Nondestructive testing and antenna measurements using UWB radar in industrial applications

Licentiate Thesis in Electrical Engineering

Nondestructive testing and antenna measurements using UWB radar in industrial applications

VIPIN CHOUDHARY

Stockholm, Sweden 2021

kth royal institute of technology

Nondestructive testing and antenna measurements using UWB radar in industrial applications

VIPIN CHOUDHARY

Licentiate Thesis in Electrical Engineering KTH Royal Institute of Technology Stockholm, Sweden 2021

Academic Dissertation which, with due permission of the KTH Royal Institute of Technology, is submitted for public defence for the Degree of Licentiate of Engineering on Tuesday the 23th March 2021, at 1:00 p.m. in house 99, room 99:131, Kungsbäcksvägen 47, Gävle.

© Vipin Choudhary TRITA-EECS-AVL-2021:16 ISBN 978-91-7873-795-6

Printed by: Universitetsservice US-AB, Sweden 2021

iii

Abstract

Many industries are rapidly substituting the manual test operations and move towards automated operations using modern technologies.

Modern technologies such as digital cameras, sonic sensors, infrared sensors, and radar and lidar systems are used for non-destructive test- ing operations. Among all the different sensors, radar systems have the ability to penetrate built structures (dielectric materials), which makes them flexible and suitable for a wide range of industrial and military applications in non-destructive sensing. Such examples are the detec- tion of damages in goods manufacturing, monitoring the health of many structures, object detection through the wall for security purposes, etc.

In particular, ultra-wide-band (UWB) radar systems are beneficial in providing high measurement accuracy and simultaneously reduced sen- sitivity to passive interference (such as rain, smoke, mist etc.), immunity to external radiation and noise.

The objectives of this thesis are: I) to investigate electrically small concealed structures using synthetic aperture radar (SAR), II) to deter- mine the complex refractive index of objects using an UWB radar sys- tem, and III) to answer to the question how we can reduce the mutual coupling (cross talk) in an UWB radar system with collocated transmit and receive antennae. In objective I, the aim is non-destructive testing of built structures, such as in concrete slab manufacturing or for use in the renovation process. In addition electrically small periodic meshes, and their orientation, could not be distinguished in conventional SAR images. The proposed polarimetric analysis method demonstrates the usefulness of the singular value decomposition (SVD) using back pro- jection algorithm (BPA) in extracting information about shape and for classifying an electrically small object.

Further in this thesis for objective II, a new method for determin- ing the complex refractive index (or equivalently the complex relative permittivity) of objects with planar interfaces is presented. The pro- posed method is relatively insensitive to hardware-impairments such as frequency-dependence of antennas and analog front end. The objects can be finite in size and at a finite distance. The limits in size and distance for the method to be valid are experimentally investigated.

Hence, the method is designed for industrial in-line measurements on objects on conveyor belts. Furthermore, in the following parts of this thesis −objective III− we investigate and show how a microwave meta- material based absorber can be used to improve the performance of a radar system for short range applications, when positioned between the transmit and receive antennas. As results, the error in estimated target distance is reduced and clutter reduction is improved.

iv

Sammanfattning

Många branscher ersätter snabbt de manuella testoperationerna och går mot automatiserad drift med modern teknik. Modern teknik såsom digitalkameror, soniska sensorer, infraröda sensorer och radar och lidar- system används för i icke-förstörande tester. Bland alla olika sensorer har radarsystem förmågan att tränga igenom byggda strukturer (di- elektrisk material), vilket gör dem flexibla och lämpliga för ett brett spektrum av industriella och militära applikationer vid icke-förstörande avkänning. Sådana exempel är upptäckt av skador vid tillverkning av varor, övervakning av hälsa hos många strukturer, detektering av ob- jekt genom väggen av säkerhetsskäl etc. Speciellt är radarsystem med ultrabredband (UWB) fördelaktiga då de ger hög mätnoggrannhet och samtidigt minskad känslighet mot passiva störningar (såsom regn, rök, dimma etc.), och immunitet mot yttre strålning och buller.

Syftet med denna avhandling är : I) att undersöka elektriskt små dol- da struktur med syntetisk bländaradar (SAR), II) att bestämma kom- plex brytningsindex för objekt som använder UWB radarsystem, och III) att svar på frågan hur vi kan minska den ömsesidiga kopplingen (överhörning) i ett UWB radarsystem med sändar- och mottagaran- tenner nära varandra. I mål I, är målet icke-förstörande provning av byggda struktures såsom vid tillverkning av betongplattor eller vid re- novering. I tillägg kunde inte elektriskt små strukturer och deras inre struktur urskiljas i konventionella SAR-bilder. Den föreslagna polari- metriska analysmetoden visar på hur användbar singulärvärdesuppdel- ning (SVD) med bakåtprojektion (BPA) är för att få information om och för att klassificera elektriskt små objekt.

Vidare i denna avhandling visas för mål II en ny metod för att be- stämma komplexa brytningsindex (eller motsvarande komplexa relativa permittiviteten) hos objekt med plana ytor. Den föreslagna metoden är relativt okänslig för svagheter hos hårdvaran, såsom frekvensberoende hos antennener och analog front-end. Objekten kan vara av ändlig stor- lek och på ändligt avstånd. Begränsningarna i storlek och avstån för metoden att vara giltig undersöktes experimentellt. Sålunda är meto- den utformad för industriella mätningar på föremål på transportband. I de följande delarna av avhandlingen - mål III - undersöker och visar vi dessutom hur en absorbator för mikrovågor, baserad på metamaterial, kan användas för att förbättra prestanda hos ett radarsystem för korta avstånd, när absorbatorn placeras mellan sändar- och mottagantenner.

Resultatet blir att felet i det bestämda avståndet till målet minskar och undertryckning av klotter ökar.

vi

Acknowledgments

Finally I came to this halfway point towards doing my Ph.D. and it was an educational and an exciting journey.

First of all I would like to thank my supervisors, Professor Magnus Jansson, Professor Daniel Rönnow and Professor Niclas Björsell for their supervision, resources, funding acquisition, scientific help, support and feedback during this thesis.

I also want to thank all my colleagues of the information science and engineering department (ISE) at KTH and Academy of Technology and the Environment (ATM) department at University of Gävle (HiG) for providing a inspiring, supporting and helping environment.

In addition, I would like to thank my doctorate colleagues and my friends: Oscar Bautista Gonzalez, Ali Bemani, Rabe Andersson, Sm- ruti Ranjan Panigrahi, Zain Ahmed Khan, Mahmoud Alizadeh, Shveta Soam, ... for all our amazing times, friendly discussions and collabora- tions.

I would also like to have this chance to thank my old friends and having lots of fun and nice conversations.

Finally, I am very grateful and thankful to my parents and family for their unconditional love, understanding and supports. At last, my dear daughter, who lights up like a full moon at night and greets me with joy, hugs, and a beautiful smile every day when I return home.

You gives me a reason to continue.

Vipin Choudhary Gävle, March, 2021.

Contents

Contents vii

List of Tables ix

List of Figures x

List of Acronyms & Abbreviations xiii

I Comprehensive summary 1

1 Introduction 3

1.1 Motivation . . . 3

1.2 Thesis contribution . . . 4

1.3 List of research articles included in this thesis . . . 5

2 Theory 7 2.1 EM wave propagation . . . 7

2.2 UWB radar . . . 11

2.3 Synthetic aperture radar (SAR) . . . 12

2.4 Polarimetry . . . 13

2.5 Radar absorber . . . 14

3 UWB radar system 17 3.1 UWB antenna . . . 17

3.2 RF front and data acquisition . . . 18

4 SAR polarimetry 21 4.1 Short range UWB SAR data collection . . . 21

vii

viii CONTENTS

4.2 SAR imaging . . . 23 4.3 Singular value decomposition (SVD) and object classification . 24

5 Radar absorber 29

5.1 Design . . . 29 5.2 EM simulation and analysis . . . 31 5.3 Radar performance . . . 33

6 Dielectric properties 35

6.1 Complex refractive index determination . . . 35 6.2 Experiment . . . 40 6.3 Results . . . 46

7 Conclusion and Future Research 53

7.1 Conclusion . . . 53 7.2 Future research . . . 54

Bibliography 57

II Paper reprints 63

List of Tables

6.1 Refractive index of SW (k and ⊥ components) in various polar- ization states. The real and imaginary parts are determined for the k and ⊥ polarization of the radar unit. In k polarization, the EM wave is parallel to fiber orientation in wood, and so on. Radar- determined distance D₂is 0.327±0.03 m, while the ruler-measured distance D₂is 0.30 ± 0.02 m. . . . 49 6.2 Refractive index of WCs (k and ⊥ components) in different polar-

ization states. The real and imaginary parts are determined for the k and ⊥ polarization of the radar unit. Radar-determined dis- tance D2is 0.426 ± 0.03 m, while the ruler-measured distance D2

is 0.40 ± 0.02 m. . . . 50

ix

List of Figures

2.1 The geometry of the experiment for determining the time delay of the reflected pulse. Tx and Rx are the transmit and receive antennas. D1, D2, and D3 are the distances between the antennas and the reflecting interfaces; a0 is the pulse emitted from the Tx antenna, and a₁, a₂, and a₃are the pulses from the first reflections in the respective interfaces and reach the receive antenna. u₀ is the reference pulse, and u_i (i=1,2,3,. . .,r) represents the recorded pulses. The object’s refractive index is ˜n = n + jk. At D₃, there is a reference object. . . 9 2.2 Illustration of the different path loss effects that affect the ampli-

tude of the measured pulses. . . 9 2.3 A basic block diagram of a M-sequence UWB radar system. . . 11 2.4 An outline of the short-range-based polarimetric SAR system. . . . 13 2.5 The general classification of materials depending on values of  and

µ [38] . . . . 15

3.1 (a) Radar unit: 1) Tx Vivaldi antenna, 2) shielding plate, 3) Rx Vivaldi antenna, and 4) rotatory axis. (b) Experimental radiation pattern of the Vivaldi antennas (blue line). Tx antenna was rotated while the Rx was fix. Long-dashed black line: perfectly linearly po- larized antennas. Short-dashed red line: perfectly omni-directional antennas [9]. . . 18 3.2 (a) Loop-back signal, (b) radar echo . . . . 20

4.1 Photograph of the SAR system built at University of Gävle (HIG), Sweden. . . 22

x

LIST OF FIGURES xi

4.2 BPA images and their corresponding threshold images of cross- range (x and y axis) scanning area; (a), (b), (c), and (d) for 1D periodic mesh as an object; (e), (f), (g), and (h) for 2D periodic meshes as an object (where (a), (b), (e), (f) having HH-polarization and (c), (d), (g), (h) having VV-polarization state of the radar system respectively). . . 23 4.3 The singular-values of the C-scan image matrix for the different

objects in the scene, (a) 1D periodic mesh, (c) 2D periodic meshes having HH polarization state, whereas (b) 1D periodic mesh, and (d) 2D periodic meshes having VV polarization state. . . . 26 4.4 The γ_i for the different objects in the scene, (a), (b) 1D periodic

meshes, (c) and (d) 2D periodic meshes. . . 27 4.5 The first singular value vs. equivalent antenna rotation angle θ

for the different objects in the scene, (a), with horizontal and ver- tical objects orientation, and (b) with ϕ = 40^◦ objects orienta- tion (where 1D-HH, 2D-HH, and ϕ-1DHH represents 1D mesh, 2D meshes, and 40^◦ oriented 1D periodic mesh in HH polarization state respectively). . . 28

5.1 The strucutre of the proposed unit-cell, (a) side view and (b) top view. . . 30 5.2 Simulated S₁₁ and absorption vs. frequency for the unit cell in

Figure 5.1, with design parameters optimized for maximum abso- prtion. . . 31 5.3 The normalized impedace vs frequency for the array of the unit

cell in Figure 5.1, with design paramets optimized for maximum absoprtion. . . 32 5.4 The simulated surface current-distributions at 3 GHz (left) and at

9 GHz (right). . . 32 5.5 Simulated amplitude of the received waveform for 1) the case with-

out and 2) with the proposed absorber between the transmit and receive antennas. . . 33 5.6 Simulated amplitude of the received waveform for 1) the case with

two metallic targets 2) with the proposed absorber positioned in front of one of the targets to reduce clutter. . . 34

xii LIST OF FIGURES

6.1 Schematic illustration of a detected time domain signal, with the three reflected waves, a1, a2, and a3, at times τ1, τ2, and τ3. The part illustrates the time windows and stating times used in the analysis. A signal (a) with three interfaces, and (b) with two interfaces (D3 = 0), where the reference object is at the second interface. . . 37 6.2 Samples: Wood chips (WCs) (left) and solid wood (SW) (right). . 41 6.3 Experimental values of (a) amplitude vs. object side length for

different object distance, and (b) Y_s1 = ln(| ^A_A¹⁰

r |), Ys2 = ln(|

A20

A_r |), Ys3= ln(| ^A_A³⁰

r |), and Ys4= ln(| ^A_A⁴⁰

r |) vs. frequency, where A10, A20, A30, and A40 represent pulses from objects with 10 cm, 20 cm, 30 cm, and 40 cm side lengths respectively, and Ar is the reference pulse (dashed lines represent least square fits). . . 44 6.4 Photographs of (a) Setup I: reference measurement (top) and mea-

surement of Object A (bottom). (b) Setup II: reference measure- ment (left) and measurement of Object D (right). . . 45 6.5 (a) Measured time domain signals. (b) Magnitude of frequency

domain signals. . . 47 6.6 Experimental values of Y_3r = ln(| ^A_A³

r |), Y_1r = ln(| ^A_A¹

r |), and Y31 = ln(| ^A_A³

1 |) vs. the frequency for different moisture content values (for Object A) and for polarization states ⊥⊥ and kk as shown in the figures. . . 49 6.7 The refractive index of dry SW and dry WCs for different antenna

rotation angles, (a) real part, n, and (b) imaginary part, k. Notice that θ = 0^◦, ±180^◦ corresponds to kk and θ = ±90^◦ corresponds to ⊥⊥. . . 51 6.8 Comparison of the refractive index for SW and WCs as measured

by the two different set up geometries (Setups I and II) for different moisture content values: (a) the real part, n, of SW (Object C vs.

Object A), (b) the imaginary part, k, of SW (Object C vs. Object A), (c) the real part, n, of WCs (Object D vs. Object B), and (d) the imaginary part, k, of WCs (Object D vs. Object B). . . . 52

List of Acronyms &

Abbreviations

2D Two-Dimensional

3D Three-Dimensional

BPA Back Projection Algorithm DRP Digital Radar Processor

EM Electromagnetic

FCC Federal Communication Comission

FD Frequency Domain

FMCW Frequency Modulated Continuous Wave HH Horizontal Horizontal

HV Horizontal Vertical

Rx Receiver

SAR Synthetic Aperture Radar SFR Step Frequency Radar SVD Singular Value Decompostion

SW Solid Wood

TD Time Domain

Tx Transmitter

xiii

xiv LIST OF ACRONYMS & ABBREVIATIONS

UWB Ultra Wide Band VH Vertical Horizontal VV Vertical Vertical

WCs Wood Chips

Part I

Comprehensive summary

1

Chapter 1

Introduction

1.1 Motivation

UWB radar systems are used because of their ability to perform non-destructive testing and detect and classify different targets or objects at certain distances.

The ability to penetrate built structures (dielectric materials) makes them flexible as well as suitable for a wide range of industrial, civilian, and military applications in non-destructive sensing [1]- [4]. Due to the ultra wide band- width of the signal, high resolution images in the azimuth and range directions can be achieved using UWB synthetic aperture radar (SAR) system. A major advantage of using UWB radar system is their ability to provide high mea- surement accuracy, high resolution in time domain, insensitive to disturbing ambient conditions (such as fog , rain, mist etc) and external noise in com- parsion to other radar and different sensor systems. Therefore, UWB radar systems applications can be found in non-destructive industrial testing such as imaging and determination of dielectric properties of objects. Moreover, UWB radar systems also have other short range applications such as through the wall monitoring, ground penetration etc., which attract the attention of researchers in different fields.

In [5], a non destructive testing method using UWB signals was presented, in which a sensor detected the delay between two signals induced by a change in the dielectric property of concrete. Similarly, a method using reflected UWB signals for detecting defective and healthy carbon fiber sheets was presented in [6]. In [7, 8], free space UWB methods for determining the dielectric per- mittivity and thickness of multiple liquids levels in tanks are presented. In [9], the moisture content of wood chips was determined from the anisotropy of the

3

4 CHAPTER 1. INTRODUCTION

dielectric permittivity using UWB radar in transmission mode. The ability of electromagnetic (EM) waves to penetrate built structures has been harnessed to determine the thickness and dielectric function of walls by UWB mea- surements [10]. Various building materials dielectric function are reported in [11, 12], determined from time domain transmittance measurements. The measurement of pavement thickness and dielectric function is reported in [13].

In [14], the moisture content of grains was determined from the dielectric function in the range 3-5 GHz; a UWB sensing probe and a mode matching technique was used. Anisotropy caused by inhomogeneities on length scales shorter than the wavelength has been characterized, e.g., in [9, 14].

As modern technologies are shrinking in physical scale it becomes possible to create compact UWB systems. Researchers have shown large interest in EM absorbers because of their various applications such as in EM shielding, reduc- tion in radar cross section (RCS), and in EM interference and compatibility solutions [15], [16]. EM absorbers can be designed in various ways, such as wedge tapered absorbers [15] and absorbers made using plasmas [17]. How- ever, these absorbers are bulky, expensive, and need maintenance. Various metamaterial absorbers are reported in the literature, that have configura- tions that are simple to fabricate and are inexpensive [18].

1.2 Thesis contribution

The thesis presents nondestructive testing methods using UWB radar system and a radar absorber.

Several conventional non-destuctive testing using UWB radar have been reported in the literature [9, 14]. In non-destuctive testing using UWB radar, SAR imaging is not widely used in industrial testing at short range. The image pixel size can be smaller than the operating wavelength of the radar system, as a result, electrically small objects cannot be distinguished in conventional SAR imaging in short range. Moreover, due to smaller object size, object ori- entation, unwanted noise and measurement errors, the measured radar output tends to provide insufficient object information for relevant classification (i.e.

objective I)). In paper [A], to overcome this problem, the object may be examined from a radar system mounted on a moving platform (i.e., in a line or a grid displacement) to change the angle-of-view, and imaged using mul- tiple polarization states (VV, VH, HV, and HH, where ‘V’ and ‘H’ denote vertically and horizontally polarized received and transmitted signals). We use a back projection algorithm (BPA) to form images, and a singular value decomposition (SVD) approach to detect the dominating components in the

1.3. LIST OF RESEARCH ARTICLES INCLUDED IN THIS THESIS 5

radar image of the object, rather than analysing individual pixels. We can find information about an inhomogeneous object’s structure, as well as some information about the geometry (in particular anisotropy).

Short range non-destructive testing as well as compact radar systems with collocated Tx and Rx antennas leads to higher crosstalk between Tx and Rx units of radar system. The crosstalk of the radar system may affect the radar performance, [19], in short range application, particularly, when the target is close to the radar system (i.e. objective III)). In paper [B], a dual band metamaterial absorber (which is insensitive to polarization) is proposed and we show how the microwave absorber can be used to improve the performance of a radar system for short range applications, when positioned between the transmit and receive antennas. The error in estimated target distance is re- duced and clutter reduction is improved.

Conventional techniques for determining dielectric properties commonly used in laboratory applications, in which samples of a known geometry are placed inside specifically designed cells [11] or inside waveguides [20]. In paper [C], a new method for determining the complex refractive index (or equiva- lently the complex relative permittivity) of objects with planar interfaces is presented. Real and imaginary parts of the permittivity (or the refractive in- dex) are determined, which makes it suitable for classification in nondestruc- tive testing at short range. Examples are given of solid wood (SW) and wood chips (WCs) with different moisture content and anisotropic dielectric prop- erties. The method provides a robust in-line industrial measurement method suitable for large volumes (which includes objective II)). It can be used on objects with planar interfaces, which is common in industrial applications and makes the algorithm for determining the dielectric function simpler than for, e.g., cylindrical objects, as in [21] .

1.3 List of research articles included in this thesis

In this thesis, the included conference and journal research articles are the following:

[A] Choudhary, V., Rönnow, D., and Jansson, M. A, A Singular Value De- composition Based Approach for Classifying Concealed Objects in Short Range Polarimetric Radar Imaging, Prog. Electromagn. Res. Sympo- sium, Rome, Italy, June 2019; pp. 4109-4115.

Author’s contribution: The author of this thesis was involved in concep- tualization, developing the methodology , experimental work, developing

6 CHAPTER 1. INTRODUCTION

algorithms, data analysis, investigation and writing original draft. The co-authors were involved in validation, formal analysis, resources, su- pervision, writing review and editing.

[B] Choudhary, V., Rönnow, D., and Tripathy, M.R., Metamaterial-based- absorber to improve the performance of S and X band radar systems, 7th Inter. Conf. on Sig. Proc. and Int. N. (SPIN), Noida, India Feb.

2020, pp. 126-129.

Author’s contribution: The author of this thesis have been the main con- tributor of this article and was involved in conceptualization, developing the methodology, software work, simulation, data analysis, and writing original draft. The co-authors were involved in validation, formal anal- ysis, resources, supervision, writing review and editing.

[C] Choudhary, V. and Rönnow, D., A Nondestructive Testing Method for the Determination of the Complex Refractive Index Using Ultra Wideband Radar in Industrial Applications, Sensors, vol. 11, pp.3161, June 2020.

Author’s contribution: The author of this thesis was involved in concep- tualization, developing the methodology, software, experimental work, data curation, developing algorithms, data analysis, investigation and writing original draft preparation. The co-author was involved in con- ceptualization, validation, formal analysis, investigation, feedback, re- sources, supervision, funding acquisition, writing review and editing.

Chapter 2

Theory

In this chapter, the fundamentals of EM wave propagation, UWB radar, SAR, radar polarimetry and radar absorber are presented. The chapter also explains the theory and formulas, which are used to develop the nondestructive testing methods, algorithms and techniques.

2.1 EM wave propagation

This subsection describes propagation of EM waves, which takes place in air as well as in a dielectric medium with veloctiy, v (v6 c0, where c₀is speed of light in vaccum). We assume homogeneous linear media without any ferro- or ferri-magnetic properties. The assumption of homogeneous media means that any heterogeneities must be on length scales much smaller than the wavelength of the electromagnetic radiation, i.e., an effective medium [22].

The electromagnetic interaction is then described by the complex relative dielectric permittivity ˜ε = ε⁰−jε⁰⁰(or the complex refractive index ˜n = n+jk, where ε⁰= n²− k²and ε⁰⁰= 2nk). We assume that the objects have smooth interfaces, such that they reflect the radiation specularly. This assumption is valid if the objects are large compared to the wavelength and the roughness is much smaller than the wavelength [23]; this is valid for many industrial surfaces. The reflections in the planar interfaces are described by the Fresnel’s formulae [24]. The geometry of the experiment with EM wave propagation is shown in Figs. 2.1 and 2.2, and used in [C] to determine the complex refractive index. Figure 2.1 illustrates the reflection in the different interfaces, and Figure 2.2 shows the wavepropagation and how the different interfaces as a consequence of refraction are illuminated differently. In an alternative

7

8 CHAPTER 2. THEORY

geometry, the object is placed directly at the reference object, in which case D3 = 0. The radar pulse, a0, is emitted by the Tx antenna; reflected pulses, a1, a2, and a3, from the different interfaces are received by the Rx antenna.

The distance between the antennas and the object is D1, the object⁰s thickness is D2, and the distance from the object to the reflector is D3.

The distance from the antennas is large enough such that the objects are not in the reactive near field region, but in the Fresnel region or beyond, where the E- and H-fields are perpendicular, i.e. D1> 2D²_a/λ, where Dais the antennas’ maximum dimension, and λ is the wavelength of the electromagnetic radiation [25]. D2/n is the apparent distance from interface 1 to interface 2, as given by Snell’s law for refraction and the small angle approximation.

The frequency dependence of the complex refractive index, ˜n = n + jk, is assumed to be small, such that an effective frequency independent refractive index can be used within the experimental bandwidth; such an approximation is motivated by the small frequency dependence of several materials used in industrial applications, such as wood [26], plastic [27], [28], concrete [29], and glass [30]. For liquid water, the dielectric function has a resonance around 20 GHz [31]. At lower frequency − where the absorption is smaller − the frequency dependence is moderate. The refractive index of ice is practically flat in the region 0.1 to 300 GHz [32]. Frequency dependence in n and k are related through Kramers-Kronig relations [33]. Furthermore, we investigate materials for which n >> k, in which case the EM-wave will propagate through the object and pulses due to reflections in the different interfaces will be detectable at the Rx antenna. The reflection of EM-waves by stratified media is well studied in, e.g., optics [24], in which case an infinite number of multiple reflections are combined. We use the same approach, but we do not consider multiple reflections, since in our case we can separate the different reflected pulses in the time domain. This approach has been used for UWB radar signals in stratified media [7], [10], [34].

The used linearly polarized antennas, have wide lobes and the radiated field is close to isotropic [9]. The reflecting interfaces of the object are not always at the same distance, and the reflecting area may vary between objects. Hence, the power of the radiation reaching the object varies. Furthermore, parts of the reflected radiation from the second interface will not be transmitted through the first interface, but through the sides of the object (see Figure 2.2). In the case of the object’s interface going to infinity in both directions, all radiation would be mirrored. A path loss model with the amplitude ∝ D₁⁻¹ would be used as in [34]. If the illuminated were finite but the distance goes to infinity, a path loss model with the amplitude ∝ D₁⁻²would be used as in the

2.1. EM WAVE PROPAGATION 9

Figure 2.1: The geometry of the experiment for determining the time delay of the reflected pulse. Tx and Rx are the transmit and receive antennas.

D₁, D2, and D3 are the distances between the antennas and the reflecting interfaces; a₀is the pulse emitted from the Tx antenna, and a₁, a₂, and a₃are the pulses from the first reflections in the respective interfaces and reach the receive antenna. u₀ is the reference pulse, and u_i (i=1,2,3,. . .,r) represents the recorded pulses. The object’s refractive index is ˜n = n + jk. At D₃, there is a reference object.

Figure 2.2: Illustration of the different path loss effects that affect the ampli- tude of the measured pulses.

10 CHAPTER 2. THEORY

”radar equation,” see, e.g., Chapter 14 in [35]. In our case, the objects have finite areas and are at finite distance and we use a path loss model where the amplitude is ∝ D^−γ₁ , where 1 ≤ γ ≤ 2 and γ is different for different objects and distances.

The measured, transmitted, and received pulses are related by

a0(t) = u0(t) ∗ gt(t), (2.1) ui(t) = ai(t) ∗ gr(t), (2.2) where gt(t) is the Tx antenna’s impulse response, gr(t) is the Rx antenna’s impulse response, u0 and ui are the emitted and detected EM-pulses, and

∗ denotes the convolution. gt and g_r also include the effects of the analog front end. For the pulse reflected in the first interface and received at the Rx antenna we obtain

a1(t) =a0(t − τ1) (2D)^γ1 ∗√

σ1, (2.3)

τ₁=2D₁ c0

, (2.4)

where σ₁ is the radar cross section (RCS) for Interface 1 of the object, τ₁ is the time delay of a1, and c0is the speed of light in vacuum, and γ1is the path loss coefficient for the wave propagating between the antennas and Interface 1. For the pulse reflected in the second interface, we obtain

a2(t) = a0(t − τ2) ∗ t12∗ t21∗ α12∗ α21

(2(D₁+^D_n²))^γ2 ∗√

σ2, (2.5)

τ2= 2(D1+ nD2)

c₀ , (2.6)

where t12and t21are the Fresnel transmission coefficients, and σ2is the radar cross section of Interface 2 of the object, and α12 and α21 is the attenuation of the wave propagating through the object between Interface 1 and 2. τ2

is the time delay of pulse a2, and the term nD2 is due to the change of the phase velocity of the EM-wave in the medium. The term D2/n describes that the apparent distance from Interface 1 and Interface 2 is changed by the refraction in Interface 1, and this affects the received signal’s amplitude at the Tx antenna. In the same way, we obtain for a₃,

a3(t) = a0(t − τ2) ∗ t12∗ t23∗ t32∗ t21∗ α12∗ α21

(2(D1+^D_n² + D3))^γ3 ∗√

σr, (2.7)

2.2. UWB RADAR 11

τ₃= 2(D₁+ nD₂+ D₃) c0

. (2.8)

In a reference measurement, the object is removed and the received wave- form is

a_r(t) = a₀(t − τr)

(2(D1+ D2+ D3))^γr ∗√

σ_r, (2.9)

τ_r= (D₁+ D₂+ D₃) c0

, (2.10)

where σr is the radar cross section of the reference target.

2.2 UWB radar

The first radar system was introduced in 1935. Since then, several radar sys- tems have been reported in the literature. In 1974, ultra-wide-band (UWB) radar system was designed, which transmits and receives EM signals over a much broader EM spectrum than conventional radar systems. There are dif- ferent types of UWB radar systems evolved over time and they are classified based on the type of excitation signal. Some examples of UWB radar sys- tems are pulse noise radar, step frequency radar (SFR), M-sequence radar, Frequency Modulated Continuous Wave radar (FMCW).

System clock N-stage shift register

M-sequence

Signal

processing ∑/ADC/T&H

Target response Binary

divider

Tx

Rx

Target

Correlated data

M-sequence generator

Figure 2.3: A basic block diagram of a M-sequence UWB radar system.

12 CHAPTER 2. THEORY

In this thesis work, we have used a M-sequence radar system, which is commercially available and manufactured by Radarbolaget AB, Gävle, Swe- den. The UWB radar system is following the American Federal Communi- cations (FCC) and European (CE) standards [36]. A basic block diagram of a M-sequence UWB radar system is shown in Figure 2.3. In the M- sequence UWB radar technique [37] the transmitted signal, v(t), is a binary sequence, which is distributed over the entire measurement time, in contrast to impulse signals. The signal measured after reflection is u(t). The corre- lation u_c(t) = u(t) ∗ v(−t) is calculated, where ∗ denotes convolution. An advantage with the correlation technique is noise suppression. Notice that u(t) = h(t) ∗ v(t), where h(t) is the impulse response of the object, and u_c(t) = h(t) ∗ v_c(t), where v_c(t) is the autocorrelation of v(t), i.e., the sig- nal uc(t) depends on the objects impulse response in the same way as for an impulse signal.

2.3 Synthetic aperture radar (SAR)

A SAR system is a form of radar system whose aperture is synthesized using motion of the radar transmitter and receiver. SAR systems are used to recon- struct 2D or 3D images of an object.The synthesized aperture is much larger than the practical length of the Tx and Rx antennas. The synthesized aper- ture of the movement of the platform is used to provide good resolution in the range and azimuth directions. Some examples of applications of airborne sys- tems are sea mapping, land monitoring etc. Airborne-based SAR is seen as a powerful method for remote sensing and monitoring. A radar system can also be attached to any moving platform such as a vechicle, a motorized platform or a robot arm, which is known as short-range-based SAR (or ground-based SAR).

An outline of a short-range-based SAR system is shown in Figure 2.4. In Figure 2.4, the UWB radar unit (with collocated Tx and Rx antennas) can be moved in the x and y axis (or 2D) using a motorized platform. For each aperture antenna position, the UWB radar transmits an EM wave towards an illuminated object of interest. This EM wave propagates towards the object in the area of observation. A back reflected object response will be recieved by the Rx unit of the radar system.

2.4. POLARIMETRY 13

Figure 2.4: An outline of the short-range-based polarimetric SAR system.

2.4 Polarimetry

In polarimetry an object’s response to EM radiation of different polarization states is measured. We use the Jones matrix formalism to analyze EM-waves’

interaction with anisotropic materials [24], which is formulated in the fre- quency domain. The transmitted signal is described as a vector with the components related to the used coordinate system. The pulses from the Tx antenna are

A = A_k(f ) A_⊥(f )



, (2.11)

where A_⊥(f ) and A_k(f ) are the Fourier transforms of the perpendicular and parallel components of time domain pulse a, respectively. The reflection of EM wave in an interface or an object are described by

R = r_kk r_k⊥

r_⊥k r_⊥⊥



(2.12)

where r_kk, r_k⊥, r_⊥k and r⊥⊥ are the Fresnel coefficients. The response of an EM-wave of arbitrary polarization can be described by R. We will calculate the response corresponding to a rotation of the coordinate system of the antennas using the Jones-rotation matrix,

14 CHAPTER 2. THEORY

T =cos(θ) −sin(θ) sin(θ) cos(θ)



. (2.13)

The emitted and recieved signals (before and after the antenna units) i.e.

u0(t) and ur(t) are scalar. Their Fourier transforms are related to the Jones vectors of transmitted pulse A0, and recieved pulse Ar. For A0 and U0, we write

A0= GtU0= G_t,k Gt,⊥



U0, (2.14)

where Gt,k= Gtcos(θ − θ0) + Gt,c, and Gt,⊥ = Gtsin(θ − θ0) + Gt,c; Gtis the antenna gain, θ is the rotation angle of the transmit antenna, θ0is an offset in the rotation angle, and Gt,c is the cross-talk that describes that the antenna may transmit an EM-wave perpendicular to its plane. In the same way for the received signal U_i, we write

U_i=G_r,k G_r,⊥Ai, (2.15) where G_r,k= G_rcos(θ − θ₀) + G_r,c, and G_r,⊥= G_rsin(θ − θ₀) + G_r,c; G_r,crep- resent the corresponding angles and crosstalk for the receive antenna. Notice that θ0≈ 0, Gt,c << Gt, and Gr,c<< Gr, and we assume that Gr= Gt, since we use the same type of linear antenna for both the Tx and Rx antennas.

2.5 Radar absorber

Specially selected or designed materials that can prevent transmission or re- flection of EM radiation are used as radar absorbers. There are different types of materials, which are used for radar absorbers as discussed in Chapter 1.

In this subsection, we discuss metamaterial absorbers, which are inexpensive, light in weight and need no maintenance [18].

Metamaterials are specially engineered artifical materials. They are made up of conductive and non conductive composite materials such as metals and dielectrics, which are commonly found in nature. The resonant unit cells (in printed metamaterials) are usually arranged in periodical arrays of sub- wavelength size. This periodic structure obtains its new properties or unusual characteristics, which are not seen in natural materials (such as capable of manipulating EM wave: by complete absorbing, bending etc.).

Most isotropic materials present in nature have positive values of permit- tivity, , and permeability, µ, or , µ > 1. They are thus termed double

2.5. RADAR ABSORBER 15

Figure 2.5: The general classification of materials depending on values of  and µ [38] .

positive (DPS) materials. Such materials where  < 0 or µ < 0 are termed as

-negative (ENG ) or µ-negative ( MNG) materials. Further, materials with

, µ < 0 are not present in nature, so they are specially engineered artificially and such media are named double negative (DNG) materials [38]. The general classification of materials depending on values of  and µ and some examples of refraction of EM wave in the different media are shown in Figure 2.5.

Chapter 3

UWB radar system

This chapter discusses the UWB antenna and the RF front used in the ex- perimental measurements. The experimental results of the radiation pattern are shown for the directional antenna (used in this thesis) versus perfectly omni-directional antenna. The features such as frequency spectrum band- width, polarimetric housing, radar processing unit are discussed in depth. In addition, the data acquisition is discussed.

3.1 UWB antenna

As we know, a UWB radar system transmits and receives wide band signals, which requires antennas capable of operating on the same wide frequency band. Thus, the Tx and Rx antennas should have a small and well defined frequency dependence in the signals’ band. Practically, S-parameters and ra- diation pattern (in Fresnel near field and far field region) should be consistent over time across all measurements. Further, UWB radar systems are often using a pulse-based technology, and therefore characteristics of the antennas such as time domain (TD) effects, antenna frequency dependence as well as S-parameters properties must be known [39]. Antenna characterization can be performed using TD and FD analysis [39]. In this thesis, the radar system consists of two Vivaldi antennas which were collocated as a transmitter and a receiver as shown in Figure 3.1 a. The Vivaldi antenna was developed by uni- versity of Gävle and Radarbolaget AB. The antenna is a quasi-vivaldi antenna with a taper leaf shape design. The design of the antenna allows to match to the free space impedance over the entire operating frequency spectrum, which provides a smooth directional pattern. Therefore, the antenna has rela-

17

18 CHAPTER 3. UWB RADAR SYSTEM

tively small side lobes compared to other UWB antennas. Figure 3.1 b, shows the experimental results of the radiation pattern of the vivaldi antennas vs.

perfectly omni-directional antennas.

(a)

(b)

Figure 3.1: (a) Radar unit: 1) Tx Vivaldi antenna, 2) shielding plate, 3) Rx Vivaldi antenna, and 4) rotatory axis. (b) Experimental radiation pattern of the Vivaldi antennas (blue line). Tx antenna was rotated while the Rx was fix.

Long-dashed black line: perfectly linearly polarized antennas. Short-dashed red line: perfectly omni-directional antennas [9].

3.2 RF front and data acquisition

The system consists of a digital radar processor (DRP), a transmitter and receiver unit, with the ability to connect one or more antenna pairs. In a pair of antennas, one antenna acts as transmitting, while another as receiving antenna. The transmit antenna emits the M-sequence binary code and the receive antenna detects the radar echo. The DRP is responsible for the pre- processing of radar signals and synchronisation of the transmitter and receiver unit. Pre-processing refers to the procedure of processing transmit signal

3.2. RF FRONT AND DATA ACQUISITION 19

and object echo detected by receiver unit of the system before any further processing. The transmitter and receiver units are connected internally via a loop-back circuit, which allows the system to periodically synchronize the data as well as the user to study pulse distortion due to the antenna and object echo.

In pre-processing, the transmitted and received signals are synchronized and the synchronized signals are correlated to give a narrow pulse in time domain as shown in Figure 3.2 a and b. The system’s transmit gain can be manually adjustable (up to -10dBm).

The antennas can be rotated to perform measurements for different po- larization modes (such as HH-, HV-, VH-, and VV-polarization) as shown in Figure3.1 a. The system operates in the frequency range 0.5-3 GHz (wave- length range 0.5-0.1 m).The radar system is connected to a PC via a USB connection. Software to control, operate and export radar data was also de- veloped by Radarbolaget AB. Using the software, the system can be configured to transmit and receive for short duration of time (ns) as well as for continu- ously scanning. These output signals can be presented as radar echoes in time domain as shown in Figure 3.2 b. The x-axis represents the time, d/(2 × c0), where d is distance between radar system and object, c0 is the speed of light in vaccum. The y-axis represents the amplitude of the correlated signal.

20 CHAPTER 3. UWB RADAR SYSTEM

(a)

(b)

Figure 3.2: (a) Loop-back signal, (b) radar echo

Chapter 4

SAR polarimetry

The fundamentals of UWB radar, polarimetry and SAR are presented in Chapter 2 (see above). This chapter aims at the SAR imaging method of UWB radar and SAR polarimetry, and the steps which are mainly used for the classification of electrically small objects. This chapter also summarizes the results of paper [A].

4.1 Short range UWB SAR data collection

The SAR system uses a UWB radar from Radarbolaget, Gävle, Sweden and was built at University of Gävle (HIG), in Gävle, Sweden. It is a short-range- based SAR system. The aperture of the UWB radar system is synthesized using the 2D motorized platform as shown in Figure 4.1.

For a good SAR image forming, the data collected by the SAR system must have a good signal to noise ratio. Initially to reduce the internal and external noise, a reference measurement was made. Reference measurement refers to a measurement without an object for each antenna position and orientation.

The object was then positioned and measurements were made for the same antenna positions and orientations that were used in the reference measure- ment. The reference measurement was then subtracted from the measurement of the object, to subtract the clutter. The measurements were carried out at 36 antenna positions in a quadratic pattern with 0.18m step size. The antenna orientations were HH, VV , and HV (VH was omitted due to symmetry).

21

22 CHAPTER 4. SAR POLARIMETRY

Figure 4.1: Photograph of the SAR system built at University of Gävle (HIG), Sweden.

Objects

The experiments were carried out on metallic (copper) bars behind a concrete slab, replicating different types of building elements with reinforcement bars:

(i) a 1D periodic mesh with 15 cm spacing between four vertical bars (1D object), (ii) a 2D periodic mesh (or grid) with equal spacing between four vertical and four horizontal bars of approximately 15 cm (2D object). (iii) The 1D mesh rotated approximately φ = 40^◦clockwise as seen from the radar.

The length and diameter of the bars were 0.85 m and 1.2 cm, respectively.

The area of the compound object was approximately 1 m². The bars were tied together with thin metal wires and fastened to the wooden frame to form the meshes. Notice that the spacing between the bars was similar to or smaller than the signal’s wavelength.

4.2. SAR IMAGING 23

Figure 4.2: BPA images and their corresponding threshold images of cross- range (x and y axis) scanning area; (a), (b), (c), and (d) for 1D periodic mesh as an object; (e), (f), (g), and (h) for 2D periodic meshes as an object (where (a), (b), (e), (f) having HH-polarization and (c), (d), (g), (h) having VV-polarization state of the radar system respectively).

4.2 SAR imaging

Radar cross-range images are obtained by using the back projection method [40]. To form the cross-range images the measured radar signals of differ-

24 CHAPTER 4. SAR POLARIMETRY

ent antenna positions are combined. For each antenna position (xn; yn) and measured signal uc(xn; ynt) the discrete Fourier transform, Uc(xn; ynωi); is calculated. These spectra are then combined in phase,

Q(x⁰, y⁰, z⁰, ωi) = Σ^N_n=1Uc(xn, yn, ωi)e^−jωitr (4.1) where tr = rn = c0 with rn being the distance between antenna position (xn; yn) and image position (x0; y0; z0) and c0 the speed of light in vacuum.

A radar C-scan image is then obtained for each z⁰

I(x⁰, y⁰) = Σ_i| Q(x⁰, y⁰, z⁰, ω_i) |². (4.2) Thus, we get one image for each polarization state. We did not take into account the refraction and different speed of light in the concrete slab, since it is thin compared to the object size and wavelength.

Radar images were obtained as described in equations (4.1) and (4.2) from the experimental data as shown in Figures 4.2. Figures 4.2 (a), (c), (e) and (g) show the different radar images (HH and VV polarization) of the objects. As expected, the compound objects are clearly seen in the figure. However, the structure of the compound objects, i.e., the individual bars or their orientation cannot be distinguished, regardless of polarization state. The reason is - of course - that the distance between the bars is of the same order as or smaller than the radar signal’s wavelength. The object reflection varied with the polarization state (see the colour scale). For example, it can be observed in Figures 4.2 (a) and (b) that the intensity for the HH-image is relatively low compared to the VV-image for the 1D periodic mesh. Thus, these radar images contain information about the objects (anisotropy, orientation and ORCS area of the objects), which require further analysis. In a first attempt, thresholding of the images was performed to help identifying the significant pixels that belong to the object (only provide the information about an object cover area in the scene). These threshold images are shown in Figures 4.2 (b), (d), (f) and (h).

4.3 Singular value decomposition (SVD) and object classification

In Section 4.2, the radar images are discussed. To classify the object from the images in Figure 4.2, the SVD was applied. The size of the C-scan matrices, I, is 20 × 20 pixels; each row and column represents steps of 5 cm in x and y cross range direction, respectively. We analyse the radar cross-range images

4.3. SINGULAR VALUE DECOMPOSITION (SVD) AND OBJECT

CLASSIFICATION 25

using the SVD method. Using the SVD method, the matrix I (equation (4.2)), is decomposed as [40]

I = PΣW^T (4.3)

where Σ is a non-zero diagonal matrix that contains the singular values σi, P and W are complex unitary matrices, comprising the left and right singular vectors of I. The diagonal matrix Σ contains σi in decreasing order (i.e., σ1

> σ2. . . > 0) which means that the first few singular-components are the dominant ones.

Figure 4.3 shows the singular values of Σ ( in equation (4.3)) for the images (a), (c), (e), and (g), where (a) and (c) are HH- and V V -images of the 1D object and (e) and (g) are HH- and VV-images of the 2D object, respectively.

In Figure 4.3 we see that for all images the first singular value is an order of magnitude larger than the other (note the logarithmic scale of the vertical axis).

In order to enable classification of objects, we introduce the ratio γi=σi,HH

σ_{i,V V} . (4.4)

In Figure 4.4 , γ_i and 1/γ_i calculated from the data in Figure 4.3 are shown. In Figure 4.4 (a) - for the 1D object - γ_i is approximately zero for indices up to 10. The object only contains vertical bars. The horizontal E- field is not reflected and the HH-image has low intensity. The vertical E-field is reflected and the VV-image has high intensity. For indices above 10, γi is large; the singular values are only due to noise. Thus, from Figures 4.4 (a) and (b) one can draw the conclusion that the object has interior structure that is one-dimensional, i.e., highly anisotropic properties, whereas, Figures 4.4 (c) and (d) show γiand 1/γifor the 2D object. Both γiand 1/γi are close to unity; i.e., the singular values of the HH and VV-images are approximately the same (where unity means perfectly identical). Thus, we can conclude from Figures 4.4 (c) and (d) that the object has essentially isotropic electromagnetic properties.

Furthermore, to illustrate how the orientation of an anisotropic inhomoge- neous object can be detected. We use the rotation matrix in (Section 2.4) to calculate the Jones matrix equivalent to a certain antenna rotation; the radar images is obtained using the BPA, and then the SVD is used to determine the first singular component. In Figure 4.5 (a) the first singular value of the HH and VV-images are shown for the horizontal 1D and 2D objects as a function of the equivalent rotation angle.

26 CHAPTER 4. SAR POLARIMETRY

Figure 4.3: The singular-values of the C-scan image matrix for the different objects in the scene, (a) 1D periodic mesh, (c) 2D periodic meshes having HH polarization state, whereas (b) 1D periodic mesh, and (d) 2D periodic meshes having VV polarization state.

For the 1D object there is a clear maximum of the VV values at 0^◦ and 180^◦, and corresponding minimum at 90^◦. For the 2D object the variation with angle is smaller. Thus, the 1D and 2D periodic objects are easily separated.

Figure 4.5 (b) shows the first singular value vs. equivalent rotation angle for the vertical 1D object and for the 1D object rotated 40^◦. The behaviour with angle is the same, except a shift of 40^◦. Thus, we can clearly identify the orientation of the 1D object due to its anisotropy, though its interior structure cannot be distinguished due to the length scale of the inhomogeneities being shorter than the operating wavelength.

4.3. SINGULAR VALUE DECOMPOSITION (SVD) AND OBJECT

CLASSIFICATION 27

Figure 4.4: The γi for the different objects in the scene, (a), (b) 1D periodic meshes, (c) and (d) 2D periodic meshes.

28 CHAPTER 4. SAR POLARIMETRY

Figure 4.5: The first singular value vs. equivalent antenna rotation angle θ for the different objects in the scene, (a), with horizontal and vertical objects orientation, and (b) with ϕ = 40^◦ objects orientation (where 1D-HH, 2D-HH, and ϕ-1DHH represents 1D mesh, 2D meshes, and 40^◦ oriented 1D periodic mesh in HH polarization state respectively).

Chapter 5

Radar absorber

In this chapter, we present a metamaterial-based radar absorber. The struc- ture of the absorber consists of an array of closed ring resonators on a low profile substrate. The structure is optimized for high absorption by properly selecting the design geometry and design parameters, as discussed in paper [B]. The absorptance is calculated taking into account both co- and cross- polarization of reflected waves. This chapter also summarizes and discusses the simulation results of paper [B], which show that high absorption was achieved (absorptance > 90 %). Further, we show how the radar absorber can be used to improve the performance and clutter reduction at short range.

5.1 Design

The unit-cell of the proposed radar absorber consists of three layers: 1) a modified closed square ring resonator enclosed in a thin microstrip line as a top metallic layer, 2) a low profile FR-4 epoxy substrate ( r = 4.39, tanδ

= 0.004 , with thickness t ) as a dielectric layer, and 3) a back-plane as a ground metallic layer. The top and bottom metallic layers are 35 × 10⁻⁶m thick copper sheets (with conductivity of 5.8 × 10¹³ S/µm) attached on the dielectric layer as shown in Figure 5.1 (a); the structure of the resonator on the top layer is shown in Figure 5.1 (b).

The proposed unit-cell is square in shape with side, LS. The presented unit cell was designed, analyzed, and optimized using periodic-boundary conditions along the x-axis and y-axis. A linearly polarized wave with two different modes (x-axis and y-axis) propagates into the proposed unit-cell along z-axis, i.e. at normal incidence. The total absorption is calculated as,

29

30 CHAPTER 5. RADAR ABSORBER

A(ω) = 1− | S11(ω) |²− | S21(ω) |² (5.1) where S11(ω) and S21(ω) are the complex reflection and transmission coef- ficients, respectively (1 and 2 in subscript denote the respective ports). As the absorber structure has a complete metallic layer on the back-plane (see Figure 5.1), the transmittance becomes zero (S₂₁(ω) = 0 ). The reflection coefficient’s magnitude is expressed as | S₁₁(ω) |=p| rxx(ω) |²+ | r_yx(ω) |², where r_xxand r_yxdenote the co-polarized and cross-polarized reflected x-axis polarized waves, respectively. Further, the impedance of the periodic struc- ture and the input-impedance of the grounded lossy substrate are expressed as the total normalized complex impedance (z = re(z) + im(z) × j), which is equal to the combination of the two impedances normalized to free space impedance [42], [35]. Ideally, therefore, the reflection coefficient must be zero and the total normalized impedance should have real and imaginary parts close to unity and zero, respectively, for perfect impedance matching to free- space to achieve complete absorption. The normalized impedance can also be written as a function of the S11 and S21 reflection coefficient [35] in,

z = s

(1 + S₁₁)²− S₂₁²

(1 − S11)²− S₂₁² = (1 + S₁₁)

(1 − S11) (5.2)

Figure 5.1: The strucutre of the proposed unit-cell, (a) side view and (b) top view.

5.2. EM SIMULATION AND ANALYSIS 31

5.2 EM simulation and analysis

The electromagnetic simulation and numerical simulations of the absorber were carried out using ANSYS Electronics simulator and MATLAB R2019a.

A linearly polarized wave propagates into the proposed unit-cell along the z-axis through the top layer, (i.e. port 1 and the port 2: other side). The proposed absorber design was examined for two different modes (i.e. x-axis and y-axis) and its absorption properties using equation (5.1) are presented in Fig 5.2.

Figure 5.2: Simulated S₁₁ and absorption vs. frequency for the unit cell in Figure 5.1, with design parameters optimized for maximum absoprtion.

The structure was optimized for absorption; it is observed through sim- ulations that the lower resonant frequency band depends on parameter, t_c, while the higher resonant frequency depends on tc2 and tR. Absorption of 94.8 % at 3 GHz and 90.2% at 9 GHz for linearly polarized wave respectively was achieved. It is observed that the reflectance from the x-axis and y-axis polarization modes are identical, due to symmetrical shape of the unit-cell absorber. The complex normalized impedance (z) of the proposed structure, presented in Figure 5.3, is 1.51 − 0.06j and 0.93 − 0.14j at 3 GHz and 9 GHz frequencies, respectively. So, we can say that it is a good match with free space impedance, which results in a reduction in the reflection from the structure.

In order to understand the absorption mechanisms of the unit-cell, we analyze surface current distributions at both absorption frequencies as shown in Figure 5.4. It is clearly seen in the surface current distributions that the incident wave generates high currents mainly at the edges of the closed ring

32 CHAPTER 5. RADAR ABSORBER

Figure 5.3: The normalized impedace vs frequency for the array of the unit cell in Figure 5.1, with design paramets optimized for maximum absoprtion.

resonator. The flow of current is opposed by the inductance components of the microstrip-structure, which introduces insertion losses in the top layer. The current induced electric and magnetic resonances in the closed ring resonator, which is coupled through the lossy grounded substrate, further introduces additional dielectric and ohmic losses in the structure [35]. Hence, these losses in the structure cause the absorption at mentioned frequencies.

Figure 5.4: The simulated surface current-distributions at 3 GHz (left) and at 9 GHz (right).

5.3. RADAR PERFORMANCE 33

5.3 Radar performance

The simulation of the radar performance was also performed with the EM simulator (see above). The simulated radar system corresponds to the actual radar system described in Chapter 3; it operates with a center frequency of 3 GHz (i.e. the wavelength is 0.1 m). The radar simulations were carried out for flat (large and small) metallic objects, as described below.

Antenna cross-talk and target distance

In the short range applications, the crosstalk of the radar system may affect the radar performance [19]. The single large metallic target (1 × 1 m²) is placed at 0.6 m distance from the radar unit. We estimate the target distance from the peak of the received wavelet. The array of proposed unitcell is used as absorber positioned between the transmitting and receiving antennas. As a result, in Figure 5.5, it is seen that the crosstalk between the Tx and Rx antenna as well as the error in estimated target position are reduced. The crosstalk was reduced by a factor of 4 with the absorber and the estimated target positions were found to be 0.622 m without absorber, and 0.605 m with absorber.

Figure 5.5: Simulated amplitude of the received waveform for 1) the case without and 2) with the proposed absorber between the transmit and receive antennas.