Automotive radar is an important sensor technology for self-driving cars and Advanced Driver-Assistance Systems (ADAS). Current automotive radars lack the ability to classify and categorize objects due to their limited angular resolution. A new generation of automotive radar systems, known as automotive imaging radars, proposes to overcome this limitation by using larger apertures with more antenna elements. During the radar operation, automotive imaging radar systems face challenges in the accurate estimation of the Direction-of-Arrival (DoA) due to phase incoherency in the spatially sampled information caused by hardware imperfections, temperature variations, and aging effects. This work proposes a method combining convex optimization and alternating updates to first jointly calibrate the phase incoherencies and estimate the DoAs, and then update them iteratively. It further derives the Cramér-Rao Bound (CRB) and investigates the impact of the phase incoherency on DoA estimation using the CRB. In the proposed approach, the MUltiple SIgnal Classification (MUSIC) algorithm is applied to estimate the DoAs after each calibration. Additionally, the eigenvalue decomposition process in MUSIC is replaced by the Projection Approximation Subspace Tracking (PAST) algorithm to reduce computational complexity while maintaining the accuracy of DoA estimation. Experimental results illustrate the effectiveness of these techniques, highlighting their potential in improving next-generation automotive radar systems.

While the success of improving direction of arrival (DOA) estimation with linear coded covers using a single acoustic vector sensors (AVS) has been established, the extension of this theory to arraybased systems remains unexplored. To address this gap, we employ a specially designed coded cover and leverage compressed sensing (CS) and compressed covariance sensing (CCS) methods, extending their application from single AVS systems to an array-based acoustic measurement system. Our results demonstrate that a 14×10 coded cover with 12 PU probes enables accurate localization of 100 sound sources in 3D, even at a signal to noise ratio (SNR) as low as 10 dB, showcasing the scalability and robustness of this approach. To further enhance localization accuracy, we implement a selfcalibration method in the covariance domain to correct phase and gain errors in each receiving channel. Additionally, we combine selfcalibration with CCS to improve resolution and reduce side lobes. For geometric mismatch, we first investigate the sparsity-cognizant total least-squares (STLS) with multiple measurement vectors (MMV) variant of the fast iterative shrinkage-thresholding algorithm (FISTA) method. Then a grid-searching strategy is employed to compensate for these mismatches, ensuring better estimation accuracy. Experimental validation confirms that these techniques significantly enhance DOA estimation under non-ideal conditions, contributing to the advancement of acoustic sensing and localization methodologies.

Graph signal processing (GSP) extends classical signal processing to signals on graphs, enabling the analysis of complex data structures through graph theory. A core challenge in GSP is graph topology identification, which aims to deduce the graph structure that best explains observed signal dependencies.

This project addresses graph topology identification for applications where the underlying structure of systems like brain and social networks is not directly observable. Traditional approaches based on signal matching and spectral templates have limitations, particularly in handling scale issues and sparsity assumptions. We introduce a novel covariance matching methodology that efficiently reconstructs the graph topology using observable data. For the structural equation model (SEM) using an undirected graph, we demonstrate that our method can converge to the correct result under relatively soft conditions. Furthermore, we extend our methodology to polynomial models, sparse directed graphs, and any known Gaussian distribution of latent variables, broadening its applicability and utility in diverse graph-based systems. Experimental results demonstrate that our method outperforms existing techniques, offering new directions for future research in graph topology identification.

The rapid development of Advanced Driver Assistance Systems (ADAS) necessitates enhanced performance in automotive radar systems, with Phase Modulated ContinuousWave (PMCW) radar emerging as a key technology due to its high resolution, interference resistance, and robust performance. Despite these advantages, PMCW radar faces challenges such as high computational complexity and Doppler-induced range sidelobes. This thesis addresses these challenges by proposing an adaptive block FFT correlation method to reduce computational complexity and enhance processing efficiency, ensuring reliable target detection. Additionally, we tackle Dopplerinduced range sidelobes by introducing code diversity and novel frame designs for MIMO systems, leveraging cyclic shifts and Hadamard matrices to balance sidelobe attenuation and sequence set size requirements. Through extensive analysis and simulations, the proposed methods demonstrate significant improvements in radar performance, especially in detecting weak targets behind strong reflectors. The findings contribute to developing more efficient, reliable, and scalable PMCW radar systems for advanced automotive applications.

Pursuing higher communication rates is a perpetual goal, especially in today's age of information explosion. To increase line rate without extending the optical and electrical bandwidth, advanced modulation formats such as probabilistic constellation shaping (PCS) and partial response signaling (PRS) have been researched. PCS offers up to 1.53 dB sensitivity gains by modifying the uniform distribution of transmitted symbols into the Maxwell-Boltzmann distribution to approximate a Gaussian distribution; PRS, also known as faster-than-Nyquist signaling, increases the symbol rate beyond the ideal Nyquist bandwidth limit by introducing controlled inter-symbol interference (ISI). However, when applied to PCS-enabled or PRS-enabled systems, digital signal processing (DSP) algorithms developed for conventional QAM with uniform probabilities and free ISIs often perform poorly, degrading the expected gain.

To maximize the benefits of PCS and PRS, thereby enhancing the performance of single-carrier coherent communication systems, this thesis focuses on addressing the problem of optimal degradation in the carrier recovery stage. In coherent optical communication systems, carrier recovery is a crucial DSP subsystem that compensates for time-varying carrier frequency offset and phase noise caused by both lasers at the transmitter and receiver.

We first propose a carrier recovery scheme using generalized maximum likelihood estimation with negligible pilot overhead (approximately 0.2%) in the context of PCS. Through simulations and 100 GBaud experiments with PCS-64QAM, our proposed scheme doubles computational efficiency, provides better estimation accuracy, and exhibits greater stability, leading to up to 0.25 dB sensitivity gain compared to other algorithms. We also determine the practical optimal shaping factors of PCS-64QAM for different SNR intervals to guide future experimental work.

Additionally, in a popular PRS scheme, Tomlinson-Harashima precoding combined with polybinary shaping (THP + Polybinary), we compare two 2M modulo formats and investigate their impact on carrier recovery. Based on simulations and 96 GBaud experiments with THP+Polybinary-16QAM, our carrier recovery scheme enhances both accuracy and stability, effectively mitigating issues caused by zero symbols and residual ISIs.

With its superior overall performance, the proposed carrier recovery scheme is a competitive algorithm for addressing carrier imperfections in both PCS-enabled and PRS-enabled high-speed coherent optical communications. For the future, modifying the timing recovery algorithm and the blind equalization algorithm to suit PCS/PRS systems is prioritized to maximize PCS/PRS gains. Given the vast amount of communication data, machine learning-based DSP algorithms also present an interesting avenue for future research.

Doppler ultrasound imaging of cerebral blood flow faces challenges arising from a low signal-to-noise ratio (SNR) and a wide dynamic range. Echo signals received from blood cells are significantly weaker compared to surrounding tissues, such as the skull or brain soft tissue, resulting in inhibited visualization of small blood vessels and deep brain areas. To address this issue, this thesis explored the feasibility of employing and improving coded excitation techniques to enhance the SNR of Doppler ultrasound images. Furthermore, an optimized code for Doppler ultrasound imaging is designed, represented by a generalized encoding matrix.
The research begins with the definition of a linear signal model that incorporates the encoding matrix. Subsequently, a trace-constraint optimization problem is formulated based on maximizing the Fisher information matrix to find the optimized encoding matrix. The feasibility and performance of the optimized encoding matrix are assessed through simulations on both small and large array settings, which operate above Nyquist sampling frequency and under Nyquist sampling frequency respectively. The imaging results indicate that the optimized code exhibits higher SNR in deep image regions compared to existing coded excitation methods like Barker code while using the same number of transmissions, bit length, and same average transmit energy, albeit with a trade-off of decreased axial resolution. Nonetheless, this resolution degradation can be mitigated through the application of the iterative imaging technique LSQR. Finally, the optimized code is tested in a clinical transducer setting, and a blood flow simulation is conducted. The outcomes showcase the capacity of the proposed optimized code to enable higher SNR in Doppler ultrasound imaging and more accurate and informative clinical assessments.

Ultrasound images are typically generated using the Delay-And-Sum (DAS) method, which assumes a homogeneous propagation medium. When an aberrating layer is situated between the sensor array and the imaging target, this assumption does not hold, and DAS is replaced with model-based methods. These methods are computationally expensive and require to accurately model the aberrations caused by the layer. This thesis investigates novel methods for image formation and aberration estimation. The effect of the layer is described using a set of transfer functions from the sensor array to a virtual array placed after the layer. In the first part, we assume the transfer functions are known, and we propose a new method for image formation. The transfer functions allow to map the signal from the sensor array to the virtual array, and the DAS method is used on the virtual array signal. This technique is equivalent to model-based matched filtering in terms of image quality, without requiring expensive matrix computations. In the second part, the transfer functions are unknown, and a novel technique is introduced for their estimation. Using pulse-echo data, a focus-quality metric is computed to quantify the accuracy of the transfer function estimate. The transfer functions are modeled using a dictionary and the dictionary coefficients are iteratively updated to increase the defined metric. The optimization leads to improved focus quality and sharper images. In the case the layer model requires a limited dictionary, the proposed algorithm generates an accurate estimate of the transfer functions.

In this work, we deal with the problem of reconstructing a complete bandlimited graph signal from partially sampled noisy measurements. For a known graph structure, some efficient centralized algorithms are proposed to partition the nodes of the graph into disjoint subsets such that sampling the graph signal from any of these subsets leads to a sufficiently accurate reconstruction. Furthermore, we consider the situation when the graph has a massive size, where processing the data centrally is impractical anymore. To overcome this issue, a distributed framework is proposed that allows us to implement the centralized algorithms in a parallelized fashion. Finally, we provide numerical simulation results on synthetic and real-world data to show that our proposals outperform state-of-the-art node partitioning techniques.

The edge flow reconstruction task improves the integrity and accuracy of edge flow data by recovering corrupted or incomplete signals. This can be solved by a regularized optimization problem, and the corresponding regularizers are chosen based on prior knowledge. However, obtaining prior information is challenging in some fields. Thus, we consider exploiting the learning ability of neural networks to acquire prior knowledge. In this paper, we propose a new optimization problem for the simplicial edge flow reconstruction task, the simplicial ElasticNet, which is a regularized optimization problem that combines the advantages of the L1 and L2 norm. It is solved iteratively by the multi-block ADMM algorithm, and the convergence conditions are illustrated. By unrolling the simplicial ElasticNet's iterative steps, we propose a neural network with high interpretability and low requirement for the number of training data for the reconstruction task of simplicial edge flows. The unrolling network replaces the fixed parameters in the iterative algorithm with the learnable weights in the neural networks, thus exploiting the neural network's learning capability while preserving the iterative algorithm's interpretability. The core component of this unrolling network is simplicial convolutional filters with learnable weights to aggregate information from the edge flow neighbors, thus enhancing the learning and expressive ability of the network. We conduct extensive experiments on real-world and artificial datasets to validate the proposed approach. It is demonstrated that the simplicial unrolling network is significantly more advantageous than the traditional iterative algorithms and standard non-model-based neural networks in the case of limited training data.

Existing sonar systems typically rely on a minimum signal strength of a single echo, which limits their performance in low signal-to-noise conditions. This thesis explores the concept of coherent integration for active sonar, with the aim of improving imaging and detection capabilities under low signal-to-noise conditions. The goal is to provide signal processing methods that achieve long-time coherent integration of the received echoes, thereby maximising the processing gain. Additionally, this research explores waveform design by comparing the performance of pseudo-random noise with chirps. Two applications are seen in this thesis: moving target detection, which involves static sonar sensors, and synthetic aperture imaging, where the sensors move while the imaging scene remains static. For moving target detection, a processing methods is proposed which achieves coherent integration for constant velocity targets in a computationally efficient manner, and improves the detection performance by implementing a clutter filtering stage. For the second application, a processing method for imaging from a moving sensor pair is proposed. The resulting point-spread function for a circular sensor trajectory is investigated, from which a set of design rules are established. Additionally, a least squares algorithm is applied, which shows that the resulting image can be improved in terms of resolution and sidelobe interference. Finally, the imaging and detection methods are tested and verified using an in-air demonstrator.

Subgraph matching is a fundamental problem in various fields such as machine learning, computer vision, image processing, and bioinformatics, where detecting specific substructures within an object is often crucial. In these domains, not only structure plays an essential role, but also the feature information on nodes should be incorporated, thus highlighting the necessity for comprehensive analytical approaches.

In this thesis, we propose two novel subgraph matching frameworks using the Fused Gromov-Wasserstein (FGW) distance, namely the Subgraph Optimal Transport (SOT) and the Sliding Subgraph Optimal Transport (SSOT). Both frameworks integrate a dummy node strategy to handle the discrepancy between two graphs of different sizes. The SSOT extends upon the SOT by incorporating a sliding window framework and Wasserstein pruning to enhance the performance, especially for sparse large graphs. Our frameworks can be easily implemented and are adaptable for problems of exact matching, top-k approximate matching, and inexact matching.

We further propose a normalized FGW distance to cater to the practical interests and enhance the performance evaluation. We adopt the Frank-Wolfe algorithm for optimization and develop computation-reducing techniques by isolating the dummy node.

By conducting experiments on both synthetic and real-world datasets, we demonstrate that the SOT method achieves excellent performance on small graphs, and the SSOT method improves the accuracy over the SOT on large graphs. Both these two methods show the ability to outperform the state-of-the-art methods in noisy environments in terms of accuracy and efficiency.

This study delves into the application of coded covers in enhancing Acoustic Vector Sensor (AVS) performance for sound source localization. We initially explored the use of a coded mask inspired by ultrasound imaging. However, our analysis indicated that the coded mask primarily acts as a scaling factor without substantial benefits for direction of arrival (DOA) estimation.
In response, we investigated an alternative approach using a larger cover with spaced channels, positioned above the AVS sensor. In this setup, each channel operates independently, and their combined acoustic outputs are analyzed upon reaching the sensor. Importantly, the upper surface channels can be viewed as a virtual uniform linear array (ULA), allowing the application of compressed analysis methods.
Two distinct DOA estimation approaches were developed: the compressive sampling (CS) method and the compressive covariance sensing (CCS) method. Both methods were validated, showing improved accuracy in angle estimation. Notably, the CCS method exhibited the potential to expand the number of detectable sound sources using a single AVS.
In summary, while the coded mask did not offer significant advantages, the coded cover design, along with the CS and CCS methods, improved DOA accuracy and extended the detection capabilities of single AVS.

In recent years, neural networks (NNs) have seen a surge in popularity due to their ability to model complex patterns and relationships in data. One of the challenges of using NNs is the requirement for large amounts of labelled data to train the model effectively. In many real-world applications such as radar, labelled data may be scarce due to the high cost of acquiring measurements together with privacy and security concerns.

To overcome the lack of data, researchers have resorted to data augmentation (DA), a technique that aims to solve the problem at the root by generating new training samples by leveraging the available ones. In computer vision, image transformations and generative networks are used to perform DA. These techniques, however, may lead to the production of physically unfeasible samples that may hinder the generalization capabilities of classifiers in domains where the data has an underlying physical meaning.

Physics-informed machine learning aims to incorporate physical prior knowledge and governing equations of the target domain into the machine learning pipeline to improve the performance of NNs in fields with limited available data but with well-defined physical models. In this thesis, physics-informed DA in the radar domain is addressed to improve the task of classifying armed and unarmed walking individuals through micro-Doppler spectrograms.

To begin with, the usage of model-driven micro-Doppler radar simulations to improve the existing generative augmentations is investigated. After introducing several generative NN architectures, the quality and diversity of the produced synthetic spectrograms are evaluated together with their effect on the downstream classification task.


Next, the impact of visual transformations on micro-Doppler spectrograms is studied. Their effect on the underlying physics of the micro-Doppler spectrograms and their impact on feature extraction is assessed. Based on the results, a new DA technique is devised to improve the feature extraction process by informed segmentation of the input spectrogram, halving the size of the NN model and reducing the risk of overfitting.

The underwater acoustic environment is amongst the most challenging mediums for wireless communications. The three distinct challenges of underwater acoustic communication are the low and nonuniform propagation speed, frequency-dependent attenuation and time-varying multipath propagation.
To cope with these challenges, physical layer communication systems allow the selection of communication parameters based on environmental conditions and constraints. This is also known as link adaptation. In this thesis, the frequency-repetition spread-spectrum (FRSS) physical layer is studied. Various channel parameters are used to classify the optimal FRSS format. Furthermore, different machine learning classifiers are implemented to solve the classification problem. It is determined that the output signal-to-noise ratio provides enough information to switch effectively between transmission formats. Among the implemented machine learning classifiers, the decision tree strikes a good balance between performance and computational complexity. It is shown that a small performance gain can be achieved when custom channel parameters are extracted from the estimated impulse response and the equalizer error sequence using a deep neural network.
Optimizing the equalization process is another method to better cope with difficult environmental conditions. Various adaptive filter algorithms are implemented for the decision feedback equalizer used in the FRSS receiver. The optimal algorithm parameters are found by means of algorithm unrolling. It is shown that the standard least mean squares algorithm cannot be outperformed by various other optimization algorithms that use linear or non-linear filters.
The Watermark channel simulator is used to study the performance of the link adaptation and equalization optimization solutions for a wide range of underwater channels.

In recent years, researchers proposed several universal caching policies. These universal caching policies aim to work well with any request sequence. However, with this universal well-working property, these caching policies sometimes do not work as well as conventional caching policies such as Least-Recently-Used and Least-Frequently-Used. This thesis introduces an online learning approach to dynamically switch between caching policies. The dynamical switching selects the most suitable caching policy for the request sequence and thus ensures the best of both worlds, working well under any request sequence and having comparable performance to the conventional caching policies. The Dynamic Expert Caching (DEC) policy designed in this thesis uses algorithms from the expert selection problem to achieve the dynamic caching policy selection. The DEC policy is evaluated using various datasets where it is shown to have comparable performance to the best caching policies in the simulations. The DEC policy is also adapted to work in a network of caches, named MultiDEC. In this setting, MultiDEC has significant advantages over other universal caching policies where each caching node can have a different caching policy that is optimal.

In the current Big Data era, large amounts of data are collected from complex systems, such as sensor networks and social networks. The emerging field of graph signal processing (GSP) leverages a network structure (graph) to process signals on an irregular domain. This thesis studies the forecasting of multi-dimensional graph processes, i.e., where each entity in the network carries a multivariate time series. Recent research has proposed to use product graphs to model the dependencies between different variables in multi-dimensional graph processes and employ them in graph-based vector autoregressive models to predict future values. A problem with these product graph-based models is that they can be too restrictive. In this work, it is proposed to combine product graph-based models with multiple one-dimensional models to implement more estimation flexibility. To further increase the degrees of freedom, the use of multiple-input-multiple-output graph filters is also proposed. The proposed models are implemented and tested on synthetic and real-world data sets, which shows an improved forecasting performance compared to state-of-the-art alternatives.

Microphones are the most popular devices used to convert sound into electrical signals. However, with the advent of sensor technology, transducers capable of measuring vector quantities are opening up many new possibilities. One such device is an acoustic vector sensor (AVS), which measures both acoustic pressure and particle velocity, and has shown promising results with distinct advantages. In this work, we explore the characteristics of AVS arrays and their variations in comparison to the conventional microphone arrays for the purpose of direction-of-arrival estimation of far-field sound sources. Furthermore, we also look into one of the practical aspects of calibrating the AVS arrays and propose novel techniques to address this issue.

At the Center for Ultrasound and Brain imaging at Erasmus MC in Rotterdam, a mouse's visual cortex had been imaged using the fUS technique. The mouse had been exposed to different visual stimuli. The stimuli varied in position, size, and shape. We investigate how the measured task-based fUS signals differ depending on the visual stimuli presented to the mouse. For that purpose, we decompose the fUS data with four different methods giving different levels of sparsity. This thesis compares the performance of the four methods, and provides neurological insights obtained with these methods. For modeling the data, we consider four data-driven decomposition methods: ICA and three sDL variants. The methods decompose the data into better interpretable spatial maps and time courses. Every decomposition is further examined by training L1-regularized prediction models that optimize for sparsity. The goal is to predict the presented stimulus based on the decomposed data. Furthermore, the potential of group lasso regularization in prediction models is illustrated. The decompositions extract spatial maps anatomically linked to the visual cortex, superior colliculus and the hippocampus. All decompositions achieve considerable performance in the position prediction but have low success in the size and shape prediction. ICA outperformed the three sDL variants in all prediction tasks. Furthermore, group lasso regularization is found to be a useful tool to obtain discriminatory information in the time dynamics.

Federated learning is an upcoming machine learning concept which allows data from multiple sources be usedfor training of classifiers without said data leaving its origin. In certain research cases using highly privatedata, the step of gathering data can be quite tedious. In such cases, federated learning has the potential tovastly speed up the research cycle. However, the question arises whether such a federated framework givessimilar performance compared to a central model with access to all data, in other words: Whether it mightbe worth the hassle of gathering all data anyway due to the performance difference. In this work, we providean extensive set of experiments comparing central and federated models, using multiple classifiers on multipledatasets. Results show that federated learning indeed has the potential to provide similar results, but thatits nature might enable use cases in which challenges with regards to batch effects between different datasetscould become prevalent

Graphs can be models for many real-world systems, where nodes indicate the entities and edges indicate the pairwise connections in between. In various cases, it is important to detect informative subsets of nodes such that the nodes within the subsets are ’closer’ to each other. For example, in a cellular network, determining appropriate node subsets can reduce the operation costs. A subset is usually called a cluster. This leads to the graph clustering problem. Furthermore, plenty of systems in the real world are changing over time, and consequently, graphs as models vary with time as well. It is thus also important to update the clusters when the graph changes.

In this thesis work, we studied two problems from the cellular network background. We needed to partition graphs that have certain structures and cluster their nodes to minimize certain cost functions. In the first problem, we partitioned a bipartite graph by minimizing the so-called MinMaxCut cost function, while in the second problem, we partitioned a structured graph by minimizing the so-called Modified-MinMaxCut cost function. The structural property of the graph is incorporated in defining this new cost function. The solutions we proposed are under the framework of spectral clustering, where one relies on the eigenvectors of the graph matrices, e.g., the Laplacian matrix or the adjacency matrix, and any clustering algorithm, e.g., K-means, to partition nodes into disjoint clusters.

Furthermore, for the time-variant graph, we decomposed the problem into two steps. First, we transformed the variations in the graph topology into perturbations to the graph matrices. Then we transformed the update of the clusters into an update of the (generalized) eigenvectors of these graph matrices. We utilized matrix perturbation theory to update the generalized eigenvectors and then update the clusters. Our simulations showed that on synthetic data, the proposed method can efficiently track the eigenvectors and the clusters generated by the updated eigenvectors have almost the same cost function value as that of exact computation.