sixteen of the twenty-six chapters in this edition have authors or coauthors who were not involved in the previous editions. The hard work of preparing these chapters was done by the individual expert authors of the various chapters. Thus the value of the Radar Handbook is the result of the diligence and expertise of the authors who contributed their time, knowledge, and experience to make this handbook a useful addition to the desk of radar system engineers and all those people vital to the development, production, and employment of radar systems. I am deeply grateful to all the contributing authors for their fine work and the long hours they had to apply to their task. It is the chapter authors who make any handbook a success. My sincere thanks to them all. As stated in the Preface of the previous edition, readers who wish to reference or quote material from the Radar Handbook are asked to mention the names of the individual chapter authors who produced the material. MERRILL SKOLNIK Baltimore, Maryland

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.R C NUMBEROFINDEPENDENTRANGESAMPLESPROCESSEDPER)00IN#ONFIRM

.F CUE NUMBEROFINDEPENDENTDOPPLERFILTERSINTHE#ONFIRMWINDOWCENTERED ABOUTTHEDOPPLEROFTHE!LERTDETECTIONCUE

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4&2 OVERALL!LERT#ONFIRMFALSEREPORTTIME 4HE- OF .RANGINGUSEDIN-273REQUIRESCORRELATIONINRANGEANDCANBEVIEWED ASABINARYDETECTOR-273ISTYPICALLYAMEDIUM 02&WAVEFORMWITHRANGEANDDOP PLERAMBIGUITIES$OPPLERISUSEDFORCLUTTERMITIGATIONINEACHLOOK ANDTHEDOPPLER AMBIGUITYMAYNOTNEEDTOBERESOLVEDSINCETHETRACKERCANDETERMINERANGERATEFROM SUCCESSIVEDWELLS!TYPICAL-273- OF .CORRELATIONWOULDBETHREEDETECTIONSOUT OFEIGHTLOOKSIE MANDN &ORRANGE ONLYCORRELATION THE0&!INEACHRANGE DOPPLERCELLISGIVENBY M

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FOR 3WERLING ) TARGGET CHI SQUARED DISTRIBUTION WITH  DEGRESSS OF FREEDOM FOR 3WERLING )) TARGET CHI SSQUARED DISTRIBUTION WITH . PDI DEGRESS OF FREEDOM FOR 3WERLING ))) TARGET CHI SQUARRED DISTRIBUTION WITH  DEGRESS OF FREEDOM FOR 3WERLING )6 TARGET CHI SQUARED DISTRIIBUTION WITH . PDI DEGRESS OF FREEDOM

¤ D X³ + M  X D   0 ¥ ´ CHI SQUAREDDISTRIBUTIONSURVIVALFUNCTION ¦  µ +  M P D INVERSECHI SQUAREDDISTRIBUTIONSURVIVALFUNCTION X

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4HEINTEGRALOFTHECHI SQUAREDDISTRIBUTION+MX D ANDITSINVERSE+  M P D AREOFTEN INCLUDEDINMATHEMATICALCOMPUTATIONSOFTWAREPACKAGES 7HEN- OF .DETECTIONIE BINARYDETECTION ISUSEDWITHINADWELL THEPROBABIL ITYOFDETECTIONFOREACHLOOK0D LOOK ISUSEDTOCOMPUTETHEPROBABILITYOFDETECTION FORADWELL0D DWELL 7HENADWELLREQUIRESMDETECTIONSOUTOFNLOOKSFORATARGET DECLARATION THE0D DWELLIS N

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0D CUM ;K =   “ ; 0D SS ;I== I 

 0D CUM ;K = 0D SS ;K =  0D CUM ;K =



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