An Introduction to RF Stealth (Radar, Sonar and Navigation) [2 ed.] 1839531592, 9781839531590

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An Introduction to RF Stealth 2nd Edition

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An Introduction to RF Stealth 2nd Edition David Lynch Jr.

The Institution of Engineering and Technology

Published by SciTech Publishing, an imprint of The Institution of Engineering and Technology, London, United Kingdom The Institution of Engineering and Technology is registered as a Charity in England & Wales (no. 211014) and Scotland (no. SC038698). † The Institution of Engineering and Technology 2021 First published 2004 Second edition 2021 This publication is copyright under the Berne Convention and the Universal Copyright Convention. All rights reserved. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may be reproduced, stored or transmitted, in any form or by any means, only with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publisher at the undermentioned address: The Institution of Engineering and Technology Michael Faraday House Six Hills Way, Stevenage Herts, SG1 2AY, United Kingdom www.theiet.org While the author and publisher believe that the information and guidance given in this work are correct, all parties must rely upon their own skill and judgement when making use of them. Neither the author nor publisher assumes any liability to anyone for any loss or damage caused by any error or omission in the work, whether such an error or omission is the result of negligence or any other cause. Any and all such liability is disclaimed. The moral rights of the author to be identified as author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.

British Library Cataloguing in Publication Data A catalogue record for this product is available from the British Library

ISBN 978-1-83953-159-0 (hardback) ISBN 978-1-83953-160-6 (PDF)

Typeset in India by MPS Limited Printed in the UK by CPI Group (UK) Ltd, Croydon Cover image: Sukhoi Su-57, 5th Generation Jet Fighter. Source – Sukhoi Design Bureau, Author – Anna Zvereva, Tallinn, Estonia. Creative Commons Attribution-Share Alike 2.0 Generic License

Contents

About the author Preface

xiii xv

1 Introduction to stealth systems 1.1 Introduction 1.1.1 Introduction to survivability 1.1.2 Brief history of radar and ladar 1.1.3 Brief history of signature reduction 1.1.4 Great thoughts of stealth/LO technology 1.1.5 Brief history of LPI systems 1.1.6 LPIR program accomplishments 1.1.7 LPI modes demonstrated through test 1.1.8 LPIR program results summary 1.2 The stealth design challenge 1.2.1 The stealth approach 1.2.2 Balanced design 1.2.3 RCS and power management summary 1.3 Low probability of intercept systems: an introduction 1.3.1 Great thoughts of LPI systems design 1.3.2 Passive detection and intercept probability 1.3.3 Reduced detectability: effective radiated peak power 1.3.4 Reduced detectability: maximum signal uncertainty 1.3.5 LPI performance example 1.3.6 LPIS typical technology 1.3.7 LPI maximizes uncertainty 1.4 Basic LPI equations 1.4.1 Radar and beacon equations 1.4.2 Intercept power relations and LPIS figures of merit 1.4.3 Detection range versus intercept range equations 1.5 Introduction to RCS 1.5.1 Mathematical basis 1.5.2 RCS phenomenology 1.5.3 Estimating RCS 1.5.4 Edge diffraction 1.6 Introduction to signature balance 1.6.1 Radar threat

1 1 1 4 7 8 10 10 10 11 13 13 17 18 19 19 20 21 23 24 25 26 27 27 29 30 36 36 38 42 49 52 52

viii

An introduction to RF stealth, 2nd edition 1.6.2 Infrared threat 1.6.3 Visual threat 1.6.4 Intercept threat 1.7 Exercises References

55 59 60 67 68

2

Introduction to materials and shaping 2.1 Introduction 2.2 Detailed RCS calculation 2.2.1 Plates or facets 2.2.2 Edges 2.2.3 Wedges 2.2.4 Dihedrals 2.2.5 Ogives 2.3 Radiation absorbing materials 2.3.1 Bulk RAM 2.3.2 Circuit analogs 2.3.3 Metamaterials 2.4 Blending 2.5 More complex shapes 2.6 Exercises References

71 71 82 84 88 92 96 102 106 106 113 115 116 118 120 121

3

Interceptibility parameters and analysis 3.1 Interceptability parameters 3.1.1 Interceptability footprints 3.1.2 Interceptor time response 3.1.3 Receiver sensitivity versus intercept probability 3.1.4 Power management 3.2 Interceptibility analysis 3.2.1 Intercept receiver sensitivity 3.2.2 Sidelobe intercept range 3.2.3 Interceptor detection probabilities 3.2.4 Interceptability time constraints 3.2.5 Interceptability frequency constraints 3.2.6 Antenna gain mismatch 3.2.7 Cumulative probability of intercept 3.3 Example mode interceptability calculations 3.3.1 Data link mode interceptability example 3.4 Footprint calculation 3.4.1 “Cookie cutter” footprints 3.4.2 More accurate footprints 3.5 Bistatics 3.5.1 Bistatic properties 3.5.2 Bistatic threats

123 123 124 127 128 133 135 135 138 139 140 143 144 146 148 156 157 157 168 172 172 179

Contents 3.6 Exercises References

ix 181 182

4 Intercept receivers 4.1 Survey of current and future intercept receivers 4.2 Receiver types (similar to Schleher) 4.2.1 Crystal video receiver 4.2.2 Instantaneous frequency measurement 4.2.3 Scanning superheterodyne receivers 4.2.4 Channelized receivers 4.2.5 Transform intercept receivers 4.2.6 Hybrid or cueing receivers 4.2.7 Software-defined radios 4.2.8 Intercept receiver processing 4.2.9 Cross correlation processing 4.3 Interceptor measurement accuracy 4.3.1 Frequency measurement 4.3.2 Pulse amplitude and width measurement 4.3.3 Time of arrival and PRI measurement 4.3.4 Angle of arrival measurement 4.3.5 Range estimation 4.4 Intercept receiver threat trends 4.4.1 Typical response threats – elastic threat (after Gordon) 4.4.2 Corresponding specification of LPIS emissions 4.4.3 Typical response threats—radiometric 4.4.4 Typical response threats – correlation 4.5 LPIS versus interceptor 4.5.1 Screening jamming 4.5.2 Spoofing 4.6 Typical deployed intercept receivers 4.7 Exercises References

185 185 186 187 189 191 192 195 200 202 203 213 221 223 224 224 225 238 244 246 249 250 261 263 263 264 265 267 267

5 Exploitation of the environment 5.1 Atmospheric attenuation 5.2 Clutter 5.3 Terrain masking 5.4 Electronic order of battle 5.4.1 Radar and EW intercept EOB 5.4.2 Radar emitter EOB 5.4.3 Electronic countermeasures EOB 5.5 RF Spectrum masking 5.5.1 Example ambient spectra

271 271 274 289 300 303 306 309 310 310

x

An introduction to RF stealth, 2nd edition 5.5.2 Estimating ambient spectra 5.5.3 Estimating ambient pulse density 5.6 Example scenario analysis 5.6.1 Classification usable sensitivity 5.6.2 Monte Carlo simulations 5.7 Typical deployed emitters 5.8 Exercises References

314 331 332 332 336 346 346 347

6

Stealth waveforms 6.1 Waveform criteria 6.2 Frequency diversity 6.2.1 Simultaneous transmit and receive cross talk 6.2.2 Low noise adaptive multifrequency generation 6.2.3 Detection by multifrequency waveforms 6.3 Power management 6.4 Pulse compression 6.4.1 Linear FM/chirp 6.4.2 LPI performance loss incurred by use of chirp 6.4.3 Stretch processing 6.4.4 Pulse compression waveform sidelobe measures 6.5 Discrete phase codes 6.5.1 Barker codes 6.5.2 Frank and digital chirp codes 6.5.3 Complementary codes 6.6 Hybrid waveforms 6.6.1 Hybrid spread spectrum stretch (S-cubed) 6.6.2 Hybrid spread spectrum stretch processing 6.6.3 Waveform and processing parameters 6.7 Noise propagation in pulse compressors 6.8 Waveform summary 6.9 Analog to digital conversion 6.10 Exercises References

349 349 350 351 357 362 365 367 367 369 371 372 374 374 388 390 409 409 410 414 416 417 418 426 427

7

Stealth antennas and radomes 7.1 Introduction 7.2 Antenna parameters 7.2.1 Fundamental definitions (adapted from Skolnik and Silver) 7.2.2 Antenna radiation pattern and aperture distribution 7.3 Single radiators 7.3.1 The electric dipole (adapted from Radiation Laboratories) 7.3.2 The magnetic dipole or small loop

429 429 429 429 432 436 436 440

Contents 7.3.3 Slot radiators (Adapted from Blass) 7.3.4 Broadband radiators 7.4 Antenna arrays 7.4.1 Simple apertures 7.4.2 Sidelobe reduction functions 7.4.3 Error induced antenna pattern degradation 7.4.4 Arrays of elements 7.5 Electronically scanned arrays 7.5.1 Single beam antennas 7.5.2 Multibeam antennas 7.5.3 Active electronic scan antennas 7.5.4 AESA antenna example 7.5.5 AESA bandwidth and pulse compression 7.5.6 AESA exciter 7.5.7 AESA unique noise contributions 7.6 Multichannel receivers 7.6.1 Receiver noise sources: thermal noise 7.6.2 Thermal noise example 7.7 Antenna scattering 7.7.1 Basic notions 7.7.2 Estimating antenna RCS 7.7.3 Estimating AESA RCS 7.7.4 Estimating errors due to circuit variations 7.8 Low RCS radomes 7.8.1 Introduction 7.8.2 Antenna and radome integration 7.8.3 General formulas 7.8.4 Composite radomes 7.8.5 Thick frequency-selective layers 7.8.6 Edge treatment 7.8.7 Coordinate rotations 7.8.8 Radome and antenna RCS 7.9 Exercises References 8 Passive observables testing 8.1 Introduction 8.2 Indoor ranges 8.3 Inverse synthetic aperture radar (ISAR) 8.4 Typical RCS range performance 8.5 Ground to air RCS testing 8.6 Air to air RCS testing 8.7 Ship ISAR from aircraft 8.8 Exercises References

xi 441 444 446 446 451 457 459 462 462 470 472 473 476 478 479 480 482 484 484 484 494 501 505 510 510 510 513 514 520 523 527 529 534 536 539 539 539 544 548 550 552 557 559 560

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An introduction to RF stealth, 2nd edition

Appendices Appendix Appendix Appendix Appendix Appendix Appendix Appendix Appendix Glossary Index

of of of of of of of of

Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter

1 2 3 4 5 6 7 8

563 563 564 566 567 569 572 573 576 577 591

About the author

David Lynch Jr. is an IEEE Life Fellow, senior member of the AIAA, former President of Pioneers of Stealth, and winner of Hyland Award and the Minta Martin Prize. He was involved in stealth programs as technical contributor including LPIR, Have Blue, F-117, Tacit Blue, Advanced Cruise Missile, and many others. Mr. Lynch was an inventor of or contributor to many world firsts, including manned space flight, telecommunications, digital signal processing, SAR, and stealth.

Supplementary material Software appendices for this book can be obtained by: ●

●

downloading from the IET Digital Library at https://digital-library.theiet.org/ content/books/ra/sbra540e. Once on the page, click on the “Supplementary Material” tab to access the files. Alternatively email [email protected] to be sent a copy of the files. requesting a DVD-R from the author by email at [email protected]. The cost is USD 15.00 inside the United States and USD 50.00 outside the United States to cover mailing.

The appendices contain data files and counterpart Adobe Acrobat files of most of the programs with output for a user to read first. They are supplied for information only.

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Preface

Much has changed since the first edition of Introduction to RF Stealth. The Russians, Chinese, and others have introduced stealth and counter-stealth systems. The material in the first book was based on work from the 1970s which finally became unclassified in the mid-1990s. In the mid-1990s, many countries became aware of stealth technologies. This book updates some progress since then. It is based entirely on unclassified open literature sources. It is amazing how many things forgotten are rediscovered by the current generation and maybe this will save some time. Much stealth technology is retrospectively obvious and mathematically simple but before it is explained, it is not so easy to see. The book is a “How to” allowing estimation of radar cross section (RCS), emitter interceptability, infrared (IR) signature with speed, emitter footprints, terrain obscuration and target visibility, ambient spectra, ambient pulse density, detection performance, stealthy antenna design including active electronic scanned antennas (AESA), filter and pulse compression sidelobes, emitter location accuracy, stealthy pulse compression design, and more. This introductory book presents first principles in a simple and approximate way. It will introduce technologists to the essential elements of RF Stealth from both a hardware and waveform point of view, using simple Mathcad, Excel, and Excelimbedded Basic examples. The programs are contained in the appendices for each chapter, along with an Adobe Acrobat file of the text of the programs as well as the plotted results of a program run. Everything from platform shaping, passive target detection and tracking, radar detection, waveforms, low RCS antenna design, and RCS testing. The Mathcad software should allow the curious to experiment with their own parameters and notions (play-with) to achieve a greater understanding of the underlying behaviors. Some may find this book trivial and too simple even for an introductory text. Again, please accept apologies, the simplicity is because the author did not include anything he could not understand himself. Besides, if the book seems trivial, you are already beyond the point of need anyway. Mathematicians may be bothered by some of the approximations but the approximations have proven to be adequate for real applications. The text is oriented toward undergraduate seniors and graduate engineers with some prior background in radar, communications, and basic physics. It approaches each topic from a system engineering perspective. The book is a summary of the courses, which my colleagues and your author taught between 1977 and 2015 on the general topic of RF Stealth. As you might imagine, there were many ideas. The author does not claim anything original in this

xvi

An introduction to RF stealth, 2nd edition

book, but it will be new to many. Much of this material is in the public domain and first appeared in un-copyrighted sources. It appears in many places, although I created much of it over the last 30–45 years. There are several references to formerly classified documents. The author may have the only copies in existence since the government usually destroys them when they become unclassified. Every attempt has been made to give credit where it is due but the early originators were not as careful as they should have been in citing references and some readers will undoubtedly find subjects in the text in which references are not properly cited. The author apologizes in advance for these errors but 25 years in the black makes them difficult to correct. In addition, try as one will there will always be mistakes which escape into the text; please notify me of those you find so that they may be corrected. A few photos, tables, and figures in this intellectual property were made at Hughes Aircraft Company and first appeared in public documents that were not copyrighted. These photos, tables, and figures were acquired by Raytheon Company in the merger of Hughes and Raytheon in December 1997 and are identified as Raytheon photos, tables, or figures.

Organization of the book The book covers two major topics low observables and low probability of intercept (LO and LPI) of radars and data links, collectively sometimes called stealth. In most sections, both are covered since the signatures often interact. Each chapter has examples, student exercises, references, and counterpart appendices that describe the associated software for download or DVD. Most of the analysis has been verified by experiment or computer simulation by the “Famous Names of the Radar/ Stealth World.” Chapter 1 provides an introduction and history of radio frequency (RF)/ microwave LPI/LO techniques and some basic LPI/LO equations similar to the first edition but with more info on new and current systems including more on infrared. Chapter 2 covers radiation absorbing materials and shaping. It is a completely new chapter focused on materials, meta-materials, and detailed platform shaping and structures including ships. Chapter 3 covers interceptability parameters and analysis with corrections, updates, and simulations. Chapter 4 covers current and future intercept receivers and some of their limitations with more information and tracking techniques. Chapter 5 surveys exploitation of both the natural and the threat environment with extensive threat table updates including Russian S300, S400, S500, and more info on cellular systems. It gives examples of one of the “great thoughts” of LPI/LO design, electronic order of battle (EOB) exploitation. Chapter 6 deals with LPIS waveforms and pulse compression with new material and simulations of new codes. It covers another “great thought” of LPIS: HudsonLarson complementary code pulse compression. Chapter 7 introduces some hardware techniques associated with LO/LPIS low sidelobe/cross section antenna and radome design with emphasis on active electronic scan arrays. It includes another of the “great thoughts” of LPI design: separable antenna illumination functions. Chapter 8 is a new chapter on RCS testing of subsystems and platforms.

Preface

xvii

Acknowledgments The mid-1970s found the happy coincidence of very bright, hard-working leaders, scientists, and engineers in both the United States Department of Defense (DoD) and Industry working on the stealth problem. The author was probably the least of these great people and lucky to be along for the ride. The early government leaders included: Jack Twigg, Bill Elsner, Skip Hickey, Ron Longbrake, Pete Worch, Ken Perko, Bruce James, Nick Willis, Bobby Bond, Harlan Jones, and a little later Ken Staten, Joe Ralston, Bob Swarts, Jerry Baber, Dave Englund, Don Merkl, Allen Koester, Hans Mark, Tom Swartz, Dick Scofield, Ken Dyson, John Sumerlot, John Griffen, Keith Glenn, Allen Atkins, Jim Tegnelia, John Entzminger, Tony Diana, Carl O’Berry, Jim Evatt, George Heilmeir, Allen Wiechman, and many others. The early industry leaders were Ben Rich, Ed Martin, Alan Brown, Norm Nelson, Dick Sherrer, Denys Overholtzer, John Cashen, Fred Oshiro, and Irv Waaland. Your author made many contributions to these technologies, but most methods and notions in this book are the creation of others including: Stan Aks, Pete Bogdanovic, Gary Graham, Joel Mellema, fred harris, Ralph Hudson, Eddie Phillips, Sam Thaler, Jim Uphold, Jack Pearson, Sam Blackman, Dave Green, Nate Greenblatt, Ralph Gifford, Jeff Hoffner, Jack Stein, Dan Rivers, Rudy Marloth, Ivan Bottlik, Tom Kennedy, Kan Jew, Howie Nussbaum, John Pearson, Hugh Washburn, Lee Tower, Steve Iglehart, Fred Rupp, Fred Williams, Don Stuart, Milt Radant, Dave Kramer, Charlie Smith, Charlie Strider, Wolf Kummer, Bob Hanson, Steve Panaretos, Mark Landau, Gene Gregory, Atul Jain, Bill Milroy, Don Parker, David Whelan, Chuck Krumm, Hank McCord, Mike O’Sullivan, and many others. The “author” is the editor and compiler of the material in this book. The ideas contained here are the products of an array of very bright people, and it is my privilege to summarize. As often happens when conditions are right, smart people invent the same thing without the knowledge that others are also doing it. We made lots of mistakes as happens in every new technology but fortunately there were enough creative people that we worked our way through each failure to success. Like all new technologies you cannot give it away at the beginning and much of the very early effort was not classified because it had never worked yet. Thanks also go to Dr. Brian Kent and his U.S. Air Force coworkers for a careful assessment of the security compliance of the book. David Lynch Jr. IEEE Life Fellow, Senior Member AIAA, Stealth Pioneer, Life Member Sigma Xi

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Chapter 1

Introduction to stealth systems

1.1 Introduction Guessing and knowing are two completely different things. The objective of stealth is to keep the adversary guessing until it is too late. Over the past few decades, stealth platforms, especially aircraft, have come into public consciousness. However, stealth research work was conducted in earnest beginning in the mid1970s and was spearheaded by the Defense Advanced Research Projects Agency (DARPA) in both U.S. Air Force and Navy programs. Most of those programs are still shrouded in secrecy, but a few, especially the earliest, are now declassified, and the basic notions of stealth technology can be described. For reasons of classification, nothing can be said about aircraft like the F-117A and the B-2, pictured in Figures 1.1 and 1.2, respectively, but they grew out of those early programs. Several generations of technology have now passed, as embodied by such aircraft, but the basic stealth concepts remain the same.

1.1.1 Introduction to survivability Survivability is the system engineering discipline of finding the best way to perform a mission with the greatest chance of success and survival of the weapon system designed to perform that mission. Each mission, counterpart threats, and potential countermeasures have different attributes that influence the design. ●

●

●

●

●

●

Mission, for example, defend a point on earth, control the sea, monitor potential adversaries, and defend a region or a country Threats to the mission, for example, nuclear, high explosive, chemical, biological, and electromagnetic. Threat platform, for example, intercontinental ballistic missile (ICBM), intermediate range ballistic missile (IRBM), airplane, submarine, guided bomb, buried improvised explosive device (IED), explosive vest, and explosive shoe. Countermeasure, for example, indications and warning (I&W), deeply buried bunker, early warning, stealth, jamming, antisubmarine warfare (ASW), air defense, and airport screening. How to counter, for example, spies, space surveillance, airborne early warning (AEW) radar, offshore SOSUS nets, ELINT, and chemical/biological sensors. Identify limits, for example, the shorter the distance in space/time and the more resource intensive.

2

An introduction to RF stealth, 2nd edition

Figure 1.1 F117A stealth attack fighter. Photo courtesy: author

Figure 1.2 B-2 stealth bomber. Photo courtesy: D. Whelan. Adapted from [1]

●

● ●

Threat direction, for example, airports, seaports, high altitude, underwater, nose on, and broadside. Threat range, for example, 10s of feet, miles, horizon, and intercontinental. Threat timeline, for example, 10
3 s (EMP or high power laser weapon), 10s of seconds (surface to air missile), 30 min (ICBM), and years (terrorist).

For example, Figure 1.3 shows a ship in which each threat direction may have completely different types of threat with different timelines and different ship vulnerabilities. One sector might be submarines with a timeline of an hour. While another sector might be ballistic missiles with a timeline of minutes. There are multiple ways a threat might be detected and set in motion a series of actions to counter that threat. Table 1.1 lists different sensors, their usable range, their direction of use, timeline, and exploitable feature on the threat. Eyes and ears were used extensively in World War II (WW II) to detect aircraft attacking England. There are short-range sensors that detect magnetic materials and

Introduction to stealth systems

Top sector

3

High elevation

Rear sector Low elevation

Side sector Front sector Lower sector

Figure 1.3 Identify the threat direction Table 1.1 Counter threat sensors Type

Typical range (ft)

Direction

Timeline (s)

Exploitable feature

Nose Eyes Ears

10 104 100

5–10 5–30 5–30

HE/chem/bio Platforms Platform acoustics

Magnetic Chem/bio UV LWIR MWIR EO Acoustic Radar/ladar

100 100 1000 105 5  104 2  104 103 or 107 107

Omni Nose on cone Best forward hemisphere Omni Omni Focused cone Focused cone Focused cone Focused cone Focused cone Focused cone

1–10 10–105 10
3–5 10
3–5 10
3–5 10
3–5 1–10 10
3–5

Magnetic materials Chem/bio Missile combustion Hot/cold platforms Hot/cold platforms Illuminated platforms Platform acoustics Electromagnetic discontinuities

antipersonnel chemical or biological agents. Ultraviolet is used to detect missile propulsion exhaust. Infrared is used to detect hot or cold platforms that differ from the background. Electro-optical sensors rely on starlight, moonlight, or sunlight. Acoustic sensors such as sonar detect sounds from platforms in some cases at a very long range. Radar and ladar sensors have the longest detection ranges and hence provide the greatest warning time. Since radar and ladar provide the longest detection range, that is the first focus for a stealth platform on the surface, in the air, and in space. Sonar provides the longest detection range underwater and so acoustic emissions are the first focus for a stealthy submarine.

4

An introduction to RF stealth, 2nd edition

1.1.2

Brief history of radar and ladar

Because radar and ladar (which is just a very short wavelength radar) have such long-range performance, the history of radar development is important to gauge what new evolutions may occur. The 130-year history of radar begins with Heinrich Hertz demonstrating radio waves reflected from metal objects. Tesla showed a radio-controlled boat at a world’s fair anticipating radio guidance of missiles and bombs. Ship detection and later aircraft detection were demonstrated by 1930. During the 1930s, radar developments improved dramatically. With the onset of WW II, radar development accelerated and both ground-based and airborne radars were developed and used in combat. Both the United States and UK used radar for early warning, navigation, and fire control. The dropping of the atomic bombs on Japan used radar for navigation and target location designation. The invention of solid-state lasers at Hughes Research Labs in 1958 led to ladar developments in 1960. By 1970, lasers were used for weapon guidance. High-power lasers were being designed into weapon tracking and target kill systems. By 1980, there were laser target weapon guidance deployed. Table 1.2 summarizes these advances. A simple radar block diagram is given in Figure 1.4. The essential elements are an antenna, a transmitter, an exciter, a stable frequency source, low noise receiver, signal processor, a display, and a controller. For a radar or ladar to be useful, the signal-to-noise ratio (SNR) must be adequate to detect a target at the desired range. One version of the radar equation development is given in Figure 1.5. The radar signal propagates through space spherically, encounters a target that reflects a fraction of the incoming energy toward a receiver. That reflected Table 1.2 History of radar and ladar Dates

Events

1886

Hertz demonstrates radio waves are reflected from metal and dielectric objects Tesla demonstrates radio control of a small ship Hulsmeyer detects radio waves reflected from ships Marconi urges the use of short waves for detection of objects Hyland detects aircraft with CW radar Watson-Watt (UK) and Page (US) demonstrate pulsed radar Radar developed in the US, UK, France, Germany, USSR, and Japan prior to WW II UK suggests the United States develop air-intercept and antiaircraft fire control radar MIT Radiation Laboratory established to develop radar—4000 staff and publication of Rad Lab 28 volume series at war end Digital signal processing, masers, high power klystrons, low noise TWT’s, parametric amplifiers, gyrotrons, synthetic aperture, and over-the-horizon radar Active arrays, photonic devices, multiple phase center arrays, space-time-adaptive-processing, MIMO radar, and laser radars demonstrate missile detection and track at 100s of miles.

1889 1903 1922 1930 1934–1936 Late 1930s 1940 1940–1945 1945–1970 1970–present

Introduction to stealth systems

5

energy is usually small when it arrives at the receiver. There is both ambient noise and noise in the receiver itself competing with the returned signal. Gathering all those factors together results in the radar equation SNR.

Drive

Transmitter

Exciter

Target Propagation

Circulator Antenna

L.O.

Clutter Signal processor

Receiver Modes, timing ETC.

Display Controller Operator

Figure 1.4 A simple radar

Target

1 (4∙)∙R2 R

G

G

σ PT R 1

TRF

XMIT

Noise k∙TA

A

Transmitter

Receiver

SNR1 =

RCVR TEX,B

(4∙)∙R2

Total noise temperature Te = TEX + TRF + TA

PT · G · A · σ · √n (4 ∙ )2 ∙ R4 ∙ kB ∙ Te ∙ B

Number of pulses & chips integrated n = TOT ∙ PRF ∙ PCR

Figure 1.5 Radar/ladar equation development

6

An introduction to RF stealth, 2nd edition

Laser radars or ladars are not very different than the radar block diagram of Figure 1.4. The primary difference is that the antenna is now a set of lenses or mirrors as shown in Figure 1.6. The coherent reference (local oscillator) is mixed optically with the return signal and sent to a detector. There still must be some front-end filtering just as in microwave radar. A more detailed version of a ladar receiver is given in Figure 1.7. In this case, the receiver is a Cassegrain telescope. Often in space communications and space radars, the antenna is also a Cassegrain. In this case, the secondary optics does not totally focus the signal, allowing the filter aperture to be a little larger. Following the filter is a refocusing mirror that bends the light to a detector. Because the reference signal is so much larger than the received signal, the detector nonlinearities result in harmonics producing sum and difference frequencies for further processing. All of the techniques used at radar frequencies are usable for ladars. Just as with radar, the amount of signal that is backscattered from a ladar target depends on the surface treatment relative to the wavelength of illumination. Some ladar target backscattering examples are given in Figures 1.8 and 1.9. Because surface roughness plays a much bigger role in ladar illumination, bistatic cross section is large over a wide range of angles relative to radar cross section (RCS) as seen in Figures 1.8 and 1.9. Transmit optics Display

CW Laser

Modulator

Coherent reference Processor

Detector

Filter Receive optics

Figure 1.6 Typical ladar block diagram. Adapted from [2] Enclosure barrel Filter Refocusing mirror

Entrance pupil Detector Primary mirror

Secondary mirror

Figure 1.7 Ladar receiver detail. Adapted from [2]

Introduction to stealth systems

7

0.4 0.35 Reflection factor

White untinted polyurethane on aluminum

0.3 0.25

White spectralon

White paper

0.2

Flat white paint on aluminum

0.15 0.1

0

13

27

53 40 Bistatic angle (deg.)

67

80

Figure 1.8 Ladar target surfaces I. Adapted from [2] 0.01

Reflection factor

0.008 Black spectralon

0.006 Black corduroy cloth

0.004 Black flocked paper

0.002 Martin black

0.001

0

15

45 30 Bistatic angle (deg.)

60

75

Figure 1.9 Ladar target surfaces II. Adapted from [2]

1.1.3 Brief history of signature reduction As radars and sonars got better, there were natural efforts to counter these sensors. The impetus for radar and sonar during WW II caused nations to develop signature reduction. Table 1.3 summarizes signature reduction efforts. Subsequent to WW II progress on stealth slowed until the 1970s by that time understanding of signature sources and mathematical tools became quite good. In the mid to late 1970s, multiple programs showed the feasibility of stealth. Once other nations knew it could be done, they started their own stealth programs. Today there are dozens of stealth programs all over the world. Figures 1.10–1.12 show examples of firstgeneration stealth platforms.

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Table 1.3 History of signature reduction Dates

Events

1940–1945

British propose aircraft RCS reduction; Germany uses radiation absorber on submarines USAF ballistic missile reentry vehicles, SR-71 USAF countermeasures decoys, USAF-Lockheed efforts to reduce aircraft signatures with wires and ferrites, Navy submarine quieting designs, and sneaker program USAF low RCS remotely piloted vehicles, USAF Have Blue, F-117, Tacit Blue, USAF/Navy LPIR, and others USAF AGM-129, B-1B, B-2, Navy A-12, Sea Shadow, Outlaw Bandit, Army Comanche, and others USAF F-22, USAF/Navy F-35, and others Russian PAK-50, Chinese J-20, USAF RQ-170, Swedish stealth UAV, Navy-Northrop X47-B, and many others

1950–1960 1960–1970 1970–1980 1980–1990 1990–2000 2000–present

Although these platforms are very different, they all exhibit all of the basic techniques used to reduce radar, ladar, and EO/IR shaping. Low reflectivity material selection—paints, surface coatings, and radiation absorbing material (RAM). They use low emissivity materials and surfaces. They use passive cancellation with 1/4 wave coatings. Although this is quite dangerous if you get it wrong, they could use active cancellation, that is, transmit a signal equal and opposite to the reflected signal. Large surfaces are chosen to deflect radar and ladar to angles which are not tactically useful. Propulsion is mostly hidden. Edges are aligned and loaded with RAM.

1.1.4

Great thoughts of stealth/LO technology

The essential elements of passive signature control (LO) are summarized below. More details are provided in Section 1.5 and Chapter 6. ● ● ● ● ● ●

Planform alignment/isomorphism Facets and shape Edge treatment by convolution Impedance control Edge treatment by impedance matching Exploitation of environment

With respect to a radar or data link in an LO platform, the first element is a shaped radome. The radome usually will be bandpass, that is, only passing those frequencies in the normal emitter band of operation. Outside of that band, the radome should be lossy and properly reflective. With appropriate radome shaping, out-ofband RCS can be quite low over a wide range of angles. The radome also can be switchable, which means that even in-band, the radome may be closed when the emitter is not operating. Under these circumstances, the radome may take on crosssection properties of a lossy reflective and properly shaped surface (see Chapter 7).

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Figure 1.10 Tacit Blue first-generation stealth. Adapted from [3]

Figure 1.11 Have Blue first-generation stealth. Adapted from [3].

Figure 1.12 Sea Shadow first-generation stealth. Adapted from [3]. However, when the emitter is on, the radome must be open and relatively transparent, which can cause the antenna to present a very large RCS in both of its surface normal and its pointing direction. Usually, the antenna face must be canted relative to the beam pointing direction. In addition, the antenna should be dynamically stowed when it is off, so that it presents the lowest possible RCS to the radar horizon or threat direction. Inside the compartment that contains the antenna, radiation-absorbing material (RAM) should be applied so the energy that does enter the radome is well terminated and not retro-reflected. Any other internal surfaces inside a radome antenna cavity, such as gimbals, mounting plates, auxiliary horns, etc., that might be visible at some viewing or multibounce angles should be faceted with their surface normals aligned along the platform planform.

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1.1.5

Brief history of LPI systems

RF stealth is not new. The British were proposing RCS reduction techniques in 1941 [4]. The first complete modern demonstration of an LO platform was the DARPA/USAF/Lockheed Have Blue aircraft. So much has been written about Have Blue that no discussion is necessary here [5]. The first modern demonstration of LPI techniques was the Navy/Westinghouse Sneaker program. The first complete LPI system program was the LPIR started in the mid-1970s by DARPA, the U.S. Air Force and Navy, with Hughes Aircraft Company as the prime contractor. That program resulted in the conclusive demonstration that LPI techniques could be employed and still provide a complete airborne radar weapon system. The performance, modes, and accomplishments are summarized in this section. Flight tests of the first airborne LPIR system were completed in 1979 and 1980. The system was tested against an AN/ALR-62-equipped F-111 from the 57th Test Wing at McClellan Air Force Base. The ALR-62 is a radar homing and warning (RHAW) receiver that has full 360 coverage over a wide range of frequencies. It has a potential equivalent sensitivity of
65 dBm. The ALR-62 used in these tests was especially programmed to detect and identify LPIR waveforms. All available parameters of the LPIR system were provided to the programmers of the RHAW receiver so that an adequate algorithm could be incorporated to detect an LPI system [6–9].

1.1.6

LPIR program accomplishments

First complete airborne LPIR system. ●

●

●

●

System tested against RHAW (ALR-62) equipped F-111F from 57th Test Wing, McClellan AFB. Air-to-air modes demonstrated with 40 km detection, acquisition, and track to crossover without intercept. Ground-to-air roofhouse demonstration in January 1979 and air-to-air demonstration in November 1979. Air-to-ground modes (ground moving target detection and tracking) demonstrated in April and May 1980, successful LPI detection, and track of ground vehicles at a maximum range of 20 km.

The second program to incorporate LPI features was the DARPA/USAF Pave Mover program which began flight test shortly after the conclusion of the LPIR program. It continued to demonstrate a wider set of LPI modes and features including alternative LPI strategies, longer-range operation, LPI data links, more air-to-ground modes, adaptive ECM nulling, weapon delivery, and the LPI benefits of electronic scanning. Subsequently, there were many programs that have applied LO/LPI features and most of which are still classified.

1.1.7

LPI modes demonstrated through test

Listed below in Table 1.4 are the stealthy radar and data link which have been demonstrated in unclassified or declassified test programs. For example, air-to-air

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Table 1.4 Demonstrated LPI modes Air-to-Air

Air-to-Ground

Search Target acquisition Track Track while scan Air combat Missile data link Stealth weapon delivery ECCM

Real beam ground map Ground moving target indication Ground target track moving and stationary Doppler beam sharpening Terrain following Synthetic aperture All weather weapon delivery Air to ground station data links

medium PRF modes were demonstrated with 40 km detection, acquisition, and tracking (shown in Figure 1.20). Power management was employed with a typical maximum power per frequency of 3 watts. Tracking lock-on near maximum range was consistently achieved and track was maintained all the way to crossover/ gimbal limit without any intercepts occurring. In January 1979, there were groundto-air roofhouse demonstrations and in November 1979, air-to-air demonstrations. The following year, air-to-ground modes were tested. Both ground moving target detection (GMTD) and ground moving target tracking (GMTT) were demonstrated in April and May 1980, with successful LPI detection and track at the maximum design range of 20 km. The surface vehicles tracked in these tests carried a responsive jammer with an intercept receiver that could be used to detect the LPI signal. In addition, these tests were conducted in an ECM environment and, in most cases, the LPIR was not only able to detect, acquire, and track both air-to-air and air-to-ground targets but also to defeat the countermeasures. The program was very successful, and the LPI system met its program objectives. The only time this radar was ever detected by any intercept receiver or ECM gear was when radiated power was intentionally augmented to 100 watts per frequency and fixed so that the radar could be detected for intercept receiver performance verification. Even to this day, there are skeptics about achievable stealth system performance but this is mostly from those who are uninformed. Especially silly are claims about some Eastern European intercept systems. The stealth weapon systems, which have been shot down, owe that primarily to poor tactics as will be discussed in Chapter 4. Any system is susceptible to bad tactics or the “golden BB”; just remember, an aborigine shot down a UN helicopter with a bow and arrow and killed the UN secretary general.

1.1.8 LPIR program results summary The performance results demonstrated almost 40 years ago in LPIR program are summarized below. The total intercept threat system sensitivity, PI /GI, given below is the intercept receiver sensitivity at the threshold device referred to the

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front end divided by the interceptor antenna gain including all radome and cabling losses. ●

●

●

Radar performance Air-to-air: 5 m2 target, lookdown mode, search, acquisition, track, and missile guidance—detection range 40 km Air-to-ground: RB map, GMTI/T (trucks), and DBS (0.3 ) detection range 80 km Weapon delivery targeting accuracy: 0.46 milliradian CEP, stationary and moving targets, and ECCM: Like F-16 against DLQ-3B jammer Flight test RWR: specially modified ALR-62 in F-111F, the best RHAW the United States had at that time 18 passes, Jan 11
12, 1979 ALR-62 detected LPIR only when the test profile intentionally allowed it using 100 W peak, 14 km typical intercept range, consistent with ALR-62 specification performance, 1 year, 400 passes against military and civilian targets, LPIR detection ranges: 22–35 km, track acquisition ranges: 14–22 km, track ranges: 0–40 km, and power: 3 W peak, 0.75 W average. Intercept threat RWR mainlobe: RI  10 km, PI /GI
60 dBm, and 1 GHz bandwidth ELINT sidelobes: RI  20 km, PI /GI
120 dBm, and 5 MHz bandwidth ARM sidelobes: RI  5 km, PI /GI
75 dBm, and 30 MHz bandwidth

These demonstrations give rise to an obvious question: how does one verify and validate that an LO/LPI system is succeeding at its mission? Perhaps the intercept receiver or jamming equipment is broken. Is there any difference between a broken intercept receiver or countermeasures equipment and one that is actually being fooled by an LPIS? There must be a sequence of techniques used to verify that the countermeasures or interceptors are actually working during the course of a LO/LPI test program. Most LPI evaluation is identical to conventional emitter evaluation. LPI is measured by placing an intercept receiver at the target or with a fixed offset with respect to the target. Power management is then switched off so that full power will be transmitted to verify that the intercept receiver is working. One of the items often requested, but usually virtually impossible to do, is suppression of the pseudorandom dynamic waveform selection that is incorporated into the mode design of every LPIS. It is generally not technically feasible to shut off dynamic waveform selection during LPI verification and validation. Finally, the RCS of an LO/LPIS is usually measured statically on indoor or outdoor ranges, and finally, its performance is measured in air to air RCS tests on the LO vehicle. The upper bound on the installed RCS of an LO/LPIS is the vehicle cross section in the emitter band, about 60 with respect to the antenna normal. What then are typical LPIS performance parameters? First, antenna sidelobes are typically less than
55 dB rms below the mainlobe over the half-space. Second, power management is often conducted over a 70 dB dynamic range. Time bandwidth products of 4  106 are typically achieved in LPI systems. Even with modern processing technology, that is a great deal of integration. Typical instantaneous bandwidths are between 1 and 4 GHz. In order to achieve very high time-bandwidth

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products, fully coherent frequency agility and corresponding stability of 1 in 1010 are required. A typical number of channels simultaneously processed are on the order of 6 to 9. Tracking is normally performed with a 3 dB SNR. All these performance parameters are achieved with a full complement of modes.

1.2 The stealth design challenge ●

●

Survive and prosper in the future environment of improved sensors, dense countermeasures, antiradiation weapons, and emitter locators Become invulnerable or invisible

Stealth requires the reduction of active and passive signatures. Signatures are the acoustic, optical, RF, infrared, ultraviolet, magnetic, and chemical emissions from the platform. Some early stealth examples are camouflage, blinds, for example, duck blinds, downwind approaches, disguises, submarines, fake animal calls, etc. RF signatures are detectable at the longest ranges for surface, airborne, and spaceborne platforms. RF signatures must be suppressed first. Stealth is not one item but an assemblage of techniques, which makes a system harder to find and attack. Stealth radar and data link design involve the reduction of active and passive signatures. Active signature is defined as all the observable emissions from a stealth platform: acoustic, chemical (soot and contrails), communications, radar, IFF, IR, laser, and UV. Passive signature is defined as all the observables on a stealth platform that require external illumination: magnetic and gravitational anomalies, reflection of sunlight and cold outer space, reflection of acoustic, radar and laser illumination, and reflection of ambient RF (sometimes called splash track). Active radar and data link signature reduction requires the use of techniques that minimize radiated power density at possible intercept receiver locations. Active signature reduction also depends on the implementation of tactics that reduce exposure time during emission.

1.2.1 The stealth approach ●

●

●

●

●

Force the threats to use active sensors sparingly by employing antiradiation missiles and electronic countermeasures. Decrease predictability and increase “randomness” to force the threats to increase complexity and cost of intercept receivers, surveillance, fire control, and missiles. Reduce active and passive signatures and increase “hiding” to make weapon systems less visible. Use tactics that combine with the order of battle as well as the natural and manmade environment to enhance the effect of the reduced observables. Use prior knowledge and offboard sensor cueing to minimize onboard active and passive exposure.

The Radar Cross Section (RCS) and Laser Cross Section (LCS) notion is a combination of geometric cross section, reflectivity of the surface, and directivity of the surface as shown in Figure 1.13. The active signature reduction methods are

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An introduction to RF stealth, 2nd edition Scatter

σ=

Geometric cross section

×

Reflectivity

×

Directivity

Scatter

Figure 1.13 The RCS notion

Low cross section Maximum signal uncertainty

Minimum peak power

Figure 1.14 LO/LPIS objective commonly called low probability of intercept (LPI) techniques and are illustrated in Figure 1.14. Passive signature reduction techniques are often called low observables (LO). They require the development of radome, antenna cavity, and antenna designs as interactive elements of a common subsystem that yields low in and outof-band RCS. Additionally, passive radar signatures are reduced in-band by employing special antenna design techniques that minimize retro-reflective echoes. Low probability of intercept system (LPIS) design is an engineering problem with a larger set of optimization constraints and hence no different than every other modern design challenge. The stealth designer must always create designs in which complete knowledge of the design is not much help to the threat. Conventional antenna designs have side and mainlobe patterns that do not differ fundamentally from that shown in Figure 1.15(a). There are a few close-in sidelobes and, of course, the mainlobe, which are above isotropic. The remainder of the sidelobes average 3 dB to 6 dB below isotropic for a conventional antenna. On the other hand, an LO/LPI antenna has sidelobes that are
10 dB to
30 dB below isotropic and may average more than 20 dB below isotropic. These low sidelobes are realized at the expense of mainlobe gain and full utilization of the total aperture area. An idealized LO/LPI antenna pattern is shown in Figure 1.15(b). Similarly, conventional aircraft RCS may be noise-like, but it is generally well above 5 m2 in most directions, as shown in Figure 1.16(a). In most cases, very little

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40 dB 30 dB 20 dB 10 dB 0 dB (Isotropic)

–30 dB –20 dB –10 dB 0 dB (Isotropic) 10 dB 20 dB 30 dB

(a)

(b)

40 dB

Figure 1.15 (a) Conventional and (b) LO/LPI antenna patterns effort in conventional platform design was devoted to the reduction of the platform RCS. Some of this lack of effort was due to the belief that low RCS vehicles would have undesirable aerodynamic, hydrodynamic, or functional shapes. It is now known that this is not the case; it is the lack of planform alignment in the direction of the threat that results in many RCS spikes. A typical stealth aircraft signature strategy might be as shown in Figure 1.16(b), where there are five main spikes that contain most of the RCS signature. The total RCS integrated over all directions will not be much better than that of a nonstealthy platform. By pushing most of the RCS into a few large spikes then everywhere else can be much lower. If those directions are in areas that the threat cannot exploit, then the platform can be stealthy. Figure 1.17 suggests that spikes from each edge result in a signature like that shown on the right in Figure 1.16(a). The strategy for a stealth aircraft signature is not fundamentally different from that for an LO/LPI antenna. The idea is to design a platform in such a way that there are only a few RCS spikes in carefully controlled directions. The vast majority of angle space is occupied by RCS that is substantially below that of a conventional platform. The rest of the angle space is occupied by relatively low RCS lobes. This can be thought of as similar to the radar signal ambiguity function, where the total volume under the curve must be preserved. Others have pointed out that the average RCS of a smooth body (see Table 1.6 for eggs and spheres) is on the order of ¼ the total surface area. As a result, concentrating all of the reflections in a few directions can reduce the RCS in all other directions. RCS enhancement can be designed so that those spikes are not tactically useful to threat sensors because the geometry is poor relative to either the threat radar horizon or the threat platform velocity vector. The first “great thought” of stealth is planform alignment or spike alignment of all of the major scatterers on a platform. Most RCS reduction comes from shaping. Radar absorbing materials (RAM) are only applied in areas where there are special problems and they have very little to do with the

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An introduction to RF stealth, 2nd edition 35 dB 30 25 20 15 10 5

(a)

40 dB 30 dB 20 dB Low observables aircraft objective

10 dB 0 dB –10 dB

(b)

Figure 1.16 (a) Conventional and (b) stealth aircraft RCS signatures

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Specular radar scattering directions

Figure 1.17 Lack of planform alignment results in many RCS spikes average RCS. Furthermore, mismatches between RAM and free space create a first scatter which must not be reflected in a tactically useful direction.

1.2.2 Balanced design Active and passive signatures must be balanced relative to a threat. This requires that cross section reduction and management of the active emissions be controlled in a combined and concerted way. First, the active emission of an LPI system (LPIS) must be controlled in each operating mode, using only the power that is necessary for that mode. In addition, the power must be programmed while tracking a target or communicating by data link so that, as a target or link destination opens or closes in range, the power is adjusted accordingly. This is the first “great thought” of LPIS technology. Next, emitter on-times must be limited. The emitter active signature when the emitter is not transmitting still exists, but it is orders of magnitude lower than when it is on. By using a radar or data link only when necessary and by making maximum use of a priori information, the off-time of the emitter can be 60% or more, and the system can still perform very successful, useful missions. This is the second “great thought” of LPI design. Active emissions control must be coupled with platform cross-section reduction. There are a number of techniques used for RCS reduction that will be presented in Chapters 3 and 6 of this book. The other “great thoughts”, in addition to planform alignment, are facets and shape, that is, selecting shapes that reflect very low sidelobes in the direction of illumination/threat, edge treatment by convolution, that is, using a mathematical function such as a Gaussian convolved on the junction of two surfaces to create a “blend” which has very low RCS sidelobes, impedance control, that is, insuring there are no discontinuities in the platform surface impedance, edge treatment by impedance matching of the platform skin to free space, and exploitation of the environment.

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Unfortunately, stealth techniques are more expensive both to design and to maintain. As a result, a stealth designer must strive to balance all the signatures of the system. The detection or threat range for each signature component should be similar. For example, the infrared threat range should be roughly the same as the radar or intercept threat ranges. Each threat system has a characteristic engagement balloon as shown in Figure 1.18. The balloons will not be the same shape, in general, but in a modern stealth system, they should be close as depicted in the figure. This means, for example, that the intercept range for a threat antiradiation missile should be roughly comparable to the range at which a threat radar-guided missile would be effective against the platform RCS. Each signature should be balanced to the corresponding threat—UV, visible, IR, radar, RF, acoustic, magnetic, etc. As previously mentioned, the stealth designer must always create designs in which complete knowledge of the LPIS does not help much. These constraints are discussed in detail in Chapters 3 and 5. Future and response threats are analyzed in Chapter 4 including massive noncoherent integration (sometimes called radiometry).

1.2.3

RCS and power management summary

The essential elements of RCS and power management are summarized below. More details are provided in Chapters 3, 6, and 7. ● ● ● ● ● ● ● ●

LPIS power controlled by mode, a program in track (Chapters 3 and 6) LPIS on-times limited to 40% or less (Chapter 3) Shaped low RCS radome (Chapter 7) Radome frequency selective (Chapter 7) Radome reflective during off-time (Chapter 7) Antenna face canted with respect to beam pointing angle (Chapter 7) Antenna dynamically stowed during off-time (Chapter 7) Antenna cavity lined with radiation-absorbent-material (RAM) (Chapter 7) Surveillance zone

Surveillance zone Side view central cut Planning and coordination time

Planning and coordination time

Maximum possible threat altitude

Radar weapon 80% employment range

80% weapon employment range

Surface

Defensive volume Plan view

– Terminal – No escape plus reaction time

Figure 1.18 Balanced engagement balloons

Antiradiation weapon 80% employment range

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1.3 Low probability of intercept systems: an introduction There are a number of “simple” thoughts which are robust counters to passive threats to emitters. Some of these have already been introduced in the proceeding section. Some will require more background to appreciate. All of these simple but great thoughts will be described in more detail in the Chapters 3–7. There are many stealth ideas but the “great thoughts” have been demonstrated to work the best in the real environment of modern civil and military electronic systems [10].

1.3.1 Great thoughts of LPI systems design The essential elements of active signature control (LPI) are summarized below. More details are provided in Chapters 3, 4, 5, 6, and 7. ● ● ● ● ● ● ●

Maximum bandwidth (Chapters 3, 4, and 6) Power management (Chapters 3 and 6) Emission time control (Chapter 3) Creation and exploitation of gain mismatches (Chapter 3) Separable antenna illumination functions (Chapter 7) Hudson-Larson complementary code pulse compression (Chapter 6) Electronic order of battle exploitation (Chapter 5)

LPI counters the many passive threats to emitters such as radars and data links. Table 1.5 summarizes some of those threats with respect to threat type, type of intercept receiver, threat objective, and whether the threat operates primarily in the sidelobes or in the mainlobe of the emitter antenna. The threats range from antiradiation missiles (ARM), direction of arrival (DOA) systems, radar warning receivers (RWR), electronic countermeasures (ECM) equipment, and electronic intelligence (ELINT) systems. All of these threats are designed to degrade the performance of the emitter in its mission either immediately or over a span of time and ultimately to destroy the usefulness of the weapons system. All of these passive threat systems depend on some type of intercept receiver. The intercept receiver performs three basic functions: detection, sorting, and classification. The intercept receiver detection function depends on single-pulse peakpower detection at the outset, and little or no processing gain is obtained for the first detection. This is primarily due to uncertainty about the angle of arrival, actual operating frequency, and waveform of emitters, which may include LPI radars or data links. This initial large signal mismatch is one of the principal advantages of an LPIS. The third “great thought” of LPI design is the creation and exploitation of gain mismatches. The second intercept receiver function, sorting, is achieved by a combination of hardware and software. Sorting is designed to operate in a dense signal environment in which there are many intercept signals; perhaps all in the same band, all arriving from different directions. The task of sorting is the separation of individual emitters from this environment so they may be recognized or classified.

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Table 1.5 Passive threats to radars and data links Threat type

ARM DOA RWR ECM ELINT

Intercept receiver function

Threat objective

Missile guidance Emitter location Pilot warning ECM control Jammer turn-on, set-on, pointing Warning Electronic order of battle (EOB)

Operation through antenna Sidelobes

Mainlobe

Hard kill Attack or avoidance Maneuvers Jamming, chaff, and flares Degraded detection and track

Yes Yes No Yes Yes

No No Yes Yes Yes

Intelligence, battle planning, operations control, and ECM design

Yes Yes

Yes Yes

The third intercept receiver function is classification. It identifies or recognizes emitter type, or even the specific emitter, and from that, the weapon system in which the emitter is carried. Once the weapon system is identified, suitable countermeasures can be employed. The waveforms selected also must make countermeasures difficult to employ. LPI systems must be designed to degrade all three intercept receiver functions. In the course of the next six chapters, many techniques will be discussed that work on each of these three properties. Obviously, if an emitter is never detected, it cannot be sorted or classified but usually mission performance suffers too much to depend on never being detected. There will inevitably be detections but selected waveform properties such as large duty ratio over significant bandwidths enhance the chance of embedment of multiple emitter signals making sorting very difficult. Sometimes, in spite of careful waveform selection and bad luck, an LPI emitter will be sorted and the waveform must also be made hard to classify by spoofing or other agility features.

1.3.2

Passive detection and intercept probability

Passive detection probability is associated with detection and intercept by a threat receiver. Passive detection probability is the probability that an intercept receiver will detect an emitter, given that the intercept receiver antenna, RF front end, and processor are directed at the emitter while the emitter is transmitting toward the intercept receiver. Intercept probability is the product of the detection probability and the emitter on-time divided by the intercept receiver scan time (1.1). The intercept receiver requires a certain amount of time to cover both the frequency range in which the emitter may transmit and the angle space over which it surveys. Since an LPI system is not on or pointing in the same direction all the time, these scan-on-scan probabilities reduce the intercept probability below that which would occur based on power and antenna gain alone.

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Intercept probability is: Intercept Probability =

Detection Probability × Emitter-On-Time Intercept Receiver Scan-Time

(1.1)

Obviously, not all systems scan, in which case the emitter-on-time/interceptorscan-time is one. It usually turns out that even if the RF or antenna does not scan, the signal/computer processing has a scan or frame or refractory time. Many intercept systems which form simultaneous multiple antenna beams or RF filters have such poor sidelobes (
25 dB.) that false alarms overwhelm their sensitivity and stealth targets are thresholded out. They would have been better off scanning if stealth targets were the only threat. Such basic observations lead to an obvious set of elements for an LPIS design. To defeat detection, an LPIS must minimize required effective radiated power, effective intercept receiver sensitivity, and required on-time. To minimize effective radiated power, the transmitter power must be managed to the minimum necessary for a given range and mode or function. In addition, low sidelobe antennas must be used for minimum sidelobe effective radiated power. Minimizing required effective radiated power implies that the shortest operating range, based on usable weapon system mission parameters, must be employed at all times and the largest possible antenna aperture or gain and maximum transmitter duty ratio is required. If receive losses are high, more transmit power must be emitted; therefore, an LPIS requires minimum receive losses and the lowest possible noise figure. Furthermore, because losses are important, maximum coherent integration must be used to save processing losses. To minimize realized intercept receiver performance, the maximum use of a priori knowledge and passive sensing is required whenever possible. The weapon system should not emit to determine information that could be obtained by some other method. This, in turn, implies maximum use of prebriefed missions and accurate navigation systems on the weapon system platform. Lastly, LPIS must minimize required on-time and utilize maximum extrapolation between measurements. The least detectable LPIS is one that is off.

1.3.3 Reduced detectability: effective radiated peak power The definition of effective radiated peak power (ERPP) is the root mean square power in the transmitted pulse through the antenna mainlobe, sidelobes, and radome into free space. There are two thoughts here. The exact power which can be detected and where to reference it. It is the free space power which is immediately outside the radome and vehicle skin which is detectable. On a stealth vehicle, one can think of the antenna as the feed and the platform as the actual radiator. Minimizing antenna sidelobes may minimize the sidelobe ERPP if the radome and antenna installations are carefully done. Minimizing receive losses minimizes the power that must be propagated in free space. Since total signal energy determines detection performance, average power over the observation period is what counts for the LPIS, not peak power. The essential elements of ERPP control are summarized below. More details are provided in Chapters 3, 4, 6, and 7.

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● ●

An introduction to RF stealth, 2nd edition Signal uncertainties and broad threat spectrum force intercept receivers to depend on single-pulse peak power detection (Chapters 3 and 4). LPI systems require low peak power and high average power (Chapter 3). LPI systems are ERPP limited and therefore require very low receive losses and energy management (Chapters 3 and 6).

Figure 1.19 shows one of the simplest kinds of gain mismatch exploitation in LPI, single pulse peak power detection. Because an interceptor must deal with a wide range of threats, its predetection bandwidth is set by considerations other than the transmitted pulse width of an LPIS; therefore, noise power in the interceptor’s bandwidth is independent of the LPIS transmitted waveform. That being the case, the appropriate LPI strategy is to go to the lowest peak and highest average power waveform obtainable for a given mode of operation. This is shown in simple pictorial form in Figure 1.19. Either the interceptor must deal with large numbers of false alarms or the probability of detection must be very low. This mismatch can be expanded if an LPIS intentionally uses a wide range of pulse or chip powers and pulse widths. Increased sensitivity without selectivity in a dense signal environment just leads to false alarms and recognitions [10–12]. Minimizing effective radiated peak power requires transmitter power management. Most current radars and data links always transmit the maximum peak power available. They typically use the same power for a 1-mile communication or dogfight mode as for a 100-mile detection or data-sharing mode. In fact, many current radars and data links have no power management capability whatsoever. Power

No noise

With noise 1 Watt second

High peak power; Threshold low false alarm detection

1 Watt second Threshold

1/2 peak power; harder detection

1 Watt second 1/4 peak power; Threshold no detection without high flase alarms

Figure 1.19 Single pulse peak power detection (SP3D)

Introduction to stealth systems

23

management doctrine dictates that minimum power is transmitted at all times, and the minimum acceptable signal-power-to-noise-power ratio (SNR) is used under every condition. Therefore, for each mode, such as air-to-air search, air-to-air track or low bandwidth data handling, and for each selected range, such as 5 miles or 50 miles, transmitter power is adjusted to the minimum value, which will give acceptable performance. For example, a typical target may require 5,000 W peak for 80 mile detection in an air-to-air search mode. On the other hand, to track that same target at 5 miles requires only 75 milliWatts (mW) peak. The intercept range is then cut by a factor of 1/256 of the maximum under this condition [13]. Every designer who is first introduced to LPIS proposes large noncoherent integration to counter a stealthy emitter. It is the easiest interceptor performance parameter to counter. Section 3.2 deals with the constraints necessary to create time, frequency, and antenna gain mismatches. Those constraints coupled with the ambient spectra present on a battlefield as analyzed in Sections 5.4–5.6 overwhelm high sensitivity but unselective intercept receivers. As long as there is a 10% probability of at least one conventional emitter in the same resolution cell, long coherent integration is overwhelmed by other/false targets. Even some of the most modern intercept equipments cannot use the sensitivity they already have because of processing, false alarms, and resolution limitations. The statements made in 1975 are still true as of 2000. Nowadays almost every radar and data-link mode uses coherent transmission and processing but it is anything but single frequency as shown in Chapter 6. Waveforms are completely geometry dependent and so even the emitter would not know what waveform will be transmitted until the control frame immediately preceding the emission. How then is the interceptor to match filter the waveform unless every possibility is processed? If only noncoherent integration is used, then the LPIS emission only needs to be significantly lower than all the other emitters in that interceptor resolution cell. This is discussed in Section 3.2. These facts force initial detection on the basis of SP3D.

1.3.4 Reduced detectability: maximum signal uncertainty An LPIS must also defeat sorting and classification. This, in turn, requires maximum signal uncertainty at all times. Waveform parameters, such as pulse repetition frequency (PRF), chip rate, encryption code, frequency, and on-time must be randomized so that the interceptor cannot predict how and when the next emission will occur. The waveform location inside the operating band is selected on a pseudo-random basis for each coherent array. The waveform itself is geometry dependent [14]; some examples are given in Chapters 5 and 6. The PRF is “FMed” and adaptively changed to account for maneuvers during a coherent array. The next PRF from a compatible set is chosen on a pseudo-random basis. Other techniques that are commonly used are mimicking another system or spoofing the interceptor. This is achieved either by transmitting an easily detectable mimic waveform that is interleaved with the LPI waveform and that mimics a benign or an adversary weapon system or by using a cooperative jammer that transmits a low-level spoofing signal, masking the LPIS signal. Simultaneous multibeam antennas are used to more rapidly search the required volume but they must be implemented in

24

An introduction to RF stealth, 2nd edition

such a way that the same frequency does not visit the same region of space very often. The essential elements of maximum signal uncertainty are summarized below. More details are provided in Chapters 3, 4, 5, 6, and 7. ●

● ●

Direction of arrival—low sidelobes, multibeams, and movement between emissions Frequency—large instantaneous bandwidth Time of arrival—multiple PRFs, low peak power, time spread, and multibeams

1.3.5

LPI performance example

As an example of what can be accomplished using stealth notions to achieve the same weapon system mission, consider a high peak power fighter radar such as those found in the French Mirage (Cyrano Series) [15] and a similar performing LPIS. Table 1.6 summarizes the improvements which have been demonstrated with stealth principles. The corresponding intercept sensitivities for the table are given in Section 1.1. The threats are typical of 5,000 to 10,000 currently deployed worldwide (Chapters 3 and 5). LPI and electronic counter-countermeasure (ECCM) features go hand in hand. Both LPI and ECCM designs require antennas that have narrow main beams and very low sidelobes. They both require transmitters that have frequency agility, PRF agility, and large instantaneous bandwidths. Furthermore, they both require processors with large time-bandwidth products and integration times. LPI technology also augments ECCM. The combination of LPI operation and low platform RCS reduces detection by electronic support measures (ESM) equipment because neither the active emissions nor cueing from threat sensors can be used by the ESM systems to exploit an LPI/LO platform. Low antenna sidelobes and adaptive null steering also negate sidelobe jammers. The impact of very low antenna sidelobes coupled with modern adaptive null steering provides many orders of magnitude improvement against sidelobe jamming threats. An LPIS must operate over a large band or the jammer will place all its power in the narrower band. The jammer cannot know what part of the wider band to jam and so some of the jam power is wasted. Narrowband systems are extremely easy to jam with swept noise. LPIS requires frequency agility for maximum signal uncertainty, but frequency agility controlled by a sniff feature defeats mainlobe continuous wave (CW) and spot noise jammers as well. LPIS with high duty ratios usually requires high pulse or data compression ratios. High compression ratios, in turn, enable signal-to-jam processing gain improvements of an Table 1.6 LPIS performance comparison A/A LOOKDOWN EXAMPLE (range nautical miles)

Target Detect

Threat RHAW

Threat ELINT

Threat ARM

Typical fighter radar LPI radar

20 20

187 4.6

1181 10.4

29.7 0.26

System parameters: 5 W/beam, 9 beams, 320 MHz bandwidth,
55 dB rms, sidelobes, and LPI waveform for both radar and missile

Introduction to stealth systems

25

order of magnitude under most circumstances. The net effect of these LPI technologies is to greatly decrease LPIS susceptibilities to some types of countermeasures. LPI capabilities are not free by any means. First, maximum antenna gain and very low sidelobes have many undesirable effects. The aperture is always bigger than the platform designer wants. A narrow beam limits dwell time in volume search scan, and multiple simultaneous beams may be required in order to cover a volume adequately. Low sidelobes increase required manufacturing accuracy and always compromise gain. Not surprisingly, these requirements are conflicting and thus carry some weapon system level costs. Second, multiple agile simultaneous antenna beams inevitably result in higher levels of complexity. Each beam should be on a different frequency to limit sideloberadiated power density in any direction. The transmission of multiple simultaneous frequencies through a typical modern traveling wave tube (TWT) or semiconductor power amplifier-based transmitter is no problem, but the need for a separate receiver and processor channels for each frequency greatly increases complexity and cost. Third, high duty ratios often result in diminishing returns, especially in large range blind zones or eclipsing losses that complicate mode design or may require multiple waveforms to get complete desired coverage. Furthermore, a high duty ratio usually requires significant amounts of compression. Compression usually has range sidelobes, which may greatly limit performance, so it is not always desirable to have large compression ratios. Fourth, a large coherent integration time may conflict with mode and target type. For example, in a synthetic aperture radar mode, integration time is determined by geometry, not by the convenience of the mode designer. In air-to-air modes, large coherent integration time is usually limited by potential target geometrical acceleration. In the presence of large accelerations, large coherent integration times may require multiple simultaneous integrations, each using a different target acceleration hypothesis. This greatly increases the complexity of the processing. Fifth, wide instantaneous bandwidth inevitably results in more costly hardware. Such things as analog-to-digital (A/D) converters, processor memory, and signal processor arithmetic throughput are usually substantially more expensive as they get faster. More instantaneous bandwidth increases both signal processor required speed and memory capacity requirements. For example, a 500 MHz bandwidth gives 1-foot range bins and, to cover a 20-mile search range, requires 120,000 range bins per channel. This is a lot of processing just to improve SNR. In addition, small range bins will not necessarily improve performance if the target extent is greater than 1 foot, which is typical. Similarly, small chip widths for data compression require massive “defruiting” due to multipath.

1.3.6 LPIS typical technology ● ● ● ●

Current unclassified LPIS performance is summarized below. Antenna sidelobes of <
55 dB rms over half-space relative to mainbeam Power management over a 70 dB dynamic range Large coherent integration gain—time bandwidth products of at least 4  106

26 ● ● ●

● ● ●

An introduction to RF stealth, 2nd edition Instantaneous bandwidth of 2 GHz, hopped bandwidths of 6 GHz Fully coherent frequency agility/stability of 1:1012 Dynamic waveform selection—full mode complement/minimum dwell and minimum power Low peak power/high duty waveforms—3 dB SNR tracking Multibeam, multifrequency search—6
9 channels Adaptive data link spectral spreading—300:1

There are two LPI strategies that have been used that will be described later in the text: the minimum dwell strategy and the minimum power strategy. These strategies are other examples of the creation and exploitation of gain mismatches. Typical dynamic waveform selection is summarized below. Figure 1.20 shows actual performance for an LPI system at two different powers and target positions.

1.3.7

LPI maximizes uncertainty

The current unclassified LPI emitter parameters that are variable are: ● ● ● ● ● ● ●

PRF: 1000:1 variation Pulse width: 8000:1 variation Bandwidth: 100:1 variation Data link chip width: 100:1 variation Power: 107:1 variation Dwell time: 10:1 variation Frequency: 0.5–4 GHz variation No. of unique pulse or data compression codes: 105 easily obtainable, 1020 feasible 0.99 0.98

10 watts/ beam

a b

0.95 Cumulative detection probability

●

0.9 0.8 0.7

a. Target at search bar center b. Target off search bar center by 1 degree Range rate search Look up mode 600 ft/s ownship speed

0.5 0.3 0.2 0.1 0.05 0

a b 40

20

16 watts/ beam 60

Range (km)

Figure 1.20 Performance of MPRF demonstration radar

Introduction to stealth systems

27

1.4 Basic LPI equations The basic LPI equations are specialized applications of the well-known radar equation (1.2) and beacon equations (1.3) and (1.4) [16,17]. The power received in the radar equation is inversely proportional to R4. The power received in the beacon or intercept receiver equation is inversely proportional to R2. At first glance, it appears that the interceptor has an insurmountable advantage, but the condition that typically occurs is shown in Figure 1.21. There is a radar or data link operating range, RDmax at which the required transmitted peak power crosses over the corresponding intercept receiver required power. This range is usually less than the radar horizon, RH.

1.4.1 Radar and beacon equations In order to review the radar and beacon equations begin by defining the following parameters: Then, the radar receiver threshold detector input power is: PT ⋅ G T2 ⋅ G RP ⋅ l 2 ⋅ s ⋅ L R

(4 ⋅p )

3

(1.2)

⋅ R D4

RT RI

Required peak power (watts)

PR =

Intercept receiver, R2

Horizon limit

Radar, R4

Range

RDMAX

RH

Figure 1.21 Interceptor has R2 advantage at long range

28

An introduction to RF stealth, 2nd edition The data link receiver threshold detector input power is: PT ⋅ GT ⋅ GDL ⋅ GDP ⋅ LDL ⋅ l 2

PR =

(4 ⋅p )

2

2 ⋅ RDL

(1.3)

The intercept receiver threshold detector input power is: Pi =

PT ⋅ GTI ⋅ GI ⋅ l 2 ⋅ GIP ⋅ LI

(4 ⋅p )

2

⋅ Ri2

(1.4.1)

Where RD , RDL s l PR GT

Emitter design range

Target RCS Emitter wavelength RMS power required at radar or link receiver Emitter antenna gain

GRP , GDP , GIP LR , LDL LI

Radar, data link, and interceptor processor

net gain, respectively Emitter total path losses (numbers less than 1)

(1.4.2)

Losses between emitter and interceptor (numbers less than 1)

PI

Power required at intercept receiver for detection

Pi

Power received at the intercept detector

Ri

Intercept receiver to emitter range

GI

Intercept receiver antenna gain

GDL

Data link receive antenna gain

GTI

Emitter gain in interceptor direction

The intercept power relations are summarized in (1.5)–(1.13). The required transmitter power, PT, can be represented as a figure of merit constant, K, times the detection or link range, RD, divided by the radar antenna gain, GT (1.5). K is the effective radiated peak power (ERPP) normalized by the design range raised to a power of either 2 or 4 depending on whether a one way or two-way path is involved. K depends on the emitter design and operating mode. The power received at the interceptor threshold, Pi, is equal to an interceptor figure of merit, J, times the emitter transmitter power, PT, times the emitter antenna gain in the interceptor direction, GTI, divided by the intercept receiver to emitter range squared, Ri2, as shown in (1.7) (one-way path). Substitution of the PT (1.5) into the Pi (1.9) provides a form that contains ratios of radar-to-intercept range and radar-to-interceptor gain (1.11). For an intercept to occur, the power received at the interceptor threshold, Pi, must equal or exceed the power required for detection, PI, as shown in (1.9). The object for every LPI mode is to minimize K. Radar processing gains, GRP, are defined in Section 1.6.1.

Introduction to stealth systems

29

Duty factor, integration time, and receiver bandwidth are specifically called out. Similarly, interceptor processing gains, GIP, are described in Sections 3.2 and 3.3. These gains are obviously SNR gains at the detection threshold and are dealt with more completely in those sections. Let the radar equation for required transmitted power for a given target detection range, RD, be written as PT =

K R ⋅ R D4 GT

(Required radiated peak power for RD)

(1.5)

Where KR is a radar figure of merit, which depends on the mode and mission and is defined as KR =

(4 ⋅p )

3

⋅ PR ⇒ 10 −16 W/m4 typical value l ⋅ G T ⋅ G RP ⋅ s ⋅ L R 2

(1.6)

And similarly for a data link, the required transmitted power for a given range, RDL, can be written as PT

2 K DL ˜ R DL GT

(Required power for RDL)

(1.7)

Where KDL is a data link figure of merit, which depends on the mode and mission and is defined as K DL =

(4 ⋅p )

2

⋅ PR ⇒ 10 −8 W/m2 typical value l ⋅ G DL ⋅ G DP ⋅ L DL 2

(1.8)

Let the beacon equation for a given transmitted power and emitter-tointerceptor range, Ri, be written as Pi = J I

PT ⋅ G TI (Power received by intercept receiver at range Ri) Ri2

(1.9)

1.4.2 Intercept power relations and LPIS figures of merit Where JI is an interceptor figure of merit, which also depends on the mode and mission of the interceptor and is defined as JI =

G I ⋅ G IP ⋅ l 2 ⋅ L I

(4 ⋅p )

2

⇒ 2 ⋅ 10 −3 m2 typical value

(1.10)

Substituting (1.5) into (1.9) yields: Pi = J I ⋅ K R

R D4 ⋅ G TI Ri2 ⋅ G T

(1.11)

30

An introduction to RF stealth, 2nd edition And similarly substituting (1.7) into (1.9) yields: Pi = J I ⋅ K DL ⋅

2 R DL ⋅ G TI R i2 ⋅ G T

(1.12)

For example, let Pi ¼ PI and GTI ¼ GT (i.e., the interceptor is in mainlobe), then the intercept range for specified RD and PI is: RI = J ⋅ K R

R D4 R2 = J 1/ 2 ⋅ K R 1/ 2 1/D2 PI PI

(1.13)

The LPIS concept is to minimize KR or KDL for each operating mode.

1.4.3

Detection range versus intercept range equations

As previously mentioned and used below, the radar, data link, and the interceptor have figures of merit, shown in (1.6), (1.8), and (1.10), respectively. More insight into how LPI radar is successful against an interceptor can be gained by comparing equations for radar detection range versus intercept range. The radar range equation for a given required receive power, PR, is: PT ⋅ G RP ⋅ G T2 ⋅ l 2 ⋅ s ⋅ L R

R D4 =

(4 ⋅p )

3

⋅ PR

=

PT ⋅ G T KR

(1.14)

And similarly the data link (beacon) range equation for a given required receive power, PR, is: 2 R DL =

PT ⋅ G T ⋅ G DL ⋅ G DP ⋅ L DL ⋅ l 2

( 4 ⋅ p ) ⋅ PR 2

=

PT ⋅ G T K DL

(1.15)

The interceptor (beacon) range equation for a given required receive power, PI, is: R I2 =

PT ⋅ G TI ⋅ G I ⋅ G IP ⋅ l 2 ⋅ L I

(4 ⋅p )

2

⋅ PI

=

PT ⋅ G TI ⋅ J PI

(1.16)

The ratio of RD4 to RI2 [(1.14) and (1.16)] is given in (1.17). By grouping like elements, it can be seen that the best performance for the radar relative to the interceptor occurs when each ratio in (1.17) is maximized. Maximizing each ratio means maximum radar antenna gain relative to radar-to-interceptor gain, smaller radar detection power relative to required interceptor power, and greater radar processing gain relative to interceptor processing gain: R D4 ⎛ G T2 P G L ⎞ s =⎜ ⋅ I ⋅ RP ⋅ R ⎟ ⋅ R I2 ⎝ G TI ⋅ G I PR G IP L I ⎠ 4 ⋅ p

(1.17)

Introduction to stealth systems

31

If the maximum range where LPI is maintained is defined as the range at which the radar detection range just equals the intercept range, as in (1.18), then R2Dmax is equal to (1.19). Because R2I is proportional to R4D , then once RD is less than RDmax, the intercept range decreases faster than the detection range, as in (1.21). Thus, to find the maximum LPI radar range, set RD equal to RI which defines RDmax: R D = R I ≡ R Dmax

Maximum LPI Range

(1.18)

Substituting (1.18) into (1.17) and grouping like parameters yields: ⎛ G T2 P G L ⎞ s R D2 max = ⎜ ⋅ I ⋅ RP ⋅ R ⎟ ⋅ ⎝ G TI ⋅ G I PR G IP L I ⎠ 4 ⋅ p

(1.19)

Further, since both R2i and R4D are proportional to transmitted power, PT : Ri2 ∝ PT ∝ R D4 And normalizing Ri and RD to RDmax yields:

(1.20) Ri R D max

§ RD · ¨ ¸ © R D max ¹

2

(1.21)

Therefore, there is no intercept if RD < RDmax. The intercept probability gets very small inside RDmax. As will be seen in Chapter 3, the intercept probability never quite goes to zero, but does become adequately small, for example, the PD ¼ 3  10
3 to 3  10
5 at 1/2 of RDmax. Similarly taking the ratio of (1.14) into (1.15) yields: 2 ⎛ G ⋅G R DL P G L ⎞ = ⎜ T DL ⋅ I ⋅ DP ⋅ DL ⎟ 2 RI ⎝ G TI ⋅ G I PR G IP L I ⎠

(1.22)

There are two cases for LPI data links associated with radars. The first is for a data link between close station keeping platforms or between a platform and a missile, so that R Dmax ≥ R DL

(1.23)

The right side of (1.22) is almost always greater than 1 but by (1.23), the left side of (1.22) will be less than or equal to 1 so there will never be an intercept. The second case occurs when an LPI radar sensor must transmit data to a remote processing station, so that R I ≥ R DL ≥ R Dmax

(1.24)

For this case, RDLmax, is dependent on the specific parameters and geometry. For example, suppose the processing station and the interceptor have the same antenna gain, required received power is about the same, data link bandwidth compression is 100, the interceptor is in the sidelobes, and data link losses are

32

An introduction to RF stealth, 2nd edition

double interceptor losses; then R DLmax = R I ⋅ 3 ⋅ 10 5 ⋅ 1 ⋅ 1 ⋅ 100 ⋅ 0.5 = R I ⋅ 3.9 ⋅ 10 3

(1.25)

If the interceptor is in the mainlobe, RDLmax can easily be very close to RDmax. Comparison of three different fighter radars with similar missions dramatizes what can be done both in terms of figure of merit and mainlobe intercept range against a typical RWR. Improvements of two orders of magnitude are achievable. Another example based on the LPIR system, a typical RWR, and (1.19) is shown in Table 1.7. The table compares the various performance elements of the radar and the interceptor and provides an explanation of the differences. Note that the maximum safe range can be a very large number and thus is operationally useful in many real scenarios. One important factor in this example is the adjustment of transmitter power based on the interceptor’s known or assumed sensitivity. An alternative formulation for RDmax is given in (1.28). It substitutes aperture areas for gains and required SNRs, detection bandwidths, and noise figures for required detection powers. Equation (1.19) can be rewritten in terms of antenna areas, SNRs, bandwidths, and noise figures. Since PI = SNR I ⋅ B I ⋅ NFI ⋅ k B ⋅ T0

and PR = SNR R ⋅ B R ⋅ NFR ⋅ k B ⋅ T0

(1.26)

and And: G T =

4 ⋅ p ⋅ AeT 4 ⋅ p ⋅ AeI 4 ⋅ p ⋅ AeTI and G I = and G TI = 2 2 l l l2

(1.27)

Substituting into (1.17) yields: R D2 max =

AeT2 SNR I ⋅ B I ⋅ NFI G RP L R s ⋅ ⋅ ⋅ ⋅ AeTI ⋅ AeI SNR R ⋅ B R ⋅ NFR G IP L I 4 ⋅ p

(1.28)

Table 1.7 Mainlobe/RWR intercept ranges Air to air lookdown, transmitter power adjusted for 40 km detection range* Weapon/sensor system

K (w/km4,2)

K0.5 (REL)

Typ. RWR RI (km)

F4E/APQ-120* F-16/APG-66* LPIR (HPRF mode) LPI missile data link

23.7* 10.9* 0.0067 1.610
6

59.5 40.3 1 0.015

595* 403* 10 3.7510
3

*Estimated from unclassified sources

Introduction to stealth systems

33

Similarly, substituting into the corresponding data link (1.21) yields: R DLmax

RI ˜

AeT ˜ AeD SNR I ˜ B I ˜ NFI G L s ˜ ˜ DP ˜ DL ˜ AeTI ˜ AeI SNR DL ˜ B DL ˜ NFDL G IP L I 4 ˜ p

Where: NFR , NFDL , NFI kB AeTI

noise figure - radar, data link, interceptor, respectively

Boltzmann’s constant, T0

AeT , AeD , AeI

(1.29.1)

standard temperature

antenna effective area - radar, data link, interceptor

emitter antenna effective area in interceptor direction

SNRR , SNRDL , SNRI

required signal-to-noise ratio - radar, data link, interceptor

BR , BDL , BI

noise bandwidth - radar, data link, interceptor

LR , LDL , LI

loss fraction - radar, data link, interceptor

(1.29.2) The effective antenna area for the radar usually will be higher than the interceptor for operational reasons. The intercept receiver must search all the resolution cells, the radar, or data link scans but in addition must search more angle and signal space because in the beginning, it cannot know where the LPIS emitter is. More interceptor bandwidth causes poorer low noise amplifier impedance match and most noise figure increases are caused by mismatch loss (a microwave circuit limitation). Allowable radar SNR can be lower because the radar coverage is smaller. The radar bandwidth is smaller because the waveform is more completely known, and the radar noise figure is lower because the bandwidth is smaller. A white paper prepared for DARPA by Mitre Corporation on August 22, 1978 concluded that it is extremely difficult to hide a radar or data link from a decent intercept receiver. The theoretical analysis was correct, but it assumed a radar state-ofthe-art that was far behind the times, especially in terms of achievable time-bandwidth product, antenna gain, and noise figure advantage over an intercept receiver. It also assumed a substantially better interceptor signal processor than that in the radar and that the interceptor has a priori knowledge of the radar direction and waveform, which is impossible in a dense emitter environment as will be shown in Chapters 3 and 5. A more realistic example is given in Table 1.8 for equally good radars and interceptors. Mitre, Lincoln Laboratories, and NRL were funded to develop and test interceptors and ECM for the LPIR and Pave Mover Programs. These systems were so unsuccessful in actual flight tests that one could conclude that the state-of-the-art of ECM and intercept systems is considerably behind counterpart radars and data links. These organizations are on the US government dole (fixed percentage funding independent of expertise or need) and may not be representative of what a real adversary might be able to mount. Even though it appears that ECM and intercept systems lag the state of the art, any deployed LPIS will steadily become more vulnerable over time as threat systems improve through the application of more modern RF and signal processing technologies. Any LPIS will require steady upgrades to maintain its stealth advantage.

34

An introduction to RF stealth, 2nd edition

Table 1.8 LPIR—how it is done example Inverse square beats inverse fourth power, but Parameter

Rader (dB)

Interceptor (dB)

Advantage ratio (dB)

Comment

Detection power SNR Antenna gain

13.5

16

2.5

37

0

37

Processor loading Direction unknown Frequency unknown

Receiver bandwidth (dB Hz) Noise figure

16.5

90

73.5

2

10

8

Integration gain

9

10


1

Total system Losses, Duty ratio


9.1


8


1.1


3.5

0


3.5

RCS per steradian (dB km2)


64

0


64

RDmax2 (dB km2) It is all in the numbers!

Bandwidth matching Better intercept SNR Radar complexity Central band filter Nature

51.4 RDmax ¼ 372 km

Example applications of (1.28) and (1.29) for various tradeoff parameters are shown in Figures 1.22 and 1.23. Those parameters, which are held fixed in the tradeoffs, are summarized in Table 1.9. It is instructive to look at mainlobe intercept versus radar predetection bandwidth with fixed postdetection integration, as shown in Figure 1.22. This is really a trade-off between radar data rate and maximum safe detection range. The update period varies from a low of 28 ms with maximum safe radar range (RDmax) of 12 km to a high of 4 min, 40 s with maximum safe range of 1131 km. Figure 1.22 shows the dramatic increase in maximum safe operating range as a function of decreasing detection bandwidth (longer coherent integration time). Long coherent integration time requires complex signal processing because changing Doppler and geometric acceleration require a different filter for each target extent and path. The antenna gain has been set at a value typical of many deployed radar systems (see Chapter 5). The intercept receiver for this example is very simple. Nonetheless, there are over 10,000 intercept receivers currently deployed worldwide similar to the one used in the examples of Tables 1.8 and 1.9 and Figures 1.22 and 1.23 (also see Chapter 5). The performance parameters are typical of modern fighter radars and RWRs. A second comparison as a function of antenna gain with fixed (32 Hz) predetection bandwidth and all other parameters, as in Figure 1.22, is shown in

Introduction to stealth systems

35

1,400

Maximum safe detection range (km)

1,200 Radar antenna gain = 37 dB 1,000 800 600 400 200 0

0.1

0.3

1

31.5 3.1 9.9 Radar bandwidth (Hz)

99.8

315.7 998.2

Figure 1.22 Mainlobe intercept versus radar predetection (fig1-12.xls) 110

Maximum safe detection range (km)

100 90

Radar BW = 32 Hz

80 70 60 50 40 30 20 10 0

20.0 21.5 23.0 24.5 26.0 27.5 29.0 30.5 32.033.5 35.0 36.5 38.0 39.5 41.0 Radar antenna gain (dB)

Figure 1.23 Mainlobe intercept versus radar antenna gain (fig1-12.xls) Figure 1.23. The detection filter bandwidth in Figure 1.23 is set to a value, which is typical and allows simple signal processing (not too stealthy). The antenna gain varies from a low of 20 dB with RDmax¼ 9 km to a high of 41 dB with RDmax ¼ 108 km. Large antenna gains are required to obtain operationally useful safe detection range. The antenna must still be constrained to superior sidelobes.

36

An introduction to RF stealth, 2nd edition

Table 1.9 Mainlobe intercept parameters (Figures 1.22 and 1.23) Emitter parameter

Emitter value

Interceptor value

Noise figure Wavelength Processor gain (postdetection) Required SNR Antenna gain Bandwidth Target RCS

3 dB 0.03 m 28 20 See figures See figures 1 m2

6 dB 0.03 m 3 40 10 1 GHz N/A

The obvious conclusion from these curves is to choose the largest gain consistent with good sidelobe performance and the smallest predetection bandwidth consistent with threat response time for an LPIS design. The appendices describe the contents of the accompanying analysis software available for download or DVD-R. They contain an Excel
spreadsheet in .XLS format for Figures 1.22 and 1.23 for student manipulation. Each chapter has a similar counterpart appendix. Excel
, Mathcad
, and Basic programs for many of the figures throughout the text are described in the appendices. The appendices contain the computational details for these figures and many others which do not appear in the text. These programs are meant to be the jumping off point for the book user’s own analysis.

1.5 Introduction to RCS 1.5.1

Mathematical basis

Whether an observation of an object is optical, infrared, or radar, it is governed by the physics of electromagnetic radiation. James Clerk Maxwell in a surprisingly modern and prescient book around 1850 laid out a set of equations describing electromagnetic theory. These equations have stood the test of time quite well and most microwave engineers use them daily in one form or another. Equations (1.30) below give one form of Maxwell’s equations [2,5,15,18–22]: ∇×H = J +

∂D ∂t

∇×E = −

∂B ∂t

∇•D = r

Where: H = vector magnetic field intensity J = vector current density D = vector electric flux density t = time E = vector electric field intensity B = vector magnetic flux density r = electric charge density

∇•B = 0

(1.30.1)

(1.30.2)

Fortunately, most of us do not have to solve this set of differential equations for every problem because very smart people have spent the last 150 years solving

Introduction to stealth systems

37

these equations one way or another for most practical problems. Maxwell’s equations are solved as summarized below. Exact solutions—separation of variables, orthogonal coordinate systems, and boundary value problems Integral forms—Stratton-Chu integrals and vector Green’s functions Approximate techniques—geometrical optics (GO), microwave optics (MO), physical optics (PO), geometrical theory of diffraction (GTD), physical theory of diffraction (PTD), uniform theory of diffraction (UTD), method of moments (MM), finite difference time domain (FDTD), finite difference frequency domain (FDFD), and conjugate gradient fast Fourier transform (CG-FFT) [18,20,21,28] Hybrids—combinations of several of the above techniques A related set of equations which are easier to visualize are the wave equations. If the fields are in homogeneous regions with no current or charge sources, the wave equations are given in (1.31): ∂E ∂ 2E −e ⋅m 2 = 0 ∂t ∂t ∂H ∂ 2H ∇ 2H − s c ⋅ m ⋅ −e ⋅m 2 = 0 ∂t ∂t

∇ 2E − s c ⋅ m ⋅

(1.31.1)

Where: s c = conductivity of the homogeneous medium m = magnetic permeability of the homogeneous medium

(1.31.2)

e = electric permittivity of the homogeneous medium

Note that in free space or dry air, sc is close to zero and on a conductor sc is very large ( for copper sc ¼ 5.8  107 Siemens/m ) so that the center terms in (1.31) either drop out or are dominant. If the fields are assumed made up of E(x,y,z) exp(jw t) and H(x,y,z)exp(jw t) components, then (1.31) simplify to (1.32): ∇ 2E + k 2 ⋅ E = 0 Where: k 2 mr , e r

∇ 2H + k 2 ⋅ H = 0

w 2em -js cw and e

e re 0 , m

(1.32.1) m r m0

permeability and permittivity relative to free space, respectively.

(1.32.2) If the fields are in free space, then sc ¼ 0, mr ¼ 1, and er ¼ 1 and the equation for k is the familiar form given in (1.33): k 2 = w 2 ⋅ e 0 ⋅ m 0 = w 2 c 2 = ( 2 ⋅ p l ) and h = m e 2

free space impedance h 0 = m 0 e 0 ≅ 377Ω

(1.33)

Where the permittivity of free space is e0 ¼ 8.85  10
12 farads/m, the permeability of free space is m0 ¼ 4p  10
7 henrys/m, and the velocity of light in free space is c ¼ 2.9979  108 m/s.

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An introduction to RF stealth, 2nd edition

One way of thinking about Maxwell’s equations and the counterpart wave equations is that they are conservation of energy equations in space and time. The basic definition of radar cross section (RCS) is the ratio of the scattered power to the incident power in the direction of an observer at infinity. Equation (1.34) shows the fundamental RCS equation in terms of the electric or magnetic fields: s = 4 ⋅ p lim R 2 R →∞

Es

2

Ei

2

= 4 ⋅ p lim R 2 R →∞

Hs

2

Hi

2

(1.34.1)

Where: R = range to the observer Ei , H i = vector incident electric and magnetic fields Es , Hs = vector scattered electric and magnetic fields

1.5.2

(1.34.2)

RCS phenomenology

As a propagating wavefront meets a boundary or discontinuity in the medium, some energy must be reflected, some are transmitted, and some are reradiated in order to satisfy the physics described by (1.30), (1.31), and (1.32). Figure 1.24 summarizes the five major sources of reradiation which can result in observable RCS. The first and the one that everyone is familiar with is specular or mirror-like reflection or scattering. Although the reflection has a lobe structure, the dominant reflection is at the complement of the incidence angle of the illumination relative to the surface

Pi

Pr Complement to normal

Pi

Pr

Pr

Surface discontinuity Tangent Pr ray Creeping wave Currents in exposed Pi region flow into shadow region

Pi n

Diffraction Tip of cone, edge Pr

Change in material

Traveling wave

Specular Mirror like

Pr

End of body

Shadow boundary

Pr

Pr Changes in EM boundary

Pr

Pi

Change in material

Pr

Gap

Surface slope discontinuity

Pr

Figure 1.24 Sources of electromagnetic scattering. Adapted from Fuhs [15]

Introduction to stealth systems

39

normal. Almost everyone has experienced the mirror-like glint from the sun on a window. A second source of reradiation is diffraction in which a tip scatters spherically or an edge scatters in a specular torus (donut) about the complement to the edge normal. A third source of scattering is traveling waves which arise when the illuminating wave couples into a surface at a shallow angle. This creates currents propagating on the surface. The effect is most pronounced in long thin bodies such as wires, egg (prolate ellipsoid) shapes, and ogives. As these surface currents encounter shape discontinuities, material changes (different m or e ), or the end of the body, then, in order for the physics to be satisfied, some reradiation usually occurs. A fourth source of reradiation or scattering is creeping waves. The illuminating wave couples into the surface creating currents propagating in the surface which flow from the region of illumination to shadowed regions. These currents can flow all the way around a body and then interact with the specular reflection to create a resonance effect. The effect is most pronounced in objects which are good conductors and bodies of revolution (cylinders, spheres, eggs, and ogives). The last category is any coupled-wave currents which encounter a change in the electromagnetic boundary conditions such as gaps, surface curvature changes, material changes, conductivity changes, and even smashed bugs. So what does this all mean in terms of real objects? Almost every single radar or ladar observable depends on the laser or RCS of the object creating that effect. The overall RCS determines detection performance but the unique features of that RCS determine target recognition performance. The recognition of a target is based on its signature which in turn is made up of RCS from individual sources. A list of typical RCS signature sources is given below. ● ● ● ● ● ●

Jet engine, propeller, or vibration modulation Roll, pitch, yaw motions about the object center Polarization conversion Resolution of individual scatterers Nonlinear frequency interactions Near resonance frequency response

These features may have small RCS in many cases thus forcing recognition using these sources to short-range relative to first target detection. The object of a stealth platform must be, first, to prevent detection but, next, to prevent recognition on the basis of the above observables. Some examples of the less obvious sources of RCS are helpful in understanding resonance and edge diffraction. Two examples of the effects of near resonance response are given in Figures 1.25 and 1.26. Figure 1.25 shows the RCS of a sphere as a function of wavelength relative to the radius. There are three regions of RCS behavior for a sphere. When the wavelength is large relative to the circumference, the RCS is proportional to l
4 and is called the Rayleigh region. When the circumference is between ½ and 10 wavelengths, creeping waves are important and constructive interference can enhance the RCS by up to a factor of 4 as suggested in Figure 1.25. This is called the resonance region. When the circumference is large relative to wavelength, the cross section is independent of

40

An introduction to RF stealth, 2nd edition 10 Resonance region Optical region 1.0 Constructive interference gives max

σSphere / a2

Rayleigh region

Specular

0.1

Creeping

a

E Destructive interference gives min

0.01

Specular reflected wave

Specular Backscattered creeping wave Creeping

0.001 0.1

0.2 0.3

0.5 0.8 1.0 3 4 5 6 Circumference/wavelength = 2a/λ

8 10

20

Figure 1.25 RCS of a sphere relative to wavelength

4

Cylinder σll

σ

1.0 0.8 0.6

Rayleigh region

σ

L σll

Optical/ region

0.4

E

σ = kaL2

Resonance region

1.0

E

T

kaL2

λ=a 0.2 0.1 0.1

σ

4 2a

λ = 2a

1

ka = 0.2

0.4 0.6

1.0

ka

2

4 6

10

T

2

20

2a λ

Figure 1.26 RCS of a cylinder relative to wavelength. Adapted from Barton [19] wavelength and proportional to the projected area, pa2. This is called the optical region. Similar to the resonance of a sphere, when the incident electric field is perpendicular to the axis of a cylinder as shown in Figure 1.26, a cylinder exhibits a resonance effect due to creeping waves. When the incident electric field is parallel to the axis of the cylinder, the effect of creeping waves is very small. In the

Introduction to stealth systems

41

7-17 GHz, 1.6 cm sp. res., 0º. Az., VV 1 0.8

Down-range (m)

0.6

Target drone Log mag (dBsm)

–30

0.4 0.2 0 –0.2

–40 –30

–50

–40

–0.4

–60

–50

–70 1

–60 0.6

–70 –0.6

–0.4 –0.2 Cross-range (m)

0

0.2 0.4

0.2 –0.2 Down -range (m) 0.6 –0.6

–0.6 –0.6

–0.4

–0.2 0 0.2 0.4 Cross-range (m) Contour plot of target drone RCS

0.6

ISAR image of target drone RCS

Figure 1.27 Example sources of scattering. Adapted from Raytheon [23] Rayleigh region, a cylinder exhibits the same l
4 RCS dependence for perpendicular polarization as a sphere, but for parallel polarization, the RCS exhibits l0.5 dependence! This last property is one of the bases for fiber chaff radar countermeasures. The optical region is entered as the wavelength gets smaller relative to the dimensions; then, the RCS is proportional to the circumference divided by l times the length squared independent of polarization (to a first order!). As the radius of a cylinder gets very small relative to length and wavelength, the parallel polarization RCS approaches L2/p and the perpendicular polarization RCS approaches 0. An example of edge diffraction is shown in Figure 1.27. These high-resolution images of the RCS of a small drone show that nose-on scattering comes primarily from the inlet edges and inlet interior components, the junctions of major structural features, and the tips of the wings and tail. The physical outline of the drone has been added to the contour plot to assist in visualization of the sources of scattering. Note that the trailing tips have a significantly higher cross section than the leading tips due to traveling wave scattering. The images have a resolution of 5/8th of an inch using a 10 GHz bandwidth stepped FM waveform and inverse synthetic aperture radar (ISAR) processing. The high-resolution image allows identification of the individual sources of the RCS signature of the object under test. As can be seen from the amplitude plot in the lower left of the figure, the cross-section of each source may be quite small but the summation of all of them may yield a significant RCS. Clearly, low RCS vehicles require some type of edge treatment. Some

42

An introduction to RF stealth, 2nd edition

examples are provided in Figure 1.24 and Chapter 6. Obviously, at other angles, a different set of RCS sources may dominate the signature such as the wing leading edges or body.

1.5.3

Estimating RCS

Figure 1.27 would suggest that RCS is made up of discrete independent sources which could be summed to provide overall estimates of a vehicle signature (this is not really true but can provide a reasonable estimate under many circumstances). A first-order approximation of RCS for a platform or complex object can be obtained by summing the major specular RCS components as given in (1.35): s≈

∑

M m =1

2

s m ⋅ exp ( j⋅ 4 ⋅ p ⋅ rm l )

Where: s m = RCS of the individual simple scatterer

(1.35)

rm = distance to the observer (or some local reference plane)

This formula, which can be used to obtain a second-order approximation to a complex object RCS, can be simplified by dropping the phase term and forming a noncoherent sum for first-order approximations. The idea, which is not new, is to break the object into simple components whose RCS performance is well understood. Then the specular/major RCS components in each angular region are summed with all the other components in that region to obtain an estimate of RCS. Table 1.10 summarizes the geometrical optics (GO) approximations for the specular components of simple RCS shapes that can be used for a first-order estimate. These components consist of reflections normal to the surface (broadside), principal diffraction from edges and tips at their normals, travelling wave reflections, and reflections from cavities or holes. The formulas in Table 1.9 assume that the components are perfect electrical conductors (sometimes called PEC in textbooks) at the illumination wavelength. Obviously, real objects are not perfect conductors and so the scattered fields and RCS are usually somewhat smaller (usually not nearly enough without special effort for stealth platforms). The complex nature of scattering objects can be modeled on a first-order basis by applying a complex reflection factor, G 2, to each RCS component. Geometrical optics assumes each photon or ray is like a billiard ball, that is, the ray is reflected from a surface at the complement of the angle between the incident ray and the surface normal. Thus only rays which are normal to a surface—the specular— would be retroreflective and give rise to monostatic RCS. Obviously, there is the potential that a complex object could have multiple reflections which in combination would be retroreflective. The obvious examples of this are right dihedrals and corner reflectors. Stealth vehicles must avoid such configurations at all costs. Usually, ray tracing is used until the last bounce and the RCS of this last surface is then applied to estimate the overall RCS (sometimes called shooting and bouncing rays). As an example of the use of (1.35) and Table 1.10, consider the hypothetical aircraft shown in Figure 1.28. From an RCS point of view, there are seven major components of the hypothetical example aircraft as listed in the figure (marked

Introduction to stealth systems

43

Table 1.10 First-order specular RCS components. Adapted from [20]. Scattering source

Type of scatter

Approx. RCS equation (M2) • G2

Approx. Beamwidth ( )

Flat plate

Broadside Front edge Back edge

4pAe2/l2 Leff2/p 7 20V 10

s84

18V 10V 13V 8V

*Average of both polarizations except where noted. s0 ¼ median or mean backscatter coefficient in decibels below 1 m2/m2. s84 ¼ reflectivity that 84% of the cells are below. Composite of references [1–4].

Table 5.4 Land clutter reflectivity, 5 –10 grazing angle Reflectivity, dB below 1 m2/m2 @ band, GHz*

Terrain type

Desert Farmland Open woods Wooded hills Residential Cities

UHF

L

S

C

X

Ku

Ka

0.5–1

1–2

2–4

4–8

8–12

12–18

31–36

s0 s84 s0 s84 s0 s84 s0 s84 s0 s84 s0

s84

40 36 23 22 23 9

13V 25 11V 18V 10V 15V 14V 13V 8V 11 3V

34 30 20 18 17

39 30 26 23 26 20 15

36 28 33 26 24 23 18

33 26 23 35 26 18

30 26 30 22 23 30 24 16

18V 22 22 20 18V 9V

s0

s84

*Average of both polarizations except where noted. s0 ¼ median or mean backscatter coefficient in decibels below 1 m2/m2. s84 ¼ reflectivity that 84% of the cells are below. Composite of references [1–4].

steeper, clutter backscatter typically rises. There are some notable exceptions for this, such as commercial and industrial areas that may contain high-rise buildings and many vertical features with large RCS. Furthermore, commercial and industrial areas typically have dramatically higher cross sections than areas that are largely devoid of cultural features. In addition, backscatter from clutter is conservative: most of the energy that a radar places on the ground either intentionally or unintentionally is reflected, a fraction back in the direction of the radar observer, but much scattered in other directions. This multidirectional scatter can be an advantage in commercial, industrial, and heavy vegetation areas because it confuses angle-of-arrival intercept

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An introduction to RF stealth, 2nd edition 20 Aircraft

Back-scatter coefficient, dB sq.m/sq.m

Industrial 10

\ Urban

0

Terrain

Suburban –10 20

Woods

Wind, knots =

–20 Desert

0

–30 Sea –40 0

10

20

30 40 50 Grazing angle,˚

60

Figure 5.3 Summary of X-band clutter reflection data. Adapted from [5] systems and direction finding. Angle of arrival differences of 10 with only 5 dB of attenuation over path lengths of 50 miles are common occurrences. In areas with many cultural features, the scattering in other directions may be so strong as to punch through the sidelobes of the antenna on the intercept receiver and dramatically degrade dynamic range and signal discrimination characteristics. Over calm sea water or smooth desert sand, however, clutter is not as easily exploitable. One alternative is to enhance the clutter with ground bounce ECM. Another attribute of clutter that is an important property and beneficial for stealth vehicles is the probability density function of RCS with respect to size. For example, Ku-band data taken over rural terrain at medium resolution (40  40 ft. cell) can be approximated by a normal probability density function, as shown in Figure 5.4. The data shown is prior to pulse compression out of 6 bit A/D converters. A little over 20,000 sample points were used with a postpulse compression dynamic range of 60 dB and a median reflectivity of –24.9 dBsm. The input is almost white noise but the output is most decidedly not as will be shown in the figures which follow. Some representative statistics with and without smoothing for populated areas are given in Figures 5.6–5.9. These data are from the USAF FLAMR program which was declassified in 1987 and 1988 [4]. One clutter feature important to stealth platforms is bright discretes. Figure 5.5 shows a summary collection of data for bright discretes in terms of density per square nautical mile versus equivalent radar cross section in square meters. There are several important features to the clutter in populated areas. The mean and the median clutter reflectivity can differ by as much as 10:1 (very much nonGaussian!). Commercial areas have large statistical tails and hence a significant

Exploitation of the environment

Probability density

0.05

0.05

Mean = 0.01 Q’s Sigma = 8.49 Q’s

0.04

277

Mean = 0.3 Q’s Sigma = 8.49 Q’s

0.04 Data

0.03

Gaussian

Data

0.03

0.02

Gaussian

0.02 Inphase

0.01 0 –30

–24

–16

Quadrature

0.01

–8 0 8 Quantum level

16

24

30

0 –30

–24

–16

–8 0 8 Quantum level

16

24

30

Figure 5.4 Rural terrain raw I-Q data histograms. Adapted from [4,8,20,21]

104 FLAMR data (Ku band) Additional data as labeled Discrete density, no. per sq. nmi.

103 Downtown austin, TX 102

Bakersfield airport / vandenburg AFB

10 General rural (C band)

1

Typical USAF specification San joaquin valley farmland AWACS

Nominal discrete clutter spec. J = –10 to –15 dB

0.1 0

10

20

30 40 Discrete size, dBsm

50

60

Figure 5.5 Density of bright discretes. Adapted from [5,20,21] probability of a very large cross section. This means that there is a small but finite probability that there will be some very large RCS scatterers, over any reasonable observation space. Similarly, an RCS probability density function over heavily populated terrain (e.g., Los Angeles) has a greatly distributed density function, which has an even larger probability of a few extremely large scatters in any observation space. The probability of a 105 m2 scatterer can be as high as 0.001 in a city. There is a small but finite probability that a “bright discrete” scatterer will be in a range cell. A USAF specification used on many programs expects a bright

278

An introduction to RF stealth, 2nd edition Individual image areas (four to one data averaging) 30 Flight line

Frequency, percent

24

Tree 20.1 dB-Ft2

Airplane Truck 35.2 dB-Ft2 2 23.7 dB-Ft

Brush area 18

Trees

12

Built up area (buildings)

6

0 –46.4

–40.4

–34.4

–28.4

–22.4

–16.4

–10.4

–4.4

1.6

7.6

13.6

Cross section per unit area (V0), dB

Figure 5.6 Clutter histograms for Vandenberg AFB vicinity. Adapted from [4]



Individual image areas (four to one data averaging)

Frequency, percent

Dark agricultural field  Runway 

Bright agricultural field Trees

  –56.0 –47.9 –39.8 –31.7 –23.6 –15.5 –7.4 0.7 Cross section per unit area (V0), dB

8.8

16.9

25.0

Figure 5.7 Clutter histograms for Point Mugu, CA, vicinity. Adapted from [4]

discrete of 105 m2 in every 10 nmi2 and similarly a bright discrete of 106 m2 in every 100 nmi2 and so on. The sidelobes of these scatterers can be in hundreds of cells which can mask a small target for quite an area over densely populated areas. The measurements of Ku-band reflectivity made with a synthetic aperture radar have high enough resolution so that individual terrain features can be separated, compared to ground truth and categorized as to the type of clutter as shown in Figures 5.6–5.9. These typically use thousands of data points to estimate the underlying statistics. Notwithstanding the large sample sizes and averaging, the four figures still show significant variability for terrain that does not seem that different in the SAR imagery. The grazing angles in these cases were typically 5 – 10 . Clutter has been measured by many researchers since the 1930s. There are many approximate equations which characterize the main aspects of clutter which

Exploitation of the environment

279

Overall map (one-to-one data) Frequency percent

12 Mean 6

0 17.7

23.7

29.7

35.7

(a)

53.7 41.7 47.7 Magnitude, dB

59.7

65.7

71.7

77.7

Individual image areas (one-to-one data) Frequency percent

18 Fields 12

Vacant lot Residential Grass

6

0 –46

Commercial

–40

–34

–28

–22

–16

–10

–4

2

8

14

Cross section per unit area (V0), dB

(b)

Individual image areas (four to one data averaging) 30 Canal Pol tanks Fence

Frequency percent

24 Vacant lot

Fields

18 Residential 12 Grass 6

0 –46

(c)

Commercial

–40

–34

–28 –22 –16 –10 –4 Cross section per unit area (V0), dB

2

8

14

Figure 5.8 Clutter histograms for Bakersfield, CA, airport vicinity. Adapted from [4] will be given in the following paragraphs but they are by no means the final word on the subject and the references throughout the book give many more examples. These higher resolution clutter histograms typically use thousands of data points to estimate the underlying statistics. Note that in Figure 5.9(a), when all data are collapsed, clutter statistics seem to be Rayleigh power distributed implying an underlying normal or Gaussian distributed amplitude variation. This is what one would expect based on the central limit theorem and very large sample sizes. Notwithstanding the large sample sizes and averaging, the four previous

280

An introduction to RF stealth, 2nd edition 18

Overall map (one-to-one date)

Frequency percent

Mean 12

6

0 2.6

(a)

Frequency percent

18

10.7

18.8

26.9

35.0

43.1 51.3 Magnitude, dB Individual image areas (one-to-one date) River bed

–49.1

–41.0

–32.9 –24.8 –16.7 –8.6 –0.5 Cross section per unit area (V0), dB Individual image areas (four to one data averaging)

River bed Frequency percent

83.7

7.6

15.7

23.8

7.6

15.7

23.8

Residential

0 –57.2

Terrain

18

12

Bridge

6

Residential

0 –57.2

(c)

75.6

Terrain

6

24

67.5

Bridge

12

(b)

59.4

–49.1

–41.0

–32.9

–24.8

–16.7

–8.6

–0.5

Cross section per unit area (V0), dB

Figure 5.9 Clutter histograms for Austin, TX, vicinity. Adapted from [4]

figures still show significant variability for terrain that does not seem that different in SAR imagery. Therefore, when examining the fine structure of mixed terrain surface returns, the statistical distribution more closely resembles a log-normal distribution. The grazing angles in these cases were typically 5 to 10 . Clutter has been measured by many researchers since the 1930s. There are many approximate equations which characterize the main aspects of clutter which will be given in the following paragraphs but they are by no means the final word on the subject and the references throughout this document give many more examples. Because of the wide variation in terrain cross section and the nature of radar measurements, radar targets and clutter are typically measured in decibels as shown in Figures 5.4–5.9. Since the random value of the surface terrain radar cross section

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281

can be approximated by a log-normal distribution, often it is both convenient and accurate to model clutter for GMTI as log-normal. The log-normal probability density function for unit clutter cross section, s0, in linear units is given in (5.1): P s 0 P s 0

§ § § s 0 ¨ exp ¨  ¨ ln ¨© s med © 2 ˜ p ˜ s2 ˜ s 0 ¨ © 2 ˜ s2 0 otherwise 1

2 ·· · ¸ ¸ ¸ for s 0 t 0 ¹¹ ¸ ¸ ¹

(5.1)

where: s med is the median cross section in linear units, s mean is the mean cross section in linear units, §s · which is always larger than the median and s = 2 ˜ ln ¨ mean ¸ s © med ¹

This density function can be fitted to measured data by adjusting the mean and median cross section coefficients. An example curve fit to the trees in Figure 5.6 is given in Figure 5.10. Note that s0 has been converted into dB to match the prior experimental data. Land and sea clutter are proportional to illuminated area. They are strongly grazing angle dependent. Often grazing angle and depression angle are close 0.2 Log-norma1 trees Median=0.45, mean=0.7

Probability of occurrence

0.15

0.1

0.05

0 –35

–30

–10 –5 –25 –20 –15 Cross section per unit area (V0), dB

0

5

Figure 5.10 Log-normal clutter model fit to trees of Figure 5.6 (LogNormal1)

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An introduction to RF stealth, 2nd edition

enough in value so that they can be used interchangeably but for extended clutter purposes, grazing angle must take into account the earth’s curvature. The grazing angle independent of atmospheric refraction is given in the first equation in (5.2). If the radar line-of-sight is entirely in the atmosphere, then the 4/3 earth approximation for atmospheric refraction [25] is often included in the grazing angle calculation. Under those circumstances, the second equation in (5.2) is accurate to better than 0.1%: ⎛h ⎛ h ⎞ R ⎞ y = sin −1 ⎜⎜ r ⎜ 1 + r ⎟ − ⎟⎟ ⎝ R ⎝ 2 ⋅ Re ⎠ 2 ⋅ Re ⎠ If line-of-sight entirely in atmosphere, then:

(5.2)

⎛h 3⋅ Rs ⎞ y ≅ sin −1 ⎜ r − ⎟ ⎝ Rs 2 ⋅ 4 ⋅ Re ⎠

Where hr is the height of the radar, Rs is the slant range to the target, and Re is the average earth radius with a typical value of 6,370,880 m [3]. The grazing angle dependancy of terrain cross section has been modeled by many different researchers. There are three simple models for the grazing angle dependence of reflectivity to be described in what follows. The emphasis in the equations is simple first-order approximations. The simplest is the constant g model [7]. A second more accurate model is the exponential model. It requires the selection of the minimum expected backscatter, smin. A third model called the Muhleman planetary model is probably the most accurate [8]. It is a “platelet” or facet model of the type used to predict first order RCS. It assumes that the platelets are randomly oriented. Muhleman is the only one which matches the underlying physics of scattering [9]. It requires the selection of two parameters: a scale factor K0 and a roughness factor a. All three models are given in (5.3) in dB m2/m2 units. Then the unit area radar cross section of ground clutter is one of the following: Constant g Model: s 0 Exponential Model: s 0 Muhleman Model: s 0

10 ˜ log  g  10 ˜ log  siny (dB) s min  8 ˜y  4 ˜ log y  S § siny 10 ˜ log ¨ ¨  cos sin



2 3

(dB) · ¸  10 ˜ log  K 0 (dB) ¸

(5.3) Where g is a backscatter coefficient that is reasonably constant for a given frequency. When designing for MTI clutter rejection, g is usually chosen high with a typical s84 value of 3. However, when designing for mapping, g is usually chosen low with a value of 0.03–0.1 because interesting map features may be small. When using the exponential model the minimum backscatter, smin, in dB for a given frequency must be chosen, 15 dB is typical for forested, brushy terrain. However, as can be seen from Tables 5.3 and 5.4 as well as Figures 5.5–5.9, smin

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283

varies significantly with both terrain and frequency. When using the Muhleman model, the factor, K0, can be thought of as the backscatter coefficient at mid grazing angles, that is, 45 and the roughness factor, a, which might be between 0.2 and 0.4 dominates very steep grazing angles, that is, near 90 . A comparison of the constant g model, exponential model, and Muhleman model is given in Figure 5.11. In this graph, g ¼ 0.3, K0 ¼ 0.2, smin ¼ 15 dB, and a ¼ 0.4, which might be used for typical GMTI analysis. The constant g model provides a simple approximation for mid-range and low grazing angles. The exponential model provides a somewhat more complex estimate of grazing angle dependance, which is more accurate at medium and high angles. The exponential model fits recent data fairly accurately but provides no insight into the physics. The Muhleman model fits both space-based and land clutter data very well. Sea surface return is strongly dependent on grazing angle, root mean square (rms) wave height, ocean currents, wind direction, and operating wavelength. Wave height is related to surface winds, sea bottom features, and location on the Earth. The simplest model is again a platelet or facet model based on geometrical optics and Rayleigh rough surface scattering. It is a function of roughness (wave height) relative to wavelength and the foreshortening of facets caused by grazing angle. Since the model is based on geometrical optics, it predicts nothing about polarization sensitive scattering. Although polarization sensitivity of sea clutter data is anomalous, historically over-land radars have used vertical polarization and overwater radars have used horizontal polarization. Typically designers said, “It might help who knows?” Equation (5.6) is one of many approximations to unit area sea clutter. Another aspect of clutter is from the point of view of its equivalent cross section per radar cell as a function of range for a fixed antenna size. For surfacebased threat radars, the earth’s curvature dramatically reduces RCS with range. Such a typical graph is shown in Figure 5.12 for various kinds of surface clutter.

Backscatter coefficient (dB)

5 Const. gamma Exponential Muhleman

0 –5 –10 –15 –20 –25 –30 90

80

70

60

50 40 30 ψ, grazing angle (˚)

20

10

0

Figure 5.11 Comparison of land clutter models (CluttervsGrazing1)

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Land clutter

6 4 Sea state 5

1.0 0.8

Sea state 4

0.6 Clo uds Typic al equ ivalen t rece iver n ois

e

0.4

der ate rain ,4

0.1 0.08

Mo

0.06

Ch

aff

0.04

sq. Lig m. ht r / cu ain . km ,1 mm /hr

mm /hr

0.2

10

Radar cross section, sq.m.

2

0.02

150 m resolution 1.4° x 1.4° beamwidth Antenna sidelobes –3 dBi Horiz. polarization C-band 4 dB noise figure

0.01 2

7.5

15

75

150

300

Slant range, km

Figure 5.12 Typical surface radar clutter. Adapted from Nathanson [2]

This graph shows typical clutter returns and equivalent cross section for land clutter, several different sea states, and various amounts of rain and chaff as a function of range. Also plotted on the graph for reference is typical equivalent receiver noise and where it limits performance. As can be seen, surface clutter rapidly drops away with range because of radar horizon effects. However, volume clutter from such things as chaff and rain steadily increases as the range increases because the cell size grows dramatically with range. Usually, the range at which a threat radar detects an LPIS, as limited by receiver noise, is far greater than its equivalent performance in the presence of surface and atmospheric clutter. Land and sea clutter are proportional to illuminated area. They are strongly grazing angle dependent. Often grazing angle and depression angle are close enough in value so that they can be used interchangeably but for extended clutter purposes grazing angle must take into account the earth’s curvature. In this case grazing angle and reflectivity is typically approximated when operating in the atmosphere as shown in (5.4) and (5.5). The emphasis in the equations which follow is simple first-order approximations.

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The grazing angle is: ⎛h ⎞ Rs y ≅ sin −1 ⎜ r − ⎟ R R 2 4 / 3 ⋅ ⋅ e ⎠ ⎝ s

(5.4 from 5.2)

The unit area radar cross section is: s 0 LAND

§h · Rs g ˜ sin y # g ˜ ¨ r  ¸ © Rs 2 ˜ 4 / 3 ˜ Re ¹

Where: g backscatter coefficient - reasonably constant at a given frequency with a typical s 84 value of 3 h r height of the radar R s slant range to the target R e average earth radius with a value of 6,370,880 m

(5.5)

Sea clutter is strongly dependent on grazing angle, rms wave height, and operating wavelength. Wave height is related to surface winds and location on the earth. Equation (5.6) is one of many approximations to unit area sea clutter: 2 ⎡ ⎛ s ⋅y ⎞ ⎤ s 0 SEA = exp ⎢ -8 ⋅ p 2 ⋅ ⎜ h ⎟ ⎥ ⎝ l ⎠ ⎥⎦ ⎣⎢

(5.6)

Where sh is the rms wave height and typically, 0.107 m for sea state 1, 0.69 m for sea state 4, 1.07 m for sea state 5, and for the Perfect Storm, sea state 8, 6 m. The author has been in sea state 5 in a 27 ft sailboat; it is amazingly rough. Similarly, rain clutter is proportional to illuminated volume. Equation (5.7) is one approximation to unit volume rain clutter assuming Rayleigh scattering [1]: s 1RAIN ≅ 7.03 ⋅ 10 −12 ⋅ f 4 ⋅ r 1.6

(5.7)

Where f is operating frequency in GHz and r is rainfall rate in millimeters per hour. Equation (5.7) must be coupled with the rain scattering volume to determine the total rain cross section competing with targets whether they are target movers or stationary. The final rain RCS is given in (5.8): p ⋅ R 2 ⋅ q az ⋅ e el ⋅ d r 8 Where: d r = range resolution in meters, R = slant range in meters,

s RAIN = s 1rain ⋅

q az = azimuth beamwidth in radians, e el = elevation beamwidth in radians.

(5.8) Yet, another aspect of clutter is its velocity distribution as a function of range. A clutter velocity model for various types of backscatter is shown in Figure 5.13. This figure shows apparent radial velocity as a function of range. Notice that as

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range increases, the apparent radial velocity of chaff and rain gets larger and is determined by the velocity of either the storm cell or the chaff cloud. A similar condition exists at shorter range for sea and land clutter. There are many land clutter items such as rooftop ventilators and fans, which have apparent velocities similar to aircraft, and all land vehicles. The only way to sort these scatterers out is to track them long enough to determine that their location is unchanged. In addition, there is a region of velocities occupied by insects and birds, which fills in additional parts of the range-velocity space at lower altitudes. Insects and birds can be especially problematic for radars attempting to detect and track stealth vehicles. As suggested by Figure 5.13, at low altitudes there is significant natural moving clutter arising from insects and birds. Table 5.5 tabulates the RCS, flock size, and aspect for three different radar bands for several common birds and insects. As can be seen from Table 5.5, even though the individual insect or bird cross sections are extremely low, their aggregate RCS can be significant depending on the quantity in a radar cell. Grackles, for instance, flock in large numbers at night to feed on insects and it is not uncommon for 1,000 grackles to be in a single radar cell. A flock of grackles can have a 1 m2 RCS in a single radar cell and have internal Doppler which easily masks a stealth aircraft. These conditions have been observed regularly on radar programs such as the TPQ-36 and 37. The old saying “birds of a feather flock together,” comes into play in fact, forcing higher false alarms, more processing, or lower sensitivity. Furthermore, wing speed as well as velocity can be high enough, especially in certain kinds of hummingbirds and geese, that these birds can easily be confused for aircraft. These sources of clutter

Apparent radial velocity (meters/second)

40

std = 2

std = 1 standard deviation std = 1

High altitude chaff

35 std = 3.5 std = 1 Rainstorm

30

Not change

10

Rainstorm velocity limits

Insects and birds std = 1.0

5 Land clutter std = 0.25 at 30 kt wind

Sea state 4

0 0

5

10

15

20 130 Range, km

135

140

145

Figure 5.13 Clutter velocity model. Adapted from Nathanson [3]

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Table 5.5 Reasons to stay low in a stealth vehicle Type of bird or insect

Flock size per cell

Sparrow Pigeon Duck Grackle Hawkmoth Honeybee Dragonfly

10 100 10 1000 10 1000 10

Individual RCS (dBsm) UHF

S-band

X-band

Typical net RCS per cell (dBsm)

56 30 12 43 54 52 52

28 21 30 26 30 37 44

38 28 21 28 18 28 30

18 to 46 1 to 10 2 to 20 þ4 to 13 8 to 44 þ2 to 22 20 to 42

can be rejected, of course, but a major increase in signal processing is required and in many cases, dramatically lower exposure times for a stealth system are the result. In late July 2019, there was a large migration of grasshoppers that showed up on NEXRAD weather radars as violent rain storms covering tens of square miles. The conclusions from Figure 5.13 and Table 5.5 are that there is significant moving clutter at lower altitudes which results in a major increase in threat processing and lower stealth vehicle exposure times. Land clutter has a velocity spread which has been extensively analyzed and modeled. The internal motion of brush and trees places a lower limit on both subclutter visibility. The accepted model for velocity distribution is exponential as given in (5.9): ⎞ ⎟⎟ ⎠ Where: s v is the velocity deviation and

s 0v =

⎛ 2⋅ v 1 ⋅ exp ⎜ ⎜ sv 2 ⋅s v ⎝

(5.9)

v is the velocity variable

A plot of this model for standard deviation, sv, corresponding to wind conditions ranging from calm to gale force (0.12 to 0.3 m/s) is shown in Figure 5.14.

Rain Doppler spread Another issue especially for aircraft and spacecraft is rain, fog, and dust. Usually, the particle size for all of these obscurants is much less than a wavelength but they still cause Rayleigh backscattering and attenuation. The author has been in tests in which each of these obscurants reduced detection range to ½ of the expected in clear air at X-band, Ku-band, and above. Of course, obscuration under these conditions is much worse at IR, visible, and UV wavelengths. In the Mideast at some times of the year, one can only see 100’ in a combination of haze and dust. One cannot tell where the sun is even though it is daylight.

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Calm Breezy Windy Gale

Relative power (dB)

0 –5 –10 –15 –20 –25 –30 –35 –40 –2

–1.5

–1

–0.5 0 0.5 Velocity spread (m/s)

1

1.5

2

Figure 5.14 Land clutter velocity spread (ClutterSpectralSpread)

One rainfall Doppler model is given in (5.10) [2]. It consists of the root sum square of four terms: a term associated with wind shear in elevation and distance, a term associated with turbulence, a term associated with velocity spread across the azimuth beamwidth, and a term associated with apparent distributions in falling droplet velocities with grazing angle. In most cases, wind shear is the dominant term. The values for each of these terms has been approximated empirically: 2 2 2 2 2 = s SHEAR + s TURB + s BEAM + s FALL m 2 /s2 s VR Where: s SHEAR ≅ 0.84 ⋅ R ⋅ e el , s TURB ≈ 1.0; s BEAM ≅ 0.42 ⋅ DV ⋅ q az ; s FALL ≅ siny ; R is slant range to scattering volume in kilometers, y is grazing angle, DV is line of sight wind speed, q az is azimuth beamwidth.

(5.10)

Example 5.1 For example, suppose the azimuth beamwidth is 50 mrad, platform velocity is 200 m/s, wavelength is 0.03 m, angle off the velocity vector is 45 , range is 120 km, elevation beamwidth is 105 mrad, grazing angle is 105 mrad, and line-ofsight wind velocity is 5 m/s. Then the Doppler spread for rain would be 832 Hz as shown in Figure 5.15. Depending on the targets of interest, the rain will interfere with only a part of the spectrum. Nonetheless, rain makes a dramatic reduction in detection range. This is especially true in South East Asia.

Exploitation of the environment Ground clutter bandwidth 2V 'FC = O qaz SIN q

Amplitude Ground clutter

'FR

–PRF 2

= 471 HZ Where: V = 200 M/S, O = 0.03M

Rain clutter

'FC

289

q= 45°, qaz = 50 MRAD Rain clutter bandwidth 'FC2 + 2∙VVR 2 O = 832 HZ Where: R = 120 km., 'V = 5 M/S eel= 6°, y = 6°

'FR =

'V 0 Frequency

PRF 2

Figure 5.15 Rain spectral situation

5.3 Terrain masking Another important issue is terrain and local feature masking. As grazing angles become very low, the amount of the terrain and the space immediately above the terrain actually visible decreases dramatically. Figure 5.16 shows terrain and local feature masking comparisons for two different depression angles at 8 and 4 for the Fulda Gap region in Germany. The black areas are masked from the observer’s viewing direction. Note also that the city in the upper left corner of the images is also partially masked at lower grazing angles. It can be seen that significant parts of the terrain and thus, a stealth vehicle, will be masked if it is flying low or on the surface at shallow viewing angles. A study of terrain masking versus elevation angle was performed at the University of Southern California under contract to Hughes Aircraft in the late 1970s for the Cooperative Weapon Delivery program [10]. One result of that study is summarized in Figure 5.17. The figure shows the fraction of the surface terrain that is masked as a function of elevation or grazing angle for various types of terrain. What can be observed is that, for terrain that contains woods and urban areas, as much as 40% of the terrain is masked at a grazing angle of 5 . This study used hypsographic (topographical relief) map data for a wide range of areas in both Germany and the United States. One can observe that a significant fraction of the terrain is masked because of the height of urban features or trees. There are a number of classified and unclassified terrain masking studies from which data can be obtained for more accurate modeling [4,11]. These terrain features can be used by an LO/LPI system not only to mask itself from conventional radar detection but also to scatter its emissions and prevent reception by an interceptor. One possible terrain-masking model that fits the experimental data reasonably well is a calculation of the cumulative probability of obscuration along the line of sight between the surveillor and the target or emitter. The instant probability of obscuration can be modeled as a function of the apparent height of the line of sight (LOS) above mean terrain altitude. The cumulative terrain height in a range cell, DR, determines

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14 km

14 km

–8°

Viewing direction

14 km

–4°

Figure 5.16 Terrain and local masking comparison

Fulda gap region of Germany

Fraction of terrain masked

0.80

0.60 Terrain + woods + urban areas

0.40

Incremental heights: 20 M average Woods: Urban areas: 10 M average

Terrain + woods

0.20

Terrain + urban areas Terrain only

0 0

5

10 Grazing angle (º)

15

20

Figure 5.17 Terrain masking versus grazing angle

whether the observer can see beyond that cell to the next. The probable height in a cell is a function of the terrain roughness. Cell height statistics can be approximated by a Chi-squared amplitude distribution with 2 degrees of freedom. One minus the cumulative Chi-squared distribution with LOS altitude as the independent variable determines the instant probability that the remaining terrain is obscured as shown in (5.11). (This is not

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291

exactly true but almost true when most LOS cells are higher than the terrain). The LOS height must be normalized by the terrain roughness or variance and the cell size in which the roughness was calculated. Summarizing, (5.11) gives a simple approximation for the probability of obscuration per range cell: ha

Pob = 1 −

∫ 0

⎛ ( x ⋅ Cell ) 2 ⎞ x ⋅ Cell 2 ⋅ exp ⎜ − ⎟ dx ⎜ 2 ⋅ C r 2 ⎟⎠ C r2 ⎝

Where: Cell = normalizing coefficient accounting for range cell correlation length D R & terrain roughness statistic in that size range cell h a = apparent height or altitude of the line of sight above mean terrain in a specific range cell, D R C r = terrain roughness in the same units as the apparent height (typically feet).

(5.11) For example, for a range cell, DR, of a nautical mile and a cumulative experimental probable rms terrain height, Cell is 1.41, that is, the square root of 2 sigma of a cumulative Chi-squared function. Each incremental height for additional terrain features is a square root sum squared with the basic terrain roughness to approximate overall roughness. Typical rms values for 1 nautical mile range cell size for Cr are 50 ft for steppe terrain (typical of Siberia, Canadian Territories, Kansas and Florida—no glacial moraines however in Florida), 150 ft for grassy terrain (typical of Indiana, Oklahoma, Northern Africa—no grass however in North Africa), 250 ft for wooded terrain (typical of Eastern New York and Canada, Germany, Austria, and Viet Nam) and 1000 ft for mountainous terrain (typical of the Rockies, Sierras, Switzerland, Urals, Afghanistan, Himalayas, and Columbia). Figure 5.18 shows plots of (5.11) for the parameters mentioned above and a range cell size of 1500 feet. The microwave horizons in nautical miles for the 4/3-earth model for surveillor, RHs and target, RHt, respectively, are given in (5.12): 5280 5280 0.5 and R Ht = (1.998 ⋅ h t ) ⋅ 6076.1 6076.1 Where: h s = height of the surveillor above the earth's surface in feet R Hs = (1.998 ⋅ h s )

0.5

⋅

(5.12)

ht = height of the emitter or target above the earth's surface in feet

The maximum visible slant range is less than or equal to the sum of the horizon distances for the surveillor and the target/emitter as shown in (5.13). If the target is inside the slant range to the horizon, then obviously the maximum range is the distance between the surveillor and target: R smax ≤ R Hs + R Ht

(5.13)

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Probability of obscuration in range cell

1

0.1 Mountains Woods Grassy Steppe

0.01

1‧10–3 10

100

1‧103 Apparent altitude (feet)

1‧104

Figure 5.18 Instant probability of obscuration for different terrains (Visible10. mcd) The apparent altitude is the height of the line of sight between the surveillor and the target over a 4/3 earth for every possible slant range. The apparent altitude in feet for a given slant range with all units in feet is shown in (5.14): 0.5 ⎡ ⎡⎛ ⎤ ⎤ ⎞ ⎢ ⎢ ⎜ 1 − Rs ⎟ ⋅ ( R e 43 + h s ) 2 + R s2 ⎥ ⎥ ⎢ ⎢ ⎝ Rsmax ⎠ ⎥ ⎥ ha = ⎢ − R e 43 ⎥ ⎢ ⎥ ⎢ ⎢ + ⎡( R + h ) 2 − R 2 ⎤ ⋅ R s ⎥ ⎥ e 43 t ⎢ ⎥ ⎢ ⎢⎣ ⎣ ⎥ smax ⎦ Rsmax ⎥ ⎦ ⎣ ⎦ Where: R s = slant range to the range cell at the height, h a

R e 43 = mean radius of the 4/3 earth generally taken to be 27,871,086 ft ∗

(5.14) *(Yes, this value is slightly different than what one would calculate using the value in (5.2) [2]. The same controversy surrounds the velocity of light.) Figure 5.19 shows the geometry for (5.12), (5.13), and (5.14). The surveillor, the target, and the center of the earth form a triangle from which the apparent height can be estimated. The distance to the surveillor from the center of the earth is hs þ Re, in order to take atmospheric refraction into account, the earth radius to be used is Re43. The second leg of the triangle is the distance to the target from the center of the earth ht þ Re, again the earth radius to be used is Re43. The third leg is the line of

Exploitation of the environment Target

293

ht Earth surface

LOS Rs

Rsmax

Surveillor Earth center

ha hs

Re

Figure 5.19 Apparent altitude geometry

1‧104

Apparent altitude (feet)

1‧103

100

10

1 0

20

40 60 Range (nautical miles)

80

100

Figure 5.20 Apparent altitude versus range (Visible9a.mcd) sight between the surveillor and the target with slant range Rsmax. Since the triangle is completely known, ha þ Re can be calculated from the slant range to a specific range cell Rs and subtracting Re yields ha, the apparent height above the local surface. Obviously, ha is a small difference in large numbers and one must be careful to prevent ridiculous results. An example plot of apparent altitude versus range for a surveillor altitude of 6000 ft and a target altitude of 10 ft is shown in Figure 5.20. Note that the apparent altitude drops to essentially zero because the LOS grazes the limb of the earth at the maximum range. Clearly, visibility is very improbable at maximum range. Even very smooth terrain such as steppe will not provide much visibility near maximum range. Let Rs ¼ iDR, where,DR, is the length at which cells are 75% decorrelated (not radar or ladar range bins). Then the cumulative probability of obscuration out to the ith range cell, Rs, is one minus the product of the instant visibilities (one

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minus the probability of obscuration equals the probability of visibility) for all the range cells to the range Rs as shown in (5.15): Rs =i⋅D R

Pcumob = 1 −

∏(

1 − Pob ( h a ( i ⋅ D R ) )

i =1

)

(5.15)

Repeated calculation of the cumulative obscuration at successive values of Rs, (iDR), out to Rsmax allows the generation of plots of obscuration versus range or grazing angle similar to the experimental data. For example, consider two cases: one where the surveillor altitude is 30,000 ft and the target altitude is 100 ft (or vice versa) in wooded or grassy terrain typical of AEW aircraft detecting a cruise missile and second where the surveillor altitude is 6,000 ft and the target altitude is 10 ft in wooded or mountainous terrain typical of mountaintop, UAV or helicopter surveillance of covert military operations. A graph of obscuration probability for case one using a DR size of 1 nmi and a range bin to cell normalizing factor of 0.248 is shown in Figures 5.21 and 5.22 as a function of range and grazing angle, respectively. Note that the visibility is down to

Surveillor altitude 30 kft Target altitude 100 ft 1 0.9

Terrain masking probabilities

0.8 0.7 0.6 0.5 0.4 0.3 0.2

Mountainous LOS obscuration Woods LOS obscuration Grassy LOS obscuration Steppe LOS obscuration

0.1 0 5

25

45

65

85

105 125 145 165 185 205 225

Range (nautical miles)

Figure 5.21 Terrain masking versus range – case 1 (Visible10a.mcd)

Exploitation of the environment Surveillor altitude 30 kft.

295

Target altitude 100 ft.

1 0.9

Terrain masking probabilities

0.8 0.7 0.6 0.5 0.4 0.3 Mountainous LOS obscuration Woods LOS obscuration Grassy LOS obscuration Steppe LOS obscuration

0.2 0.1 0 0

2

4

6

8

10

12

Grazing angle (°)

Figure 5.22 Terrain masking versus grazing angle – case 1 (Visible11.mcd)

50% for wooded terrain at 85 to 90 nmi which is roughly 40% of maximum range. For grassy terrain, visibility is 50% at roughly 65% of maximum range. Figures 5.23 and 5.24 show visibility for wooded and mountainous terrain when the surveillor altitude is 6,000 ft and the target altitude is 10 ft with a cell size, DR, of 1 nmi, Cell is 0.248, Cr has rms values (i.e., 63% of all cells will not rise more than Cr in one nautical mile) of 50 ft for steppe, 150 ft for grassy, 250 ft for wooded, and 1000 ft for mountainous terrain. As can be seen, the visible range is almost nil for mountainous terrain and low altitude surveillance. For example, such conditions exist in the Balkans, Alps, and Dolomites in Europe. The maximum range for this case is approximately 98 nmi, so the 50% visibility range for wooded terrain is a poor 15% of maximum. The grazing angle for low altitude targets can be approximated by (5.16): ⎡⎛ h ⎞ ⎛ h ⎞ R y = sin -1 ⎢ ⎜ s ⎟ ⋅ ⎜ 1 + s ⎟ − smax ⎣⎢ ⎝ R smax ⎠ ⎝ 2 ⋅ R e ⎠ 2 ⋅ R e

⎤ ⎥ ⎦⎥

(5.16)

One very rough rule of thumb from the foregoing is that visibility is typically down to 10% at approximately 80% of maximum range between the surveillor and the target for their respective operating altitudes.

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Target altitude 10 ft

1

Terrain masking probabilities

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2

Mountainous LOS obscuration Woods LOS obscuration Grassy LOS obscuration Steppe LOS obscuration

0.1 0 0

10

20

30 40 50 60 Range (nautical miles)

70

80

90

Figure 5.23 Terrain masking versus range—case 2 (Visible10.mcd)

Surveillor 6 kft Target 10 ft 1

Terrain masking probability

0.9 0.8 0.7 0.6 0.5 0.4 0.3

Mountainous LOS obscuration Woods LOS obscuration Grassy LOS obscuration Steppe LOS obscuration

0.2 0.1 0 0

2

4

6 8 Grazing angle (°)

10

12

Figure 5.24 Terrain masking versus grazing angle—case 2 (Visible10.mcd)

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Another aspect of the visibility issue for low altitude targets is the persistence of visibility with travel in the cross range dimension. Assuming that the target is detected at a specific range, Rs, what is the probability that it will stay visible for a cross range distance of Rc ¼ (j-1)DR. As the target moves a given number of cells laterally, it is repeatedly subject to the LOS visibility probability associated with the range, Rs. However, one cell lateral displacement means that most cells along the line-of-sight are still the same or almost the same. In fact, the new set of cells overlap the old set by more than 50% for ½ the range between the observer and the target. Clearly for the highly correlated cells, if they permitted visibility before, they still permit visibility. An arbitrary offset is three cells in which less than ¼ of the cells are correlated. The cumulative lateral obscuration per cell of offset on the basis of the foregoing assumption is shown in (5.17): Pcumobl = 1 − (1 − Pcumob ( D R ) )

j −1 3

= 1 − Pcumvis ( D R )

j −1 3

(5.17)

Where j is the cell index described above, DR is the cell length, and the cumulative visibility is Pcumvis ¼ 1Pcumob. For wooded terrain with the surveillor at 30,000 ft and target at 100 ft, lateral visible lengths are quite short until the target is less than 50% of maximum range as shown in Figure 5.25. In other words, exposure times are less than 20 s 50% of the time if the target is traveling at Mach 0.85 laterally to the surveillor at greater than ½ of maximum range. As surveillor altitude goes down, the situation gets even better for the low altitude penetrator. Parenthetically, cross range visibility for low altitude targets makes one of the most compelling arguments for E-3 AWACS type surveillance aircraft since visibility is dramatically better the higher the surveillor operates.

Surveillor altitude 30 kft

Target altitude 100 ft

Wooded visibility probability

0.99 0.88 0.77 0.66 0.55 0.44

20% max range 40% max range 60% max range 80% max range 100% max range

0.33 0.22 0.11 0 0

2

4

6

8

10

12

14

16

Cross range (nautical miles)

Figure 5.25 Typical wooded visibility versus cross range (Visible10a.mcd)

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Target altitude 100 ft

1

Grassy visibility probability

0.9 0.8 0.7 0.6 0.5 0.4 0.3 20% max range 40% max range 60% max range 80% max range 100% max range

0.2 0.1 0 0

4

8

12

16

20

24

28

32

Cross range (nautical miles)

Figure 5.26 Typical grassy visibility versus cross range (Visible10a.mcd)

Usually, a simple exponential approximation can be made to the obscuration curves of the form shown in (5.18):

(

c Pˆcumob = 1 − exp − a ⋅ ( R s − b )

)

(5.18)

Where a, b, and c are best-fit values for an exponential regression to the curves generated from (5.15) and (5.17). Terrain masking is beaten to death in the appendices. The situation is significantly different if the terrain is gently rolling or grassy as shown in Figure 5.26. For the same conditions mentioned above, the exposure time is 50 s 50% of the time at ½ maximum range. Staying low in featureless terrain will not provide adequate masking and other types of masking or signature reductions are a necessity. Figure 5.27 may help to visualize the process that reduces cross range visibility. The figure plots visibility on a log scale and since visibility decreases are a power series they appear as straight lines on a log scale. Another question to ask is “What is the effect of surveillance altitude on persistence of visibility for a given grazing angle?” Figures 5.28 and 5.29 compare 30 kft with 6 kft operating altitude. Note that there is a 7.5:1 difference in range scales.

Exploitation of the environment

Wooded visibility probability

1

Surveillor altitude 6 kft Target altitude 10 ft

0.1

0.01 20% max range 40% max range 60% max range 80% max range 100% max range

–3

10

10–4

0

0.5

1

1.5

2

2.5

3

3.5

4

Cross range (nautical miles)

Figure 5.27 Low altitude visibility versus cross range (Visible9a.mcd)

Surveillor alt 40 kft

Target alt 100 ft

4º grazing angle

1

Target visibility probability

0.9 0.8 0.7 0.6 0.5 0.4 0.3

Mountainous Wooded Grassy Steppe

0.2 0.1 0 0

10

20

30

40

50

Cross range (nautical miles)

Figure 5.28 Persistence of visibility for 30 kft surveillor altitude (Visible10a.mcd)

60

299

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Target alt 10 ft

4º grazing angle

1

Target visibility probability

0.9 0.8 0.7 0.6 0.5

Mountainous Wooded Grassy Steppe

0.4 0.3 0.2 0.1 0 0

1

2

3 4 5 Cross range (nautical miles)

6

7

8

Figure 5.29 Persistence of visibility for 6 kft surveillor altitude (Visible9a.mcd)

5.4 Electronic order of battle The next important stealth consideration is exploitation of the electronic order of battle (EOB). The EOB is the deployment and utilization of various kinds of radar, ECM, and radar intercept equipment in adversary military doctrine and tactics. The examples given here are somewhat dated but show a method of assessing stealth designs and tactics, which is generally useful. The latest adversary training and doctrine are necessary to evaluate the efficacy of a given stealth design. The training and doctrine are typically obtained by long-term observation with national technical and other means. An overview of the EOB threat for ground forces is given in Figure 5.30. As shown in panel 1 in Figure 5.30, each front will have a hierarchy of military units which will have threat systems attached to them based on coverage and numbers deployed. These systems will range from air defense batteries, to intercept and direction finding, to jamming, to early warning, to electronic intelligence, and ultimately national technical means. A stealthy weapon system must concern itself first with the immediate threats and having dealt with those then the longer-term threat. For an airborne penetrator, the primary threat is air defense. Panels 2 and 3 in Figure 5.30 show a typical regimental air defense complement. In addition to air defense that may be organic to a regiment, there will be air defense regiments in a division. Usually, a division-level air defense regiment will have longer-range threats than the air defense battalion organic to a regiment. This may include surveillance, communications specific to targeting, and some jamming. At the combined arms army level, there will be air defense regiments and

Exploitation of the environment 1

2

301

SA-8/-15 regiment

Front SA-8/-15 battery

x

Front air defense ESM/ECM reg

SA-4/-12 brigade

xxxx Army

Army air defense ESM/ECM BN

SA-4/-11 regiment

xx Division

Each regiment has 1 air defense battalion (ADA BN) ADA BN HQ unit 2 dog ear TA radars 2S6

Regiment

TA battery

Each battery Has 4 vehicles Each vehicle Has 6 missiles 1 land roll radar 3

SA-8/-15 regiment

HQ

Each 2S6 Has 8 SA-19 or ADATS 2 or 4 30 mm guns 1 hot shot TA/TT Radar

BMP-2 Each BMP-2 Has 1 ATGM 1 30 mm guns 6 crewman/SA-16

SA-13 FU 1 hat box ESM on PLT CMDR Vehicle

Figure 5.30 Overview of EOB threat—ground forces air defense electronic support measures (ESM), and electronic countermeasures (ECM). Finally, at the front or regional command level, there will be a SAM brigade and ESM/ECM regiment. Although this EOB example is quite specific, none of the details should be taken too seriously. What is important is the approach and manner of thinking about EOB threat scenarios. As will be seen in the following EOB scenario description, the build-up of emitters results in surprisingly large numbers. These emitters, even if far away, are so numerous that the ambient power spectrum can be the limiting factor in interceptor sensitivity. Appendix A.5 contains a table, which lists a large number of emitter types and their performance parameters. Section 5.7 lists a smaller table of typical emitters that could be expected on a battlefield. The parameters are gathered primarily from unclassified sources; however, in some cases, the author has made plausible guesses based on photos and observation of the equipments at international defense shows (be skeptical!). The organization of a generic surface-to-air missile (SAM) regiment is given in Figure 5.31. SAM regiments will have a command post that includes battle management with data links and communications for target handoff (as well as other command and control communications). There will be long and short-range acquisition radars. The missile batteries will have fire control radars and electro-optical systems (EOS). Each complement of missiles will have a transporter-erector-launcher (TEL or TELAR) with data links for both the missile and target handoff. Usually, there will also be service vehicles for fuel, replenishment, and personnel support that have radios and data links. The idea of EOB can be understood by schematically sketching out some hypothetical battle order based on tactics and doctrines. Figure 5.32 shows a typical

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SAM regiment

HQ

TABN SAM BTRY

Command post element

2-3 long range acquisition radars

Battery target acquisition radar 4 fire control radars

Figure 5.31 Generic SAM regiment

1st echelon armies 10 TK div 10 MR div

2nd echelon armies 5 TK div 5 MR div

NATO scenario schematic order of battle Legend FEBA Division XX 400 km Army or corps XXXX Division HQ

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35 km

50 75

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100 km 150

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Figure 5.32 Typical schematic order of battle

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EOB based on Warsaw Pact tactics and doctrines for 1990 for the utilization of radar, ECM, and radar intercept equipment on the central German front. The central German front is a much-studied area that has been subjected to many wars and war games over the last 150 years. Shown schematically is a 400 km battlefront, behind which are deployed first and second echelon armies. In the first 35 km behind the forward edge of the battle area (FEBA) across a 400 km front, 10 tank divisions and 10 motorized rifle divisions might be deployed and be moving toward or at the front. From 35 to 100 km behind the FEBA, reinforcements would be deploying and flowing toward the battle area. From 100 to 250 km behind the front, reinforcing second echelon armies would be flowing toward the battle area as quickly as they could be transported into the battle. The second echelon armies might contain an additional five tank divisions and five motorized rifle divisions flowing as reinforcements toward the front. As part of these first and second echelon armies, large numbers of radar, ECM, radar intercept, and air defense systems are routinely deployed. The total area covered by the adversary side of the FEBA is 100,000 km2 or roughly 38,500 mi2. There is a comparable amount of territory on the friendly side of the FEBA with similar forces. As pointed out earlier in this section, what is important here is a manner of thinking not the specific accidentals of the electronic order of battle described in the following sections.

5.4.1 Radar and EW intercept EOB Each first echelon division will have radar intercept and direction finding capability as shown schematically in Figure 5.34. Each division has a reconnaissance battalion with a radio and radar reconnaissance company containing modern systems like the Vega/Orion radar intercept and direction finding system. The system consists of a control station and three intercept receivers deployed on a 20 to 30 km long baseline for accurate two dimensional localization by triangulation. Each division artillery regiment also contains a target acquisition battery with similar equipment to allow attack of detected emitters. Localization of emitters is partially manual and typically takes 10 s to update. These sensors cover 150 km beyond the FEBA and are deployed 2 to 6 km behind the FEBA. There is overlapping coverage across the entire line of the FEBA as shown. Twenty-six sites are required to provide full coverage of the FEBA. The primary objective of the first echelon intercept and direction finding equipments is to detect the location of battlefield surveillance, counter battery, and air defense radars. So that they can be attacked with artillery, rockets or missiles, or neutralized with jamming. As such, long range is not necessary and sensitivity is required only for location accuracy. The more modern systems have some sidelobe interference cancellation capabilities but only for a few (1 or 2) interferers. In the second echelon, equipments similar to Vega/Orion in Figure 5.33 or Trash Can are deployed with division reconnaissance battalions and division artillery regiments. These are shown dashed and bold in Figure 5.34 for typical second echelon and Combined Arms Army (CAA) deployments. Those units

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0.2 to 2.0 GHz antenna system

Up to 30 km. Power cart

Power cart

Data link

Data link

Individual intercept receiver

Control station

Target # bearing signal parameters

Target # target Information location to user target recognition

Power carts

Figure 5.33 Russian Vega/Orion intercept and direction finding system. Adapted from [12] 1st echelon arimes 10 TK div 10 MR div

2nd echelon arimes 5 TK div 5 MR div

Army general and direct support of division capability utilizing assets of Army radar intercept and DF BN Radar intercept and DF BN

Intercept and DF site

Target Acq Btry, Army artillery div

Intercept and DF site

Targets detected and located by the army radar intercept/DF capability are engaged by artillery and rocket fire as a first priority for neutralization. Active jamming is a secondary course of action

250

200

150 0

100 25

50

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50 75

100

FEBA 150

100 km 200

250 km

250

Kilometers

Figure 5.34 Division intercept and direction finding (DF) deployed in the second echelon may not all be in operation because they are moving toward the front, but some fraction will be used to cover the line of march. Intercept/direction finding (I/DF) systems in the second echelon will have significantly degraded capabilities due both to distance from the FEBA, terrain

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masking, and their semimobile deployment along the routes of movement to the front. Notwithstanding the limitations, some capabilities will exist for the intercept of airborne radar coverage of the deployment, movement, and targeting of second echelon forces. These intercepts could lead to alerting of air defense, hiding, or jamming. In addition, at the CAA level, there will be additional radar intercept and direction finding capabilities over and above those that are attached to first and second echelon divisions. At this level, there will be longer-range intercept and direction finding systems in addition to the short-range units. Their primary mission is to counter air defense units of the opposing forces as well as to counter close air support attack aircraft and associated ground control. More specifically, the mission of the I/DF is detection and accurate location of the operating radars and data links of SAM batteries, counter battery field artillery, ground surveillance, ground attack/target designation control, and unmanned air vehicle (UAV) control stations. One major challenge associated with longer-range detection is visibility of emitters at low or zero altitude above ground level (AGL). Additionally at low altitudes, multipath and ducting are significant problems which limit location accuracy independent of signal-to-noise ratio (SNR). The primary methods of low altitude visibility are locating at higher altitude AGL, if available, or from aircraft. The minimum altitude for 90% short range visibility is probably 5,500 ft AGL. Such emitter location can be accomplished from medium utility or attack helicopters or medium aircraft. Surface or airborne I/DF systems may not have a unique signature other than their large RCS created by the I/DF antennas or by their data link signatures. Whether ground-based, airborne or mixed, there will be a minimum of 17 sites to provide full coverage of the battlespace. At the next highest level, there are also radar intercept and direction finding sites to support army groups. There may be as many as 80 positions at 23 sites that contain radio and radar intercept regiments supporting multiple armies across a broad front. They are targeted against all military radars, data links, and communications within their coverage range. In general, the frequency coverage of these multiple systems ranges from approximately 30 MHz to a little less than 40 GHz. For I/DF at the Ka-band frequencies, the intercept range is very limited by decreased sensitivity and increased atmospheric attenuation. In addition, some of these systems have excellent direction finding accuracy, perhaps as low as a fraction of a degree in a few cases. The primary weaknesses of ground-based systems are the limitations imposed by low altitude visibility, multipath, and ducting. Larger airborne I/DF and radar systems will be deployed in support of the full battlefront. These systems will include sensitive ELINT and COMINT recognition equipment. They will be limited primarily by their signal processing number smashing capabilities since thousands of emitters and tens of thousands of potential targets will be within their line of sight. One to three systems will be required continuously on orbits over the battlespace. This, in turn, requires a total of seventeen systems to allow refueling, replenishment, maintenance, crew replacement, travel to-from orbits, phase maintenance, etc. Although the resources required are much smaller than for counterpart ground I/DF systems, the resources

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required in the theater are still substantial (up to 1000 personnel). Counterpart Allies systems include E-2, E-3, E-8, RC-135, RC-12, Global Hawk, Astor, Reaper, and Wedgetail. Additionally at the theater level, space national assets may be dedicated to the battlefront.

5.4.2

Radar emitter EOB

In addition to the intercept equipment described in Section 5.4.1, there are numerous electronic warfare, early warning radar, and air defense radar systems deployed with the army across the front. Many older Russian and Chinese systems have been upgraded to AESAs using modern semiconductor T/R channels. Three separate classes of radar are normally deployed: early warning radars with reasonably long ranges, height finding radars, and target acquisition/fire control radars. Each of these radar companies might have three or four radars for the functions described above. These systems are capable of detecting aircraft and missiles out to 250 km depending on radar site and aircraft operating altitudes. For an early warning radar to detect targets at 250 km, the sum of the aircraft or missile altitude and the radar site altitude must be greater than 12,000 ft. The modern Russian and Chinese concept to counter stealth aircraft with battlefield surveillance radars is to use them in a network as shown in Figure 5.35. The good news is that range and angle resolution is so poor that target handoff is very difficult. Site location is critical to the success of these radars and, in a major battle, the site choices may be very limited. One purpose behind short-range air defense and other passive measures is to force attacking aircraft to higher altitudes where the early warning assets can actually give early warning. SVU

Networked control station RLM-Ku RLM-S VHF-band track

X-band track

RLM-D

L-band track

Figure 5.35 Long range detection and track. Adapted from [12]

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The NEBO UYe/Tall Rack may be able to detect an 0.01 m2 RCS stealth vehicle at a range of 40 mi under ideal conditions. In addition, the NEBO SVU AESA radar is capable of detecting stealth aircraft and missiles because its operating wavelength of roughly 6 ft is near the vehicle resonance region. Other radars such as the L-band Protivinik GE AESA (RLM-D in Figure 5.35) may have some capability against stealth vehicles and better resolution as well but, at a wavelength of roughly 1 ft, the effects of modern stealth techniques are fully in play. The Gamma S1 AESA (RLM-S in Figure 5.35) is an S/X-band target acquisition radar and stealth limits its performance significantly. A CAA will have an early warning battalion, and within that battalion, there will be early warning companies typically deployed as shown in Figure 5.36. In addition, there are early warning companies associated with a front early warning regiment, and each early warning regiment will have companies containing as many as 84 radars across the front. Location for front early warning radars is easier since they are further from the FEBA and may be able to choose high ground. These limitations are what have given rise to airborne radars to surveil and control assets in the battle space. There may be up to 96 early warning class radars associated with a front.

1st echelon armies 10 TK div 10 MR div

2nd echelon armies 5 TK div

5 MR div

Early warning company of the front early warning regiment Early warning company of the army early warning battalion Early EW battalion consists of 3 EW companies Each EW company contains three or four radars Each EW regiment consists of 6 EW companies

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200

150 0

100 25

50

35 km

50 75

100

100 km FEBA 150

250 km 200

250

Kilometers

Figure 5.36 Army and front early warning companies

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Not only are there early warning radars, but also there are radars associated with air defense guns and surface-to-air missile (SAM) systems. These systems usually operate at higher frequencies and have short radar ranges. However, because they typically are high peak power, low duty ratio systems, their intercept ranges can be extremely long. Air defense guns such as the upgraded ZSU23 and mobile surface-to-air missiles such as the SA8 through SA21 will be deployed at the division level in both the first and second echelon. Even SA2, SA3, and SA6 systems have upgrades and are deployed by some countries. These air defense systems will be deployed where there are troop concentrations as well as along lines of march. In addition, there will be the longer range SAMs deployed at the Corp and Army level to defend Command, Control and Communications (C3) and Leadership concentrations. Within the front, there may be as many as 480 Gun Dish radars (ZSU23) and 600 Land Roll (SA8) or Snow Drift (SA11/17) radars. Furthermore, there are radars associated with SA4, SA6 (Straight Flush), SA10 (Tin Shield, Flap Lid, Clam Shell, Tombstone), SA13 (Dog Ear), and SA12 (Bill Board, High Screen) fire units, which may contain as many as 212 radars across a front. As well as the newer SA20, SA21, and SA22 are with the very capable Tomb Stone and Pantsir radars. One concept for the deployment within the example EOB is given in Figure 5.37. The figure also tabulates the detection and engagement range performance of some (but not all) of the systems in the battlespace. Similar numbers of radar emitters will exist on the friendly side of the FEBA. All this “music” greatly complicates the 1st echelon armies 10 TK div10 MR div

2nd echelon armies 5 TK div 5 MR div

There are acquisition and fire control radars of the air defense units organic to divisions. A front might consist of 30 divisions with 7 armies in amajor battlefront. Each division will have 16 air defense guns and perhaps 20 short range SAM batteries. The missile batteries could range from upgraded SA-2 to SA-8. They also might contain SA-10 thru SA-22. As many as 164 radars associated with armies and front air defense will be deployed. These systems may cover 180 MHz to 30 GHz in frequency. Both Russian and Chinese systems will have a war band that they have never used. There may be signatures never seen before. The newer systems such as S-200, S-300, S-400 and S-500 will also be deployed. These newer systems use X band range gated HPRF pulse Doppler. Most of these systems also have IFF emissions. As many as 70 radars associated with army SA-6,SA-11, SA-17, SA-20 SA-21 Fire units and regiments Gun dish radar W/ZSU 23/4 (Range: 26 km search; 13 km track) Land roll radar W/SA-8 SAM system (Range: 54 km Acq; 13 km track)

250

200

150 0

100 25

50

35 km

50 75 100

FEBA 150

100 km

200

250 km

250

Kilometers

Figure 5.37 Radars associated with air defense guns and SAMs

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interceptor’s sorting problems and, as will be shown in a later section, limits usable sensitivity. The spectrum congestion can be so bad that it is not uncommon to see another’s video marching through your radar window.

5.4.3 Electronic countermeasures EOB On top of the radar emitters described above, there are significant numbers of jammers used to deny opposing forces’ use of their radar sensors, navigation, and communication equipment [21,22]. Some of the jammers are designed to deny accurate navigation data to attacking aircraft or missiles and may be oriented toward such systems as TACAN and GPS. As many as 54 jammers may be deployed across the front. Some will have effective radiated powers high enough to reach 200 km to the friendly side of the FEBA at higher altitudes (greater than 8000 ft). These cover X- and Ku-band primarily but do reach down to UHF. The typical deployment of these jammers is shown in Figure 5.38. In addition, there will be some number of airborne standoff jammers to reach lower altitude targets. Modern jamming systems are netted and coordinated by a control station. In addition, there will be radar defensive aids such as decoy emitters to prevent antiradiation missiles from targeting the true radar. There may also be look alike decoy missile TELARs (Transporter Erector Launcher) with fake missile data links. Jamming can be of many types including broadband noise, spot or swept noise, set-on (requires detection first), repeater, deception (requires detection first), etc. Usually, an LPIS has so much coherent gain that broadband, spot and swept noise

1st echelon armies 10 TK div10 MR div

2nd echelon armies 5 TK div 5 MR div

Single jamming site Jamming range capability TACAN / GPS jammer The jamming coverage shown here requires the support of a battalion and a half, or three radar jamming companies and Four TACAN / GPS jammers Each radar jamming company has 18 jamming sites. Because of the size of the central front (This scenario), Three companies (54 jamming sites) is a typical allocation of resources Of the 54 jammers, 36 are I-band jammers and 18 are J-band

Jammer CPN-2 CPN-4 TACAN/GPS SPN-2, 3, 4

Transmitter DF Freq (GHz) Power (kW ERP) Accuracy J-band I-band 0.5–2.0 2–20

50–250 50–250 50 50–250

r1° r3° – r1°

35 km

250

200

150 0

100 25

50

50 75 100

FEBA 150

100 km 200

Figure 5.38 Front jamming capabilities

250 Kilometers

250 km

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as well as deception jamming is invisible. The type that usually works best against both LPIS and GPS is repeater jamming since detection is not required and the repeater sends the complex LPI or GPS signal with a small delay which by definition will be match filtered at the receiver. Since the SNR at the repeater jammer will be less than unity, the repeated signal will return with a high level of noise, which can be detected and then nulled with an antenna canceller. Since sidelobe/ mainlobe cancellers are typically limited by the available number of degrees of freedom in the antenna, they can be overwhelmed if there are enough repeater jammers (usually 10s). For the threat interceptor, jamming greatly complicates detection of LPI emitters since the jamming is usually blind as to LPI location. Adversary jammer sidelobes will usually mask an LPIS. It can be seen that large numbers of both interceptors as well as radar and data link emitters are deployed along a front. In summary, possibly 100 to 200 intercept receivers will be deployed in the battle area. Fortunately for a stealth system, there will be 2000 to 5000 friendly and adversary force emitters potentially visible to a high sensitivity intercept receiver. These make up the environment that can be exploited by a stealth system. These emitters can be used to mask and confuse by careful choice of stealth waveforms and emission strategy.

5.5 RF Spectrum masking 5.5.1

Example ambient spectra

Ambient RF spectra can be another form of masking for LPI systems. Figures 5.39– 5.41 show typical ambient raw low-frequency spectra at three different altitudes:

–56

Received power (dBW)

–66

–76

–86

–96

–106 Noise floor-108.5 dBW@ front end in 3 MHz band –116 0.1

0.2

0.3

0.4

0.5 0.6 0.7 Frequency (GHz)

0.8

0.9

1.0

1.1

Figure 5.39 Ambient power spectrum: 18,000 feet AGL, Southern California in 1997. Adapted from [6]

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–56

Received power (dBW)

–66

–76

–86

–96

–106 Noise floor –108.5 dBW @ front end in 3 MHz band –116 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

Frequency (GHz)

Figure 5.40 Low-frequency ambient power spectrum: 3,000 feet AGL, Southern California in 1997. Adapted from [6]

18,000 feet above ground level (AGL), 3,000 feet AGL, and 200 feet AGL. They were also taken at different times and cities. The plots of Figures 5.39 and 5.40 were made in an aircraft flying over the Antelope Valley in Northern Los Angeles county. The only smoothing applied is that inherent in the chart recorder servo. Note that the total ambient spectral power decreases with decreasing altitude but local emitter power increases with lower altitude. The minimum discernable signal for these two figures is 108.5 dBW in a 3 Megahertz bandwidth. Some spectral masking is provided by the mountains which surround the Antelope Valley and reach an altitude of almost 12,000 ft, so this spectrum may be optimistic. Figure 5.41 shows the ambient spectrum for Washington, DC from a different study [13]. It is at a lower altitude but more than a decade later. The sensitivity is better and the ambient power is dramatically higher. The natural trend to have more users of RF spectrum means there will be more spectral masking even on a battlefield. At GM Hughes, we regularly received cell phone calls from Middle East battlefields requesting help with spare parts and information about a specific weapon system. This trend will only grow. Figure 5.42 shows very smoothed data for the ambient power spectrum from ground emitters taken by the Institute for Telecommunications Sciences spectrum survey in Los Angeles, CA in 1997 [6]. The data used for Figure 5.42 was collapsed into 100 MHz bins, mean power was estimated and scaled to power in a 3 MHz band. The data were gathered with several measurement strategies and the compromise estimate for the minimum discernable signal is 116 dBW. A small amount of smoothing was applied for the plot.

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Power (dBW)

–60 –70 –80 –90 –100 –110 Ambient spectrum in 3 MHz band, MDS –116 dBm –120 30 80 130 180 230 280 330 380 430 480 530 580 630 680 730 780 830 880 930 980 Frequency (MHz)

Figure 5.41 Low-frequency ambient spectrum: 200 ft AGL, Washington DC in 2010. Adapted from [13] (Table 5.6E.xls)

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Power (dBW)

–70 –80 –90 –100 –110 –120 –130 –140 –150 1000

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11000

13000

15000

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Frequency (MHz)

Figure 5.42 Microwave ambient power spectrum: 0 feet AGL, 3 MHz bandwidth, Los Angeles, CA in 1997. Adapted from [6]

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Ambient spectrum in 30 MHz band

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Power (dBw)

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6

8

10 12 14 Frequency (GHz)

16

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Figure 5.43 Microwave ambient power spectrum: 200 feet AGL, 30 MHz bandwidth, Denver, CO in 2013. Adapted from [14] (Table 5.6E.xls)

Figure 5.43 shows the ambient power spectrum for Denver, CO in a 30 MHz band at 200 feet AGL. Although the analysis bandwidth is 30 MHz rather than 3 MHz, it is obvious that compensating for bandwidth the ambient is roughly 20 dB higher in 2013 up to 10 GHz above that the ambient has changed very little. In cities like San Diego, which contain many military facilities, the ambient is 20 dB higher yet in the radar bands [15]. The demand for bandwidth and hence more ambient power will continue to rise. One could expect this level of civilian spectral emissions over a large metropolitan area even during wartime. Using the Excel program, Table 5.6E assuming a battle somewhere in the Pacific yields the spectrum shown in Figure 5.44. All the figures show that there are many segments of the spectrum that have power far above the noise-limited sensitivity. The ambient will mask and break up LPIS emissions that are lower than the ambient spectrum as described in Chapter 4. During a battle in which jamming may also be used, the ambient power will be much higher and will further limit interceptor sensitivity. The Excel program Table 5.6E is associated with Table 5.6 in the last section of this chapter. It is a compilation of most of the military emitters in the world as well as ambient powers in multiple US cities. The program allows one to calculate both power and pulse density across the spectrum from 100 MHz to 24 GHz. The user can thus create any electronic battlefield environment. As more information becomes available about existing emitters, the program can be updated and more

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Military @ 30 MHz bandwidth Military + civilian @ 30 MHz bandwidth

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Figure 5.44 Hypothetical future battle combined with Denver ambient spectrum (Table 5.6E.xls)

accurate potential spectra can be estimated. It should be a working tool for any stealth or EW engineer.

5.5.2

Estimating ambient spectra

The ambient spectrum for a battlefield can be estimated based on an assumed EOB as presented in the previous sections. Using the extended Table 5.6 later in this chapter and some assumed EOB (i.e., some set of ground and airborne emitters), the average ambient power spectrum over a battlefield at an interceptor with an omnidirectional antenna can be calculated using an Excel spreadsheet. The spectrum will also contain the emissions of many civilian sources which will be present in any modern EOB as well. This ambient power limits the usable interceptor sensitivity and can mask a stealth system. Many studies have been made of forecast pulse traffic in the European theater [17]. Once an EOB scenario is chosen, then pulse traffic can be estimated using the models provided in this section. The basic assumption is that there are emitters distributed uniformly and randomly over the battlespace. Further, a small fraction of the emitter antenna mainbeams are pointed in the direction of the interceptor and they are also random. There are four elements of the total spectrum. The first element, and the largest in number, is ground emitter sidelobes. The second element, and the largest in instantaneous power, is ground emitter mainlobes. Only some mainlobes are pointed at the interceptor at any time. An emitter dwell time on the interceptor is proportional to mainlobe beamwidth and scan rate. When there are a large number of emitters and since their scan rates are slow relative to interceptor detection time, the number of mainlobe emitters illuminating the interceptor is proportional to their beamwidth and the solid angle scanned. The third element is airborne and spaceborne emissions from

Table 5.6 Typical deployed emitter parameters. Adapted from [16,17,26–30] System type

Air radar Communist China F-7 F-8 FBC-1 H-20 J-11 J-15 J-20 J-31 France Mirage Entendard Jaguar Rafale EFA Germany F4G Tornado Typhoon International F-5 F-4 F-104 Mirage F-16 F-35

Operating band low (GHz)

Operating band high (GHz)

Average instant bandwidth (MHz)

Antenna mainlobe gain (dB)

Peak power (kW)

Mainlobe ERPP (dBW)

Antenna sidelobe gain (dBi)

Sidelobe ERPP (dBW)

Average power (W)

Sidelobe ERAP (dBW)

PRF high (kHz)

PRF low (kHz)

No. of systems in theater

9.5 9.6 16.0 15.5 9.5 9 8 8

10.0 9.9 16.2 16.5 10.5 10.5 11 11

1 1 3 5 3 3 10 3

30 32 30 35 33 35 36 34

5 8 75 10 5 4 30 8

67 71 79 75 70 71 81 73

3 6 3 10 10 10 15 10

34 33 46 30 27 26 30 29

40 160 300 500 1000 400 100 400

13 16 22 17 20 16 5 16

3.0 3.0 5.0 5.0 5.0 300 30 300

1.0 1.0 0.5 1.0 1.0 0.5 0.5 0.5

200 200 30 10 100 100 100 100

9.5 9.5 9.5 9.5 9.5

10.0 10.0 10.0 10.0 10.0

1 1 1 1 5

35 33 33 35 36

200 50 50 5 5

88 80 80 72 73

6 3 3 10 10

47 44 44 27 27

200 50 50 500 400

17 14 14 17 16

5.0 3.0 3.0 20.0 20.0

0.5 1.0 1.0 1.0 1.0

100 25 25 25 50

9.6 9.6 9.6

10.2 9.8 10.2

5 3 5

35 36 35

4 10 4

71 76 71

10 3 10

26 37 26

400 400 400

16 23 23

20.0 5.0 20

1.0 0.5 1

50 50 50

9.6 9.6 9.6 8.0 9.6 8.5

9.8 9.8 9.8 10.0 9.8 11

1 1 1 1 1 300

32 35 34 35 33 33

50 150 100 200 17 20

79 87 84 88 75 76

3 3 3 6 6 15

44 49 47 47 36 28

50 150 150 200 200 200

14 19 19 17 17 8

5.0 5.0 3.0 5.0 30.0 300

1.0 1.0 1.0 1.0 1.0 1

200 100 50 50 200 100

(Continues)

Table 5.6 System type

Russia MIG-21 MIG-23 MIG-29/33 MIG-31 SU-27 TU-16/22 A-50 T-50 Sweden JA-37 JA-39 U.K. Tornado AV-8 Typhoon U.S.A. E-2 E-3 E-8 P-3 P-8 F-14 F-15 F-16 F-18 F-22 F-35

(Continued) Operating band low (GHz)

Operating band high (GHz)

Average instant bandwidth (MHz)

Antenna mainlobe gain (dB)

Peak power (kW)

Mainlobe ERPP (dBW)

Antenna sidelobe gain (dBi)

Sidelobe ERPP (dBW)

Average power (W)

Sidelobe ERAP (dBW)

PRF high (kHz)

PRF low (kHz)

No. of systems in theater

12.9 12.9 9.5 9.5 9.5 8.0 0.5 8

13.2 13.2 10.5 10.2 10.5 15.0 1.5 10

1 1 3 2 3 1 0.5 3

30 35 33 37 33 33 37 37

8 100 5 10 5 100 10 10

69 85 70 77 70 83 77 77

3 3 10 10 10 3 3 10

36 47 27 30 27 47 37 30

150 300 1000 3000 1000 100 1000 500

19 22 20 25 20 17 27 17

3.0 3.0 20.0 300.0 5.0 3.0 1.5 300

1.0 1.0 1.0 5.0 1.0 1.0 0.3 5

100 100 100 100 100 10 5 100

9.5 9.5

10.0 10.0

1 1

34 34

5 10

71 74

6 10

31 30

500 1000

21 20

20.0 20.0

5.0 5.0

25 25

9.6 9.6 9.6

9.8 10.2 10.2

3 1 5

36 32 35

10 100 4

76 82 71

3 3 10

37 47 26

400 300 400

23 22 16

5.0 5.0 20.0

0.5 1.0 1.0

50 25 50

0.5 2.0 8.5 9.0 8.5 9.5 9.6 9.7 8.5 8.5 8.5

0.6 3.0 9.0 9.5 9.5 10.2 10.2 9.9 11 11 11

0.5 1 12.5 150 500 1 3 1 150 150 150

29 38 40 37 37 37 37 33 35 36 33

500 750 25 100 100 10 5 17 8 15 5

86 97 84 87 87 77 74 75 71 78 70

3 10 3 3 3 6 10 6 10 10 10

54 49 41 47 47 34 27 36 26 32 27

20 25 5 300 300 5000 1200 200 400 3000 500

10 4 4 22 22 31 21 17 16 25 17

1.0 5.0 5.0 5.0 10 300.0 250.0 30.0 300.0 30.0 300

0.2 0.2 0.5 0.5 0.5 1.0 1.0 1.0 0.5 0.5 1

3 3 3 5 5 25 100 100 100 100 100

AC-130 9.6 AV-8 9.5 AH-64 90.0 Global Hawk 8.4 V-22 9.3 C-130 9.35 C-5 9.3 C-141 9.3 C-17 9.3 C-2 9.3 B-52 16 B-1 9.6 Aerostat 9.6 Typ. Commercial 9.35 Air EW Communist China BM/KG 8601 2.0 BM/KG 8605/6 8.0 J-16D 1.0 France Remora 6.0 ABD 2000 6.0 Germany Sky Buzzer 6.0 USA ALQ-99 0.1 ALQ-136 8 ALQ-165 0.80 ALQ-176 0.80 ALQ-214 0.5 ALQ-227 0.1 ASQ-239 0.5 ALE-50 5

9.8 10.2 100.0 8.9 9.4 9.41 9.4 9.4 9.4 9.4 16.4 9.8 9.9 9.41

10 3 5 50 1 4 1 1 1 1 1 3 5 4

37 35 35 40 33 30 33 33 33 33 35 37 42 30

5 4 5 3 10 10 10 10 10 10 100 15 17 10

74 71 72 75 73 70 73 73 73 73 85 79 84 70

10 10 3 6 6 6 6 6 6 6 3 6 6 6

27 26 34 29 34 34 34 34 34 34 47 36 36 34

1200 400 50 400 5 5 5 5 5 5 150 150 200 5

21 16 14 20 1 1 1 1 1 1 19 16 17 1

30.0 300.0 50.0 5.0 2.0 1.6 2.0 2.0 2.0 2.0 3 20 5 1.6

1.0 0.5 5.0 1.0 0.2 0.2 0.2 0.2 0.2 0.2 0.5 0.5 0.5 0.2

10 50 50 2 5 50 5 4 10 5 20 20 5 100

8.0 18.0 16

20 20 10

3 3 20–35

25 50 2

47 50 53–68

3 3 3

41 44 24–39

25 50 500

11 14 21

100.0 100.0 100.0

1.0 1.0 1.0

300 300 10

18.0 18.0

20 20

9 9

50 25

56 53

3 3

44 41

50 25

14 11

100.0 100.0

1.0 1.0

50 300

18.0

20

9

100

59

3

47

100

17

100.0

1.0

300

18 18 35.0 15.5 40 18 35 18

20 25 25 25 30 20 30 30

20 10 15 7 20 20 20 10

1000 500 2000 400 1000 1000 500 100

80 67 78 63 80 80 77 6

3 3 3 3 3 3 3 3

57 54 60 53 57 57 54 47

1000 250 500 400 500 500 100 25

27 21 24 23 24 24 17 11

100 500 500.0 500 500 1000 500 500

1 0.5 0.5 1 1 1 1 1

30 50 50 10 10 5 100 100

(Continues)

Table 5.6 System type

Air Comm. International SatComm ARC-840 USA ATX-2740 JTIDS JTIDS SatComm GPS TACAN AXQ-14 Link 16 Air IFF International Typical Typical Typical Surface Radar Communist China LD2000 LD2000 FM90 Sino Crotale FM90 Sino Crotale FM90 Sino Crotale

(Continued) Operating band low (GHz)

Operating band high (GHz)

7.9 0.2

8.4 0.4

11.0 0.96 0.96 7.9 1.2 1.0 1.5 1.5

14.5 1.22 1.22 8.4 1.6 1.2 1.8 1.7

Average instant bandwidth (MHz)

Antenna mainlobe gain (dB)

1.5 0.025

27 6

275 4 4 1.5 0.5 0.1 5 0.5

30 9 9 27 50 0 10 10.0

Peak power (kW)

0.1 0.025 0.025 1 0.2 0.1 100 0.75 0.05 0.0

Mainlobe ERPP (dBW)

47 20 44 39 32 47 100 29 27 26.0

Sidelobe ERPP (dBW)

Average power (W)

3 3

17 11

100 25

3 9 9 3 3 0 3 3.0

11 39 32 17 47 29 14 13.0

Antenna sidelobe gain (dBi)

Sidelobe ERAP (dBW)

17 11

25 1000 100 100 100 100 40 50.0

11 39 29 17 17 20 13 14.0

2 10 6

1 1 1

15 35 20

2 1 1

48 65 50

3 6 3

30 24 27

10 10 10

7 4 7

14.6 2 2.3

16.6 4 2.4

2.5 0.5 0.25

40 36 32

20 5 5

83 73 69

3 6 3

40 31 34

200 200 200

16.0

16.4

1

40

20

83

3

40

9.5

10.5

0.5

25

5

62

3

34

1 8 4

PRF high (kHz)

PRF low (kHz)

1500.0 25.0

No. of systems in theater

1500 1.0

275000 275000 3700 3700 3700 3700 1500 1500 500.0 500 5.4 5.4 500.0 0.0 500.0 1.0

30 300 30 30 1000 30 1 20 100 100.0

20 20 20

0.3 0.3 0.3

10000 500 500

20 17 20

10 4.5 6

8 3.5 5

50 7 10

200

20

9

8

50

100

17

5

4.5

50

SJ-202 SJ-202 CLC-1 CLC-2 HT-233 HT-233 YLC-2V HQ-2J JY11B JY11B Yitian France Crotale Crotale Shahine Shahine Roland Roland Roland Germany Gepard AA Gepard AA Roland Roland Roland Wildcat International Cobra Fire Can Super Fledermaus Crotale

33 35 40 36 45 40 33 33 38,5 20 40

600 1500 20 5 100 100 100 350 700 1 5

91 97 83 73 95 90 83 88 97 50 77

3 3 3 6 10 3 10 3 10 6 10

55 59 40 31 40 47 40 52 48 24 27

600 1500 200 200 5000 2500 1000 600 4000 100 200

25 29 20 17 27 31 20 25 26 14 13

2.8 2.8 9 3.5 120 1.2 1.2 0.4 1.2 1.2 6.5

0.8 0.8 8 2.5 90 0.8 0.8 0.3 0.8 0.8 5.5

100 100 100 12 70 8 100 12 20 20 100

0.25 1 0.25 1 0.25 1 3

32 40 32 40 32 30 40

5 20 5 20 4 50 10

69 83 69 83 68 77 80

3 3 3 3 3 3 3

34 40 34 40 33 44 37

200 200 200 200 200 100 200

20 20 20 20 20 17 20

6 9 6 9 6 6 6

5 8 5 8 5 5 5

10 50 50 50 50 50 50

2.4 16.4 1.4 5.9 16.4 10.0

0.25 3 0.25 1 3 3

27 37 32 30 40 27

5 10 4 50 10 10

64 77 68 77 80 67

3 3 3 3 3 3

34 37 33 44 37 37

200 200 200 100 200 100

20 20 20 17 20 17

6.0 9.0 9.0 6.0 6.0 10.0

5.0 8.0 8.0 5.0 5.0 9.0

100 100 50 50 50 100

5.7 2.7 15.9

5.9 2.9 17.1

5 1.5 5

36 33 39

20 300 65

79 88 87

10 3 3

33 52 45

2000 500 50

23 24 14

10.0 1.9 8

5.0 1.8 7

20 20 50

16

16.4

1

40

20

83

3

40

200

20

9

8

50

2.9 4.9 14.6 2 6 1 2 0.14 2 1 8

3.1 5.1 16.6 4 8 2 3 0.16 3.5 2 9

0.5 0.5 1 0.5 3 0.2 0.5 0.2 1.5 1 1

2.3 16.0 2.3 5.0 1.3 5.7 16.0

2.4 16.4 2.4 16.4 1.4 5.9 16.4

2.3 16.0 1.4 5.7 16.0 8.0

(Continues)

Table 5.6

(Continued)

System type

Russia Dog Ear Gun Dish AA Big Fred Pat Hand Thick/Thin Skin Land Roll Land Roll Land Roll Bar Lock Spoon Rest Long Track Squat Eye Flat Face Side Net Big Back Straight Flush Straight Flush Flap Lid Hot Shot AA Hot Shot AA 9S18M1 Snow Drift Fan Song AandB Fan Song CandD Gauntlet Gauntlet Snap Shot

Operating band low (GHz)

3.0 14.6 34.6 6.4 6.0 6.0 8.0 14.5 2.7 0.1 2.5 0.8 0.8 2.6 1.0 8.0 5.0 9.5 2 14.6 8.0 4 2.9 4.9 4 34.6 14.6

Operating band high (GHz)

6.0 15.6 35.3 6.9 7.0 7.0 9.0 14.6 3.1 0.5 2.6 0.9 0.9 2.7 2.0 9.0 6.0 10.5 3 15.6 9.0 6 3.1 5.1 5 35.3 15.6

Average instant bandwidth (MHz) 0.5 3 3 1 0.5 0.5 3 3 0.5 0.1 0.2 0.1 0.3 0.2 0.2 1 1 2 0.5 3 1 0.3 0.5 0.5 1 3 3

Antenna mainlobe gain (dB)

37 37 40 35 32 32 27 38 36 30 36 34 34 36 40 38 35 40 33 37 38 20 33 35 33 40 35

Peak power (kW)

200 135 50 250 500 100 100 100 650 350 650 500 900 650 900 300 300 300 25 200 300 500 600 1500 10 50 100

Mainlobe ERPP (dBW)

90 88 87 89 89 82 77 88 94 85 94 91 94 94 100 93 90 95 77 90 93 47 91 97 73 87 85

Antenna sidelobe gain (dBi)

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 10 3 3 3 6 3 3 3 10 10

Sidelobe ERPP (dBW)

Average power (W)

50 48 44 51 54 47 47 47 55 52 55 54 57 55 57 52 52 45 41 50 52 21 55 59 37 37 47

400 200 50 200 500 100 100 100 650 700 650 500 2500 650 2500 300 300 5000 200 200 300 100 600 1500 500 50 100

Sidelobe ERAP (dBW)

23 20 14 20 24 17 17 17 25 25 25 24 31 25 31 22 22 27 20 20 22 14 25 29 24 7 17

PRF high (kHz)

4.0 9.0 4.4 2.0 0.5 2.0 4.0 6.0 0.4 0.4 0.8 0.8 0.8 0.5 0.3 100.0 1.5 10.0 10 9.0 1.5 200 2.8 2.8 8.0 10.0 10.0

PRF low (kHz)

1.0 8.0 2.5 1.0 0.3 1.0 2.0 4.0 0.4 0.3 0.4 0.4 0.2 0.4 0.2 50.0 1.0 5.0 5 8.0 1.0 1 0.8 0.8 7.0 5.0 5.0

No. of systems in theater

30 500 200 100 20 250 250 250 6 15 30 15 15 6 5 35 35 100 25 200 50 50 50 50 20 100 100

90K6E1 9S32 1L220UK Big Bird Tombstone TOR TOR NEBO M RLM-S RLM-D RLM-Ku Sweden Track Fire 9KA500 9KA500 Sky Guard LeopardAA LeopardAA U.K. Rapier Rapier Cymbeline TPS-32 Watchman Martello U.S.A. TPQ-36 TPQ-37 MPQ-53 MPQ-64 Hawk PAR Hawk CWAR T/MPQ32/49

3 6 6 2 7 14.6 6 0.18 7 1 14

4 8.5 8 4 9 16.6 8 0.22 9 2 16

0.5 3 5 0.5 3 3 0.5 0.75 1.3 1.3 1

38 42 40 40 42 40 33 39 42 41 20

500 300 10 500 300 20 10 12 500 125 1

95 97 80 97 97 83 73 80 99 92 50

10 10 10 6 10 10 10 3 10 10 3

47 45 30 51 45 33 30 38 47 41 27

7000 5000 200 7000 5000 100 200 3000 5000 12000 200

28 27 13 32 27 10 13 32 27 31 20

6.0 120 10.0 3 120 6 5 0.6 1 0.6 100

3.0 90 5.0 1 90 4 3 0.3 0.5 0.3 1

50 50 100 30 100 100 25 25 25 25 75

15.9 15.9 8.6 8.6 8.6 34.0

17.1 17.1 9.5 9.5 9.5 35.0

5 5 3 3 3 5

39 39 36 36 36 40

65 65 200 26 26 10

87 87 89 80 80 80

3 3 3 3 3 3

45 45 50 41 41 37

50 50 150 250 250 50

14 14 19 21 21 14

8.0 8.0 8.1 8.1 8.1 10.0

7.0 7.0 4.8 4.8 4.8 5.0

30 30 30 50 100 100

3.0 13.4 8.0 2.9 2.8 1.0

4.0 14.0 10.0 3.1 3.1 2.0

0.5 3 5 0.3 0.5 1

33 38 36 41 34 41

100 100 100 2200 58 132

83 88 86 104 82 92

3 3 3 10 3 10

47 47 47 53 45 41

100 100 100 22000 1300 5000

17 17 17 33 28 27

5.0 10.0 10.0 0.3 1.0 0.3

4.0 5.0 5.0 0.1 0.4 0.1

50 50 50 4 10 4

9.0 2.9 5.7 9.0 1.2 9.0 1.2

9.5 3.1 5.9 9.5 1.4 9.5 1.4

3 3 1 3 0.3 0.1 0.3

42 40 38 40 30 36 27

25 125 200 5 50 5 15

86 91 91 77 77 73 69

10 10 10 10 3 3 3

34 41 43 27 44 34 39

500 5000 1000 500 1000 5000 150

17 27 20 17 27 34 19

10.0 6.0 10 10.0 1.0 100.0 4.8

5.0 3.0 5 5.0 0.5 100.0 4.2

50 15 20 50 50 50 50

(Continues)

Table 5.6

(Continued)

System type

Operating band low (GHz)

Operating band high (GHz)

Average instant bandwidth (MHz)

TPS-32 TPS-43/70 TPS-43/75 TPS-73 ASR-9 FPS-8/88 FPN-66 PPS-5 MPN-25 Condor 2 TPN-18 VPS-2 TPN-22 TPN-24 GPN-22 TPN-25 FPS-117 WSR-88D Wind Shear ASR-3 Surface EW Communist China BM/DJG8715 970 Russia Tub Brick King Pin

2.9 2.9 2.9 2.7 2.7 1.3 2.7 16.0 9.0 1.0 9.0 9.2 9.0 2.7 2.7 9.0 1.2 2.7 0.4 1.3

3.1 3.1 3.1 2.9 2.9 1.4 2.9 16.5 9.2 1.1 9.6 9.3 9.2 2.9 2.9 9.2 1.4 3 0.4 1.4

8.0 8.0

16.0 12.0

100 120

2.9 8.0

10.4 10.4

50 50

0.3 0.3 0.3 3 1 0.3 1 4 1 5 5 5 1 1 1 1 0.5 0.8 0.5 0.5

Sidelobe ERPP (dBW)

Sidelobe ERAP (dBW)

PRF high (kHz)

PRF low (kHz)

No. of systems in theater

Mainlobe ERPP (dBW)

2200 4000 4000 10 1000 1000 10 1 5 2 200 1.4 50 500 500 12.5 25 750 2000 5000

104 102 102 76 93 87 77 62 75 60 92 65 90 94 94 86 80 104 93 101

10 10 10 3 3 3 3 3 10 10 3 3 6 3 3 10 10 3 3 3

53 56 56 37 57 57 37 27 27 23 50 28 41 54 54 31 34 56 60 64

22000 6700 6700 1100 600 1100 1000 1 500 100 250 10 300 500 500 40 2000 1500 1000 3600

33 28 28 27 25 27 27 3 17 10 21 7 19 24 24 6 23 29 27 33

1.0 0.3 0.3 1.0 1.2 0.4 1.2 4.0 4.5 5.0 1.2 20.0 5.0 1.2 1.2 4.3 0.5 1.3 0.1 0.4

0.3 0.2 0.2 0.5 0.7 0.3 0.8 3.0 2.5 0.5 1.1 15.0 4.0 0.8 0.8 2.7 0.2 0.3 0.1 0.3

4 10 10 5 5 5 2 100 5 5 10 100 5 5 5 5 10 3 20 5

32 32

0.2 0.2

55 55

3 3

20 20

200 120

20 18

100.0 100.0

1.0 1.0

50 50

30 35

0.2 0.15

53 53

3 3

20 19

200 150

20 19

50.0 50.0

1.0 1.0

10 20

41 36 36 36 33 27 37 32 38 27 39 34 43 37 37 45 36 45.5 30 34

Antenna sidelobe gain (dBi)

Average power (W)

Peak power (kW)

Antenna mainlobe gain (dB)

Cheese Brick TACAN/GPS SPN-2,3,4 USA MGARJS Surface Comm. France ST-701 lowband ST-701 midband ST-701 high Alcat. 179 Russia R-423 USA GRC-201 TRC-170 Typical MLS Cellular MilSat-Uplink Milstar TCM-600 USC-60 Surface IFF International Typical Typical Typical Typical

8.6 0.5 2.0

10.4 2.0 20.0

50 10 50

35 20 30

0.15 0.5 0.25

57 57 47

3 3 3

19 24 21

150 500 250

19 24 21

0.4

18.0

100

30

0.25

54

3

21

250

21

0.6 1.4 4.4 4.4

0.9 1.9 5.0 5.0

2 2 2 2

3 9 13 30

0.005 0.003 0.002 1

10 14 16 60

2 3 3 3

5 2 0 27

0.005 25 0.003 28 0.002 30 1000 27

4.4

5.0

2

33

1.5

65

3

29

1500

4.4 4.4 5.0 0.8 7.9 43 7.0 11.0

5.0 5.0 5.1 1.8 8.4 46 8.4 14.5

2 2 3 0.005 40 1.6 45 45

30 33 30 0 42 40 30 43

1 2 500 0.001 0.5 10 0.005 0.5

60 66 87 0 69 80 37 70

3 3 3 0 3 6 3 3

27 30 54 0 24 34 4 24

1 4 8 36

2 6 10 38

0.5 0.5 0.5 0.5

25 25 36 40

4 4 4 0.5

61 61 76 67

3 3 6 6

33 33 30 21

50.0 50.0 50.0

1.0 1.0 1.0

20 10 20

0

20

2000 2000.0 2000 2000

2000 2000 2000 2000

100 100 100 10

29

2000

2000

10

1000 2000 50 1 500 500 5 500

27 30 14 0 24 21 4 24

2000 2000 5.0 5.0 45000 45000 45000 45000

200 200 200 75

20 20 17 13

100 100 100 100

300

2000 100 2000 10 5.0 10 5.0 100000 45000 25 1500 100 45000 100 45000 100

0.3 0.3 0.3 0.3

10000 1200 500 500

324

An introduction to RF stealth, 2nd edition

sidelobes. The last element is airborne mainlobe emissions. Again, only a small fraction proportional to the beamwidth of the mainlobes is pointed at the interceptor at any time. The ground emitters exhibit an area density and the airborne/spaceborne emitters exhibit a volume density. Each emitter power as received at the interceptor is a function of its ERPP, instant and total bandwidth, distance from the interceptor, atmospheric attenuation, and wavelength. The actual locations of the emitters with respect to the interceptor are random to a first order. There are several techniques that could be used to estimate average power per unit of bandwidth under these circumstances including Monte Carlo simulation and probability-weighted summation. One of the examples provided in Section 5.6.2 is based on a Monte Carlo simulation. The technique selected for this section is probability-weighted power summation which is adequate if there are enough emitters of each type and enough resolution cells (which is usually true in a major battle). The earth is assumed flat for the analysis which follows. Since emitter power decreases as 1/R2, a flat earth approximation makes very little difference in the estimate. Consider the geometry of Figure 5.45 using spherical coordinates for airborne emitters and cylindrical coordinates for surface emitters. Define the following variables: Rg = ground range, Rs = slant range, D f = analysis bandwidth h = interceptor altitude, q = angle from z or up axis to Rs f = angle from x or East axis to the projection of Rs in the x - y plane N m = number of the mth emitter type IBWm = instant bandwidth of the mth emitter type f um = upper end of the operating band of the mth emitter type f lm = lower end of the operating band of the mth emitter type PSerpm = effective radiated peak power mth emitter type in its sidelobes PM erpm = effective radiated peak power mth emitter type in its mainlobe PUL( f , m ) = 1 if f lm ≤ f ≤ f um , PUL( f , m ) = 0 if f ≤ f lm or f um ≤ f pulse function is used to allow summation of multiple emitters and bands Q ( m ) = 1 if emitter is airborne and = 0 otherwise Perpm = mainlobe or sidelobe effective radiated peak power

(5.19.1) At each emitter site, an emitter’s probable frequency is assumed uniformly random. The emission spectra will be spaced at intervals roughly the instant bandwidth apart. The apparent power density is the interceptor analysis bandwidth divided by the instant bandwidth. Its contribution to the average ambient spectral power density assuming all frequencies in the operating band are used or visited is approximately as shown in (5.19.2): PFm =

IBW m ⋅ PUL( f , m ) ⋅ D f ( f um − f lm ) ⋅ IBWm

(5.19.2)

Exploitation of the environment

325

Z

Maximum altitude plane

hmax

Rt

dV

Rsdθ dRs Rssinθdf Rs

θ

y

Interceptor

f

Ground plane

h Rgdf Rg dRg dA

x

Figure 5.45 Ambient spectrum estimation geometry

Of course, the ambient power density at the interceptor from each emitter in its operating band is subject to the range equation (1.4) given in Chapter 1 with GIP and GI equal to 1 and PT  GTI equal to Perpm as well as the probability, PEm, of an emitter of the mth type at range, Rs; therefore, the probable differential power is given in (5.20): dPm ( f , R s ) =

Perpm ⋅ l m2 ⋅ Lm ⋅ d PEm ⋅ PFm

(4 ⋅p )

2

⋅ R s2

(5.20)

The probability of an emitter in a differential cell in this case is approximately the volume or area of coverage times the density of emitters, DEm, of the mth type given in (5.21): d PEm = ( D Em ⋅ dA) or

( D Em ⋅ dV )

(5.21)

326

An introduction to RF stealth, 2nd edition

Where the density is the total number of emitters of that type divided by the total volume or area considered in the battlespace: DEm = ( N m Vbat ) or ( N m Abat )

(5.22)

The area, Abat, and volume, Vbat, of the battlespace can be related to some maximum range, Rmax, which is related to the horizon or to the size of the front as

(

)

2 2 2 and Vbat ≅ p ⋅ R max Abat ≅ p ⋅ R max h + 2 h max ≈ p ⋅ R max ⋅ h max 3

(5.23)

Note that in Figure 5.45, slant range, Rs, and ground range, Rg, as well as the mean operating wavelength, lm, and operating frequency range between fum and flm are related by (5.24): R s = h 2 + R g2 and l m = ( 2 ⋅ c )

( f um + f lm )

(5.24)

Where c is the velocity of light and is approximately 0.983 feet/nanosecond. Then for the ground emitter elements, sidelobes and mainlobes of the total spectrum in cylindrical coordinates are given in (5.25): PG m ( f ) =

∫∫

Perpm ⋅ l m2 ⋅ Lm ⋅ PFm

( 4 ⋅ p ) 2 ⋅ R s2

Amax

d PEm

(5.25)

Referring to Figure 5.45 and noting that dA and Amax in cylindrical coordinates are 2 dA = R g ⋅ d f ⋅ dR g and Amax = p ⋅ R gmax

(5.26)

Substituting for lm, PFm, and dPEm, using (5.19.2)–(5.26), assuming that loss is a constant (for simplification) and integrating into angle, then the ambient peak power for the mth type ground emitter as a function of frequency is PGS m ( f ) = PUL ( f , m ) ⋅ D Em ⋅ PS erpm ⋅ D f ⋅ Lm ⋅ c 2

(

)

2 − f lm2 ⋅ ( f um + f lm ) 2 ⋅ p ⋅ f um

R gmax

∫ 0

Rg h 2 + R g2

(5.27) dR g

Exploitation of the environment

327

Therefore, integrating again [23,24] and substituting for Rgmax using (5.24), the ambient peak power attributable to ground emitter sidelobes is given in the following (5.28): PGS m ( f ) = PUL ( f , m ) ⋅

(

2 D Em ⋅ PS erpm ⋅ D f ⋅ Lm ⋅ c 2 ⋅ ln R smax h2

4 ⋅p ⋅

(

2 f um

−

f lm2

)⋅( f

um

+ f lm )

)

(5.28)

For clarity, define the above equation in two parts. The first part is all the characteristics of the mth emitter type and is independent of geometry. The second part is the interceptor geometry which is independent of emitter type. For a given altitude and presumed maximum range, part 2 is constant over all emitters. Then, part 1 as a function of frequency is KS m ( f ) =

PUL( f , m ) ⋅ D Em ⋅ PS erpm ⋅ D f ⋅ Lm ⋅ c 2

(5.29)

2 ⋅ p ⋅ ( f um2 − f lm2 ) ⋅ ( f um + f lm )

and combining with part 2, then PGS m ( f ) = KS m ( f ) ⋅ ln ( R smax h )

(5.30)

Element 2 of the total ambient power frequency spectrum uses the same formula except that the number of emitters is reduced to those that are pointed at the interceptor and PMerpm is the peak mainlobe ERP. For surface emitters, one can assume that the mainlobes are uniformly distributed in azimuth and will rapidly visit or continuously cover elevations up to 30 (antenna patterns often are csc2 or multibeamed in elevation). Total coverage is a little over p steradians or roughly ¼ of isotropic. The probability of mainlobe illumination will be approximately proportional to beamwidth: d PEm =

D Em ⋅ 4 ⋅ dA G MLm

(5.31)

Substituting the mainlobe probability density (5.31) into the total spectrum integral for the mth emitter type (5.25) yields the ambient peak power density attributable to ground emitter mainlobes for the mth type in its operating band:

PGM m ( f ) = 2 ⋅ PUL ( f , m ) ⋅

(

2 D Em ⋅ PM erpm ⋅ D f ⋅ Lm ⋅ c 2 ⋅ ln R smax h2

p ⋅ G MLm ⋅

(

2 f um

−

f lm2

)⋅( f

um

+ f lm )

) (5.32)

328

An introduction to RF stealth, 2nd edition Again for clarity, define KMm and substitute: KM m ( f ) =

2 ⋅ PUL ( f , m ) ⋅ D Em ⋅ PM erpm ⋅ D f ⋅ Lm ⋅ c 2

(

)

(5.33)

2 p ⋅ G MLm ⋅ f um − f lm2 ⋅ ( f um + f lm )

And thus the power for ground emitter mainlobes is PGM m ( f ) = KM m ( f ) ⋅ ln ( R smax h )

(5.34)

Similarly for the airborne emitters which are distributed according to a volume density as summarized in (5.35) which follows: PAm ( f ) =

∫∫∫ V max

Perpm ⋅ l m2 ⋅ Lm ⋅ PFm

( 4 ⋅ p ) 2 ⋅ R s2

d PEm

(5.35)

The above integration is best carried out in three sectors. The first sector is a cone centered on the zenith axis with apex at the interceptor/surveillor altitude, h, with base at the maximum altitude, hmax, and with base radius, Rtmax. This sector is integrated into cylindical coordinates. The second sector is a sphere with conical boring centered at the surveillor altitude, h, with radius, Rsmax. This sector is best integrated into spherical coordinates for q angles given in (5.36): ⎛h −h⎞ ⎛ h ⎞ q = p / 2 − asin ⎜ max ⎟ to p / 2 + asin ⎜ ⎟ ⎝ R smax ⎠ ⎝ R smax ⎠

(5.36)

The third sector is a cone centered on the zenith axis with apex at the interceptor/surveillor altitude, h, with a base at the ground level and with a base radius, Rgmax. This sector is integrated into cylindrical coordinates. Substituting and noting that in the two coordinate systems dV for spherical and cylindrical coordinates, respectively, is dV sphere = R s ⋅ d f ⋅ R s ⋅ sinq ⋅ dq ⋅ dR s or dV cylinder = R g or t ⋅ d f ⋅ dZ ⋅ dR g or t

(5.37) And also noting that Rgmax and Rtmax are given by (5.38): 2 2 R gmax = R smax − h 2 and R tmax = R smax − ( h max − h )

2

(5.38)

And in anticipation of the integration to follow define two intermediate variables, a and b: a=

h2 2 R smax − h2

and b =

( h max − h ) 2 2 2 R smax − ( h max − h )

(5.39)

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Then the three-segment integrals are p 2 + a sin ( h R smax )

2⋅p

PAS m =

∫

2⋅p

+

sin q ⋅ dq

p 2 − a sin ( h max − h ) R smax )

0

+

∫ (

df

R smax

(1− Z h )⋅ R gmax

h

∫ ∫ df

dZ

0

0

2⋅p

h max

∫ ∫ h

0

PS erpm ⋅ l m2 ⋅ Lm ⋅ PFm ⋅ R g

( Z ( hmax − h ) )⋅Rtmax dZ

( 4 ⋅ p ) 2 ⋅ R s2

( 4 ⋅ p ) 2 ⋅ ( R g2 + h 2 )

0

df

0

∫

∫

PS erpm ⋅ l m2 ⋅ Lm ⋅ PFm ⋅ R s2

∫ 0

dR s

dR g

PS erpm ⋅ l m2 ⋅ Lm ⋅ PFm ⋅ R t

( 4 ⋅ p ) 2 ⋅ ( Rt2 + ( hmax − h ) 2 )

dR t

(5.40)

After integrating [23,24] and much algebra:

( (

) )

⎡ ⎛ b2 ⋅ h2 + a 2 ⎞ ⎤ 2 ⎞ ⎛ 2 ⎢ h max ⋅ ln ⎜ h max + b ⎟ + h ⋅ ln ⎜ ⎟ ⎥ ⎜ ⎟ 2 ⎢ 2 ⎜ a 2 ⋅ h2 + b2 ⎟ ⎥ b2 ⎝ ⎠ PAS m ( f ) = KS m ( f ) ⋅ ⎢ ⎝ ⎠ ⎥ ⎢ ⎥ ⎞ −1 ⎛ h −1 ⎛ h ⎞ −1 ⎛ h ⎞ ⎢ +b ⋅ tan ⎜ max ⎟ − b ⋅ tan ⎜ ⎟ + a ⋅ tan ⎜ ⎟ ⎥ ⎝b⎠ ⎝ a ⎠⎦ ⎝ b ⎠ ⎣ (5.41)

For all cases of practical interest Rsmaxh, so the arctangent terms in the interceptor geometry portion of (5.41) are very small relative to the other terms, thus ⎡ h max ⎛ h2 + b2 ⎞ ⎤ ⋅ ln ⎜ max 2 ⎢ ⎟ ⎥ ⎝ b ⎠ ⎥ ⎢ 2 PAS m ( f ) ≅ KS m ( f ) ⋅ ⎢ 2 2 2 ⎛ ⎞⎥ ⎢ + h ⋅ ln ⎜ b ⋅ ( h + a ) ⎟ ⎥ 2 2 ⎢ 2 ⎜ 2 ⎟⎥ ⎝ a ⋅ ( h + b ) ⎠⎦ ⎣

(5.42)

Furthermore, the second term in (5.42) can also be dropped with a maximum geometry error penalty of 18%. The author recommends dropping the second term in most cases since the EOB will not be known with 20% accuracy. Similarly, the mainlobe differential probability density of airborne emitter pointing directions is approximately distributed over ¼ of isotropic but for completely different reasons ( aircraft scan volumes are usually small but they are typically maneuvering even when on station which expands the covered volume), thus d PEm =

D Em ⋅ 4 ⋅ dV G MLm

(5.43)

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Integrating similarly to above, using (5.35) and breaking the integration space into three regions as done in (5.40) but for mainlobe emitter pointing probabilities, making the same substitutions and approximations, the airborne contribution to the ambient spectrum from the mth emitter is given in (5.44) below: ⎡ h max ⎛ h2 + b2 ⎞ ⎤ ⋅ ln ⎜ max 2 ⎢ ⎟ ⎥ ⎝ b ⎠ ⎥ ⎢ 2 PAM m ( f ) ≅ KM m ( f ) ⋅ ⎢ 2 2 2 ⎛ ⎞⎥ ⎢ + h ⋅ ln ⎜ b ⋅ ( h + a ) ⎟ ⎥ ⎢ 2 ⎜ a 2 ⋅ ( h 2 + b 2 ) ⎟⎥ ⎝ ⎠⎦ ⎣

(5.44)

Recall from (5.12) and (5.13) that Rsmax is approximately:

(

)

(5.45) R smax ≤ h I0.5 + h E0.5 ⋅ 7463 feet Where hI is the interceptor altitude and hE is the emitter altitude. Therefore, h ¼ hI þ hE is always very small compared to Rsmax which is the reason the approximation of (5.42) and (5.44) are so accurate. Since most ground emitters are at relatively low altitude, hE is often assumed to be 20 feet. Most airborne emitters are above 1000 feet and often hE is assumed to be 1000 feet. If these assumptions are made, then h and Rsmax are different for the airborne and ground contributions to the overall spectrum. (Figures 5.46 and 5.47 make this assumption.) Recall that each of the individual spectral contributions is a function of frequency. Accumulating all the emitters in both the sidelobes and mainlobes, the –30.0 Military + civilian @ 30 MHz bandwidth

–40.0

Military @ 30 MHz bandwidth

–50.0

Power (dBw)

–60.0 –70.0 –80.0 –90.0 –100.0 –110.0 –120.0 1.0

3.0

5.0

7.0

9.0 11.0 Frequency (GHz)

13.0

15.0

17.0

19.0

Figure 5.46 Estimated battlefield spectrum 18,000 feet AGL in 30 MHz band (Table 5.6E.xls)

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331

10000 Military @ 30 MHz bandwidth and –60 dBm

Pulse density (106 per second)

1000

100

10

1

0.1

0.01 0

2

4

6

8 10 12 Frequency (GHz)

14

16

18

20

Figure 5.47 Estimated battlefield pulse density 18,000 feet AGL in 30 MHz band, sensitivity – 60 dBm (Table 5.6E.xls)

overall ambient spectrum can be estimated for a set of systems in a given scenario, then m max

Pamb ( f ) =

∑ m =1

⎡ (1 − Q ( m ) ) ⋅ ( PGS m + PGM m ) ⎤ ⎢ ⎥ ⎢⎣ +Q ( m ) ⋅ ( PAS m + PAM m ) ⎥⎦

(5.46)

Using parameters from Table 5.6 or a larger table in the download or DVD appendix, a typical battlefield spectrum can be estimated as shown in Figures 5.44 and 5.46. That spectrum when combined with a typical civilian spectrum (Figures 5.39–5.43) shows what might be expected over some modern battlefield. Whether this spectrum is representative of a real battlefield is not important but rather the method used should be applied to a predicted EOB to obtain the expected spectrum. Interestingly, as noted in the civilian spectrum discussion, the ambient power may go up as the altitude goes down because most airborne emitters are still visible and surface emitters are closer.

5.5.3 Estimating ambient pulse density Several studies have been reported that forecast intercept receiver pulse traffic [16,17]. Pulse traffic can be estimated using the model presented in Section 5.5.2 with a few additions. The mth emitter type has an assumed population on the battlefield as represented by Nm and a characteristic range of or average PRFm. Thus the total number of pulses emitted is the product, PRFm  Nm, and if the interceptor had infinite sensitivity it would detect and be forced to process all of them. Since interceptors have limited sensitivity (often intentionally), a lower number of emitted pulses weighted by their power probability will be detected and must

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be processed. If one assumes a biased detector with exponential characteristic, then the number of pulses detected can be modeled as given in (5.47): PPD ( f ) =

∑ m

⎛ ⎛ −P ( f ) ⎞ ⎞ N m ⋅ PRFm ⋅ ⎜ 1 − exp ⎜ amb ⎟ ⎟⎟ ⎜ TH ⎝ ⎠⎠ ⎝

(5.47)

Where TH is the threshold power bias, Nm is the total quantity of emitters of the mth type in the battlespace and PRFm is the average pulse repetition frequency of the mth emitter type. The use of a soft threshold as shown in (5.47) is consistent with multipath and anomalous propagation typical of real environments. Similar to Section 5.5.2 using the table in Section 5.6 or Appendix A.5, the pulse density can also be estimated for a given sensitivity as shown in Figure 5.47. The threshold, altitude, and analysis bandwidth, in this case, have been chosen to be –60 dBm, 18,000 ft AGL, and 30 MHz, respectively.

5.6 Example scenario analysis 5.6.1

Classification usable sensitivity

Two stealth scenarios will be analyzed in this section. The first provides a typical LPI and intercept receiver scenario. It will derive an average number of emitters visible for given sensitivity and make classification software loading estimates. Classification limited present and ultimate usable sensitivity will be discussed. The second uses conventional attrition analysis to estimate the benefits of stealth system survival rates as a function of observables. Figure 5.48 shows a typical LPIS scenario similar to the early days of Desert Shield/Desert Storm/Kosovo. A penetrating stealthy aircraft must fly from a base somewhere in friendly territory to the target somewhere in enemy territory. The total one way travel might be 400 nmi of which some fraction is over enemy controlled or threat territory. During such a flight, the penetrator will be in the engagement range or presence of perhaps 100 each friendly and enemy air defense systems with radar and data link emitters. In addition, there will be possibly 100 battlefield surveillance radars. In the air, there will be up to 400 aircraft emitters within the line of sight as suggested in the figure. Some or all of these units will be emitting at any time. The total number of emitters could be a little less than 2,000 with an average density of 3.3 per 100 nmi2 or roughly 1 per 30 nmi2. The emitters will be distributed on average over the battle area 1 every 5 1/2 nmi in any direction and their antenna mainlobes will be almost uniformly distributed in azimuth. The stealth penetrator might operate at altitudes from 30,000 ft to 200 ft AGL at various times during a mission. Extending the scenario, suppose the enemy interceptors have a 1 GHz instant bandwidth receiver with sensitivities including antenna gain of –60, 40, 30 dBm, and quadrant angle sorting (i.e., a typical RWR). The enemy interceptors are operating at an altitude of 5000 ft AGL (higher altitude hardly makes any difference). In this example during the time in enemy territory, the stealthy penetrator is flying at night at an altitude of 1000 ft AGL (lower altitude improves

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333

penetrator stealth). The unfriendly aircraft and surface threats must operate and detect the stealth aircraft in this environment. The threat systems must detect, sort, and classify LPI emissions in the presence of all the other emitters. The natural question is, “How well can they do”? To determine the answer, the ambient spectrum needs to be estimated and the corresponding intercept receiver loading must be calculated. Using (5.32)–(5.44) with the parameters assumed, the ambient spectrum can be calculated with and without the sidelobe contribution to power. The mainlobes of the emitters will be visible to the threat intercept receivers all the way to the RF horizon. The sidelobes of the emitters will be visible out to a ground range equivalent to the interceptor detection threshold signal level. For example, the typical enemy fighter in the table below will be detected in its sidelobes at 18 km with a –60 dBm sensitivity receiver. Table 5.7 summarizes the assumed parameters for the example scenario. Obviously, all these systems would not have identical parameters but the values in the table are quite common and represent a good average. One could argue about any of the numbers in the example; the important idea is the method. Emitter density 3.3 per 100 sq. nmi.

Typical flight path all weather

Friendly SAM’s radar guns Base

75 mi

>1000 Comm.

FEBA

Enemy:180 interceptors Friendly:180 interceptors, 20 Reece/Surv. Battlefield surveillance radars: 100

200 mi

Enemy Target SAM’s radar guns GCI radars

75 mi

75 mi

Figure 5.48 Example stealth penetrator scenario

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Table 5.7 Battlefield emitter parameters Type

Q N

PS

PM

Friendly fighter 1 180 2500 Recce/surveillance 1 20 5000 Enemy fighter 1 180 5104 Air defense 0 200 5104 Bomber 1 20 5000 SatComm 0 50 105 Battle surveillance/ GCI 0 100 105 Communications 0 200 500 Short range comm. 0 1000 83.3 Long range comm. 0 20 1.7105

GML GSL fu

fl

IBW PRF

8

5000 0.125 10 9 3 10 5000 0.25 9 8 500 108 5108 5000 0.5 8 7 1 109 10000 0.5 17 5 1 5000 0.25 16.5 16 5 108 3108 1500 0.5 5 4 5 6108 3000 0.5 4 3 1 1000 0.5 3 2 5 106 30 0.5 2 1 0.5 5103 109 3000 0.5 1 0.5 5

50 10 50 5 5 50 3 50 10 0.3

10 Pulse density per sec. in 1 GHz bands, all quadrants, sensitivities –60, –40, –30 dBm, altitude 5k ft

Pulse density (MPPS)

1 –60 dBm –40 dBm –30 dBm 0.1

0.01

0.001 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17

Frequency (GHz)

Figure 5.49 Example scenario pulse density for several sensitivities (AmbientPWR7.xmcd) Where Q in the table is 1 if airborne, N is the number of systems in theater, PS is the sidelobe ERPP in Watts, PM is the mainlobe ERPP in Watts, GML is the mainlobe gain, GSL is the sidelobe gain, fu is the upper edge of the operating band in GigaHertz, fl is the lower edge of the operating band in GigaHertz, IBW is the instantaneous bandwidth in megaHertz, PRF is the average PRF in kiloHertz. With these parameters, the ambient pulse density can be calculated for several different intercept sensitivities as shown in Figure 5.49. The sensitivities chosen are the probable

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335

hardware limited sensitivity and two probable software limited sensitivities. The actual calculation of the graph below is given in the download or DVD Appendix A.5. With estimates of the pulse density in each band as a function of sensitivity, the equivalent intercept processor loading can be calculated. Since a radar warning receiver (RWR) that gives a warning too late has no military utility, the maximum usable sensitivity can be estimated. Returning to the loading equation of Section 4.2.8 which is restated as (5.48), the intercept processor loading can be estimated for the various intercept receiver sensitivities given in Figure 5.49: OPS sec = 225 ⋅ N p ⋅ log 2 ( N p ) ⋅ 10 3 + 2.9 ⋅ 10 6

(5.48)

Where Np is the number of pulses intercepted per millisecond. The highest sensitivity shown in Figure 5.49, 60 dBm, has a total pulse traffic from 1 to 17 GHz of roughly 5 107 pulses per second. The traffic is made up of four bands of 107 pulses/s and twelve bands of roughly 106 pulses/s. Since the RWR is assumed to have quadrant angle separation and millisecond processing the four bands each require: OPS sec = 225 ⋅ 2500 ⋅ log 2 ( 2500 ) ⋅ 10 3 + 2.9 ⋅ 10 6 = 6.35 ⋅ 10 9

(5.49)

Similarly, the 12 other bands each require: OPS sec = 225 ⋅ 250 ⋅ log 2 ( 250 ) ⋅ 10 3 + 2.9 ⋅ 10 6 = 0.32 ⋅ 10 9

(5.50)

This requires a total number of processor operations for the entire band of 29109. Assuming the best militarized processor is currently deployed, the update time would be a second or two assuming the processors are dedicated only to this task. When the processing time exceeds the emitter dwell time, emitters appear to sparkle or scintillate in angle and are much more difficult to track if they are moving. Mainlobe dwell times are typically 30 to 300 ms and the interceptor must complete its processing in some fraction of that minimum time, which is why the 1 ms assumption was used in the analysis. So what sensitivity is usable in the assumed battlefield scenario? The two other sensitivities, 40 dBm and –30 dBm, shown in Figure 5.49 require 11.9109 and 3.83109 OPS, respectively. Using the best available military processors, 30 dBm would require much less than a second for updates. This update rate would be acceptable for surface targets, which either do not move or are moving slowly as well as airborne emitters which are far away. For stealth vehicles that move, even slowly, low update rates prevent tracking and may prevent detection due to scan on scan discussed in Chapter 3. The intercept receiver designer has several options: increase complexity dramatically, limit sensitivity, or accept very low update rates. Most deployed RWRs have chosen low update rates and reduced sensitivity. Typical intercept sensitivities in a dense signal environment are limited to –45 to 60 dBm and update rates will be about a second. The objective is to limit intercepts to a few emitters per band. Normally RWRs focus primarily on threats to the carrying platform limiting intercepts to mainlobe only. This is not the case for air

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Number of emitters in 1 GHz band

Number of emitters detected in 1 GHz band at 5 kft altitude and interceptor sensitivities of –60, –40, –30 dBm

100 –60 dBm –40 dBm –30 dBm

10

1 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17

Frequency (GHz)

Figure 5.50 Example scenario emitters detectable in 1 GHz band (AmbientPWR7. xmcd) defense suppression with antiradiation missiles (ARM) of course. Present classification is limited to about 5 to 10 intercepts in the same bin (RF, AOA). Figures 5.50 and 5.51 show the number of emitters as opposed to pulses detectable in each band. Returning to Figures 5.46 and 5.47, one can see the attraction for scanning superhet intercept receivers. Even though they do not have instant band coverage, the lower per band pulse density and ambient power make classification software loading much easier which produces a more balanced hardware and software design. In turn, the narrower instant bandwidth allows higher sensitivity if more processing is available. In summary, most current intercept receivers have more intrinsic sensitivity than can be used with current processing. Dramatic reductions in bin size are required to match existing intrinsic sensitivity to existing processing in a dense signal environment. In turn, stealth systems must use waveforms which neutralize small bin sizes and increase processing load. The actual usable sensitivity is dependent on the friendly/threat environment and the interceptor processing strategies. Therefore, an analysis similar to the foregoing must be performed for each new design and weapon system mission.

5.6.2

Monte Carlo simulations

The second example will cover superficially a low altitude penetrator simulation (LAPSIM) software program based on the engagement balloon concept introduced in Chapter 1 [18,19]. Simulations of this type attempt to model more accurately

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Number of emitters in 30 MHz band

1000

Example scenarioNumber of emitters detectable in 30 MHz band at 5 kft altitude and sensitivities of –60, –40, –30 dBm

100

–60 dBm –40 dBm –30 dBm 10

1 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17

Frequency (GHz)

Figure 5.51 Example scenario emitters detectable in a 30 MHz band (AmbientPWR6.xmcd) engagement geometries in terms of terrain, threat deployment, threat performance in the radar equation sense, threat response times, and flight trajectories. This simulation does not cover other emitter masking or penetrator end game countermeasures but does include electronic order of battle, threat strategy, terrain masking, stealth platform cross section, flight trajectory, and multilayer engagement timelines. The fundamental notions involve a random laydown of air defense threats, a random penetrating aircraft flight trajectory, typical threat timeline performance, and a terrain database. The visibility limitations of Section 5.3 are taken into account in an encounter. The resulting “missile intercepts” are thus just the missile arriving in the vicinity of the target penetrator while still in track. Figure 5.52 shows the overall block diagram for a LAPSIM type program. The stealth penetrator independent variables are altitude, radar cross section, and speed. Terrain databases can be specific world locations and threat performance/deployment can be as realistic as computing will allow. The environment functions of sensors, communications, command and control, and missile batteries can be everything from simple timelines to functional block simulations. Functional simulations allow not only time delay factors but also designation accuracies and battle degradation evaluation. The outputs are encounter statistics as well as typical visibility-time histories. Figure 5.53 shows a typical threat laydown for the much-studied Fulda Gap region of Germany. Normally, there is a topographic map underlay for Figure 5.53 but the composite does not reproduce well and confuses understanding of the basic

338

An introduction to RF stealth, 2nd edition Inputs

Environment functions

Terrain data base

True threat deployment

Acquisition tracking

Surveillance Command and control

Threat performance data base

Outputs

Threat evaluation and weapon assignment

Track distribution and hand-over

Acquisitions Launches Intercepts

Track prioritization engagement analysis fire unit assignment

Fire control

Tracking launch decision

Missile engagement

Missile guidance missile flyout

Aircraft trajectory

Statistics

Visibility-time histories

Figure 5.52 Low altitude penetrator simulator diagram. Adapted from Raytheon [5] 5660

Fulda gap laydown

Northing

5635

5610

Typical flight paths

5585 FEBA 5560 500

525

550

575

600

625

Easting

Figure 5.53 Typical random laydown of air defense threats. Adapted from Raytheon [5] geometry. Each box in the figure represents an air defense threat. Flight paths can be chosen at random and for short periods can be thought of as segments of constant altitude great circle routes. Although encounters on some flight paths could be simultaneous, mathematically they will be dealt with individually and then summed (a good first approximation). The specific results for real aircraft in various real-world locations are classified but the basic models provide good first-order approximations. The simulation operates by calculating the encounter probability to each threat as the penetrator travels along its flight path. That probability is made up of several parts. First, the probability that the penetrator is visible, second the probability that the penetrator could be detected in the radar equation sense, and third that the detection lasts long enough for acquisition, handoff, launch, and intercept. As mentioned earlier,

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each encounter is modeled as an independent one-on-one encounter and then all the encounters are summed to arrive at an overall statistic. The number of detections, acquisitions, launches, and intercepts are accumulated over the entire flight path. This process is repeated for multiple trajectories and statistics can be built up. When or if the detection probability goes above some preset threshold, an acquisition timer is started. If the detection probability drops below a second threshold, the acquisition is abandoned. If the detection probability stays above the acquisition threshold long enough, a launch timer is started which runs until intercept, missile flight time-out, or the penetrator detection probability drops below the second threshold. The acquisition timer includes surveillance frame time, acquisition designation and track stabilization, target threat assessment, and fire unit assignment through missile launch. The launch timer includes launch, missile stabilization, and flyout. The only math is the continuous calculation of the range between each air defense site and the penetrator as a function of time, the apparent altitude, and thus visibility along that line of sight (5.21)–(5.29) and the range equation for a characteristic radar type as given in Table 1.12. In Chapter 1, Figures 1.36 and 1.37 assumed detection thresholds set for PD ¼ 90% and PFA ¼ 1012 and thus detection was either certain if inside that range or zero if outside that range. For the current case, a Rayleigh fading single frequency channel is often assumed with a radar square law detector with unknown phase in both inphase and quadrature channels followed by noncoherent integration (It is not exactly correct but it is easy to calculate). The probability of detection is ⎛ -ln ( PFA ) ⎞ PD ( R s ) = G Eu ⎜⎜ 1, ⎟⎟ ⎝ 1 + SNR ( R s ) ⎠

(5.51)

Where G Eu(1,y) is the incomplete Euler gamma function with y the lower limit of integration and ? is the upper integration limit. All other variables are as defined before. The probability of acquisition is: Pacq = C acq ⋅ PD ( R s ) ⋅ (1 − Pcumobl ( R s , h a , D R c1 ) ) Where: Cacq PD ( Rs )

(5.52.1)

constant to account for acquisition probability and timing

probability of detection in the radar equation sense and is a function of range, Rs

Pcumob , Pcumobl D Rc1

as defined in equations (5.18) and (5.17), respectively

cross range length necessary for acquisition

(5.52.2) Similarly, the probability of launch depends on the probability of acquisition, the probability of continued detection and an extended cross range length: Plaunch = C launch ⋅ Pacq ⋅ PD ( R s ) ⋅ (1 − Pcumobl ( R s , h a , D R c1 + D R c2 ) )

(5.53)

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Where Claunch is a constant to account for intercept probability and timing and DRc2 is the additional cross range length necessary for launch: Pintercept

C intercept ˜ Plaunch ˜ PD  R s ˜ 1  Pcumobl  R s , h a , D R c1  D R c2  D R c3

(5.54) Where Cintercept is a constant to account for intercept probability and timing and DRc3 is the additional cross range length necessary for intercept. Because apparent altitude and range may change dramatically during an encounter the visibility and detection probabilities must be continuously calculated. The independent variables in (5.51)–(5.52) do not seem to match the need since the above probabilities are usually time-dependent not displacement dependent. In order for (5.51)–(5.52) to be useful, a penetration geometry and speed must be invoked. Assume a penetrator flying “constant speed, straight and level” is traveling a segment of a great circle route. Assuming such a route with an arbitrary offset with respect to an observer near the earth’s surface allows the displacements to be converted to timelines. Although the results shown in Figures 5.58–5.61 are an accumulation of many Monte Carlo runs, the basic idea can be understood by considering the geometry of Figures 5.51 and 5.52. A whole earth cutaway view of the threat-penetrator geometry in the plane intersecting the threat, the penetrator, and the center of the earth is shown in Figure 5.51. Assume that the altitudes ht and hs do not change during the time of the encounter and the penetrator flies a segment of a great circle route. The distance between the threat and the penetrator is Rs. Assuming no winds and a constant speed along a great circle route implies a constant angular velocity about the earth’s center. Then arbitrarily setting t ¼ 0 at Earth tangent plane

z

Threat

Rs

hs

Penetrator ht Constant altitude

ht + Re

ht + Re

θ

y

Roff

x

Earth Radius 3960 mi. Apparent radius Re = 5267(4/3 earth)

Figure 5.54 Whole earth view of penetrator geometry

Exploitation of the environment

Penetrator flying great circle trajectory altitude=ht

341

Speed=SAC Earth tangent xy plane, z =Re

DR Rg

Rsmax

Observer / air defense threat altitude=hs

Roff

Rsmax Apparent horizon for a given altitude

Figure 5.55 Plan view of penetrator geometry the time that the penetrator crosses the xz plane in Figure 5.54 yields the following form for the penetrator motion: y = ( R e + h t ) ⋅ sin ( w ⋅ t ) x = ( R e + h t ) ⋅ cos ( w ⋅ t ) ⋅ sin (q ) z = ( R e + h t ) ⋅ cos ( w ⋅ t ) ⋅ cos (q ) Where: w =

S AC R e + ht

(5.55)

⎛ Roff ⎞ and q = atan ⎜ ⎟ ⎝ Re ⎠

Where SAC is the penetrator speed and Roff is the range at the point of closest approach (t ¼ 0). The y, x, z speeds are Sy =

⎛ S ⋅t ⎞ dy = S AC ⋅ cos ⎜ AC ⎟ dt ⎝ Re + ht ⎠

Sx =

⎛ S ⋅t ⎞ dx = S AC ⋅ sin (q ) ⋅ sin ⎜ AC ⎟ dt ⎝ Re + ht ⎠

Sz =

⎛ S ⋅t ⎞ dz = S AC ⋅ cos (q ) ⋅ sin ⎜ AC ⎟ dt ⎝ Re + ht ⎠

(5.56)

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1 0.9

Terrain masking probability

0.8 0.7 0.6 Surveillor altitude 10 ft penetrator altitude 200 ft

0.5 0.4 0.3

Mountain Wooded Grassy Simple approximation to wooded obscuration

0.2 0.1

0 1

0

2

3

4

5

Range (nautical miles)

Figure 5.56 Terrain masking for the example penetrator geometry (Visible10.mcd)

Surveillor altitude 10 ft penetrator altitude 200 ft 0.99

Wooded visibility probability

0.88

20% max range 40% max range 60% max range 80% max range 100% max range

0.77 0.66 0.55 0.44 0.33 0.22 0.11 0 0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

Cross range (nautical miles)

Figure 5.57 Cross range visibility for the example penetrator geometry (Visible10.mcd)

Exploitation of the environment 35

RCS: 102 meters

30

Acquisitions Launches Intercepts

25 Encounters

343

20 15 10 5 0 165

200

330

500

Penetrator altitude (ft. AGL)

Figure 5.58 Effect of altitude on threat missile intercepts. Adapted from Raytheon [5]

The slant range between the penetrator and the surveillor is Rs2 = ( z − ( Re + hs ) ) + x 2 + y 2 and thus: 2

Rs ( t ) =

⎛ S AC ⋅ t ⎝ Re + ht

( Re + ht ) 2 − 2 ⋅ ( Re + hs ) ⋅ ( Re + ht ) ⋅ cos (q ) ⋅ cos ⎜

⎞ 2 ⎟ + Re ⎠

(5.57) For most geometries of interest where Roff is less than 500 mi, the following (5.58) approximation is useful: cos (q ) ≈ 1 −

2 Roff

2 ⋅ Re2

(5.58)

Now that an equation for range as a function of time has been developed, a version of the radar equation suitable to determine the probability of detection with time can be stated: SNR ( R s , s ) =

PT ⋅ G T2 ⋅ Duty ⋅ T D ⋅ l 2 ⋅ L R s ⋅ ( 4 ⋅ p ) 2 ⋅ k B ⋅ T0 ⋅ NFR R s4

(5.59)

Where all the variables are as previously defined in Chapter 1. The cross range term can be approximated by DRc ≈

R s ( t1 ) − R s ( t 2 ) ⎛ 2 ⋅ Roff ⎛ ⎞⎞ tan ⎜ acos ⎜ ⎟ ⎜ ⎟⎟ ⎝ R s ( t1 ) + R s ( t 2 ) ⎠ ⎠ ⎝

(5.60)

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Where t1 is the start of an acquisition, launch, or intercept interval and t2 is the end of the same interval. With these basic equations, it is now possible to calculate individual encounters. Figure 5.55 shows a plan view of the penetrator geometry and the trajectory projected on a tangent plane under the surveillor is a segment of an ellipse. Some segment of the trajectory DR must have good visibility and good SNR for a full engagement. The penetrator will appear to rise above the horizon in a segment of an ellipse. The point of closest approach is Roff. All of the curvatures are exaggerated to illustrate the geometrical effects. For example, consider the case of an encounter between a penetrator flying at 200 ft over wooded terrain at a speed of 850 ft/s with radar cross section of 20 dBsm and the X-band fire control radar of Table 1.12 with an offset range of 5 mi. Assume acquisition time of 30 s, launch time of 30 s, and maximum missile time of flight of 15 s. Then, using the equations of Section 5.3, the probability of terrain masking is given in Figure 5.56. The penetrator is not visible in wooded terrain for ranges greater than 2 nmi as shown in Figure 5.56 and thus PD in the radar equation sense does not make any difference. At this offset range, all encounters result in no acquisitions, launches, or intercepts. Note, however, that grassy or steppe (not shown) terrain can result in an acquisition. If all offsets between 5 and 0 nmi are tested in a regular or Monte Carlo sense, then 7.5% of the total will be visible and those visible will be well within the 95% probability of detection envelope. The transit time will range from 12 s to 0 and no launches will occur since 30 s has been assumed. If, however, acquisition time of 5 s is assumed (some systems make this claim), then there could be 7.5%  (12 þ 0)/(2  5) ¼ 9% launches. No launch would result in an intercept because the cross range visibility is too short as shown in Figure 5.57. But if the launched missile had an autonomous seeker that could detect a stealth target in clutter and if the missile had a lofted trajectory (5000 ft altitude) so that the grazing angle was greater than 6 as shown in Figure 5.24, for example, then an intercept might occur. In most cases, the penetrator would be an opening target at the time of missile launch, the penetrator must be more than 3.5 nmi from the missile launcher at the time of launch (e.g., 6 nmi missile range in 15 s versus 3.5 nmi at missile launch þ 2.5 nmi penetrator travel during missile time of flight). Line of sight missiles would have no chance due to cross range loss of visibility. The coefficients for the simple approximation in Figure 5.56 using (5.18) are a ¼ 1.52, b ¼ 0.11, and c ¼ 1.56. Figures 5.58–5.61 show a summary of multiple runs of the type just described for a lofted trajectory missile and 5 s acquisition time for various cross sections and penetrator altitudes using the random laydown of Figure 5.53. The absolute numbers in this example mean nothing—only the ratios between columns because the numbers are a function of the number of Monte Carlo runs. Figure 5.58 shows for a conventional aircraft target RCS of 10 m2 of 200 feet that it gets very dangerous with increasing altitude. Figure 5.59 shows the improvement with reduced RCS for a practical penetrator altitude of 200 feet above the local ground level. The ride is still very rough at

Exploitation of the environment 35

345

Average altitude 200 ft. AGL

30

Encounters

25 Acquisitions Launches Intercepts

20 15 10 5 0 10

0 –20 –30 Penetrator RCS (dBsm)

–40

Figure 5.59 Radar cross section versus threat missile intercepts. Adapted from Raytheon [5]

25

High threat density, average altitude 200 ft.

Encounters

20

Straight – acq Straight – Lau Straight – Int Optimal – Acq Optimal – Lau Optimal – Int

15 10 5 0 10

0

–20

–30

–40

RCS (dBsm)

Figure 5.60 Straight and optimal penetration route versus threat. Adapted from Raytheon [5] 200 feet but easily doable for modern military aircraft. The author has been at air defense sites when going against low altitude military aircraft. The timeline is very short requiring almost perfect response time. When the shock wave from the aircraft hits you, it is awesome and easily knocks you flat. Obviously, if the deployment of air defense assets is known, then the penetrator can fly an optimal trajectory which minimizes the number of exposures to air defense. That coupled with reduced RCS dramatically reduces the probability of an encounter as shown in Figure 5.60. Finally, when the air defense threat density is half as much, the reduction in successful encounters is more than cut in half as shown in Figure 5.61. (Successful for the air defense site and bad for the aircraft.)

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35

35 Altitude as above 1/2 fulda gap density

30

30

25

25

20 15

Acquisitions Launches Intercepts

10 5 0

Encounters

Encounters

Average altitude 200 ft. AGL fulda gap laydown

20 15

Copyright, Raytheon Company, 2003. All rights reserved. Raytheon is a registered trademark of Raytheon Company Reproduced with permission from Raytheon Company.

10 5

10

0

–20

–30

–40

RCS (dBsm)

0

10

0

–20

–30

–40

RCS (dBsm)

Figure 5.61 Effect of penetrating at lower threat density. Adapted from Raytheon [5]

5.7 Typical deployed emitters There are both formidable, combat proven, numerous airborne and surface emitters, which will fill the battlefield spectrum. These systems emit from VHF to Ka-band. There also are many new civilian emitters such as Wi-Fi, Bluetooth, and 5G cellular, which will be found in or near a battle area. The primary change since the first edition of this book is not so much new emitters although there are a few. But rather many existing systems and platforms have been upgraded with modern solid state transmitters or active arrays and dramatic improvements in signal processing enabled with programmable signal processors that have orders of magnitude more execution rates and memories. These state of the art improvements allow systems not only to cover more bandwidth in the same frequency band but also to provide more ECM and ECCM features. Another new feature is networking of systems to provide target detection and designation to other in theater assets. Table 5.6 contains typical parameters for deployed emitters, all taken from open literature and thus may contain some disinformation. It was used to make the spectrum power estimates earlier in this chapter using the Excel Table 5.6E.xls. The table in the appendix can be easily modified by the reader as more information becomes available. In some cases, I have made educated guesses of parameters based on hardware photos and thoughts on, “What would I do using the current state of the art?”

5.8 Exercises 1.

2.

Using the parameters of Table 1.12 LREW column, calculate the probability of detection, PD, using (5.51) with Rs equal to 100 nmi and s equal to –10 dBsm with PFA equal to 1010. Calculate the received power from sea clutter and rain clutter for a sea state 4 storm at a range of 100 nmi using the parameters of the JAS-39 from Table 5.6.

Exploitation of the environment 3.

4. 5. 6.

347

Find the pulse density in a 300 MHz band at 16 GHz for an intercept receiver at 30 kft and –85 dBm total sensitivity using the example parameters of Table 5.7. Calculate the ambient spectrum in 1 GHz bands using the EOB from Figure 5.48 including both the quantities and coverage bands given in the figure. Assume an observer at 20 kft, what is the apparent altitude for an emitter at 1000 ft 240 nmi away? What is the cross range 60% visibility distance for steppe terrain for observer and target both at 1000 ft and separation of 80 nmi range?

References [1] Skolnik, M. Introduction to radar systems, 2nd ed. McGraw Hill, p. 449. [2] Nathanson, F. Radar design principles. McGraw Hill, pp. 33, 15, 169, 206. [3] Nathanson, F. Radar design principles. 2nd ed. McGraw Hill, pp. 33–36, 317–320, 371. [4] Stipulkosky, T. “Statistical radar cross section measurements for tactical target and terrain backgrounds: Phase I and phase II.” Hughes Reports P76–482, December 1976 and P77-251, pp. 3-1 to 3-30, August 1977, pp. 41 to 4-116. Declassified 12/31/1987. [5] A few photos, tables, and figures in this intellectual property were made by Hughes Aircraft Company and first appeared in public documents that were not copyrighted. These photos, tables, and figures were acquired by Raytheon Company in the merger of Hughes and Raytheon in December 1997 and are identified as Raytheon photos, tables, or figures. All are published with permission. [6] Sanders, F., Ramsey, B., and Lawrence, V. “Broadband spectrum survey of Los Angeles, CA.” Institute For Telecommunication Sciences - NTIA Report 97-336, May 1997, pp. 9–104. [7] Skolnik, M., ed. Radar handbook, 1st ed. McGraw Hill; 1970, pp. 25-2–2510. [8] Muhleman, D. O. “Radar scattering from venus and the moon.” Astronomy Journal. 1964; 69:34–41. [9] Katzin, M. “On the mechanisms of radar sea clutter.” Proceedings of IRE. 1957; 45: 44–54. [10] Air Force Avionics Laboratory. “Cooperative weapon delivery study.” Technical Report AFAL-TR-78-154. October 1978. pp. 2-1 to 2-29, 3-1 to 371. Declassified 12/31/1991. [11] Biron, S. and Francois, R. “Terrain masking in the European Soviet Union.” MIT Lincoln Laboratory Report. CMT-31, Vol. 2, March 9, 1983. [12] Kopp, C, and Goon, P. http://www.ausairpower.net. [13] Shared Spectrum Company. “General survey of radio frequency bands: 30 MHz to 3 GHz.” Version 2, September 23, 2010 Chriss Hammerschmidt, Heather E. Ottke, J. Randy Hoffman.

348 [14]

[15]

[16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30]

An introduction to RF stealth, 2nd edition Hammerschmidt, C., Heather E., Ottke, B., and Hoffman, J.R. “Broadband spectrum survey in the Denver and Boulder, Colorado, metropolitan areas.” National Institute For Telecommunications and Information Administration NTIA Report TR-13-496, August 2013. Hammerschmidt, C., “Broadband spectrum survey in the San Diego, California, area.” National Institute for Telecommunications and Information Administration: NTIA Report TR-14-498, November 2013. Cullen, T. and Foss, C., eds. Janes land-based air defence 2001–2002. Janes Information Group; 2001, pp. 109–196. Williamson, J., ed. Janes military communications 2001–2002. Janes Information Group; 2001. pp. 163–377, 459–480, 715–770. Craig, D. and Hershberger, M. “Operator performance research.” Hughes Report P74-504, December 1974. Craig, D. and Hershberger, M. “FLAMR operator target/OAP recognition study.” Hughes Report P75-300, 1975. Declassified 12/31/1987. Pearson, J., Robinson, P. N. and Garlick, R. A. “SAR data precision study.” Hughes Report P75-459, December 1975. Declassified 12/31/1987. Peot, M. A. “Electronic warfare signal processing in the year 2000.” Microwave Journal. February 1987, pp. 169–176. Schleher, D. C. Introduction to electronic warfare. Artech House, Inc.; 1986, pp. 33–35. Selby, S. M., ed. Standard mathematical tables. CRC; 1968, p. 394, eq. 70. Gradshteyn, I.S. and Ryzhik, I. M. Table of integrals, series, and products. Academic Press, Inc.; 1965, p. 205, eq. 2.733-1. ITT Staff. Reference data for radio engineers, 6th ed., Howard W. Sams & Co., Indianapolis, IN, pp. 28-12 to 28-15. Streetly, M., ed. Janes radar and electronic warfare systems 1999–2000. Janes Information Group; 1999, pp. 29–37, 41–64, 377–391, 435–530. Pretty, R.T. Janes Weapon Systems 1984–85. Janes Information Group; 1984, pp. 84–125, 157–197, 229–285, 424–499, 543–580, 581–678. Brinkman, D., ed. Janes avionics 1990–91. Janes Information Group; 1990, pp. 20–89, 134–199. Downs, E., ed. Janes avionics 2001–2002. Janes Information Group; 2001, pp. 347–524. International electronic countermeasures handbook, 2001 ed. Horizon House, pp. 307–337.

Chapter 6

Stealth waveforms

6.1 Waveform criteria The primary unique criterion for stealth waveform design is reasonably flat total operating frequency band coverage. This objective is not always compatible with best data link or radar mode performance. Some obvious criteria are stated in this section. These criteria are then applied to various spread spectrum strategies such as frequency diversity, discrete phase codes, linear FM, and hybrid waveforms. Low probability of intercept (LPI) requirements, in addition to signal-to-noise ratio (SNR) considerations, dictate the use of high duty cycle waveforms. This result has two implications: (1) that the transmitted pulse period must be incrementally variable and (2) that large expansion/compression ratios usually are involved. Another result based on stealth requirements is that the instantaneous (not just the average) bandwidth of the transmitted signal is as large and as uniform as possible. For each geometry, the power must be managed to the lowest level consistent with acceptable performance or bit error rate (BER) as mentioned in Section 3.1.4. It is obviously desirable to keep the preprocessing and the bandwidth to a minimum; therefore, the waveforms chosen should result in the lowest possible data rate prior to compression or decompression. Lastly, LPI time and frequency constraints described in Sections 3.2.4 and 3.2.5 require noncontinuous or burst transmission for both data links and radars. Some systems naturally operate in a burst mode such as the JTIDS, which uses a TDMA format. As mentioned earlier in Section 3.2.4, the stealth platform whether aircraft, ship, or vehicle must move between transmissions to create an uncertainty volume. These requirements outlined above are summarized below: ● ● ● ● ● ● ●

Incrementally variable transmit period Power management Large compression ratios Wide instantaneous bandwidth Uniform instantaneous bandwidth Minimum preprocessing Minimum required data rate

With the advent of active electronic scan antenna (AESA) radars and data links, the T/R channels may have 4 to 8 GHz potential bandwidth. An LPI system

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must use as much of that as possible either by continuous occupation or jumping over that bandwidth in a pseudo-random way. Also, for antijam and clutter cancellation requirements, modern systems have multiple independent receive channels.

6.2 Frequency diversity There are a number of methods that have been used to achieve a wide bandwidth while minimizing hardware complexity. The most common stealth bandwidth expansion schemes are summarized in Figure 6.1. They are listed in no particular order in Figure 6.1. The simplest and least effective is frequency hopping because it requires the highest ERPP (notwithstanding some authors’ arguments to the contrary). In this scheme, a single modulated center frequency is transmitted for each coherent array and a single receiver channel is tuned to that frequency. The frequency is chosen pseudo-randomly, should be known only to the transmitter and the receiver and the next frequency must not be easily derivable from the current frequency. The transmitted power should be programmed to be just enough for the chosen path length (one way or two way). The interceptor is required to cover the entire hop band and thus is limited by total noise bandwidth. The next scheme in complexity is stacked frequency transmission. Multiple modulated center frequencies are simultaneously transmitted and separately received in multiple independent channels. The channel spacing and modulation

Stacked frequency Transmission Amplitude Separate receiver channels F1

Frequency hopping Amplitude Single receiver channel

F1

F2

F2

F3

F3

F4

F4

F1

Time

Simultaneous transmit and receive (STAR)

F2

F3

FN

Power F? Time

Stacked STAR Separate diplexed Amplitude receiver channels F11

F22

F33

F44

F11

F21

F32

F43

F14

F21

F31

F42

F13

F24

F31

F41

F12

F23

F34

F41

Amplitude Single diplexed receiver channel F1

F2

F3

F4

F1

Time

Figure 6.1 Alternative frequency diversity strategies

Time

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351

should be chosen to cover the entire band of operation in a reasonably uniform manner. The frequency set is chosen pseudo-randomly, should be known only to the transmitter and the receiver and the next frequency set must not be easily derivable from the current frequency set. As in frequency hopping the transmitted power should be programmed to be just enough for the chosen path length (one way or two way). The interceptor is required to cover the entire operating band and thus is limited by total noise bandwidth. The total ERPP is the same as frequency hopping but for a channelized interceptor the per channel power is less. This reduces the effectiveness of channelization. Since all channels transmit at once channel to channel cross talk is a minor problem and the individual channels can be “shoulder to shoulder” almost completely filling the band. The natural question to ask is: Why not create this same spectral spread with direct chip coding of a single channel? The answer is often multipath interference and antenna bandwidth make multiple channels easier to separate and process than direct encoding. The main weakness is that the duty cycle is limited typically to 33% or less. The next most complex scheme is simultaneous transmit and receive (STAR). It is like frequency hopping in which reception occurs on every frequency not being transmitted. Transmit frequencies are visited in a pseudo-random manner. All other frequencies are received in diplexed separate channels. This allows the transmitter to obtain almost 100% duty cycle while allowing all other frequencies to be received with maximum processing gain. The ERPP is lowest; however, the band of operation is incompletely covered at any one time because the channel to cross talk is difficult to control. Pseudo-random frequency hopping must be used to fill the entire operating band. The most complex scheme is a combination of stacked transmission and STAR. Almost 100% transmit duty cycle and wider frequency coverage is achieved. The price in hardware complexity is very precise and difficult frequency diplexing so that the transmit frequency of one band does not leak into the receivers of the other bands thus limiting the dynamic range. Again the ERPP is lowest; however, the band of operation is incompletely covered at any one time. Pseudorandom frequency hopping must be used to fill the entire operating band. This scheme typically requires octave bandwidth which is good from an intercept point of view but a challenge in terms of antenna and receiver complexity. Each of these schemes has been tested. Cost and complexity is the tradeoff.

6.2.1 Simultaneous transmit and receive cross talk Frequency hopping has been described many times and needs minimal discussion [5]. The other three schemes are not as well known. Their essential or unique design elements will be described in Sections 6.2.1–6.2.3. The first element to be described is cross talk between elements. STAR is the stressing case for cross talk. A simple STAR example is shown in Figure 6.2. A low frequency, fL, is transmitted with a 50% duty cycle and a low-frequency receiver listens during the lowfrequency transmitter off time. A high frequency, fH, is transmitted with a 50% duty cycle and a high-frequency receiver listens during the high-frequency transmitter

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Transmitted waveform

fL

fL fL

RCVR fL

fL

fL

Transmitted waveform

fH

fH

RCVR fH

fH fH

fH

Figure 6.2 Simultaneous transmit and receive (STAR) concept

off time. (For many reasons explained later, 25% duty cycle and four frequencies are much better.) The high and low-frequency channels alternate with a small switching guard time to allow diplexer settling. The transmit duty cycle approaches 100%. The high and low frequencies including their modulation sidebands must be sufficiently separated so that the leakage through the diplexer does not limit performance. This requires sidelobe weighting and a frequency guard band so frequency band filling is not complete for any single transmission set, fL and fH. The band gaps can be filled on subsequent coherent arrays by selecting a different channel set. A block diagram of a STAR transmitter and receiver for multiple frequency bands is shown in Figure 6.3. In order to get sufficient isolation, there must be high power filtering on both the transmitter output and the receiver inputs as well as high power switching on both. Each receiver channel is subject to high power transmitter leakage and must be protected from burnout as well as dynamic range limitations. Each receiver channel is processed independently until magnitude detection and then combined noncoherently. The exciter input which contains all the waveform modulation may be a single frequency or multiple frequencies. The filters are 4–6 poles each and require approximately linear phase for the pulse code. Each transmitted frequency must not limit sensitivity in the other channels and each received frequency must not suppress a signal in an adjacent channel. Consider the spectral situation in Figure 6.4. The adjacent channel can interfere in two different ways. First, power from the adjacent channel can come through the front end filter and influence the gain control settings limiting the channel dynamic range. Second, the smaller processed region filters and pulse compression can have their noise floors set by adjacent channel interference. The total power in the receiver that may influence the gain control is sometimes called near end cross talk (NEXT). It is the integral of adjacent channel

Stealth waveforms

From Feed network

Band pass filter (F1)

Switch 1

Band pass filter (F1)

Band pass filter (F2)

Switch 2

Band pass filter (F2)

Receive LNA 1

Receiver protector 1

Band pass filter (F1)

Receive LNA 2

Receiver protector 2

Band pass filter (F2)

Transmit amplifier

353

To antenna aperture radiating elements

Etc. Etc.

To feed network

Etc.

Figure 6.3 Multifrequency transmit-receive block diagram

Amplitude

Front end filter

Processed region

Transmitted or received spectrum in adjacent channel Additional AGC interference Interference power Frequency

F1

F2

F3

F4

Figure 6.4 Adjacent channel interference concept waveform power spectrum times, the transmitter filter times, and the receiver filter as shown in (6.1) [1]: PNEXT =

∫

S ( f − f n ) ⋅ H T ( f − f n ) ⋅ H R ( f ) ⋅ df

Where: S ( f ) = transmitted spectrum H T ( f ) = frequency response of the transmitter output filter H R ( f ) = frequency response of the front end receiver filter

(6.1)

For example, consider the case of a power spectrum for a 13 chip Barker code with 50 ns chip width, tc. This waveform is transmitted through an n pole

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transmitter filter and received through an n pole filter in an adjacent channel (more details in the appendices and Section 6.5). The normalized transmitted spectrum for a Barker code through a six-pole Butterworth filter is shown in Figure 6.5. Figure 6.6 shows a multiline spectrum made up of adjacent channels each with a binary phase code. Today, a spectrum such as Figure 6.6 would span 2–4 GHz with a chip width of 0.5 ns rather than only 200 MHz. Depending on the spacing between channels and filter skirt selectivity, a significant fraction of the spectrum will appear in the adjacent channel. The adjacent channel center frequency in Figure 6.7 is 2/tc or 40 MHz away from the transmit channel. The receiver cross talk spectrum and the six-pole Butterworth receive filter frequency response are shown in Figure 6.7. The value of the total PNEXT calculated using (6.1) normalized to 1 is approximately –44 dB. If the transmit power amplifier was 100 watts peak, then the power in the receiver channel would be approximately –22 dBW and it would very likely be setting the front end gain and sensitivity. The noise floor in the receiver with the filter described above would probably be –121 dBW. A typical receiver of this type might have a spur free dynamic range of 75 dB and a 1 dB compression point of –20 dBW. Thus, the desensitization would be NEXT Degradation = −121 dBW − ( −75 − 24 dBW ) = −22 dB

(6.2)

10 0 –10

Normalized power (dB)

–20 –30 –40 –50 –60 –70 –80 –90 –100 0.1

1

10

100

Frequency (MHz)

Figure 6.5 Single channel Barker code transmitted spectrum (ChanSep1a.mcd)

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355

10 5 0 –5 –10 Normalized power (dB)

–15 –20

13 Chip-50 ns/ch Barker code 20 MHz channel spacing 10 Pole transmit filter

–25 –30 –35 –40 –45 –50 –55 –60 –65 –70 –100

–80

–60

20 40 60 –40 –20 0 Frequency offset from band center (MHz)

80

100

Figure 6.6 Barker coded stacked frequency spectrum (ChanSep2a.xmcd) Such a reduction probably would be unacceptable and thus more filter skirt selectivity must be used to prevent performance limitations. The maximum allowable leakage that will not limit performance is Maximum Allowable NEXT = −121 dBW − ( −75) = −46 dBW

(6.3)

Consider a second case in which all the parameters are the same but the transmit and receive filters are 10 poles. Then the NEXT spectrum would be as shown in Figure 6.8. The integrated sidelobe ratio is –67 db. In both cases, the filter break frequency has been chosen to be 1/(1.35 tc) to allow bit transitions to be 40% of the chip time (about the maximum allowable). In the case of 10 pole filters and 100 Watts peak power from the transmitter, the power in the adjacent receiver channel would be –47 dBW just below that maximum allowable of –46 dBW. The second potential limitation from NEXT is in the processed band noise floor. As can be seen in Figure 6.8, parts of the processed band have power densities as high as –65 dB below the transmitter power. One solution when using phase codes is to choose adjacent channel center frequencies to be offset by exact multiples of 1/tc. This offset results in perfect decorrelation in the pulse compressor and thus zero output. That is why in the example above, the channel spacing was

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An introduction to RF stealth, 2nd edition 10 0 –10 –20 –30

Normalized power (dB)

–40

13 chip-50ns/ch Barker code 40 MHz channel spacing Receive filter response Transmit leakage

–50 –60 –70 –80 –90 –100 –110 –120 –130 –140 –150 –100–90 –80 –70 –60 –50 –40 –30 –20 –10 0 10 20 30 40 50 60 70 80 90 100 Frequency offset from band center (MHz)

Figure 6.7 Example Barker code transmitted spectrum in adjacent receiver channel—six pole filters (ChanSep2a.xmcd) chosen to be 2/tc. Usually, however, if the dynamic range problem is solved, then the noise floor limit is also solved. In the example given, transmit and receive channels are the same bandwidth. For data links, this is often not the case. For example, SAR mapping radars may transmit very broadband data to ground stations but the ground station to mapping radar bandwidth may be quite narrow. There are arguments for making up-links more broadband to improve signal to interference ratios since the antennas may be smaller (as they often are on missiles or aircraft). The same general analysis applies. In multifrequency STAR, stacked frequencies, and frequency hopping, there can also be cross talk between receive channels in which a strong received signal in one channel interferes with a weak signal in another channel. This is sometimes called far end cross talk, FEXT. Dynamic range differences of 60 dB frequently occur. Note that the skirt selectivity in Figure 6.8 at the upper 3 dB point of the next lower band is –80 dB and so the interferer could be roughly even in power to the weak signal before compression. Again by selecting channels in multiples of 1/tc, perfect or good decorrelation can be achieved in pulse compression and bit detection. The result is that once the transmit problem is solved, the other cross talk

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357

10 0 –10 –20 –30

Normalized power (dB)

–40

13 chip-50 ns/ch Barker code 40 Mhz channel spacing 10 pole transmit & receive filters

–50 –60 –70 –80 –90 –100 –110 –120 –130 –140 –150 –100–90 –80 –70 –60 –50–40 –30 –20 –10 0 10 20 30 40 50 60 70 80 90 100 Frequency offset from band center (MHz)

Figure 6.8 Barker code spectrum in adjacent receiver channel—10 pole filters (ChanSep1a.mcd) problems usually are solved. The spectrum filling shown in Figure 6.6 for stacked frequencies will not work with any version of STAR because the cross talk and pulse compression requirements prevent a realizable transmit and receive filter set.

6.2.2 Low noise adaptive multifrequency generation All of the frequency diversity approaches described in Section 6.1 still require very low noise stable frequency references. The brute force approach of adding together multiple stable oscillator outputs results in the noise sidebands growing proportionally to the number of simultaneous channels. This would be an unacceptable degradation in performance. Fortunately, there is a way to generate multiple simultaneous reference signals which will go through saturated power amplifiers and result in a noise degradation of at most 3 dB. The scheme was invented by Gregory and Katz more than 50 years ago [2,3]. It is possible to generate an adaptive pure FM multitone waveform using the method diagrammed in Figure 6.9. A low noise signal generator (reference oscillator) output is split into two paths. One path is used to generate the third harmonic of

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An introduction to RF stealth, 2nd edition Var phase shift

BPF 3 ωm

Limiter

Var attenuator Signal gen

ωm

Divider

∑

VCO Output

Var attenuator

Figure 6.9 Example pure FM multifrequency generation the signal which is then adjusted in amplitude and phase. It is summed with the reference signal in the other path which is then used to frequency modulate a voltage controlled oscillator (VCO). Long-term stability for the VCO output is obtained by phase locking it to the low noise signal generator (not shown in Figure 6.9). The simplest basic equation governing approximately equal amplitude multifrequency FM waveforms is given in (6.4). The object is to generate a number of frequencies with very low FM noise of substantially equal amplitude with a pure FM waveform. The pure FM is necessary so that the waveform can pass through saturated amplifiers with low distortion to preserve pulse compression sidelobes. The modulation strategy used in (6.4) generates 3Nþ1 central spectral lines: v t

§ sin ¨ 2 ˜ ˜ f 0  ¨ ©

N

˜

¦ n 0



sin 3n ˜ 2 ˜ ˜ f m ˜ t 

·

n

¸¸

(6.4)

¹

Where f0 is the carrier or center frequency of the multiline spectrum, fm is the modulation frequency, b is the modulation index which is chosen so that J0(b) ¼ J1(b). For example, if N ¼ 1, a0 ¼ 0, and a1 ¼ p/2, then

(

v ( t ) = sin 2 ⋅ p ⋅ f 0 + b ⋅ ⎡⎣ cos ( 6 ⋅ p ⋅ f m ⋅ t ) + sin ( 2 ⋅ p ⋅ f m ⋅ t ) ⎤⎦

)

(6.5)

A typical hardware implementation of a multiline spectrum generator is shown in Figure 6.10. This particular example produces an output at X-band and is based on a low noise fifth overtone crystal oscillator at roughly 106 MHz with modulation at 11.8/12 MHz and its harmonics. Those signals are generated in the dual divide by 3 circuits followed by bandpass filtering and variable attenuation. The modulation is then amplified and applied to the VCO after the LO phase comparator. The VCO is then multiplied up to the operating frequency (12). Not shown are all the other outputs to the receiver channels to provide local oscillator signals, pulse compression and A/D clocking. There is a sweep circuit inside the LO phase comparator for initial lockup of the phase-locked loop since such loops are narrow band. The diagram shows an FM modulation on-off switch for noise measurements with and without modulation. A typical spectrum analyzer output from the circuit of Figure 6.10 is shown for a nine spectral line FM modulation of 11.8 and 35.4 MHz and center frequency of

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Transmitter output chain Low noise crystal oscillator

3 DB hybrid 100 MHz buffer amplifier

70 DB active isolator

Frequency divider

Reference outputs

Bandpass filters & combiner Variable attenuator

800 MHz VCO

r e s .

cap.

800 MHz isolator coupler assembly

res. L.O. phase comparator Sweep disable switch

800 MHz amplifier

X12 multiplier

Modulation on-off switch 30 DB amplifier

X-band output

Figure 6.10 Example multifrequency hardware block diagram 9.7 GHz in Figure 6.11. The vertical scale was 2 dB/cm and the horizontal scale was 20 MHz/cm. Spectral line spacing is, of course, 11.8 MHz. Final output frequency spacing is determined by the multiplier which follows the modulation scheme. The FM noise also is increased by the square of the multiplication ratio and so starting FM noise must be very low. The modulation equation (6.4) generates the set of frequencies shown in Table 6.1. An important question is whether the multiline spectrum preserves the noise performance of the low noise reference oscillator. Figures 6.12 and 6.13 show the noise spectrum with no modulation and with multiline modulation. Figure 6.12 is a plot of the single sideband FM noise with a calibration scale (because most noise measuring test sets are nonlinear) for SNR in a 1 kHz band relative to the center carrier. Note that the noise hovers around 92 dB below the carrier with no modulation. This noise level will allow detection of weak targets after filtering, compression and space-time-adaptive-processing (STAP) down to about –135 dBW. This 3 dB degradation is the lowest multiline noise spectrum achievable for a given master oscillator noise performance. A similar noise plot with modulation is shown in Figure 6.13. At larger separations from the carriers the SNR hovers around 89–90 dB. This is no greater than a 3 dB degradation as expected. The explanation of the better SNR near the carriers is that the modulation noise is correlated to the master oscillator and the correlated noise cancels. A more general theory indicates that any odd number of roughly equal tones can be generated but it requires the selection of two modulation indices. An

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Figure 6.11 Nine-line spectrum. Adapted from Raytheon [4]

Table 6.1 Example multifrequency modulation Frequency

Power relative to F0

dB

f0 f0 f0 f0 f0 f0 f0 f0 f0 f0

1 1.17 1.14 1.02 1.02 0.312 0.167 0.156 0.034 0.011

0 0.7 0.6 0.1 0.1 5.1 7.8 8.1 14.7 19.6

        

fm 2fm 3fm 4fm 5fm 6fm 7fm 8fm 9fm

example spectrum for the two modulation index scheme is given in Figure 6.14. Explanation of the mathematical criteria for two or higher modulations is beyond the scope of this text. The spectrum analyzer display on the left in the figure has a horizontal scale of 50 MHz/cm and a vertical scale of 10 dB/cm. The display on the right in the figure has a horizontal scale of 20 MHz/cm and a vertical scale of 10 dB/cm. Three modulation frequencies are used 11.8, 23.6 and 35.4 MHz. The noise performance is similar since all the modulation is derived from the same master oscillator. The beauty of this scheme is that the spacing can always be matched to the chip width of a pulse code selected for operating mode reasons not hardware limitations.

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Single sideband signal-to-noise ratio (dB/kHz) DB = 70 72 74 75 76 77 78 79 80 81 82

83

84 85

6 FM deviation (Hz)

86 5

87 88 89 90 91 92 93 94 95 96 97

4 3 2 1 0

25

50

150 175 75 100 120 Modulation frequency (KHz)

200

225

250

Figure 6.12 FM noise measurement – no modulation

7

Single sideband signal-to-noise ratio (dB/kHz) DB = 7071 73 7475 76 78 79 80 81 82

83

84 85

6 FM deviation (Hz)

86 87

5

88 89 90 91 92 93 94 95 96 97

4 3 2 1

0

25

50

75

175 100 125 150 Modulation frequency (kHz)

200

225

Figure 6.13 FM noise measurement with modulation

250

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An introduction to RF stealth, 2nd edition

Figure 6.14 Thirteen line spectrum. Adapted from Raytheon [4]

6.2.3

Detection by multifrequency waveforms

Multifrequency waveforms provide improved detection performance in the presence of fading and jamming providing the desired detection performance probability is high or the required bit error rate, BER, is low. As more frequencies are used, the power per frequency goes down. At low SNRs, this results in worse detection or BER performance since some frequencies are faded or jammed and the power is wasted. At high required SNRs, there is already enough power for detection and the issue is the probability of a fade or jamming at any one frequency. In this case, more frequencies improve detection performance or reduce BER. One possible approximation for Rayleigh fading frequency channels and fixed total energy transmission across all frequencies with a square law detector in inphase and quadrature channels and unknown arrival phase followed by noncoherent integration of the individual frequency channels is given in (6.6) [5–8]:

PD  N Freq

§ PTH  N Freq · ¸ * Eu ¨ N Freq , ¨ 1  SNR N Freq ¸ © ¹  N Freq  1 !

Where: * Eu  x, y x

N Freq , y

³

f

t x 1 ˜ exp  t d t

(6.6)

y

PTH  N Freq

1  SNR N Freq

Where G Eu(x, y) is the incomplete Euler Gamma function and y is the lower limit of integration with an upper limit of ?. All the other variables are as defined before. NFreq is the number of frequency channels, SNR is the rms signal-to-noise power ratio, and PTH is the power threshold. One example of (6.6) is given in Figure 6.15. For simplicity, an approximation to the optimum threshold is used as given in (6.7):

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1 0.9 0.8

Probability of detection

0.7 0.6 0.5 0.4 0.3

1 freq. 3 freq. 5 freq. 9 freq. 13 freq.

0.2 0.1 0

0

20 10 15 Signal-to-noise ratio (dB)

5

25

30

Figure 6.15 Multifrequency detection performance (Multifreq1a.mcd)



PTH N Freq



§ P · 0.11 ˜ ln ¨ 2FA ¸  1 N Freq  N Freq ¨ N Freq ¸ © ¹

(6.7)

Where PFA is the desired probability of false alarm as previously defined. Similarly, the multifrequency bit error rate, BER, for binary signaling and a Rayleigh fading channel, fixed total energy across all frequencies, matched filter bit waveform correlation, square law detection, unknown phase (i.e., center frequency phase is not recovered from signal), and noncoherent integration of each frequency channel is given in (6.8):

(

)

(

BER N Freq = F N Freq

)

N Freq −1 N Freq

⋅

∑ i =0

(

) )

⎛ N Freq − 1 + i ! ⎞ ⎜ ⎟ ⋅ 1 − F N Freq ⎜ i ! ⋅ N Freq − 1 ! ⎟ ⎝ ⎠

(

(

(

))

i

(6.8) Where F(NFreq) is a convenient intermediate variable as given in (6.9).

(

)

F N Freq =

2 N Freq 2 + SNR 2 ⋅ N Freq

(6.9)

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An introduction to RF stealth, 2nd edition

0.1

Bit error rate

0.01

1∙10–3

1∙10–4

1 freq. 3 freq. 5 freq. 9 freq. 13 freq.

1∙10–5

1∙10–6

0

5

10

15 20 25 Signal-to-noise ratio (dB)

30

35

40

Figure 6.16 Bit error rate for fading multifrequency channels (Multifreq1a.mcd) For example, consider the radar case of a required PFA of 106 and a Rayleigh fading target where the same total detection energy across all frequencies is used in each case. The probabilities of detection as a function of SNR for 1, 3, 5, 9, and 13 frequencies are given in Figure 6.15. The frequency sets chosen are easily generated with multiline FM as described in Section 6.2.2. Up to the point where PD is 0.6, a single frequency has the best performance even in the presence of fading. Similarly consider the same situation and parameters for a data link as shown in Figure 6.16. These curves may look different than many texts because typically SNR is plotted on a per frequency basis rather than on a total SNR basis across all frequencies. Again the single frequency BER is lower until the SNR is 17 to 25 dB. Of course, all these performances are significantly better with coherent integration and fine Doppler tracking. Because of the nature of the waveforms described, they are all mutually coherent and could allow coherent integration if Doppler can be sorted out. Resolving Doppler on a short term basis as required for most stealth transmissions is problematical but possible. These somewhat counter-intuitive results emphasize the problem with all diversity schemes because they generally do not have perfect integration. What they do have is more robust performance in the presence of jamming and better stealth performance. As in almost everything, there is a price to pay which is significant unless SNR is quite high.

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Duplexer XX

Ferrite power divider

Bypass

365

XX

Incident power monitor

RF switch RF switch TWT amplifier Driver

Driver

Harmonic filter Diode attn (40 dB)

Microprocessor

From exciter

From controller

Power monitor

Diade limiter To receiver

Figure 6.17 Typical TWTA transmitter power management block diagram

6.3 Power management As was mentioned in Section 6.1, power management or transmitting exactly the power necessary to achieve the required BER or detection performance is an essential element of stealthy waveforms. Hardware implementation of power management is really quite simple. The power management design follows ideas first used in the AN/ TPS-32 and described in 1976. A typical power-managed TWT transmitter block diagram is shown in Figure 6.17. It consists of both input and output attenuators that are controlled by a microprocessor in a closed-loop fashion. In the subsystem diagram shown, the TWT amplifier (TWTA) is operated primarily in its linear or unsaturated mode. Maximum power still is delivered from the TWTA saturated state. The input attenuation to the TWT is steadily applied as the required output power drops. This improves power efficiency, but at the expense of noise figure. Usually, the noise figure of a TWT is about 40 dB, but that value does not limit radar or data link performance if it is not allowed to deteriorate too much further. Once the input attenuator is decreased as far as is reasonable based on allowable noise performance,

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the power out of the TWT is low enough that power dividers can then be used at the TWT output to further reduce output power. Finally, when very low power levels are required and the attenuation exceeds the TWTA gain, there is usually an RF switch at the TWT input and output to allow the amplifier to be bypassed altogether; thus, the 1–1,000 milliwatts that comes from the exciter can be attenuated by the cascaded power dividers and attenuators to provide the output. The directional coupler in the duplexer is used to verify that the commanded power output is within the required tolerance. Attenuation is not set on a closed-loop basis because experiment has shown such loops susceptible to countermeasures and loop instability [9,10]. A TWT is reasonably nonlinear; therefore, an output power monitor must measure power from the TWT at all times. This measurement is utilized in a microprocessor that contains a premeasured and stored profile of attenuation versus output power as a function of frequency using the incident power monitor. The strategy is to apply the attenuation in such a way that the SNR at the output of the TWTA is maintained as close to optimum as possible and at the same time power efficiency degradation is minimized. This typically means that the first 10 dB of power management is applied from the diode attenuator at the input to the TWT. The power out of the TWT drops to 0.1 of its peak power, at which point ferrite power dividers can be utilized at the TWT output, and the next 30 dB is applied with the output power dividers. Even at 10% of maximum output, the power that must be dissipated in the power dividers is significant and they are usually liquid-cooled. Typical TWTAs have somewhere between 40 dB and 50 dB of gain, and once the attenuation equals the gain of the TWTA, the amplifier is switched out and the attenuation is applied to the local oscillator signal. In this way, very large power management ranges can be achieved (typically 70 dB or more), while maintaining the overall transmitter noise figure somewhere between 40 dB and 50 dB. The receiver protection and diplexing must be adequate to handle the leakage and broadband noise from the TWT even when the transmit power is low. A similar method must be used for modern AESAs as shown in Figure 6.18. The same 70 dB of power management must be achieved but starting at 20 watts and going to 2 microwatts per channel. The amplitude control in a T/R channel is usually only Power MGMT switch

Main power Bus

Transmit input Receive output

Power regulator

Amplitude & phase control

Driver amplifier

T/R switches Low noise amplifier LNA

Timing & control

Power MGMT switch

Power amplifier Circulator or T/R duplexer T/R switch & limiter

Channel control logic

Figure 6.18 T/R channel power management

Antenna Radiator

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30–40 dB. Thus another 30–40 dB is required which must come from bypassing the power amplifier and then the driver amplifier. These bypasses also greatly reduce emitter power consumption from the platform. Usually, the power biases to the amplifiers are also reduced to save power in the AESA which usually dissipates 1/2 of the system power.

6.4 Pulse compression 6.4.1 Linear FM/chirp Linear FM or “chirp” is one of the oldest pulse compression methods [37]. From an LPI point of view, it is probably the worst method of band spreading. The basic process is shown in Figure 6.19. The waveform output from each functional (lettered) block is shown at the bottom of the figure. A rectangular pulse of length, T, is generated by the

Pulse generator (A)

Mixer (B)

Transmitter (C)

Free space

Frequency

(A)

Frequency

t1

t2

Time

t1

t2

Time

(D)

f2 B f1 t1

t2

Time

f2 B f1

Amplitude

(B)

(C)

Time

Amplitude

Amplitude

T

A

Detector (E)

Demodulator (D)

Receiver

(E)

BT

Time 2 B

Figure 6.19 Basic chirp process. Adapted from [11]

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pulse generator timing circuit. The pulse enables or selects a section of a steadily increasing or decreasing FM waveform. The linear FM or chirp bandwidth, B, from the mixer output is amplified by the transmitter, launched by the antenna and propagates to the target. The wavefront scattered from the target is received and amplified. This signal is then mixed in the demodulator with the opposite slope FM. This approximate matched filter results in an output pulse whose amplitude is proportional to the square root of the time bandwidth product BT. For large bandwidths and unweighted matched filtering, the null to null width of the output pulse is 2/B. For high-resolution systems, this leads to very high bandwidth front end signal processing. Since the processed range swath in such systems is small relative to the PRF, this high bandwidth was very inefficiently used and systems were invented to stretch the processing over the entire interpulse interval. Those approaches are called “stretch” processing. To simultaneously achieve long-range detection and high range resolution requires a very long pulse and large frequency excursion. The long, linear FM waveform in which the pulse length exceeds the swath width has some very nice processing characteristics, which can be exploited by stretch processing. The chirp transmitted signal is of the form shown in (6.10): 'f 2· § · § ˜t ¸ j0 ¸ A ˜ PUL  t , T ˜ cos ¨ 2 ˜ p ˜ ¨ f 0 ˜ t  ˜ 2 T © ¹ © ¹ Where: A transmitted amplitude, j 0 starting phase PUL(t , T ) rectangular pulse of length T f 0 center of the operating band, D f total frequency excursion s (t )

(6.10)

The output power from a filter matched to this waveform is given in (6.11): Pmatch ( t ) = c match ⋅ SNR ⋅ exp ( j ⋅ 2 ⋅ p ( f 0 − f D ) ⋅ (t − t 0 ) )

⋅ X ((t − t0 ) , ( f 0 − f D )) Where: c match = constant representing the transmitted amplitude, range equation and receiver performance including the matched filter f D = received signal Doppler offset from the carrier f 0 t 0 = time of the matched filter sampling instant X = chirp waveform matched filter output given in equation (6.12)

(6.11)

Define 'fD = f0 – fD and 'T = t – t0 then: X  'T , ' f D

'T · § T ¨1  ¸ T ¹ ©

§ 'T · · § sin ¨¨ p ˜  ' f ˜ 'T  ' f D ˜ T ˜ ¨ 1  ¸¸ T ¹ ¸¹ © ˜ exp(  j ˜ p ˜ ' f D ˜ 'T ) ˜ © 'T · § p ˜  ' f ˜ 'T  ' f D ˜ T ˜ ¨ 1  ¸ T ¹ ©

(6.12)

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For example, consider the case of a compression ratio of 20:1 and 100-foot resolution with Df of 5 MHz. Then the matched filter response as a function of time delay and Doppler offset using (6.12) is as shown in Figure 6.20. The figure is a top view contour plot (i.e., like a topographic map) with 10 dB contour lines. The dark bands are very low sidelobes that are rapidly varying. The diagonal large central lobe shows one of the principal weaknesses of linear FM, which is the large ambiguity between range and Doppler. Another stealth weakness shown in the plot is that any cut in Doppler has significant power for much of the range/time axis [12]. That fact makes detection of chirp waveforms and jamming thereof relatively easy. In addition, there are many range-Doppler sidelobes, which allow easy detection of the true center frequency if the interceptor has guessed incorrectly. The problem is that the very feature of chirp is a slow progression of frequency and a relatively small instantaneous frequency bandwidth. This is a very poor waveform for an LPI platform. The only reason for an LPIR to use chirp is to detect passive UHF radars, which are a real threat to stealth systems [13].

6.4.2 LPI performance loss incurred by use of chirp Unfortunately, the instantaneous bandwidth is narrow for a long, linear FM waveform, concentrating all the output power in one interceptor detection filter for a significant time. For example, for a pulse compression ratio (PCR) of 2000 and 10 feet resolution, the transmitted pulse width is 40 ms and the FM slope is 1.25 MHz/ms for a total excursion of 50 MHz. The transmit signal dwells in a single, 5 MHz wide detection filter for 4 ms, or about 20 filter time constants.

Doppler offset (megahertz)

10

10 dB contours, max. 0 dB, min. –60 dB

0

–10 –1

0 Time offset (microseconds)

1

Figure 6.20 20:1 Linear FM ambiguity contour plot (BarkDopp2a.mcd)

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An introduction to RF stealth, 2nd edition 0 Peak power at intercept receiver input Peak power at intercept receiver output for channelized receiver 50 MHz chirp 50 MHz phase code

Normalized power (dB)

–10

–20

Chirp LPI loss Versus phase code

–30

–40

–50

1

1,000 10 100 Pulse compression ratio

10,000

Figure 6.21 Peak power input and output in 5.0 MHz intercept receiver for 50 MHz chirp and phase code Not only is the detection filter fully rung-up but also this action takes place sequentially along the filter bank. Clearly, conventional linear FM is not a good LPI waveform. Figure 6.21 shows the LPI performance loss for a chirp waveform. The peak power associated with a pulse of fixed average power, without regard to the type of pulse compression used, is shown in the upper straight line in Figure 6.21. If a single pulse, or binary code, is used, the peak power will be instantaneously spread over 50 MHz and a 5 MHz wide intercept receiver would pass only one-tenth of the peak power as shown by the lower line. However, if a chirp waveform is used, the filter in the receiver passes the full peak power unless the chirp rate is very fast (curved line). Very fast chirp rates occur only with low PCRs. Since LPI requires high pulse compression ratios, chirp is not usually an acceptable waveform. The LPI loss inherent in using chirp instead of a spreadspectrum waveform is the difference between the two curves in Figure 6.21 [14]. A typical hybrid pulse compression code required for good LPI might consist of a 50 MHz chip-rate cyclic phase code with a slow superimposed chirp to resolve the ambiguities of the cyclic code. Hybrids will be discussed in Section 6.6. However, sophisticated receiver techniques other than the ones currently in use can counter some phase codes as shown in Section 4.1.9 of Chapter 4 [5]. Therefore, if more sophisticated threats are to be countered, a polyphase complementary code should be implemented for the best LPI.

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6.4.3 Stretch processing If linear FM is such a poor LPI waveform, why ever use it? The answer is that there are processing means available for linear FM that are so simple and advantageous that the LPI performance loss against channelized intercept receivers is often balanced by this simplicity. Furthermore, chirp waveforms are effective against many wide-open receiver types. This simple processing method is known as stretch [15]. Some discussion of the fundamentals of stretch processing is appropriate to lay the groundwork for what follows. The basis for the derivation of the stretch processing parameters is shown in Figure 6.22, where SW is the swath width time and E is the effective pulse length (the time during which returns from the entire swath come in simultaneously; hence the time during which data are taken) [15–19]. Similarly, the actual frequency excursion is DfT, while the effective frequency excursion over TE is Df. From simple geometrical arguments, the required IF bandwidth DfIF could be as small as shown in (6.13). Since the total frequency excursion can be resolved into range bins equal to the reciprocal of Df, then Df ¼ 1/Trb. Therefore D f IF =

T SW ⋅D f TE

and D f IF =

T SW N = rb T E ⋅ T rb T E

(6.13)

Where Nrb is the number of range cells across the swath and Trb is the range resolution or cell time. A typical stretch mechanization is shown in Figure 6.23(a). The received signal is deramped with a center frequency matched to the center of the swath minus the IF frequency. The output of a narrowband IF matched to the frequency excursion over the swath width is heterodyned to the baseband. The baseband is I/Q sampled at a sample rate of Ns¼ 1/(2DfIF) to meet the Nyquist criterion. This is typically followed by an FFT in two dimensions (Doppler and range).

Frequency

T=TSW+TE

ΔfIF

ΔfT Δf

TSW

TE

Time

Figure 6.22 Stretch processing basic parameter derivation

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An introduction to RF stealth, 2nd edition Transmitter

Receiver Mixer

ΔfIF IF A/D (Narrowband)

Ramp generator Deramp generator (a)

FFT Based Filter BankSidelobe Weighted

Conventional stretch mechanization-functional

Δf IF

A/D

Pre-summer

ΔfIF

(Wideband) (b)

Equivalent replacement for narrowband IF and A/D converter

Figure 6.23 Functional stretch mechanization The total number of I and Q samples across TE is then N s = T E ⋅ D f IF = N rb

(6.14)

Which demonstrates one advantageous processing feature of stretch pulse compression processing. In particular, the number of samples required prior to range compression (which can be accomplished efficiently with an FFT) equals the number of samples after range compression, thus minimizing the precompression data rate. In addition, the pulse length is easily varied and preprocessing is minimal. The range compression can be accomplished by a simple FFT because after deramping, targets at a given range within the swath are characterized by an almost constant frequency within the DfIF band. Two functional approaches to mechanizing stretch are shown in Figure 6.23. The first approach (6.23a) is the one conventionally described. The second approach (6.23b) shows that the narrowband IF and A/D converter, whose bandwidth and sample rate are DfIF, can be replaced by a wider band IF of bandwidth, Df, followed by an A/D converter and a digital presummer. With the advent of higher speed A/D converters, it often turns out that greater dynamic range can be achieved by digital filtering after conversion rather than analog filtering before conversion in the IF.

6.4.4

Pulse compression waveform sidelobe measures

An important issue with any pulse compression waveform is the sidelobe performance since it limits the dynamic range in adjacent bins just as shown in Section 6.2.1 for multifrequency operation. There are several important pulse compression figures of merit including: the ratio of the peak compressed signal to the peak sidelobe (PSLR), the ratio of the peak signal to the rms sidelobes (RMSLR), and the ratio of the peak signal to the integral of all the sidelobes

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(ISLR). If X(t) is the output from the pulse compressor, then (6.15) defines the ISLR. The RMSLR is the ISLR divided by the PCR:

ISLR =

∫

T 2 −T 2

X ( t ) dt − 2

∫

Trb 2

∫

2.3⋅Trb 2 −2.3⋅Trb 2

X ( t ) dt 2

(6.15)

X ( t ) dt 2

− Trb 2

Equation (6.15) can often be integrated from 0 to the upper limit only if the sidelobes are symmetrical or Hermitian. The stretch processing time is converted to frequency (if one ignores the Doppler effects) and often the ISLR is calculated in the frequency domain. As a practical matter weighting must be applied to reduce sidelobes in the analysis filters so individual bandwidths are usually significantly larger than 1/Trb. For a chirp waveform, the swept frequency residue after deramp must lie in a single filter and the spurious FM noise covering the entire analysis band must be low enough that its integrated power does not limit the dynamic range of adjacent channels and vice versa. Therefore, linearity for the combination of the transmit waveform and its receiver demodulation must be on the order of Trb/T usually split evenly between transmit and receive. Furthermore, the integral of the FM noise and clutter in the analysis filter mainlobe and sidelobes must be as given in (6.16) otherwise distributed clutter, broadband noise jamming, or FM noise will limit the desired Dynamic Range, DRd, in every other bin since the FM spreads this signal over the entire band: Dynamic Range d

Pmatch  t max § ¨ ¨ ¨ ©

³

TE 2 TE 2



· 2 2 2  s clutter ˜ h  t dt ¸ s FM ¸ ¸ ¹



(6.16)

In addition, the pulse compression filter bank ratio of minimum signal to peak sidelobes for each filter must be greater than the desired dynamic range otherwise bright discretes (Figure 5.5 of Chapter 5) or repeater jammers will limit dynamic range. Thus Dynamic Range d

Pmatch  t min § ¨ ¨ ¨ ©

³

TE 2 TE 2

BrtDis  DT h  t

2

· dt ¸ ¸ ¸ ¹

(6.17)

For example, if the desired dynamic range is 106, then the product of the filter ISLR and the noise variance must be 106. So the FM noise must be approximately

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2.5106 below the carrier if there is no interfering clutter. Assuming a weighted filter bank using a 4th power Parzen window and using the 10 dB mainlobe width yields an ISLR of –15.3 dB. It would provide some margin for interfering clutter as well as allow some relaxation of the FM noise requirement. Parzen window far sidelobes are low enough that a bright discrete 20 bins away will be attenuated by more than 60 dB. Over the bandwidth of a typical chirp, these requirements are very difficult to achieve [12]. One of the main weaknesses with chirp is that it is easy to detect and jam, even inadvertently. Another weakness is that linearity and long-term stability often degrade as hardware ages. How to get simple processing and good LPI? One method, complementary coding, is described in Section 6.5.3 [11,12,15,18].

6.5 Discrete phase codes Discrete phase codes include binary phase codes, such as Barker and compound Barker, random, pseudo-random, and complementary codes, and polyphase codes, such as Frank codes and discrete chirp as well as many others. Typically the PCR of a discrete phase code is the ratio of the chip time, tc, to the pulse time, T, or alternatively the number of chips in the code [1,11,12,20–24]. The major problem with long, discrete phase codes, such as those required by typical LPI criteria, is that the number of range samples required before range compression is large; in fact, equal to the number of range cells plus the PCR. For example, for a swath width of 512 range cells and a PCR of 2000:1, 2512 range samples are needed, which is five times the number required with stretch. This problem can be resolved for some codes such as the complementary codes by using the Hudson Larson decoder. If range pulse compression can be accomplished in a single ASIC, then this large number of samples is not a problem. Simple processing is possible for the more structured codes such as the Barker, compound Barker, and complementary codes, but they do not lend themselves to incremental variation in pulse length. On the other hand, the random-like codes, which can be chopped off or extended to any desired pulse length, require complicated, inverse filter processing to improve their relatively poor integrated sidelobe ratios (ISLR) resulting from matched filtering. (It is easy to show that the ISLR of a random discrete phase code approaches 0 dB as the code length increases.) Such processing could be done in a surface acoustic wave device for a few code lengths, but for large numbers of code lengths, this approach is inappropriate [36]. For a 10 to 1 pulse length variation, for example, 25 different code lengths would be required to cover this range in approximately 10% increments.

6.5.1

Barker codes

The basic notions of discrete phase code can be illustrated with a 13 chip Barker code as shown in Figures 6.24 and 6.25. Figure 6.25 shows the waveform generation block diagram of a phase code. Figure 6.25 shows the waveforms at three

Stealth waveforms CW source

C

0/180° phase shifter

RF amplifier

A

Phase code Timing and control

375

B

PRF pulse

Modulator

Figure 6.24 Phase coded transmitter Bit or chip designation

φ0

φ1

φ2

φ3

φ4

φ5

φ6

φ7

φ8

φ9

φ10

Binary source

+

+

+

+

+

–

–

+

+

–

+

φ11 φ12 –

+

Pulse point B

Video amplifier modulation Point A 0° 180° Phase reversal CW signal Point C

Figure 6.25 Waveforms for a Barker code of 13 chips points, A, B, and C in Figure 6.24. The phase code waveform shown at A in Figure 6.25 is applied to an RF phase shifter with a net phase difference between the two states of 180 at the source frequency. The phase reversal CW signal at point C in Figures 6.24 and 6.25 is shifted upward in frequency in an RF amplifier and transmitted to the target. Usually, the overall transmitted pulse envelope is determined separately and the modulation at B in Figures 6.24 and 6.25 is used to turn the RF amplifier on and off. On reflection from the target and receipt by the radar, the signal is amplified, demodulated, and presented to a pulse compressor, as shown in Figure 6.26. The pulse compressor is often a “matched filter” and has the property that the output pulsewidth, Trb, is the chip width, tc, and the amplitude is equal to the number of chips (sometimes called bits) in the phase code. For many reasons such as sidelobe suppression and straddling loss, the compressed output only approaches the matched filter. One example of a binary phase code pulse compressor is shown in more detail in Figure 6.27. The example shows a five-chip Barker code decoder in which a shift register slides the received detected signal past a correlator, which multiplies the detected signal by phase weights of 1 or –1 corresponding to the transmitted phase waveform and sums the weighted results to produce a discrete output as shown by the dots (connected for visualization). This process is the discrete autocorrelation

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1

2

3

4

Amplitude

Amplitude

6 6

5

1 –1

4 2 Time

0

tc

Trb Baseband coded pulse

Pulse compressor

Compressed pulse

Code reference

Figure 6.26 Phase code pulse compressor

Transmitted signal

Time

Detected signal

+

+

+

+ –

Shift register correlator

Time ∑

Direction of shift +1

–1

+1

+1

+1

–1

+1

+1

+1

Output

Multiplier weights

+1 5

Output 1 0

5

Shift number

Figure 6.27 Example binary phase code pulse compressor function, of course, whose general form is shown in Figure 6.28. Since the returned waveform is not the transmitted waveform, the pulse compressor is performing a cross-correlation which digs out scattering from point targets in the range cell. The correlation is just the chip by chip product of the prototype waveform and the received waveform summed over all chips with successive offsets of an integral number of chips. The zero time offset case is just the sum of the square-law detection of all the chips in the code (in the example, five chips).

Stealth waveforms X(0)

377

If X( j), 0> l is E (q , f = 0 ) =

∫

+a 2 −a 2

2 ⋅ p ⋅ x′ ⎞ ⎛ F ( x ′ ) ⋅ exp ⎜ j⋅ sin (q ) ⋅ ⎟ ⋅ dx ′ l ⎠ ⎝

(7.13)

Where F(x’) ¼ current at distance x’, assumed to be flowing in the y’ direction. F(x’), the aperture distribution, may be written as a complex quantity, including both the amplitude and phase distributions: F ( x ′ ) = F ( x ′ ) ⋅ exp ( j⋅ x ( x ′ ) ) Where: | F ( x ') |= amplitude distribution, x ( x ') = phase distribution

(7.14)

Equation (7.13) represents the summation, or integration, of the individual contributions from the current distribution across the aperture according to Huygens’ principle (every incremental element on a wavefront gives rise to a secondary spherical wavefront which when superimposed gives the field at the observation point). At an angle q, the contribution from a particular point on the aperture will be advanced or retarded in phase by 2psin(q )(x’/l) radians. Each of these contributions is weighed by the factor F(x’). The field intensity is the integral of these individual contributions

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b E(θ,ϕ) x’ a

y’

θ

y

z ϕ

Figure 7.4 Aperture geometry for far-field calculation in cardinal plane across the face of the aperture. For F(x’) equal to a constant, the integral of (7.13) is obviously: E (q , f = 0 ) =

4 ⋅ p ⋅ a ⋅ b ⎡ sin ( p ⋅ sin (q ) ⋅ a l ) ⎤ 4 ⋅ p ⋅ a ⋅ b ⋅⎢ ⋅ sinc (U ) ⎥= l2 l2 ⎣⎢ p ⋅ sin (q ) ⋅ a l ⎦⎥

(7.15) One way of thinking about (7.15) as well as most aperture and RCS patterns is that the area determines the maximum amplitude and the edges determine the shape of the pattern. The function in the brackets in (7.15) occurs so often that it has its own symbol sinc(U) where, in this case, U ¼ (pa/l)sin(q)cos(0). Another important observation about the aperture in Figure 7.4 is that there must be a discontinuity at the edges sometimes called the Gibbs phenomenon. That edge phenomenon has been modeled in various ways, the simplest is to assume an independent wire loop traversing the perimeter of the aperture (more about this later in the chapter). The aperture distribution can be defined in terms of the current iy. It may also be defined in terms of the magnetic field component Hx for polarization in the y direction, or in terms of the electric field component Ex for polarization in the x direction, provided these field components are confined to the aperture [3].

7.3 Single radiators 7.3.1

The electric dipole (adapted from Radiation Laboratories)

In the preceding Section 7.2.2, a radiation field arising from an aperture distribution of time-varying currents was described [2]. Now some small-scale idealized current distributions and their associated electromagnetic fields will be discussed. These elements are useful models in real low sidelobe and low RCS antennas.

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z

+q

δ

y

ℓ

–q

x (a)

(b)

Figure 7.5 The electric dipole: (a) mathematical dipole and (b) dipole antenna. Adapted from [2] The simplest form of idealized radiator is the electric dipole shown in Figure 7.5. A dipole consists mathematically of a pair of equal and opposite charges, each of magnitude q, separated by an infinitesimal distance d. If a vector d is directed from q to þq, then the dipole moment is a vector defined as  exp(j⋅ w ⋅ t ) ⋅δ p = q 0 ⋅ exp(j⋅ w ⋅ t ) ⋅ δ = I 0 ⋅ l ⋅ j⋅ w Where: I 0 = maximum rate of change of charge, q l = length of the dipole

(7.16)

The closest real-life example of such an antenna is the AM radio antenna embedded in the windshield in some cars. An antenna equivalent to a dipole also is shown in Figure 7.5(b). It consists of thin wires terminated in small spheres, the assumed dimensions are very small compared with a wavelength. The spheres form the capacitive element of the structure, and the charge at any instant can be considered localized to them. If the antenna is energized by RF applied across the gap at the center, the charges on the spheres are given by the magnitude of the dipole moment q0 which corresponds to the current flowing in the infinitesimal antenna of I0 ‘/jw. The electromagnetic field set up by a dipole can be described in spherical coordinates as shown in Figure 7.6. The components of the E and H fields are as shown in the figure. Since the dipole is infinitesimal, the equations which follow are good everywhere not on the dipole. Although Silver references Stratton for the derivation of the dipole fields, a more accessible text is Antenna Theory by Balanis [4]. Equations (7.17) stated below are from that reference. The one inconvenient fact in this description is that arrays of dipoles usually want the z coordinate to be normal to the dipole not parallel with the dipole axis.

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Er Hϕ

θ

r

Eθ

y

ϕ

x

Figure 7.6 Geometry for electric dipole oriented along the z-axis Assuming that the dipole is at the origin and oriented along the z-axis and dropping the exp(jw t) since it is in all terms, then the far-field pattern in spherical coordinates is given in (7.17). As a consequence of the axial symmetry of the radiator, the field of the dipole is independent of f. The dipole is a true point source because the equiphase surfaces are spheres with centers at the origin; it is directive because the intensity of the field varies with the direction of observation. In design specifications, it is customary to characterize such cuts in the three-dimensional (3D) polar diagram by two widths if they exist, the “half-power width”, q3dB, which is the full angle in that cut between the two directions in which the power radiated is one-half the maximum value, and the “tenth-power width”, q10dB, the angle between the directions in which the power radiated is one-tenth of the maximum. These two values and their counterparts in u, v space from (7.12) are useful for estimating mainlobe and sidelobe antenna performance. h ⋅ I 0 ⋅ l ⋅ cos (q ) ⋅ exp ( − j⋅ k ⋅ r ) ⎡ 1 ⎤ ⋅ ⎢1 + 2 j ⋅ ⋅ r ⎥⎦ k 2 ⋅p ⋅ r ⎣ j⋅ k ⋅ h ⋅ I 0 ⋅ l ⋅ sin (q ) ⋅ exp ( − j⋅ k ⋅ r ) ⎡ 1 1 ⎤ ⋅ ⎢1 + − Eq = ⎥ 2 4 ⋅p ⋅ r ⎢⎣ j⋅ k ⋅ r ( k ⋅ r ) ⎥⎦ j⋅ k ⋅ I 0 ⋅ l ⋅ sin (q ) ⋅ exp ( − j⋅ k ⋅ r ) ⎡ 1 ⎤ ⋅ ⎢1 + Hf = ⋅ ⋅ r ⎥⎦ k 4 ⋅p ⋅ r j ⎣ H r = H q = Ef = 0 Er =

(7.17)

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Where the propagation constant, k, and the intrinsic impedance, h, are defined in (7.18): k 2 = w 2 ⋅ m ⋅ e = (2 ⋅p l )

2

and h = m e

(7.18)

and the free space impedance is: h 0 = m 0 e 0 ≅ 377Ω

In the far-field kr >> ‘, (7.17) reduce to j⋅ k ⋅ h ⋅ I 0 ⋅ l ⋅ sin (q ) ⋅ exp ( − j⋅ k ⋅ r ) 4 ⋅p ⋅ r j⋅ k ⋅ I 0 ⋅ l ⋅ sin (q ) ⋅ exp ( − j⋅ k ⋅ r ) Hf = 4 ⋅p ⋅ r E r ≈ H r = H q = Ef = 0

Eq =

(7.19)

The gain function of the dipole when oriented along the z-axis is shown in (7.20). The gain is maximum at q ¼90
(The formula is slightly more complex for other orientations but nothing has changed but the coordinates.): G e (q ) =

3 ⋅ sin 2 (q ) 2

(7.20)

The power pattern of the dipole is independent of f and is toroidal shaped. It can be represented by a normalized cut in any one plane containing the z-axis as shown in Figure 7.7. Up to l/4 dipole length, the q3dB beamwidth only changes by 3
z 0°

20°

40°

50°

60° 70°

P(θ) 80° θ 0.2

0.4

0.6

90° x, y

0.8

100°

1.0 180°

160°

140°

130°

110°

120°

Figure 7.7 Power pattern of an electric dipole in cardinal plane. Adapted from [2]

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from 90
to 87
and from l/4 to l/2 dipole length, the q3dB beamwidth only changes by 9
from 87
to 78
, so the small dipole is an excellent model for many real cases.

7.3.2

The magnetic dipole or small loop

The magnetic counterpart of the electric dipole antenna is a current loop with small radius compared with the wavelength as shown in Figure 7.8. Such a current loop is equivalent to a magnetic dipole along the axis normal to the plane of the loop. As before, this vector will be assumed along the z-axis in a spherical coordinate system (Figure 7.6). As will be seen, the electric dipole E field in q corresponds to the magnetic dipole H field in q and the electric dipole H field in f corresponds to the magnetic dipole E field in f. The complementary nature of the fields is useful since it can simplify analysis and help visualization, for example, replacing slots with dipoles and vice versa. j⋅ k ⋅ a 2 ⋅ I 0 ⋅ cos (q ) ⋅ exp ( − j⋅ k ⋅ r ) ⎡ 1 ⎤ ⋅ ⎢1 + ⎥ 2 2⋅ r ⎣ j⋅ k ⋅ r ⎦ 2 − ( k ⋅ a ) ⋅ I 0 ⋅ sin (q ) ⋅ exp ( − j⋅ k ⋅ r ) ⎡ 1 1 ⎤ Hq = ⋅ ⎢1 + − 2⎥ 4⋅ r ⎢⎣ j⋅ k ⋅ r ( k ⋅ r ) ⎥⎦ 2 h ⋅ ( k ⋅ a ) ⋅ I 0 ⋅ sin (q ) ⋅ exp ( − j⋅ k ⋅ r ) ⎡ 1 ⎤ Ef = ⋅ ⎢1 + ⎥ 4⋅ r ⎣ j⋅ k ⋅ r ⎦ E r = Eq = H f = 0 Hr =

(7.21)

The current in the loop is assumed to be a complex sinusoid with a peak value I0 just as for the electric dipole. The counterpart to the electric dipole length is the loop radius, a. The field components are given in (7.21). The far-field approximations for z

m

y I

x

Figure 7.8 Magnetic dipole and equivalent current loop. Adapted from [2]

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kr >>1 should be obvious from the electric dipole (7.19). Again out to a dipole radius of a ¼ l/5, the beamwidth is almost unchanged. The far-field patterns of noncircular loops have almost the same field equations as the circular loop as long as the loop enclosed area is the same. This is also true of the loop as a scatterer.

7.3.3 Slot radiators (Adapted from Blass) The next important type of radiating element (or scatterer) is the small slot radiator [4]. The metal surfaces in which the slots are cut will be large compared with a wavelength, but the slots themselves are less than one wavelength in extent. Such slots may be excited by a cavity placed behind it, through a waveguide, or by a transmission line connected across the slot. The simplest example of such a radiator consists of a rectangular slot cut in an extended thin flat sheet of metal with the slot free to radiate on both sides of this sheet, as shown in Figure 7.9. The slot is excited by a voltage source from a transmission line connected to the opposite edges of the slot. The electric-field distribution in the slot can be obtained from the relationship between slot radiators and complementary dipole radiators. It has been shown that the electric-field distribution (magnetic current) in the slot is identical with the electric-current distribution on a complementary dipole. In the case of the rectangular slot of Figure 7.9, the electric field is perpendicular to the long dimension and its amplitude vanishes at the ends of the slot. The electric field is everywhere normal to the surface of the slot antenna except in the region of the slot itself. The radiation of the currents in the sheet can be deduced directly from the distribution of the electric field in the slot. Consequently, the radiated field of an elementary magnetic dipole within the slot boundaries should include the contributions of the electric currents flowing on a

y

z θ

x

E(θ, ϕ) Eθ x

dx

z

y

E dy

y

z

ϕ x

Eθ

Eϕ

Figure 7.9 Principal plane field diagrams for thin rectangular slot, Adapted from Blass [4]

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metal surface. The field can be thought of as toroidal (donut) shaped with an axis through the long dimension of the slot as suggested by the three cuts in Figure 7.9. Of course, most slot radiators are not free to radiate on both sides of the surface on which the slot is cut since one side often is completely enclosed, for example, the slotted waveguide antenna. In these cases, the influence of the enclosed cavity region on the excitation and impedance of the slot radiator is significant to the design.

7.3.3.1

Small rectangular slot in infinite ground plane

The theoretical properties of a radiating slot in a flat sheet can be obtained from Booker’s extension of Babinet’s principle, which shows that the field on the slot can be deduced from those surrounding a dipole of the same dimensions by interchanging the electric and magnetic vectors. Alternatively, the field can be found from the equivalence principle. The two-sided radiation field of a small rectangular slot such as shown in Figure 7.9 is given by cos ( f ) ⋅ dx ⋅ dy ⋅ exp( − j⋅ k ⋅ r ) 2⋅ r ⋅l cos (q ) ⋅ sin ( f ) ⋅ dx ⋅ dy ⋅ exp( − j⋅ k ⋅ r ) E f = j⋅ E x ⋅ 2⋅ r ⋅l

Eq = − j⋅ E x ⋅

(7.22)

Where Ex is the x component of the electric field in the slot and it is assumed that the electric field is parallel to the x-axis, dx is the slot dimension in the x direction, and dy is the slot dimension in the y direction. The principal plane radiation patterns of this magnetic-current dipole also are shown in Figure 7.9. It is seen that the radiation pattern in the xz plane is omnidirectional, and the pattern in the yz plane varies as cos(q). Note that the phase of the radiated field reverses on the two sides of the ground plane even though the amplitude patterns are identical.

7.3.3.2

Near half-wave radiating slot in infinite ground plane

A rectangular slot cut in a flat sheet of metal will be resonant when it is approaching half wavelength. As in the case of the complementary dipole, the magnetic-current distribution for the thin slot is approximately cosinusoidal. The far-field radiation pattern of the near half-wave slot is given in (7.23): sin (U ) U V −p 4 cos (V ) sin (U ) ⋅ Ef = −Cr ⋅ cos (q ) ⋅ sin ( f ) ⋅ 2 U V −p 2 4 Er = H r = 0 and Hf = Eq h , Hq = − Ef h a⋅k ⋅u p ⋅a sin (q ) ⋅ cos ( f ) = and U= 2 l p ⋅b b⋅k ⋅v V= sin (q ) ⋅ sin ( f ) = 2 l − j⋅ a ⋅ b ⋅ E0 ⋅ exp ( − j⋅ k ⋅ r ) Cr = 2⋅ r⋅l Eq = Cr ⋅ cos ( f ) ⋅

cos (V ) 2

2

⋅

(7.23)

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Where Ex ¼ E0 cos (p y’/b) is the field strength of the cosine distribution in the slot used in (7.22) to obtain (7.23) and a is the x dimension and b is the y dimension of the slot. Of course, in all these equations, exp(jw t) as well as exp(jkr) has been dropped since it is in all terms. For the case of a half-wave slot, that is, b ¼l/2 and a