Time-Frequency techniques for the detection of signals in non-stationary environments

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(1)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.

(2) 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. ii.

(3) 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. iii.

(4) 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. iv.

(5) 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 v.

(6) 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. vi.

(7) 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.. vii.

(8) 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 tiempofrecuencia, transformada de Fourier de tiempo corto (STFT), enventanado, señales no estacionarias.. viii.

(9) 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 noncoherent 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. ix.

(10) 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. x.

(11) 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. xi.

(12) 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.. 1.

(13) 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. 2.

(14) 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.. 1. Taken from http://www.radartutorial.eu/. 3.

(15) 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 2. Taken from: http://www.globalsecurity.org/ Taken from http://www.radartutorial.eu/. 3. 4.

(16) 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 R interceptor to radar as I > 1, where R I is the detection distance of a radar from an RR. interceptor, and R R is the detection distance of an interceptor from a radar. Using the radar equation, the power received by the radar is: S|R =. The. S N. PGTR GRR λ2 σ (4π)3 R4 LR. (1). relation without processing after the detector could be calculated as: S PGTR GRR λ2 σ | = N R (4π)3 R4 KT0 FR BR LR. (2). If exist processing after detection, the equivalent bandwidth receptor radar (BER) is B the one should be usedBER = G R . PR. P GTR , GRR. Radar peak power. Gain of the transmition antenna radar, Gain of the reception antenna radar. λ σ R FR BR LR GPR. Wave length of signal transmitted.. Target cross section. Radar-Interceptor distance. Noise factor radar receiver. Wideband radar receiver. Radar losses. Proccesing gain radar. Signal received by the interceptor is: S|I =. PGTR GRI λ2 (4π)2 R2 LI. (3). And signal to noise ratio in the interceptor is: S PGTR GRI λ2 | = N I (4π)2 R2 KT0 FI BeI LI. P GRI λ FI BEI LI. (4). Radar peak power. Gain of the receiver antenna interceptor Wavelength of signal transmitted. Noise factor interceptor. Equivalent bandwidth of interceptor Interceptor losses.. 5.

(17) By relating the equations (2) and (4): S S 4πR2 GRI FR LR BeR | = | . N I N R σ GRR FI LI BeI. (5). Some important considerations are derived from that: 4πR2. Factor : Advantage of the interceptor due the distance and the inconvenience of σ its radar cross section. G Factor RI : Radar advantage accounting for the fact of having a directive reception GRR. antenna. F R LR : Receptor quality factor for both systems. F I LI 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 GRR FI LI BeI ] 4π GRI FR LR BeR. 1⁄ 2. 1⁄ 2. ≈[. σ GRR FI LI t R−I ] 4π GRI FR LR t I−R. , 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: t R−I (Observation time on interceptor by radar) and t I−R (Obervation time on the radar by the interceptor). To defined radar-interceptor battle is necessary to calculate the signal to noise ratio S in R = R E , | and compared to that required for a given probability of detection N RE. (Pd ), and a probability of false alarm (Pfa ), which are assumed to be equal for radar S and interceptor, | ≈ 13 dB with Pfa = 10−6 and Pd = 90%, associated with a N Pfa− Pd. maximum range R D , If R D < R E , 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 R E measure decreases, trying minimize B the eR factor in equation (5). BeI. 6.

(18) 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).. 7.

(19) 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.. 8.

(20) 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.. 9.

(21) 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.. 10.

(22) 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. 11.

(23) ➢ 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.. 12.

(24) 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.. 13.

(25) 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 TEXAS INSTRUMENTS ADC12J4000 TEXAS INSTRUMENTS ADC12D1800RF TEXAS INSTRUMENTS ADC12D1600RF. MAXIM MAX 109 ANALOG DEVICES AD9680-1000. Sampling frequency (Gsps). Bits. Analog input BW (GHz). Input tension levels (V). SNR. Common 1.2 fin= 2.4 GHz 4 12 3.3 Differential 55 dB 0.2 Common fin= 1.44 GHz 2.2 3.6 12 2.7 54.3 / 54.6 Differential dB 0.10 Common 2.2 fin= 1.44 GHz 3.2 12 2.7 Differential 57 / 59 dB 0.10 Common 2.5 fin= 1.6 GHz 2.2 8 2.8 Differential 44 / 44.6 dB 0.2 Common fin= 1.9 GHz 2.5 1.0 12 2.0 57 / 67.2 Differential dBFS 0.2 Table 4-1 Main specifications in high speed ADCs. SFDR. Jitter (ps). fin= 2.4 GHz 68.3 / 74.9 dBFS. 0.12 RMS. fin= 1.44 GHz 61 / 68.1 dBc. 0.2 RMS. fin= 1.44 GHz 67.3 / 67.9 dBc. 0.2 RMS. fin= 1.6 GHz 50.3 / 61.7 dBc. 0.2 RMS. fin= 1.9 GHz 68 / 88 dBFS. 0.3 RMS. It is important consider the current trend in ADC performance, whose tendency is sample closer to the receiving antenna directly in RF in addition with the search high dynamic range and wide signal bandwidth that enable implementation advanced multi-function digital receiver systems, leading to significant reduction cost, size, weight and power dissipation of current systems [13] [14].. to of of of. 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.. 14.

(26) 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 Microcontrollers (MCUs) Microprocessors DSPs GPUs FPGAs. ASSPs. ASICs. BENEFITS Low cost, miniaturization, easy to program. Higher levels of clock for highperformance, easy to program. Dedicated components for signal processing, floating point arithmetic. Parallel processing to speed CPUs. Flexible Hardware defined by software, reprogrammable circuits inherent parallel processing. Speed and optimization for specific applications, offers standard commercially available chips. Fully Configurable Chips, constrained optimization and a single package for one application.. CONSIDERATIONS Insufficient power (HP) for high performance applications. More power, sequential processing architecture. Inherently sequential processing. More power, necessarily requires a CPU. Programming complexity in hardware description languages. Without flexibility to modify designs.. High initial investment and feasible only in high volumes.. Table 4-2 Actual processor technologies. 4. Taken from: II Curso de Telecomunicaciones y Guerra Electrónica de la ACING- Tecnologías ESM- ETSIT. 15.

(27) 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 Programming Language Ease of software programming Performance. VHDL, Verilog Fairly easy, however a programmer needs to understand the hardware architecture before programming. Can be very fast in an appropriate architecture is design.. Reconfigurability. SRAM type FPGA can be reconfigurable infinite times. Reconfiguration method. Reconfiguration is done by downloading configuration data to a chip electronically.. Areas where FPGAs can outperform DSPs, or vice versa. FIR filter, IIR filter, correlator, FFT, etc.. Power consumption. Can be minimized if the circuit is designed to save power, or the power is dynamically controlled. Implementation method of MAC. Parallel multiplier/adder arithmetic.. 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.. Parallelism. Can be parallelized to achieve high performance.. or. distributed. DSPs C, Assembly language Easy Speed is limited by the clock speed of a DSP chip. Can be reconfigurable by changing program memory content. Reconfiguration is done by simply reading a program at a different memory address. A signal processing program of sequential nature. 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. Repeated operation of MAC function. 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. DSP chip programming is usually sequential and cannot be parallelized.. Table 4-3 FPGAs vs DSPs comparative. 16.

(28) 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. 17.

(29) 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 pseudonoise (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 , t 2 , … , t n ) 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.. 18.

(30) 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. (7). k=−∞. That representation let getting a Fourier series representation, where the coefficients are given by (8). ak =. 1 ∫ x(t). e−jnω0t T0 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).. 19.

(31) ∞. 1 ∫ X(ω). ejωt dω x(t) = 2π. (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. ( 11 ). k=⟨n⟩. ak =. 1 ∑ X[n]e−jk(2π/N)n N. ( 12 ). k=⟨n⟩. •. 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:. 20.

(32) • • • • •. 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 Signal with 1,024 s time duration, Superposition of three sinusoidal signals composed by three consecutive pulses of with frequencies: 10 Hz, 50 Hz and 300 same frequencies, and 340 ms individual Hz, fs=1000 Hz, 1,024 s time duration. 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.. 21.

(33) s(n) vs n 1. s(n). 0.5 0 -0.5 -1 0. 100. 200. 300. 400. 500 n. 600. 700. 800. 900. 1000. 0.4. 0.35. 0.35. 0.3. 0.3. 0.25. 0.25. 40 30 20 10. Amplitude. 0.45. 0.4. d. 0.45. f. f. d. signal spectrum. 0 -10. 0.2. 0.2. 0.15. 0.15. -20. 0.1. 0.1. -30. 0.05. 0.05. -40. 0. 0 60. 40. 20 Amplitude[dB]. 0. -20. 5. 10. 15. 20. 25. M. Figure 5-2 Non-Stationary signal s(n) vs n. s(n). 2. 0. -2 0. 100. 200. 300. 400. 500 n. 600. 700. 800. 900. 1000. 40. 0.45. 0.4. 0.4. 0.35. 0.35. 20. 0.3. 0.3. 10. 0.25. 0.25. 0.2. 0.2. 0.15. 0.15. 0.1. 0.1. 0.05. 0.05. 0 60. 30. Amplitude. d. 0.45. f. f. d. signal spectrum. 0 -10 -20 -30 -40. 0 50. 40 30 20 Amplitude[dB]. 10. 0. 5. 10. 15. 20. 25. M. 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. 22.

(34) 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 nonstationary 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. 23.

(35) An example decision tree for selecting a TFR presented by [24] is shown in Figure 5-5 TFR selection. yes known parameters? no. yes. Bank of correlators. FFT. STFT. t-f. Waveform signal known?. Match Filter or correlator. Stochastic models?. Stationary model. Classic radiometer. others. no. Radiometer. Cyclostationary model. Wigner Ville Distribution yes. Atomic Descomposition Multivariate detector. Spectral correlators. Ambiguity function no. Known parameters? Monocyclic detector. Cyclostationary detector. 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.. 24.

(36) At last, some applications fields of common TFR are extracted from [25] and shown in Table 5-2. TFR STFT. Wavelet Transform Spectrogram Wigner Distribution. Ambiguity function. Common applications 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 Signal and image coding, acoustic and seismic signal processing, stochastic signal processing, fractal analysis, system analysis and detection Analysis of speech signals 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. 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.. 25.

(37) 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). n+(L−1). STDFTxω[n, k]). k L. −j2π m. ∑ x[m]ω[m − n]e. ( 13 ). , k = 0, … , L − 1. m=n. 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 , k ∶ 0, … , L − 1 L. ( 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].. 26.

(38) 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. 27.

(39) 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). SNR out =. BT SNR in Bv. ( 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 2𝜋 bandwidth will correspond to , where K corresponds with the total number of filters. K. 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: K SNR in 2. ( 17 ). SNR out K = SNR in 2. ( 18 ). SNR out =. And the processing gains will be: Gp =. 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.. 28.

(40) 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): K. k. K. K e = 2 − 1, each one centered at K, k = 1, … , 2 − 1. ( 19 ). Channels centered at 0 and 0,5 won’t be taken into account, due to their different statistical.. 29.

(41) 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. Log 10 (rp . ra ) − 13 +1 2,324 . Btr. ( 20 ). Where, Btr = 2π(fa − fp ). ( 21 ). B𝑡𝑟 : Transition band (rad). Band pass ripple and attenuation in stop band relation in dB (R a , R b )and in natural units (ra , rb ) are shown in (21) and (22). R p = 20. Log10 (1 + rp ). ( 22 ). R a = −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. 30.

(42) 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 holdingR 𝑎 , what is required is increasing R p . 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 1 ≥ 2. M K M≤. K 2. ( 24 ). ( 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) K ) x ( − 1) M 2. ( 26 ). 31.

(43) ➢ 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/(2Lins Bn ). ( 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 Li .m. Ii (m, k) =. ∑. |STFT(rM, k). r=1+Li .(m−1). |2. , m = 1, … ,. (. 1−L M. )+1. ( 28 ). Li. 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 1 2. 𝐋𝐢 1 5. 3. 25. Optimal in pattern Short duration signals Intermediate duration signals Long duration signals. Description Pulsed radar without intrapulse modulation. Pulsed signals with intrapulse modulation, for example: Chirp, Barker. 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. 32.