Analysis of angular accuracy in the IFF Monopulse...

Department of Science and Technology Institutionen för teknik och naturvetenskap Linköping University Linköpings universitet

gnipökrroN 47 106 nedewS ,gnipökrroN 47 106-ES

LiU-ITN-TEK-A--18/015--SE

Analysis of angular accuracy inthe IFF Monopulse receiver

Filip Bengtsson

David Sköld

2018-06-08

LiU-ITN-TEK-A--18/015--SE

Analysis of angular accuracy inthe IFF Monopulse receiver

Examensarbete utfört i Elektroteknikvid Tekniska högskolan vid

Linköpings universitet

Filip BengtssonDavid Sköld

Handledare Anna LombardiExaminator Adriana Serban

Norrköping 2018-06-08

Upphovsrätt

Detta dokument hålls tillgängligt på Internet – eller dess framtida ersättare –under en längre tid från publiceringsdatum under förutsättning att inga extra-ordinära omständigheter uppstår.

Tillgång till dokumentet innebär tillstånd för var och en att läsa, ladda ner,skriva ut enstaka kopior för enskilt bruk och att använda det oförändrat förickekommersiell forskning och för undervisning. Överföring av upphovsrättenvid en senare tidpunkt kan inte upphäva detta tillstånd. All annan användning avdokumentet kräver upphovsmannens medgivande. För att garantera äktheten,säkerheten och tillgängligheten finns det lösningar av teknisk och administrativart.

Upphovsmannens ideella rätt innefattar rätt att bli nämnd som upphovsman iden omfattning som god sed kräver vid användning av dokumentet på ovanbeskrivna sätt samt skydd mot att dokumentet ändras eller presenteras i sådanform eller i sådant sammanhang som är kränkande för upphovsmannens litteräraeller konstnärliga anseende eller egenart.

För ytterligare information om Linköping University Electronic Press seförlagets hemsida http://www.ep.liu.se/

Copyright

The publishers will keep this document online on the Internet - or its possiblereplacement - for a considerable time from the date of publication barringexceptional circumstances.

The online availability of the document implies a permanent permission foranyone to read, to download, to print out single copies for your own use and touse it unchanged for any non-commercial research and educational purpose.Subsequent transfers of copyright cannot revoke this permission. All other usesof the document are conditional on the consent of the copyright owner. Thepublisher has taken technical and administrative measures to assure authenticity,security and accessibility.

According to intellectual property law the author has the right to bementioned when his/her work is accessed as described above and to be protectedagainst infringement.

For additional information about the Linköping University Electronic Pressand its procedures for publication and for assurance of document integrity,please refer to its WWW home page: http://www.ep.liu.se/

© Filip Bengtsson, David Sköld

Abstract

This master thesis investigates how certain components error margin may affect the accuracyof a IFF monopulse receiver. The IFF monopulse receiver measures the angle of arrival ofthe incident signal by comparing sum and difference signals created in the receiver. Thecomponents of interest are phase shifters and attenuators, where both can give individualand different errors depending on the antenna steering angle.

The project is conducted at Saab Aeronautics, based on a receiver in development forthe Gripen E aircraft. A model of the receiver was made as close as possible for an idealcase using the program Matlab Simulink. The model is an ideal model based on componentcharacteristics coded with function blocks, based on theory. Simulated measurements of theantenna pattern and the values of look-up tables for the existing receiver have been providedfor comparison. Further, the ideal model is compared with the non-ideal model where thecomponents have their errors enabled.

Although the simulation environment Simulink may not be ideal for simulations of thistype of system, the results of the thesis generated results showing that the angular accuracydecreases with the increase of steering angle. The angular deviation can for some cases beseen as sufficiently small for the receiver to work properly in the ideal case.

i

Acknowledgments

We would like to thank our supervisor at Saab, Mikael Håkansson Borg, for his feedback andsupport throughout this thesis. Also, we would like to thank other colleagues at Saab fortheir technical support and for welcoming us to the office.

We would also like to thank both our supervisor, Anna Lombardi, and our examiner,Adriana Serban, at Linköpings University for their feedback on the report and for theirencouragement.

David Sköld and Filip BengtssonNorrköping, June 20, 2018

iii

Contents

Contents iv

List of Figures vi

List of Tables viii

Abbreviations and acronyms ix

Symbols xi

1 Introduction 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.4 Research questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.5 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.6 Delimitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.7 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Radar technology 5

2.1 Antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Secondary Surveillance Radar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3 Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.4 Monopulse SSR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.5 Identification Friend or Foe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.6 IFF monopulse antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.7 Single pulse detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.8 System design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.9 Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3 Signal model 23

3.1 System design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.2 Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4 Receiver model 35

4.1 Receiver system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.2 Transmit receive unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.3 Low-noise amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.4 Phase shifter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.5 Attenuator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.6 Random error generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.7 Wilkinson power divider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.8 The 180˝ hybrid coupler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

iv

4.9 Diff/Sum ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5 Data management 49

5.1 Simulink to Matlab file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495.2 Matlab file to graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

6 Simulation results and discussion 55

6.1 Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556.2 System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566.3 Input signals and parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566.4 Signal modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566.5 Transmit receive unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576.6 Couplers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586.7 Model validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596.8 Ideal antenna pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596.9 Steer 0˝ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606.10 Steer 10˝ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 676.11 Steer 20˝ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 696.12 Steer 30˝ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 706.13 Steer 40˝ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 726.14 Steer 50˝ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 746.15 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

7 Conclusion and future work 79

7.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 797.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

Bibliography 81

Webography 83

Appendices

A Simulink blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .B Matlab code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

v

List of Figures

2.1 (a) Radiation pattern polar diagram. (b) Radiation pattern rectangular diagram. . . 62.2 Radiation pattern example for broadside linear array with different elements. . . . 72.3 Incident wave with angle of arrival θ. . . . . . . . . . . . . . . . . . . . . . . . . . . 82.4 Phased array antenna operation principle. . . . . . . . . . . . . . . . . . . . . . . . . 92.5 Radar operation principle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.6 Illustration of the interrogation signal. . . . . . . . . . . . . . . . . . . . . . . . . . . 112.7 Illustration of the reply signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.8 Illustration of the sliding-window method. . . . . . . . . . . . . . . . . . . . . . . . 132.9 The beam pattern of the monopulse SSR. . . . . . . . . . . . . . . . . . . . . . . . . 142.10 Top of the beam pattern of the monopulse SSR. . . . . . . . . . . . . . . . . . . . . . 152.11 Interrogate and control beam patterns. . . . . . . . . . . . . . . . . . . . . . . . . . . 182.12 The 180˝ hybrid coupler. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.1 Conceptual image of the system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.2 The entire system in Simulink. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.3 The SBB system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.4 Inside the SBB system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.5 The propagation block. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.6 The configuration of the propagation system. . . . . . . . . . . . . . . . . . . . . . . 263.7 The relative speed function block. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.8 The Doppler function block. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.9 The Friis function block. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.10 The distance calculation function block. . . . . . . . . . . . . . . . . . . . . . . . . . 293.11 The effective area function block. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.12 Input_signal subsystem of the SBB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.13 Inside the Input_signal subsystem of the SBB. . . . . . . . . . . . . . . . . . . . . . . 313.14 The phase calculation block. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.15 The phase calculation function block. . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.16 Phase shifter block in the SBB subsystem. . . . . . . . . . . . . . . . . . . . . . . . . 343.17 Phase shifter function in the SBB subsystem. . . . . . . . . . . . . . . . . . . . . . . 34

4.1 Conceptual block model of the receiver. . . . . . . . . . . . . . . . . . . . . . . . . . 354.2 Receiver system block. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.3 Inside receiver system subsystem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.4 TRU block. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.5 Inside the TRU block. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.6 The steer calculation function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.7 The RF module block. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.8 The subsystems of the RF module block. . . . . . . . . . . . . . . . . . . . . . . . . . 384.9 The LNA block. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.10 Inside the LNA block. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.11 The phase shifter block. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

vi

4.12 Inside the phase shifter block. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.13 The steer function block. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.14 The state generator function block. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.15 The attenuator block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.16 Inside the attenuator block. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.17 The attenuator function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.18 The Random Matlab function block. . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.19 The WPD block. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.20 The WPD function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.21 The rat-race block. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.22 Rat-race function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.23 Ratio calculation block. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.24 Inside the ratio calculation block. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5.1 The to_matfile function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

6.1 The received signal at one antenna element. . . . . . . . . . . . . . . . . . . . . . . . 566.2 The phase shifted signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576.3 The attenuated signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586.4 The sum and difference signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586.5 Antenna pattern of the ideal system. . . . . . . . . . . . . . . . . . . . . . . . . . . . 596.6 Sum diff ratio of ideal the system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606.7 Sum diff signals with phase shifter error enabled. . . . . . . . . . . . . . . . . . . . 616.8 Sum diff signals with attenuation error enabled. . . . . . . . . . . . . . . . . . . . . 616.9 Sum diff signals with attenuator and phase shifter error enabled. . . . . . . . . . . 626.10 Ratio with attenuator error for steer 0˝. . . . . . . . . . . . . . . . . . . . . . . . . . 636.11 Ratio with phase shifter error for steer 0˝. . . . . . . . . . . . . . . . . . . . . . . . . 636.12 Ratio with attenuator error for steer 0˝. . . . . . . . . . . . . . . . . . . . . . . . . . 646.13 Ratio with attenuator and phase shifter error for steer 0˝. . . . . . . . . . . . . . . . 646.14 Ratio deviation for steer 0˝. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656.15 Maximum, minimum and ideal ratio for steer 0˝. . . . . . . . . . . . . . . . . . . . . 666.16 Max and min angle deviation for steer 0˝. . . . . . . . . . . . . . . . . . . . . . . . . 666.17 Sum and difference with attenuator and phase shifter error enabled for steer 10˝. . 676.18 Ratio with attenuator and phase shifter error for steer 10˝. . . . . . . . . . . . . . . 686.19 Max and min angular deviation with both errors enabled for steer 10˝. . . . . . . . 686.20 Sum and difference with attenuator and phase shifter error enabled for steer 20˝. . 696.21 Ratio with attenuator and phase shifter error for steer 20˝. . . . . . . . . . . . . . . 696.22 Max and min angular deviation with both errors enabled for steer 20˝. . . . . . . . 706.23 Sum and difference pattern with attenuator and phase shifter error for 30˝ steer. . 716.24 Ratio with both attenuator and phase shifter error for 30˝ steer. . . . . . . . . . . . 716.25 Max and min angular deviation with both errors enabled for steer 30˝. . . . . . . . 726.26 Sum difference pattern with attenuator and phase shifter error for 40˝ steer. . . . . 726.27 Ratio with attenuator and phase shifter for 40˝ steer. . . . . . . . . . . . . . . . . . . 736.28 Maximum and minimum angular deviation with both errors enabled for steer 40˝. 736.29 Sum difference pattern with attenuator and phase shifter error for 50˝ steer. . . . . 746.30 Ratio with attenuator and phase shifter for 50˝ steer. . . . . . . . . . . . . . . . . . . 746.31 Max and min angular deviation with both errors enabled for steer 50˝. . . . . . . . 756.32 Angular deviation for all the different steering angles with attenuator error enabled. 766.33 Angular deviation for all the different steering angles with phase shifter error en-

abled. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 766.34 Ideal ratio for different steer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 776.35 Angular deviation for all the different steering angles with both errors enabled. . . 77

vii

List of Tables

2.1 Interrogation modes for SSR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4.1 Maximum phase variance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

viii

Abbreviations and acronyms

Abbreviation Description

IFF Identification Friend or FoeSSR Secondary Surveillance RadarAoA Angle-of-ArrivalESA Electrically Scanned SystemAESA Active Electrically Scanned SystemATC Air Traffic ControlMSSR Monopulse Secondary Surveillance RadarSLS Side Lobe SuppressionSPI Special Position PulseFRUIT False Replies Unsynchronized In TimeLNA Low-Noise AmplifierNF Noise FigureISLS Interrogation Side Lobe SuppressionWPD Wilkinson Power DividerTRU Transmit Receive UnitSBB Signal Black BoxDSP Digital Signal Processing

ix

Symbols

Notation Description

D DirectivityU RatioPtot Total power transmittedAe Antenna apertureλ WavelengthN Number of antenna elements∆ϕ Phase differencen Number of the antenna elementx Space difference between antenna elementsAF Array factorwi Weight factork Wavenumberθ Angle deviationvp Speed of the signalc Speed of lightR Distance from targetttravel Travel time for wavePr Power receivedPt Power transmittedGr Gain of receiving antennaGt Gain of transmitting antennaAr Antenna aperture of receiving antennaAt Antenna aperture of transmitting antennaσ Antenna cross-sectiond Distance between antennasfd Doppler frequencyfs Signal frequencyV0 Velocity of observerVw Velocity of signalVr Radial velocityL LossesS Scattering parameter∆ Difference signalΣ Sum signalFi Noise factorGi GainSi Signal

xi

Chapter One

Introduction

This master thesis investigates how certain components error margin may affect the accuracyof the new IFF monopulse receiver for Gripen E. The project was done as a Master thesisat the Electronic Design Engineering program at Linköpings University provided by SaabAeronautics in Linköping, Sweden.

1.1 Background

Saab is currently developing the new JAS 39E Gripen. This new aircraft will use a new typeof Monopulse IFF radar which is electronically controlled instead of mechanically controlled.The project will analyze and validate data of different parameters for this radar.

Aeronautics, a business area of Saab offers advanced airborne systems, related subsystems,unmanned aerial systems, aerostructures and services to defense customers and commercialaerospace industries, worldwide. Aeronautics is also responsible for development, produc-tion, marketing, selling and supporting of the Gripen fighter.

The section Radar and IFF (Identification, Friend or Foe) works with integration of to-day’s and future radar and IFF systems. This work will be a part of the tactical systems areawho develops functions in the fields of communication and data links, target acquisition,electronic warfare, navigation, reconnaissance and decision support.

1.2 Motivation

Identification of aircrafts is important for both daily travel and for military purposes. Toidentify an aircraft, a radar could be used and the aircraft could be contacted through radioto request identification and purpose. However, this solution requires a lot of manpowerand has been replaced by a Secondary Surveillance Radar (SSR) which handles the describedproblem. This system contacts the aircraft, requests information and processes the answer,which can be presented in a manageable way for the operators. SSR can in some cases alsodetermine where the aircraft is sending its reply from, effectively producing a more or lessreliable map of where nearby aircrafts are. Depending on how accurate the position data is,more aircrafts can be directed in a finite area with less risk for accidents to happen.

This project evaluates a new model of a SSR system to determine the angular accuracyof the system. The project is conducted at Saab Aeronautics in Linköping, Sweden.

1

1. INTRODUCTION

1.3 Aim

The goal of this work is to analyze and calculate the angular accuracy and uncertainty of theIFF receiver system developed for Gripen E.

A monopulse IFF receiver system determines the “angle-of-arrival” (AoA) of a transpon-der reply by comparing the reply amplitude in different antenna lobes; the main and controllobe. In an Electrically Scanned Array (ESA) the lobe characteristics change depending onthe desired steering angle.

The scope of the work is to identify parameters that have an impact on the accuracy ofthe measured AoA within the antenna system and receiver system and to evaluate the per-formance of the system. The goal is to present a model of how much the measured valuediffers from the true AoA. What this project is designed to achieve is the following:

1. Model the receiver system in software, taking into consideration as many relevant vari-ables as possible.

2. Acquire data from the system for the nominal case and the non nominal case.

3. By comparing the different cases, angular dependency will be analyzed and evaluated.

4. Summarize and present the results of the analysis.

1.4 Research questions

The main questions of the project are presented here and will be answered in the conclusion.Although there are several more questions that undoubtedly will be of interest to the masterthesis, these were the questions that guided this project.

1. At what accuracy can this specific system measure the angle of arrival of a signal?

2. Which factors is the accuracy most dependent on?

3. How close is this theoretical system to the real system?

1.5 Method

The work will be separated into stages that will be evaluated in Chapter 6. The theory willbe presented in Chapter 2 to get a good understanding of the technology used in the system.This chapter includes a background study for similar projects and old work. It is mostly theunderstanding of microwave theory, the secondary surveillance radar and how to model itusing mathematic equations that are of importance.

A model will show a system of the radar which will be analyzed. This will give an un-derstanding of how this specific radar system works, which parameters are unique to it andwhich parameters could be changed for testing. The model will be presented in Chapters 3, 4and 5. All the different components and contributing factors will be identified to make surethe model which is created in a later stage will be as similar to the real system as possible. Inthis part it is important to consider how each and every part of the system affects the signalfor the next stage to be as successful as possible.

Simulation results can be analyzed and used to evaluate the radar system in the softwares

2

1.6. Delimitations

Matlab and Simulink. The purpose is to make the model as close to the real system as pos-sible and trying to include as many variables as possible. The model will be simulated withvarious settings and parameters to extract data which will reveal e.g., angular dependency.

The data from the simulations will be analyzed and processed in a way, were the char-acteristics of the radar system become more visible and easier to understand. The accuracyof the project will be taken into consideration to make a valid conclusion of the results.

1.6 Delimitations

The work will focus on a specific IFF monopulse SSR developed by Saab. The subject ofprimary surveillance systems will be explained briefly to highlight the differences betweenthis system and the SSR. The results will be published in two different forms:

• One redacted version which will be public and accessible to all.

• One complete version presented only to Saab.

In this project, specific components in the receiver chain have been studied. Therefore, anominal model of the system has been implemented which does not take into considerationsome factors which can affect the performance of the system. For instance, the model hasno noise implemented. The low noise amplifiers have no gain errors implemented, insteadthe attenuators have errors in gain, and the attenuator is variable making its impact moreinteresting in the model.

Some of the theory explained is not applicable in the final model since the use of isotropicantenna elements. However, all the theory discussed has been implemented at some stage ofthe system and is kept by the authors to be used for future work. This is not included in thisthesis.

1.7 Outline of the thesis

Chapter 2 explains theory of the radar technology and the signals in the system. This includesthe Identical Friend or Foe theory and system design.

Chapter 3 describes the signal model.

Chapter 4 describes the hardware part of the receiver model.

Chapter 5 describes how the model data is processed.

Chapter 6 shows the results of the simulations and calculations of the model. It will alsoevaluate the result as it is presented.

Chapter 7 concludes the entire project.

3

Chapter Two

Radar technology

This Section will explain the theory behind radar technology. At first, antennas antennaarray and antenna parameters are introduced. Then, the primary radar operation principle isexplained. After this, the Secondary Surveillance Radar (SSR), monopulse SSR and Identifi-cation Friend or Foe (IFF) technology are introduced. Also, signals, radar equation, Dopplereffect and system design aspects are shortly presented in this chapter.

The word radar is an abbreviation for radio detection and ranging. The concept of radar isnot a new one, the technology has been used since at least the beginning of the 19th centuryand later improved and developed to be applicable to different situations. In most cases,radar systems use modulated waveforms and directive antennas to transmit electromagneticenergy into a specific volume in space to search for targets. Objects within a search volumewill reflect portions of the incident energy in the direction of the radar. These echoes are thenprocessed by the radar receiver to extract target information such as range, velocity, angularposition, and other target identifying characteristics [16].

Radars can be located in different places and can be classified as ground-based, airborne,space borne, or ship-based radar systems. These can be separated into numerous categoriesbased on the radar characteristics, such as the frequency band, antenna type, and wave-forms. Radar systems using continuous waveforms, modulated or otherwise, are classifiedas continuous wave radars. Radar systems using time-limited pulsed waveforms are clas-sified as Pulsed Radars. Another radar systems classification are with the mission and thefunctionality of the specific radar. This includes: weather, acquisition and search, tracking,track-while-scan, fire control, early warning, over-the-horizon, terrain following, and terrainavoidance radars [16].

There are different types of radar available today for applicable in aeronautics, the twomain categories are primary surveillance radar and secondary surveillance radar, SSR.

2.1 Antennas

Antennas are used to transmit and receive electromagnetic pulses traveling through the air.Antennas come in all different sizes and forms, which affect their performance. All antennashowever can be operated in two modes: transmitting and receiving. Antennas have theuseful property of reciprocity which states that an antenna transmits and receives signals inthe same radiation pattern.

When transmitting, an antenna is fed with a signal which radiates electromagnetic waveswhen propagating through the conducting antenna element. Depending on the phase, fre-quency and amplitude of the signal as well as the characteristics of the antenna, the signal

5

2. RADAR TECHNOLOGY

will radiate from the antenna according to a radiation pattern. An arbitrary radiation patternis shown in Figure 2.1.

Figure 2.1: (a) Radiation pattern polar diagram. (b) Radiation pattern rectangular diagram[5].

Antenna radiation patterns represent graphically radiation properties such as electric fieldand magnetic field magnitude or radiated power as a function of direction. In Figure 2.1,the pattern is represented in polar coordinates. In both graphs, the patterns are shown withnormalized dB scale. Hence, 0 dB corresponds to a normalized value of 1, e.g., the power ismaximum power value for that direction [13].

Directivity is a measure of the degree to which the radiation that is emitted is concen-trated in a single direction and is an important property of the antenna. The directivity iscalculated as in (2.1) where U is the maximum radiation intensity in the main beam and Ptot

is the total power transmitted [2], [13].

D =UPtot4π

(2.1)

The antenna aperture, also called effective area and receiving cross-section, is a measure ofhow effectively an antenna can receive power. In the case of an isotropic antenna it can beexpressed as in (2.2), where Ae is antenna aperture and λ is wavelength. Antenna aperturecan be used to calculate the antenna gain and is used in the Friis transmission equation whichwill be explained in Section 2.3.1 [13].

Ae =λ2

4π(2.2)

6

2.1. Antennas

Antenna arrays

Antenna arrays can be used to create different antenna patterns, achieve higher gain anddirectivity. The antenna array used in this project is a broadside linear array with N elementsand distance d between the elements. A broadside linear array is a one dimensional lineararray with the main lobe directed perpendicular to the antenna plane. An illustration of abroadside linear array can be seen in Figure 2.4. The number of elements in the array affectsthe radiation pattern and with more elements comes a narrower beamwidth for the mainlobe, as illustrated in Figure 2.2 [2].

Figure 2.2: Radiation pattern example for broadside linear array with different elements [7].

In Figure 2.2, the three different lines shows the radiation pattern for different number ofantenna elements in the array. As can be observed, the beamwidth of the main lobe reduceswith the increase antenna elements and the damping of the sidelobes increases. Also, thenumber of antenna elements affect the gain of the main lobe. It is therefore common incomplex military systems to use a lot of antenna elements to achieve a high gain and narrowbeam. This reduces interferences and increases the range of the antenna array. The powerof the incident signal is equally divided between the antenna elements, e.g., if there are twoantenna elements, they receive half of the power, each.

When using an antenna array, the distance between the antenna elements creates bothphase delays (∆ϕ) and amplitude differences in the signals received by antenna elements inthe array. The amplitude difference is explained by the losses in power as the wave prop-agates, and it is mathematically quantified in Friis transmission equation, see Section 2.3.1.The phase difference is the phase delay that every signal acquires when propagating. Forexample, in Figure 2.3, there is a phase delay in the signal received by Antenna 2 due to theextra distance, ∆x, it needs to travel.

If the antennas are identical, isotropic antennas, then the ideal phase delay between Antenna1 and Antenna 2 in Figure 2.3 is given by (2.3).

φ(t) = k∆x =2π

λx sin θ

arrayÝÝÝÑ=

2π

λnx sin θ (2.3)

Where k is the propagation constant or wave factor, k = 2πλ and λ is the wavelength.

7

2. RADAR TECHNOLOGY

Figure 2.3: Incident wave with angle of arrival θ.

When antenna array is of interest, a way to express e.g., the total electrical field of thearray is by assuming that the total field is equal with the field of one single antenna elementpositioned in the origin multiplied by the array factor, AF.

The array factor is an important factor for optimizing the functionality of antenna arrays. Itis an equation of the positions of the antenna elements and a weight factor. The array factor,AF, can be calculated using (2.4).

AF =ÿ

wie´jkri (2.4)

In (2.4) the variable k is a wave vector which describes the phase variation of a plane wave inx, y and z directions. It can be expressed as in (2.5).

k = (kx, ky, kz) =2π

λ(sin θ cos φ, sin θ sin φ, cos θ) (2.5)

The r variable in (2.4) refers to the position of the antenna element as ri = (xi, yi, zi). Theweight factor can be interpreted as a complex amplitude which can be represented with phaseshifters and amplifiers in the system to apply beam steering which will be explained further.

Active electronically scanned array

An active electronically scanned array (AESA) is a type of phased array. A phased arrayis an antenna array which can be electronically controlled to steer the radiation in differentdirections without rotating the antenna array. This is widely used within radar systemsand is achieved by introducing phase shifters to every antenna element. The phase shiftersare controlled by a computer system which calculates the required phase shift to steer theradiation to the specified angle. This is illustrated in Figure 2.4.

The phase shifters create a phase delay which creates a delay in radiation from the antennaelements, just as the phase delay due to the distance between antenna elements discussedin the previous section. E.g., for Figure 2.4, if the desired angle of radiation is θ = 20°, thewavelength is 20 cm and the distance between elements is half the wavelength. Then theantenna element at the top must radiate without phase delay; then the phase delay which isapplied for certain beam steering is calculated using (2.3). ∆φ = 2π

0.2 ¨ 1 ¨ 0.1 ¨ sin 20° yields the

8

2.1. Antennas

Figure 2.4: Phased array antenna operation principle [19].

phase delay ∆φ = 61.56° which is added to the closest antenna element. Then, this phasedelay is incremented for each antenna element further away from the top element, this isdone by incrementing n in (2.3).

What separates AESA from other phased arrays is that it has a transmit/receive modulefor each antenna element instead of just one. This allows the AESA to radiate multiple beamsat different frequencies, making it more difficult to detect the radar system.

2.1.1 Primary radar

The model of the radar system as described at the beginning of Section 2.1 is called primaryradar. To determine the range to an object, a strong electromagnetic signal in the form of apulse is transmitted by the antenna. The reflected signal is then received by the radar deviceand the range can be calculated from the time between the transmission of the signal and thetime at which the reflected signal was received. This time is twice the time it took for thesignal to travel to the object, meaning that if the signals speed is known, then the distance tothe object is also known. A simple radar illustration is shown in Figure 2.5. Since the speedof the signal in air is the same as the speed of light in vacuum, the distance to the object canbe calculated with (2.6).

Air : vp = c Ñ 2 ¨ R = ttravel ¨ c Ñ R =ttravel

2c (2.6)

Using a rotating antenna, the surroundings of the antenna can be scanned. For example,the direction of an aircraft can be deduced from the direction of the radar antenna when thesignal is received. However, this points out one of the weakness of the primary radar, i.e.,any object that can reflect enough signal power will be picked up by the radar. The distanceto the object the signal reflected of is given by the radar equation:

R = 4

d

PtG2λ2σ

Pr(4π)3(2.7)

9

2. RADAR TECHNOLOGY

Figure 2.5: Radar operation principle [8].

In (2.7) G is the gain of the transmitting antenna, Pt is the power being transmitted, R is thedistance between the radar and the object, σ is the antenna cross-section and Pr is the powerreceived.

2.2 Secondary Surveillance Radar

A Secondary Surveillance Radar (SSR), used in air traffic control (ATC), sends out an electro-magnetic pulse towards a target. But in this case the transmitting radar also encodes somedata. Instead of being reflected by the aircraft, the signal is received by the aircraft via atransponder. The transponder then replies to the SSR in a different frequency. Thereforethe energy required is less, than of the primary radar since the SSR is not dependent on areflected response which needs to be sufficiently strong to identify. The SSR relies on targetswith a radar transponder equipped on the aircraft.

The transmitter to receiver system is called an "interrogator". The interrogator requestsinformation from the aircraft such as identity and height. The aircraft transponder thenanswers by sending the requested information, simply called a "reply". This is one of themain advantages of a SSR compared to the primary radar, the communication between theaircrafts to relay additional information. Also, the power and size of the radar can be signif-icantly reduced and still cover long ranges, making it more cost effective. What often limitsthe range of a SSR system placed on the ground is the screening of the target by the horizon.The range increases with the height of the antenna and the height of the aircraft which resultsin (2.8) where ha and ht is the height of the antenna and the aircraft [6].

R = 1.23(h12a + h

12t ) (2.8)

In the equation presented above, a "four-thirds earth" is assumed. This is a common assump-tion in radar calculations were the earth radius Re is replaced by the factor kRe with k = 4

3 tocompensate for the attenuation by the atmosphere for higher frequencies [18].

2.3 Signals

The signal transmitted by the interrogator and the reply are at two different frequencies.Typically, the interrogator transmits at 1090 MHz and the reply is at 1030 MHz. By havingtwo different frequencies some of the problems experienced by the primary radar can beavoided, e.g., the reflected interrogator signal will not be confused with a response from theaircraft.

10

2.3. Signals

Interrogation can be done in different modes depending on what information is requiredfrom the aircraft and who is using the SSR system. The interrogation signal consists of 3pulses named P1, P2 and P3. The spacing of the two main beams, the pulses P1 and P3,determine what interrogating mode is used. The different modes are presented in Table 2.1,where the spacing for different modes are specified [6].

Table 2.1: Interrogation modes for SSR.

Mode Purpose User P1-P3 pulse spacing in micro S3/A Identity Military/Civil 8B Undefined Civil 17C Altitude Civil 21D Undefined Civil 25S Multipurpose Civil 3.5

When used by the military, the SSR distinguishes a friendly aircraft from an enemy aircraft,naming the process Identify Friend or Foe (IFF). There are more modes than what is dis-played in Table 2.1 that are in use by the military, but these are the most common ones. Othermodes include more combat specified functions such as encryption of replies.

The second pulse named P2 is radiated from the control beam and has a lower amplitude.This allows the aircraft transponder to compare the pulses P1 and P2 to determine if thesignal received originates from the main or side lobe to determine if a response is necessary.By doing this evaluation of the signal, the transponder can minimize the risk of respondingseveral times causing errors in the identification process. This is known as interrogator sidelobe suppression (SLS). Combining these three pulses, the form of the interrogator signal canbe illustrated as in Figure 2.6 [6].

Figure 2.6: Illustration of the interrogation signal [6].

This simple signal is enough to request different forms of information from aircrafts. Thereply signal is a bit more complex since it contains more information, it needs a total of 16pulses in the following way: two framing pulses to mark the start and end of transmission,twelve data pulses giving a total of 4096 permutations, one pulse named x which remainsunused and a Special Position Pulse (SPI), which is only used when the ATC requests it forfurther identification.

11

2. RADAR TECHNOLOGY

Figure 2.7: Illustration of the reply signal [21].

In Figure 2.7, the data pulses, named A, B, C and D with suffixes 1, 2 and 4, are framed bythe framing pulses F1 and F2. The figure also illustrates the following time specifications:

• Pulse duration: 0.45 µs ˘0.1 µs

• Duration between pulses: 1 µs ˘0.1 µs

• Time from F1 to F2: 20.3 µs ˘0.1 µs

• Delay from pulse F2 to the SPI pulse: 4.35 µs ˘0.1 µs

Depending on the mode of communication, not all 4096 codes are used, e.g., mode C doesnot use the D1 pulse which leaves it with 2048 codes. The military mode S uses 24 bits, whichallows for 16 million permutations [12], [21].

To relay height information, mode C is most commonly used and, as mentioned earlier,it has 2048 permutations which are used to indicate the height according to the aneroidbarometer. These 2048 permutations are sufficient to indicate the height in 100 ft incrementin the range of -1000 ft to +121000 ft.

Since the SSR system relies on a response of the airborne transponder, it cannot deter-mine the direction of the airplane in the same way as the primary radar, by receiving thereflected signal. Instead the SSR system uses a method called the "sliding-window" whichdetermines the direction of the airplane by monitoring when communication starts and stopswith the aircraft. Replies from the aircraft are received by the antenna when the leadingedge of the rotating antenna points towards the direction of the aircraft and the antennastops receiving when the trailing edge of the antenna passes it. The average from these twopositions reveals the direction of the antenna. The sliding-window method is illustrated inFigure 2.8 [6].

A problem that is present in this system is due to continuous communication. Since a largeamount of replies are being requested from the transponder it presents a problem for thetransponder, which can handle a finite amount of signals during a period of time. The groundstation also receives replies which have been requested by other SSR systems, these repliesare called false replies unsynchronized in time (FRUIT). Fruit signals can affect the accuracyof the direction measurements since the signals can overlap, which confuses the equipmentand can create phantom aircrafts [6].

A more advanced type of SSR is the Monopulse SSR which will be discussed in Section2.4.

12

2.3. Signals

Figure 2.8: Illustration of the sliding-window method [6].

2.3.1 Friis Transmission equation

To calculate the power received at each antenna terminal of the receiving antenna elements,the Friis transmission equation (2.9) can be used. This equation uses the ideal case of freespace transmission. The equation depends on the transmitted power, the distance betweenthe transmitting antenna and the receiving antenna, the wavelength and the gain of the an-tennas [13].

Pr = PtGtGrλ2

(4π)2R2(2.9)

2.3.2 Doppler effect

The Doppler effect describes how the frequency of a signal can be affected for an observer,by the movement of the source of the signal. For example, if the source moves towards theobserver the frequency is higher than it would have been if the source was moving awayfrom the observer. The relation between speed and frequency can be seen as in the equationfor the Doppler frequency in (2.10).

fd = fs ¨ (1 ˘Vo

Vw) (2.10)

In (2.10), fd is the Doppler frequency, fs is the transmitted signal frequency, Vo is the observervelocity relative to the source and Vw is the velocity of the signal, which is the speed of lightin vacuum. This is the case when a stationary source is used and the ˘ part would be positiveif moving towards the source and negative if moving away from the source. If instead theobserver was stationary the equation would change to that in (2.11). Where Vs is the velocityof the source relative to the observer

fd = fs ¨ (1 ˘Vw

Vs) (2.11)

Combining (2.10) and (2.11), the frequency that the observer detects can be found when boththe source and observer are moving. This is given in (2.12).

fd = fs ¨ (1 ˘ Vo

c

1 ˘ Vsc

) = fs ¨c ˘ Vo

c ˘ Vs(2.12)

13

2. RADAR TECHNOLOGY

The ˘ in the numerator is positive when the observer is moving towards the source andnegative when moving away from the source. The ˘ in the denominator is positive whenmoving away from the source and negative when moving towards the source. This resultsin the frequency which is observed by the observer is greater when observer and source aremoving towards each other. The velocity of the observer in (2.10) and (2.11) are relative to thesource and the velocity of the source is relative to the observer. This implies that the radialvelocity is to be used in (2.12).

The radial velocity is the velocity which is proportional to the increase or decrease be-tween the observer and source. Using Cartesian coordinates in a 3D-space, the velocity canbe defined as the vector Vt = [VxVyVz] where Vt is the total velocity and the three elements inthe vector are the velocities in each dimension. The radial velocity is then defined as in (2.13).

Vr =b

V2x + V2

y + V2z (2.13)

Using this, radars can extract the targets radial velocity using the difference in frequencybetween the transmitted signal and the received signal. This enables the radar systems tomore successfully identify clutter and separate aircrafts flying in proximity of each other.Monopulse antennas can be susceptible to interference from such sources as stationary ob-jects and weather-phenomena.

2.4 Monopulse SSR

The monopulse SSR system uses a single reply to determine the direction of arrival of thesignal instead of the sliding-window method. This is made possible by introducing a secondbeam pattern called the difference beam. The difference beam has a lower gain than the sumbeam at boresight and a higher gain at the sidelobes of the sum beam. The beam pattern isshown in Figure 2.9. A more specified figure of the top of the graph in Figure 2.9 is shown inFigure 2.10 [6].

Figure 2.9: The radiation pattern of the monopulse SSR [6].

Seen in Figure 2.10, the notch along the boresight which is important to the functionality ofthe monopulse SSR. Similar to interferometry technique, the system can determine the angleof arrival (AoA) by comparing the received signal at the sum and difference channels. An

14

2.5. Identification Friend or Foe

Figure 2.10: Top of the radiation pattern of the monopulse SSR [6].

interferometer can be implemented with two or more antennas placed side-by-side whichproduces a single high-gain beam with low sidelobes. Combined by a 180° hybrid coupler,which will be discussed in Section 2.8.4, the sum output of the ring produces the originalhigh-gain sum beam and the difference output produces the difference beam. With a differ-ence in phase related to the extra distance traveled to the antenna which is the furthest away.The relative phase delay can be calculated using the method described in Section 2.1.

If the incident signal aligns with the antenna boresight, the relative phase difference iszero and the signal on the difference beam is greatly dampened. In an ideal case this wouldeliminate the signal on the difference channel since there would be total destructive inter-ference. In other cases, the ratio between the sum and difference signals can be analyzed toindicate the incident signals angle of arrival. The receiver in this project uses the L1 process-ing method, therefore all other methods will not be discussed. The L1 processing methoduses that the ambiguity is located at the beam center, the phase difference between the sumand difference channels must be analyzed to reveal at which side of the ambiguity point thesignal arrives as discussed in Section 2.8.5 [9].

The monopulse SSR is similar to an interferometer. However, one difference is for trans-mission between antenna and receiver the signals are converted to sum and difference beamform. There are two different monopulse processing methods: the amplitude processing andphase processing method. The amplitude processing method compares the amplitude of thesum and difference channel to find the angle of arrival and the phase processing method usesthe phase information.

2.5 Identification Friend or Foe

The Identification Friend or Foe (IFF) system is a military and civil system; mainly dedicatedto identification. SSR is based on the military IFF technology originally developed duringWorld War II. The system is composed, like SSR, of the two active devices: an interrogatingdevice, interrogator, and a replying device, transponder. The interrogating device sendsan interrogation using a carrier frequency in the direction of the object equipped with atransponder. The replying device receives and decodes the interrogation, then, a coded replyis sent on a different carrier frequency. When received by the interrogation device, the replysignal is processed and decoded. The result is presented in a suitable way, for examplevisually or in the form of digital data. To decode the encrypted data, both systems must use

15

2. RADAR TECHNOLOGY

the same predetermined encryption which can vary depending on the user. For instance,the encryption used by NATO and the encryption used by Brazil is not the same. If theencryption is the same, the replying object is recognized as a friend. If not, it is treated as anunidentified object or foe [4].

The generation of undesirable replies by a properly working transponder can occur inthe following cases:

• Interrogations from other interrogators.

• Reception of reflected signals, interrogations, from the friendly interrogator, not exceed-ing the receiver dynamic range.

• Reception of interrogation from the friendly interrogator, not exceeding the receiver dy-namic range and not responding to Interrogation Side Lobe Suppression (ISLS) criteria.

The interrogator and transponder devices are characterized by following parameters.

• Transmission frequency

• Output power

• Sensitivity

• Antenna gain

• System losses

Other parameters are as follows:

• Atmospherically attenuation

• Free space range

2.6 IFF monopulse antenna

The purpose of the Identification Friend or Foe (IFF) system is to minimize own losses com-ing from friendly fire. The main feature of the system should be high identification and datatransmission reliability. The problems with these transmission signals are sidelobe elevationcovering characteristics, reflection from field objects known as multipath, replies generatedby transponders for other interrogators’ requests.

The secondary search radar’s issue is an important part of radio location technology. Inpractice, the simplest antenna solutions could not fulfill the severe requirements concerningcharacteristics of radiation pattern in IFF systems. The solution is the suppression of thesidelobes in the antenna pattern. Two methods that can result in sidelobe suppression.

• Monopulse directional antenna with sidelobes suppression units forming by an addi-tional omni-directional antenna.

• Monopulse antenna with sidelobes suppression based on dependencies between sig-nals in both channels sum and difference one.

Monopulse antennas are meant to work in short range interrogators which have monopulsepattern in azimuth axis and/or in elevation axis. Short range interrogator devices are in-stalled on self-propelled systems or on naval weapons. The weight and dimension of thoseinterrogators must be minimal, especially in hand-held applications. In mobile systems itis important to assure synchronization of antenna movement with the movement of devicesinstalled on vehicles like anti-aircraft guns or missile launchers. This synchronization can beimplemented in different ways, depending on the complexity of the system [10].

16

2.7. Single pulse detection

2.7 Single pulse detection

In its simplest form, a radar signal can be represented by a single pulse comprising a sinu-soid of known amplitude and phase. A returned signal will also comprise a sinusoid. Underthe assumption of completely known signal parameters, a returned pulse from a target hasknown amplitude and known phase with no random components; and the radar signal pro-cessor will attempt to maximize the probability of detection for a given probability of falsealarm. In this case, detection is referred to as coherent detection or coherent demodulation.A radar system will declare detection with a certain probability of detection if the receivedvoltage signal envelope exceeds a pre-set threshold value. In this kind of detection, envelopedetectors are used [16].

2.8 System design

Given the operation of a SSR, the range R can be calculated from Friis transmission equation(2.14), presented in Section 2.3.1.

R =λ

4π

d

PtGtGr

LPr(2.14)

Where a supplementary factor L was added to model losses in the system. Reciprocally, thereceived power in a SSR can be written as:

Pr =PtGtGr

L(

λ

4π ¨ R)2 (2.15)

2.8.1 Dynamic range

The dynamic range for the radar is the power ratio between minimum and maximum forthe echo signals in close range or of objects from a long distance. If there is a large powerdifference it will be difficult to process the digital data. It can be described with (2.16), whereD is the dynamic range and Pr is the power.

D =Prmax

Prmin

(2.16)

The dynamic range is highly sensitive to the radar cross-section σ and the range R, as theother parameters in (2.15) do not vary. Hence, the received power and the dynamic range Dcan be rewritten as (2.17) and (2.18) [20].

Pr =PtλG2σ

(4π)3R4= k

σ

R4(2.17)

D =Prmax

Prmin

=kσmax/R4

min

kσmin/R4max

=σmaxR4

max

σminR4min

(2.18)

2.8.2 Horizontal characteristics

The horizontal characteristics refer to the accuracy of the aircraft bearing measurement, toidentify separate aircrafts which are close to each other and minimize the interference of theaircraft replies outside the main beam. The antenna has two different beams in its beampattern, one interrogate beam and one control beam [6].

17

2. RADAR TECHNOLOGY

Interrogate beam

An interrogate beam, also called a main beam, has a radiation pattern for the horizontalantenna. The beam has a high-gain and narrow main lobe with low sidelobes. The sidelobesshould be at least 24 dB below the main lobe. If the interrogation beam is lower than thecontrol beam at the sidelobes, attenuation is applied on the variable attenuator in the receiverwhich will lower the gain of the interrogation beam. The interrogate beam transmits thepulses P1 and P3. If the interrogate beam is too broad it will be more sensitive to groundreflections [6].

Control beam

The control signal is the second antenna beam that is broader but has a lower peak gainaround boresight. As seen in Figure 2.11, the control signal has a higher gain than the interro-gate beam except for the main lobe. It is used to prevent the aircraft from replying to signalsfrom the interrogate beam sidelobes. Using the interrogate beam distribution the controlsignal can be formed while the center element in the array is in anti-phase. The signal of thecontrol beam transmit the pulse P2. The transponder compares the pulse amplitudes of P1and P2 to determine if the signal is received from the antenna sidelobes or from the mainbeam. Depending on whether if P1 is greater than P2 by more than 9 dB, the transpondermust reply. The transponder does not need to reply if P2 is larger than P1.

When an aircraft is at close range, the transponder receiver dynamic range can cause ampli-tude limiting. Leading to a weaker signal for P1 and can be compared with P2. Therefore theamplitude of P2 at the direction of P1 will be reduced [6].

Figure 2.11: Interrogate and control beam patterns.

Difference beam

To find the angle of arrival of the incident signal a difference beam is used. To get both thesum beam and the difference beam a hybrid ring coupler is used which will produce two out-puts. The hybrid ring coupler is explained in Section 2.8.4. If the difference peak gain is highthe accuracy will be increased. The smaller peaks will not affect the monopulse performanceand therefore it is good if they have a low amplitude so it wont be any extraneous signals [6].

18

2.8. System design

2.8.3 Changes in the horizontal characteristics with elevation

In a perfect antenna the three horizontal beam pattern originates from a common phase cen-ter and will have the relative shape with elevation. In reality the three beam shapes will bebroaden with elevation angle. This is because the radar assumes that bearing measurementsare made in the horizontal plane even when the incident signal is arriving from a significantelevation angle. This broadening effect is of importance for the monopulse direction findingand for elevation angles above 20°. The error can be corrected by dividing the measuredangle by the cosine of the elevation angle with slant range and the Mode C height. Eitherside of the boresight is of the monopulse direction is measured and averaged which leads toa reduced error [6].

The beam patterns produced are dependent on the distribution of power across the an-tenna aperture which can be maintained at all elevation angles but is difficult to achieve inpractice. The control beam may in some cases not cover the sidelobes of the interrogate beamwhich will give erroneous replies [6].

2.8.4 The 180° hybrid coupler

The 180° hybrid is a passive network usually easily implemented using microstrip transmis-sion lines of 50 Ω characteristic impedance at a given frequency of operation and for a spec-ified substrate on a printed circuit board. The structure of a 180° hybrid is shown in Figure2.12. Four ports are available and they can be assigned as input and output ports. The hybriduses transmission line of quarter wave length λ/4. The port is assumed to work on loads of50 Ω impedance, e.g., following elements are of 50 Ω impedance. In (2.19), the S-parametersmatrix of the hybrid is shown [14].

Figure 2.12: The 180° hybrid coupler [14].

[S] =´j?

2

0 1 1 01 0 0 ´11 0 0 10 ´1 1 0

(2.19)

The way the 180° hybrid can be used can be understood knowing that a λ/4 length con-tribute to a phase delay of 90°. Main operation are as combiner of two incoming signals anddivider of one signal. Combiner: With reference to Figure 2.12, it can be seen that if signalsare applied at ports 2 and 3, they will reach port 1 in phase hence, they add, Σ. In opposite,

19

2. RADAR TECHNOLOGY

at port 4, the signals are coming with 180° phase difference, hence they subtract, ∆. Divider:If the input signal is applied to port 1, the signal will be evenly split at port 2, 3 and port 4will be isolated 180° out of phase. Port 1 is the sum and port 4 is the difference.

The amplitudes of the scattering waves can be calculated by decomposing the case intoa superposition of the two simpler circuits and excitations, using the even-odd mode analy-sis technique. The amplitudes of the scattered waves shows that the input port is matched,port 4 is isolated, and the input power is evenly divided and in phase between ports 2 and 3.These results form the first row and column of the scattering matrix (2.19) [14].

If a unit amplitude wave incident at port 4, the difference port, of the ring hybrid, thetwo wave components on the ring will arrive in phase at port 2 and at port 3, with a relativephase difference of 180° between these two ports. The two wave components will be 180° outof phase at port 1. This case can also be decomposed into a superposition of the two simplercircuits and excitations [14].

2.8.5 Ratio calculations

The 180° hybrid coupler produces a sum Σ and difference ∆ signal. The ratio of these signals,U, contains information about how much the angle of arrival differs from the angle of theinterrogation beam. The ratio can be calculated according to (2.20) [3].

U =∆

Σ(2.20)

By using the ratio the sum and difference signals can be evaluated using a look-up table. Foran ideal system the ratio should relate to the error angle according to (2.21).

U = j tan

(

k ¨ d ¨ sin θ

2

)

(2.21)

In (2.21), the angular wavenumber k = 2πλ , d is the distance between antenna elements and θ

is the angle deviation from the boresight. The j factor determines which side of the boresightthe signal is arriving on and when crossing the boresight it changes from j to ´j representinga phase difference of π. To determine which side of the lobe the signal is coming from anone-bit ambiguity comparison is made in the system. In the interval where the sum has ahigher gain the ratio will be lower than 1. At two points, on each side of the boresight, theratio will be one as the sum and difference signals crossing each other, i.e. has the samegain. For larger angles the difference gain will be higher than the sum gain and the ratiowill therefore be larger than 1. This can be seen in Figure 2.10, which shows the top of thesum and difference pattern. The sum and difference beam could have the same gain for evenhigher angles as Punch-Through can occur. Although this can occur the angles are mostlikely not of importance [3].

The radiation pattern is different for each elevation angle and also changes when beamsteering is applied. To apply beam steering, a look-up table is used to find the phase delayneeded in the phase shifters. The angles are not likely to be exactly on point, but are of goodapproximation. An uncertainty of the angle exist as there is an interval in the look-up table,and angle uncertainty in the phase shifter. In the realization of the system it is also impossibleto gain ideal characteristics, therefore look-up tables containing measured data is used toreveal a more realistic result.

20

2.9. Errors

2.8.6 Interrogation side lobe suppression

Interrogation side lobe suppression (ISLS) is similar to the SLS. But for the interrogator itis implemented using attenuation. Attenuation is applied to the sum beam to lower theamplitude. The ratio of the un-dampened difference beam and the dampened sum beamis analyzed. With variable attenuators the user can make sure that the sidelobes of the in-terrogator beam all have a lower amplitude than the resulting control beam as discussed inSection 2.8.2.

2.9 Errors

The angle error is created from the difference signal by calculating a complex ratio. This isdone for the left/right difference beams, as well as for the up/down difference beams. Inthis project, only one difference beam is used. An explanation of how real and imaginaryparts are used with radar can be found in the description of Pulse Doppler. The outcome ofthe calibration process is to rotate the complex antenna angle error vector onto the real axisto reduce signal processing losses. The angle error is used to make an adjustment to positionthe target along the centerline of the antenna.

The error sources for the monopulse bearing measurement system are as follows:

• Antenna pattern errors.

• Effects of receiver noise.

• Receiver errors dependent upon frequency.

• Receiver errors dependent upon reply signal strength.

• Errors in the conversion of video to angle units.

• Electrical errors and azimuth encoder.

Some of the errors are random with different degrees of error. Other errors are fixed with thesame error [6].

21

Chapter Three

Signal model

In this Section the signal model will be presented with Simulink blocks and Matlab code.

3.1 System design

To measure signals for the receiver, a model will be made and simulated using Matlab andSimulink. There are some common blocks used in the model already existing in Simulink.The more uncommon blocks are listed in Appendix A for explanation. Most of those un-common blocks are in the DSP Toolbox or the Communication System Toolbox in Simulink.Throughout the model, different signal sinks will be added for troubleshooting and verifi-cation of the system and will not be discussed in detail and will not be shown in any figure.All Matlab code can be found throughout the text under corresponding function block. Thegray blocks in the figures are subsystem blocks which are used to divide a larger system intosmaller subsystems and the white blocks with Matlab symbols are Matlab functions. TheMatlab functions have the same name in the box as the Matlab code name.

Figure 3.1: Conceptual image of the system.

Figure 3.1 shows a conceptual block diagram of the system. The system consists of: thesignal black box block, the receiver system block and the output signal. Figure 3.2 showsthe entire system in Simulink. There is also a function outside of the Simulink model tocalculate the angle error. The function of the signal black box is described in this Chapter.The Steer_angle block, the Attenuation block, the Enable_error_attenuator andthe Enable_error_phaseshifter are data memory block. These blocks are used in theSystem blocks seen in the Figure 3.2. The on-off switches are connected to the constant blocksand are used to enable or disable the attenuator and phase shifter errors.

23

3. SIGNAL MODEL

Figure 3.2: The entire system in Simulink.

3.2 Signal

To model the signal from the transmitter to the receiver a system which calculates theDoppler effect, the Friis transmission, the received phase at each antenna element and theeffective area of the antenna elements is needed. These functions are considered to be themost important to produce a good signal. This subsystem is named the Signal Black

Box (SBB). All that is required by the user to operate this subsystem is to define the inputsinto the subsystem. The inputs of the SBB subsystem are seen in Figure 3.3. From this blockeight signals are produced for each antenna element and also the angle of the transmitters’position, which is used for calculations in Matlab.

• Velocity of the transmitter, given in a X Y Z vector.

• Velocity of the receiver, given in a X Y Z vector.

• Position of the receiver, given in a X Y Z vector.

• Position of the transmitter, given in a X Y Z vector.

• Frequency of the transmitted signal is always 1090 MHz.

• Power of the transmitted signal is in watts.

24

3.2. Signal

Figure 3.3: The SBB system.

The system block, which is shown in Figure 3.3, consists of several subsystems shown inFigure 3.4. There is a propagation block which calculates what happens to the signalbefore it reaches the antenna elements. The Input_signal block creates the specified sinesignals. These blocks will produce eight signals at each antenna element. The Phase_calcand Phase_shifting blocks calculates and applies a phase difference between the antennaelements. The subsystems of the SBB are further explained in Sections 3.2.1 to 3.2.4. The restof the system is presented in Chapters 4 and 5.

Figure 3.4: Inside the SBB system.

3.2.1 Propagation subsystem

Figure 3.5 shows the propagation subsystem block. The input parameters for this block arethe same as for the entire system. The output signals are used in the Input_signal blockand the Phase_Calc block. The propagation subsystem is configured as in Figure 3.6.

25

3. SIGNAL MODEL

Figure 3.5: The propagation block.

Figure 3.6: The configuration of the propagation system.

The relativespeed function calculates the speed of the transmitter and receiver relativeto each other. This is needed in the calculations of the Doppler frequency. Since the Dopplerfrequency is calculated differently depending on if the objects are moving towards or awayfrom each other, as described in Section 2.3.2, the relative_speed function also works as astate machine. It therefore tells the Doppler function what equation to use according to thesestates:

• 1. The transmitter is moving away from the receiver, the receiver is moving towards thesource.

• 2. The transmitter and receiver are moving towards each other.

• 3. The transmitter is moving towards the receiver, the receiver is moving away from thesource.

• 4. The transmitter and receiver is moving away from each other.

The relative speed is calculated using the Matlab function radialspeed shown in Figure3.7 with the Matlab code shown in Code block 3.1, which returns the radial speed of an

26

3.2. Signal

object relative to another object. It also takes into consideration the speed of the other object.However, in the Doppler equation (2.12) the relative speed is divided into two separatevariables. Therefore the relative_speed function is used to calculate the speed vector ofone object relative to a stationary second object. This is done as in (3.1), where the functionradialspeed is used. The function, which is part of the Phased Array Toolbox, calculatesthe relative radial speed between two objects. In (3.1) the P variables are the position of thereceiver and transmitter and the V variables are the velocity vectors of the transmitter andreceiver. The second of the velocity vectors is set to zero to calculate the radial velocity forboth the transmitter and receiver relative to each other when the other part is stationary. TheMatlab code is also using the function ge(A, B) which determines if A is greater than B.

Vr = radialspeed(Pr, Vr, Pt, Vt) (3.1)

Figure 3.7: The relative speed function block.

1 function [V_relative_transmitter, V_relative_receiver, state] = ...

relativespeed(V_transmitter, V_receiver, P_transmitter, P_receiver)

2

3 c = physconst('LightSpeed');

4

5 V_relative_receiver = radialspeed(P_receiver,V_receiver,P_transmitter,[0;0;0]);

6 V_relative_transmitter = ...

radialspeed(P_transmitter,V_transmitter,P_receiver,[0;0;0]);

7

8 if ge(V_relative_receiver,0)

9 if ge(V_relative_transmitter,0)

10 state = 2;

11 else

12 state = 1;

13 end

14 else

15 if ge(V_relative_transmitter,0)

16 state = 3;

17 else

18 state = 4;

19 end

20 end

21

22 end

Code block 3.1: Relative speed Matlab code.

The relative velocity is passed on to the Doppler function shown in Figure 3.8 with cor-responding code presented in Code block 3.2, which calculates the Doppler frequency ac-cording to the theory described in Section 2.3.2. The Doppler function outputs the Dopplerfrequency which is used in the Friis function shown in Figure 3.9, with the correspondingcode in Code block 3.3. The Friis function calculates the received power for the different

27

3. SIGNAL MODEL

antenna elements, which were described in Section 2.3.1. The Friis function also requiresthe distance from the transmitter to the receiver, or more accurately it requires the distancefrom the transmitter to each antenna element. This is calculated using the Distance_calcfunction shown in Figure 3.10. The code used in the Distance_calc function is presentedin Code block 3.4. This function identifies the position of each antenna element dependingon the position of the receiver, interpreted as the center of the array, and the distance betweenantenna elements. For simplicity, the receiving antenna array is fixed with the boresightparallel to the x-axis which means that the position of each antenna element only varies fromthe position of the receiver on the y-axis. An example of this, is the case of two antennaelements with the distance λ/4 between:

Receiver_Position = [0 0 0]

Distance between elements: d = λ4

Position of antenna element 1: Pos_A1 = [0 d2 0]

Position of antenna element 2: Pos_A2 = [0 - d2 0]

Figure 3.8: The Doppler function block.

1 function f_doppler = doppler(V_r_transmitter,V_r_receiver,state,f_source)

2


4

5 Va_receiver = abs(V_r_receiver);

6 Va_transmitter = abs(V_r_transmitter);

7

8 switch state

9 case 1

10 f_doppler = f_source * ((c+Va_receiver)/(c+Va_transmitter));

11 case 2

12 f_doppler = f_source * ((c+Va_receiver)/(c-Va_transmitter));

13 case 3

14 f_doppler = f_source * ((c-Va_receiver)/(c-Va_transmitter));

15 case 4

16 f_doppler = f_source * ((c-Va_receiver)/(c+Va_transmitter));

17 otherwise

18 f_doppler = f_source;

19 end

20

21 end

Code block 3.2: Doppler effect Matlab code.

28

3.2. Signal

Figure 3.9: The Friis function block.

1 function [A1,A2,A3,A4,A5,A6,A7,A8] = Friis(d_A1,d_A2,d_A3, ...

d_A4,d_A5,d_A6,d_A7,d_A8,f,Pt,Ar,At)

2


4 lambda = c/f;

5

6 A1 = (Pt/4)*((At*Ar)/((d_A1^2)*lambda^2));








14

15 end

Code block 3.3: Friis equation Matlab code.

Figure 3.10: The distance calculation function block.

29

3. SIGNAL MODEL

1 function [d_A1,d_A2,d_A3,d_A4,d_A5,d_A6,d_A7,d_A8] = ...

distance_calc(pos_tran,pos_rec,f)

2


4 lambda = c/f;

5 d = lambda/4;

6 pos_A1 = [pos_rec(1) pos_rec(2)+3.5*d pos_rec(3)];




10 pos_A5 = [pos_rec(1) pos_rec(2)-0.5*d pos_rec(3)];




14

15 d_A1 = sqrt((pos_tran(1)-pos_A1(1))^2 + (pos_tran(2)-pos_A1(2))^2 + ...

(pos_tran(3)-pos_A1(3))^2);















23 end

Code block 3.4: Distance calculations Matlab code.

The effective area is calculated using the effective_area function in Figure 3.11 whichuses the code in Code block 3.5. The area outputs is used in the Friis function explainedpreviously.

Figure 3.11: The effective area function block.

1 function [A_eff_r,A_eff_t] = effective_area(fr,ft)


3 lambda_t = c/f_t;

4 lambda_r = c/f_r;

5

6 A_eff_t = lambda_t^2/(4*pi);

7 A_eff_r = lambda_r^2/(4*pi);

8 end

Code block 3.5: Effective area Matlab code.

30

3.2. Signal

3.2.2 Input signal subsystem

The Input_signal subsystem, seen in Figure 3.12, creates a sinusoidal signal with thecorrect amplitude and frequency. Figure 3.13 shows the inside of the signal create subsystem.

Figure 3.12: Input_signal subsystem of the SBB.

Figure 3.13: Inside the Input_signal subsystem of the SBB.

The subsystem consists of a DSP-sine block and one multiplier for each antenna element, ascan be observed in Figure 3.13. The DSP-sine block, from the DSP toolbox, outputs samplesof a specified sine wave. The configurable parameters are configured as follows:

• Amplitude = 1

• Frequency = Doppler frequency from the propagation subsystem.

• Phase Offset = 0

• Sample mode = Discrete

• Output complexity = Complex

• Computation method = Trigonometric fcn

• Sample time = 1/1000000000000

• Samples per frame = 1

31

3. SIGNAL MODEL

The frequency is 1090 MHz, there is no need for a phase offset, the sample mode is discreteand output complexity is set to complex because both a real and a complex signal are needed.The sample time follows the Nyquist criteria and samples per frame is default value. Theamplitude is set to 1 because the input of the subsystem is the received power for each of thespecified antenna element, which is multiplied with the signal from the DSP-sine block to getthe correct amplitude and then passed on to the output.

3.2.3 Phase calculation subsystem

The Phase_calc subsystem shown in Figure 3.14, calculates the shift in phase for eachantenna element depending on the distance between the antenna elements and the anglebetween receiver boresight and transmitter. These computations require the position of thereceiver, position of the transmitter and the Doppler frequency previously calculated in thepropagation subsystem.

Figure 3.14: The phase calculation block.

Inside the Phase_Calc subsystem, as illustrated in Figure 3.15, there is a single Matlabfunction block named phase_calc. It outputs the required phase shift for each antennaelement. It positions the antenna elements in the same way as in the propagation subsystem,calculates the angle of arrival for the incident signal and the individual phase difference foreach antenna element relative to the element closest to the transmitter. This is describedin Section 2.1. It also outputs the angle of arrival in both azimuth and elevation for trou-bleshooting and verification. The code which implements this can be seen in Code block 3.6.

Figure 3.15: The phase calculation function block.

32

3.2. Signal

1 function [p_A1,p_A2,p_A3,p_A4p_A5,p_A6,p_A7,p_A8,Theta] = ...

phase_calc(f_doppler,pos_rec,pos_tran)

2


4 lambda = c/f_doppler;

5 d = lambda/4;

6

7 theta_rad = atan2(pos_tran(2)-pos_rec(2), pos_tran(1)-pos_rec(1));

8 Theta =rad2deg(theta_rad);

9

10 if Theta > 0

11 p_A1 = 0;

12 p_A2 = 2*pi*d*sin(theta_rad)/lambda;

13 p_A3 = 2*pi*2*d*sin(theta_rad)/lambda;






19 elseif Theta < 0

20 p_A8 = 0;

21 p_A7 = 2*pi*d*sin(abs(theta_rad))/lambda;

22 p_A6 = 2*pi*2*d*sin(abs(theta_rad))/lambda;






28 else

29 p_A4 = 2*pi*0.5*d*sin(theta_rad)/lambda;




33 p_A5 = p_A4;

34 p_A6 = p_A3;

35 p_A7 = p_A2;

36 p_A8 = p_A1;

37 end

38 end

Code block 3.6: Phase calculation Matlab code.

3.2.4 Phase shifting subsystem

The Phase_Shifting subsystem shown in Figure 3.16 contains a single Matlab functionblock also named Phase_Shifting shown in Figure 3.17. This function takes the createdsignals from the Input_signal subsystem and the phase shift from the Phase_Calc sub-system and applies the specified phase shift to the signal for each antenna element.

The Matlab uses the Equation (3.2) to apply the desired phase shift without affecting theamplitude or frequency of the signals. This is shown in Code block 3.7. The variable φ is thephase in radians, which is applied.

Out = e´iφ ¨ signal (3.2)

The output of the subsystem is the shifted signals with the correct amplitude for each of theantenna elements. This phase shifting technique is used and explained further in Section 4.4.

33

3. SIGNAL MODEL

Figure 3.16: Phase shifter block in the SBB subsystem.

Figure 3.17: Phase shifter function in the SBB subsystem.

1 function ...

[Signal_A1,Signal_A2,Signal_A3,Signal_A4,Signal_A5,Signal_A6,Signal_A7, ...

2 Signal_A8] = Phase_Shifting(A_1,A_2,A_3,A_4,A_5,A_6,A_7,A_8, ...

p_A1,p_A2,p_A3,p_A4,p_A5,p_A6,p_A7,p_A8)

3

4 Signal_A1 = exp(-1i*p_A1)*A_1;








12

13 end

Code block 3.7: Phase shifter Matlab code.

34

Chapter Four

Receiver model

In this Chapter, the receiver model created in Simulink is presented and explained includingthe Simulink blocks and Matlab code.

4.1 Receiver system

The receiver model follows the Signal Black Box model. As shown in Figure 4.1, the modelincludes three main processing components, the low-noise amplifier (LNA), the phase shifterand the attenuator. The input signal number corresponds to the number of antenna elementsin the array. The expected output signals are the sum (Σ), the difference (∆) and the ratio ∆

Σ

signals, as indicated in Figure 4.2.

Figure 4.1: Conceptual block model of the receiver.

As detailed in Figure 4.3, the Receiver_System block gets the input signals A1 to A8and processes them firstly in the Transmit receive unit (TRU). Then, TRU results arefurther processed by means of microwave passive components, i.e., the Wilkinson powerdivider (WPD) and the rat-race, 180° hybrid combiner. The WPD-network implementsuperposition of the signals coming out from TRU, and the 180° hybrid delivers the desiredsum Σ and difference ∆ signals. Finally, the ratio is calculated. These systems are furtherdescribed in Sections 4.2 to 4.9.

35

4. RECEIVER MODEL

Figure 4.2: The Receiver_system block.

Figure 4.3: Inside the Receiver_system block.

4.2 Transmit receive unit

The TRU shown in Figure 4.3 mainly contain the modules modeling the radio frequency(RF) circuits, i.e., the LNA, the phase shifter and the attenuator. From Figures 4.4 and 4.5,it can be seen that two other input signals are assigned to the TRU, i.e., Steer_angle andAttenuation.

Figure 4.4: TRU block.

In Figure 4.5, the TRU is detailed as implemented in Simulink. The Steer_calc block calcu-lates the required phase delay for the phase shifters so that the desired beam steer is appliedto each of eight RF modules. Shown in Figure 4.8 in detail and as implemented in Simulink,the RF module block perform amplification, controlled phase shifting and attenuation ontoeach signal coming from the eight antenna elements in the array.

36

4.2. Transmit receive unit

Figure 4.5: Inside the TRU block.

Figure 4.6: The steer calculation function.

The code of the Steer_calc function is shown in Code block 4.1. It implements (2.3), i.e.,the phase delay for each antenna element when the desired beam steer is specified. It can beseen that the phase delay increase linearly with the position of the antenna element relativeto the antenna element closest to the transmitter.

37

4. RECEIVER MODEL

1 function [steer_A1, steer_A2, steer_A3, steer_A4, steer_A5, steer_A6, ...

steer_A7, steer_A8] = Steer_calc(steer)

2

3 f = 1090e6;


5 lambda = c/f;

6 k = 2*pi/lambda;

7 d = lambda / 4;

8

9 steering_rad = deg2rad(steer);

10 ∆_phi = k*d*sin(steering_rad);

11

12 if ge(steer,0)

13 steer_A1 = 0;

14 steer_A2 = ∆_phi;

15 steer_A3 = ∆_phi*2;






21 else

22 steer_A8 = 0;

23 steer_A7 = ∆_phi;







30 end

31

32 end

Code block 4.1: Steer calculation Matlab code.

Figure 4.7: The RF module block.

Figure 4.8: The subsystems of the RF module block.

38

4.3. Low-noise amplifier

4.3 Low-noise amplifier

In RF/microwave front-end systems, the first active circuit is the LNA. The low-noise ampli-fier has the task to a) amplify usually weak signals and b) to minimize the noise figure at itsoutput.

From Friis noise figure equation for cascaded stages in (4.1), it can be seen that first ac-tive stage in a receiver front-end with e.g., gain G1, minimize the noise figure of followingstages, Fi, observe division with G1. Also from (4.1), it can be seen that it is important thatthe noise figure of the first stage F1 is minimized. The minimization of the noise figure atthe output of the amplifier is the main characteristic of the LNA and it is realized throughamplifier special design.

Ftotal = F1 +F2 ´ 1

G1+

F3 ´ 1

G1G2+ ... +

Fn ´ 1

G1G2...Gn´1(4.1)

The receiver model in this project includes only one active block, the LNA block in Figure4.1, so that (4.1) can be simplified as (4.2). The phase shifter and attenuator in Figure 4.8are usually passive components contributing only with losses, losses that translate into noisefigure contribution, denoted with Frest in (4.2). In this project, the LNA block was modeled asa gain block of 20 dB. No noise figure aspects were considered [13].

Freceiver = FLNA +Frest ´ 1

GLNA(4.2)

Figure 4.9: The LNA block.

Figure 4.10: Inside the LNA block.

4.4 Phase shifter

In an active electronically scanned array (AESA), the phase shifters are crucial to applysteering. It is used to apply a phase delay to steer the beam as described in Section 2.1. Whenphase shifting, there will be an insertion loss which will change the amplitude of the wave.For an active phase shift the amplitude will increase and for the passive it will decreases,which is why it is good to have an attenuator after the phase shifter. In this ideal modelinsertion loss is not applied. In the receiver a variable phase shifter is implemented to beable to steer the beam. This gives a phase error which depends on the size of the phase delay.When the phase delay is increased the phase error increases according to Table 4.1 which isbased on an existing phase shifter, model 984-1. The phase shifter block seen in Figure 4.11,is placed between LNA and attenuator in the model. Figure 4.12 shows the inside of thePhase_shifter subsystem, containing a State_generator Matlab function, a random

Matlab function, a Steer_function Matlab function, a Random Integer block and somemath operation blocks [17].

39

4. RECEIVER MODEL

Figure 4.11: The phase shifter block.

Figure 4.12: Inside the phase shifter block.

Table 4.1: Maximum phase variance [17].

Maximum phase variance0-10° 20° 40° 80° 160° 320°˘1.5° ˘2° ˘3.5° ˘5.5° ˘10° ˘10°

The steer_function shown in Figure 4.13 shifts the phase with (4.3) and is dependent onthe State_generator to apply the correct phase shift. The code for the steer_functionis shown in Code block 4.2

Out = eiφ ¨ signal (4.3)

40

4.4. Phase shifter

Figure 4.13: The steer function block.

1 function shifted_signal = steer_function(signal,state,P1,P2,P3,P4,P5)

2

3 if state == 1

4 shifted_signal = signal;

5 shift = 0;

6 elseif state == 2

7 shifted_signal = exp(1i*P1)*signal;

8 shift = P1;

9 elseif state == 3


11 shift = P2;

12 elseif state == 4


14 shift = P3;



17 shift = P4;



20 shift = P5;

21 else

22 shifted_signal = 0;

23 shift = 0;

24 end

25 end

Code block 4.2: Steer function Matlab code.

Five separate states indicate the different degree intervals of shifting according to Table 4.1.The states are generated by the Matlab function state_generator, seen in Figure 4.14with the corresponding code presented in Code block 4.3. Depending on the input from theSteer_calc, different states will be chosen and for each state the corresponding phase erroris applied. This function does not affect the amplitude of the signal.

41

4. RECEIVER MODEL

Figure 4.14: The state generator function block.

1 function [state,phase_out] = state_generator(phase_steer)

2

3 phase_steer_deg = rad2deg(phase_steer);

4 phase_shift = phase_steer_deg;

5 phase_out = phase_steer_deg;

6

7 if phase_shift == 0

8 state = 1;

9 elseif ((abs(phase_shift) > 0) && (abs(phase_shift) ď 15))

10 state = 2;


12 state = 3;


14 state = 4;


16 state = 5;


18 state = 6;

19 else

20 state = 7;

21 end

22

23 end

Code block 4.3: State generator Matlab code.

The required phase shift is the output from the State_generator and an error signal isadded from the Random function, seen in Figure 4.12. The Random function will generate aphase error between 0 and 1. The amplifiers will then amplify the error to match the intervalsin Table 4.1. The random generator is presented in Section 4.6. The non-selected states willnot affect the chosen state since the steer_function only uses the signal corresponding tothe active state.

4.5 Attenuator

The attenuator decreases the amplitude of the signal. It is used to improve impedance match-ing and to lower the amplitude of the signal for measuring and protection. Attenuation isoften expressed in decibel, this means that 3 dB attenuation will decrease the power by ahalf. Some requirements are low deviation, for instance coaxial structure, and low SWR. Inthe receiver, a variable attenuator is used to apply sidelobe suppression. Accuracy can differfor different attenuation levels, for example: a specific attenuator AT-264 has the accuracy of˘0.3 dB +5% of the attenuation setting for the frequency used [1].

The subsystem for the attenuator is shown in Figure 4.15. The implementation of the at-tenuator functions are shown in Figure 4.16. The model has a gain with negative constantwhich will add up with the accuracy of the attenuator implemented as a Matlab functionAttenuator seen in Figure 4.17. The accuracy is modeled with a Matlab random function

42

4.5. Attenuator

just like in the phase shifter. The equation for the attenuator is modeled as (4.4), where A isattenuation level, Aloss is attenuation accuracy and signal is the input signal. The code whichimplements this can be seen in Code block 4.4.

Out = A ¨ Aloss ¨ signal (4.4)

Figure 4.15: The attenuator block

Figure 4.16: Inside the attenuator block.

Figure 4.17: The attenuator function

1 function out = attenuator(in,rand_in,attenuation_dB)

2

3 rand_number = rand_in*(0.05*attenuation_dB);

4 rand_number_pwr = 10^(rand_number/10);

5 attenutation_pwr = 10^(-attenuation_dB/10);

6

7 out = attenuation_pwr*rand_number_pwr*in);

8

9 end

Code block 4.4: Attenuator Matlab code.

43

4. RECEIVER MODEL

4.6 Random error generator

Simulink has different toolboxes containing blocks which generate pseudo random numbers.Also, Matlab has different functions for generating pseudo random numbers. When usinga Matlab function block in Simulink to generate a random number, the same seed is used atevery simulation unless manually changed. This means that it generates the same numberevery time. To generate a random number within a specified range the following methodcan be used. For this simulation, a finite array of random numbers can be predefined by aMatlab function and then one of these numbers can be chosen by a separate Simulink block.By using the function rand(1000,1) a vector of 1000 random numbers between 0 and 1 canbe generated. If a different range of numbers is required the range is specified by doing thefollowing:

1 a = 50 b = 100;

2 x = (b-a).*rand(1000.1)+a

This generates a vector of 1000 random numbers between 50 and 100. It uses a randominteger block from Simulink DSP Toolbox. With this block a random number from the vectorcan be chosen at random each simulation.

Generating a random number to the attenuator and phase shifter errors it is sufficient togenerate a finite vector of numbers within the required range. This vector is predefinedin the Matlab functions random and generated beforehand in a Matlab script. Then aRandom_integer block can be used to generate an integer between 1 and the size of thevector. This integer is used as input to the Matlab function and the integer determines whichvalue is used from the vector. The system is displayed in Figure 4.18. A variable is used asan input which enables the error generator. If set to zero, the errors are disabled. The codeimplemented in the random is shown in Code block 4.5. However, the 1000 random numbershave been excluded.

Figure 4.18: The Random Matlab function block.

One of these systems is used for each attenuator and for each of the phase shifters of theTRU. The enable variable is stored in a Data Store Memory, which can be used as input tothe Matlab function block. The Data Store Memory block is, as the name suggests, a storageblock for variables. This storage can be accessed by write or read blocks. The write blockinputs data to the storage, overwriting the previous value. The read block outputs the valuefrom the storage. This enables the user to enable all errors at once by changing the value inthe Data Store Memory. The errors have been divided into phase shifter errors and attenuatorerrors which both have an enable button each. This can be seen in Figure 3.2.

44

4.7. Wilkinson power divider

1 function random_number = random(random_int,enable)

2

3 x = [ "Array with 5318 numbers" ];

4

5 if enable == 0

6 number = 0;

7 else

8 random_number = x(random_int+1);

9 end

10

11 end

Code block 4.5: Random generator Matlab code.

4.7 Wilkinson power divider

Power dividers are microwave components used for power division, i.e., one input powerwill be split into two outputs with less power. It can also be used the other way aroundas a combiner with two inputs and one output. The equal 3 dB Wilkinson power divider(WPD) is used as a combiner in this model. A great advantage with the WPD is that theoutputs are isolated, S23 = S32 = 0, so it is lossless when perfectly matched. The lengthof the transmission lines between input ports and output port is λ/4, which means that thesignal will be 90° phase shifted. Figure 4.19 shows the WPD block and Figure 4.20 shows theMatlab function WPD in Simulink [14]. Code block 4.6 shows the code implemented in theWPD block.

Figure 4.19: The WPD block.

Figure 4.20: The WPD function.

1 function port_1 = WPD(port_2,port_3)

2

3 port_1 = port_2*exp(1i*pi/4) + port_3*exp(1i*pi/4);

4

5 end

Code block 4.6: WPD Matlab code.

45

4. RECEIVER MODEL

4.8 The 180° hybrid coupler

The hybrid, also referred to as rat-race coupler, is a four-port network with two inputs andtwo outputs. The coupler will be used as a combiner with the outputs phase shifted 180° toproduce the difference signal and with a tuned output to which the signals are coming inphase, hence producing the sum of the signals. The input signals are applied at port 2 and 3so that the sum signal will be produced at port 1 and the difference signal will be producedat port 4.

As described in Section 2.8.4, the distance between the input ports 2 and 3 to port 1 isλ/4. The same distance will produce the same phase shifting so that the signals will addup like Σ = S1 + S2. The distance from the inputs ports 2 and 3 to port 4 is unequal. Thisresults in different phase shift for the signals: 90° for port 3 and 270° for port 2. This meansthat there will be destructive interference and the signals will be subtracted ∆ = S1 ´ S2.Ideally, if the signals on the input ports are in phase, port 4 is zero in amplitude. Figure 4.21shows the rat-race subsystem block and Figure 4.22 shows the rat_race Matlab function inSimulink with the corresponding code shown in Code block 4.7. In the function block port1 is called sum_1 and port 4 is called diff_4. The outputs of this subsystem can be used tomake a graph of the antenna pattern as described in Chapter 2 [14].

Figure 4.21: The rat-race block.

Figure 4.22: Rat-race function.

1 function [sum_1,diff_4] = rat_race(port_2,port_3)

2

3 sum_1 = port_2*exp(1i*pi/4) + port_3*exp(1i*pi/4);

4

5 diff_4 = port_2*exp(1i*pi/4) + port_3*exp(-3i*pi/4);

6

7 end

Code block 4.7: Rat-race Matlab code.

46

4.9. Diff/Sum ratio

4.9 Diff/Sum ratio

Equation (4.5) shows how the monopulse ratio is calculated, where U is the monopulse ratio,∆ is the difference signal, Σ is the sum signal and ϕ is the phase difference between twoantennas. Equation (4.6) shows how the ratio phase can be calculated, where R1 and R2

are the distances between the transmitter and the antennas, λ is wavelength, d is distancebetween the antennas and θ is the deviation angle from boresight [3], [15], [16].

U =|∆|

|Σ|= tan(

ϕ

2) (4.5)

U =2π

λ(R1 ´ R2) =

2π

λd sin θ (4.6)

The amplitude comparison subsystem block, in Figure 4.23, calculates the max sum anddifference values of the signal, and also the ratio by using these values. The max value istaken because in theory the signal is a pulse. The amplitude comparison block is modeled asin Figure 4.24, with the difference and sum signals as input.

Figure 4.23: Ratio calculation block.

Figure 4.24: Inside the ratio calculation block.

47

Chapter Five

Data management

In this Chapter, the method for how the data is processed is explained, using Matlab code.

The high frequency sine wave is making pulses, which are analyzed. Because it is a pulsewhich is received, only the max value is used for calculating the ratio. These are the maxvalues of the sum and difference signals from the rat-race. With signals measured for thedifferent positions of the transmitter relative to the receiver, these angles will give differentresults. By summarizing a set of data the antenna pattern is achieved. This antenna patternwill be plotted with 10 different measurement values of 5° interval. There will be differentcases of measurement setups:

• The ideal system.

• Only the phase shifter error enabled.

• Only the attenuation error enabled.

• Both the phase shifter error and the attenuation error enabled.

With this method, the phase shifters and the attenuators can be evaluated separately. Fur-thermore, the ideal pattern is used as comparison to calculate how much the errors affect theangle measurements.

5.1 Simulink to Matlab file

By using the to_matfile function in Figure 5.1, the simulated data is sent to a Matlab filethat can be processed by Matlab code. The variables needed are ratio, sum signal, differencesignal and the angle theta. The ratio has also been calculated with a Matlab script, whichyielded the same results.

Figure 5.1: The to_matfile function.

49

5. DATA MANAGEMENT

1 function to_file = to_matfile(theta,ratio,sum,diff)

2

3 to_file = [theta ratio sum diff];

4

5 end

Code block 5.1: To file Matlab code.

The function in Figure 5.1 works as a multiplexer, which can be seen in Code block 5.1. AMatlab function block was used instead of a regular multiplexer block because of its flexi-bility. Meaning that it is easier to output parts of the string, which will be sent to the file, inSimulink for verification. The block can be modified to take as many inputs as required.

5.2 Matlab file to graph

The Matlab code in Code block 5.2, loads data from Matlab files and sorts the values to theright position in a Matlab workspace variable. It sorts it in the following way: column oneis always the θ corresponding to the measurements, column two is the ratio of the first mea-surement followed by the sum and difference values in columns three and four. The samesorting is used for all performed measurements.

1 row = 1;

2

3 load('Results.mat');

4 load('Results2.mat');



7

8 s_a = size(sim_results_attenuator);

9 s_p = size(sim_results_phase_shifter);

10 s_i = size(sim_results_ideal);

11 s_a_p = size(sim_results_attenuator_phaseshifter);

12

13 DS_a_p(row,1) = sim_results_attenuator_phaseshifter(2,s_a_p(2));

14 DS_a_p(row,2:(s_a_p(1)-1)) = ...

sim_results_attenuator_phaseshifter(3:s_a_p(1),s_a_p(2));

15 DS_a(row,1) = sim_results_attenuator(2,s_a(2));

16 DS_a(row,2:(s_a(1)-1)) = sim_results_attenuator(3:s_a(1),s_a(2));

17 DS_p(row,1) = sim_results_phase_shifter(2,s_p(2));

18 DS_p(row,2:(s_p(1)-1)) = sim_results_phase_shifter(3:s_p(1),s_p(2));

19 DS_ideal(24+row,1) = sim_results_ideal(2,s_i(2));

20 DS_ideal(24+row,2:(s_i(1)-1)) = sim_results_ideal(3:s_i(1),s_i(2));

Code block 5.2: Sorting Matlab code.

In the Matlab code in Code block 5.2, there is a row variable. This variable is used to specifywhich row in the dataset the results of the simulation should be put in. For simplicity, it issuggested that the user starts at the lowest angle and increments the row variable for eachangle.

The files are then processed by the following code to sort out, calculate and plot: ratiodata and the sum and difference signals in dB. The first part in Code block 5.3 extracts theratio data from the file and puts them in a new variable named ratio_ f ile. Only some keyparts of the code is presented here, the entirety of the code is presented in Appendix B.

50

5.2. Matlab file to graph

1 %% Ratioextractor

2 % Extracts the ratio data out of the file and gives a file with only ratio ...

data and corresponding angle.

3 file = DS; % Name of your data set as file here.

4 file_size = size(file);

5

6 ratio_file(:,1) = file(:,1);

7 i = 1;

8

9 while le(i,file_size(1)+2)

10 u = 2;

11 p = 2;

12 while le(p,file_size(2))

13 ratio_file(i,u) = file(i,p);

14 p = p + 3;

15 u = u +1;

16 end

17 i = i + 1;

18 end

Code block 5.3: Ratio extracting Matlab code.

The sum and diff data can also be extracted by the code in Code block 5.4, which uses thesame principle as the code which extracts the ratio.

1 %% SUM DIFF EXTRACTOR

2 % Extracts the sum and diff values out of your file

3 file = DS; % Name of your dataset as file here


5

6 sum_diff_file(:,1) = file(:,1);

7 i = 1;

8


10 u = 2;

11 p = 3;


13 sum_diff_file(i,u) = file(i,p);

14 sum_diff_file(i,u+1) = file(i,p+1);

15 p = p + 3;

16 u = u +2;

17 end

18 i = i + 1;

19 end

Code block 5.4: Sum and diff extracting Matlab code.

From the code presented above, the ratio file is used to calculate the deviation with the codein Code block 5.5. The code plots all the different ratio measurements. Calculates and plotsthe absolute value of the deviation from the ideal ratio to the different ratio measurements.The code also adapts to small errors in the datasets by finding the angle in the ideal datasetwhich is closest to the angle in the non-ideal dataset. Since the non-ideal dataset and theideal dataset can deviate from each other for the same measurement. For instance, whenmeasuring for 10° the ideal dataset might end up measuring for 9.997° and the non-ideal10.002°. The code will pair them with each other even though there is a small deviation.

51

5. DATA MANAGEMENT

1 % Find the closest angle in the ideal dataset corresponding to the angle in ...

the non-ideal dataset

2 % Non-ideal file must consist of only ratios at columns 2 and beyond

3 steer = 0; % Input the steer of your dataset here to formate the plot function.

4 ideal_file = DS; % Name of the ideal ratio dataset as file

5 non_ideal_file = DS_a_p_r; % Name of the non ideal ratio dataset as ...

non_ideal_file

6

7 size_ideal_file = size(ideal_file);

8 size_non_ideal = size(non_ideal_file);

9

10 dev_file = zeros(size_non_ideal);

11 dev_file(:,1) = non_ideal_file(:,1);

12 dev_file_procent(:,1) = non_ideal_file(:,1);

13 i = 1;

14 while le(i,size_non_ideal(1))

15 value_check = 0;

16 save_value = 0;

17 save_row = 1;

18 row = 1;

19

20 while le(row,size_ideal_file(1))

21 value_check = abs(ideal_file(row,2) - non_ideal_file(i,2));

22 if ge(row,2)

23 if le(value_check,save_value)

24 save_value = value_check;

25 save_row = row;

26 end

27 else


29 end

30 row = row + 1;

31 end

32

33 row_angle = save_row;

Code block 5.5: Processing Matlab code part 1.

The while loop in the code presented in Code block 5.5 loops through the ideal_ f ile and findsthe row number of the angle in the ideal file which has the smallest difference from the anglein the non-ideal file as stated previously. This loop is used to perform the same task severaltimes in the code and will not be presented again. The deviation is calculated as in (5.1),where the absolute value is taken of the difference between the ideal and non-ideal value.

deviation =a

ideal_value2 ´ non_ideal_value2 (5.1)

Then the percental deviation is calculated and plotted. It is calculated as in (5.2).

percental_deviation =deviation

ideal_ratio(5.2)

The code which implements this is shown in Code block 5.6.

52

5.2. Matlab file to graph

1 % Calculate the absolute value of the deviation from the ideal pattern as ...

well as the percental deviation

2 io = 1;

3

4 while le(io,size_non_ideal(2)-1)

5 dev_file(i,1+io) = abs(ideal_file(row_angle,2)-non_ideal_file(i,1+io));

6 dev_file_procent(i,1+io) = dev_file(i,1+io)/ideal_file(row_angle,2);

7 io = io + 1;

8 end

9 i = i + 1;

10 end

11 % Find the maximum value of the percental deviation for each measured point

12 dev_file_procent_max(:,1) = dev_file_procent(:,1);

13 size_procent = size(dev_file_procent);

14 mo = 1;

15

16 while le(mo,size_procent(1))

17 dev_file_procent_max(mo,2) = max(dev_file_procent(mo,2:size_procent(2)));

18 mo = mo + 1;

19 end


Then the code in Code block 5.6 finds the maximum and minimum deviation in each mea-sured point by using a max() and min() functions, which are standard Matlab functions.The functions return the maximum and minimum value of an array, which are then appliedto the ideal value as in (5.3) and yields the ratio with the maximum and minimum deviationin each measured point. This is implemented in Code block 5.7.

maximum_deviation_ratio = ideal_value ¨ (1 + max_procentual_deviation) (5.3)

1 % Calculate maximum error ratio: ideal_ratio + (ideal_ratio * ...

max_percental_deviation)

2 max_deviation_ratio(i,2) = ...

ideal_file(ideal_row,2)+(ideal_file(ideal_row,2).*dev_file_procent_max(i,2));

3

4 if le(max_error_ratio(i,1),steer)

5 max_iteration = row_steer;

6 else

7 max_iteration = size_ideal_file(1)-row_steer;

8 end


These values are then inputed to a look-up table which uses the ideal antenna pattern forthe steer degree corresponding to the dataset to find the incident angle corresponding to thevalue of the ratio. The look-up table works similarly as the while loop presented above, buthas more conditions as can be seen in Code block 5.8. Such as the ambiguity variable whichmakes sure that the look-up table is choosing the correct side of the steer angle to comparethe values with.

53

5. DATA MANAGEMENT

1 %% Find the angle corresponding to the ratio with maximum error in the ideal ...

pattern

2 y2 = 0;

3 s2 = 1;

4 s = 1;

5 while le(s,max_iteration)


7 ambiguity = 0;

8 y1 = abs(ideal_file(s,2) - max_deviation_ratio(i,2));

9 else

10 ambiguity = 1;

11 y1 = abs(ideal_file(row_steer+s,2) - max_deviation_ratio(i,2));

12 end

13 if ge(s,2)

14 if le(y1,y2)

15 y2 = y1;

16 if ambiguity == 1

17 s2 = row_steer+s;

18 else

19 s2 = s;

20 end

21 end

22 else

23 y2 = y1;

24 end

25 s = s + 1;

26 end


The absolute value of the difference between the angle which correlates with the ratiofrom the max_deviation_ratio and the real angle from the ideal_ f ile is then saved in theangle_deviation_maximum. The code which performs this can be seen in Code block 5.9.

1 % Calculate the angular deviation

2 angle_deviation_maximum(i,1) = dev_file_procent_max(i,1);

3 angle_deviation_maximum(i,2) = abs(max_deviation_ratio(i,1)-ideal_file(s2,1));

4 i = i + 1;

5 end


The values calculated from this code are then saved by the user and functions can be used toplot the data so that it is comparable in the same graph. These functions are also included inAppendix B.

54

Chapter Six

Simulation results and discussion

Simulation results and discussion explain the final model result. In graphical form, it isshown how the different components affect the signal. First the scenario is presented, then themodel results are presented with graphs of how the signals look throughout the model. Thenthe measurements are presented for different steering angles. The result will be discussedas it is presented, with a comparison discussed in Section 6.15. This will be the basis for theconclusion in Chapter 7. Simulations will be made for different positions for the transmitterrelative to the receiver position. These positions will give data with graphs for different steer-ing angles. With all this data, the angular deviation will be presented in this Chapter. For theresult, the relevant data is around ˘ 20° of the steering angle.

6.1 Scenario

The scenario for the simulations have been briefly discussed in previous chapters. Here itwill be summarized and explained to give an accurate representation of how the simulationswere performed.

• The receiving antenna boresight is assumed parallel to the x-axis. It implies that theposition of the antenna elements varies along the y-axis, as discussed in Section 3.2.1.

• 8 antenna elements are implemented.

• The distance between the antenna elements is set to λ4 .

• Isotropic antenna elements are used.

• Friis transmission equation is modelled and used. All other transmission related lossesare neglected.

• Sinusoidal waves are used to represent the signals.

• Both aircrafts are stationary.

• The angular deviation will be analyzed for both the phase shifter and attenuator errorsseparate as well as together.

• Ten simulations are made for each of the three error cases: phase shifter, attenuator andboth together.

• The simulations are made for the same distance between transmitter and receiver. Thisdistance is D = 10 km. The model has been tested to make sure that it yields the sameresults for different distances.

• The attenuation is the same for all simulations A = 12 dB.

55

6. SIMULATION RESULTS AND DISCUSSION

6.2 System

The entire model of the system includes initial variables set by the user and also some vary-ing variables which are the moving objects around and parts of the system. The signal ismodulated by a propagation block so the realistic signal could be processed by the TransmitReceive Unit (TRU). The TRU will produce eight signals which are connected to the couplers.These couplers will give the sum signal and the difference signal.

6.3 Input signals and parameters

The initial parameters are the position and velocity of the transmitting aircraft and the re-ceiving aircraft. The phase steering of the phase shifters and attenuation in the TRU can bevaried as well, but the attenuation will be set to 12 dB for these measurements. It is importantthat the distance between the antenna elements are correct in all subsystems which are usedas a variable, otherwise the shape of the radiation pattern can deviate greatly.

6.4 Signal modulation

The signal is processed by a signal box consisting of a propagation block, a phase shiftcalculator and a phase shifter. The output of the propagation block for one antenna elementcan be seen in Figure 6.1. The graph shows both the real part, the red line, and the imaginarypart, the blue line, of the signal. All graphs later will not necessarily have the imaginary part.This signal can be compared with the later modified signal.

Figure 6.1: The received signal at one antenna element.

56

6.5. Transmit receive unit

6.5 Transmit receive unit

The TRU contains eight RF modules which in turn consist of a LNA, a phase shifter and anattenuator. The output signal for a phase shifter is shown in Figure 6.2, where it is comparedwith the input signal of the phase shifter. The red line is the real part of the signal beforethe phase shifter and the blue line is the real part of the signal after the phase shifter. In thegraph it can be seen that the signal is shifted as expected.

Figure 6.2: The phase shifted signal.

The output of the attenuator is compared with the input signal in Figure 6.3. The blue lineshows the real part of the input signal and the red line shows the attenuated signal. In thegraph the signal is attenuated by 12 dB as it should.

57


Figure 6.3: The attenuated signal.

6.6 Couplers

The WPD is used to combine two signals into one. The rat-race will then receive two signalsand produce a sum and a difference signal. These signals are shown in Figure 6.4. The differ-ence signal, the blue line, varies much more than the sum signal, the red line, depending onthe incoming angle of the transmitter, around boresight.

Figure 6.4: The sum and difference signal.

58

6.7. Model validation

6.7 Model validation

The antenna pattern produced by this model was compared with the antenna pattern of thesystem that Saab is developing. To make sure that the antenna pattern was similar in the casewhen e.g., the same distance between antenna elements and the same amount of antennaelements are used. Using scopes and display throughout the whole system the signals canbe traced and evaluated. The model simulates results for an ideal system and a system witherrors. The nominal result is compared with the simulated results for the interrogator toachieve reasonable values. The system with errors is then compared with the ideal system tosee how the errors affect the signals.

To evaluate the system, different angles between the transmitter and receiver were simu-lated. To calculate these angles a Matlab function was created to calculate the desired anglesbetween 0° and 180° for a set distance. It generates coordinates for the transmitter whichcorresponds to the angle. The values for the sum and difference signals, in dB, can now beplotted using a plot function in Matlab.

6.8 Ideal antenna pattern

The results from the simulation were sent into the selected Matlab folder in a file where thedata is stored. All ideal datasets are simulated with a precision of 0.2°. The measured anglesare ˘50° around the steering angle. The antenna pattern plots shows dB watt on the y-axisand incident angle in degrees on the x-axis. Figure 6.5 shows the plot for the ideal systemwith 0° steer. The blue line is the sum signal and the red line is the difference signal.

Figure 6.5: Antenna pattern of the ideal system.

59


The ratio which is calculated from the data used in Figure 6.5 is displayed in Figure 6.6. Inboth these figures the critical point is around ˘15° where the sum and difference cross eachother and where the ratio in Figure 6.6 becomes 1.

Figure 6.6: Sum diff ratio of ideal the system.

6.9 Steer 0°

Figure 6.7 shows the ten different antenna patterns with phase shifter error enabled andFigure 6.8 shows the ten different antenna patterns with the attenuator error at 0° steer. Mostof the figures in Section 6.9 to Section 6.15 have been calculated or processed by the codepresented in Section 5.1.

Unlike the radiation pattern for the ideal system, Figure 6.5, the curves do not have the samesmooth lines. These small deviations will give a ratio different from the ideal system, and itis this ratio deviation that can be used to calculate the angular deviation.

When processing the data from the figures, it can be stated that the attenuator error graphdoes not deviate as much as the phase shifter error graph. This result shows that the phaseshifter error will have a bigger impact on the angular accuracy than the attenuator. For theother steering angles only the antenna pattern and the ratio plot with both errors will beshown. Because the attenuator errors do not increase as the phase shifter errors does forlarger steering angles, the attenuator antenna pattern will have a similar error interval forthe different measured angles.

60

6.9. Steer 0°

Figure 6.7: Sum diff signals with phase shifter error enabled.

Figure 6.8: Sum diff signals with attenuation error enabled.

61


When enabling both error sources a greater deviation is acquired. Figure 6.9 shows theantenna pattern with both phase shifter and the attenuator error at 0° steer. With these smalldeviations for the attenuator Figure 6.9 is similar to Figure 6.7.

Figure 6.9: Sum diff signals with attenuator and phase shifter error enabled.

Figure 6.10 shows the ratio for steer 0° with phase shifter and attenuator errors enabled. Thisgraph shows how the ratio increase to values above 50 when the sum signal approacheszero. Since the most important data is where the ratio is lower than 1, the rest of the graphscontaining the ratio will be presented without these peaks. Figure 6.11 to 6.13 shows croppedgraphs of the ratio for the three different error cases for steer 0°. These different cases for theratio will only be presented for steer 0°. For the other steer values, only the ratio deviationfor the case when both errors are enabled will be shown.

For these graphs, the most important area is where the ratio is below 1 since the real systemuses RSLS processing to get rid of the other signals. But it can be important to know howthe angular accuracy varies for the case when the ratio is higher than 1. The deviation whichoccurs at boresight is mostly due to the amplitude offset between the ideal and non-idealratio. Since the ideal ratio approaches zero at boresight it generates a higher deviation.

Figure 6.14 shows the ratio deviation and the percental ratio deviation where the rele-vant angles are from ´30° to 30°. The small peak between ´5° and 5° is expected because theideal difference signal is approaching zero at 0°. This however, is more visible in the secondgraph where the percental deviation peaks at a value much higher than 100 %. Which isexpected since the deviation in the upper graph is around 0.01 ´ 0.03 at 0° and the ideal ratioat 0° has a magnitude around ˚10´4. The method of calculating the percental ratio deviationis explained in Chapter 5.

62

6.9. Steer 0°

Figure 6.10: Ratio with attenuator error for steer 0°.

Figure 6.11: Ratio with phase shifter error for steer 0°.

63


Figure 6.12: Ratio with attenuator error for steer 0°.

Figure 6.13: Ratio with attenuator and phase shifter error for steer 0°.

64

6.9. Steer 0°

Figure 6.14: Ratio deviation for steer 0°.

Using the function described in Section 5.1, the maximum and minimum percental devi-ation from the data shown in Figure 6.14 can be calculated. This is applied to the ideal ratiofrom Figure 6.13 which can be used to calculate the angular deviation. Figure 6.15 showsthe ideal ratio together with the plots for the maximum and minimum deviation applied to it.

The data from the maximum deviation ratio and minimum deviation ratio in Figure 6.15 isput through a look-up table as described in Chapter 5. The look-up table finds the anglecorresponding to the value of the ratio. The real angle is subtracted from the angle found inthe look-up table to calculate the angular deviation.

The maximum and minimum angular deviations for steer 0° are shown in Figure 6.16.The blue line is the maximum angular deviation and the red line is the minimum angulardeviation. All look-up tables have a precision of 0.2°, this precision directly affects the preci-sion of the angular deviation. If the angular deviation is 0° it could be up to 0.1° because ofthis precision. The graph in Figure 6.16 shows that the angular deviation are at most 0.2° forboth max and min.

65


Figure 6.15: Maximum, minimum and ideal ratio for steer 0°.

Figure 6.16: Max and min angle deviation for steer 0°.

66

6.10. Steer 10°

6.10 Steer 10°

Figure 6.17 shows the sum and difference signals with 10° steering angle. The black linesshow the ideal pattern for both the sum and difference signal. This line can easiest be spottedat ´20° and 40°. Compared with Figure 6.9 the pattern differs. The sum for steer 0° has anotch for ˘30°. For steer 10° the notch at the right side in the graph is more than +30° abovethe steer. This notch moves further and further away with the increase of steering angle.

Figure 6.17: Sum and difference with attenuator and phase shifter error enabled for steer 10°.

Figure 6.18 shows the ratio for the phase shifter and attenuator error case. Seen in thesefigures is that the ratio in the right side of the graph seems to gradually flatten out.

The maximum and minimum angular deviations for steer 10° are shown in Figure 6.19. Theblue line is the max angular deviation and the red line is the min angular deviation. Thegraph shows that the angular deviation are at most 1° for both max and min. Comparedwith steering angle 0° the angular deviation has increased by around 0.6° around the steerangle. The pattern has no particular form but the minimum deviation has its maximumat the steering angle for both steering 0° and 10°, meaning that it will always be an an-gular deviation at the boresight. This is because of how the difference signal is changingaround the steering angle. As can be seen in Figure 6.19, there are spikes with an interval of 5°for some intervals. These spikes are because of the interval of the measured incident angle, 5°.

67



Figure 6.19: Max and min angular deviation with both errors enabled for steer 10°.

68

6.11. Steer 20°

6.11 Steer 20°

Figure 6.20 shows the sum and difference signals with 20° steering angle. The black linesshow the ideal patterns for both the sum and difference signals. These lines can easiest bespotted at ´10° and 55°. The signal at the higher incident angle becomes more and moredifferent for higher steering angle. This can be seen in Figure 6.21, which shows the ratio forthe phase shifter and attenuator error case.

Figure 6.20: Sum and difference with attenuator and phase shifter error enabled for steer 20°.


69


The maximum and minimum angular deviations for steer 20° are shown in Figure 6.22. Theblue line is the maximum angular deviation and the red line is the minimum angular devi-ation. The graph shows that the angular deviation is at most 2° for maximum and 0.2° forminimum. Compared with steering angle 0° the angular deviation has increased by around1.4° around the steer angle. The minimum value has a deviation, as usual, at the steeringangle.


6.12 Steer 30°

Figure 6.23 shows the sum and difference signals with 30° steering angle. The black linesshows the ideal patterns for both the sum and difference signals. These lines can easiestbe spotted at 0°. When applying this much steering, the pattern will differ more and moreon the right hand side of the graph. Figure 6.24 shows the ratio for the phase shifter andattenuator error case. The notch in the sum plot which was visible in Figure 6.20 is not visiblefor steer 30° anymore. The notch would appear if the simulations had covered higher angles.

The maximum and minimum angular deviations for steer 30° are shown in Figure 6.25. Theblue line is the max angular deviation and the red line is the min angular deviation. Thegraph shows that the angular deviation is at most 3° for maximum and 0.2° for minimum.Compared with steering angle 0° the angular deviation has increased by around 1.3° aroundthe steer angle. The minimum value has no deviation at the steering angle. The deviation forthe maximum case has the same form as for steer 20° but with a higher deviation.

70

6.12. Steer 30°

Figure 6.23: Sum and difference pattern with attenuator and phase shifter error for 30° steer.

Figure 6.24: Ratio with both attenuator and phase shifter error for 30° steer.

71



6.13 Steer 40°

Figure 6.26 shows the sum and difference signals with 40° steering angle. The black linesshows the ideal patterns for both the sum and difference signals. These lines can easiest bespotted at 5°. For this high steer, the sum signal on the right hand side will not have a notch,similar to steer 30°. Figure 6.27 shows the ratio for the phase shifter and attenuator errorcase. Because the sum and difference pattern is different at high incident angles the ratio willnot have a high value at those angles.

Figure 6.26: Sum difference pattern with attenuator and phase shifter error for 40° steer.

72

6.13. Steer 40°

Figure 6.27: Ratio with attenuator and phase shifter for 40° steer.

The maximum and minimum angular deviations for steer 40° are shown in Figure 6.28. Theblue line is the maximum angular deviation and the red line is the minimum angular devi-ation. The graph shows that the angular deviation is at most 5° for maximum and 0.5° forminimum. Compared with steering angle 0° the angular deviation has increased by around2° around the steer angle. The minimum plot deviates when the ratio is 1 and at the steeringangle. The deviation angles are relatively high and increasing for higher incident angles.

Figure 6.28: Maximum and minimum angular deviation with both errors enabled for steer40°.

73


6.14 Steer 50°

Figure 6.29 shows the sum and difference signals with 50° steering angle. The black linesshows the ideal patterns for both the sum and difference signals which are in the middle ofall the deviation plots. In the graph it can be seen that the difference signal is not crossingthe sum signal for at the right hand side. Meaning that the ratio will not exceed 1 for thesimulated incident angles. This result was not expected and will result in a flatter ratio curveas shown in Figure 6.30, where the ratio for the phase shifter and attenuator error case isshown.

Figure 6.29: Sum difference pattern with attenuator and phase shifter error for 50° steer.

Figure 6.30: Ratio with attenuator and phase shifter for 50° steer.

74

6.15. Comparison

The maximum and minimum angular deviations for steer 50° are shown in Figure 6.31.The blue line is the maximum angular deviation and the red line is the minimum angulardeviation. The graph shows that the angular deviation is at most 11° for maximum and 0.5°for minimum. Compared with steering angle 0° the angular deviation has increased by 4.2°around the steer angle. The angular min value deviate at the steering angle.


6.15 Comparison

In this Section, a comparison between the angular deviations for different steer angles willbe presented. In the following figures the deviation for attenuator error, phase shifter errorand both errors are shown.

In Figure 6.32 the maximum angular deviation for different steer angles simulations isshown. In this figure it can be seen that the attenuator error does not affect the angularaccuracy more than 0.5° for steer below 40°. For steer above 40°, the angular accuracy is moreaffected by the attenuator error. Giving us a deviation of up to 5°. However, it can also beseen that most of the angular deviation happens around the steer point except for steer 50°where the maximum deviation happens at 85°.

In Figure 6.33, the maximum angular deviation for the different steer angle simulations withphase shifter error enabled is shown. It can be seen by comparing Figure 6.33 and Figure 6.32the phase shifter error has a bigger impact on the angular accuracy of the receiver than theattenuator error since it in almost all angles in the figure has a higher deviation. The excep-tion is around the steer point where the attenuator error yields similar deviation. Figure 6.33also shows the same trend as for the attenuator error, that the angular accuracy gets worsewith the increase of steering angle.

75


Figure 6.32: Angular deviation for all the different steering angles with attenuator error en-abled.

Figure 6.33: Angular deviation for all the different steering angles with phase shifter errorenabled.

It also seems that the highest deviation for steer 20° to steer 50° happens around 30° abovethe steering angle. This could largely be due to the fact that the ratio slope gets flatter athigher incident angles when the steering increases. This can be seen in Figure 6.34, where

76

6.15. Comparison

the ideal ratios for the different steer angles are shown. Meaning that the percental deviationhas a higher impact on the accuracy in these areas.

Figure 6.34: Ideal ratio for different steer.

Figure 6.35 shows the maximum angular deviation for the case when both errors are en-abled. As can be seen in Figure 6.35, this is the case when the maximum angular deviation isachieved. The maximum deviation seen in the figure is 11.2°.

Figure 6.35: Angular deviation for all the different steering angles with both errors enabled.

77

Chapter Seven

Conclusion and future work

In this Chapter, the project work is concluded. Also, considerations about future work areshortly presented.

7.1 Conclusion

The main task of this project was the realization of a model for a Monopulse SecondarySurveillance Radar in Matlab Simulink. The modeling has focused on blocks that generateand process signals that are specific for Monopulse SSRs. Monopulse SSR in this projectassumes antenna array with sum Σ and difference ∆ patterns. The receiver gets a sequence ofinput signals as coming from the antenna array, calculate the Σ-signal, the ∆-signal and theratio signal ∆

Σ. From the ratio signal and a look-up table (LUT), the AoA can be identified.

The receiver block model includes models for three main operations: amplification (LNAblock), phase shifting and attenuation. After the model implementation in Matlab, simula-tions were performed and results were analyzed and interpreted. The model validation wasdone through comparison to known results provided by the company in form of a designfile. The main expected result from simulations was the Angle-of-Arrival (AoA) as a functionof several model parameters.

First, a nominal AoA was calculated for different steering angles. Then, non-ideal caseswere modeled in the receiver by assuming random errors in the phase shifter and attenuatorparameter values. Then, the difference between nominal and non-ideal calculated AoA wasanalyzed.

• It was shown that the accuracy of the calculated AoA was mostly dependent on thephase shifter error margins.

• Moreover, the deviation from the ideal case was higher than expected.

• The random deviation of the two component parameters result in higher deviation forhigher steering angles.

• The ∆ ´ Σ pattern was deformed when the steering angle increased that also con-tributed to higher deviation.

• Also, the pattern lost its symmetry around the steering angle with increase steeringangle.

There are some other aspects of the model that can be concluded. E.g., simulations were per-formed for a static scenario, i.e., both the transmitter and receiver were stationary. However,the model can be used also for the case when both the transmitter and receiver are in motion

79

7. CONCLUSION AND FUTURE WORK

as the Doppler effect is implemented in the Propagation_block.

As for the design aspects of the IFF monopulse receiver, it depends on the field of appli-cation. If the system is implemented with fewer antenna elements it results in a broadersum beam. This broader sum beam results in a ratio pattern which is more prone to biggerangular deviation. However, more antenna elements results in a higher cost for the system.

The choice of components greatly affects the precision of the system and if a high preci-sion system is required, the price of the components increase. However, knowing the angulardeviation for the different steer angles you could implement this deviation into the look-uptables to reduce the angular deviation.

7.2 Future work

The measurements of the ideal patterns for the different steer angles could have better preci-sion. This would give a better precision for the angular deviation, higher than 0.2°. Smallerinterval for the measurements of the non-ideal error data to get a smoother graph. Moremeasurements per incident angle could be made to get a better and more accurate mathe-matical result, not just 10 measurements. All these aspects will give a more reliable result.

The attenuator value could be changed to see how much it would affects the result. Theattenuator value could be implemented to be changed depending on the amount of steering.

An easy way to set the inputs could be implement, for example the position of the transmit-ter. The entire model could be compatible with an interface which contain both a commandpanel and results.

There are more components in the receiver chain that could be investigated for instancethe WPD and the rat race.

More error sources could be implemented such as: white noise, thermal effects and non-ideal antennas could be used. Measurements could also be done for already implementedparameters such as how the angular accuracy is affected by the velocity of the transmittingand receiving aircrafts.

80

Bibliography

[2] Constantine A. Balanis. “Antenna Theory Analysis And Design Second Edition”. In:John Wiley and sons (1997).

[3] Samuel M. Sherman. David K. Barton. “Monopulse Principles and Techniques”. In:Artech House (2011).

[4] Marek Borejko. “Monopulse IFF interrogator antenna with optimised parameters, min-imising the possibility of generating false replies by transponder”. In: ().

[6] Michael C.Stevens. “Secondary Surveillance Radar”. In: (1988).

[9] G. Jacovitti. “Performance analysis of monopulse receivers for secondary surveillanceradar”. In: (1983).

[10] W Kołosowski. E Sedek. M Borejko. A Jeziorski. “Monopulse of IFF antennas”. In: ().

[12] International Civil Aviation Organization. “Agenda item 3: Overview of Primary andSecondary Surveillance Radars”. In: (2011).

[13] David M. Pozar. “Microwave and RF design of wireless systems”. In: John Wiley andsons (2001).

[14] David M. Pozar. “Microwave engineering, Fourth edition”. In: John Wiley and sons(2011).

[15] Cai Fei. Fan Hongqi. Song Zhiyong. Fu Qiang. “Difference beam aided target detectionin monopulse radar”. In: (2015).

[16] Bassem R.Mahafza. “Radar Systems Analysis And Design Using Matlab”. In: CRC Press(2013).

[18] Shaun Quegan Simon Kingsley. “Understanding Radar Systems”. In: SciTech Publishing(1999).

[21] Christian Wolff. “Internet: The Reply message”. In: (2018).

81

Webography

[1] Attenuator. AT-264. URL: https : / / www . rf - microwave . com / resources /products_attachments/5a4386c8af228.pdf. (accessed: 03.19.2018).

[5] Cisco. Antenna patterns and their meaning. URL: https://www.cisco.com/c/en/us/products/collateral/wireless/aironet-antennas-accessories/

prod_white_paper0900aecd806a1a3e.html. (accessed: 12.04.2018).

[7] Peter M. Grant. CDMA Array Processing: Why use a receive array? URL: http://www.wirelesscommunication.nl/reference/chaptr05/cdma/cdmaarr1.htm.(accessed: 12.03.2018).

[8] Illumin. Motion Sensors. URL: http : / / illumin . usc . edu / 165 / motion -sensors/. (accessed:01.09.2016).

[11] Matlab. Blocklist. URL: https://se.mathworks.com/help/simulink/block-libraries.html. (accessed: 12.04.2018).

[17] Phase shifter. Weinschel model 984-1. URL: http://weinschel.apitech.com/weinschel/pdfiles/wmod984.pdf. (accessed: 03.19.2018).

[19] Wiki. Phased Array. URL: https://en.wikipedia.org/wiki/Phased_array.(accessed:04.12.2016).

[20] Christian Wolff. Dynamic Range of a Receiver. URL: http://www.radartutorial.eu/09.receivers/rx52.en.html. (accessed: 12.03.2018).

83

Appendices

A Simulink blocks

The complete blocks used for the model in Simulink are listed here. Most of the descriptionsare taken from Mathworks. [11]

dB gain. The dB Gain block multiplies the input by the decibel valuesspecified in the Gain parameter.

Complex to Magnitude-Angle. The Complex to Magnitude-Angle blockoutputs the magnitude and/or phase angle of the input signal, dependingon the setting of the Output parameter. The outputs are real values of thesame data type as the block input. The input can be an array of complexsignals, in which case the output signals are also arrays. The magnitudesignal array contains the magnitudes of the corresponding complex inputelements. The angle output similarly contains the angles of the inputelements.

Max value. Saves the maximum value of the simulated data.

dB converter. The dB Conversion block converts a linearly scaled poweror amplitude input to dB or dBm. The reference power is 1 Watt forconversions to dB and 1 mWatt for conversions to dBm.

Math Function block. The Math Function block performs numerous com-mon mathematical functions.

MATLAB Function. With a MATLAB Function block, you can write aMATLAB® function for use in a Simulink® model. The MATLAB functionyou create executes for simulation and generates code for a SimulinkCoder™ target. Double-clicking the MATLAB Function block opens itseditor, where you write the MATLAB function.

Random integer. The Random Integer Generator block generates uniformlydistributed random integers in the range [0, M-1], where M is the Set sizedefined in the dialog box.

Data Store Memory. The Data Store Memory block defines and initializes anamed shared data store, which is a memory region usable by Data StoreRead and Data Store Write blocks that specify the same data store name.

WEBOGRAPHY

Radian to degree, degree to radian. Converts radian value to degree value. Inthe block it can be set to convert degree value to radian value.

Toggle switch. The Toggle Switch block toggles the value of the connectedblock parameter between two values during simulation. For example, youcan connect the Toggle Switch block to a Switch block in your model andchange its state during simulation. Use the Toggle Switch block with otherDashboard blocks to create an interactive dashboard for your model.

Complex to Real-Imag. The Complex to Real-Imag block outputs the realand/or imaginary part of the input signal, depending on the settingof the Output parameter. The real outputs are of the same data typeas the complex input. The input can be an array (vector or matrix) ofcomplex signals, in which case the output signals are arrays of the samedimensions. The real array contains the real parts of the correspondingcomplex input elements. The imaginary output similarly contains theimaginary parts of the input elements.

Complex phase difference. The Complex Phase Difference block acceptstwo complex input signals that have the same size and frame status. Theoutput is the phase difference from the second to the first, measured inradians. The elements of the output are between ´π and π.

To file. The To File block inputs a signal and writes the signal data into aMAT-file. Use the To File block to log signal data.

B. Matlab code

B Matlab code

Read to mat-file

1 function to_file = to_matfile(ratio,sum,diff,theta)

2

3 to_file = [ratio sum diff theta];

4

5 end

Data sorting function which writes data from the simulations into variables in the workspace.

1 row = 9;

2

3 load('Results.mat');




7

8 s_a = size(sim_results_attenuator);

9 s_p = size(sim_results_phase_shifter);

10

11 s_a_p = size(sim_results_attenuator_phaseshifter);

12

13 DS_a_p(row,1) = sim_results_attenuator_phaseshifter(2,s_a_p(2));

14 DS_a_p(row,2:(s_a_p(1)-1)) = ...

sim_results_attenuator_phaseshifter(3:s_a_p(1),s_a_p(2));

15 DS_a(row,1) = sim_results_attenuator(2,s_a(2));

16 DS_a(row,2:(s_a(1)-1)) = sim_results_attenuator(3:s_a(1),s_a(2));

17 DS_p(row,1) = sim_results_phase_shifter(2,s_p(2));

18 DS_p(row,2:(s_p(1)-1)) = sim_results_phase_shifter(3:s_p(1),s_p(2));

Position generator code. Generates the position of the transmitter for different angles withthe same distance.

1 Pos_rec = [0 0 0];

2 distance = 10000;

3 precision = 0.2;

4 angle1 = -50;

5 angle2 = 50;

6

7 x = angle1;

8 i = 1;

9 while le(x,angle2)

10 angle_steps(i) = x;

11 x = x + precision;

12 i = i+1;

13 end

14 if angle_steps(i-1) ‰ angle2

15 angle_steps(i) = angle2;

16 end

17 j = 1;

18 while le(j,length(angle_steps))

19 yvarde = sin(deg2rad(angle_steps(j)))*distance;

20 xvarde = cos(deg2rad(angle_steps(j)))*distance;

21 Save(j,:) = [angle_steps(j) xvarde yvarde];

22 j = j+1;

23 end

WEBOGRAPHY

Ratio and sum/diff extractor

1 %% Ratio extractor

2 file = DS_ideal; % File name in the workspace here


4

5 ratio_file(:,1) = file(:,1);

6 i = 1;

7


9 u = 2;

10 p = 2;


12 ratio_file(i,u) = file(i,p);

13 p = p + 3;

14 u = u +1;

15 end

16 i = i + 1;

17 end

Ratio plotter

1 % Ratio plotter

2 file = DS_ideal_r;


4 steer = 50; % Change the steer

5

6 % put to = inf if you want all of the data showed in the plot

7 % limits the plot on the x-axis to this value on both positive and negative side.

8 limit_degree = 40;

9 limit_amplitude = 4;

10

11 if steer ‰ 0

12 lim_degree_min = steer - limit_degree;

13 lim_degree_max = steer + limit_degree;

14 else

15 lim_degree_min = -limit_degree;

16 lim_degree_max = limit_degree;

17 end

18

19 i = 2;

20

21 while le(i,file_size(1)-1)

22 hold on

23 plot(file(:,1),file(:,i))

24 title('Ratio deviation')

25 xlabel('Incident angle[]')

26 ylabel('Ratio')

27 xlim([lim_degree_min lim_degree_max])

28 ylim([0 limit_amplitude])

29 i = i + 1;

30 end

B. Matlab code

Sum diff extractor

1 %% SUM DIFF EXTRACTOR

2 file = DS_ideal;


4

5 sum_diff_file(:,1) = file(:,1);

6 i = 1;

7


9 u = 2;

10 p = 3;


12 sum_diff_file(i,u) = file(i,p);

13 sum_diff_file(i,u+1) = file(i,p+1);

14 p = p + 3;

15 u = u +2;

16 end

17 i = i + 1;

18 end

dB conversion

1 %% To dB

2 file = sum_diff_file;


4

5 sum_diff_file2(:,1) = file(:,1);

6 i = 1;

7


9 u = 2;

10 while le(u,file_size(2))

11 sum_diff_file2(i,u) = mag2db(file(i,u));

12 u = u +1;

13 end

14 i = i + 1;

15 end

WEBOGRAPHY

Sum diff plot

1 %% sum diff plotter

2 file = sum_diff_file2;


4

5 % put to = inf if you want all of the data showed in the plot

6 % limits the plot on the x-axis to this value on both positive and negative side.

7 limit_degree = 40;

8 limit_amplitude = inf;

9

10 if steer ‰ 0

11 lim_degree_min = steer - limit_degree;

12 lim_degree_max = steer + limit_degree;

13 else

14 lim_degree_min = -limit_degree;

15 lim_degree_max = limit_degree;

16 end

17

18 figure()

19 i = 2;

20 while le(i,file_size(1))

21 hold on

22 plot(file(:,1),file(:,i))

23 title('Sum diff deviation')

24 xlabel('Incident angle[]') % x-axis label

25 ylabel('Magnitude [dBW]') % y-axis label

26 xlim([lim_degree_min lim_degree_max])

27 ylim([-190 limit_amplitude])

28 i = i + 1;

29 end

Deviation calculations

1 % ideal file must have ratio at column 2.

2 % non ideal file must consist of only ratios at columns 2.. inf

3 steer = 50;

4 ideal_file = DS_ideal;

5 non_ideal_file = DS_a_p_r;

6 size_ideal = size(ideal_file);


8 if steer == 20

9 ideal_file = ideal_file(12:202,1:2);

10 non_ideal_file = non_ideal_file(3:16,:);

11 elseif steer == 10

12 ideal_file = ideal_file(30:135,1:2);



15 ideal_file = ideal_file(16:204,:);



18 ideal_file = ideal_file(12:size_ideal(1),:);

19 non_ideal_file = non_ideal_file(3:size_non_ideal(1),:);


21 ideal_file = ideal_file(12:size_ideal(1),1:2);



24 ideal_file = ideal_file(5:size_ideal(1),1:2);


26

27 end

B. Matlab code

1 size_ideal_file = size(ideal_file);


3

4 xlim_max = non_ideal_file(size_non_ideal(1),1);

5 xlim_min = non_ideal_file(1,1);

6

7 plot(ideal_file(:,1),ideal_file(:,2))

8 xlim([xlim_min xlim_max])

9 ylim([0 5])

10 title('Ideal ratio')

11 ylabel('Ratio')


13

14 dev_file = zeros(size_non_ideal);

15 dev_file(:,1) = non_ideal_file(:,1);

16 dev_file_procent(:,1) = non_ideal_file(:,1);

17 i = 1;

18 while le(i,size_non_ideal(1))

19 value_check = 0;

20 save_value = 0;

21 save_row = 1;

22 row = 1;


24 value_check = abs(ideal_file(row,1) - non_ideal_file(i,1));

25 if ge(row,2)



28 save_row = row;

29 end

30 else


32 end

33 row = row + 1;

34 end

35 row_angle = save_row;

36 io = 1;

37 while le(io,size_non_ideal(2)-1)

38 dev_file(i,1+io) = abs(ideal_file(row_angle,2)-non_ideal_file(i,1+io));

39 dev_file_procent(i,1+io) = dev_file(i,1+io)/ideal_file(row_angle,2);

40 io = io + 1;

41 end

42 i = i + 1;

43 end

44

45 dev_file_procent_max(:,1) = dev_file_procent(:,1);


47 mo = 1;


49 dev_file_procent_max(mo,2) = max(dev_file_procent(mo,2:size_procent(2)));

50 mo = mo + 1;

51 end

52

53 dev_file_procent_min(:,1) = dev_file_procent(:,1);


55 mo = 1;


57 dev_file_procent_min(mo,2) = min(dev_file_procent(mo,2:size_procent(2)));

58 mo = mo + 1;

59 end

WEBOGRAPHY

Plot settings for ratio deviation

1 %% plotting

2 i = 1;

3 figure()

4 while le(i,size_non_ideal(2)-1)

5 hold on

6 subplot(2,1,1)

7 plot(dev_file(:,1),dev_file(:,i+1))

8 ylim([-inf 0.5])


10 title('Ratio deviation')

11 ylabel('Ratio')


13 hold on

14 subplot(2,1,2)

15 plot(dev_file_procent(:,1),dev_file_procent(:,i+1))

16 ylim([0 0.5])


18 title('Ratio deviation %')

19 ylabel('Deviation[]')


21 hold on

22

23 i = i+1;

24 end

25 figure()

26 subplot(2,1,1)

27 plot(dev_file_procent_max(:,1),dev_file_procent_max(:,2))

28 ylim([0 1.5])


30 title('Ratio deviation procentual max')

31 ylabel('Deviation max []')


33 subplot(2,1,2)

34 plot(dev_file_procent_min(:,1),dev_file_procent_min(:,2))

35 ylim([0 0.1])


37 ylabel('Deviation min[]')


39 title('Ratio deviation procentual min')

B. Matlab code

Angle deviation calculation

1 %% Angle deviation calculation (MAX ERROR)

2 max_error_ratio(:,1) = dev_file_procent_max(:,1);

3 min_error_ratio(:,1) = dev_file_procent_max(:,1);

4 i = 1;

5

6 while le(i, size_non_ideal(1)) % create maximum error ratio dataset

7 value_check = 0;

8 save_value = 0;

9 ideal_row = 1;

10 row = 1;


12 value_check = abs(ideal_file(row,1) - dev_file_procent_max(i,1));

13 if ge(row,2)



16 ideal_row = row;

17 end

18 else


20 end

21 row = row + 1;

22 end

23 % Find steer row

24 value_check = 0;

25 save_value = 0;

26 row_steer = 1;

27 row = 1;


29 value_check = abs(ideal_file(row,1) - steer);

30 if ge(row,2)



33 row_steer = row;

34 end

35 else


37 end

38 row = row + 1;

39 end

40 % Maximum/minimum error ideal ratio + (ideal ratio * max percentage deviation)

41 max_error_ratio(i,2) = ideal_file(ideal_row,2) + ...

(ideal_file(ideal_row,2).*dev_file_procent_max(i,2));

42 min_error_ratio(i,2) = ideal_file(ideal_row,2) + ...

(ideal_file(ideal_row,2).*dev_file_procent_min(i,2));

43


45 max_iteration = row_steer;

46 else

47 max_iteration = size_ideal_file(1)-row_steer;

48 end

WEBOGRAPHY

Continued...

1 % find the corresponding angle

2 y2 = 0;

3 s2 = 1;

4 s = 1;

5 while le(s,max_iteration)


7 ambiguity = 0;

8 y1 = abs(ideal_file(s,2) - max_error_ratio(i,2));

9 else

10 ambiguity = 1;

11 y1 = abs(ideal_file(row_steer+s,2) - max_error_ratio(i,2));

12 end

13 if s == 1

14 y2 = y1;

15 end

16 if le(y1,y2)

17 y2 = y1;


19 s2 = row_steer + s;

20 else

21 s2 = s;

22 end

23 end

24 s = s + 1;

25 end

26 angle_deviation_maximum(i,1) = dev_file_procent_max(i,1);

27 angle_deviation_maximum(i,2) = abs(max_error_ratio(i,1)-ideal_file(s2,1));

28 p2 = 0;

29 u2 = 1;

30 u = 1;

31 while le(u,max_iteration)

32 if le(min_error_ratio(i,1),steer)

33 ambiguity = 0;

34 y1 = abs(ideal_file(u,2) -min_error_ratio(i,2));

35 else

36 ambiguity = 1;

37 y1 = abs(ideal_file(row_steer+u,2) - min_error_ratio(i,2));

38 end

39 if u == 1

40 p2 = y1;

41 end

42 if le(y1,p2)

43 p2 = y1;


45 u2 = row_steer + u;

46 else

47 u2 = u;

48 end

49 end

50 u = u + 1;

51 end

52 angle_deviation_minimum(i,1) = dev_file_procent_min(i,1);

53 angle_deviation_minimum(i,2) = abs(min_error_ratio(i,1)-ideal_file(u2,1));

54 if le(angle_deviation_minimum(i,2),0.19)

55 angle_deviation_minimum(i,2) = 0;

56 end

57 i = i + 1;

58 end

B. Matlab code

Plot

1 %% plot

2 figure()

3 plot(max_error_ratio(:,1),max_error_ratio(:,2))

4 ylim([0 5])


6 hold on

7 title('Ideal ratio*(1+max procentual deviation)')

8 ylabel('Ratio')


10 figure()

11 plot(angle_deviation_maximum(:,1),angle_deviation_maximum(:,2))

12 ylim([0 inf])


14 hold on

15 title('Max deviation in angles')

16 ylabel('Degrees[]')


18

19 figure()

20 plot(min_error_ratio(:,1),min_error_ratio(:,2))

21 ylim([0 5])


23 hold on

24 title('Ideal ratio*(1+min procentual deviation)')

25 ylabel('Ratio')


27 figure()

28 plot(angle_deviation_minimum(:,1),angle_deviation_minimum(:,2))

29 ylim([0 inf])


31 hold on

32 ylabel('Degrees[]')


34 title('Min deviation in angles')

Analysis of angular accuracy in the IFF Monopulse...

Documents

Transcript of Analysis of angular accuracy in the IFF Monopulse...