1.INTRODUCTION TOSYSTEMSRADAR SYSTEMS Second Edition Second Merrill I. SkolnikMcGRAW-HILL BOOK COMPANYMcGRAW-HILL BOOK COMPANYAuckland Bogotii Guatemala Hamburg Lisbon Auckland Bogota Guatemala Hamburg LisbonLondon Madrid Mexico New Delhi Panama ParisLondon Madrid Mexico New Delhi Panama Paris San Juan S5o Paulo Singapore Sydney Tokyo San Juan Sao Paulo Singapore Sydney Tokyo

2. INTRODUCTION TO RADAR SYSTEMSINTRODUCTION TO RADAR SYSTEMS International Edition 1981International Edition 1981 Exclusive rights by McGraw-Hill Book Co.-- Singapore forExclusive rights by McGraw-Hili Book Co.-- Singapore for manufacture and export. This book cannot be re-exportedmanufacture and export. This book cannot be re-exported from the country to which it is consigned by McGraw-Hill.from the countlY to which it is consigned by McGraw-Hill.Copyright 1980, 1962 by McGraw-Hill, Inc. Copyright @ 1980,1962by McGraw-Hill, Inc. All rights reserved. Except as permitted under the United States CopyrightAll rights reserved. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed inAct of 1976, no part of this publication may be reproduced or distributed inany form or by any means, or stored in aadata base or retrieval system, any form or by any means, or stored in data base or retrieval system, without the prior written permission of the publisher.without the prior written permission of the publisher.I 2 3 4 5 6 7 8 9 2 0 BJE 9 8 7 6 5 4 This book was set in Times Roman.This book was set in Times Roman. The editor w s Frank J. Cerra. aThe editor was FrankJ. Cerra. Theproduction supervisor was GayleAngelson.Theproduction supervisor was Gayle Angelson. Library of Congress Cataloging in Pubilcation DataLibrary of Congress Cataloging In Publication Data Skolnik, Merrill Ivan, dateSkolnik, Merrill Ivan, date Introduction to radar systems.Introduction to radar systems. Includes bibliographical references and index.Includes bibliographical references and index. 1. Radar. I. Title. 11. Series.1. Radar. I. Title. II. Series. TK6575S477 1980 621.3848 79-15354TK6575.s477 1980 621.3848 79-15354 ISBN 0-07-057909-1ISBN 0-07-057909-1When ordering this title use ISBN 0-07-066572-When ordering this title use ISBN 0-07-066572~ 99 Printed in SingaporePrinted in Singapore 3. CONTENTSPreface IX1 The Nature of Radar 1 1.1lntroductiorlIntroduction 1 1.2*llle Sirnple Fortn Kadar EquatiorlThe Simple Form of the Radar Equation 3 1.3 1.3HlockRadar Block Diagram and Operation 5 1.4 1.4Radar Frequencies 7 1.5 1.5Radar Development Prior to World War IIDcvcloprnent I1 8 1.6 1.6 KadarApplications of Radar 12References142 The Radar Equation15 2.1Range PerformancePrediction of Range Performance 15 2.2Mirlimurn SignalMinimum Detectable Signal 16 2.3Receiver Noise18 2.4Probability-density FunctionsFunctions 20 2.5Signal-to-noise RatioSignal-to-noise Ratio 23 2.6PulsesIntegration of Radar Pulses 29 2.7Radar Cross Sectiorl TargetsRadar Cross Section of Targets33 2.8Cross-section FluctuationsCross-section 46 2.9TransmitterTransmitter Power 522.10Pulse Repetition andPulse Repetition Frequency and Range Ambiguities532.11 ~arametersAntenna Parameters542.12System LossesSystem Losses 562.1 JPropagation EffectsPropagation Effects 622.14Other ConsideratiorlsOther Considerations62 RefererlcesReferences65 3 C W and 3 CW and Frequency-Modulated Radar 68 2.1 3.tTile Iloppler EffectThe Doppler ElTect68 3.2 3.2C W RadarCW Radar70 3.3 3.3Frequency-modulated C W RadarFrequency-modulated CW Radar81 4. JCONTENTS3.4Airl>or-neDoppler NavigationAirhorne Doppler Navigation l)~3.5M ultiple-Frequency C W RadarMultiple-Frequency CW Radar LJS ReferencesRekrences l)K 4MTI and Pulse Doppler RadarMTI and Pulse Doppler Radar10l4.1Introd~ictionIntroduction 10/4.2Delay-Line CancelersDelay-Line Cancelers 1064.3Multiple, or Staggered, Pulse Repetition FreqiirncicsMultiple, or Staggered, Pulse Repetition Frequencies I 144.4 Range-Gated Doppler Filters Range-Gated Doppler Filters 1174.5Digital Signal ProcessingDigital Signal ProcessingI 194.6Other MTI Delay LinesOther MTI Delay Lines1264.7Example of an MTI Radar ProcessorExample of an MTI Radar Processor1274.HLimitations to MTI PerformanceLimitations to MTI Performance 12L)4.9 Noncoherent MTI NoncoherentMTIDH 4.10Pulse Doppler RadarPulse Doppler RadarDtJ 4.11 MTI from a aMoving Platform MTI from Moving Platform140 4.12 Ot her Types of MTI Other Typesof MTI 147 ReferencesReferences 14~Tracking Radar 5 Tracking Radar152 5.1 Tracking with RadarTracking with Radar152 5.2 Sequential LobingSequential Lobing15. 5.3 Conical ScanConical Scan 155 5.4 Monopulse Tracking RadarMonopulse Tracking Radar 160 5.5Target-Reflection Characteristics and Angular Accuracy Target-ReflectionCharacteristics and Angular Accuracy 167 5.6Tracking ininRange Tracking Range176 5.7 AcquisitionAcquisition177 5.R Other TopicsOther Topics In 5.9 Comparison of TrackersComparison of Trackers IX:25.10 Tracking with Surveillance RadarTracking with Surveillance Radar 1~3 ReferencesReferences IX6 6 Radar TransmittersRadar Transmitters 1906.1 IntroductionIntroduction 1906.2The Magnetron OscillatorThe Magnetron Oscillator 1926.3 Klystron AmplifierKlystron Amplifier 20()6.4Traveling-Wave-Tube AmplifierTraveling-Wave-Tube Amplifier2066.5 Hybrid Linear-Beam AmplifierHybrid Linear-Beam Amplifier lOX6.6 Crossed-Field AmplifiersCrossed-Field Amplifiers 20X6.7 Grid-Con trolled TubesGrid-Controlled Tubes2.1(d~ ModulatorsModulators 2/)6.9 Solid-State TransnlittersSolid-Slale Transmitters 2 IIIReferencesReferences no 7 Radar AntennasRadar Antennas 2237.1Antenna ParametersAntenna Parameters 2217.2Antenna Radiation Pattern and Aperture DistributionAntenna Radiation Pattern and Aperture Distribution22~7.3 Parabolic-Reflector AntennasParabolic-Reflector Antennas 2357.4Scanning-Feed Reflector AntennasScanning-Feed Reflector Antennas 2447.5 Lens AntennasLens Antennas24~ 5. CONTENTS vii 7.6 7.6Pattern SynthesisPattern Sy~~rlicsis254 7.7 7.7Cosecant-Squared Antenna PatternCosecarit-Squared Arttenna Pattern 258 7.R 7.8FlTect of Frrors on Radiation Palernsi:fTccl of Errors Radiatiot~Patterns 262 7.97.9 RadolllesKadomcs2647.107.10Stabilization of AntennasStabili7ation of Antcnnas270Referencesf~cfcrcrlccs 273 8 The ElectronicaJJy Steered Phased 8 llle Electrot~icallySteered Array Antennat in Radar Array AI278 H.I11111r od ud ion I r r l otlr~ctior~ 278H.2 Basic l(or~ccl>ts1t:tsic onccpts 279lUPhase S C . sl1irlct.sII ~ ~ ~ Shifters 286 XA hequellcy-Scan ArraysI,requc~~cy-Scar1 Arritys 298X.5 Array IllcnieritsArray Elemcnts 305X.6 lcccls for ArraysFeeds for Anays306X.7 Sil~lultarlcousMultil>lc 13ea1lisfrom Array AriterlliasSimultaneous Multiple Beams from Array Antennas310X.X Random Errors in ArraysRandom Errors in Arrays3188.9 Computer Control of Phased-Array RadarComputer Control of Phased-Array Radar 3221.10 Otlicr Array TopicsOther Array Topics 3288.11Applications of the Array in RadarApplications of the Array in Radar 334~.12Advantages arid LimitationsAdvantages and Limitations 335Kcfcrcl~ccsRefercnces 337 9Receivers, Displays, and DuplexersReceivers, Displays, and Duplexers 343 9.1The Radar ReceiverThe Radar Receiver 343 9.2 Noise FigureNoise Figure 344 9.3 MixersMixers 347 9.4Low- Noise Front-Ends Low-Noise Front-Erids 351 9.5 [)is playsDisplays 353 9.6 1)uplexers and Receiver ProtectorsDuplexers and Receiver Protectors359ReferencesReferences 366 10 Detectiotl of Radar Signals in NoiseDetection or Radar Signals In Noise36910.1 Introductiot~Introduction 36910.2 Matched-Filter ReceiverMatched-Filter Receiver36910.3 Correlation DetectioriCorrelation Detection37510.4 Detection CriteriaDetection Criteria 37610.5 Detector CliaracteristicsDetector Characteristics 38210.6 Performance of the Radar OperatorPerformance of the Radar Operator38610.7 Automatic DetectionAutomatic Detection38810.8 Constant-False-Alarm-Rate (CFAR) ReceiverConstant-False-Alarm-Rate (CFAR) Receiver392 ReferencesReferences 3951Extractio~~ Information and Waveformof 111 Extraction of Information and Waveform Design Design399 11.111.1Introduction Introduction399 11.211.2 Information Available from aa RadarInformation Available from Radar 399 1 1.3 Theoretical Accuracy of Radar Measurements11.3 Theoretical Accuracy of Radar Measurements400 1 1.4 Ambiguity Diagram11.4Ambiguity Diagram411 6. viiiviii CONTENTS CONTENTS11.511.5 Pulse Compression Pulse 42011.6 Classification of Targets with Radarof with434 References438 12 Propagation of Radar Wavesof 44112.1 Introduction4412.2 Propagation over a Plane Earth44212.3 The Round Earth 44612.4 Refraction44712.5 Anomalous Propagation 45012.6 Diffraction 45612.7 Attenuation by Atmospheric Gases45912.8 Environmental Noise Environmental 46112.9 Microwave-Radiation Hazards 465 References466 13Radar Clutter 47013.1 Introduction to Radar Clutter 47013.2 Surface-,Clutter Radar Equations Surface-ClutterEquations47113.3 Sea Clutter 47413.4 Detection of Targets in Sea Clutter 48213.5 Land Clutter48913.6 Targets Detection of Targets in Land Clutter49713.7 Effects of Weather on Radar 49813.8 Detection of Targets in Precipitation Precipitation 50413.9Echoes Angel Echoes508 References References, 512 14Other Radar Topics51714.1 Synthetic Aperture Radar Synthetic Aperture Radar51714.2 Over-the-Horizon HF Over-the-Horizon Radar 52914.3 Air-Surveillance Air-Surveillance Radar53614.4 Height-Finder and 3D Radars Height-Finder3D Radars54114.5 Electronic Counter-Countermeasures Electronic Counter-Countermeasures54714.6 Bistatic Radar Bistatic Radar55314.7 Millimeter Waves and Beyond Millimeter Waves and Beyond 560 References References566 Index Index 571 7. PREFACEAlthough the fundamentals of radar have changed little since the publication of the first tlie firstedition,edition. there has been continual development of new radar capabilities and continual im-provements to the technology and practice of radar. This growth has necessitated extensivearid tlierevisions and the introduction of topics not found in the original. (moving One of the major changes is in the treatment of MTI (moving target indication) radar(Chap. 4).(Chap. 4). Most of the basic MTI concepts that have been added were known at the time of theGattliefirst edition, but they had not appeared in the open literature nor were they widely used infirst lhey i11practice. Inclusion in the first edition would havebeen largely academic since the analogdelay-line technology available at that time did not make it practical to build the sophisticatedsignal processors that were theoretically possible. However, subsequent advances in digitallechnology, originally developed for applications other than radar, have allowed the practicaltechnology,implementation of the multiple delay-line cancelers and multiple pulse-repetition-frequencypulse-repetition-frequencyMTI radars indicated by the basic MTI theory.(Secs. 5.1010.7). Automatic detection and tracking, or ADT (Sees. 5)0 and 10.7), is another important evelopment fordevelopment whose basic theory was known for some time, but whose practical realizationilad to await advances in digital technology. The principle of ADT was demonstrated in the ad1950s. .ofearly 1950s, using vacuum-tube technology, as part of the United States Air Forces SAG ESAGE Laboratory.air-defense system developed by MIT Lincoln Laporatory. In this form ADT was physicallyexpensive,1960slarge, expensive, and difficult to maintain. The commercial availability in the late 1960s of thesolid-slate minicomputer, however, permitted ADT to be relatively inexpensive, reliable, and of small size so that it can be used with almost any surveillance radar that requires it. sniallit it. Anotlcr radar area that has seen much development is that of the electronically steered Another ptiased-array antenna. In tlie first edition, the radar antenna was the subject of a single phased-arraythe cliaptcr. I11 tliis chapter. In this edition, one chapter covers the conventional radar antenna (Chap. 7) and a (Chap. 8). separate chapter covers the phased-array antenna (Chap. 8). Devoting a single chapter to the array antenna is more a reflection of interest rather than recognition of extensive application. antenria inore rellection application. The chapter on radar clutter (Chap. 13) has been reorganized to include methods for the o~i(Ctiap. 13) clutter. detection of targets in the presence of clutter. Generally, the design techniques necessary for the detection of targets in a clutter background are considerably different from.those necessary ttieclutter, fromthose for detection in a noise background. Other subjects that are new or which have seen significant cliaiiges" on-axis" changes in the current edition include low-angle tracking, "on-axis" tracking, solid-state RFRFources,antet~na,stabilization, sources, the mirror-scan antenna, antenna stabilization, computer control of phased arrays,arrays,olid-stateCFAR, )Olid-state duplexers, CFAR, pulse compression, target classification, synthetic-aperture radar,synthetic-aperture ver-the-horizonair-surveillance 3D over-the-horizon radar, air-surveillance radar, height-finder and 3D radar, and ECCM. The ECCM. bistatic radar and millimeter-wave radar are also included even though their applications have 8. x PREFACEX been limited. Omitted from this second edition is the chapter on Radar Astronomy since interest in this subject has dccrcascti with tltc i~vi~ilithility space prolws tthat cilll explore ttlcsub.ject decreased the availability o fof probes l l i i l callthe planets at close range. The basic material of the first edition that covers the radar equation,range.the detection of signals in noise, the extraction of information, and the propagation of radarofwaves has not changed significantly. The reader, ttowcvcl., wilt find only a fcw pagcs ofsignificantly. however, willfew pages the original edition that have not been modified in some manner.One of the features of the first edition which Ilas hcen contintled is the inclt~sionofOnefeatures has been continuedinclusion ofextensive references at the end of each chapter. These are provided to acknowlcdgc the sources chapter.acknowledge of material used in the preparation of the book, as well as to permit the interested reader to learn more about some particular subject. Some references that appeared in the first edition have been omitted since they have been replaced by more current references or appear in publications that are increasingly difficult to find. The references included in the first edition find. represented a large fraction of those available at the time. I t woilld have been difficult to add to fractionIt wouldthem extensively or to include many additional topics. This is not so with the second edition.The current literature is quite large; and, because of the limitations of.space, only a milch The of space, muchsmaller proportion of what is available could be cited.In addition to changes in radar technology, there have been changes also in style and thercnomenclature. For example, db has been changed to dB, and Mc is replaced by M iIlL.~ Also, tthenomenclature.example, d b i AIso, he .letter-band nomenclature widely employed by the radar engineer for designating the commonradar frequency bands (such as L, S, and X ) has been officially adopted as a standard by thefrequency (suchX)IEEE.IEEE.The material in this book has been used as the basis for a graduate course in radar taughtby the author at the Johns Hopkins University Evening College and, before that, at several.Universityother institutions. This course is different from those usually found in most graduate electricalinstitutions.engineering programs. Typical EE courses cover topics related t o circuits, components, de- tovices, and techniques that might make up an electrical or electronic system; but seldom is the vices, orstudent exposed to the system itself. It is the system application (whether radar, communica-itself.tions, navigation, control, information processing, or energy) that is the raison ditre for the tions, control,dctreelectrical engineer. The course on which this book is based is a proven method for introducingengineer.the student to the subject of electronic systems. It integrates and applies the basic concepts systems.found in the students other courses and permits the inclusion of material important to foundof the practice of electrical engineering not usually found in the traditional curriculum. the Instructors of engineering courses like to use texts that contain a variety of problems that th3;tof can be assigned to students. Problems are not included in this book. Althoirgh the author toAlthough assigns problems when using this book as a text, they are not considered a major learning assigns technique. Instead, the comprehensive term paper, usually involving a radar design problem o rInstead,comprehensive or a study in depth of some particular radar technology, has been found to be a better means for bctter having the student reinforce what is covered in class and in the text. Even more important, itthe allows the student to research the literature and to be a bit more creative than is possible by allows the tosimply solving simply solving standard problems. a A book of this type which covers a wide variety of topics cannot be written in isolation. I t isolation. It would not have been possiblewithoutthe many contributions on radar that have appeared in possible,withoutthe the open literature and which have been used here as the basic source-material. A largethesource material.measure of gratitude must be expressed to those radar engineers who have taken the time anci toand energy to ensure that the results,:of their work were made available by publication iinenergy t o ensure results of puhlication l lrecognized journals..I. On a more personal note, neither edition of this book could have been written without theOnth~complete support complete support and patience of my wife Judith and my entire family who allowed me tllcthe totime necessary to undertake this work.Merrill 1. SkolrlikI. Skolnik 9. CHAPTER ONE THE NATURE OF RADAR1.1 INTRODUCTIONRadar is an electromagnetic system for the detection and location of objects. It operates byis a ntransmitting a particular type of waveform, a pulse-modulated sine wave for example, andpulse-modulateddetects the nature of the echo signal. Radar is used to extend the capability of ones senses fordetects theof signal. to of onesobserving the environment, especially the sense of vision. The value of radar lies not in being aenvironment,substitute for the eye, but in doing what the eye cannot do...Radar cannot resolve detail as wellsi~hstitute for eye, do-Radar the eye, nor is it capable of recognizing the" color" of objects to the degree of sophisticationas the eye,is the "color" of sophisticationof which the eye is capable. However, radar can be designed to see through those conditions the eye isimpervious to normal human vision, such as darkness, haze, fog, rain, and snow. In addition,irnpervioris t orairi,radar has the advantage of being able to measure the distance or range t o the object. This is has thetoitsattribute.probably its most important attribute. An elementary form of radar consists of a transmitting antenna emitting electromagnetic formradiation generated by an oscillator of some sort, a receiving antenna, ~nd an energy-detectingoscilIator anddevice. or receiver. A portion of the transmitted signal is intercepted by a reflecting objectdevice,reRecting(target) and is reradiated in all directions. I.t is the energy reradiated in the back direction that (target) and isall1.tis of prime interest to the radar. The receiving antenna collects the returned energy and isdelivers it to a receiver, where it is processed to detect the presence of the target and t o extractdelivers t o to toits location and relative velocity. The distance to the target is determined by measuring the itsandtotime taken for the radar signal to travel to the target and back. The direction, or angularfor toposition, of the target may be determined from the direction of arrival of the reflected wave- position, thefront. The usual method of measuring the direction of arrival is with narrow antenna beams. Iffront. TheIfrelative motion exists between target and radar, the shift in the carrier frequency of therelativeexistsofreflected wave (doppler elTect) is a measure of the targets relative (radial) velocity and may be(doppler effect)used to distinguish moving targets from stationary objects. In radars which continuously tracktothe movement of a target, a continuous indication of the rate of change of target position istheofalso available.also available.1 10. 2 INTRODUCTION TO RADAR SYSTEMSSYSTEMS The name radar reflects the emphasis placed by the early experimenters on a device todetect the presence of a target and measure its range. Radar is a contraction of the words radio ofdetection and ranging. It was first developed as a detection device to warn of the approach ofof approach ofhostile aircraft and for directing antiaircraft weapons. Although a well-designed modern radar modern radarcan usually extract more information from the target signal than merely range, the measure-thement of range is still one of radars most important functions. There seem to be no otherof radarscompetitive techniques which can measure range as well or as rapidly as can a radar. The most common radar waveform is a train of narrow, rectangular-shape pulses modu-modu-lating a sinewave carrier. The distance, or range, to the target is determined by measuring theTRtime TR taken by the pulse to travel to the target and return. Since electromagnetic energyenergy 8 ofe= 10 mis,propagates at the speed of light c = 3 x 10 m/s, the range R isRR = eTR(1.1 ) 2The factor 2 appears in the denominator because of the two-way propagation of radar. With propagation of radar. Withthe range in kilometers or nautical miles, and TR in microseconds, E q . (1.1) becomes o m e sTREq. bec orEach microsecond of round-trip travel time corresponds to a distance of 0.081 nautical mile,ofof 0.081 nautical mile,0.093 statute mile, 150 meters, 164 yards, or 492. feet. 492 feet. Once the transmitted pulse is emitted by the radar, a sufficient length of time must elapse of must elapseto allow any echo signals t o return and be detected before the next pulse may be transmitted. tonext be transmitted.Therefore the rate at which the pulses may be transmitted is determined by the longest range at determined by longest range atIfwhich targets are expected. If the pulse repetition frequency is too high, echo signals from some repetitionecho sometargets might arrive after the transmission of the next pulse, and ambiguities in measuringof measuring I I!.. .III~E0u 1,000:;:::l0c:.u0> c:0.0100E0c::J10 L-_l...-..I..-I-1...J....1-U-L_-.J..---L--1-....L....L..l...L.J---_...1.--4-~ ...................10 100 1,000 Pulse repetition frequency, Hzfrequency, HzFigure 1.1 Plot of maximum unambiguous range as a function of the pulse repetition frequency.of of the pulse repetition frequency. 11. THE NATURE OF RADAR3range might result. Echoes that arrive after the transmission of the next pulse are calledrange result.second-time-arOlmd (or multiple-time-around) echoes. Such an echo would appear to be at asecorrd-tinte-arotrrtd (ormuch shorter range than the actual and could be misleading if it were not known to be asecond-time-around echo. The range beyond which targets appear as second-time-aroundsecond-time-around echo. second-time-aroundechoes is called the maximum unambiguous range and isechoes isrna.uintttrn trr~arnhigtrousrattgecRunamb = 2fp(1.2)where fp = pulse repetition frequency, in Hz. A plot of the maximum unambiguous range as awhere./, = Hz.function of pulse repetition frequency is shown in Fig. 1.1. Although the typical radar transmits a simple pulse-modulated waveform, there are anumber of other suitable modulations that might be used. The pulse carrier might befrequency- or phase-modulated to permit the echo signals to be compressed in time afterfrequency-reception.reception. This achieves the benefits of high range-resolution without the need t o resort to a to. short pulse. The technique of using a long, modulated pulse to obtain the resolution of a shortofpulse, but with the energy of a long pulse, is known as pulse compression. Continuouspulse, pulsewaveforms (CW)) also can be used by taking advantage of the doppler frequency shift to (CWseparate the received echo from the transmitted signal and the echoes from stationary clutter.separatefromUnmodulated CW waveforms do not measure range, but a range measurement can be made CW do measurement by applying either frequency- or phase-modulation.1.2 THE SIMPLE FORM OF THE RADAR EQUATION1.2 THE SIMPLEThe radar equation relates the range of a radar to the characteristics of the transmitter,Theofreceiver. antenna, target, and environment. It is useful not just as a means for determining thereceiver, antenna, justmaximum distance from the radar to the target, but it can serve both as a tool for under-fromstanding radar operation and as a basis for radar design. In this section, the simple form oftheisthe radar equation is derived. If the power of the radar transmitter is denoted by P,, and if an isotropic antennaIf P" ifis used (one which radiates uniformly in all directions), the power density (watts per unit area)is (one powerat a distance R from the radar is equal to the transmitter power divided by the surface areadistance from4nR2rapius4n:R 2 of an imaginary sphere of radius R, orI ptPower density from isotropic antenna = - = 4 P, 2 (1.3) 4nR2n:RRadars employ directive antennas to channel, or direct, the radiated power Pt into someP,particular direction. The gain G of an antenna is a measure of the increased power radiated indirection. gain ofofthe direction of the target as compared with the power that would have been radiated from anthe directionisotropic antenna. It may be defined as the ratio of the maximum radiation intensity from theisotropic antenna. from asubject antenna to the radiation intensity from a lossless, isotropic antenna with the same antennapower input. (The radiation intensity is the power radiated per unit solid angle in a giveninput. (Thedirection.) The power density at the target from an antenna with a transmitting gain G isdirection.) fromPower density from directive antenna = :::~2Power density from directive antenna = -Pt G(1.4) 4nR2The target intercepts a portion of the incident power and reradiates it in vqrious directions.The target intercepts a portion of the incident power and reradiates it in v~rious directions. 12. 4 INTRODUCTION TO RADAR SYSTEMSR A D A R SYSTEMSThe measure of the amount of incident power intercepted by the target and reradiated back inthe direction of the radar is denoted as the radar cross section (J, and is defined by the relation a, P,G a= P, G2 ~Power density of echo signal at radar = ---- - (1.5)4nR2 4nR24rrR 4n:RThe radar cross section (J has units of area. It is a characteristic of the particular target and is aameasure of its size as seen by the radar. The radar antenna captures a portion of the echopower. If the effective area of the receiving antenna is denoted A., the power P, received by the A",radar is (1.6) RmaxThe maximum radar range R max is the distance beyond which the target cannot be detected. Itoccurs when the received echo signal power P, just equals the minimum detectable signal Smin. P,just S,,,Therefore 1 P GA(J ]1/ 4R max = [ (4~)2S:in (1. 7)This is the fundamental form of the radar equation. Note that the importantpar~ antenna par-ameters are the transmitting gain and the receiving effective area. Antenna theory gives the relationship between the transmitting gain and the receivingeffectiveeffective area of an antenna as (1.8)Since radars generally use the same antenna for both transmission and reception, Eq. (1.8) can(1.8)be substituted into Eq. (1.7), first for A,e then for G, to give two other forms of the radar (1.7), AequationR max = [P G:AI 2(4n:) Smin (J r/4 (1.9)Rmax =[ P, A;O ] 1/4( 1.10)4rrA. 2Smln These three forms (Eqs. 1.7, 1.9, and 1.10) illustrate the need to be careful in the inter- forms (Eqs.1.7, 1.9,1.10)pretation of the radar equation. For example, from Eq. (1.9) it might be thought that the range A. 1/2 , A. - 1/2of a radar varies as All2, but Eq. (1.10) indicates a 1-12 relationship, and Eq. (1.7) shows therange to be independent of 1.The correct relationship depends on whether it is assumed theA.. introduc~gain is constant or the effective area is constant with wavelength. Furthermore, the introduc-istion of other constraints, such as the requirement to scan a specified volume in a given time,can yield a different wavelength dependence. These simplified versions of the .radar equation do not adequately describe the perfor-of radar domance of practical radar. Many important factors that affect range are not explicitly included.In practice, the observed maximum radar ranges are usually much smaller than what would bepredicted by the above equations, sometimes by as much as a factor of two. There are manyreasons for the failure of the simple radar equation to correlate with actual performance, as the failureperformance,discussed in Chap. 2. .2._ ,9 , .. ...... .1 1 13. THE N A T U R E OF RADART H E NATURE RADAR5S1.31.3 RADAR BLOCK DIAGRAM AND OPERATIONThe operation of a typical pulse radar may be described with the aid of the block diagramTtleshown in Fig. 1.2. The transmitter may be an oscillator. such as a magnetron. that is "pulsed"i n Fig. 1.2. Tlle transtnitteroscillator, magnetron," pulsed"(turned on and off) by the modulator to generate a repetitive train of pulses. The magnetron on) rnodulator prohnhly beenhas prohahly heen the most widely used of the various microwave generators for radar. A radar.typical radar for the detection of aircraft at ranges of 100 or 200 nmi might employ a peaktypicrtl tile dctcctionpower of the order of a megawatt. an average power of several kilowatts, a pulse width of megawatt,several microseconds. and a pulse repetition frequency of several hundred pulses per second.microseconds,second.The waveform generated by the transmitter travels via a transmission line to the antenna. antenna, space.where it is radiated into space. A single antenna is generally used for both transmitting and pro~ectedreceiving. The receiver must be protected from damage caused by the high power of the duplexer. totransmitter. This is the function of the duplexer. The duplexer also serves to channel thereturned echo signals to the receiver and not to the transmitter. The duplexer might consist ofdevices,two gas-discharge devices. one known as a TR (transmit-receive) and the other an ATR(anti-transmit-receive). The TR protects the receiver during transmission and the ATR directs(anti-transmit-receive). ferritethe echo signal to the receiver during reception. Solid-state ferrite circulators and receiverprotectors with gas-plasma TR devices and/or diode limiters are also employed as duplexers. duplexers. The receiver is usually of the superheterodyne type. The first stage might be a low-noiseRF amplifier. such as a parametric amplifier or a low-noise transistor. However. it is not amplifier, However,always desirable to employ a low-noise first stage in radar. The receiver input can simply be stage,the mixer stage. especially in military radars that must operate in a noisy environment.Although a receiver with a low-noise front-end will be more sensitive, the mixer input can range,have greater dynamic range. less susceptibility to overload, and less vulnerability to electronicinterference.interference.(LO)RFThe mixer and local oscillator (LO) convert the RF signal to an intermediate frequency(IF). A " typical" I F(IF). / "typical" IF amplifier for an air-surveillance radar might have a center frequency of 30MHzor 60 MHz and a bandwidth of the order of one megahertz. The IF amplifier should bedesigned as a matc/ted filter; i.e., its frequency-response function H ( f ) should maximize the n~atcltedfilter; i.e.,frequency-responseH(f)peak-sigtial-to-mean-noise-powerratio at the output. This occurs when the magnitude of thepeak-signal-to-mean-noise-power1frequency-response function [H(f) I is equal to the magnitude of the echo signal spectrum H(f)(I S(.f) 1, IS(f) I. and the phase spectrum of the matched filter is the negative of the phase spectrum of(Sec. 10.2).the echo signal (Sec. 10.2). In a radar whose signal waveform approximates a rectangularpulse, the conventional IF filter bandpass characteristic approximates a matched filter whenpulse.IF raAfter maximizing the signal-to-noise ratio in the IF amplifier, the pulse modulation is amplifier,extracted by the second detector and amplified by the video amplifier to a level where it can be acd-the product of the IF bandwidth B and the pulse width t is of the order of unity, that is, Bt ~ 1. 1. TronsrnitlerPulseDuplellermodulalorAntenna4-Low - noiseRFRF MixerIF amplifier amplifier(matched filter).. IFigure 1.2 Block diagram of a pulse radar. diagramradar. 14. 6 INTRODUCTION TO RADAR SYSTEMS, -~(a) (b)modulation); ( h A-scop~ pr~sentaFigure 1.3 (a) PPI presentation displaying range vs. angle (intensity modulation); (0)) A-scope presenta-(a)tion displaying amplitude vs. range (deflection modulation).modulation). "4(CRT).properly displayed, usually on a cathode-ray tube (CRT). Timing signals are also supplied to signals suppliedthe indicator to provide the range zero. Angle information is obtained from the pointing zero.fromdirection of the antenna. The most common form of cathode-ray tube display is the planformposition indicator, or PPI (Fig. 1.3a), which maps in polar coordinates the location of the(Fig. 1.3a),target in azimuth and range. This is an intensity-modulated display in which the amplitude ofthe receiver output modulates the electron-beam intensity (z axis) as the electron beam is madeaxis)to sweep outward from the center of the tube. The beam rotates in angle in response to the Aantenna position. A B-scope display is similar to the PPI except that it utilizes rectangular,rather than polar, coordinates to display range vs. angle. Both the B-scope and the PPI, being angle.intensity modulated, have limited dynamic range. Another form of display is the A-scope,range.formshown in Fig. 1.3b, which plots target .amplitude (y axis) vs. range (x axis), for some fixed Fig.amplitudeaxis) axis),fixeddirection. This is a deftectiort:inodulated display. It is more suited for tracking-radar applica-deflection-modulated tion than for surveillance radar.The block diagram of Fig. 1.2 is a simplified version that omits many details. I t does not include several devices often found in radar, such as means for automatically compensating the(AFC) receiver for changes in frequency (AFC) or gain (AGe), receiver circuits for reducing interfer- (AGC), interfer- ence from other radars and from unwanted signals, rotary joints in the transmission lines to signals, allow movement of the antenna, circuitry for discriminating between moving targets and unwanted stationary objects (MTn and pulse compression for achieving the resolution benefits (MTI), achieving of a short pulse but with the energy of along pulse. If the radar is used for tracking, some a longIf means are necessary for sensing the angular location of a moving target and allowing the antenna automatically to lock-on and to track the target. Monitoring devices are usuallydevices included to ensure that the transmitter is delivering the proper shape pulse at the properdelivering power level and that the receiver sensitivity has not degraded. Provisions may also be in-sensitivity corporated in the radar for locating equipment failures so that faulty circuits can be easilyfor failuresfaulty found and replaced.the " raw-video"Instead of displaying the" rawvideo" output of a surveillance radar directly on the CRT,CRT, it might first be processed by an automatic detection and tracking (ADT) device that quantizesfirst anautornaticdetection(ADT) device the radar coverage into range-azimuth resolution cells, adds (or integrates) all the echo pulses cells, received within each cell, establishes a threshold (on the basis of these integrated pulses) thatcell, establishes (onpulses) permits only the strong outputs due to target echoes to pass while rejecting noise, establishesrejecting noise, and maintains the tracks (trajectories) of each target, and displays the processed information 15. THE NATURE OF RADAR 7NATURE OF to the operator. These operations of an ADT are usually implemented with digital computer operator. technology.techriology. A common form of radar antenna is a reflector with a parabolic shape, fed (illuminated) A from a point source at its focus. The parabolic reflector focuses the energy into a narrow beam, from focus. just as does a searchlight or an automobile headlamp. The beam may be scanned in space by mechanical pointing of the antenna. Phased-array antennas have also been used for radar. In a phased array. the bcam is scanned by electronically varying the phase of the currents acrosspllascd array, tllc beamof the aperture.aperture. 1.4 RADAR FREQUENCIES R A D A R FREQUENCIES Conventional radars generally have been operated at frequencies extending from about 220 M Hz to 35 G Hz, a spread of more than seven octaves. These are not necessarily the limits,MHz 35 GHz,., since radars can be, and have been, operated at frequencies outside either end of this range. since of Skywave HF over-the-horizon (OTH) radar might be at frequencies as low as 4 or 5 MHz, and HF(OTH)frequencies groundwave HF radars as low as 2 MHz. At the other end of the spectrum, millimeter radarsHF have operated at 94 GHz. Laser radars operate at even higher frequencies. GHz.The place of radar frequencies in the electromagnetic spectrum is shown in Fig. 1.4. Some frequencies1.4. of the nomenclature employed to designate the various frequency regions is also shown.Early in the development of radar, a letter code such as S, X, L, etc., was employed to designate radar frequency bands. Although its original purpose was to guard military secrecy, desigr~ate the designations were maintained, probably out of habit as well as the need for some conven- ient short nomenclature. This usage has continued and is now an accepted practice of radarof1.1 lists engineers. Table 1.1 lists the radar-frequency letter-band nomenclature adopted by the engineers. IEEE. 15 These are related to the specific bands assigned by the International Telecommunica- IEEE. These are to tions Union for radar. For example, although the nominal frequency range for L band is 1000 to 2000 MHz, an L-band radar is thought of as being confined within the region from 1215 to to 2000 L-band12151400 MHz since 1400 MHz since that is the extent of the assigned band. Letter-band nomenclature is not a Wovelenath Wavelength10 kmfOkm Ikm l km100 m 100m 10m 10mIm1mlOcm!Oem tcm 1cm1mmlmmO.lnm OIMm I I --VlF -LF-+-MF -VLF-+HF-t-VHF-+LF--------+ ---MF- - H F - -VHF- fo- UHF-I-SHF- ..... E H F --+UHF---c+SHF-+k EHF-Very lowVery lowLowLow MediumMedium High Very high Ultrohigh high UltrohighSuperExtremely frequency frequencyfrequency frequency frequency frequency frequency high hrgh hiqhfrequencyfrequency frequency I Myriometric Myriometric Kilometric Hectometric Kilometric Hecrometric Decometric Metric Decimetric Centimetric Millimetric Decimilli- Decimilli- woves woves woveswoves woves waveswoveswoveswovcs woves woveswaveswoves metric wovesBondBond 4 Bond 5 Bond 5 Bond 6Bond 6 Bond Bond 7Bond 8 Bond 8I Bond 9 Bond Bond 1 0Bond 10Bond l lII12 Bond 12mg!~e9~~ry~i~s r~d::i~~~OiA fwSubmillimelerI --- For Fo r ~roodcost OTH OTH infra redm in f m >------lbond rodor II t - - -- - - *I designotions LLetter designotions LJC X Ku KaS C X Ku Ka. II..4Audio frequenciesAudio frequenciesc ,Microwove region Microwave rtQionI --1IVideo frequenciesVideo frequencies I I III * 30 Hzz 30H300Hz300Hz3kHz 3kHz30kHz 30kHz 300kHz 300kHz3MHz 3MHz 30MHz30MHz 300 M H z3 0 0 MHz 3GHz3GHz30GHz30GHz300GHz 300GHz 3 , 0 0 0 GHr3,000 GHz Frequency FrequencyFigure 1.4 Radar frequencies and electromagnetic spectrum.Figure 1.4 Radar frequencies and the electromagnetic spectrum. 16. 8 INTRODUCTION TO RADAR SYSTEMSSYSTEMSTable 1.1 Standard radar-frequency letter-band nomenclature1.1letter-band Specific radiolocatio~l Specific radio locationBandNominal(radar) bands based ondesignation frequency rangeITU assignments for region 22HFHF 3-30 MHzVHFVHF 30-300 MHz 138-144 MHz 138-144 216-225 2 16-225UHFUHF300-1000 MHz420-450 420-450 MHz 890-942 890-942L 1000-2000 MHz 1215-1400 MHz1215-1400S 2000-4000 MHz2300-2500 MHz 2300-2500 2700-3700 2 700-3 700C 4000-8000 MHz5250-5925 MHz 5250-5925X 8000-12,000 MHz8500-10,680 MHz 8500- 10,680Ku 12.0-18 GHz13.4-14.0 GHz 13.4-14.0 15.7-17.7 15.7- 17.7,K 18-27 GHz24.05-24.25 G H z 24.05-24.25 GHz .. _,;KgK,27-40 GHz 33.4-36.0 G H z33.4-36.0 GHzrnrnmm40-300 GHzsubstitute for the actual numerical frequency limits of radars. The specific numerical frequency forfrequencylimits should be used whenever appropriate, but the letter designations of Table 1.1 may belimits shouldappropriate,of desired.used whenever a short notation is desired.1.5 RADAR DEVELOPMENT PRIOR TO WORLD WAR I11.5 DEVELOPMENTIIAlthough the development of radar as a full-fledged technology did not occur until World WarAlthough full-fledgedII, the basic principle of radar detection is almost as old as the subject of electromagnetism11,itself. Heinrich Hertz, in 1886, experimentally tested the theories of Maxwell and demonstrateditself. 1886,Lthe similarity between radio and light waves. Hertz showed that radio waves could be reflectedthe ,Iby metallic and dielectric bodies. It is interesting to note that although Hertzs experimentswere performed with relatively short wavelength radiation (66 cm), later work in radio engin-were (66 cm),eering was almost entirely at longer wavelengths. The shorter wavelengths were not activelyeeringwas wavelengths.toused to any great extent until the late thirties. 1903 a In 1903 a German engineer by the name of Hiilsmeyer experimented with the detection of engineer of radio wavesfrom ships.1904radio waves reflected from ships. He obtained a patent in 1904 in several countries for a n anobstacle detector and ship navigational device. 2e His methods were demonstrated before theship de~ic .~German Navy, but generated little interest. The state of technology at that time was not Germansufficiently adequate to obtain ranges of more than about a mile, and his detection technique sufficiently adequate rangeswas dismissed on the grounds that it was little better than a visual observer. wason the grounds Marconi recognized the potentialities of short waves for radio detection and strongly Marconi recognizeduse in 1922 for urged their use in 1922 for this application. In a speech delivered before the Institute of Radio Engineers, he said: 3 Engineers, he said: As was first shown by Hertz, electric waves can be completely reflected by conducting bodies. In As was first shown Hertz, electric reflected bodies. some my tests I have noticed the effects reflection some of iny tests J have noticed the effects of reflection and detection of these waves by metallic objects miles away. objects miles away.It ~eems to me that it should be possible to design apparatus by means of which a ship could !eems to me that shoulddesign apparatus means 17. THE NATURE RADAR T H E N A T U R E OF R A D A R 9 radiate or project a divergent beam of these rays in any desired direction, which rays, if coming if across a metallic object, such as another steamer or ship, would be reflected back to a receiver screened reflected backreceiver from the local transmitter on the sending ship, and thereby, immediately reveal the presence and immediately presence bearing of the other ship in fog or thick weather. inAlthough Marconi predicted and successfully demonstrated radio communication be-successfullytween continents, he was apparently not successful in gaining support for some of his otherofideas involving very short waves. One was the radar detection mentioned above; the other waswaves.the suggestion that very short waves are capable of propagation well beyond the optical line of ofsight-a phenomenon now know11 as tropospheric scatter. He also suggested that radio wavessight-a phenometlon knownbe used for the transfer of power from one point to the other without the use of wire or otheroftrat~smissiot~transmission lines.lit~cs. In the autumn of 1922 A. ti. Iaylor arid L. C. Young of tile Naval Research LaboratoryaututnrlH. Taylor andthedetected a wooden ship using a CW wave-interference radar with separated receiver andtransmitter. The wavelength was 5 m. A proposal was submitted for further work but was not wavelerlgthaccepted.accepted.The first application of the pulse technique to the measurement of distance was in the ofbasic scientific investigation by Breit and Tuve in 1925 for measuring the height of the 1925 ofionosphere. 4 .1 6 ~ .~i ~ n o s p h e r e . However, more than a decade was to elapse before the detection of aircraft bydetection of bypulse radar was demonstrated. The first experimental radar systems operated with CW and depended for detection uponfirstthe interference produced between the direct signal received from the transmitter and theinterferencetransmitter thedoppler-frequency-shifted signal reflected by a moving target. This effect is the same as the therhythmic flickering, or flutter, observed in an ordinary television receiver, especially on weakflickering, weakstations, when an aircraft passes overhead. This type of radar originally was called C Wstations,ofCWwal}e-inte~rerelceradar. Today, such a radar is called a bistatic C W radar. The first experimen-wqaoe-irtfer-erence bistatic CWtal detections of aircraft used this radar principle rather than a monostatic (single-site) pulse pulseradar because CW equipment was readily available. Successful pulse radar had to await the thedevelopment of suitable components, especially high-peak-power tubes, and a better under- high-peak-power betterstanding of pulse receivers. The first detection of aircraft using the wave-interference effect was made in June, 1930, by firstwave-interference byL. 1... tlyland of the Naval Research Laboratory. It was made accidentally while he wasA HylandLaboratory.lwas working with a direction-finding apparatus located in an aircraft on the ground. The transmit- ter at a frequency of 33 MHz was located 2 miles away, and the beam crossed an air lane from a nearby airfield. When aircraft passed through the beam, Hyland noted an increase in the the received signal. This stimulated a more deliberate investigation by the NRL personnel, but the but the work continued at a slow pace, lacking official encouragement and funds from the govern- ment. although it was fully supported by the NRL administration. By 1932 the equipment was nrent. was demonstrated to detect aircraft at distances as great as 50 miles from the transmitter. The NRL NRL work on aircraft detection with CW wave interference was kept classified until 1933, when several Bell Telephone Laboratories engineers reported the detection of aircraft during theof the course of other experiments.5 The N R L work was disclosed in a patent filed and granted to experiments. NRL patentgranted to Taylor, Young, and Hyland6 on a "System for Detecting Objects by Radio." The type of radar Hyland 6 a" System Radio." type of radar described in this patent was a CW wave-interference radar. Early in 1934, a 60-MHz CWwave-interference6O-MHz CW wave-interference radar was demonstrated by NRL.The early CW wave-interference radars were useful only for detecting the preserrce of thepresence of the target. The problem of extracting target-position information from such radars was a difficult was a difficult one and could not be readily solved with the techniques existing at that time. A proposal was thatA proposal was made by N R L in 1933 to errlploy a chain of transmitting and receiving stations along a line to RL1933 employ ofa line to be guarded. for the purpose of obtaining some knowledge of distance and velocity. This wasofof and velocity. This was 18. to INTRODUCTION TO RADAR SYSTEMS10 SYSTEMS never carried out, however. The limited ability of C W wave-interference radar to be anything however.CW wave-interference more than a trip wire undoubtedly tempered what little official enthusiasm existed for radar.It was recognized that the limitations to obtaining adequate position information coiildcould be overcome with pulse transmission. Strange as it may now seem, in the early days pulsetransmission:radar encountered much skepticism. Nevertheless, an effort was started at NRL in the spring Nevertheless,N RLof 1934 to develop a pulse radar. The work received low priority and was carried out prin-1934cipally by R. M. Page, but he was not allowed to devote his full time to the effort.The first attempt with pulse radar at NRL was at a frequency of60 MHz. According to firstfrequency of 60Guerlac,t the first tests of the 6O-MHz pulse radar were carried out in late December, 1934,Guerlac, 60-MHzand early January, 1935. These tests were "hopelessly unsuccessful and a grievous disappoint-1935. were" hopelesslyment." No pulse echoes were observed on the cathode-ray tube. The chief reason for thischieffailure was attributed to the receivers being designed for CW communications rather than forfailurepulse reception. The shortcomings were corrected, and the first radar echoes obtained atreception.NRL using pulses occurred on April 28, 1936, with a radar operating at a frequency of 1936,of28.3 MHz and a pulse width of 5 ,US. The range was only 24 miles. By early June the range was28.3 IlS.2!miles.25 miles.It was realized by the NRL experimenters that higher radar frequencies were desired,frequenciesespecially for shipboard application, where large antennas could not be tolerated. However,the necessary components did not exist. The success of the experiments at 28 MHz encouraged ofthe NRL experimenters to develop a 200-MHz equipment. The first echoes at 200 MHz werereceived July 22, 1936, less than three months after the start of the project. This radar was also1936,ofthe first to employ a duplexing system with a common antenna for both transmitting and firsttransmitting receiving. The range was only 10 to 12 miles. In the spring of 1937 it was installed and tested onreceiving.12 of 1937the destroyer Leary. The range of the 200-MHz radar was limited by the transmitter. The ofdevelopment of higher-powered tubes by the Eitel-McCullough Corporation allowed animproved design of the 200-MHz radar known as XAF. This occurred in January, 1938. Although the power delivered to the antenna was only 6 kW, a range of 50 miles-the limit of of miles-the of the sweep-was obtained by February. The XAF was tested aboard the battleship New York, sweep-was in maneuvers held during January and February of 1939, and met with considerable success.of considerable Ranges of 20 to 24 kiloyards were obtained on battleships and cruisers. By October, 1939,wereorders were placed for a manufactured version called the CXAM. Nineteen of these radarsof were installed on major ships of the fleet by 1941.ofThe United States Army Signal Corps also maintained an interest in radar during the early 1930s. 7 The beginning of serious Signal Corps work in pulse radar apparently resulted1930s. of apparentlyfrom a visit to NRL in January, 1936. By December of that year the Army tested its first pulse1936.ofpulse radar, obtaining a range of 7 miles. The first operational radar used for antiaircraft fire controlantiaircraft was the SCR-268, available in 1938, The SCR-268 was used in conjunction with searchlights SCR-268, 1938!8 for radar fire control. This was necessary because of its poor angular accuracy. However, itsfire of its range accuracy was superior to that obtained with optical methods. The SCR-268 remained the standard fire-control equipment until January, 1944, when it was replaced by the SCR-584replaced microwave radar. The SCR-584 could control an antiaircraft battery without the necessity for antiaircraft battery searchlights or optical angle tracking, .tracking..In 1939 the Army developed the SCR-270, a long-range radar for early warning. The attack(n 1939attackon Pearl Harbor in December, 1941, was detected by an SCR-270, one of six in Hawaii at theof thetime. (There were also 16 SCR-268s assigned to units in Honolulu.) But unfortunately, thetime.!16unfortunately, thetrue significance of the blips on the scope was not realized until after the bombs had fallen. Asignificance Amodified SCR-270 was also the first radar to detect echoesfrom the moon in 1946. SCR-270 echoes!The early developments of pulse radar were primarily concerned with military applica- oftions. Although it was not recognized as being a radar at the time, the frequency-modulated 19. R A D A R 11 THE N A T U R E OF RADAR 11 NATURE aircraft radio altimeter was probably the first commercial application of the radar principie.tlietlie principle.first The first equipments were operated in aircraft as early as 1936 and utilized the same principle1936 Sec. 3.3. of operation as the FM-CW radar described in Sec. 3.3. In the case of the radio altimeter, thetlie ground. target is the ground .. In Brit.ain the development of radar began later than in the United States. S - 11 But111 13rit.aiti [lieit1 States.- because they felt the nearness of war more acutely and were in a more vulnerable position with felt effort respect to air attack, the British expended a large amount of effort on radar development. By the time the United States entered the war, the British were well experienced in the militarytlie applications of radar. British interest in radar began in early 1935, when Sir Robert Watson- applications 1935, Watt was asked about the possibility of producing a death ray using radio waves. Watson- Watt concluded that this type of death ray required fantastically large amounts of power and could he regarded as not being practical at that time. Instead, he recommended that it wouldbe recotnmended be more promising to investigate means for radio detection as opposed to radio destruction.destruction. (The only available means for locating aircraft prior to World War n were sound locators (Theaircraft IE whose maximum detection range under favorable conditions was about 20 miles.) Watson- Watt was allowed to explore the possibilities of radio detection, and in February, 1935, he 1935, effective issued two memoranda outlining the conditions necessary for an effective radar system. In that same month the detection of an aircraft was carried out, using 6-MHz communication equip- ment, by observing the beats between the echo signal and the directly received signal (wavetlie (wave interference). interference). The technique was similar to the first United States radar-detection experiments.experiments.miles. The transmitter and receiver were separated by about 5.5 miles. When the aircraft receded from the receiver, it was possible to detect the beats to about an 8-mile range. froinBy June, 1935, the British had demonstrated the pulse technique to measure range of an 1935, aircraft target. This was almost a year sooner than the successful NRL experiments with pulse radar. By September, ranges greater than 40 miles were obtained on bomber aircraft. The September, 12 frequency was 12 MHz. Also, in that month, the first radar measurement of the height of aircraft above ground was made by measuring the elevation angle of arrival of the reflected signal. In March, 1936, the range of detection had increased to 90 miles and the frequency was signal.1936,of raised to 25 MHz. CH HomejA series of CH (Chain Home) radar stations at a frequency of 25 MHz were successfullysuccessfully demonstrated in April, 1937. Most of the stations were operating by September, 1938, and 1937.September, 1938,,J plotted the track of the aircraft which flew Neville Chamberlain, the British Prime Minister atChamberlain, that time, to Munich to confer with Hitler and Mussolini. In the same month, the CH radar stations began 24-hour duty, which continued until the end of the war.The British realized quite early that ground-based search radars such as CH were not sufficiently accurate to guide fighter aircraft to a complete interception at night or in bad weather. Consequently, they developed, by 1939, an aircraft-interception radar (AI), mounted 1939, aircraft-interception aircraft, aircraft.A1 on an aircraft, for the detection and interception of hostile aircraft. The AI radar operated at aA1frequency of 200 MHz. During the development of the AI radar it was noted that radar couldbe used for the detection of ships from the air and also that the character of echoes from theground was dependent on the nature of the terrain. The former phenomenon was quicklyexploited for the detection and location of surface ships and submarines. The latter effect wasnot exploited initially, but was later used for airborne mapping radars. Until1940 tliein Unlil the middle of 1940 the development of radar in Britain and the United States was carried out independently of one another. In September of that year a British technical mission developmentsvisited the United States to exchange information concerning the radar developments in thetwo countries. The British realized the advantages to be gained from the better angularresolution possible at the microwave frequencies, especially for airborne and naval applica-tions. They suggested that the United States undertake the development of a microwave AIA1 20. 12 R A D A R SYSTEMS INTRODUCTION TO RADAR SYSTEMSradar and a microwave antiaircraft fire-control radar. The British technical miSSIonmissiondemonstrated the cavity-magnetron power tube developed by Randell and Boot and furnished manufacturers.design information so that it could be duplicated by United States manufacturers. The Randell10and Boot magnetron operated at a wavelength of 10 cm and produced a power output ofabout 1 kW, an improvement by a factor of 100 over anything previously achieved at cen-100cen-timeter wavelengths. The development of the magnetron was one of tile most importantwavelengths. thecontributions to the realization of microwave radar.radar. 1940.The success of microwave radar was by no means certain at the end of 1940. Therefore the States ServiceUnited States Service Laboratories chose to concentrate on the development of radars at thefrequencies,frequency (VHF)lower frequencies, primarily the very high frequency (VHF) band, where techniques andcomponents were more readily available. The exploration of the microwave region for radarapplication became the responsibility of the Radiation Laboratory, organized in November,1940,1940, under the administration of the Massachusetts Institute of Technology. developmentsIn addition to the developments carried out in the United States and Great Britain, radar Russia,was developed essentially independently in Germany, France, Russia, Italy, and Japan duringthe middle and late thirties. 12 The extent of these developments and their subsequent militarythirties.12 however.deployment varied, however. All of these countries carried out experiments with CW waveinterference,interference, and even though the French and the Japanese deployed such radars opera-opera-tionally, they proved of limited value. Each country eventually progressed to pulse radar value.operation and the advantages pertaining thereto. Although the advantages of the higherfrequencies recognized,frequencies were well recognized, except for the United States and Great Britain none of theothers deployed radar at frequencies higher than about 600 MHz during the war.frequencies600 war.several differentThe Germans deployed several different types of radars during World War II. Ground-11.based radars were avt,lilable for air search and height finding so as to perform ground control avgilable finding(GCI). shipboard, successfullyof intercept (GCI). Coastal, shipboard, and airborne radar were also employed successfully insignificant numbers. An excellent description of the electronic battle in World War 11 between I1lessonsbook " Instrllmetlts oj Darkness"the Germans and the Allies, with many lessons to offer, is the book" It~strtlrnerttsf Dcrrkt~ess"o by Price. 13 Price.I3energeticallyThe French efforts in radar, although they got an early start, were not as energetically supported as in Britain or the United States, and were severely disrupted by the German occupation in 1940. 12 The development of radar in Italy also started early, but was slow. There 1940.12slow.few were only relatively few Italian-produced radars operationally deployed by the time they left leftSeptember, 1943. the war in September, 1943. The work in Japan was also slow but received impetus from fromallies 1940 disclosures by their German allies in 1940 and from the capture of United States pulse radars1942. in the Philippines early in 1942. The development of radar in the Soviet Union was quite elsewhere.1941 similar to the experience elsewhere: By the summer of 1941 they had deployed operationally adefense number of 80-MHz air-search radars for the defense of Moscow against the German invasion. 14 Their indigenous efforts were interrupted by the course of the war. invasion.14 efforts Thus, radar developed independently and simultaneously in several countries just prior toseveral World War II. It is not possibleto single out any one individual as the inventor; there were 11. possible to many fathers of radar. This was brought about not only by the spread of radio technology to many coun~ries, but by the maturing of the airplane during this same time and the commoncountries,recognition of its military threat and the need to defend against it.. :; ,1.6 APPLICATIONS OF RADARRadar has been employed onthe ground, in the air, on the sea, and in space. Ground-hased onthe space. Ground-basedradar has been applied chiefly to the detection, location, and tracking of aircraft or spacetothetargets. Shipboard radar isused a~ anavigation aid and safet~ device to locate buoys, shore is used as a navigationsafety 21. THE NATURE OF RADAR13lines,ships.aircraft.lines. and other ships, as well as for observing aircraft. Airborne radar may be used to detectships,other aircraft, ships, or land vehicles, or itt may be used for mapping of land, storm avoidance,iavoidance,terrain avoidance, and navigation. In space, radar has assisted in the guidance of spacecraftand for the remote sensing of the land and sea.sea. The major user of radar, and contributor of the cost of almost all of its development, hasbeen the military: although there have been increasingly important civil applications, chieny chieflyfor marine and air navigation. The major areas of radar application, in no particular order ofniaririe tiavigation. niajorirnpo~ ta~icc, Ijrieflyareimportance. arc hriefly described below.Air. Traffic COlltrol (A TC). . Radars are employed throughout the world for the purpose ofAir Trclffic Corrtrol ( A T C )coritrollit~g tlic safely controlling air traffic en route and in the vicinity of airports. Aircraft and ground vclliculararetliearis vehicular traffic at large airports arc monitored by means of high-resolution radar. Radar st has been used with GCA (ground-control approach) systems to guide aircraft to a safe landing in bad weather. In addition, the microwave landing system and the widely used weather.ATC radar-beacon system are based in large part on radar technology.technology.Aircv-aft Nac~iqatiotl.The weather-avoidance radar used on aircraft to outline regions of preci-Aircr~fi Navigatioll.to pitation to the pilot is a classical form of radar. Radar is also used for terrain avoidance and terrain following. Although they may not always be thought of as radars, the radiofollowing.FM/CW altimeter (either FMjCW or pulse) and the doppler navigator are also radars. Sometimes ground-mapping radars of moderately high resolution are used for aircraft navigationpurposes.S},i" Safety. Radar is used for enhancing the safety of ship travel by warning of potentialShip Safety. collision with other ships, and for detecting navigation buoys, especially in poor visibility. ships,In terms of numbers, this is one of the larger applications of radar, but in terms of physicalI11 size and cost it is one of the smallest. It has also proven to be one of the most reliablesystems.radar systems. Automatic detection and tracking equipments (also called plot extractors)are commercially available for use with such radars for the purpose of collision avoi-dance.dance. Shore-based radar of moderately high resolution is also used for the surveillance ofliarbors as an aid to navigation.harborsSpace. Space vehicles have used radar for rendezvous and docking, and for landing on theSpace..docking,moon.moon. Some of the largest ground-based radars are for the detection and tracking ofsatellites. Satellite-borne radars have also been used for remote sensing as mentionedsatellites. Satcllitc-bornemeritioriedbelow.Remote Setrsirrg. A 11Rer~roteSellsillg. All radars are remote sensors; however, as this term is used it implies thesensing of geophysical objects, or the""environment." For some time, radar has been usedthe environment."as a remote sensor of the weather. It was also used in the past to probe the moon and the astronomy).planets (radar astronomy). The ionospheric sounder, an important adjunct for HF (short communications,wave) communications, is a radar. Remote sensing with radar is also concerned with Earth resources, which includes the measurement and mapping of sea conditions, water resources, ice cover, agriculture, forestry conditions, geological formations, and environ-agriculture, formations, mental pollution. The platforms for such radars include satelJites as weB as aircraft. niental satellites well Law Erfircentenr. In addition to the wide use of radar to measure the speed of automobileLa~vEnforcement. traffic by highway police, radar has also been employed as a means for the detection of intruders.Alilitnrv. Many of the civilian applications of radar are also employed by the military. TheMilitary.traditional role of radar for military application has been for surveillance, navigation, andsurveillance,for the control and guidance of weapons. It represents, by far, the largest use of radar. for far, 22. 14 INTRODUCTION TO RADAR SYSTEMS SYSTEMSREFERENCES 1. Guerlac, H. E.: "OSRD Long History," vol. V, Division 14, "Radar," available from Office of 1. Guerlac, vol. 14,OfficeTechnical Services, U.S. Department of Commerce. Services, 2. British Patent 13,170, issued to Christian Hiilsmeyer, Sept. 22, 1904, entitled" Hertzian-wave Project- 13,170, Hiilsmeyer, 1904,entitled "ing and Receiving Apparatus Adapted to Indicate or Give Warning of the Presence of a MetallicBody, Such as a Ship or a Train, in the Line of Projection of Such Waves." 3. Marconi, S. G.: Radio Telegraphy, Proc. IRE, vol. 10, no. 4, p. 237, 1922. IRE, vol. 10, 237, 1922. 4. Breit, G., and M. A. Tuve: A Test of the Existence of the Conducting Layer, Phys Rev., vol. 28, Phys. Rev., vol. 28,pp. 554-575, September, 1926. September, 1926. 5. 5. Englund, C. R., A. B. Crawford, and W. W. Mumford: Some results of a Study of Ultra-short-wave Mumford:Ultra-short-waveTransmission Phenomena, Proc. IRE, vol. 21, pp. 475-492, March, 1933.475-492,1933.CIS.1,981,884,Radio," C. Young, 6. U.S. Patent 1,981,884, "System for Detecting Objects by Radio," issued to A. H. Taylor, L. C. Young,and L. A. Hyland, Nov. 27, 1934. 1934. 7. Vieweger, A. L.: Radar in the Signal Corps, IRE Trans., vol. MIL-4, pp. 555-561, October, 1960.Vieweger,1960. Commission, Wireless World, vol. 58, 8. Origins of Radar: Background to the Awards of the Royal Commission, Wireless World, vol. 58,pp. 95-99, March, 1952.95-99, 1952. 9. Wilkins, F.: 9. Wilkins, A. F.: The Story of Radar, Research (London), vol. 6, pp. 434-440, November, 1953.(London), 1953.10. Rowe, A. P.: "One Story of Radar," Cambridge University Press, New York, 1948. A very readable10. Rowe, Radar," 1948. .i(Telecommunicationsdescription of the history of radar development at TRE (Telecommunications Research Establish-ment, England) and how TRE went about its business from 1935 to the end of World War II.1935 11.11."Three1957;11. Watson-Watt, Sir Robert: "Three Steps to Victory," Odhams Press, Ltd., London, 1957; "The Pulse ofRadar," The Dial Press, Inc., New York, 1959.Radar," 1959.12. Susskind, c.: "The Birth of the Golden Cockerel: The Development of Radar," in preparation12.C.:preparation.13.13. Price, A.: "Instruments of Darkness," Macdonald and Janes, London, 1977. 1977.14. Lobanov, M. M.: "Iz Proshlovo Radiolokatzii" (Out of the Past of Radar), Military Publisher of the14.Radar), Ministry of Defense, USSR, Moscow, 1969.Defense, 1969.15. IEEE Standard Letter Designations for Radar-Frequency Bands, IEEE Std 521-1976, Nov. 30, 1976.15. 521-1976, 30, 1976.16. Villard, O. G., k: The Ionospheric Sounder and Its Place in the History of Radio Science, Radio16. 0.Jr.:Science, Science, vol. 11, pp. 847-860, November, 1976. Science,11,847-860,1976. 23. CHAPTERTWO THE RADAR EQUATION2.1 PREDICTION OF RANGE PERFORMANCE2.1iThe simple form of the radar equation derived in Sec. 1.2 expressed the maximum radar range of radarRmu. in terms of radar and target parameters:R,,, Rmu. = [r~2Ae(J]1/4 (2.1) 41t SmlnP =where P,t = transmitted power, wattsG = antenna gain=A =A,r = antenna emective aperture, m2 effective m2 (J = a = radar cross section, m2m 2Smln =Smin = minimum detectable signal, wattsAll the parameters are to some extent under the control of the radar designer, except for thefor the (J.target cross section a. The radar equation states that if long ranges are desired, the transmitted iflongthe transmittedpower must be large, the radiated energy must be concentrated into a narrow beam (high concentrated beam (hightransmitting antenna gain), the received echo energy must be collected with a large antenna belarge antennaaperture (also synonymous with high gain), and the receiver must be sensitive to weak signals. to weak signals. In practice, however, the simple radar equation does not predict the range performance ofpredict performance ofactual radar equipments to a satisfactory degree of accuracy. The predicted values of radarof values of radarrange are usually optimistic. In some cases the actual range might be only half that predicted.1be only halfthat predicted.Part of this discrepancy is due to the failure of Eq. (2.1) to explicitly include the various lossesofinclude the various lossesthat can occur throughout the system or the loss in performance usually experienced when usually experienced whenelectronic equipment is operated in the field rather than under laboratory-type conditions.than under laboratory-type conditions. 4nother important factor that must be considered in the radai equation is the statistical or &.nother the radatis the statistical orunpredictable nature of several of the parameters. The minimum detectable signal S, and the of,,signal Smln and the~arget(Jtarget cross section cr are both statistical in nature and must be expressed in statistical terms.be in statistical terms. 24. 16 INTRODUCTION TO R A D A R SYSTEMS RADAR Other statistical factors which do not appear explicitly in Eq. (2.1) but which have an effectoneffect the radar performance are the meteorological conditions along the propagation path and thc propagation paththe performance of the radar operator, if one is employed. The statistical nature of these several of ifofparameters does not allow the maximum radar range to be described by a single number. Its byItsspecification must include a statement of the probability that the radar will detect a certainprobability radar willtype of target at a particular range. ofparticularIn this chapter, the simple radar equation will be extended to include most of the impor-most of the impor-tant factors that influence radar range performance. If all those factors affecting radar range performance. If factorsradar rangewere known, it. would be possible, in principle, to make an accuratc prediction of radaraccurate prediction of radarperforpance. But, as is true for most endeavors, the quality of the prediction is a function of perfoqnance. of prediction is a function ofthe amount of effort employed in determining the quantitative effects of the various pa- ofof the various pa-rameters. Unfortunately, the effort required to specify completely the effects of all radar pa-Unfortunately,effort of all radar pa-rameters to the degree of accuracy required for range prediction is usually not economicallyofpredictionnot economicallyjustified. A compromise is always necessary between what one would like to have and what whatto have and whatone can actually get with reasonable effort. This will be better appreciated as we proceedbe betteras we proceedthrough the chapter and note the various factors that must be taken into account. must be takenJA complete and detailed discussion of all those factors that influence the prediction ofAof that influence the prediction ofradar range is beyond the scope of a single chapter. For this reason many subjects will appear Forreason many subjects will appearto be treated only lightly. This is deliberate and is necessitated by brevity. More detailedby brevity. More detailed information will be found in some of the subsequent chapters or in the references listed at the ofin the references listed at the end of the chapter.of2.2 MINIMUM DETECTABLE SIGNAL. 6The ability of a radar receiver to detect a weak echo signal is limited by the noise energy that of weak signal limited by the noise energy thatoccupies the same portion of the frequency spectrum as doesthe signal energy. The weakest portion as does the energy. The weakestsignal the receiver can detect is called the minimum detectable signal. The specification of thecalled.minimum detectable signal. The specification of theminimum detectable signal is sometimes difficult because of its statistical nature and becausebecause of its statistical nature and becausethe criterion for deciding whether a target is present or not may not be too well defined. target present or not may not be too well defined.Detection is based on establishing a threshold level at the output of the receiver. If theDetectionlevel at the output of the receiver. If thereceiver output exceeds the threshold, a signal is assumed to be present. This is called thresholdto be present. This is called thresholddetection. Consider the output of a typical radar receiver as a function of time (Fig. 2.1). This radar receiver as a function of time (Fig. 2.1). Thismight represent one sweep of the video output displayed on an A-scope. The envelope has a the video output displayed on an A-scope. The envelope has afluctuating appearance caused by the random nature of noise. If a large signal is present suchby the random nature of noise. If a large signal is present suchas at A in Fig. 2.1, it is greater than the surrounding noise peaks and can be recognized on the Athan the surrounding noise peaks and can be recognized on thebasis of its amplitude. Thus, if the threshold level were set sufficiently high, the envelope would of if the threshold level were set sufficiently high, the envelope wouldnot generally exceed.the threshold if noise alone were present, but would exceed it if a strongexceed. threshold if noise alone were present, but would exceed it if a strongsignal were present. If the signal were small, however, it would be more difficult to recognize its present.Uthe were small, however, it would be more difficult to recognize itspresence. The threshold level mustbe low if weak signals are to be detected, but it cannot be so must.be low if weak signals are to be detected, but it cannot be solow that noise peaks cross the threshold and give a false indication of the presence of targets. peaks threshold and give a false indication of the presence of targets.The voltage envelope :of. Fig. 2.1 .is assumed to be from a matched-filter receiverlof Fig. 2.1 is assumed to be from a matched-filter receiver ,(Sec. 10.2). A matched filter is one designed to maximize the output peak signal to average (Sec. 10.2). A matched filter isdesigned to maximize the output peak signal to averagenoise (power) ratio. It has a frequency-response function which is proportional to the complexratio. It has a frequency-response function which is proportional to the complexconjugate of the signa1,spectrum. (This is not the same as the concept of" impedance match " ofsignalspectrum. (Thi.s is not the same as the concept of" impedance match"of circuit theory.) The ideal matched-filterreceiver cannot always be exactly realized in prac- of ideal matched-filter receiver cannot always be exactly realized in prac-tice, but it is possible to approach.it with practical receiver circuits. A matched filter for a radarbut possible to approach it with practical receiver circuits. A matched filter for a radartransmitting a rectangular-shaped .pulse is usually characterized by a bandwidth B approxi- transmitting rectangular-shaped .pulse is usually characterized by a bandwidth B approxi-mately the reciprocal of the pulse width 7, or Br = 1. The output of a matched-filter receiver isreciprocal of the pulse width f, or Br ;::: 1. The output of a matched-filter receiver is 25. THE RADAR EQUATION17 _Thresho~ve~ Threshold l e v e l , A Rms value of noiseQ)-0oo> Time- Time - -Fi~unFigure 2.1 Typical envelope orthe radar receiver output as a runction ortime. A , and B, and C represent of tilefunction of time. A, andsignal plus noise. ,4 and B would be valid detections, but C is a missed detection. A arid receivedthe cross correlation between the received waveform and a replica of the transmittedwaveform. Hence it does not preserve the shape of the input waveform. (There is no reason towish to preserve the shape of the received waveform so long as the output signal-to-noise ratio maximized.)is maximized.) us tlieLet liS return to the receiver output as represented in Fig. 2.1. A threshold level is estab-lished,lished. as shown by the dashed line. A target is said to be detected if the envelope crosses thetliethresliold. ifsigrialthreshold. If the signal is large such as at A, it is not difficult to decide that a target is present.I3uttlie B andatnplitudc. IlicBut consider the two signals at Band C, representing target echoes of equal amplitude. Thenoise voltage accompanying the signal at B is large enough so that the combination of signalpIlls noise exceeds the threshold. At C the noise is not as large and the resultant signal plusplustlireshold.noise does not cross the threshold. Thus the presence of noise will sometimes enhancerioisetlireshold.enhancethe detection of weak signals but it may also cause the loss of a signal which would otherwisebe detected.CriotWeak signals such as C would not be lost if the threshold level were lower. But too Iowalow athreshold increases the likelihood that noise alone will rise above the threshold and be takentliresholdsignal. afalse alarm.for a real signal. Such an occurrence is called afalse alarm. Therefore, if the threshold is set toolow, falselow. false target indications are obtained, but if it is set too high, targets might be missed. Theselection of the proper threshold level is a compromise that depends upon how important it isif a mistake is made either by (1) failing to recognize a signal that is present (probability of a(1)z miss)falselyfalse miss) or by (2) falsely indicating the presence of a signal when none exists (probability of a false alarm). alarm).When the target-decision process is made by an operator viewing a cathode-ray-tubedisplay, it would seem that the criterion used by the operator for detection ought to be arialogoussubconsciously.analogous to the setting of a threshold, either consciously or subconsciously. The chief differ- differ- tlie ence between the electronic and the operator thresholds is that the former may be determined with some logic and can be expected to remain constant with time, while the latters thresholdfixed. might be difficult to predict and may not remain fixed. The individuals performance as part of the radar detection process depends upon the state of the operators fatigue and motivation, astraining. well as training,The capability of the human operator as part of the radar detection process can be determined only by experiment. Needless to say, in experiments of this nature there are likely to be wide variations between different experimenters. Therefore, for the purposes of the preserit present discussion, the operator will be considered the same as an electronic threshold detec- tor, an assumption that is generally valid for an alert, trained operator.signal-to.noiseThe signal-to ,noise ratio necessary to provide adequate detection is one of the important 26. 18 INTRODUCTION TO RADAR SYSTEMSparameters that must be determined in order to compute the minimum detectable signal. comptitesignal,Although the detection decision is usually based on measurements at the video otrtput, it isoutput,easier to consider maximizing the signal-to-noise ratio at the output of the IF amplifier ratherofthan in the video. The receiver may be considered linear irp to the output of the IF. I t is shown video.upofIt 3by Van Vleck and Middleton that maximizing the signal-to-noise ratio at the output of the IF Vieck Middleton3 ofis equivalent to maximizing the video output. The advantage of considering the signal-to-noiseis equivalentIF isratio at the IF is that the assumption of linearity may be made. It is also assumed that the IFratiofilter characteristic approximates the matched filter, so that the oirtput signal-to-noise ratio isfilterfilter,outputmaximized.2.3 RECEIVER NOISE2.3 RECEIVERSince noise is the chief factor limiting receiver sensitivity, it is necessary to obtain some meansSinceisof describing it quantitatively. Noise is unwanted electromagnetic energy which interferes with quantitatively.the ability of the receiver to detect the wanted signal. It may originate within the receiver itself,the to Ifor it may enter via the receiving antenna along with the desired signal. If the radar were tooperate in a perfectly noise-free environment so that no external sources of noise accompanied ofthe desired signal, and if the receiver itself were so perfect that it did not generate any excessthesignal,noise, there would still exist an unavoidable component of noise generated by the thermal an ofmotion of the conduction electrons in the ohmic portions of the receiver input stages. This is conductionelectronsofcalled thermal noise, or Johnson noise, and is directly proportional t o the temperature of the orto ofb a n d ~ i d t 60 Theohmic portions of the circuit and the receiver bandwidth.h . ~available thermal-noise powerohmic B,generated by a receiver of bandwidth BII (in hertz) at a temperature T (degrees Kelvin) is atTequalequal to = kTB II Available thermal-noise power = kTB, (2.2)(2.2)where k = Boltzmanns constant = 1.38 x 10- 23 J/deg. If the temperatiire T is taken to be== 1.38Jjdeg. Iftemperature bl: K,290 K, which corresponds approximately to room temperature (62"F), the factor kT is to (62F),kT4 x 10- 21 WjHz of bandwidth. If the receiver circuitry were at some other temperature, ttie lo-" W/Hz thl:thermal-noise power would be correspondingly different. A receiver with a reactance input such as a parametric amplifier need not have any ::!significant ohmic loss. The limitation in this case is the thermal noise seen by the antennii andinthe ohmicline.the ohmic losses in the transmission line. For radar receivers of the superheterodyne type (the type of receiver used for most radarreceiversapplications), the receiver bandwidth is approximately that of the intermediate-freqire~lcyapplications), intermediate-frequencystages. B,stages. It should be cautioned that the bandwidth BII of Eq. (2.2) is not the 3-dB, or half-power, half-power.bandwidth commonly employed by electronic engineers. It is a n integrated bandwidth and is anbandwidthgiven by( IH(f) 12 df B = . - all H(fo) 2 II 1(2.3)where H(f) = frequency-response characteristic of I F amplifier (filter) and fo = frequency of H(f ) = frequency-response IF fo =ofmaximum response (usually occurs at midband). H(f is normalized t o When H(f)) is normalized. to unity at midband (maximum-response frequency), frequency).H (fo) = 1. The bandwidth B II is called,the noise bandwidth and is the bandwidth of an equiva-H(fo)= 1. Bn called the bandwidth oflent rectangular filter whose noise~poweroutput is the same as the filter with characteristicnoise-power output 27. THE RADAR EQUATIONTHE RADAR EQUATION 19 1911(1), The J-t1B handwidthi t li tsl defined as the separation in hertz hetween the points on theI ! ( / ) 1 lic 3-ti13 I ~ i ~ r ~ t l w is itlcfirictl as tlic scparntioti it1 licrtz betwceri tlie poitits oti tlicfrequency-response characteristic whcrc thc responsc is reduced to 0.707 (3 dB) from its maxi-frequericy-resi~otisccliaractcristic wliere the response is reduced to 0.707 (3 dB) fro111its r~iaxi- nlilm valric. Tllc 3-dl3 t~i~ndwicith widely i~sed,mUIll valuc. Thc 3-d B handwidth is widely lIscd. since it is easy to measure. The measurementis since it is easy to measure. The meastire~nentof noise bandwidth. however. involves a complctcknowlcdge of the respollse charactcristicof rioisc t)aridwicftli. I~owcvcr,irivolves a coriiplete knowledge of tlie resporrse cliaractet.istic /-1(/).). The frequcncy-responsc characteristics of many practical radar receivers are such thatN ( / Tlie rreqiicncy-response cliaracteristics of many practical receivers are suchtlic 3-dl3 i ~ r i tlic tioisc I~nt~tlwidtlis riot differ appreciably. Tlierefore tlie 3-dl3 I~itnciwidtlithc 3-dB and c ithe noise handwidths do 1I0t differ appreciahly. Therefore the 3-dB bandwidth tlomay be used in many cases as an approximation to the noise bandwidth. 2rnay be used in niatiy cases as an approximation to the rioise bandwidth.The noise power in practical receivers is often greater than canThe noise power in practical receivers is often greater than can be accounted for by accounted for thertnal noise alone. The additional noise cotnpotlents are due tothermal noise alone. The additional noise components are due to mechanisms other than the than thetlierrnal agitation of tlie conduction electrons. For purposes of thethermal agitation of the conduction electrons. For purposes of the present discussion.discussion,tiowever, the exact origin of tlie extra noise components is not important except tohowever, the exact origin of the extra noise components is not important except to know thatit exists. N o matter whether the noise is generated by a thermalit exists. No matter whether the noise is generated by a thermal mechanism or by some other orsome mechanism. tile total tloise at tlie output of the receiver may be considered t o equal t omechanism. the total noise at the output of the receiver may be considered to be equal to the thermal-noise power obtained from an " ideal " receiver multiplieda factorthermal-noise power obtained from an " ideal" receiver multiplied by a factor called the "oisethe iroisefig~rre.The noise figure Fn of a receiver is defined by the equationfigure. The noise figure F n of a receiver is defined by the equationi rI: =~!-__ =N = ----"-.. -- noise out of practical receivertloise out of practical (2.40) (2.4a) " nkTo BnG,kToBnG onoise out of ideal receiver at std temp Tonoise out of ideal receiver at std temp Towhere No = noise output from receiver, and Go = available gain. The standard temperature To where No = rioise output from receiver, and G, = available gain. The standard temperature To is taken to be 290 K according to the Institute of Electrical and Electronics Engineersis taken to be 290 K., according to the Institute of Electrical and Electronics Engineers definition. Tlie noise No is measured over the linear portion of the receiver input-outputdefinition. The 1I0ise No is mcasured over the linear portion of the receiver input-output characteristic, usually at the output of tlie IF amplifier before the nonlinear second detector.characteristic. usually at the output of the IF amplifier before the nonlinear second detector. The receiver bandwidth Bn is that of tlie IF aniplifier in most receivers. The available G, isThe receiver bandwidth B n is that of the IF amplifier in most receivers. The available gain Go isthe ratio of the signal out So to the signal in Sj, and kTo Bn is the input noise N jiin an ideal tlie ratio of the signal out So to the signal in Si, and kTo Bn is the input noisein anreceiver. Equation (2.40) may be rewritten asreceiver. Equation (2.4a) may be rewritten as (2.4b)The noise figure may be interpreted, therefore, as a measure off the degradation of signal-to-The noise figure may be interpreted, therefore, as a measure o the degradation of signal-to-noise-ratio as the signal passes through the receiver.noise-ratio as the signal passes through the receiver.j Rearranging Eq. (2.417). the input signal may be expressed as Rearranging Eq. (2.4"). the input signal may be expressed as(2.5)Iff the minimum detectable signal Smln is that value of SIIcorresponding to the minimum ratio of I the minimum detectable signal S,,, is that value of S corresponding to the minimum ratio ofoutput (IF) signal-to-noise ratio ( S