Spectrum sensing is the process of identifying the frequencies of a spectrum in which Signals Of Interest (SOI) are present. In case of continuous time signals present in a wideband spectrum, the information rate is seen to be much less than that suggested by its bandwidth and are therefore known as sparse signals. A review of the literature in [1] and [2] indicates that two of the many techniques used in wideband spectrum sensing of sparse signals are the Wideband Compressive Radio Receiver (WCRR) for multitoned signals and the mixed analog digital system for multiband signals. In both of these techniques even though the signals are sampled at sub-Nyquist rates using Compressive Sampling (CS), the recovery algorithms used by them are different from that of CS. In WCRR, a simple correlation function is used for the detection of carrier frequencies and in a mixed analog digital system, a simple digital algorithm is used for the identification of frequency support. Through a literature survey, we could identify that a VHSIC hardware descriptive ModelSim simulation model for wideband spectrum sensing of multitoned and multiband signals using sub Nyquist sampling does not exist. If a ModelSim simulation model can be developed using VHDL codes, it can be easily adapted for FPGA implementation leading to the development of a realistic hardware prototype for use in Cognitive Radio (CR) communication systems. The research work reported through this dissertation deals with the implementation of simulation models of WCRR and mixed analog digital system in ModelSim by making use of VHDL coding. Algorithms corresponding to different blocks contained in the conceptual design of these models have been formulated prior to the coding phase. After the coding phase, analyses of the models are performed using test parameter choices to ensure that they meet the design requirements. Different parametric choices are then assigned for the parametric study and a sufficient number of iterations of these simulations were carried out to verify and validate these models. / MIng (Computer and Electronic Engineering), North-West University, Potchefstroom Campus, 2014

Spectrum sensing is the process of identifying the frequencies of a spectrum in which Signals Of Interest (SOI) are present. In case of continuous time signals present in a wideband spectrum, the information rate is seen to be much less than that suggested by its bandwidth and are therefore known as sparse signals. A review of the literature in [1] and [2] indicates that two of the many techniques used in wideband spectrum sensing of sparse signals are the Wideband Compressive Radio Receiver (WCRR) for multitoned signals and the mixed analog digital system for multiband signals. In both of these techniques even though the signals are sampled at sub-Nyquist rates using Compressive Sampling (CS), the recovery algorithms used by them are different from that of CS. In WCRR, a simple correlation function is used for the detection of carrier frequencies and in a mixed analog digital system, a simple digital algorithm is used for the identification of frequency support. Through a literature survey, we could identify that a VHSIC hardware descriptive ModelSim simulation model for wideband spectrum sensing of multitoned and multiband signals using sub Nyquist sampling does not exist. If a ModelSim simulation model can be developed using VHDL codes, it can be easily adapted for FPGA implementation leading to the development of a realistic hardware prototype for use in Cognitive Radio (CR) communication systems. The research work reported through this dissertation deals with the implementation of simulation models of WCRR and mixed analog digital system in ModelSim by making use of VHDL coding. Algorithms corresponding to different blocks contained in the conceptual design of these models have been formulated prior to the coding phase. After the coding phase, analyses of the models are performed using test parameter choices to ensure that they meet the design requirements. Different parametric choices are then assigned for the parametric study and a sufficient number of iterations of these simulations were carried out to verify and validate these models. / MIng (Computer and Electronic Engineering), North-West University, Potchefstroom Campus, 2014

ITC/USA 2014 Conference Proceedings / The Fiftieth Annual International Telemetering Conference and Technical Exhibition / October 20-23, 2014 / Town and Country Resort & Convention Center, San Diego, CA / Massive amounts of data are typically acquired in third generation full-waveform (FW) LIDAR systems to generate image-like depthmaps of a scene of acceptable quality. The sampling systems acquiring this data, however, seldom take into account the low information rate generally present in the FW signals and, consequently, they sample very inefficiently. Our main goal here is to compare two efficient sampling models and processes for the individual time-resolved FW signals collected by a LIDAR system. Specifically, we compare two approaches of sub-Nyquist sampling of the continuous-time LIDAR FW return pulses: (i) modeling FW signals as short-duration pulses with multiple bandlimited echoes, and (ii) modeling them as signals with finite rates of innovation (FRI).

ITC/USA 2013 Conference Proceedings / The Forty-Ninth Annual International Telemetering Conference and Technical Exhibition / October 21-24, 2013 / Bally's Hotel & Convention Center, Las Vegas, NV / Third generation LIDAR full-waveform (FW) based systems collect 1D FW signals of the echoes generated by laser pulses of wide bandwidth reflected at the intercepted objects to construct depth profiles along each pulse path. By emitting a series of pulses towards a scene using a predefined scanning patter, a 3D image containing spatial-depth information can be constructed. Unfortunately, acquisition of a high number of wide bandwidth pulses is necessary to achieve high depth and spatial resolutions of the scene. This implies the collection of massive amounts of data which generate problems for the storage, processing and transmission of the FW signal set. In this research, we explore the recovery of individual continuous-time FW signals at sub-Nyquist rates. The key step to achieve this is to exploit the sparsity in FW signals. Doing this allows one to sub-sample and recover FW signals at rates much lower than that implied by Shannon's theorem. Here, we describe the theoretical framework supporting recovery and present the reader with examples using real LIDAR data.

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Ultrawideband (UWB) is one of the promising technologies for future short-range high data rate communications (e.g. for wireless personal area networks) and longer range low data rate communications (e.g. wireless sensor networks).Despite its various advantages and potentials (e.g. low-cost circuitry, unlicensed reuse of licensed spectrum, precision ranging capability etc.), UWB also has its own challenges. The goal of this dissertation is to identify and address some of those challenges, and provide a framework for practical UWB transceiver design.In this dissertation, various modulation options for UWB systems are reviewed in terms of their bit error rate (BER) performances, spectral characteristics, modem and hardware complexities, and data rates. Time hopping (TH) code designs for both synchronous (introduced an adaptive code assignment technique) and asynchronous UWB impulse radio (IR) systems are studied. An adaptive assignment of two different multiple access parame ters (number of pulses per symbol and number of pulse positions per frame)is investigated again considering both synchronous and asynchronous scenarios, and a mathematical framework is developed using Gaussian approximations of interference statistics for different scenarios. Channel estimation algorithms for multiuser UWB communication systems using symbol-spaced (proposed a technique that decreases the training size), frame-spaced (proposed a pulse-discarding algorithm for enhanced estimationperformance), and chip-spaced (using least squares (LS) estimation) sampling are analyzed.A comprehensive review on multiple accessing andinterference avoidance/cancellation for IR-UWB systems is presented.BER performances of different UWB modulation schemes in the presence of timing jitter are evaluated and compared in static and multipath fading channels, and finger estimation error, effects of jitter distribution, and effects of pulse shape are investigated. A unified performance analysis app roach for different IR-UWB transceiver types (stored-reference, transmitted-reference, and energy detector) employing various modulation options and operating at sub-Nyquist sampling rates is presented. The time-of-arrival (TOA) estimation performance of different searchback schemesunder optimal and suboptimal threshold settings are analyzed both for additive white Gaussian noise (AWGN) and multipath channels.

The Shannon sampling framework is widely used for discrete representation of analog bandlimited signals, starting from samples taken at the Nyquist rate. In many practical applications, signals are not bandlimited. In order to accommodate such signals within the Shannon-Nyquist framework, one typically passes the signal through an anti-aliasing filter, which essentially performs bandlimiting. In applications such as RADAR, SONAR, ultrasound imaging, optical coherence to-mography, multiband signal communication, wideband spectrum sensing, etc., the signals to be sampled have a certain structure, which could manifest in one of the following forms: (i) sparsity or parsimony in a certain bases; (ii) shift-invariant representation; (iii) multi-band spectrum; (iv) finite rate of innovation property, etc.. By using such structure as a prior, one could devise efficient sampling strategies that operate at sub-Nyquist rates. In this Ph.D. thesis, we consider the problem of sampling and reconstruction of finite-rate-of-innovation (FRI) signals, which fall in one of the two classes: (i) Sum-of-weighted and time-shifted (SWTS) pulses; and (ii) Sum-of-weighted exponential (SWE). Finite-rate-of-innovation signals are not necessarily bandlimited, but they are specified by a finite number of free parameters per unit time interval. Hence, the FRI reconstruction problem could be solved by estimating the parameters starting from measurements on the signal. Typically, parameter estimation is done using high-resolution spectral estimation (HRSE) techniques such as the annihilating filter, matrix pencil method, estimation of signal parameter via rotational invariance technique (ESPRIT), etc.. The sampling issues include design of the sampling kernel and choice of the sampling grid structure. Following a frequency-domain reconstruction approach, we propose a novel technique to design compactly supported sampling kernels. The key idea is to cancel aliasing at certain set of uniformly spaced frequencies and make sure that the rest of the frequency response is specified such that the kernel follows the Paley-Wiener criterion for compactly supported functions. To assess the robustness in the presence of noise, we consider a particular class of the proposed kernel whose impulse response has the form of sum of modulated splines (SMS). In the presence of continuous-time and digital noise cases, we show that the reconstruction accuracy is improved by 5 to 25 dB by using the SMS kernel compared with the state-of-the-art compactly supported kernels. Apart from noise robustness, the SMS kernel also has polynomial-exponential reproducing property where the exponents are harmonically related. An interesting feature of the SMS kernel, in contrast with E-splines, is that its support is independent of the number of exponentials. In a typical SWTS signal reconstruction mechanism, first, the SWTS signal is trans formed to a SWE signal followed by uniform sampling, and then discrete-domain annihilation is applied for parameter estimation. In this thesis, we develop a continuous-time annihilation approach using the shift operator for estimating the parameters of SWE signals. Instead of using uniform sampling-based HRSE techniques, operator-based annihilation allows us to estimate parameters from structured non-uniform samples (SNS), and gives more accurate parameters estimates. On the application front, we first consider the problem of curve fitting and curve completion, specifically, ellipse fitting to uniform or non-uniform samples. In general, the ellipse fitting problem is solved by minimizing distance metrics such as the algebraic distance, geometric distance, etc.. It is known that when the samples are measured from an incomplete ellipse, such fitting techniques tend to estimate biased ellipse parameters and the estimated ellipses are relatively smaller than the ground truth. By taking into account the FRI property of an ellipse, we show how accurate ellipse fitting can be performed even to data measured from a partial ellipse. Our fitting technique first estimates the underlying sampling rate using annihilating filter and then carries out least-squares regression to estimate the ellipse parameters. The estimated ellipses have lesser bias compared with the state-of-the-art methods and the mean-squared error is lesser by about 2 to 10 dB. We show applications of ellipse fitting in iris images starting from partial edge contours. We found that the proposed method is able to localize iris/pupil more accurately compared with conventional methods. In a related application, we demonstrate curve completion to partial ellipses drawn on a touch-screen tablet. We also applied the FRI principle to imaging applications such as frequency-domain optical-coherence tomography (FDOCT) and nuclear magnetic resonance (NMR) spectroscopy. In these applications, the resolution is limited by the uncertainty principle, which, in turn, is limited by the number of measurements. By establishing the FRI property of the measurements, we show that one could attain super-resolved tomograms and NMR spectra by using the same or lesser number of samples compared with the classical Fourier-based techniques. In the case of FDOCT, by assuming a piecewise-constant refractive index of the specimen, we show that the measurements have SWE form. We show how super-resolved tomograms could be achieved using SNS-based reconstruction technique. To demonstrate clinical relevance, we consider FDOCT measurements obtained from the retinal pigment epithelium (RPE) and photoreceptor inner/outer segments (IS/OS) of the retina. We show that the proposed method is able to resolve the RPE and IS/OS layers by using only 40% of the available samples. In the context of NMR spectroscopy, the measured signal or free induction decay (FID) can be modelled as a SWE signal. Due to the exponential decay, the FIDs are non-stationary. Hence, one cannot directly apply autocorrelation-based methods such as ESPRIT. We develop DEESPRIT, a counterpart of ESPRIT for decaying exponentials. We consider FID measurements taken from amino acid mixture and show that the proposed method is able to resolve two closely spaced frequencies by using only 40% of the measurements. In summary, this thesis focuses on various aspects of sub-Nyquist sampling and demonstrates concrete applications to super-resolution imaging.

Electrical bioimpedance spectroscopy (EBIS) has been used to assess the status or composition of various types of tissue, and examples of EBIS include body composition analysis (BCA) and tissue characterisation for skin cancer detection. EBIS is a non-invasive method that has the potential to provide a large amount of information for diagnosis or monitoring purposes, such as the monitoring of pulmonary oedema, i.e., fluid accumulation in the lungs. However, in many cases, systems based on EBIS have not become generally accepted in clinical practice. Possible reasons behind the low acceptance of EBIS could involve inaccurate models; artefacts, such as those from movements; measurement errors; and estimation errors. Previous thoracic EBIS measurements aimed at pulmonary oedema have shown some uncertainties in their results, making it difficult to produce trustworthy monitoring methods. The current research hypothesis was that these uncertainties mostly originate from estimation errors. In particular, time-varying behaviours of the thorax, e.g., respiratory and cardiac activity, can cause estimation errors, which make it tricky to detect the slowly varying behaviour of this system, i.e., pulmonary oedema. The aim of this thesis is to investigate potential sources of estimation error in transthoracic impedance spectroscopy (TIS) for pulmonary oedema detection and to propose methods to prevent or compensate for these errors.   This work is mainly focused on two aspects of impedance spectrum estimation: first, the problems associated with the delay between estimations of spectrum samples in the frequency-sweep technique and second, the influence of undersampling (a result of impedance estimation times) when estimating an EBIS spectrum. The delay between frequency sweeps can produce huge errors when analysing EBIS spectra, but its effect decreases with averaging or low-pass filtering, which is a common and simple method for monitoring the time-invariant behaviour of a system. The results show the importance of the undersampling effect as the main estimation error that can cause uncertainty in TIS measurements.  The best time for dealing with this error is during the design process, when the system can be designed to avoid this error or with the possibility to compensate for the error during analysis. A case study of monitoring pulmonary oedema is used to assess the effect of these two estimation errors. However, the results can be generalised to any case for identifying the slowly varying behaviour of physiological systems that also display higher frequency variations.  Finally, some suggestions for designing an EBIS measurement system and analysis methods to avoid or compensate for these estimation errors are discussed. / <p>QC 20140604</p>

One way of reducing the examination time in magnetic resonance imaging (MRI) is to reduce the amount of raw data acquired, by performing so-called undersampling. Conventionally, MRI data is acquired line-by-line on a Cartesian grid. In the field of Cardiovascular Magnetic Resonance (CMR), however, radial k-space sampling is seen as a promising emerging technique for rapid image acquisitions, mainly due to its robustness against motion disturbances occurring from the beating heart. Whereas Cartesian undersampling will result in image aliasing, radial undersampling will introduce streak artifacts. The objective of this work was to train the deep learning architecture, CycleGAN, to reduce streak artifacts in radially undersampled CMR images, and to evaluate the model performance. A benefit of using CycleGAN over other deep learning techniques for this application is that it can be trained on unpaired data. In this work, CycleGAN network was trained on 3060 radial and 2775 Cartesian unpaired CMR images acquired in human subjects to learn a mapping between the two image domains. The model was evaluated in comparison to images reconstructed using another emerging technique called GRASP. Whereas more investigation is warranted, the results are promising, suggesting that CycleGAN could be a viable method for effective streak-reduction in clinical applications.