Fractional Focusing and the Chirp Scaling Algorithm With Real Synthetic Aperture Radar Data

abstract: For synthetic aperture radar (SAR) image formation processing, the chirp scaling algorithm (CSA) has gained considerable attention mainly because of its excellent target focusing ability, optimized processing steps, and ease of implementation. In particular, unlike the range Doppler and range migration algorithms, the CSA is easy to implement since it does not require interpolation, and it can be used on both stripmap and spotlight SAR systems. Another transform that can be used to enhance the processing of SAR image formation is the fractional Fourier transform (FRFT). This transform has been recently introduced to the signal processing community, and it has shown many promising applications in the realm of SAR signal processing, specifically because of its close association to the Wigner distribution and ambiguity function. The objective of this work is to improve the application of the FRFT in order to enhance the implementation of the CSA for SAR processing. This will be achieved by processing real phase-history data from the RADARSAT-1 satellite, a multi-mode SAR platform operating in the C-band, providing imagery with resolution between 8 and 100 meters at incidence angles of 10 through 59 degrees. The phase-history data will be processed into imagery using the conventional chirp scaling algorithm. The results will then be compared using a new implementation of the CSA based on the use of the FRFT, combined with traditional SAR focusing techniques, to enhance the algorithm's focusing ability, thereby increasing the peak-to-sidelobe ratio of the focused targets. The FRFT can also be used to provide focusing enhancements at extended ranges.Dissertation/ThesisM.S. Electrical Engineering 201

Advanced signal processing solutions for ATR and spectrum sharing in distributed radar systems

Previously held under moratorium from 11 September 2017 until 16 February 2022This Thesis presents advanced signal processing solutions for Automatic Target Recognition (ATR) operations and for spectrum sharing in distributed radar systems. Two Synthetic Aperture Radar (SAR) ATR algorithms are described for full- and single-polarimetric images, and tested on the GOTCHA and the MSTAR datasets. The first one exploits the Krogager polarimetric decomposition in order to enhance peculiar scattering mechanisms from manmade targets, used in combination with the pseudo-Zernike image moments. The second algorithm employs the Krawtchouk image moments, that, being discrete defined, provide better representations of targets’ details. The proposed image moments based framework can be extended to the availability of several images from multiple sensors through the implementation of a simple fusion rule. A model-based micro-Doppler algorithm is developed for the identification of helicopters. The approach relies on the proposed sparse representation of the signal scattered from the helicopter’s rotor and received by the radar. Such a sparse representation is obtained through the application of a greedy sparse recovery framework, with the goal of estimating the number, the length and the rotation speed of the blades, parameters that are peculiar for each helicopter’s model. The algorithm is extended to deal with the identification of multiple helicopters flying in formation that cannot be resolved in another domain. Moreover, a fusion rule is presented to integrate the results of the identification performed from several sensors in a distributed radar system. Tests performed both on simulated signals and on real signals acquired from a scale model of a helicopter, confirm the validity of the algorithm. Finally, a waveform design framework for joint radar-communication systems is presented. The waveform is composed by quasi-orthogonal chirp sub-carriers generated through the Fractional Fourier Transform (FrFT), with the aim of preserving the radar performance of a typical Linear Frequency Modulated (LFM) pulse while embedding data to be sent to a cooperative system. Techniques aimed at optimise the design parameters and mitigate the Inter-Carrier Interference (ICI) caused by the quasiorthogonality of the chirp sub-carriers are also described. The FrFT based waveform is extensively tested and compared with Orthogonal Frequency Division Multiplexing (OFDM) and LFM waveforms, in order to assess both its radar and communication performance.This Thesis presents advanced signal processing solutions for Automatic Target Recognition (ATR) operations and for spectrum sharing in distributed radar systems. Two Synthetic Aperture Radar (SAR) ATR algorithms are described for full- and single-polarimetric images, and tested on the GOTCHA and the MSTAR datasets. The first one exploits the Krogager polarimetric decomposition in order to enhance peculiar scattering mechanisms from manmade targets, used in combination with the pseudo-Zernike image moments. The second algorithm employs the Krawtchouk image moments, that, being discrete defined, provide better representations of targets’ details. The proposed image moments based framework can be extended to the availability of several images from multiple sensors through the implementation of a simple fusion rule. A model-based micro-Doppler algorithm is developed for the identification of helicopters. The approach relies on the proposed sparse representation of the signal scattered from the helicopter’s rotor and received by the radar. Such a sparse representation is obtained through the application of a greedy sparse recovery framework, with the goal of estimating the number, the length and the rotation speed of the blades, parameters that are peculiar for each helicopter’s model. The algorithm is extended to deal with the identification of multiple helicopters flying in formation that cannot be resolved in another domain. Moreover, a fusion rule is presented to integrate the results of the identification performed from several sensors in a distributed radar system. Tests performed both on simulated signals and on real signals acquired from a scale model of a helicopter, confirm the validity of the algorithm. Finally, a waveform design framework for joint radar-communication systems is presented. The waveform is composed by quasi-orthogonal chirp sub-carriers generated through the Fractional Fourier Transform (FrFT), with the aim of preserving the radar performance of a typical Linear Frequency Modulated (LFM) pulse while embedding data to be sent to a cooperative system. Techniques aimed at optimise the design parameters and mitigate the Inter-Carrier Interference (ICI) caused by the quasiorthogonality of the chirp sub-carriers are also described. The FrFT based waveform is extensively tested and compared with Orthogonal Frequency Division Multiplexing (OFDM) and LFM waveforms, in order to assess both its radar and communication performance

Instantaneous Frequency Estimation and Signal Separation Using Fractional Continuous Wavelet Transform

In the signal processing field, time-frequency representations (TFR\u27s) have intensively been improved to provide effective and powerful tools for reliable signal analysis. One of the most valuable and frequently used tools is Fourier transform (FT) which has been used to study the frequency content of stationary signals in the Fourier domain (FD). However, FT is not sufficient to study the frequency of non-stationary signals. For this particular type of signals to be best analyzed, some transforms such as the short time Fourier transform (STFT) and the continuous wavelet transform (CWT) have been introduced to provide us with a signal representation in the time-frequency plane. Another transform based on STFT and CWT; namely, the synchrosqueezing transform (SST), was introduced to improve the sharpness of the TFR\u27s by assigning the coefficient value to a different point in the TF plane. Also, TFR\u27s with satisfactory energy concentration and the corresponding SST’s involving both time and frequency variables were introduced; namely, the instantaneous frequency-embedded STFT (CWT) (IFE-STFT/IFE-CWT), where a rough estimation of the IF of a targeted component was used to achieve an accurate IF estimation. Recently, the STFT, the CWT and the corresponding SST’s with a time-varying window width are proposed and studied. These transforms have shown the confidence in the accuracy of both sharpening the TFR and separating the components of a multicomponent non-stationary signal, which then led to obtain a more accurate component retrieval formula at any local time. In order to improve the time-frequency resolutions, the concept of fractional Fourier transform (FrFT) was introduced as a potent tool to analyze time-varying signals; however, it fails in locating the frequency content in the fractional Fourier domain (FrFD). To this regard, the short time fractional FT (STFrFT) and the fractional CWT (FrCWT) were proposed to solve this issue by displaying the time and FrFD-frequency contents jointly in the time-FrFD-frequency plane. In this dissertation, we provide a component retrieval formula for a multicomponent signal from its FrCWT with integral involving only the scale variable and then introducing the corresponding SST (FrWSST). We also introduce the first and second order SST based on the IFE-CWT (IFE-WSST) and then propose time-FrFD-frequency representations with satisfactory energy concentration; namely, IFE-FrCWT and the corresponding SST (IFE-FrWSST). Lastly, we consider the FrCWT with a time-varying window width; namely, the adaptive FrCWT (AFrCWT) and the corresponding SST (AFrWSST). We propose these TFR\u27s in the FrFD for the purpose of not only improving the accuracy of the IF estimation and the energy concentration of these transforms, but also enhancing the separation conditions for the components of a multicomponent signal to be retrieved more accurately

Sensor Signal and Information Processing II

In the current age of information explosion, newly invented technological sensors and software are now tightly integrated with our everyday lives. Many sensor processing algorithms have incorporated some forms of computational intelligence as part of their core framework in problem solving. These algorithms have the capacity to generalize and discover knowledge for themselves and learn new information whenever unseen data are captured. The primary aim of sensor processing is to develop techniques to interpret, understand, and act on information contained in the data. The interest of this book is in developing intelligent signal processing in order to pave the way for smart sensors. This involves mathematical advancement of nonlinear signal processing theory and its applications that extend far beyond traditional techniques. It bridges the boundary between theory and application, developing novel theoretically inspired methodologies targeting both longstanding and emergent signal processing applications. The topic ranges from phishing detection to integration of terrestrial laser scanning, and from fault diagnosis to bio-inspiring filtering. The book will appeal to established practitioners, along with researchers and students in the emerging field of smart sensors processing

Analysis and decomposition of frequency modulated multicomponent signals

Frequency modulated (FM) signals are studied in many research fields, including seismology, astrophysics, biology, acoustics, animal echolocation, radar and sonar. They are referred as multicomponent signals (MCS), as they are generally composed of multiple waveforms, with specific time-dependent frequencies, known as instantaneous frequencies (IFs). Many applications require the extraction of signal characteristics (i.e. amplitudes and IFs). that is why MCS decomposition is an important topic in signal processing. It consists of the recovery of each individual mode and it is often performed by IFs separation. The task becomes very challenging if the signal modes overlap in the TF domain, i.e. they interfere with each other, at the so-called non-separability region. For this reason, a general solution to MCS decomposition is not available yet. As a matter of fact, the existing methods addressing overlapping modes share the same limitations: they are parametric, therefore they adapt only to the assumed signal class, or they rely on signal-dependent and parametric TF representations; otherwise, they are interpolation techniques, i.e. they almost ignore the information corrupted by interference and they recover IF curve by some fitting procedures, resulting in high computational cost and bad performances against noise. This thesis aims at overcoming these drawbacks, providing efficient tools for dealing with MCS with interfering modes. An extended state-of-the-art revision is provided, as well as the mathematical tools and the main definitions needed to introduce the topic. Then, the problem is addressed following two main strategies: the former is an iterative approach that aims at enhancing MCS' resolution in the TF domain; the latter is a transform-based approach, that combines TF analysis and Radon Transform for separating individual modes. As main advantage, the methods derived from both the iterative and the transform-based approaches are non-parametric, as they do not require specific assumptions on the signal class. As confirmed by the experimental results and the comparative studies, the proposed approach contributes to the current state of the-art improvement

The Fractional Fourier Transform and Its Application to Fault Signal Analysis

To a large extent mathematical transforms are applied on a signal to uncover information that is concealed, and the capability of such transforms is valuable for signal processing. One such transforms widely used in this area, is the conventional Fourier Transform (FT), which decomposes a stationary signal into different frequency components. However, a major drawback of the conventional transform is that it does not easily render itself to the analysis of non-stationary signals such as a frequency modulated (FM) or amplitude modulated (AM) signal. The different frequency components of complex signals cannot be easily distinguished and separated from one another using the conventional FT. So in this thesis an innovative mathematical transform, Fractional Fourier Transform (FRFT), has been considered, which is more suitable to process non-stationary signals such as FM signals and has the capability not only of distinguishing different frequency components of a multi-component signal but also separating them in a proper domain, different than the traditional time or frequency domain. The discrete-time FRFT (DFRFT) developed along with its derivatives, such as Multi-angle-DFRFT (MA-DFRFT), Slanted Spectrum and Spectrogram Based on Slanted Spectrum (SBSS) are tools belonging to the same FRFT family, and they could provide an effective approach to identify unknown signals and distinguish the different frequency components contained therein. Both artificial stationary and FM signals have been researched using the DFRFT and some derivative tools from the same family. Moreover, to accomplish a contrast with the traditional tools such as FFT and STFT, performance comparisons are shown to support the DFRFT as an effective tool in multi-component chirp signal analysis. The DFRFT taken at the optimum transform order on a single-component FM signal has provided higher degree of signal energy concentration compared to FFT results; and the Slanted Spectrum taken along the slant line obtained from the MA-DFRFT demonstration has shown much better discrimination between different frequency components of a multi-component FM signal. As a practical application of these tools, the motor current signal has been analyzed using the DFRFT and other tools from FRFT family to detect the presence of a motor bearing fault and obtain the fault signature frequency. The conclusion drawn about the applicability of DFRFT and other derivative tools on AM signals with very slowly varying FM phenomena was not encouraging. Tools from the FRFT family appear more effective on FM signals, whereas AM signals are more effectively analyzed using traditional methods like spectrogram or its derivatives. Such methods are able to identify the signature frequency of faults while using less computational time and memory

Mobile node-aided localization and tracking in terrestrial and underwater networks

In large-scale wireless sensor networks (WSNs), the position information of individual sensors is very important for many applications. Generally, there are a small number of position-aware nodes, referred to as the anchors. Every other node can estimate its distances to the surrounding anchors, and then employ trilateration or triangulation for self-localization. Such a system is easy to implement, and thus popular for both terrestrial and underwater applications, but it suffers from some major drawbacks. First, the density of the anchors is generally very low due to economical considerations, leading to poor localization accuracy. Secondly, the energy and bandwidth consumptions of such systems are quite significant. Last but not the least, the scalability of a network based on fixed anchors is not good. Therefore, whenever the network expands, more anchors should be deployed to guarantee the required performance. Apart from these general challenges, both terrestrial and underwater networks have their own specific ones. For example, realtime channel parameters are generally required for localization in terrestrial WSNs. For underwater networks, the clock skew between the target sensor and the anchors must be considered. That is to say, time synchronization should be performed together with localization, which makes the problem complicated. An alternative approach is to employ mobile anchors to replace the fixed ones. For terrestrial networks, commercial drones and unmanned aerial vehicles (UAVs) are very good choices, while autonomous underwater vehicles (AUVs) can be used for underwater applications. Mobile anchors can move along a predefined trajectory and broadcast beacon signals. By listening to the messages, the other nodes in the network can localize themselves passively. This architecture has three major advantages: first, energy and bandwidth consumptions can be significantly reduced; secondly, the localization accuracy can be much improved with the increased number of virtual anchors, which can be boosted at negligible cost; thirdly, the coverage can be easily extended, which makes the solution and the network highly scalable. Motivated by this idea, this thesis investigates the mobile node-aided localization and tracking in large-scale WSNs. For both terrestrial and underwater WSNs, the system design, modeling, and performance analyses will be presented for various applications, including: (1) the drone-assisted localization in terrestrial networks; (2) the ToA-based underwater localization and time synchronization; (3) the Doppler-based underwater localization; (4) the underwater target detection and tracking based on the convolutional neural network and the fractional Fourier transform. In these applications, different challenges will present, and we will see how these challenges can be addressed by replacing the fixed anchors with mobile ones. Detailed mathematical models will be presented, and extensive simulation and experimental results will be provided to verify the theoretical results. Also, we will investigate the channel estimation for the fifth generation (5G) wireless communications. A pilot decontamination method will be presented for the massive multiple-input-multiple-output communications, and the data-aided channel tracking will be discussed for millimeter wave communications. We will see that the localization problem is highly coupled with the channel estimation in wireless communications

The Discrete Linear Chirp Transform and its Applications

In many applications in signal processing, the discrete Fourier transform (DFT) plays a significant role in analyzing characteristics of stationary signals in the frequency domain. The DFT can be implemented in a very efficient way using the fast Fourier transform (FFT) algorithm. However, many actual signals by their nature are non--stationary signals which make the choice of the DFT to deal with such signals not appropriate. Alternative tools for analyzing non--stationary signals come with the development of time--frequency distributions (TFD). The Wigner--Ville distribution is a time--frequency distribution that represents linear chirps in an ideal way, but it has the problem of cross--terms which makes the analysis of such tools unacceptable for multi--component signals. In this dissertation, we develop three definitions of linear chirp transforms which are: the continuous linear chirp transform (CLCT), the discrete linear chirp transform (DLCT), and the discrete cosine chirp transform (DCCT). Most of this work focuses on the discrete linear chirp transform (DLCT) which can be considered a generalization of the DFT to analyze non--stationary signals. The DLCT is a joint frequency chirp--rate transformation, capable of locally representing signals in terms of linear chirps. Important properties of this transform are discussed and explored. The efficient implementation of the DLCT is given by taking advantage of the FFT algorithm. Since this novel transform can be implemented in a fast and efficient way, this would make the proposed transform a candidate to be used for many applications, including chirp rate estimation, signal compression, filtering, signal separation, elimination of the cross--terms in the Wigner--Ville distribution, and in communication systems. In this dissertation, we will explore some of these applications