Department of Science and Technology
Institutionen för teknik och naturvetenskap
Linköping University
Linköpings universitet
Analysis of angular accuracy in
the IFF Monopulse receiver
Filip Bengtsson
David Sköld
LiU-ITN-TEK-A--18/015--SE
Analysis of angular accuracy in
the IFF Monopulse receiver
Examensarbete utfört i Elektroteknik
vid Tekniska högskolan vid
Linköpings universitet
Filip Bengtsson
David Sköld
Handledare Anna Lombardi
Examinator Adriana Serban
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Abstract
This master thesis investigates how certain components error margin may affect the accuracy of a IFF monopulse receiver. The IFF monopulse receiver measures the angle of arrival of the incident signal by comparing sum and difference signals created in the receiver. The components of interest are phase shifters and attenuators, where both can give individual and different errors depending on the antenna steering angle.
The project is conducted at Saab Aeronautics, based on a receiver in development for the Gripen E aircraft. A model of the receiver was made as close as possible for an ideal case using the program Matlab Simulink. The model is an ideal model based on component characteristics coded with function blocks, based on theory. Simulated measurements of the antenna pattern and the values of look-up tables for the existing receiver have been provided for comparison. Further, the ideal model is compared with the non-ideal model where the components have their errors enabled.
Although the simulation environment Simulink may not be ideal for simulations of this type of system, the results of the thesis generated results showing that the angular accuracy decreases with the increase of steering angle. The angular deviation can for some cases be seen as sufficiently small for the receiver to work properly in the ideal case.
Acknowledgments
We would like to thank our supervisor at Saab, Mikael Håkansson Borg, for his feedback and support throughout this thesis. Also, we would like to thank other colleagues at Saab for their 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 their encouragement.
David Sköld and Filip Bengtsson Norrköping, June 20, 2018
Contents iv
List of Figures vi
List of Tables viii
Abbreviations and acronyms ix
Symbols xi 1 Introduction 1 1.1 Background . . . 1 1.2 Motivation . . . 1 1.3 Aim . . . 2 1.4 Research questions . . . 2 1.5 Method . . . 2 1.6 Delimitations . . . 3
1.7 Outline of the thesis . . . 3
2 Radar technology 5 2.1 Antennas . . . 5
2.2 Secondary Surveillance Radar . . . 10
2.3 Signals . . . 10
2.4 Monopulse SSR . . . 14
2.5 Identification Friend or Foe . . . 15
2.6 IFF monopulse antenna . . . 16
2.7 Single pulse detection . . . 17
2.8 System design . . . 17 2.9 Errors . . . 21 3 Signal model 23 3.1 System design . . . 23 3.2 Signal . . . 24 4 Receiver model 35 4.1 Receiver system . . . 35
4.2 Transmit receive unit . . . 36
4.3 Low-noise amplifier . . . 39
4.4 Phase shifter . . . 39
4.5 Attenuator . . . 42
4.6 Random error generator . . . 44
4.7 Wilkinson power divider . . . 45
4.9 Diff/Sum ratio . . . 47
5 Data management 49 5.1 Simulink to Matlab file . . . 49
5.2 Matlab file to graph . . . 50
6 Simulation results and discussion 55 6.1 Scenario . . . 55
6.2 System . . . 56
6.3 Input signals and parameters . . . 56
6.4 Signal modulation . . . 56
6.5 Transmit receive unit . . . 57
6.6 Couplers . . . 58
6.7 Model validation . . . 59
6.8 Ideal antenna pattern . . . 59
6.9 Steer 0˝ . . . . 60 6.10 Steer 10˝ . . . . 67 6.11 Steer 20˝ . . . . 69 6.12 Steer 30˝ . . . . 70 6.13 Steer 40˝ . . . . 72 6.14 Steer 50˝ . . . . 74 6.15 Comparison . . . 75
7 Conclusion and future work 79 7.1 Conclusion . . . 79 7.2 Future work . . . 80 Bibliography 81 Webography 83 Appendices A Simulink blocks . . . . B Matlab code . . . .
2.1 (a) Radiation pattern polar diagram. (b) Radiation pattern rectangular diagram. . . 6
2.2 Radiation pattern example for broadside linear array with different elements. . . . 7
2.3 Incident wave with angle of arrival θ. . . . 8
2.4 Phased array antenna operation principle. . . 9
2.5 Radar operation principle. . . 10
2.6 Illustration of the interrogation signal. . . 11
2.7 Illustration of the reply signal. . . 12
2.8 Illustration of the sliding-window method. . . 13
2.9 The beam pattern of the monopulse SSR. . . 14
2.10 Top of the beam pattern of the monopulse SSR. . . 15
2.11 Interrogate and control beam patterns. . . 18
2.12 The 180˝hybrid coupler. . . . 19
3.1 Conceptual image of the system. . . 23
3.2 The entire system in Simulink. . . 24
3.3 The SBB system. . . 25
3.4 Inside the SBB system. . . 25
3.5 The propagation block. . . 26
3.6 The configuration of the propagation system. . . 26
3.7 The relative speed function block. . . 27
3.8 The Doppler function block. . . 28
3.9 The Friis function block. . . 29
3.10 The distance calculation function block. . . 29
3.11 The effective area function block. . . 30
3.12 Input_signal subsystem of the SBB. . . 31
3.13 Inside the Input_signal subsystem of the SBB. . . 31
3.14 The phase calculation block. . . 32
3.15 The phase calculation function block. . . 32
3.16 Phase shifter block in the SBB subsystem. . . 34
3.17 Phase shifter function in the SBB subsystem. . . 34
4.1 Conceptual block model of the receiver. . . 35
4.2 Receiver system block. . . 36
4.3 Inside receiver system subsystem. . . 36
4.4 TRU block. . . 36
4.5 Inside the TRU block. . . 37
4.6 The steer calculation function. . . 37
4.7 The RF module block. . . 38
4.8 The subsystems of the RF module block. . . 38
4.9 The LNA block. . . 39
4.10 Inside the LNA block. . . 39
4.12 Inside the phase shifter block. . . 40
4.13 The steer function block. . . 41
4.14 The state generator function block. . . 42
4.15 The attenuator block . . . 43
4.16 Inside the attenuator block. . . 43
4.17 The attenuator function . . . 43
4.18 The Random Matlab function block. . . 44
4.19 The WPD block. . . 45
4.20 The WPD function. . . 45
4.21 The rat-race block. . . 46
4.22 Rat-race function. . . 46
4.23 Ratio calculation block. . . 47
4.24 Inside the ratio calculation block. . . 47
5.1 The to_matfile function. . . 49
6.1 The received signal at one antenna element. . . 56
6.2 The phase shifted signal. . . 57
6.3 The attenuated signal. . . 58
6.4 The sum and difference signal. . . 58
6.5 Antenna pattern of the ideal system. . . 59
6.6 Sum diff ratio of ideal the system. . . 60
6.7 Sum diff signals with phase shifter error enabled. . . 61
6.8 Sum diff signals with attenuation error enabled. . . 61
6.9 Sum diff signals with attenuator and phase shifter error enabled. . . 62
6.10 Ratio with attenuator error for steer 0˝. . . . 63
6.11 Ratio with phase shifter error for steer 0˝. . . . 63
6.12 Ratio with attenuator error for steer 0˝. . . . 64
6.13 Ratio with attenuator and phase shifter error for steer 0˝. . . . 64
6.14 Ratio deviation for steer 0˝. . . . 65
6.15 Maximum, minimum and ideal ratio for steer 0˝. . . . 66
6.16 Max and min angle deviation for steer 0˝. . . . 66
6.17 Sum and difference with attenuator and phase shifter error enabled for steer 10˝. . 67
6.18 Ratio with attenuator and phase shifter error for steer 10˝. . . . 68
6.19 Max and min angular deviation with both errors enabled for steer 10˝. . . . 68
6.20 Sum and difference with attenuator and phase shifter error enabled for steer 20˝. . 69
6.21 Ratio with attenuator and phase shifter error for steer 20˝. . . . 69
6.22 Max and min angular deviation with both errors enabled for steer 20˝. . . . 70
6.23 Sum and difference pattern with attenuator and phase shifter error for 30˝steer. . 71
6.24 Ratio with both attenuator and phase shifter error for 30˝steer. . . . 71
6.25 Max and min angular deviation with both errors enabled for steer 30˝. . . . 72
6.26 Sum difference pattern with attenuator and phase shifter error for 40˝steer. . . . . 72
6.27 Ratio with attenuator and phase shifter for 40˝steer. . . . 73
6.28 Maximum and minimum angular deviation with both errors enabled for steer 40˝. 73 6.29 Sum difference pattern with attenuator and phase shifter error for 50˝steer. . . . . 74
6.30 Ratio with attenuator and phase shifter for 50˝steer. . . . 74
6.31 Max and min angular deviation with both errors enabled for steer 50˝. . . . 75
6.32 Angular deviation for all the different steering angles with attenuator error enabled. 76 6.33 Angular deviation for all the different steering angles with phase shifter error en-abled. . . 76
6.34 Ideal ratio for different steer. . . 77
2.1 Interrogation modes for SSR. . . 11 4.1 Maximum phase variance. . . 40
Abbreviations and acronyms
Abbreviation Description
IFF Identification Friend or Foe SSR Secondary Surveillance Radar AoA Angle-of-Arrival
ESA Electrically Scanned System AESA Active Electrically Scanned System ATC Air Traffic Control
MSSR Monopulse Secondary Surveillance Radar SLS Side Lobe Suppression
SPI Special Position Pulse
FRUIT False Replies Unsynchronized In Time LNA Low-Noise Amplifier
NF Noise Figure
ISLS Interrogation Side Lobe Suppression WPD Wilkinson Power Divider
TRU Transmit Receive Unit SBB Signal Black Box
Symbols
Notation Description
D Directivity
U Ratio
Ptot Total power transmitted
Ae Antenna aperture
λ Wavelength
N Number of antenna elements ∆ϕ Phase difference
n Number of the antenna element
x Space difference between antenna elements AF Array factor
wi Weight factor
k Wavenumber
θ Angle deviation vp Speed of the signal
c Speed of light R Distance from target ttravel Travel time for wave
Pr Power received
Pt Power transmitted
Gr Gain of receiving antenna
Gt Gain of transmitting antenna
Ar Antenna aperture of receiving antenna
At Antenna aperture of transmitting antenna
σ Antenna cross-section d Distance between antennas
fd Doppler frequency fs Signal frequency V0 Velocity of observer Vw Velocity of signal Vr Radial velocity L Losses S Scattering parameter ∆ Difference signal Σ Sum signal Fi Noise factor Gi Gain Si Signal
Chapter One
Introduction
This master thesis investigates how certain components error margin may affect the accuracy of the new IFF monopulse receiver for Gripen E. The project was done as a Master thesis at the Electronic Design Engineering program at Linköpings University provided by Saab Aeronautics in Linköping, Sweden.
1.1
Background
Saab is currently developing the new JAS 39E Gripen. This new aircraft will use a new type of 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 commercial aerospace 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 area who 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. To identify an aircraft, a radar could be used and the aircraft could be contacted through radio to request identification and purpose. However, this solution requires a lot of manpower and has been replaced by a Secondary Surveillance Radar (SSR) which handles the described problem. 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 also determine where the aircraft is sending its reply from, effectively producing a more or less reliable 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 accuracy of the system. The project is conducted at Saab Aeronautics in Linköping, Sweden.
1.3
Aim
The goal of this work is to analyze and calculate the angular accuracy and uncertainty of the IFF 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 control lobe. In an Electrically Scanned Array (ESA) the lobe characteristics change depending on the desired steering angle.
The scope of the work is to identify parameters that have an impact on the accuracy of the 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 value differs 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 master thesis, 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 will be 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 the understanding of microwave theory, the secondary surveillance radar and how to model it using 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 and which parameters could be changed for testing. The model will be presented in Chapters 3, 4 and 5. All the different components and contributing factors will be identified to make sure the model which is created in a later stage will be as similar to the real system as possible. In this part it is important to consider how each and every part of the system affects the signal for the next stage to be as successful as possible.
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 pospos-sible. The model will be simulated with various 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 accuracy of 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 of primary surveillance systems will be explained briefly to highlight the differences between this 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, a nominal model of the system has been implemented which does not take into consideration some factors which can affect the performance of the system. For instance, the model has no noise implemented. The low noise amplifiers have no gain errors implemented, instead the attenuators have errors in gain, and the attenuator is variable making its impact more interesting in the model.
Some of the theory explained is not applicable in the final model since the use of isotropic antenna elements. However, all the theory discussed has been implemented at some stage of the system and is kept by the authors to be used for future work. This is not included in this thesis.
1.7
Outline of the thesis
Chapter 2 explains theory of the radar technology and the signals in the system. This includes the 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 also evaluate the result as it is presented.
Chapter Two
Radar technology
This Section will explain the theory behind radar technology. At first, antennas antenna array and antenna parameters are introduced. Then, the primary radar operation principle is explained. After this, the Secondary Surveillance Radar (SSR), monopulse SSR and Identifi-cation Friend or Foe (IFF) technology are introduced. Also, signals, radar equation, Doppler effect 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 is not a new one, the technology has been used since at least the beginning of the 19thcentury and later improved and developed to be applicable to different situations. In most cases, radar systems use modulated waveforms and directive antennas to transmit electromagnetic energy into a specific volume in space to search for targets. Objects within a search volume will reflect portions of the incident energy in the direction of the radar. These echoes are then processed by the radar receiver to extract target information such as range, velocity, angular position, 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 categories based on the radar characteristics, such as the frequency band, antenna type, and wave-forms. Radar systems using continuous waveforms, modulated or otherwise, are classified as 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 the functionality of the specific radar. This includes: weather, acquisition and search, tracking, track-while-scan, fire control, early warning, over-the-horizon, terrain following, and terrain avoidance radars [16].
There are different types of radar available today for applicable in aeronautics, the two main 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 antennas however can be operated in two modes: transmitting and receiving. Antennas have the useful property of reciprocity which states that an antenna transmits and receives signals in the same radiation pattern.
When transmitting, an antenna is fed with a signal which radiates electromagnetic waves when 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
will radiate from the antenna according to a radiation pattern. An arbitrary radiation pattern is 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 field and 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 with normalized dB scale. Hence, 0 dB corresponds to a normalized value of 1, e.g., the power is maximum 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 is calculated 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= PU
tot
4π
(2.1)
The antenna aperture, also called effective area and receiving cross-section, is a measure of how effectively an antenna can receive power. In the case of an isotropic antenna it can be expressed as in (2.2), where Ae is antenna aperture and λ is wavelength. Antenna aperture
can be used to calculate the antenna gain and is used in the Friis transmission equation which will be explained in Section 2.3.1 [13].
Ae= λ 2
2.1. Antennas
Antenna arrays
Antenna arrays can be used to create different antenna patterns, achieve higher gain and directivity. The antenna array used in this project is a broadside linear array with N elements and distance d between the elements. A broadside linear array is a one dimensional linear array with the main lobe directed perpendicular to the antenna plane. An illustration of a broadside linear array can be seen in Figure 2.4. The number of elements in the array affects the radiation pattern and with more elements comes a narrower beamwidth for the main lobe, 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 of antenna elements in the array. As can be observed, the beamwidth of the main lobe reduces with the increase antenna elements and the damping of the sidelobes increases. Also, the number of antenna elements affect the gain of the main lobe. It is therefore common in complex military systems to use a lot of antenna elements to achieve a high gain and narrow beam. This reduces interferences and increases the range of the antenna array. The power of the incident signal is equally divided between the antenna elements, e.g., if there are two antenna elements, they receive half of the power, each.
When using an antenna array, the distance between the antenna elements creates both phase delays (∆ϕ) and amplitude differences in the signals received by antenna elements in the 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. For example, in Figure 2.3, there is a phase delay in the signal received by Antenna 2 due to the extra distance, ∆x, it needs to travel.
If the antennas are identical, isotropic antennas, then the ideal phase delay between Antenna 1 and Antenna 2 in Figure 2.3 is given by (2.3).
φ(t) =k∆x= 2π
λ x sin θ
array
ÝÝÝÑ= 2π
λ nx sin θ (2.3)
Where k is the propagation constant or wave factor, k= 2π
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 the array is by assuming that the total field is equal with the field of one single antenna element positioned in the origin multiplied by the array factor, AF.
The array factor is an important factor for optimizing the functionality of antenna arrays. It is an equation of the positions of the antenna elements and a weight factor. The array factor, AF, can be calculated using (2.4).
AF=ÿwie´jkri (2.4)
In (2.4) the variable k is a wave vector which describes the phase variation of a plane wave in x, 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). The
weight factor can be interpreted as a complex amplitude which can be represented with phase shifters 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 array is an antenna array which can be electronically controlled to steer the radiation in different directions without rotating the antenna array. This is widely used within radar systems and is achieved by introducing phase shifters to every antenna element. The phase shifters are controlled by a computer system which calculates the required phase shift to steer the radiation 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 antenna elements, just as the phase delay due to the distance between antenna elements discussed in the previous section. E.g., for Figure 2.4, if the desired angle of radiation is θ = 20°, the wavelength is 20 cm and the distance between elements is half the wavelength. Then the antenna element at the top must radiate without phase delay; then the phase delay which is applied for certain beam steering is calculated using (2.3). ∆φ= 2π0.2¨ 1 ¨ 0.1 ¨ sin 20° yields the
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 phase delay is incremented for each antenna element further away from the top element, this is done by incrementing n in (2.3).
What separates AESA from other phased arrays is that it has a transmit/receive module for each antenna element instead of just one. This allows the AESA to radiate multiple beams at 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 primary radar. To determine the range to an object, a strong electromagnetic signal in the form of a pulse is transmitted by the antenna. The reflected signal is then received by the radar device and the range can be calculated from the time between the transmission of the signal and the time at which the reflected signal was received. This time is twice the time it took for the signal to travel to the object, meaning that if the signals speed is known, then the distance to the object is also known. A simple radar illustration is shown in Figure 2.5. Since the speed of the signal in air is the same as the speed of light in vacuum, the distance to the object can be calculated with (2.6).
Air : vp=c Ñ 2 ¨ R=ttravel¨ c Ñ R=
ttravel
2 c (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 the signal 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 distance to the object the signal reflected of is given by the radar equation:
R= 4
d
PtG2λ2σ
Figure 2.5: Radar operation principle [8].
In (2.7) G is the gain of the transmitting antenna, Ptis the power being transmitted, R is the
distance between the radar and the object, σ is the antenna cross-section and Pr is the power
received.
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 some data. Instead of being reflected by the aircraft, the signal is received by the aircraft via a transponder. The transponder then replies to the SSR in a different frequency. Therefore the energy required is less, than of the primary radar since the SSR is not dependent on a reflected response which needs to be sufficiently strong to identify. The SSR relies on targets with a radar transponder equipped on the aircraft.
The transmitter to receiver system is called an "interrogator". The interrogator requests information from the aircraft such as identity and height. The aircraft transponder then answers by sending the requested information, simply called a "reply". This is one of the main advantages of a SSR compared to the primary radar, the communication between the aircrafts 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 limits the 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 results in (2.8) where haand htis the height of the antenna and the aircraft [6].
R=1.23(h12
a +h
1 2
t) (2.8)
In the equation presented above, a "four-thirds earth" is assumed. This is a common assump-tion in radar calculaassump-tions were the earth radius Reis replaced by the factor kRewith k= 43 to
compensate 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 having two different frequencies some of the problems experienced by the primary radar can be avoided, e.g., the reflected interrogator signal will not be confused with a response from the aircraft.
2.3. Signals
Interrogation can be done in different modes depending on what information is required from the aircraft and who is using the SSR system. The interrogation signal consists of 3 pulses 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 S
3/A Identity Military/Civil 8
B Undefined Civil 17
C Altitude Civil 21
D Undefined Civil 25
S 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. Other modes 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 the signal 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 responding several times causing errors in the identification process. This is known as interrogator side lobe suppression (SLS). Combining these three pulses, the form of the interrogator signal can be 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. The reply signal is a bit more complex since it contains more information, it needs a total of 16 pulses 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 remains unused and a Special Position Pulse (SPI), which is only used when the ATC requests it for further identification.
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 by the framing pulses F1and 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 F1to F2: 20.3 µs ˘0.1 µs
• Delay from pulse F2to 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 does not use the D1pulse which leaves it with 2048 codes. The military mode S uses 24 bits, which
allows 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 aneroid barometer. These 2048 permutations are sufficient to indicate the height in 100 ft increment in 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 the reflected signal. Instead the SSR system uses a method called the "sliding-window" which determines the direction of the airplane by monitoring when communication starts and stops with the aircraft. Replies from the aircraft are received by the antenna when the leading edge of the rotating antenna points towards the direction of the aircraft and the antenna stops receiving when the trailing edge of the antenna passes it. The average from these two positions reveals the direction of the antenna. The sliding-window method is illustrated in Figure 2.8 [6].
A problem that is present in this system is due to continuous communication. Since a large amount of replies are being requested from the transponder it presents a problem for the transponder, which can handle a finite amount of signals during a period of time. The ground station also receives replies which have been requested by other SSR systems, these replies are called false replies unsynchronized in time (FRUIT). Fruit signals can affect the accuracy of the direction measurements since the signals can overlap, which confuses the equipment and can create phantom aircrafts [6].
A more advanced type of SSR is the Monopulse SSR which will be discussed in Section 2.4.
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 free space transmission. The equation depends on the transmitted power, the distance between the transmitting antenna and the receiving antenna, the wavelength and the gain of the an-tennas [13].
Pr =Pt GtGrλ 2
(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 the observer the frequency is higher than it would have been if the source was moving away from the observer. The relation between speed and frequency can be seen as in the equation for the Doppler frequency in (2.10).
fd= fs¨(1 ˘ Vo
Vw) (2.10)
In (2.10), fdis the Doppler frequency, fsis the transmitted signal frequency, Vois the observer
velocity relative to the source and Vwis the velocity of the signal, which is the speed of light
in vacuum. This is the case when a stationary source is used and the ˘ part would be positive if moving towards the source and negative if moving away from the source. If instead the observer was stationary the equation would change to that in (2.11). Where Vsis the velocity
of 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 both the source and observer are moving. This is given in (2.12).
fd= fs¨(1 ˘ Vo c 1 ˘Vs c ) = fs¨c ˘ Vo c ˘ Vs (2.12)
The ˘ in the numerator is positive when the observer is moving towards the source and negative when moving away from the source. The ˘ in the denominator is positive when moving away from the source and negative when moving towards the source. This results in the frequency which is observed by the observer is greater when observer and source are moving towards each other. The velocity of the observer in (2.10) and (2.11) are relative to the source and the velocity of the source is relative to the observer. This implies that the radial velocity 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 can be defined as the vector Vt= [VxVyVz]where Vtis the total velocity and the three elements in
the vector are the velocities in each dimension. The radial velocity is then defined as in (2.13). Vr=
b V2
x +Vy2+Vz2 (2.13)
Using this, radars can extract the targets radial velocity using the difference in frequency between the transmitted signal and the received signal. This enables the radar systems to more 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 the signal instead of the sliding-window method. This is made possible by introducing a second beam pattern called the difference beam. The difference beam has a lower gain than the sum beam at boresight and a higher gain at the sidelobes of the sum beam. The beam pattern is shown in Figure 2.9. A more specified figure of the top of the graph in Figure 2.9 is shown in Figure 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 of the monopulse SSR. Similar to interferometry technique, the system can determine the angle of arrival (AoA) by comparing the received signal at the sum and difference channels. An
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 which produces 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 original high-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 is zero and the signal on the difference beam is greatly dampened. In an ideal case this would eliminate 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 to indicate 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 processprocess-ing method uses that the ambiguity is located at the beam center, the phase difference between the sum and difference channels must be analyzed to reveal at which side of the ambiguity point the signal 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 beam form. There are two different monopulse processing methods: the amplitude processing and phase processing method. The amplitude processing method compares the amplitude of the sum and difference channel to find the angle of arrival and the phase processing method uses the phase information.
2.5
Identification Friend or Foe
The Identification Friend or Foe (IFF) system is a military and civil system; mainly dedicated to identification. SSR is based on the military IFF technology originally developed during World War II. The system is composed, like SSR, of the two active devices: an interrogating device, interrogator, and a replying device, transponder. The interrogating device sends an interrogation using a carrier frequency in the direction of the object equipped with a transponder. The replying device receives and decodes the interrogation, then, a coded reply is sent on a different carrier frequency. When received by the interrogation device, the reply signal is processed and decoded. The result is presented in a suitable way, for example visually or in the form of digital data. To decode the encrypted data, both systems must use
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 the encryption is the same, the replying object is recognized as a friend. If not, it is treated as an unidentified object or foe [4].
The generation of undesirable replies by a properly working transponder can occur in the 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 data transmission reliability. The problems with these transmission signals are sidelobe elevation covering characteristics, reflection from field objects known as multipath, replies generated by transponders for other interrogators’ requests.
The secondary search radar’s issue is an important part of radio location technology. In practice, the simplest antenna solutions could not fulfill the severe requirements concerning characteristics of radiation pattern in IFF systems. The solution is the suppression of the sidelobes 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-direcaddi-tional 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 monopulse pattern 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 those interrogators must be minimal, especially in hand-held applications. In mobile systems it is important to assure synchronization of antenna movement with the movement of devices installed on vehicles like anti-aircraft guns or missile launchers. This synchronization can be implemented in different ways, depending on the complexity of the system [10].
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 sinusinu-soid. Under the assumption of completely known signal parameters, a returned pulse from a target has known 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 false alarm. 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 received voltage signal envelope exceeds a pre-set threshold value. In this kind of detection, envelope detectors 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, the received 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 for the echo signals in close range or of objects from a long distance. If there is a large power difference it will be difficult to process the digital data. It can be described with (2.16), where D is the dynamic range and Pris the power.
D= Prmax
Prmin
(2.16) The dynamic range is highly sensitive to the radar cross-section σ and the range R, as the other parameters in (2.15) do not vary. Hence, the received power and the dynamic range D can be rewritten as (2.17) and (2.18) [20].
Pr = PtλG 2σ (4π)3R4 =k σ R4 (2.17) D= Prmax Prmin = kσmax/R 4 min kσmin/R4max = σmaxR 4 max σminR4min (2.18)
2.8.2
Horizontal characteristics
The horizontal characteristics refer to the accuracy of the aircraft bearing measurement, to identify separate aircrafts which are close to each other and minimize the interference of the aircraft replies outside the main beam. The antenna has two different beams in its beam pattern, one interrogate beam and one control beam [6].
Interrogate beam
An interrogate beam, also called a main beam, has a radiation pattern for the horizontal antenna. The beam has a high-gain and narrow main lobe with low sidelobes. The sidelobes should be at least 24 dB below the main lobe. If the interrogation beam is lower than the control beam at the sidelobes, attenuation is applied on the variable attenuator in the receiver which will lower the gain of the interrogation beam. The interrogate beam transmits the pulses P1 and P3. If the interrogate beam is too broad it will be more sensitive to ground reflections [6].
Control beam
The control signal is the second antenna beam that is broader but has a lower peak gain around 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 signals from the interrogate beam sidelobes. Using the interrogate beam distribution the control signal can be formed while the center element in the array is in anti-phase. The signal of the control beam transmit the pulse P2. The transponder compares the pulse amplitudes of P1 and P2 to determine if the signal is received from the antenna sidelobes or from the main beam. Depending on whether if P1 is greater than P2 by more than 9 dB, the transponder must 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 the amplitude 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 the sum 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 high the accuracy will be increased. The smaller peaks will not affect the monopulse performance and therefore it is good if they have a low amplitude so it wont be any extraneous signals [6].
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 be broaden with elevation angle. This is because the radar assumes that bearing measurements are made in the horizontal plane even when the incident signal is arriving from a significant elevation angle. This broadening effect is of importance for the monopulse direction finding and for elevation angles above 20°. The error can be corrected by dividing the measured angle by the cosine of the elevation angle with slant range and the Mode C height. Either side of the boresight is of the monopulse direction is measured and averaged which leads to a 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 in practice. The control beam may in some cases not cover the sidelobes of the interrogate beam which 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 Figure 2.12. Four ports are available and they can be assigned as input and output ports. The hybrid uses transmission line of quarter wave length λ/4. The port is assumed to work on loads of 50 Ω impedance, e.g., following elements are of 50 Ω impedance. In (2.19), the S-parameters matrix of the hybrid is shown [14].
Figure 2.12: The 180° hybrid coupler [14].
[S] = ?´j 2 0 1 1 0 1 0 0 ´1 1 0 0 1 0 ´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 and divider of one signal. Combiner: With reference to Figure 2.12, it can be seen that if signals are applied at ports 2 and 3, they will reach port 1 in phase hence, they add, Σ. In opposite,
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 4 will 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 into a 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, the two wave components on the ring will arrive in phase at port 2 and at port 3, with a relative phase difference of 180° between these two ports. The two wave components will be 180° out of phase at port 1. This case can also be decomposed into a superposition of the two simpler circuits 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 the interrogation 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. For an 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= 2π
λ , d is the distance between antenna elements and θ
is the angle deviation from the boresight. The j factor determines which side of the boresight the signal is arriving on and when crossing the boresight it changes from j to ´j representing a phase difference of π. To determine which side of the lobe the signal is coming from an one-bit ambiguity comparison is made in the system. In the interval where the sum has a higher gain the ratio will be lower than 1. At two points, on each side of the boresight, the ratio will be one as the sum and difference signals crossing each other, i.e. has the same gain. For larger angles the difference gain will be higher than the sum gain and the ratio will therefore be larger than 1. This can be seen in Figure 2.10, which shows the top of the sum and difference pattern. The sum and difference beam could have the same gain for even higher angles as Punch-Through can occur. Although this can occur the angles are most likely not of importance [3].
The radiation pattern is different for each elevation angle and also changes when beam steering is applied. To apply beam steering, a look-up table is used to find the phase delay needed in the phase shifters. The angles are not likely to be exactly on point, but are of good approximation. 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 impossible to gain ideal characteristics, therefore look-up tables containing measured data is used to reveal a more realistic result.
2.9. Errors
2.8.6
Interrogation side lobe suppression
Interrogation side lobe suppression (ISLS) is similar to the SLS. But for the interrogator it is implemented using attenuation. Attenuation is applied to the sum beam to lower the amplitude. The ratio of the un-dampened difference beam and the dampened sum beam is 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 in Section 2.8.2.
2.9
Errors
The angle error is created from the difference signal by calculating a complex ratio. This is done for the left/right difference beams, as well as for the up/down difference beams. In this project, only one difference beam is used. An explanation of how real and imaginary parts are used with radar can be found in the description of Pulse Doppler. The outcome of the calibration process is to rotate the complex antenna angle error vector onto the real axis to reduce signal processing losses. The angle error is used to make an adjustment to position the 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 the same error [6].
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 and Simulink. 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. The gray blocks in the figures are subsystem blocks which are used to divide a larger system into smaller subsystems and the white blocks with Matlab symbols are Matlab functions. The Matlab 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: the signal black box block, the receiver system block and the output signal. Figure 3.2 shows the entire system in Simulink. There is also a function outside of the Simulink model to calculate 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 and the Enable_error_phaseshifter are data memory block. These blocks are used in the System blocks seen in the Figure 3.2. The on-off switches are connected to the constant blocks and are used to enable or disable the attenuator and phase shifter errors.
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 the Doppler effect, the Friis transmission, the received phase at each antenna element and the effective area of the antenna elements is needed. These functions are considered to be the most 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 inputs into the subsystem. The inputs of the SBB subsystem are seen in Figure 3.3. From this block eight 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.
3.2. Signal
Figure 3.3: The SBB system.
The system block, which is shown in Figure 3.3, consists of several subsystems shown in Figure 3.4. There is a propagation block which calculates what happens to the signal before it reaches the antenna elements. The Input_signal block creates the specified sine signals. These blocks will produce eight signals at each antenna element. The Phase_calc and Phase_shifting blocks calculates and applies a phase difference between the antenna elements. The subsystems of the SBB are further explained in Sections 3.2.1 to 3.2.4. The rest of 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 are the same as for the entire system. The output signals are used in the Input_signal block and the Phase_Calc block. The propagation subsystem is configured as in Figure 3.6.
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 relative to each other. This is needed in the calculations of the Doppler frequency. Since the Doppler frequency is calculated differently depending on if the objects are moving towards or away from each other, as described in Section 2.3.2, the relative_speed function also works as a state machine. It therefore tells the Doppler function what equation to use according to these states:
• 1. The transmitter is moving away from the receiver, the receiver is moving towards the source.
• 2. The transmitter and receiver are moving towards each other.
• 3. The transmitter is moving towards the receiver, the receiver is moving away from the source.
• 4. The transmitter and receiver is moving away from each other.
The relative speed is calculated using the Matlab function radialspeed shown in Figure 3.7 with the Matlab code shown in Code block 3.1, which returns the radial speed of an
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 separate variables. Therefore the relative_speed function is used to calculate the speed vector of one object relative to a stationary second object. This is done as in (3.1), where the function radialspeedis used. The function, which is part of the Phased Array Toolbox, calculates the relative radial speed between two objects. In (3.1) the P variables are the position of the receiver and transmitter and the V variables are the velocity vectors of the transmitter and receiver. The second of the velocity vectors is set to zero to calculate the radial velocity for both the transmitter and receiver relative to each other when the other part is stationary. The Matlab 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 Doppler frequency which is used in the Friis function shown in Figure 3.9, with the corresponding code in Code block 3.3. The Friis function calculates the received power for the different
antenna elements, which were described in Section 2.3.1. The Friis function also requires the distance from the transmitter to the receiver, or more accurately it requires the distance from the transmitter to each antenna element. This is calculated using the Distance_calc function shown in Figure 3.10. The code used in the Distance_calc function is presented in Code block 3.4. This function identifies the position of each antenna element depending on the position of the receiver, interpreted as the center of the array, and the distance between antenna elements. For simplicity, the receiving antenna array is fixed with the boresight parallel to the x-axis which means that the position of each antenna element only varies from the position of the receiver on the y-axis. An example of this, is the case of two antenna elements 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 3 c = physconst('LightSpeed'); 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
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 3 c = physconst('LightSpeed'); 4 lambda = c/f; 5 6 A1 = (Pt/4)*((At*Ar)/((d_A1^2)*lambda^2)); 7 A2 = (Pt/4)*((At*Ar)/((d_A2^2)*lambda^2)); 8 A3 = (Pt/4)*((At*Ar)/((d_A3^2)*lambda^2)); 9 A4 = (Pt/4)*((At*Ar)/((d_A4^2)*lambda^2)); 10 A5 = (Pt/4)*((At*Ar)/((d_A5^2)*lambda^2)); 11 A6 = (Pt/4)*((At*Ar)/((d_A6^2)*lambda^2)); 12 A7 = (Pt/4)*((At*Ar)/((d_A7^2)*lambda^2)); 13 A8 = (Pt/4)*((At*Ar)/((d_A8^2)*lambda^2)); 14 15 end
Code block 3.3: Friis equation Matlab code.
