design of a wideband jammer detector · design of a wideband jammer detector m.sc. thesis jeroen...

Design of a Wideband JammerDetector

M.Sc. Thesis

Jeroen A.H. Harmsen

Thales NetherlandsDepartment of Joint Radar SensorsProcessing group (JRS-PRO)P.O. Box 427550 GD Hengelo Ov.The Netherlands

University of TwenteDepartment of Electrical Engineering,

Mathematics & Computer Science (EEMCS)Signals & Systems Group (SAS)P.O. Box 2177500 AE EnschedeThe Netherlands

Report Number: SAS2203Report Date: 24th August 2003Period of Work: 20/01/2003 – 29/08/2003Thesis Committee: Prof. Dr. ir. C.H. Slump

ir. F.W. HoeksemaDr. ir. A.M. BazenDr. ir. H. Schurer (Thales NL)Ing. J.P. Mol (Thales NL)

Abstract

This report describes a method for jammer detection in a wideband radar signal. No wideband detectionmechanisms are available at the moment due to the relative low speed analog to digital converters (ADC).New, high speed ADCs offers the opportunity to analyze wideband radar signals without mixing themback to baseband or filter them to decrease the signal bandwidth.

Jammers are manmade interference and intended for interfering with or precluding the normal operationof enemy radio system. This project focusses on bandlimited noise jammers which can be detected onthe received power compared to the noise floor. Therefore first some different power spectrum densityestimators are examined. For jammer detection no frequency components have to be found which areclosely situated to each other, but noise bandlimited signals. For this reasons, and because a large datasequence is available, classical estimators give results which are sufficient for detecting jammers. Themain advantage of classical estimators is there repeating and non-conditional structure for implemen-tation in hardware. Therefore, the classical method is used for estimating the power spectrum. Thismethod is also implemented in an FPGA by another parallel project by Wolkotte [1], calculating thepower spectrum within 1 ms, which is seven times as fast as the specifications required.

Once the power spectrum has been estimated, the jammed frequency bands can be determined. A detectorhas been designed which needs only the power spectrum as input, and the number of averages which wereneeded to calculate the power spectrum. Therefore no interaction with other parts of the radar systemis needed and this will make integration into the system easier. Though this detector is not optimal,the results from the theoretical analysis are very promising. The detector is capable of detecting 3 dBjammers (meaning the jammer to noise ratio is 3 dB) within300 µs with a mean time between failuresof minimal 41 hour.

In order to simulate the designed algorithm and to test the implementation in hardware, a model has beendeveloped which generates broadband radar signals. This model is capable of simulating noise, targetsand jammers. Clutter signals are not implemented yet, but they are also irrelevant for the implementedtype of jammer detection. A graphical user interface is build to generate the signals and export them tothe FPGA where the power spectrum algorithm is implemented by Wolkotte [1]. The calculated powerspectrum is returned to the computer and then the developed jammer detection algorithm detects thejammed frequency bands.

I

Preface

Radar systems make use very advanced and complicated digital algorithms and it was very fascinatingto work in this area. After this project I understand several possibilities of radars, but even more thedifficulties which have to overcome. The development of high speed analog to digital converters withsufficient resolution will open even more possibilities and digital signal processing will become moreand more important. In radar systems is digital signal processing an increasing investigation area wheremuch research still has to be done.

This project is the final assignment for my Master degree in Electrical Engineering at the University ofTwente. Many aspects of my study were very helpful during this assignment and not the less the lectureson Advance Digital Signal Processing by Prof. C.H. Slump. I wish to thank Prof. C.H. Slump forintroducing me to digital signal processing which is a very interesting and inspiring subject.

Also I would like to thank my parents, who supported me throughout my study unconditional. Especially,I wish to express my gratitude to my girlfriend Esther, who not only supported me but also kept onbelieving in me and for encouraging me to finish my study.

Enschede, August 2003

Jeroen A.H. Harmsen

III

CONTENTS

Contents

1 Introduction 1

1.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 The radar system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.1 Development in radar technique . .. . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 SMART-L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.4 Jammers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.5 Assignment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.6 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 Power Spectrum Estimators 9

2.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2 Non-parametric methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.1 Periodogram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.2 Properties of the periodogram . . .. . . . . . . . . . . . . . . . . . . . . . . . 12

2.2.3 Averaging periodograms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2.4 Averaging modified periodograms .. . . . . . . . . . . . . . . . . . . . . . . . 14

2.2.5 Periodogram smoothing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2.6 Properties of averaging (modified) periodograms. . . . . . . . . . . . . . . . . 15

2.3 Parametric power estimators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.3.1 Prediction .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.3.2 Yule-Walker Method for the AR Model Parameters. . . . . . . . . . . . . . . . 18

2.3.3 Burg Method for the AR Model Parameters. . . . . . . . . . . . . . . . . . . . 18

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CONTENTS

2.3.4 Experimental results of the Yule-Walker and Burg algorithm. . . . . . . . . . . 19

2.4 Classical versus Parametric methods for Jammer Detection. . . . . . . . . . . . . . . . 21

2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3 Simulation of Radar Signals 23

3.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2 Definition of the simulated radar system. . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2.1 Definitions of pulse radars. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2.2 Functional Radar Blocks .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2.3 Signal Radar Blocks . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.2.4 Jammer types and there properties. . . . . . . . . . . . . . . . . . . . . . . . . 26

3.2.5 Simulating the radar signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.3 Results . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4 System Definition 33

4.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.2 Fixed system parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.3 Algorithm choice and optimization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.3.1 Sampling Frequency choice. . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.3.2 Algorithm optimization . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.3.3 Size of the FFT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.3.4 Optimization of the preprocessing blocks. . . . . . . . . . . . . . . . . . . . . 38

4.3.5 Final structure choice . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.4 Implementation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5 Detector 45

5.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.2 Systematic Description of the Detector. . . . . . . . . . . . . . . . . . . . . . . . . . . 45

VI

CONTENTS

5.3 Probability Density Function of Frequency bins. . . . . . . . . . . . . . . . . . . . . . 46

5.3.1 PDF of a single frequency bin . . .. . . . . . . . . . . . . . . . . . . . . . . . 47

5.3.2 PDF after summation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5.3.3 Consequences of averaging on the mean and variance. . . . . . . . . . . . . . . 47

5.3.4 Practical example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5.4 Determination of jammed subbands. . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

5.4.1 Histogram .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.4.2 PDF of subbands. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.5 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

6 Conclusions and Recommendations 59

6.1 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

6.2 Recommendations .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

A Levinson-Durbin algorithm 63

A.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

A.2 Function: levdub .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

B Forward linear prediction 67

C PSD Estimators 71

C.1 Function: PSDWelch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

C.2 Function: PSDyulewalker. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

C.3 Function: PSDburg. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

D Generation of Radar Signals, Matlab script 75

D.1 Function: r2d . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

D.2 Function: d2r . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

D.3 Function: Jdefant .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

D.4 Function: Jdefjammer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

VII

CONTENTS

D.5 Function: defnoise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

D.6 Function: Jdeftarget. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

D.7 Function: defwave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

D.8 Function: defsources. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

D.9 Function: getmod. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

D.10 Function: simnoise. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

D.11 Function: Jsimjammer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

D.12 Function: Jsimtarget. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

D.13 Function: Jsimradarsig. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

D.14 Function: RxRadarSigT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

D.15 Function: Ran2SampleNo. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

D.16 Function: uisaveSignalSimulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

D.17 Function: UISignalSimulationexport . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

E Matlab scripts general 115

E.1 Function: plotting PD and PFA . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

F Abbreviation list 117

Bibliography 119

VIII

Chapter 1

Introduction

1.1 Introduction

This Master’s Thesis is concerned with the realization of a demonstrator for smallband jammer detectionin a wideband radar signal. In this introduction chapter some facts and figures will be given after whichbasic principles of radars will be treated. Next, the focus will be on jammers and the specific radarsystem for which the detector is designed: SMART-L from Thales NL. Finally the assignment descriptiontogether with the outline of this report will be given.

Modern air defense systems are unimaginable without radars. The radars are the ”eyes” of a ship or landdefense system against several aggressors. A single radar is only a part of the complete radar system. Insuch a system every radar is made for different kind of tasks. From surveillance to highly specializedsearch and track radars. A magnificent example is the new Air Defence and Command frigate (LCF) ofthe Royal Netherlands Navy the ”Zeven Provincien” shown in figure 1.1, where several different types ofradars are situated. Because a system is not able to see under all different kind of conditions every radaruses specific frequency areas. Every frequency area is useful for sensing at a different circumstance.

The basic principle of radar detection is almost as old a the subject of electromagnetism itself. HeinrichHertz, in 1886, experimentally tested the theories of Maxwell and demonstrated the similarity betweenradio and light waves. Hertz showed that radio waves could be reflected by metallic and dielectric bodies,where light waves are reflected by a non-transparent body. After this discovery the radar was developedindependently and simultaneously in several countries just prior to World War II. The first radar systemswere only able to detect objects in their direction of view. Gradually the information extracted from thesignal increased together with the types of signalling used. For example a radar sensitive for infraredlight is able to indicate heated targets. And a radar, which uses radiowaves, does not need an external”light” source to be able to ”see”.

For an operator of a radar system it is important to detect (see) a possible aggressor as soon as possible.However, the aggressor wants to stay invisible as long as possible. Staying invisible is possible with forexample stealth techniques. Stealth technique is a technique where the reflected signal towards the radarsensor is minimized. For example, a blue airplane in a blue sky can not be seen if the radar based onsensing visible light. Another way to prevent detection is to transmit a (noisy) signal, so the radar cannot properly detect the reflected signal anymore. This type of interference is called active jamming.

One of the aims of the radar developer is to design the radar in such way this active jamming is noteffective, meaning it will not degrade the system in such a way that it can’t perform its mission. This can

1

1. Introduction

Figure 1.1: The new Air Defence and Command frigate (LCF) the ”Zeven Provincien” of the RoyalNetherlands Navy with several different types of radars. Some radars from Thales are: Smart-L, APAR,Goalkeeper, Sabre.

be achieved by improving the quality of the processed signal. This improvement is possible with a betterprocessing of the received signal or minimizing the amount of received noise. This amount of noise willdiffer among the different operating frequencies of the radar. Choosing for the least noisy frequency willbe only possible if the amount of noise in all the different operating frequencies are known.

Current radar systems are already able to handle parts of the problems regarding jamming as describedabove. Used techniques are sidelobe cancellation, Skolnik [11], which adaptively places nulls from thebeam pattern at the direction of the external noise source. An other possibility is a so-called burnthroughwhich means that the radar energy will be increased in the direction of the jammer in the hope of receivingthe radar echo power above the jamming noise.

Though there are much more smart and advance anti-jamming techniques, one other is interesting tomention. If a radar system is capable of unpredictable changing its frequency from time to time, thejammer is forced to spread its power over a wide band, Maksimov et al. [14]. This will reduce theeffective jammer power over a smaller band in which the radar transmits its signal. This project is acontinuation on this idea. Suppose that the radar system is capable of changing its frequency. Thechange of frequency of the radar system should be unpredictable, but also the change should be intonot-jammed frequency bands. The second restriction is harder to accomplish than the first one, becauseif the frequency band is jammed it is sure that echo’s can not be interpreted. The purpose of this project isthe design and prototype implementation of a method for detecting jammed bands within the total band

2

1.2. The radar system

in which the radar system can transmit its pulses.

The next section will discuss some radar systems and explain their general concepts. Also a step to newradar systems is made, due to new generations of analog to digital converter (ADC) having high samplingfrequencies. The new ADCs enable make it possible to do broadband signal processing, where previousradar system first had to mix (analogue) the band back to baseband.

1.2 The radar system

The principle of radars is easy to understand. The radar transmits a signal which will be reflected by atarget. A receiver (usually the same radar) tries to detect this reflection. The time between transmissionand detection is a measurement for the distance and if the target has a velocity relative to the radar, thiswill also be measurable in the reflected signal.

Radar systems can be divided in 2 major categories based on there transmitted signal, Skolnik [11]:

• Continuous Wave Radar

• Pulse Doppler Radar

One can define more subcategories, but these two types are the most important. In both cases the radartransmits a well known signal and observes the returned echo. The transmitted signal has always acarrier frequencyfc which could be varied, according to its specific application. The receiver part of theradars are completely matched on the characteristics of the transmitted wave. Ideally at the output of thismatched receiver a pulse will appear if the target has reflected the transmitted signal.

Figure 1.2:The basic radar principle where the transmitter and receiver use the same antenna and inthis case the SMART-L radar is shown.

Continuous Wave Radars

A continuous wave (CW) radar transmits continuously and separates the weak echo from the strongtransmitted signal at the receiver. A feasible technique for this separation, when there is a relative motionbetween radar and target, is based on recognizing the change in the echo-signal frequency caused by

3

1. Introduction

the doppler effect. This technique for separation and examining the echo forms the basis of CW radar,Skolnik [11].

The necessary isolation between the transmitted and the received signals is achieved via separation infrequency as a result of the doppler effect. In practise, it is not possible to completely eliminate thetransmitter leakage of the transmitted energy directly to the receiver. However the send frequency couldbe used as a reference necessary for the detection of the doppler frequency shift. The chief use of simple,unmodulated CW radar is for the measurement of the relative velocity of a moving target, as in the policespeed monitor. But for long-range applications the utility of unmodulated CW radar are limited due tothe necessary high transmitted power.

One of the greatest shortcomings of the simple CW radar is its inability to obtain a measurement of time(∼ distance). A timing mark, such as a changing frequency, permits the time of transmission and thetime of return to be recognized. Using a change of frequency in the transmitted signal, the radar is calledFrequency Modulated CW radar or shortly FM-CW.

Pulse Doppler Radar

Pulse radars use the doppler frequency shift to separate small moving targets in the presence of largeclutter (e.g. clouds, sea). A pulse doppler radar transmits pulses of electromagnetic waves instead oftransmitting continuously. This has the main advantage that the receiver and transmitter do not worksimultaneously, but successively. Therefore the transmitter is capable of transmitting a much higherpower signal.

The time between the transmitted pulse and received echo gives an indication for the distance of thetarget. From the frequency difference between the reflected signal and the transmitted signal the rela-tive frequency can be determined. This relative frequency gives the doppler information, which is anindication of the speed of an object. Clutter (having a speed of zero) can be extracted from the possiblereflections with this doppler information.

As well as measuring the distance and speed of a target by analyzing the signal, it is also possible to detectthe exact position of the target in the 3D world. By measure the incoming direction of the received signalthe elevation (vertical angle, of altitude) and azimuth (horizontal angle) can be calculated. For examplefor a rotating radar, which is only sensitive in the direction of view, the azimuth can be determined fromthe position of the radar.

1.2.1 Development in radar technique

An important device in many products is the analog to digital converter (ADC). This device separates theanalog from the digital processing part. Digital processing has several advantages like being independentof the inaccuracy of components, but properly even a larger advantage is the reconfigurability. Newprocessing and/or features can be implemented without changing the hardware. Finally it is a lot easierto implement advance and large algorithms in digital devices as to design and implement an equivalentin the analog domain. Therefore a lot of signal analysis (like spectrum estimation and target detection)are performed in the digital domain.

New ADC having a (very) high sample rate (e.g. GHz range) offer also another very important property,namely the opportunity to analyze wideband signals. Due to the Nyquist criterium, the sample rate isresponsible for the maximal bandwidth which can be analyzed. If new ADC’s have sample rates which

4

1.3. SMART-L

are higher as twice the broadband (> 200 MHz) frequency information of the radar signal, it should(theoretical) be possible to analyze the whole bandwidth digitally. Otherwise signals have to be mixedback to baseband and are then low pass filtered and digitized. The enormous possibilities which newADC’s offer, will be discussed shortly in the next sections, with special attention for the SMART-L radarsystem.

1.3 SMART-L

Figure 1.3:The SMART-L radar system

SMART-L is the D band (1.2 GHz≤ f ≤ 1.4 GHz) version of the successful family of SMART multi-beam 3D radars. This family of multibeam radars are operational on board ships of various NATOcountries. The SMART-L antenna consists of a stack of 24 linear arrays. All 24 arrays are used duringreception while 16 arrays are used during transmission. By controlling the phase of the RF energy, con-nected to the 16 elements, the illumination pattern can be controlled and level stabilized. The receivedradar energy is processed by 24 receiver channels and fed to a beamforming network in which 14 beamsare formed in the elevation coverage from0o to 70o (as is visible in figure 1.4). The output signals of thebeam former are further processed for the extraction of the target and environment information.

0.2

0.4

0.6

30o

60o

90o

0o

Single beam

Figure 1.4: The beam pattern generated by the beamforming network of the SMART-L. Every singlebeam is sensitive in a specific elevation.

A schematic view of the SMART-L radar for the receiving part is visible in figure 1.5. The receiveralready contains a large amount of digital processing, but the matched filter is still an analog part in the

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1. Introduction

system. A wideband signal analysis algorithm is developed to analyze the complete frequency band ofSMART-L. This algorithm is realized a demonstrator to show the possibilities of high speed digital signalprocessing in an FGPA in a parallel project by Wolkotte [1]. The result will give an idea of the furtherpossibilities for developing a complete digital radar receiver. This digital radar receiver is only possiblewith the use of a high speed ADC, which maintains the wideband frequency information.

Initially this demonstrator will be coupled directly after the antenna (position 1 in figure 1.5), whichresults in small system parallel to the existing receiver. Another option would be to place this demon-strator after the analog matched filter (position 2 in figure 1.5). This would give a signal improvementdue to the matched filter. But the improvement is only achieved in a small frequency band, because ofthe presence of several small bandpass filters in the analog processing. The rest of the wideband signalwill be attenuated and therefore cannot be analyzed.

If in a new generation of radar systems more of the analog processing will be replaced by digital version,it is also possible to place a wideband jammer detector after the beamformer (position 3 in figure 1.5).This would require 24 parallel high speed AD-converter and a very calculation demanding beamformingnetwork, but it will give extra elevation information for the jammer detector.

Figure 1.5:The current front end of the Smart-L antenna. The antenna consists of a stack op 24 lineararrays. The analog signal processing is a matched filter for the received radar signal. After a digitaliza-tion of these 24 signals, the beamforming network creates 14 beams in the elevation coverage from0o to70o. These beams are used for the extraction of the target and environment information.

The above reasons indicate to place the jammer detection ideally behind the beamformer, so more in-formation about (the position of) the jammer is available. Placing the jammer detector after the beamformer also makes the detection easier, because a jammer cannot be situated in all the frequencies andcomplete (elevation) range of the radar. So defining the threshold(s) can rely on 2 different (uncorrelated)dimensions (elevation and frequency).

1.4 Jammers

Producing a radio signal by a special radio transmitter intended for interfering with or precluding thenormal operation of enemy radio system is called active jamming. Active jamming produces at the inputof a victim system a background signal. This signal impedes the detection and recognition of usefulsignals and determination of their parameters. Jamming interference is usually linearly added to thesignal at the receiver input and is therefore called additive interference.

6

1.5. Assignment

Active jamming may be divided into three classes: continuous noise, random pulse noise and regularpulse noise. But any of the three classes reduces the probability of correct signal detection, increases theprobability of false alarm and reduces measurement accuracy. The effectiveness of jamming depends onmany factors, especially on the time and frequency structure both of the noise and of the signal, and alsoon the power ratio of the interference and signal at the input of the receiver of the victim system.

The enemy radio system wants to be immune to the interference of the jamming signal. This immunityis described as the ability to perform effectively while an enemy is simultaneously engaged in electronicsurveillance and jamming [14]. The control of the interference is based essentially on knowing theparameters of the transmitted signal and use this in matched filter of the radar receiver. This is forexample accomplished by: preventing the overloading of receivers, by cancellation of radio interferenceor adaptation of the radar system.

Adaptation involves a change in the structure and parameters of an electronic system to perform at itsbest during any kind of jamming. This adaptation makes it possible stay unpredictable or to change to abetter measurable condition. In this project an extra measurement system is realized, which can improvethe speed and possibilities of adaptation. In essence the measurement system quantifies the amount ofjamming in a specific band. Knowing this amount makes it possible to change the frequency band to anun-jammed one.

1.5 Assignment

There has always been a desire to build flexible radar/receiver systems. Digital re-configurable or re-programmable hardware systems by software combined with possibilities of full band analysis are sig-nificant. Because of the analog nature of the air interface, a so-called digital receiver will always havean analog front-end. Ideally, the ADC should be positioned directly after the antenna, requiring a highspeed ADC. With the arrival of new low power, high speed ADCs, it is possible to place the ADC almostdirectly after the antenna.

These high speed ADCs will result in large data sequences which have to be processed at a very highspeed. Many people at Thales asked themselves whether current hardware systems are capable of pro-cessing the amount of data at high speeds. The digital radar project has therefore the basic question:

Is it possible to replace the current analog processing with a new digital design immediately after theantenna?

In order to concretize this question a subproblem has been identified, concerning the design of a sim-ple wideband jammer detector for a D-band radar system. Important constraints are the use of a highspeed ADC and the implementation of the designed algorithm in hardware. This master thesis concernsthe development of the algorithm for this detection system. Another parallel project by Wolkotte [1],implemented the designed algorithm.

This project has to give a proposal for an algorithm which is capable of detecting jammers in a widebandradar signal for the SMART-L radar. The radar bandwidth is from 1200 to 1400 MHz and the minimumJammer to Noise ratio which should be detectable is 3 dB. Another requirement is that the processing ofthe algorithm should be ready before the start of a next burst, resulting in a maximum time for processingof 7 ms.

In order to simulate the designed algorithm and to test the implementation in hardware, a model has tobe developed which simulates the received radar signals. This models should simulate at least jammers

7

1. Introduction

and targets.

1.6 Overview

This introductory chapter provided some overview in the different aspects of the development of thejammer detector. Above all things, the detector should be implementable in a hardware device chosenby Wolkotte [1] as well as the probability of false decision should be low. The next chapters will dealwith the selection of an algorithm which can be implemented in hardware. Also a simulation model forwideband radar signals will be derived.

Chapter 2 starts with theory about spectral analysis. It distinguish two different methods, parametric andnon-parametric or classical method. The differences in quality and computational load will be discussed,concluded with a well-founded choice for a specific method.

A simulation model for simulating wideband radar signals will be described in chapter 3. Several prop-erties of radar signals are discussed. Several definitions for pulse radars will be given. Several differenttypes of jammers are discussed and are clear choice will be made which type of jammer will be simulatedand recognized by this project.

Chapter 4 will give a definition of the designed system. Since the algorithm is implemented in hardwareby Wolkotte [1], some optimizations were necessary. These optimizations, together with the paramtriza-tion, are given in chapter 4, which has been written together with Wolkotte.

The detector will be described in chapter 5. The conceptual blocks will be discussed, together with someprobability theory. A definition will be given for the robustness of the system which will be underpinnedwith some theoretical results.

The last chapter of this thesis will summarise the results of the conducted research, followed by conclu-sions and recommendations for further research.

8

Chapter 2

Power Spectrum Estimators

2.1 Introduction

There are two classes of methods for power spectrum estimation: non-parametric methods and parametricmethods. In each class there are a set of methods with all different performance. The performance of allthese different estimation methods is evaluated by looking into the expected value (bias) and the varianceof the estimate. First two classes are distinguished and different methods within a class will be described,see figure 2.1. The basic method for the nonparametric class is the Periodogram method as introduced bySchuster [2]. Others have modified it in order to obtain a different (better) result [3] [4]. The parametricmethods are based on modelling the data first, after which the power spectrum is estimated from theparameters of the model. These methods are described in paragraph 2.3

Figure 2.1:Different ways to estimate the Power Spectrum Density (PSD) divided in two classes.

9

2. Power Spectrum Estimators

2.2 Non-parametric methods

The nonparametric methods are also called the classical methods. These methods make no assumptionabout how the data were generated, or contents of the data. Since the estimates are based entirely on afinite record of data, the frequency resolution of these methods is, at best, equal to the spectral width ofthe rectangular window of lengthN . Below, the methods for nonparametric power spectrum estimationwill be explained.

2.2.1 Periodogram

The power spectrum is often estimated with help of the Fourier Transform, though important classes ofsignals (most periodic signals and random signals) are power signals and thus do not possess a FourierTransform. They do have a finite average power and hence are characterized by a power spectral den-sity. The Wiener-Khinchin theorem states that the PSD of a stationary random process is the FourierTransform of the autocorrelation function [4].

In practice, the true autocorrelation function is not known, due to a single realization of the randomprocess. Though from a finite, single realizationx(n), 0 ≤ n ≤ N−1, the time-averaged autocorrelationsequence may be computed,

rxx(m) =1

N − |m|N−|m|−1∑n=0

x∗(n)x(n + m) m = 0, 1, . . . , N − 1 (2.1)

where ·∗ denotes the complex conjugate. Notice that at this pointm is allowed to have the values0 ≤ m ≤ N − 1, otherwise wouldx(n + m) result in non-existing samples. To obtain the negative partof rxx the complex conjugate has to be taken, according torxx(−m) = r∗xx(m). So for calculating theautocorrelationm is allowed to obtain only positive values and otherwise:−(N−1) ≤ m ≤ N−1. If thestationary random process is ergodic in the first and second moment, the time-averaged autocorrelationwill be the true autocorrelation function in the limit,N → ∞.The normalization factorN − |m| forcomputing the autocorrelation sequence, results in an estimate with mean value

E [rxx(m)] =1

N − |m|N−|m|−1∑n=0

E [x∗(n)x(n + m)] (2.2)

= γxx(m) (2.3)

whereγxx(m) is the (statistical) autocorrelation sequence ofx(n).

Then the discrete Fourier Transform ofγxx(m) provides the true discrete power spectral density;

Γxx(f) =N−1∑

m=−N+1

γxx(m)e−j2πfm (2.4)

The discrete Fourier Transform ofrxx(m) (rxx(m) being an estimate of the autocorrelation) provides anestimatePxx(f) of the PSD; The variance of the estimaterxx(m) is approximately,

var[rxx(m)] ≈ N

(N − |m|)2∞∑

n=−∞

(|γxx(m)|2 + γ∗xx(n−m)γxx(n + m)

)(2.5)

which is a result given by Jenkins and Watts [5]. For largem, especially asm approachesN , the estimaterxx(m) has a large variance. As an alternative, the following estimate of the autocorrelation sequence

10

2.2. Non-parametric methods

may be used,

rxx(m) =1N

N−|m|−1∑n=0

x∗(n)x(n + m) (2.6)

which has a bias of|m|N γxx(m), since its mean value is,

E[rxx(m)] =1N

N−|m|−1∑n=0

E [x∗(n)x(n + m)] (2.7)

=N − |m|

Nγxx(m) =

(1 − |m|

N

)γxx(m) (2.8)

In return, this estimate has a smaller variance, given approximately as

var[rxx(m)] ≈ 1N

∞∑n=−∞

(|γxx(m)|2 + γ∗xx(n−m)γxx(n + m)

)(2.9)

It can be seen thatrxx(m) is asymptotically unbiased;

limN→∞

E[rxx(m)] = γxx(m) (2.10)

and its variance converges to zero asN → ∞. Therefore, the estimate is a so-calledconsistent estimateof γxx(m) [4]. Consistent means that in the limit the expectation of the estimate should converge to thetrue value and the variance to zero. The corresponding estimate of the PSD is,

Pxx(f) =N−1∑

m=−N+1

rxx(m)e−j2πfm (2.11)

=1N

∣∣∣∣∣N−1∑n=0

x(n)e−j2πfn∣∣∣∣∣2

(2.12)

=1N

|X(f)|2 (2.13)

whereX(f) is the Fourier transform of the sample sequencex(n). This well-known form of the PSDestimate is called theperiodogram, which was originally introduced by Schuster [2]. The average (ormean) value of the periodogram estimatePxx(f) is,

E[Pxx(f)] = E

[N−1∑

m=−N+1

rxx(m)e−j2πfm]

(2.14)

=N−1∑

m=−N+1

E[rxx(m)]e−j2πfm (2.15)

=N−1∑

m=−N+1

(1 − |m|

N

)γxx(m)e−j2πfm (2.16)

=N−1∑

m=−N+1

γxx(m)e−j2πfm − 1N

N−1∑m=−N+1

|m| · γxx(m)e−j2πfm (2.17)

The estimated spectrum is asymptotically unbiased, since,

limN→∞

E

[N−1∑

m=−N+1

rxx(m)e−j2πfm]

=∞∑

m=−∞γxx(m)e−j2πfm = Γxx(f) (2.18)

11


The variance of the estimatePxx(f) for a data sequence of a Gaussian random process is [4],

var[Pxx(f)] = Γ2xx(f)

(1 +

[sin 2πfNN sin 2πf

]2)

(2.19)

which, in the limit asN → ∞, becomes

limN→∞

var[Pxx(f)] = Γ2xx(f) (2.20)

Hence, we conclude that the periodogram isnot a consistent estimate of the true PSD (i.e., it does notconverge to the true PSD, since in the limit asN → ∞ the variance does not converge to zero).

2.2.2 Properties of the periodogram

It has been shown in the previous section that the periodogram is not a consistent estimate of the truePSD, because the variance does not converge to zero. This is not the only problem with periodograms.Two other properties, bias and leakage, determine the quality of the estimate of the PSD. As notationfrom this pointPxx = P periodogram

xx , where the superscript indicates the method used for calculatingPxx.

Periodogram bias

Equation 2.17 shows that for data sequences less with length than infinity, the expected value for theperiodogram will contain abiasand thus will not be the true spectrum. The periodogram is calculatedat discrete values, where each value is supposed to be a representative of a whole discrete frequencyvalue extending from halfway from the preceding discrete frequency to halfway to the next one. ThenPxx(fk), indicating the periodogram estimate at a discrete frequencyfk, shouldbe expected to be somekind of average ofPxx(f) (the continuous true spectrum) over a narrow window function centered onits fk. Equation 2.17 is logical in this point of view, since as the number of discrete values (N ) goes toinfinity, the bias should go to zero, see 2.18.

Leakage

In practice, only a finite-duration sequencex(n) is available for computing the spectrum of the signal,which is equivalent to multiplyingx(n) by a rectangular windoww(n). From the basic Fourier transformproperties, it is known that multiplication of two sequences is equivalent to convolution of their spectra.By this convolution the sidelobes of the window functionW (f) (see figure 2.2) will result in significantleakagefrom one frequency to another in the periodogram estimate. The solution for the problem ofleakage is called time windowing, and will be discussed below.

Time windowing

As indicated, the finite-duration sequencex(n) has already been windowed by a rectangular window(becausex(n) is finite). Besides a rectangular window, there are various different window types withdifferent properties. Time windowing could be an answer for sidelobe reduction, but this can only beachieved by broadening the window’s mainlobe frequency response, resulting in a reduction of the spec-tral resolution, see figure 2.2. A trade-off must, therefore, be made between mainlobe width and the

12


0 20 40 600

0.2

0.4

0.6

0.8

1

Rectangle (Uniform) window

Samples

0 20 40 600

0.2

0.4

0.6

0.8

1

Weighted Cosines (Blackman−Harris) window

Samples

0 0.2 0.4 0.6 0.8 1−20

−10

0

10

20

30

40

Normalized Frequency (×π rad/sample)

Mag

nitu

de (

dB)

0 0.2 0.4 0.6 0.8 1−150

−100

−50

0

50

Normalized Frequency (×π rad/sample)

Mag

nitu

de (

dB)

Figure 2.2:Two different windows: rectangular and Blackman-Harris window. Though the Blackman-Harris window has significant lower sidelobes (which will reduce the leakage effect), the mainlobe hasbeen broadened and therefore the spectral resolution will be less.

level of sidelobe suppression. Unfortunately there is no objective measurement for chosing the best win-dow and in each case this trade-off should be made. If the rectangular window has not been used, theperiodogram is calledmodified periodogram. Before the Fourier Transform will be calculated, eachsample is first multiplied with its appropriate window coefficient. If equation (2.13) is used, the powerspectrum density estimation can be computed by the Fourier transform. Themodified periodogrammaybe calculated by windowing the data segments prior to computing the periodogram, as given by;

Pmodifiedxx (f) =

1NU

∣∣∣∣∣N−1∑n=0

x(n)w(n)e−j2πfn∣∣∣∣∣2

(2.21)

whereU is a scaling factor for the power in the window function and is defined as;

U =1N

N−1∑n=0

|w(n)|2 (2.22)

2.2.3 Averaging periodograms

Bartlett introduced a method for reducing the variance in the periodogram, involving three steps [4]:

1. SubdivideN -point sequence intoK non-overlapping segments of lengthM .

2. Compute for each segment the periodogram.

13


3. Average the periodograms for theK segments.

The reduction in variance has to be paid back in the frequency resolution. The window has now a lengthof M , whereM = N

K , instead of the original lengthN . The spectral width of this window has beenincreased by a factorK. Consequently, the frequency resolution has been reduced by a factorK. Onthe other hand the variance has been improved by a factorK.

Extending equation 2.13 for averaging overK periodogram estimates, will result:

PBartlettxx (f) =

1K

K∑r=1

1N

|Xr(f)|2 (2.23)

WhereXr(f) is the Fourier Transform of segmentr of x(n).

There is a second variant, not introduced by Bartlett, which can be used when the estimated average ofthe data has to be updated continuously. This approach is calledexponential averageand defined as;

P exponentialxx,r (f) ≈ K − 1

K· P exponential

xx,r−1 +1

N ·K |Xr(f)|2 r ≥ 1 (2.24)

WhereP exponentialxx,0 (f) = 0. This approach has the advantage that the calculations can be stopped as

soon as the result is good enough. Secondly if the power is estimated for several segments,nonstationary trends can be observed and the final power estimate can be calculated by taken theweighted average of calculated power estimates.

2.2.4 Averaging modified periodograms

Averaging modified periodograms, or better known as the ’Welch method’, has two basic modificationsto the Bartlett method.

1. Data segments are allowed to overlap

2. Window the data segments prior to computing the periodogram (hence, ’modified’ periodogram)

These modifications have as a result that there are more segments (in case of overlap) and animprovement of the variance (due to the windowing). A consequence of the windowing is thebroadening in frequency resolution, where in return a smaller variance is given. In fact equation 2.21and 2.23 will be combined and give

PWelchxx (f) =

1N · U ·K

K∑r=1

∣∣∣∣∣N−1∑n=0

xr(n)w(n)e−j2πfn∣∣∣∣∣2 (2.25)

A throughout treatment of the Welch’s approach can be found in his paper [3].

14


2.2.5 Periodogram smoothing

Blackman and Tukey proposed and analyzed the method in which the sample autocorrelation sequenceis windowed first, and then Fourier transformed to yield the estimate of the power spectrum, giving;

PBTxx (f) =

M−1∑m=−M+1

rxx(m)w(m)e−j2πfm (2.26)

whereM N , i.e. the autocorrelation functionrxx(m) is calculated by taking the whole datasequence ofN -points.

The windoww(m) should be much smaller compared to the triangular window (also known as theBartlett window), so the (extra) smoothing of the periodogram will be effective. Otherwise the effect ofthe Bartlett window would prevail the effect of windoww(m), see equation 2.8. The disadvantage ofthis method is that first the autocorrelation function has to be estimated, after which the windowfunction can be applied (indirect method).

Subsequently the Fourier Transform can be applied. Therefore it needs more operations (multiplicationsand adders) than the direct method of taking the absolute value of the Fourier Transform of the datasequence squared.

2.2.6 Properties of averaging (modified) periodograms

The periodogram has several properties. These properties are summated.

Periodogram Properties for all periodogram methods

• Frequency resolution is controlled by the number of points,N (frequency bins), in the FFT

• The periodogram gives a asymptotically unbiased estimate of the power spectrum density

• The periodogram is not a consistent estimate of the true PSD

Windowing Consequences of windowing the input sequencex(n)

• Leakage is controlled by the time window

• There will be a trade-off between leakage suppression and spectral resolution

• Spectrum smoothing is achieved by the time window

Averaging Properties of averaging the periodograms

• Averaging does not improve the bias of the periodogram estimate, it decreases the spectralresolution when segmenting the data

• The variance of the estimated power spectrum decreases proportional to the increase in thenumber of segments

• Nonstationary trends can be observed by monitoring shorter intermediate spectrum resultsbefore the number of averages

• Overlapping makes maximal use of the data and yields the smallest achievable variance fora given input record length

• The variance decreases at a slower rate as the overlap increases and studies have shown that50% overlap is near optimal [3].

15


2.3 Parametric power estimators

The parametric methods considered in this section (see e.g. [4]) are based on modelling the datasequencex(n) as the output of a linear system with white-noise inputw(n), characterized by a rationalsystem function of the form:

H(z) =B(z)A(z)

=∑q

k=0 bkz−k

1 +∑p

k=1 akz−k (2.27)

The corresponding difference equation is

x(n) = −p∑k=1

akx(n− k) +q∑k=0

bkw(n− k) (2.28)

wherew(n) is the input sequence to the system and the observed data,x(n), represent the outputsequence. This system is schematically given in figure 2.3. In power spectrum estimation, the input

Figure 2.3:Schematic model of a linear system characterized by a rational system function.

sequence is not observable. However, if the observed data is characterized as a stationary randomprocess, the input sequence is also assumed to be a stationary random process. In such a case the PSDof the observed data is

Γxx(z) = |H(z)|2 Γww(z) (2.29)

whereΓww(z) is the PSD from−π to π of the input sequence andH(z) is the frequency response ofthe model. It is convenient to assume that the input sequencew(n) is a zero-mean, white noisesequence with autocorrelation

γww(m) = σ2wδ(m) (2.30)

whereσ2w is the variance (i.e.,σ2

w = E[|w(n)|2

]). Then the PSD of the observed data is

Γxx(z) = σ2w |H(z)|2 = σ2

w

|B(z)|2|A(z)|2 (2.31)

16

2.3. Parametric power estimators

In the model-based approach, the spectrum estimation procedure consists of two steps:

• Given the data sequence,0 ≤ n ≤ N − 1, estimate the parametersak andbk

• From these estimates, compute the power spectrum estimate according to 2.31

2.3.1 Prediction

The random processx(n) generated by the pole-zero model in 2.27 and 2.28 is called anautoregressive-moving average (ARMA) processof order(p, q) and it is usually denoted asARMA(p, q). Autoregressive (AR) or moving-average (MA) processes are extracted according to:

ARMA(p, q) : H(z) = B(z)A(z) =

∑qk=0 bkz

−k

1 +∑p

k=1 akz−k (2.32)

AR(p) : H(z) = 1A(z) =

11 +

∑pk=1 akz

−k (2.33)

MA(q) : H(z) = B(z)1 =

∑qk=0 bkz

−k

1(2.34)

The decomposition theorem due to Wold [6] asserts that any ARMA or MA process may be representeduniquely by an AR model of possible infinite order. In view of this theorem, the issue of model selectionis selecting the model that requires the smallest number of calculations. Suppose a ARMA model withp+ q parameters, which can be represented by an AR model withm, m > p+ q, parameters. Due to thefact that the AR parameters can be calculated with simple linear equations, the total required number ofcalculations for am order AR model could be less than the ARMA model withp + q parameters.

Autoregressive predictors

If an AR(p) model is adopted for the observed data, the relationship between the AR parameters and theautocorrelation sequence are given by theYule-Walkeror normalequations:

γxx(m) =

−∑p

k=1 akγxx(m− k) , m > 0−∑p

k=1 akγxx(m− k) + σ2w , m = 0

γ∗xx(−m) , m < 0

(2.35)

In this case, the AR parametersak are obtained from the solution of the Yule-Walker or normalequations

γxx(0) γxx(−1) · · · γxx(−p + 1)γxx(1) γxx(0) · · · γxx(−p + 2)

......

. .....

γxx(p− 1) γxx(p− 2) · · · γxx(0)

a1

a2...ap

= −

γxx(1)γxx(2)

...γxx(p)

(2.36)

and the varianceσ2w can be obtained from the equation

σ2w = γxx(0) +

p∑k=1

akγxx(−k) (2.37)

17


The equations 2.36 and 2.37 are usually combined into a single matrix equation of the formγxx(0) γxx(−1) · · · γxx(−p)γxx(1) γxx(0) · · · γxx(−p + 1)

......

. .....

γxx(−p) γxx(−p + 1) · · · γxx(0)

1a1...ap

= −

σ2w(1)0...0

(2.38)

Since the correlation matrix in 2.38 is Toeplitz, the normal equations can be efficiently solved by use ofthe Levinson-Durbin algorithm [4], see appendix A.

Thus all the system parameters in theAR(p) model are easily determined from knowledge of theautocorrelation sequenceγxx(m) for 0 ≤ m ≤ p. Furthermore, 2.35 may be used to extend theautocorrelation sequence form > p once theak are determined.

2.3.2 Yule-Walker Method for the AR Model Parameters

The Yule-Walker method estimates the autocorrelationγxx(m) from the data and uses it to obtain theAR model parameters. Then using the Levinson-Durbin algorithm (see appendix A) withrxx(m)substituted forγxx(m) yields the AR parameters. The corresponding power spectrum estimate is

P YWxx (f) =

σ2wp∣∣1 +

∑pk=1 ap(k) e−jπfk

∣∣2 (2.39)

whereap(k) are estimates of the AR parameters obtained from the Levinson-Durbin recursion and

σ2wp = Ef

m = rxx(0)p∏k=1

[1 − |ak(k)|2

](2.40)

is the estimated minimum mean-square value for thepth-order predictor.

2.3.3 Burg Method for the AR Model Parameters

The Burg method for estimating the AR parameters may be viewed as an order-recursive, least-squareslattice method based on the minimization of the forward and backward errors in linear predictors, withthe constraint that the AR parameters satisfy the Levinson-Durbin recursion. Some theory aboutforward linear prediction (which is necessary for this subsection) is given in appendix B.

First, consider the forward and backward linear prediction estimates of orderm, which are given as

x(n) = −∑mk=1 am(k)x(n− k)

x(n−m) = −∑mk=1 x

∗m(k)x(n + k −m)

(2.41)

and the corresponding forward and backward errorsfm(n) andgm(n) defined asfm(n) = x(n)− x(n)andgm(n) = x(n−m) − x(n−m), wheream(k), 0 ≤ k ≤ m− 1, m = 1, 2, . . . , p are theprediction coefficients. The least-squares error is

LSE(m) =N−1∑n=m

[|fm(n)|2 + |gm(n)|2

](2.42)

18

2.3. Parametric power estimators

This error (form = p) is to be minimized by selecting the prediction coefficients. The forward andbackward errors can be calculated in a recursive fashion;

f0(n) = g0(n) = x(n)fm(n) = fm−1(n) + Km gm−1(n− 1), m = 1, 2, . . . , pgm(n) = K∗

m fm−1(n) + gm−1(n− 1), m = 1, 2, . . . , p(2.43)

WhereKm is the reflection coefficient, more details can be found in appendix B and Proakis [4].

If equation 2.43 is substituted into equation 2.42 and LSE is minimized with respect tot thecomplex-valued reflection coefficientKm, will give the result

Km =−∑N−1

n=m fm−1(n) g∗m−1(n− 1)12

∑N−1n=m

[|fm(n)|2 + |gm(n)|2

] , m = 1, 2, . . . , p

=−∑N−1

n=m fm−1(n) g∗m−1(n− 1)12LSEm−1

, m = 1, 2, . . . , p (2.44)

Due to Anderson [7] the denominator, orLSE can be computed in an order-recursive fashion accordingto the relation1:

LSEm =(1 − |Km−1|2

)LSEm−1 − |fm−1(m− 1)|2 − |gm−1(N −m + 1)|2 (2.45)

The power spectrum can be estimated from the estimates of the AR parameters according to

PBUxx (f) =

LSEp∣∣1 +∑p

k=1 ap(k) e−j2πfk∣∣2 (2.46)

The major advantages of the Burg method for estimating the parameters of the AR model are:

1. Results in high-frequency resolution

2. Yields a stable AR model

3. Computationally efficient (due to the Levinson-Durbin algorithm)

2.3.4 Experimental results of the Yule-Walker and Burg algorithm

In this subsection some experimental results of the Yule-Walker and Burg algorithm will be presented.As a reference also Welch method 2.2.4 is presented in the graphs.

Before looking to the results it should be mentioned that, although there are advantages of parametricmethods over the classical methods, there are still some difficulties. A very important disadvantage isthe proble of estimating the model order. A order which is too low will result in a highly smoothedspectrum, where on the other hand a too high order will results in spurious peaks in the spectrum.Several proposals have been made for selecting the model order [8] [9]. Unfortunately, the selectioncriteria do not yield conclusive results, however for practical use orders can be adapted givingacceptable results [10]. Much research has been done in finding frequency components which aresituated closely to each other in short data lengths. Parametric methods are very suitable is this case, butwhen large data records are available nonparametric methods are a very good alternative.

1Proakis [4] page 504 formula 8.3.19, comes to another relation which is not correct. The correct relation is given in theoriginal article by Anderson [7]

19


Next some results are given for a data set which is typical for a medium PRF (pulse repetitionfrequency) radar, consisting of a sweep time of approximal310 µs [11]. For a specific configuration ofthe processing with ADC having a sample rate of 250 MSPS or higher, the data length of a single sweepwill be minimal77.000 samples. The signal in figure 2.4 consists of four different subsignals:

• Chirp signal of 2 [W], representing a reflection at 1280 MHz with a bandwidth of 2 MHz

• White noise of 2 [W], representing the noise floor

• Band-limited white noise of 8 [W], from 1200 to 1270 MHz, representing a weak jammer

• Band-limited white noise of 40 [W], from 1320 to 1360 MHz, representing a strong powerfuljammer

1200 1250 1300 1350 14000

5

10

15

20

25

30Influence of poles, 76670 samples

PS

D in

[dB

]

D−band frequency from 1200 to 1400 [Hz]

Welch, 1024 p−FFTBurg, 20 polesYule−Walker, 20 poles

1200 1250 1300 1350 14000

5

10

15

20

25


PS

D in

[dB

]



1200 1250 1300 1350 14000

5

10

15

20

25


PS

D in

[dB

]



1200 1250 1300 1350 14000

5

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PS

D in

[dB

]



Figure 2.4:The PSD is calculated of a signal of 77k samples. For the parametric methods a differentnumber of poles is selected. The Burg method gives almost the same results as the Yule-Walker and cantherefore not been seen in this graph.

It is obvious from figure 2.4 that a low number of poles has difficulties with representing a flat spectrumof white noise, where a higher number of poles will overcome this problem. The problem with a highernumber of poles is the presence of many spurious peaks in the power spectrum. Though each model canbe uniquely represented by an AR model of possible infinite order, this would not be ideal for powerestimators and other models could give better results, Waele [12].

20

2.4. Classical versus Parametric methods for Jammer Detection

2.4 Classical versus Parametric methods for Jammer Detection

De Waele [12] states that for many problems in statistical inference, estimators that use a parametricmodel for the data yield more accurate results than non-parametric estimators, ifthe correct type ofmodelis used. However, the correct model type is often unknown in practical situations. So the type ofmodel (ARMA, MA or AR) has to be chosen, together with the number of poles or zeros. As mentionedbefore, selection criteria do not yield definitive results. De Waele [12] implemented a method forautomatic detection of the model structure from the data. Unfortunately this is done by calculating allthree models with a lot of different parameter settings (for large data length the number of poles andzeros goes up to 1000!), which results in a large computational load.

Broersen [10] mentions in his article: All types of models, AR, MA, and ARMA, must be estimated fordifferent model orders, before a choice can be made for data with unknown spectral density. Not onlymodels of the, afterwards selected, best order must be computed, butalso models of higher orders.Only then it is possible to conclude that lower orders are the best and should be selected.

The selected model type by the automatic algorithm of De Waele yields in a smoother estimation of thepower spectrum, see figure 2.5, but due to the large computational load it is not possible to perform thisalgorithm in realtime for large data lengths as for our case.

Besides the computational load, the quality is an important factor, after all to compare thecomputational load of different method the should be compared at equal quality. The quality of theestimation given by the classical methods is by far good enough for the purpose of jammer detection.Different article from Broersen and the PhD theses from de Waele address the problem that it is veryhard to set a fixed model type with parameters and to calculate in advance the error of the PSD of aarbitrary data sequence. On the other hand to calculate the results for all type of models and parameterswould require to many calculations. Therefore the classical methods are preferable in the case ofestimating a unknown spectrum of a large data sequence.

2.5 Conclusion

The power spectrum can only be estimated and therefore it has a variance with a non zero mean. Therehave been several proposals to improve the variance by means of more complex algorithms. Thesimples power estimation (with the smallest computational load) is the periodogram where the FourierTransform from the data samples are taken. Then the squared absolute value of the Fourier coefficientswill give an estimation of the power spectrum.

The data sequence could be cut into several segments from which the power spectra are averaged. Thisaveraging will decrease the variance of the estimate and give the possibility of observing non-stationarytrends.

Another approach is to use a parametric power estimator. The main problem is the larger computationalload, since the ideal model and its parameters (poles and/or zeros) are not known. So from the data itshould be calculated which model type and parameters have to be chosen. Though it is possible tocalculate always an AR model (which is most computational efficient) with a fixed number of poles,most likely this will not result in a better result as a non-parametric method.

Concluding, no frequency components have to be found which are closely situated to each other, butnoise bandlimited signals. Large data sequences are available as a result of which the variance of the

21


1220 1240 1260 1280 1300 1320 1340 1360 1380 1400

5

10

15

20

25


Pow

er S

pect

rum

Den

sity

in [d

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Comparison between classical and parametric methods, 76670 observations, 1024 points FFT

Welch 148 av.ARMA, 105 poles, 104 zeros

Figure 2.5: The PSD is calculated of a signal of 77k samples. The ARMASEL algorithm by S. deWaele [12] has been used for selecting the optimal model and parameters.

PSD estimation of classical methods will decrease significantly. Selecting the best model type withparameters requires to calculate all the model types for several parameters, resulting in manycalculations. Therefore the classical methods are chosen to be used for the PSD estimation.

22

Chapter 3

Simulation of Radar Signals

3.1 Introduction

Thales NL is investigating to what extent the radar receiver can be realized with digital processing. NewAD-convertors with high sample rates offer the opportunity for wideband signal processing. To developnew algorithms and perform some validation tests on the new design, several wideband test signals arenecessary.

The present radar system mix the band back to baseband and filters it low pass with a pass band equal tothe transmitted bandwidth. Therefore no wideband signals from these systems are available. Using highspeed ADC’s for generating wideband test signals is not very practical, since only very limited signalproperties can be generated (very small jammers< 10 MHz) due to limitations of the available signalgenerators. For these reasons a simulation model has been made to create some wideband signals.

A digital model has been developed which is capable of generating radar signals. Though the code hasbeen rewritten, the basis of the code (including much more than just signal modelling) was the opensource code ofDBT R2.14: A MATLAB Toolbox for Radar Array Processing[13].

3.2 Definition of the simulated radar system

Since the jammer detection project focusses on a pulse doppler radar, the simulation model has beendesigned for this type of radar. Both internal and external factors influence the radar signal. Internalfactors like antenna, modulation and wave-form are indicated with green blocks in figure 3.1, whereexternal factors like targets, clutter, thermal noise or jammers are indicated with blue blocks. Thecurrent implementation does not support clutter due to the complex signal properties. Nevertheless,because of the systematic generation of the final radar signal, a clutter definition could be easily addedand taken into account when generating the radar signal.

3.2.1 Definitions of pulse radars

In the radar ’world’ there are several terms which are explained in this section. Terms like range bins,pulse repetition frequency or Air-Burst Pulse (ABP) will be explained in this subsection. For basic

23

3. Simulation of Radar Signals

Figure 3.1:Different blocks to generate radar signals for test purposes. More than one target or jammercan be added by adding an extra Definition block where the properties of this extra target/jammer areset down. The clutter definition has not be implemented yet.

radar principle see section 1.2 or Skolnik [11].

If a pulse radar system send some successive pulses, they are arranged and grouped according to acertain strategy, where a group is called a burst. For every pulse radar system this arrangement isdifferent. The following example of a pulse radar system will be the basic radar waveform used for thisproject.

A burst is organized as follows (see figure 3.2): a clutter pulse (also referred asABP0), followed by xABP’s (x > 1).

Figure 3.2:Burst organization with some guidelines for timing.

The time from the start of a ABP till the start of the next ABP is called a sweep, which is on average330 µs. The duration of the clutter measurementtclutter meas. is approximate1.6 ms and the durationof a single ABPtsend is approximate28 µs. The duration of a sweep varies with the varying repetitionfrequency of the ABP’s, called Pulse Repetition Frequency (PRF). The total duration of a burst varies

24

3.2. Definition of the simulated radar system

with this PRF, but the given values will not vary more than60 µs. So the total burst time (forxmax = x16) is given by;

Tburst = 17 · tsend + tclutter meas. + 16 · tsweep≈ 17 · 28 10−6 + 1.6 10−3 + 16 · 330 10−6 [s]≈ 7.4 · 10−3 [s]

(3.1)

The variation of a burst time, due to the variation of the PRF are in the range of6.4 − 8.4 ms.

The burst will be sampled when it is received back from e.g. target reflections. Therefor the ABP,clutter measurement and sweeps will consists of a number of samples. Because the radar signals travelswith the speed of light, each sample represents a certain distance and is called a range quantum (RQ).The distance of a single range bin is called a range bin length (RBL) and is given by;

RBL = Ts·c02 = c0

Fs·2 [m]c0 = 299792458

[ms

] (3.2)

wherec0 is the speed of light in vacuum at0 K, Ts the sample time andFs the sample frequency. Thetime of, for example, the clutter measurement, is often defined in range quanta, because the sample timeis fixed. Suppose a sample time ofTs = 1.33 ns, giving a sample rate of approximate 750 MSPS. Thenumber of range quanta (NofRQ) for the clutter measurement (of1.6 ms) is consequently:

NofRQ = tclutter measurementTs

[RQ]= 1.6 10−3

1.33 10−9 ≈ 1.200.000 [RQ](3.3)

And the RBL can be calculated with Equation 3.2:

RBL|750 MSPS =3.0 108

750 106 · 2 ≈ 0.20 [m] (3.4)

3.2.2 Functional Radar Blocks

There are some basic radar properties represented by functional blocks, which define the type of pulseradar. According to the type of radar, the signal will have a certain number of properties. Thesefunctional blocks are summarized below with some information about the way they are implemented inthe built signal generation toolbox. Therefore it should not be read as a general description of a pulseradar, but as a specific implementation which can be changed according to other preferences.

Antenna definition defines the antenna type, e.g. ULA (Uniform Linear Array) and element type, e.g.Isotropic element.

Modulation definition constructs the send signal, where rectangular, sine or chirp pulses can bechosen. This toolbox mixes all these pulses up to the carrier frequency. The input for thisfunction should contain at least the type of wave, sampling timeTs , carrier frequencyFc and thetime tsend of the ABP. In case of a sine the frequencyFsine of this sine, together with themaximum frequency deviation of the chirpFchirp,max has to be given. The outputABP iscalculated according to:

ABPsine(t) = ej 2π Ts t(Fsine+Fc) (3.5)

ABPchirp(t) = ej 2π Ts t(Fchirp,maxt

tmax+Fc) (3.6)

Note that in case of a rectangular pulse, the frequency of the sine could be set to zero. Sobasically three types of waves can be defined:rectangular, sine andchirp pulses. Moreover, thechirp signal has been implemented as a so-called ’chirp-up’ only.

25


Wave definition defines the wavelength of the carrier frequencyFc and number of Range Quanta. Infact the number of range quanta (= number of samples) specify the simulation time. This meansthatonlysweep number 1 (see figure 3.2) will be generated. If other sweeps will be implemented,they will be copies of sweep 1, added with ambiguous and multiple reflections. Because thecurrent model only generate sweep 1, no information about number of pulses or PRF is needed.

At this point the following parameters are defined for generating the radar signal:

• Sample timeTs of the ADC

• Wavelengthλ of the carrier frequencyFc

• Modulation information for the transmitted pulseABP (e.g. chirp)

• Number of range quanta for the total simulation timeNofRQ, giving the number of samples.

3.2.3 Signal Radar Blocks

As mentioned previously, there are four major external factors which influence the final radar signal.The parameters which have to be specified for this toolbox are also mentioned. Because the definitionsof the parameters are separated from the actual generation, new parameters could be introduced easilyadded, resulting in a more advance simulation of the radar signal.

Target reflections The parameters are: received power, range and velocity. It is assumed that the targetis in line with the beam. The power is the received power at the radar, so the data is easy to verify.Another choice could be to define the target cross section (effective reflection area of the target)and calculate the received power, according to the send power and attenuation due to theenvironment.

Noise The received power of the noise has to be given by the user. The noise modelled here is forexample noise from the antenna channels (receiver noise), thermal or outside noise (other thanjammers).

Jammers The parameters for the jammer are: Power, range, velocity, jammer bandwidth and startfrequency of the jammer. The modelled jammer is an active wideband noise jammer (for moreinformation on jammers see next section)

Clutter This signal type is not implemented yet, since the properties are not known. Clutter arereflected signals from, for example, sea and clouds. The power will therefore be in the same bandas the targets and give the power spectrum a higher value in this band.

3.2.4 Jammer types and there properties

There are a lot of different types of jammers. When people speak of jammers, they often do not specifyexactly which kind of jammers they mean. Each jammer is intended for interfering with or precludingthe normal operation of an enemy radio system. If this jammer produces a radio signal, it is calledactive jamming. Its oppositepassive jamming does not use radio signals, but for example largequantities of chaff, which are thin metallized passive resonators, which are thrown out a plane. Thoughpassive jamming can be very effective and useful, the focus in this project will be on active jamming.

Active jamming may be divided into three classes [14]:

26

3.2. Definition of the simulated radar system

Continuous noise This type of jamming is implemented in our simulation model. It may be assumedthat the voltage of the interference at the receiver input is a stationary ergodic narrowbandrandom process, in which the instantaneous values have a normal distribution and the frequencyspectrum is uniform within the radar band. Narrowband could mean narrow compared to theradar band or narrow compared to the central frequency (so in this case it could exist on thewhole radar band). From the text where narrowband is mentioned, the definition should be clear.

random pulse noise jamming of this kind may be represented as a burst of radio pulses with a givenduty cycle, the amplitudes and durations of which, and also the spaces between adjacent pulses,change randomly. It is effective against command guidance radio links, radio communicationslinks and certain types of radars

regular pulse an example of this kind is multiple synchronous pulses, which consists of a series ofradio pulses, radiated in response to a signal received from a radar by an electroniccountermeasure system. The goal can be twofold, the information channels are overloaded bydeception jamming or the victims radar measures several false targets. Both detection as well asautomatic tracking systems will have problems with this type of jamming.

The focus of this project will be mainly on continuous noise jammers with their specific properties.Other types, like regular pulse jamming can be intercepted with so-called electronic counter-countermeasures, which means that the jammer will be separated from reflection basically on the receivedpower. Continuous noise jammers are also detected on the received power, with the difference that theyare compared to the noise floor and not to the reflected signal.

There are several ways to generate direct-noise (noise which approximates Gaussian noise). The first isto use an SHF noise generator [14]. The signals produced at the output of such a generator are amplifiedand radiated into space. Gas discharge tube may be used as primary SHF noise generators. They obeythe property to be extreme wide-band sources of high-frequency noise and have a highly uniformspectrum. In most cases the whole radar band will be jammed.

The second way is to use the heterodyning method to transfer the noise from a low-frequency oscillatorto the high-frequency range. This can be done in two different ways. The first one is to use a fixedcarrier frequency. The noise will be bandlimited and probably does not jam the whole radar band. Thesecond one is to use a varying carrier frequency. The speed of this varying should be that fast thatwithin the time of a sweep, it should cover the whole radar band.

To classify the effectiveness (power) of a jammer, a parameter can be identified and is called thejammer to noise ratio (JNR) which is defined as follows,

JNR = 10 · log10

(PjammerPnoise

)[dB]

in whichPjammer andPnoise is the jammer respectively noise power. So, if the jammer power is equalto the noise power, the jammer to noise ratio is0 dB. But, since the jammer produces an additive signal,the received power will be twice the noise floor, which is normally indicated as a ratio of3 dB. Thoughthis could be confusing, it is convenient to have the most widely used definition, which is the first one.

3.2.5 Simulating the radar signal

Now the generation of the radar signal by the developed model will be explained. When the all theparameters for the green and blue blocks in figure 3.2 are given, the radar signal can be generated. The

27


radar signal is generated by calculating the influences of the major input signals; target reflections,noise and jammers. For these calculations also information about the Air-Burst pulseABP , wavelengthof the carrier frequencyλ , sample timeTs and simulation timeNofRQ is needed.

First the target reflections will be calculated, which consists of 2 steps:

1. Calculate the range quantum where the first sample of the Air-Burst pulse (ABP) will return

2. Calculate the phase shifts for each sample of the ABP due to the target range and velocity.

To start with step 1: we need to calculate the range bin length (RBL), given by equation 3.2. With thisRBL, the first range quantum where the target will appearRQtarget can be calculated and is defined fora target distanceDtarget by:

RQtarget =[2Dtarget

RBL

]rounding

(3.7)

where the rounding to integers is needed for proper indexing in Matlab. Next the phase shifts for eachsample of the ABP due to the target range and velocity have to be calculated. The phase shift due to thetarget rangeDtarget is the same for each sample, since it is assumed that the target is not moving withinone ABP:

Movementtarget < RBL ⇐⇒ (3.8)

tsend · vtarget < c0Fs·2 ⇐⇒

28 10−6 · 3300 < 3.0 108

750 106·2 ⇐⇒0.092 < 0.200 ⇐⇒

A speed of3300 m/s (= Mach 10 (3300330 = 10), is taken because this could be the speed of an incomingmissile. The phase shiftφdistTarget can be calculated by determining the modulo (mod) of thewavelengthλ in twice the target distanceDtarget:

φdistTarget = 2π2Dtarget MOD λ

λ(3.9)

Besides the start phase, there is another phase shift due to the velocity of the target. This phase shiftφvi

influences each send sampleSi, wherei represents the sample number of the send pulse;

φvi =Si 2π 2 Ts

λvtarget i = 0, 1, . . . , N − 1 (3.10)

The phase shiftφvi is an array of lengthN . To calculate the returned ABP, each sample should becorrected for the target velocity (for this example a chirp pulse is used):

ABPvi = ABPchirpi ejφvi (3.11)

The phase shifts due to the range, as well as the target’s velocity are calculated next. The ABP still hasto be corrected due to the phase shift introduced by the target distance, so equation 3.11 becomes:

ABP i = ABPchirpi ejφvi ejφdistTarget

= ABPchirpi ej(φvi+φdistTarget) (3.12)

Equation 3.7 gives the first sample of a target reflection. The phase shiftABPi of this reflection hasbeen calculated in Equation 3.12. Finally the samples have to get the correct amplitude (since the

28

3.3. Results

amplitude is still 1 and only frequency operations have been performed), which is the square root of thereceived power:

ABPreturned i =√

Ptarget ABP i (3.13)

These calculated samples can be placed at the correct positions, or if you like, at the correct rangequanta. From equation 3.7 and 3.13, each sweep can be defined for the target:

Target i = ABPreturned (i+RQtarget)(3.14)

Secondly the noise will be considered. The noise is modelled as normally distributed random numberswith meanµ = 0 and varianceσ2 = Pnoise, so the probability density function of a single noise samplex is:

f(x) =1√

2πσ2e−

12· (x−µ)2

σ2 (3.15)

Because the (other) signals are complex at this stage, the modelled noise is also a complex signal.Having for the real values the stochastic variable X and for the complex values the stochastic variable Y,which has the same probability density function as described by 3.15, the noiseN becomes:

Ni = X(i) + j Y (i) (3.16)

Final part is to generate jammer signals. A more extensive look at jammers was presented in the abovesection, but in the developed model only bandlimited noise jammers are shown. These signals are verysimilar to the noise signals, with the difference that they are bandlimited. The major difference is tofilter the white noise with a low pass filter and mix it to the desired frequency. Schematically it lookslike figure 3.3.

Figure 3.3:Generating band limited white noise for generating jammer signals.

wheref0 is the center frequency of the noise band. The white noise generates numbers which aredistributed according to the probability density function, given by equation 3.15, and their power can bechanged by changing the variance of this noise. To be sure that the filtering does not change the averagepower, the sumB of the filter coefficients,bi, i = 1, 2, . . . , N , should be equal to one:

B =N∑i=1

bi = 1 (3.17)

3.3 Results

This section shows some results for signals which can be generated with this model. The result of”undersampling” with the ADC, which will be described in chapter 4, is already implemented. Figure3.4 shows four different cases, where the lowest jammer to noise ratio is given in the title (note that thetrue jammer to noise ratio in the spectrum is different from the jammer to noise ratio according to thedefinition, see equation 3.7).

29


0 0.5 1 1.5 2

−15

−10

−5

0

Frequency "Ω" normalized from 0 to 2π [rad/sample]

Pow

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in [d

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A) Welch PSD estimation, 350 averages; −3 dB J/N

0 0.5 1 1.5 2

−15

−10

−5

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Pow

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in [d

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B) Welch PSD estimation, 350 averages; 0 dB J/N

0 0.5 1 1.5 2

−15

−10

−5

0


Pow

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in [d

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C) Welch PSD estimation, 350 averages; 3 dB J/N

0 0.5 1 1.5 2

−15

−10

−5

0


Pow

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in [d

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D) Welch PSD estimation, 350 averages; 6 dB J/N

Figure 3.4:Four different examples of radar signals.

The properties of the signals are as follows: Each figure has, except for the received noise power thesame properties:

1. Target 1: received power 0.1 W,Fc = 1300 MHz, at a distance of 1 km

2. Target 2: received power 0.01 W,Fc = 1300 MHz, at a distance of 10 km

3. Jammer 1: received power 1 W, bandlimited continuous noise from1333 to 1400 MHz

4. Jammer 2: received power 2 W, bandlimited continuous noise

The noise(floor) has the following properties:

• Figure 3.4a: power 2 W

• Figure 3.4b: power 1 W

• Figure 3.4c: power 0.5 W

• Figure 3.4d: power 0.25 W

30

3.4. Conclusion

Figure 3.5 shows the graphical user interface (GUI) for generating the wideband radar signals. Thereare only a few parameters that have to be provided. The PSD of the generated signal will also bevisualized in the same figure. This GUI has been written within the Matlab program, since this programis also needed to generate the radar signals.

Figure 3.5: The graphical user interface (GUI) for simulating radar signals. A same GUI has been buildfor exporting the generated signal to a hardware device (e.g. FPGA). Also the detector from chapter 5is implemented in this other GUI.

The total simulation time for this signal was approximately 30 seconds on an Intel Celeron 1.7 GHzpersonal computer.

3.4 Conclusion

This chapter explains some basic principles of pulse radar signals. With this knowledge a simulationmodel has been build. Though clutter signals are not implemented, they can easily be added. For theproject there was not really a need for clutter signals, since they appear in the same band as thereflection of targets.

A graphical user interface (GUI) has been build in Matlab to have an easy interface and possibility togenerate simulation signals. The model, together with the GUI gives an easy to use simulation packagefor a first analysis of the algorithms developed for use with a high speed ADC. If the model is extendedand validated it may be suitable for using it for first testing of more advanced algorithms like

31


beamforming, target search or clutter suppression.

32

Chapter 4

System Definition

4.1 Introduction

From chapter 2 can be concluded that the classical PSD estimators will need less calculations thanparametric PSD estimators. The quality of the PSD estimator is sufficient to detect jammers properly aschapter 5 will show. For these reasons (sufficient quality with the fewest number of calculations) theclassical PSD estimator has been chosen to implement in hardware.

The first part of the algorithm which has to determine the jammed frequency bands will consist of anPSD estimator based on the Welch method. The second part is the detector after the PSD estimator andis not implemented in hardware yet. The Welch method for PSD estimation involves that on the data anFFT has to be performed. The input sequences should also be windowed and of the FFT the absolutevalue has to be calculated. Finally the results should be averaged over a specific interval. Themathematical representation for this algorithm is given by (see chapter 2),

PWelchxx (f) =

1L ·N · U

L∑r=1

∣∣∣∣∣N−1∑n=0

xr(n)w(n)e−j2πfn∣∣∣∣∣2 (4.1)

whereL is the number of averages,N is the size of the FFT andU is the scaling factor for the power inthe windoww(n). This is schematically drawn in figure 4.1

Figure 4.1: The basic algorithm for detecting jammers in subbands. This shows a power estimationbased on the Welch method. The power is a signal property from which jammers can be detected.

The main issue in this chapter will be the optimization and parametrization of the algorithm above. Theoptimization is necessary for implementing the algorithm in hardware, because of the largecomputational load. There are several parameters which can be varied, or optimized, in order to achievea minimal number of calculations for the given Welch PSD estimate. For example the size of the FFT,or the use of preprocessing resulting in less computations of the total system. First, the next section willidentify the fixed parameters of the system.

33

4. System Definition

4.2 Fixed system parameters

The system has several fixed parameters which are given. These parameters will be identified in thissection. Furthermore, the most important parameters of the ADC which generates the samples for thissystem will be given. Figure 4.2 shows the functional processing resulting in the data sequence, whichhas to be analyzed.

Figure 4.2: The functional processing parts before the jammer detector. LNA stands for Low NoiseAmplifier, BPF Band Pass Filter, ADC Analog to Digital Converter and PSD Power Spectral Density.

Low noise amplifier and band pass filter

First two blocks are the low noise amplifier (LNA) and the band pass filter BPF. The LNA amplifies thereceived signal, after which the BPF selects the interesting frequency band and filters out other signals.Although the specific parameters of these two functional parts are not known exactly, this is also notnecessary. For now, it is enough that the analog BPF is not of a very high order, and it filters outfrequencies outside the band of 1200 to 1400 MHz. The presence of this bandpass filter makes itpossible to ”undersample” the frequency band, because the ADC also operates as a mixer.

ADC

The used ADC is fabricated by AMTEL and is a 10-bit 2 GSPS ADC. The most import parameters ofde ADC for this project are:

• 10-bit Resolution

• 2 GSPS Sampling Rate

• 3.3 GHz Full Power Input Bandwidth

This ADC has been tested at Thales NL resulting in a measured ENOB of 7.5 bits at 750 MSPS. Thetesting equipment was capable of testing the ADC at a maximum of 800 MSPS. Since no high speedconnection is possible between the ADC and the test board for this jammer project, the maximalallowed speed is 800 MSPS. The complete data sheet of this device (TS83102G0B) can be found athttp://www.atmel.com.

34

4.3. Algorithm choice and optimization

Other parameters

From the ENOB of the ADC the dynamic range can be deduced, resulting in 46.9 dB SNR (Signal toNoise Ratio) at the input of the jammer detector. Moreover the minimal detectable JNR (Jammer toNoise Ratio) should be 3 dB and the maximal JNR is 40 dB. The processing is allowed to have aduration of maximal one burst of radar pulses, which is approximately 7 ms.

The input for the detector is only the data sequence from the ADC and this is only the received data,since the analog system is turned of while transmitting the signal. Other inputs to the detector system isnot allowed, because the necessary interaction with the system is probably too difficult.

4.3 Algorithm choice and optimization

4.3.1 Sampling Frequency choice

The selection of the sampling frequencyFs of the ADC has a very large influence on the processingarchitecture. Unfortunately we had not much influence on the testingFs of the ADC, since it waslimited to 800 MSPS. The Nyquist theorem for sampling states that the minimal sampling frequencyshould be twice the bandwidth of the signal. Since the radar signal has a bandwidth of 200 MHz, theminimal sampling frequency is 400 MSPS.

It is known that this jammer project is proceeding from a D-band long distance radar with a bandwidthof 200 MHz. The frequencies allowed for this radar range from 1200 to 1400 MHz. Sampling this radarband directly with an ADC (so without analog mixing), will result in multiple frequency bands over thewhole frequency axis depending on the sampling frequencyFs. This is schematically reflected forseveral different sampling frequencies in figure 4.3.

Figure 4.3 shows several possibilities for sampling frequencies with there consequences. First, somevalues ofFs will result in frequency bands for which the positive and negative frequency bands will bejoined together, e.g. at 800, 700 and 400 MSPS. Other frequencies, e.g. 750 MSPS, will result in clearlyseparate positive and negative frequency bands. Separated frequency bands could have the advantagethat in case of not ideally sharp filtered analogue input, a somewhat wider bandwidth will notimmediately form an overlap in the other band as joined frequency bands will do.

Another difference is whether the resulting frequency bands are centered around zero or not. If possiblea reduction in data could be achieved by decimation. This will have consequences for the frequencybands and then it is convenient to have them centered around zero.

The radar band is limited by an analogue bandpass filter, before its signal arrives at the ADC. To have aless strict analogue filter, the separate frequency bands offer a great advantage. Therefore the samplingfrequencyFs has been set at 750 MSPS. The algorithm choice and optimization will be for this specificsampling frequency.

4.3.2 Algorithm optimization

The algorithm of figure 4.1 can be implemented in several ways. In this section different optimizationsare highlighted which results in the final algorithm of section 4.4. The optimization basically is toreduce the amount of calculations, without changing the functionality of the algorithm. The main block

35


Figure 4.3:Consequences for the radar bands of the sampling frequency of the ADC. The sampling ofthe ADC results in many frequency bands on the whole frequency axis, where the exact position dependson the sampling frequency.

of figure 4.1 that can be optimized is the DFT block. There are several options for the architecture toimplement the DFT, but the Radix-2 FFT seems to be the best structure for implementation in a FPGA.The main reason for this choice, is that it has a very regular structure and is therefore easy scalable andhas a small design effort as described in chapter 2by Wolkotte [1]. This small design effort is veryimportant, because of the limited time to realize the complete PSD algorithm in an FPGA.

After choosing for the radix-2 FFT algorithm we are able to optimize the PSD algorithm in two ways(see also figure 4.4):

• Add a preprocessing block before the PSD-algorithm. This block mix and decimate (factor 3,resulting inFs = 250 MSPS) the real valued to complex valued-data, which then need aN1 pointcomplex-valued FFT.

• Use aN2 point real-valued FFT, because the data from the ADC is also real.

Option 1 requires a low pass filter (LPF) to prevent aliasing, but then needs a smaller points DFT(N1 < N2) to get the same frequency resolution after the DFT. This will be explained in in the nextsubsection.

The real-valued radix 2 FFT can reduce the number of calculations by not calculating redundant points.

36


These redundant point occur, because the outputX[k] will have the following characteristics (with areal-valued inputx[n]):

• X[0] andX[N/2] are real

• X[k] = X∗[N − k], for 1 ≤ k ≤ N/2 − 1

It is also possible to combine 2 real-valued data-blocks into a complex data block and separate themagain after the FFT-output. Both options reduce the amount of calculations by≈ 50% compared to acomplex DFT as described in [15].

After looking into some optimizations of the different pre-processing subblocks (mixer and LPF), insection 4.3.5, the final structure is chosen. Notice that the block ”Preprocessing” is called ”Hilbert

Figure 4.4:The two possible processing structures 1 and 2.

Filter” at Thales NL, including mixing, low pass filtering and decimation. The length of the two FFT’s(Nx in figure 4.4) will be explained in the next subsection.

4.3.3 Size of the FFT

To compare the different structures, it is assumed that the total radar band (of 200 MHz) is required toconsistsN frequency bins after the FFT. Because the both structure 1 and 2 are not maximallydecimated, this will have consequences for each individual size of the FFT, indicated byNx. This willhave as a consequence that a smaller length of the DFT can be used, at the expense of some extra preprocessing. The position of the D-band after preprocessing are illustrated in figure 4.5. The total size ofthe FFTNtotal as a function ofN can be calculated for both structures as follows:

Ntotal, structure 1(N) =58· 2 ·N (4.2)

Ntotal, structure 2(N) =158

· 2 ·N (4.3)

37


Figure 4.5:The two different structures with the position of the radar band on the normalized frequencyband. From these positions the total FFT size can be calculated

4.3.4 Optimization of the preprocessing blocks

Further reduction can be achieved by implementing the sub-blocks (mixer and LPF) from figure 4.4 in adedicated way. This make the structure somewhat less flexible, but also requires less arithmetic.

This reduction which could be achieved by

• Implement the mixer withΩmix = π2 . This gives only the mixing values 1,j,-1,-j which require

no complex multiplications.

• Choose an IIR filter for the LPF which can reduce the order of the filter (since for powerestimation linear phase is no requirement).

In general an IIR filter has a lower order to achieve the same requirements compared to a FIR filter. Butthe order does not take the used multiplication and additions into account. In this section the filters arecompared on the computational load, which is necessary to achieve the same filter performance.Stability and accuracy of both filters is not taken into account. The structures which are used forcomparing these two filter types are given in figure 4.6. The transfer functions are given in the report byWolkotte [1].

For both structures it is assumed that:

• The filter coefficients in the forward path are symmetrical.

• The inputx[n] is the result of the complex mixer withΩmix = π2 . This means that the input

values are (alternately) real or imaginary.

For both structures an equation can be deduced for the necessary amount of multiplications andadditions per sample. This amount only depends on the order of the filter.

In the next part the length of the filter coefficient vector in the forward path is calledM , having a orderequal toM − 1 (see Wolkotte [1] chapter 2). For IIR filters it is assumed thatL (which is the length of

38


(a) IIR-filter (b) FIR-filter

Figure 4.6:Structures of digital filters assuming symmetric filter coefficients in the forward path.

the filter coefficients in the feedback path) equalsM . For the FIR filter the amount of additions/sampleare:

AdditionFIR(M) = round

(M − 1

2

)︸︷︷︸

pre addition

+ floor

(M − 1

2

)︸︷︷︸

complex addition after multiplication

(4.4)

But knowing the characteristic ofx[n] the pre addition is not necessary if the order of the filter is odd(M is even), because a real value will be added with a imaginary value. In contradiction, if the order ofthe filter is even (M is odd) this pre addition is necessary, but after the multiplication it requires onlyreal additions, because the output of the multiplications are real or imaginary. The total amount of realadditions for a FIR equals:

AdditionFIR(M) =

(M − 1) − 1 (M) = even

(M − 1) (M) = odd(4.5)

From the figure 4.6b. the number of real multiplications equals:

MultiplicationsFIR(M) = (M − 1) + 1 (4.6)

because every multiplier has a complex input. But using the characteristics ofx[n], the inputs of themultipliers will be real if the order of the filter is even. This reduce the number of multipliers with 50%.

For the forward part of the IIR filter the same number of additions and multiplications are necessary.The intermediate value of this part will be complex and therefore the number of real addition for thefeedback part equals:

AdditionIIR(low)(M) = 2 · (M − 1), whereM = L (4.7)

The same accounts for the number of real multiplications of the lower part of the filter. Because everyreal valueda[l] is multiplied with a complex value.

MultiplicationIIR(low)(M) = 2 · (M − 1), whereM = L (4.8)

39


Order IIR FIR# Adders # Multi # Adders # Multi

Even 3 · (M − 1) − 1 52 · (M − 1) + 1 (M − 1) (M−1)

2 + 1Odd 3 · (M − 1) − 1 3 · (M − 1) + 1 (M − 1) − 1 (M − 1) + 1

Table 4.1:Used arithmetic operations in IIR and FIR filters

These results are combined into table 4.3.4. Comparing these values for the computation of IIR and FIRat a comparable filter response, the IIR filter is favorable comparing to FIR if the order of the IIR is 3times smaller then the order of the FIR. If the order of the FIR-filter is even, the IIR is favorable it itsorder is 5 times smaller.

Section 4.3.1 gives the positions of the radar band with a sample frequency of 750 MSPS. With a mixerof Ωmix = π

2 , the left frequency band (−0.8π ≤ Ω ≤ −0.27π) will shift approximately around zero.The right frequency band (0.27π ≤ Ω ≤ 0.8π) is situated aroundΩ = π. This frequency band has to befiltered with a LPF, to prevent aliasing after the decimator. The maximal JNR is 40 dB, resulting in anecessary stop band of at least -40 dB. The requirements for the LPF filter are;

• An |Ωpass| frequency< 0.3π [rad/sample]

• An |Ωstop| frequency> 0.7π [rad/sample]

• Stop band attenuation of -40 dB

With help of the FDAtool of Matlab it appeared that the necessary order of the FIR and IIR dependsmainly on the transition-band and the ripple in the stop-band. It turned out that the order of the FIRfilter had to be approximately two times the order of the IIR filter, to get a comparable filter response.Therefore, the FIR filter will always need less arithmetic operations than an IIR filter (see table 4.1).Because we want to minimize the arithmetic operations, the FIR filter is selected for a comparisonbetween structure 1 and 2.

4.3.5 Final structure choice

So, with the use of the formulas of table 4.1 and formulas of the FFT-research (see Wolkotte chapter2 [1]), a comparison in arithmetic operations between the two structures of figure 4.4 can be made. Thiscomparison in necessary arithmetic operations can be made by summing all the necessary arithmeticoperations to calculate a specific number (=N) of FFT-coefficients in the given 200 MHz band. Theorder (= M − 1) of the FIR filter also can be varied.

In figure 4.7 this comparison between structures 1 and 2 is given. In this figure the relative difference(DIFF(N,M)) between the number of arithmetic operations (NOFOP(N,M)) of both structures is given,which is calculated by:

DIFF (N,M) =NOFOPstructure 2(N) −NOFOPstructure 1(N,M)

NOFOPstructure 1(N,M)(4.9)

As visible in the equation, the relative difference depends on theN and length (M ) of the filter, becausein structure 1 this length still has to be chosen. The color in figure 4.7 indicates the relative difference,and the black line indicates an equal number of arithmetic operations. Because the order of the FIRfilter will never exceed the order of 14 (giving at least a 100 dB stop band, which is not necessary with a

40

4.4. Implementation

Usable frequency values (=N)

Ord

er o

f FIR

Multiplications

Structure2 better

Structure1 better

1000 2000 3000 4000

4

12

20

28

36

−60

−40

−20

0

20

40

60

Usable frequency values (=N)

Ord

er o

f FIR

Additions

Structure2 better

Structure1 better

1000 2000 3000 4000

4

12

20

28

36

−60

−40

−20

0

20

40

60

Figure 4.7:

SNR = 46.9 [dB] of the ADC) the complex structure 1 will be the best solution. Comparison of thearithmetic operations of the structures 1 and 2. The color of the image gives the relative differencebetween the number of arithmetic operations of both structures, as can be calculated by equation 4.9.The black line indicate the equilibrium between both structures.

4.4 Implementation

In the previous section, it has been investigated what structure is the most efficient for calculation of thePSD, based on the Welch method. This turned out to be structure 1, giving a maximal FIR order up to14. Next it is important to calculate the exact necessary FIR order.

The maximum jammer to noise ratio (JNR) is given to be 40 dB for the given system. Restrictions fromthe optimization requires the filter order always to be even (see table 4.1). A filter order of 6 is mostefficient to implement in hardware, since a higher order will need extra hardware resources in de orderof 5%. Question is whether a filter could be designed with the following specifications:

• Filter order of 6

• An |Ωpass| frequency< 0.3π [rad/sample]

• An |Ωstop| frequency> 0.7π [rad/sample]

• Minimum ripple in the pass band

• Minimal -40 dB stop band

The fourth item ”Minimal ripple in the pass band” implies an equiripple filter, so this has been used.The filter coefficients are found with the ’fdatool’ (Filter Design and Analysis Tool) in the Matlabprogram using a weight value of 1.2 for the passband and 40 for the stopband. With this configuration

41


Figure 4.8: The total system for determining jammed frequency bands. The input for the Smart Detectionis an averaged PSD estimate.

the ripple (or magnitude difference) in the pass band is 4.7 dB and the minimal difference between passand stop band is 39.4 dB.

Other parameters, like mixing frequency and decimation factor, have already been subtracted in theprevious section. A mixing frequency of Ωmix = π

2 in combination with a sampling frequency ofFs = 750 MSPS results very efficient in a good placement of the frequency band as can be seen infigure 4.8. Then decimation with a factor 3 results that the 200 MHz D-band is placed from−0.9π ≤ Ω ≤ 0.7π

[rad

sample

]in the normalized frequency band, visualized at the right of the

decimation block in figure 4.8.

Finally something should be said on the D-band frequency which ranges from 1200 to 1400 MHz. For

42

4.5. Conclusion

communication issues, some other (interfering) signals surround this band. The preprocessing of thesystem places the D-band in the normalized frequency plot from−0.9π ≤ Ω ≤ 0.7π. This means that0.4 π adjacent to the end of the band will not be used for detection and will also not interfere. At thegiven sample frequency of 750 MHz this is equivalent to a non interfering frequency band around theD-band of 50 MHz. Observing this, frequencies which are outside 1150 to 1450 MHz interfere with thesystem as proposed in this project and therefore have to be filtered before the decimation. Frequencieswithin this range will not interfere.

4.5 Conclusion

A system has been defined which estimate the power of a D-band radar signal. This system uses theWelch method (meaning a modified averaged periodogram) for spectral power estimation. This has anadvantage over other methods, due to the fewer calculations it needs for a sufficient quality of theestimation.

The algorithm has been optimized for a processing architecture which will be build in an FPGA. It hasbeen found that a sampling frequency of 750 MSPS is an acceptable choice. Together with a mixingfrequency ofΩ = π

2 and a decimation with factor 3, the D-band will have a good location on thenormalized frequency axis.

Finally it has been found that the use of a FIR filter in the pre-processing will need less arithmeticoperations than an IIR filter with a comparable filter response. This is only valid for a real datasequence which is mixed atΩ = π

2 and an even filter order.

43


44

Chapter 5

Detector

5.1 Introduction

Once the PSD has been estimated, the final step is to determine whether a subband is jammed or not. Acommon way to do this is to set a certain threshold value on the power of each frequency bin and if thevalue is above this threshold, the frequency bin is denoted jammed, and otherwise not jammed. In casea certain number of frequency bins is jammed in a subband, theentiresubband is considered jammed.The problem is that the PSD estimators will always have a certain variance and thus it can never beexactly determined whether a frequency bin is jammed or not.

First the global idea of the detector will be explained. A conceptual overview of the detector will begiven in figure 5.1. A method for determining the threshold value from the PSD will be proposed. Next,some theoretical results about the accuracy and the mean time between failures will be given.

5.2 Systematic Description of the Detector

Figure 5.1 gives a conceptual overview of the different parts of the detector. First the PSD will beestimated, using the Welch method as explained in chapter 2. This will result in aN -points PSD,calculated withL averages. These two variables are the input for the detector.

The introduction states that the detector has to determine whether a subband is jammed. A subband isdefined to have a bandwidth which is equal to the bandwidth of a transmitted signal (see section 3.2.2).So the detector does not have to decide whether a single frequency bin belongs to a jammer or not, butwhether a subband is jammed or not. The number of subbands is determined by the number subbands inwhich the radars frequency bandwidth can be divided. Suppose a total radar frequency bandwidth of200 MHz (part of the D-band) and a transmitted signal (chirp) with a bandwidth of e.g.3.1 MHz, thetotal number of subbandsK will be:

K =BWradar

BWsend signal=

2003.1

≈ 64 (5.1)

TheN -point PSD input is first divided intoK subbands (according to equation 5.1), giving eachsubbandNK bins. The next block, calledCalculate BAT(Bins Above Threshold), has two inputs. Thefirst is N

K frequency bins (bandwidth of a subband) from the PSD estimate, where the second input is

45

5. Detector

Figure 5.1: Conceptual overview of the detector, with the PSD as estimated according to the Welchmethod as input. The N-point PSD will be subdivided into K subbands. From each subband the numberof frequency bins which are above a threshold (BAT, bins above threshold) are calculated. Finally ifthis number exceeds a certain value, given by the BAT LUT (LUT = look up table), the subband will bedenoted as jammed. The threshold value follows from a LUT which has been calculated in advance.

the threshold value. For each subband the number of frequency bins above this threshold is calculated.The determination of the threshold value will be concerned in a later stadium. Finally according to thenumber of bins above threshold in each subband, the subband will be denoted as jammed if this numberexceeds the number given by the block BAT. The report will exist of K values, indicating whethersubband K is jammed or not.

The BAT as well as the threshold are stored in a LUT (look up table). To find the correct value in thisLUT, two inputs are necessary. First the power of the noise floor and and a candidate lowest jammer areneeded. These two values will result in a JNR, which is the first input to the LUTs. The threshold valuewill be different for a 3 dB JNR than for example a 9 dB JNR, therefore the JNR is needed. The secondinput is the number of averages L, that is needed to establish the ”degrees of freedom” (see nextsection), needed to assers the PDF of a single frequency bin. The compilation of these LUTs will betreated in sections 5.4.2 and 5.4.2.

5.3 Probability Density Function of Frequency bins

This section will introduce the probability density functions (pdf) of a frequency bin, calculated bytaking the absolute value of the Fourier coefficients, see equation 2.13. If the input to a FourierTransform is white noise (normally distributed values), the Fourier coefficients will also be normallydistributed with variance σ2. First the case of a white noise input having a variance equal to 1 will be

46

5.3. Probability Density Function of Frequency bins

5.3.1 PDF of a single frequency bin

SupposeXn is normally distributed with the parameters meanµ and varianceσ2. The probabilitydensity function is:

PDF(x|µ,σ2

)= N(µ, σ2) =

1σ√

2πe

−(x−µ)2

2σ2 (5.2)

If Xn ∼ N(0, 1) (meaning thatXn has a normal distribution withµ = 0 andσ2 = 1), thenX2n will be

Chi-squared distributed with parameterv (= degrees of freedom, dof with in this casev = 1):X2n ∼ χ2(1), (see [16] definition 11.2.1). The summation of several mutually independent variables of

typeXn will have consequences for the number of degrees of freedom (dof)v of the Chi-squareddistribution as follows:

Y1 =v∑

n=1

X2n (5.3)

Y1 ∼ χ2(v)

E[Y1] = v

var[Y1] = 2v

If Xn is complex, the absolute value squared is the summation of the real and imaginary part squared asgiven by,

|Xn|2 = Re Xn2 + Im Xn2 (5.4)

5.3.2 PDF after summation

As in the determination of the PSDL averages are taken, the single frequency bin is summatedL timesfirst. A new stochastic variableY2 will be introduced which represent the summation ofL complexabsolute values squared and is defined as;

Y2 =L∑n=1

|Xn|2 (5.5)

=L∑n=1

[Re Xn2 + Im Xn2

](5.6)

and thus will be distributed according to,

Y2 ∼ χ2(2L) (5.7)

The distribution function for a Chi-squared distribution with different dof’s are given in figure 5.2. Itcan be seen that theχ2 distribution resembles more and more a gaussian as the number of dof’s isincreasing.

5.3.3 Consequences of averaging on the mean and variance

Till this point, it has been assumed that the variableXn has a variance equal to 1. Next, suppose theinput sequence isN(0, σ2) distributed, instead ofN(0, 1). The PSD is the squared absolute value of theFourier coefficients, which also follow a normal distribution with varianceσ2, see [4]. Let us introducea stochastic variableY3, which is the square of the absolute value of the Fourier coefficients and thus

47

5. Detector

0 1 2 3 40

0.1

0.2

0.3

0.4

0.5Distribution of χ2(v)

χ2(2) dist.

0 2 4 6 80

0.05

0.1

0.15


χ2(4) dist.

0 10 20 30 400

0.01

0.02

0.03

0.04

0.05

0.06


χ2(20) dist.

0 50 100 150 2000

0.005

0.01

0.015

0.02

0.025


χ2(100) dist.

Figure 5.2:PDF distributions ofχ2v for dof or v equals 2, 4, 20 and 100

has aχ2(v) distribution. MoreoverY3 has been summatedL times and scaled by1L to obtain anaveraged PSD.Y3 can be obtained fromY1 with an appropriate scaling factor, which is found to be,

Y3 =σ2

vY1 (5.8)

This will have consequences for the expected mean and variance

E[Y3] = E[σ2

v Y1] = σ2

v E[Y1] = σ2

v v = σ2

var[Y3] = var[σ2

v Y1] =(σ2

v

)2var[Y1] =

(σ2

v

)22v = 2σ4

v

(5.9)

From 5.9, it can be concluded that a larger number of degrees of freedom (i.e. more averaging), will notaffect the expected mean, but will reduce the expected variance.

5.3.4 Practical example

The theory presented so far is for a single frequency bin. At this stage two different probabilities aredefined: noise floor and jammer. If the distribution functions of these probabilities are known, thevariable can be classified into a category (noise floor or jammer) with a certain confidence value. Thereare two important parameters, False Rejection Rate (FRR) and False Acceptance Rate (FAR). Theseparameters are defined as follows:

FRR = P (noise detected| there is a jammer)

FAR = P (jammer detected| there is only noise)

in which P (X|Y ) is the probability ofX on the conditionY .

48

5.3. Probability Density Function of Frequency bins

Example: a noise floor is given with a mean of 3 [W] and a jammer with a mean of 6 [W]. The PSD hasbeen calculated withL = 20 averages. Question is to determine the FRR and FAR with a threshold of4.5 [W].

First from Equation 5.7 is known that the PSD has a Chi-squared distribution with2L = 40 degrees offreedom. From chapter 3, we know that the power of white noise is equal to the variance of white noise.SetV1 as the noise floor andV2 as the jammer. According to Equation 5.8 the mean and variance ofV1

andV2 are:,

E[V1] = σ2noise floor = 3

E[V2] = σ2jammer = 6

var[V1] =2σ4

noise floor

v = 0.45

var[V2] =2σ4

jammer

v = 1.80

(5.10)

A function has been written in Matlab which gives the pdf of a noise and jammer signal, when the meanof the noise and jammer are given together with the number of averagesL for the PSD estimation, seeappendix E.1. Final input for the function should be a threshold value and the function returns a figurecontaining the FAR, FRR and pdf’s, see figure 5.3

0 2 4 6 8 10 120

0.1

0.2

0.3

0.4

0.5

0.6

0.7FAR (green) = 0.022; FRR (yellow) = 0.12; Threshold = 4.5

PSD output value

Pro

babi

lity

dens

ity

PDF noise floorPDF jammer

Figure 5.3:PDF’s of Noise and Jammer, with the PSD calculated with 20 averages. The FAR (green)and FRR (yellow) are also shown.

In the ”radar world” two probabilities are important:

• PD: Probability of Detection (a jammer)

• PFA: Probability of False Alarm

These two probabilities are related to the FRR and FAR and can be calculated for each frequency bin.Suppose the threshold value is set atxthreshold, then ifX is a jammer it will be detected with the

49

5. Detector

following probability (PD):

PD = P (jammer detected| there is a jammer) = 1 − P (X < xthreshold) (5.11)

= 1 − FRR

and the same for can be done for the PFA. IfX represents the noise floor, the probability on false alarmwill be:

PD = P (jammer detected| there is only noise) = 1 − P (X < xthreshold) (5.12)

= FAR

This is illustrated in figure 5.4.

0 2 4 6 8 10 120

0.1

0.2

0.3

0.4

0.5

0.6

0.7PD and PFA, with a threshold of 4.5

PSD output value

Pro

babi

lity

dens

ity

X2: PDF noise floor

X1: PDF jammer

Probability Detection

Probability False Alarm

xthreshold

Figure 5.4:Figure shows the definitions of PD and PFA, which are colored. Also the threshold valuexthreshold is shown.

5.4 Determination of jammed subbands

The pdf, which has a Chi squared distribution, is determined by a single parameter:v. However, fromsubsection 5.3.3 can be deduced that this pdf needs a scaling, according to the variance of the input.This variance results in an expected mean of the pdf, see equation 5.9. So if the mean is measured andthe number of averages are known (givingv), the pdf is completely defined. When the pdf’s of thepower of the noise floor and a candidate jammer are known, an optimal threshold value can becalculated. If this is done in advance for several noise floors and possible jammers, these thresholdvalues can be stored in a LUT. Next section will give a method for determining the noise floor andcandidates jammers.

50

5.4. Determination of jammed subbands

5.4.1 Histogram

A histogram of the PSD and the PSD itself is given in figure 5.5. From this histogram the mean of the

−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1−15

−10

−5

0

5

10

15

PS

D e

stim

ate

[ dB

]

Normalized frequency [ Ω ]

# averages: 49x, # points FFT: 1024, # samples: 25602

PSD of the signalHistogram

Noise floor

Jammer 1

Jammer 2

Figure 5.5:Histogram of a wideband radar signal. The three major peaks indicate the noisefloor andthe two jammers. Also the PSD itself is given in the figure.

noise floor and candidate jammers can be determined as can be seen in the figure. The problem is,however, that the histogram has a certain spacing or resolution normally called bins, butblocksin thiswork to avoid confusion with frequency bins. A very high resolution will result in many peaks, where avery low resolution will not result in separate peaks for a jammer close to the noise floor. Figure 5.6illustrates this behavior. Experimentally has been found that a resolution of 64 blocks on a logarithmicdensity spectrum of 46 dB gives good results. The 46 dB is exactly the dynamic range of the ADC,which was 7.5 bits effective (see chapter 1).

The big advantage of using a histogram for determining the noise floor and possible jammer levels isthat this will result in a system where no other external measured inputs are needed. With this methodonly the input sequence is needed and from this input sequencex[n] the noise floor will be determined.

5.4.2 PDF of subbands

As already stated in the introduction, if the mean of the noise floor (and a possible jammer) is known,together with the number of averages, the pdf of a single frequency bin is known. However, thequestion was to determine if a subband (consisting ofN

K frequency bins) was jammed. It is assumed

51

5. Detector

−1 −0.5 0 0.5 1−20

−15

−10

−5

0

5

10

15

PS

D e

stim

ate

[ dB

]


Histogram with 64 "blocks"


−1 −0.5 0 0.5 1−20

−15

−10

−5

0

5

10

15

PS

D e

stim

ate

[ dB

]




−1 −0.5 0 0.5 1−20

−15

−10

−5

0

5

10

15

PS

D e

stim

ate

[ dB

]




−1 −0.5 0 0.5 1−20

−15

−10

−5

0

5

10

15

PS

D e

stim

ate

[ dB

]




Figure 5.6:Histogram with different spacings, resulting for high resolution in many peaks for the noisefloor and jammers.

from this point that a subband is or completely jammed or not. After all an effective jammer shouldcover several subbands. Consequence is that all the frequency bins in a subband belong to the samedistribution function.

A single frequency bin in a subband can be considered as a trial in a Bernoulli experiment. The subbandrelated probabilities can now be computed. A Bernoulli experiment comes from probability theory. Asuccess will be defined as when a frequency bin belongs to a jammer. Subsequently,Bk is the event thatthere arek successes atn Bernoulli experiments with a success probability equal top. Then theprobabilityBk will be,

P (Bk) =(

n

k

)pk(1 − p)n−k, k = 0, 1, . . . , n (5.13)

where the probabilityp can be PD from equation 5.11 or PFA from equation 5.12. Suppose that for ajammer detectionminimal s out of then frequency values in a subband should be abovexthreshold toregard the subband as jammed.PDsubband andPFAsubband are then defined as (note PD or PFAwithouta subscript are the probabilities of a single frequency bin):

PDsubband = P (Bs|p=PD) + P (Bs+1|p=PD) + . . . + P (Bn|p=PD) (5.14)

PFAsubband = P (Bs|p=PFA) + P (Bs+1|p=PFA) + . . . + P (Bn|p=PFA) (5.15)

52

5.4. Determination of jammed subbands

In this case there should ben− s timesn Bernoulli experiments,

PDsubband =n∑k=s

(n

k

)PDk(1 − PD)n−k (5.16)

PFAsubband =n∑k=s

(n

k

)PFAk(1 − PFA)n−k (5.17)

However, if the data is windowed, before calculating the Fourier Transform, the frequency bins willcorrelate and therefore the quality of detection will change. For simplicity, the frequency bins areassumed to be mutually exclusive.

BAT LUT

Equation 5.16 shows the change of probability on PD and PFA for different values ofs. It is obviousthat the less the value ofs (0 ≤ s ≤ n), the higher the total probability on PD and PFA. But the demandis a PD which is as high as possible and a PFA as low as possible. Moreover if the penalty for PD andPFA is made equal, the optimal value fors can be determined. This optimal value represents thenumber of bins above threshold (BAT).

Threshold LUT

If the number of averages is known, together with the mean of the power of the noise floor and jammer,thePDsubband andPFAsubband can be calculated for different threshold values. The optimal thresholdis now defines as,

Thresholdoptimal = min (α · (1 − PD) + β · PFA) (5.18)

whereα andβ are parameters for giving the PD and PFA different weights. For the moment the weightsα andβ are assumed to be equal.

Calculating the system PD and PFA

The Bernoulli experiments, as explained in the previous section, are performed for each subband. Forsystem performance, the total systemPD andPFA needs to be known (meaning one report for allsubbands in the radar signal). For this, the total system performance is always less than the singlesubband PD and PFA. ThePDsystem andPFAsystem can be calculated according to,

PDsystem = (PDsubband)Number of Subbands (5.19)

PFAsystem = 1 − (1 − PFAsubband)Number of Subbands (5.20)

The consequences of this adjustment is visualized in figure 5.7a. The dashed and solid lines with thesame color belong to each other. The dotted lines represent the pdf of a single frequency bin. It can beseen that for a fixed probability of PD and PFA the threshold variation for the total system is less thanfor a single subband.

Figure 5.7b shows the consequences of averaging. The more averages, the less sensitive the PD andPFA are for threshold variation (for equal probabilities), due to the wider gap between the1 − PD line

53

5. Detector

1 2 3 4 5 6 7 80

0.2

0.4

0.6

0.8

1

Threshold value in [dB]

Pro

babi

lity

a) Difference between subband detection and total system. 3 dB J/N, 1024−pnt FFT

1 2 3 4 5 6 7 80

0.2

0.4

0.6

0.8

1

Threshold value in [dB]

Pro

babi

lity

b) Influence of averaging on the threshold value. 3 dB J/N, 1024−pnt FFT

PDFA Total System1−PD Total SystemPDFA Subband1−PD SubbandPDF Noise /binPDF Jammer /bin

25x Av. (PFA)25x Av. (1−PD)50x Av. (PFA)50x Av. (1−PD)75x Av. (PFA)75x Av. (1−PD)100x Av. (PFA)100x Av. (1−PD)

Optimal Threshold

Maximum probability level, givingthe acceptable threshold variation

Figure 5.7:Threshold characteristics for different situations. Ad a) Here the influence of compensatingsingle subband probabilities for system probabilities are shown. Ad b) The more number of averages,the more wider the range where the threshold values can be chosen, without exceeding the maximumprobability level.

and the correspondingPFA line. A measurement for robustness of the detector could be the variationin the threshold where the system does not degrade (too) much.

Another way of representing the PD and PFA is in so-called Receiver Operating Curves (ROC) curves,given in figure 5.8. These curves represent the probabilities by setting them into one figure with thePFA on the x-axes and the PD on the y-axes. The threshold is varied and will result in the curve lines.The figure shows these threshold variations for different number of bins which are above the threshold,different BAT. The disadvantage of this way of representing that it cannot be seen what happens to thePD andPFA with slight variations of the threshold.

5.5 Results

In this section the consequences for this jammer detection project of the designed detector will beshown. The system has an input rate of 750 MSPS and by decimation this will reduce to 250 MSPScomplex values (see chapter 4). The signal band of the D-band radar signal is for normalized

54

5.5. Results

0 1 2

x 10−4

0.9998

0.9998

0.9999

0.9999

1ROC 3 dB J/N, 25x av. 1024−pnt FFT

Probability False Alarm: PFA (or FAR)

Pro

babi

lity

Det

ectio

n: P

D (

or 1

−F

RR

)

4 bins above threshold5 bins above threshold6 bins above threshold7 bins above threshold8 bins above threshold

Figure 5.8:ROC curves for a wideband system scan. For this case 6 bins above the threshold will givethe best result in the Bernoulli experiment. This figure is for a 3 dB JNR where the PSD is averaged 25times having 1024 points.

frequencies in the range from−0.9π to 0.7π. The total radar signal has 64 subbands, so each subbandhas a (normalized) width ofΩ

K = 1.664 = 0.025 [rad].

The size of the FFT, together with the width of a single subband, determines the number of frequencyvalues that fall within a subband. In experiments it was found that the number of frequency values for asingle subband should be around 12 or 6 for this specific system, giving a FFT length of 1024 or 512.

Section 5.4.2 explained the consequences of threshold variation and the spacing of the histogram.Because the system has a effective SNR of 46 dB (by influences of the SNR from the ADC and thecalculation noise by the fixed point FFT, see [1]) and the spacing of the histogram is 64, the thresholdvariation is allowed to be,

V ariationthreshold ≈ 4664

≈ 0.7 [dB] (5.21)

If the size of the FFT (N ) has been set, the time required for a certain number of averages (L) can becalculated according to,

tNofAv =N · Lfsample

=1024 ∗ 25250 · 106

≈ 100 µs (5.22)

wherefsample is the sample rate after decimation. So averaging over 25 different PSD estimations takesapproximate100 µs, plus a latency of approximate6 µs, see [1].

Figure 5.9 is a picture where the different parameters come together. It shows the necessary calculationtime for a certain maximal error. It has been taken into account that the threshold variation is allowed tobe 0.7 [dB]. Moreover the parameterα andβ from Equation 5.18 are chosen both equal to one. BothPD and PFA have to be below an error ofPmax,

Pmax = max((1 − PD) , PFA) (5.23)

It can be seen that a J/N ratio of 3 dB can be detected within±230 µs with a maximal errorPmax = 10−9. The input for this system is:

55

5. Detector

• size of FFT is 1024

• allowed threshold variation is 0.7 dB

• there are 64 subbands in the radar band of 200 MHz

• the preprocessing from chapter 4 has been used withL = 25 averages.

• there is a variable number of bins above threshold (BAT) which have to be found in a LUT

• there is a variable threshold level for different JNR and these can be found in a LUT

1 1.5 2 2.5 3 3.5 4 4.5 5 5.50

100

200

300

400

500

600

700

800

J/N ratio [ dB ]

Tim

e [ µ

s ]

Minimum time for different error values and J/N ratios

Emax

= 10−9

Emax

= 10−8

Emax

= 10−7

Emax

= 10−6

Emax

= 10−5

Emax

= 10−4

Emax

= 10−3

Figure 5.9:J/N ratio versus time. Each100µs represent appr. 25 averages.Emax, which should bePmax, represents the probability of an error.

To give an idea about the mean time between failure (MTBF), an errorPmax = 10−9 gives a cumulativeerror of2 · 10−9. In case every300 µs a report is generated the MTBF can be calculated;

MTBF =time report generation

maximal error probability=

300 · 10−6

2 · 10−9 · 3600= 41.7 [hours] (5.24)

5.6 Conclusion

The detector is capable of detecting jammers within one sweep time (approximate300µs). The minimalJNR which can be detected within one sweep depends on the required error rate. For the minimaldemand of detecting jammers with a JNR of 3 dB, the mean time between failures is minimal 41 hour.This has as a consequence that a jammed subband will not be marked or a clean subband will beillegally marked as jammed.

56

5.6. Conclusion

The robustness of this detector is defined as a variation in the threshold level. It is not possible todetermine the mean of the noise floor and the jammer exactly, due to the accuracy of the histogram.Therefore a variation in the threshold level should not influence the result of detection too much. Theacceptable variation in threshold level for the jammer detection system has been set to 0.7 dB.

This performance of this detector is capable of having such good results due to the possibility ofaveraging the PSD. The averaging is responsible of reducing the variance of the PSD estimation.

57

5. Detector

58

Chapter 6

Conclusions and Recommendations

6.1 Conclusions

The main goal of this project was to develop an algorithm which could be implemented in hardware inorder to find jammers in a D-band radar system, for example the SMART-L. Moreover a simulationmodel had to be developed in order to test the processing functionality of this algorithm in thehardware. These two goals have been achieved and are documented in this report.

First the basic question at the beginning of this project was formulated as follows:Is it possible toreplace the current analog processing with a new digital design immediately after the antenna?Ofcourse the answer is more nuanced than just yes or no. From chapter 2 can be deduced that in case ofestimating the power spectrum, the large amount of data samples offers the possibility of estimating thepower spectrum with a very small variance. The parallel project by Wolkotte [1] has as a result that thisalgorithm can be implemented in hardware. Concluding from Wolkotte [1] the current hardware iscapable of processing this algorithm at a speed which is fast enough to handle the incoming data.Restrictions are, however, that the algorithm cannot be too complex and not have many conditionalaspects. Therefore other parts of the (analog) processing can probably also be changed for handlinglarge amounts of data at high speed, though some (conditional) algorithms might give problems. Afterworking some time on this project, I strongly have the perception that it is not possible to replace thecurrent analog processing completely with a new digital design yet, but that it will be in the near future.

As can be concluded from chapter 5, jammers with a jammer to noise ratio of 3 dB can be detected bythe developed algorithm within300 µs. This can be achieved with an accuracy ofPmax = 10−9

resulting in a mean time between failures of 41 hour. A failure means a jammed subband will not bemarked or a clean subband will be illegally marked as jammed. The time is considerably within thespecifications of detecting a 3 dB jammer within one burst of approximately 7 ms.

A simulation model has been developed for testing the designed algorithm and the implementation of itin hardware. This model is capable of generating wideband radar signals including noise, targets andjammers. There is a possibility of implementing other signals like clutter in a relative easy way. Agraphical user interface has been written for generating signals and for uploading these signals to theFPGA on which Wolkotte [1] implemented the algorithm.

Final conclusion involves the use of classical power estimators (FFT-based estimators) over otheralgorithms like the parametric class. Dependent of the application the classical power estimator or aparametric one will have the preference. Parametric power estimators are very good in separating

59

6. Conclusions and Recommendations

closed frequencies where the classical ones will always be limited due to the spectral width of thewindow as given in chapter 2. On the other hand in case there is a large amount of data available, thevariance of the classical power estimators can be reduced significantly by means of averaging.Moreover due to the regular structure the classical power estimators can be implemented in hardwarevery efficient, see Wolkotte [1].

Summarized

• Parts of the current analog processing can already be replaced by digital algorithms, and probablyin the near future all the processing can be replaced.

• Bandlimited noise jammers with 3 dB JNR can be detected within a time of300 µs.

• A simulation model have been designed for generating wideband radar signal with an orderlygraphical user interface.

• Dependently of the application a choice should be made between classical power estimators andother, e.g. parametric, power estimators.

6.2 Recommendations

The high sample rate of the ADCs in digital radar receivers will result in large amounts of data. Becauseof this the available information will increase. When extracting more information from the radar signalit should be possible to get higher performance of the current algorithms. But if the performance is keptequal, the quality of the incoming data may be allowed to decrease. Then fast ADCs that have a smalleffective number of bits might result in the same quality of detection compared to relative slow ADCswith a higher effective number of bits. So it should be investigated to which extend current algorithms(like the matched filter) improve due to the larger amount of information offered by high speed ADCs.

Secondly the developed simulation model should be extended in case other algorithms have to be testedon functional behavior. More pulses could be added, including ambiguous and multiple reflections.Then also different pulse repetition frequencies can be implemented. Finally also a clutter (or more thanone) definition could be added in order to simulate more realistic radar signals.

The developed jammer detection algorithm is capable of producing results before the next pulse will betransmitted. To use this information, the control of setting the parameters for the transmitted pulsesshould be able to adapt very fast to this information. This control is currently not capable of adapting sofast. Therefore it is not advisable to set up single projects, but to use the full improvements digital radarreceiver concept offers, a complete new design has to be build. However, to investigate possibleproblems in advance, pilot projects should be launched in order to identify important obstacles in theprocessing chain.

Summarized

• Investigate to what extent current algorithms like the matched filter improve, due to moreinformation in the larger amount of data.

• Extend the simulation model with more pulses and clutter definitions in order to simulate morerealistic radar signals and test more algorithms.

60

6.2. Recommendations

• Launch some pilot projects to identify important obstacles in the processing chain for high speedprocessing. However, implement a new design integrally since the control of many parameters inthe radar system will completely change.

61

6. Conclusions and Recommendations

62

Appendix A

Levinson-Durbin algorithm

A.1 Theory

The Levinson-Durbin algorithm [17] [18] is a computationally efficient algorithm for solving thenormal equation in 2.35for the prediction coefficients. This algorithm exploits the special symmetry inthe autocorrelation matrix

Γp =

γxx(0) γ∗

xx(1) · · · γ∗xx(p− 1)

γxx(1) γxx(0) · · · γ∗xx(p− 2)

......

. .....

γxx(p− 0) γxx(p− 2) · · · γxx(0)

(A.1)

Note thatΓp(i, j) = Γp(i− j), so that the autocorrelation matrix is aToeplitz matrix. SinceΓp(i, j) = Γ∗

p(j, i), the matrix is also Hermitian.

The key to the Levinson-Durbin method of solution that exploits the Toeplitz property of the matrix isto proceed recursively, beginning with a predictor of orderm = 1 (one coefficient) and to increase theorder recursively, using the lower-order solutions to obtain the solution to the next higher order. Thusthe solution to the first-order predictor obtained by solving 2.35 is

a1(1) = −γxx(1)γxx(0)

(A.2)

and the resulting MMSE (minimum mean-square error) is

Ef1 = γxx(0) + a1(1) γxx(−1)

= γxx(0)[1 − |a1(1)|2

] (A.3)

Recall thata1(1) = K1, the first reflection coefficient in the lattice filter.

The next step is to solve for the coefficientsa2(1) anda2(2) of the second-order predictor and expressthe solution in terms ofa1(1). The two equations obtained from 2.35 are

a2(1) γ(xx(0) + a2(2) γ∗xx(1) = −γxx(1)

a2(1) γ(xx(1) + a2(2) γ∗xx(0) = −γxx(2)

(A.4)

63

A. Levinson-Durbin algorithm

By using the solution in A.2 to eliminateγxx(1), we obtain the solution

a2(2) = −γxx(2)+a1(1) γxx(1)

γxx(0)[1−|a1(1)|2]= −γxx(2)+a1(1) γxx(1)

Ef1

a2(1) = a1(1) + a2(2) a∗1(1)

(A.5)

Thus the coefficients of the second-order predictor are obtained. Again, we note thata2(2) = K2, thesecond reflection coefficient in the lattice filter.

Proakis [4] shows on pages 224-225 that theKm coefficients can be determined recursively according to

Km = −γxx(m) + Aγbtm−1Aam−1

γxx(0) + Aγbtm−1Aab∗m−1

= −γxx(m) + Aγbtm−1Aam−1

Efm−1

(A.6)

where·b : takes the elements in reverse order·∗ : takes the complex conjugate·t : takes the transpose

which can be rewritten into the recursion for the predictor coefficients in the Levinson-Durbinalgorithm:

am(m) = Km = −γxx(m) + Aγbtm−1Aam−1

Efm−1

(A.7)

am(k) = am−1(k) + Km a∗m−1(m− k)

= am−1(k) + am(m) a∗m−1(m− k),k = 1, 2, . . . ,m− 1m = 1, 2, . . . , p

(A.8)

A.2 Function: levdub

f u n c t i o n v a r a r g o u t = levdub ( r , p )

% LevDub Levinson−Durbin r e c u r s i o n .%−−−−

5 % USAGE : [ a , E ] = levdub ( r )% [ a , E ] = levdub ( r , p )%% So lves t h e T o e p l i t z normal e q u a t i o n s% R a = e p s i l o n [ 1 0 . . . 0 ] ’

10 % where R = t o e p l i t z ( r ) i s a T o e p l i t z m a t r i x t h a t c o n t a i n s% t h e a u t o c o r r e l a t i o n sequence r ( k ) .%% [ r ( 0 ) r (−1) r (−2) . . . r (−p ) ] [ 1 ] = [ E ]% [ r ( 1 ) r ( 0 ) r (−1) . . . r (−p + 1 ) ] [ a1 ] = [ 0 ]

15 % [ . . . . ] [ . ] = [ . ]% [ r ( p ) r ( p−1) r ( p−2) . . . r ( 0 ) ] [ ap ] = [ 0 ]%% The o u t p u t s a r e t h e c o e f f i c i e n t s o f t h e a l l−po le model a ( k )% of o r d e r p , and t h e c o n s t a n t E .

20

% ( c ) o p y r i g h t Tha les Neder land BV% Crea ted on 08−05−2003 by JAH Harmsen

%∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ VERIFY INPUT ∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗%25 i f n a r g i n < 2 | i sempty( p )

p = l e n g t h( r )−1;e l s e i f p < 1 | p > l e n g t h( r )−1;

e r r o r (’order p should be between [ 1 , length(r)-1 ]’ )end

64

A.2. Function: levdub

30

%∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ THE ALGORITHM ∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗%r = r ( : ) ; % Giv ing [ r ( 0 ) r ( 1 ) . . . r ( p ) ] ’ ; a lways column a r r a ya = 1 ; % a ( 0 ) = 1 ;E = r ( 1 ) ; % e p s i l o n = r ( 0 ) : s i n c e Mat lab i n d i c e s b e g i n s wi th 1

35 % r ( 1 ) r e p r e s e n t s r ( 0 ) !

f o r m = 2 : p+1K = − r ( 2 :m) . $ ’ $ ∗ f l i p u d ( a ) / E ;a = [ a ; 0 ] + K ∗ [ 0 ; con j ( f l i p u d ( a ) ) ] ;

40 E = E ∗ ( 1 − abs(K ) ˆ 2 ) ;end

%∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ SET OUTPUT∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗%i f n a r g o u t = = 0

45 f p r i n t f ( 1 ,’WARNING: Let me give you at least one output’ )e l s e

v a r a r g o u t1 = a ;i f n a r g o u t >= 2 , v a r a r g o u t2 = E ; end

end

65

A. Levinson-Durbin algorithm

66

Appendix B

Forward linear prediction

A one-step forward linear predictor[4], which forms the prediction of the valuex(n) by a weightedlinear combination of the past valuesx(n− 1), x(n− 2), . . . , x(n−m), will be considered. The linearpredicted value ofx(n) is

x(n) = −m∑k=1

am(k)x(n− k) (B.1)

where the−am(k) represent the weights in the linear combination. These weights are called theprediction coefficientsof the one-step forward linear predictor oforderm. The difference of thispredicted valuex(n) with the real valuex(n) is called theforward prediction errorfm(n),

fm(n) = x(n) − x(n)

= x(n) +p∑k=1

am(k)x(n− k) (B.2)

Proakis [4] gives a realization of the prediction-error filter which takes the form of a lattice structure,

Figure B.1: p-stage lattice filter

see figure B.1. The lattice filter is generally described by the following set oforder-recursive equations:

f0(n) = g0(n) = x(n)fm(n) = fm−1(n) + Km gm−1(n− 1), m = 1, 2, . . . , pgm(n) = K∗

m fm−1(n) + gm−1(n− 1), m = 1, 2, . . . , p(B.3)

Suppose a predictor of orderp = 2. In this case the prediction error is:

f2(n) = a2(0)x(n) + a2(1)x(n− 1) + a2(2)x(n− 2) (B.4)

67

B. Forward linear prediction

The lattice structure would give the followingKm parameters:

f1(n) = x(n) + K1 x(n− 1)g1(n) = K∗

1x(n) + x(n− 1)(B.5)

where for the second stage the outputs are defined as:

f2(n) = f1(n) + K2 g1(n− 1)g2(n) = K∗

2f1(n) + g1(n− 1)(B.6)

so, focussing onf2(n), and substitute forf1(n) andg1(n− 1) from B.5 into B.6,

f2(n) = x(n) + Kz x(n− 1) + K2 [K∗1 x(n− 1) + x(n− 2)]

= x(n) + (K1 + K∗1K2)x(n− 1) + K2 x(n− 2) (B.7)

Equation B.7 is identical to B.4 giving for the coefficients:

a2(2) = K2, a2(1) = K1 + K∗1K2, a2(0) = 1

K2 = a2(2), K1 = a1(1)(B.8)

The output of them-stage lattice filter could be expressed as:

fm(n) =m∑k=0

am(k)x(n− k), am(0) = 1 (B.9)

The mean-square value of the forward linear prediction errorfm(n) is:

Errfm = E[|fm(n)|2

∣∣∣ (B.10)

= γxx(0) + 2[m∑k=1

a∗m(k) γxx(K)

]+

m∑k=1

m∑k=1

a∗m(l) ap(k) γxx(l − k)

Errfm is a quadratic function of the predictor coefficients, and its minimization leads to the set of linearequations

γxx(l) = −m∑k=1

am(k) γxx(l − k), l = 1, 2, . . . ,m (B.11)

These are called thenormal equationsfor the coefficients of the linear predictor. The minimummean-square prediction error is

min[Errfm

]≡ Ef

m = γxx(0) +m∑k=1

am(k) γxx(−k) (B.12)

Since each new coefficient can be calculated by the recursive algorithm, only theKm coefficients andthe initial conditions have to be calculated. The mean-square value of the prediction error could be aparameter to be minimized in order to get the ”optimal”Km coefficients. The forward prediction errorin the lattice filter is expressed as

fm(n) = fm−1(n) + Km gm−1(n− 1) (B.13)

The minimization ofE[|fm(n)|2

]with respect to the reflection coefficientKm yields the result

Km =−E

[fm−1(n) g∗m−1(n− 1)

]E

[|gm−1(n− 1)|2

] (B.14)

68

or equivalently,

Km =−E

[fm−1(n) g∗m−1(n− 1)

]√Efm−1 E

bm−1

(B.15)

whereEfm−1 = Eb

m−1 = E[|gm−1(n− 1)|2

]= E

[|fm−1(n)|2

]Since it is apparent from B.14 that|Km| ≤ 1, it follows that the minimum mean-square value of theprediction error, which may be expressed recursively as

Efm =

(1 − |Km|2

)Efm−1 (B.16)

is a monotonically decreasing sequence.

The parameters of anAR(m) process are intimately related to a predictor of orderp for the sameprocess. In fact, if the underlying processx(n) is AR(m), the prediction coefficients of themth-orderpredictor will be identical toak.

69

B. Forward linear prediction

70

Appendix C

PSD Estimators

This appendix gives several Matlab codes for PSD estimators

C.1 Function: PSDWelch

f u n c t i o n v a r a r g o u t = PSDWelch ( x , N , ove r l ap , win , s h i f t )

% Syntax : [ Pxx , xsh , k ] = PSDWelch ( x , N , ove r l ap , win , s h i f t )%

5

% Crea ted on 20−03−2003 by JAH Harmsen% ( c ) Tha les Neder land BV

i f n a r g i n < 510 s h i f t = ’noshift’ ;

e l s e i f ˜ i s c h a r ( s h i f t )e r r o r (’HAR-info: 5th input into WelchPSD should be of type char’ )

end i f n a r g i n < 4win = ’hamming’ ;

15 win = s t r 2 f u n c ( win ) ;e l s e i f ˜ i s c h a r ( win )

e r r o r (’HAR-info: 4th input into WelchPSD should be of type char’ )end i f n a r g i n < 3

o v e r l a p = 0 . 5 ;20 e l s e i f o v e r l a p >= 1 | o v e r l a p < 0

e r r o r (’HAR-info: overlap for WelchPSD should be between [ 0,1 >’ )end i f n a r g i n < 2

N = 5 1 2 ;end i f n a r g i n < 1

25 e r r o r (’HAR-info: no input samples for WelchPSD to estimate the Power Spectrum’ )end i f mod (N, 2 )

N = f i x (N−1);end i f s i z e( x , 1 ) > 1

i f s i z e ( x , 2 ) = = 130 x = x .’;

elseerror(’d a t a i n p u t f o r welchpsd shou ld be a ve c t o r and no t a mat r i x ’ )

endend

35

xsh = ( 0 : N−1) / (N−1)∗2; % Normal ized f r e q u e n c yWin = window ( win ,N ) ; % Window

% Welch wi th compensa t ion f o r window power .40 Pxx =0; k = 0 ; f o r i = 1 : round(N∗(1− o v e r l a p ) ) : l e n g t h( x)−(N−1)

k=k +1;tmp1 = f f t ( x ( i : i +N−1).∗Win ’ ) ;tmp1 = ( ( abs( tmp1 ) ) . ˆ 2 ) /sum( Win . ˆ 2 ) ;

71

C. PSD Estimators

Pxx = Pxx + tmp1 ;45 end Pxx = Pxx . / k ;

i f s t r cmp( s h i f t ,’shift’ )Pxx = f f t s h i f t ( Pxx ) ;xsh = xsh−1;

50 end

%∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ SET OUTPUT∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗%i f n a r g o u t = = 0

f i g u r e , p l o t ( xsh ,10∗ l og10( Pxx ) ) % p l o t i n new f i g u r e55 x l t x t =[ ’Frequency "\Omega" normalized from 0 to 2\pi [rad/sample]’ ] ;

x l a b e l ( x l t x t ) ; y l a b e l (’Power Spectrum Density in [dB]’ ) ,t t x t =[’Welch PSD estimation, ’ , num2st r( k ,’%0.5g’ ) ,’ averages’ ] ;t i t l e ( t t x t )

e l s e % d e l i v e r t h e asked o u t p u t60 i f n a r g o u t = = 3 , v a r a r g o u t3 = k ; end

i f n a r g o u t >= 2 , v a r a r g o u t2 = xsh ; endv a r a r g o u t1 = Pxx ;

end

C.2 Function: PSDyulewalker

f u n c t i o n v a r a r g o u t = PSDyulewalker ( x , NofPoles , fs , NofPo in ts , s h i f t )

% Use :% [ Pxx , a , e p s i l o n ] = PSDyulewalker ( x , po les , f s )

5 % I f no o u t p u t a rguments a r e s e l e c t e d , t h i s f u n c t i o n w i l l p l o t t h e PSD . I f% no f s i s g iven , t h e p l o t w i l l d i s p l a y t h e no rma l i zed f requency .%% This f u n c t i o n c a l c ul a t e s t h e Yule−Walker Power spec t rum e s t i ma t i o n by% e s t i m a t i n g t h e a u t o c o r r e l a t i o n f i r s t . Second ly t h e a ( k ) p a r a me t e r s w i l l

10 % be e s t i m a t e d wi th t h e Levinson−Durbin a l g o r i t h m . F i n a l l y t h e PSD i s% e s t i m i t e d wi th t h e a ( k ) p a r a m e t e r s .

% ( c ) o p y r i g h t Tha les Neder land BV% Crea ted on 0 8 0 5 2 0 0 3 by JAH Harmsen

15

%∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ VERIFY INPUT ∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗%i f n a r g o u t > 3

e r r o r (’Too much output arguments for PSDYuleWalker’ )end i f n a r g i n < 5

20 s h i f t = ’noshift’ ;e l s e i f ˜ i s c h a r ( s h i f t )


No fPo in t s = 5 1 2 ;25 end i f n a r g i n < 3

f s = 2 ;end i f n a r g i n < 2 | i sempty( NofPo les ) | NofPo les > l e n g t h( x)−1

NofPo les = l e n g t h( x )−1;end

30

%∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ THE ALGORITHM ∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗%[ rxx , p ] = x c o r r ( x ,’unbiased’ ) ; % c a l c u l a t i n g a u t o c o r r e l a t i o n

% c o e f f i c i e n t s : n o r ma l i z e !Rxx = rxx ( f i n d ( p>= 0 ) ) ; % S e l e c t i n g poss c o e f f

35

[ a , e p s i l o n ] = levdub ( Rxx , NofPo les ) ; % c a l c u l a t i n g a c o e f f w i th t h e% Levinson−Durbin a l g o r i t h m

Pxx = e p s i l o n . / (abs( f f t ( a , No fPo in t s ) ) ) . ˆ 2 ;% c a l c u l a t i n g t h e PSD40

i f s t rcmp( s h i f t ,’shift’ )Pxx = f f t s h i f t ( Pxx ( : ) ) ;f = ( 0 : f s / No fPo in t s : fs−f s / No fPo in t s )−( fs−f s / No fPo in t s ) / 2 ; % s e t t i n g x a x i s f o r p l o t

e l s e45 Pxx = Pxx ( : ) ;

f = ( 0 : f s / No fPo in t s : fs−f s / No fPo in t s ) ;end

72

C.3. Function: PSDburg

%∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ SET OUTPUT∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗%50 i f n a r g o u t = = 0

f i g u r e , p l o t ( f ,10∗ l og10( Pxx ) ) % p l o t i n new f i g u r ei f f s = = 2

x l t x t =[ ’Frequency "\Omega" normalized from 0 to 2\pi [rad/sample]’ ] ;e l s e

55 x l t x t =[ ’Frequency "f" from 0 to ’ , num2st r( fs ,’%0.5g’ ) ,’ [Hz]’ ] ;endx l a b e l ( x l t x t ) ; y l a b e l (’Power Spectrum Density in [dB]’ ) ,t t x t =[’Yule Walker PSD estimation, ’ , num2st r( NofPoles ,’%0.5g’ ) ,’ poles’ ] ;t i t l e ( t t x t )

60 e l s e % d e l i v e r t h e asked o u t p u ti f n a r g o u t = = 3 , v a r a r g o u t3 = e p s i l o n ; endi f n a r g o u t >= 2 , v a r a r g o u t2 = a ; endv a r a r g o u t1 = Pxx ;

end

C.3 Function: PSDburg

f u n c t i o n v a r a r g o u t = PSDburg ( x , NofPoles , fs , NofPo in ts , s h i f t )

% Use :% [ Pxx , a , e p s i l o n ] = PSDburgJ ( x , NofPoles , fs , NofPo in ts , s h i f t )

5 % I f no o u t p u t a rguments a r e s e l e c t e d , t h i s f u n c t i o n w i l l p l o t t h e PSD . I f% no f s i s g iven , t h e p l o t w i l l d i s p l a y t h e no rma l i zed f requency .%% This f u n c t i o n c a l c u l a t e s t h e Burg Power spec t rum e s t i ma t i o n by% min imiz ing t h e r e s i d u e l e r r o r . Second ly t h e a ( k ) p a r a me t e r s w i l l

10 % be e s t i m a t e d wi th t h e Levinson−Durbin a l g o r i t h m . F i n a l l y t h e PSD i s% e s t i m i t e d wi th t h e a ( k ) p a r a m e t e r s .

% ( c ) o p y r i g h t Tha les Neder land BV% Crea ted on 0 8 0 5 2 0 0 3 by JAH Harmsen

15

%∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ VERIFY INPUT ∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗%i f n a r g o u t > 3

e r r o r (’Too much output arguments for PSDburg’ )end i f n a r g i n < 5

20 s h i f t = ’noshift’ ;e l s e i f ˜ i s c h a r ( s h i f t )


No fPo in t s = 5 1 2 ;25 end i f n a r g i n < 3

f s = 2 ;end i f n a r g i n < 2 | i sempty( NofPo les ) | NofPo les > l e n g t h( x)−1

NofPo les = l e n g t h( x )−1;end

30

%∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ THE ALGORITHM ∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗%%INITIALISATIONSx = x ( : ) ; %S e t t i n g x i n a column v e c t o re f = x ; %Forward e r r o r i n s t a g e 0 i s x ( n )

35 eg = x ; %Backward e r r o r i n s t a g e 0 i s x ( n )a = 1 ; %F i r s t a p a r a m e t e r i s 1E = 2∗ abs( x ) .’*abs(x); %Total mean square error is:

% sum_n=0ˆN-1 ef_0(n)ˆ2 + eg_0(n)ˆ2P = abs(x).’∗abs( x ) / l e n g t h( x ) ; %\ s igma wp ˆ2

40 K = 0 ; %I n i t i a l K p a r a m e t e r i s 0

f o r m = 1 : NofPo lese f s = e f ( 2 :end) ;egs = eg ( 1 :end−1);

45 %CALCULATE NUMERATOR AND TOTAL LEAST−SQUARES ERRORnum = − ( e f s ) .’ * conj(egs);E = (1-abs(K)ˆ2)*E - abs(ef(1))ˆ2 - abs(eg(end))ˆ2;K = num ./ (0.5 * E);%RESETTING THE MEAN SQUARED VALUE

50 P = P * (1-abs(K)ˆ2);

73

C. PSD Estimators

%UPDATE ERROR ESTIMATESef = efs + K * egs;eg = egs + conj(K) * efs;%UPDATE THE a PARAMETERS OF THE AR-MODEL

55 a = [a;0] + K * [0;conj(flipud(a))];

end

Pxx = P./(abs(fft(a,NofPoints))).ˆ2; % calculating the PSD60

if strcmp(shift,’ s h i f t ’ )Pxx = f f t s h i f t ( Pxx ( : ) ) ;f = ( 0 : f s / No fPo in t s : fs−f s / No fPo in t s )−( fs−f s / No fPo in t s ) / 2 ; % s e t t i n g x a x i s f o r p l o t

e l s e65 Pxx = Pxx ( : ) ;

f = ( 0 : f s / No fPo in t s : fs−f s / No fPo in t s ) ;end

%∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ SET OUTPUT∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗%70 i f n a r g o u t = = 0

f i g u r e , p l o t ( f ,10∗ l og10( Pxx ) ) % p l o t i n new f i g u r ei f f s = = 2

x l t x t =[ ’Frequency "\Omega" normalized from 0 to 2\pi [rad/sample]’ ] ;e l s e

75 x l t x t =[ ’Frequency "f" from 0 to ’ , num2st r( fs ,’%0.5g’ ) ,’ [Hz]’ ] ;endx l a b e l ( x l t x t ) ; y l a b e l (’Power Spectrum Density in [dB]’ ) ,t t x t =[’Burg PSD estimation, ’ , num2st r( NofPoles ,’%0.5g’ ) ,’ poles’ ] ;t i t l e ( t t x t )

80 e l s e % d e l i v e r t h e asked o u t p u ti f n a r g o u t = = 3 , v a r a r g o u t3 = P ; endi f n a r g o u t >= 2 , v a r a r g o u t2 = a ; endv a r a r g o u t1 = Pxx ;

end85

%∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ TEST ENVIRONMENT∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗%% hold on , Pxx = P . / ( 1 + abs ( f f t ( a , l e n g t h ( a ) ) ) ) . ˆ 2 ;% p l o t ( f ,10∗ l og10 ( Pxx ) , ’ r ’ ) , l egend ( ’ f i r s t ’ , ’ second ’ )

74

Appendix D

Generation of Radar Signals, Matlabscript

D.1 Function: r2d

f u n c t i o n deg = r2d ( rad )

% f u n c t i o n deg = r2d ( rad )%

5 % Conver t s from r a d i a n s t o d e g r e e s .

deg = 180∗ rad /p i ;

D.2 Function: d2r

f u n c t i o n rad = d2r ( d e g r e e s )

% f u n c t i o n rad = d2r ( d e g r e e s )%

5 % Conver t s from d e g r e e s t o r a d i a n s .%

rad = p i ∗ d e g r e e s / 1 8 0 ;

D.3 Function: Jdefant

f u n c t i o n a n t = J d e f a n t ( an tennaType )

% f u n c t i o n r e t u r n s a s t r u c t u r e ’ ant ’ where t h e an tenna ande lement t ype a r e% d e f i n e d .

5 % C u r r e n t l y s u p p o r t e d t y p e s :% − l i n e a r a r r a y w i th an i s o t r o p i c a l an tenna e lement%% Use :% a n t = J d e f a n t ( ’ isotropULA ’ ) ;

10 % or% a n t = J d e f a n t ( ) ;

% Las t mod i f i ed JAH Harmsen

15 i f n a r g i n > 1e r r o r (’HAR-Error: Too many input parameters.’ )

e l s e i f s t rcmp( antennaType ,’isotropULA’ ) | n a r g i n = = 0a n t . an tennaType =’ULA’ ;

75

D. Generation of Radar Signals, Matlab script

a n t . e lemen t . an tennaType =’elem’ ;20 a n t . e lemen t . pa t t e r n T y p e =’isotrop’ ;

a n t . e lemen t . beamSpaceTrans = 1 ;a n t . beamSpaceTrans = 1 ;%ones ( noChannels , 1 ) ;

e l s ee r r o r (’HAR-Error: Only Isotrop Uniform Linear Array antenna are modelled, with 1 Channel’ )

25 end

D.4 Function: Jdefjammer

f u n c t i o n jammerdef = Jdef jammer ( jamPower , jamRange , jamVel ,jamBW ST )

5 %Use :% jamerde f = def jammer% jamerde f = def jammer ( jamPower )% jamerde f = def jammer ( jamPower , t rgRange )% jamerde f = def jammer ( jamPower , t rgRange , jamVel )

10 % jamerde f = def jammer ( jamPower , t rgRange , jamVel , jamBWST )%%D e s c r i p t i o n :%% Def i nes a s t r u c t v a r i a b l e c o n t a i n i n g a l l i n f o r m a t i o n needed by t h e

15 % f u n c t i o n ” s i m r a d a r s i g ” i n comb ina t i on wi th t h e f u nc t i o n ” simjammer ”% t o s i m u l a t e t h e r a d a r s i g n a l from a jammer .%%I n p u t :% jamPower : Power o f jammer a t r e c i e v i n g an tenna

20 % t rgRange : Range t o Jammer . D e f a u l t i s 2 0 0 0 [m] .% jamVel : R a d i a l v e l o c i t y o f t a r g e t r e l a t i v e r a d a r . D e f a u l t i s 0 [m/ s ] .% jamBW ST : The bandwid th and s t a r t f r e q u e n c y o f t h e jammer

%25 %OutPut :

% jammerdef ( JammerDefT ) : A d e f i n i t i o n o f t h e jammer i n a s t r u c t .%%−−−−−−−−%

30 %See a l s o :% d e f n o i s e d e f c l u t t e r d e f t a r g e t s i m r a d a r s i g

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−%−−−− In−p a r a m e t e r c o n t r o l & d e f a u l t v a l u e s h a n d l i n g −−−−

35 %−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

i f n a r g i n < 4 | i sempty( jamBW ST )jamBW ST = [ 4 0 1 2 5 0 ] ; % D e f a u l t bandwid th o f 40MHz s t a r t i n g a t 1 2 5 0 MHz

end40

i f n a r g i n < 3 | i sempty( jamVel )jamVel = 0 ; % D e f a u l t r a d i a l v e l o c i t y i n m/ s .

end

45 i f n a r g i n < 2 | i sempty( jamRange )jamRange = 2 0 0 0 ; % D e f a u l t s t o 2 km d i s t a n t

end

i f n a r g i n < 1 | i sempty( jamPower )50 jamPower = 1 0 ;

end

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−%−−−− S e t t i n g up t h e o u t p u t p a r a m e t e r −−−−

55 %−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

jammerdef . da taType =’Jjammer’ ;jammerdef . Power = jamPower ; % Might be r e p l a c e d by RCS l a t e r onjammerdef . Range = jamRange ; jammerdef . V e l o c i t y = jamVel ;

60 jammerdef . Bandwidth = jamBWST ( 1 ) ; jammerdef . BWStart =

76

D.5. Function: defnoise

jamBW ST ( 2 ) ;

D.5 Function: defnoise

f u n c t i o n n o i s e d e f = d e f n o i s e ( no isePower )

%Use :% n o i s e d e f = J d e f n o i s e ( no isePower )

5 %%D e s c r i p t i o n :% De f i nes a s t r u c t v a r i a b l e c o n t a i n i n g a l l i n f o r m a t i o n needed by f u n c t i o n% ” s i m r a d a r s i g ” i n comb ina t i on wi th f u nc t i o n ” s imno i se ” t o s i m u l a t e t h e% r a d a r s i g n a l from n o i s e t h a t a r e c r e a t e d i n t h e r e c e i v i n g rada rsys tem ’ s

10 % c h a n n e l s . see s imno i se f o r more d e t a i l e d i n f o r ma t i o n .%%I n p u t :% no isePower : Power o f n o i s e i n r e c e i v i n g an tenna c h a n n e l s . D e f a u l t i s 1 [W] .%

15 %OutPut :% n o i s e d e f : A d e f i n i t i o n o f t h e n o i s e i n a s t r u c t .%%−−−−−−−−%N o t a t i o n s :

20 %%Examples :% n o i s e S r c 1 = J d e f n o i s e ( 0 . 3 ) ;% Th is d e f i n e s a n o i s e s o u r c e o f t h e t ype ’ Gauss ian ’ which i s a% complex g a u s s i a n n o i s e s o u r c e wi th t h e power 0 . 3 . i . e t h e v a r i a n c e

25 % of t h e complex n o i s e i s eq u a l t o 0 . 3 .%

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−%−−−− In−p a r a m e t e r c o n t r o l & d e f a u l t v a l u e s h a n d l i n g −−−−

30 %−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

i f n a r g i n < 1no isePower = 1 ; % D e f a u l t s t o t h e power 1 [W] .

end%i f35

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−%−−−− S e t t i n g up t h e o u t p u t p a r a m e t e r −−−−%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

40 n o i s e d e f . da taType =’Jnoise’ ; n o i s e d e f . Power = no isePower ;

D.6 Function: Jdeftarget

f u n c t i o n t a r g e t d e f = J d e f t a r g e t ( t rgPower , t rgRange , trgDOA ,t r g V e l )

%Use :5 % t a r g e t d e f = d e f t a r g e t

% t a r g e t d e f = d e f t a r g e t ( t rgPower )% t a r g e t d e f = d e f t a r g e t ( t rgPower , t rgRange )% t a r g e t d e f = d e f t a r g e t ( t rgPower , t rgRange , trgDOA )% t a r g e t d e f = d e f t a r g e t ( t rgPower , t rgRange , trgDOA , t r g V e l )

10 %%D e s c r i p t i o n :% De f i nes a s t r u c t v a r i a b l e c o n t a i n i n g a l l i n f o r m a t i o n needed by f u n c t i o n% ” s i m r a d a r s i g ” i n comb ina t i on wi th f u nc t i o n ” s i m t a r g e t ” t o s i m u l a t e t h e% r a d a r s i g n a l from a t a r g e t .

15 %%I n p u t :% t rgPower : Power ( l i n e a r s c a l e ) o f t a r g e t i n r e c i e v i n g an tenna c h a n n e l s% D e f a u l t i s 1 [W] .% t rgRange : Range t o t a r g e t . D e f a u l t i s 1 0 0 0 [m] .

20 % trgDO : D i r e c t i o n t o t a r g e t . D e f a u l t i s s t r a i g h t fo rward .% t r g V e l : R a d i a l v e l o c i t y o f t a r g e t r e l a t i v e r a d a r . D e f a u l t i s 0 [m/ s ] .

77


%%OutPut :% t a r g e t d e f : A d e f i n i t i o n o f t h e t a r g e t i n a s t r u c t .

25 %%%Examples :% t r g = d e f t a r g e t ( 4 . 7 , 6 0 0 0 , [ d2r ( 2 5 ) ; 0 ] , 2 ) ;% Th is d e f i n e s a c o n s t a n t ( s w e r l i n g 0 ) t a r g e t w i th a power o f 4 . 7 [W]

30 % a t t h e d i s t a n c e 6 [ km ] and t h e d i r e c t i o n 2 5 [ d e g r e e s ] h o r i s o n t a l l y% from t h e c e n t e r d i r e c t i o n o f t h e an tenna and wi th t h e v e l o c i t y% 2 [m/ s ] .%

35 %−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−%−−−− In−p a r a m e t e r c o n t r o l & d e f a u l t v a l u e s h a n d l i n g −−−−%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

i f n a r g i n < 4 | i sempty( t r g V e l )40 t r g V e l = 0 ; % D e f a u l t s t o a s t a t i o n a r y t a r g e t

end%i f

i f n a r g i n < 3 | i sempty( trgDOA )trgDOA = [ 0 ; 0 ] ; % D e f a u l t s t o s t r a i g h t fo rward

45 end%i f

i f n a r g i n < 2 | i sempty( t rgRange )t rgRange = 1 0 0 0 ; % D e f a u l t s t o 1 km d i s t a n t

end%i f50

i f n a r g i n < 1 | i sempty( t rgPower )t rgPower = 1 ; % D e f a u l t s t o t h e power 1

end%i f

55

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−%−−−− S e t t i n g up t h e o u t p u t p a r a m e t e r −−−−%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

60

t a r g e t d e f . da taType =’Jtarget’ ;t a r g e t d e f . Power = t rgPower ;% Might be r e p l a c e d by RCS l a t e r ont a r g e t d e f . Range = t rgRange ; t a r g e t d e f .DOA = trgDOA ;t a r g e t d e f . V e l o c i t y = t r g V e l ;

65

%End Of F i l e−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

D.7 Function: defwave

f u n c t i o n waveform = defwave ( wave length , noRangeBins , pModulat ion ,sampleTime )

%DEFWAVE De f i nes t h e t ime p r o p e r t i e s o f a r a d a r or r a d i o s i g n a l .5 %

%Use :% waveform=defwave ( wave length , noRangeBins , noPu lses , pModulat ion , . . .% sampleTime , noCPI )%

10 %D e s c r i p t i o n :% De f i nes t h e t ime p r o p e r t i e s o f a r a d a r or r a d i o s i g n a l , e . g . number o f% t ime samples , sample t ime and waveform modu la t i on .%%

15 %I n p u t :% wave leng th : Wavelength o f t h e c a r r i e r [m] .% OR% wave leng th : Wavelengths o f t h e c a r r i e r [m ] . Th is means% t h a t d i f f e r e n t wave leng ths a r e used i n d i f f e r e n t c o h e r e n t p u l s e

20 % i n t e r v a l l s ( CPI : s ) , i . e . l e n g t h ( wave leng th ) ( must be ) = noCPI .% wave leng th ( 1 ) i s used i n t h e f i r s t CPI and so on .% noRangeBins : The s e p a r a t i o n between d i f f e r e n t p u l s e s or

78

D.8. Function: defsources

% PRIs e x p r e s s e d i n number o f range b i n s . Th is i s t h e same as t h e% maximum unambiguous range . The number o f range b i n sa c t u a l l y p r e s e n t

25 % i n t h e s i g n a l i s l e s s or eq u a l t o ” noRangeBins ” . The p a r a m e t e r% ” noRangeBins ” i s used t o c a l c u l a t e t h e PRI [ s ] as% PRI = noRangeBins∗ sampleTime [ s ] .% noPu l ses : Number o f p u l s e s∗ PRI = CPI ( c o h e r e n t% p r o c e s s i n g i n t e r v a l ) .

30 % pModu la t ion : The c o e f f i e n t o f t h e p u l s e modu la t i on . See% he lp ” getmod ” f o r more i n f o r m a t i o n .% sampleTime : Sample p e r i o d t ime i n t r a n s m i t t e r and% r e c e i v e r . One sampleTime c o r r e s p o n d s t o one range b in .% noCPI : Number o f c o h e r e n t p r o c e s s i n g i n t e r v a l s ( CPI : s ) .

35 %%Output :% waveform : The r e c o r d v a r i a b l e c o n t a i n i n g t h e combined d a t a .%

40 i f ( n a r g i n < 4)e r r o r (’HAR-Error: To few input parameters to defwave.’ ) ;

end%i f

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−45 %−−−− C o n s t r u c t t h e waveform s t r u c t v a r i a b l e . −−−−

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

waveform . wave leng th = wave leng th ;

50 waveform . noRangeBins = noRangeBins ;

% waveform . noPu l ses = noPu l ses ;

waveform . sampleTime = sampleTime ;55

waveform . pModu la t ion = pModu la t ion ;

% End Of F i l e

D.8 Function: defsources

f u n c t i o n s rcDe f = d e f s o u r c e s ( s r c L i s t , t rgCorrMx )

%Synops i s :% srcDe f = d e f s o u r c e s ( s r c L i s t )

5 % srcDe f = d e f s o u r c e s ( s r c L i s t , t rgCorrMx )%%D e s c r i p t i o n :% De f i nes a s t r u c t v a r i a b l e c o n t a i n i n g a l l i n f o r m a t i o n needed by% f u n c t i o n ” s i m r a d a r s i g ” i n comb ina t i on wi th t h e f u nc t i o n s ” s i m t a r g e t ” ,

10 % ” s imno i se ” , ” s i m c l u t t e r ” and ” simjammer ” t o s i m ul a t e t h e r a d a r s i g n a l% from a l l d i f f e r e n t s o u r c e s . V a r i a b l e s i s c o l l e c t e d i n a more e f f i c i e n t% way , so t h a t t h e s i m u l a t i o n p r o c e s s can be made as f a s t as p o s s i b l e .%%I n p u t :

15 % s r c L i s t : C e l l a r r a y w i th d e f i n i t i o n s o f s o u r c e s .%% trgCorrMx : C o r r e l a t i o n m a t r i x f o r t a r g e t s . C o r r e l a t i o n between t a r g e t s .% D e f a u l t i s no c o r r e l a t i o n .%

20 %OutPut :% srcDe f : A d e f i n i t i o n o f t h e s o u r c e s i n a s t r u c t v a r i a b l e%

%25 %Examples :

% t r g 1 = J d e f t a r g e t ( 1 0 , 2 0 0 0 , [ 0 ; 0 ] , 0 ) ;% t r g 2 = J d e f t a r g e t ( 3 , 7 0 0 0 , [ 0 ; 0 ] ,−2 0 0 ) ;% n o i s e S r c 1 = J d e f n o i s e ( 3 ) ;% jam1 = Jdef jammer ( 1 5 , 2 0 0 , 3 0 0 , [ 9 0 1 2 0 0 ] ) ;

30 % jam2 = Jdef jammer ( 2 0 , 3 0 0 , 4 0 0 , [ 6 6 1 2 0 0 ] ) ;% s o u r c e s = J d e f s o u r c e s ( t r g 1 t r g 2 n o i s e S r c 1 jam1 jam2 ) ;

79


% F i r s t a d e f i n i t i o n o f s e v e r a l t a r g e t s and then f i n a l l y combin ing a l l% t h e s e s o u r c e s i n t o a s t r u c t so t h a t s i m u l a t i o n can be made e a s i e r .% The l i s t o f s o u r c e s does no t need t o be i n any s p e c i f i c o r d e r .

35 %%

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−%−−−− In−p a r a m e t e r c o n t r o l & d e f a u l t v a l u e s h a n d l i n g −−−−

40 %−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

i f n a r g i n < 2trgCorrMx = [ ] ; % D e f a u l t s t o no c o r r e l a t i o n between t a r g e t s

end %i f45 i f n a r g i n < 1

e r r o r (’To few input parameters, give me atleast one source!’ ) ;end %i f

50 %−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−%−−−− S e t t i n g up t h e o u t p u t p a r a m e t e r −−−−%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

noSrcs = l e n g t h( s r c L i s t ) ;55

n o T a r g e t s = 0 ; % Number o f t a r g e t snoNo iseSrcs = 0 ; % Number o f n o i s e s o u r c e sn o C l u t t e r S r c s = 0 ; % Number o f c l u t t e r s o u r c e snoJammers = 0 ; % Number o f jammers

60

s rcDe f . da taType =’Jsources’ ;

65 f o r s r c I x = 1 : noSrcs

c u r r e n t S r c = s r c L i s t s r c I x ;

i f ( ˜ i sempty( c u r r e n t S r c ) )70 i f ( s t rcmp( c u r r e n t S r c . dataType ,’Jtarget’ ) )

n o T a r g e t s = n o T a r g e t s + 1 ;f p r i n t f (’\nAdding a TARGET of type: "Swerling 0" ’ ) ;s r cDe f . T a r g e t s . Powers ( n o T a r g e t s ) = c u r r e n t S r c . Power ;s r cDe f . T a r g e t s . Ranges ( n o T a r g e t s ) = c u r r e n t S r c . Range ;

75 s rcDe f . T a r g e t s . DOAs ( : , n o T a r g e t s ) = c u r r e n t S r c .DOA;s rcDe f . T a r g e t s . V e l o c i t i e s ( n o T a r g e t s ) = c u r r e n t S r c . V e l oc i t y ;

e l s e i f s t rcmp( c u r r e n t S r c . dataType ,’Jnoise’ )f p r i n t f ( ’\nAdding NOISE of type: "Gaussian"’ ) ;

80 noNo iseSrcs = noNo iseSrcs + 1 ;s rcDe f . Noise . PowersnoNo iseSrcs = c u r r e n t S r c . Power ;

e l s e i f s t rcmp( c u r r e n t S r c . dataType ,’Jclutter’ )f p r i n t f ( ’\nAdding CLUTTER of type: "MIT-LCE"’ ) ;

85 n o C l u t t e r S r c s = n o C l u t t e r S r c s + 1 ;s rcDe f . C l u t t e r s . TypeParam ( n o C l ut t e r S r c s , : ) = c u r r e n t S r c . TypeParam ;s rcDe f . C l u t t e r s . Power ( n o C l ut t e r S r c s ) = c u r r e n t S r c . Power ;s r cDe f . C l u t t e r s .DOAs( n o C l ut t e r S r c s , : ) = c u r r e n t S r c .DOAs ;s rcDe f . C l u t t e r s . Pl a t H e i g h t ( n o C l u t t e r S r c s ) = c u r r e n t S r c . P l a t H e i g h t ;

90 s rcDe f . C l u t t e r s . Pl a t V e l o c i t y ( n o C l u t t e r S r c s ) = c u r r e n t S r c . P l a t V e l o c i t y ;

e l s e i f s t rcmp( c u r r e n t S r c . dataType ,’Jjammer’ )f p r i n t f ( ’\nAdding a JAMMER of type: "Gaussian"’ ) ;noJammers = noJammers + 1 ;

95 s rcDe f . Jammers . Powers ( noJammers ) = c u r r e n t S r c . Power ;s r cDe f . Jammers . Ranges ( noJammers ) = c u r r e n t S r c . Range ;s rcDe f . Jammers . V e l o c i t i e s ( noJammers ) = c u r r e n t S r c . V e l oc i t y ;s r cDe f . Jammers . Bandwidths ( noJammers ) = c u r r e n t S r c . Bandwidth ;s r cDe f . Jammers . BWStarts ( noJammers ) = c u r r e n t S r c . BWStart ;

100

endend%i f ( ˜ i sempty ( c u r r e n t S r c ) )

end%f o r s r c I x

80

D.9. Function: getmod

105

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−%−−−− S e t t i n g up t h e c o r r e l a t i o n m a t r i c e s −−−−%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

110 i f i s f i e l d ( s rcDef , ’Targets’ ) % I f t h e r e was any t a r g e t s d e f i n e d .i f i sempty( t rgCorrMx )

t rgCorrMx = eye( n o T a r g e t s ) ;end %i fs r cDe f . T a r g e t s . CorrMx = trgCorrMx ;

115 end %i f

%End Of F i l e−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

D.9 Function: getmod

f u n c t i o n mod = getmod ( method , Fs , Tsweep , methodParam , Fc ,phaseF lag , permFlag )

%GETMOD Retu rns t h e c o e f f i e n t s f o r a s e l e c t e d modu la t ion , e . g . Ch i rp .5 %

%Synops i s :% mod = getmod ( method , Fs , Tsweep )% mod = getmod ( method , Fs , Tsweep , methodParam , Fc )% mod = getmod ( method , Fs , Tsweep , methodParam , Fc , phaseF lag )

10 % mod = getmod ( method , Fs , Tsweep , methodParam , Fc , phaseF lag , permFlag )%%D e s c r i p t i o n :% Re tu rns t h e ( complex ) c o e f f i e n t s f o r a s e l e c t e d modu la t ion , e . g . Ch i rp .% Th is modu la t i on w i l l be r e pe a t e d once f o r eve ry PRI ( p u l s e r e p e t i t i o n

15 % i n t e r v a l ) when used i n s i m u l a t i o n s .%%Output and I n p u t :% mod : The complex c o e f f i c i e n t s f o r t h e modu la t i on code .% method : Type of modu la t i on .

20 % = ’ r e c t ’ : R e c t a n g u l a r p u l s e . See below f o r d e s c r i p t i o n .% = ’ ch i rp ’ : Ch i rp ( l i n e a r FM) cod ing . See below f o r d e s c r i p t i o n .% = ’ f i x f r e q ’ : F ixed f r e q u e n c y complex wave% Fs : Sampl ing Frequency% Tsweep : Time d u r a t i o n o f a s i n g l e sweep

25 % methodParam : Parame te r f o r ’ f i x f r e q ’ and ’ ch i rp ’% Fc : C a r r i e r Frequency% phaseF lag : 1 i f a p h a s e s h i f t o f p i r a d i a n s o f t h e code% i s wanted . D e f a u l t s t o ze ro .% permFlag : 1 i f a f l i p a r o u n d of t h e code i s wanted .

30 % D e f a u l t s t o ze ro .%

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−%% Handle i n p u t p a r a me t e r s .

35 %−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−%

i f ( n a r g i n < 4)e r r o r (’DBT-Error: To few input parameters.’ )

end40

% ∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ Add miss ing i n p u t p a r a me t e r s ∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗

arg inNo = 6 ; i f ( n a r g i n < arg inNo )phaseF lag = [ ] ;

45 end arg inNo = arg inNo + 1 ; i f ( n a r g i n < arg inNo )permFlag = [ ] ;

end

50 % ∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ Pick ou t some f i e l d s from i n p u t p a r a me t e r s .∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗

% ∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ D e f a u l t v a l u e s∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗

i f i sempty( phaseF lag )

81


55 phaseF lag = 0 ;end%i fi f i sempty( permFlag )

permFlag = 0 ;end%i f

60

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−%% C a l c u l a t e t h e modu la t i on code .%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−%l e n = round( Fs∗Tsweep ) ;

65

%−−−−−−−−−−−−−−−−−−−−−−−− R e c t a n g u l a r Coding −−−−−−−−−−−−−−−−−−−−−−−−−−

i f s t r cmp( method ,’rect’ )phaseCode =exp( j ∗2∗ p i ∗Fc / Fs∗ ( 1 : l e n ) ) ;

70

%−−−−−−−−−−−−−−−−−−−−−−−−−−− Chi rp Coding −−−−−−−−−−−−−−−−−−−−−−−−−−−−

e l s e i f s t rcmp( method ,’chirp’ )fModMax = methodParam ;

75 phaseCode =exp( j ∗2∗ p i ∗ ( fModMax / Fs∗ ( ( 1 : l e n ) . ˆ 2 / l e n )+ Fc / Fs∗ ( 1 : l e n ) ) ) ;

%−−−−−−−−−−−−−−−−−−−−−−−−−−− Sine Coding −−−−−−−−−−−−−−−−−−−−−−−−−−−−

e l s e i f s t rcmp( method ,’fixfreq’ )80 f s i n e = methodParam ;

phaseCode =exp( j ∗2∗ p i ∗ ( ( f s i n e ) / Fs )∗ ( 1 : l e n ) ) ;

%−−−−−−−−−−−−−−−−−−−−−−−−−− The ELSE branch −−−−−−−−−−−−−−−−−−−−−−−−−−−

85 e l s ee r r o r (’HAR-Error: The desired modulation does not exist.’ )

end%i f

90 %−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−%% M o d i f i c a t i o n s o f t h e modu la t i on code .%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−%

i f phaseF lag = = 195 phaseCode =− phaseCode ;

end%i f

i f permFlag = = 1phaseCode =f l i p l r ( phaseCode ) ;

100 %phaseCode = phaseCode ( l e n g t h ( phaseCode ) :−1 : 1 ) ;end%i f

mod = phaseCode .’; % Transpose to make it a column vector.

105

% End Of File

D.10 Function: simnoise

f u n c t i o n n o i s e = s imno i se ( no i seSou rces , noRangeBins ) ;

%SIMNOISE i s t h e co re s i m u l a t i n g eng ine f o r s i m u l a t i n g n o i s e s o u r c e s .%

5 %Use :% n o i s e = s imno i se ( no i seSou rces , noRangeBins ) ;%%D e s c r i p t i o n :% S i m u l a t e s r a d a r s i g n a l s and s t o r e s t h e d a t a i n a ve c t o r

10 % The s i m u l a t o r assumes t h a t t h e n o i s e i s borne i n t h e an tenna channe ls ,% i n c o n t r a s t t o i n t h e an tenna e lemen ts or o u t s i d e o f t h e an tenna .% The n o i s e t h a t i s s i m u l a t e d i s a complex g a u s s i a n n o i s e wi th mean 0 and% v a r i a n c e eq u a l t o t h e wanted power .%

15 % Th is f u n c t i o n i s c a l l e d upon by t h e f u n c t i o n ” s i m r a d a r s i g ” and i s

82

D.11. Function: Jsimjammer

% norma l l y no t used by t h e end u s e r .%%I n p u t :% n o i s e S o u r c e s : C e l l a r r a y o f t h e n o i s e s o u r c e s t h a t w i l l be

20 % s i m u l a t e d .% noRangeBins : Number o f r a n g e b i n s i n s i m u l a t i o n .%%OutPut :% n o i s e : v e c t o r w i th t h e s i m u l a t e d d a t a .

25 %

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−%−−−− I n i t i a l i z e v a r i a b l e s . −−−−

30 %−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

n o i s e = 0 ;

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−35 %−−−− I n i t i a l i z e random g e n e r a t o r . −−−−

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

randn(’state’ , sum(100∗ c l ock ) ) ; %every t ime a d i f f e r e n t sequence of numbersrand(’state’ , sum(100∗ c l ock ) ) ;

40

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−%−−−− S imu la te n o i s e s i g n a l s . −−−−%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

45 f o r n o i s e I d x = 1 :l e n g t h( n o i s e S o u r c e s . Powers )%dev ide by 2 due t o complex n o i s e !

n o i s e = ( n o i s e + s q r t ( n o i s e S o u r c e s . Powers n o i s e I d x / 2 ) ∗ . . .( randn( noRangeBins , 1 ) + j∗ randn( noRangeBins , 1 ) ) ) .’;

% [Pss,fs,noAv] = PSDWelch (noise, 1024, 0.5, ’hamming ’ ) ;50 % f i g u r e , p l o t ( fs ,10∗ l og10 ( Pss ) ) , y l a b e l ( ’ Welch PSD i n [ dB ] ’ ) ,

% x l a b e l ( ’ Frequency ( no rma l i zed ) ’ ) ;% t x t = [ ’N: complex n o i s e P n o i s e = ’ , num2st r ( n o i s e S o u r c e s . Powers n o i s e I d x ) , ’ ;% P xx = ’ , num2st r ( mean ( Pss ) , ’%2.1 f ’ ) ] ; t i t l e ( t x t )

55 end

D.11 Function: Jsimjammer

f u n c t i o n JammerSig1D = Jsimjammer ( jammerPowers , jammerRanges ,j ammerVe loc i t i e s , . . .

jammerBandwidths , jammerBWStarts , noRangeBins , sampleTime )

5 %JSIMJAMMER i s t h e co re s i m u l a t i n g eng ine f o r s i m u l a t i n g jammer s o u r c e s .%%Use :% JammerSig1D = Jsimjammer ( jammerPowers , jammerRanges , j ammerVe loc i t i e s , . . .% jammerBandwidths , jammerBWStarts , noRangeBins , sampleTime )

10 %%D e s c r i p t i o n :% S i m u l a t e s r a d a r s i g n a l s and s t o r e s t h e d a t a i n a ve c t o r%% This f u n c t i o n i s c a l l e d upon by t h e f u n c t i o n ” s i m r a d a r s i g ” and i s

15 % norma l l y no t used by t h e end u s e r .%%I n p u t :% jammerPowers : Powers o f d i f f e r e n t jammer% jammerRanges : Ranges of t h e jammers

20 % j a m m e r V e l o c i t i e s : v e l o f t h e jammers% jammerBandwidths : BW of t h e jammers% jammerBWStarts : S t a r t f r e q u e n c y o f t h e jammer% noRangeBins : Number o f r a n g e b i n s i n s i m u l a t i o n .% sampleTime : Sample t ime used i n t h e s i m u l a t i o n

25 %%OutPut :% JammerSig1D : v e c t o r w i th t h e s i m u l a t e d d a t a .

83


%

30 %−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−%−−−− C o n s t a n t s used i n f u n c t i o n −−−−%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

noJammers =l e n g t h( jammerPowers ) ;35

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−%−−−− S imu la te t h e s i g n a l s . −−−−%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

40 i f ˜ i sempty( noJammers )f o r i = 1 : noJammers

% Make some b a n d l i m i t e d wh i te n o i s e% S e l e c t bandwid thF = [ jammerBandwidths ( i ) / 2 jammerBandwidths ( i ) / 2 + 0 . 1∗ jammerBandwidths ( i ) ]∗1 0 ˆ 6 ;

45 [ Nf ,Wn, be ta , t yp ] = k a i s e r o r d ( F , [ 1 0 ] , [ 0 . 0 1 0 . 1 ] , 1 / sampleTime ) ;b = f i r 1 ( Nf , Wn, typ , k a i s e r ( Nf +1 ,b e t a) ) ;

% F i l t e r , n o i s e dev ided by 2 because of complex n o i s e !n o i s e = s q r t ( jammerPowers ( i ) / 2 ) .∗ ( randn( 1 , noRangeBins )+ j∗ randn( 1 , noRangeBins ) ) ;

50

% [ Pss , fs , noAv ] = PSDWelch ( no ise ,1 0 2 4 , 0 . 5 , ’ hamming ’ , ’ s h i f t ’ ) ;% f i g u r e , s u b p l o t ( 2 1 1 ) , p l o t ( fs ,10∗ l og10 ( Pss ) ) , y l a b e l ( ’ Welch PSD i n [ dB ] ’ )% x l a b e l ( ’ Frequency ( no rma l i zed ) ’ ) ;% t x t = [ ’ J : complex no ise , P jammer = ’ , num2st r ( jammerPowers ( i ) ) , ’ ;

55 % P xx = ’ , num2st r ( mean ( Pss ) , ’%2.1 f ’ ) ] ; t i t l e ( t x t ) ,pFFT = s i z e( no ise , 2 ) ;B = f f t ( b , pFFT ) ;NOISE = f f t ( no ise , pFFT ) ;n t = i f f t (B.∗NOISE , pFFT ) ;

60 %c a l c u l a t i o n below i s more a c c u r a t e , bu t appr . 2 . 5 t im es s lower%n t = f i l t e r ( b , 1 , n o i s e ) ;

% [ Pss , fs , noAv ] = PSDWelch ( nt , 1 0 2 4 , 0 . 5 , ’ hamming ’ , ’ s h i f t ’ ) ;% s u b p l o t ( 2 2 3 ) , p l o t ( fs ,10∗ l og10 ( Pss ) ) , y l a b e l ( ’ Welch PSD i n [ dB ] ’ )

65 % x l a b e l ( ’ Frequency ( no rma l i zed ) ’ ) ;% t x t = [ ’ J : f i l t e r e d complex no ise , P jammer = ’ , num2st r ( jammerPowers ( i ) ) ] ;% t i t l e ( t x t )

% Mix t h e n o i s e t o t h e a p p r o p r i a t e f r e q u e n c y70 Fc = ( jammerBWStarts ( i ) + jammerBandwidths ( i ) / 2 )∗ 1 0 ˆ 6 ;

n ( i , : ) = n t .∗ exp( j ∗2∗ p i ∗Fc∗sampleTime∗ ( 1 : noRangeBins ) ) ;

% [ Pss , fs , noAv ] = PSDWelch ( n ,1 0 2 4 , 0 . 5 , ’ hamming ’ , ’ s h i f t ’ ) ;% s u b p l o t ( 2 2 4 ) , p l o t ( fs ,10∗ l og10 ( Pss ) ) , y l a b e l ( ’ Welch PSD i n [ dB ] ’ )

75 % x l a b e l ( ’ Frequency ( no rma l i zed ) ’ ) ;% t x t = [ ’ J : s h i f t e d f i l t e r e d complex no ise , P jammer = ’ , num2st r ( jammerPowers ( i ) ) ] ;% t i t l e ( t x t )

end

80 SumUp = ones ( 1 , noJammers ) ;JammerSig1D =z e r o s ( 1 , noRangeBins ) ;JammerSig1D = SumUp∗ n ;

%[ Pss , fs , noAv ] = PSDWelch ( r e a l ( JammerSig1D ) , f i x ( noRangeBins / 6 ) , 0 . 5 , ’ hamming ’ ) ;85 %p l o t ( fs ,10∗ l og10 ( Pss ) ) , y l a b e l ( ’ Welch PSD i n [ dB ] ’ ) , x l a b e l ( ’ Frequency i n [ Hz ] ’ ) ;

%t i t l e ( ’JAMMER’ ) , u i w a i te l s e

JammerSig1D = 0 ;end

D.12 Function: Jsimtarget

f u n c t i o n radarS ig1D = J s i m t a r g e t ( lambda , pulseMod , sampleTime , . . .t a r g e t P o w e r s , t a r g e t V e l , t a r g e t R a n g e s , t a r g e t S t a r t P h a s e s , noRangeBins )

%SIMTARGET i s t h e co re s i m u l a t i n g eng ine f o r s i m u l a t i n g narrowband r a d a r5 % s i g n a l s from t a r g e t s

84

D.12. Function: Jsimtarget

%%Synops i s :% radarS ig1D = J s i m t a r g e t ( lambda , pulseMod , sampleTime , t a r g e t P o w e r s , . . .% t a r g e t V e l , t a r g e t R a n g e s , t a r g e t S t a r t P h a s e s , noRangeBins )

10 %%D e s c r i p t i o n :% S i m u l a t e i n g t h e Number Of RangeBins , o r sample numbers% The range t o t h e t a r g e t i s t r a n s l a t e d i n t o a c o r r e sp o n d i n g range b in% wi th t h e f u n c t i o n ” Ran2SampleNo ” where a l l t a r g e t s t h a t a r e beyond t h e

15 % range d e s c r i b e d by t h e ” Ran2SampleNo ” w i l l be d i s r e g a r d e d . T a r g e t r a n g e s% a r e a l s o used t o d e t e r m i n e t h e s t a r t phase ofeach t a r g e t . These phases% a r e then a l t e r e d from p u l s e t o p u l s ea c c o r d i n g t o t h e t a r g e t ’ s v e l o c i t y%% This f u n c t i o n i s c a l l e d upon by ” J s i m r a d a r s i g ” and shou ld be

20 % h idden from t h e everyday u s e r .%%I n p u t :% lambda ( Rea lSca la rT ) : Wavelength [m] .% pulseMod ( CxVectorT ) : Pu l se modu la t i on we igh t s . see ” Jgetmod ” .

25 % sampleTime ( Rea lSca la rT ) : Time between range b i n s [ s ] .% t a r g e t P o w e r s ( CxVectorT ) : Power re c e i v e d from each t a r g e t s [W] .% t a r g e t V e l ( CxVectorT ) : R a d i a l v e l o c i t i e s t o r a d a r an tenna f o r% each t a r g e t [m/ s ] .% t a r g e t R a n g e s ( CxVectorT ) : D i s t a n c e between t a r g e t and r a d a r [m] .

30 % t a r g e t S t a r t P h a s e s : S t a r t phase of t h e r a d a r% noRangeBins ( I n t S c a l a r T ) : Number o f range b i n s .%%Output :% r a d a r S i g ( CxMatrixT ) : ve c t o r w i th s i m u l a t e d d a t a

35 %%−−−−−−−−%L i m i t a t i o n s :% 1 ) Only t a r g e t s o f t ype ” s w e r l i n g 0 ” ( c o n s t a n t ) i s implemented .%

40 % 2 ) T a r g e t s beyond t h e umambiguous range , i . e . i n a range b in beyond% ” noRangeBins ” a r e d i s r e g a r d e d%% 3 ) In a s i t u a t i o n wi th t a r g e t s i n some of t h e l a s t range b i n s and when% p u l s e modu la t i on i s chosen t h e p u l s e code shou ld s p i l l over t o t h e

45 % nex t p u l s e .%

%∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗50

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−%−−−− C o n s t a n t s used i n f u n c t i o n −−−−%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

55 n o T a r g e t s = l e n g t h( t a r g e t P o w e r s ) ;pulseMod = pulseMod .’;

%-------------------------------------------------------------------------%---- Simulate the signals. ----

60 %-------------------------------------------------------------------------

%- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -%--- Create empty preRadarSig variable. Each row corresponds to a ---%--- range bin. Each Column corresponds to a target. ---

65 %- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

preRadarSig = zeros(noRangeBins, noTargets);

% -- Convert Targetrange to corresponding RangeBin or SampleNo--70 TimeRange = noRangeBins*sampleTime;

SampleNo = Ran2SampleNo(targetRanges, sampleTime, TimeRange);noTargets = length(SampleNo);if ˜isempty(SampleNo)

75 %- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -%--- An index to a 2D matrix is a linear array columnwise. I.e. 2nd ---%--- column and 5th row is 1*noRows + 5 ---%- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

85


80 idxes2D = ((1:noTargets) - 1) * noRangeBins + SampleNo;

%- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -%--- We now have a signal where the rows represent range bins and the ---%--- columns represent targets ---

85 %- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

%- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -%--- Calculate velocity dependent phase shifts due to target motion ---%--- within a single pulse, i.e. different positions of the targets ---

90 %--- at each subpulse. One of the two’s a r e t h e r e because of t h a t −−−%−−− t h e wave t r a v e l l e s back and f o r t h . −−−%− − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − −

p h S h i f t s = ( ( ( ( 1 :l e n g t h( pulseMod ) )−1 ) ∗ 2∗ p i ∗ 2 ∗ sampleTime / . . .95 lambda ) .’ * targetVel).’ ;

% T e s t v a r i a b l e s :% noRangeBins = 2 0 ; t a r g e t P o w e r s = [ 4 1 ] ; t a r g e t S t a r t P h a s e s = [ 0 0 ] ;% idxes2D = [ 1 5 2 3 ] ; pulseMod = ones ( 1 , 6 ) ; p h S h i f t s = z e r o s ( 2 , 6 ) ;

100

p reRadarS ig =z e r o s( noRangeBins , n o T a r g e t s ) ;i f ˜ i sempty( pulseMod )

f o r i =1: l e n g t h( idxes2D )idx = idxes2D ( i ) ;

105 PowerT = s q r t ( t a r g e t P o w e r s ( i ) ) .∗ exp( j ∗ t a r g e t S t a r t P h a s e s ( i ) ) ;d a t a = PowerT∗ pulseMod .∗ exp( j ∗ p h S h i f t s ( i , : ) ) ;i f l e n g t h ( d a t a ) > noRangeBins−rem( idx , noRangeBins )

d a t a = d a t a ( 1 : noRangeBins−rem( idx , noRangeBins ) + 1 ) ;end

110 p reRadarS ig ( i dx : i dx +l e n g t h( d a t a )−1) = d a t a .’;end

end

%- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -115 %--- We now have a 2D-signal where the 1:st index represent rangebins ---

%--- and the 2:nd index represents the targets ---%- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

SumUp = ones(1,noTargets);120 radarSig1D = zeros(1,noRangeBins);

radarSig1D = (SumUp * (preRadarSig.’ ) ) ;% f i g u r e , p l o t ( r e a l ( radarS ig1D ) ) , u i w a i t% [ Pss , fs , noAv ] = PSDWelch ( ( r e a l ( radarS ig1D ) ) , f i x ( noRangeBins / 6 ) , 0 . 5 , ’ hamming ’ ) ;% p l o t ( fs ,10∗ l og10 ( Pss ) ) , y l a b e l ( ’ Welch PSD i n [ dB ] ’ ) , x l a b e l ( ’ Frequency i n [ Hz ] ’ ) ;

125 % t i t l e ( ’ Targe t ’ ) , u i w a i te l s e

radarS ig1D = 0 ;end

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−130 %− F i n a l l y we have a 3D−s i g n a l where t h e 1 s t index r e p r e s e n t p u l s e s and−−

%− t h e 2 nd index r e p r e s e n t s r a n g e b i n s and 3 rd index r e p r e s e n t t h e c h a n n e l s−%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

%End Of F i l e

D.13 Function: Jsimradarsig

f u n c t i o n r a d a r S i g S = J s i m r a d a r s i g ( recAnt , sou rces , waveform , B)

%SIMRADARSIG s i m ul a t e s r a d a r s i g n a l s from t a r g e t s , n o i s e and c l u t t e r .%

5 %Synops i s :% r a d a r S i g S = s i m r a d a r s i g ( recAnt , sou rces , waveform , B)%%D e s c r i p t i o n :% S i m u l a t e s r a d a r s i g n a l s and s t o r e s t h e d a t a i n a 3D m a t r i x

10 % ( Number P u l s e s x Number Of RangeBins x Number Of Channe ls )% R a d a r s i g n a l s i m u l a t i o n i s dev ided i n t o ( so f a r ) t h r e e d i f f e r e n t p a r t s ,

86

D.13. Function: Jsimradarsig

% n o i s e s i m u l a t i o n , t a r g e t s i m ul a t i o n and c l u t t e r s i m u l a t i o n . The t a s k s% t o s i m u l a t e d t h e s e c o n t r i b u t i o n s a r e per fo rmed i n s e p a r a t e f u n c t i o n s% such as ” s imno i se .m” , ” s i m t a r g e t .m” and ” s i m c l u t t e r .m” . These f u n c t i o n s

15 % a r e c a l l e d one t ime f o r each c o h e r e n t p u l s e i n t e r v a l ( CPI ) . A l t e r na t i o n% of wave leng ths between c p i : s a r e suppor ted , see f u nc t i o n ” defwave .m”% f o r more i n f o r m a t i o n . The s i m u l a t e d d a t a i s then a r r a n g e d i n a% s t r u c t u r e v a r i a b l e o f t h e t ype ” RxRadarSigT ” . A l l t a r g e t s a r e seen as% s t a t i o n a r y i n t h a t r e s p e c t t h a t t hey does no t move from r a n g e b i n t o

20 % r a n g e b i n nor move i n d i r e c t i o n between CPIs . The v e l o c i t y o f t h e% t a r g e t s a r e used t o d e t e r m i n e t h e p h a s e s h i f t s between p u l s e s and% s u b p u l s e s ( r a n g e b i n s ) .%% For t h e n o i s e s i m u l a t i o n , t h e an tenna d e f i ni t i o n ” recAnt ” i s no t used .

25 % See he lp t e x t o f f u n c t i o n ” s imno i se ” f o r more i n f o r m a t i o n on t h e n o i s e% s i m u l a t i o n .%%I n p u t :% recAnt : D e f i n i t i o n o f t h e r e c e i v i n g an tenna .

30 % s o u r c e s : S t r u c t u r e v a r i a b l e w i th t h e s i g n a l s o u r c e s to be s imu la ted ,% i . e . t a r g e t s , n o i s e or c l u t t e r ( so f a r ) .% waveform : Waveform of t h e t r a n s m i t t e d r a d a r s i g n a l .% B : f i l t e r which has t o be a p p l i e d a t t h e o u t p u t ( o p t i o n a l )%

35 %%OutPut :% r a d a r S i g S : S t r u c t w i th t h e s i m u l a t e d r a d a r s i g n a l .%%−−−−−−−−

40 f i l t e r e n d = 1 ;i f ( n a r g i n < 3)

e r r o r (’HAR-Error: To few input parameters.’ )e l s e i f n a r g i n = = 3

f i l t e r e n d = 0 ;45 e l s e i f n a r g i n > 4

e r r o r (’HAR-Error: To many input parameters.’ )end

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−50 %−−−− Handle d e f a u l t s −−−−

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

g l o b a l c0

55 propSpeed = c0 ;%s p e e d o f l i g h t

%f o c u s D i s t = I n f ; Always f o r c a l c u l a t i o n s t e e r i n g m a t r i x ! ! !

p u l I x = [ ] ;60

r a n I x = [ ] ;

spa I x = [ ] ;

65 %−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−%−−−− Pick ou t f i e l d s from i n p u t p a r a me t e r s . −−−−%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

wave leng th = waveform . wave leng th ;70 noRangeBins = waveform . noRangeBins ;

% noPu l ses = waveform . noPu l ses ;pMod = waveform . pModu la t ion ;sampleTime = waveform . sampleTime ;

75 p r i = sampleTime ∗ noRangeBins ;%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−%−−−− S imu la te r a d a r s i g n a l . −−−−%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

80 r a d a r S i g = z e r o s( 1 , noRangeBins ) ;

lambda = wave leng th ;

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

87


85 %−−−− S i m u l a t i o n o f T a r g e t s −−−−%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

i f i s f i e l d ( sou rces ,’Targets’ )t i c

90 t a r g e t P o w e r s = s o u r c e s . T a r g e t s . Powers ;t a r g e t S p e e d s = s o u r c e s . T a r g e t s . V e l o c i t i e s ;t a r g e t R a n g e s = s o u r c e s . T a r g e t s . Ranges ;t a r g e t S t a r t P h a s e s =rem( t a r g e t R a n g e s , lambda ) / lambda∗2∗ p i ;

95 f p r i n t f (’\nsimradarsig: Simulating targets... ’ ) ;r a d a r S i g T a r g = J s i m t a r g e t ( lambda , pMod , sampleTime , t a r g e t P o w e r s , . . .

t a r g e t S p e e d s , t a r g e t R a n g e s , t a r g e t S t a r t P h a s e s , noRangeBins ) ;T imeI tTook=t o c ; f p r i n t f (’done in %1.2f sec’ , T imeI tTook )

e l s e100 r a d a r S i g T a r g = 0 ;

end

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−105 %−−−− S i m u l a t i o n o f Noise −−−−

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

i f i s f i e l d ( sou rces ,’Noise’ )t i c , f p r i n t f (’\nsimradarsig: Simulating noise... ’ ) ;

110 r a d a r S i g N o i s e = J s i m n o i s e ( s o u r c e s . Noise , noRangeBins ) ;T imeI tTook=t o c ; f p r i n t f (’done in %1.2f sec’ , T imeI tTook )

e l s er a d a r S i g N o i s e = 0 ;

end %i f115

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−%−−−− S i m u l a t i o n o f C l u t t e r −−−−%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

120

i f i s f i e l d ( sou rces ,’Clutters’ )t i cd b t i n f o (’simradarsig: Simulating clutter...’ , 1 ) ;i f s t r cmp( s o u r c e s . C l u t t e r . TransAnt ,’recAnt’ )

125 s o u r c e s . C l u t t e r . TransAnt = recAnt ;end%i fp l a t H e i g h t = s o u r c e s . C l u t t e r . P l a t H e i g h t ;p l a t V e l = s o u r c e s . C l u t t e r . Pl a t V e l o c i t y ;

130 spec = p a n t p a t 3 ( s o u r c e s . C l u t t e r . TransAnt , [ ] , [ ] , [ ] , [ ] , [ ] , [ ] , . . .s o u r c e s . C l u t t e r . DOAs , lambda , [ ] , [ ] , [ ] , [ ] , [ ] , . . .’noplot’ ) ; % n o p l o t Main D i re c t i o n o f T r a n s m i t t i n g an tenna i s :

% t h e t a = 0 ;

135 t r a n s m i t G a i n = spec . specSmpl ;

s t e e r i n g M a t r i x C l u t t e r = s p a s t e m a t ( recAnt , s o u r c e s . C l u t t e r . DOAs, lambda , . . .f o c u s D i s t , s u b A r r P o i n t ) ;%Rece i v i ng an tenna

140 r a d a r S i g C l u t t e r = s i m c l u t t e r ( s o u r c e s . C l ut t e r , t r a n s m i t G a i n , . . .s t e e r i n g M a t r i x C l u t t e r , lambda , . . .sampleTime , noPu lses , noRangeBins , . . .propSpeed , p r i , p l a t H e i g h t , p l a t V e l ) ;

t ime I tTook = t o c ;145 i n f o S t r = s p r i n t f (’ done (%2.1f secs).’ , t ime I tTook ) ;

d b t i n f o ( i n f o S t r , [ ] , 1 ) ;e l s e

% d b t i n f o ( ’ s i m r a d a r s i g : No c l u t t e r p r e s e n t ’ ) ;r a d a r S i g C l u t t e r = 0 ;

150 end %i f

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−%−−−− S i m u l a t i o n o f Jammers −−−−%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

155

i f i s f i e l d ( sou rces ,’Jammers’ )t i c , f p r i n t f (’\nsimradarsig: Simulating jammers... ’ ) ;

88

D.14. Function: RxRadarSigT

jammerPowers = s o u r c e s . Jammers . Powers ;jammerRanges = s o u r c e s . Jammers . Ranges ;

160 j a m m e r V e l o c i t i e s = s o u r c e s . Jammers . V e l o c i t i e s ;jammerBandwidths = s o u r c e s . Jammers . Bandwidths ;jammerBWStarts = s o u r c e s . Jammers . BWStarts ;radarS igJammer = Jsimjammer ( jammerPowers , jammerRanges , j ammerVe loc i t i e s , . . .

jammerBandwidths , jammerBWStarts , noRangeBins , sampleTime ) ;165 TimeI tTook=t o c ; f p r i n t f (’done in %1.2f sec\n’ , T imeI tTook )

e l s eradarS igJammer = 0 ;

end

170 %−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−%−−−− Combine a l l s i m u l a t e d s i g n a l s i n t o a comple te r a d a r s i g n a l .−−−−%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% [ Pss , fs , noAv ] = PSDWelch ( r ad a r S ig No i se ,1 0 2 4 , 0 . 5 , ’ hamming ’ ) ;175 % f i g u r e , p l o t ( fs ,10∗ l og10 ( Pss ) ) , y l a b e l ( ’ Welch PSD i n [ dB ] ’ )

% x l a b e l ( ’ Frequency ( no rma l i zed ) ’ ) ;% t x t = [ ’R : n o i s e b e f o r e r a d a r S i g , Pxx = ’ , num2st r ( mean ( Pss ) , ’%2.1 f ’ ) ] ;% t i t l e ( t x t )

180

r a d a r S i g = r a d a r S i g T a r g + r a d a r S i g N o i s e + r a d a r S i g C l u t t e r + radarS igJammer ;

% [ Pss , fs , noAv ] = PSDWelch ( r a d a r S i g , 1 0 2 4 , 0 . 5 , ’ hamming ’ ) ;% f i g u r e , p l o t ( fs ,10∗ l og10 ( Pss ) ) , y l a b e l ( ’ Welch PSD i n [ dB ] ’ )

185 % x l a b e l ( ’ Frequency ( no rma l i zed ) ’ ) ;% t x t = [ ’R : n o i s e and jammer ’ ] ; t i t l e ( t x t )

i f f i l t e r e n d = = 1pFFT = max( [ s i z e( r a d a r S i g , 2 ) ,s i z e(B , 2 ) ] ) ;BF = f f t (B , pFFT ) ;

190 RADARSIG = f f t ( r a d a r S i g , pFFT ) ;r a d a r S i g = i f f t (BF .∗RADARSIG, pFFT ) ;%r a d a r S i g = f i l t e r (B, 1 , r a d a r S i g ) ;

end%

195 % [ Pss , fs , noAv ] = PSDWelch ( r a d a r S i g , 1 0 2 4 , 0 . 5 , ’ hamming ’ , ’ s h i f t ’ ) ;% f i g u r e , p l o t ( fs ,10∗ l og10 ( Pss ) ) , y l a b e l ( ’ Welch PSD i n [ dB ] ’ )% x l a b e l ( ’ Frequency ( no rma l i zed ) ’ ) ;% t x t = [ ’R : f i l t e r e d n o i s e and jammer ’ ] ; t i t l e ( t x t )%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

200 %−−−− Complete t h e s t r u c t & d e l i v e r t h e r e s u l t . −−−−%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

r a d a r S i g S = RxRadarSigT ( r a d a r S i g , recAnt , waveform ) ;% S t o r e a l s o ” p u l I x ” , ” r a n I x ” , ” sp a I x ” ? !

205 %End Of F i l e−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

D.14 Function: RxRadarSigT

f u n c t i o n s igOu t = RxRadarSigT ( s i g n a l s , model , param , pu l I x , ran Ix ,spaIx , e x t r a I x , cp i I x , t r i a l I x , pu lT rans , ranTrans , spaTrans ,f reqPos , rangePos , doaPos , spaPu lT rans , spaRanTrans , pulRanTrans ,a l l T r a n s )

5

%RXRADARSIGT C o n s t r u c t o r f o r r a d a r s i g n a l s .%%−−−−−−−−%Synops i s :

10 % s igOu t = RxRadarSigT% s igOu t = RxRadarSigT ( s i g n a l s , antenna , waveform , propSpeed ,% pu l I x , ran Ix , spaIx , e x t r a I x , cp i I x , t r i a l I x , pu lT rans , ranTrans , spaTrans ,% f reqPos , rangePos , doaPos )%

15 %D e s c r i p t i o n :% C o n s t r u c t o r f o r r a d a r s i g n a l s , i . e . t h e d a t a t ype ” RxRadarSigT ” .% More i n f o r m a t i o n on t h i s d a t a t ype and t h e i n p u t p a r a me t e r s o f t h i s% f u n c t i o n can be found i n [ 1 ] ( t ype t h e command ” d b t r e f g u i d e ” ) .%

89


20 %Output and I n p u t :% s igOu t ( RxRadarSigT ) : The o u t p u t r a d a r s i g n a l .%% s i g n a l s ( CxMul t iMatr ixT ) : The complex r a d a r s i g n a l v a l u e s i n a% m u l t i d i m e n s i o n a l m a t r i x w i th t h e i n d i c e s ( p u l s e I x , t i m e I n P u l s e I x ,

25 % channe l I x , e x t r a I x , cp i I x , t r i a l I x ) . A l l i n d i c e s e x c e p t f o r p u l s e I x% a r e o p t i o n a l .% an tenna ( AntDefT ) : The an tenna d e f i n i t i o n t o use i n s u b s e q u e n t s i g n a l% p r o c e s s i n g o f t h i s r a d a r s i g n a l .% waveform ( WaveformT ) : The t ime p r o p e r t i e s ( WaveformT ) o f t h e r a d a r s i g n a l

30 % t o use i n s u b s e q u e n t s i g n a l p r o c e s s i n g .% propSpeed [ D] ( R e a l S c a l a r T ) : P r o p a g a t i o n speed of t h e r a d a r wave [m/ s ] .% D e f a u l t i s ? . Th is i n p u t p a r a me t e r i s no t used . What i s t h e purpose% wi th i t ?% p u l I x [ D] ( IndexT ) : P r e s e n t p u l s e or d o p p l e r channe l numbers i n t h e s i g n a l .

35 % r a n I x [ D] ( IndexT ) : P r e s e n t range b i n s ( numbers ) i n t h e s i g n a l .% sp a I x [ D] ( IndexT ) : P r e s e n t s p a t i a l c h a n n e l s i n t h e s i g n a l .% e x t r a I x [ D] ( IndexT ) : P r e s e n t e x t r a i n d i c e s i n t h e s i g n a l .% c p i I x [ D] ( IndexT ) : P r e s e n t CPIs i n t h e s i g n a l .% t r i a l I x [ D] ( IndexT ) : P r e s e n t t r i a l s i n t h e s i g n a l .

40 % p u lT r an s [ D] ( CxMatrixT ) : T r a n s f o r ma t i o n m a t r i x used f o r d o p p l e r o r% f r e q u e n c y f i l t e r i n g , i . e . f i l t e r i n g i n t h e t ime d imens ion .% r an T r an s [ D] ( CxMatrixT ) : T r a n s f o r ma t i o n m a t r i x used f o r p u l s e compress ion ,% i . e . f i l t e r i n g i n t h e range d imens ion .% spaTrans [ D] ( CxMatrixT ) : T r a n s f o r ma t i o n m a t r i x used f o r beamforming , i . e .

45 % f i l t e r i n g i n t h e s p a t i a l d imens ion .% f r e q P o s [ D] ( Rea lVectorT ) : Frequency i n Her tz f o r t h e d i f f e r e n td o p p l e r% or f r e q u e n c y c h a n n e l s .% rangePos [ D] ( Rea lVectorT ) : Range i n meter f o r t h e d i f f e r e n t range b i n s .% doaPos [ D] ( Rea lVectorT ) : Beam p o s i t i o n s i n r a d i a n s f o r t h e d i f f e r e n t beams .

50 %%−−−−−−−−%N o t a t i o n s :% Data t ype names a r e shown i n p a r e n t h e s e s and they s t a r t w i th a c a p i t a l% l e t t e r and end wi th a c a p i t a l T . Data t ype d e f i n i t i o n s can be found i n [ 1 ]

55 % or by ” he lp d b t d a t a ” .% [D ] = Th is p a r a m e t e r can be o m i t t e d and then a d e f a u l t v a l u e i s used .% When t h e [ D]− i n p u t p a r a me t e r i s no t t h e l a s t used i n t h ec a l l , i t must be% g iven t h e v a l u e [ ] , i . e . an empty m a t r i x .% . . . = There can be more p a r a m e t e r s . They a r e e x p l a i n e dunder r e s p ec t i v e

60 % metod or c h o i c e .%

% The s t r u c t u r e o f t h i s f u n c t i o n i s p r e p a r e d f o r u s i n g MATLAB’ sc l a s s e s .65 g l o b a l c0

i f ( n a r g i n = = 0 )s igOu t = b a s e d e f ;

e l s e i f i s a ( s i g n a l s ,’RxRadarSigT’ )70 s igOu t = s i g n a l s ;

e l s ei f ( n a r g i n < 2)

e r r o r (’DBT-Error: To few input parameters.’ )end

75

% ∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ Add miss ing i n p u t p a r a me t e r s ∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗

arg inNo =3;i f ( n a r g i n < arg inNo )

80 param = [ ] ;endarg inNo = arg inNo + 1 ;

i f ( n a r g i n < arg inNo )85 p u l I x = [ ] ;

endarg inNo = arg inNo + 1 ;i f ( n a r g i n < arg inNo )

r a n I x = [ ] ;90 end

arg inNo = arg inNo + 1 ;i f ( n a r g i n < arg inNo )

90

D.14. Function: RxRadarSigT

spa I x = [ ] ;end

95 arg inNo = arg inNo + 1 ;i f ( n a r g i n < arg inNo )

e x t r a I x = [ ] ;endarg inNo = arg inNo + 1 ;

100 i f ( n a r g i n < arg inNo )c p i I x = [ ] ;


105 t r i a l I x = [ ] ;endarg inNo = arg inNo + 1 ;

i f ( n a r g i n < arg inNo )110 p u l T r a n s = [ ] ;


r a n T r a n s = [ ] ;115 end

arg inNo = arg inNo + 1 ;i f ( n a r g i n < arg inNo )

spaTrans = [ ] ;end

120 arg inNo = arg inNo + 1 ;

i f ( n a r g i n < arg inNo )f r e q P o s = [ ] ;

end125 arg inNo = arg inNo + 1 ;

i f ( n a r g i n < arg inNo )rangePos = [ ] ;

endarg inNo = arg inNo + 1 ;

130 i f ( n a r g i n < arg inNo )doaPos = [ ] ;

endarg inNo = arg inNo + 1 ;

135

% ∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ D e f a u l t v a l u e s∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗

i f i sempty( param )140 param = c0 ;

end%i fi f i sempty( p u l I x )

p u l I x = 1 : s i z e( s i g n a l s , 1 ) ;end%i f

145 i f i sempty( r a n I x )r a n I x = 1 : s i z e( s i g n a l s , 2 ) ;

end%i fi f i sempty( sp a I x )

spa I x = 1 :s i z e( s i g n a l s , 3 ) ;150 end%i f

i f i sempty( e x t r a I x )e x t r a I x = 1 :s i z e( s i g n a l s , 4 ) ;

end%i fi f i sempty( c p i I x )

155 c p i I x = 1 : s i z e( s i g n a l s , 5 ) ;end%i fi f i sempty( t r i a l I x )

t r i a l I x = 1 : s i z e( s i g n a l s , 6 ) ;end%i f

160

% ∗∗∗∗∗∗∗∗∗∗∗∗∗ Pick ou t some more f i e l d s from i n p u t p a r a me t e r s .∗∗∗∗∗∗∗∗∗∗∗∗∗

an tenna = model1 ;165 waveform = model2 ;

91


%propSpeed = param1 ;

% ∗∗∗∗∗∗∗∗∗∗∗∗∗ Base d e f i n i t i o n .∗∗∗∗∗∗∗∗∗∗∗∗∗170

s igOu t = b a s e d e f ;

% ∗∗∗∗∗∗∗∗∗∗∗∗∗ Ass ign v a l u e s .∗∗∗∗∗∗∗∗∗∗∗∗∗175

s igOu t . s i g n a l s = s i g n a l s ;s i gOu t . an tenna = an tenna ;s igOu t . waveform = waveform ;s igOu t . p u l I x = p u l I x ;

180 s igOu t . r a n I x = r a n I x ;s i gOu t . sp a I x = sp a I x ;s i gOu t . e x t r a I x = e x t r a I x ;s i gOu t . c p i I x = c p i I x ;s i gOu t . t r i a l I x = t r i a l I x ;

185

s igOu t . t r a n s . p u l T r a n s = p u l T r a n s ;s igOu t . t r a n s . r an T r an s = r an T r an s ;s igOu t . t r a n s . spaTrans = spaTrans ;

190 s igOu t . f r e q P o s = f r e q P o s ;s igOu t . rangePos = rangePos ;s igOu t . doaPos = doaPos ;

end%i f%e n d f u n c t i o n RxRadarSigT

195

f u n c t i o n s igOu t = b a s e d e f200 s igOu t . da taType =’RxRadarSigT’ ;

s i gOu t .v e r s i o n = 2 ;% The v e r s i o n number must be changed a f t e r i m p o r t a n t changes of t h i s% d a t a type , changes r e q u i r i n g changes of t h e f u n c t i o n s which a r e% u s in g t h i s d a t a t ype .

205 s igOu t . s i g n a l s = [ ] ;s i gOu t . an tenna = [ ] ;s i gOu t . waveform = [ ] ;s i gOu t . p u l I x = [ ] ;s i gOu t . r a n I x = [ ] ;

210 s igOu t . sp a I x = [ ] ;s i gOu t . e x t r a I x = [ ] ;s i gOu t . c p i I x = [ ] ;s i gOu t . t r i a l I x = [ ] ;

215 s igOu t . t r a n s . p u lT r an s = [ ] ;s i gOu t . t r a n s . r an T r an s = [ ] ;s i gOu t . t r a n s . spaTrans = [ ] ;

s i gOu t . f r e q P o s = [ ] ;220 s igOu t . rangePos = [ ] ;

s i gOu t . doaPos = [ ] ;

%p a r e n t = SigT ( . . . )%s igOu t = c l a s s ( s igOut , ’ RxRadarSigT ’ , p a r e n t ) ;

225 % I n h e r i t a n c e from c l a s s ” SigT ” .%e n d f u n c t i o n b a s e d e f

D.15 Function: Ran2SampleNo

f u n c t i o n [ SampleNo , ranBinLen ] = Ran2SampleNo ( t a r g e t R a n g e s ,sampleTime , TimeRange )

%RAN2RANBIN : Conve r t s r a n g e s t o r a n g e b i n s & ca l c u l a t e s l e n g t h o f a r a n g e b i n5 %

%Synops i s :

92

D.16. Function: uisaveSignalSimulation

% [ SampleNo , ranBinLen ] = Ran2SampleNo ( t a r g e t R a n g e s , sampleTime , TimeRange )%%D e s c r i p t i o n :

10 % Conver t s r a n g e s ( i n meter ) t o a p p r o p ri a t e r a n g e b i n a c c o r d i n g t o% p r o p a g a t i o n speed o f l i g h t i n c u r r e n t medium and sample t ime .% I f t h e r e s u l t exceeds t h e maximum noRangeBins i t t hen s t a r t s over% a t r a n g e b i n # 1 ag a i n . I f t h e max no of r a n g e b i n s i s o m i t t e d then% t h e r e i s no wrap back t o r a n g e b i n # 1 . The f u n c t i o n a l s oc a l c u l a t e s

15 % t h e range r e s o l u t i o n , i . e . t h e l e n g t h ( i n me te rs ) o feach r a n g e b i n .%%I n p u t :% r a n g e s : D i s t a n c e between t a r g e t and r a d a r [m] .% noRanBins : Maximum number o f r a n g e b i n s .

20 % sampleTime : Time between r a n g e b i n s [ s ] .% propSpeed : P r o p a g a t i o n speed of t h e beam [m/ s ] .%%Output :% ranB ins : The r a n g e b i n s c o r r e s p o n d i n g t o i n p u t r a n g e s .

25 % ranBinLen : Length o f t h e c a l c u l a t e d range b i n s [m] .

i f ( n a r g i n < 3)30 e r r o r (’Not enough input arguments in Ran2SampleNo’ )

end%i f

g l o b a l c0

35 ranBinLen = sampleTime∗ c0 / 2 ;

unModRange = c e i l ( t a r g e t R a n g e s / ranBinLen ) ;

i f sum( f i n d ( unModRange> TimeRange∗1/ sampleTime ) )> 040 f p r i n t f (’\nTargat at range %1.0f [m] was ambiguous. Proceeding...\n’ , . . .

t a r g e t R a n g e s (f i n d ( unModRange> TimeRange∗1/ sampleTime ) ) ) ;

end SampleNo = unModRange (f i n d ( unModRange<=TimeRange∗1/ sampleTime ) ) ; i f i sempty( SampleNo ) ,

45 f p r i n t f (’\nWARNING: all ranges were ambiguous\n’ ) , end% ranB ins = mod( unModRange , noRanBins ) ;% ranB ins ( f i n d ( ranB ins = = 0 ) ) = noRanBins ;%End Of F i l e

D.16 Function: uisaveSignalSimulation

f u n c t i o n u i s a v e S i g n a l S i m u l a t i o n ( v a r i a b l e s )%UISAVE GUI He lper f u nc t i o n f o r SAVE%% See a l s o u isave , u i p u t f i l e

5

% Copy r i gh t 1984−2002 The MathWorks , Inc .% $Rev i s i on : 1 . 1 3 $ $by JAH Harmsen$

i f n a r g i n = = 010 % whooutput = e va l i n ( ’ c a l l e r ’ , ’ who ’ , ’ ’ ) ;

% i f i sempty ( whooutput )% e r r o r d l g ( ’No v a r i a b l e s t o save ’ )% r e t u r n ;% end

15 % v a r i a b l e s = whooutput ; % f o r no in p u t save a l l v a r i a b l e s i n workspacee r r o r d l g (’No input variables given’ )r e t u r n;

end

20 i f ˜ i s c e l l s t r ( v a r i a b l e s ) & ˜ i s c h a r ( whooutput )e r r o r (’VARIABLES argument must be a string or cell array of strings’ ) ;

end

i f i s c e l l ( v a r i a b l e s )25 v a r i a b l e s = s p r i n t f (’’’%s’’,’ , v a r i a b l e s : ) ;

93


v a r i a b l e s = v a r i a b l e s ( 1 :end − 1 ) ;end

seed = ’*.mat’ ,’MAT-files (*.mat)’ ; ’*.*’ ,’All Files (*.*)’ ;30 f i l e = ’Untitled.mat’ ; [ fn , pn , f i l t e r i n d e x ] = u i p u t f i l e ( seed , ’Save

Workspace Variables for Signal Simulation’ , f i l e ) ;

i f ˜ a l l ( pn = = 0 ) & ˜ a l l ( fn = = 0 )t r y

35 fn = s t r r e p( f u l l f i l e ( pn , fn ) , ’’’’ , ’’’’’’ ) ;sz = s i z e( seed ) ;i f ( f i l t e r i n d e x <= sz ( 1 ) & f i n d s t r ( seed f i l t e r i n d e x , ’.mat’ ) )

e v a l i n (’caller’ , [ ’save(’’’ fn ’’’, ’ v a r i a b l e s ’);’ ] , ’error(lasterr)’ ) ;e l s e i f ( f i l t e r i n d e x <= sz ( 1 ) & f i n d s t r ( seed f i l t e r i n d e x , ’.txt’ ) )

40 e v a l i n (’caller’ , [ ’save(’’’ fn ’’’, ’ v a r i a b l e s ’, ’’-ASCII’’);’ ] , ’error(lasterr)’ ) ;e l s e

e v a l i n (’caller’ , [ ’save(’’’ fn ’’’, ’ v a r i a b l e s ’);’ ] , ’error(lasterr)’ ) ;end

c a t c h45 e r r o r d l g ( l a s t e r r)

endend

D.17 Function: UISignalSimulation export

f u n c t i o n v a r a r g o u t = U I S i g n a l S i m u l a t i o ne x p o r t ( v a r a r g i n )% UISIGNALSIMULATION EXPORT M− f i l e f o r U I S i g n a l S i m u l a t i o n e x p o r t . f i g% UISIGNALSIMULATION EXPORT , by i t s e l f , c re a t e s a new UISIGNALSIMULATION EXPORT% or r a i s e s t h e e x i s t i n g s i n g l e t o n∗ .

5 %% H = UISIGNALSIMULATION EXPORT r e t u r n s t h e hand le t o a new% UISIGNALSIMULATION EXPORT or t h e hand le t o t h e e x i s t i n g s i n g l e t o n∗ .%% UISIGNALSIMULATION EXPORT( ’CALLBACK’ , hObject , even tData , hand les , . . . ) c a l l s t h e

10 % l o c a l f u n c t i o n named CALLBACK i n UISIGNALSIMULATION EXPORT .M wi th t h e g iven in p u t% arguments .%% UISIGNALSIMULATION EXPORT( ’ P rope r t y ’ , ’ Value ’ , . . . ) c re a t e s a new% UISIGNALSIMULATION EXPORT or r a i s e s t h e e x i s t i n g s i n g l e t o n∗ . S t a r t i n g from t h e

15 % l e f t , p r o p e r t y v a l u e p a i r s a r e a p p l i e d t o t h e GUI b e f o r e% U I S i g n a l S i m u l a t i o n e x p o r t O p e n i n g F u n c t i o n g e t s c a l l e d . An u n r e c o g ni z e d p r o p e r t y% name or i n v a l i d v a l u e makes p r o p e r t y a p p l i c a t i o n s t o p . A l l i n p u t s a r e passed t o% U I S i g n a l S i m u l a t i o n e x p o r t O p e n i n g F c n v i a v a r a r g i n .%

20 % ∗See GUI Opt ions on GUIDE’ s Too ls menu . Choose ” GUIa l l o w s on ly one% i n s t a n c e t o run ( s i n g l e t o n ) ” .%% See a l s o : GUIDE , GUIDATA , GUIHANDLES

25 % E d i t t h e above t e x t t o modi fy t h e r e sp o n s e t o he lp U I S i g n a l S i m ul a t i o n e x p o r t

% Las t Mod i f ied by GUIDE v2 .5 01−Aug−2003 14:46:35

% Begin i n i t i a l i z a t i o n code− DO NOT EDIT30 g u i S i n g l e t o n = 1 ; g u i S t a t e = s t r u c t (’gui_Name’ , mf i lename ,

. . .’gui_Singleton’ , g u i S i n g l e t o n , . . .’gui_OpeningFcn’ , @UIS igna lS imu la t i onexpor t Open ingFcn , . . .’gui_OutputFcn’ , @UIS igna lS imu la t i onexpo r t Ou tpu tFcn , . . .

35 ’gui_LayoutFcn’ , @UIS igna lS imu la t i onexpo r t Layou tFcn , . . .’gui_Callback’ , [ ] ) ;

i f n a r g i n & i s s t r ( v a r a r g i n1 )g u i S t a t e . g u i C a l l b a c k = s t r 2 f u n c ( v a r a r g i n1 ) ;

end40

i f n a r g o u t[ v a r a r g o u t1: n a r g o u t ] = g u i m a i n f c n ( g u i S t a t e , v a r a r g i n : ) ;

e l s eg u i m a i n f c n ( g u i S t a t e , v a r a r g i n : ) ;

45 end

94

D.17. Function: UISignalSimulationexport

% End i n i t i a l i z a t i o n code− DO NOT EDIT

%−−− Execu tes j u s t b e f o r e U I S i g n a l S i m u l a t i o ne x p o r t i s made v i s i b l e .f u n c t i o n U I S i g n a l S i m u l a t i o n e x p o r t O p e n i n g F c n ( hObject , e v e n t d a t a ,

50 hand les , v a r a r g i n )% Th is f u n c t i o n has no o u t p u t a rgs , see OutputFcn .% hOb jec t hand le t o f i g u r e% e v e n t d a t a r e s e r v e d− t o be d e f i n e d i n a f u t u r e v e r s i o n o f MATLAB% h a n d l e s s t r u c t u r e w i th h a n d l e s and u s e r d a t a ( see GUIDATA)

55 % v a r a r g i n command l i n e arguments t o U I S i g n a l S i m u l a t i o ne x p o r t ( see VARARGIN)

% Choose d e f a u l t command l i n e o u t p u t f o r U I S i g n a l S i m ul a t i o n e x p o r th a n d l e s . o u t p u t = hOb jec t ;

60 % Update h a n d l e s s t r u c t u r eg u i d a t a ( hObject , h a n d l e s ) ;

% Th is s e t s up t h e i n i t i a l p l o t− on ly do when we a r e i n v i s i b l e% so window can g e t r a i s e d u s in g U I S i g n a l S i m ul a t i o n e x p o r t .

65 i n i t i a l i z e g u i ( hObject , h a n d l e s ) ;

% UIWAIT makes U I S i g n a l S i m u l a t i o ne x p o r t wa i t f o r u s e r r e sp o n s e ( see UIRESUME)% u i w a i t ( h a n d l e s . f i g u r e 1 ) ;

70

% −− I n i t i a l i z a t i o n f u n c t i o n .f u n c t i o n i n i t i a l i z e g u i ( f i g h a n d l e , h a n d l e s )

%f p r i n t f ( 1 , ’ I n i t i a l i z e f u n c t i o n works !\n ’ )d a t a .v e r s i o n = 0 . 1 ; d a t a . P t a r g e t 1 = 0 ;

75 d a t a . D t a r g e t 1 = 0 ; d a t a . P t a r g e t 2 = 0 ;d a t a . D t a r g e t 2 = 0 ; d a t a . SimTime = 300 e−6;d a t a . pmod =’rect’ ; d a t a . f s i n e = 0 ;d a t a . c a r r i e r F r e q = 1280 e6 ; d a t a . Pn o i s e = 0 ;d a t a . P jammer 1 = 0 ; d a t a . S t a r t F r e qj a m m e r 1 = 0 ;

80 d a t a . Bandwidthjammer 1 = 0 ; d a t a . Pjammer 2 = 0 ;d a t a . S t a r t F r e qj a m m e r 2 = 0 ; d a t a . Bandwidthjammer 2 = 0 ;s e t a p p d a t a ( f i gh a n d l e ,’inputdata’ , d a t a ) ; s e t( h a n d l e s . r e c t,’Value’ , 1 ) ; s e t( h a n d l e s . s i n e ,’Value’ , 0 ) ;s e t( h a n d l e s . ch i r p ,’Value’ , 0 ) ;

85

%−−− Outpu ts from t h i s f u n c t i o n a r e r e t u r n e d t o t h e command l i n e .f u n c t i o n v a r a r g o u t = U I S i g n a l S i m u l a t i o ne x p o r t O u t p u t F c n ( hObject ,e v e n t d a t a , h a n d l e s )% v a r a r g o u t c e l l a r r a y f o r r e t u r n i n g o u t p u t a r g s ( see VARARGOUT) ;

90 % hOb jec t hand le t o f i g u r e% e v e n t d a t a r e s e r v e d− t o be d e f i n e d i n a f u t u r e v e r s i o n o f MATLAB% h a n d l e s s t r u c t u r e w i th h a n d l e s and u s e r d a t a ( see GUIDATA)

% Get d e f a u l t command l i n e o u t p u t from h a n d l e s s t r u c t u r e95 v a r a r g o u t1 = h a n d l e s . o u t p u t ;

%−−− Execu tes d u r i n g o b j e c t c r e a t i o n , a f t e r s e t t i n g a l l p r o p e r t i e s .f u n c t i o n D t a r g e t 1 C r e a t e F c n ( hObject , e v e n t d a t a , h a n d l e s )

s e t( hObject ,’BackgroundColor’ ,’white’ ) ;100 f u n c t i o n P t a r g e t 2 C r e a t e F c n ( hObject , e v e n t d a t a , h a n d l e s )

s e t( hObject ,’BackgroundColor’ ,’white’ ) ;f u n c t i o n maxFDev CreateFcn ( hObject , e v e n t d a t a , h a n d l e s )

s e t( hObject ,’BackgroundColor’ ,’white’ ) ;s e t( hObject ,’Visible’ ,’off’ ) ;

105 f u n c t i o n f s i n e C r e a t e F c n ( hObject , e v e n t d a t a , h a n d l e s )s e t( hObject ,’BackgroundColor’ ,’white’ ) ;s e t( hObject ,’Visible’ ,’off’ ) ;

f u n c t i o n c a r r i e r F r e q C r e a t e F c n ( hObject , e v e n t d a t a , h a n d l e s )s e t( hObject ,’BackgroundColor’ ,’white’ ) ;

110 s e t( hObject ,’Visible’ ,’off’ ) ;f u n c t i o n SimTime CreateFcn ( hObject , e v e n t d a t a , h a n d l e s )

s e t( hObject ,’BackgroundColor’ ,’white’ ) ;f u n c t i o n Bandwid th jammer 2 Crea teFcn ( hObject , e v e n t d a t a , h a n d l e s )

s e t( hObject ,’BackgroundColor’ ,’white’ ) ;115 f u n c t i o n S t a r t F r e q j a m m e r 2 C r e a t e F c n ( hObject , e v e n t d a t a , h a n d l e s )

s e t( hObject ,’BackgroundColor’ ,’white’ ) ;f u n c t i o n P jammer 2 Crea teFcn ( hObject , e v e n t d a t a , h a n d l e s )

s e t( hObject ,’BackgroundColor’ ,’white’ ) ;

95


f u n c t i o n Bandwid th jammer 1 Crea teFcn ( hObject , e v e n t d a t a , h a n d l e s )120 s e t( hObject ,’BackgroundColor’ ,’white’ ) ;

f u n c t i o n S t a r t F r e q j a m m e r 1 C r e a t e F c n ( hObject , e v e n t d a t a , h a n d l e s )s e t( hObject ,’BackgroundColor’ ,’white’ ) ;

f u n c t i o n P jammer 1 Crea teFcn ( hObject , e v e n t d a t a , h a n d l e s )s e t( hObject ,’BackgroundColor’ ,’white’ ) ;

125 f u n c t i o n P n o i s e C r e a t e F c n ( hObject , e v e n t d a t a , h a n d l e s )s e t( hObject ,’BackgroundColor’ ,’white’ ) ;

f u n c t i o n D t a r g e t 2 C r e a t e F c n ( hObject , e v e n t d a t a , h a n d l e s )s e t( hObject ,’BackgroundColor’ ,’white’ ) ;

f u n c t i o n P t a r g e t 1 C r e a t e F c n ( hObject , e v e n t d a t a , h a n d l e s )130 s e t( hObject ,’BackgroundColor’ ,’white’ ) ;

%−−− Execu tes on b u t t o n p r e s s i n pushbu t t on1 .f u n c t i o n p u s h b u t t o n 1C a l l b a c k ( hObject , e v e n t d a t a , h a n d l e s )

% The main f u n c t i o n , g e t a l l v a r i a b l e s and c a l c u l a t e t h e r a d a r s i g n a l135 % Make a message box wi th a p i c tog ram c a l l e d ’ P i c t ’

P i c t = 1 : 6 4 ; P i c t =( P i c t ’∗ P i c t ) / 6 4 ; MsgSt r ing = [’Please wait ...This may take a while’ ] ; MsgT i t le = [’Simulating Radar Signals’ ] ;h=msgbox ( MsgStr ing , MsgTi t le ,’custom’ , P i c t , ho t ( 6 4 ) ) ;% De f i n i ng non changeb le v a r i a b l e s

140 g l o b a l c0Fs = 3 . 7 5 e9 ; % Sampl ing f r e q u e n c y wi th d e c i m a t i o n o f 5 g i v e s

% t h e wanted 7 5 0 MHzTsweep = 28 e−6; % Time d u r a t i o n o f a sweep ( 2 8 usec )c0 = 2 9 9 7 9 2 4 5 8 ; % Speed of l i g h t [m/ s ]

145 s o u r c e s = ; d a t a = g e t a p p d a t a ( gcb f ) ; sampleTime = 1 / Fs ;noRangeBins = c e i l ( d a t a . i n p u t d a t a . SimTime / sampleTime ) ;% Check f o r f i e l d si f i s f i e l d ( d a t a . i n p u t d a t a ,’maxFDev’ ) &s t rcmp( d a t a . i n p u t d a t a . pmod ,’chirp’ ) . . .

150 & i s f i e l d ( d a t a . i n p u t d a t a ,’carrierFreq’ )methodParam = d a t a . i n p u t d a t a . maxFDev ;Fc = d a t a . i n p u t d a t a . c a r r i e r F r e q ;%c a r r i e r f r e q . o r LO

e l s e i f s t rcmp( d a t a . i n p u t d a t a . pmod ,’chirp’ ) %shou ld no t be n e s se c a r r ymethodParam = 1 . 8 7 5 e6 / 2 ;

155 Fc = 1280 e6 ;e l s e i f i s f i e l d ( d a t a . i n p u t d a t a ,’fsine’ ) &s t rcmp( d a t a . i n p u t d a t a . pmod ,’fixfreq’ )

methodParam = d a t a . i n p u t d a t a . f s i n e ;Fc = methodParam ;

160 e l s e i f s t rcmp( d a t a . i n p u t d a t a . pmod ,’fixfreq’ ) %shou ld no be n e s se c a r r ymethodParam =1 2 8 0 e6 ;Fc = 1280 e6 ;

e l s emethodParam = 0 ;

165 Fc = 1280 e6 ;end a n t = J d e f a n t (’isotropULA’ ) ; pmod =Jgetmod ( d a t a . i n p u t d a t a . pmod , Fs , Tsweep , methodParam , Fc ) ; waveform =Jdefwave ( c0 / Fc , noRangeBins , pmod , 1 / Fs ) ;i fd a t a . i n p u t d a t a . Pt a r g e t 1 > 0

170 t r g 1 = J d e f t a r g e t ( d a t a . i n p u t d a t a . Pt a r g e t 1 , d a t a . i n p u t d a t a . Dt a r g e t 1 , . . .[ 0 ; 0 ] , 0 ) ;

s o u r c e s = [ s o u r c e s t r g 1 ] ; endi f d a t a . i n p u t d a t a . Pt a r g e t 2 > 0

t r g 2 = J d e f t a r g e t ( d a t a . i n p u t d a t a . Pt a r g e t 2 , d a t a . i n p u t d a t a . Dt a r g e t 2 , . . .175 [ 0 ; 0 ] , 0 ) ;

s o u r c e s = [ s o u r c e s t r g 2 ] ; endi f d a t a . i n p u t d a t a . Pn o i s e > 0

n o i s e S r c 1 = J d e f n o i s e ( d a t a . i n p u t d a t a . Pn o i s e ) ;s o u r c e s = [ s o u r c e s n o i s e S r c 1 ] ; end

180 i f d a t a . i n p u t d a t a . Pjammer 1 > 0jam1 = Jdef jammer ( d a t a . i n p u t d a t a . Pjammer 1 , 2 0 0 , 3 0 0 , . . .

[ d a t a . i n p u t d a t a . Bandwidthjammer 1 d a t a . i n p u t d a t a . S t a r t F r e qj a m m e r 1 ] ) ;s o u r c e s = [ s o u r c e s jam1 ] ; end

i f d a t a . i n p u t d a t a . Pjammer 2 > 0185 jam2 = Jdef jammer ( d a t a . i n p u t d a t a . Pjammer 2 , 0 , 0 , . . .

[ d a t a . i n p u t d a t a . Bandwidthjammer 2 d a t a . i n p u t d a t a . S t a r t F r e qj a m m e r 2 ] ) ;s o u r c e s = [ s o u r c e s jam2 ] ; end

s o u r c e s d a t a = J d e f s o u r c e s ( s o u r c e s ) ;%Model ing ana log Bandpass f i l t e r

190 %F = [ 1 1 9 0 1 2 0 0 1 4 0 0 1 4 1 0 ]∗1 0 ˆ 6 ;%A = [ 0 1 0 ] ;

96


%DEV = [ 0 . 1 0 . 0 1 0 . 1 ] ;%[ Nf , Fo , Ao ,W] = REMEZORD( F ,A,DEV, 1 / sampleTime ) ;%B = remez ( Nf , Fo , Ao ,W) ;

195 B = [ 0 . 0 1 3 8 3 1 0 .026669 0 .0092641−0.0010959 −0.0150870 . 0 1 7 7 9 5 −0.0091945 0.0013692−3.4166 e−005 0.0013977−0.00019865 −0.0032921 0 .0046698 −0.001606 −0.00316840 .0050385 −0.0025289 −0.0015128 0 .0033217 −0.0020047−0.00024556 0.0010926 −0.00047281 4.3657 e−006 −0.00058688

200 0 .0012701−0.00061987 −0.0012394 0 .0024724 −0.0015338−0.00097289 0 .0027427 −0.002107−0.00026924 0.002126−0.001931 0 .00026843 0 .001053 −0.0010118 0.000232848.2921 e−005 0.00028861−0.00043517−0.00034497 0.0014237−0.0014167−0.00013001 0 .0019447 −0.0021996 0.00046163

205 0 .0017152 −0.0023415 0 .00093367 0 .00097814 −0.00171350 .00084844 0.0002419 −0.00054444 0 .00010743 4 .9001 e−0060 .00063493 −0.0010726 0 .00035026 0 .0012501 −0.00216710 .0011153 0 .0011895 −0.0025941 0 .0017478 0.00056722−0.0022008 0.0017718−2.9547 e−005 −0.0011622 0.00094891

210 −0.00015366−3.9841 e−005 −0.00041239 0 .00045138 0.00057785−0.0017789 0 .0015327 0 .00047282 −0.0025088 0.0024766−0.00018351 −0.0023095 0.0027195 −0.00082162 −0.0014170.0019783−0.00082175−0.00040791 0 .00049137 4 .4288 e−0059.5808 e−005 −0.0010652 0.0014994 −0.00022635 −0.0019846

215 0 .0028802 −0.0011325 −0.001939 0 .0034679 −0.0019493−0.0011357 0 .0029027 −0.0019799−0.00022575 0.0014375−0.00092962 6.5065 e−005 −0.00019476 0.00090332−0.00061164−0.0011772 0 .0027453 −0.0019526 −0.0011131 0.0037338−0.0031829−0.00025873 0 .0034167 −0.0034444 0.00064011

220 0 .0020699 −0.0023498 0 .00073767 0.00049592−0.00023281−0.00035267−0.00036634 0 .0020036 −0.0022946−7.3935 e−0050 .0033486 −0.0041403 0 .0010913 0 .0032724 −0.00485650 .0021922 0 .0020485 −0.0039223 0 .0022437 0.00060044−0.0016846 0 .00076046 2 .6131 e−006 0 .0008088 −0.0018459

225 0 .000767 0 .0023734 −0.0044491 0 .0025437 0.0023683−0.0057954 0 .0042079 0 .0011062 −0.0052013 0.0044967−0.00029697 −0.0030237 0.0028073−0.00058526−0.00046073−0.00042826 0 .00087939 0 .0010893 −0.0038552 0.00362790 .00085036 −0.005902 0.0062473 −0.00077543 −0.005733

230 0 .0071979 −0.0024564 −0.0036678 0 .0055859 −0.0025958−0.0011456 0 .0 0 1 8 7 1 −0.0003454 9.8689 e−005 −0.00227230.0036853−0.00081121 −0.0049939 0 .0078036 −0.0034453−0.0051051 0 .0098923 −0.0060208 −0.0030072 0.0087465−0.0064568−0.00044331 0 .0047754 −0.0035441 0.00036756

235 −2.444e−005 0 .0021221 −0.0018243 −0.0031799 0.0082942−0.0064387 −0.0031304 0 .0 1 2 1 4 5 −0.011099−0.000305790 . 0 1 1 8 5 2 −0.012826 0 .0029451 0 .0077245 −0.00965710 .0034829 0 .0022826 −0.0020179−0.00072939 −0.00100770 .0071888 −0.0091931 0 .00029568 0 .013851 −0.018586

240 0 . 0 0 5 8 5 9 2 0 . 0 1 4 8 7 −0.024149 0 .0 1 2 2 1 2 0.010128−0.02204 0 .0 1 4 0 2 0 . 0 0 3 1 5 3 5 −0.011645 0.0066746−0.00012425 0 .0034913 −0.01114 0 .0059941 0.016665−0.03607 0 .0 2 4 0 1 8 0 . 0 2 0 7 6 4 −0.060886 0.0514990 . 0 1 1 4 9 3 −0.077124 0 .0 8 1 3 7 5 −0.010321 −0.078623

245 0 . 1 0 4 4 8 −0.038616 −0.064249 0 .1 1 3 1 7 −0.064249−0.038616 0 .1 0 4 4 8 −0.078623 −0.010321 0.081375−0.077124 0 .0 1 1 4 9 3 0 . 0 5 1 4 9 9 −0.060886 0.0207640 . 0 2 4 0 1 8 −0.03607 0 .016665 0 .0059941 −0.011140.0034913−0.00012425 0 .0066746 −0.011645 0.0031535

250 0 . 0 1 4 0 2 −0.02204 0 .0 1 0 1 2 8 0 . 0 1 2 2 1 2 −0.0241490 . 0 1 4 8 7 0 . 0 0 5 8 5 9 2 −0.018586 0 .0 1 3 8 5 1 0.00029568−0.0091931 0 .0071888 −0.0010077−0.00072939 −0.00201790 .0022826 0 .0034829 −0.0096571 0 .0077245 0.0029451−0.012826 0.011852 −0.00030579 −0.011099 0.012145

255 −0.0031304 −0.0064387 0 .0082942 −0.0031799 −0.00182430.0021221−2.444 e−005 0 .00036756 −0.0035441 0.0047754−0.00044331 −0.0064568 0 .0087465 −0.0030072 −0.00602080 .0098923 −0.0051051 −0.0034453 0 .0078036 −0.0049939−0.00081121 0 .0036853 −0.0022723 9.8689 e−005 −0.0003454

260 0 . 0 0 1 8 7 1 −0.0011456 −0.0025958 0 .0055859 −0.0036678−0.0024564 0 .0071979 −0.005733−0.00077543 0.0062473−0.005902 0 .00085036 0 .0036279 −0.0038552 0.00108930.00087939−0.00042826−0.00046073−0.00058526 0.0028073−0.0030237−0.00029697 0 .0044967 −0.0052013 0.0011062

97


265 0 .0042079 −0.0057954 0 .0023683 0 .0025437 −0.00444910 .0023734 0 .000767 −0.0018459 0 .0008088 2 .6131 e−0060 .00076046 −0.0016846 0 .00060044 0 .0022437 −0.00392230 .0020485 0 .0021922 −0.0048565 0 .0032724 0.0010913−0.0041403 0.0033486−7.3935 e−005 −0.0022946 0.0020036

270 −0.00036634−0.00035267−0.00023281 0 .00049592 0.00073767−0.0023498 0 .0020699 0 .00064011 −0.0034444 0.0034167−0.00025873 −0.0031829 0 .0037338 −0.0011131 −0.00195260 .0027453 −0.0011772−0.00061164 0.00090332−0.000194766.5065 e−005 −0.00092962 0.0014375 −0.00022575 −0.0019799

275 0 .0029027 −0.0011357 −0.0019493 0 .0034679 −0.001939−0.0011325 0 .0028802 −0.0019846−0.00022635 0.0014994−0.0010652 9.5808 e−005 4.4288 e−005 0.00049137−0.00040791−0.00082175 0 .0019783 −0.001417−0.00082162 0.0027195−0.0023095−0.00018351 0 .0024766 −0.0025088 0.00047282

280 0 .0015327 −0.0017789 0 .00057785 0.00045138−0.00041239−3.9841e−005 −0.00015366 0 .00094891 −0.0011622−2.9547 e−0050 .0017718 −0.0022008 0 .00056722 0 .0017478 −0.00259410 .0011895 0 .0011153 −0.0021671 0 .0012501 0.00035026−0.0010726 0 .00063493 4 .9001 e−006 0.00010743−0.00054444

285 0 .0002419 0 .00084844 −0.0017135 0 .00097814 0.00093367−0.0023415 0 .0017152 0 .00046163 −0.0021996 0.0019447−0.00013001 −0.0014167 0.0014237−0.00034497−0.000435170 .00028861 8 .2921 e−005 0 .00023284 −0.0010118 0.0010530 .00026843 −0.001931 0.002126 −0.00026924 −0.002107

290 0 .0027427−0.00097289 −0.0015338 0 .0024724 −0.0012394−0.00061987 0.0012701 −0.00058688 4.3657 e−006 −0.000472810.0010926−0.00024556 −0.0020047 0 .0033217 −0.0015128−0.0025289 0 .0050385 −0.0031684 −0.001606 0.0046698−0.0032921−0.00019865 0.0013977−3.4166 e−005 0.0013692

295 −0.0091945 0 .0 1 7 7 9 5 −0.015087 −0.0010959 0.00926410 . 0 2 6 6 6 9 0 . 0 1 3 8 3 1 ] ;%C r e a t i n g Radar S i g n a lr a d a r S i g = J s i m r a d a r s i g ( ant , s o u r c e sd a t a , waveform , B ) ;%Sav ing t h e d a t a i n a v a r i a b l e

300 s d a t a . RangeBinLength = sampleTime∗5 ∗ c0 / 2 ;s d a t a . NumberOfRangeBins = noRangeBins / 5 ; samples =r e a l ( r a d a r S i g . s i g n a l s ) ; s d a t a . S i m u l a t e d S i g n a l =samples ( 5 : 5 :end) ; s e t a p p d a t a ( gcbf ,’simulated_data’ , s d a t a ) ;[ Pxx , fs , noAv ] = PSDWelch ( s d a t a . S i m ul a t e d S i g n a l , 1 0 2 4 , 0 . 5 ,

305 ’hamming’ ) ; axes( h a n d l e s . axes1 ) ;c l a ;%P l o t t h e d a t ap l o t ( fs ,10∗ l og10( Pxx ) ,’EraseMode’ ,’background’ ) x l a b e l (’Frequency"\Omega" normalized from 0 to 2\pi [rad/sample]’ ) ; y l a b e l (’PowerSpectrum Density in [dB]’ ) ;

310 T t x t = [ ’Welch PSD estimation, ’ , num2st r( noAv ,’%0.5g’ ) ,’ averages’ ] ;t i t l e ( T t x t )

%Close t h e message box ( i f i t e x i s t ) .i f i s h a n d l e ( h ) , c l o s e( h ) , end

315 %−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−f u n c t i o n F i l eMenu Ca l l back ( hObject , e v e n t d a t a , h a n d l e s )

f u n c t i o n OpenMenuI temCal lback ( hObject , e v e n t d a t a , h a n d l e s ) d=pwd;d t =’c:/tmp’ ; cd(’c:/’ ) ; warn ing o f f MATLAB:MKDIR: D i r e c t o r y E x i s t s ,

320 mkdir tmp ; cd tmp ; save backup cd( d ) ; u iopen (’load’ ) i f( e x i s t (’file_info’ )==1)

i f i s f i e l d ( f i l e i n f o ,’content’ )i f s t r cmp( f i l e i n f o . c o n t e n t ,’Variables_from_SignalSimulation’ )

%c o r r e c t !325 s e t a p p d a t a ( gcbf ,’simulated_data’ , d a t a s i m u l a t e d ) ;

s e t a p p d a t a ( gcbf ,’inputdata’ , d a t a i n p u t ) ;s e t( h a n d l e s . Pt a r g e t 1 ,’String’ , d a t a i n p u t . P t a r g e t 1 ) ;s e t( h a n d l e s . D t a r g e t 1 ,’String’ , d a t a i n p u t . D t a r g e t 1 ) ;s e t( h a n d l e s . Pt a r g e t 2 ,’String’ , d a t a i n p u t . P t a r g e t 2 ) ;

330 s e t( h a n d l e s . D t a r g e t 2 ,’String’ , d a t a i n p u t . D t a r g e t 2 ) ;s e t( h a n d l e s . SimTime ,’String’ , d a t a i n p u t . SimTime∗1 e6 ) ;s e t( h a n d l e s . f s i n e ,’String’ , d a t a i n p u t . f s i n e / 1 e6 ) ;s e t( h a n d l e s . c a r r i e r F r e q ,’String’ , d a t a i n p u t . c a r r i e r F r e q / 1 e6 ) ;s e t( h a n d l e s . Pno ise ,’String’ , d a t a i n p u t . P n o i s e ) ;

335 s e t( h a n d l e s . Pjammer 1 ,’String’ , d a t a i n p u t . P jammer 1 ) ;s e t( h a n d l e s . S t a r t F r e qj a m m e r 1 ,’String’ , d a t a i n p u t . S t a r t F r e qj a m m e r 1 ) ;s e t( h a n d l e s . Bandwidthjammer 1 ,’String’ , d a t a i n p u t . Bandwidth jammer 1 ) ;

98


s e t( h a n d l e s . Pjammer 2 ,’String’ , d a t a i n p u t . P jammer 2 ) ;s e t( h a n d l e s . S t a r t F r e qj a m m e r 2 ,’String’ , d a t a i n p u t . S t a r t F r e qj a m m e r 2 ) ;

340 s e t( h a n d l e s . Bandwidthjammer 2 ,’String’ , d a t a i n p u t . Bandwidth jammer 2 ) ;s e t( h a n d l e s . maxFDev ,’String’ , d a t a i n p u t . maxFDev / . 5 e6 ) ;s w i t c h d a t a i n p u t . pmod

case ’rect’s e t( h a n d l e s . r e c t ,’Value’ , 1 ) ;

345 s e t( h a n d l e s . s i n e ,’Value’ , 0 ) ;s e t( h a n d l e s . ch i r p ,’Value’ , 0 ) ;s e t( h a n d l e s . f s i n e ,’Visible’ ,’off’ ) ;s e t( h a n d l e s . maxFDev ,’Visible’ ,’off’ ) ;s e t( h a n d l e s . c a r r i e r F r e q ,’Visible’ ,’off’ ) ;

350 s e t( h a n d l e s . f s i n et x t ,’Visible’ ,’off’ ) ;s e t( h a n d l e s . f s i n et x t 1 ,’Visible’ ,’off’ ) ;s e t( h a n d l e s . maxFDevtxt ,’Visible’ ,’off’ ) ;s e t( h a n d l e s . maxFDevtxt1 ,’Visible’ ,’off’ ) ;s e t( h a n d l e s . maxFDevtxt2 ,’Visible’ ,’off’ ) ;

355 s e t( h a n d l e s . maxFDevtxt3 ,’Visible’ ,’off’ ) ;case ’fixfreq’

s e t( h a n d l e s . r e c t ,’Value’ , 0 ) ;s e t( h a n d l e s . s i n e ,’Value’ , 1 ) ;s e t( h a n d l e s . ch i r p ,’Value’ , 0 ) ;

360 s e t( h a n d l e s . f s i n e ,’Visible’ ,’on’ ) ;s e t( h a n d l e s . maxFDev ,’Visible’ ,’off’ ) ;s e t( h a n d l e s . c a r r i e r F r e q ,’Visible’ ,’off’ ) ;s e t( h a n d l e s . f s i n et x t ,’Visible’ ,’on’ ) ;s e t( h a n d l e s . f s i n et x t 1 ,’Visible’ ,’on’ ) ;

365 s e t( h a n d l e s . maxFDevtxt ,’Visible’ ,’off’ ) ;s e t( h a n d l e s . maxFDevtxt1 ,’Visible’ ,’off’ ) ;s e t( h a n d l e s . maxFDevtxt2 ,’Visible’ ,’off’ ) ;s e t( h a n d l e s . maxFDevtxt3 ,’Visible’ ,’off’ ) ;

case ’chirp’370 s e t( h a n d l e s . r e c t ,’Value’ , 0 ) ;

s e t( h a n d l e s . s i n e ,’Value’ , 0 ) ;s e t( h a n d l e s . ch i r p ,’Value’ , 1 ) ;s e t( h a n d l e s . f s i n e ,’Visible’ ,’off’ )s e t( h a n d l e s . maxFDev ,’Visible’ ,’on’ ) ;

375 s e t( h a n d l e s . c a r r i e r F r e q ,’Visible’ ,’on’ ) ;s e t( h a n d l e s . f s i n et x t ,’Visible’ ,’off’ ) ;s e t( h a n d l e s . f s i n et x t 1 ,’Visible’ ,’off’ ) ;s e t( h a n d l e s . maxFDevtxt ,’Visible’ ,’on’ ) ;s e t( h a n d l e s . maxFDevtxt1 ,’Visible’ ,’on’ ) ;

380 s e t( h a n d l e s . maxFDevtxt2 ,’Visible’ ,’on’ ) ;s e t( h a n d l e s . maxFDevtxt3 ,’Visible’ ,’on’ ) ;

end[ Pxx , fs , noAv ] = PSDWelch ( d a t as i m u l a t e d . S i m ul a t e d S i g n a l , 1 0 2 4 , 0 . 5 ,’hamming’ ) ;axes( h a n d l e s . axes1 ) ;

385 c l a ;%P l o t t h e d a t ap l o t ( fs ,10∗ l og10( Pxx ) ,’EraseMode’ ,’background’ )x l a b e l (’Frequency "\Omega" normalized from 0 to 2\pi [rad/sample]’ ) ;y l a b e l (’Power Spectrum Density in [dB]’ ) ;

390 T t x t = [ ’Welch PSD estimation, ’ , num2st r( noAv ,’%0.5g’ ) ,’ averages’ ] ;t i t l e ( T t x t )

e l s ee r r o r d l g (’Incorrect file’ )c l e a r

395 cd( d t ) ; l oad backup , cd( d ) ;end





f u n c t i o n P r i n tMenu I t em Ca l l back ( hObject , e v e n t d a t a , h a n d l e s )410 p r i n t d l g ( h a n d l e s . f i g u r e 1 )

99


f u n c t i o n CloseMenuI temCal lback ( hObjec t , e v e n t d a t a , h a n d l e s )s e l e c t i o n = q u e s t d l g ( [’Close ’ g e t( h a n d l e s . f i g u r e 1 ,’Name’ )’?’ ] , . . .

415 [ ’Close ’ g e t( h a n d l e s . f i g u r e 1 ,’Name’ ) ’...’ ] , . . .’Yes’ ,’No’ ,’Yes’ ) ;

i f s t r cmp( s e l e c t i o n ,’No’ )r e t u r n;

end d e l e t e( h a n d l e s . f i g u r e 1 )420

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−f u n c t i o n D t a r g e t 1 C a l l b a c k ( hObject , e v e n t d a t a , h a n d l e s )D t a r g e t 1 = s t r 2 d o u b l e (g e t( hObject ,’String’ ) ) ; i fi s n a n( D t a r g e t 1 )

425 s e t( hObject ,’String’ , 0 ) ;D t a r g e t 1 = 0 ;e r r o r d l g (’Input must be a number’ ,’Error’ ) ;

end d a t a = g e t a p p d a t a ( gcbf ,’inputdata’ ) ; d a t a . D t a r g e t 1 =D t a r g e t 1 ; s e t a p p d a t a ( gcbf ,’inputdata’ , d a t a ) ;

430

f u n c t i o n P t a r g e t 2 C a l l b a c k ( hObject , e v e n t d a t a , h a n d l e s )P t a r g e t 2 = s t r 2 d o u b l e (g e t( hObject ,’String’ ) ) ; i fi s n a n( P t a r g e t 2 )

s e t( hObject ,’String’ , 0 ) ;435 P t a r g e t 2 = 0 ;

e r r o r d l g (’Input must be a number’ ,’Error’ ) ;end d a t a = g e t a p p d a t a ( gcbf ,’inputdata’ ) ; d a t a . P t a r g e t 2 =P t a r g e t 2 ; s e t a p p d a t a ( gcbf ,’inputdata’ , d a t a ) ;

440 f u n c t i o n D t a r g e t 2 C a l l b a c k ( hObject , e v e n t d a t a , h a n d l e s )D t a r g e t 2 = s t r 2 d o u b l e (g e t( hObject ,’String’ ) ) ; i fi s n a n( D t a r g e t 2 )

s e t( hObject ,’String’ , 0 ) ;D t a r g e t 2 = 0 ;

445 e r r o r d l g (’Input must be a number’ ,’Error’ ) ;end d a t a = g e t a p p d a t a ( gcbf ,’inputdata’ ) ; d a t a . D t a r g e t 2 =D t a r g e t 2 ; s e t a p p d a t a ( gcbf ,’inputdata’ , d a t a ) ;

f u n c t i o n P t a r g e t 1 C a l l b a c k ( hObject , e v e n t d a t a , h a n d l e s )450 P t a r g e t 1 = s t r 2 d o u b l e (g e t( hObject ,’String’ ) ) ; i f

i s n a n( P t a r g e t 1 )s e t( hObject ,’String’ , 0 ) ;P t a r g e t 1 = 0 ;e r r o r d l g (’Input must be a number’ ,’Error’ ) ;

455 end d a t a = g e t a p p d a t a ( gcbf ,’inputdata’ ) ; d a t a . P t a r g e t 1 =P t a r g e t 1 ; s e t a p p d a t a ( gcbf ,’inputdata’ , d a t a ) ;

f u n c t i o n P n o i s e C a l l b a c k ( hObject , e v e n t d a t a , h a n d l e s ) Pn o i s e =s t r 2 d o u b l e (g e t( hObject ,’String’ ) ) ; i f i s n a n( P n o i s e )

460 s e t( hObject ,’String’ , 0 ) ;P n o i s e = 0 ;e r r o r d l g (’Input must be a number’ ,’Error’ ) ;

end d a t a = g e t a p p d a t a ( gcbf ,’inputdata’ ) ; d a t a . P n o i s e =P n o i s e ; s e t a p p d a t a ( gcbf ,’inputdata’ , d a t a ) ;

465

f u n c t i o n P jammer 1 Ca l l back ( hObject , e v e n t d a t a , h a n d l e s )P jammer 1 = s t r 2 d o u b l e (g e t( hObject ,’String’ ) ) ; i fi s n a n( P jammer 1 )

s e t( hObject ,’String’ , 0 ) ;470 P jammer 1 = 0 ;

e r r o r d l g (’Input must be a number’ ,’Error’ ) ;end d a t a = g e t a p p d a t a ( gcbf ,’inputdata’ ) ; d a t a . P jammer 1 =P jammer 1 ; s e t a p p d a t a ( gcbf ,’inputdata’ , d a t a ) ;

475 f u n c t i o n S t a r t F r e q j a m m e r 1 C a l l b a c k ( hObject , e v e n t d a t a , h a n d l e s )S t a r t F r e q j a m m e r 1 = s t r 2 d o u b l e (g e t( hObject ,’String’ ) ) ; i fi s n a n( S t a r t F r e q j a m m e r 1 )

s e t( hObject ,’String’ , 0 ) ;S t a r t F r e q j a m m e r 1 = 0 ;

480 e r r o r d l g (’Input must be a number’ ,’Error’ ) ;end d a t a = g e t a p p d a t a ( gcbf ,’inputdata’ ) ;d a t a . S t a r t F r e qj a m m e r 1 = S t a r t F r e q j a m m e r 1 ;s e t a p p d a t a ( gcbf ,’inputdata’ , d a t a ) ;

100


485 f u n c t i o n Bandw id th jammer 1 Ca l lback ( hObject , e v e n t d a t a , h a n d l e s )Bandwidth jammer 1 = s t r 2 d o u b l e (g e t( hObject ,’String’ ) ) ; i fi s n a n( Bandwidth jammer 1 )

s e t( hObject ,’String’ , 0 ) ;Bandwidth jammer 1 = 0 ;

490 e r r o r d l g (’Input must be a number’ ,’Error’ ) ;end d a t a = g e t a p p d a t a ( gcbf ,’inputdata’ ) ;d a t a . Bandwidthjammer 1 = Bandwidth jammer 1 ;s e t a p p d a t a ( gcbf ,’inputdata’ , d a t a ) ;

495 f u n c t i o n P jammer 2 Ca l l back ( hObject , e v e n t d a t a , h a n d l e s )P jammer 2 = s t r 2 d o u b l e (g e t( hObject ,’String’ ) ) ; i fi s n a n( P jammer 2 )

s e t( hObject ,’String’ , 0 ) ;P jammer 2 = 0 ;

500 e r r o r d l g (’Input must be a number’ ,’Error’ ) ;end d a t a = g e t a p p d a t a ( gcbf ,’inputdata’ ) ; d a t a . P jammer 2 =P jammer 2 ; s e t a p p d a t a ( gcbf ,’inputdata’ , d a t a ) ;

f u n c t i o n S t a r t F r e q j a m m e r 2 C a l l b a c k ( hObject , e v e n t d a t a , h a n d l e s )505 S t a r t F r e q j a m m e r 2 = s t r 2 d o u b l e (g e t( hObject ,’String’ ) ) ; i f

i s n a n( S t a r t F r e q j a m m e r 2 )s e t( hObject ,’String’ , 0 ) ;S t a r t F r e q j a m m e r 2 = 0 ;e r r o r d l g (’Input must be a number’ ,’Error’ ) ;

510 end d a t a = g e t a p p d a t a ( gcbf ,’inputdata’ ) ;d a t a . S t a r t F r e qj a m m e r 2 = S t a r t F r e q j a m m e r 2 ;s e t a p p d a t a ( gcbf ,’inputdata’ , d a t a ) ;

f u n c t i o n Bandw id th jammer 2 Ca l lback ( hObject , e v e n t d a t a , h a n d l e s )515 Bandwidth jammer 2 = s t r 2 d o u b l e (g e t( hObject ,’String’ ) ) ; i f

i s n a n( Bandwidth jammer 2 )s e t( hObject ,’String’ , 0 ) ;Bandwidth jammer 2 = 0 ;e r r o r d l g (’Input must be a number’ ,’Error’ ) ;

520 end d a t a = g e t a p p d a t a ( gcbf ,’inputdata’ ) ;d a t a . Bandwidthjammer 2 = Bandwidth jammer 2 ;s e t a p p d a t a ( gcbf ,’inputdata’ , d a t a ) ;

f u n c t i o n SimTime Cal lback ( hObject , e v e n t d a t a , h a n d l e s ) SimTime =525 s t r 2 d o u b l e (g e t( hObject ,’String’ ) )∗1 e−6; i f i s n a n( SimTime )

s e t( hObject ,’String’ ,300 e−6);SimTime = 3 0 0 e−6;e r r o r d l g (’Input must be a number’ ,’Error’ ) ;

end d a t a = g e t a p p d a t a ( gcbf ,’inputdata’ ) ; d a t a . SimTime =530 SimTime ; s e t a p p d a t a ( gcbf ,’inputdata’ , d a t a ) ;

%−−− Execu tes on b u t t o n p r e s s i n r e c t .f u n c t i o n r e c t C a l l b a c k ( hObject , e v e n t d a t a , h a n d l e s )s e t( h a n d l e s . r e c t ,’Value’ , 1 ) ; s e t( h a n d l e s . s i n e ,’Value’ , 0 ) ;

535 s e t( h a n d l e s . ch i r p ,’Value’ , 0 ) ; d a t a =g e t a p p d a t a ( gcbf ,’inputdata’ ) ; d a t a . pmod =’rect’ ; d a t a . f s i n e = 0 ;s e t a p p d a t a ( gcbf ,’inputdata’ , d a t a ) ;s e t( h a n d l e s . f s i n e ,’Visible’ ,’off’ ) ;s e t( h a n d l e s . maxFDev ,’Visible’ ,’off’ ) ;

540 s e t( h a n d l e s . c a r r i e r F r e q ,’Visible’ ,’off’ ) ;s e t( h a n d l e s . f s i n et x t ,’Visible’ ,’off’ ) ;s e t( h a n d l e s . f s i n et x t 1 ,’Visible’ ,’off’ ) ;s e t( h a n d l e s . maxFDevtxt ,’Visible’ ,’off’ ) ;s e t( h a n d l e s . maxFDevtxt1 ,’Visible’ ,’off’ ) ;

545 s e t( h a n d l e s . maxFDevtxt2 ,’Visible’ ,’off’ ) ;s e t( h a n d l e s . maxFDevtxt3 ,’Visible’ ,’off’ ) ;

%−−− Execu tes on b u t t o n p r e s s i n s i n e .f u n c t i o n s i n e C a l l b a c k ( hObject , e v e n t d a t a , h a n d l e s )

550 s e t( h a n d l e s . r e c t ,’Value’ , 0 ) ; s e t( h a n d l e s . s i n e ,’Value’ , 1 ) ;s e t( h a n d l e s . ch i r p ,’Value’ , 0 ) ; d a t a =g e t a p p d a t a ( gcbf ,’inputdata’ ) ; d a t a . pmod =’fixfreq’ ; d a t a . f s i n e =1280 e6 ; se t a p p d a t a ( gcbf ,’inputdata’ , d a t a ) ;s e t( h a n d l e s . f s i n e ,’Visible’ ,’on’ ) ;

555 s e t( h a n d l e s . maxFDev ,’Visible’ ,’off’ ) ;s e t( h a n d l e s . c a r r i e r F r e q ,’Visible’ ,’off’ ) ;

101


s e t( h a n d l e s . f s i n et x t ,’Visible’ ,’on’ ) ;s e t( h a n d l e s . f s i n et x t 1 ,’Visible’ ,’on’ ) ;s e t( h a n d l e s . maxFDevtxt ,’Visible’ ,’off’ ) ;

560 s e t( h a n d l e s . maxFDevtxt1 ,’Visible’ ,’off’ ) ;s e t( h a n d l e s . maxFDevtxt2 ,’Visible’ ,’off’ ) ;s e t( h a n d l e s . maxFDevtxt3 ,’Visible’ ,’off’ ) ;

%−−− Execu tes on b u t t o n p r e s s i n c h i r p .565 f u n c t i o n c h i r p C a l l b a c k ( hObject , e v e n t d a t a , h a n d l e s )

s e t( h a n d l e s . r e c t ,’Value’ , 0 ) ; s e t( h a n d l e s . s i n e ,’Value’ , 0 ) ;s e t( h a n d l e s . ch i r p ,’Value’ , 1 ) ; d a t a =g e t a p p d a t a ( gcbf ,’inputdata’ ) ; d a t a . pmod =’chirp’ ; d a t a . maxFDev =1 .8 e6 / 2 ; s e t a p p d a t a ( gcbf ,’inputdata’ , d a t a ) ;

570 s e t a p p d a t a ( gcbf ,’inputdata’ , d a t a ) ;s e t( h a n d l e s . f s i n e ,’Visible’ ,’off’ )s e t( h a n d l e s . maxFDev ,’Visible’ ,’on’ ) ;s e t( h a n d l e s . c a r r i e r F r e q ,’Visible’ ,’on’ ) ;s e t( h a n d l e s . f s i n et x t ,’Visible’ ,’off’ ) ;

575 s e t( h a n d l e s . f s i n et x t 1 ,’Visible’ ,’off’ ) ;s e t( h a n d l e s . maxFDevtxt ,’Visible’ ,’on’ ) ;s e t( h a n d l e s . maxFDevtxt1 ,’Visible’ ,’on’ ) ;s e t( h a n d l e s . maxFDevtxt2 ,’Visible’ ,’on’ ) ;s e t( h a n d l e s . maxFDevtxt3 ,’Visible’ ,’on’ ) ;

580

f u n c t i o n f s i n e C a l l b a c k ( hObject , e v e n t d a t a , h a n d l e s ) f s i n e =s t r 2 d o u b l e (g e t( hObject ,’String’ ) )∗1 e6 ; i f i s n a n( f s i n e )

s e t( hObject ,’String’ , 0 ) ;f s i n e = 0 ;

585 e r r o r d l g (’Input must be a number’ ,’Error’ ) ;end d a t a = g e t a p p d a t a ( gcbf ,’inputdata’ ) ; d a t a . f s i n e = f s i n e ;s e t a p p d a t a ( gcbf ,’inputdata’ , d a t a ) ;

f u n c t i o n maxFDev Cal lback ( hObject , e v e n t d a t a , h a n d l e s ) maxFDev =590 s t r 2 d o u b l e (g e t( hObject ,’String’ ) )∗1 e6 / 2 ; i f i s n a n( maxFDev )

s e t( hObject ,’String’ , 1 . 8 7 5 ) ;maxFDev = 1 . 8 7 5 e6 / 2 ;e r r o r d l g (’Input must be a number’ ,’Error’ ) ;

end d a t a = g e t a p p d a t a ( gcbf ,’inputdata’ ) ; d a t a . maxFDev =595 maxFDev ; s e t a p p d a t a ( gcbf ,’inputdata’ , d a t a ) ;

f u n c t i o n c a r r i e r F r e q C a l l b a c k ( hObject , e v e n t d a t a , h a n d l e s )c a r r i e r F r e q = s t r 2 d o u b l e (g e t( hObject ,’String’ ) )∗1 e6 ; i fi s n a n( c a r r i e r F r e q )

600 s e t( hObject ,’String’ , 1 2 8 0 ) ;maxFDev = 1 2 8 0 e6 ;e r r o r d l g (’Input must be a number’ ,’Error’ ) ;

end d a t a = g e t a p p d a t a ( gcbf ,’inputdata’ ) ; d a t a . c a r r i e r F r e q =c a r r i e r F r e q ; s e t a p p d a t a ( gcbf ,’inputdata’ , d a t a ) ;

605

f u n c t i o n S a v e s i m u l a t e d s i g n a l C a l l b a c k ( hObject , e v e n t d a t a ,h a n d l e s ) d a t a = g e t a p p d a t a ( gcb f ) ;i f˜ i s f i e l d ( da ta ,’simulated_data’ )

610 e r r o r d l g (’Er is nog geen signaal gesimuleerd!’ ,’Foutmelding’ )e l s e i f i s f i e l d ( d a t a . s i m u l a t e dd a t a ,’SimulatedSignal’ ) &i s f i e l d ( d a t a . s i m u l a t e dd a t a , . . .

’NumberOfRangeBins’ ) & i s f i e l d ( d a t a . s i m u l a t e dd a t a ,’RangeBinLength’ )s = f i x ( c l ock ) ;

615 f i l e i n f o . d a t e = d a t e;f i l e i n f o . t ime = [ num2st r( s ( 4 ) ) ,’:’ , num2st r( s ( 5 ) ) ,’:’ , num2st r( s ( 6 ) ) ] ;f i l e i n f o . v e r s i o n = num2st r( d a t a . i n p u t d a t a .v e r s i o n) ;f i l e i n f o . c o n t e n t =’Variables_from_SignalSimulation’ ;d a t a s i m u l a t e d . S i m ul a t e d S i g n a l = d a t a . s i m ul a t e d d a t a . S i m u l a t e d S i g n a l ;

620 d a t a s i m u l a t e d . NumberOfRangeBins = d a t a . s i m u l a t e dd a t a . NumberOfRangeBins ;d a t a s i m u l a t e d . RangeBinLength = d a t a . s i m u l a t e dd a t a . RangeBinLength ;d a t a i n p u t . v e r s i o n = d a t a . i n p u t d a t a .v e r s i o n;d a t a i n p u t . P t a r g e t 1 = d a t a . i n p u t d a t a . Pt a r g e t 1 ;d a t a i n p u t . D t a r g e t 1 = d a t a . i n p u t d a t a . Dt a r g e t 1 ;

625 d a t a i n p u t . P t a r g e t 2 = d a t a . i n p u t d a t a . Pt a r g e t 2 ;d a t a i n p u t . D t a r g e t 2 = d a t a . i n p u t d a t a . Dt a r g e t 2 ;d a t a i n p u t . SimTime = d a t a . i n p u t d a t a . SimTime ;d a t a i n p u t . pmod = d a t a . i n p u t d a t a . pmod ;d a t a i n p u t . f s i n e = d a t a . i n p u t d a t a . f s i n e ;

102


630 d a t a i n p u t . c a r r i e r F r e q = d a t a . i n p u t d a t a . c a r r i e r F r e q ;d a t a i n p u t . P n o i s e = d a t a . i n p u t d a t a . Pn o i s e ;d a t a i n p u t . P jammer 1 = d a t a . i n p u t d a t a . Pjammer 1 ;d a t a i n p u t . S t a r t F r e qj a m m e r 1 = d a t a . i n p u t d a t a . S t a r t F r e qj a m m e r 1 ;d a t a i n p u t . Bandwidth jammer 1 = d a t a . i n p u t d a t a . Bandwidthjammer 1 ;

635 d a t a i n p u t . P jammer 2 = d a t a . i n p u t d a t a . Pjammer 2 ;d a t a i n p u t . S t a r t F r e qj a m m e r 2 = d a t a . i n p u t d a t a . S t a r t F r e qj a m m e r 2 ;d a t a i n p u t . Bandwidth jammer 2 = d a t a . i n p u t d a t a . Bandwidthjammer 2 ;d a t a i n p u t . maxFDev = d a t a . i n p u t d a t a . maxFDev ;l oadVars = ’file_info’ ,’data_simulated’ ,’data_input’ ;

640 u i s a v e S i g n a l S i m u l a t i o n ( l oadVars )

e l s ee r r o r d l g (’Er is geen gesimuleerd signaal beschikbaar’ ,’Foutmelding’ ) ;

end645

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−f u n c t i o n window Cal lback ( hObjec t , e v e n t d a t a , h a n d l e s )

%do n o t h i n g650

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−f u n c t i o n FPGA connect Ca l lback ( hObjec t , e v e n t d a t a , h a n d l e s )

% 1 ) c l o s e t h i s f u n c t i o n655 % 2 ) opens t h e o t h e r

% 3 ) c l o s e a l l h a n d l e s .d a t a = g e t a p p d a t a ( gcb f ) ;i f ˜ i s f i e l d ( da ta ,’simulated_data’ )

e r r o r d l g (’Er is nog geen signaal gesimuleerd!’ ,’Foutmelding’ )e l s e i f i s f i e l d ( d a t a . s i m u l a t e dd a t a ,’SimulatedSignal’ ) &

660 i s f i e l d ( d a t a . s i m u l a t e dd a t a , . . .’NumberOfRangeBins’ ) & i s f i e l d ( d a t a . s i m u l a t e dd a t a ,’RangeBinLength’ )

s = f i x ( c l ock ) ;f i l e i n f o . d a t e = d a t e;f i l e i n f o . t ime = [ num2st r( s ( 4 ) ) ,’:’ , num2st r( s ( 5 ) ) ,’:’ , num2st r( s ( 6 ) ) ] ;

665 f i l e i n f o . v e r s i o n = num2st r( d a t a . i n p u t d a t a .v e r s i o n) ;f i l e i n f o . c o n t e n t =’Variables_from_SignalSimulation’ ;d a t a s i m u l a t e d . S i m ul a t e d S i g n a l = d a t a . s i m ul a t e d d a t a . S i m u l a t e d S i g n a l ;d a t a s i m u l a t e d . NumberOfRangeBins = d a t a . s i m u l a t e dd a t a . NumberOfRangeBins ;d a t a s i m u l a t e d . RangeBinLength = d a t a . s i m u l a t e dd a t a . RangeBinLength ;

670 d a t a i n p u t . v e r s i o n = d a t a . i n p u t d a t a .v e r s i o n;d a t a i n p u t . P t a r g e t 1 = d a t a . i n p u t d a t a . Pt a r g e t 1 ;d a t a i n p u t . D t a r g e t 1 = d a t a . i n p u t d a t a . Dt a r g e t 1 ;d a t a i n p u t . P t a r g e t 2 = d a t a . i n p u t d a t a . Pt a r g e t 2 ;d a t a i n p u t . D t a r g e t 2 = d a t a . i n p u t d a t a . Dt a r g e t 2 ;

675 d a t a i n p u t . SimTime = d a t a . i n p u t d a t a . SimTime ;d a t a i n p u t . pmod = d a t a . i n p u t d a t a . pmod ;d a t a i n p u t . f s i n e = d a t a . i n p u t d a t a . f s i n e ;d a t a i n p u t . c a r r i e r F r e q = d a t a . i n p u t d a t a . c a r r i e r F r e q ;d a t a i n p u t . P n o i s e = d a t a . i n p u t d a t a . Pn o i s e ;

680 d a t a i n p u t . P jammer 1 = d a t a . i n p u t d a t a . Pjammer 1 ;d a t a i n p u t . S t a r t F r e qj a m m e r 1 = d a t a . i n p u t d a t a . S t a r t F r e qj a m m e r 1 ;d a t a i n p u t . Bandwidth jammer 1 = d a t a . i n p u t d a t a . Bandwidthjammer 1 ;d a t a i n p u t . P jammer 2 = d a t a . i n p u t d a t a . Pjammer 2 ;d a t a i n p u t . S t a r t F r e qj a m m e r 2 = d a t a . i n p u t d a t a . S t a r t F r e qj a m m e r 2 ;

685 d a t a i n p u t . Bandwidth jammer 2 = d a t a . i n p u t d a t a . Bandwidthjammer 2 ;d a t a i n p u t . maxFDev = d a t a . i n p u t d a t a . maxFDev ;l oadVars = ’file_info’ ,’data_simulated’ ,’data_input’ ;d=pwd ; d2=’c:/tmp’ ;cd(’c:/’ ) ; warn ing o f f MATLAB:MKDIR: D i r e c t o r y E x i s t s , mkdir tmp ; cd tmp ;

690 save backup f i l e i n f o d a t a ∗cd( d ) ;

e l s ee r r o r d l g (’Er is geen gesimuleerd signaal beschikbaar’ ,’Foutmelding’ ) ;

695 end

d e l e t e( h a n d l e s . f i g u r e 1 )

u i s i g n a l s i m u l a t i o n e x p o r t700

%−−− C r e a t e s and r e t u r n s a hand le t o t h e GUI f i g u r e .f u n c t i o n h1 = U I S i g n a l S i m u l a t i o ne x p o r t L a y o u t F c n ( p o l i c y )

103


% p o l i c y − c r e a t e a new f i g u r e or use a s i n g l e t o n . ’ new ’ or ’ reuse ’ .

705 p e r s i s t e n t h s i n g l e t o n ;i f s t r c m p i ( po l i c y , ’reuse’ ) &i s h a n d l e ( h s i n g l e t o n )

h1 = h s i n g l e t o n ;r e t u r n;

end710

h1 = f i g u r e ( . . . ’Units’ ,’characters’ , . . .’Color’ , [ 0 .752941176470588 0 .7529411764705880 . 7 5 2 9 4 1 1 7 6 4 7 0 5 8 8 ] , . . .’Colormap’ , [ 0 0 0 . 5 6 2 5 ; 0 0 0 . 6 2 5 ; 0 00 . 6 8 7 5 ; 0 0 0 . 7 5 ; 0 0 0 . 8 1 2 5 ; 0 0 0 . 8 7 5 ; 0 0 0 . 9 3 7 5 ; 0 0 1 ; 0 0 . 0 6 2 5 1 ; 0

715 0 . 1 2 5 1 ; 0 0 . 1 8 7 5 1 ; 0 0 . 2 5 1 ; 0 0 . 3 1 2 5 1 ; 0 0 . 3 7 5 1 ; 0 0 . 4 3 7 5 1 ; 0 0 . 51 ; 0 0 . 5 6 2 5 1 ; 0 0 . 6 2 5 1 ; 0 0 . 6 8 7 5 1 ; 0 0 . 7 5 1 ; 0 0 . 8 1 2 5 1 ; 0 0 . 8 7 5 1 ; 00 . 9 3 7 5 1 ; 0 1 1 ; 0 . 0 6 2 5 1 1 ; 0 . 1 2 5 1 0 . 9 3 7 5 ; 0 . 1 8 7 5 1 0 . 8 7 5 ; 0 . 2 5 10 . 8 1 2 5 ; 0 . 3 1 2 5 1 0 . 7 5 ; 0 . 3 7 5 1 0 . 6 8 7 5 ; 0 . 4 3 7 5 1 0 . 6 2 5 ; 0 . 5 10 . 5 6 2 5 ; 0 . 5 6 2 5 1 0 . 5 ; 0 . 6 2 5 1 0 . 4 3 7 5 ; 0 . 6 8 7 5 1 0 . 3 7 5 ; 0 . 7 5 1

720 0 . 3 1 2 5 ; 0 . 8 1 2 5 1 0 . 2 5 ; 0 . 8 7 5 1 0 . 1 8 7 5 ; 0 . 9 3 7 5 1 0 . 1 2 5 ; 1 1 0 . 0 6 2 5 ; 1 10 ; 1 0 . 9 3 7 5 0 ; 1 0 . 8 7 5 0 ; 1 0 . 8 1 2 5 0 ; 1 0 . 7 5 0 ; 1 0 . 6 8 7 5 0 ; 1 0 . 6 2 5 0 ; 10 . 5 6 2 5 0 ; 1 0 . 5 0 ; 1 0 . 4 3 7 5 0 ; 1 0 . 3 7 5 0 ; 1 0 . 3 1 2 5 0 ; 1 0 . 2 5 0 ; 1 0 . 1 8 7 50 ; 1 0 . 1 2 5 0 ; 1 0 . 0 6 2 5 0 ; 1 0 0 ; 0 . 9 3 7 5 0 0 ; 0 . 8 7 5 0 0 ; 0 . 8 1 2 5 0 0 ; 0 . 7 50 0 ; 0 . 6 8 7 5 0 0 ; 0 . 6 2 5 0 0 ; 0 . 5 6 2 5 0 0 ] , . . .’IntegerHandle’ ,’off’ , . . .

725 ’InvertHardcopy’ , g e t ( 0 ,’defaultfigureInvertHardcopy’ ) , . . .’MenuBar’ ,’none’ , . . . ’Name’ ,’UISignalSimulation’ , . . .’NumberTitle’ ,’off’ , . . .’PaperPosition’ , g e t ( 0 ,’defaultfigurePaperPosition’ ) , . . .’Position’ , [ 1 2 8 . 6 4 . 3 0 7 6 9 2 3 0 7 6 9 2 3 1 1 8 8 5 0 ] , . . .

730 ’Renderer’ , g e t ( 0 ,’defaultfigureRenderer’ ) , . . .’RendererMode’ ,’manual’ , . . . ’Resize’ ,’off’ , . . .’HandleVisibility’ ,’callback’ , . . . ’Tag’ ,’figure1’ , . . .’UserData’ , z e r o s( 1 , 0 ) ) ;

735 s e t a p p d a t a ( h1 ,’GUIDEOptions’ , s t r u c t ( . . . ’active_h’ ,1 .770002 e + 0 0 2 , . . .’taginfo’ , s t r u c t ( . . . ’figure’ , 2 , . . . ’axes’ ,2 , . . . ’pushbutton’ , 3 , . . . ’popupmenu’ , 3 , . . . ’frame’ , 1 2 , . . .’text’ , 4 3 , . . . ’edit’ , 2 0 , . . . ’radiobutton’ , 4 , . . . ’listbox’ ,2 ) , . . . ’override’ , 0 , . . . ’release’ , 1 3 , . . . ’resize’ , ’none’ ,

740 . . . ’accessibility’ , ’callback’ , . . . ’mfile’ , 1 , . . . ’callbacks’ ,1 , . . . ’singleton’ , 1 , . . . ’syscolorfig’ , 1 , . . . ’lastSavedFile’ ,’C:\MatlabWork\GoodScripts\UISignalSimulation.m’ ) ) ;

745 h2 = axes( . . . ’Parent’ , h1 , . . . ’ALim’ , g e t ( 0 ,’defaultaxesALim’ ) , . . .’ALimMode’ ,’manual’ , . . . ’CameraPosition’ , [ 0 . 5 0 . 59 . 1 6 0 2 5 4 0 3 7 8 4 4 3 9 ] , . . .’CameraPositionMode’ ,’manual’ , . . .’CameraTarget’ , [ 0 . 5 0 . 5 0 . 5 ] , . . . ’CameraTargetMode’ ,’manual’ , . . .’CameraUpVector’ , [ 0 1 0 ] , . . . ’CameraUpVectorMode’ ,’manual’ , . . .

750 ’CameraViewAngle’ , 6 . 6 0 8 6 1 0 3 6 0 3 1 1 9 2 , . . .’CameraViewAngleMode’ ,’manual’ , . . .’CLim’ , g e t ( 0 ,’defaultaxesCLim’ ) , . . . ’CLimMode’ ,’manual’ , . . .’Color’ , g e t ( 0 ,’defaultaxesColor’ ) , . . .’ColorOrder’ , g e t ( 0 ,’defaultaxesColorOrder’ ) , . . .

755 ’DataAspectRatio’ , g e t ( 0 ,’defaultaxesDataAspectRatio’ ) , . . .’DataAspectRatioMode’ ,’manual’ , . . .’PlotBoxAspectRatio’ , g e t ( 0 ,’defaultaxesPlotBoxAspectRatio’ ) , . . .’PlotBoxAspectRatioMode’ ,’manual’ , . . .’Position’ , [ 0 .324468085106383 0 .0507692307692308 0 .661702127659574

760 0 . 6 0 9 2 3 0 7 6 9 2 3 0 7 6 9 ] , . . .’TickDir’ , g e t ( 0 ,’defaultaxesTickDir’ ) , . . .’TickDirMode’ ,’manual’ , . . . ’XColor’ , g e t ( 0 ,’defaultaxesXColor’ ) , . . .’XLim’ , g e t ( 0 ,’defaultaxesXLim’ ) , . . . ’XLimMode’ ,’manual’ , . . .’XTick’ , [ 0 0 . 2 0 . 4 0 . 6 0 . 8 1 ] , . . .’XTickLabel’ , ’0 ’ ’0.2’ ’0.4’’0.6’ ’0.8’ ’1 ’ , . . . ’XTickLabelMode’ ,’manual’ , . . .

765 ’XTickMode’ ,’manual’ , . . . ’YColor’ , g e t ( 0 ,’defaultaxesYColor’ ) , . . .’YLim’ , g e t ( 0 ,’defaultaxesYLim’ ) , . . . ’YLimMode’ ,’manual’ , . . .’YTick’ , [ 0 0 . 2 0 . 4 0 . 6 0 . 8 1 ] , . . .’YTickLabel’ , ’0 ’ ’0.2’ ’0.4’’0.6’ ’0.8’ ’1 ’ , . . . ’YTickLabelMode’ ,’manual’ , . . .’YTickMode’ ,’manual’ , . . . ’ZColor’ , g e t ( 0 ,’defaultaxesZColor’ ) , . . .

770 ’ZLim’ , g e t ( 0 ,’defaultaxesZLim’ ) , . . . ’ZLimMode’ ,’manual’ , . . .’ZTick’ , [ 0 0 . 5 1 ] , . . . ’ZTickLabel’ ,’’ , . . .’ZTickLabelMode’ ,’manual’ , . . . ’ZTickMode’ ,’manual’ , . . .’Tag’ ,’axes1’ , . . . ’UserData’ , z e r o s( 1 , 0 ) ) ;

775

104


h3 = g e t( h2 ,’title’ ) ;

s e t( h3 , . . . ’Parent’ , h2 , . . . ’Color’ , [ 0 0 0 ] , . . .’HorizontalAlignment’ ,’center’ , . . . ’Position’ , [0 .496575342465753

780 1 . 0 4 4 5 2 0 5 4 7 9 4 5 2 1 1 . 0 0 0 0 5 4 5 9 9 3 7 2 0 5 ] , . . .’VerticalAlignment’ ,’bottom’ , . . . ’HandleVisibility’ ,’off’ ) ;

h4 = g e t( h2 ,’xlabel’ ) ;

785 s e t( h4 , . . . ’Parent’ , h2 , . . . ’Color’ , [ 0 0 0 ] , . . .’HorizontalAlignment’ ,’center’ , . . . ’Position’ , [0 .496575342465753−0 .160958904109589 1 .00005459937205 ] , . . .’VerticalAlignment’ ,’cap’ , . . . ’HandleVisibility’ ,’off’ ) ;

790 h5 = g e t( h2 ,’ylabel’ ) ;

s e t( h5 , . . . ’Parent’ , h2 , . . . ’Color’ , [ 0 0 0 ] , . . .’HorizontalAlignment’ ,’center’ , . . . ’Position’ , [ −0.07196969696969690 . 4 9 6 2 1 2 1 2 1 2 1 2 1 2 1 1 . 0 0 0 0 5 4 5 9 9 3 7 2 0 5 ] , . . .’Rotation’ , 9 0 , . . .

795 ’VerticalAlignment’ ,’bottom’ , . . . ’HandleVisibility’ ,’off’ ) ;

h6 = g e t( h2 ,’zlabel’ ) ;

s e t( h6 , . . . ’Parent’ , h2 , . . . ’Color’ , [ 0 0 0 ] , . . .800 ’HorizontalAlignment’ ,’right’ , . . . ’Position’ , [ −1.05681818181818

1 . 5 5 4 2 9 2 9 2 9 2 9 2 9 3 1 . 0 0 0 0 5 4 5 9 9 3 7 2 0 5 ] , . . .’HandleVisibility’ ,’off’ , . . . ’Visible’ ,’off’ ) ;

h7 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .805 ’CData’ , z e r o s( 1 , 0 ) , . . . ’ListboxTop’ , 0 , . . . ’Position’ , [ 9

7 . 5 3 8 4 6 1 5 3 8 4 6 1 5 4 4 0 . 2 9 . 3 0 7 6 9 2 3 0 7 6 9 2 3 1 ] , . . .’String’ , ’’ , . . .’Style’ ,’frame’ , . . . ’Tag’ ,’frame10’ , . . . ’UserData’ , z e r o s( 1 , 0 ) ) ;

810 h8 = uimenu( . . . ’Parent’ , h1 , . . .’Callback’ ,’UISignalSimulation_export(’’FileMenu_Callback’’,gcbo,[],guidata(gcbo))’ , . . .’Label’ ,’File’ , . . . ’Tag’ ,’FileMenu’ ) ;

h9 = uimenu( . . . ’Parent’ , h8 , . . .815 ’Callback’ ,’UISignalSimulation_export(’’OpenMenuItem_Callback’’,gcbo,[],guidata(gcbo))’ , . . .

’Label’ ,’Open ...’ , . . . ’Tag’ ,’OpenMenuItem’ ) ;

h10 = uimenu( . . . ’Parent’ , h8 , . . .’Callback’ ,’UISignalSimulation_export(’’PrintMenuItem_Callback’’,gcbo,[],guidata(gcbo))’ , . . .

820 ’Label’ ,’Print ...’ , . . . ’Tag’ ,’PrintMenuItem’ ) ;

h11 = uimenu( . . . ’Parent’ , h8 , . . .’Callback’ ,’UISignalSimulation_export(’’CloseMenuItem_Callback’’,gcbo,[],guidata(gcbo))’ , . . .’Label’ ,’Close’ , . . . ’Separator’ ,’on’ , . . . ’Tag’ ,’CloseMenuItem’ ) ;

825

h12 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’ListboxTop’ , 0 , . . . ’Position’ , [ 4 7 . 2 4 7 . 0 7 6 9 2 3 0 7 6 9 2 3 1 8 6 . 82 . 2 3 0 7 6 9 2 3 0 7 6 9 2 3 ] , . . .’String’ , ’’ , . . . ’Style’ ,’frame’ , . . .’Tag’ ,’frame8’ ) ;

830

h13 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’CData’ , z e r o s( 1 , 0 ) , . . . ’ListboxTop’ , 0 , . . . ’Position’ , [ 8 . 43 7 . 7 6 9 2 3 0 7 6 9 2 3 0 8 3 9 . 8 8 . 3 8 4 6 1 5 3 8 4 6 1 5 3 9 ] , . . .’String’ , ’’ , . . .

835 ’Style’ ,’frame’ , . . . ’Tag’ ,’frame1’ , . . . ’UserData’ , z e r o s( 1 , 0 ) ) ;

h14 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’ListboxTop’ , 0 , . . . ’Position’ , [ 8 . 4 3 7 . 3 8 4 6 1 5 3 8 4 6 1 5 4 3 9 . 8

840 4 . 2 3 0 7 6 9 2 3 0 7 6 9 2 3 ] , . . .’String’ , ’’ , . . . ’Style’ ,’frame’ , . . .’Tag’ ,’frame2’ ) ;

h15 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’normalized’ , . . .845 ’Callback’ ,’UISignalSimulation_export(’’pushbutton1_Callback’’,gcbo,[],guidata(gcbo))’ , . . .

’CData’ , z e r o s( 1 , 0 ) , . . . ’ListboxTop’ , 0 , . . .’Position’ , [ 0 .66088840736728 0 .815580286168521 0 .2448537378114840 . 1 0 9 6 9 7 9 3 3 2 2 7 3 4 5 ] , . . .’String’ ,’Execute’ , . . .

105


’Tag’ ,’pushbutton1’ , . . . ’UserData’ , z e r o s( 1 , 0 ) ) ;850

h16 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’ListboxTop’ , 0 , . . . ’Position’ , [ 1 3 . 6 4 2 8 . 4 1 . 1 5 3 8 4 6 1 5 3 8 4 6 1 5 ] , . . .’String’ ,’Distance’ , . . . ’Style’ ,’text’ , . . . ’Tag’ ,’text2’ ) ;

855

h17 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’BackgroundColor’ , [ 1 1 1 ] , . . .’Callback’ ,’UISignalSimulation_export(’’D_target_1_Callback’’,gcbo,[],guidata(gcbo))’ , . . .

860 ’ListboxTop’ , 0 , . . . ’Position’ , [ 2 4 . 6 4 1 . 8 4 6 1 5 3 8 4 6 1 5 3 8 1 41 . 4 6 1 5 3 8 4 6 1 5 3 8 4 6 ] , . . .’String’ ,’0’ , . . . ’Style’ ,’edit’ , . . .’CreateFcn’ ,’UISignalSimulation_export(’’D_target_1_CreateFcn’’,gcbo,[],guidata(gcbo))’ , . . .’Tag’ ,’D_target_1’ ) ;

865

h18 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’ListboxTop’ , 0 , . . . ’Position’ , [ 4 0 . 2 4 2 3 . 2 1 . 1 5 3 8 4 6 1 5 3 8 4 6 1 5 ] , . . .’String’ ,’[m]’ , . . . ’Style’ ,’text’ , . . . ’Tag’ ,’text4’ ) ;

870

h19 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’ListboxTop’ , 0 , . . . ’Position’ , [ 1 5 . 6 3 9 . 9 2 3 0 7 6 9 2 3 0 7 6 9 6 . 41 . 1 5 3 8 4 6 1 5 3 8 4 6 1 5 ] , . . .’String’ ,’Power’ , . . . ’Style’ ,’text’ , . . .’Tag’ ,’text5’ ) ;

875

h20 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’ListboxTop’ , 0 , . . . ’Position’ , [ 1 3 . 6 3 8 . 3 0 7 6 9 2 3 0 7 6 9 2 3 8 . 41 . 1 5 3 8 4 6 1 5 3 8 4 6 1 5 ] , . . .’String’ ,’Distance’ , . . . ’Style’ ,’text’ , . . .

880 ’Tag’ ,’text6’ ) ;

h21 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’BackgroundColor’ , [ 1 1 1 ] , . . .

885 ’Callback’ ,’UISignalSimulation_export(’’P_target_2_Callback’’,gcbo,[],guidata(gcbo))’ , . . .’ListboxTop’ , 0 , . . . ’Position’ , [ 2 4 . 6 3 9 . 7 6 9 2 3 0 7 6 9 2 3 0 8 1 41 . 4 6 1 5 3 8 4 6 1 5 3 8 4 6 ] , . . .’String’ ,’0’ , . . . ’Style’ ,’edit’ , . . .’CreateFcn’ ,’UISignalSimulation_export(’’P_target_2_CreateFcn’’,gcbo,[],guidata(gcbo))’ , . . .’Tag’ ,’P_target_2’ ) ;

890

h22 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’ListboxTop’ , 0 , . . . ’Position’ , [ 4 0 . 2 3 9 . 9 2 3 0 7 6 9 2 3 0 7 6 9 3 . 21 . 1 5 3 8 4 6 1 5 3 8 4 6 1 5 ] , . . .’String’ ,’[W]’ , . . . ’Style’ ,’text’ , . . .

895 ’Tag’ ,’text7’ ) ;


900 ’Callback’ ,’UISignalSimulation_export(’’D_target_2_Callback’’,gcbo,[],guidata(gcbo))’ , . . .’ListboxTop’ , 0 , . . . ’Position’ , [ 2 4 . 6 3 8 . 1 5 3 8 4 6 1 5 3 8 4 6 2 1 41 . 4 6 1 5 3 8 4 6 1 5 3 8 4 6 ] , . . .’String’ ,’0’ , . . . ’Style’ ,’edit’ , . . .’CreateFcn’ ,’UISignalSimulation_export(’’D_target_2_CreateFcn’’,gcbo,[],guidata(gcbo))’ , . . .’Tag’ ,’D_target_2’ ) ;

905

h24 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’ListboxTop’ , 0 , . . . ’Position’ , [ 4 0 . 2 3 8 . 3 0 7 6 9 2 3 0 7 6 9 2 3 3 . 21 . 1 5 3 8 4 6 1 5 3 8 4 6 1 5 ] , . . .’String’ ,’[m]’ , . . . ’Style’ ,’text’ , . . .

910 ’Tag’ ,’text8’ ) ;

h25 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’CData’ , z e r o s( 1 , 0 ) , . . . ’ListboxTop’ , 0 , . . . ’Position’ , [ 1 5 . 6

915 4 3 . 6 1 5 3 8 4 6 1 5 3 8 4 6 6 . 4 1 . 1 5 3 8 4 6 1 5 3 8 4 6 1 5 ] , . . .’String’ ,’Power’ , . . .’Style’ ,’text’ , . . . ’Tag’ ,’text1’ , . . . ’UserData’ , z e r o s( 1 , 0 ) ) ;

h26 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .920 ’BackgroundColor’ , [ 1 1 1 ] , . . .

’Callback’ ,’UISignalSimulation_export(’’P_target_1_Callback’’,gcbo,[],guidata(gcbo))’ , . . .

106


’CData’ , z e r o s( 1 , 0 ) , . . . ’ListboxTop’ , 0 , . . . ’Position’ , [ 2 4 . 64 3 . 4 6 1 5 3 8 4 6 1 5 3 8 5 1 4 1 . 4 6 1 5 3 8 4 6 1 5 3 8 4 6 ] , . . .’String’ ,’0’ , . . .’Style’ ,’edit’ , . . .

925 ’CreateFcn’ ,’UISignalSimulation_export(’’P_target_1_CreateFcn’’,gcbo,[],guidata(gcbo))’ , . . .’Tag’ ,’P_target_1’ , . . . ’UserData’ , z e r o s( 1 , 0 ) ) ;

h27 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .930 ’CData’ , z e r o s( 1 , 0 ) , . . . ’ListboxTop’ , 0 , . . . ’Position’ , [ 4 0 . 2

4 3 . 6 1 5 3 8 4 6 1 5 3 8 4 6 3 . 2 1 . 1 5 3 8 4 6 1 5 3 8 4 6 1 5 ] , . . .’String’ ,’[W]’ , . . .’Style’ ,’text’ , . . . ’Tag’ ,’text3’ , . . . ’UserData’ , z e r o s( 1 , 0 ) ) ;

935 h28 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’CData’ , z e r o s( 1 , 0 ) , . . . ’ListboxTop’ , 0 , . . . ’Position’ , [ 8 . 4 3 3 3 9 . 83 . 2 3 0 7 6 9 2 3 0 7 6 9 2 3 ] , . . .’String’ , ’’ , . . . ’Style’ ,’frame’ , . . .’Tag’ ,’frame3’ , . . . ’UserData’ , z e r o s( 1 , 0 ) ) ;

940

h29 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’CData’ , z e r o s( 1 , 0 ) , . . . ’ListboxTop’ , 0 , . . . ’Position’ , [ 1 5 . 63 3 . 9 2 3 0 7 6 9 2 3 0 7 6 9 6 . 4 1 . 1 5 3 8 4 6 1 5 3 8 4 6 1 5 ] , . . .’String’ ,’Power’ , . . .’Style’ ,’text’ , . . . ’Tag’ ,’text9’ , . . . ’UserData’ , z e r o s( 1 , 0 ) ) ;

945

h30 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’BackgroundColor’ , [ 1 1 1 ] , . . .’Callback’ ,’UISignalSimulation_export(’’P_noise_Callback’’,gcbo,[],guidata(gcbo))’ , . . .

950 ’CData’ , z e r o s( 1 , 0 ) , . . . ’ListboxTop’ , 0 , . . . ’Position’ , [ 2 4 . 63 3 . 7 6 9 2 3 0 7 6 9 2 3 0 8 1 4 1 . 4 6 1 5 3 8 4 6 1 5 3 8 4 6 ] , . . .’String’ ,’0’ , . . .’Style’ ,’edit’ , . . .’CreateFcn’ ,’UISignalSimulation_export(’’P_noise_CreateFcn’’,gcbo,[],guidata(gcbo))’ , . . .’Tag’ ,’P_noise’ , . . . ’UserData’ , z e r o s( 1 , 0 ) ) ;

955

h31 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’CData’ , z e r o s( 1 , 0 ) , . . . ’ListboxTop’ , 0 , . . . ’Position’ , [ 4 0 . 23 3 . 9 2 3 0 7 6 9 2 3 0 7 6 9 3 . 2 1 . 1 5 3 8 4 6 1 5 3 8 4 6 1 5 ] , . . .’String’ ,’[W]’ , . . .

960 ’Style’ ,’text’ , . . . ’Tag’ ,’text10’ , . . . ’UserData’ , z e r o s( 1 , 0 ) ) ;

h32 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’CData’ , z e r o s( 1 , 0 ) , . . . ’ListboxTop’ , 0 , . . . ’Position’ , [ 8 . 4

965 2 0 . 7 6 9 2 3 0 7 6 9 2 3 0 8 3 9 . 8 1 1 ] , . . .’String’ , ’’ , . . .’Style’ ,’frame’ , . . . ’Tag’ ,’frame4’ , . . . ’UserData’ , z e r o s( 1 , 0 ) ) ;

h33 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .970 ’ListboxTop’ , 0 , . . . ’Position’ , [ 8 . 4 2 0 . 3 0 7 6 9 2 3 0 7 6 9 2 3 3 9 . 8

5 . 6 1 5 3 8 4 6 1 5 3 8 4 6 2 ] , . . .’String’ , ’’ , . . . ’Style’ ,’frame’ , . . .’Tag’ ,’frame5’ ) ;

975 h34 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’CData’ , z e r o s( 1 , 0 ) , . . . ’ListboxTop’ , 0 , . . . ’Position’ , [ 1 5 . 62 9 . 4 6 1 5 3 8 4 6 1 5 3 8 5 6 . 4 1 . 1 5 3 8 4 6 1 5 3 8 4 6 1 5 ] , . . .’String’ ,’Power’ , . . .’Style’ ,’text’ , . . . ’Tag’ ,’text11’ , . . . ’UserData’ , z e r o s( 1 , 0 ) ) ;

980

h35 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’ListboxTop’ , 0 , . . . ’Position’ , [ 1 1 . 8 2 7 . 6 9 2 3 0 7 6 9 2 3 0 7 7 1 0 . 21 . 3 0 7 6 9 2 3 0 7 6 9 2 3 1 ] , . . .’String’ ,’Start Freq.’ , . . .’Style’ ,’text’ , . . . ’Tag’ ,’text12’ ) ;

985

h36 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’BackgroundColor’ , [ 1 1 1 ] , . . .’Callback’ ,’UISignalSimulation_export(’’P_jammer_1_Callback’’,gcbo,[],guidata(gcbo))’ , . . .

990 ’CData’ , z e r o s( 1 , 0 ) , . . . ’ListboxTop’ , 0 , . . . ’Position’ , [ 2 4 . 62 9 . 3 0 7 6 9 2 3 0 7 6 9 2 3 1 4 1 . 4 6 1 5 3 8 4 6 1 5 3 8 4 6 ] , . . .’String’ ,’0’ , . . .’Style’ ,’edit’ , . . .’CreateFcn’ ,’UISignalSimulation_export(’’P_jammer_1_CreateFcn’’,gcbo,[],guidata(gcbo))’ , . . .’Tag’ ,’P_jammer_1’ , . . . ’UserData’ , z e r o s( 1 , 0 ) ) ;

107


995

h37 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’CData’ , z e r o s( 1 , 0 ) , . . . ’ListboxTop’ , 0 , . . . ’Position’ , [ 4 0 . 22 9 . 4 6 1 5 3 8 4 6 1 5 3 8 5 3 . 2 1 . 1 5 3 8 4 6 1 5 3 8 4 6 1 5 ] , . . .’String’ ,’[W]’ , . . .

1000 ’Style’ ,’text’ , . . . ’Tag’ ,’text13’ , . . . ’UserData’ , z e r o s( 1 , 0 ) ) ;


1005 ’Callback’ ,’UISignalSimulation_export(’’StartFreq_jammer_1_Callback’’,gcbo,[],...guidata(gcbo))’ , ’ListboxTop’ , 0 , . . . ’Position’ , [ 2 4 . 62 7 . 6 9 2 3 0 7 6 9 2 3 0 7 7 1 4 1 . 4 6 1 5 3 8 4 6 1 5 3 8 4 6 ] , . . .’String’ ,’0’ , . . .’Style’ ,’edit’ , . . .’CreateFcn’ ,’UISignalSimulation_export(’’StartFreq_jammer_1_CreateFcn’’,...

1010 gcbo,[],guidata(gcbo))’ ,’Tag’ ,’StartFreq_jammer_1’ ) ;

h39 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’ListboxTop’ , 0 , . . . ’Position’ , [ 4 0 . 2 2 7 . 8 4 6 1 5 3 8 4 6 1 5 3 8 5 . 4

1015 1 . 1 5 3 8 4 6 1 5 3 8 4 6 1 5 ] , . . .’String’ ,’[MHz]’ , . . . ’Style’ ,’text’ , . . .’Tag’ ,’text14’ ) ;

h40 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .1020 ’ListboxTop’ , 0 , . . . ’Position’ , [ 1 1 . 6 2 6 . 2 3 0 7 6 9 2 3 0 7 6 9 2 1 0 . 4

1 . 1 5 3 8 4 6 1 5 3 8 4 6 1 5 ] , . . .’String’ ,’Bandwidth’ , . . . ’Style’ ,’text’ , . . .’Tag’ ,’text15’ ) ;

1025 h41 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’BackgroundColor’ , [ 1 1 1 ] , . . .’Callback’ ,’UISignalSimulation_export(’’Bandwidth_jammer_1_Callback’’,gcbo,[],...guidata(gcbo))’ , ’ListboxTop’ , 0 , . . . ’Position’ , [ 2 4 . 62 6 . 0 7 6 9 2 3 0 7 6 9 2 3 1 1 4 1 . 4 6 1 5 3 8 4 6 1 5 3 8 4 6 ] , . . .’String’ ,’0’ , . . .

1030 ’Style’ ,’edit’ , . . .’CreateFcn’ ,’UISignalSimulation_export(’’Bandwidth_jammer_1_CreateFcn’’,gcbo,[],...guidata(gcbo))’ , ’Tag’ ,’Bandwidth_jammer_1’ ) ;

1035 h42 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’ListboxTop’ , 0 , . . . ’Position’ , [ 4 0 . 2 2 6 . 2 3 0 7 6 9 2 3 0 7 6 9 2 5 . 41 . 1 5 3 8 4 6 1 5 3 8 4 6 1 5 ] , . . .’String’ ,’[MHz]’ , . . . ’Style’ ,’text’ , . . .’Tag’ ,’text17’ ) ;

1040

h43 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’CData’ , z e r o s( 1 , 0 ) , . . . ’ListboxTop’ , 0 , . . . ’Position’ , [ 1 5 . 62 4 . 3 8 4 6 1 5 3 8 4 6 1 5 4 6 . 4 1 . 1 5 3 8 4 6 1 5 3 8 4 6 1 5 ] , . . .’String’ ,’Power’ , . . .’Style’ ,’text’ , . . . ’Tag’ ,’text23’ , . . . ’UserData’ , z e r o s( 1 , 0 ) ) ;

1045

h44 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’ListboxTop’ , 0 , . . . ’Position’ , [ 1 1 . 8 2 2 . 6 1 5 3 8 4 6 1 5 3 8 4 6 1 0 . 21 . 3 0 7 6 9 2 3 0 7 6 9 2 3 1 ] , . . .’String’ ,’Start Freq.’ , . . .

1050 ’Style’ ,’text’ , . . . ’Tag’ ,’text24’ ) ;


1055 ’Callback’ ,’UISignalSimulation_export(’’P_jammer_2_Callback’’,gcbo,[],guidata(gcbo))’ , . . .’CData’ , z e r o s( 1 , 0 ) , . . . ’ListboxTop’ , 0 , . . . ’Position’ , [ 2 4 . 62 4 . 2 3 0 7 6 9 2 3 0 7 6 9 2 1 4 1 . 4 6 1 5 3 8 4 6 1 5 3 8 4 6 ] , . . .’String’ ,’0’ , . . .’Style’ ,’edit’ , . . .’CreateFcn’ ,’UISignalSimulation_export(’’P_jammer_2_CreateFcn’’,gcbo,[],...

1060 guidata(gcbo))’ , ’Tag’ ,’P_jammer_2’ , . . . ’UserData’ , z e r o s( 1 , 0 ) ) ;


1065 2 4 . 3 8 4 6 1 5 3 8 4 6 1 5 4 3 . 2 1 . 1 5 3 8 4 6 1 5 3 8 4 6 1 5 ] , . . .’String’ ,’[W]’ , . . .’Style’ ,’text’ , . . . ’Tag’ ,’text25’ , . . . ’UserData’ , z e r o s( 1 , 0 ) ) ;

108



’Callback’ ,’UISignalSimulation_export(’’StartFreq_jammer_2_Callback’’,gcbo,[],...guidata(gcbo))’ , ’ListboxTop’ , 0 , . . . ’Position’ , [ 2 4 . 62 2 . 6 1 5 3 8 4 6 1 5 3 8 4 6 1 4 1 . 4 6 1 5 3 8 4 6 1 5 3 8 4 6 ] , . . .’String’ ,’0’ , . . .’Style’ ,’edit’ , . . .

1075 ’CreateFcn’ ,’UISignalSimulation_export(’’StartFreq_jammer_2_CreateFcn’’,gcbo,[],...guidata(gcbo))’ , ’Tag’ ,’StartFreq_jammer_2’ ) ;

h48 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .1080 ’ListboxTop’ , 0 , . . . ’Position’ , [ 4 0 . 2 2 2 . 7 6 9 2 3 0 7 6 9 2 3 0 8 5 . 4

1 . 1 5 3 8 4 6 1 5 3 8 4 6 1 5 ] , . . .’String’ ,’[MHz]’ , . . . ’Style’ ,’text’ , . . .’Tag’ ,’text26’ ) ;

1085 h49 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’ListboxTop’ , 0 , . . . ’Position’ , [ 1 1 . 6 2 1 . 1 5 3 8 4 6 1 5 3 8 4 6 2 1 0 . 41 . 1 5 3 8 4 6 1 5 3 8 4 6 1 5 ] , . . .’String’ ,’Bandwidth’ , . . . ’Style’ ,’text’ , . . .’Tag’ ,’text27’ ) ;

1090

h50 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’BackgroundColor’ , [ 1 1 1 ] , . . .’Callback’ ,’UISignalSimulation_export(’’Bandwidth_jammer_2_Callback’’,gcbo,[],...guidata(gcbo))’ , ’ListboxTop’ , 0 , . . . ’Position’ , [ 2 4 . 6 2 1 1 4

1095 1 . 4 6 1 5 3 8 4 6 1 5 3 8 4 6 ] , . . .’String’ ,’0’ , . . . ’Style’ ,’edit’ , . . .’CreateFcn’ ,’UISignalSimulation_export(’’Bandwidth_jammer_2_CreateFcn’’,gcbo,[],...guidata(gcbo))’ , ’Tag’ ,’Bandwidth_jammer_2’ ) ;

1100 h51 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’ListboxTop’ , 0 , . . . ’Position’ , [ 4 0 . 2 2 1 . 1 5 3 8 4 6 1 5 3 8 4 6 2 5 . 41 . 1 5 3 8 4 6 1 5 3 8 4 6 1 5 ] , . . .’String’ ,’[MHz]’ , . . . ’Style’ ,’text’ , . . .’Tag’ ,’text28’ ) ;

1105

h52 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’ListboxTop’ , 0 , . . . ’Position’ , [ 1 1 . 2 4 5 . 3 0 7 6 9 2 3 0 7 6 9 2 3 1 0 . 21 . 1 5 3 8 4 6 1 5 3 8 4 6 1 5 ] , . . .’String’ ,’Target(s)’ , . . . ’Style’ ,’text’ , . . .’Tag’ ,’text29’ ) ;

1110

h53 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’ListboxTop’ , 0 , . . . ’Position’ , [ 1 1 . 2 3 5 . 6 1 5 3 8 4 6 1 5 3 8 4 6 71 . 1 5 3 8 4 6 1 5 3 8 4 6 1 5 ] , . . .’String’ ,’Noise’ , . . . ’Style’ ,’text’ , . . .

1115 ’Tag’ ,’text30’ ) ;

h54 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’ListboxTop’ , 0 , . . . ’Position’ , [ 1 1 . 2 3 1 1 1 . 8 1 . 3 0 7 6 9 2 3 0 7 6 9 2 3 1 ] , . . .

1120 ’String’ ,’Jammer(s)’ , . . . ’Style’ ,’text’ , . . . ’Tag’ ,’text31’ ) ;


1125 3 5 . 2 3 0 7 6 9 2 3 0 7 6 9 2 5 5 . 8 1 0 . 9 2 3 0 7 6 9 2 3 0 7 6 9 ] , . . .’String’ , ’’ , . . .’Style’ ,’frame’ , . . . ’Tag’ ,’frame7’ , . . . ’UserData’ , z e r o s( 1 , 0 ) ) ;


1 . 2 3 0 7 6 9 2 3 0 7 6 9 2 3 ] , . . .’String’ ,’Simulation time (micro sec)’ , . . .’Style’ ,’text’ , . . . ’Tag’ ,’text32’ ) ;

1135 h57 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’BackgroundColor’ , [ 1 1 1 ] , . . .’Callback’ ,’UISignalSimulation_export(’’SimTime_Callback’’,gcbo,[],guidata(gcbo))’ , . . .’CData’ , z e r o s( 1 , 0 ) , . . . ’ListboxTop’ , 0 , . . . ’Position’ , [ 854 3 . 2 3 0 7 6 9 2 3 0 7 6 9 2 1 4 1 . 4 6 1 5 3 8 4 6 1 5 3 8 4 6 ] , . . .’String’ ,’300’ , . . .

1140 ’Style’ ,’edit’ , . . .

109


’CreateFcn’ ,’UISignalSimulation_export(’’SimTime_CreateFcn’’,gcbo,[],guidata(gcbo))’ , . . .’Tag’ ,’SimTime’ , . . . ’UserData’ , z e r o s( 1 , 0 ) ) ;

1145 h58 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’Callback’ ,’UISignalSimulation_export(’’rect_Callback’’,gcbo,[],guidata(gcbo))’ , . . .’ListboxTop’ , 0 , . . . ’Position’ , [ 5 5 . 8 4 1 . 6 9 2 3 0 7 6 9 2 3 0 7 7 1 5 . 21 . 1 5 3 8 4 6 1 5 3 8 4 6 1 5 ] , . . .’String’ ,’Rectangular’ , . . .’Style’ ,’radiobutton’ , . . . ’Tag’ ,’rect’ ) ;

1150

h59 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’Callback’ ,’UISignalSimulation_export(’’sine_Callback’’,gcbo,[],guidata(gcbo))’ , . . .’ListboxTop’ , 0 , . . . ’Position’ , [ 5 5 . 8 4 0 7 . 8 1 . 1 5 3 8 4 6 1 5 3 8 4 6 1 5 ] , . . .

1155 ’String’ ,’Sine’ , . . . ’Style’ ,’radiobutton’ , . . . ’Tag’ ,’sine’ ) ;

h60 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’Callback’ ,’UISignalSimulation_export(’’chirp_Callback’’,gcbo,[],guidata(gcbo))’ , . . .

1160 ’ListboxTop’ , 0 , . . . ’Position’ , [ 5 5 . 8 3 8 . 2 3 0 7 6 9 2 3 0 7 6 9 2 8 . 61 . 1 5 3 8 4 6 1 5 3 8 4 6 1 5 ] , . . .’String’ ,’Chirp’ , . . .’Style’ ,’radiobutton’ , . . . ’Tag’ ,’chirp’ ) ;

1165 h61 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’ListboxTop’ , 0 , . . . ’Position’ , [ 6 4 . 4 3 9 . 9 2 3 0 7 6 9 2 3 0 7 6 9 1 1 . 61 . 2 3 0 7 6 9 2 3 0 7 6 9 2 3 ] , . . .’String’ ,’: Frequency’ , . . .’Style’ ,’text’ , . . . ’Tag’ ,’fsine_txt’ , . . . ’Visible’ ,’off’ ) ;

1170

h62 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’ListboxTop’ , 0 , . . . ’Position’ , [ 6 5 . 2 3 8 . 1 5 3 8 4 6 1 5 3 8 4 6 2 2 0 . 81 . 2 3 0 7 6 9 2 3 0 7 6 9 2 3 ] , . . .’String’ ,’: Frequency deviation’ , . . .’Style’ ,’text’ , . . . ’Tag’ ,’maxFDev_txt’ , . . . ’Visible’ ,’off’ ) ;

1175

h63 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’BackgroundColor’ , [ 1 1 1 ] , . . .’Callback’ ,’UISignalSimulation_export(’’fsine_Callback’’,gcbo,[],guidata(gcbo))’ , . . .

1180 ’CData’ , z e r o s( 1 , 0 ) , . . . ’ListboxTop’ , 0 , . . . ’Position’ , [ 783 9 . 7 6 9 2 3 0 7 6 9 2 3 0 8 1 4 1 . 4 6 1 5 3 8 4 6 1 5 3 8 4 6 ] , . . .’String’ ,’1280’ , . . .’Style’ ,’edit’ , . . .’CreateFcn’ ,’UISignalSimulation_export(’’fsine_CreateFcn’’,gcbo,[],guidata(gcbo))’ , . . .’Tag’ ,’fsine’ , . . . ’UserData’ , z e r o s( 1 , 0 ) , . . . ’Visible’ ,’off’ ) ;

1185

h64 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’BackgroundColor’ , [ 1 1 1 ] , . . .’Callback’ ,’UISignalSimulation_export(’’maxFDev_Callback’’,gcbo,[],guidata(gcbo))’ , . . .

1190 ’CData’ , z e r o s( 1 , 0 ) , . . . ’ListboxTop’ , 0 , . . . ’Position’ , [ 8 8 3 8 1 41 . 4 6 1 5 3 8 4 6 1 5 3 8 4 6 ] , . . .’String’ ,’1.8’ , . . . ’Style’ ,’edit’ , . . .’CreateFcn’ ,’UISignalSimulation_export(’’maxFDev_CreateFcn’’,gcbo,[],guidata(gcbo))’ , . . .’Tag’ ,’maxFDev’ , . . . ’UserData’ , z e r o s( 1 , 0 ) , . . . ’Visible’ ,’off’ ) ;

1195

h65 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’ListboxTop’ , 0 , . . . ’Position’ , [ 9 3 . 2 3 9 . 6 9 2 3 0 7 6 9 2 3 0 7 7 5 . 41 . 3 8 4 6 1 5 3 8 4 6 1 5 3 8 ] , . . .’String’ ,’[MHz]’ , . . . ’Style’ ,’text’ , . . .’Tag’ ,’fsine_txt1’ , . . . ’Visible’ ,’off’ ) ;

1200

h66 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’ListboxTop’ , 0 , . . . ’Position’ , [ 1 0 2 . 8 3 8 5 . 4 1 . 3 8 4 6 1 5 3 8 4 6 1 5 3 8 ] , . . .’String’ ,’[MHz]’ , . . . ’Style’ ,’text’ , . . . ’Tag’ ,’maxFDev_txt1’ , . . .

1205 ’Visible’ ,’off’ ) ;

h67 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’ListboxTop’ , 0 , . . . ’Position’ , [ 6 4 3 6 . 0 7 6 9 2 3 0 7 6 9 2 3 1 2 0 . 8

1210 1 . 2 3 0 7 6 9 2 3 0 7 6 9 2 3 ] , . . .’String’ ,’: Carrier frequency’ , . . .’Style’ ,’text’ , . . . ’Tag’ ,’maxFDev_txt2’ , . . . ’Visible’ ,’off’ ) ;

110



’Callback’ ,’UISignalSimulation_export(’’carrierFreq_Callback’’,gcbo,[],guidata(gcbo))’ , . . .’CData’ , z e r o s( 1 , 0 ) , . . . ’ListboxTop’ , 0 , . . . ’Position’ , [ 8 8 3 6 1 41 . 4 6 1 5 3 8 4 6 1 5 3 8 4 6 ] , . . .’String’ ,’1280’ , . . . ’Style’ ,’edit’ , . . .’CreateFcn’ ,’UISignalSimulation_export(’’carrierFreq_CreateFcn’’,gcbo,[],...

1220 guidata(gcbo))’ , ’Tag’ ,’carrierFreq’ , . . . ’UserData’ , z e r o s( 1 , 0 ) , . . .’Visible’ ,’off’ ) ;

h69 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .1225 ’ListboxTop’ , 0 , . . . ’Position’ , [ 1 0 3 3 6 5 . 4 1 . 3 8 4 6 1 5 3 8 4 6 1 5 3 8 ] , . . .

’String’ ,’[MHz]’ , . . . ’Style’ ,’text’ , . . . ’Tag’ ,’maxFDev_txt3’ , . . .’Visible’ ,’off’ ) ;

1230 h70 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’FontAngle’ ,’italic’ , . . . ’FontSize’ , 1 2 , . . . ’ListboxTop’ , 0 , . . .’Position’ , [ 4 9 . 2 4 7 . 3 8 4 6 1 5 3 8 4 6 1 5 4 8 3 1 . 5 3 8 4 6 1 5 3 8 4 6 1 5 4 ] , . . .’String’ ,’Graphical User Interface (GUI) for Radar SignalSimulation’ , . . . ’Style’ ,’text’ , . . . ’Tag’ ,’text39’ ) ;

1235

h71 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’ListboxTop’ , 0 , . . . ’Position’ , [ 1 1 1 6 . 2 3 0 7 6 9 2 3 0 7 6 9 2 1 0 . 21 . 1 5 3 8 4 6 1 5 3 8 4 6 1 5 ] , . . .’String’ ,’Output’ , . . . ’Style’ ,’text’ , . . .

1240 ’Tag’ ,’text40’ ) ;

h72 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’ListboxTop’ , 0 , . . . ’Position’ , [ 1 4 1 4 . 3 0 7 6 9 2 3 0 7 6 9 2 3 1 7 . 6

1245 1 . 4 6 1 5 3 8 4 6 1 5 3 8 4 6 ] , . . .’String’ ,’* Real value signal’ , . . .’Style’ ,’text’ , . . . ’Tag’ ,’text41’ ) ;


1 . 1 5 3 8 4 6 1 5 3 8 4 6 1 5 ] , . . .’String’ ,’* Sampled at 750 MSPS’ , . . .’Style’ ,’text’ , . . . ’Tag’ ,’text42’ ) ;

1255 h74 = u i c o n t r o l ( . . . ’Parent’ , h1 , . . . ’Units’ ,’characters’ , . . .’Callback’ ,’UISignalSimulation_export(’’Save_simulated_signal_Callback’’,gcbo,[],...guidata(gcbo))’ , ’ListboxTop’ , 0 , . . . ’Position’ , [ 1 2 . 88 . 3 8 4 6 1 5 3 8 4 6 1 5 3 9 3 4 . 2 3 . 8 4 6 1 5 3 8 4 6 1 5 3 8 5 ] , . . .’String’ ,’Accept andsave simulated signal’ , . . . ’Tag’ ,’Save_simulated_signal’ ) ;

1260

h75 = uimenu( . . . ’Parent’ , h1 , . . .’Callback’ ,’UISignalSimulation_export(’’window_Callback’’,gcbo,[],guidata(gcbo))’ , . . .’Label’ ,’window’ , . . . ’Tag’ ,’window’ ) ;

1265

h76 = uimenu( . . . ’Parent’ , h75 , . . .’Callback’ ,’UISignalSimulation_export(’’FPGA_connect_Callback’’,gcbo,[],guidata(gcbo))’ , . . .’Label’ ,’FPGA connect’ , . . . ’Tag’ ,’FPGA_connect’ ) ;

1270

h s i n g l e t o n = h1 ;

%−−− Handles d e f a u l t GUIDE GUI c r e a t i o n and c a l l b a c k d i s p a t c h1275 f u n c t i o n v a r a r g o u t = g u i m a i n f c n ( g u i S t a t e , v a r a r g i n )

% GUI MAINFCN p r o v i d e s t h e s e command l i n e APIs f o r d e a l i n g wi th GUIs%

1280 % UISIGNALSIMULATION EXPORT , by i t s e l f , c r e a t e s a new UISIGNALSIMULATIONEXPORT% or r a i s e s t h e e x i s t i n g s i n g l e t o n∗ .%% H = UISIGNALSIMULATION EXPORT r e t u r n s t h e hand le t o a new UISIGNALSIMULATIONEXPORT% or t h e hand le t o t h e e x i s t i n g s i n g l e t o n∗ .

1285 %% UISIGNALSIMULATION EXPORT( ’CALLBACK’ , hObject , even tData , hand les , . . . ) c a l l s t h e l o c a l

111


% f u n c t i o n named CALLBACK i n UISIGNALSIMULATION EXPORT .M wi th t h e g iven in p u t a rguments .%% UISIGNALSIMULATION EXPORT( ’ P rope r t y ’ , ’ Value ’ , . . . ) c re a t e s a new

1290 % UISIGNALSIMULATION EXPORT or r a i s e s t h e e x i s t i n g s i n g l e t o n∗ . S t a r t i n g from t h e l e f t ,% p r o p e r t y v a l u e p a i r s a r e a p p l i e d t o t h e GUI b e f o r e u n t i t l e dO p e n i n g F u n c t i o n g e t s% c a l l e d . An u n r e c o g n i z e d p r o p e r t y name or i n v a l i d v a l u e makes p r o p e r t y a p p l i c a t i o n% s t o p . A l l i n p u t s a r e passed t o u nt i t l e d O p e n i n g F c n v i a v a r a r g i n .%

1295 % ∗See GUI Opt ions on GUIDE’ s Too ls menu . Choose ” GUIa l l o w s on ly one% i n s t a n c e t o run ( s i n g l e t o n ) ” .

% Copy r i gh t 1984−2002 The MathWorks , Inc .% $Rev i s i on : 1 . 4 $ $Date : 2 0 0 2 / 0 5 / 3 1 2 1 : 4 4 : 3 1 $

1300

g u i S t a t e F i e l d s = ’gui_Name’’gui_Singleton’’gui_OpeningFcn’’gui_OutputFcn’

1305 ’gui_LayoutFcn’’gui_Callback’ ;

g u i M f i l e = ’’ ; f o r i =1: l e n g t h( g u i S t a t e F i e l d s )i f ˜ i s f i e l d ( g u i S t a t e , g u i S t a t e F i e l d s i )

e r r o r (’Could not find field %s in the gui_State struct in GUI M-file %s’ , . . .1310 g u i S t a t e F i e l d s i , g u i M f i l e ) ;

e l s e i f i s e q u a l ( g u i S t a t e F i e l d s i , ’gui_Name’ )g u i M f i l e = [ g e t f i e l d ( g u i S t a t e , g u i S t a t e F i e l d s i ) , ’.m’ ] ;

endend

1315

numargin = l e n g t h( v a r a r g i n ) ;

i f numargin = = 0% UISIGNALSIMULATION EXPORT

1320 % c r e a t e t h e GUIg u i C r e a t e = 1 ;

e l s e i f numargin > 3 & i s c h a r ( v a r a r g i n1 ) & i s h a n d l e ( v a r a r g i n2 )% UISIGNALSIMULATION EXPORT( ’CALLBACK’ , hObject , even tData , hand les , . . . )g u i C r e a t e = 0 ;

1325 e l s e% UISIGNALSIMULATION EXPORT (. . . )% c r e a t e t h e GUI and hand v a r a r g i n t o t h e open ing f cng u i C r e a t e = 1 ;

end1330

i f g u i C r e a t e = = 0v a r a r g i n1 = g u i S t a t e . g u i C a l l b a c k ;i f n a r g o u t

[ v a r a r g o u t1: n a r g o u t ] = f e v a l ( v a r a r g i n : ) ;1335 e l s e

f e v a l ( v a r a r g i n : ) ;end

e l s ei f g u i S t a t e . g u i S i n g l e t o n

1340 g u i S i n g l e t o n O p t =’reuse’ ;e l s e

g u i S i n g l e t o n O p t =’new’ ;end

1345 % Open f i g f i l e w i th s t o r e d s e t t i n g s . Note : Th is e x e c u t e s a l l component% s p e c i f i c C r e a t e F u n c t i o n s wi th an emptyHANDLES s t r u c t u r e .

% Do f e v a l on l a y o u t code i n m− f i l e i f i t e x i s t si f ˜ i sempty( g u i S t a t e . gu i Layou tFcn )

1350 g u i h F i g u r e = f e v a l ( g u i S t a t e . gu i LayoutFcn , g u i S i n g l e t o n O p t ) ;e l s e

g u i h F i g u r e = l o c a l o p e n f i g ( g u i S t a t e . guiName , g u i S i n g l e t o n O p t ) ;% I f t h e f i g u r e has I n G U I I n i t i a l i z a t i o n i t was no t c o m pl e t e l y c re a t e d% on t h e l a s t pass . D e l e t e t h i s hand le and t r y ag a i n .

1355 i f i s a p p d a t a ( g u ih F i g u r e , ’InGUIInitialization’ )d e l e t e( g u i h F i g u r e ) ;g u i h F i g u r e = l o c a l o p e n f i g ( g u i S t a t e . guiName , g u i S i n g l e t o n O p t ) ;

endend

112


1360

% Set f l a g t o i n d i c a t e s t a r t i n g GUI i n i t i a l i z a t i o ns e t a p p d a t a ( g u ih F i g u r e ,’InGUIInitialization’ , 1 ) ;

% Fe tch GUIDE A p pl i c a t i o n o p t i o n s1365 g u i O p t i o n s = g e t a p p d a t a ( g u ih F i g u r e ,’GUIDEOptions’ ) ;

i f ˜ i s a p p d a t a ( g u ih F i g u r e ,’GUIOnScreen’ )% Ad jus t background c o l o ri f g u i O p t i o n s . s y s c o l o r f i g

1370 s e t( g u i h F i g u r e ,’Color’ , g e t ( 0 ,’DefaultUicontrolBackgroundColor’ ) ) ;end

% Genera te HANDLES s t r u c t u r e and s t o r e w i th GUIDATAg u i d a t a ( g u i h F i g u r e , g u i h a n d l e s ( g u ih F i g u r e ) ) ;

1375 end

% I f u s e r s p e c i f i e d ’ V i s i b l e ’ , ’ o f f ’ i n p / v p a i r s , don ’ t make t h e f i g u r e% v i s i b l e .gu i MakeV i s i b l e = 1 ;

1380 f o r i nd = 1 : 2 : l e n g t h( v a r a r g i n )i f l e n g t h ( v a r a r g i n ) = = ind

break;endlen1 = min ( l e n g t h(’visible’ ) , l e n g t h( v a r a r g i n i nd ) ) ;

1385 l en2 = min ( l e n g t h(’off’ ) , l e n g t h( v a r a r g i n i nd + 1 ) ) ;i f i s c h a r ( v a r a r g i n i nd ) & i s c h a r ( v a r a r g i n i nd + 1 ) & . . .

s t r n c m p i ( v a r a r g i n i nd ,’visible’ , l en1 ) & len2 > 1i f s t r n c m p i ( v a r a r g i n i nd +1 ,’off’ , l en2 )

gu i MakeV i s i b l e = 0 ;1390 e l s e i f s t r n c m p i ( v a r a r g i n i nd +1 ,’on’ , l en2 )

gu i MakeV i s i b l e = 1 ;end

endend

1395

% Check f o r f i g u r e param v a lu e p a i r sf o r i ndex = 1 : 2 :l e n g t h( v a r a r g i n )

i f l e n g t h ( v a r a r g i n ) = = indexbreak;

1400 endt r y , s e t( g u i h F i g u r e , v a r a r g i n i ndex , v a r a r g i n i ndex + 1 ) , ca tch , break , end

end

% I f hand le v i s i b i l i t y i s s e t t o ’c a l l b a c k ’ , t u r n i t on u n t i l f i n i s h e d1405 % wi th OpeningFcn

g u i H a n d l e V i s i b i l i t y = g e t( g u i h F i g u r e ,’HandleVisibility’ ) ;i f s t r cmp( g u i H a n d l e V i s i b i l i t y , ’callback’ )

s e t( g u i h F i g u r e ,’HandleVisibility’ , ’on’ ) ;end

1410

f e v a l ( g u i S t a t e . gu i OpeningFcn , g u ih F i g u r e , [ ] , g u i d a t a ( g u ih F i g u r e ) , v a r a r g i n : ) ;

i f i s h a n d l e ( g u i h F i g u r e )% Update hand le v i s i b i l i t y

1415 s e t( g u i h F i g u r e ,’HandleVisibility’ , g u i H a n d l e V i s i b i l i t y ) ;

% Make f i g u r e v i s i b l ei f gu i MakeV i s i b l e

s e t( g u i h F i g u r e , ’Visible’ , ’on’ )1420 i f g u i O p t i o n s . s i n g l e t o n

s e t a p p d a t a ( g u ih F i g u r e ,’GUIOnScreen’ , 1 ) ;end

end

1425 % Done wi th GUI i n i t i a l i z a t i o nrmappdata ( g u ih F i g u r e ,’InGUIInitialization’ ) ;

end

% I f hand le v i s i b i l i t y i s s e t t o ’c a l l b a c k ’ , t u r n i t on u n t i l f i n i s h e d wi th1430 % OutputFcn

i f i s h a n d l e ( g u i h F i g u r e )g u i H a n d l e V i s i b i l i t y = g e t( g u i h F i g u r e ,’HandleVisibility’ ) ;

113


i f s t rcmp( g u i H a n d l e V i s i b i l i t y , ’callback’ )s e t( g u i h F i g u r e ,’HandleVisibility’ , ’on’ ) ;

1435 endg u i H a n d l e s = g u i d a t a ( g u ih F i g u r e ) ;

e l s eg u i H a n d l e s = [ ] ;

end1440

i f n a r g o u t[ v a r a r g o u t1: n a r g o u t ] = f e v a l ( g u i S t a t e . gu i Outpu tFcn , g u i h F i g u r e , [ ] , g u i H a n d l e s ) ;

e l s ef e v a l ( g u i S t a t e . gu i Outpu tFcn , g u i h F i g u r e , [ ] , g u i H a n d l e s ) ;

1445 end

i f i s h a n d l e ( g u i h F i g u r e )s e t( g u i h F i g u r e ,’HandleVisibility’ , g u i H a n d l e V i s i b i l i t y ) ;

end1450 end

f u n c t i o n g u i h F i g u r e = l o c a l o p e n f i g ( name , s i n g l e t o n )i fn a r g i n(’openfig’ ) = = 3

g u i h F i g u r e = o p e n f i g ( name , s i n g l e t o n ,’auto’ ) ;1455 e l s e

% OPENFIG d id no t a c c e p t 3 rd i n p u t argument u n t i l R13 ,% t o g g l e d e f a u l t f i g u r e v i s i b l e t o p r e v e n t t h e f i g u r e% from showing up too soon .g u i O l d D e f a u l t V i s i b l e = g e t ( 0 ,’defaultFigureVisible’ ) ;

1460 s e t( 0 ,’defaultFigureVisible’ ,’off’ ) ;g u i h F i g u r e = o p e n f i g ( name , s i n g l e t o n ) ;s e t( 0 ,’defaultFigureVisible’ , g u i O l d D e f a u l t V i s i b l e ) ;

end

114

Appendix E

Matlab scripts general

E.1 Function: plotting PD and PFA

f u n c t i o n NoiseJammerPlo t ( Pno ise , Pjammer , noAv , t h r e s h o l d )

%NoiseJammerPlo t% P l o t s t h e PDF of a Chi−squa red d i s t r i b u t i o n f o r t h e g iven number o f

5 % a v e r a g e s ( o f t h e PSD ) , w i th t h e n o i s e f l o o r power and jammer power . The% t h r e s h o l d g i v e s t h e FAR ( F a l s e Alarm Rate ) and FRR ( F a l s e R e j e c t i o n% Rate )

%Checking i n p u t10 i f n a r g i n < 4 | n a r g i n > 4

e r r o r (’Requires 4 input arguments: Pnoise,Pjammer,noAv,threshold’ ) ;e l s e i f Pno i se <= 0 | Pjammer<=0

e r r o r (’Pnoise and/or Pjammer should have a value larger than zero’ ) ;e l s e i f mod ( noAv , 1 ) ˜ = 0 | noAv <= 0

15 e r r o r (’Number of Averages should be a positive integer’ ) ;e l s e i f t h r e s h o l d ==− I n f | t h r e s h o l d = = I n f

e r r o r (’Threshold cannot be a infinite element’ ) ;end

20 prob = ( 0 . 0 0 0 1 : 0 . 0 0 0 3 : 0 . 9 9 9 9 ) ’ ;%’%i t i s assumed t h a t t h e d a t a i s complex , so dof i s tw i ce t h e number o f Averagesdof = 2∗noAv ;%c a l c u l a t e p r o b a b i l i t y d e n s i t y f u n c t i o nx = c h i 2 i n v ( prob , dof ) ; y = c h i 2 p d f ( x , dof ) ;

25 %Set up c o r r e c t x− and y−a x i s f o r t h e d i f f e r e n tx1 = Pno ise / dof ∗ x ; x2 = Pjammer / dof ∗ x ; y1 = dof / Pno i se ∗ y ;y2 = dof / Pjammer ∗ y ;

%C a l c u l a t e t h e t o t a l chance f o r FRR and FAR30 FRR = c h i 2 c d f ( t h r e s h o l d∗dof / Pjammer , dof ) ; FAR =

1−c h i 2 c d f ( t h r e s h o l d∗dof / Pno ise , dof ) ;

%p l o t t h e d i s t r i b u t i o n shh = p l o t ( x1 , y1 ,’b-’ , x2 , y2 ,’r-’ ) ; l egend(’PDF noise floor’ ,’PDF

35 jammer’ )np = g e t( gca,’NextPlot’ ) ; %t o s e t a t t h e end t h e o ld v a lu e backs e t( gca,’Nextplot’ ,’add’ ) ;

%C a l c u l a t e y v a lu e o f v e r t i c l e l i n e s40 xa = g e t( gca,’Xlim’ ) ;

xv l = [ t h r e s h o l d ; t h r e s h o l d ] ; y v l1 =c h i 2 p d f ( t h r e s h o l d∗dof / Pno ise , dof ) ∗ dof / Pno i se ; y v l 2 =c h i 2 p d f ( t h r e s h o l d∗dof / Pjammer , dof )∗ dof / Pjammer ; yv l = [ 0 ;

45 max( [ y v l 1 ; y v l 2 ] ) ] ;

%p l o t v e r t i c l e l i n e s

115

E. Matlab scripts general

hh1 = p l o t ( xv l , yv l , ’k-’ ) ;

50 %%%%CALCULATE FOR PD i n s t e a d of FRR ; PD = 1− FRR%%%%% k3 = f i n d ( x2 > t h r e s h o l d & x2 < i n f ) ;% x f i l l 3 = x ( k3 )∗Pjammer / dof ;% i f ˜ i sempty ( x f i l l 3 )% x f i l l 3 = [ xv l ( 1 ) ; x f i l l 3 ; x f i l l 3 ( end ) ] ;

55 % y f i l l 3 = [ 0 ; y2 ( k3 ) ; 0 ] ;% f i l l ( x f i l l 3 , y f i l l 3 , ’ y ’ ) ;% end%%%%%%%%%%%%%%%%%%%%%%END%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%FRR%%%%%%%%%%%%%%%%%%%%%%%%%%%%

60 k2 = f i n d ( x2 > − i n f & x2 < t h r e s h o l d ) ; x f i l l 2 =x ( k2 )∗Pjammer / dof ; i f ˜ i sempty( x f i l l 2 )

x f i l l 2 = [ x f i l l 2 ( 1 ) ; x f i l l 2 ; x f i l l 2 ( end) ] ;y f i l l 2 = [ 0 ; y2 ( k2 ) ; 0 ] ;f i l l ( x f i l l 2 , y f i l l 2 ,’y’ ) ;

65 end%%%%%%%%%%%%%%%%%%%%%%END%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%f i l l t h e p l o t f o r t h e FARk1 = f i n d ( x1 > t h r e s h o l d & x1 < i n f ) ; x f i l l 1 =

70 x ( k1 )∗ Pno ise / dof ; i f ˜ i sempty( x f i l l 1 )x f i l l 1 = [ xv l ( 1 ) ; x f i l l 1 ; x f i l l 1 ( end) ] ;y f i l l 1 = [ 0 ; y1 ( k1 ) ; 0 ] ;f i l l ( x f i l l 1 , y f i l l 1 ,’g’ ) ;

end75

%To p l a c e p l o t above t h e f i l l e d area ’ shh = p l o t ( x1 , y1 ,’b-’ , x2 , y2 ,’r-’ ) ;s t r = [’FAR (green) = ’ , num2st r(FAR,’%0.2g’ ) , . . .’; FRR (yellow) = ’ , num2st r(FRR ,’%0.2g’ ) ,’; Threshold = ’ , num2st r( t h r e s h o l d ) ] ;

80 t i t l e ( s t r ) ; i f ˜ i sempty( np )s e t( gca,’NextPlot’ , np ) ;

end x l a b e l(’PSD output value’ ) y l a b e l (’Probability density’ )x a x i s = r e f l i n e ( 0 , 0 ) ;%adds a r e f e r e n c e l i n e y=0

116

Appendix F

Abbreviation list

ABP Air-Burst PulseADC Analog to Digital ConverterAR Auto-RegressiveARMA Auto-Regressive Moving AverageBT Blackman and TukeyBW BandwidthD DecimationDFT Discrete Fourier TransformENOB Effective Number Of BitsFAR False Acceptance RateFFT Fast Fourier TransformFPGA Field Programmable Gate ArrayFRR False Rejection RateGUI Graphical User InterfaceHPF High Pass FilterHz HertzIm ImaginaryJNR Jammer to Noise RatioLPF Low Pass FilterMA Moving AverageMSPS Mega Samples Per SecondNofAv Number of AveragesNofRQ Number of Range QuantaPD Probability DetectionPDF Probability Density FunctionPFA Probability False AlarmPRF Pulse Repetition FrequencyPSD Power Spectrum DensityQMF Quadrature Mirror FilterRBL Range Bin LengthRQ Range QuantumRe RealSINAD SIgnal to Noise And Distortion ratioSNR Signal to Noise RatioULA Uniform Linear Array

117

F. Abbreviation list

W WattdB deci Belldof degree(s) of freedomm meters secondvar variance

118

BIBLIOGRAPHY

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