Joint Transmit and Receive Filter Optimization for Sub-Nyquist Delay-Doppler Estimation

In this article, a framework is presented for the joint optimization of the analog transmit and receive filter with respect to a parameter estimation problem. At the receiver, conventional signal processing systems restrict the two-sided bandwidth of the analog pre-filter $B$ to the rate of the analog-to-digital converter $f_s$ to comply with the well-known Nyquist-Shannon sampling theorem. In contrast, here we consider a transceiver that by design violates the common paradigm $B\leq f_s$. To this end, at the receiver, we allow for a higher pre-filter bandwidth $B>f_s$ and study the achievable parameter estimation accuracy under a fixed sampling rate when the transmit and receive filter are jointly optimized with respect to the Bayesian Cram\'{e}r-Rao lower bound. For the case of delay-Doppler estimation, we propose to approximate the required Fisher information matrix and solve the transceiver design problem by an alternating optimization algorithm. The presented approach allows us to explore the Pareto-optimal region spanned by transmit and receive filters which are favorable under a weighted mean squared error criterion. We also discuss the computational complexity of the obtained transceiver design by visualizing the resulting ambiguity function. Finally, we verify the performance of the optimized designs by Monte-Carlo simulations of a likelihood-based estimator.Comment: 15 pages, 16 figure

Sparse Signal Processing Concepts for Efficient 5G System Design

As it becomes increasingly apparent that 4G will not be able to meet the emerging demands of future mobile communication systems, the question what could make up a 5G system, what are the crucial challenges and what are the key drivers is part of intensive, ongoing discussions. Partly due to the advent of compressive sensing, methods that can optimally exploit sparsity in signals have received tremendous attention in recent years. In this paper we will describe a variety of scenarios in which signal sparsity arises naturally in 5G wireless systems. Signal sparsity and the associated rich collection of tools and algorithms will thus be a viable source for innovation in 5G wireless system design. We will discribe applications of this sparse signal processing paradigm in MIMO random access, cloud radio access networks, compressive channel-source network coding, and embedded security. We will also emphasize important open problem that may arise in 5G system design, for which sparsity will potentially play a key role in their solution.Comment: 18 pages, 5 figures, accepted for publication in IEEE Acces

Learning Sub-Sampling and Signal Recovery with Applications in Ultrasound Imaging

Limitations on bandwidth and power consumption impose strict bounds on data rates of diagnostic imaging systems. Consequently, the design of suitable (i.e. task- and data-aware) compression and reconstruction techniques has attracted considerable attention in recent years. Compressed sensing emerged as a popular framework for sparse signal reconstruction from a small set of compressed measurements. However, typical compressed sensing designs measure a (non)linearly weighted combination of all input signal elements, which poses practical challenges. These designs are also not necessarily task-optimal. In addition, real-time recovery is hampered by the iterative and time-consuming nature of sparse recovery algorithms. Recently, deep learning methods have shown promise for fast recovery from compressed measurements, but the design of adequate and practical sensing strategies remains a challenge. Here, we propose a deep learning solution termed Deep Probabilistic Sub-sampling (DPS), that learns a task-driven sub-sampling pattern, while jointly training a subsequent task model. Once learned, the task-based sub-sampling patterns are fixed and straightforwardly implementable, e.g. by non-uniform analog-to-digital conversion, sparse array design, or slow-time ultrasound pulsing schemes. The effectiveness of our framework is demonstrated in-silico for sparse signal recovery from partial Fourier measurements, and in-vivo for both anatomical image and tissue-motion (Doppler) reconstruction from sub-sampled medical ultrasound imaging data

Compressive Sensing and Its Applications in Automotive Radar Systems

Die Entwicklung in Richtung zu autonomem Fahren verspricht, künftig einen sicheren Verkehr ohne tödliche Unfälle zu ermöglichen, indem menschliche Fahrer vollständig ersetzt werden. Dadurch entfällt der Faktor des menschlichen Fehlers, der aus Müdigkeit, Unachtsamkeit oder Alkoholeinfluss resultiert. Um jedoch eine breite Akzeptanz für autonome Fahrzeuge zu erreichen und es somit eines Tages vollständig umzusetzen, sind noch eine Vielzahl von Herausforderungen zu lösen. Da in einem autonomen Fahrzeug kein menschlicher Fahrer mehr in Notfällen eingreifen kann, müssen sich autonome Fahrzeuge auf leistungsfähige und robuste Sensorsysteme verlassen können, um in kritischen Situationen auch unter widrigen Bedingungen angemessen reagieren zu können. Daher ist die Entwicklung von Sensorsystemen erforderlich, die für Funktionalitäten jenseits der aktuellen advanced driver assistance systems eingesetzt werden können. Dies resultiert in neuen Anforderungen, die erfüllt werden müssen, um sichere und zuverlässige autonome Fahrzeuge zu realisieren, die weder Fahrzeuginsassen noch Passanten gefährden. Radarsysteme gehören zu den Schlüsselkomponenten unter der Vielzahl der verfügbaren Sensorsysteme, da sie im Gegensatz zu visuellen Sensoren von widrigen Wetter- und Umgebungsbedingungen kaum beeinträchtigt werden. Darüber hinaus liefern Radarsysteme zusätzliche Umgebungsinformationen wie Abstand, Winkel und relative Geschwindigkeit zwischen Sensor und reflektierenden Zielen. Die vorliegende Dissertation deckt im Wesentlichen zwei Hauptaspekte der Forschung und Entwicklung auf dem Gebiet der Radarsysteme im Automobilbereich ab. Ein Aspekt ist die Steigerung der Effizienz und Robustheit der Signalerfassung und -verarbeitung für die Radarperzeption. Der andere Aspekt ist die Beschleunigung der Validierung und Verifizierung von automated cyber-physical systems, die parallel zum Automatisierungsgrad auch eine höhere Komplexität aufweisen. Nach der Analyse zahlreicher möglicher Compressive Sensing Methoden, die im Bereich Fahrzeugradarsysteme angewendet werden können, wird ein rauschmoduliertes gepulstes Radarsystem vorgestellt, das kommerzielle Fahrzeugradarsysteme in seiner Robustheit gegenüber Rauschen übertrifft. Die Nachteile anderer gepulster Radarsysteme hinsichtlich des Signalerfassungsaufwands und der Laufzeit werden durch die Verwendung eines Compressive Sensing-Signalerfassungs- und Rekonstruktionsverfahrens in Kombination mit einer Rauschmodulation deutlich verringert. Mit Compressive Sensing konnte der Aufwand für die Signalerfassung um 70% reduziert werden, während gleichzeitig die Robustheit der Radarwahrnehmung auch für signal-to-noise-ratio-Pegel nahe oder unter Null erreicht wird. Mit einem validierten Radarsensormodell wurde das Rauschradarsystem emuliert und mit einem kommerziellen Fahrzeugradarsystem verglichen. Datengetriebene Wettermodelle wurden entwickelt und während der Simulation angewendet, um die Radarleistung unter widrigen Bedingungen zu bewerten. Während eine Besprühung mit Wasser die Radomdämpfung um 10 dB erhöht und Spritzwasser sogar um 20 dB, ergibt sich die eigentliche Begrenzung aus der Rauschzahl und Empfindlichkeit des Empfängers. Es konnte bewiesen werden, dass das vorgeschlagene Compressive Sensing Rauschradarsystem mit einer zusätzlichen Signaldämpfung von bis zu 60 dB umgehen kann und damit eine hohe Robustheit in ungünstigen Umwelt- und Wetterbedingungen aufweist. Neben der Robustheit wird auch die Interferenz berücksichtigt. Zum einen wird die erhöhte Störfestigkeit des Störradarsystems nachgewiesen. Auf der anderen Seite werden die Auswirkungen auf bestehende Fahrzeugradarsysteme bewertet und Strategien zur Minderung der Auswirkungen vorgestellt. Die Struktur der Arbeit ist folgende. Nach der Einführung der Grundlagen und Methoden für Fahrzeugradarsysteme werden die Theorie und Metriken hinter Compressive Sensing gezeigt. Darüber hinaus werden weitere Aspekte wie Umgebungsbedingungen, unterschiedliche Radararchitekturen und Interferenz erläutert. Der Stand der Technik gibt einen Überblick über Compressive Sensing-Ansätze und Implementierungen mit einem Fokus auf Radar. Darüber hinaus werden Aspekte von Fahrzeug- und Rauschradarsystemen behandelt. Der Hauptteil beginnt mit der Vorstellung verschiedener Ansätze zur Nutzung von Compressive Sensing für Fahrzeugradarsysteme, die in der Lage sind, die Erfassung und Wahrnehmung von Radarsignalen zu verbessern oder zu erweitern. Anschließend wird der Fokus auf ein Rauschradarsystem gelegt, das mit Compressive Sensing eine effiziente Signalerfassung und -rekonstruktion ermöglicht. Es wurde mit verschiedenen Compressive Sensing-Metriken analysiert und in einer Proof-of-Concept-Simulation bewertet. Mit einer Emulation des Rauschradarsystems wurde das Potential der Compressive Sensing Signalerfassung und -verarbeitung in einem realistischeren Szenario demonstriert. Die Entwicklung und Validierung des zugrunde liegenden Sensormodells wird ebenso dokumentiert wie die Entwicklung der datengetriebenen Wettermodelle. Nach der Betrachtung von Interferenz und der Koexistenz des Rauschradars mit kommerziellen Radarsystemen schließt ein letztes Kapitel mit Schlussfolgerungen und einem Ausblick die Arbeit ab.Developments towards autonomous driving promise to lead to safer traffic, where fatal accidents can be avoided after making human drivers obsolete and hence removing the factor of human error. However, to ensure the acceptance of automated driving and make it a reality one day, still a huge amount of challenges need to be solved. With having no human supervisors, automated vehicles have to rely on capable and robust sensor systems to ensure adequate reactions in critical situations, even during adverse conditions. Therefore, the development of sensor systems is required that can be applied for functionalities beyond current advanced driver assistance systems. New requirements need to be met in order to realize safe and reliable automated vehicles that do not harm passersby. Radar systems belong to the key components among the variety of sensor systems. Other than visual sensors, radar is less vulnerable towards adverse weather and environment conditions. In addition, radar provides complementary environment information such as target distance, angular position or relative velocity, too. The thesis ad hand covers basically two main aspects of research and development in the field of automotive radar systems. One aspect is to increase efficiency and robustness in signal acquisition and processing for radar perception. The other aspect is to accelerate validation and verification of automated cyber-physical systems that feature more complexity along with the level of automation. After analyzing a variety of possible Compressive Sensing methods for automotive radar systems, a noise modulated pulsed radar system is suggested in the thesis at hand, which outperforms commercial automotive radar systems in its robustness towards noise. Compared to other pulsed radar systems, their drawbacks regarding signal acquisition effort and computation run time are resolved by using noise modulation for implementing a Compressive Sensing signal acquisition and reconstruction method. Using Compressive Sensing, the effort in signal acquisition was reduced by 70%, while obtaining a radar perception robustness even for signal-to-noise-ratio levels close to or below zero. With a validated radar sensor model the noise radar was emulated and compared to a commercial automotive radar system. Data-driven weather models were developed and applied during simulation to evaluate radar performance in adverse conditions. While water sprinkles increase radome attenuation by 10 dB and splash water even by 20 dB, the actual limitation comes from noise figure and sensitivity of the receiver. The additional signal attenuation that can be handled by the proposed compressive sensing noise radar system proved to be even up to 60 dB, which ensures a high robustness of the receiver during adverse weather and environment conditions. Besides robustness, interference is also considered. On the one hand the increased robustness towards interference of the noise radar system is demonstrated. On the other hand, the impact on existing automotive radar systems is evaluated and strategies to mitigate the impact are presented. The structure of the thesis is the following. After introducing basic principles and methods for automotive radar systems, the theory and metrics of Compressive Sensing is presented. Furthermore some particular aspects are highlighted such as environmental conditions, different radar architectures and interference. The state of the art provides an overview on Compressive Sensing approaches and implementations with focus on radar. In addition, it covers automotive radar and noise radar related aspects. The main part starts with presenting different approaches on making use of Compressive Sensing for automotive radar systems, that are capable of either improving or extending radar signal acquisition and perception. Afterwards the focus is put on a noise radar system that uses Compressive Sensing for an efficient signal acquisition and reconstruction. It was analyzed using different Compressive Sensing metrics and evaluated in a proof-of-concept simulation. With an emulation of the noise radar system the feasibility of the Compressive Sensing signal acquisition and processing was demonstrated in a more realistic scenario. The development and validation of the underlying sensor model is documented as well as the development of the data-driven weather models. After considering interference and co-existence with commercial radar systems, a final chapter with conclusions and an outlook completes the work

Development of a Feasible Elastography Framework for Portable Ultrasound

Portable wireless ultrasound is emerging as a new ultrasound device due to the advantages such as small size, lightweight and affordable price. Its high portability allows practitioners to make diagnostic and therapeutic decisions in real-time without having to take the patients out of their environment. Recent portable ultrasound devices are equipped with sophisticated processors and image processing algorithms providing high image quality. Some of them are able to deliver multiple ultrasound modes including color Doppler, echocardiography, and endovaginal examination. Nevertheless, they are still lack of elastography functions due to the limitations in computational performance and data transfer speed via wireless communication. In order to implement the elastography function in the wireless portable ultrasound devices, this thesis proposes a new strain estimation method to significantly reduce the computation time and a compressive sensing framework to minimize the data transfer size. Firstly, a robust phase-based strain estimator (RPSE) is developed to overcome the limited hardware performance of portable ultrasound. The RPSE is not only computationally efficient but also robust to variations of the speed of sound, sampling frequency and pulse repetition. The RPSE has been compared with other representative strain estimators including time-delay, displacement-gradient, and conventional phase-based strain estimators (TSE, DSE and PSE, respectively). It has been shown that the RPSE is superior in several elastographic image quality measures, including signal-to-noise (SNRe) and contrast-to-noise (CNRe), and the computational efficiency. The study indicates that the RPSE method can deliver the acceptable level of elastography and fast computational speed for the ultrasound echo data sets from the numerical and experimental phantoms. According to the results from the numerical phantom experiment, RPSE can achieve highest values of SNRe and CNRe (around 5.22 and 47.62 dB) among all strain estimators tested, and almost 100 times higher computational efficiency than TSE and DSE (around 0.06 vs. 5.76 seconds per frame for RPSE and TSE, respectively). Secondly, as a means to reduce the large amount of ultrasound measurement data that has to be transmitted via wireless communication, the compressive sensing (CS) framework has been applied to elastography. The performance of CS is highly dependent on the selection of model basis to represent the sparse expansion as well as the reconstruction algorithm to recover the original data from the compressed signal. Therefore, it is essential to compose the optimal combination of model basis and reconstruction algorithm for CS framework to achieve the best CS performance in terms of image quality and the maximum data reduction. In this thesis, three model bases, discrete Fourier transform (FT), discrete cosine transform (DCT), and wave atoms (WA), along with two reconstruction algorithms, L1 minimization (L1) and Block sparse Bayesian learning (BSBL) are tested. Using B-mode and elastogram images of simulated numerical phantoms, the quality of CS reconstruction is assessed in terms of three image quality measures, mean absolute error (MAE), SNRe, and CNRe, at varying data reduction (subsampling) rates. The results illustrate that BSBL based CS frameworks can generally deliver much higher image quality and subsampling rate compared with L1-based ones. In particular, the CS frameworks adopting DCT and BSBL offer the best CS performance. The results also suggests that the maximum subsampling rates without causing image degradation are 40% for L1-based framework and 60% for BSBL-based framework, respectively. The contributions of this thesis help realize elastography functionality in portable ultrasound, thereby significantly expanding its utility. For example, the diagnosis of malignant lesions, even when a patient cannot be moved to hospital immediately, is possible with the portable ultrasound. Furthermore, the SPSE method and the CS framework can be individually employed for the conventional ultrasound device as well as other telemedicine applications, to enhance computational efficiency and image quality

Experimental Investigations of Millimeter Wave Beamforming

The millimeter wave (mmW) band, commonly referred to as the frequency band between 30 GHz and 300 GHz, is seen as a possible candidate to increase achievable rates for mobile applications due to the existence of free spectrum. However, the high path loss necessitates the use of highly directional antennas. Furthermore, impairments and power constraints make it difficult to provide full digital beamforming systems. In this thesis, we approach this problem by proposing effective beam alignment and beam tracking algorithms for low-complex analog beamforming (ABF) systems, showing their applicability by experimental demonstration. After taking a closer look at particular features of the mmW channel properties and introducing the beamforming as a spatial filter, we begin our investigations with the application of detection theory for the non-convex beam alignment problem. Based on an M-ary hypothesis test, we derive algorithms for defining the length of the training signal efficiently. Using the concept of black-box optimization algorithms, which allow optimization of non-convex algorithms, we propose a beam alignment algorithm for codebook-based ABF based systems, which is shown to reduce the training overhead significantly. As a low-complex alternative, we propose a two-staged gradient-based beam alignment algorithm that uses convex optimization strategies after finding a subregion of the beam alignment function in which the function can be regarded convex. This algorithm is implemented in a real-time prototype system and shows its superiority over the exhaustive search approach in simulations and experiments. Finally, we propose a beam tracking algorithm for supporting mobility. Experiments and comparisons with a ray-tracing channel model show that it can be used efficiently in line of sight (LoS) and non line of sight (NLoS) scenarios for walking-speed movements