Radar and Radionavigation: Pre-professional Training for Aviation Radio Specialists 9811961905, 9789811961908

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Anatoly Ivanovich Kozlov · Yuri Grigoryevich Shatrakov · Dmitry Alexandrovich Zatuchny

Radar and Radionavigation Pre-professional Training for Aviation Radio Specialists

Anatoly Ivanovich Kozlov Moscow State Technical University of Civil Aviation Moscow, Russia

Yuri Grigoryevich Shatrakov St. Petersburg State University of Aerospace Instrumentation St. Petersburg, Russia

Dmitry Alexandrovich Zatuchny Moscow State Technical University of Civil Aviation Moscow, Russia

ISSN 1869-1730 ISSN 1869-1749 (electronic) Springer Aerospace Technology ISBN 978-981-19-6190-8 ISBN 978-981-19-6191-5 (eBook) https://doi.org/10.1007/978-981-19-6191-5 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Introduction

The main reason for the appearance of this book was the fact that currently there is quite a lot of literature on the training of aviation specialists in the field of electronic equipment of aircraft, trained in the relevant educational institutions, but there is practically no literature designed to guide potential aircraft engineers in choosing this profession. At the same time, it should be noted that the process aimed at attracting interest and popularizing the profession of an aviation specialist before entering an educational institution is necessary due to at least the fact that students in the future do not have the idea of choosing the wrong specialty, which can lead to negative psychological and economic consequences. This determines the relevance of this work, which is aimed at popularizing in the pre-professional environment such basic areas for any radio engineer engaged in the maintenance of aviation equipment as radar, radio wave propagation, and air navigation. It should be noted that, for example, in a country like the United States of America, there are more than 13,500 airports that require proactive and highly qualified specialists who consciously chose their profession. The purpose of this book is to demonstrate the capabilities and limitations of engineering science in some of the technical areas necessary for the future aviation specialist: radar and air navigation. The book discusses issues related to the physical principles of the existence of an electromagnetic field, the structure of radar information, and the methods of its transmission. The authors paid great attention to the classification of radio waves used for transmitting radar information, as well as to the physical description of their propagation media. The third part of the paper addresses issues related to the current state of navigation systems used in civil aviation, and the prospects for their development in the future, as well as the history of satellite radio navigation systems. The level of presentation of the book’s material ensures its productive perception by high school students, their parents, and teachers who want to understand the basics of the disciplines necessary for the development of their future profession as an aviation specialist.

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Contents

1 Radar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 The Electromagnetic Field Around Us . . . . . . . . . . . . . . . . . . . . . . . . 1.2 How to Describe the Electromagnetic Field . . . . . . . . . . . . . . . . . . . 1.3 What Are Electromagnetic Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 What Tasks Does Radar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 What Signals Are Used in Radar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6 That Carries the Radar Information . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7 What Is a Permission Element? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.8 How to Improve the Detection of Radar Targets . . . . . . . . . . . . . . . . 1.9 What Signals Affect the Input of the Radar . . . . . . . . . . . . . . . . . . . . 1.10 How to Select Useful Signal Against the Background Noise . . . . . 1.11 How to Make a Decision About the Presence of a Radar Target . . 1.12 What Errors Occur, When Making a Decision . . . . . . . . . . . . . . . . . 1.13 When and by What Criteria to Make a Decision . . . . . . . . . . . . . . . . 1.14 Equation Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.15 What Determines the Accuracy of Measurement and How to Improve It . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.16 What Non-classical Types of Radar Exist . . . . . . . . . . . . . . . . . . . . . 1.17 Where Today Can Not Do Without Radar . . . . . . . . . . . . . . . . . . . . . 1.18 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 2 4 8 12 13 14 16 17 19 21 22 23 24 25

2 Propagation of Radio Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Propagation of Radio Waves in Free Space . . . . . . . . . . . . . . . . . . . . 2.1.1 Environment Without Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 The Medium with Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.3 Line-of-Sight Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Areas of Radio Wave’s Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Soil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Troposphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33 33 33 36 38 39 40 40

28 29 30 30 31

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Contents

2.2.3 Stratosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.4 Ionosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Features of Propagation of Radio Waves in the Troposphere . . . . . 2.4 Features of Propagation of Radio Waves in the Ionosphere . . . . . . 2.5 The Area of Space, That Is Essential for the Propagation of Radio Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Classification of Radio Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 Features of Radio Wave Propagation in Different Bands . . . . . . . . . 2.7.1 Ultra-Long Waves (ULW) and Long Waves (LW) . . . . . . . . 2.7.2 Medium Waves (MW) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7.3 Short Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7.4 Ultra-Short Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7.5 Decimeter, Centimeter, and Millimeter Waves . . . . . . . . . . . 2.7.6 Waves of Optical Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41 41 45 47

3 Aero Radionavigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Basics of Aero Radionavigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 General Approaches to Solving Problems of Aircraft Navigation Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Basic Concepts, Used in Aero Radionavigation . . . . . . . . . . 3.2 Traditional Navigation Equipment, Used for Aircraft Navigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Automatic Radio Compass . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Flight and Navigation System . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 Radio Engineering Systems for Long-Range and Short-Range Navigation . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.4 Radiobeacons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Satellite Radio Navigation Systems . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Reasons for Switching to Satellite Radio Navigation Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 History of the SRNS Development . . . . . . . . . . . . . . . . . . . . 3.3.3 Requirements for SRNS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Principles of SRNS’s Functioning . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Ground Control Complex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Joint Use of GLONASS and GPS Systems . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

69 69

Appendix A: Lecture “About the Laws of the Electromagnetic World” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49 53 54 54 60 61 62 64 65 66 67

69 70 71 71 73 75 76 77 77 79 80 81 82 84 86

89

Appendix B: Lecture “Navigation, Communication and Observation—Eyes, Speech and Hearing of the Aircraft in the Past, Present and Future” . . . . . . . . . . 115

Abbreviations

A AC Af AM ARC ASE ATC BC CA CC CCRS CMS CS DA DC Df DI DMT EA EAS EI ERS ES ESA ESCS FANS FM FTC GA GCC GH

Azimuth Aircraft Air force Amplitude Modulation Automatic Radio Compass Artificial satellite of the Earth Air Traffic Control Ballistic center Civil aviation Compass course Corner of course for the radio station Command and measurement station The central synchronizer Demolition angle Directional coefficient of the antenna The directivity factor Digital information Digital map of the terrain The efficiency of the antenna The effective area of scattering Ephemeris information Effective reflecting surface Ephemeris support Effective scattering area The effective scattering cross-section Future air navigation system Frequency modulation Frequency-time corrections Gain of the antenna Ground control complex Given heading ix

x

GLONASS GPS GWA ICAO IR radar LRRNS LSP LW MAF MBRS MC MSD MSF MW NES NF NFME NO NSC OBTS OG PM PND PNI PRW RBRS RCR RME RNS RS RSA SC SMF SMT SRNS SRRNS SW TC TFS TS ULF ULW USW UTS

Abbreviations

Global navigation satellite system of the Russian Federation Global Position System A given way angle International civil aviation organization Radar in the infrared wave range L-range radio navigation system Line of the specified path Long waves The maximum applicable frequency Magnetic bearing of the radio station Magnetic course A mean square deviation Military space forces Medium waves Navigation equipment for consumers Naval forces Navigation field monitoring equipment The navigation object Navigation spacecraft On-board time scale Orbital grouping Phase modulation Planned navigation device The planned navigation instrument Propagation of radio waves The relative bearing of the radio station Radio compass reading Receiving measuring equipment Radio navigation system A radar station Radar with a synthesized aperture Spacecraft Strategic missile forces Selection of moving targets Satellite radio navigation system Short-range radio navigation system Short waves True course Time-frequency support Time scale Ultra-low frequencies Ultra-long waves Ultra-short waves Unified time service

Chapter 1

Radar

Somewhere in the fifties, most people first heard the word “radar”. It was pronounced, as a rule, in a low voice, with great reverence and respect for this word and carried an element of the fact that the person who uttered this word was involved in some higher military or scientific secrets. Mass popular publications of that time in newspapers and magazines, detective stories, and films convinced readers and viewers of the existence of a very complex, capable of creating a miracle means that will protect sky from uninvited guests, allow planes to fly in any weather, in any visibility and see everything that is happening in the sky, on Earth, and at sea. But as time went on, and as always happens, mass interest in radar faded, it was replaced by new scientific and technical advances, and radar itself began to take shape in a strict scientific discipline with clearly defined boundaries of capabilities and applications. Today we have, on the one hand, a classic educational and scientific discipline that is included in the mandatory training program for specialists in the field of radio engineering, on the other hand, various numerous radar stations and devices that are really able to do the impossible and “see” what is basically impossible to “see” in everyday life [1]. The fantastic progress in science and technology that has taken place over the past 50 years has led to the fact that the radio world has entered the life of each of us as a natural attribute of our lives. The Internet, mobile phones and iPhones, computers and complexes, digital television, and car navigators have become so “their own” that it is difficult to imagine how we used to live without them. Well, the pinnacle of radio technology—Moon’s rovers and Mars’s rovers, people on the moon, radar and photographing distant planets and their satellites, with details that even allow you to look at the rocks on the surface of the planet Pluton [2]. All these achievements are based on the knowledge of the laws of electromagnetism, electrodynamics, and electronics. Therefore, to understand how miracles of the radio world are born and generated by them the wonders of radar, navigation, and telecommunication, first of all, try with the most common positions to approach the concept of the electromagnetic field.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 A. I. Kozlov et al., Radar and Radionavigation, Springer Aerospace Technology, https://doi.org/10.1007/978-981-19-6191-5_1

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1 Radar

1.1 The Electromagnetic Field Around Us We will begin our consideration of the laws of electromagnetism by paying attention to the following fact, which is somehow not paid much attention to due to its apparent naturalness. So, dear reader, imagine that you are sitting in front of the TV and easily switch its channels—1, 2, 3, 4, etc., and see the changing pictures. Without getting up from your seat, you pick up the radio receiver, and just as easily, by scrolling the receiver settings, you can hear voices from Moscow and Beijing, London, Rome, etc. What was the source of the information you received? The answer is simple—the currents induced in the antenna of your devices. But the antenna did not change its appearance or position in space with your settings. So where the antenna is located, “there is” information about all (!!!) sources of radio waves, wherever they are located. Naturally, this statement is true for any location of the antenna. As you know from the course of physics, any body with a temperature other than absolute zero (−273 °C) is a source of electromagnetic radiation, which is also “transported” through any small volume of space, including the one where our antenna is located and carries information about its source. Similar reasoning in relation to stars leads to a generalization of the statement formulated for the entire Universe, which will sound like this: “Through any small volume (and bolder, any point!) of space is transferred information about all natural and artificial sources of electromagnetic radiation, located on Earth and throughout the Universe (!)”. Figure 1.1 schematically shows the flows of electromagnetic radiation from a radio station, a person, a tree, a planet, and a star flowing into a small volume (point) of space.

ALL information generated by ALL natural and artificial SOURCES of radio radiation of the UNIVERSE is transferred through ANY infinite small VOLUME of space

Fig. 1.1 Illustration of the “electromagnetic unity of the world”

1.1 The Electromagnetic Field Around Us

3

In this formulation, the negligible power of most fields should not be confused. The question is about the fundamental side of the issue, and not about the technology of dividing and separating information. Thus, we can talk about a kind of electromagnetic “unity” of nature and man in particular [3]. As for the possibility of allocating insignificant signals, dear reader, estimate the power of the signal, reaching the Earth from the orbit of the planet Pluton, located at a distance of 5 billion km with a transmitter power of only 60 W. And such a signal was highlighted! The “quality” of this selection is shown in Fig. 1.2. Photos of Mars’s surface with its legendary sphinxes are not inferior in quality (Fig. 1.3). These photos should not leave anyone in doubt about the possibility of identifying the smallest traces of the electromagnetic field. Fig. 1.2 Photo of the Pluton and its surface

Fig. 1.3 Photo of Mars’s surface

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1 Radar

1.2 How to Describe the Electromagnetic Field In this context, we would like to emphasize that the electromagnetic field is not a synonym for electromagnetic waves or radio waves, which are only a special case of the electromagnetic field. The authors believe that the most successful definition is: “The electromagnetic field is a form of existence of matter that can transfer energy and information”. And nothing more! In the framework of modern physics, if we do not intrude into the area of the microworld and quantum effects, to describe the properties of the electromagnetic field, i.e. the quantitative characteristics of the named form, at each point (!) of space at each moment of time (!), it is necessary to use independent 52 (!) numbers. It took many decades of efforts of geniuses from different countries: Ampere, Volt, Gauss, Hertz, Joule, Kirchhoff, Lenz, Lorentz, Maxwell, Ohm, Faraday, and a number of others to be able to see that this is exactly 52 numbers [4, 5]. In most modern approaches, 4 vectors are used as basic concepts—the electric E (3 numbers) and magnetic H (3 numbers) field strength vectors, as well as the electric D (3 numbers) and magnetic B (3 numbers) induction vectors describing the electromagnetic field at a given point in space Q with coordinates (x, y, z). These vectors are connected by Maxwell’s equations, which are four differential equations, two of which are written in vector and two in scalar forms, i.e. we are talking about eight scalar differential equations, in which the products of each component of the vectors E, H, D, B in time t, i.e. the rate of their change (total 3 × 4 = 12 numbers) appear. In addition, the equal terms of these equations are also the derivatives of each of the components for each of the spatial coordinates x, y, z, i.e. another 9 × 4 = 36 numbers. Thus, we are talking about 12 + 12 + 36 = 60 variables related to each other by 8 Maxwell equations, which gives reason to talk about 60 − 8 = 52 independent numbers, that characterize the electromagnetic field at the point Q (x, y, z) at time t. The question is quite appropriate here, the essence of which boils down to the following. So, Maxwell described the electromagnetic field based on the vectors E, H, D, B and their derivatives in all four space–time coordinates. From a formal point of view, Maxwell’s equations are 8 equations, that connect 52 variables. Couldn’t we have chosen a different combination of these variables and also linked them with some other equations? The answer is clear: “Of course, you can”. For a complete description of the electromagnetic field in a number of problems, it is much more convenient to use other characteristics of the field, such as the vector A and scalar ϕ potentials, the Hertz vector P, which can be easily converted into the classical vectors E, H, D, and B. So why is preference given to vectors E, H, D, and B and what is in nature? Historically, the electromagnetic field, or rather its manifestation, was observed in the form of some force action on electric charges, for which it was convenient to introduce the electric field strength vector E (electric vector), as a force, acting on a single charge. As for the second part of the question: “So what is there in nature”? You

1.2 How to Describe the Electromagnetic Field

5

can answer, that in nature there is neither E, nor A, nor P. There is an electromagnetic field, and E, A, and P are tools for describing its properties. In the future, we will rely on the classical description of the electromagnetic field in terms of the vectors E, H, D, and B. It is very important to note, that Maxwell’s equations state the fact that any (!) medium in the framework of electromagnetic theory is described, using only 3 (!) characteristics: permittivity—ε, conductivity—σ, and magnetic permeability—μ (this does not apply to electrically and magnetically anisotropic media). For isotropic media the vectors D and B can be expressed via the remaining two vectors E and H with equality: D = εε0 E and B = μμ0 H, where ε0 = 8.85 × 10−12 F/m and μ0 = 4π × 10−7 Gn/m—electrical and magnetic constant, respectively. So, let the “observer” be located at point Q with coordinates (x, y, z), and the observation is made at time t. Thus, the problem is reduced to determining the vectors E and H at point Q at the same time. In other words, you should represent E and H as some functions of four variables, i.e. find E(x, y, z, t) and H(x, y, z, t). This is the problem solved by Maxwell’s equations, which essentially connect only the derivatives of the components of the vectors E(x, y, z, t) and H(x, y, z, t) with respect to all four variables by linear dependencies. Moreover, only ε, ε0 , and μ0 are used as coefficients for these production terms that are part of linear combinations [6]. We introduce the notation: ˙ = (E x, E y, E z)—derivatives of the components of the vector E in time, Et E mn —a derivative of the m-component (m = x, y, z) of the vector E in one of the spatial coordinates n = x, y, z. Similarly, the notation for the components of the H vector is introduced. Taking into account the introduced notation, six Maxwell equations can be represented as two vector equalities, where Icm is the density of the external current. ( ) ( ) FE E yz − E zy , E zx − E xz , E xy − E yx + μ0 H t Hxt , Hyt , Hzt = 0,

(1.1)

( ) ( ) FH Hyz − Hzy , Hzx − Hxz , Hxy − Hyx − εε0 E t E xt , E yt , E zt = Icm .

(1.2)

Vectors F E and F H are the expanded entry of the “rotor” operator, i.e. F E = rotE and F H = rotH. Expressions in round brackets—the expanded record of the “divergence” operator, i.e. divE = ρ/εε0 , a divH = 0. The remaining 2 equations are represented as simple equations: E xx + E yy + E zz = ρ/εε0 ,

(1.3)

Hxx + Hyy + Hzz = 0,

(1.4)

where ρ is the volume charge density. As you can see, the left parts of all equations are absolutely identical with respect to the vectors E and H. The difference occurs in the right parts of the equations.

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The volume charge density appears on the right side of Eq. (1.3), which means, that Eq. (1.3) states the presence of electric charges. The zero on the right side of Eq. (1.4) indicates, on the contrary, the absence of magnetic charges. So, one of the sources of the electric field is electric charges [7]. Equation (1.1) shows that, if vector H does not change in time, i.e. Ht ≡ 0, then vector E has the same property, and, consequently, the electric and magnetic fields exist separately independently of each other. Well, what generates a magnetic field? To find the answer to this question, consider Eq. (1.2). Let now, contrary, the vector )E does not change in time, i.e. E t ≡ 0, ( on the y y then FH Hyz − Hz , Hzx − Hxz , Hx − Hyx = Icm . As you can see, the source of the magnetic field is a constant electric current. What is the source of the electromagnetic field and how can it be artificially created? The presence of an alternating current will lead to a change in the magnetic field over time, which will lead to the appearance of an alternating electric field, etc., and this already makes it possible to talk about the appearance of an electromagnetic field. An electromagnetic field also occurs, when the electric charge density changes over time, i.e. an alternating electric current occurs, which leads to a chain of variable vector E—variable vector H, etc. A few words about electric charges. The most common models, that explain electromagnetic processes, use the concept of an elementary charge that an electron has. However, this interpretation does not follow Maxwell’s equations. They include a slightly different characteristic of matter—the volume charge density ρ. They claim that there may be points in space, where the concentration of “charge” can be very high and no more. Here, the charge is again understood as a form of existence of matter with spatial inhomogeneities. For all electrical and radio engineering, the electronic model is quite acceptable, and therefore generally accepted. In quantum electrodynamics, such a charge model, alas, is not acceptable in any way. Therefore, there are completely different approaches [8]. Similar reasoning can be carried out in relation to electric current and in the framework of generally accepted models, it can be considered as the movement of electric charges. However, in some cases, such as, when a current passes through a capacitor, this interpretation of the current is not acceptable in principle. To satisfy the requirement of the current continuity between the capacitor plates, the concept of “displacement current”, equal to the derivative of the vector magnetic field time—Ht , which, again, is numerically equal to the conduction current in the external circuit of the capacitor is introduced. Being within the framework of the classical models of current as the movement of charged particles, we must answer the question of what is the source of the electromagnetic field: “EVERYTHING!”. Since, in the framework of our “electronic” model, all atoms contain electrons, that are in continuous motion, all (!) material objects, whose temperature is different from absolute zero are a source of electromagnetic radiation, i.e. each of us continuously generates an electromagnetic field.

1.2 How to Describe the Electromagnetic Field

7

All the furniture around us, walls and floors, tables and chairs, doors and windows have the same property. Of course, the power of this radiation is very small, but in the framework of our reasoning, this is not at all important. The most powerful natural source of radiation is the Sun. Thunderbolts are a powerful emitter. Finally, we must say about the cosmic radiation, that continuously affects our planet [2]. What was said above demonstrates natural sources of electromagnetic radiation, which are essentially continuously operating generators of the electromagnetic field. From the point of view of the Earth’s inhabitants, this is the so-called background radiation. Let’s focus on one more point. Maxwell’s equations describe the electromagnetic field at any point in space Q (x, y, z) at any time t. Let the source of the electromagnetic field be located at some point P and let the electrical conductivity be non-zero and equal to σ at point Q where the observation is made. In this case, to ensure equality in Eq. (1.2), it will be necessary to take into account the occurrence of the induced current, the density of which will be equal to I ind = σ E. This current will be the source of its own electromagnetic field, which is called the scattered field, and, if it is observed at point P, then the reflected field. Taking Maxwell’s equations as “true”, the fact of propagation of the electromagnetic field in space is elementary proved. The basis for this statement is the fact that the field can be determined, using these formulas at any point in space at any time. It is clear, that as we move away from the source of the electromagnetic field, the length of the vectors E and H, i.e. their modules, should decrease. The question arises about the laws of this reduction. It is known from electrodynamics [9], that the density of the energy flux carried by an electromagnetic field at a sufficiently large distance from its source is proportional |E|2 , and the ratio |E|/|H |=120π . We assume that |E|2 depending on the distance to the source R decreases according to the law |E|2 = Rαn , where α is some coefficient, that does not play a role in this case, and n is a parameter to be determined [10]. In this case, the energy, carried by the electromagnetic field through any sphere surrounding the sphere must be a constant value, which requires the condition of energy transfer in free space, i.e. |E|2 · Ssph =

α · 4π R 2 = 4π α R 2−n = const, Rn

therefore, n = 2. Thus, the condition of energy transfer requires a dependency |E|2 ≈ therefore, |E| ≈ R1 .

1 R2

and,

8

1 Radar

1.3 What Are Electromagnetic Waves So, at observation point Q with coordinates (x 0 , y0 , z0 ) at a sufficiently large distance from the source of electromagnetic radiation, the main characteristic of the electromagnetic field is the vector E(x 0 , y0 , z0 ; t), which changes in the direction and time, which makes it possible to “read” information, that is transmitted to the observer by changing the current I in the source. The observer, wishing to extract the information transmitted to him, ultimately relies on some parameter S(t), measured by him, and studies its change in time, and, if this parameter is a vector S(t), then its spatial change. So, the observer is dealing with a certain function S(t). The great theorem of the great mathematician J. Fourier states, that any physically realizable function can be represented as a sum of sinusoidal functions of various frequencies ω from zero to infinite (Fig. 1.4a), i.e. S(t) = A0 + A1 sin(ω1 t + ϕ1 ) + A2 sin(ω2 t + ϕ2 ) + A3 sin(ω3 t + ϕ3 ) + · · · , where each term is called a harmonic (spectral) component or simply a harmonic, the coefficients An (n = 0, 1, 2, …) of the amplitude of the components, ωn —the frequency of the n-th harmonic, ϕn —the initial phase of the n-th harmonic. Often, instead of the frequency ω measured in rad/s, the frequency f = ω/2π, measured in Hz is used [11].

Fig. 1.4 To illustrate the Fourier transform

1.3 What Are Electromagnetic Waves

9

The entire set of frequencies is called the spectrum, and the difference between the maximum and minimum frequencies is called the spectrum width—∆f . In this case, the maximum and minimum frequencies are understood as the limit values of frequencies, whose amplitude (intensity) exceeds a certain conditionally set level, for example, the level of 0.1 or 0.2, etc., in relation to the maximum intensity amplitude, that one of the harmonics has (Fig. 1.4b). The values of An , ωn , ϕ n i n are determined by a specific type of function S(t). If you go to a different observation point, then the representation S(t) should be written in exactly the same form. To avoid confusion, it is advisable to “synchronize” these expressions, i.e. take into account the phase shift ∆ψ from the source to the observation point, located at a distance R from it: ∆ψ =

2π ω R= R = k R, c λ

where c = 3 × 108 m/s is the speed of light, λ—the wavelength, k = number. Thus, the general expression entry for S(t) will take the form:

2π —the λ

wave

[ ( [ ( ] ] ) ) R R S(t) = A0 + A1 sin ω1 t − + ϕ1 + A2 sin ω2 t − + ϕ2 + · · · c c As you can see, the desired parameter, that characterizes the electromagnetic field, is represented as the sum of vibrational (wave) processes. This allows us to assume that the electromagnetic field is the sum of electromagnetic waves of different frequencies. With this interpretation, in the future, we will deal with electromagnetic waves of a particular frequency [12]. The number of terms in the written sum is determined by the degree of difference between the function S(t) and the sinusoid. The more abrupt changes and jumps the function S(t) has, the more summands are required, and the higher frequencies must be used to describe it. In accordance with the principle of superposition and linearity of Maxwell’s equations, it can be argued, that the source of the electromagnetic field, and this will be considered an alternating current I(t), can also be represented as a set of current harmonics of the same frequencies: I (t) = B0 + B1 sin(ω1 t + β1 ) + B2 sin(ω2 t + β2 ) + B3 sin(ω3 t + β3 ) + · · · Let’s illustrate what was said. Let’s assume that, at the point M with coordinates (x M , yM , zM ) there is a source, generating a radio wave at the frequency ω0 : E(t) = B sin(ω0 t + ϕ0 ). At a distance R at point Q, this radio wave is observed, which results in the appearance of a signal of the same frequency:

10

1 Radar

S(t) =

] [ ( ) R αB sin ω0 t − + ϕ0 , R c

where α is a certain coefficient that does not play any role in the consideration carried out, taking into account the radiation direction and the propagation conditions of the radio wave. In such a statement, the information that an observer can get consists only in stating the fact of the presence of a radio wave of frequency ω0 , i.e. in the formation of the function S 0 (t) known to him. If the observer receives another function S 1 (t), it will indicate the appearance of some unknown information [13, 14]. Figuratively speaking, the “distortion” introduced in the function S0(t) is the transmitted information. To change S 0 (t), you need to make changes to the current distribution I, which will cause a change in the function E(t) = B sin(ω0 t + ϕ0 ). The amplitude—B (amplitude modulation—AM), the frequency—ω0 (frequency modulation—FM), and initial phase—ϕ 0 can be changed. Finally, you can add an additional time-varying phase—ψ(t) (phase manipulation—PM). For E(t), we write a new relation: E(t) = B(t) sin(ω0 t + ψ(t) + ϕ0 (t)). The resulting function can be decomposed into a Fourier series, i.e. it is represented as a sum of sinusoids of different frequencies. Therefore, at the observation point Q, the function S(t), will represent a similar sum. The width of the spectrum of the received signal will be equal to the width of the spectrum of the emitted one (we will discuss the special case related to the Doppler effect below). The situation of transmitting information from the source to the consumer is typical for radio communications, television, and, in some cases, radio navigation. Let’s focus on the simplest case of AM. Suppose we are talking about transmitting information in the form of a sinusoidal frequency Ω signal, using an electromagnetic wave of frequency ω0 (carrier frequency). In this case [7, 15], [ ] B(t) = B0 1 + m sin(Ωt + γ0 ) , where m is the so-called modulation index, then [ ] S(t) = B0 1 + m sin(Ωt + γ0 ) sin(ω0 t + ϕ0 ) = B0 [sin(ω0 t + ϕ0 ) ] [ ]] [ sin (ω0 − Ω)t + (ϕ0 − γ0 ) − sin (ω0 + Ω)t + (γ0 + ϕ0 ) +m , 2

1.3 What Are Electromagnetic Waves

11

i.e. amplitude modulation leads to two additional harmonics at frequencies (ω0 − Ω) i (ω0 + Ω) and the width of the spectrum is 2Ω. We assume that the frequency Ω is the maximum frequency in the spectrum of the transmitted signal, which ensures the recovery of the transmitted information with the required accuracy. It is clear, that in order to be able to transfer other similar information, the carrier frequency ω1 must defend from the frequency ω0 , at least by an amount greater than 2Ω, i.e. ω1 > ω0 + 2Ω or ω1 < ω0 + 2Ω. When transmitting a voice signal, the value of 2Ω does not exceed 20 kHz, and for transmitting a television signal, this value is 6.5 MHz. A similar situation occurs with frequency modulation and phase manipulation [16]. Figures 1.5, 1.6 and 1.7 shows signals with amplitude modulation (AM), frequency modulation (FM), and phase manipulation. Consider the situation related to radar. Here, the radiation and reception of radio waves occur at the same point. The received signal still looks like this E(t) = B(t) sin(ω0 t + ϕ0 ). The wave, having reached a stationary target, induces a current I on its surface, which generates a new electromagnetic wave of the same configuration and frequency ω with an initial phase ϕ 1 . After reaching the receiving point, the signal will look like the following: S(t) =

] ) [ ( R α1 Bδ t − + ϕ sin ω + ϕ 0 0 1 , R2 c

where α 1 is a certain coefficient that does not play any role in the current consideration, taking into account the radiation direction and the conditions for radio wave propagation to and from, σ —a coefficient that takes into account the configuration and electrophysical characteristics of a radar target, it is called the effective cross-section (area) of scattering (ECSS) or the effective reflecting surface (ERS), the dimension of this value is m2 .

Fig. 1.5 Signal with amplitude modulation

Fig. 1.6 Signal with frequency modulation

12

1 Radar

•

•

•

•

•

•

•

•

•

Fig. 1.7 Signal with phase manipulation

What information does the reflected wave carry? First, the presence of this wave indicates the very fact of having a goal. Second, the appearance of the reflected wave, after a time of 2R/c, carries information about the distance to the target. Finally, the intensity of the reflected wave in the presence of some calibration estimates makes it possible to evaluate the effective area of scattering (EAS) of the target—σ, i.e. to make a conclusion about the type of target. The EAS strongly depends on the angular orientation of the target, and even a small rotation of the target strongly affects the value of σ, and therefore, most often, its average and square average values are used. In this case, if the target is moving and the component of its velocity in the direction of the transmit-receive point vR is different from zero, then the frequency of the reflected signal increases or decreases by the value of the so-called Doppler R , i.e. write (ω0 ± = 2πν ) instead ω0 , which makes it possible, frequency λ while at the receiving point, to estimate the radial velocity of the target. Next, we will look at the physical principles that underlie radar, consider its capabilities and some of the problems it faces as a science, and illustrate some of the achievements in the field of radar technology with a number of examples.

1.4 What Tasks Does Radar Let’s start with the statement of the main task of radar. This task can be formulated as follows [17]: Let the observer, being at point 0, want to know what is at some other point 1 and what physical and geometric characteristics “it” has. What does the observer have? It has the ability to emit radio waves and concentrate the main part of the radiated energy in a given direction, using an antenna. (The fundamental point: despite the fact that the main flow of energy is somehow concentrated in space, energy is radiated in all directions without exception). The observer can receive reflected radio waves from the desired direction. (A fundamental point: the reception of reflected radio waves is carried out, however, from all directions without exception). The observer may also have certain information about the object of observation (radar target) and the environment. This makes it possible to assign radar to the class of remote sensing tasks. To sum up, we can formulate three key tasks of radar: 1. Detect the target.

1.5 What Signals Are Used in Radar

13

Fig. 1.8 Example of performing a radar task

2. Measure the parameters of the target, namely—the distance to the target, the angular position of the target, and the speed of the target. 3. To make the classification of the target (Fig. 1.8). Let us now consider, what physical processes occur during the implementation of radar sensing. So, the observer emits a radio wave, which, after some time, reaches point 1, where it induces electric and magnetic currents on the object under study, which, in turn, generate radio waves, that propagate in all directions, including in the direction of point 0. The reflected radio wave reaches point 0, where the corresponding signal (current, voltage) appears in the radar receiver [18]. It is clear, that all the information, received (and this is a change in the amplitude, phase, and frequency of the radiated wave, i.e. its distortion) about the observed target, can only be obtained from comparing the radiated and received signals. Once extracted, this information will be expressed in the language of electrical signals, rather than in the language of any physical or geometric characteristics of the target. Translating from one language to another is another independent task.

1.5 What Signals Are Used in Radar Radar uses radio waves with a wavelength that falls within the centimeter (less often decimeter) and millimeter ranges. The very type of emitted signal is quite simple. As a rule, this is a sequence of short pulses in time, following one after another through a time much longer than the duration of these pulses. The width of the spectrum of such signals is ∆f in the vast majority of cases is many times less than the carrier frequency of the emitted signal f 0 , that is, for radar signals (except in special cases), the ratio ∆f /f 0 1. However, in environments, where electrically charged particles are present, this inequality is violated, and depending on the concentration of such particles ε, it becomes less than 1, equal to 0, or even a negative value. Quite often (as a rule,√in medium with low losses), instead of the permittivity ε, the refractive index n = ε, which is uniquely associated with it, is used. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 A. I. Kozlov et al., Radar and Radionavigation, Springer Aerospace Technology, https://doi.org/10.1007/978-981-19-6191-5_2

33

34

2 Propagation of Radio Waves

RADIOWAVE PROPAGATION MEDIUM

RADIOWAVES SOURCE

RECEIVER

Fig. 2.1 Scheme of information exchange using radio waves

The main characteristics of a radio wave, that describe it, are the vectors of electric E (electric vector) and magnetic H (magnetic vector) strengths. In the framework of the following, since the processes taking place are considered far enough away from the sources of electromagnetic √ radiation, the lengths of the vectors E and H are related by the ratio E = 120π H/ ε. Find the field strength E of a radio wave, generated at a distance R from a point source of electromagnetic radiation Q with power PΣ . Let’s draw a sphere of radius R with the center at the location of this source. Obviously, the density of power flow ρ on the surface of the sphere will be equal ∑ ρ = SPsph = 4πP∑R 2 . It is known from electrodynamics that, on the other hand, this value is equal to the length of the so-called Umov-Poynting vector, which in this E2 case is the product of the lengths of the vectors E and H, i.e. ρ = E · H = 120π , from which it follows elementary [2] √ E=

30 · P∑ R

.

(2.1)

If we assume, that the antenna has directional properties, then this can be easily taken into account by entering a certain parameter into the formula, that takes these properties into account. This parameter G is called the directivity coefficient of the antenna (DC), which shows the ratio of the concentration of energy, radiated in a given direction, to the average energy, radiated in all directions. With this in mind, formula (2.1) will take the form: √ E=

30 · P∑ D R

.

This ratio is called the ideal radio transmission formula. The obtained relations essentially solve the problem of radio wave’s propagation in a homogeneous medium (ε and μ are constants, σ = 0), which can include space and atmosphere. For this purpose, we write down the instantaneous value of the electric

2.1 Propagation of Radio Waves in Free Space

35

field strength at a point, located at a distance x from the source of the electromagnetic wave frequency ω [2, 3]: ] ) [ ( ( x) ω + φ0 = E 0 sin ωt − x + φ0 = E 0 sin(ωt − kx + φ0 ), E = E 0 sin ω t − c c (2.2) where E 0 is the amplitude, ϕ 0 is the initial phase, k = ω/c = 2π /λ is the wave number, λ is the wavelength, and c = 3 · 108 m/s is the speed of light. It is known that the effective value of the intensity E, defined √ by formula (2.1), is related to its amplitude value E m , using the relation E m = 2E. Thus, formula (2.2) will take the form: √ E=

60 · P∑ sin(ωt − kx + φ0 ). x

(2.3)

In the future, where during the analysis amplitude dependence from distance and value of the initial phase does not play a special role, so as not to clutter the formulas, they will fall, and instead of formula (2.3), we write ( ω ) E = E 0 sin(ωt − kx) = E 0 sin ωt − x . c

(2.4)

If the wave propagates in a dielectric with a permittivity ε, then the electric vector is written as follows: ) ( ( √ ) ω (2.5) E = E 0 sin ωt − k εx = E 0 sin ωt − √ x , c/ ε that is, the dielectric affects the √ phase of the wave√and, consequently, the phase velocity, which is reduced by ε times. The value ε = n is called the refractive index of the medium. Here, the question is quite appropriate: “Does the permittivity ε depend on the frequency ω?”. The answer to this question is yes. There are special reference tables, that reflect this dependency for different environments. Some information on this issue will be provided below. The given relations related to the situation, when the second parameter of the medium—its conductivity σ was equal to zero, i.e. σ = 0. If we take into account the energy loss during PRW, then the formula requires modification, which is successfully performed by the attenuation multiplier V (ω, R, δ, ε, μ), which leads to the ratio [3] √ E=

30 · P∑ D R

− V (ω, R, δ, ε, μ).

36

2 Propagation of Radio Waves

Most of the real problems of propagation of radio waves are reduced to determining the attenuation multiplier, which primarily depends on the frequency and distance.

2.1.2 The Medium with Losses The situation changes abruptly for the case of finite conductivity σ, which is caused by the presence of conduction currents and, as a consequence, the occurrence of ohmic, i.e. heat losses. Instead of dependency (2.2), we now have E = E 0 · e−αkx cos(ωt − βkx) = E 0 · 10−0.434αkx cos(ωt − βkx),

(2.6)

where / ( ) / 1 2 2 α= (60λδ) + ε − ε , 2 / ( ) / 1 β= (60λδ)2 + ε2 + ε . 2

(2.7)

(2.8)

The fundamental difference between formula (2.6) and formula (2.5) is, first of all, in the dependence of the wave amplitude from the distance, which has a decreasing character, according to the exponential law. The second difference is that both the defining parameters α and β depend fundamentally on the wavelength (frequency). In the future, for convenience, we will refer α to as the attenuation coefficient and the parameter β as the phase coefficient. As mentioned above, the propagation of radio waves significantly depends on the electrophysical characteristics of the propagation’s medium, and therefore the characteristics of the soil and atmosphere are discussed below. Consider the nature of changes in amplitude and phase [4]. As you move away from the radiation source, the amplitude of the radio wave decreases, firstly, as 1/R, which is a consequence of energy transfer in space, and, secondly, according to the exponential law, which is a consequence of energy absorption by the molecules of the propagation’s medium. As can be seen from the above relations, these losses in the same medium significantly depend on the wavelength—λ (frequency—ω) of the propagating radio wave. At low frequencies, when the wavelength λ is large enough, we have 60λσ >> ε, and therefore the medium behaves like a conductor by its properties. That is why the Earth’s surface behaves like an ideal conductor on long and ultra-long radio waves. In contrast, if 60λσ > ε, then α and β are approximately the same: / α ≈ β ≈ 2π

30δ . λ

The phase velocity of the wave will be: V ph ≈ √

c 30λδ

, where c is the speed of light,

and the wavelength in the medium: λme

V ph = = f

/

λ0 . 30δ

2. Poorly conducting environment. In this case, 60λσ