introduction to radar systems1 2nd

1. INTRODUCTION TO RADAR SYSTEMS Second Edition Merrill I. Skolnik McGRAW-HILL BOOK COMPANY Auckland Bogotii Guatemala Hamburg Lisbon London Madrid Mexico New Delhi Panama Paris San Juan S5o Paulo Singapore Sydney Tokyo

2. INTRODUCTIONTO RADAR SYSTEMS International Edition 1981 Exclusive rights by McGraw-Hill Book Co.--Singapore for manufactureand export.This book cannot be re-exported from the country to which it is consigned by McGraw-Hill. Copyright @ 1980,1962by McGraw-Hill, Inc. All rights reserved. Except as permitted under the United States Copyright Act of 1976,no part of thispublication may be reproduced or distributed in any form or by anymeans, or stored in a data base or retrieval system, without the prior written permission of the publisher. This book was set in Times Roman. The editor wasFrank J. Cerra. The production supervisorwas Gayle Angelson. Library of Congress Cataloging in PubilcationData Skolnik,Merrill Ivan,date Introduction to radar systems. Includesbibliographical references and index. 1. Radar. I. Title. 11. Series. TK6575S477 1980 621.3848 79-15354 ISBN 0-07-057909-1 When orderingthis title use ISBN 0-07-066572- 9 Printed in Singapore

3. CONTENTS Preface 1 The Nature of Radar 1.1 lntroductiorl 1.2 *l'lleSirnple Fortn of the Kadar Equatiorl 1.3 Radar Hlock Diagram and Operation 1.4 Radar Frequencies 1.5 Radar Dcvcloprnent Prior to World War I1 1.6 Applications of Kadar References The Radar Equation Prediction of Range Performance Mirlimurn Detectable Signal Receiver Noise Probability-density Functions Signal-to-noise Ratio Integration of Radar Pulses Radar Cross Sectiorl of Targets Cross-section Fluctuations Transmitter Power Pulse Repetition Frequency and Range Ambiguities Antenna ~aramete'rs System Losses Propagation Effects Other Consideratiorls Refererlces 3 CW and Frequency-Modulated Radar 2.1 Tile Iloppler Effect 3.2 CW Radar 3.3 Frequency-modulated CW Radar

4. Airl>or-neDoppler Navigation Multiple-Frequency CW Radar References MTI and Pulse Doppler Radar Introd~iction Delay-Line Cancelers Multiple, or Staggered, Pulse Repetition Freqiirncics Range-Gated Doppler Filters Digital Signal Processing Other MTI Delay Lines Example of an MTI Radar Processor Limitations to MTI Performance Noncoherent MTI Pulse Doppler Radar MTI from a Moving Platform Other Types of MTI References Tracking Radar Tracking with Radar Sequential Lobing Conical Scan Monopulse Tracking Radar Target-Reflection Characteristics and Angular Accuracy Tracking in Range Acquisition Other Topics Comparison of Trackers Tracking with Surveillance Radar References Radar Transmitters Introduction The Magnetron Oscillator Klystron Amplifier Traveling-Wave-Tube Amplifier Hybrid Linear-Beam Amplifier Crossed-Field Amplifiers Grid-Controlled Tubes Modulators Solid-State Transnlitters References Radar Antennas Antenna Parameters Antenna Radiation Pattern and Aperture Distribution Parabolic-Reflector Antennas Scanning-Feed Reflector Antennas Lens Antennas

5. CONTENTS vii 7.6 Pattern Sy~~rlicsis 7.7 Cosecarit-Squared Arttenna Pattern 7.8 i:fTccl of Errors on Radiatiot~Patterns 7.9 Kadomcs 7.10 Stabili7ation of Antcnnas f~cfcrcrlccs 8 l'lle Electrot~icallySteered Phased Array A t I Radar I r r l r otlr~ctior~ 1t:tsic ('or~ccl>ts I ' I ~ ~ ~ S C .sl1irlct.s I,'requc~~cy-Scar1Arritys Array Illcnierits l'cccls for Arrays Sil~lultarlcousMultil>lc13ea1lisfrom Array Ariterllias Random Errors in Arrays Computer Control of Phased-Array Radar Otlicr Array Topics Applications of the Array in Radar Advantages arid Limitations Kcfcrcl~ccs Receivers, Displays, and Duplexers The Radar Receiver Noise Figure Mixers Low-Noise Front-Erids [)isplays 1)uplexers and Receiver Protectors References Detectiotl of Radar Signals in Noise Introductiot~ Matched-Filter Receiver Correlation Detectiori Detection Criteria Detector Cliaracteristics Performance of the Radar Operator Automatic Detection Constant-False-Alarm-Rate (CFAR) Receiver References 11 Extractio~~of Information and Waveform Design 11.1 Introduction 11.2 Information Available from a Radar 1 1.3 Theoretical Accuracy of Radar Measurements 1 1.4 Ambiguity Diagram

6. viii CONTENTS 11.5 Pulse Compression 11.6 Classification of Targets with Radar References Propagation of Radar Waves Introduction Propagation over a Plane Earth The Round Earth Refraction Anomalous Propagation Diffraction Attenuation by Atmospheric Gases Environmental Noise Microwave-Radiation Hazards References Radar Clutter Introduction to Radar Clutter Surface-Clutter Radar Equations Sea Clutter Detection of Targets in Sea Clutter Land Clutter Detection of Targets in Land Clutter Effects of Weather on Radar Detection of Targets in Precipitation Angel Echoes References Other Radar Topics Synthetic Aperture Radar HF Over-the-Horizon Radar Air-Surveillance Radar Height-Finder and 3D Radars Electronic Counter-Countermeasures Bistatic Radar Millimeter Waves and Beyond References Index

7. PREFACE Although tlie fundamentals of radar have changed little since the publication of the first 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 extensive revisions arid tlie introduction of topics not found in the original. One of the major changes is in the treatment of MTI (moving target indication) radar (Chap. 4). Most of the basic MTI concepts Gat have been added were known at the time of tlie first edition, but they had not appeared in the open literature nor were they widely used i11 practice. Inclusion in the first edition would have'been largely academic since the analog delay-line technology available at that time did not make it practical to build the sophisticated signal processors that were theoretically possible. However, subsequent advances in digital technology, originally developed for applications other than radar, have allowed the practical implementation of the multiple delay-line cancelers and multiple pulse-repetition-frequency MTI radars indicated by the basic MTI theory. Automatic detection and tracking, or ADT (Secs. 5.10 and 10.7). is another important evelopment whose basic theory was known for some time, but whose practical realization ad to await advances in digital technology. The principle of ADT was demonstrated in the early 1950s. using vacuum-tube technology, as part .of the United States Air Force's SAGE air-defense system developed by MIT Lincoln Laboratory. In this form ADT was physically large, expensive, and difficult to maintain. The commercial availability in the late 1960sof the solid-slate minicomputer, however, permitted ADT to be relatively inexpensive, reliable, and of sniall size so that it can be used with almost any surveillance radar that requires it. Anotlcr radar area that has seen much development is that of the electronically steered ptiased-array antenna. In tlie first edition, the radar antenna was the subject of a single cliaptcr. I11 tliis edition, one chapter covers the conventional radar antenna (Chap. 7) and a separate chapter covers the phased-array antenna (Chap. 8). Devoting a single chapter to the array antenria is inore a reflection of interest rather than recognition of extensive application. The chapter o ~ iradar clutter (Ctiap. 13) has been reorganized to include methods for the detection of targets in the presence of clutter. Generally, the design techniques necessary for ttie detection of targets in a clutter,background are considerably different from.those necessary for detection in a noise background. Other subjects that are new or which have seen significant cliaiiges in the current edition include low-angle tracking, "on-axis" tracking, solid-state RF ources, the mirror-scan antet~na,antenna stabilization, computer control of phased arrays, olid-state duplexers, CFAR, pulse compression, target classification, synthetic-aperture radar, ver-the-horizon radar, air-surveillance radar, height-finder and 3D radar, and ECCM. The bistatic radar and millimeter-wave radar are also included even though their applications have

8. X PREFACE been limited. Omitted from this second edition is the chapter on Radar Astronomy since interest in this sub.ject has dccrcascti with tltc i~vi~ilithilityo f space prolws tlliil cilll explore ttlc planets at close range. The basic material of the first edition that covers the radar equation, the detection of signals in noise, the extraction of information, and the propagation of radar waves has not changed significantly. The reader, ttowcvcl., wilt find only a fcw pagcs of 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~sionof extensive references at the end of each chapter. These are provided to acknowlcdgc the sources 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 represented a large fraction ofthose available at the time. It woilld have been difficult to add to them 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 smaller proportion of what is available could be cited. In addition to changes in radar technology, there have been changes also in style and nomenclature. For example, db has been changed to dB, and Mc is replaced by M i i ~ .Also, t he letter-band nomenclature widely employed by the radar engineer for designating the common radar frequency bands (such as L, S, and X) has been officially adopted as a standard by the IEEE. The material in this book has been used as the basis for a graduate course in radar taught by the author at the Johns Hopkins .University Evening College and, before that, at several other institutions. This course is different from those usually found in most graduate electrical engineering programs. Typical EE courses cover topics related to circuits, components, devices, and techniques that might make up an electrical or electronic system; but seldom is the student exposed to the system itself. It is the system application (whether radar, communications, navigation, control, information processing, or energy) that is the raison d'itre for the electrical engineer. The course on which this book is based is a proven method for introducing the student to the subject of electronic systems. It integrates and applies the basic concepts found in the student's other courses and permits the inclusion of material important to the practice of electrical engineering not usually found in the traditional curriculum. Instructors of engineering courses like to use texts that contain a variety of problems that can be assigned to students. Problems are not included in this book. Althoirgh the author assigns problems when using this book as a text, they are not considered a major learning technique. Instead, the comprehensive term paper, usually involving a radar design problem or a study in depth of some particular radar technology, has been found to be a better means for having the student reinforce what is covered in class and in the text. Even more important, it allows the student to research the literature and to be a bit more creative than is possible by simply solving standard problems. A book of this type which covers a wide variety of topics cannot be written in isolation. It would not have been possible,without'themany contributions on radar that have appeared in the open literature and which have been used here as the basic source -material. A large measure of gratitude must be expressed to those radar engineers who have taken the time anci energy to ensure that the results :of their work were made available by publication ill recognized journals. I . On a more personal note, neither edition of this book could have been written without the complete support and patience of my wife Judith and my entire family who allowed me tllc time necessary to undertake this work. Merrill 1. Skolrlik

9. CHAPTER ONE THE NATURE RADAR 1.1 INTRODUCTION Radar is an electromagnetic system for the detection and location of objects. It operates by transmitting a particular type of waveform, a pulse-modulated sine wave for example, and detects the nature of the echo signal. Radar is used to extend the capability of one's senses for observing the environment, especially the sense of vision. The value of radar lies not in being a si~hstitutefor the eye, but in doing what the eye cannot do-Radar cannot resolve detail as well the eye, nor is it capable of recognizing the "color" of objects to the degree of sophistication which the eye is capable. However, radar can be designed to see through those conditions irnpervioris to normal human vision, such as darkness, haze, fog, rain, and snow. In addition, radar has the advantage of being able to measure the distance or range to the object. This is probably its most important attribute. An elementary form of radar consists of a transmitting antenna emitting electromagnetic radiation generated by an oscilIator of some sort, a receiving antenna, and an energy-detecting device. or receiver. A portion of the transmitted signal is intercepted by a reflecting object (target)and is reradiated in all directions. 1.t is the energy reradiated in the back direction that is of prime interest to the radar. The receiving antenna collects the returned energy and delivers it to a receiver, where it is processed to detect the presence of the target and to extract its location and relative velocity. The distance to the target is determined by measuring the time taken for the radar signal to travel to the target and back. The direction, or angular position, of the target may be determined from the direction of arrival of the reflected wave- front. The usual method of measuring the direction of arrival is with narrow antenna beams. If relative motion exists between target and radar, the shift in the carrier frequency of the reflected wave (doppler effect) is a measure of the target's relative (radial) velocity and may be used to distinguish moving targets from stationary objects. In radars which continuously track the movement of a target, a continuous indication of the rate of change of target position is also available. 1

10. 2 INTRODUCTION TO RADAR SYSTEMS The name radar reflects the emphasis placed by the early experimenters on a device to detect the presence of a target and measure its range. Radar is a contraction of the words radio detection and ranging. It was first developed as a detection device to warn of the approach of hostile aircraft and for directing antiaircraft weapons. Although a well-designed modern radar can usually extract more information from the target signal than merely range, the measurement of range is still one of radar's most important functions. There seem to be no other competitive 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- lating a sinewave carrier. The distance, or range, to the target is determined by measuring the time TRtaken by the pulse to travel to the target and return. Since electromagnetic energy propagates at the speed of light c = 3 x 10' m/s, the range R is The factor 2 appears in the denominator because of the two-way propagation of radar. With the range in kilometers or nautical miles, and TRin microseconds, Eq. (1.1) becomes Each microsecond of round-trip travel time corresponds to a distance of 0.081 nautical mile, 0.093 statute mile, 150 meters, 164 yards, or 492.feet. Once the transmitted pulse is emitted by the radar, a sufficient length of time must elapse to allow any echo signals to return and be detected before the next pulse may be transmitted. Therefore the rate at which the pulses may be transmitted is determined by the longest range at which targets are expected. If the pulse repetition frequency is too high, echo signals from some targets might arrive after the transmission of the next pulse, and ambiguities in measuring I I . . . Pulse repetition' frequency, Hz Figure 1.1 Plot of maximum unambiguous range as a function of the pulse repetition frequency.

11. THE NATURE OF RADAR 3 range might result. Echoes that arrive after the transmission of the next pulse are called secorrd-tinte-arotrrtd (or multiple-time-around) echoes. Such an echo would appear to be at a much shorter range than the actual and could be misleading if it were not known to be a second-time-around echo. The range beyond which targets appear as second-time-around echoes is called the rna.uintttrn trr~arnhigtrousrattge and is where./, = pulse repetition frequency, in Hz. A plot of the maximum unambiguous range as a function of pulse repetition frequency is shown in Fig. 1.1. Although the typical radar transmits a simple pulse-modulated waveform, there are a number of other suitable modulations that might be used. The pulse carrier might be frequency- or phase-modulated to permit the echo signals to be compressed in time after reception. This achieves the benefits of high range-resolution without the need to resort to a . short pulse. The technique of using a long, modulated pulse to obtain the resolution of a short pulse, but with the energy of a long pulse, is known as pulse compression. Continuous waveforms (CW) also can be used by taking advantage of the doppler frequency shift to separate the received echo from the transmitted signal and the echoes from stationary clutter. Unmodulated CW waveforms do not measure range, but a range measurement can be made by applying either frequency- or phase-modulation. 1.2 THE SIMPLE FORM OF THE RADAR EQUATION The radar equation relates the range of a radar to the characteristics of the transmitter, receiver, antenna, target, and environment. It is useful not just as a means for determining the maximum distance from the radar to the target, but it can serve both as a tool for under- standing radar operation and as a basis for radar design. In this section, the simple form of the radar equation is derived. I f the power of the radar transmitter is denoted by P,, and if an isotropic antenna is used (one which radiates uniformly in all directions), the power density (watts per unit area) at a distance R from the radar is equal to the transmitter power divided by the surface area 4nR2of an imaginary sphere of rapius R, or pt Power density from isotropic antenna = - 4nR2 Radars employ directive antennas to channel, or direct, the radiated power Pt into some particular direction. The gain G ofan antenna is a measure of the increased power radiated in the direction of the target as compared with the power that would have been radiated from an isotropic antenna. It may be defined as the ratio of the maximum radiation intensity from the subject antenna to the radiation intensity from a lossless, isotropic antenna with the same power input. (The radiation intensity is the power radiated per unit solid angle in a given direction.) The power density at the target from an antenna with a transmitting gain G is Pt GPower density from directive antenna = - 4nR2 The target intercepts a portion of the incident power and reradiates it in vqrious directions.

12. 4 INTRODUCTION TO RADAR SYSTEMS The measure of the amount of incident power intercepted by the target and reradiated back in the direction of the radar is denoted as the radar cross section a,and is defined by the relation P,G a Power density of echo signal at radar = ---- - 4nR24nR2 The radar cross section a has units of area. It is a characteristic of the particular target and is a measure of its size as seen by the radar. The radar antenna captures a portion of the echo power. If the effective area of the receiving antenna is denoted A., the power P, received by the radar is The maximum radar range Rmaxis the distance beyond which the target cannot be detected. It occurs when the received echo signal power P, just equals the minimum detectable signal S,,, . Therefore 1 This is the fundamental form of the radar equation. Note that the important antenna parameters are the transmitting gain and the receiving effective area. Antenna theory gives the relationship between the transmitting gain and the receiving effective area of an antenna as Since radars generally use the same antenna for both transmission and reception, Eq. (1.8)can be substituted into Eq. (1.7), first for A, then for G, to give two other forms of the radar equation These three forms (Eqs. 1.7, 1.9, and 1.10) illustrate the need to be careful in the inter- pretation of the radar equation. For example, from Eq. (1.9) it might be thought that the range of a radar varies as All2,but Eq. (1.10) indicates a 1-'12 relationship, and Eq. (1.7) shows the range to be independent of 1.The correct relationship depends on whether it is assumed the gain is constant or the effective area is constant with wavelength. Furthermore, the introduction 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 performance 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 be predicted by the above equations, sometimes by as much as a factor of two. There are many reasons for the failure of the simple radar equation to correlate with actual performance, as discussed in Chap. 2. _ , 9 , 1 1 ' .

13. T H E N A T U R E OF RADAR 5 1.3 RADAR BLOCK DIAGRAM AND OPERATION Ttle operation of a typical pulse radar may be described with the aid of the block diagram shown in Fig. 1.2. Tlle transtnitter may be an oscillator, such as a magnetron, that is " pulsed" (turned on and on) by the rnodulator to generate a repetitive train of pulses. The magnetron has prohnhly been the most widely used of the various microwave generators for radar. A typicrtl radar for tile dctcction of aircraft at ranges of 100 or 200 nmi might employ a peak power of the order of a megawatt, an average power of several kilowatts, a pulse width of several microseconds, and a pulse repetition frequency of several hundred pulses per second. The waveform generated by the transmitter travels via a transmission line to the antenna, where it is radiated into space. A single antenna is generally used for both transmitting and receiving. The receiver must be protected from damage caused by the high power of the transmitter. This is the function of the duplexer. The duplexer also serves to channel the returned echo signals to the receiver and not to the transmitter. The duplexer might consist of 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 the echo signal to the receiver during reception. Solid-state ferrite circulators and receiver protectors with gas-plasma TR devices and/or diode limiters are also employed as duplexers. The receiver is usually of the superheterodyne type. The first stage might be a low-noise RF amplifier, such as a parametric amplifier or a low-noise transistor. However, it is not always desirable to employ a low-noise first stage in radar. The receiver input can simply be 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 have greater dynamic range, less susceptibility to overload, and less vulnerability to electronic interference. The mixer and local oscillator (LO)convert the RF signal to an intermediate frequency (IF).A " typical" IF amplifier for an air-surveillance radar might have a center frequency of 30 or 60 MHz and a bandwidth of the order of one megahertz. The IF amplifier should be designed as a n~atcltedfilter; i.e., its frequency-response function H ( f ) should maximize the peak-sigtial-to-mean-noise-powerratio at the output. This occurs when the magnitude of the frequency-response function 1H ( f ) ( is equal to the magnitude of the echo signal spectrum IS(.f')1, and the phase spectrum of the matched filter is the negative of the phase spectrum of the echo signal (Sec. 10.2). In a radar whose signal waveform approximates a rectangular pulse, the conventional IF filter bandpass characteristic approximates a matched filter when the product of the IF bandwidth B and the pulse width r is of the order of unity, that is, Bt -1. After maximizing the signal-to-noise ratio in the IF amplifier, the pulse modulation is extracted by the second detector acd amplified by the video amplifier to a level where it can be Tronsrnitler Pulse modulalor 4 Low - noise RF Mixer amplifier I.. Figure 1.2 Block diagram of a pulse radar.

14. Figure 1.3 (a) PPI presentation displaying range vs. angle (intensity modulation); ( h ) A-scope presentation displaying amplitude vs. range (deflection modulation)."4 properly displayed, usually on a cathode-ray tube (CRT).Timing signals are also supplied to the indicator to provide the range zero. Angle information is obtained from the pointing direction of the antenna. The most common form of cathode-ray tube display is the plan position indicator, or PPI (Fig. 1.3a), which maps in polar coordinates the location of the target in azimuth and range. This is an intensity-modulated display in which the amplitude of the receiver output modulates the electron-beam intensity (z axis)as the electron beam is made to sweep outward from the center of the tube. The beam rotates in angle in response to the antenna 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 intensity modulated, have limited dynamic range. Another form of display is the A-scope, shown in Fig. 1.3b, which plots target .amplitude (y axis) vs. range (x axis), for some fixed direction. This is a deflection-modulated display. It is more suited for tracking-radar application 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 receiver for changes in frequency (AFC)or gain (AGC),receiver circuits for reducing interference from other radars and from unwanted signals, rotary joints in the transmission lines to allow movement of the antenna, circuitry for discriminating between moving targets and unwanted stationary objects (MTI),and pulsecompression for achievingthe resolution benefits of a short pulse but with the energy of a 'long pulse. If the radar is used for tracking, some 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 usually included to ensure that the transmitter is delivering the proper shape pulse at the proper power level and that the receiver sensitivity has not degraded. Provisions may also be in- corporated in the radar for locating equipment failures so that faulty circuits can be easily found and replaced. Instead of displaying the "raw-video" output of a surveillance radar directly on the CRT, it might first be processed by an'autornaticdetection and tracking (ADT)device that quantizes the radar coverage into range-azimuth resolution cells, adds (or integrates) all the echo pulses received within each cell, establishes a threshold (on the basis of these integrated pulses) that permits only the strong outputs due to target echoes to pass while rejecting noise, establishes and maintains the tracks (trajectories) of each target, and displays the processed information

15. THE NATURE OF RADAR 7 to the operator. These operations of an ADT are usually implemented with digital computer techriology. A common form of radar antenna is a reflector with a parabolic shape, fed (illuminated) from a point source at its focus. The parabolic reflector focuses the energy into a narrow beam, 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 pllascd array, tllc bcam is scanned by electronically varying the phase of the currents across the aperture. 1.4 RADAR FREQUENCIES Conventional radars generally have been operated at frequencies extending from about 220 MHz to 35 GHz, a spread of more than seven octaves. These are not necessarily the limits, . , since radars can be, and have been, operated at frequencies outside either end of this range. Skywave H F over-the-horizon (OTH)radar might be at frequenciesas low as 4 or 5 MHz, and groundwave H F radars as low as 2 MHz. At the other end of the spectrum, millimeter radars have operated at 94 GHz. Laser radars operate at even higher frequencies. The place of radar frequencies in the electromagnetic spectrum is shown in Fig. 1.4.Some 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 desigr~ateradar frequency bands. Although its original purpose was to guard military secrecy, the designations were maintained, probably out of habit as well as the need for some convenient short nomenclature. This usage has continued and is now an accepted practice of radar engineers. Table 1.1 lists the radar-frequency letter-band nomenclature adopted by the IEEE.' These are related to the specific bands assigned by the International Telecommunica- 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 1215to 1400 MHz since that is the extent of the assigned band. Letter-band nomenclature is not a Wovelenath 3 0 H z 3 0 0 H z 3kHz 30kHz 3 0 0 k H z 3 M H z 3 0 M H z 3 0 0 M H z 3GHz 30GHz 300GHz 3,000 GHr Frequency 10 km l k m 100 m 1 0 m Im lOcm t c m 1mm O . l n m Figure 1.4 Radar frequencies and the electromagnetic spectrum. UHF---c+SHF-+k Super high frequency Centimetric woves I- V L F Very low frequency I Myriometric woves -+HF-t-VHF-+ High frequency Decometric waves 4 E H F --+ Extremely hrgh frequency Millimetric waves --LF-+-MF Low frequency Kilometric woves 1 I I I Bond 7 Very high frequency Metric woves Decimilli- metric woves Medium frequency Hectometric woves Video frequencies Ultrohigh frequency Decimetric wovcs Bond 4 Audio frequencies c Bond 8 I Bond 9 Bond 10 Bond l l mdgf r w Bond 12 Submillimeler Bond 5 IFor in f m m Bond 6 t------* IOTH rodor I Letter designotions L S C X Ku Ka * I Microwove region I

16. 8 INTRODUCTION TO RADAR SYSTEMS Table 1.1 Standard radar-frequency letter-band nomenclature Specific radiolocatio~l Band Nominal (radar) bands based on designation frequency range ITU assignments for region 2 HF VHF UHF K K , rnrn 138-144 MHz 216-225 420-450 MHz 890-942 1215-1400 MHz 2300-2500 MHz 2700-3 700 5250-5925 MHz 8500- 10,680 MHz 13.4-14.0 GHz 15.7- 17.7 24.05-24.25 GHz 33.4-36.0 GHz substitute for the actual numerical frequency limits of radars. The specific numerical frequency limits should be used whenever appropriate, but the letter designations of Table 1.1 may be used whenever a short notation is desired. 1.5 RADAR DEVELOPMENT PRIOR TO WORLD WAR I1 Although the development of radar as a full-fledged technology did not occur until World War 11, the basic principle of radar detection is almost as old as the subject of electromagnetism itself. Heinrich Hertz, in 1886,experimentally tested the theories of Maxwell and demonstrated the similarity between radio and light waves. Hertz showed that radio waves could be reflected L ,I by metallic and dielectric bodies. It is interesting to note that although Hertz's experiments were performed with relatively short wavelength radiation (66 cm), later work in radio engineering was almost entirely at longer wavelengths. The shorter wavelengths were not actively used to any great extent until the late thirties. In 1903a German engineer by the name of Hiilsmeyer experimented with the detection of radio waves reflected from ships. He obtained a patent in 1904 in several countries for an obstacle detector and ship navigational d e ~ i c e . ~His methods were demonstrated before the German Navy, but generated little interest. The state of technology at that time was not sufficiently adequate to obtain ranges of more than about a mile, and his detection technique was dismissed on the grounds that it was little better than a visual observer. Marconi recognized the potentialities of short waves for radio detection and strongly urged their use in 1922 for this application. In a speech delivered before the Institute of Radio Engineers, he said:' As was first shown by Hertz, electric waves can be completely reflected by conducting bodies. In some of 'my tests I have noticed the effects of reflection and detection of these waves by metallic objects miles away. It !eems to me that it should be possible to design apparatus by means of which a ship could

17. 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 across a metallic object, such as another steamer or ship, would be reflected back to a receiver screened from the local transmitter on the sending ship, and thereby, immediately reveal the presence and bearing of the other ship in fog or thick weather. Although Marconi predicted and successfully demonstrated radio communication between continents, he was apparently not successful in gaining support for some of his other ideas involving very short waves. One was the radar detection mentioned above; the other was the suggestion that very short waves are capable of propagation well beyond the optical line of sight-a phenometlon now know11as tropospheric scatter. He also suggested that radio waves be used for the transfer of power from one point to the other without the use of wire or other trat~smissiot~lit~cs. In the aututnrl of 1922 A. ti. I'aylor arid L. C. Young of tile Naval Research Laboratory detected a wooden ship using a CW wave-interference radar with separated receiver and transmitter. The wavelerlgth was 5 m. A proposal was submitted for further work but was not accepted. The first application of the pulse technique to the measurement of distance was in the basic scientific investigation by Breit and Tuve in 1925 for measuring the height of the i~nosphere.~.'~However, more than a decade was to elapse before the detection of aircraft by pulse radar was demonstrated. The first experimental radar systems operated with CW and depended for detection upon the interference produced between the direct signal received from the transmitter and the doppler-frequency-shifted signal reflected by a moving target. This effect is the same as the rhythmic flickering, or flutter, observed in an ordinary television receiver, especially on weak stations, when an aircraft passes overhead. This type of radar originally was called CW wqaoe-irtfer-erenceradar. Today, such a radar is called a bistatic CW radar. The first experimental detections of aircraft used this radar principle rather than a monostatic (single-site) pulse radar because CW equipment was readily available. Successful pulse radar had to await the development of suitable components, especially high-peak-power tubes, and a better under- standing of pulse receivers. The first detection of aircraft using the wave-interference effect was made in June, 1930,by L. A. tlyland of the Naval Research Laboratory.' It was made accidentally while he was working with a direction-finding apparatus located in an aircraft on the ground.The transmitter 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 received signal. This stimulated a more deliberate investigation by the NRL personnel, but the work continued at a slow pace, lacking official encouragement and funds from the govern- nrent. although it was fully supported by the NRL administration. By 1932the equipment was demonstrated to detect aircraft at distances as great as 50 miles from the transmitter. The 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 the course of other experiments.' The NRL work was disclosed in a patent filed and granted to Taylor, Young, and Hyland6 on a "System for Detecting Objects by Radio." The type of radar described in this patent was a CW wave-interference radar. Early in 1934, a 60-MHz CW wave-interference radar was demonstrated by NRL. The early CW wave-interference radars were useful only for detecting the preserrce of the target. The problem of extracting target-position information from such radars was a difficult one and could not be readily solved with the techniques existing at that time. A proposal was made by NRL in 1933 to errlploy a chain of transmitting and receiving stations along a line to be guarded. for the purpose of obtaining some knowledge of distance and velocity. This was

18. 10 INTRODUCTION TO RADAR SYSTEMS never carried out, however. The limited ability ofCW wave-interferenceradar to be anything 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 coiild be overcome with pulse transmission. Strange as it may now seem, in the early days pulse radar encountered much skepticism. Nevertheless,an effort was started at NRL in the spring of 1934 to develop a pulse radar. The work received low priority and was carried out prin- cipally 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 Guerlac,' the first tests of the 60-MHz pulse radar were carried out in late December, 1934, and early January, 1935.These tests were "hopelessly unsuccessful and a grievousdisappoint- ment." No pulse echoes were observed on the cathode-ray tube. The chief reason for this failure was attributed to the receiver's being designed for CW communications rather than for pulse reception. The shortcomings were corrected, and the first radar echoes obtained at NRL using pulses occurred on April 28, 1936, with a radar operating at a frequency of 28.3 MHz and a pulse width of 5 ,US. The range was only 24 miles. By early June the range was 25 miles. It was realized by the NRL experimenters that higher radar frequencies were desired, especially 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 the NRL experimenters to develop a 200-MHz equipment. The first echoes at 200 MHz were received July 22, 1936,less than three months after the start of the project. This radar was also the first to employ a duplexing system with a common antenna for both transmitting and receiving. The range was only 10to 12miles. In the spring of 1937it was installed and tested on the destroyer Leary. The range of the 200-MHz radar was limited by the transmitter. The development of higher-powered tubes by the Eitel-McCullough Corporation allowed an improved 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 the sweep-was obtained by February. The XAF was tested aboard the battleship New York, in maneuvers held during January and February of 1939,and met with considerable success. Ranges of 20 to 24 kiloyards were obtained on battleships and cruisers. By October, 1939, orders were placed for a manufactured version called the CXAM. Nineteen of these radars were installed on major ships of the fleet by 1941. The United States Army Signal Corps also maintained an interest in radar during the early 1930s.' The beginning of serious Signal Corps work in pulse radar apparently resulted from a visit to NRL in January, 1936.By December of that year the Army tested its first pulse radar, obtaining a range of 7 miles.The first operational radar used for antiaircraft firecontrol was the SCR-268,available in 1938,' The SCR-268 was used in conjunction with searchlights for radar fire control. This was necessary because of its poor angular accuracy. However, 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-584 microwave radar. The SCR-584 could control an antiaircraft battery without the necessity for searchlights or optical angle tracking, In 1939the Armydeveloped the SCR-270,a long-range radar for early warning. The attack on Pearl Harbor in December, 1941,was detected by an SCR-270, one of six in Hawaii at the time.' (There were also 16 SCR-268s assigned to units in Honolulu.) But unfortunately, the true significanceof the blips on the scope was not realized until after the bombs had fallen. A modified SCR-270 was also the first radar to detect echoesfrom the moon in 1946. The early developments of pulse radar were primarily concerned with military applications. Although it was not recognized as being a radar at the time, the frequency-modulated

19. THE NATURE OF RADAR 11 aircraft radio altimeter was probably tlie first commercial application of tlie radar principie. The first equipments were operated in aircraft as early as 1936and utilized the same principle of operation as the FM-CW radar described in Sec. 3.3. In the case of the radio altimeter, the target is tlie ground. 111 13rit.aiti [lie development of radar began later than it1 the United States.'-'' But because they felt the nearness of war more acutely and were in a more vulnerable position with respect to air attack, the British expended a large amount of efforton radar development. By the time the United States entered tlie war, the British were well experienced in the military applications of radar. British interest in radar began in early 1935,when Sir Robert Watson- 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 be regarded as not being practical at that time. Instead, he recotnmended that it would be more promising to investigate means for radio detection as opposed to radio destruction. (The only available means for locating aircraft prior to World War IE were sound locators 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 issued two memoranda outlining the conditions necessary for an effectiveradar system. In that same month the detection of an aircraft was carried out, using 6-MHz communication equipment, by observing tlie beats between the echo signal and the directly received signal (wave interference). The technique was similar to the first United States radar-detection experiments. The transmitter and receiver were separated by about 5.5 miles. When the aircraft receded froin the receiver, it was possible to detect the beats to about an 8-mile range. By June, 1935, the British had demonstrated the pulse technique to measure range of an 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 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 raised to 25 MHz. A series of CH (Chain Homej radar stations at a frequency of 25 MHz were successfully demonstrated in April, 1937. Most of the stations were operating by September, 1938, and plotted the track of the aircraft which flew Neville Chamberlain, the British Prime Minister at 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 on an aircraft, for the detection and interception of hostile aircraft. The A1 radar operated at a frequency of 200 MHz. During the development of the A1 radar it was noted that radar could be used for the detection of ships from the air and also that the character of echoes from the ground was dependent on the nature of the terrain. The former phenomenon was quickly exploited for the detection and location of surface ships and submarines. The latter effect was not exploited initially, but was later used for airborne mapping radars. Until the middle of 1940 tlie 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 visited the United States to exchange information concerning the radar developments in the two countries. The British realized the advantages to be gained from the better angular resolution possible at the microwave frequencies, especially for airborne and naval applications. They suggested that the United States undertake the development of a microwave A1

20. 12 INTRODUCTION TO RADAR SYSTEMS radar and a microwave antiaircraft fire-control radar. The British technical mission demonstrated the cavity-magnetron power tube developed by Randell and Boot and furnished design information so that it could be duplicated by United States manufacturers. The Randell and Boot magnetron operated at a wavelength of 10 cm and produced a power output of about 1 kW, an improvement by a factor of 100 over anything previously achieved at cen- timeter wavelengths. The development of the magnetron was one of tile most important contributions to the realization of microwave radar. The success of microwave radar was by no means certain at the end of 1940.Therefore the United States Service Laboratories chose to concentrate on the development of radars at the lower frequencies, primarily the very high frequency (VHF) band, where techniques and components were more readily available. The exploration of the microwave region for radar application became the responsibility of the Radiation Laboratory, organized in November, 1940, under the administration of the Massachusetts Institute of Technology. In addition to the developments carried out in the United States and Great Britain, radar was developed essentially independently in Germany, France, Russia, Italy, and Japan during the middle and late thirties.12The extent of these developments and their subsequent military deployment varied, however. All of these countries carried out experiments with CW wave interference, and even though the French and the Japanese deployed such radars operationally, they proved of limited value. Each country eventually progressed to pulse radar operation and the advantages pertaining thereto. Although the advantages of the higher frequencies were well recognized, except for the United States and Great Britain none of the others deployed radar at frequencies higher than about 600 MHz during the war. The Germans deployed several different types of radars during World War 11. Ground- based radars were avgilable for air search and height finding so as to perform ground control of intercept (GCI).Coastal, shipboard, and airborne radar were also employed successfully in significant numbers. An excellent description of the electronic battle in World War I1 between the Germans and the Allies, with many lessons to offer, is the book " It~strtlrnerttsof Dcrrkt~ess" by Price.I3 The 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 1940.12The development of radar in Italy also started early, but was slow.There were only relatively few Italian-produced radars operationally deployed by the time they left the war in September, 1943. The work in Japan was also slow but received impetus from disclosures by their German allies in 1940and from the capture of United States pulse radars in the Philippines early in 1942. The development of radar in the Soviet Union was quite similar to the experience elsewhere. By the summer of 1941they had deployed operationally a number of 80-MHz air-search radars for the defense' of Moscow against the German invasion.14Their indigenous efforts were interrupted by the course of the war. Thus, radar developed independently and simultaneously in severalcountries just prior to World War 11. It is not possible to single out any one individual as the inventor; there were many fathers of radar. This was brought about not only by the spread of radio technology to many countries, but by the maturing of the airplane during this same time and the common recognition of its military threat and the need to defend against it. . ' 1.6 APPLICATIONS OF RADAR Radar has been employed on'the ground, in the air, on the sea, and in space. Ground-based radar has been applied chiefly to'the detection, location, and tracking of aircraft or space targets. Shipboard radar is used as a navigation aid and safety device to locate buoys, shore

21. lines, and other ships. as well as for observing aircraft. Airborne radar may be used to detect other aircraft, ships, or land vehicles, or it may be used for mapping of land, storm avoidance, terrain avoidance, and navigation. In space, radar has assisted in the guidance of spacecraft and for the remote sensing of the land and sea. The major user of radar, and contributor of the cost of almost all of its development, has been the military: although there have been increasingly important civil applications, chiefly for niaririe and air tiavigation. The niajor areas of radar application, in no particular order of irnpo~ta~icc,are Ijriefly described below. Air. Trclffic Corrtrol ( ATC). Radars are employed throughout the world for the purpose of safely coritrollit~gair traffic en route and in tlic vicinity of airports. Aircraft and ground vcllicular traffic st large airports are monitored by tliearis of high-resolution radar. Radar 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 ATC radar-beacon system are based in large part on radar technology. Aircv-aft Nac~iqatiotl.The weather-avoidance radar used on aircraft to outline regions of precipitation 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 radio altimeter (either FM/CW or pulse) and the doppler navigator are also radars. Sometimes ground-mapping radars of moderately high resolution are used for aircraft navigation purposes. Ship Safety. Radar is used for enhancing the safety of ship travel by warning of potential collision with other ships, and for detecting navigation buoys, especially in poor visibility. I11 terms of numbers, this is one of the larger applications of radar, but in terms of physical size and cost it is one of the smallest. It has also proven to be one of the most reliable radar systems. Automatic detection and tracking equipments (also called plot extractors) are commercially available for use with such radars for the purpose of collision avoidance. Shore-based radar of moderately high resolution is also used for the surveillance of liarbors as an aid to navigation. Space.. Space vehicles have used radar for rendezvous and docking, and for landing on the moon. Some of the largest ground-based radars are for the detection and tracking of satellites. Satcllitc-borne radars have also been used for remote sensing as meritioried below. Rer~roteSetrsirrg. A11 radars are remote sensors; however, as this term is used it implies the sensing of geophysical objects, or the "environment." For some time, radar has been used as a remote sensor of the weather. It was also used in the past to probe the moon and the planets (radar astronomy).The ionospheric sounder, an important adjunct for HF (short 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- niental pollution. The platforms for such radars include satellites as well as aircraft. La~vErfircentenr. In addition to the wide use of radar to measure the speed of automobile 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. The traditional role of radar for military application has been for surveillance, navigation, and for the control and guidance of weapons. It represents, by far, the largest use of radar.

22. 14 INTRODUCTION TO RADAR SYSTEMS REFERENCES 1. Guerlac, H. E.: "OSRD Long History," vol. V, Division 14, "Radar," available from Office of Technical Services, U.S. Department of Commerce. 2. British Patent 13,170,issued to Christian Hiilsmeyer, Sept. 22, 1904,entitled " Hertzian-wave Project- ing and Receiving Apparatus Adapted to Indicate or Give Warning of the Presence of a Metallic Body, 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. 4. Breit, G., and M. A. Tuve: A Test of the Existence of the Conducting Layer, Phys Rev., vol. 28, pp. 554-575, September, 1926. 5. Englund, C. R., A. B. Crawford, and W. W. Mumford: Some results of a Study of Ultra-short-wave Transmission Phenomena, Proc. IRE, vol. 21, pp. 475-492, March, 1933. 6. CIS. 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. 7. Vieweger, A. L.: Radar in the Signal Corps, IRE Trans., vol. MIL-4, pp. 555-561, October, 1960. 8. Origins of Radar: Background to the Awards of the Royal Commission, Wireless World, vol. 58, pp. 95-99, March, 1952. 9. Wilkins, A. F.: The Story of Radar, Research (London), vol. 6, pp. 434-440, November, 1953. 10. Rowe, A. P.: "One Story of Radar," Cambridge University Press, New York, 1948. A very readable .i description 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 11. 11. Watson-Watt, Sir Robert: "Three Steps to Victory," Odhams Press, Ltd., London, 1957;"The Pulse of Radar," The Dial Press, Inc., New York, 1959. 12. Susskind, C.: "The Birth of the Golden Cockerel: The Development of Radar," in preparation 13. Price, A.: "Instruments of Darkness," Macdonald and Janes, London, 1977. 14. Lobanov, M. M.: "Iz Proshlovo Radiolokatzii" (Out of the Past of Radar), Military Publisher of the Ministry of Defense, USSR, Moscow, 1969. 15. IEEE Standard Letter Designations for Radar-Frequency Bands, IEEE Std 521-1976, Nov. 30, 1976. 16. Villard, 0.G., Jr.: The Ionospheric Sounder and Its Place in the History of Radio Science, Radio Science, vol. 11, pp. 847-860, November, 1976.

23. TWO THE RADAR EQUATION 2.1 PREDICTION OF RANGE PERFORMANCE The simple form of the radar equation derived in Sec. 1.2expressed the maximum radar range R,,, in terms of radar and target parameters: where P, = transmitted power, watts G = antenna gain A, = antenna emective aperture, m2 a = radar cross section, m2 Smin= minimum detectable signal, watts All the parameters are to some extent under the control of the radar designer, except for the target cross section a. The radar equation states that iflong ranges are desired,the transmitted power must be large, the radiated energy must be concentrated into a narrow beam (high transmitting antenna gain), the received echo energy must be collected with a large antenna aperture (also synonymous with high gain),and the receiver must be sensitiveto weak signals. In practice, however, the simpleradar equation does not predict the range performance of actual radar equipments to a satisfactory degree of accuracy. The predicted values of radar range are usually optimistic. In some cases the actual range might be only half that predicted.' Part of this discrepancy is due to the failure of Eq. (2.1) to explicitly include the various losses that can occur throughout the system or the loss in performance usually experienced when electronic equipment is operated in the field rather than under laboratory-type conditions. 4nother important factor that must be considered in the radai equation is the statistical or unpredictable nature of several ofthe parameters. The minimum detectable signalS,,, and the target cross section cr are both statistical in nature and must be expressed in statistical terms.

24. 16 INTRODUCTION TO RADAR SYSTEMS Other statistical factors which do not appear explicitly in Eq. (2.1)but which have an effecton the radar performance are the meteorological conditions along the propagation path and thc performance of the radar operator, if one is employed. The statistical nature of these several parameters does not allow the maximum radar range to be described by a single number. Its specification must include a statement of the probability that the radar will detect a certain type of target at a particular range. In this chapter, the simple radar equation will be extended to include most of the important factors that influence radar range performance. If all those factors affecting radar range were known, it. would be possible, in principle, to make an accuratc prediction of radar perforpance. But, as is true for most endeavors, the quality of the prediction is a function of the amount of effort employed in determining the quantitative effects of the various parameters. Unfortunately, the effort required to specify completely the effects of all radar parameters to the degree of accuracy required for range prediction is usually not economically justified. A compromise is always necessary between what one would like to have and what one can actually get with reasonable effort. This will be better appreciated as we proceed through the chapter and note the various factors that must be taken into account. J A complete and detailed discussion of all those factors that influence the prediction of radar range is beyond the scope of a single chapter. For this reason many subjects will appear to be treated only lightly. This is deliberate and is necessitated by brevity. More detailed information will be found in some of the subsequent chapters or in the references listed at the end of the chapter. ' . 6 The ability of a radar receiver to detect a weak echo signal is limited by the noise energy that occupies the same portion of the frequency spectrum as does'the signal energy. The weakest signal the receiver can detect is called the minimum detectable signal. The specification of the minimum detectable signal is sometimes difficult because of its statistical nature and because the criterion for deciding whether a target is present or not may not be too well defined. Detection is based on establishing a threshold level at the output of the receiver. If the receiver output exceeds the threshold, a signal is assumed to be present. This is called threshold detection. Consider the output of a typical radar receiver as a function of time (Fig. 2.1). This might represent one sweep of the video output displayed on an A-scope. The envelope has a fluctuating appearance caused by the random nature of noise. If a large signal is present such as at A in Fig. 2.1, it is greater than the surrounding noise peaks and can be recognized on the basis of its amplitude. Thus, if the threshold level were set sufficiently high, the envelope would not generally exceed.the threshold if noise alone were present, but would exceed it if a strong signal were present. If the signal were small, however,it would be more difficult to recognize its presence. The threshold level mustbe low if weak signals are to be detected, but it cannot be so low that noise peaks cross the 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 receiver (Sec. 10.2). A matched filter is one designed to maximize the output peak signal to average noise (power) ratio. It has a frequency-response function which is proportional to the complex conjugate of the signa1,spectrum.(This is not the same as the concept of" impedance match " of circuit theory.) The ideal matched-filterreceiver cannot always be exactly realized in practice, but it is possible to approach.itwith practical receiver circuits. A matched filter for a radar transmitting a rectangular-shaped .pulse is usually characterized by a bandwidth B approximately the reciprocal of the pulse width 7, or Br = 1.The output of a matched-filter receiver is

25. Threshold level , A Time - Figure 2.1 Typical envelope of tile radar receiver output as a function of time. A , and B, and C represent signal plus noise. ,4 arid B would be valid detections, but C is a missed detection. the cross correlation between the received waveform and a replica of the transmitted waveform. Hence it does not preserve the shape of the input waveform. (There is no reason to wish to preserve the shape of the received waveform so long as the output signal-to-noise ratio is maximized.) Let us return to tlie receiver output as represented in Fig. 2.1. A threshold level is estab- lished, as shown by the dashed line. A target is said to be detected if the envelope crosses tlie thresliold. if the sigrial is large such as at A, it is not difficult to decide that a target is present. I3ut consider tlie two signals at B and C, representing target echoes of equal atnplitudc. 'I'lic noise voltage accompanying the signal at B is large enough so that the combination of signal plus noise exceeds the tlireshold. At C the noise is not as large and the resultant signal plus rioise does not cross the tlireshold. Thus the presence of noise will sometimes enhance' the detection of weak signals but it may also cause the loss of a signal which would otherwise be detected. Weak signals such as C would riot be lost if the threshold level were lower. But too low a tlireshold increases the likelihood that noise alone will rise above the threshold and be taken for a real signal. Such an occurrence is called afalse alarm. Therefore, if the threshold is set too low, false target indications are obtained, but if it is set too high, targets might be missed. The selection of the proper threshold level is a compromise that depends upon how important it is if a mistake is made either by (1) failing to recognize a signal that is present (probability of z miss) or by (2) falsely indicating the presence of a signal when none exists (probability of a false alarm). When the target-decision process is made by an operator viewing a cathode-ray-tube display, it would seem that the criterion used by the operator for detection ought to be arialogous to the setting of a threshold, either consciously or subconsciously. The chief differ- ence between tlie 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 latter's threshold might be difficult to predict and may not remain fixed.The individual's performance as part of the radar detection process depends upon the state of the operator's fatigue and motivation, as 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 discussion, the operator will be considered the same as an electronic threshold detector, an assumption that is generally valid for an alert, trained operator. The signal-to.noise ratio necessary to provide adequate detection is one of the important

26. parameters that must be determined in order to comptite the minimum detectable signal. Although the detection decision is usually based on measurements at the video otrtput, it is easier to consider maximizing the signal-to-noise ratio at the output of the IF amplifier rather than in the video. The receiver may be considered linear irp to the output of the IF. It is shown by Van Vieck and Middleton3 that maximizing the signal-to-noise ratio at the output of the IF is equivalent to maximizing the video output. The advantage of considering the signal-to-noise ratio at the IF is that the assumption of linearity may be made. It is also assumed that the IF filter characteristic approximates the matched filter, so that the oirtput signal-to-noise ratio is maximized. 2.3 RECEIVER NOISE Since noise is the chief factor limiting receiver sensitivity, it is necessary to obtain some means of describing it quantitatively. Noise is unwanted electromagnetic energy which interferes with the ability of the receiver to detect the wanted signal. It may originate within the receiver itself, or it may enter via the receiving antenna along with the desired signal. If the radar were to operate in a perfectly noise-free environment so that no external sources of noise accompanied the desired signal, and if the receiver itself were so perfect that it did not generate any excess noise, there would still exist an unavoidable component of noise generated by the thermal motion of the conduction'electrons in the ohmic portions of the receiver input stages. This is called thermal noise, or Johnson noise, and is directly proportional to the temperature of the ohmic portions of the circuit and the receiver band~idth.~'The available thermal-noise power generated by a receiver' of bandwidth B, (in hertz) at a temperature T (degrees Kelvin) is equal to Available thermal-noise power = kTB, (2.2) where k = Boltzmann's constant = 1.38 x J/deg. If the temperatiire T is taken to be 290 K, which corresponds approximately to room temperature (62"F), the factor kT is 4 x lo-" W/Hz of bandwidth. If the receiver circuitry were at some other temperature, ttie 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 and the ohmic losses in the transmission line. For radar receivers of the superheterodyne type (the type of receiver used for most radar applications), the receiver bandwidth is approximately that of the intermediate-freqire~lcy stages. It should be cautioned that the bandwidth B, of Eq. (2.2) is not the 3-dB, or half-power, bandwidth commonly employed by electronic engineers. It is an integrated bandwidth and is given by where H(f ) = frequency-response characteristic of I F amplifier (filter) and fo = frequency of maximum response (usually occurs at midband). When H(f) is normalized .to unity at midband (maximum-response frequency), H(fo) = 1.The bandwidth Bnis called the noise bandwidth and is the bandwidth of an equivalent rectangular filter whose noise-power output is the same as the filter with characteristic

27. THE RADAR EQUATION 19 I ! ( / ) '1 lic 3-ti13 I ~ i ~ r ~ t l w i t l t l iis tlcfirictl as tlic scparntioti it1 licrtz betwceri tlie poitits oti tlic frequericy-resi~otisccliaractcristic wliere the response is reduced to 0.707 (3 dB) fro111its r~iaxi- nlilm valric. Tllc 3-dl3 t~i~ndwicithis widely i~sed,since it is easy to measure. The meastire~nent of rioisc t)aridwicftli. I~owcvcr,irivolves a coriiplete knowledge of tlie resporrse cliaractet.istic N(/). Tlie rreqiicncy-response cliaracteristics of many practical radar receivers are such that tlic 3-dl3 i~ricitlic tioisc I~nt~tlwidtlistlo riot differ appreciably. Tlierefore tlie 3-dl3 I~itnciwidtli rnay be used in niatiy cases as an approximation to the rioise bandwidth.' The noise power in practical receivers is often greater than can be accounted for by thertnal noise alone. The additional noise cotnpotlents are due to mechanisms other than the tlierrnal agitation of tlie conduction electrons. For purposes of the present discussion, tiowever, the exact origin of tlie extra noise components is not important except to know that it exists. No matter whether the noise is generated by a thermal mechanism or by some other mechanism. tile total tloise at tlie output of the receiver may be considered to be equal to the thermal-noise power obtained from an " ideal " receiver multiplied by a factor called the iroise fig~rre.The noise figure Fn of a receiver is defined by the equation i NI: = ----"-.. - tloise out of practical receiver - " kToBnG, noise out of ideal receiver at std temp To (2.40) 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 Engineers definition. 'Tlie noise No is measured over the linear portion of the receiver input-output characteristic, usually at the output of tlie IF amplifier before the nonlinear second detector. 'The receiver bandwidth Bn is that of tlie IF aniplifier in most receivers. The available gain G, is tlie ratio of the signal out Soto the signal in Si,and kToBn is the input noise Niin an ideal receiver. Equation (2.40) may be rewritten as The noise figure may be interpreted, therefore, as a measure of the degradation of signal-to- noise-ratio as the signal passes through the receiver. j Rearranging Eq. (2.417). the input signal may be expressed as If the minimum detectable signal S,,, is that value of SIcorresponding to the minimum ratio of output (IF)signal-to-noise ratio ( S o / N o ~ i nnecessary for detection, then Substituting Eq. (2.6) into Eq. (2.1) results in the following form of the radar equation: Before continuing the discussion of the factors involved in the radar equation, it is necessary to digress and review briefly some topics in probability theory in order to describe the signal-to-noise ratio in statistical terms.

28. 20 INTRODUCTION TO RADAR SYSTEMS 2.4 PROBABILITY-DENSITY FUNCTIONS The basic concepts of probability theory needed in solving noise problems may be found in any of several In this section we shall briefly review probability and the probability-density function and cite some examples. Noise is a random phenomenon. Predictions concerning the average performance of random phenomena are possible by observing and classifying occurrences, but one cannot predict exactly what will occur for any particular event. Phenomena of a random nature can be described with the aid of probability theory. Probability is a measure of the likelihood of occurrence of an event. The scale of probability ranges from 0to 1.t An event which is certain is assigned the probability 1. An impossible event is assigned the probability 0.The intermediate probabilities are assigned so that the more likely an event, the greater is its probability. One of the more useful concepts of probability theory needed to analyze the detection of signals in noise is the probability-density function. Consider the variable x as representing a typical measured value of a random process such as a noise voltage or current. Imagine each x to define a point on a straight line corresponding to the distance from a fixed reference point. The distance of x from the reference point might represent the value of the noise current or the noise voltage. Divide the line into small equal segments of length Ax and count the number of times that x falls in each interval. The probability-density function p(x) is then defined as (number of values in range AXat x)/Ax p(x) = lim (2.8) AX-o total number of values = N N-rm The probability that a particular measured value lies within the infinitesimal width ds centered at x is simply p(x) dx. The probability that the value of x lies within the finite rangz from xl to x2 is found by integrating p(x) over the range of interest, or X2 Piobability (x, < x < x2)= 1 p(x) dx X I By definition, the probability-density function is positive. Since every measurement must yield some value, the integral of the probability density over all values of x must be equal to unity; .j that is, The average value of a variable function, +(x), that is described by the probability-density function, p(x), is This follows from the definition of an average value and the probability-density function. The mean, or average, value of x is t Probabilities are sometimes expressed in percent (0 to 100) rather than 0 to 1.

29. and tlie mean square value is THE RADAR EQUATION 21 'Tlie quantities in, and l,lz are sometimes called the first and second moments of the random variable .u.I f .urepresents an electric voltage or current, inl is the d-c component. It is the value read by a direct-curretlt voltmeter or ammeter. The mean square value (nt,) of the current wl~erirrlllltiplied by tile resistaricet gives the mean power. The mean square value of voltage times tlie conductance is also the mean power. The variarlce is defined as The variance is tile meall square deviation of x about its mean and is sometimes called the secorld ceiltral rnonrcllt. If the random variable is a noise current, the product of the variance '/a and resistance gives the mean power of the a-c component. The square root of the variance o is called the stclrldard deviatioit and is the root-mean-square (rms) value of the a-c component. We shall consider four examples of probability-density functions: the uniform, gaussian, Rayleigh, and exponential. The uniform probability-density (Fig. 2 . 2 ~ )is defined as Ik f o r a < x < a + b /I(.Y) = O for .w < a and x > a + b t 111 ~ioisetheory it is customary to take the resistance as 1 ohm or the conductance as 1 mho. Figure 2.2 Examples of probability-density functions. (a) Unlform; (6)Gaussian; (c) Rayleigh (voltage); ( d ) Rayleigtl (power) or exponential.

30. 22 INTRODUCTION TO RADAR SYSTEMS where k is a constant. A rectangular, or uniform, distribution describes the phase of a random sine wave relative to a particular origin of time; that is, the phase of the sine wave may be found, with equal probability, anywhere from 0 to 2n, with k = 1121s.It also applies to the distribution of the round-off (quantizing) error in numerical computations and in analog-to- digital converters. The constant k may be found by applying Eq. (2.10); that is, The average value of x is This result could have been determined by inspection. The second-moment, or mean square, value is and the variance is a = standard deviation = b rJj The gaussian, or normal, probability density (Fig. 2.2b) is one of the most important in noise theory, since many sources of noise, such as thermal noise or shot noise, may be represented by gaussian statistics. Also, a gaussian representation is often more convenient to manipulate mathematically. The gaussian density function has a bell-shaped appearance and is defined by where exp [ ] is the exponential function, and the parameters have been adjusted to satisfy the normalizing condition of Eq. (2.10). It can be shown that * - m -02 The probability density of the sum of a large number of independently distributed quantities approaches the gaussian probability-density function no matter what the individual dis- tributions may be, provided that the contribution of any one quantity is not comparable with the resultant of all others. This is the central limit theorem. Another property of the gaussian distribution is that no matter how large a value x we may choose, there is always some finite probability of finding a greater value. If the noise at the input of the threshold detector were truly gaussian, then no matter how high the threshold were set, there would always be a chance that it would be exceeded by noise and appear as a false alarm. However, the probability diminishes rapidly with increasing x, and for all practical purposes the probability of obtaining an exceedingly high value of x ,isnegligibly small. The Rayleigh probabi~itydensit~function is also of special interest to the radar systems

31. erigirice~ 11 tlescr il~cstl~ceriveloi~cof (lie~ioiscoutlxrt fro111ii rlar r.owbatld filtcr (sucli as tile IF filter iri a sr~pcrheterotlynereceiver). tile cross-section fluctuatioris of certain types of conlplex radar targets. arid rnariy kinds of clutter arid weather echoes. The Rayleigh density function is Tliis is plottetf iri Fig. 2.2~.Tlie parameter .u might represent a voltage, and (.u2),, the mean, or average, valirc of tlic voltage squar-ed.If .uZis replaced by w, wlierc kc represents power instead of voltage (assuming the resistance is I ohm), Eq. (2.17) becomes 1 P ( w )= exp (- ,v 2 o "'0 where H., is tlie average power. This is tlie exponential probability-density function, but it is sornetiriie5 called the Rayleigh-power probability-density function. It is plotted in Fig. 2.2d. , ?'lie starid:trd dcviatiori of the Kayleigli density of Eq. (2.17) is equal to J(4/n) - 1 times tlie mean valuc, arid for tile cxponeritial density of Eq. (2.18)tlie standard deviation is equal to w o . 'l'licrc ate otlicr pr ot~ability-densityfunctions of interest in radar, such as the Rice, log norrnal, arid tlie chi square. I'liese will be introduced as needed. Ariotlicr rriathcrnatical description of statistical phenomena is the probability distrihrrtiot~ Jirr~c.tir,r~f'(u), dclined as tile probability tliat tile value x is less than some specified value 111 sorrie cases, tlie distribution function may be easier to obtain from an experimental set of data tlian the derisity function. Tlie density function may be found from the distribution futiction by dilferentiatiori. 2.5 SIGNAL-TO-NOISE RATIO : In this section tile results of statistical noise theory will be applied to obtain the signal-to-noise ratio at the output of the IF amplifier necessary to achieve a specified probability of detection without exceeding a specified probability of false alarm. The output signal-to-noise ratio thus obtained rnay be substituted into Eq. (2.6) to find the minimum detectable signal, which, in turn. is used in the radar equation, as in Eq. (2.7). Corisider an IF amplifier with bandwidth BIFfollowed by a second detector and a video arnplificr witli baridwidth B,.(Fig. 2.3). Tlie second detector and video amplifier are assumed to form an envelope detector, that is, one which rejects the carrier frequency but passes the niodulation envelope. To extract the modulation envelope, the video bandwidth must be wide enough to pass the low-frequency components generated by the second detector, but not so wide as to pass the high-frequency components at or near the intermediate frequency. The video bandwidth B,,must be greater than BIF/2in order to pass all the video modulation. Most radar receivers used in conjunction with an operator viewing a CRT display meet this condition and Second detector - V~deo amplifier (Bv) . : Figure 2.3 Envelope detector.

32. 24 INTRODUCTION TO RADAR SYSTEMS may be considered envelope detectors. Either a square-law or a linear detector may be assumed since the effect on the detection probability by assuming one instead of the other is iisually small. The noise entering the I F filter (the terms filter and amplifier are used interchangeably) is assumed to be gaussian, with probability-density function given by where p(v) do is the probability of finding the noise voltage v between the values of 11 and v +dl,, $o is the variance, or mean-square value of the noise voltage, and the mean value of 11 is taken to be zero. If gaussian noise were passed through a narrowband IF filter-one whose bandwidth is small compared with the midfrequency-the probability density of the envelope of the noise voltage output is shown by Riceg to be where R is the amplitude of the envelope of the filter output. Equation (2.21) is a form of the Rayleigh probability-density function. The probability that the envelope of the noise voltage will lie between the values of V, and V2 is v 2 R Probability (V, < R < V2)= - exp (- 5)d R v, +o 2+0 The probability that the noise voltage envelope will exceed the voltage threshold V,- is " R Probability (VT< R < m) = [ - exp (- c)dR v7.$0 2$ 0 = exp (- 2)= P,, Whenever the voltage envelope exceeds the threshold, a target detection is considered to have -? occurred, by definition. Since the probability of a false alarm is the probability that noise will cross the threshold, Eq. (2.24) gives the probability of a false alarm, denoted PI,. The average time interval between crossings of the threshold by noise alone is defined as the filse-alarm time 3,, I N Ta= lim -- N - + W N k = ~ where & is the time between crossings of the threshold VT by the noise envelope, when the slope of the crossing is positive. The false-alarm probability may also be defined as the ratio of the duration of time the envelope is actually above the threshold to the total time it coirld have been above the threshold, or N-

33. Time - Figure 2.4 Envelope of receiver output illustrating false alarms due to noise. where t, and & are defined in Fig. 2.4. The average duration of a noise pulse is approximately the reciprocal of the bandwidth B, which in the case of the envelope detector is BIF.Equating Eqs. (2.24) and (2.25) we get 1 v", 3,= -exp - BIF 21//0 A plot of Eq. (2.26) is shown in Fig. 2.5, with V;/2t,bo as the abscissa. If, for example, the bandwidth of the IF amplifier were 1 MHz and the average false-alarm time that could be tolerated were 15 nlin, the probability of a fdse alarm is 1.11 x lo-'. From Eq. (2.24) the threshold voltage necessary to achieve this false-alarm time is 6.45 times the rms value of the noise voltage. The false-alarm probabilities of practical radars are quite small.The reason for this is that the false-alarm probability is the probability that a noise pulse will cross the threshold during an interval of time approximately equal to the reciprocal of the bandwidth. For a 1-MHz bandwidth, there are of the order of 106 noise pulses per second. Hence the false-alarm probability of any one pulse must be small ( < if false-alarm times greater than 1 s are to be obtained. The specification of a tolerable false-alarm time usually follows from the requirements desired by the customer and depends on the nature of the radar application. The exponential relationship between the false-alarm time Tfa and the threshold level VT results in the false- alarm time being sensitive to variations or instabilities in the threshold level. For example, if' the batidwidtll were 1 MHz, a value of 10 log (V$/2t,bo)= 12.95 dB results in an average false-alarm time of 6 min, while a value of 14.72 dB results in a false-alarm time of 10,000 h. Thus a change in the threshold of only 1.77 dB changes the false-alarm time by five orders of magnitude. Such is the nature of gaussian noise. In practice, therefore, the threshold level would probably be adjusted slightly above that computed by Eq. (2.26), so that instabilities which lower the threshold slightly will not cause a flood of false alarms. If the receiver were turned off (gated) for a fraction of time (as in a tracking radar with a servo-controlled range gate or a radar which turns off the receiver during the time of transmission), the false-alarm probability will be increased by the fraction of time the receiver is not operative assuming that the average false-alarm time remains the same. However, this is usually not important since small changes in the probability of false alarm result in even smaller changes in the threshold level because of the exponential relationship of Eq. (2.26). Thus far, a receiver with only a noise input has been discussed. Next, consider a sine-wave signal of amplitude A to be present along with noise at the input to the IF filter. The frequency

34. 26 INTRODUCTION TO RADAR SYSTEMS 1 yeor 6 months 30 doys 2 weeks l week 15 rnin Figure 2.5 Average time between false alarms as a function of the threshold level I/, and thc receiver bandwidth 8;(I/, is the mean square noise voltage. 3 of the signal is the same as the IF midband frequencyhF.The outpul or the envelope detector has a probability-density function given by9 where lo(Z) is the modified Bessei function of zero order and argument Z. For Z large, an asymptotic expansion for i o ( Z )is When the signal is absent, A = 0 and Eq. (2.27)reduces to Eq. (2.21),the probability-density function for noise alone. Equation (2.27) is sometimes called the Rice probability-density function. The probability that the ;ignal will be detected (which is the probability ofdetenio,,)is the same as the probability that the envelope R will exceed the predetermined threshold VT.The

35. probability' of detection f', is therefore This cannot he evaluated by sirnple nleans, and numerical techniques or a series approximation must be used. A series approximation valid when RA/$o % 1, A 9 IR - A 1, and terms in A - and beyond can be neglected is9 VT - A 1 + (VT - A)2/$oX [ I - 4 ~ - -+ - - . . . 8A2/rC/0 where tlie error fu~lctionis defined as erf Z = - A graphic illustratior~of the process of threshold detection is shown in Fig. 2.6. The probability density for noise alone [Eq. (2.21)] is plotted along with that for signal and noise [Eq. (2.27)Jwith /I/(/:!* = 3. A tl~resl~oldvoltage VT/$;12= 2.5 is shown. The crosshatched area to the right of I ~ , / $ : ' ~under the curve for signal-plus-noise represents the probability of detection. while the double-crosshatched area under the curve for noise alone represents the probability of a false alarm. If v ~ / $ ; ' ~is increased to reduce the probability of a false alarm, the probability of detection will be reduced also. Equation (2.29)may be used to plot a family of curves relating the probability of detection to the threshold voltage and to the amplitude of tlie sine-wave signal. Although the receiver designer prefers to operate with voltages, it is more convenient for the radar system engineer to ernploy power relationships. Equation (2.29) may be converted to power by replacing the signal - to -rrns-noise-voltageratio with the following: .I signal amplitude fi(rms signal voltage). - . -- -- = ( 2 signal power) ' I 2 = (:) - ' 1 2 d,:,I2 - rrns noise voltage rms noise voltage noise power We shall also replace If;/2rC/, by In (l/P,,)[from Eq. (2.24)). Using the above relationships, the probability of detection is plotted in Fig. 2.7 as a function of the signal-to-noise ratio with the probability of a false alarm as a parameter. Figure 2.6 Probability-density function for noise alone arid for signal-plus-noise, illustrating the process of tl~resl~olddetection.

36. 28 INTRODUCTION TO RADAR SYSTEMS 4 6 8 " 10 12 14 16 18 20 (S/N ), , signal-to-noise ratio, dB Figure 2.7 Probability of detection for a sine wave in noise as a function of the signal-to-noise (power) ratio and the probability of false alarm. .I Both the false-alarmtime and the detection probability are specified by the system requirements. The radar designer computes the probability of the false alarm and from Fig. 2.7 determines the signal-to-noise ratio. This is the signal-to-noise ratio that is used in tht: eqlta- tion for minimum detectable signal [Eq. (2.6)].The signal-to-noise ratios of Fig. 2.7 apply to a single radar pulse. For example, suppose that the desired false-alarm time was 15 min and tllc IF bandwidth was 1 MHz. This gives a false-alarm probability of 1.11 x lo-'. Figure 2.7 indicates that a signal-to-noise ratio of 13.1 dB is required to yield a 0.50 probability of detection, 14.7dB for 0.90, and 16.5 dB for 0.999. There are several interesting facts illustrated by Fig. 2.7. At first glance, it m

introduction to radar systems1 2nd

Engineering

radar tracking

radar dcvcloprnent

radar frequencies

nature of radar

frequencymodulated radar

radar hlock diagram

frequencymodulated cw

pulse doppler radar