Radar Basic Principles : учебно-методическое пособие

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Министерство науки и высшего образования Российской Федерации Сибирский федеральный университет

RADAR BASIC PRINCIPLES Учебно-методическое пособие

Электронное издание

Красноярск СФУ 2020

УДК 811.111:621.396.967(07) ББК 81.432.1я73+32.95я73 R13 Составители: Андюсева Валентина Германовна Поликарпова Светлана Витальевна Руковишников Юрий Сергеевич Рыбакова Екатерина Владимировна Шагалина Ольга Вениаминовна

R13 Radar Basic Principles : учеб.-метод. пособие / сост. : В. Г. Андюсева, С. В. Поликарпова, Ю. С. Руковишников, Е. В. Рыбакова, О. В. Шагалина. – Электрон. дан. (1,4 Мб). – Красноярск : Сиб. федер. ун-т, 2020. – Систем. требования: PC не ниже класса Pentium I ; 128 Mb RAM ; Windows 98/XP/7 ; Adobe Reader V8.0 и выше. – Загл. с экрана. Включает в себя оригинальные профессиональные тексты на английском языке для автономного чтения и перевода, методические рекомендации по подготовке устного ответа по содержанию прочитанного текста, а также тематические глоссарии. Предназначено для самостоятельной работы студентов первого и второго курсов Военно-инженерного института, обучающихся по направлению 11.05.01 «Радиоэлектронные системы и комплексы», 11. 05.02 «Специальные радиотехнические системы». . УДК 811.111:621.396.967(07) ББК 81.432.1я73+32.95я73 © Сибирский федеральный университет, 2020 Электронное учебное издание Подготовлено к публикации издательством Библиотечно-издательского комплекса Подписано в свет 06.03.2020. Заказ №11190 Тиражируется на машиночитаемых носителях Библиотечно-издательский комплекс Сибирского федерального университета 660041, г. Красноярск, пр. Свободный, 82а Тел. (391)206-26-16; http://rio.sfu-kras.ru E-mail: [email protected]

CONTENT First course ......................................................................................................... 4 Section 1. Historical overview ........................................................................ 4 Section 2. Radar basic principles .................................................................... 7 Section 3. Signal routing\timing ................................................................... 9 Section 4. Ranging ...................................................................................... 12 Section 5. Radar waveforms minimum range ............................................... 15 Section 6. True bearing ................................................................................ 18 Section 7. Accuracy...................................................................................... 21 Section 8. Range resolution .......................................................................... 24 Second course .................................................................................................. 27 Section 9. Theoretical maximum range equation .......................................... 27 Section 10. Antenna aperture ........................................................................ 39 Section 11. Free-space path loss ................................................................... 32 Section 12. Converting the equation ............................................................. 35 Section 13. MDS – echo ............................................................................... 37 Section 14. Radar range Equation................................................................. 40 Section 15. Frequency-diversity radar .......................................................... 43 Section 16. Training questions ..................................................................... 46 References ........................................................................................................ 47

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FIRST COURSE Section 1 Vocabulary: radar (radio detecting and ranging) – радар (радио обнаружение и определение дальности) high frequency engineer – инженер СВЧ equipment – оборудование super-heterodyne receiver – супергетеродинный приемник electro-magnetic light theory – электромагнитная теория света parabolic dish – параболическая зеркальная антенна backscattering – обратное рассеивание intermediate frequency – помехоустойчивая частота denomination – обозначение inventor – изобретатель amplifier – усилитель мощности transmitting tube – передающая трубка Task 1. Fill in the blanks with the words from the box. Equipment, inventor, parabolic dish, frequency, amplifier, light 1. Outdated ________has been replaced. 2. Visible________ is visible to the human eye and is responsible for the sense of sight. 3. The largest radar tracking facility in western Europe was using a 34 metre ________ antenna. 4. For cyclical processes, such as rotation, oscillations, or waves, ________ is defined as a number of cycles per unit time. 5. Alexander Popov is considered to be the ________ of radio. 6. Electronic ________ or (informally) amp is an electronic device that can increase the power of a signal. Task 2. Read the text and answer the questions. 1. Who is considered to be the inventor of radar? 2. Who developed electro-magnetic light theory? What’s this theory about? 3. Who proved Maxwell’s electro-magnetic light theory? 4. When were electro-magnetic waves discovered? 5. What made it possible to calculate the distance between “Telemobiloskop” and an object (ship)? 6. When was Magnetron invented? 7. What company first presented Klystron?

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Historical Overview Neither a single nation nor a single person is able to say, that he (or it) is the inventor of the radar method. One must look at the “Radar” than an accumulation of many developments and improvements earlier, which scientists of several nations parallel made share. There are nevertheless some milestones with the discovery of important basic knowledge and important Figure 1. “Würzburg Riese”, inventions: World War II radar produced 1865 The Scottish physicist James Clerk in 1940 by Telefunken Maxwell developed his electro-magnetic light (Germany) theory (Description of the electro-magnetic waves and their propagation) 1886 The German physicist Heinrich Rudolf Hertz discovers the electromagnetic waves and proves the theory of Maxwell with that. 1904 The German high frequency engineer Christian Hülsmeyer invents the “Telemobiloskop” to do the traffic supervision on the water. He measures the running time of electro-magnetic waves to a metal object (ship) and back. A calculation of the distance is thus possible. This is the first practical radar test. Hülsmeyer registers his invention to the patent in Germany and in the United Kingdom. 1917 The French engineer Lucien Lévy invents the super-heterodyne receiver. He uses as first the denomination “Intermediate Frequency”, and alludes the possibility of double heterodyning. 1921 The invention of the Magnetron as an efficient transmitting tube by the US-American physicist Albert Wallace Hull. 1922 The American electrical engineers Albert H. Taylor and Leo C. Young of the Naval Research Laboratory (USA) locate a wooden ship for the first time. 1930 Lawrence A. Hyland (also of the Naval Research Laboratory) locates an aircraft for the first time. 1931 A ship is equipped with radar. As antennae are used parabolic dishes with horn radiators. 1936 The development of the Klystron by the technicians George F. Metcalf and William C. Hahn, both from General Electric. This will be an important component in radar units as an amplifier or an oscillator tube. 1940 Different radar equipment is developed in the USA, Russia, Germany, France and Japan.

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Figure 2. Cover of the patent script

The reasoning to use of electric magnetic waves to the locating of ships has been registered of the engineer of Düsseldorf, Christian Hülsmeyer, already 1904 in Germany and England as a patent. One finds the illustration in the patent specification of a steamer which detects an approaching ship with help of the backscattering. Tests carried out on the Rhine River had in principle yielded the usefulness of this method. (https://www.radartutorial.eu/04.history/hi04.en.html) Task 3. Make all possible two-words phrases with the words from the opposite columns. to prove metal high frequency basic practical light electro-magnetic neither research super-heterodyne

nor theory waves receiver test object engineer knowledge laboratory principle

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Section 2 Vocabulary: detecting – обнаружение ranging – определение дальности reflection – отражение sound-reflecting – звуковое отражение determine – определять range – дальность аngle – угол highly sensitive – высокочувствительный contraction – сокращение measure – измерять pulse – импульс estimate – оценивать Task 1. Fill in the blanks with the words from the box. Ranging, estimate, reflection, pulse detection, measuring, 1. The term RADAR was coined in 1940 by the United States Navy as an acronym for Radio ________ And ________. 2. I saw my ________in the mirror. 3. The builders ________ the cost of repairing the roof at $600. 4. The metre is the standard unit for ________ length in the SI system. 5. A ________ in signal processing is a rapid change in the amplitude of a signal from a baseline value to a higher or lower value, followed by a rapid return to the baseline value. Task 2. Read the text and answer the questions. 1. What is returned energy? 2. How can we produce an echo? 3. How is the distance to the object determined? 4. What is the basic principle of radar operation? 5. What is radar used for? Radar Basic Principles The electronic principle on which radar operates is very similar to the principle of sound-wave reflection. If you shout in the direction of a soundreflecting object (like a rocky canyon or cave), you will hear an echo. If you know the speed of sound in air, you can then estimate the distance and general direction of the object.

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The time required for an echo to return can be roughly converted to distance if the speed of sound is known.

Figure 3. Radarprinciple

Radar uses electromagnetic energy pulses in much the same way, as shown in Figure 3. The radio-frequency (RF) energy is transmitted to and reflected from the reflecting object. A small portion of the reflected energy returns to the radar set. This returned energy is called an ECHO, just as it is in sound terminology. Radar sets use the echo to determine the direction and distance of the reflecting object. The word radar is a contraction of RAdio Detecting And Ranging. As implied by this contraction, radars are used to detect the presence of an aim (as object of detection) and to determine its location. The contraction implies that the quantity measured is range. While this is correct, modern radars are also used to measure range and angle. The following figure shows the operating principle of primary radar. The radar antenna illuminates the target with a microwave signal, which is then reflected and picked up by a receiving device. The electrical signal picked up by the receiving antenna is called echo or return. The radar signal is generated by a powerful transmitter and received by a highly sensitive receiver.

Figure 4. Block diagram of a primary radar with the signal flow

(https://www.radartutorial.eu/01.basics/Radar%20Principle.en.html) 8

Task 3. Make all possible two-words phrases with the words from the opposite columns. basic speed electromagnetic roughly echo to determine radar primary reflecting

signal converted location object set of sound principle radar energy Section 3

Vocabulary: short duration high-power RF- pulses – короткие радиочастотные импульсы высокой мощности switching – переключение transfer – передавать reception – приём travel – распространяться (о волне) velocity – скорость duplexer – антенный переключатель amplify – усиливать demodulate – демодулировать (выделять модулирующий сигнал из модулированного колебания несущей частоты) backscatter – обратное рассеивание incident ray – падающий луч plan position indicator (PPI) – индикатор знакографической информации bearing – азимут time synchronization – синхронизация времени time-dependent – зависимый от времени pulse width – ширина импульса returning echo – вернувшиеся импульсы эхо circuit – схема pulse-repetition time (PRT) – время повторения импульса reciprocal – обратная величина affect – влиять

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Task 1. Fill in the blanks with the words from the box. Velocity, affect, switch, circuit, duplexer, amplify 1. You can ________ between modes using the Up-Down keys. 2. Another term for «speed» is ________. 3. In radar and radio communications systems ________ isolates the receiver from the transmitter while permitting them to share a common antenna. 4. These amplifiers are also useful when you need to ________ low-level signals in multi-channel applications. 5. The________ consists of a voltage source, a resistor and conductor. 6. New technologies can ________ how science is conducted and applied. Task 2. Read the text and answer the questions. 1. What does radar transmitter produce? 2. What is the function of duplexer? 3. In what form are transmitted pulses radiated from antenna? 4. What does indicator provide? 5. How do you define backscatter? 6. What is synchronization between the transmitter and receiver of a radar set is required for? 7. What is the function of synchronizer? 8. What does PRT stand for? 9. How is number of pulses that are transmitted per second designated? 10. Can the frequency of pulse transmission affect the maximum range of displayed pulses? Signal Routing  The radar transmitter produces short duration high-power RF- pulses of energy.  The duplexer alternately switches the antenna between the transmitter and receiver so that only one antenna need be used. This switching is necessary because the high-power pulses of the transmitter would destroy the receiver if energy were allowed to enter the receiver.  The antenna transfers the transmitter energy to signals in space with the required distribution and efficiency. This process is applied in an identical way on reception.  The transmitted pulses are radiated into space by the antenna as an electromagnetic wave. This wave travels in a straight line with a constant velocity and will be reflected by an aim.  The antenna receives the back scattered echo signals.

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 During reception the duplexer lead the weakly echo signals to the receiver.  The hypersensitive receiver amplifies and demodulates the received RFsignals. The receiver provides video signals on the output.  The indicator should present to the observer a continuous, easily understandable, graphic picture of the relative position of radar targets. All targets produce a diffuse reflection i.e. it is reflected in a wide number of directions. The reflected signal is also called scattering. Backscatter is the term given to reflections in the opposite direction to the incident rays. Radar signals can be displayed on the traditional plan position indicator (PPI) or other more advanced radar display systems. A PPI has a rotating vector with the radar at the origin, which indicates the pointing direction of the antenna and hence the bearing of targets. It shows a map-like picture of the area covered by the radar beam. Signal Timing Most functions of a radar set are time-dependent. Time synchronization between the transmitter and receiver of a radar set is required for range measurement. Radar systems radiate each pulse during transmit time (or Pulse Width τ), wait for returning echoes during listening or rest time, and then radiate the next pulse, as shown in Figure 5. A so called synchronizer coordinates the timing for range determination and supplies the synchronizing signals for the radar. It sent simultaneously signals to the transmitter, which sends a new pulse, and to the indicator, and other associated circuits.

Figure 5. A typical radar time line

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The time between the beginning of one pulse and the start of the next pulse is called pulse-repetition time (PRT) and is equal to the reciprocal of PRF as follows: 1 PRT = PRF The Pulse Repetition Frequency (PRF) of the radar system is the number of pulses that are transmitted per second. The frequency of pulse transmission affects the maximum range that can be displayed, as we shall see later. (https://www.radartutorial.eu/01.basics/Radar%20Principle.en.html) Task 3. Make all possible two-words phrases with the words from the opposite columns. to travel reflected radiated constant alternately hypersensitive identical backscattered video

way switches echo signals signals by an aim receiver in a straight line velocity into space Section 4

Vocabulary: running time – время прохождения (продолжительность) high-frequency transmitted signal – высокочастотный переданный сигнал propagation – распространение slant range – угол места line of sight distance – линия прямой видимости target – цель target's elevation – высота цели round trip time – время, прохождения сигнала до цели и обратно pulsed radars – импульсные радары sequence of pulses – последовательность импульсов leading edge – передний фронт pulse repetition time (PRT) – время повторения импульса ambiguous – неоднозначный, неопределенный

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Task 1. Fill in the blanks with the words from the box. Round-trip, target, propagation, leading, elevation, sequence 1. The free electrons in the ionosphere had a strong influence on the ________ of radio signals. 2. The radar antenna illuminates the ________ with a microwave signal, which is then reflected and picked up by a receiving device. 3. Space beyond the ________ of approximately 100 kilometers above sea level of the Earth. 4. Each of the above expressions can be represented by a ________ of bits and bytes. 5. The ________edge is the part of the wing that first contacts the air; alternatively it is the foremost edge of an airfoil section. 6. In telecommunications, the________ delay time (RTD) is the length of time it takes for a signal to be sent plus the length of time it takes for an acknowledgement of that signal to be received. Task 2. Read the text and answer the questions. 1. How is the distance of the aim determined? 2. What is slant range? 3. What knowledge is needed to calculate ground range? 4. How is the distance between a target and the radar set calculated? 5. How is the maximum unambiguous range for given radar system found? Ranging The distance of the aim is determined from the running time of the highfrequency transmitted signal and the propagation c0. The actual range of a target from the radar is known as slant range. Slant range is the line of sight distance between the radar and the object illuminated. While ground range is the horizontal distance between the emitter and its target and its calculation requires knowledge of the target's elevation. Since the waves travel to a target and back, the round trip time is divided by two in order to obtain the time the wave took to reach the target. Therefore the following formula arises for the slant range: 𝑅=

𝑡𝑑𝑒𝑙𝑎𝑦 ∗ 𝑐0 2

Where tdelay is the time taken for the signal to travel to the target and teturn, c0 is the speed of light (approximately 3·108 m/s). If the respective running time 𝑡𝑑𝑒𝑙𝑎𝑦 is known, then the distance R between a target and the radar set can be calculated by using this equation.

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Maximum Unambiguous Range A problem with pulsed radars and range measurement is how to unambiguously determine the range to the target if the target returns a strong echo. This problem arises because of the fact that pulsed radars typically transmit a sequence of pulses. The radar receiver measures the time between the leading edges of the last transmitting pulse and the echo pulse. It is possible that an echo will be received from a long range target after the transmission of a second transmitting pulse.

Figure 6. А second-sweep echo in a distance of 400 km assumes a wrong range of 100 km

In this case, the radar will determine the wrong time interval and therefore the wrong range. The measurement process assumes that the pulse is associated with the second transmitted pulse and declares a much reduced range for the target. This is called range ambiguity and occurs where there are strong targets at a range in excess of the pulse repetition time. The pulse repetition time defines a maximum unambiguous range. To increase the value of the unambiguous range, it is necessary to increase the PRT, this means: to reduce the PRF. Echo signals arriving after the reception time are placed either into the  transmit time where they remain unconsidered since the radar equipment isn't ready to receive during this time, or  into the following reception time where they lead to measuring failures (ambiguous returns). The maximum unambiguous range for given radar system can be determined by using the formula: R unamb = (PRT − τ) ∗ c0 /2 The pulse repetition time (PRT) of the radar is important when determining the maximum range because target return-times that exceed the PRT of the radar system appear at incorrect locations (ranges) on the radar screen. Returns that appear at these incorrect ranges are referred as ambiguous returns or second time around (second-sweep) echoes. The pulse width τ in this equation indicates that the complete echo impulse must be received. (https://www.radartutorial.eu/01.basics/Maximum%20Unambiguous%20 Range.en.html)

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Task 3. Make all possible two-words phrases with the words from the opposite columns. running pulsed line speed measurement range leading slant round high

of light frequency trip time time range edge process radar of sight measurement Section 5

Vocabulary: avoid – избегать value – значение suffer – терпеть pulse compression radar – импульсивно-компрессионный радар surface movement radar – радар наземного движения air-defense radar – зенитныйрадар ATC air surveillance radar – радар воздушного наблюдения slope range – диапазон наклона topographical distance – топографическое расстояние false measurement – ложное измерение directivity – направленность directive antenna – направленная антенна point – метка Task 1. Fill in the blanks with the words from the box. Avoid, radar, false, directivity, measurement, surface 1. Military should always ________ civilian casualties. 2. SI units are the standard units of________ used all over the world. 3. In electromagnetics, ________ is a parameter of an antenna or optical system which measures the degree to which the radiation emitted is concentrated in a single direction. 4. One ________ move could mean war. 5. These waves reach the earth ________ from the outer space. 6. All ground-based primary________ systems are capable of aircraft detection and tracking. 15

Task 2. Read the text and answer the questions. 1. What does the minimum detectable range depend on? 2. Why is the receiver disconnected from the transmitter during transmission? 3. What is typical pulse width for: air-defense radar, ATC air surveillance radar, surface movement radar? 4. Can false measurement be corrected? How? 5. How is directivity defined? Radar Waveforms Minimum Range The minimum detectable range (or blind distance) is also a consideration. When the leading edge of the echo pulse falls inside the transmitting pulse, it is impossible to determine the “round trip time”, which means that the distance cannot be measured. The minimum detectable range R min depends on the transmitters pulse with τ, and the recovery time trecovery of the duplexer. 𝑅𝑚𝑖𝑛 =

(𝜏 + 𝑡𝑟𝑒𝑐𝑜𝑣𝑒𝑟𝑦 ) ∗ 𝑐0 2

The receiver does not listen during the transmitting pulse, because it needs to be disconnected from the transmitter during transmission to avoid damage. In that case, the echo pulse comes from a very close target. Targets at a range equivalent to the pulse width from the radar are not detected. A typical value of 1 µs for the pulse width of short range radar corresponds to a minimum range of about 150 m, which is generally acceptable. However, radars with a longer pulse width suffer a relatively large minimum range, notably pulse compression radars, which can use pulse lengths of the order of tens or even hundreds of microseconds. Typical pulse widthτ for  Air-defense radar: up to 800 μs (R min = 120 km)  ATC air surveillance radar: 1.5 μs (R min = 250 m)  Surface movement radar: 100 ns (R min = 25 m) Slant Range Cause by the fact that the radar unit measures a slope range, the radar measures different ranges of two airplanes, which exactly one above the other flies (therefore having the same topographical distance to the radar unit exactly). This false measurement could be corrected by software, or module in modern radar sets with digital signal processing.

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Figure 7. Different height causes a different slant range

Direction determination Bearing The direction to the target is determined by the directivity of the antenna. Directivity, sometimes known as the directive gain, is the ability of the antenna to concentrate the transmitted energy in a particular direction. An antenna with high directivity is also called a directive antenna. By measuring the direction in which the antenna is pointing when the echo is received, both the azimuth and elevation angles from the radar to the object or target can be determined. The accuracy of angular measurement is determined by the directivity, which is a function of the size of the antenna.

Figure 8. True Bearing

(https://www.radartutorial.eu/01.basics/Direction-determination.en.html)

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Task 3. Make all possible two-words phrases with the words from the opposite columns. to correspond to blind pulse hundreds recovery to avoid transmitting leading sometimes close

time edge damage known as pulse target of microseconds width a minimum range distance Section 6

Vocabulary: true bearing – истинный азимут clockwise direction – по часовой стрелке relative angle – относительный угол turn table – поворотный стол mounted antenna – установленная антенна scope – осциллограф servosystem – система автоматического регулирования missile launcher – ракета-носитель synchro torque transmitters – сельсин-датчик (датчик крутящего момента) synchro torque receiver – сельсин-приемник Azimuth-Change-Pulses (ACP) – сигнал изменения азимута electronic phase scanning – электронное фазированное сканирование elevation angle – угол места altitude – высота refraction – преломление wavelength – длина волны Task 1. Fill in the blanks with the words from the box. Refraction, clockwise, elevation angle, missile launcher, altitude, wavelength 1. In the case of a rotary switch, operation of the switch in a________ direction shall engage the vehicle's position. 2. Detection became possible when the aircraft gained ________.

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3. When the ultimate use was precise positioning, such________ was considered a source of error that had to be removed with the appropriate mathematical treatment. 4. The distance between adjacent waves is called the________. 5. The geographical area where these conditions are met is based on coverage data and ________ recommendations provided by INTELSAT. 6. A mobile ballistic missile defence system uses mobile ________, missile interceptors and radar systems. Task 2. Read the text and answer the questions. 1. How is true bearing measured? 2. What is the relative bearing? 3. Which radars use electronic phase scanning? 4. How is elevation angle measured? 5. What factors affect the electromagnetic wave propagation? True Bearing The True Bearing (referenced to true north) of a radar target is the angle between true north and a line pointed directly at the target. This angle is measured in the horizontal plane and in a clockwise direction from true north. The bearing angle to the radar target may also be measured in a clockwise direction from the centerline of your own ship or aircraft and is referred to as the relative bearing. The rapid and accurate transmission of the bearing information between the turn table with the mounted antenna and the scopes can be carried out for:  servo systems and  counting of azimuth change pulses. Servo systems are used in older radar antennas and missile launchers and works with help of devices like synchro torque transmitters and synchro torque receivers. In other radar units we find a system of Azimuth-Change-Pulses (ACP). In every rotation of the antenna a coder sends many pulses, these are then counted in the scopes. Some radar sets work completely without or with a partial mechanical motion. These radars employ electronic phase scanning in bearing and/or in elevation (phased-array-antenna).

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Elevation Angle The elevation angle is the angle between the horizontal plane and the line of sight, measured in the vertical plane. The Greek letter Epsilon (ε) describes the elevation angle. The elevation angle is positive above the horizon (0° elevation angle), but negative below the horizon. Figure 9. Definition of elevation angle

Height The height of a target over the earth's surface is called height or altitude. This is denominated by the letter H (like: Height) in the following formulae and figures. True altitude is the actual airplane distance above mean sea level. The altitude can be calculated with the values of distance R and elevation angle ε, as shown in Figure 11, where: R = aims slant range ε = measured elevation angle re = earth's equivalent radius (about 6370 km)

Figure 10. Altitude vs Height

In practice, however, the propagation of electromagnetic waves is also subject to refraction, this means, the transmitted beam of the radar unit isn't a straight side of this triangle but this side is also bent and it depends on:  the transmitted wavelength,  the barometric pressure,  the air temperature and  the atmospheric humidity. Therefore, all these equations are an approximation only. Figure 11. Calculation of height

(https://www.radartutorial.eu/01.basics/Measurement%20of%20the%20el evation%20angle.en.html) 20

Task 3. Make all possible two-words phrases with the words from the opposite columns. measure radar accurate missile mechanical to send clockwise

direction angle target motion transmission launcher pulse Section 7

Vocabulary: accuracy – точность conformance – соответствие cоnfuse – путать, смешивать radar resolution – разрешающая способность радара uncertainty – неопределенность residual bias – остаточная систематическая погрешность true value – истинное значение deviation – отклонение mean value – среднее значение exposure – подвергание, подверженность, воздействие Task 1. Fill in the blanks with the words from the box. Accuracy, residual, value, confuse, deviation, resolution 1. ________ of measurement is achieved by suppression of noise. 2. I always________ this man with his brother. 3. At the moment, the ________is limited to about 1 metre so it cannot be used to identify the shape of small targets. 4. Car imports’ ________ grew 50% due to the significant increase in the number of imported cars. 5. ________ from standard ratio was due to operational requirements. 6. ________ means resulting or left from something that was previously present. Task 2. Read the text and answer the questions. 1. What is accuracy? 2. What does the stated value of required accuracy represent? 3. Can the recommended probability level be near 50 percent? 21

4. Can you explain the meaning of true value? 5. What does the target resolution of radar distinguish? 6. What is angular resolution? Accuracy Accuracy is the degree of conformance between the estimated or measured position and/or the velocity of a platform at a given time and its true position or velocity. Radio navigation performance accuracy is usually presented as a statistical measure of system error. Accuracy should not be confused with radar resolution. The stated value of required accuracy represents the uncertainty of the reported value with respect to the true value and indicates the interval in which the true value lies with a stated probability The recommended probability level is 95 per cent, which corresponds to 2 standard deviations of the mean for a normal (Gaussian) distribution of the variable. The assumption that all known correction are taken into account implies that the errors in the reported values will have a mean value (or bias) close to zero. Any residual bias should be small compared with the stated accuracy requirement. The true value is that value which, under operational conditions, characterizes perfectly the variable to be measured or observed over the representative time, area and/or volume interval required, taking into account siting and exposure.

Figure 12. Dependence of the accuracy of the range (Source: MIT Lincoln Laboratory)

Radar Resolution The target resolution of radar is its ability to distinguish between targets that are very close in either range or bearing. Weapons-control radar, which requires great precision, should be able to distinguish between targets that are only yards apart. Search radar is usually less precise and only distinguishes between targets that are hundreds of yards or even miles apart. Radar resolution is usually divided into two categories; range resolution and angular (bearing) resolution. 22

Angular Resolution Angular resolution is the minimum angular separation at which two equal targets at the same range can be separated. The angular resolution characteristics of a radar are determined by the antenna beam width represented by the -3 dB angle Θ which is defined by the halfpower (-3 dB) points. The half-power points of the antenna radiation Figure 13. Angular resolution pattern (i.e. the -3 dB beam width) are normally specified as the limits of the antenna beam width for the purpose of defining angular resolution; two identical targets at the same distance are, therefore, resolved in angle if they are separated by more than the antenna beam width. An important remark has to be made immediately: the smaller the beam width, the higher the directivity of the radar antenna, the better the bearing resolution. The angular resolution as a distance between two targets depends on the slant-range. (https://www.radartutorial.eu/01.basics/Radars%20Accuracy.en.html) Task 3. Make all possible two-words phrases with the words from the opposite columns. mean radio operational system with respect radar residual performance to take

accuracy error to the true value resolution into account conditions navigation value bias

23

Section 8 Vocabulary: range resolution – разрешающая способность по дальности distinguish – отличать, различать, дифференцировать depend on – зависеть pulse compression system – система сжатия импульсов bandwidth – ширина полосы пропускания higher average power – более высокая средняя мощность resolution cell – элемент ячейки; разрешающая способность ячейки Doppler shifts – доплеровский сдвиг по частоте aperture angle – угловая апертура Task 1. Fill in the blanks with the words from the box. Doppler shifts, bearing, resolution, depend, bandwidth. 1. The display modes or ________ of a digital television, computer monitor or display device is the number of distinct pixels in each dimension that can be displayed. 2. Specific operations can vary and ________ on the type of data displayed and rules of processing of this data. 3. ________ indicates the maximum capacity of a network link transmitting bits of data on a per-second basis. 4. Radar systems provide range and ________ to the target. 5. The change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source is called ________. Task 2. Read the text and answer the questions. 1. What is range resolution? 2. What does the degree of range resolution depend on? 3. How can a well-designed radar system distinguish targets? 4. How is the range-resolution of the radar given? 5. What allows very high resolution to be obtained with long pulses and a higher average power? 6. What do the range and angular resolutions lead to? Range Resolution Range resolution is the ability of a radar system to distinguish between two or more targets on the same bearing but at different ranges. The degree of range resolution depends on the width of the transmitted pulse, the types and sizes of targets, and the efficiency of the receiver and indicator. Pulse width is the primary factor in range resolution. A well-designed radar system, with all other factors at 24

maximum efficiency, should be able to distinguish targets separated by one-half the pulse width time. Therefore, the theoretical range resolution of a radar system can be calculated from the following formula: 𝑐 ∗𝜏

𝑆𝑟 = 0 [𝑚]𝑐0= speed of light 2 τ = transmitters pulse width Sr= range resolution as a distance between the two targets

Figure 14. Two aims with too small spacing

Figure 15. Two aims, when the spacing is large enough

In a pulse compression system, the range-resolution of the radar is given by the bandwidth of the transmitted pulse (Btx), not by its pulse width. 𝑆𝑟 ≥

𝑐0 2𝐵𝑡𝑥

[𝑚]𝑐0 = speed of light

𝐵𝑡𝑥 = band width of the transmitted pulse Sr = range resolution as a distance between the two targets Resolution Cell The range and angular resolutions lead to the resolution cell. The meaning of this cell is very clear: unless one can rely on eventual different Doppler shifts it is impossible to distinguish two targets which are located inside the same resolution cell. The shorter the pulse with τ (or the broader the spectrum of the transmitted pulse) and the narrower the aperture angle are, the smaller the resolution cell, and the higher the interference Figure 16. The resolution cell immunity of the radar station is. (https://www.radartutorial.eu/01.basics/Range%20Resolution.en.html)

25

Task 3. Make all possible two-words phrases with the words from the opposite columns. ability clear high Doppler pulse maximum size aperture resolution interference

shift efficiency of a target compression cell angle immunity to distinguish resolution meaning

26

2 COURSE Section 9 Vocabulary: range equation – основное уравнение дальности действия рлк станции dependence – зависимость relate – устанавливать связь или отношение affect – воздействовать value – величина antenna gain – усиление антенны, коэффициент усиления average – средний directive gain – коэффициент направленного действия arbitrary direction – произвольное направление figure of merit – критерий качества Task 1. Fill in the blanks with the words from the box. Range, dependence, affect, value, average, directive, gain, direction 1. According to statistics, the _________ income of women is 64 per cent of the income of men across the country. 2. The bearing angle to the radar target may also be measured in a clockwise _________ from the centerline of your own ship or aircraft. 3. This _________ shall be calculated using intervals of five nanometres. 4. The country's _________ on foreign sources of food supply has increased. 5. This transmitter records everything from the camera but would go out of _________ outside of 50 feet. 6. Directivity, sometimes known as the _________, is the ability of the antenna to concentrate the transmitted energy in a particular direction. 7. The only force strong enough to _________ global weather is the sun. Task 2. Read the text and answer the questions. 1. What does the radar equation represent? 2. Give and describe the formula of the equation. 3. What is expressed by P and Prx? 4. How are returned power and transmitted power related? 5. What power is required to detect a target? 6. What does antenna gain mean? 7. What parameters are associated with the antenna gain 8. Can antenna gain serve as a figure of merit?

27

Theoretical Maximum Range Equation The radar equation represents the physical dependences of the transmit power, that is the wave propagation up to the receiving of the echo-signals. Furthermore one can assess the performance of the radar with the radar equation. The received energy is an extremely small part of the transmitted energy. How small is it? 𝐺 2 ∙ 𝜆2 ∙ 𝜎𝑡 𝑃𝑟𝑥 = 𝑃𝑡𝑥 [ ] (4𝜋)3 ∙ 𝑅 4 ∙ 𝐿𝑆 The radar equation relates the important parameters affecting the received signal of radar. The derivation is explained in many texts. Now we want to study, what kinds of factors are expressed in this radar equation. Ptx is the peak power transmitted by the radar. This is a known value of the radar. It is important to know because the power returned is directly related to the transmitted power. P rx is the power returned to the radar from a target. This is an unknown value of the radar, but it is one that is directly calculated. To detect a target, this power must be greater than the minimum detectable signal of the receiver. Antenna Gain The antenna gain of the radar is a known value. This is a measure of the antenna's ability to focus outgoing energy into the directed beam.

𝐺=

maximum radiation intensity average radiation intensit

Antenna gain describes the degree to which an antenna concentrates electromagnetic energy in a narrow angular beam. The two parameters associated with the gain of an antenna are the directive gain and directivity. The gain of an antenna serves as a figure of merit relative to an isotropic source with the directivity of an isotropic antenna being equal to 1. The power received from a given target is directly related to the square of the antenna gain, while the antenna is used both for transmitting and receiving.  The antenna gain increases the transmitted power in one desired direction.  The reference is an isotropic antenna, which equally transmits in any arbitrary direction. For example, if the focused beam has 50 times the power of an omni directional antenna with the same transmitter power, the directional antenna has a gain of 50 (or 17 Decibels). 28

Figure 16. Pattern of a highly directional antenna compared with a ball-shaped isotropic pattern

(https://www.radartutorial.eu/01.basics/The%20Radar%20Range%20Equ ation.en.html) Task 3. Make all possible two-words phrases with the words from the opposite columns. radar wave received physical known antenna directly extremely peak detectable

dependences small value related signal power energy gain equation propagation Section 10

Vocabulary: process – обрабатывать pick up – улавливать within – впределах, внутри deliver – доставлять antenna load – антеннаянагрузка power density – плотность мощности dish antennas – спутниковая антенна irregularities – нарушения radar cross-section – радиолокационное поперечное сечение incident energy – энергия падающей волны

29

Task 1. Fill in the blanks with the words from the box. Dish antenna, deliver, within, processes, antenna load, irregularities, incident energy 1. Tracking Server _________ radar video data to extract plots, from which it tracks targets of interest. 2. The atmospheric temperature should be _________ the range of 278 up to and including 313 K. 3. The United Nations is able to mobilize, _________ and coordinate humanitarian assistance. 4. Transmitter power is rated based on a 0-db _________ —that is, the resistance and output of the antenna are assumed to be exactly the same as those of the transmitter feeding it. 5. _________ is a type of parabolic antenna. 6. Election _________ in the country were certainly a problem. 7. The polarization property of microwaves was very useful in differentiating objects on the ground, as surfaces reflect differently depending on the polarization of the _________. Task 2. Read the text and answer the questions. 1. How does transmission differ from reception? 2. What is antenna's aperture? 3. What is the relation between the dimensions of an antenna, gain and frequency? 4. What does RCS stand for? 5. In what case the radar cross section would be equal to the target's crosssectional area? 6. Why is the radar cross-section difficult to estimate? 7. What does the target radar cross sectional area depend on? Antenna Aperture Remember: the same antenna is used during transmission and reception. In case of transmission the whole energy will be processed by the antenna. In case of receiving, the antenna has got the same gain, but the antenna receives a part of the incoming energy only. But as a second effect is that of the antenna's aperture, which describes how well an antenna can pick up power from an incoming electromagnetic wave.

30

As a receiver, antenna aperture can be visualized as the area of a circle constructed broadside to incoming radiation where all radiation passing within the circle is delivered by the antenna to a matched load. Thus incoming power density (watts per square meter) • aperture (square meters) = available power from antenna (watts). Antenna gain is directly proportional to aperture. An isotropic antenna has an aperture of λ² / 4π. An antenna with a gain of G has an aperture of G • λ² / 4π. The dimensions of an antenna depend of their gain G and/or of the used wavelength λ as the expression of the radar transmitters’ frequency. The higher the frequency, the smaller the antenna, or the higher is its gain by equal dimensions. Large dish antennas like radar antennas have an aperture nearly equal to their physical area, and have got a gain of normally 32 up to 40 Decibels. Changes of the quality of the antenna (antenna-irregularities, like deformations or ice) have a very big influence. Radar Cross Section The size and ability of a target to reflect radar energy can be summarized into a single term, σt, known as the radar cross-section RCS, which has units of m². If absolutely all of the incident radar energy on the target were reflected equally in all directions, then the radar cross section would be equal to the target's cross-sectional area as seen by the transmitter. In practice, some energy is absorbed and the reflected energy is not distributed equally in all directions. Therefore, the radar cross-section is quite difficult to estimate and is normally determined by measurement. The target radar cross sectional area depends of:  the airplane’s physical geometry and exterior features,  the direction of the illuminating radar,  the radar transmitters frequency,  used material types of the reflecting surface.

Figure 17. The experimental radar cross section of the B-26 aircraft at 3 GHz frequency as a function of azimuth angle

31

Table 1 Examples of Radar Cross Section Targets RCS [m2] Jumbo Jet 100 jet airliner 20 … 40 large fighter 6 helicopter 3 four-passenger jet 2 small aircraft 1 stealth jet 0.1 … 0.01

RCS [dB] 20 13 … 16 7.8 4.7 3 0 -10 …-20

(https://www.radartutorial.eu/01.basics/Radar%20Cross%20Section.en.h tml) Task 3. Make all possible two-words phrases with the words from the opposite columns. incoming to be processed within directly constructed antenna's matched electromagnetic to depend equal

aperture wave broadside load the circle energy proportional on the gain by the antenna dimensions Section 11

Vocabulary: free-space path loss – потери (дорожки, ориентира) в свободном пространстве target range – дальность цели atmospheric loss – потери при атмосферных помехах line-of-sight path – линия прямой видимости diffraction – преломление obstacle – препятствие power loss – потери мощности quantity – величина attenuation – ослабление, затухание precipitation – осадки elevation angle – угол повышения

32

Task 1. Fill in the blanks with the words from the box. Precipitation, obstacle, power loss, diffraction quantity, target range, attenuation 1. The existence of the condensate was determined by light _________ on a microscopic specimen. 2. In physics, acceleration is defined as the rate of change of velocity, or, equivalently, as the second derivative of position. It is thus a vector_________ with dimension length/ time. 3. This can be due to many factors including interference and, in the case of long transmissions, signal _________. 4. Two indicators under climate change are temperature and_________ . 5. Capacities to measure _________ and other factors, such as speed, are also required. 6. We need to overcome that _________ if we are finally to make progress. 7. There is electric _________ in the third sector, but I'll fix it tomorrow. Task 2. Read the text and answer the questions. 1. How can the target range be calculated? 2. What does free-space path loss mean? 3. What is the reason of the loss in signal strength? 4. Why is it necessary to calculate a value of external and internal losses? 5. What is the attenuation by precipitation? 6. What will occur by 3Decibels loss? Free-space Path Loss P is the target range of the term in the equation. This value can be calculated by measuring the time it takes the signal to return. The range is important since the power obtaining a reflecting object is inversely related to the square of its range from the radar. Free-space path loss is the loss in signal strength of an electromagnetic wave that would result from a line-of-sight path through free space, with no obstacles nearby to cause reflection or diffraction. The power loss is proportional to the square of the distance between the radars transmitter and the reflecting obstacle. The expression for freespace path loss actually encapsulates 33

two effects. Firstly, the spreading out of electromagnetic energy in free space is determined by the inverse square law. The intensity (or illuminance or irradiance) of linear waves radiating from source (energy per unit of area perpendicular to the source) is inversely proportional to the square of the distance from the source as shown in Figure 18. An area of surface A1 (as of the same size as an area of surface A2) twice as far away, receives only a quarter of the energy SA1. The same is true for both directions: for the transmitted, and the reflected signal. So this quantity is used as squared in the equation.

Figure 18. Non-directional power density diminishes as geometric spreading of the beam

External and Internal Losses This is the sum of all loss factors of the radar. This is a value that is calculated to compensate for attenuation by precipitation, atmospheric gases, and receiver detection limitations. The attenuation by precipitation is a function of precipitation intensity and wavelength. For atmospheric gases, it is a function of elevation angle, range, and wavelength. Since all of this is taken in account for e.g. 3 Decibels loss, all signals are weakened by half the value. Some of these losses are unavoidable. Some of these can be influenced by radar technicians. (https://www.radartutorial.eu/01.basics/Typical%20Search%20Radar%2 0Loss%20Budget.en.html) Task 3. Make all possible two-words phrases with the words from the opposite columns. free inversely

strength obstacle 34

area signal path electromagnetic square reflecting atmospheric as shown

law gases loss related of surface in the Figure wave space Section 12

Vocabulary: beam shape loss – потери, обусловленные формой диаграммы направленности антенны beam width factor – коэффициент ширины луча filter matching loss – потери на согласовании c фильтром fluctuation loss – потери колебаний integration loss – потери в степени интеграции (низкая, средняя, высокая, сверхвысокая и т.д.) miscellaneous signal-processing loss – непредвиденные потери при обработке сигналов receive line loss – потери линии при приеме transmit line loss – потери линии при передачи factors of influence – факторы воздействия theoretical maximum range – теоретически максимально-возможная дальность Task 1. Fill in the blanks with the words from the box. Influence, signal processing, range, beam, loss, width 1. When traditional linear polarizer acts on unpolarized light flux, the resulting ________ of intensity is about 50%. 2. Transport and communications ________ greatly the environment. 3. Radar is a detection system that uses radio waves to determine the ________, angle, or velocity of objects. 4. ________ is an electrical engineering subfield that focuses on analysing, modifying and synthesizing signals such as sound, images and biological measurements. 5. The volume of a rectangle is: ________ × length × height. 6. A laser-________ guided missile allows to fire on the move if the line of sight is stable.

35

Task 2. Read the text and answer the questions. 1. What does radar equation transformation provide? 2. What is called Minimum Discernible Signal? 3. Can maximum range of given radar set be calculated theoretically? 4. What is the dependence between transmitted power and power of range? 5. How can the maximum range be doubled? Converting the Equation This radar equation can be transformed to see the factors of influence of some technical characteristics of given radar set, and to determine its theoretical maximum range. Perhaps the most important feature of this converted equation is the fourth-root dependence. The smallest signal that can be detected by the radar is called Minimum Discernible Signal. Smaller powers than this PMDS aren't usable since they are lost in the noise of the receiver and its environment. The minimum power is detected at the maximum range Rmax as seen from the equation. So the theoretically maximum range of given radar set can be calculated. Transmitters Power The more transmitted power, the more power of range, but: Note this fourth root! To double the maximum range you must increase the transmitted power 16-fold! The inversion of this argument is also permissible: if the transmit power is reduced by 1/16 (e.g. failures into two of 32 transmitter modules), then the change on the maximum range of the radar set is negligible in the practice: 4

4

√15/16 = √0.9375 = 0.982 < 2%

36

Figure 19. Decreased maximum range by defect or missing power modules in a solid state transmitter with 32 power modules

(https://www.radartutorial.eu/01.basics/The%20Radar%2equation%20in %20practice.en.html) Task 3. Make all possible two-words phrases with the words from the opposite columns. power factors important radar minimum fourth negligible solid Discernible converted

set power root in the practice state module of influence feature equation Signal Section 13

Vocabulary: minimum discernible signal – минимально различимый сигнал echo power – мощность отражённого сигнала input jack – входной разъём Signal-to-Noise-Ratio – соотношение сигнал-шум agitation of electrons – возбуждение электронов front-endcomponent – подсистема первичной обработки данных low-noise preamplifier – малошумящий предусилитель

37

Task 1. Fill in the blanks with the words from the box. Low-noise, minimum detectable signal, power, agitation, input 1. A ________ is a signal at the input of a system whose power produces a signal-to-noise ratio of m at the output. In practice, m is usually chosen to be greater than unity. In some literature, the name sensitivity is used for this concept. 2. Thermal noise is caused by the thermal ________ of electrons in resistances. 3. A ________ amplifier (LNA) is an electronic amplifier that amplifies a very low-power signal without significantly degrading its signal-to-noise ratio. 4. These ________ jacks and connectors are used to input audio to the BR1600CD. 5. We will need new technologies to mobilize large-scale solar, wind, and geothermal ________. Task 2. Read the text and answer the questions. 1. What is the minimum discernible signal? 2. What are the typical radar values of the MDS echo? 3. Name the main source of noise. What is it due to? 4. What does noise arise from? 5. How can a very low noise figure receiver be achieved? 6. What does LNA stand for? What is it used for? MDS- Echo The minimum discernible signal is defined as the useful echo power at the reception antenna, which gives on the screen a discernible blip. The minimum discernible signal at the receiver input-jack leads to the maximum range of the radar; all other nominal variables are considered as constant. A reduction of the minimal received power of the receiver gets an increase of the maximum range. 𝑃𝑡𝑥 ∙ 𝐺 2 ∙ 𝜆2 ∙ 𝜎𝑡 𝑅𝑚𝑎𝑥 = √ (4𝜋)3 ∙ 𝑃𝑀𝐷𝑆 ∙ 𝐿𝑆 4

For every receiver there is a certain receiving power as of which the receiver can work at all. This smallest workable received power is frequently often called MDS – Minimum Discernible Signal or Minimum Detectable Signal in radar technology. Typical radar values of the MDS echo lie in the range of –104 dBm to – 113 dBm.

38

Figure 20. Signal-Noise-Ratio 3dB shown on an A-Scope

Noise The value of the MDS echo depends on the Signal-to-Noise-Ratio, defined as the ratio of the signal energy to the noise energy. All radars, as with all electronic equipment, must operate in the presence of noise. The main source of noise is termed thermal noise and is due to agitation of electrons caused by heat. The noise can arise from:  received atmospheric or cosmic noise  receiver noise – generated internally in the radar receiver. The overall receiver sensitivity is directly related to the noise figure of the radar receiver. It becomes clear, that a low noise figure receiver is accomplished by a good design in the very front-end components. An aspect to a very low noise figure receiver is achieved through minimizing the noise factor of the very first block. This component usual is characterized by a low noise figure with high gain.

Figure 21. Didactical Primary Radar

This is the reason for the often used denomination, low noise preamplifier (LNA). (https://www.radartutorial.eu/01.basics/Radar%20Coverage.en.html)

39

Task 3. Make all possible two-words phrases with the words from the opposite columns. reception generated radar frequently typical discernible electronic atmospheric low noise directly

blip called technology values equipment antenna internally noise related receiver Section 14

Vocabulary: false-alarm rate – частота ложных тревог interfering signals – помеха detection threshold – обнаружение порогового значения spurious signal – сигнал помехи valid target – важная цель erroneous detection – ложное обнаружение momentary blip – кратковременная вспышка CRT display – монитор с электронно-лучевой трубкой Task 1. Fill in the blanks with the words from the box. Blip, target, threshold, CRT displays, interfering signals, erroneous 1. Since 2000 all Wincor Nixdorf ATMs have been equipped with LCD displays service life of which is 2-3 times longer than of ________. 2. Undesirable ________ that are caused by components of the radar sensor itself are not modulated and can thus be separated by filtering from the wanted signal. 3. The ________ shall not exceed 60 seconds. 4. Current efforts to achieve that ________ were insufficient. 5. A small spot of light, sometimes with a short, sharp sound, that appears on a computer screen is called a ________. 6. They were also, I noted, "misleading, ________ and therefore unacceptable.

40

Task 2. Read the text and answer the questions. 1. What does a radar range equation determine? 2. What is a false alarm? 3. When are false alarms generated? 4. How can false alarms be shown? 5. What is the way to reduce false alarms? 6. What happens if the detection threshold is set too high or too low? 7. How should the threshold be balanced? Radar Range Equation (Example given) One of the important uses of the radar range equation is in the determination of detection range, or the maximum range at which a target has a high probability of being detected by the radar. Table 3 Example of a real radar set Radar Range Equation Parameter Metric units Radiated Power Ptx 1- 10 6 W Antenna Gain G 1900 Transmitters Wavelength Z (at 2,700 0.11m MHz)a (e.g. of a small Radar Cross Section 1 m2 aircraft) MDS echo PMDS 5 • 10 -15 W Sum of losses (see: Table 2) LS 128.8

Decibels 60 dBW 32.8 dB

-113 dBm 21.1 dB

If we substitute the metric values from the upper table into the radar range equation we get: 4

𝑅𝑚𝑎𝑥 = √

4 1 ∙ 106 𝑊 ∙ 19002 ∙ 0.112 ∙ 1 𝑚 4 𝑃𝑡𝑥 ∙ 𝐺 2 ∙ 𝜆2 ∙ 𝜎𝑡 √ = = 76.5 𝑘𝑚 (4𝜋)3 ∙ 𝑃𝑀𝐷𝑆 ∙ 𝐿𝑆 (4𝜋)3 ∙ 5 ∙ 10−15 𝑊 ∙ 128.8

The result expressed in nautical miles is 41.3 NM. False Alarm Rate A false alarm is “an erroneous radar target detection decision caused by noise or other interfering signals exceeding the detection threshold”. In general, it is an indication of the presence of a radar target when there is no valid target. The False Alarm Rate (FAR) is calculated using the following formula:

41

FAR =

𝑓𝑎𝑙𝑠𝑒 𝑡𝑎𝑟𝑔𝑒𝑡𝑠 𝑝𝑒𝑟 𝑃𝑅𝑇 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑟𝑎𝑛𝑔𝑒𝑐𝑒𝑙𝑙𝑠

False alarms are generated when thermal noise exceeds a pre-set threshold level, by the presence of spurious signals (either internal to the radar receiver or from sources external to the radar), or by equipment malfunction. A false alarm may be manifested as a momentary blip on a cathode ray tube (CRT) display, a digital signal processor output, an audio signal, or by all of these means. If the detection threshold is set too high, there will be very few false alarms, but the signal-to-noise ratio required will inhibit detection of valid targets. If the threshold is set too low, the large number of false alarms will mask detection of valid targets. Probability of Detection The received and demodulated echo signal is processed by threshold logic. This threshold shall be balanced so that as of certain amplitude wanted signals being able to pass and noise will be removed. Since high noise exists in the mixed signal tops which lie in the range of small wanted signals the optimized threshold level shall be a compromise. Wanted signals shall on the one hand reach the indication as of minimal amplitude; on the other hand the false alarm rate may not increase. PD =

𝑑𝑒𝑡𝑒𝑐𝑡𝑒𝑑 𝑡𝑎𝑟𝑔𝑒𝑡𝑠 𝑝𝑒𝑟 𝑛𝑎𝑙𝑙 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑏𝑙𝑖𝑏𝑠

∙ 100 %

The system must detect, with greater than or equal to 80% probability at a defined range, a one square meter radar cross section. (https://www.radartutorial.eu/01.basics/The%20Radar%20equation%20i n%20practice.en.html) Task 3. Make all possible two-words phrases with the words from the opposite columns. range spurious valid signal-to-noise high lie minimal square cross threshold

ratio amplitude in the range meter equation target noise signal section level

42

Section 15 Vocabulary : frequency diversity radar – РЛС с частотным разнесением fluctuations – колебания illumination frequency – частота сигнала облучения carrier frequency – несущая частота backscatter – обратное рассеяние in terms of – с точки зрения assume – предполагать sufficient gap – достаточный промежуток, пространство sum – сумма alter – видоизменять power doubling – увеличение мощности smoothing – нивелирование Task 1. Fill in the blanks with the words from the box. In terms of, fluctuation, alter, assume, carrier frequency, sum, backscatter 1. A change, or the process of changing, especially continuously between one level or thing and another is called ________. 2. Device is equipped with built-in QPSK modulator with ________ that can be set in the range of 950-1750 MHz. 3. In physics, ________is the reflection of waves, particles, or signals back to the direction from which they came. 4. We need better aid ________ quantity and quality. 5. Let's ________ you are right about acceleration and gravity. 6. How does gravity ________ the trajectory of light? 7. The________ of $6.6 million was spent on transportation supplies. Task 2. Read the text and answer the questions. 1. Why do many radars use two or more different illumination frequencies? 2. What makes it possible to achieve a higher maximum range? 3. Why are extreme values (minima and maxima) moved against each other? 4. What causes smoothing of the resulting signal? 5. Why must the reflected single signal be independent? 6. What leads to a target visible to the enemy? 7. What can be done to increase detection probability of frequency diversity radar?

43

Frequency-diversity Radar In order to overcome some of the target size fluctuations many radars use two or more different illumination frequencies. Frequency diversity typically uses two transmitters operating in tandem to illuminate the target with two separate frequencies like shown in the following picture. With the multiple frequency radar procedure it is possible to achieve a fundamentally higher maximum reach, equal probability of detection and equal false alarm rate. That is, if the probability of detection and the false alarm rate are equal in both systems, then by using two or more frequencies it is possible to achieve a higher maximum range. The smoothing of the fluctuation of the complex echo signal is the physical basis for this. The extreme values (minima and maxima) are moved against each other because of the differences in the secondary radiation diagram of the target for the different carrier frequencies. If the backscatter of the first frequency has a maximum, then the backscatter of the second frequency has a minimum for most part. The sum of both signals doesn’t alter the average of the single signals.

Figure 22. Block diagram of a frequency-diversity radar

This causes a smoothing of the resulting signal at an addition of the single received signals. The reflected single signals must be independent in order to increase the maximum range by increasing the probability of detection of the target. The disadvantage of this process is that the signals have different spectra and therefore they are easily detected, making a target visible to the enemy. In addition to the 3dB gain in performance achieved by using two transmitters in 44

parallel, the use of two separate frequencies improves the radar performance by decreasing the fluctuation loss by (typically) 2.8dB (see Tables 2 and 3) 4

𝑅𝑚𝑎𝑥 = √

4 2 ∙ 106 𝑊 ∙ 19002 ∙ 0.112 ∙ 1 𝑚 4 𝑃𝑡𝑥 ∙ 𝐺 2 ∙ 𝜆2 ∙ 𝜎𝑡 =√ = 106.8 𝑘𝑚 (4𝜋)3 ∙ 𝑃𝑀𝐷𝑆 ∙ 𝐿𝑆 (4𝜋)3 ∙ 5 ∙ 10−15 𝑊 ∙ 67.6

The result expressed in nautical miles is 57.7 NM. In order to increase detection probability of frequency diversity radar two pulses of different frequency are radiated one after another at very short intervals. Assuming a sufficient gap between the frequencies of the pulses radiated exists, echo signals of a fluctuating target are statistically decorrellated. Smoothing of fluctuation can be expressed in terms of signal-to-noise ratio gain, maximum range gain or improved detection probability. In Frequency Diversity Radar the decreasing of fluctuation loss can effectuate either an increased maximum range or an increased probability of detection. By putting aside the power doubling achieved with two transmitters at constant frequencies, the maximum range through frequency diversity mode can never be better due losses caused by fluctuation (3 to 8 dB). (https://www.radartutorial.eu/01.basics/Frequency%20Diversity%20Rad ar.en.html) Task 3. Make all possible two-words phrases with the words from the opposite columns. in order illumination equal maximum false smoothing echo extreme easily secondary

probability range of fluctuation alarm signal to overcome values frequencies radiation detected

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Section 16 Training Questions Please try to answer some of the more frequently asked training questions. The reasonable time to frame the answers is about 30 minutes. You can use pocket calculator, but the chosen here numerical examples are optimized to perform with mental arithmetic. 1. Specify the flow of radar signals from the originating device in given radar set to the users display. 2. Describe the field of functions of a duplexer and state a case on that condition given radar can work without a duplexer. 3. A frequency-diversity radar with two identically transmitters use one transmitter only. 4. Please calculate the decreasing the range of the radar (without consideration of the fluctuation loss) according the radar equation. 5. How the additional influences of the fluctuation loss affect the radar range tendentiously? 6. The transmitters pulse width of pulsed radar is 1.5 µs and the duplexers recovery time is 0.5 µs. How far-off the antenna an airplane must be located at the least as to be detecting by the radar?

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REFERENCES 1. Kingsley S., Quegan S. Understanding Radar Systems / Scitech Publishing, 1999, 11 p. 2. Hovanessian S. A. Radar System Design and Analysis / Artech House, 1984, 369 p. 3. Nathanson F. E. Radar Design Principles / McGraw-Hill Book Company, 1969, 720 p. 4. Chang K. RF and Microwave Wireless Systems / John Wiley and Sons, 2000. 198 p. 5. Radartutorial: Radar Basics. C. B.W. Wolff. [Электронный ресурс]. URL: http://www.radartutorial.eu/internetsite/01.basics/rb13.en.html

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