designing an rwr

Document identity Saab REPORT Prepared by (dept, name) Classification acc. to FHL Issue date Issue

ATVYS, Robert ter Vehn COMPANY UNCLASSIFIED 2009-01-15 PA4 Approved by (dept, name) Classification acc. to SekrL No of appendices Page

ÖPPEN/UNCLASSIFIED 1 (85)

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ABSTRACT

A Tracking Method for Pulse Measurements in a Dense Radar Signal Environment

Electronic warfare is vital on today’s battlefield. Technology improvements continuously lead to more advanced radars and weapons and in environments with many radio frequency (RF) emitters the chance of pulses overlapping in time is rather high.

For a fighter aircraft to survive it is necessary to detect incoming RF signals. Fighter aircrafts use radar warning receivers (RWR) with commonly four antennas to be able to detect, categorize and identify potential threats such as hostile surveillance radars and radar guided weapons. RWRs usually use Detector Log Video Amplifiers (DLVA) to measure the power of incoming RF signals but due to the function of DLVAs it is difficult to differentiate between overlapping pulses.

This master’s thesis presents two possible solutions that interpret DLVA signals from four antennas and output a digital pulse descriptor word (PDW) for, at best, each pulse. The first solution uses a pulse stack and comparisons to keep track of numerous incoming pulses but encounter problems when pulses start or end simultaneously.

The second solution tracks a maximum of four overlapping pulses and is less error prone. Simulations show that the second solution constitutes a very good candidate for use in future RWR systems although frequency measurements remain to be implemented.




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REFERAT

En metod för att mäta pulser i en tät radarsignalmiljö

Elektronisk krigföring är kritiskt på dagens slagfält. Teknologiska framsteg leder kontinuerligt till mer avancerad radarutrustning och i en miljö med många emittrar som emitterar radiofrekvenssignaler är risken för att pulser överlappar i tid ganska stor.

För att ett stridsflygplan ska överleva är det nödvändigt att upptäcka inkommande radiofrekvenssignaler. Stridsflygplan använder radarvarnare med vanligtvis fyra antenner för att upptäcka, kategorisera och identifiera potentiella hot som till exempel övervakningsradar och radarmålsökande robotar. Radarvarnare använder vanligtvis en komponent kallad DLVA (Detector Log Video Amplifier) för att mäta effekten av inkommande radiofrekvenssignaler men på grund av DLVA-komponentens funktion är det svårt att särskilja mellan överlappande pulser.

Detta examensarbete presenterar två möjliga lösningar som tolkar signalerna från fyra DLVA-komponenter och genererar en digital pulsdeskriptor (PDW) för, i bästa fall, varje puls. Den första lösningen använder sig av en pulsstack och jämförelser för att spåra åtskilliga inkommande pulser men stöter på problem när pulser startar eller slutar samtidigt.

Den andra lösningen spårar maximalt fyra överlappande pulser och är mindre benägen att råka ut för fel. Simuleringar visar att den andra lösningen utgör en mycket bra kandidat för användning i framtida radarvarnare trots att frekvensmätningar återstår att implementera.




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PREFACE

This report is the written record of a master’s thesis project at the KTH School of Information and Communications Technology (ICT) as part of the fulfillment of the requirements for a Master’s Degree in Computer Science and Engineering at the Royal Institute of Technology (KTH), Sweden. The project was carried out during the winter semester of 2008/2009 at Saab Avitronics in Järfälla.

I would like to thank my supervisors at Saab; Sven Tegsveden, for his tremendous support and guidance, and Fredrik Hoffman, for his assistance and initiative which led to this master’s thesis. I also want to express my gratitude to all the coworkers at Saab who contributed to this thesis by answering my questions even when time was short.

Further, I would like to express my appreciation to Associate Professor Svante Signell and Professor Ben Slimane at the Department of Communication Systems (CoS) at ICT for the opportunity to carry out this project.

Last, but not least, I wish to thank Ellen Venderlöf for her encouragement and understanding and our daughter Tilda for being who she is.

Stockholm, December 2008 Robert ter Vehn




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CONTENTS

1 Introduction.............................................................................................. 6 1.1 Background................................................................................................... 6 1.2 The Problem in General ................................................................................ 7 1.3 Previous Work .............................................................................................. 7 1.4 Motivation..................................................................................................... 8 1.5 Outline of Thesis........................................................................................... 8

2 Problem Definition................................................................................... 9 2.1 Purpose and Goals ........................................................................................ 9 2.2 Conditions..................................................................................................... 9 2.3 Scope............................................................................................................. 9

3 Task Break Down................................................................................... 11

4 Background Study ................................................................................. 12 4.1 Radars and Radar Warning Receivers ........................................................ 12

4.1.1 Radars ............................................................................................... 12 4.1.2 Examples of Radar Types................................................................. 13 4.1.3 Radar Warning Receivers................................................................. 14

4.2 Detector Log Video Amplifiers .................................................................. 15 4.2.1 Logarithmic Video Amplifiers ......................................................... 15 4.2.2 Detector Log Video Amplifiers ........................................................ 16 4.2.3 Pulse-on-Pulse DLVAs .................................................................... 19

4.3 Instantaneous Frequency Measurement Receivers ..................................... 20 4.4 Pulse Parameters ......................................................................................... 22

4.4.1 Pulse Amplitude ............................................................................... 23 4.4.2 Amplitude Triggered Thresholds...................................................... 24 4.4.3 Pulse Width ...................................................................................... 24 4.4.4 Time of Arrival................................................................................. 25 4.4.5 Angle of Arrival ............................................................................... 25 4.4.6 Frequency ......................................................................................... 26

5 Research Approach................................................................................ 27 5.1 Tools ........................................................................................................... 27

5.1.1 Matlab............................................................................................... 27 5.1.2 Laboratory Equipment...................................................................... 27

5.2 Simulations ................................................................................................. 27 5.3 Experiments ................................................................................................ 28

6 Implementation ...................................................................................... 29 6.1 Modelling a DLVA..................................................................................... 29




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6.1.1 Base Curve........................................................................................ 29 6.1.2 Noise................................................................................................. 30 6.1.3 Leading- and Trailing Edges ............................................................ 31 6.1.4 Result ................................................................................................ 31

6.2 Antennas ..................................................................................................... 32 6.3 Direction Finding........................................................................................ 33 6.4 Frequency Measurements ........................................................................... 34 6.5 Creating Scenarios ...................................................................................... 34 6.6 Sample Rate ................................................................................................ 34

7 Proposed Solutions................................................................................. 36 7.1 Edge Detection............................................................................................ 36 7.2 Solution 1: Overlapping Pulses................................................................... 39 7.3 Solution 2: Simultaneous and Overlapping Pulses ..................................... 41

8 Simulations ............................................................................................. 47 8.1 Test Scenarios ............................................................................................. 47

8.1.1 Scenario 1: A Single Pulse ............................................................... 47 8.1.2 Scenario 2: Two Overlapping Pulses................................................ 49 8.1.3 Scenario 3: Three Overlapping Pulses.............................................. 50 8.1.4 Scenario 4a: Simultaneous Pulses .................................................... 52 8.1.5 Scenario 4b: Simultaneous Pulses .................................................... 53

8.2 Test Results................................................................................................. 55 8.2.1 Scenario 1 ......................................................................................... 55 8.2.2 Scenario 2 ......................................................................................... 56 8.2.3 Scenario 3 ......................................................................................... 57 8.2.4 Scenario 4 ......................................................................................... 57

9 Discussion................................................................................................ 59 9.1 Evaluation ................................................................................................... 59

9.1.1 Solution 1.......................................................................................... 59 9.1.2 Solution 2.......................................................................................... 60 9.1.3 Comparison....................................................................................... 60

9.2 Frequency Measurements ........................................................................... 61 9.3 Conclusions................................................................................................. 62 9.4 Further Work .............................................................................................. 62

Appendices .................................................................................................... 64 Appendix A Abbreviations and Acronyms.............................................. 64 Appendix B List of Figures ..................................................................... 65 Appendix C List of Tables....................................................................... 67 Appendix D Detailed Results .................................................................. 68 Appendix E A Specific Test Case ........................................................... 82

Bibliography.................................................................................................. 83




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1 INTRODUCTION

1.1 Background

Since the beginning of the 20th century Electronic Warfare has grown to become an important component of warfare [1]. For a fighter aircraft this poses a serious threat. Radars are used to detect the aircraft and “smart” radar guided weapons have been developed and are continuously improved. To be able to avoid these hazards counter-measures are developed in parallel to the development of new and improved weapons and radars (as well as counter-countermeasures). For a fighter aircraft to survive on today’s battlefield it is necessary to detect these radio frequency (RF) signals and take the appropriate actions.

A fighter aircraft typically has at least four antennas [2] to retrieve surrounding RF signals and process these. The reason to use at least four is to maximize detection probability. By having an antenna in each direction, detection probability increases as the antennas together have a 360° field of view.

The signal from each RF receiver is fed through a component called a Detector Log Video Amplifier (DLVA). A DLVA receives RF pulses from a large dynamic range, amplifies them logarithmically and outputs a video signal which changes linearly over the input range [3, 4, 5]. The typical range of the input signal is in the order of 40 dB and very often the detector in the DLVA is paralleled by another with a RF preamplifier to extend the overall dynamic range to greater than 70 dB [5, 6], e.g. -65dBm (≈0.32 nW) to +5 dBm (≈3.2 mW) [7]. 1 dBm is the power ratio in dB with 1 milliwatt as reference power.

The video signal from each DLVA is processed by the radar warning receiver (RWR) system, which performs pulse measurements and geometric triangulation to determine the main pulse parameters: pulse width (PW), pulse amplitude (PA; the power of the signal), angle of arrival (AOA) or bearing, time of arrival (TOA) and frequency (ƒ) [8, 9]. These parameters form a digital description of the pulse (or signal) in what is commonly called a pulse descriptor word (PDW).

Typical frequencies of radar signals are 0.4–40 GHz [10]. Lower frequencies are often used for surveillance radars while higher frequencies are used for target acquisition radars [1]. A commonly used type of antenna is the planar spiral antenna which, despite a small size and weight, can retrieve RF signals from a large range, typically 2–18 GHz [11]. This is often referred to as a “wide band” (WB) antenna because its wide frequency range.

There are multiple algorithms and techniques focused on sorting and analyzing PDWs coming from multiple emitters, a process called radar pulse deinterleaving. Radar pulse deinterleaving is the process of categorizing different PDWs and group them together so that, ideally, all pulses generated by an emitter is grouped together in a single group. Groups of PDWs can then be analyzed as a fingerprint of what type of emitter the RF signals where sent from, e.g. surveillance radar, radar guided missile or a fishing boat with surface search radar [11].




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1.2 The Problem in General

In environments with many RF emitters the, so-called dense radar signal environ-ments, the chance of pulses overlapping is rather high [12]. When two or more pulses are received by the RWR system simultaneously the RF signal receiver (the DLVA with the antenna connected to it) will output a voltage which corresponds to the sum of the power of the pulses. Due to the design pattern of DLVAs the difficulty is to differentiate between the pulses since the logarithmic change of the output voltage might be small or completely hidden in the normal fluctuation level of the output voltage [9].

1.3 Previous Work

The importance of radars and electronic warfare (EW) has resulted in lots of literature on the subject. References [1] and [9] both describe the most important aspects of radar developments and how it is used in EW in general terms, which give a good overview of the subject. Reference [8] is another very useful literature which goes into more detail and covers the basic EW components thoroughly.

Two components, the DLVA and the IFM (instantaneous frequency measurement) receiver, create input data to the algorithms this thesis aims to develop. To understand how these components work, a literature study and experimental measurements have been conducted. References [3] and [13] describe the characteristics of DLVAs and are really helpful when it comes to understanding how DLVAs work.

Despite the numerous books and papers in the area of radars and electronic warfare, no open sources have been found which focuses on tracking multiple simultaneous pulses. The lack of information is most likely due to the nature of EW where much work is conducted behind closed doors for military purposes. There are, however, sources which mention pulse-on-pulse and pulse-on-CW (Continuous Wave RF signal) situations and how these can be treated, but only within the scope of IFM receivers [8, 9, 12, 14]. Despite that none of these discuss how the other important parameters of the pulses can be measured during pulse-on-pulse situations; their ideas will still be helpful.

A brief simplified explanation by Saab describes how the problem is attacked today. The explanation doesn’t uncover the whole truth, but can be used as a starting point of the thesis. Basically, various actions are taken to ensure that incorrect measurements are avoided; e.g. the frequency is checked during the pulse and if the frequency changes it is a sign that the pulse (input power received by the antenna) which is currently being measured actually consist of multiple simultaneous pulses. If the power level during a pulse measurement significantly rises, that indicates that a much stronger pulse is received simultaneously. In this case the algorithm adapts and updates thresholds etc. to the new circumstances.




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1.4 Motivation

Current algorithms can be improved regarding the detection of multiple overlapping and simultaneous pulses. By keeping track of changes in the output voltage of the four DLVAs and the frequency of the incoming signal, it might be possible to track multiple simultaneous pulses more efficiently. This would improve the measurement algorithms and provide more pulse data which later stages, such as pulse deinterleaving and threat identification, can analyze. By reducing the number of missed pulses the detection probability of the RWR system could potentially be improved and the false alarm rate decreased.

1.5 Outline of Thesis

The following chapter defines the problem which this thesis aims at solving. Chapter 3 describes the various sub tasks and the initial time plan set up during the beginning of the project.

The most important topics and components covered in this report are summarized in chapter 4 while chapter 5 describes the research approach. The implementation phase is described in chapter 6 where descriptions on how the simulation models were designed and implemented.

The solutions proposals are described in chapter 7 and chapter 8 presents some test scenarios and the corresponding results.

In chapter 9 a discussion is held where the solutions are evaluated and conclusions are drawn.




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2 PROBLEM DEFINITION

2.1 Purpose and Goals

The purpose of the thesis is to investigate and develop new algorithms capable of tracking multiple simultaneous pulses using four channels (RF signal receivers) and instantaneous frequency measurements.

2.2 Conditions

Since the idea of the thesis is to come up with new algorithms to solve the problem, I will not be limited by current hardware structure and speed in regards to calculation capacity and logic. To keep the algorithms implementable and to solve the actual problem (instead of only an ideal one) the models and simulations will be based on real data provided by today’s RF signal receivers and DLVAs.

An important factor in these kinds of applications is the ability to function in a real-time perspective. The real-time aspect implies that the algorithms must work by comparing old values with current ones (in an increasing time lime) and that batch processing of entire scenarios must not be a prerequisite for the algorithms.

Since most aircrafts with RWR systems have at least four antennas which retrieve RF signals from the surroundings, the output of four DLVAs will be used as input to the algorithms.

I also have four IFMs at hand and will—if there is time—investigate how the algorithms will be affected if only a single IFM is available, which is likely since IFMs are rather expensive and large compared to other components of RWR systems.

2.3 Scope

To keep this thesis within a reasonable extent I will focus on signals in the frequency range of 2–18 GHz since this is the typical range of wide band planar spiral antennas commonly used in RWRs together with DLVAs.

The polarization of incoming RF signals will be disregarded as simulations and experiments will be conducted with signals from models and synthesizers which will be connected directly to antenna ports, thereby bypassing the actual antennas.

A possible source of trouble is when multiple RF signals with similar frequency interact which will result in interference patterns. These cases will be disregarded since the chances of this happening are rather slim and need special handling with or without the algorithms I will develop. To avoid interference, I will use test cases where the frequencies of the incoming RF signals clearly differ.

Another possible cause of constructive or destructive interference is multipath. Since multipath signals require more advanced models and especially since it cannot be simulated in the laboratory equipment I have access to, I will disregard the possible multipath effects during this thesis project.




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DLVAs often have a feature called CW-immunity. The CW-immunity means that a DLVA can adapt to a continuous incoming RF signal and suppress it from the output voltage of the DLVA. Since the CW-suppression will behave similar to an ordinary pulse ending when it springs into action, the algorithms will not need to handle these cases in any special way. After the CW-immunity adaptation the basic problem will remain the same as it did before the CW-suppression.




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3 TASK BREAK DOWN

The first seven weeks of the project were dedicated to literature and background studies and to define the scope of the master’s thesis. At first time was spent on getting familiarized with the problem and the components involved. During the background study it became clear that a DLVA model needed to be developed in order to simulate scenarios and evaluate proposed solutions efficiently. The literature study also showed that frequency measurements are quite system specific, with large timing and delay differences between different IFMs, thus a decision was made to prioritize amplitude comparison methods over frequency measurements but to at least reason on how IFMs may be used. Three sub tasks were set up to guide the remaining work:

• Implement and evaluate algorithms tracking multiple overlapping pulses (where start and end times differ) by amplitude comparisons

• Modify the algorithms or develop new ones to also handle simultaneous pulse starts/ends, evaluate the results

• Incorporate frequency measurements, evaluate the results

A rough description of the initial time plan is shown in table 1:

TaskLiterature & SpecificationOverlapping pulsesSimultaneous pulsesFrequency MeasurementsEvaluationsReport

Week

Table 1: Gantt chart of project time plan

The initial time plan was roughly followed. More tasks were done in parallel than indicated in the figure and more time was spent on situations where pulses start or end simultaneously which proved very difficult to handle. As a consequence, time dedicated to investigating how frequency measurements can be used was decreased to a minimum to allow more time to investigate and try out solutions for simultaneous pulses.




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4 BACKGROUND STUDY

4.1 Radars and Radar Warning Receivers

4.1.1 Radars

Radar, short for radio detection and ranging, was invented during World War II for military purposes and has since then rapidly been extended to other areas. Today radar is also used in civil aviation, weather forecasting and ground surveys, to name a few [8]. Radar uses electromagnetic radio waves in the frequency range of 1–40 GHz which have wave lengths of 30–0.75 cm, usually called microwaves [1, 11].

In military applications the radar is a vital piece of equipment. It is used to detect hostile aircraft, vehicles, ships as well as guide weapons and in high resolution ground mapping [8, 11, 15].

Radars emit two basic RF wave forms, pulse modulated and continuous wave (CW). Pulse modulated, or pulsed, wave forms are the by far most common. By sending out short RF waves and measure the time it takes for the signal to bounce of the target and return the radar, the distance to an object can be determined. By measuring the frequency change of the echo (the Doppler effect), the speed of the target can be determined. The pulse width (PW), the length of a pulse, of pulsed radars may range from tens of nanoseconds to several milliseconds [15].

CW signals are usually weaker than pulsed signals and can be used to track a target continuously. A disadvantage with pure CW signals is that the range to the target cannot be measured. Various actions have been taken to overcome this problem, e.g. frequency modulated CW signals and burst (interrupted) CW signals [1, 8, 11, 12].

The power, or amplitude, of a RF signal depends on a number of factors according to the one-way radar equation [5]:

2

4 ⎟⎟⎠

⎞⎜⎜⎝

⎛=

fRcGGPP rttr π

(4-1)

where: Pr = received power (W) Pt = transmitter power (W) Gt = gain of transmitter antenna in the direction of the target (ratio) Gr = gain of receiver antenna in the direction of the emitter (ratio) c = speed of light (m/s) ƒ = frequency of the signal (Hz) R = distance between the radar and the target (m)

The equation is valid for signals travelling in free space (vacuum). It is worth noting that the atmospheric losses are heavily dependant on the frequency of the RF signal,




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thus long range radars use lower frequencies because of the lesser power loss of the signals.

Radio waves have a property called polarization. The polarization of an RF signal describes the orientation of the oscillation in the plane perpendicular to the propagation direction. Radars use linear or circular polarization and by using different polarizations radars can target specific requirements, such as minimizing the effects of rain and indicate the type of material the signals are reflected off.

4.1.2 Examples of Radar Types

Military radars can roughly be divided into the following groups; early warning-, target acquisition- and target tracking radars.

Early warning radars scan large areas and transmit RF signals with high power, thus making them detectable over long distances. Historically, early warning radars were large ground based systems due to the size and power requirements of the systems but nowadays much focus lay on AEW (Airborne Early Warning) systems. Since AEW systems operate at high altitude they have a longer line-of-sight compared to ground based systems where the curvature of the earth constitutes an obstacle.

An example of ground based long-range surveillance radars which is currently in use is the TRS-2215 radar. The TRS-2215 radar uses the E/F-band (2–4 GHz) with a peak power of 700 kW. The radar transmits 3×13 µs pulses (frequency modulated to achieve a resolution of 0.2 µs) and has a range of about 510 km [16, 17]. The antenna gain is 38.5 dB [18].

Target acquisition radars have shorter range than early warning radar systems but the acquisition radar is likely to present a greater threat due to the fact that the purpose often is to guide target tracking radars [19], and thus weapon systems. An example of acquisition radars is the APG-66 multimode fire control radar installed in numerous fighting aircraft, e.g. the F16A/B. The APG-66(V)2 uses the frequency band 9.7–9.9 GHz and has a pulse width between 0.81–4 µs. The maximum range is approximately 140 km [20] and the antenna gain is 32.6 dB [21]. Peak power is in the order of 16 kW [22].

Target tracking radars are closely connected to weapon systems and the purpose is to guide the weapons, e.g. missiles or anti-aircraft cannons, toward the target. Target tracking radars often use RF signals in the 4–12 GHz band and pulsed signals with high pulse repetition frequency (several kHz) or CW [19]. Homing devices in for example Surface-to-Air missiles can be either active or semi-active. Active devices actively send out radar signals and track the target while semi-active devices passively detects the RF signals—sent by an external (“off-board”) emitter—as they reflect off the target, thus the device itself isn’t detectable by a RWR system.

The modern battlefield doesn’t just involve military equipment; an aircraft operating in built-up areas is likely to pass airports and airfields. A common air traffic control radar is the ASR-E radar manufactured by EADS. It uses the frequency band 2.7–3.0 GHz and send out pulses with alternating pulse width, either 1 µs or 2.45 µs. The peak power is 25 kW and the range is 100 km [23]. The antennas used have a gain of approximately 34 dB [24].




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4.1.3 Radar Warning Receivers

For an aircraft to survive on today’s battlefield it is vital to detect and identify hostile radars. Hostile radars, as discussed, are likely closely connected to weapon systems; e.g. Surface-to-Air Missiles (SAM). To counter these threats military aircrafts are equipped with radar warning receivers (RWR). By using passive detectors the RF signals can be detected without revealing the position of the aircraft. A RWR has an advantage towards radars; the power of the signal at the location of the aircraft is considerably stronger than the power of the returned echo. The reason is that the signal must travel double the distance to the target (the aircraft) before it returns to the radar, as a consequence the signal suffers double attenuation in addition to any reflection loss. RWR systems can therefore use simpler detectors with lower sensitivity and still be able to detect the emitter before the aircraft itself gets detected [12, 25].

The purpose of a RWR is to detect and identify an emitter (radar) and display the information to the pilot. Intelligent RWRs may also determine the optimum response—depending on the emitter—and even initiate electronic countermeasures (ECM) automatically if the emitter is considered an imminent threat. ECM actions may include initiating a jammer, activate a towed decoy and/or dispense chaff (aluminum strips which generate a larger echo in order to disengage the hostile radar from the aircraft and instead track the cloud of false echoes).

RWR systems commonly use variants of planar spiral antennas because of their wide frequency range (typically 2–18 GHz), despite the small size and weight. The planar spiral antenna has a maximum antenna gain of around 0 dB and a half-power (3 dB) beamwidth of approximately 70° [5, 11]. Figure 1, from [26], show a typical antenna diagram of a commonly used antenna type:

Figure 1: Typical pattern of a cavity-backed spiral antenna (courtesy of SciTech Publishing, Inc.)

The antenna diagram above show both vertically and horizontally polarized signals, hence the ripple in the curve. Worth noting is the back-lobe gain which is very low




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(less than -20 dB), this show why this type of antenna is popular for direction finding as there is essentially no ambiguity in signal strength versus angle of arrival.

4.2 Detector Log Video Amplifiers

4.2.1 Logarithmic Video Amplifiers

A logarithmic amplifier compresses an input of a large dynamic range into an output of small dynamic range. This property is extremely useful in radar receivers and similar equipment where voltage changes from microvolts to volts in very short time intervals.

In an ordinary linear amplifier the output dynamic range is limited by the signal-to-noise ratio (threshold level) at the low end and the saturation level at the high end. Therefore, the output dynamic range is the saturation level minus the threshold level. The input dynamic range is the same as the output dynamic range due to the linearity. A variable gain control can be used to increase the input dynamic range by lowering the gain when the output signal nears saturation; however, the instantaneous input dynamic range will remain the same (usually less than 30 dB). This is where the logarithmic amplifier excels; it has an instantaneous input dynamic range which can be greater than 100 dB while the output dynamic range remains the same as for the linear amplifier [27]. Figure 2 illustrates the difference between the two types of amplifiers; for a very different input range the output range is the same:

Figure 2: A comparison of linear and logarithmic amplifiers

Because of the large dynamic input range, the input signals of logarithmic amplifiers are usually expressed in decibels (dB) compared to a reference level of 1 volt. A voltage described in dB with 1 volt as the reference is usually denoted dBV (1 volt = 0 dBV).

A logarithmic amplifier has an input-output relationship given by [27]:

( )in21out eKKe log= (4-2)

where: K1 = slope (V/dB; often given in mV/dB) K2 = logarithmic offset (dBV)




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ein = input voltage (V) eout = output voltage (V)

The term video can be referred to the bandwidth of the logarithmic amplifier. In short, the incoming signal is linearly amplified in stages and rectified. The outputs of each stage are summed together and pass the last component of the LVA. The last component consists of a low pass filter which even out the incoming signal, to describe the envelope (amplitude) instead of the actual signal [3]. The process is illustrated in figure 3:

Figure 3: A simplified description of a LVA design (courtesy of E. Nash)

The low pass filter of the LVA works in the so called video bandwidth, which is in the range of MHz. The shortest pulse which a RWR typically must be able to measure is 50 ns [13, 14]. A wave length of 50 ns corresponds to bandwidth of 20 MHz. Thus a bandwidth of 20 MHz in the low pass filter should be sufficient to describe the envelope of the RF signal. In practice 20 MHz is likely insufficient to describe the pulse envelope in enough detail, [13] states that a 70 MHz bandwidth is necessary to detect a 50 ns pulse. The exact figures are unimportant, the point is that the high frequency RF signal is converted to a relatively low frequency (hence; video) signal describing the envelope.

4.2.2 Detector Log Video Amplifiers

A detector log video amplifier (DLVA) is a logarithmic video amplifier with a detector at the input port. As a consequence, a DLVA measures input power instead of voltage. The power of an incoming RF signal is given by its amplitude and is measured in dBm. A dBm is the power (watt) expressed in dB with 1 mW as the reference power [3, 4]. Modern DLVAs are similar in size as medium sized boxes of matches, which can be seen in figure 4 from [7]:




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Figure 4: Photograph of a DLVA (courtesy of Chengdu AINFO, Inc.)

The input–output characteristics of a DLVA are illustrated by figure 5:

Figure 5: The input to output characteristics of a DLVA, note the logarithmic dBm unit

A DLVA has a specified range for which this linearity is valid, e.g. -65 dBm to 0 dBm, within a specified acceptance value (e.g. ±1 dB). If the signal power exceeds the linear range, linearity cannot be guaranteed [3, 27]. The output of the DLVA above the linear range can be approximated by a quadratic polynomial curve until it reaches its limit value (goes into saturation). The same applies below the lower end of the linear range.

When input power is given in dBm, the following equation describes the input to output relationship within the linear range [3]:

( )interceptPslopeV inout −×= (4-3)

The slope variable has the same meaning as in equation (4-2); it determines how much the output voltage increases with each 1 dB increase in the input power. The intercept is the value in dBm for which the linear curve (if extended below the threshold) crosses the x-axis, where the output voltage is 0:




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Figure 6: Characteristics of the AD8313 DLVA (courtesy of E. Nash)

The DLVA measured in figure 6 has a ±1.0 dB output accuracy within a 65 dB range and ±3.0 dB within a 70 dB range [28]. The error curves describe how much the DLVA differs from its intended linear input-output relationship and show that it is perfectly reasonable to approximate the output edges with a quadratic polynomial curve. The measurements of the DLVA also show that the output is temperature dependant; this is due to the physical characteristics of the components in the DLVA, such as conductance at different temperatures.

Ideally the output of a DLVA would respond instantly to changes in the input signal but due to physical characteristics of the components a rise and fall time is unavoidable [27]. Figure 7 illustrates the rise and fall time:

Figure 7: Rise and fall time of the AD8313 DLVA (courtesy of E. Nash)

The rise time is commonly defined as the time required for the leading edge of a video output to change from 10% to 90% of its final value for the specified output value of the input signal but other definitions also exist. The fall time is commonly defined as the time it takes for the trailing edge of the signal to drop from 90% to 10% of its stable value [8, 29, 30].




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4.2.3 Pulse-on-Pulse DLVAs

The recovery process of DLVAs can cause pulse misses. Figure 8 illustrates the problem where a short pulse is hidden in the aftermath of a previous stronger pulse:

Figure 8: Example where a pulse is hidden in the "backporch" of another pulse

The development of the pulse-on-pulse DLVA was prompted by the need to reduce the recovery time after strong signals. During the beginning of 1980’s American Electronic Laboratories (AEL), Inc.—nowadays part of Cobham Defense Electronic Systems—developed a DLVA which used delay lines to subtract the pulse from itself, thus allowing only a part of the incoming pulse to be amplitude logged [25]. The approach permits reception of a second pulse before the first has disappeared but the pulse width information is lost in the process, as can be seen in the lower of the two graphs in figure 9, from [26]. By matching a starting flank with an ending flank, the pulse width can presumably be determined anyhow. The pulse-on-pulse DLVA will, however, still encounter problems during simultaneous pulse starts or pulse ends, similar to those discussed later in this master’s thesis.




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Figure 9: The pulse-on-pulse DLVA (courtesy of SciTech Publishing, Inc.)

The information about the pulse-on-pulse DLVA developed and manufactured in large quantities by AEL wasn’t discovered until half way into the master’s thesis thanks to a Saab-employee who had seen a demonstration of it during the 1980’s. Once the manufacturer was known a three page chapter could be found in [25] which still is the only source found which discusses the pulse-on-pulse problems of DLVAs and proposes a method of separating the pulses using hardware. Even more interesting is the fact that the pulse-on-pulse DLVA information was so hard to find; the only text found referring to it was written 1987. Whether the secrecy of military components or an overestimation of the need is the reason for this lack of information is hard to tell.

4.3 Instantaneous Frequency Measurement Receivers

An instantaneous frequency measurement (IFM) receiver is a relatively simple component which measures the frequency of an incoming signal. It measures the frequency by splitting up the input signal into two paths where one has a constant time delay. By measuring the phase of the signal at the end of the two paths the frequency can be determined. The delay time must be short enough for the IFM to be able to measure short pulses, but at the same time long enough for the measurement to settle [8, 12]. In practice, multiple delay lines are used so that ambiguities can be resolved [14].

An IFM receiver can cover a wide dynamic range, e.g. 0.5–18 GHz [31], which suits EW systems well. The receiver can measure short pulses with high resolution, i.e. 1 MHz resolution on a 100 ns pulse [8].




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There is, however, one major deficiency with IFMs; they can only measure the frequency of a single incoming signal at a time. If multiple signals arrive at the input port of the IFM receiver the result will, at best, correspond to the frequency of the strongest signal, but the result may just as well be completely wrong [8, 12]. Erroneously reported frequencies may confuse the following stages in the RWR system and complicate emitter identifications.

One way of measuring frequency in a more controlled way is to digitize the measurements by using a trigger signal to initiate the IFM. A fixed time interval after the leading edge of the triggering signal, the output is sampled and returned by the IFM receiver [12]. By monitoring the amplitude of the incoming signal, one can detect the presence of any other signals and, if any exist, discard the measurement as erroneous or label it as unsafe.

Wiley [14] distinguishes between two types of pulse-on-pulse situations; the static case and a dynamic case. The static case refers to the situation where two pulses with constant amplitude are present during the frequency measurement. He shows, analytically, that if the amplitude ratio between the stronger signal, S1, and the weaker, S2, is at least 10 dB, the weaker signal has little effect on the frequency measurement of the stronger one.

The dynamic case is when two pulses overlap during an ongoing frequency measurement, according to figure 10:

Figure 10: Overlapping pulses

In tests of an IFM the probability of frequency measurement errors were significant, e.g. 20%, even if the S1/S2 ratio was in excess of 20 dB. The error probability can, however, be greatly improved by keeping track of the signal amplitude. The method can decrease the probability of errors to less than a few percent, if S1/S2 ratio exceeds 2 dB. Wiley states there are three cases of interest:

1. For S1 > S2 there are no transient problems and the frequency of S1 will be correctly measured if S1/S2 exceeds a few decibels.

2. If S2 > S1, the frequency of S2 will be correctly determined if the delay is less than that required by the IFM video bandwidth to give a stable voltage (e.g., 100 ns typical). The circuitry to process the video can detect the transients and simply delays the reading until the video voltage stabilizes (provided S2/S1 > a few decibels).




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3. If the delay between the pulses (t2-t1) exceeds that for producing a stabilized video voltage after the second pulse arrives, the frequency of S1 is correctly determined, and the frequency of S2 is correctly determined if S2/S1, exceeds a few decibels.

There are hardware components which can be used to filter the incoming signals, thus enabling the IFM to conduct measurements with sufficient accuracy despite of the overlapping signals. One approach is to use a tunable notch filter, which can be used to block out a CW signal from the IFM receiver, assuming the frequency of the CW signal is known. Another method is to use circuitry to divide the incoming RF signals into two paths, one which holds pulsed signals and one for CW signals. In the end, however, most discussion fall back on techniques and circuitry to detect pulse-on-pulse situations and discard or flag the IFM receiver measurements as possibly unreliable due to the pulse-on-pulse situation [8].

4.4 Pulse Parameters

The most important pulse parameters measured by RWR systems are pulse amplitude (PA), pulse width (PW), time of arrival (TOA), angle of arrival (AOA) or bearing and frequency (ƒ) [8, 9]. The pulse parameters are combined and form a digital description of the pulse, commonly called a Pulse Descriptor Word (PDW). PDWs differ in bit-length, and thus resolution, among different systems. A common PDW consist of 60 to 80 bits, possibly divided according to table 2 [9]:

Parameter Resolution Span Bits

TOA 0.1 µs 1.7 s 24AOA 0.7 ° 360 ° 9ƒ 1 MHz 2-18 GHz 14PW 50 ns 100 µs 11PA 1 dB 60 dB 6

Table 2: A possible bit-pattern of a 64 bit PDW

All pulse parameters, except the pulse frequency, can be determined by analyzing the output of the DLVAs. The pulse parameters are used to sort the pulses and categorize the emitters in the deinterleaving process which follows after the PDWs are generated [8, 9]. The parameter definitions are illustrated in figure 11:




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Figure 11: Pulse parameters: (a) Angle of Arrival definition; (b) Parameters of an incoming RF pulse

Figure 11 (b) shows the output from a DLVA; hence the frequency information is lost. However, since frequency measurements are conducted directly on the signal from the RF receiver and not the DLVA output the frequency of the signal can be determined.

Radar Warning Receiver systems must not necessarily measure all parameters on each pulse. Since an emitter most likely will illuminate the aircraft with multiple pulses any missing parameters can usually be determined when additional pulses have been measured and identified as coming from the same emitter [9].

4.4.1 Pulse Amplitude

The pulse amplitude (PA) is a measurement of the power received by the RF receiver. The amplitude of a signal depends on the transmit power of the RF emitter (e.g. radar) and the distance the signal has travelled, according to the radar equation, eq. (4-1).

Theoretically the amplitude may be used to estimate the distance to an emitter but due to the physics of RF signals it is difficult to know whether a received RF pulse is sent from a weak emitter nearby or strong emitter far away [8].

The signal power is usually measured in dBm, which is the power in watt compared to a reference power of 1 milliwatt. The main reason is to be able to cover a large dynamic range, as discussed in chapter 4.2. The other advantage of expressing the amplitude in decibels is that the difference in decibels is equivalent to the ratio of the two signals. This can provide AOA information of the input signals when multiple receiver channels (antennas) are used [8].

Depending on the characteristics of the DLVAs in the RWR system as well as the characteristics of the emitter, the leading and trailing edges of pulses have different rise and fall times. The trailing edge of a pulse may also be affected by multipath. Multipath means that a signal reaches the receiver via different paths, e.g.




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via reflections [8, 9]. The effect of multipath is likely to be worse when the aircraft is flying at low altitude because of ground reflections. Multipath may also cause constructive or destructive interference due to phase differences between the main signal path and the reflected paths [9].

Another effect which must be taken into account is any overshoot caused by the DLVAs. The overshoot, if any, is the initial peak at the start of the video output when a pulse hits the receiver. Using the peak value of the overshoot as the overall PA would result in an erroneous PA, thus actions must be taken to ignore the peak value or at least minimize the error. Ideally the PA would be measured at the center of the video signal representation of the pulse, but since one cannot predict the center of the video pulse, a sampling window is often chosen after a fixed time delay from the leading edge. The PA measured with this technique is quite accurate [8].

The PA measurement also depends on the AOA of the receiving antenna and the antenna gain. If the pulse is detected in the center of the main lobe of the antenna the PA will be accurate, but if the signal hits the antenna with an angle the amplitude will appear weaker. To compensate, a collection of antennas are used and the reported amplitude is normalized. The normalization is further described in chapter 4.4.5.

4.4.2 Amplitude Triggered Thresholds

If a fixed threshold is used to determine if the input signal is affected by a pulse an unwanted effect called multiple triggering may occur. The multiple triggering problem refers to cases where an increase in the input signal will cause the signal to rise above the threshold, thus indicating an active pulse, but due to noise and multipath fluctuate around the threshold. This will cause the receiver to report multiple short pulses with very close TOAs which complicates the sorting problem in later stages.

A better approach is to use a double-threshold scheme, or hysteresis. In the double-threshold scheme the signal must first cross the upper threshold to be seen as a pulse start. For the signal change to be declared a pulse end the signal must drop below the lower threshold. This approach will allow the signal to fluctuate, which in practice is inevitable, within a certain range. The range between the threshold can be chosen arbitrarily but a to large span may cause the receiver to loose sensitivity while a to narrow span may cause the receiver to falsely report pulse starts and pulse endings caused by fluctuations in the signal. In general, the separation is about 3 dB [8].

4.4.3 Pulse Width

The pulse width (PW) can be used to categorize and identify different RF emitters. Surveillance radars tend to use longer pulses in the lower end of the 2–18 GHz band while weapon guidance radars usually use shorter pulses with higher frequency [1, 8].

Due to the effects of multipath the falling edge can, as previously discussed, be quite long and if a fixed threshold is used the PW will be incorrectly reported as too




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long. The double-threshold scheme solves the issue and enables the PW measurement to be conducted independent of the PA. Multipath, however, may still cause the measured value to be an overestimate of the real pulse width [9].

The PW can range from tens of nanoseconds to continuous wave (CW) signals [8, 13, 14]. In practice one can predetermine a maximum PW and any signal longer than the designated value is considered a CW signal. It would be impractical to wait until the end of a CW signal to process it since a CW signal may stay locked on the aircraft during a long time. In most receivers the maximum PW is programmable. It is also important to notify the RWR system of the CW signal, since CW signals often correspond to threats such as weapon guidance radars [8, 12].

4.4.4 Time of Arrival

By keeping track of the time of arrival (TOA) of multiple pulses emitter patterns can be analyzed. An important parameter which may be used to identify an emitter is the pulse repetition frequency (PRF). The PRF describes how often pulses are sent out by an emitter. Pulse repetition interval (PRI) is another commonly used term which is the opposite; PRI is the time between pulses sent out by an emitter. The timing parameters can, in addition to identify the emitter, also be used to predict incoming pulses, information which can be used by a possible jammer to jam radar signals [8].

The radar scan time is usually in the order of seconds; therefore the clock period usually lasts a few seconds before it laps around. The important parameter isn’t the exact TOA, but rather the difference between the TOA of multiple pulses [8]. A larger time span of course exists within the RWR system, but a relatively small time span of a TOA value is sufficient for the immediate pulse handling [9].

4.4.5 Angle of Arrival

The angle of arrival (AOA) is the angle to the emitter relative to the aircraft pointing direction, as could be seen in figure 11. In electronic warfare the AOA information is extremely important. Since AOA is obtained from the position of the emitter, this is the only parameter a hostile emitter cannot easily change. Thus, the AOA becomes the most reliable sorting parameter in a RWR system, especially when the hostile radar intentionally varies its PRF and RF.

There are numerous algorithms focused on measuring the AOA of a signal, the two most common are the amplitude comparison method and the phase comparison method [8, 12].

The phase comparison method uses two or more antennas placed close to each other and measures the phase of the incoming signal. The difference in phase of each antenna is used to determine the angle of the arriving signal. AOA determination by phase comparison is more accurate than an amplitude comparison system but requires multiple antennas with the same boresight to avoid ambiguity in the AOA measurement [8, 11]. To be able to intercept signals effectively in the 360° range surrounding the aircraft one would need 12 or more antennas (assuming at least three antennas covering each quadrant) which would be highly impractical.




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Typically, the amplitude comparison method uses four antennas, each covering its own quadrant [8, 11]. By knowing the antenna characteristics and comparing the ratios of the signal strength in the antennas the AOA can be determined [8].

Typical direction finding accuracy by amplitude comparison is 3° to 10° rms and by phase comparison 0.1° to 3° rms [5].

4.4.6 Frequency

The frequency information is important for both deinterleaving of RF signals and jamming. By knowing the frequency of the RF emitters illuminating the aircraft, the aircraft can instruct the jammer to concentrate its energy within the desired frequency range. The frequency of an incoming radar pulse is often measured by Instantaneous Frequency Measurement (IFM) receivers; which were discussed in chapter 4.3.

Since DLVAs output a video signal, the frequency information of the incoming RF signal is lost. To be able to measure the frequency of an incoming signal, the IFMs must be connected in parallel to the DLVAs.

Due to the characteristics of IFMs and the endless number of possible scenarios, it may not always be possible to measure the frequency of an incoming signal; hence the frequency parameter of a PDW can occasionally be skipped. Later stages will group together different PDWs and can thereby determine the frequency, assuming that enough of the PDWs have the frequency parameter set. The risk of placing a PDW in the wrong group might, however, increase if the frequency parameter is missing.




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5 RESEARCH APPROACH

5.1 Tools

5.1.1 Matlab

During the thesis project I will be using Matlab as the basis for developing simulation models and testing algorithms. Matlab suits the project well since its libraries and matrix operations enables me to swiftly try out new ideas and solutions. Additionally, Matlab scripts can be written like ordinary programs; with for- and while-loops as well as conditional statements.

The downside of programming Matlab scripts is that the execution time is longer than what it would be if the algorithms where implemented directly with a low level programming language such as C, but since the execution time isn’t important during simulations the benefits of using Matlab outweighs the execution speed of other programming languages. The major drawback of using a low level language such as C is the time it would take to visualize results and create functions which can easily be executed in Matlab without the need to program these functions (e.g. vector and matrix operations).

5.1.2 Laboratory Equipment

To be able to test the algorithms and the models I have created in Matlab I have been given access to a simple RWR system. Basically, the system consists of four antenna ports with DLVAs as well as IFMs and a computer which samples the output signals of the different components. The system is capable of generating simultaneous RF signals which makes it possible to execute the scenarios on real hardware. Depending on the output from the experiments I might need to adapt and enhance my Matlab models. By recording the data from the experiments I can use it to evaluate the performance of the algorithms and validate my simulation models.

Figure 12: Laboratory setup

5.2 Simulations

To be able to work efficiently, I need to set up a simulation environment in Matlab. This includes the ability to specify pulses and radars, as well as the antennas, the DLVAs and the IFMs of the RWR system.




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The first step is to develop a simplified model of a DLVA, since the characteristics of DLVAs will be important for the creation of input values to the algorithms. Initially, the model will not accurately model rise and fall time, but—depending on experimental results—I might need to adapt the model to simulate these characteristics as well.

Antenna patterns can be approximated by Gaussian functions, which eliminate the need to develop any specific antenna model.

There are several papers on monopulse (single pulse) direction finding, but in the interest of this thesis project it will be sufficient to approximate the direction by normalizing the power (amplitude) vectors of each antenna by simple linear algebra. As long as the amplitude contributions of a single RF pulse can be determined, which is necessary to fulfill the goals of the thesis project, the actual direction finding algorithm doesn’t really matter.

I will try to develop algorithms which avoid relying on frequency measurements, but measuring the frequency of incoming signals is likely to become useful in various scenarios. Therefore, I will act as if I have one IFM per channel and only allow the algorithms to acquire the frequency of the strongest signal provided the signal ratios differ sufficiently. Depending on experimental results, it might become necessary to implement a simple model of an IFM.

Since IFMs are large, compared to other components of RWR systems, and expensive, a reasonable assumption is that a RWR system relies on one IFM instead of one per channel. Therefore, a possible addition to the thesis project—provided there is time—is to evaluate and adapt the algorithms based on the precondition that there is only a single IFM at hand.

5.3 Experiments

Using laboratory equipment at Saab, I will recreate the simulated scenarios using real hardware. The equipment I have access to can generate multiple simultaneous pulses from which I can recreate my simulated scenarios and generate real data to work with.




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6 IMPLEMENTATION

6.1 Modelling a DLVA

To understand the problem and effects of the DLVA output during pulse-on-pulse situations I needed to create a simplified model of the DLVA component. The model will be simplified in the sense that it is based on real data but doesn’t take into account the effects of e.g. different temperature and signal frequencies. Data from measurements on existing DLVAs at Saab as well as external sources [3, 13, 32] have been used as the basis for the model. Parameters of particular interest are the base curve of the DLVAs’ input to output relations as well as noise levels and linear range thresholds.

My first attempt of creating a DLVA model did not include modeling leading- and trailing edges, meaning that the DLVA responded instantly to any change in the input power. The initial idea was that the simple approach would help me focus on coming up with ideas on methods to solve the problem and not get stuck on fine-tuning thresholds. This idea was scrapped very early in the project as it became obvious that leading- and trailing edges needed to be modeled in order to solve an actual problem and not just an ideal one.

6.1.1 Base Curve

To begin with, I needed to create a base curve for the power (given in dBm) to voltage (U) conversion. I decided to divide the voltage spectrum into five areas:

• below lower quadratic range (minimum voltage) • lower quadratic range • linear range • upper quadratic range • above upper quadratic (saturation voltage)

The reason the passes from the linear range to limiting voltages are called quadratic is because they are modeled with quadratic polynomials. This assumption is based on observations from real measurements on DLVAs as well as the base (dBm to U conversion) and error curves shown by different DLVA manufacturers, e.g. in figure 6.

The quadratic polynomials are fitted to three points each. If we look at the lower quadratic range, it is defined by three points. The two rightmost points are the first two adjacent values from the lower end of the linear range while the leftmost point (the start of the lower quadratic range) is positioned according to:

⎟⎟⎠

⎞⎜⎜⎝

⎛−++= min,linear

minmin,linearlowquadmin Pintercept

slopeUPP 2,

(6-1)




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The process is illustrated in figure 13(a) where the parenthesis of eq. (6-1) corresponds to the distance between the two red markers. The gray markers show the three (the two rightmost can not be separated at the current zoom-level) points through which the quadratic polynomial was fitted. The upper quadratic transitioning curve is calculated in the corresponding way (by using Umax and Pmax,linear). The remaining three parts of the conversion curve are simple straight lines. The parameters of the DLVA model, such as the extent of the linear range, slope, and intercept, are based on an IEEE article [13]. The overall base curve is shown in figure 13(b):

Figure 13: (a) Guide points of the lower quadratic transitioning curve, (b) Base curve of the modelled DLVA

The linear range of the modeled DLVA extends from -54 to +4 dBm and the voltage varies between 0 and 1 volt. By comparing figure 13(b) and figure 6, it is apparent that my DLVA model does not take into account the effects of temperature or any deviation from linearity within the linear range but still constitutes a useful simulation model.

6.1.2 Noise

As previously discussed, it soon became clear that noise needed to be modeled. I have based the noise modeling on conducted measurements and graphs of typical DLVA noise levels [32]. The noise level is modeled according to figure 14:




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Figure 14: (a) Noise generation in the DLVA model (b) DLVA base curve including noise generation

6.1.3 Leading- and Trailing Edges

To create a valid model which take into account factors such as temperature, illumination time, heat generation and frequency would be a master’s thesis of its own, thus I have created a simplified model which can be seen as an example of leading- and trailing edge behavior. My model will likely behave worse than some DLVAs and prove too simple for others. To mimic the edge behaviors, I needed to find a suitable electronic filter to approximate the DLVAs ringing behavior. By comparing filter responses with DLVA measurements and graphs I concluded that Butterworth filters would suit my model well. I experimented with different parameters and how to adjust them according to rise- and fall times (based on the power difference). Eventually I concluded that a single Butterworth filter would be sufficient for the leading edge approximation. I modeled the trailing edge using two serial coupled Butterworth filters and by calculating a weighted average the DLVA model would produce a satisfactory approximation.

6.1.4 Result

The pulse response of the DLVA model is shown in figure 15; the gray square wave constitute the envelope of simulated RF pulses and the black curve show the (simulated) DLVA response. The lower graph show which modeling method (filter combination) is used.




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Figure 15: Pulse response of the DLVA model

6.2 Antennas

I have assumed the aircraft has four antennas, since this is common in RWRs. The boresight (pointing direction) of the antenna in each receiver is directed, relative to the aircraft pointing direction, according to table 3:

Receiver Boresight directionForward Left (FL) 45°Forward Right (FR) 135°Aft Left (AL) 225°Aft Right (AR) 315°

Table 3: Antenna boresights relative aircraft north

Antenna gain is approximated by the following formula:2

, 23)( ⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

θαα dBmaxdB GG (6-2)

where α = angle of the incoming signal, relative to the antenna boresight (degrees) θ = antenna half-power (-3 dB) beamwidth (degrees) GdB = antenna gain (dB) Gmax,dB = maximum gain, depends on the signal amplitude at the location of the aircraft (dB)

The planar spiral antennas can also be reasonably well approximated by a Gaussian function [12]:




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2

2)(⎟⎟⎠

⎞⎜⎜⎝

⎛−

= Bk

eG ϕϕ

ϕ (6-3)

where φ = angle of the incoming signal (radians) φB = antenna half-power (-3 dB) beamwidth (radians) k = )50.0ln(− ≈ 0.693 (unit-less)

The two approximation methods yield very similar results, thus I have chosen the first approximation as it is more intuitive. I’ve set the maximum gain (Gmax,dB) to 0 dB which is a reasonable for typical planar spiral antennas, by doing so I also avoid having to adjust the pulse amplitude measurements according to the maximum antenna gain. I have also chosen to set a minimum gain to mimic the back-lobe behavior of the antennas. According to figure 1, a reasonable minimum gain is -30 dB. The antenna approximation I have created and used during simulations has the following characteristics:

Figure 16: Antenna diagram used in simulations

6.3 Direction Finding

I have used amplitude comparison method, which is one of the most commonly used direction finding techniques in RWR systems among aircrafts. A reasonable approximation is to use the power vectors and normalize the four vectors to a single one describing the power of the signal and the AOA. The impact this have on the algorithms is that the power in each channel must be filtered so the vector summations are conducted per signal, and not on the power sums of different signals.

More advanced algorithms would definitely be needed to correct abnormalities caused by antenna characteristics, temperature and losses in cables but the focus of the thesis is to develop methods of extracting the different signals, thus the normalization approximation will be sufficient.




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6.4 Frequency Measurements

As focused has been primarily on resolving pulse-on-pulse situations by tracking the amplitude in different channels, frequency measurements have not been implemented in the simulation model nor in the solutions. In chapter 9, where the performance of the algorithms is evaluated, a discussion on how IFMs may be used in order to improve the results of the algorithms is held.

6.5 Creating Scenarios

To be able to work efficiently I created a simulation environment where I can specify either radars (emitters) or pulses. Pulses can be specified with the following parameters:

• Time of Arrival • Pulse Width • Frequency • Pulse Amplitude • Angle of Arrival

Alternatively, radars can be specified with the following parameters:

• Angle of Arrival • Distance • Frequency • Transmitter Power • Antenna Gain

One or more pulses can be added to each radar (together with TOA and PW), together creating a realistic scenario.

The scenario simulation combines all pulses and determines the input power of each channel in the RWR and calculates the corresponding DLVA signal. Additionally, the scenario simulation plots the situation graphically and generates a collection of PDWs, one PDW for each pulse.

The four DLVA signals can be used to test the proposed solutions and the results can easily be evaluated by comparing the PDWs given by the solution algorithm with the collection of PDWs created by the scenario simulation.

6.6 Sample Rate

As discussed earlier, the pulse width can range from tens of nanoseconds to CW signals. In [13] the authors demonstrate the capability of their Extended Range DLVA (ERDLVA) to “detect short pulses” and refer to the ERDLVA response of a 50 ns pulse.

The ability to detect short pulses depends heavily on the sampling rate of the system. A sampling frequency of 1 MHz means that a sample is taken every millisecond, in which case a short pulse would easily pass undetected. In contrast, a




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100 MHz sampling rate would require very efficient, hence more expensive, systems but would reduce the time between samples to 10 ns. A reasonable approach thus seems to be to use a sampling frequency of 50 MHz, in which the time between samples is 20 ns.

The 50 MHz sampling frequency is theoretically able to detect pulses with PW greater than 20 ns. There is, however, an additional factor which need to be taken into account; how to define the PW if only a single sample is detected? The approach I have chosen requires that a valid pulse measurement is at least two samples; this approach also avoids any false alarm caused by single sample noise spikes. The minimum of two samples per pulse measurement affect the minimum detectable PW and double the minimum detectable PW to 40 ns.

I have concluded that a 50 MHz sampling frequency will be sufficient for this master’s thesis as the minimum detectable PW of 40 ns seem reasonable and pulse-on-pulse situations are more likely to occur during longer pulses.




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7 PROPOSED SOLUTIONS

7.1 Edge Detection

The first step towards coming up with solution proposals was to define pulse starts and pulse ends. I concluded early on that single sample spikes would be disregarded as unexpected noise and have therefore based the pulse detection on the precondition that a change of state requires two subsequent samples to fulfill certain criteria. I have identified four states which work on a per-channel basis:

• Stable Signal (SS) • Tentative Leading Edge (TLE) • Tentative Trailing Edge (TTE) • Confirmed Trailing Edge (CTE)

The leading edge of a pulse is considered tentative until a subsequent sample levels out the increase in which case the signal increase can be either reported as a pulse start or discarded as noise, therefore there is no need for a confirmed leading edge state. As a consequence, a pulse with a triangular envelope according to figure 17 will go undetected. This is however acceptable as the pulse shape cannot be described by a simple PDW and therefore a more advanced technique will be required to detect and describe the pulse.

Figure 17: Triangular shaped pulse envelope

The state of each channel is independent of the other channels, disregarding the potential relationship caused by the value of the measured amplitude in each channel set by a controller process. The channel states constitute a Mealy machine according to figure 18:




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Figure 18: Per-channel state machine

To describe how the state machine works, I will show an example. The example contains two pulses, A and B. The pulses have pulse widths of 10 ns and 100 ns, respectively, and are shown in figure 19. The figure also shows the response of the DLVA:




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Figure 19: Pulses in state machine example

Figure 20 shows the sampled DLVA signal and the reaction of the state machine and its pulse-detect flag. A positive pulse-detect flag indicates a pulse start while a negative pulse detect flag indicates the end of a pulse (after the recovery time). The amplitude curve shows the measured amplitude which is set by the controller process and used in the state machine in various thresholds (the amp variable in figure 18). The constants used in the leading- and trailing edge thresholds are reasonable to set to a few dB, depending on the expected signal fluctuation and noise level. The purpose of the initialization step is to set the amplitude variable at the beginning to the amplitude of the signal to avoid reporting a pulse start when the process has just started.

Figure 20: Example of the per-channel state machine in action




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As can be seen in figure 20 the pulse start of pulse A is detected, but the pulse width is hard to determine and the increase in amplitude which A contributes to could just as well be a sudden noise spike. Additionally, the DLVA doesn’t have time to adjust to the amplitude of the short pulse, which would result in an incorrect measurement. At sample 13 the state machine algorithm concludes that the potential pulse start (tentative leading edge) was a glitch and resets back to the stable signal state without reporting the pulse start. The underlying idea is that it is better to discard an erroneous measurement than to report it. The state machine also checks for amplitude drops, although not shown in the example, and if an amplitude drop occurs only within a single sample it is discarded as a glitch.

7.2 Solution 1: Overlapping Pulses

The aim of the first solution proposal was to provide a simple algorithm to handle overlapping pulses. By overlapping pulses, I refer to cases where no pulses start or end simultaneously.

The solution can be divided into three processes; the per-channel state machine, a controller process and a main loop which samples values and invokes the two subroutines. The main loop of the algorithm is illustrated in figure 21:

Figure 21: Flowchart for the main process of solution 1

The update channel states subroutine updates the state of each channel according to figure 18 and sets the pulse-detect flags (one for each channel) accordingly.

The controller process which reads the pulse-detect flags is described in figure 22, below. The global variables are shown in the upper left of the figure. Variables consisting of vectors of four are used to save a value for each channel, e.g. the amplitude vector corresponds to the amp variable in the per-channel state machine.




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The first step in the controller process is to check the four pulse-detect flags and see if any channel has reported a pulse start. If a pulse start is reported the algorithm calculates the amplitude difference of each channel by comparing the most recent sample with the latest “measured” amplitude (the value of the amplitude variable). By calculating the difference between the current (actually the mean value of the current and previous sample to avoid any overshoot) and previously measured amplitude (the amplitude variable) the power of the newly arrived pulse can be determined. Once the power has been determined the pulse is inserted into the pulse stack (pulses variable) which initiates a new “track”, which I have chosen to call it. Once the track has started, the measured amplitude is updated to hold the new measured amplitude (the mean value of the current and the previous sample) and the controller process returns.

If no channel reported a pulse start but one or more channels have reported a pulse end the algorithm tries to determine which track, hence pulse, has ended. The first action (“if time exists in t_pe_reported”) checks if the pulse end has already been handled during a previous sample or pulse detection flag handling. If no valid tracks exist in the stack the algorithm outputs a warning message and continues with the next (if any) channel. In the normal case, there would be valid tracks in the stack. Each valid track is compared channel-wise which results in four differences per track, expressed as a percentage compared to the amplitude decrease which trigged the pulse end detection. The track which has the lowest sum of the four percentage values is the track which is assumed to have ended. Once the track has been determined, the remaining pulse parameters such as AOA and PW are calculated and a PDW is created.

In the time steps where no pulse detection has occurred, the algorithm checks for recent pulse starts. The reason is to refine the amplitude measurements so any overshoots can be disregarded. In my approach I calculate the amplitude of a pulse as the average of the two first samples and, if the pulse is long enough, ultimately sets the amplitude to the mean value of the third and forth sample.




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amplitude[4] – holds the most recent amplitude measurementnew_amplitude[4] – holds the new measured amplitude samplepulse_detect[4] – detection flag set by each channelt_pd[4] – time of the latest pulse detect (pulse start) reported by each channelt_pe_reported[4] – the latest pulse end reported by each channelpulses[] – holds all active pulsespulse_count – holds the number of currently active pulsestime – current time tick

Start

pulse_detect > 0(pulse start)

Did we register a pulse start during the previous sample?

Yes

End

Yes

Register new pulse (add to

stack)

No

pulse_detect < 0(pulse end)

No

For each channel which reported a

pulse end...

Yes

Did a pulse recently (3 or 4 samples ago) start?

No

No

time exists int_pe_reported?

Yes

pulse_count <= 0

No

Yes

No

Recalculate the amplitude of the most recent pulse

Yes

Channels remaining?

No

Yes

Failure

Controller processExecuted in each time step (for each sample-period)

Compare the amplitude change with the measured amplitude of each pulse in the pulse stack, choose the pulse with the smallest procentual difference.

Calculate the remaining parameters and output a PDW and remove the pulse from the stack. Decrement pulse_count.

Figure 22: Flowchart describing the controller process of the first solution proposal

7.3 Solution 2: Simultaneous and Overlapping Pulses

The goal of the second solution is to handle simultaneous pulses. By simultaneous pulses I refer to cases where the start or ends of two or more overlapping pulses coincide in time, thus making the situation a lot harder to resolve.

The fundamental idea of the following solution is to always look at the channel which have the greatest increase or decrease in amplitude. The idea is that the channel which perceives the greatest amplitude increase during a pulse start will




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perceive the greatest decrease when the (same) pulse ends, thus the maximum number of overlapping pulses the algorithm can handle is one per channel. There is one “track buffer” entry per channel which holds the TOA, amplitude (of each channel) and frequency of an ongoing pulse. The algorithm can be divided into five processes:

• Pulse detection (the main loop) • Per-channel state machine • Pulse start detection • Pulse end detection • Pulse end processing

The pulse detection process, or main loop, differs from the previous solution as both pulse starts and pulse ends can be detected during the same time slot (sample period). The idea is that a pulse start can be detected in one channel while another reports the end of another pulse, depending on the angle and amplitude of the incoming RF pulses. The overall pulse detection process is illustrated in figure 23:




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Figure 23: Flowchart of the overall pulse detection process of solution 2

The update channel states process is the same as in the previous solution; please refer to chapter 7.1 on Edge Detection for a description on how it works.

The pulse start detection process, however, differs from the previous solution since it has four track buffers, hence can track a maximum of four overlapping pulses, compared to the infinite sized stack of the previous solution. The process is illustrated in figure 24:




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Pulse start detection

Start

Calculate amplitude difference,determine which channel has the

largest increase in amplitude

Track started at previous sample?

End

Start a track in corresponding track buffer

No

Ignored a pulse start

Yes

An idea is to check if the new pulse start has a greater amplitude than the previous one, in which case it might be a better idea to start a new track than to ignore it

Overwrites any previous track initiated by the channel

Figure 24: Pulse start detection process of solution 2

To be able to determine which channel perceives the greatest decrease in amplitude of a pulse end, the algorithm requires special techniques compared to the first solution. For the algorithm to detect which channel has the greatest decrease it is necessary to await the pulse end detection flag of each channel. Due to the characteristics of DLVAs the recovery time of the DLVA in each channel will likely differ, thus will the time of the pulse detect flag of each channel differ as well. The consequence is that the pulse end will be reported much earlier in one channel than in another. An idea is to keep all channels in the CTE state, but this will prevent the channel from reporting any new events. To solve the problem of different report times, the algorithm checks which channels perceive a pulse end (thus are in the CTE stage) and remembers those until all channels have exited the CTE stage. When the last channel exits the CTE stage, the pulse end processing occurs. The pulse end detection is illustrated in figure 25:




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Figure 25: Pulse end detection process of solution 2

The pulse end processing, which is illustrated in figure 26, compares the amplitude differences of the reported pulse end and determines which channel perceived the greatest decrease. If the track buffer which corresponds to the channel is valid (active), the track is ended and the remaining parameters are calculated before outputting a PDW. In the event where the track buffer is invalid, the algorithm checks if there are any valid track buffers at all. If there is no active signal in any channel and only one track buffer is valid the algorithm ends the track, regardless of the strongest increase/decrease mismatch, and outputs a PDW. Afterwards the process resets the involved track buffers (the track buffers of the channels who were in the CTE state) and the corresponding amplitude differences reported by each channel.




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Figure 26: Pulse end processing of solution 2




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8 SIMULATIONS

In this chapter I will present three test scenarios which will be used to evaluate the proposed algorithms. The scenarios will incorporate at most three RF emitters, which is sufficient to generate numerous difficult pulse-on-pulse situations.

The scenarios will incorporate three typical kinds of radars; the ASR-E air traffic control radar by EADS, the APG-66 multimode fire control radar installed in numerous fighting aircraft, e.g. the F16A/B, and the TRS-2215 long-range air surveillance radar.

8.1 Test Scenarios

8.1.1 Scenario 1: A Single Pulse

This scenario involves a single RF emitter; an ASR-E air traffic control radar. The radar is positioned according to figure 27 and the incoming pulse is illustrated in figure 28:

Figure 27: Map of scenario 1

Figure 28: Incoming RF pulse

The goal of the particular scenario is to verify that the algorithms can detect a single pulse, which is the simplest possible scenario and is a definite minium requirement. The incoming pulse is detected by the RWR and the output of each DLVA is shown in figure 29:




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Figure 29: DLVA outputs of scenario 1

The algorithms should produce a PDW which describes the pulse and report them as soon as possible. In the scenario given above, the expected PDW is described in table 4:

PDW TOA (µs) AOA (°) ƒ (GHz) PW (µs) PA (dBm)P1 2 90 - 2.5 -19.1

Table 4: Expected PDW of scenario 1




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8.1.2 Scenario 2: Two Overlapping Pulses

The second scenario involves two RF emitters; one long-range air surveillance TRS-2215 radar (pulse 1) and ASR-E air traffic control radar (pulse 2). They are aligned along the same bearing, which will cause the pulses to have the same AOA. This constitutes a particularly difficult case since the amplitude change in each channel will be proportional to each other. The incoming RF pulses are illustrated in figure 30 and the corresponding DLVA outputs are shown in figure 31:

Figure 30: Incoming RF pulses of scenario 2


The expected output of the algorithms is described in table 5:

PDW TOA (µs) AOA (°) ƒ (GHz) PW (µs) PA (dBm)P1 1.3 30 - 12 -35.5P2 4 30 - 2.5 -7.1

Table 5: Expected PDWs of scenario 2




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8.1.3 Scenario 3: Three Overlapping Pulses

The third scenario aims at testing the algorithms during a where three pulses overlap, one from each emitter (ASR-E, TRS-2215 and APG-66). The scenario is illustrated in figure 32 and figure 33, while the corresponding DLVA outputs are shown in figure 34.

Figure 32: RF pulses of scenario 3

Figure 33: Overview of the pulse-on-pulse situation




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The expected PDWs are described in table 6:

PDW TOA (µs) AOA (°) ƒ (GHz) PW (µs) PA (dBm)P1 1.3 45 - 12 -35.5P2 5 310 - 3 -24.1P3 7 120 - 2.5 -19.1

Table 6: Expected PDWs of scenario 3




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8.1.4 Scenario 4a: Simultaneous Pulses

The forth scenario illustrates how the algorithms behave during a simultaneous pulse start. The AOAs of the two RF pulses are illustrated in figure 35, the pulse-on-pulse situation in figure 36 and the resulting DLVA outputs are described in figure 37.

Figure 35: RF pulses of scenario 4a

Figure 36: Overview of the pulse-on-pulse situation




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Figure 37: DLVA outputs of scenario 4a

Ideally, the following PDWs would be returned:

PDW TOA (µs) AOA (°) ƒ (GHz) PW (µs) PA (dBm)P1 2 30 - 4 -20.0P2 2 75 - 2 -15.0

Table 7: Expected PDWs of scenario 4a

8.1.5 Scenario 4b: Simultaneous Pulses

This scenario is essentially the same as the previous; the only difference is the angle between the emitters which can be seen in figure 38:




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Figure 38: Incoming RF pulses of scenario 4b

The corresponding DLVA output is shown in figure 39 and the expected PDWs in table 8:

Figure 39: DLVA outputs of scenario 4b




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PDW TOA (µs) AOA (°) ƒ (GHz) PW (µs) PA (dBm)P1 2 30 - 4 -20.0P2 2 135 - 2 -15.0

Table 8: Expected PDWs of scenario 4b

8.2 Test Results

The results from the scenarios have been tagged with either Pass or Fail. A test is designated to have passed if:

• The solution outputs at least one PDW which is correct (within tolerable limits)

• The solution does not report any incorrect PDWs

There is also, apart from the pass/fail, additional information which describes the outcome of the test in more detail, marked a, b and c in the following example:

Result of test A: [ a/ b/ c] Pass Result of test B: [ a/ b/ c] Pass

The total number of incoming pulses is given by a, b is the number of correct PDWs generated by the solution algorithm while c is the number of incorrect PDWs generated. Each test case has two results; A corresponds to the result when using solution 1 and B corresponds to solution 2. In the test reports, the TOA and PW values are given in number of samples as opposed to µs.

Additional information and explanations on how the two solutions work in the following test scenarios can be found in appendix D.

8.2.1 Scenario 1

The test results are as follows:

Result of test A: [ 1/ 1/ 0] Pass Result of test B: [ 1/ 1/ 0] Pass Expected: toa: 100, pw: 125, pa: ‐19.1, f: 2.70, aoa: 90.0 A) Returned: toa: 103, pw: 125, pa: ‐21.2, f: 0.00, aoa: 89.9 B) Returned: toa: 103, pw: 125, pa: ‐21.2, f: 0.00, aoa: 89.9

The test case was run more than 7,000 times to verify the results. Tests where the AOA is altered have also been carried out to ensure this does not affect the outcome of the test.

This particular test result was chosen to highlight what might happen in solution 2 if the AOA is at an even 90° (in between two antennas). Due to noise randomness the pulse start is detected in one channel and the pulse end in another, this happens around 50% of the times (provided the AOA is at an even 90°).




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8.2.2 Scenario 2

The results of scenario 2 are:

Result of test A: [ 2/ 2/ 0] Pass Result of test B: [ 2/ 2/ 0] Pass Expected: toa: 65, pw: 600, pa: ‐35.5, f: 4.00, aoa: 30.0 Expected: toa: 200, pw: 125, pa: ‐7.1, f: 2.70, aoa: 30.0 A) Returned: toa: 203, pw: 125, pa: ‐7.6, f: 0.00, aoa: 32.9 A) Returned: toa: 68, pw: 600, pa: ‐36.0, f: 0.00, aoa: 34.0 B) Returned: toa: 203, pw: 125, pa: ‐7.6, f: 0.00, aoa: 32.9 B) Returned: toa: 68, pw: 600, pa: ‐36.0, f: 0.00, aoa: 34.0

More extensive testing have shown that when both pulses have the same AOA, noise have a great impact. Among the conducted test runs the results have been divided according to table 9:

Result Solution 1 Solution 2Pass (2 correct PDWs) 100% 15%Pass (1 correct PDW) 0% 32%Fail 0% 53%

Table 9: Approximative results of 2×30° pulses according to more than 1,000 test runs

Shifting the shorter pulse’s AOA to 32° yield:


Table 10: Results according to more than 1,000 test runs (AOA is 30° and 32°, respectively)

If the AOA of the shortest pulse is set to 28°, the results are:


Table 11: Results according to more than 1,000 test runs (AOA is 30° and 28°, respectively)




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8.2.3 Scenario 3

The results when applying the solutions to scenario 3 are described below:

Result of test A: [ 3/ 3/ 0] Pass Result of test B: [ 3/ 3/ 0] Pass Expected: toa: 65, pw: 600, pa: ‐35.5, f: 4.00, aoa: 45.0 Expected: toa: 250, pw: 150, pa: ‐24.1, f: 9.70, aoa: 310.0 Expected: toa: 350, pw: 125, pa: ‐19.1, f: 2.70, aoa: 120.0 A) Returned: toa: 253, pw: 150, pa: ‐24.3, f: 0.00, aoa: 309.2 A) Returned: toa: 353, pw: 125, pa: ‐19.6, f: 0.00, aoa: 122.7 A) Returned: toa: 68, pw: 600, pa: ‐35.6, f: 0.00, aoa: 43.5 B) Returned: toa: 253, pw: 150, pa: ‐24.3, f: 0.00, aoa: 309.2 B) Returned: toa: 353, pw: 125, pa: ‐19.6, f: 0.00, aoa: 122.7 B) Returned: toa: 68, pw: 600, pa: ‐35.6, f: 0.00, aoa: 43.5

As can be seen, both solutions managed to correctly report all three pulses. More extensive testing showed interesting results:

Result Solution 1 Solution 2Pass (2 correct PDWs) 92% 100%Pass (1 correct PDW) 0% 0%Fail 8%* 0%

Table 12: Results according to 2,000 simulations

* A closer examination showed that the failed cases reported two correct PDWs and one incorrect. The incorrectly reported pulse was the longer one, which was reported as shorter than the incoming reference pulse. Analysis showed that the pulse end caused by the -24.1 dBm pulse was reported in two channels and that the end time reported by each channel differed with 3 samples. The settings when solution 1 was applied only allowed end times of different channels to differ with ±1 sample, thus processing the pulse end twice.

8.2.4 Scenario 4

The test results of scenario 4a, below, show that the first solution failed and only reported a single incorrect PDW while the second solution managed to report at least one of the two pulses correctly:

Result of test A: [ 2/ 0/ 1] FAIL Result of test B: [ 2/ 1/ 0] Pass Expected: toa: 100, pw: 200, pa: ‐20.0, f: 0.00, aoa: 30.0 Expected: toa: 100, pw: 100, pa: ‐15.0, f: 0.00, aoa: 75.0 A) Returned: toa: 103, pw: 100, pa: ‐15.1, f: 0.00, aoa: 65.2 B) Returned: toa: 103, pw: 200, pa: ‐20.4, f: 0.00, aoa: 32.9




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In scenario 4b, however, both solutions failed to report any correct PDWs; instead an incorrect one was returned which can be seen in the following test results:

Result of test A: [ 2/ 0/ 1] FAIL Result of test B: [ 2/ 0/ 1] FAIL Expected: toa: 100, pw: 200, pa: ‐20.0, f: 0.00, aoa: 30.0 Expected: toa: 100, pw: 100, pa: ‐15.0, f: 0.00, aoa: 135.0 A) Returned: toa: 103, pw: 100, pa: ‐14.1, f: 0.00, aoa: 106.9 B) Returned: toa: 103, pw: 100, pa: ‐14.1, f: 0.00, aoa: 106.9

Numerous tests have been carried out where the AOAs of the incoming pulses have been varied but it is difficult to find any systematic pattern in the results. To evaluate the solutions further, they were applied to 10,000 simulations where the angles of the two incoming signals were set randomly. The results are shown in table 13:


Table 13: Approximative results according to 10,000 simulations




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9 DISCUSSION

9.1 Evaluation

The pulse start detection of the per-channel state machine, shown in figure 18, requires the amplitude to rise by at least a specified amount (c_dle constant) if the amplitude increase is to be reported as a pulse start. If an incoming pulse has a very gentle increase, the pulse start might pass undetected. A conclusion is that the amplitude of the incoming RF pulses, with the current per-channel state machine, must be fairly square-shaped to be detected effectively with the proposed solutions. This is, however, sufficient as wide band receivers (in this case 2–18 GHz) are often used in combination with more advanced decoding processes. The WB receiver can be used to detect signals roughly while the more advanced decoder handles other more difficult pulse shapes.

9.1.1 Solution 1

The first solution proposal was developed with simplicity in mind. Since the algorithm doesn’t take simultaneous pulse starts or pulse ends into account at all, it acts more like a theoretical solution. During simultaneous pulse starts or pulse ends the solution will track too few or keep already ended pulses, which will result in incorrect PDWs. The solution is, however, a good spring board into a more advanced solution with its pulse stack and comparison based decisions.

In the simulation environment there is no maximum stack size, which theoretically enables the algorithm to track any number of incoming RF pulses, provided the start and end times differ and the pulses have different power contributions in the four channels. As a result the algorithm should be very well suitable to detect overlapping pulses of the same size (same amplitude) if they differ in AOA, as the pulse end detection comparison is done channel-wise.

To illustrate why the first solution excels when each pulse start and end time is detected, an example is given in appendix E. The problem with the algorithm is that a single missed pulse start or end propagates and may cause every following pulse to be incorrectly reported. This is a major drawback and is the prime reason why the algorithm is not robust enough to be used in practice.

In scenario 3, the solution fails in 8% of the test cases. If the algorithm would have allowed a bigger difference in the end time reported by each channel, e.g. ±3 samples instead of ±1, the results would be 100% passed tests. This might, however, cause trouble in situations with short adjacent pulses. In the following analysis, it will be regarded as if solution 1 passed 100% of the test cases.

The conclusions above are well supported by the results of the test scenarios; the solution resolves the first three scenarios but fail when the scenario involves a simultaneous pulse start.




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9.1.2 Solution 2

During batch testing it was discovered that the second solution had trouble detecting even single pulses if the AOA was at an even 90° (between two antennas). As a consequence the algorithm needed to be modified and a check was added to see if there is any ongoing pulse and only one active track, see figure 26. By analyzing the detailed result of solution 2 in scenario 1 (see appendix D.1.2) it is clear that the situation occurs due to a start-end mismatch. Since the start of the pulse was registered as strongest in channel 4 (AR) but the largest decrease was detected in channel 2 (FR) the algorithm normally discards the detected pulse end to avoid ambiguities. This problem, which has a clear impact on the algorithm of solution 2, would not have been discovered if noise modeling would not have been added in the DLVA model.

The start-end mismatch due to noise does not constitute a problem, unless the AOA of a signal is more or less exactly between two antennas. The situation has nonetheless proven that strictly looking at the largest increase or decrease is insufficient.

At the time of a pulse start it is impossible to tell, by just analyzing the DLVA output, whether the amplitude increase is caused by a single pulse or if it consists of multiple pulses, thus the algorithms need to figure it out later on. Figure 40, below, shows an example where it is impossible to resolve the situation by only tracking the amplitude. By discarding any mismatched pulse ends the algorithm avoids reporting unreliable PDWs.

The second solution has, however, quite high likelihood of reporting incorrect PDWs when the AOA of two signals is the same, which was shown in table 9.

Figure 40: Ambiguity of a DLVA signal

9.1.3 Comparison

Both proposed solutions have a 100% detection probability of single pulses, provided the pulse start and end is detected in at least one channel, a case which a solution must be able to resolve to be usable in practice.

The second scenario is a very likely pulse-on-pulse situation which a potential solution should be very capable of resolving. Both proposed solutions resolve the situation correctly. As more extensive testing have shown, the ability of the second solution to resolve the situation is hard to predict analytically. The situation given in scenario 2, where the two RF signals have the same AOA, was resolved by solution 1 in all test runs since there was a clear amplitude difference of the two signals.




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Solution 2 could resolve the situation with various results according to table 9. An observation is that a little more than half of the test runs (53%) resulted in an incorrect PDW, while the other could either partially resolve the situation (32%) or resolve it completely (15%). As can be seen in table 10 and table 11, the results of solution 2 are greatly improved if the angle between the two signals is increased by as little as two degrees. In the former case (table 10) solution 2 only manages to report one of the two pulses, this is due to unfortunate AOAs compared to the antenna boresights which cause the second pulse start to overwrite the already ongoing track.

The results of the third scenario show that both solutions are capable of tracking three simultaneous pulses. The second solution is more sensitive to the angles between the signals, as discussed in the previous paragraph. The three incoming RF pulses are all in different sectors (quadrants) but it is worth noting that both solutions also can track multiple pulses which share sector (as can be seen in scenario 2).

The results of scenario 4 are interesting, in particular the ability for solution 1 to resolve 26% of the test cases at least partially, which is the best any solution can do to avoid ambiguity. The reason why the first solution performed so unexpectedly well is that the incoming pulses have similar power, thus the sum of the pulses is only a few dB greater than the power of strongest pulse. This slightly incorrect measured power will fall within the acceptance limit of the pass/fail test, provided the other pulse parameters fulfill similar acceptance constraints. If the angles of the incoming signals are adjacent—or the more or less exact opposite—the solution will report a too strong pulse which still is within the acceptance limits, thus passing the test.

Solution 2 shows a clear improvement over solution 1 with 50% of the test cases passed, 26% of the tests might have been passed by the same reason as solution 1 but the other 24% are definitely resolved thanks to the per-channel track buffer algorithm. Scenario 4a shows a case which the solution is able to resolve while scenario 4b shows an example where the solution fails. The likelihood of resolving a case seems to depend on the noise at the DLVA baseline as discussed in the previous chapter (9.1.2).

9.2 Frequency Measurements

Frequency measurements are very important to be able to identify an emitter. As discussed earlier, IFMs need some time between when the measurement is initiated and the result is returned. The length of the delay depends on the time it takes for the RF signal to propagate through the longest delay line.

An approach to incorporating IFMs in the algorithms of the proposed solutions could be to always initiate an IFM measurement when a pulse start is detected. If no other event occurs (e.g. another pulse start or pulse end is detected) before the result from the IFM arrives, it can be stored together with the TOA and PA values in the ongoing track. To ensure the IFM result is as reliable as possible, the result should be read from an IFM which measures the channel where the pulse start caused the largest increase in power.




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During active pulses the IFM receivers should periodically measure the frequency, in that way it is possible to compare the latest measured frequency of the channel which reported the pulse end with the corresponding ongoing track. If the frequency information in the track differs from the measured one, one can assume the pulse end doesn’t really correspond to the pulse start even though the signal strengths indicate so. It could instead be the case that some pulse starts and ends are missed and what is believed to be a single pulse actually consist of two combined pulses, by measuring the frequency in the beginning and compare it to the latest frequency measurement the number of erroneous PDWs can potentially be reduced.

In systems where only a single IFM is used, an approach can be to always measure frequency in the channel with the highest input power or, alternatively, the channel which perceives the largest power increase during a pulse start.

9.3 Conclusions

The problem with pulse-on-pulse situations has proven to be very difficult. There are endless of possible scenarios which make it hard to evaluate potential solutions. During the thesis various scenarios have been tested and the scenarios described in chapter 8 illustrate some possible and likely scenarios. The likelihood of two pulses starting or ending at the exact same sample is, however, quite low but yet interesting in an evaluation point of view.

Both solutions have been developed with simplicity and real-time constraints in mind. They are structured and designed to be relatively easy to implement in firmware.

This thesis presents two possible algorithms which can resolve pulse-on-pulse situations. The algorithm of the first solution provides proof-of-concept and show that pulse-on-pulse situations can be resolved quite easily by using amplitude comparisons. The solution works very well for overlapping pulses, but fails significantly when pulse start or end simultaneously, thus making the solution inadequately robust to be used in practice.

Solution 2 is intended to be the implementable solution which may be used in practice. Tests have shown there are cases where the algorithm reports erroneous PDWs, but these are generally very difficult scenarios which in many cases are resolved at least partially. The test scenarios in chapter 8 confirm that the algorithm is capable of handling single pulses as well as various pulse-on-pulse situations thus making it a very good candidate for use in future RWR systems. When frequency measurements are implemented the robustness of the algorithm can likely be improved furthermore than what the results in this thesis show.

9.4 Further Work

The most important future work is to incorporate frequency measurements in both the simulation model and the solutions. Thereafter it is wise to evaluate the solution algorithms according to the specific needs of the RWR system.

There are some changes which could possibly improve the performance of solution 2. During the pulse end processing the algorithm checks which channel




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perceived the greatest voltage decrease, thus the greatest increase is calculated in the decibel scale. By comparing the pulse end detect of an unmatched channel with ongoing tracks a different decision can be made if the amplitude difference of a channel with an ongoing track is similar (almost as large) as the channel with the greatest decrease. In this case the special handling of single pulses where the algorithm checks if there is any active signal still ongoing could be avoided. This would probably eliminate the need for the special check discussed in chapter 9.1.2, but also improve the likelihood of detecting pulses during pulse-on-pulse situations where the AOA is between two antennas (at an even 90°).

Another approach which could be evaluated is instead to calculate the largest increase and decrease in the linear scale (watt). This would probably limit the algorithm to tracking a maximum of one pulse per sector, but it will also impact decisions made when DLVA signals are rather high. This might improve the reliability of the PDWs but at the expense of the, quite major, limitation of one pulse per sector which will reduce the number of reported pulses.

Other areas which may be improved include the simulation model. It can be adjusted to simplify quantitative statistical evaluations and reduce run time by avoiding plotting the scenarios. There is, however, a disadvantage of avoiding plotting the figures as the traceability becomes harder. One can, of course, adapt the simulation model and output more relevant parameters as text, thereby avoiding the shortcomings of not plotting the scenarios.

The DLVA model created and used throughout this thesis can as well be improved in regards to input parameters. The behavior of a DLVA depends on factors such as temperature, frequency and illumination time and amplitude of incoming RF signals. A more realistic DLVA model can be developed, but the level of realism in the current DLVA model was sufficient for this master’s thesis.

A case which needs further investigation is how the algorithms behave when the recovery time of a DLVA is very long. The DLVA model doesn’t model long recovery times as discussed earlier and for the same reason it is difficult to generate such cases in the laboratory. Hopefully, it will be sufficient to alter the derivative parameter of the pulse end detection, but without further tests and evaluations with more advanced equipment it is hard to tell.




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APPENDICES

Appendix A Abbreviations and Acronyms

A/D Analog-to-DigitalAEL American Electronic Laboratories, Inc.AEW Airborne Early WarningAL Aft Left (receiver unit)AOA Angle of ArrivalAR Aft Right (receiver unit)ATC Air Traffic ControlCTE Confirmed Trailing Edge (state)CW Continuous WavedBm Power in dB compared to 1 milliwattdBV Voltage in dB compared to 1 voltDLVA Detector Logarithmic Video AmplifierECM Electronic CountermeasuresERDLVA Extended Range DLVAEW Electronic Warfareƒ FrequencyFL Forward Left (receiver unit)FR Forward Right (receiver unit)IFM Instantaneous Frequency Measurement (receiver)LVA Logarithmic Video AmplifierPA Pulse AmplitudePDW Pulse Descriptor WordPRF Pulse Repetition FrequencyPRI Pulse Repetition IntervalPW Pulse WidthRF Radio Frequencyrms Root Mean Square (quadratic mean)RWR Radar Warning ReceiverSAM Surface-to-Air MissileSS Stable Signal (state)TLE Tentative Leading Edge (state)TOA Time of ArrivalTTE Tentative Trailing Edge (state)WB Wide Band




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Appendix B List of Figures

Figure 1: Typical pattern of a cavity-backed spiral antenna (courtesy of SciTech Publishing, Inc.) .........................................................................................................14 Figure 2: A comparison of linear and logarithmic amplifiers ....................................15 Figure 3: A simplified description of a LVA design (courtesy of E. Nash)...............16 Figure 4: Photograph of a DLVA (courtesy of Chengdu AINFO, Inc.).....................17 Figure 5: The input to output characteristics of a DLVA, note the logarithmic dBm unit .............................................................................................................................17 Figure 6: Characteristics of the AD8313 DLVA (courtesy of E. Nash) ....................18 Figure 7: Rise and fall time of the AD8313 DLVA (courtesy of E. Nash) ................18 Figure 8: Example where a pulse is hidden in the "backporch" of another pulse ......19 Figure 9: The pulse-on-pulse DLVA (courtesy of SciTech Publishing, Inc.)............20 Figure 10: Overlapping pulses ...................................................................................21 Figure 11: Pulse parameters: (a) Angle of Arrival definition; (b) Parameters of an incoming RF pulse .....................................................................................................23 Figure 12: Laboratory setup .......................................................................................27 Figure 13: (a) Guide points of the lower quadratic transitioning curve, (b) Base curve of the modelled DLVA.....................................................................................30 Figure 14: (a) Noise generation in the DLVA model (b) DLVA base curve including noise generation .........................................................................................................31 Figure 15: Pulse response of the DLVA model .........................................................32 Figure 16: Antenna diagram used in simulations.......................................................33 Figure 17: Triangular shaped pulse envelope ............................................................36 Figure 18: Per-channel state machine ........................................................................37 Figure 19: Pulses in state machine example...............................................................38 Figure 20: Example of the per-channel state machine in action ................................38 Figure 21: Flowchart for the main process of solution 1 ...........................................39 Figure 22: Flowchart describing the controller process of the first solution proposal....................................................................................................................................41 Figure 23: Flowchart of the overall pulse detection process of solution 2.................43 Figure 24: Pulse start detection process of solution 2 ................................................44 Figure 25: Pulse end detection process of solution 2 .................................................45 Figure 26: Pulse end processing of solution 2............................................................46 Figure 27: Map of scenario 1 .....................................................................................47 Figure 28: Incoming RF pulse....................................................................................47 Figure 29: DLVA outputs of scenario 1.....................................................................48 Figure 30: Incoming RF pulses of scenario 2.............................................................49 Figure 31: DLVA outputs of scenario 2.....................................................................49 Figure 32: RF pulses of scenario 3.............................................................................50 Figure 33: Overview of the pulse-on-pulse situation .................................................50 Figure 34: DLVA outputs of scenario 3.....................................................................51 Figure 35: RF pulses of scenario 4a ...........................................................................52 Figure 36: Overview of the pulse-on-pulse situation .................................................52 Figure 37: DLVA outputs of scenario 4a ...................................................................53 Figure 38: Incoming RF pulses of scenario 4b...........................................................54




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Figure 39: DLVA outputs of scenario 4b...................................................................54 Figure 40: Ambiguity of a DLVA signal ...................................................................60 Figure 41: Overview of solution 1 in scenario 1 ........................................................68 Figure 42: Overiew of solution 2 in scenario 1 ..........................................................69 Figure 43: Overview of solution 1 in scenario 2 ........................................................71 Figure 44: Overview of solution 2 in scenario 2 ........................................................72 Figure 45: Overview of solution 1 in scenario 3 ........................................................74 Figure 46: Overview of solution 2 in scenario 3 ........................................................75 Figure 47: Overview of solution 1 in scenario 4a ......................................................77 Figure 48: Overview of solution 2 in scenario 4a ......................................................78 Figure 49: Overview of solution 1 in scenario 4b ......................................................80 Figure 50: Overview of solution 2 in scenario 4b ......................................................81 Figure 51: An example of a particularly difficult scenario ........................................82




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Appendix C List of Tables

Table 1: Gantt chart of project time plan ...................................................................11 Table 2: A possible bit-pattern of a 64 bit PDW........................................................22 Table 3: Antenna boresights relative aircraft north....................................................32 Table 4: Expected PDW of scenario 1 .......................................................................48 Table 5: Expected PDWs of scenario 2......................................................................49 Table 6: Expected PDWs of scenario 3......................................................................51 Table 7: Expected PDWs of scenario 4a ....................................................................53 Table 8: Expected PDWs of scenario 4b....................................................................55 Table 9: Approximative results of 2×30° pulses according to more than 1,000 test runs.............................................................................................................................56 Table 10: Results according to more than 1,000 test runs (AOA is 30° and 32°, respectively) ...............................................................................................................56 Table 11: Results according to more than 1,000 test runs (AOA is 30° and 28°, respectively) ...............................................................................................................56 Table 12: Results according to 2,000 simulations......................................................57 Table 13: Approximative results according to 10,000 simulations............................58




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Appendix D Detailed Results

D.1 Scenario 1

D.1.1 Solution 1

Using data from the workbench variable <data>. T104: [Ch2] pulse started at 103 T104: [Ch3] pulse started at 103 T104: [Ch4] pulse started at 103 T104: Pulse tracking started (pulse started at 103) T104: Now tracking 1 pulse_stack. T104: toa: 103, amp: [‐51.30 ‐22.44 ‐49.47 ‐22.42] dBm, f: 0.00 T105: Refined amplitude of pulse 1 (toa: 103) T105: new amp: [‐49.42 ‐24.64 ‐49.94 ‐24.63] dBm T106: Refined amplitude of pulse 1 (toa: 103) T106: new amp: [‐49.63 ‐24.23 ‐49.87 ‐24.25] dBm T231: [Ch1] pulse ended at 228 T231: Pulse end discovered, determining pulse... T231: Pulse end, amplitude difference: [‐49.67 ‐24.43 ‐49.94 ‐24.45] dBm T231: Comparing with pulse 1 (toa: 103, amp: [‐49.63 ‐24.23 ‐49.87 ‐24.25]) T231: Decided pulse 1 ended. T231: ‐‐‐> PDW(toa: 103, pw: 125, pa: ‐21.23 dBm, aoa: 89.9, f: 0.0) <‐‐‐ T233: [Ch3] pulse ended at 228 T233: Pulse end ignored (end time: 228, ch: 3) T235: [Ch4] pulse ended at 228 T235: Pulse end ignored (end time: 228, ch: 4) T236: [Ch2] pulse ended at 228 T236: Pulse end ignored (end time: 228, ch: 2) There are 0 active pulse_stack entries remaining.

Figure 41: Overview of solution 1 in scenario 1




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D.1.2 Solution 2

Using data from the workbench variable <data>. T104: [Ch2] pulse started at 103 T104: [Ch3] pulse started at 103 T104: [Ch4] pulse started at 103 T104: Pulse tracking started in Ch4 (pulse started at 103) T104: Track buffer: T104: [4] toa: 103, amp: [‐51.30 ‐22.44 ‐49.47 ‐22.42] dBm, f: 0.00 T105: Refined amplitude of track 4 (toa: 103), new amp: [‐49.42 ‐24.64 ‐49.94 ‐

24.63] dBm T106: Refined amplitude of track 4 (toa: 103), new amp: [‐49.63 ‐24.23 ‐49.87 ‐

24.25] dBm T231: [Ch1] pulse ended at 228 T233: [Ch3] pulse ended at 228 T235: [Ch4] pulse ended at 228 T236: [Ch2] pulse ended at 228 T236: Pulse end found, amplitude difference: [‐49.72 ‐24.23 ‐49.45 ‐23.57] dBm T236: Pulse end found, unmatched channel! (Ch2, end time: 228) T236: Pulse end found, assuming channel 2 T236: ‐‐‐> PDW(toa: 103, pw: 125, pa: ‐21.23 dBm, aoa: 89.9, f: 0.0) <‐‐‐ There are 0 valid trackbuffer entries remaining.

Figure 42: Overiew of solution 2 in scenario 1




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D.2 Scenario 2

D.2.1 Solution 1

Using data from the workbench variable <data>. T69: [Ch1] pulse started at 68 T69: [Ch2] pulse started at 68 T69: Pulse tracking started (pulse started at 68) T69: Now tracking 1 pulse_stack. T69: toa: 68, amp: [‐49.50 ‐35.03 ‐57.30 ‐57.30] dBm, f: 0.00 T70: Refined amplitude of pulse 1 (toa: 68) T70: new amp: [‐50.40 ‐36.45 ‐57.30 ‐57.30] dBm T71: Refined amplitude of pulse 1 (toa: 68) T71: new amp: [‐50.29 ‐36.19 ‐57.30 ‐57.30] dBm T204: [Ch1] pulse started at 203 T204: [Ch2] pulse started at 203 T204: [Ch3] pulse started at 203 T204: [Ch4] pulse started at 203 T204: Pulse tracking started (pulse started at 203) T204: Now tracking 2 pulse_stack. T204: toa: 203, amp: [‐19.48 ‐6.24 ‐36.12 ‐32.95] dBm, f: 0.00 T205: Refined amplitude of pulse 2 (toa: 203) T205: new amp: [‐21.34 ‐8.13 ‐37.45 ‐34.50] dBm T206: Refined amplitude of pulse 2 (toa: 203) T206: new amp: [‐20.98 ‐7.78 ‐37.21 ‐34.20] dBm T333: [Ch3] pulse ended at 328 T333: Pulse end discovered, determining pulse... T333: Pulse end, amplitude difference: [‐20.98 ‐7.78 ‐37.21 ‐34.20] dBm T333: Comparing with pulse 1 (toa: 68, amp: [‐50.29 ‐36.19 ‐57.30 ‐57.30]) T333: Comparing with pulse 2 (toa: 203, amp: [‐20.98 ‐7.78 ‐37.21 ‐34.20]) T333: Decided pulse 2 ended. T333: ‐‐‐> PDW(toa: 203, pw: 125, pa: ‐7.58 dBm, aoa: 32.9, f: 0.0) <‐‐‐ T334: [Ch4] pulse ended at 328 T334: Pulse end ignored (end time: 328, ch: 4) T335: [Ch1] pulse ended at 328 T335: [Ch2] pulse ended at 328 T335: Pulse end ignored (end time: 328, ch: 1) T335: Pulse end ignored (end time: 328, ch: 2) T671: [Ch1] pulse ended at 668 T671: Pulse end discovered, determining pulse... T671: Pulse end, amplitude difference: [‐51.46 ‐37.45 ‐57.30 ‐57.30] dBm T671: Comparing with pulse 1 (toa: 68, amp: [‐50.29 ‐36.19 ‐57.30 ‐57.30]) T671: Decided pulse 1 ended. T671: ‐‐‐> PDW(toa: 68, pw: 600, pa: ‐36.03 dBm, aoa: 34.0, f: 0.0) <‐‐‐ T673: [Ch2] pulse ended at 668 T673: Pulse end ignored (end time: 668, ch: 2) There are 0 active pulse_stack entries remaining.




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D.2.2 Solution 2

Using data from the workbench variable <data>. T69: [Ch1] pulse started at 68 T69: [Ch2] pulse started at 68 T69: Pulse tracking started in Ch2 (pulse started at 68) T69: Track buffer: T69: [2] toa: 68, amp: [‐49.50 ‐35.03 ‐57.30 ‐57.30] dBm, f: 0.00 T70: Refined amplitude of track 2 (toa: 68), new amp: [‐50.40 ‐36.45 ‐57.30 ‐57.30]

dBm T71: Refined amplitude of track 2 (toa: 68), new amp: [‐50.29 ‐36.19 ‐57.30 ‐57.30]

dBm T204: [Ch1] pulse started at 203 T204: [Ch2] pulse started at 203 T204: [Ch3] pulse started at 203 T204: [Ch4] pulse started at 203 T204: Pulse tracking started in Ch1 (pulse started at 203) T204: Track buffer: T204: [1] toa: 203, amp: [‐19.48 ‐6.24 ‐36.12 ‐32.95] dBm, f: 0.00 T204: [2] toa: 68, amp: [‐50.29 ‐36.19 ‐57.30 ‐57.30] dBm, f: 0.00 T205: Refined amplitude of track 1 (toa: 203), new amp: [‐21.34 ‐8.13 ‐37.45 ‐34.50]


dBm T333: [Ch3] pulse ended at 328 T334: [Ch4] pulse ended at 328 T335: [Ch1] pulse ended at 328 T335: [Ch2] pulse ended at 328 T335: Pulse end found, amplitude difference: [‐20.98 ‐7.78 ‐36.16 ‐33.36] dBm T335: Pulse end found, matched channel 1 (end time: 328) T335: ‐‐‐> PDW(toa: 203, pw: 125, pa: ‐7.58 dBm, aoa: 32.9, f: 0.0) <‐‐‐ T671: [Ch1] pulse ended at 668




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T673: [Ch2] pulse ended at 668 T673: Pulse end found, amplitude difference: [‐51.02 ‐37.33 ‐57.30 ‐57.30] dBm T673: Pulse end found, matched channel 2 (end time: 668) T673: ‐‐‐> PDW(toa: 68, pw: 600, pa: ‐36.03 dBm, aoa: 34.0, f: 0.0) <‐‐‐ There are 0 valid trackbuffer entries remaining.





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D.3 Scenario 3

D.3.1 Solution 1

Using data from the workbench variable <data>. T69: [Ch2] pulse started at 68 T69: Pulse tracking started (pulse started at 68) T69: Now tracking 1 pulse_stack. T69: toa: 68, amp: [‐57.30 ‐34.44 ‐57.30 ‐57.30] dBm, f: 0.00 T70: Refined amplitude of pulse 1 (toa: 68) T70: new amp: [‐57.30 ‐35.90 ‐57.30 ‐57.30] dBm T71: Refined amplitude of pulse 1 (toa: 68) T71: new amp: [‐57.30 ‐35.63 ‐57.30 ‐57.30] dBm T254: [Ch1] pulse started at 253 T254: [Ch3] pulse started at 253 T254: Pulse tracking started (pulse started at 253) T254: Now tracking 2 pulse_stack. T254: toa: 253, amp: [‐22.71 ‐45.20 ‐41.14 ‐54.14] dBm, f: 0.00 T255: Refined amplitude of pulse 2 (toa: 253) T255: new amp: [‐24.73 ‐45.00 ‐42.17 ‐55.17] dBm T256: Refined amplitude of pulse 2 (toa: 253) T256: new amp: [‐24.35 ‐45.15 ‐42.00 ‐54.82] dBm T354: [Ch4] pulse started at 353 T354: Pulse tracking started (pulse started at 353) T354: Now tracking 3 pulse_stack. T354: toa: 353, amp: [‐39.64 ‐32.57 ‐45.72 ‐18.09] dBm, f: 0.00 T355: Refined amplitude of pulse 3 (toa: 353) T355: new amp: [‐39.28 ‐33.02 ‐46.09 ‐20.21] dBm T356: Refined amplitude of pulse 3 (toa: 353) T356: new amp: [‐39.52 ‐32.94 ‐45.96 ‐19.82] dBm T406: [Ch3] pulse ended at 403 T406: Pulse end discovered, determining pulse... T406: Pulse end, amplitude difference: [‐24.34 ‐47.00 ‐41.79 ‐57.30] dBm T406: Comparing with pulse 1 (toa: 68, amp: [‐57.30 ‐35.63 ‐57.30 ‐57.30]) T406: Comparing with pulse 2 (toa: 253, amp: [‐24.35 ‐45.15 ‐42.00 ‐54.82]) T406: Comparing with pulse 3 (toa: 353, amp: [‐39.52 ‐32.94 ‐45.96 ‐19.82]) T406: Decided pulse 2 ended. T406: ‐‐‐> PDW(toa: 253, pw: 150, pa: ‐24.28 dBm, aoa: 309.6, f: 0.0) <‐‐‐ T409: [Ch1] pulse ended at 403 T409: Pulse end ignored (end time: 403, ch: 1) T481: [Ch1] pulse ended at 478 T481: Pulse end discovered, determining pulse... T481: Pulse end, amplitude difference: [‐50.63 ‐32.86 ‐46.53 ‐19.93] dBm T481: Comparing with pulse 1 (toa: 68, amp: [‐57.30 ‐35.63 ‐57.30 ‐57.30]) T481: Comparing with pulse 2 (toa: 353, amp: [‐39.52 ‐32.94 ‐45.96 ‐19.82]) T481: Decided pulse 2 ended. T481: ‐‐‐> PDW(toa: 353, pw: 125, pa: ‐19.61 dBm, aoa: 122.8, f: 0.0) <‐‐‐ T482: [Ch3] pulse ended at 478 T482: Pulse end ignored (end time: 478, ch: 3) T486: [Ch4] pulse ended at 478 T486: Pulse end ignored (end time: 478, ch: 4) T674: [Ch2] pulse ended at 668 T674: Pulse end discovered, determining pulse... T674: Pulse end, amplitude difference: [‐57.30 ‐35.54 ‐57.30 ‐57.30] dBm T674: Comparing with pulse 1 (toa: 68, amp: [‐57.30 ‐35.63 ‐57.30 ‐57.30]) T674: Decided pulse 1 ended. T674: ‐‐‐> PDW(toa: 68, pw: 600, pa: ‐35.61 dBm, aoa: 47.8, f: 0.0) <‐‐‐ There are 0 active pulse_stack entries remaining.




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D.3.2 Solution 2

Using data from the workbench variable <data>. T69: [Ch2] pulse started at 68 T69: Pulse tracking started in Ch2 (pulse started at 68) T69: Track buffer: T69: [2] toa: 68, amp: [‐57.30 ‐34.44 ‐57.30 ‐57.30] dBm, f: 0.00 T70: Refined amplitude of track 2 (toa: 68), new amp: [‐57.30 ‐35.90 ‐57.30 ‐57.30]


dBm T254: [Ch1] pulse started at 253 T254: [Ch3] pulse started at 253 T254: Pulse tracking started in Ch1 (pulse started at 253) T254: Track buffer: T254: [1] toa: 253, amp: [‐22.71 ‐45.20 ‐41.14 ‐54.14] dBm, f: 0.00 T254: [2] toa: 68, amp: [‐57.30 ‐35.63 ‐57.30 ‐57.30] dBm, f: 0.00 T255: Refined amplitude of track 1 (toa: 253), new amp: [‐24.73 ‐45.00 ‐42.17 ‐


54.82] dBm T354: [Ch4] pulse started at 353 T354: Pulse tracking started in Ch4 (pulse started at 353) T354: Track buffer: T354: [1] toa: 253, amp: [‐24.35 ‐45.15 ‐42.00 ‐54.82] dBm, f: 0.00 T354: [2] toa: 68, amp: [‐57.30 ‐35.63 ‐57.30 ‐57.30] dBm, f: 0.00 T354: [4] toa: 353, amp: [‐39.64 ‐32.57 ‐45.72 ‐18.09] dBm, f: 0.00 T355: Refined amplitude of track 4 (toa: 353), new amp: [‐39.28 ‐33.02 ‐46.09 ‐


19.82] dBm T406: [Ch3] pulse ended at 403




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T409: [Ch1] pulse ended at 403 T409: Pulse end found, amplitude difference: [‐24.23 ‐46.58 ‐41.72 ‐57.30] dBm T409: Pulse end found, matched channel 1 (end time: 403) T409: ‐‐‐> PDW(toa: 253, pw: 150, pa: ‐24.28 dBm, aoa: 309.6, f: 0.0) <‐‐‐ T481: [Ch1] pulse ended at 478 T482: [Ch3] pulse ended at 478 T486: [Ch4] pulse ended at 478 T486: Pulse end found, amplitude difference: [‐50.08 ‐32.91 ‐46.17 ‐19.72] dBm T486: Pulse end found, matched channel 4 (end time: 478) T486: ‐‐‐> PDW(toa: 353, pw: 125, pa: ‐19.61 dBm, aoa: 122.8, f: 0.0) <‐‐‐ T674: [Ch2] pulse ended at 668 T674: Pulse end found, amplitude difference: [‐57.30 ‐35.54 ‐57.30 ‐57.30] dBm T674: Pulse end found, matched channel 2 (end time: 668) T674: ‐‐‐> PDW(toa: 68, pw: 600, pa: ‐35.61 dBm, aoa: 47.8, f: 0.0) <‐‐‐ There are 0 valid trackbuffer entries remaining.





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D.4 Scenario 4a

D.4.1 Solution 1

Using data from the workbench variable <data>. T104: [Ch1] pulse started at 103 T104: [Ch2] pulse started at 103 T104: [Ch3] pulse started at 103 T104: [Ch4] pulse started at 103 T104: Pulse tracking started (pulse started at 103) T104: Now tracking 1 pulse_stack. T104: toa: 103, amp: [‐32.31 ‐13.53 ‐43.40 ‐22.18] dBm, f: 0.00 T105: Refined amplitude of pulse 1 (toa: 103) T105: new amp: [‐33.87 ‐16.24 ‐44.23 ‐24.34] dBm T106: Refined amplitude of pulse 1 (toa: 103) T106: new amp: [‐33.57 ‐15.74 ‐44.06 ‐23.95] dBm T206: [Ch3] pulse ended at 203 T206: Pulse end discovered, determining pulse... T206: Pulse end, amplitude difference: [‐46.38 ‐17.40 ‐44.99 ‐24.07] dBm T206: Comparing with pulse 1 (toa: 103, amp: [‐33.57 ‐15.74 ‐44.06 ‐23.95]) T206: Decided pulse 1 ended. T206: ‐‐‐> PDW(toa: 103, pw: 100, pa: ‐15.13 dBm, aoa: 65.2, f: 0.0) <‐‐‐ T209: [Ch4] pulse ended at 203 T209: Pulse end ignored (end time: 203, ch: 4) T306: [Ch3] pulse ended at 303 T306: [Ch4] pulse ended at 303 T306: Pulse end, amplitude difference: [‐33.90 ‐20.81 ‐50.85 ‐48.41] dBm T306: Failure, Found a new pulse end (end time: 303, ch: 3), but no active

pulse_stack are being tracked. T306: Pulse end, amplitude difference: [‐33.90 ‐20.81 ‐50.85 ‐48.41] dBm T306: Failure, Found a new pulse end (end time: 303, ch: 4), but no active

pulse_stack are being tracked. T309: [Ch1] pulse ended at 303 T309: Pulse end, amplitude difference: [‐49.87 ‐33.37 ‐57.30 ‐57.30] dBm T309: Failure, Found a new pulse end (end time: 303, ch: 1), but no active


pulse_stack are being tracked. There are 0 active pulse_stack entries remaining.




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Figure 47: Overview of solution 1 in scenario 4a

D.4.2 Solution 2

Using data from the workbench variable <data>. T104: [Ch1] pulse started at 103 T104: [Ch2] pulse started at 103 T104: [Ch3] pulse started at 103 T104: [Ch4] pulse started at 103 T104: Pulse tracking started in Ch2 (pulse started at 103) T104: Track buffer: T104: [2] toa: 103, amp: [‐32.31 ‐13.53 ‐43.40 ‐22.18] dBm, f: 0.00 T105: Refined amplitude of track 2 (toa: 103), new amp: [‐33.87 ‐16.24 ‐44.23 ‐


23.95] dBm T206: [Ch3] pulse ended at 203 T209: [Ch4] pulse ended at 203 T209: Pulse end found, amplitude difference: [‐46.58 ‐17.47 ‐44.80 ‐23.96] dBm T209: Pulse end found, unmatched channel! (Ch4, end time: 203) T209: Refined amplitude of track 2 (toa: 103), new amp: [‐33.79 ‐20.57 ‐52.11 ‐

48.47] dBm T306: [Ch3] pulse ended at 303 T306: [Ch4] pulse ended at 303 T309: [Ch1] pulse ended at 303 T311: [Ch2] pulse ended at 303 T311: Pulse end found, amplitude difference: [‐32.08 ‐20.57 ‐50.67 ‐48.63] dBm T311: Pulse end found, matched channel 2 (end time: 303) T311: ‐‐‐> PDW(toa: 103, pw: 200, pa: ‐20.37 dBm, aoa: 32.9, f: 0.0) <‐‐‐ There are 0 valid trackbuffer entries remaining.




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Figure 48: Overview of solution 2 in scenario 4a




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D.5 Scenario 4b

D.5.1 Solution 1

Using data from the workbench variable <data>. T104: [Ch1] pulse started at 103 T104: [Ch2] pulse started at 103 T104: [Ch3] pulse started at 103 T104: [Ch4] pulse started at 103 T104: Pulse tracking started (pulse started at 103) T104: Now tracking 1 pulse_stack. T104: toa: 103, amp: [‐32.31 ‐13.53 ‐43.40 ‐22.18] dBm, f: 0.00 T105: Refined amplitude of pulse 1 (toa: 103) T105: new amp: [‐33.87 ‐16.24 ‐44.23 ‐24.34] dBm T106: Refined amplitude of pulse 1 (toa: 103) T106: new amp: [‐33.57 ‐15.74 ‐44.06 ‐23.95] dBm T206: [Ch3] pulse ended at 203 T206: Pulse end discovered, determining pulse... T206: Pulse end, amplitude difference: [‐46.38 ‐17.40 ‐44.99 ‐24.07] dBm T206: Comparing with pulse 1 (toa: 103, amp: [‐33.57 ‐15.74 ‐44.06 ‐23.95]) T206: Decided pulse 1 ended. T206: ‐‐‐> PDW(toa: 103, pw: 100, pa: ‐15.13 dBm, aoa: 65.2, f: 0.0) <‐‐‐ T209: [Ch4] pulse ended at 203 T209: Pulse end ignored (end time: 203, ch: 4) T306: [Ch3] pulse ended at 303 T306: [Ch4] pulse ended at 303 T306: Pulse end, amplitude difference: [‐33.90 ‐20.81 ‐50.85 ‐48.41] dBm T306: Failure, Found a new pulse end (end time: 303, ch: 3), but no active

pulse_stack are being tracked. T306: Pulse end, amplitude difference: [‐33.90 ‐20.81 ‐50.85 ‐48.41] dBm T306: Failure, Found a new pulse end (end time: 303, ch: 4), but no active



pulse_stack are being tracked. There are 0 active pulse_stack entries remaining.




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Figure 49: Overview of solution 1 in scenario 4b

D.5.2 Solution 2

Using data from the workbench variable <data>. T104: [Ch1] pulse started at 103 T104: [Ch2] pulse started at 103 T104: [Ch3] pulse started at 103 T104: [Ch4] pulse started at 103 T104: Pulse tracking started in Ch2 (pulse started at 103) T104: Track buffer: T104: [2] toa: 103, amp: [‐32.31 ‐13.53 ‐43.40 ‐22.18] dBm, f: 0.00 T105: Refined amplitude of track 2 (toa: 103), new amp: [‐33.87 ‐16.24 ‐44.23 ‐


23.95] dBm T206: [Ch3] pulse ended at 203 T209: [Ch4] pulse ended at 203 T209: Pulse end found, amplitude difference: [‐46.58 ‐17.47 ‐44.80 ‐23.96] dBm T209: Pulse end found, unmatched channel! (Ch4, end time: 203) T209: Refined amplitude of track 2 (toa: 103), new amp: [‐33.79 ‐20.57 ‐52.11 ‐

48.47] dBm T306: [Ch3] pulse ended at 303 T306: [Ch4] pulse ended at 303 T309: [Ch1] pulse ended at 303 T311: [Ch2] pulse ended at 303 T311: Pulse end found, amplitude difference: [‐32.08 ‐20.57 ‐50.67 ‐48.63] dBm T311: Pulse end found, matched channel 2 (end time: 303) T311: ‐‐‐> PDW(toa: 103, pw: 200, pa: ‐20.37 dBm, aoa: 32.9, f: 0.0) <‐‐‐ There are 0 valid trackbuffer entries remaining.




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Figure 50: Overview of solution 2 in scenario 4b




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Appendix E A Specific Test Case

The following test case is chosen to illustrate the capability of the algorithms (especially the first solution) to resolve very difficult scenarios. The key to why the first solution is able to resolve the scenario is that each pulse start and pulse end is discovered by at least one channel.

Figure 51: An example of a particularly difficult scenario

The result of the test case is shown below:

Result of test A: [ 6/ 6/ 0] Pass Result of test B: [ 6/ 1/ 3] FAIL Expected: toa: 50, pw: 325, pa: ‐38.0, f: 0.00, aoa: 220.0 Expected: toa: 100, pw: 150, pa: ‐13.0, f: 0.00, aoa: 355.0 Expected: toa: 125, pw: 50, pa: ‐5.0, f: 0.00, aoa: 30.0 Expected: toa: 75, pw: 325, pa: ‐35.0, f: 0.00, aoa: 80.0 Expected: toa: 200, pw: 150, pa: ‐15.0, f: 0.00, aoa: 130.0 Expected: toa: 150, pw: 150, pa: ‐4.0, f: 0.00, aoa: 270.0 A) Returned: toa: 128, pw: 50, pa: ‐5.5, f: 0.00, aoa: 32.6 A) Returned: toa: 103, pw: 150, pa: ‐15.0, f: 0.00, aoa: 353.0 A) Returned: toa: 153, pw: 150, pa: ‐6.1, f: 0.00, aoa: 271.0 A) Returned: toa: 203, pw: 150, pa: ‐14.9, f: 0.00, aoa: 126.5 A) Returned: toa: 53, pw: 325, pa: ‐38.2, f: 0.00, aoa: 221.0 A) Returned: toa: 78, pw: 325, pa: ‐36.8, f: 0.00, aoa: 76.3 B) Returned: toa: 128, pw: 50, pa: ‐5.5, f: 0.00, aoa: 32.6 B) Returned: toa: 103, pw: 200, pa: ‐15.0, f: 0.00, aoa: 353.0 B) Returned: toa: 203, pw: 150, pa: ‐15.1, f: 0.00, aoa: 159.5 B) Returned: toa: 153, pw: 225, pa: ‐6.1, f: 0.00, aoa: 271.0




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