UNIVERSIDAD POLITÉCNICA DE MADRID

ETSIT DE TELECOMUNICACIONES

TOT & TOK PROJECT

CORPORACION DE ALTA TECNOLOGIA PARA LA DEFENSA

TIME-FREQUENCY TECHNIQUES FOR THE DETECTION OF SIGNALS IN

NON-STATIONARY ENVIRONMENTS

Master degree final work

Authors:

Raúl Andrés Romero Vásquez

John Fredy Márquez Cárdenas

2015

TUTOR: Ph.D Jesús Grajal de la Fuente

Master en radar, tecnologías, equipos y diseño de sistemas

Master degree final work

ii

TIME-FREQUENCY TECHNIQUES FOR THE DETECTION OF SIGNALS IN NON-STATIONARY ENVIRONMENTS

AUTHORS: Raúl Andrés Romero Vásquez John Fredy Márquez Cárdenas

TUTOR: Ph.D Jesús Grajal de la Fuente

Tribunal nombrado por el Mgfco. y Excmo. Sr. Rector de la Universidad Politécnica de Madrid, el día ___ de ____________ de 2015. PRESIDENTE: SECRETARIO: VOCAL: Realizado el acto de defensa y lectura de Tesis el día ___ de ____________ de 2015, en la E.T.S. de Ingenieros de Telecomunicación, Madrid.

Calificación: EL PRESIDENTE LOS VOCALES EL SECRETARIO

iii

To God and my unconditionally wife;

to my mother and my children for their

lovely support.

Raúl Andrés Romero Vásquez

To my beloved wife, daughter, parents

and sister.

Jhon Fredy Márquez Cárdenas

iv

ACKNOWLEDGMENTS

I appreciate the support and confidence of Corporación de Alta Tecnología para la Defensa, who gave me the opportunity to participate in this project. To the Universidad Politécnica de Madrid and teachers ETSIT, whose study plans let me to acquire require knowledge to make this work. A sincere thanks to Microwave and Radar Group, their teachers and scholars, whose teaching and guidance let me acquire basic knowledge in radar systems, and especially thanks to PhD. Jesús Grajal de la Fuente, who was an unconditional and devoted director, whose great effort in guidance us is reflected in the execution of this work, leading the training process.

Raúl Andrés Romero Vásquez

In the first instance to God for all blessings and opportunities given, my family and relatives for being my eternal source of inspiration, motivation and dedication, every teacher who has actively influenced learning process, CODALTEC managerial staff by trust in my abilities and become a participant of this project, faculty of Master UPM for all the knowledge shared and most specially to our thesis tutor, PhD. Jesús Grajal de la Fuente for his patience, dedication and teaching methodology, which allowed us to meet the delivery of this document and more importantly, by the innumerable knowledge acquired during its preparation.

Jhon Fredy Márquez Cárdenas

v

CONTENTS

ABSTRACT ................................................................................................................. vii

KEYWORDS .............................................................................................................. viii

LIST OF TABLES ........................................................................................................ ix

LIST OF FIGURES ....................................................................................................... x

LIST OF APPENDICES ............................................................................................... xi

1. INTRODUCTION....................................................................................................... 1

1.1. Motivation ........................................................................................................... 1

1.2. Problem background .......................................................................................... 1

1.3. Significance of research .................................................................................... 1

1.4. Formulation of the problem ................................................................................ 2

1.5. Objectives .......................................................................................................... 2

1.5.1. General Objective ....................................................................................... 2

1.5.2. Specific Objectives...................................................................................... 2

1.6. Methodology to achieve objectives.................................................................... 2

1.7. Thesis outline ..................................................................................................... 2

SECTION I. THEORETICAL FRAMEWORK AND REVIEWING THE STATUS OF

THE ART ....................................................................................................................... 3

2. IDENTIFICATION OF ELECTRONIC WARFARE ENVIRONMENT ...................... 3

2.1. Scheme of electronic warfare ............................................................................ 3

2.1.1. Classification of electronic warfare ............................................................. 3

2.1.2. Electromagnetic spectrum .......................................................................... 4

2.2. Interceptor-Radar battle analysis ....................................................................... 5

2.3. LPI systems [6] [7] ............................................................................................. 7

3. ELECTRONIC WARFARE RECEIVERS ................................................................. 9

3.1. Receivers classification ..................................................................................... 9

3.2. Selection criteria of digital channelized receiver ............................................. 11

4. CONSIDERATIONS IN CRITICAL COMPONENTS OF DIGITAL RECEIVERS . 13

4.1. Practical considerations for selecting an ADC ................................................ 13

4.2. Digital Signal Processors ................................................................................. 15

5. PARAMETERS CONSIDERED FOR SIGNAL PROCESSING TO MODEL A

RECEIVER .................................................................................................................. 17

vi

5.1. Typical signals in electronic warfare ................................................................ 17

5.2. Signals representation ..................................................................................... 19

5.2.1. Introducing frequency domain analysis .................................................... 19

5.2.2. Time-Frequency Representation (TFR) ................................................... 21

5.3. Criteria selection and basic concepts about STFT.......................................... 25

5.3.1. STFT Basic concepts ................................................................................ 26

5.3.2. STFT Time-frequency resolution .............................................................. 26

5.3.3. STFT Processing Gain ............................................................................. 27

5.4. Model description of Digital Channelized receiver to be simulated ................ 28

5.4.1. Time-Frequency Processor ...................................................................... 29

5.4.2. Detection and feature extraction............................................................... 34

5.4.3. Encoder ..................................................................................................... 36

SECTION II. IMPLEMENTATION OF THE SIMULATION ........................................ 41

6. ADVANCED DIGITAL CHANNELIZED RECEIVER MODEL IMPLEMENTATION

..................................................................................................................................... 41

6.1. Analysis of parameters in time-frequency processor block ............................ 41

6.1.1. Design of the analysis window ................................................................. 41

6.1.2. Time Decimation Factor (M) ..................................................................... 42

6.1.3. Selection of integration lengths ................................................................ 43

6.2. Analysis of parameters in detection and feature extraction block .................. 43

6.2.1. Analysis of the probability of false alarm (Pfa) ......................................... 43

6.2.2. Analysis of the probability of detection (Pd) ............................................. 51

6.2.3. Analysis of using DIFM ............................................................................. 59

6.3. Operating simulation of digital channelized receiver ....................................... 62

7. CONCLUSIONS...................................................................................................... 70

REFERENCES ............................................................................................................ 71

APPENDICES ............................................................................................................. 74

vii

ABSTRACT

This thesis is structured from the analysis of the role of a receiver in an electronic warfare scenario, the characterization of critical elements in the processing chain for subsequent implementation of a model, that uses a time-frequency technique widely implemented and studied in interceptors signal processing, called short time Fourier transform. Only the detection process is addressed in this thesis.

RESUMEN

Esta tesis se estructura a partir del análisis del papel de un receptor en el escenario de guerra electrónica, la caracterización de elementos críticos en la cadena de procesado, para posterior implementación de un modelo que hace uso de una técnica tiempo-frecuencia ampliamente implementada y estudiada en procesado de señal de interceptadores, llamada transformada de Fourier de tiempo corto. Sólo el proceso de detección es abordado en esta tesis.

viii

KEYWORDS

Electronic warfare, electronic support measures (ESM), Low Probability or Intercept radars (LPI), digital channelized receiver, analog to digital converter (ADC), digital signal processor, time-frequency representations (TFRs), short-time Fourier transform (STFT), windowing, non-stationary signals.

PALABRAS CLAVE

Guerra electrónica, medidas de apoyo a la guerra electrónica (ESM), radares con baja probabilidad de interceptación (LPI), receptor digital canalizado, conversor análogo digital (ACD), procesador digital de señales, representaciones tiempo-frecuencia, transformada de Fourier de tiempo corto (STFT), enventanado, señales no estacionarias.

ix

LIST OF TABLES

Table 4-1 Main specifications in high speed ADCs .................................................... 14 Table 4-2 Actual processor technologies ................................................................... 15 Table 4-3 FPGAs vs DSPs comparative .................................................................... 16 Table 5-1 Comparative analysis for stationary and non-stationary signals ............... 21 Table 5-2Common TFR applications .......................................................................... 25 Table 5-3 STFT criteria selection................................................................................ 25 Table 5-4 Non-coherent integration scheme .............................................................. 32 Table 6-1Comparative Pfa theoretical vs Monte Carlo estimated without normalized window coefficients. .................................................................................................... 45 Table 6-2 Behavior variance in Pfa estimation with 5000 simulations of Monte Carlo ..................................................................................................................................... 45 Table 6-3 Parameter for comparative effect of overlapping windows with non-coherent integration .................................................................................................... 47 Table 6-4 Thresholds for spectrograms I1, I2, I3 ....................................................... 50 Table 6-5 Pd vs SNR changing position of a single tone ........................................... 52 Table 6-6 Summarize SNR required as function of centered bin of a single tone..... 52 Table 6-7 Scalloping losses comparative ................................................................... 53 Table 6-8 Radar and digital communication signals to analyze with receivers ......... 54 Table 6-9 Pd curves for DFT receiver with 1024 samples ......................................... 55 Table 6-10 Pd curves for single STFT receiver .......................................................... 56 Table 6-11 Pd curves for the ADCR ........................................................................... 57 Table 6-12 Sensitivity comparison between receivers ............................................... 58 Table 6-13 Comparative wrap and unwrap index filter in DIFM (left), and frequency estimation of a single tone by using DIFM ................................................................. 59 Table 6-14 SNR effect in frequency estimation with DIFM ........................................ 60 Table 6-15 Association between index filter in STFT and the center bin .................. 61 Table 6-16 Examples of using DIFM for estimating instantaneous frequency .......... 62 Table 6-17 Parameters of Digital Channelized Receiver to be implemented ............ 62 Table 6-18 TFR CW without modulation centered at fd=8/256 and frequency change within the channel bandwidth, SNR=-2,7 dB .............................................................. 64 Table 6-19TFR CWLFM 500 MHz/1 ms, centered at fd=62/256 and within a time interval to observe transition between two filters, SNR=-3,07 dB .............................. 65 Table 6-20TFR BPSK 10 MHz, Tb=100 ns, with random code per bit period, SNR=7,555 dB ............................................................................................................ 66 Table 6-21TFR Pulse centered at fd=8/256, with phase modulation Barker 13 - 4,8 µs SNR=-2,998 dB ...................................................................................................... 67 Table 6-22 TFR conventional pulse centered fd=8/256 =1 µs SNR= -2,785 dB .... 68 Table 6-23 TFR with three signals at the same capture time, SNR=-2,785 dB......... 69 Table 7-1Receiver types vs signals types .................................................................. 74 Table 7-2Qualitative comparison of receivers ............................................................ 75

x

LIST OF FIGURES

Figure 2-1Classification of Electronic Warfare ............................................................. 3 Figure 2-2 Electromagnetic Spectrum .......................................................................... 4 Figure 2-3Electronic warfare frequency bands............................................................. 4 Figure 2-4 SNR balances in interceptor-radar battle .................................................... 7 Figure 2-5 Atmospheric Absorption for Millimeter Wave Spectrum ............................. 8 Figure 3-1Crystal video receiver ................................................................................... 9 Figure 3-2 TFR .............................................................................................................. 9 Figure 3-3 instantaneous frequency measurement ...................................................... 9 Figure 3-4 Scanned superheterodyne ........................................................................ 10 Figure 3-5 Bragg cell ................................................................................................... 10 Figure 3-6 Channelized ............................................................................................... 11 Figure 3-7 Digital ......................................................................................................... 11 Figure 4-1 ADCs state of the art ................................................................................. 15 Figure 5-1 Examples of spread-spectrum modulation techniques ............................. 17 Figure 5-2 Non-Stationary signal ................................................................................ 22 Figure 5-3 Stationary signal ........................................................................................ 22 Figure 5-4 Matrix t-f filling process by means of Spectrogram................................... 23 Figure 5-5 Example of decision tree for selecting a TFR ........................................... 24 Figure 5-6 STFT graphical description ....................................................................... 26 Figure 5-7 window length effect in spectral components ........................................... 27 Figure 5-8 window length effect .................................................................................. 27 Figure 5-9 Architecture of time-frequency receiver .................................................... 29 Figure 5-10 Approximate filters response .................................................................. 30 Figure 5-11 Parks McClellan window, Rp 0,086 dB, Rs 60 dB, L 256 ...................... 31 Figure 5-12 Time-Frequency map for different signals .............................................. 33 Figure 5-13 Detection stage of ADCRx ...................................................................... 35 Figure 5-14 In-channel AMC flow chart ...................................................................... 38 Figure 5-15 PDWs construction .................................................................................. 40 Figure 6-1 Time and frequency response of Parks McClellan window ...................... 41 Figure 6-2 Frequency response of FIR filter design with Parks McClellan method,

centered at 0,25. Amplitude and phase on left side, group delay on right side ....... 42 Figure 6-3 Bank of 31 FIR filters with Parks-McClellan method ................................ 42 Figure 6-4 Scheme for implementing Monte Carlo .................................................... 44 Figure 6-5 Pfa (T) for spectrogram I1, rectangular window without normalized window coefficients. .................................................................................................... 46 Figure 6-6 Pfa (T) for spectrograms I2 (left), I3 (right) with Monte Carlo and theoretical (56). Rectangular windows. Both cases without normalized window coefficients .................................................................................................................. 47 Figure 6-7 Comparative effect of overlapping windows (rectangular (left) and Hamming (right)) with non-coherent integration and without normalized window coefficients .................................................................................................................. 47 Figure 6-8Pfa (T) for spectrograms I2 (left), I3 (right) with Monte Carlo and theoretical (57). Rectangular windows ....................................................................... 48

xi

Figure 6-9 Pfa (T) for spectrogram I1 with Parks McClellan window ......................... 49 Figure 6-10 Pfa (T) for spectrogram I2 with Parks McClellan window ....................... 50 Figure 6-11 Pfa (T) for spectrogram I3 with Parks McClellan window ....................... 50 Figure 6-12 Scalloping losses for a single tone with rectangular and Hamming window......................................................................................................................... 53 Figure 6-13 Comparative response for a single tone varying SNR value .................. 61

LIST OF APPENDICES

Appendix A. Receiver types vs signals types [10] ...................................................... 74 Appendix BCommon Time Frequency Representations [25] [30] .............................. 76

1

1. INTRODUCTION

Advanced digital channelized receivers perform detection, classification and identification of complex waveforms, which are designed to reduce the probability of interception. The non-stationary signals of interest are immersed in difficult environments, added with noise and interferences, reason why the proper selection of elements and signal processing techniques are critical, and can give the operational advantage of an the interceptor against the equipment that seeks to detect. Within the set of time-frequency techniques, the simulation takes into account an extension of the short-time Fourier transform (STFT), also known as sliding-window Fourier transform, including non-coherent integration lengths for different signals and frequency estimation. Other advantages associated with the model of the Advanced Digital Channelized Receiver (ADCR) taken as reference [1] will be addressed at the level of indication, but not implemented, such as implementing clustering, generation of Pulse Descriptor Word (PDW) and automatic modulation classification.

1.1. Motivation

Within the context of implementation radar and radio frequency technologies by the Corporación de Alta Tecnología para la Defensa, It has shown interest in addressing analysis and signal processing technologies in the line of electronic warfare, delimiting as a first approach the study of electronic interceptors. 1.2. Problem background

Detection, classification and identification of signals and equipment in a typical warfare environment, correspond to the aim of Electronic Support Measures (ESM) equipment. The effectiveness of their operation in electromagnetically saturated environments, and the ability to process non-stationary signals in real time, may grant the tactical and operational advantage to the part who implements it, and knows the actions that can be inferred from this phase.

1.3. Significance of research

This project seeks to consolidate knowledge on topics related with receivers, from the analysis of its role in electronic warfare, to the description of its critical components and signal processing algorithms used; that allow in the short or medium term, the development of more complex algorithms which complement the processing chain, prior to implementing a physical model with the available technology.

2

1.4. Formulation of the problem

What factors should be taken into account to give operational advantage to an electronic receiver in the actual electronic warfare?

1.5. Objectives

1.5.1. General Objective

Identify the warfare environment, architecture and signal processing techniques employed by receivers, as an electronic support measure (ESM), including detection and identification phases of non-stationary signals, by modeling a high performance and widely used technique such as the STFT (Short Time Fourier Transform).

1.5.2. Specific Objectives

➢ Identify the electronic warfare environment and the importance of systems that

implement measures to capture information and electronic reconnaissance. ➢ Study the receiver architectures employed in electronic warfare. ➢ Analyze and select analog to digital conversion technologies and digital signal

processing, as critical components in the receiver performance. ➢ Analyze and select algorithms to implement time-frequency techniques for

signals detection in non-stationary environments.

1.6. Methodology to achieve objectives

The methodology used in the development of the thesis consisted of an extensive literature review of receiver equipment, in order to identify its role in electronic warfare, and more important its critical components in signal processing, architecture selection criteria and complex algorithms which provide the necessary support for integration with more complete models, prior to implementation phase. MATLAB is employed for implementing simulation of the advanced digital channelized receiver.

1.7. Thesis outline

The content of this thesis was organized trying to follow a structure to address issues from general to the specific context, in relation to the modeling of a digital channelized receiver. Topics are grouped into the following chapters: Chapter 2. Identify the electronic warfare environment and the interceptor-radar warfare analysis. Chapter 3. Describe the typical architecture of a receiver and the classification of most common technologies. Chapter 4. Related criteria and current solutions on critical design components such as ADCs and digital signal processors. Chapter 5. It contains information required for simulating the signal processing: signals used by LPI radars, time-frequency techniques and the model description of a digital channelized receiver taken as reference. Chapter 6. Relate the tasks executed to simulate a detection process, additional to an implementation of a digital instantaneous frequency measurement (DIFM), in order to improve the frequency precision. Chapter 7. Include conclusions.

3

SECTION I. THEORETICAL FRAMEWORK AND REVIEWING THE STATUS OF

THE ART

2. IDENTIFICATION OF ELECTRONIC WARFARE ENVIRONMENT

2.1. Scheme of electronic warfare

Electronic Warfare can be described as a set of measures and actions performed by the conflicting sides to detect and electronically attack enemy electronic systems for the control of forces and weapons, as well as to electronically defend one’s own electronic systems and other targets from technical intelligence [2].

2.1.1. Classification of electronic warfare

Figure 2-1Classification of Electronic Warfare1

Electronic warfare is divided in three subsets, briefly described as follows [2]: ESM: actions taken to search for, intercept, locate and analyze radiated electromagnetic energy for the purpose of exploiting these in support of military operations. ESM is based on the use of intercept or warning receivers and relies heavily on a previously compiled directory of both tactical and strategic electronic intelligence (ELINT). ESM receivers are designed to give an immediate response to the perceived threat, so the real time processing limits the computational processing load. The ELINT receivers can support processing techniques computationally more expensive, since most of the processing is delayed [3]. ECM: actions taken to prevent or reduce an enemy's use of the electromagnetic spectrum.

1Taken from http://www.radartutorial.eu/

4

ECCM: actions taken to retain the use of the electromagnetic spectrum, despite a hostile force's use of ECM techniques.

2.1.2. Electromagnetic spectrum

Range of all possible frequencies of electromagnetic radiation. This electromagnetic spectrum goes from below the low frequencies used for radio communication to gamma radiation at the short-wavelength (high-frequency) end, covering all wavelengths from thousands of kilometers to a small size of an atom, Figure 2-2.

Figure 2-2 Electromagnetic Spectrum2

Radar systems use a different set of letter band designations, and commonly operate in the range of 3 MHz to 300 GHz, though the large majority operates between about 300 MHz and 35 GHz. The radar bands are the International Telecommunications Union (ITU) frequencies authorized for radar use [4], Figure 2-3.

Figure 2-3Electronic warfare frequency bands3

2Taken from: http://www.globalsecurity.org/ 3Taken from http://www.radartutorial.eu/

5

2.2. Interceptor-Radar battle analysis

An analysis of the incidents equations in the information processing capacity, within a typical interceptor-radar battle environment will identify the strategy, technical requirements and intelligence with which it must provide, in order to give it tactical advantage [5]. Interceptor-radar battle has traditionally raised in terms of the advantage of the

interceptor to radar as RI

RR> 1, where RI is the detection distance of a radar from an

interceptor, and RR is the detection distance of an interceptor from a radar.

Using the radar equation, the power received by the radar is:

S|R =PGTRGRRλ2σ

(4π)3R4LR

( 1 )

The S

N relation without processing after the detector could be calculated as:

S

N|

R=

PGTRGRRλ2σ

(4π)3R4KT0FRBRLR

( 2 )

If exist processing after detection, the equivalent bandwidth receptor radar (BER) is

the one should be usedBER =BR

GPR.

P Radar peak power. GTR, GRR Gain of the transmition antenna radar, Gain of the reception antenna

radar λ Wave length of signal transmitted.

σ Target cross section. R Radar-Interceptor distance.

FR Noise factor radar receiver. BR Wideband radar receiver.

LR Radar losses. GPR Proccesing gain radar Signal received by the interceptor is:

S|I =PGTRGRIλ

2

(4π)2R2LI

( 3 )

And signal to noise ratio in the interceptor is: S

N|

I=

PGTRGRIλ2

(4π)2R2KT0FIBeILI

( 4 )

P Radar peak power.

GRI Gain of the receiver antenna interceptor λ Wavelength of signal transmitted.

FI Noise factor interceptor. BEI Equivalent bandwidth of interceptor

LI Interceptor losses.

6

By relating the equations (2) and (4):

S

N|

I=

S

N|

R.4πR2

σ

GRI

GRR

FR

FI

LR

LI

BeR

BeI

( 5 )

Some important considerations are derived from that:

Factor 4πR2

σ: Advantage of the interceptor due the distance and the inconvenience of

its radar cross section.

Factor GRI

GRR: Radar advantage accounting for the fact of having a directive reception

antenna. FR

FI

LR

LI: Receptor quality factor for both systems.

BeR

BeI: Summarizes the effect of both the different bandwidth systems and their

processing gains. The distance at which both ratios in equation ( 5 ) are equal:

RE = [σ

4π

GRR

GRI

FI

FR

LI

LR

BeI

BeR]

12⁄

≈ [σ

4π

GRR

GRI

FI

FR

LI

LR

tR−I

tI−R]

12⁄

, where t ∝1

B

( 6 )

In the second expression in the equation above (6)( 59 ), the equivalent bandwidth between radar and interceptor have been approximate in function of the observation time: tR−I (Observation time on interceptor by radar) and tI−R (Obervation time on the radar by the interceptor).

To defined radar-interceptor battle is necessary to calculate the signal to noise ratio

in R = RE ,S

N|

RE

and compared to that required for a given probability of detection

(Pd), and a probability of false alarm (Pfa), which are assumed to be equal for radar

and interceptor, S

N|

Pfa−Pd

≈ 13 dB with Pfa = 10−6 and Pd = 90%, associated with a

maximum range RD, If RD < RE, radar will detect the interceptor before it is observed, otherwise the interceptor will be the one who wins the battle, see Figure 2-4. So the interceptor will be more efficient if the RE measure decreases, trying minimize

the BeR

BeI factor in equation (5).

7

Figure 2-4 SNR balances in interceptor-radar battle

This ratio gives advantage to radar, due to it knows its optimal processing time, because the knowledge of the emitted signal. Processing interceptor should focus on minimizing that equivalent bandwidth, but taking into account that should exist several simultaneous signals and that each signal will required a different process. Finally, the probability of signal interception not only depends on its modulation and power, but else the knowledge of its parameters and the ability to adapt the interceptor to a specific signal.

2.3. LPI systems [6] [7]

Both Radars and communication signals are considered low-probability of intercept (LPI) signals. LPI radars have some characteristic combination which make them hard to be detect by any particular receiver, such as: ➢ Narrow antenna beam: or antennas with suppressed side lobes, in which the

antenna emit less off axis power. ➢ Emission control: Reduce the transmitter power, maintaining a minimal SNR. ➢ High duty cycle: If the signal duration is reduced, a receiver has less time to

search for the signal in frequency and/or angle or arrival. ➢ Modulation that spreads the radar signal in frequency.

LPI communication signals typically depend on the spreading modulation to make them hard to detect and jam. LPI modulations spread the signal’s energy in frequency, so that the frequency spectrum of transmitted signal is too much wider than the information bandwidth. Some common ways to spread the signal in frequency by modulating are: ➢ Periodically changing the transmission frequency (Frequency hopping). ➢ Sweeping the signal at a high rate (chirping) ➢ Modulating the signal with a high rate digital signal (direct sequence spectrum

spreading).

8

Another features about LPI radars, in terms of comparison with conventional radars are:

➢ Limited Range: An LPI radar can use frequencies of 22, 60, 118, 183, and 320

GHz at which peak absorption occurs, Figure 2-5 [7]. ➢ Coherent detection: An Electronic Warfare Support (ES) receiver cannot achieve

coherent detection of a radar signal unless it knows the parametric details of the signal

➢ Monostatic /bistatic configurations: Both configurations can be used by LPI radars. In the second case, the transmitting and receiving antennas are separated by distance.

Figure 2-5 Atmospheric Absorption for Millimeter Wave Spectrum

The proliferation of radar, altimeters, tactical airborne targeting, surveillance and navigation devices employing LPI capabilities has demonstrated that a simple power spectral analysis is not enough to intercept and extract characteristics of these signals, therefore, a more sophisticated signal processing, such as analyzing the temporal variation of the spectral composition of the signal, by means of a time frequency representation (TFR) could extract the necessary parameters of the waveform to create a proper electronic response [8]. It motivated the identification and selection of the Short Time Frequency Technique (STFT) as the TFR to simulate the detection process of some common LPI radar and communication signals. This information will be treated in chapter 5.

9

3. ELECTRONIC WARFARE RECEIVERS

3.1. Receivers classification

Receivers, often called interceptors, are an important part of almost every kind of electronic warfare system. There are many types of receivers, and their characteristics determine their roles. The most representative receivers are described by [6], [9], [10] and briefly shown here as reference.

Crystal video

Figure 3-1Crystal video receiver

It is not frequency sensitive, wideband instantaneous coverage, low sensitivity and no selectivity, primarily used to measure pulse width, down to < 30 ns pulses, and time of arrival (TOA). One of the uses for crystal video receivers are the Radar Warning Receivers (RWRs), that are often implemented with a microwave band pass filter. Including a modification on it, the Tuned Radio Frequency Receiver (TRF), use the crystal video receiver with a tunable YIG filters to isolate simultaneous signals, with slightly better sensitivity than simple crystal video.

Figure 3-2 TFR

Instantaneous frequency measurement (IFM)

Figure 3-3 instantaneous frequency measurement

Comprise a set of correlators or discriminators, present ability to detect and display frequency-agile and chirp modulation signals. They are high FAR (False Alarm Rate) in dense signal environments and poor simultaneous signal performance. Principal applications in shipboard ESM, Jammer power management and SIGNIT equipment.

10

Scanned superhetorodyne

Figure 3-4 Scanned superheterodyne

It is the most common type of receiver, have the highest Sensitivity, low FAR and flexibility to cope with new threats, present poor POI (Probability of intercept) to single pulses, and blindness to frequency-agile signals, poor jamming immunity and good frequency accuracy.

Bragg cell

Figure 3-5 Bragg cell

Wideband instantaneous coverage; low dynamic range; multiple simultaneous signals, does not demodulate. Also known as an acousto-optic receivers [11], use a narrow video bandwidth and a relatively large number of channels that can be implemented by using a time-integrating photo detector array. The effective integration time (video bandwidth) of the acousto-optic receiver can be adjusted to match the duration of the signal intercepted for maximum sensitivity. This can be accomplished by either changing the integration period on the photo detector array or changing the number of samples integrated digitally. It presents high complexity and require recent technologies.

11

Channelized

Figure 3-6 Channelized

Combines selectivity and sensitivity with wideband coverage. It is a set of fixed tuned receivers covering a frequency range to provide 100% receipt and detection of multiple simultaneous signals. Principal applications in SIGNIT equipment and Jammer power management. This type of receiver will be analyze with more detail in chapter 5.

Digital

Figure 3-7 Digital

Highly flexible; can deal with signals with unknown parameters. The computer module contains all the data analysis required, for example based on our aim, the implementation of the STFT algorithms and additional process blocks.

Taking as reference a comparative chart of receivers shown in Appendix A, and the actual flexibility and performance of digital systems for processing signal and data, the type of receiver select corresponds with a mixture performance of the two last receivers explained (channelized and digital). Some important considerations will be expanded below.

3.2. Selection criteria of digital channelized receiver

Some of the most representative considerations for selecting the architecture receiver based on a channelized structure are based on the following characteristics, from the documentary synthesis approached: ➢ Channelization function can be accomplished more easily with the advent of

digital circuitry. The main advantage in using digital channelization is the better control of filter shape. Therefore, one can see why digital techniques rather than analog are being used in the development of wide receivers [12].

➢ As indicated in Appendix A, it presents the greatest homogeneity in the process of: detection, classification and identification of LPI signals.

➢ As indicated in Appendix A, a channelized receiver presents a wide set of technical and operative characteristics better compared with the other references, like wide instantaneous analysis bandwidth, good dynamic range, very fast speed of acquisition, good retention of signal characteristics and detection of LPI signals, good simultaneous signal capability, good immunity to Jamming, high RF range, so on.

12

➢ As is reference by [1], the actual electronic warfare is developed in a difficult environment consisting of noise, interference and multiple nonstationary signals, where some waveforms are intentionally designed to reduce the probability of interception (LPI signals). These new signals has motivated the use of advanced signal processing algorithms running on digital receivers. Specifically this reference document propose and advanced digital channelized receiver (ADCR), whose main feature is the use of time-frequency analysis before detection and encoding.

13

4. CONSIDERATIONS IN CRITICAL COMPONENTS OF DIGITAL RECEIVERS

As it was shown in 2.2 Interceptor-Radar battle analysis, the information processing capacity will identify the strategy, technical requirements and intelligence with must be provided the receiver in order to get tactical advantage. The search for improving sensitivity of equipment and detection capabilities in broadband, involves identifying critical points that will impact system performance, cost, modularity and scalability of the system [5]. Receiver performance has been technologically restricted to operate in real time by some technological considerations: Digitizing speed limits in analog to digital converters (ADC) to signals with several GHz bandwidth, and signal processors limits with capacity to implement complex signals processing algorithms, with some intelligence that allows the system correlated information and adapt to the environment [3] [5].As reference, actually developments in digital receivers look for digitizing the RF signal at the output of the receiving antenna and process information using digital hardware or software

4.1. Practical considerations for selecting an ADC

When selecting and ADC there are some general considerations which can be take into account [5]:

➢ Resolution: related with number of bits. ➢ Sampling rate: limits the capacity of sampling, quantization and coding. ➢ Quantization error: Difference between quantization samples and the input

signal. Depends on quantization levels and therefore the number of bits. ➢ Spurious responses: Derived from the quantization error periodicity, spurious

components appear reducing the dynamic range, which can potentially generated false alarm in the receiver. It should optimize the input noise level, seeking to minimize spurious components, although this decrease receiver sensitivity.

➢ Noise effect and dithering: It is possible to detect signals under quantization levels by adding noise, through a process called dithering. Sensitivity receiver is related to process bandwidth, corresponding to the individual filter bandwidth in a bank of filters, so that dynamic range not only is determined by the ADC, but else by the set of ADC plus posterior channelization.

➢ Jitter: Effect associated with sampling instants uncertainty in the sampling and hold circuit of an ADC.

Should be there take into account there are no independence between the criteria selection parameters in an ADC, when is looking for getting the best performance, for example if is required the best resolution and dynamic range, less sampling frequency should require.

14

Another important parameters used to select an ADC to for a giving specific application are [13]: ➢ Signal to Noise Ratio (SNR): fidelity measurement for quantization of small

signals in an environment with strong interference. ➢ Spurious Free Dynamic Range (SFDR): fidelity measurement for accurate

detection of low level signals in an environment with strong interference. ➢ Noise Power Ratio (NPR): for interchannel crosstalk.

Manufacturer / Model

Sampling frequency

(Gsps) Bits

Analog input BW

(GHz)

Input tension

levels (V) SNR SFDR

Jitter (ps)

TEXAS INSTRUMENTS ADC12J4000

4 12 3.3

Common 1.2

Differential 0.2

fin= 2.4 GHz 55 dB

fin= 2.4 GHz 68.3 / 74.9

dBFS

0.12 RMS

TEXAS INSTRUMENTS ADC12D1800RF

3.6 12 2.7

Common 2.2

Differential 0.10

fin= 1.44 GHz 54.3 / 54.6

dB

fin= 1.44 GHz 61 / 68.1

dBc

0.2 RMS

TEXAS INSTRUMENTS ADC12D1600RF

3.2 12 2.7

Common 2.2

Differential 0.10

fin= 1.44 GHz 57 / 59 dB

fin= 1.44 GHz 67.3 / 67.9

dBc

0.2 RMS

MAXIM MAX 109

2.2 8 2.8

Common 2.5

Differential 0.2

fin= 1.6 GHz 44 / 44.6 dB

fin= 1.6 GHz 50.3 / 61.7

dBc

0.2 RMS

ANALOG DEVICES AD9680-1000

1.0 12 2.0

Common 2.5

Differential 0.2

fin= 1.9 GHz 57 / 67.2

dBFS

fin= 1.9 GHz 68 / 88 dBFS

0.3 RMS

Table 4-1 Main specifications in high speed ADCs

It is important consider the current trend in ADC performance, whose tendency is to sample closer to the receiving antenna directly in RF in addition with the search of high dynamic range and wide signal bandwidth that enable implementation of advanced multi-function digital receiver systems, leading to significant reduction of cost, size, weight and power dissipation of current systems [13] [14]. An implementation example of digitize the input signal after the antenna, and low noise amplifier, eliminating all the frequency down-conversion electronics by mean of ALGAAS/GASS HBT technology can be found in [14]. Another recent implementation reference is described by [15], which treat high speed monolithic ADC that uses Microwave Monolithic Integrated Circuits (MMIC), and the impact on the performance of a digital receiver which uses direct IF sampling. At last, an aggrupation of good performance ADC which refers the actual state of the art is shown in Figure 4-1.

15

Figure 4-1 ADCs state of the art4

4.2. Digital Signal Processors

As mentioned before, time required for processing information in digital receivers represent a critical factor. It depends on the bandwidth of the received signal, sampling rate to digitize, processor speed and complex of the algorithms required to extract information of the received signal. Some additional considerations for taking into account when selecting a processor are: dynamic range, accuracy in arithmetic, consumption, size, communications protocol, cost. A set of the common technologies with its particular benefits and consideration is shown in Table 4-2 [10].

TECHNOLOGY BENEFITS CONSIDERATIONS

Microcontrollers (MCUs) Low cost, miniaturization, easy to program.

Insufficient power (HP) for high performance applications.

Microprocessors Higher levels of clock for high-performance, easy to program.

More power, sequential processing architecture.

DSPs Dedicated components for signal processing, floating point arithmetic.

Inherently sequential processing.

GPUs Parallel processing to speed CPUs. More power, necessarily requires a

CPU.

FPGAs Flexible Hardware defined by software, reprogrammable circuits inherent parallel processing.

Programming complexity in hardware description languages.

ASSPs Speed and optimization for specific applications, offers standard commercially available chips.

Without flexibility to modify designs.

ASICs Fully Configurable Chips, constrained optimization and a single package for one application.

High initial investment and feasible only in high volumes.

Table 4-2 Actual processor technologies

4Taken from: II Curso de Telecomunicaciones y Guerra Electrónica de la ACING- Tecnologías ESM- ETSIT

16

Some implementations required high exchange of information, so global processing capacity is not only limited by the processor speed, but else by the data transfer rate from the peripheral components, memories or input/output ports, reason why should not be ignored its effect when selecting a processor [5].

Most receivers required real time processing, but there are some technological considerations that prevent this. Two common non-real time situations are: processing time less or equal than the observation time: it means any calculation in data blocks, including data transfer, it should be ready before next available data blocks to be processor. Otherwise, if time processing is greater than observation time, the last data taken should be saved in memory for post processing, typical case of ELINT systems. In order to avoid data losses, parallel processing or multiprocessor architecture should be implemented [5] . An architecture similar to the scheme taken as reference was implemented in [16]. It consist in a parallel pipelined architecture of a FFT and related algorithms for implementing a digital channelized receiver on FPGA.

A comparison between the two most common technologies widely used in this kind of implementation (FPGA and DSP) is shown in Table 4-3 [17].

FPGAs vs DSPs

FPGAs DSPs

Programming Language VHDL, Verilog C, Assembly language

Ease of software programming

Fairly easy, however a programmer needs to understand the hardware architecture before programming.

Easy

Performance Can be very fast in an appropriate architecture is design.

Speed is limited by the clock speed of a DSP chip.

Reconfigurability SRAM type FPGA can be reconfigurable infinite times

Can be reconfigurable by changing program memory content.

Reconfiguration method

Reconfiguration is done by downloading configuration data to a chip electronically.

Reconfiguration is done by simply reading a program at a different memory address.

Areas where FPGAs can outperform DSPs, or vice versa

FIR filter, IIR filter, correlator, FFT, etc. A signal processing program of sequential nature.

Power consumption Can be minimized if the circuit is designed to save power, or the power is dynamically controlled

Even if program A is larger than program B power consumption does no change as long as the number of memory chips is the same.

Implementation method of MAC

Parallel multiplier/adder or distributed arithmetic.

Repeated operation of MAC function.

Speed of MAC

Can be fast if parallel algorithm is used. If a filter is implemented using distributed arithmetic, the speed does not depend on the number of taps.

Limited by the speed of the MAC operation of a DSP chip. If a filter is implemented, the speed becomes slower if the number of taps increases.

Parallelism Can be parallelized to achieve high performance.

DSP chip programming is usually sequential and cannot be parallelized.

Table 4-3 FPGAs vs DSPs comparative

17

5. PARAMETERS CONSIDERED FOR SIGNAL PROCESSING TO MODEL A RECEIVER

5.1. Typical signals in electronic warfare

In section 2.3 was briefly introduced the main LPI systems characteristics but it wasn’t explained typical signal modulation employed. As it was indicated three common ways in which modulation is used to spread the signal in frequency are: ➢ Periodically changing the frequency ➢ Sweeping the signal frequency at a high rate, or chirping ➢ Modulating the signal with a high rate digital signal, or direct sequence-spectrum

spreading. Included in these categories there are many wideband modulation techniques available to provide secure LPI waveforms [8] [9]: ➢ Frequency Modulation ➢ Linear FM (Chirp) ➢ Non-Linear FM ➢ Frequency Modulation Continuous Wave (FMCW) ➢ Costas Array, frequency hopping ➢ Phase modulation (bi-phase coding, polyphase coding) ➢ Combined phase shift keying, frequency shift keying (PSK,FSK) ➢ Pseudo-noise modulation ➢ Polarization modulation

A comparative wave modulation of common techniques is shown in Figure 5-1 [9].

Figure 5-1 Examples of spread-spectrum modulation techniques

18

A brief descriptions of common modulation techniques are given as follows [8]: ➢ Frequency modulation (FM): Is employed in pulsed radar where a linear swept

chirp waveform is transmitted and a weighted matched filter is incorporated into the communication receiver to detect the return echo.

➢ Frequency Modulation Continues Wave (FMCW): Waveform easier to implement than phase code modulation, it shows excellent characteristics for the best use of the output power available from solid states devices. Its emitter uses a continuous 100% duty cycle waveform, so that both the target range and the Doppler information can be measured unambiguously while maintaining a low probability of intercept.

➢ Frequency hopping (FH): Frequency agile radar transmission, either on a pulse to pulse basis or on bursts of pulses. Additionally, PRI can be made agile. Pulse to pulse agility gives ECM protection which is proportional to the agile bandwidth, defeating the repeater jammer. It works under the control of pseudo-noise (PN) code. It’s one of the favored phase modulation technique for generating spread-spectrum waveform in which the transmitted RF bandwidth is controlled directly by the PN code clock rate. As reference fast FH techniques used more than 500 hops/s, and medium hop-rate FH systems used between 50-500 hops/s [9].

➢ Phase Shift Keying (PSK): Or Minimum Shift Keying (MSK) is another one favored modulation technique for generate spread spectrum waveform. It has been gaining in popularity, as the removal of distinct phase transitions, providing superior spectral properties. The transmitted RF bandwidth is controlled directly by the PN code clock rate. Nevertheless, Binary Phase Shift Keying (BPSK) it’s not a technique employed in LPI radar modulation, being excellent for test signal in evaluating the performance of the proposed signal processing [8]. As referenced in [18] BPSK is usually used by communication links via radar and surveillance aircraft.

➢ Frequency Shift Keying (FSK): Modulation technique consisting in sending different frequency tones, corresponding to a symbolic alphabet. In a binary case there is one frequency assigned to a logical value “0”, and another frequency to the logical value “1”. Alphabets with higher symbols (M>2), is known as MFSK. Its uses is common in low cost equipment as faxes, telephone modem of low capacity and communication links. As reference by [18], MFSK is usually used in radiotelephony and GSM mobile telephony systems.

➢ Frank code: It belongs the family of polyphase codes, being successfully implemented in LPI radar signals. It consists of a constant amplitude signal whose carrier frequency is modulated by the phases of Frank code. For each frequency or section of the step chirp, a phase group consisting of N phases

samples is obtained and the total number of phases isN2, which is equal to the pulse compression ratio.

➢ Costas code: In a frequency hopping system, the signal consists of one of more frequencies being chosen from a set (f1, f2, … , fn)of available frequencies, for

transmission at each of a set (t1, t2, … , tn) of consecutive time intervals. A signal is represented by a n x n permutation matrix, where n rows correspond to the n frequencies, the n columns correspond to the n intervals, and each cell xi,j of the

matrix equals 1means transmission and 0 otherwise.

19

5.2. Signals representation

5.2.1. Introducing frequency domain analysis As mentioned by [19] different signal representations can be used for different applications. Most engineering applications are usually function of time, but for studying or designing systems is often used the frequency domain. This is because many important features of the signals and systems are more easily characterized in the frequency domain than in the time domain. The most important and fundamental variables in nature are time and frequency. While the time domain functions indicate how a signal’s amplitude change over time, the frequency domain function tells how often such changes take place. The bridge between both domains is the Fourier Transform. Next frequency domain concepts were extracted from [20] [21] [22].

• Fourier series of a periodic signal (FT)

A continuous periodic signal can be represented as a linear combination of harmonically related complex exponential of the form (7).

x(t) = ∑ ak. ejkω0

+∞

k=−∞

( 7 )

That representation let getting a Fourier series representation, where the coefficients are given by (8).

ak =1

T0

∫ x(t). e−jnω0t

T0

( 8 )

The coefficients {ak} are often called the Fourier series coefficients or the spectral coefficients of x(t). These complex coefficients measure the portion of the signal x(t) that is at each harmonic of the fundamental component. These spectral coefficients can be seen as spectral lines, in which their individual intensity is a direct measure of the fraction of total energy at the frequency corresponding to the line.

• Fourier Transform of an aperiodic signal

An extended analysis for periodical signals was implemented by Fourier with aperiodic signals and related as one of his most important contribution, letting to represent it as a combination of complex exponentials. The Fourier Transform pair are presented in (9) and (10).

20

x(t) =1

2π∫ X(ω). ejωt

∞

−∞

dω

( 9 )

X(ω) = ∫ x(t). e−jωt

∞

−∞

dt

( 10 )

Equation (9) plays a role for periodic signals similar to that of equation (7) for periodic signals, since both correspond to a decomposition of a signal into a linear combination of complex exponentials. For aperiodic signals the correspond spectral coefficients occur at a continuum of frequencies, whose amplitude isX(ω)(dω/2π). The transform X(ω) of an aperiodical signal x(t) is commonly referred to as the spectrum of x(t), as it provides information concerning how x(t)is composed of sinusoidal signals at different frequencies.

• Discrete Fourier Transform (DFT)

The increasing use and capabilities of digital computers and the development of design methods for sample data systems push forward the development of discrete time techniques around 1940 and 1950. The discrete time Fourier series pair is shown in (11) and (12).

x[n] = ∑ ak. ejk(2π/N)n

k=⟨n⟩

( 11 )

ak =1

N∑ X[n]e−jk(2π/N)n

k=⟨n⟩

( 12 )

• Fast Fourier Transform (FFT)

Algorithm developed over 1960s to improve the implementation of the Discrete Fourier Transform. This algorithm proved to be perfectly suited for efficient digital implementation, and it reduced the computation time for transforms by orders of magnitude. With this tool, many impractical ideas became practical. There are many algorithms to calculated FFT depending on the nature of numbers to be analyzed, but the most used in known as Cooley-Tuckey algorithm. ➢ FFT as a filter bank [23]

Processing digital signals require algorithms which can parallelized to take advantage of multiple processing units or a signal decomposition whereby each component in the signal decomposition can be process in parallel. The filter bank presents just a way to provide a signal decomposition useful in parallel signal processing. There are several advantages in using filter banks for parallel signal processing:

21

• Each sub-band signal is independent of the others.

• The processing software of each signal component can often be made identical.

• The required performance of the sub band processing unit is lowered, due to the lower sampling rate associated with sub band signals.

• The system is scalable in that the numbers of sub-bands created in the signal decomposition can be match to the available number of processing units or processors.

• There is option of bypassing the processing of certain sub bands to reduce hardware computational requirements.

The cost in the filter band approach for parallel signal processing is the latency associated in the analysis and synthesis. A common implementation is known as polyphase, corresponding with an uniform DFT. It assumes that analysis and synthesis filters are all generated from a simple frequency shifting of the prototypes. With polyphase, analysis and synthesis filtering occur at a lower sub band sampling rate, resulting in a lower processing speed. DFT and IDFT are commonly implemented with FFT, whose combined effects result in a significant computational reduction.

5.2.2. Time-Frequency Representation (TFR)

As mentioned before, studying a signal jointly in the time and frequency domains allows to obtain information about the temporal location of the spectral components of it. Fourier Transform by itself only gives the spectral content of a signal, preventing its use for the study of non-stationary signals [5]. A comparative example of both cases is presented in Table 5-1, Figure 5-2 and Figure 5-3.

Stationary signal Non-stationary signal

Superposition of three sinusoidal signals with frequencies: 10 Hz, 50 Hz and 300 Hz, fs=1000 Hz, 1,024 s time duration.

Signal with 1,024 s time duration, composed by three consecutive pulses of same frequencies, and 340 ms individual time duration

Simulation Parameters

Windowing Hamming

Additional considerations: without noise

Table 5-1 Comparative analysis for stationary and non-stationary signals

As it can be seen in Figure 5-2 and Figure 5-3, at the low-left graph in each figure, corresponding with the frequency response of signals related in Table 5-1, the spectrums are similar with identical spectral components at same frequencies (y-axis in each rotated graph), although signals in time domain representation are different (top graph in each figure). That assessment justifies the use of the Fourier Transform for non-stationary signal analysis. Middle image corresponds a Time Frequency Representation (TFR) called spectrogram, which is going to be explain in the implementation of the digital channelized receiver.

22

Figure 5-2 Non-Stationary signal

Figure 5-3 Stationary signal

A classic approach to detect unknown signals consist in taking energy measurements during a lapse of time, within a given bandwidth, as is made by radiometers. The evolution of the waveforms transmitted by radar and communications systems used in electronic warfare (LPI signals) has caused radiometry-based receivers do not obtain adequate gain process. These receptors are affected its performance by requiring analysis of high bandwidths, causing increased noise power and the appearance of possible interfering signals. TFRs appear as a need to analyze signals with high product time-frequency, trying to keep its sensitivity as close to a matched filter (optimum filter if signals were known), being able to represent spectral components variations over time [24]. Most of content related in this apart was extracted from [25]. Time Frequency Representations (TFRs) of signals map a one-dimensional signal on time x(t), into a

0 100 200 300 400 500 600 700 800 900 1000

-1

-0.5

0

0.5

1

n

s(n

)

s(n) vs n

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

-200204060

f d

Amplitude[dB]

signal spectrum

Mf d

5 10 15 20 250

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Am

plit

ude

-40

-30

-20

-10

0

10

20

30

40

0 100 200 300 400 500 600 700 800 900 1000

-2

0

2

n

s(n

)

s(n) vs n

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0102030405060

f d

Amplitude[dB]

signal spectrum

M

f d

5 10 15 20 250

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Am

plit

ude

-40

-30

-20

-10

0

10

20

30

40

23

two-dimensional function of time and frequency Tx(t, f). Most TFR are time varying spectral representations with time running along one axis and frequency along the other axis. The values of TFR surface above time-frequency plane give an indication as to which spectral components are present at which times. A graphical example of a matrix t-f filling process by means of spectrogram is shown in Figure 5-4 (a, b), taken from [26]. TFRs have been applied to analyze, modify and synthetize non-stationary or time varying signals. Three dimensional plots of TFRs surfaces enable a signal processor to analyze how spectral components of a signal or systems vary with time. The choice of the best TFR depends on the nature of the signals to be analyzed, additional to mathematical properties required, limitations in computation, storage, etc. Once a specific TFR has been selected, should be there adjust parameters like windowing, decimation, etc. A successful application of TFR presupposes some degree of expertise on the part of the user, and some knowledge about signals to be detected, in order to adapt the TFR parameters the best possible. TFR is a wide and increasingly field of research, due to the increased complexity of the signals presented in the electronic warfare field.

a.

b. Figure 5-4 Matrix t-f filling process by means of Spectrogram

24

An example decision tree for selecting a TFR presented by [24] is shown in Figure 5-5

TFR selection

Waveform signal

known?

Spectral correlators

Match Filter or correlator

FFT t-f others

STFT Atomic Descomposition

Stationary model

known parameters?

Stochastic models?

Classic radiometer

Radiometer

Cyclostationary model

Wigner Ville Distribution

Bank of correlators

Ambiguity function

Known parameters?

Multivariate detector

Monocyclic detector

Cyclostationary detector

yes no

no yes

yes

no

Figure 5-5 Example of decision tree for selecting a TFR

A common grouping of the TFRs is made from mathematical handling of its parameters as follows:

• Linear TFRs: Most common linear TFR are Short Time Fourier Transform (STFT) and Wavelet Transform (WT). Their main advantage is that obey the principle of linear superposition, letting analyze several simultaneous signals of different frequencies.

• Quadratic TFRs: They give information on how the energy of a signal is distributed in a time-frequency representation, these don’t obey the principle of liner superposition and their main disadvantage is the appearance of cross terms and aliasing. Most common quadratic TFR are: spectrogram and scalogram, related with STFT and WT respectively, which same poor time-frequency resolution, especially in STFT case. Another one is the Wigner Vile Distribution, whose main advantage is its excellent time-frequency resolution, related with spectrogram and scalogram.

• Adaptive TFRs: Adapted versions of the pervious classification In order to appreciate the range of TFRs available, then a set with their respective name and mathematical continuous expression are shown in Appendix B.

25

At last, some applications fields of common TFR are extracted from [25] and shown in Table 5-2.

TFR Common applications

STFT Time-varying signal analysis, system identification, spectral estimation, signal detection, parameter estimation, speaker identification, speaking coding, instantaneous frequency of signals, complex demodulation, time scale modification or wrapping of speech signals, dynamic range and bandwidth compression of acoustical signals

Wavelet Transform

Signal and image coding, acoustic and seismic signal processing, stochastic signal processing, fractal analysis, system analysis and detection

Spectrogram Analysis of speech signals

Wigner Distribution

Useful analysis tool in quantum mechanics, optics, acoustics, bioengineering, image processing, analysis of time-varying systems and highly non-stationary signals, analyzing phase distortion in audio, , analyzing non-linearity or defects un systems, , analyze speech, seismic data, , mechanical vibrations, codding applications in optical communications systems, signal detection, , spectrum and instantaneous frequency estimation, pattern recognition.

Ambiguity function Radar, sonar, radio astronomy, communications, optics. Analysis tool for selection, design and evaluation of radar signals, analysis of optical systems

Table 5-2Common TFR applications

5.3. Criteria selection and basic concepts about STFT

As is referred by [5] [1]some important criteria to take into account for selecting a STFT as a TFR are shown in Table 5-3.

Characteristic

Conceptually simple, widely studied and widely used in practice.

There are very efficient algorithms for implementation

It’s linear, thus generates no cross-terms, avoiding low pass filtering post-FFT.

Let uses of Digital Instantaneous Frequency Measurement (DIFM)

Regarding the computational load, STFT is more efficient than adaptive TFRs.

It can be seen as a uniform bank of filters with constant noise power at the output of each channel.

Table 5-3 STFT criteria selection

Possibly the most appreciable disadvantage of implementing STFT is related with its poor-time frequency resolution.

26

5.3.1. STFT Basic concepts

STFT can be seen as a Fourier Transform with sliding window. To obtain spectral time variation only is needed to move a window on certain intervals with same hope size and calculate the FT at each one. A STFT graphical description is shown in Figure 5-6 [26].

Figure 5-6 STFT graphical description

The mathematical description of the discrete STFT is shown in (13).

STDFTxω[n, k]) ∑ x[m]ω[m − n]e−j2π

k

Lm, k = 0, … , L − 1

n+(L−1)

m=n

( 13 )

Where

ω[n] ∶ window without nulls between 0 and L − 1 x[m] ∶ signal under analysis

n ∶ discrete time k ∶ Channel of normalized center frequency k/L

ωk =2πk

L, k ∶ 0, … , L − 1

( 14 )

5.3.2.STFT Time-frequency resolution

STFT correspond with applying FT to a signal x[m] windowed by [m-n]. If looking for a good spectral resolution will be needed a large window, difficulty to appreciate temporal variations of the signal spectral components. If is required good temporal resolution should be apply short coefficients windows. So that it’s impossible to get simultaneously good spectral and temporal resolution. By means of the interpretation as a filter of the STFT, frequency response of each filter corresponds the FT of

[m-n] conveniently rotated and centered. This can be seen in Figure 5-7 (a,b) [26].

27

a

b

Figure 5-7 window length effect in spectral components

Due to the uncertainty principle (15), there must be a compromise between the expected temporal resolution and the spectral resolution.

δf. δt ≥ k ( 15 )

A critical decision in performance of STFT correspond with the window selection, but else another parameters should be there take into account: side-lobes ratio (SLR), band pass ripple, transition band, etc. An example of the window length was extracted from [26] and shown in Figure 5-8 window length effect. In these sub index (S) refers to short, and (L) refers to long. From these, one can identity: ➢ Short windows measures only local properties. ➢ Long windows average spectral character. ➢ Shorter window more blurred spectrum. ➢ More time detail, less frequency detail.

a b

c d Figure 5-8 window length effect

5.3.3. STFT Processing Gain

28

STFT can be seen as a digital channelized receiver due to its process similar to a bank of filters. As occur in analog channelize receivers, SNR at the output channels improve, by the noise bandwidth reduction [5]. SNR can be calculated as in (16).

SNRout =BT

BvSNRin

( 16 )

Where: BT (Total Bandwidth): Noise bandwidth at input filter bank

Bv (Video bandwidth or process bandwidth): Bandwidth of each filter

By working with sequences, the total bandwidth will be (BW:0-), and video

bandwidth will correspond to 2𝜋

K, where K corresponds with the total number of filters.

Window length is associated with filter overlapping, so if a rectangular window is selecting, the number of channels will correspond with its length (N), otherwise filter numbers will be less than window length selected. Due to work with real signals, spectral information contents in negative and positive frequencies are the same, by which it’s equivalent to work with K/2 effective channels. SNR will be then calculated as:

SNRout =K

2SNRin

( 17 )

And the processing gains will be:

Gp =SNRout

SNRin=

K

2

( 18 )

5.4.Model description of Digital Channelized receiver to be simulated

This section concerned with the explanation of process related with the theoretical consideration to simulate/implement the architecture of the digital channelized receiver taken as reference from [1] [3]. The block diagram shown in Figure 5-9will serve to identify the focus of this thesis and so on later works to being developed in order to get an implementation. Only blocks drawn in blue dashed line where implemented in MATLAB.

29

Figure 5-9 Architecture of time-frequency receiver

Descriptionof blocks: ➢ Radiant system: Antenna array covering operating band that allow getting the

DOA: Direction of Arrival. ➢ RF system: Filters the band of interest, commonly between 0,5 GHz and 18

GHz. It realizes first channelization to down-frequency signals in FI. ➢ Detection system: Process signal in FI through filtering, correlation, etc., in order

to detect signals and identify some parameters like: TOA: Time of Arrival, PA: Pulse Amplitude, PW: Pulse Width and IF: instantaneous frequency. These parameters set should be there related with DOA from radiant system. This depend on the radiant system architecture.

➢ Encoder parameters: Responsible for clustering the detected signals, identify intrapulse modulation. Characteristics parameters of each detected signal are encoded by a Pulse Descriptor Word (PDW), which is sending to a data processor through a digital communication channel.

➢ Data processor: Perform data processing prior final information display to the user.

5.4.1. Time-Frequency Processor Once selected the TFRs, corresponding with STFT (13), next step corresponds to select a temporal window. This is designed from frequency response, using the desired attenuation mask and number of filters. By means of using a method for synthesis of digital filters FIR, the window values are getting. If total numbers of channels is K, is desirable channels whose bandwidth is 1/K, covering all frequencies effectively, Figure 5-10. Assuming an even value of K, and reals signals to be detected, only should be needed as many channels as return (19):

Ke =K

2− 1, each one centered at

k

K, k = 1, … ,

K

2− 1

( 19 )

Channels centered at 0 and 0,5 won’t be taken into account, due to their different statistical.

30

Figure 5-10 Approximate filters response

➢ Parks-McClellan method:

This method obtains a FIR filter with linear phase, known length, cutoff frequency in the band pass (fp), bandpass ripple (rp), cutoff frequency in the stop band(fa),

attenuation in stop band(ra).The filter designed will correspond with STFT channel centered at null frequency.

Equation (20) related mask attenuation parameters with the minimum window length of filter.

Nmin =−10. Log10(rp. ra) − 13

2,324 . Btr+ 1

( 20 )

Where, Btr = 2π(fa − fp) ( 21 )

B𝑡𝑟: Transition band (rad) Band pass ripple and attenuation in stop band relation in dB(Ra, Rb)and in natural units (ra, rb) are shown in (21) and (22).

Rp = 20. Log10(1 + rp) ( 22 )

Ra = −20. Log10(ra) ( 23 )

➢ Attenuation mask for channelized receiver:

Next parameters are established: Band pass = 1/2K Beginning of attenuated band = 1/K

These produces a transition band = 1/2K Variations in attenuation for the stop band and the band pass ripple will allow to handle different lengths.

31

As reference the window response in time and frequency used by [5] is shown in Figure 5-11.

Figure 5-11 Parks McClellan window, Rp 0,086 dB, Rs 60 dB, L 256

Some important considerations:

• Stop band specification is related with SLR of filter designed and the dynamic range desired.

• Band pass ripple is an indication about how much receiver sensibility could change as function of positioning signal inside the channel.

• If is necessary to increase the number of channels without increasing window length and holdingR𝑎, what is required is increasing Rp.

• Window length longer than number of channels implies in STFT operations the use of L/K channels.

➢ STFT decimation

The bank filters output is multiplied by a complex exponential which demodulate signal. Once in base band, filter bandwidth considering it to stop band avoiding aliasing becomes 1/K. Having a limited band signal, is possible its decimation (M).According to Nyquist, decimation must meet (24),(25):

1

M≥ 2.

1

K

( 24 )

M ≤K

2

( 25 )

These implies STFT can be evaluated through M samples, reducing computational load by the same factor. For an N-sample block, the size of the decimated STFT matrix becomes (26).

(1 +(N − L)

M) x (

K

2− 1)

( 26 )

32

➢ Extension of STFT With purpose of counteracting the poor resolution and lack of flexibility of STFT by its no adaptive characteristics, this scheme implements different non-coherent integration, maintaining computational burden. The STFT processing gain for a narrowband signal becomes (27).

Gp = K/(2LinsBn) ( 27 )

Where Lins is the channel insertion loss at the signal frequency, and Bn the relative noise bandwidth with respect to K-tap rectangular window. To increase the processing gain by non-coherent integration the smoothed spectrogram are defined as

Ii(m, k) = ∑ |STFT(rM, k)|2

Li.m

r=1+Li.(m−1)

, m = 1, … ,(

1−L

M) + 1

Li

( 28 )

Where, Li: Integration Length ➢ Integration length [5]

At the output of the filter bank a time-frequency map of the received signal is obtained. Depending on the type of signal, this map will be subject to a certain pattern. Based on the type of signal (modulation, duration) time remaining by filter will be variable. The approximate number of samples to integrate (NI) is calculated as indicated in (29).

Ni =Nf

M

( 29 )

Where, Nf: It corresponds to the number of samples in which a signal is within a single filter. Depending on the duration of the signal, three types of patterns will be distinguished, as indicated in Table 5-4.

𝐈𝐢 𝐋𝐢 Optimal in pattern Description

1 1 Short duration signals Pulsed radar without intrapulse modulation.

2 5 Intermediate duration signals

Pulsed signals with intrapulse modulation, for example: Chirp, Barker.

3 25 Long duration signals Commonly generated by LPI radars. They can present certain frequency and phase modulation. This group is

conformed by continuous wave signals, LFM modulation, digital spread spectrum signals: BPSK with

direct sequence modulation, etc.

Table 5-4 Non-coherent integration scheme

33

The interest for using different integration lengths is shown in Figure 5-12 [5]. There can be appreciate the degree of cell resolution occupation by each pattern signal, and their proximately required cell processing. Each segment along frequency axis corresponds to a filter, and its resolution is equivalent to the filter bandwidth. Temporal axis contains the response of the bank of filters at different instant times. The interval time between two consecutive outputs of this bank corresponds to its resolution time.

Figure 5-12 Time-Frequency map for different signals

Time-frequency processing cell is defined as the number of t-f cells needed to generate a resolution t-f processed. The system engaged is the non-coherent integration. It´s important to take into account the integration process should be made by each signal. Lengths Li are assumed to be divisible by one another. At least two integration types

should be considered: Integration (I1), which holds the highest resolution, and (IF) which achieves the highest processing gain for long duration signals. The longest integrator possible within the block of samples will be (30) [3].

LF = 1 +(N − L)

M

( 30 )

Some important consideration in a non-coherent process [5]:

• The non-coherent integration is the sum of the squared modulus of the samples that come out of the filter bank. In radar, pulses are integrated, meanwhile samples of same pulse are integrated by receivers.

• It’s not possible to employ coherent integration (more efficient), due to lack of knowledge about signals, and their possible changes in frequency.

• Non-coherent integration is applied on time axis, reason by which it’s appropriate for signals without frequency modulation (detect in the same filter).

34

• Some signals appear in different filters (like LFM), reason by which simultaneous time and frequency analysis is required. It’s necessary to implement and arbitration policy for differentiating the variation in instantaneous frequency and duration of intercept signals.

• By integrating, the minimum required SNR is reduced, previously limited by operating conditions (PFA, PD).

The set of expected responses by the Time-Frequency Processor are {STFT, I1, I2, … , IF}. 5.4.2. Detection and feature extraction The detection problem is addressed as a hypothesis testing problem:

H0 ∶ x = n ( 31 )

H1 ∶ x = ∑ Sr +

r

n ( 32 )

Where, n: Real-valued zero-mean Gaussian noise of known power

Sr: Signal present in the analyzed N-sample block. The local test turns out to be (33)

Ii(m, k)

H1

><H0

thi, i = 1,2, … F

( 33 )

Thresholds are set to meet a desired value of global false alarm probability (Pfag)

(34).

Pfag = PHo (⋃{Ii(m, k) > thi}

i,m,k

) ( 34 )

A local Pfa can also be defined for every local detection. For the time-frequency

points of the ith smoothed spectrogram (35)

Pfai(m, k) = PH0(Ii(m. k) > thi), i = 1,2, … , F ( 35 )

As the noise is white, the local Pfa is constant for the local decisions in the same

smoothed spectrogram. To find the thresholds {thi} meeting the global Pfa(Pfag), it’s

being assumed the local PFA is the same for all the smoothed spectrograms. In the digital receiver is contemplated K/2 effective channels. Given specific global operating conditions (Pfag, Pdg), is necessary to establish operational conditions per

channel (Pfac, Pdc). With the assumption of independence between channels the expression to calculate these are (36) (37) [5].

35

Pfac ≈Pfag

(K/2)

(36 )

Pdc ≈ 1 − (1 − Pdg)1

𝑟⁄

( 37 )

➢ Feature vector construction

Apart from the time-frequency location of the local detection, the feature vector includes the instantaneous frequency estimation by using the DIFM. For the channel k, the DIFM is defined as (38).

DIFM(r, k) =arg{STF((r + 1)M, k)} − arg{STFT(rM, k)}

2πM

( 38 )

Where, { . }: Phase Angle The DIFM is used to estimate the carrier frequency and recognized the signal modulation. The exact structure of the feature vector is detailed as follow. If a local detection occurs at Ii(m, k) the vector (θ) contains the smoothed spectrogram index (i), its

numerical value (Ii(m, k)), time location (m) and channel (k), and the DIFMs within

the integration length (Li) for channel k (39)(40)(41).

θ = [i, Ii(m, k), m, k, DIFM(r1, k), DIFM(r1 + 1, k), … , DIFM(r2, k)]T

( 39 )

Where, r1 = 1 + (m − 1). Li

( 40 )

r2 = m. Li

( 41 )

The detection stage of the Advanced Digital Channelized Receiver taken as reference is shown in Figure 5-13.

Figure 5-13 Detection stage of ADCRx

36

The following sections weren’t include in simulation, but they are reference in order to support basic knowledge for future implementations [1]. 5.4.3. Encoder From the feature vectors built in the detection stage, the encoder estimates the number of signals in the block under analysis, and their PDWs. Depending on its SNR, bandwidth, and duration, a signal can be simultaneously detected in different points of different smoothed spectrograms, so that several feature vectors can correspond to the same signal. Therefore, clustering is required to group all the feature vectors of the same signal. The PDW of every signal is estimated from the feature vectors of the corresponding cluster. The encoder takes the advantage of the STFT filter-bank interpretation by working in two steps: in-channel and in-block. In-channel, processing clusters the features vector from the same channel, and computes an in-channel PDW by assuming only one signal per channel. In-block processing clusters the in-channel PDWs of the same signal, fuses those PDWs into an in block PWD, and removes the out-of-channel detections. ➢ In-Channel PDW:

It contains several steps which are repeated for each channel where at least, a local detection occurred.

• Signal duration: Let Θk(i)

be the set of feature vectors with smoothed

spectrogram index i and channel k, the in-channel PA estimate for each smoothed spectrogram becomes (42).

PAi = {

max {2√I(θ) Li⁄ : θ ∈ Θk(i)

}

0, otherwise, if Θk

(i)≠ ∅}

( 42 )

Using these estimates, the signal is classified into a number of categories corresponding to the different smoothed spectrograms: signals of duration similar to smoothed spectrograms: signals of duration similar to the integration length of I1,

signals of duration similar to the integration length of I2, etc. The classification is carried out by successive hypothesis test (43) (44) (45).

PAF−1

PAF

Shorther than IF

≷Duration as IF

thPAF−1,F

( 43 )

PAF−2

PAF−1

Shorther than IF − 1≷

Duration as IF − 1thPAF−2,F−1

( 44 )

37

PA1

PA2

Duration as I1

≷Duration as I2

thPA1,2

( 45 )

Each threshold thPAi−1,ishould be obtained by simulating radar pulses with a similar

length to the integrators Ii−1 and Ii and by minimizing the probability of error in the

test PAi−1/PAi.

• PA estimate: If the signal is classified into the category of signal of length similar to the integrator

Ii, the in-channel PA estimate (PA) is defined as the one corresponding to the

integrator Ii. As the noise power is known(σ2), the SNR estimation becomes (46).

SNR =PA2

2σ2

( 46 )

• TOA and PW estimate: Temporal parameters (TOA and PW) are estimated according to the prior classification. That is, if the signal has a duration similar to the integrator Ii, the feature vector comming from the smothed spectrogram Ii are used. In order to

compute TOA and PW, the initial (ninit) and final (nend) decimated samples of the signal at channel k are required (47) (48).

ninit = min{(m(θ) − 1. Li + 1: θ ∈ Θk(i)

)} ( 47 )

nend = max{m(θ). Li: θ ∈ Θk(i)

} ( 48 )

Where Ii is the smoothed spectrogram corresponding to the signal duration, and

m(θ) is the time location of each feature vector θ. For high SNR, the smoothed spectrogram I1 is used, instead of the Ii, in order to provide a more accurate

estimation. Smoothed spectrogram I1 is used when SNR is over a certain threshold (SNRth) that assures a high probability of detection (in practice, this threshold can be defined as the SNR to detect a sinusoid with a probability of 99% by means of the

I1).

• Frequency estimate: The frequency estimated is computed by the weighted average of the DIFM samples from the time sample ninit(47) to nend − 1(48) at the considered channel. The weights are the values of smoothed spectrogram I1 and the expression of the frequency estimate becomes (49).

f =∑ I1(r, k)DIFM(r, k)

nend−1r=ninit

∑ I1(r, k)nend−1r=ninit

( 49 )

38

➢ Modulation recognition The in-channel automatic modulation classifier (AMC) follows a decision-theoretic approach. It distinguishes among four categories: no modulation, LFM, PSK and FSK, which are the typical modulation encountered in radar in digital communications systems. AMC uses the DIFM outputs of the considered channel

within the signal duration between the decimate samples ninit and nend − 1. In the preprocessing steps, a number of initial and final samples are removed to avoid peaks from the signal transients, and the signal length is verified to be greater than a minimum value. If lower, the signal is considered to be no modulated. Then the AMC proceeds as depicted in Figure 5-14. First, a frequency linear model is obtained by least squares. The model error (Ɛ) help separate LFM and no modulated signals from PSK and FSK modulated ones. The discrimination between LFM and no modulated signals is made by the magnitude of the estimated chirp-rate(a). AMC discriminates between PSK and FSK by the maximum of the 1st-order difference of the DIFM sequence (Δf) (50).

Δf(r, k) = DIFM(r + 1, k) − DIFM(r, k) ( 50 )

The threshold for the estimators Ɛ and �� hold the following general structure (51).

thT(SNR, PW) = μT(SNR, PW) + CT. σT(SNR, PW) ( 51 )

Where, μT and σT are the mean and standard deviation of the considered static T. To

compute thLFM, με and σε come from the distribution model error Ɛ for both modulated and LFM signals. Regarding tha,μa and σa come from the distribution of

the chirp rate estimate a for nonmodulated signals only.

Figure 5-14 In-channel AMC flow chart

39

➢ In-block PDW: The in channel PDWs are clustered according to a number of heuristic rules. First of

the entire in-channel PDW whit the greatest SNR, (main PDW), is selected and its

adjacent channels are grouped into the cluster according to time overlapping. SNR, and main PDW modulation. For each cluster the final PDW is the corresponding main PDW except for cluster considered to come from LFM signals. In that case, a re-estimation of the parameters is performed. The reminded no grouped in-channel PDWs undergo the sample process by selecting a new main PDW. The estimated

SNR is required in order to considerate the overlapping in time, since temporal parameter estimation degrades for low SNR. A threshold SNRf is used, so that

overlapping in time is not considered for SNR<SNRf.

• PDW estimation for LFM signals: In the in-block processing, a cluster is considered as LFM if the main PDW is found to be LFM modulated. However, for last LFM signals, there could be not enough samples to carry out the in-channel modulation analysis. In those cases the LFM character becomes apparent after examining the time-frequency arrangement of the in-channel PDWs forming the cluster.

• Cancellation of out of channel detections: Once a cluster has been formed, other no grouped channels may also be removed to prevent out-of-channel detections. Two types of out-of-channel are considered: rabbit-ear effect and signal sidelobe detection. The cancellation algorithm uses two thresholds determined by simulation and proceeds as follows:

▪ The lowest threshold is related to the rabbit-ear effect. If the number of channels in the cluster is greater than the threshold, the no grouped overlapped-in-time channels with sort duration are removed.

▪ The greatest threshold eliminates signal sidelobe detections. If the number of channels in the cluster is greater than this, the signal has a very broad band and all no grouped, overlapped-in-time channels are removed (independently of their duration).

➢ PDW construction

As mentioned before, PDW contains information related with: PA, TOA, PW, f and intrapulse modulation by each detected signal. PDW construction required correlated information through several steps, as indicated in Figure 5-15 [24].

40

Figure 5-15 PDWs construction

Each step is briefly described as follow:

• Detection STFT + I: Detected signals in a capture

• In-channel PDW: PDW constructed from detections carried out at certain channel, through amplitude comparisons between integrators with detections.

• In-block PDW: PDW association per channel with its coming capture. At this stage is intended find out the channels occupied by each specific signal detected, additional to fix PDWs in just one channel (channel arbitration policy).

• PDWs between captures: PDWs association from different captures.

PDWs association between captures

In-block PDW (PDWs association intra-capture)

In-channel PDW

Detection: STFT + I

41

SECTION II. Implementation of the simulation

6. ADVANCED DIGITAL CHANNELIZED RECEIVER MODEL IMPLEMENTATION

6.1. Analysis of parameters in time-frequency processor block

6.1.1. Design of the analysis window Taking as reference criteria about Parks-McClellan method and the attenuation mask explained in 5.4.1, the window parameters are design as follow [1] [22] [24]: As initial approach were selected: Ra=60 dB, Rp=0,086 dB and K=32. By using (20)

Nmin=163 was obtained. To set parameters that are power of two, compatible with the expected capture time (1024 samples), and a number that allow direct execution of successive DFTs (for future implementation applying FFT algorithms), the next

power of two was sought, finding a value of Nmin=256. Next increasing number of channels (K) to K=64 was sought, without changing Nmin or Ra. The only parameter on which modifications can be made is Rp. Using (20)

again, but at this time solving for rp, was found rp=0,6179 or Rp=0,52 dB.

The FIR filter with linear phase was obtained with MATLAB, following the next steps and shown in Figure 6-1and Figure 6-2. ➢ Use command firpmord: Parks-McClellan optimal FIR filter order estimation

command. Syntax: ([n,fo,ao,w] = firpmord(f,a,dev,fs)). This was iterated to verify

the compliance with Nmin. This demand to change the value of Rp to Rp=0,95

dB. ➢ Use command firpm: Parks-McClellan optimal FIR filter design. Syntax:

b = firpm(n,f,a,w).

Figure 6-1 Time and frequency response of Parks McClellan window

0 50 100 150 200 250-0.005

0

0.005

0.01

0.015

0.02

0.025Temporal response

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-140

-120

-100

-80

-60

-40

-20

0

20Frequency response

dB

fd

42

Figure 6-2 Frequency response of FIR filter design with Parks McClellan method, centered at 0,25.

Amplitude and phase on left side, group delay on right side

A general aspect of the bank of filters corresponding with the architecture selected is shown in Figure 6-3.

Figure 6-3 Bank of 31 FIR filters with Parks-McClellan method

Band pass ripple causes sensibility variations around±1 dB. It’s being better than increasing window length, which could cause higher computational load and longer transients [24]. 6.1.2. Time Decimation Factor (M) As it was explained in 5.4.1 referring to the STFT decimation, knowing the total numbers of filters will be K = 64, and using the maximum value allowed by the inequality (25), then the decimation factor will be M=32.

0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3-80

-60

-40

-20

0

( x ) rad/sample

|H(

)|,

dB

Parks McClellan

0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29

-2000

-1500

-1000

-500

0

( x ) rad/sample

Phase H

( ),

degre

es

Parks McClellan

0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29

-20

-10

0

10

20

30

40

50

60

70

( x ) rad/sample

|H(

)|,

dB

Group delay FIR filter with Parks McClellan method

Parks McClellan

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-120

-100

-80

-60

-40

-20

0

20

( x ) rad/sample

|H(

)|,

dB

Bank of filters with FIR filter Parks McClellan method

Parks McClellan

43

6.1.3. Selection of integration lengths As it was explained in 5.4.1 referring to the extension of STFT proposed by [1], consisting in the implementation of different lengths of integration and applying (29) and (30), the following lengths of integration were found. For one-sample integrator, which holds de highest resolution the corresponding length integration is equal to L1=1. For long signals, the longest integrator possible within the block of samples is equal to LF=25. An intermediate length integrator is needed to match intermediate duration signals and to prevent collapsing losses of the longest integrator. Taking into account the requirement consisting of use lengths divisible by one another, the length selected for intermediate duration signals is L2=5. 6.2. Analysis of parameters in detection and feature extraction block

6.2.1. Analysis of the probability of false alarm (Pfa) The estimation of the probabilities of false alarm was made by applying the method of Monte Carlo [27]. Some special considerations in its implementation are described as follows and a reference scheme is shown in Figure 6-4.

• Definition of a characteristic parameter of the system (I). It can be for example a probability (Pfa, Pd).

• Construction of a random experiment whose statistical average match the parameter (I) who is tried to be estimated.

• Experiment repetition (M) times, (M) defines the error or precision estimation (50).

• Calculate the estimate of the mean, with the output samples of the random experiment to obtain (I).

δ =√var[μz]

E[μz]= √

1 − p

pM

( 52 )

μz|calculation =∑ zi

Mi=1

M

( 53 )

44

Figure 6-4 Scheme for implementing Monte Carlo

From Figure 6-4 is possible to identify: X: Input signals to system (In case of Pfa analysis it corresponds with white Gaussian noise in phase and quadrature, simulated from Box-Müller method [27]) Y: Signal at comparator input Z: Output sequence T: Threshold

μz: Monte Carlo estimator

The scheme was valid for calculating Pfa and Pd, making appropriate adjustments to the simulation of the input signal. The blue line block only was take into account for probabilities which require integration. The great advantage of its use is the simplicity and generality, but demand computational load, according to the degree of accuracy required in the estimation. ➢ Effect of analysis window in Pfa estimation

The equation that calculates the probability of false alarm as function of threshold for a quadratic detector is (54).

Pfa = e−T

σT2⁄

( 54 )

Where, T: Threshold

σT2: Noise power at the receiver input

However, it isn’t valid at this experiment, due to the FFT block. At this experiment where only white Gaussian noise is considered at input (31), should be there and adjust in (54), to account the effect of gain produced by the FFT block and the window selected. As mentioned in [28], the incoherent power of a windowed transform is given by (55).

E{|F(ωk)|noise|2} = σq2 ∑ W2(nT)

n

( 55 )

Where, W2(nT): Sum of squared coefficients of the analysis window.

45

Given this consideration, the expression to be used to estimate Pfa (T), taking into account the windowing effect is (56).

Pfa = e

−T

σT2 .∑ W2(nT)n

( 56 )

As a verification, Table 6-1 relate behavioral of some curves Pfa vs T for two common windows, and Table 6-2 the effect of variance between the input signal to receiver and the output of quadratic receiver (for reference see Figure 6-4).

No Rectangular No Hamming

1

2

Table 6-1Comparative Pfa theoretical vs Monte Carlo estimated without normalized window coefficients.

Rectangular window, ∑window coeff. =5000

No Phase and quadrature histograms of input noise No Phase and quadrature histograms posterior FFT block

1

2

σ2 2,0071 σ2 10036

Hamming window, ∑window coeff. =1986

No Phase and quadrature histograms of input noise No Phase and quadrature histograms posterior FFT block

1

2

σ2 2,0138 σ2 4006

Table 6-2 Behavior variance in Pfa estimation with 5000 simulations of Monte Carlo

0 0.5 1 1.5 2 2.5 3

x 104

10-2

10-1

100

T

Pfa

Pfa(T) Quadratic detector without integratioin: Simulations=5000

Pfa (MonteCarlo)

Pfa (theoretical)

0 0.5 1 1.5 2 2.5 3

x 104

10-4

10-3

10-2

10-1

100

T

Pfa

Pfa(T) Quadratic detector without integratioin: Simulations=5000

Pfa (MonteCarlo)

Pfa (theoretical)

-4 -3 -2 -1 0 1 2 3 40

100

200

300

400

500

600

700

800

I2 =0.98651

-4 -3 -2 -1 0 1 2 3 4 50

100

200

300

400

500

600

700

800

Q2 =1.0139

-250 -200 -150 -100 -50 0 50 100 150 200 2500

100

200

300

400

500

600

700

I2 =4936.6597

-300 -200 -100 0 100 200 3000

100

200

300

400

500

600

700

Q2 =4936.6597

-4 -3 -2 -1 0 1 2 3 40

100

200

300

400

500

600

700

800

I2 =1.0035

-5 -4 -3 -2 -1 0 1 2 3 4 50

100

200

300

400

500

600

700

800

900

1000

Q2 =1.0103

-200 -150 -100 -50 0 50 100 150 2000

100

200

300

400

500

600

700

800

I2 =2021.05

-150 -100 -50 0 50 100 150 2000

100

200

300

400

500

600

700

Q2 =1985.7436

46

From this apart could be concluded:

• FFT block effect is linear over samples studied, keeping Gaussian distribution of noise through this.

• It was shown Monte Carlo estimator and theoretical expression (56) are equivalent for operation blocks which include windowing, FFT, but no integration.

• Depending on the incoherent power windowing (56), also should be adjusted threshold value for the operating condition required.

• As is well known windowing process could be seen as an amplitude modulation [22] [28], reason why in comparative curves Pfa vs T for different windows, it is seen that for the same selection of Pfa, a window as Hamming with respect to the reference (Rectangular), chosen criterion is reached with lower threshold values.

➢ (Pfa vs T) curve for spectrogram without samples integration (I1, L1 = 1)

This case allows to implement directly equation (56). Its length of integration equals to the unity corresponds with no integration. Figure 6-5 shows a comparison curves of Pfa (T) theoretical versus Monte Carlo estimation.

Figure 6-5 Pfa (T) for spectrogram I1, rectangular window without normalized window coefficients.

In this case having or not overlapped windows in time don’t affect the behavioral, letting equation (56) be applied indistinctly. ➢ (Pfa vs T) curves for spectrograms with sample integration (I2, L2 = 5) and

(I3, L3 = 25)

0 2000 4000 6000 8000 10000 1200010

-12

10-10

10-8

10-6

10-4

10-2

100

th

Pfa

(Pfa

vs th) without integration, spectogram I1 -> L= 1 simulations= 6400000

MonteCarlo

theoretical

47

Those represent special cases in the architecture selected, due to equation (56) can’t be applied directly by two reasons: Both cases present non-coherent integration and overlapped windowing in time. Figure 6-6 only is used as reference to show comparison curves for both cases. From this is obvious the impossibility of using deliberately equation (56) for confirming the Monte Carlo estimation.

Figure 6-6 Pfa (T) for spectrograms I2 (left), I3 (right) with Monte Carlo and theoretical (56).

Rectangular windows. Both cases without normalized window coefficients

In order to know the overlapped windowing effect in the estimation of Pfa (T) with non-coherent integration, it was simulated a scheme with four windows for rectangular and Hamming windows as show in Table 6-3 and Figure 6-7.

Block length (N): 1024 No Overlap (%) M

Window length (L): 256 1 0,0% 256

2 75,0% 192

3 50,0% 128

4 25,0% 64

5 12,5% 32

Table 6-3 Parameter for comparative effect of overlapping windows with non-coherent integration

Figure 6-7 Comparative effect of overlapping windows (rectangular (left) and Hamming (right)) with non-coherent integration and without normalized window coefficients

0 2000 4000 6000 8000 10000 1200010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

th

Pfa

(Pfa

vs th) with integration, spectrogram I2 -> L2= 5 M= 32 simulations= 1280000

MonteCarlo

theoretical

0 0.5 1 1.5 2 2.5 3

x 104

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

th

Pfa

(Pfa

vs th) with integration, spectrogram I3 -> L3= 25 M= 32 simulations= 256000

MonteCarlo

theoretical

0 2000 4000 6000 8000 10000 1200010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

th

Pfa

Pfa

(T) with four windows with different overlapped and non-coherent integration for four samples

0%

25%

50%

75%

12,5%

0 2000 4000 6000 8000 10000 1200010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

th

Pfa

Pfa

with four windows with different overlapped and non-coherent integration for four samples

0%

25%

50%

75%

12,5%

48

As it’s shown in Figure 6-6 and Figure 6-7, the increasing of overlapping windows causes Pfa curves reduce their slopes, what could be seen as an increasing of a threshold for the same Pfa value. Similar to a previous appreciation, the effect of selecting a window different from a basic rectangular, it will be reflected in a reduction of a threshold for the same Pfa selected due to the amplitude modulation associated with this process. In this thesis have a particular importance the effect of decimation time (M=32) and non-coherent integrations with 5 and 25 samples per channel. Derived from the previous analysis three possible solutions can be considered to provide threshold values as a function of the Pfa fixed.

a. From Pfa (T) curve estimated by using Monte Carlo, tabulated characteristics values for the selected receiver architecture, so that the operator can select from a discrete set of values, this operating parameter. This would correspond with the use of curves without markers in Figure 6-6, properly simulated with a wider range of thresholds.

b. Implementing the proposed methodology by B. Maranda [29], suitable for the analysis of signals processing by successive FFTs with overlapped blocks. Its implementation would allow an operator, to adjust dynamically the Pfa in a receiver system.

c. Implementing a scheme with the integration required but avoiding windows overlapped. This configuration is easily implement in simulation by using (57) [27]. By means of Figure 6-8 curves Pfa (T) for spectrograms I2 and I3 are shown.

Pfa = e−T

2 ∑ (1

2)

k−i Tk−i

(k − i)!, k: number of integrated pulses

k

i=1

( 57 )

Figure 6-8Pfa (T) for spectrograms I2 (left), I3 (right) with Monte Carlo and theoretical (57). Rectangular

windows

This last option presents the next disadvantages:

• As a non-overlapping windowing scheme, the signal information contained in the transition between windows is lost.

0 2000 4000 6000 8000 10000 1200010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

th

Pfa

(Pfa

vs th) with integration, spectrogram I2 -> L2= 5 M= 256 simulations= 1280000

MonteCarlo

theoretical

0 0.5 1 1.5 2 2.5 3

x 104

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

th

Pfa

(Pfa

vs th) with integration, spectrogram I3 -> L3= 25 M= 256 simulations= 256000

MonteCarlo

theoretical

49

• The length of the sample block size should be increased from 1024 sample to 6400 samples (as was simulated and shown in Figure 6-8), keeping window length (L=256) and the number of temporal analysis sections (25) corresponding to the spectrogram I3.

➢ Pfa curves to use in the simulation of the channelized receiver Taking into account the previous analysis, the methodology selected to estimate each one of the three Pfa (T) curves for spectrograms I1, I2 and I3 correspond with the literal “a”, from previous page. The only case which have a mathematical expression whose results is equivalent to Monte Carlo estimation corresponds to spectrogram I1, by means of use (56). At this case were used the window design with Parks McClellan method (6.1.1) whose windows coefficients are normalized by the window length. By using MATLAB in the detection system (Figure 5-9) under the hypothesis (31) were obtained: Figure 6-9, Figure 6-10 and Figure 6-11.

Figure 6-9 Pfa (T) for spectrogram I1 with Parks McClellan window

By fixing a global Pfa of Pfag = 1𝑥10−6, the local Pfa to be used by each spectrogram

is calculated from (36) as indicated in (58):

Pfac ≈Pfag

(K

2)

=1𝑥10−6

(64

2)

= 3,125𝑥10−8 ( 58 )

Due to estimated curves don’t reach this interest value by the number of simulations used, a methodology employed to estimate the correspondence threshold values was graphically extrapolate each curve by means of a CAD software, using a spline that fit the curve and extending it to a horizontal line that intersect the axis of probability (y-axis) in both, the value of Pfag and Pfac. The summarize of thresholds is

shown in Table 6-4.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.810

-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

T

Pfa

Pfa

(T) spectrogram I1, window:Parks McClellan,simulations 1.550.000

Pfa (Monte Carlo)

Pfa (theoretical)

50

Figure 6-10 Pfa (T) for spectrogram I2 with Parks McClellan window

Figure 6-11 Pfa (T) for spectrogram I3 with Parks McClellan window

Threshold

Spectrogram Pfa=1x10^-6 Pfa=3,125x10^-8

I1 0,526 0,660

I2 1,180 1,402

I3 2,550 2,840

Table 6-4 Thresholds for spectrograms I1, I2, I3

Only for reference, the numerical value obtained for spectrogram I1 with Pfa=3,125x10^-8 was T= 0,6577.

0 0.2 0.4 0.6 0.8 1 1.2 1.410

-6

10-5

10-4

10-3

10-2

10-1

100

T

Pfa

Pfa

(T) spectrogram I2, window: Parks McClellan, simulations 1.275.000

0 0.5 1 1.5 2 2.510

-5

10-4

10-3

10-2

10-1

100

T

Pfa

Pfa

(T) spectrogram I3, window: Parks McClellan, simulations 155000

51

6.2.2. Analysis of the probability of detection (Pd) Similar to the analysis of the Pfa, firs will be shown fundamentals for estimating the probability of detection, and subsequent will be collected the interest curves for different receivers and typical signal of interest. The estimation was made by using Monte Carlo, but at this time the hypothesis to implement corresponds with (32). ➢ Pd in a single tone without integration

First it will be shown the effect of detection a single tone in three possible cases: centered at a channel frequency, in middle of two channels and in an uncertain position between two consecutive channels (simulated by assuming an uniform distribution for its generation). Table 6-5 shows a summary of cases related for a rectangular window. Curves shown in the first column show Pd vs SNR, for each of three cases mentioned. Curves shown in the third column are indicative only, with purpose to visualize the signal aspect for: signal + noise (continuous blue line), single tone simulated (dashed red line) and threshold (continuous green line). Scalloping losses can be appreciated from this at second and third simulation (curves in second and third rows), in comparison with the spectrum of a single tone bin centered at middle frequency of the channel.

window: Rectangular

Pd(SNR) |S(k)|, |X(k)|, T

Tone centered in

a cannel frequency

Tone in middle of

two channels

-30 -25 -20 -15 -10 -50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

X: -17

Y: 0.893

S/N

Pd

Pd - quadratic detector, simulations= 1000

Pfa=1e-06

0 200 400 600 800 1000 1200-300

-250

-200

-150

-100

-50

0

50

100signal+noise S(k),signal X(k) and Threshold(T), bin for single tone k= 300 SNR= -7

k

|S(k

)| [

dB

]

|S(k)|

|X(k)|

T

-30 -25 -20 -15 -10 -50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

X: -13

Y: 0.894

S/N

Pd

Pd - quadratic detector, simulations= 1000

Pfa=1e-06

0 200 400 600 800 1000 1200-10

0

10

20

30

40

50

60signal+noise S(k),signal X(k) and Threshold(T), bin for single tone k= 300.5 SNR= -7

k

|S(k

)| [

dB

]

|S(k)|

|X(k)|

T

52

Tone in an uncertain position between

two adjacent channels, simulated

by an uniform

distribution in range {k-1/2 ,k+1/2}

Table 6-5 Pd vs SNR changing position of a single tone

Receiver sensitivity, defined as the minimum SNR required to detect a signal with a probability of Pd=90% is summarize in Table 6-6.

Single tone bin reference SNR (Pd=0,9)

Tone centered in a cannel frequency -17

Tone in middle of two channels -13

Tone in an uncertain position between two adjacent channels, simulated by an uniform distribution in range

{k-1/2, k+1/2} -15

Table 6-6 Summarize SNR required as function of centered bin of a single tone

A graphical comparison of sensitivity in two common windows: rectangular and Hamming is shown in Figure 6-12, in order to compare scalloping losses with a document reference [28].

Window: Rectangular

SNR (Pd=0,9) Pd(SNR)

Tone centered in a cannel frequency

-17

Tone in middle of two

channels -13

-30 -25 -20 -15 -10 -50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

X: -15

Y: 0.907

S/N

Pd

Pd - quadratic detector, simulations= 2000

Pfa=1e-06

0 200 400 600 800 1000 1200-10

0

10

20

30

40

50

60signal+noise S(k),signal X(k) and Threshold, bin for single tonen k= 300.2214 SNR= -7

k

|S(k

)| [

dB

]

|S(k)|

|X(k)|

T

-30 -25 -20 -15 -10 -50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

S/N

Pd

Pd - scalloping losses Pfa= 1e-06 simulation= 2000

k= 300

k= 300.5

53

Window Hamming

SNR (Pd=0,9) Pd(SNR)

Tone centered in a cannel frequency

-15,7

Tone in middle of two

channels -13,8

Figure 6-12 Scalloping losses for a single tone with rectangular and Hamming window

The comparison of scalloping losses getting by simulation and the one took from [28] is shown in Table 6-7.

Window SNR with Monte Carlo

simulation SNR [28]

Rectangular 4 3,92

Hamming 1,9 1,78

Table 6-7 Scalloping losses comparative

➢ Comparative sensitivity of the advanced channelized receiver with other common receiver architectures taken as reference

In order to appreciate the behavior of the architecture selected, two common receiver architecture were selected to compare with the Advanced Digital Channelized Receiver (ADCR), those are: DFT with 1024 samples and STFT only.

-30 -25 -20 -15 -10 -50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

S/N

Pd

Pd - scalloping losses Pfa= 1e-06 simulation= 2000

k= 300

k= 300.5

54

Some typical signals related with the radar field and digital communications were selected. Those are presented in Table 6-8.

Pattern classification Signal Specific detail

Long duration signal

CW without modulation tone with central digital frequency fd=8/256 and frequency change with uniform distribution within a channel bandwidth

CWLFM 500 MHz/ 1 ms

BPSK 10 MHz

Intermediate duration signal

Pulse phase modulated with Barker code

Barker 13 - 4,8 µs

Short duration signal Conventional pulse

tone with central digital frequency fd=8/256 and frequency change with uniform distribution within a channel bandwidth, t=1 µs

Table 6-8 Radar and digital communication signals to analyze with receivers

Curves obtained by simulation in each one of the three types of receivers are shown in the next pages, through Table 6-9, Table 6-10 and Table 6-11. In each one was used the window design with Parks McClellan method, in the case of the STFT-only and the Advanced Digital Channelized Receiver (ADCR) the windows parameters correspond with the described in 6.1.1. For the DFT-1024 receiver was designed a window with 1024 samples with the same methodology for using a Parks-McClellan window, with the next parameters: Ra=60 dB, Rp=0,93 dB.

55

• Pd curves for DFT receiver of 1024 samples

a. CW without modulation b. CWLFM 500 MHz 1 ms

c. BPSK 10 MHz d. Barker 13 - 4,8 µs

d. Conventional pulse 1µs

Table 6-9 Pd curves for DFT receiver with 1024 samples

-30 -25 -20 -15 -10 -5 00

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

S/N [dB]

Pd

CW, simulations= 2000

Pdc

Pdg

-30 -25 -20 -15 -10 -5 00

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

S/N [dB]

Pd

CWLFM 500 MHz 1 ms, simulations= 2000

Pdg

Pdc

-30 -25 -20 -15 -10 -5 0 5 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

S/N [dB]

Pd

BPSK 10 MHz, simulations= 2000

Pdc

Pdg

-30 -25 -20 -15 -10 -5 00

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

S/N [dB]

Pd

Barker 13-pulse 4,8 us, simulations= 2000

Pdc

Pdg

-30 -25 -20 -15 -10 -5 00

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

S/N [dB]

Pd

Conventional pulse 10-6 s, simulations= 2000

Pdc

Pdg

56

• Pd curves for single STFT receiver

a. CW without modulation b. CWLFM 500 MHz 1 ms

c. BPSK 10 MHz d. Barker 13 - 4,8 µs

e. Conventional pulse 1µs

Table 6-10 Pd curves for single STFT receiver

-16 -14 -12 -10 -8 -6 -4 -2 0 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SNR [dB]

Pd

Pd(SNR) only STFT for CW signal

PdI1g

PdI1

-16 -14 -12 -10 -8 -6 -4 -2 0 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SNR [dB]

Pd

Pd(SNR) only STFT for CWLFM signal, 500MHz/1 ms

PdI1g

PdI1

-15 -10 -5 0 5 10 150

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SNR [dB]

Pd

Pd(SNR) only STFT for BPSK signal, 10 MHz

PdI1g

PdI1

-16 -14 -12 -10 -8 -6 -4 -2 0 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SNR [dB]

Pd

Pd(SNR) pulse phase modulated with Barker 13 4,8 us

PdI1g

PdI1

-16 -14 -12 -10 -8 -6 -4 -2 0 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SNR [dB]

Pd

Pd(SNR) for conventional pulse 1 us

PdI1g

PdI1

57

• Pd curves for the Advanced digital channelized receiver(ADCR)

a. CW without modulation b. CWLFM 500 MHz 1 ms

c. BPSK 10 MHz d. Barker 13 - 4,8 µs

f. Conventional pulse 1µs

Table 6-11 Pd curves for the ADCR

The sensitivity comparison of the three receivers is shown in Table 6-12.

-16 -14 -12 -10 -8 -6 -4 -2 0 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SNR [dB]

Pd

Pd(SNR) for CW signal

Pdg

PdI1

PdI2

PdI3

-16 -14 -12 -10 -8 -6 -4 -2 0 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SNR [dB]

Pd

Pd(SNR) for CWLFM signal, 500MHz/1 ms

Pdg

PdI1

PdI2

PdI3

-15 -10 -5 0 5 10 150

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SNR [dB]

Pd

Pd(SNR) for BPSK signal, 10 MHz

Pdg

PdI1

PdI2

PdI3

-16 -14 -12 -10 -8 -6 -4 -2 0 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SNR [dB]

Pd

Pd(SNR) for pulse phase modulated with Barker 13 4,8 us

Pdg

PdI1

PdI2

PdI3

-16 -14 -12 -10 -8 -6 -4 -2 0 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SNR [dB]

Pd

Pd(SNR) for conventional pulse 1 us

Pdg

PdI1

PdI2

PdI3

58

Sensitivity: minimum SNR for Pfag=10e-6 and Pdg=90% (Pfac=Pfag/(K/2)) Estimated probability

RECEIVER SENSITIVITY (dB)

Pattern classification

Signal Specific detail DFT_1024 STFT (only), I1 ADCRx

Long duration signal

CW without modulation

tone with central digital frequency fd=32/1024 =8/256

and frequency change with uniform distribution within a

channel bandwidth

Pdg5 -11,260 -5,512 -11,530

Pdc -8,039 -2,734

I1 -2,734

I2 -6,860

I3 -11,530

CWLFM 500 MHz/ 1 ms

Pdg -12,190 -6,698 -11,160

Pdc -8,748 -3,070

I1 -3,070

I2 -6,904

I3 -11,160

BPSK 10 MHz, Tb=100 ns

Pdg -5,929 -4,432 -8,543

Pdc 8,441 7,555

I1 7,555

I2 -3,037

I3 -8,543

Intermediate duration signal

Pulse phase modulated with Barker code

Barker 13 - 4,8 µs

Pdg -8,677 -6,878 -11,770

Pdc -4,964 -2,998

I1 -2,998

I2 -6,771

I3 -11,770

Short duration signal

Conventional pulse

Generated from a tone with central digital frequency fd=32/1024 =8/256 with

uniform distribution within a

channel bandwidth, =1 µs

Pdg -10,380 -4,876 -7,205

Pdc -8,798 -2,785

I1 -2,785

I2 -7,178

I3 -6,582

Table 6-12 Sensitivity comparison between receivers

Some important considerations in simulation: every signal simulated as real, use of quadratic detector after channelization,

sampling frequency (fs = 250 MHz), Pdg = 90%, Pfag = 10−6, signals as cw without modulation and conventional pulse were

simulated with frequency changes from a realization to another according to another, according to a uniform distribution within the channel bandwidth, pulse signal was additional simulated time centered in block. BPSK signal with random code in bit period.

5Pdg: Global probability of detection, defined as the probability of having at least a local detection under the hypothesis H1.

59

From information registered in Table 6-12 can be concluded:

• In terms of the global probability of detection, the architecture of the ADCR taken as reference presents good sensitivity in comparison with the other two receivers, with the exception of CWLFM and conventional pulse, in which case the receiver who presents more sensitivity is the corresponding with the DFT_1024. A possible explanation of this performance can be associated with the narrow channelization of this last one. For instance, the 500 MHz/1ms CWLFM sweeps a very small bandwidth in the analyzed interval6 (around 2,05 MHz).

• Due to the processing gain of the ADCR, its sensitivity is better than the one presented by the STFT-only for all cases.

• Worst sensitivity in the three receivers is present with the BPSK signal.

• As it was expected in the ADCR, long signals are best suited with spectrogram I3. Similar occurs with the intermediate duration signal with the spectrogram I2, and conventional pulse with the spectrogram I1.

• Every probability of detection per channel was realize taking into account a channel where one would expect to detect the simulated signal.

6.2.3. Analysis of using DIFM Taking as reference what was expose in 5.4.2, referring to the use of DIFM in the feature vector construction, it’s important to note the necessity to unwrap the vector with phases, prior applying equation (38) and to respect the limit imposed by the inequality (25) in order to avoid aliasing. An example to unwrap the coefficients of one row (index filter 21) in the DIFM matrix, corresponding to one of the filters having detections by simulating a single real tone in bin 85/256 is shown in Table 6-13.

Table 6-13 Comparative wrap and unwrap index filter in DIFM (left), and frequency estimation of a

single tone by using DIFM

Taking as reference the argumentation exposed in [5] about the lack of efficiency of the DIFM for low SNR, some simulations were made to check the effect of changing the SNR in the frequency estimation for a single tone generated in bins: 63.5/256, 64/256, and 64.5/256 Results are presented in Table 6-14.

6The architecture of the ADCR has a 3,9 MHz channelization and 4,1 µs signal block

0 5 10 15 20 25-60

-50

-40

-30

-20

-10

0

10Comparative wrap/unwrap vecto with phases for a single tone generated in bin 85

wrap vector

unwrap vector

0 5 10 15 20 250.3318

0.3319

0.3319

0.332

0.332

0.3321

0.3322

0.3322

0.3322

time sequence

Insta

nta

neus f

requency

DIFM for single tone generated in bin 85

60

Table 6-14 SNR effect in frequency estimation with DIFM

The general formula for accurately estimating the instantaneous frequency of a signal from DIFM matrix calculation corresponds to the equation (59)

fi =kc

256+ DIFM(k, : ) − sign(DIFM(k, : ) ). mod(k, 2).

4

256

( 59 )

Where:

kc: central bin of filter having detection (Table 6-14) DIFM(k, : ): row vector number (k) in DIFM matrix corresponding with filter having detection sign(DIFM(k, : ) ): sign of each element in the row vector number (k) in DIFM matrix mod(k, 2): remainder to divide the central bin of filter having detection by two. A simulation showing the effect of the SNR value for a single tone generated at fd=8/256 is shown in Figure 6-13.

61

Figure 6-13 Comparative response for a single tone varying SNR value

Due to the need for a reference corresponding to each filter bank center bin, the information in Table 6-15 is appended

Reference filter in STFT

matrix

central bin in filter

Reference filter in STFT

matrix

central bin in filter

1 4 16 64

2 8 17 68

3 12 18 72

4 16 19 76

5 20 20 80

6 24 21 84

7 28 22 88

8 32 23 92

9 36 24 96

10 40 25 100

11 44 26 104

12 48 27 108

13 52 28 112

14 56 29 116

15 60 30 120

31 124

Table 6-15 Association between index filter in STFT and the center bin

Three examples of using DIFM with signals tabulated in Table 6-12 with their respective parameters are presented below (Table 6-16), all simulations were made with SNR=10dB.

0 5 10 15 20 250.0295

0.03

0.0305

0.031

0.0315

0.032

0.0325

Comparative response fi for a single tone in bin 8/256 with SNR (-2,7 dB ans 10 dB)

Time sequence

dig

ital f i

fi for SNR=-2,7 dB

fi for SNR= 10 dB

fi (theoretical)

62

CW without modulation, fd=8/256=0,03125 CWLFM 500 MHz/1 ms

Pulse with fd=8/256 and phase modulation Barker 13-4,8µs

Table 6-16 Examples of using DIFM for estimating instantaneous frequency

6.3. Operating simulation of digital channelized receiver

From previous considerations, Table 6-17 summarizes the parameters of the Advanced Digital Channelized Receiver implemented by simulation in MATLAB.

Parameter Symbol Value

Block length N 1024

Total number of channels K 64

Effective number of channels K/2 -1 31

Decimation M 32

Integration lengths for I1,I2,I3 L1 1

L2 5

L3 25

Parks McClellan Analysis Window

Length L 256

Pass band ripple Rp 1 dB

Attenuation Ra 60 dB

Other paramaters

Receiver bandwidth BW 125 MHz

Sampling frequency fs 250 MHz

Capture time 4,096µs

Bandwidth per channel BWc 3,91 MHz

STFT matrix dimensions STFT [31 x 25]

Table 6-17 Parameters of Digital Channelized Receiver to be implemented

0 5 10 15 20 250.0308

0.0309

0.031

0.0311

0.0312

0.0313

0.0314

0.0315

0.0316

0.0317

Time sequence

dig

ital f i

Comparative (Instantaneus frequency vs time sequence) theoretical and estimate with DIFM

fi in filter 2

fi theoretical

0 5 10 15 20 250.254

0.255

0.256

0.257

0.258

0.259

0.26

0.261

0.262

0.263Comparative (Instantaneus frequency vs Time sequence) theoretical and estimate with DIFM

Time sequence

dig

ital f i

fi in filter 16

fi in filter 17

fi theoretical

0 5 10 15 20 250.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05Instantaneus frequency for pulse centered at fd=8/256 with phase modulation Barker 13 - 4,8 us

Time sequence

dig

ital f i

63

From signals tabulated in Table 6-12 with their respective parameters, the sensitivity values corresponding to the spectrogram I1 and the threshold values tabulated in Table 6-4, the time-frequency responses obtained by simulation are presented below, in Table 6-18, Table 6-19, Table 6-20, Table 6-21, Table 6-22. Each table presents three blocks with graphics.

• The upper block contains the time frequency response obtained by a planar response of the spectrogram I1, by using the “imagesc” command from MATLAB. Above it the time response and on left side the frequency response (rotated 90° counterclockwise).

• The lower left graph presents a 3-D colored surface of spectrogram I1 by using the “surf” command from MATLAB.

• The lower right graph presents the detections in spectrogram I1 by using the “spy” command from MATLAB.

64

➢ Long duration signal (CW without modulation)

Table 6-18 TFR7 CW without modulation centered at fd=8/256 and frequency change within the channel bandwidth, SNR=-2,7 dB

7TFR:Time Frequency Representation

0 0.5 1 1.5 2 2.5 3 3.5 4

x 10-6

-5

0

5

n

s(n

)

s(n) vs n

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

-80-60-40-200

f d

Amplitude[dB]

signal spectrum

time segments

f d

200 300 400 500 600 700 800 900

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Am

plit

ude

-40

-35

-30

-25

-20

-15

-10

-5

0

0

500

1000

0

0.2

0.4

0.6

0.8

-50

-40

-30

-20

-10

0

10

time segments

Signal spectrogram -->[N=1024 L=256 Ke=31 M=32]

fd

Am

plit

ude

-40

-35

-30

-25

-20

-15

-10

-5

0

0 5 10 15 20 250

5

10

15

20

25

30

nz = 25

Matrix detections for spectrogram I1, Pfa1c= 3.125e-08T= 0.66

65

➢ Long duration signal (CWLFM)

Table 6-19TFR CWLFM 500 MHz/1 ms, centered at fd=62/256 and within a time interval to observe transition between two filters, SNR=-3,07 dB

0 1 2 3 4

x 10-6

-5

0

5

n

s(n)

s(n) vs n

0

0.1

0.2

0.3

0.4

-100-500

f d

Amplitude[dB]

signal spectrum

time segments

f d

200 400 600 800

0.1

0.2

0.3

0.4

Am

plitu

de

-40

-30

-20

-10

0

0

500

1000

0

0.2

0.4

0.6

0.8

-50

-40

-30

-20

-10

0

10

time segments

Signal spectrogram -->[N=1024 L=256 Ke=31 M=32]

fd

Am

plit

ude

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

0 5 10 15 20 250

5

10

15

20

25

30

nz = 29

Matrix detections for spectrogram I1, Pfa1c= 3.125e-08T= 0.66

66

➢ Long duration signal (BPSK)

Table 6-20TFR BPSK 10 MHz, Tb=100 ns, with random code per bit period, SNR=7,555 dB

0 1 2 3 4

x 10-6

-10

0

10

ns(

n)

s(n) vs n

0

0.1

0.2

0.3

0.4

-1000100

f d

Amplitude[dB]

signal spectrum

time segments

f d

200 400 600 800

0.1

0.2

0.3

0.4

Am

plitu

de

-40

-30

-20

-10

0

0

500

1000

0

0.2

0.4

0.6

0.8

-50

-40

-30

-20

-10

0

10

time segments

Signal spectrogram -->[N=1024 L=256 Ke=31 M=32]

fd

Am

plit

ude

-40

-35

-30

-25

-20

-15

-10

-5

0

5

0 5 10 15 20 250

5

10

15

20

25

30

nz = 84

Matrix detections for spectrogram I1, Pfa1c= 3.125e-08T= 0.66

67

➢ Intermediate duration signal (Pulse Barker)

Table 6-21TFR Pulse centered at fd=8/256, with phase modulation Barker 13 - 4,8 µs SNR=-2,998 dB

0 1 2 3 4

x 10-6

-5

0

5

n

s(n

)

s(n) vs n

0

0.1

0.2

0.3

0.4

-100-500

f d

Amplitude[dB]

signal spectrum

time segments

f d

200 400 600 800

0.1

0.2

0.3

0.4

Am

plit

ude

-50

-40

-30

-20

-10

0

0

500

1000

0

0.2

0.4

0.6

0.8

-60

-40

-20

0

20

time segments

Signal spectrogram -->[N=1024 L=256 Ke=31 M=32]

fd

Am

plit

ude

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

0 5 10 15 20 250

5

10

15

20

25

30

nz = 18

Matrix detections for spectrogram I1, Pfa1c= 3.125e-08T= 0.66

68

➢ Short duration signal (conventional pulse)

Table 6-22 TFR conventional pulse centered fd=8/256 =1 µs SNR= -2,785 dB

0 1 2 3 4

x 10-6

-4

-2

0

2

4

ns(n

)

s(n) vs n

0

0.1

0.2

0.3

0.4

-100-500

f d

Amplitude[dB]

signal spectrum

time segments

f d

200 400 600 800

0.1

0.2

0.3

0.4

Am

plit

ude

-60

-50

-40

-30

-20

-10

0

500

1000

0

0.2

0.4

0.6

0.8

-80

-60

-40

-20

0

time segments

Signal spectrogram -->[N=1024 L=256 Ke=31 M=32]

fd

Am

plit

ude

-60

-50

-40

-30

-20

-10

0 5 10 15 20 250

5

10

15

20

25

30

nz = 6

Matrix detections for spectrogram I1, Pfa1c= 3.125e-08T= 0.66

69

The last one TFR with three signals at the same capture time is shown in Table 6-23. The signal values were assigned as indicated below, and only for showing the ability of this TFR for detecting simultaneous signals. The parameters of these three signals are described below.

• CWLFM, Tr=5µs, f=80MHz, cutoff frequency 0 Hz.

• Pulse with phase modulation Barker-13, T=2,5 µs, centered at fd=0,4. Initial time equal to the initial capture time.

• Conventional pulse centered at fd=0,05 between samples 848 and 974.

Table 6-23 TFR with three signals at the same capture time, SNR=-2,785 dB

0 1 2 3 4

x 10-6

-5

0

5

n

s(n

)

s(n) vs n

0

0.1

0.2

0.3

0.4

-100-500

f d

Amplitude[dB]

signal spectrum

time segments

f d

200 400 600 800

0.1

0.2

0.3

0.4

Am

plit

ude

-40

-30

-20

-10

0

0

500

1000

0

0.2

0.4

0.6

0.8

-50

-40

-30

-20

-10

0

10

time segments

Signal spectrogram -->[N=1024 L=256 Ke=31 M=32]

fd

Am

plit

ude

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

0 5 10 15 20 250

5

10

15

20

25

30

nz = 33

Matrix detections for spectrogram I1, Pfa1c= 3.125e-08T= 0.66

70

7. CONCLUSIONS

✓ The way in which the development of this thesis was addressed, allowed

analyzing a particular line of systems in the field of radio frequency sensors of interest to CODALTEC. From the knowledge of the common environment of electronic warfare (technologies, systems and signals) in which today´s military operations are developed, allowed to identify critical points in the architecture of a receiver, whose optimization could be reflected in improved their tactical advantage in the battlefield.

✓ The analysis of different receiver architectures allowed to know a wide variety of

schemes, whose selection is influenced by different variables, among which is important to highlight the type of signal to be detected, its instantaneous bandwidth, sensitivity, acquisition speed, ability to work with simultaneous signals, range, accuracy, etc. The specific conditions in which it is expected a receiver operates optimally addressed the selection of a channelized receiver.

✓ Although the purpose of this thesis isn’t a physical implementation of any constitutive component of a receiver of electronic warfare, relevance was given to reviewing parameters selection and review the state of the art of two critical components (ADC and Digital Signal Processor). The knowledge derived from this will serve as a basis for a future integration or implementation of a receiver.

✓ The extensive literature review done on time-frequency techniques allowed to know the criteria for selecting it, applications where it is common to use, limitations of real time implementation for complex calculations and confirm the selection of the STFT as the correct TFR for future implementation in a receiver who can operate in real time, together with their analytical properties.

✓ Although implementation phase is small compared with the building blocks of a real receiver, It’s considered an important first step for understanding the signal processing through the detection/classification scheme, This architecture is very promising, mainly based on the fact of their increased sensitivity in comparison with other receiver architectures, due to their non-coherent integration and improvement in estimating frequency and modulation arising from the implementation of the DIFM. The extensive analysis done by estimating probabilities of detection and false alarm, allowed to characterize this architecture as function of typical LPI and communication signals, and have a first idea of the performance of a receiver with similar parameters in the actual complex electromagnetically battlefield.

71

REFERENCES

[1] J. Grajal, G. Lopez y A. Sanz, «Digital Channelized Receiver Based on Time-

Frequency Analysis for Signal Interception,» IEEE Trans. Aerosp.Electron.

Syst., vol. 41, nº 3, pp. 879-898, 2005.

[2] S. Vakin, L. Shustov y R. Dunwell, Fundamentals of electronic warfare,

Norwood, M.A: Artech House, 2001.

[3] G. Lopez, Detección y análisis de señales en interceptadores mediante técnicas

tiempo-frecuencia, Tesis Doctoral UPM, Madrid, 2003.

[4] M. Richards, J. Scheer y W. Holm, Principles of Modern Radar, New York:

Sheridan Books, Inc., Chelsea, MI, 1987.

[5] J. Grajal, Curso sobre Guerra Electrónica Radar - Receptores Digitales, Madrid:

Universidad Politecnica de Madrid, 1999.

[6] D. Adamy, EW 101 A first course of electronic warfare, Norwood, Ma.: Artech

House, 2001.

[7] A. Denk, Detection and jamming low probability of intercept (LPI) radars,

Monterrey,CA.: Naval Postgraduate School, 2006.

[8] F. Taboada, Detection and classification of low probability of intercept radar

signals using parallel filter arrays and higher order statistics- Thesis Naval

Postgraduate School, Monterey, CA: Naval Postgraduate School, 2002.

[9] P. Grant y J. Collins, «Introduction to electronic warfare,» IEE PROC., vol. 129,

nº 3, pp. 113-132, 1982.

[10] Naval Air Systems Command, Electronic Warefare and Radar Systems

Engineering Hand Book, Washington, DC: Naval Air Warfare Center, 1997.

[11] J. P. Lee, Interception of LPI radar signals., 1991.

[12] J. Tsui, «Digital microwave receiver technology,» IEEE Trans. on Microwave

theory and techniques, vol. 50, nº 3, pp. 699-705, 2002.

[13] J. Wepman, «Analog to Digital Converters and their applications in radio

72

receivers,» IEEE Comminications Magazine, pp. 39-45, 1995.

[14] R. Yu, N. Sheng, V. Ho y e. al., «Multi-Gigasample per second analog to digital

converters and digital to analog converters implemented in an ALGAAS/GAAS

HBT technology,» Proc. IEE, nº 466, pp. 13-16, 1999.

[15] Z. Shenghua, X. Dazhuan y J. Xueming, «ADC limitations on the Dynamic

Range of a Digital Receiver,» Proc. IEEE, pp. 79-82, 2005.

[16] M. Sanchez, M. Garrido, J. Grajal y e. al, «Digital channelized receivers on

FPGAs platforms,» Proc. IEEE, 2005.

[17] M. Cummings, «FPGA in the software radio,» Proc. IEEE, pp. 108-112, 1999.

[18] Universidad Politécnica de Madrid, Manual de practicas de laboratorio de

señales y comunicaciones, Madrid: Universidad Politécnica de Madrid -

E.T.S.I.T, 2004.

[19] S. Qian y D. Chen, «Understanding the nature of signals whose power spectra

change with time - Joint Analysis,» Proc. IEEE Signal Processing Magazine, pp.

52-67, 1999.

[20] A. Oppenheim y R. Schafer, Signals and Systems, Prentice Hall.

[21] A. Oppenheim y R. Schafer, Discrete-Time signal processing, Prentice Hall,

1999.

[22] Universidad Politécnica de Madrid, Master en radar, Tecnologías, Equipos y

Diseño de Sistemas - class notes, Madrid, 2014-2015.

[23] F. De Leon, «On the use of filter banks for parallel digital signal processing,»

Proc. 7th NASA symposium on VLSI Design, pp. 1-9, 1998.

[24] O. Artemi, Diseño de detectores digitales para entornos de guerra electrónica-

Doctoral Thesis, Madrid: Universidad Politécnica de Madrid, 2007.

[25] F. Hlawatsch y G. Boudreaux, «Linear and quadratic Time-frequency signal

representations,» Proc. IEEE SP Magazine, pp. 21-67, 1992.

[26] D. o. E. E.-. C. University y D. Ellis, «ELEN E4810-Summer 2014 Digital Signal

Processing,» Department of Electrical Engineering- Columbia University, 11

2013. [En línea]. Available:

http://www.ee.columbia.edu/~dpwe/e4810/outline.html.

73

[27] J. Grajal, Simulación de detectores radar- Master en Radar, Tecnologías,

Equipos y Diseño de Sistemas, Madrid: ETSIT UPM, 2014.

[28] F. Harris, «On the use of windows for Harmonic Analysis with the Discrete

Fourier Transform,» Proc. IEEE, vol. 66, nº 1, pp. 51-83, 1978.

[29] Maranda B., «On the false alarm probability of an overlapped FFT processor,»

Proc. IEEE transactions on Aerosp. Elect. Sys., vol. 32, nº 4, pp. 1452-1456,

1996.

[30] L. Cohen, «Time-Frequency Distributions-A review,» Proc. IEEE, vol. 77, nº 7,

pp. 941-981, 1989.

[31] J. Moreno, Técnicas tiempo frecuencia para análisis de señal radar, Proyecto de

fin de carrera UPM, Madrid, 1999-2000.

74

APPENDICES

Appendix A. Receiver types vs signals types [10]

Table 7-1Receiver types vs signals types

75

Table 7-2Qualitative comparison of receivers

76

Appendix B. Common Time Frequency Representations [25] [30]

77