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

Dual operative radar for vehicle to vehicle and vehicle to infrastructure communication

The research presented in this Thesis deals with the concepts of joint radar and communication system for automotive application. The novel systems developed include a joint radar and communication system based on the fractional Fourier transform (FrFT) and two interference mitigation frameworks. In the joint radar and communication system the FrFT is used to embed the data information into a radar waveform in order to obtain a signal sharing Linear Frequency Modulation (LFM) characteristics while allowing data transmission. Furthermore, in the proposed system multi user operations are allowed by assigning a specific order of the FrFT to each user. In this way, a fractional order division multiplexing can be implemented allowing the allocation of more than one user in the same frequency band with the advantage that the range resolution does not depend on the number of the users that share the same frequency band but only from the assigned of the FrFT. Remarkably, the predicted simulated radar performance of the proposed joint radar and communication system when using Binary Frequency Shift Keying (BFSK) encoding is not significantly affected by the transmitted data. In order to fully describe the proposed waveform design, the signal model when the bits of information are modulated using either BFSK or Binary Phase Shift Keying (BPSK) encoding is derived. This signal model will result also useful in the interference mitigation frameworks. In multi user scenarios to prevent mutual radar interference caused by users that share the same frequency band at the same time, each user has to transmit waveforms that are uncorrelated with those of other users. However, due to spectrum limitations, the uncorrelated property cannot always be satisfied even by using fractional order division multiplexing, thus interference is unavoidable. In order to mitigate the interference, two frameworks are introduced. In a joint radar communication system, the radar also has access to the communication data. With a near-precision reconstruction of the communication signal, this interference can be subtracted. In these two frameworks the interfering signal can be reconstructed using the derived mathematical model of the proposed FrFT waveform. In the first framework the subtraction between the received and reconstructed interference signals is carried out in a coherent manner, where the amplitude and phase of the two signals are taken into account. The performance of this framework is highly depend on the correct estimation of the Doppler frequency of the interfering user. A small error on the Doppler frequency can lead to a lack of synchronization between the received and reconstructed signal. Consequently, the subtraction will not be performed in a correct way and further interference components can be introduced. In order to solve the problem of the lack of the synchronization an alternative framework is developed where the subtraction is carried out in non-coherent manner. In the proposed framework, the subtraction is carried out after that the received radar signal and the reconstructed interference are processed, respectively. The performance is tested on simulated and real signals. The simulated and experimental results show that this framework is capable of mitigating the interference from other users successfully.The research presented in this Thesis deals with the concepts of joint radar and communication system for automotive application. The novel systems developed include a joint radar and communication system based on the fractional Fourier transform (FrFT) and two interference mitigation frameworks. In the joint radar and communication system the FrFT is used to embed the data information into a radar waveform in order to obtain a signal sharing Linear Frequency Modulation (LFM) characteristics while allowing data transmission. Furthermore, in the proposed system multi user operations are allowed by assigning a specific order of the FrFT to each user. In this way, a fractional order division multiplexing can be implemented allowing the allocation of more than one user in the same frequency band with the advantage that the range resolution does not depend on the number of the users that share the same frequency band but only from the assigned of the FrFT. Remarkably, the predicted simulated radar performance of the proposed joint radar and communication system when using Binary Frequency Shift Keying (BFSK) encoding is not significantly affected by the transmitted data. In order to fully describe the proposed waveform design, the signal model when the bits of information are modulated using either BFSK or Binary Phase Shift Keying (BPSK) encoding is derived. This signal model will result also useful in the interference mitigation frameworks. In multi user scenarios to prevent mutual radar interference caused by users that share the same frequency band at the same time, each user has to transmit waveforms that are uncorrelated with those of other users. However, due to spectrum limitations, the uncorrelated property cannot always be satisfied even by using fractional order division multiplexing, thus interference is unavoidable. In order to mitigate the interference, two frameworks are introduced. In a joint radar communication system, the radar also has access to the communication data. With a near-precision reconstruction of the communication signal, this interference can be subtracted. In these two frameworks the interfering signal can be reconstructed using the derived mathematical model of the proposed FrFT waveform. In the first framework the subtraction between the received and reconstructed interference signals is carried out in a coherent manner, where the amplitude and phase of the two signals are taken into account. The performance of this framework is highly depend on the correct estimation of the Doppler frequency of the interfering user. A small error on the Doppler frequency can lead to a lack of synchronization between the received and reconstructed signal. Consequently, the subtraction will not be performed in a correct way and further interference components can be introduced. In order to solve the problem of the lack of the synchronization an alternative framework is developed where the subtraction is carried out in non-coherent manner. In the proposed framework, the subtraction is carried out after that the received radar signal and the reconstructed interference are processed, respectively. The performance is tested on simulated and real signals. The simulated and experimental results show that this framework is capable of mitigating the interference from other users successfully

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

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