An Augmented Lagrangian Based Compressed Sensing Reconstruction for Non-Cartesian Magnetic Resonance Imaging without Gridding and Regridding at Every Iteration

Background: Non-Cartesian trajectories are used in a variety of fast imaging applications, due to the incoherent image domain artifacts they create when undersampled. While the gridding technique is commonly utilized for reconstruction, the incoherent artifacts may be further removed using compressed sensing (CS). CS reconstruction is typically done using conjugate-gradient (CG) type algorithms, which require gridding and regridding to be performed at every iteration. This leads to a large computational overhead that hinders its applicability. Methods: We sought to develop an alternative method for CS reconstruction that only requires two gridding and one regridding operation in total, irrespective of the number of iterations. This proposed technique is evaluated on phantom images and whole-heart coronary MRI acquired using 3D radial trajectories, and compared to conventional CS reconstruction using CG algorithms in terms of quantitative vessel sharpness, vessel length, computation time, and convergence rate. Results: Both CS reconstructions result in similar vessel length (P = 0.30) and vessel sharpness (P = 0.62). The per-iteration complexity of the proposed technique is approximately 3-fold lower than the conventional CS reconstruction (17.55 vs. 52.48 seconds in C++). Furthermore, for in-vivo datasets, the convergence rate of the proposed technique is faster (60±13 vs. 455±320 iterations) leading to a ∼23-fold reduction in reconstruction time. Conclusions: The proposed reconstruction provides images of similar quality to the conventional CS technique in terms of removing artifacts, but at a much lower computational complexity

Design and Analysis of GFDM-Based Wireless Communication Systems

Le multiplexage généralisé par répartition en fréquence (GFDM), une méthode de traitement par blocs de modulation multiporteuses non orthogonales, est une candidate prometteuse pour les technologies de forme d'onde pour les systèmes sans fil au-delà de la cinquième génération (5G). La capacité du GFDM à ajuster de manière flexible la taille du bloc et le type de filtres de mise en forme des impulsions en fait une méthode appropriée pour répondre à plusieurs exigences importantes, comme une faible latence, un faible rayonnement hors bande (OOB) et des débits de données élevés. En appliquant aux systèmes GFDM la technique des systèmes à entrées multiples et sorties multiples (MIMO), la technique de MIMO massif ou des codes de contrôle de parité à faible densité (LDPC), il est possible d'améliorer leurs performances. Par conséquent, l'étude de ces systèmes combinés sont d'une grande importance théorique et pratique. Dans cette thèse, nous étudions les systèmes de communication sans fil basés sur le GFDM en considérant trois aspects. Tout d'abord, nous dérivons une borne d'union sur le taux d'erreur sur les bits (BER) pour les systèmes MIMO-GFDM, technique qui est basée sur des probabilités d'erreur par paires exactes (PEP). La PEP exacte est calculée en utilisant la fonction génératrice de moments(MGF) pour les détecteurs à maximum de vraisemblance (ML). La corrélation spatiale entre les antennes et les erreurs d'estimation de canal sont prises en compte dans l'environnement de canal étudié. Deuxièmement, les estimateurs et les précodeurs de canal de faible complexité basés sur une expansion polynomiale sont proposés pour les systèmes MIMO-GFDM massifs. Des pilotes sans interférence sont utilisés pour l'estimation du canal basée sur l'erreur quadratique moyenne minimale(MMSE) pour lutter contre l'influence de la non-orthogonalité entre les sous-porteuses dans le GFDM. La complexité de calcul cubique peut être réduite à une complexité d'ordre au carré en utilisant la technique d'expansion polynomiale pour approximer les inverses de matrices dans l'estimation MMSE conventionnelle et le précodage. De plus, nous calculons les limites de performance en termes d'erreur quadratique moyenne (MSE) pour les estimateurs proposés, ce qui peut être un outil utile pour prédire la performance des estimateurs dans la région de Eₛ/N₀ élevé. Une borne inférieure de Cramér-Rao(CRLB) est dérivée pour notre modèle de système et agit comme une référence pour les estimateurs. La complexité de calcul des estimateurs de canal proposés et des précodeurs et les impacts du degré du polynôme sont également étudiés. Enfin, nous analysons les performances de la probabilité d'erreur des systèmes GFDM combinés aux codes LDPC. Nous dérivons d'abord les expressions du ratio de vraisemblance logarithmique (LLR) initiale qui sont utilisées dans le décodeur de l'algorithme de somme de produits (SPA). Ensuite, basé sur le seuil de décodage, nous estimons le taux d'erreur de trame (FER) dans la région de bas E[indice b]/N₀ en utilisant le BER observé pour modéliser les variations du canal. De plus, une borne inférieure du FER du système est également proposée basée sur des ensembles absorbants. Cette borne inférieure peut agir comme une estimation du FER dans la région de E[indice b]/N₀ élevé si l'ensemble absorbant utilisé est dominant et que sa multiplicité est connue. La quantification a également un impact important sur les performances du FER et du BER. Des codes LDPC basés sur un tableau et construit aléatoirement sont utilisés pour supporter les analyses de performances. Pour ces trois aspects, des simulations et des calculs informatiques sont effectués pour obtenir des résultats numériques connexes, qui vérifient les méthodes proposées.8 372162\u a Generalized frequency division multiplexing (GFDM) is a block-processing based non-orthogonal multi-carrier modulation scheme, which is a promising candidate waveform technology for beyond fifth-generation (5G) wireless systems. The ability of GFDM to flexibly adjust the block size and the type of pulse-shaping filters makes it a suitable scheme to meet several important requirements, such as low latency, low out-of-band (OOB) radiation and high data rates. Applying the multiple-input multiple-output (MIMO) technique, the massive MIMO technique, or low-density parity-check (LDPC) codes to GFDM systems can further improve the systems performance. Therefore, the investigation of such combined systems is of great theoretical and practical importance. This thesis investigates GFDM-based wireless communication systems from the following three aspects. First, we derive a union bound on the bit error rate (BER) for MIMO-GFDM systems, which is based on exact pairwise error probabilities (PEPs). The exact PEP is calculated using the moment-generating function (MGF) for maximum likelihood (ML) detectors. Both the spatial correlation between antennas and the channel estimation errors are considered in the investigated channel environment. Second, polynomial expansion-based low-complexity channel estimators and precoders are proposed for massive MIMO-GFDM systems. Interference-free pilots are used in the minimum mean square error (MMSE) channel estimation to combat the influence of non-orthogonality between subcarriers in GFDM. The cubic computational complexity can be reduced to square order by using the polynomial expansion technique to approximate the matrix inverses in the conventional MMSE estimation and precoding. In addition, we derive performance limits in terms of the mean square error (MSE) for the proposed estimators, which can be a useful tool to predict estimators performance in the high Eₛ/N₀ region. A Cramér-Rao lower bound (CRLB) is derived for our system model and acts as a benchmark for the estimators. The computational complexity of the proposed channel estimators and precoders, and the impacts of the polynomial degree are also investigated. Finally, we analyze the error probability performance of LDPC coded GFDM systems. We first derive the initial log-likelihood ratio (LLR) expressions that are used in the sum-product algorithm (SPA) decoder. Then, based on the decoding threshold, we estimate the frame error rate (FER) in the low E[subscript b]/N₀ region by using the observed BER to model the channel variations. In addition, a lower bound on the FER of the system is also proposed based on absorbing sets. This lower bound can act as an estimate of the FER in the high E[subscript b]/N₀ region if the absorbing set used is dominant and its multiplicity is known. The quantization scheme also has an important impact on the FER and BER performances. Randomly constructed and array-based LDPC codes are used to support the performance analyses. For all these three aspects, software-based simulations and calculations are carried out to obtain related numerical results, which verify our proposed methods

6G Wireless Systems: Vision, Requirements, Challenges, Insights, and Opportunities

Mobile communications have been undergoing a generational change every ten years or so. However, the time difference between the so-called "G's" is also decreasing. While fifth-generation (5G) systems are becoming a commercial reality, there is already significant interest in systems beyond 5G, which we refer to as the sixth-generation (6G) of wireless systems. In contrast to the already published papers on the topic, we take a top-down approach to 6G. We present a holistic discussion of 6G systems beginning with lifestyle and societal changes driving the need for next generation networks. This is followed by a discussion into the technical requirements needed to enable 6G applications, based on which we dissect key challenges, as well as possibilities for practically realizable system solutions across all layers of the Open Systems Interconnection stack. Since many of the 6G applications will need access to an order-of-magnitude more spectrum, utilization of frequencies between 100 GHz and 1 THz becomes of paramount importance. As such, the 6G eco-system will feature a diverse range of frequency bands, ranging from below 6 GHz up to 1 THz. We comprehensively characterize the limitations that must be overcome to realize working systems in these bands; and provide a unique perspective on the physical, as well as higher layer challenges relating to the design of next generation core networks, new modulation and coding methods, novel multiple access techniques, antenna arrays, wave propagation, radio-frequency transceiver design, as well as real-time signal processing. We rigorously discuss the fundamental changes required in the core networks of the future that serves as a major source of latency for time-sensitive applications. While evaluating the strengths and weaknesses of key 6G technologies, we differentiate what may be achievable over the next decade, relative to what is possible.Comment: Accepted for Publication into the Proceedings of the IEEE; 32 pages, 10 figures, 5 table

Numerical modeling of seismic wave propagation in underground mines.

The phenomenon of rockburst damage localization, which is not well understood, has been observed in deep underground mines. Analysis of seismic wave propagation in underground mines is of great interest for improved understanding of the dynamic rock failure problem. This thesis aims at making a contribution for improving understanding of the seismic wave propagation in deep underground mines. Advanced numerical modeling tools are used and new modeling techniques are developed to attain this goal. In this thesis, research is emphasized on the ground motion around excavations due to seismic wave propagation that results from a fault-slip seismic event in the far-field and the near-field. It is found that moment tensor point source model seems to be suitable for the source representation in the far-field and the non-point source model (such as kinematic rupture source model) seems to be suitable for the source representation in the near-field. The modeling results confirm that ground motion is influenced by many factors such as target-source distance, slip direction, spatial location, and geometrical and geological conditions. Influence of wavelength-to-excavation span (/D) ratio on the wavefield is investigated to gain insights of ground motion behavior under both quasi-static and dynamic loading conditions. It is revealed that PPV (peak particle velocity) values increase as the /D ratio increases and the amplification effect increases as the /D ratio decreases. The loading condition maybe changed from the dynamic loading to the quasi-static condition when the /D is larger than 30. Strong dynamic loading should be considered when the /D ratio is small (less than 10, with a shear wavelength less than 50 m and an excavation span greater than 5 m) for most underground excavations. A method is proposed to estimate the quality factor (a measure of energy loss per oscillation cycle) for shear waves propagating in underground hard rocks so as to gain insight into the influence of internal attenuation on seismic wave propagation. A proper shear wave quality factor can be obtained by comparing modeling results with that from a scaling law, even if there are no high quality data for quality factor back analysis. Furthermore, the influence of different geological structures on seismic wave propagation is studied. It is shown that wave propagation patterns around an excavation can be altered and PPV amplification and shielding effect can occur near the excavation boundaries amongst other reasons due to heterogeneities such as tunnels, open and backfilled stopes, and dykes in underground mines. Finally, a coupled numerical procedure, which couples FLAC and SPECFEM2D, is developed to consider the excavation effect on ground motion. The FLAC model considers the excavationinduced stress change and rock mass failure, and passes the input data to SPECFEM2D by invoking FISH scripts. In addition, a new nonlinear velocity model that considers the influence of confinement and rock mass failure on wave velocity is presented. This nonlinear velocity model and the coupled numerical technique are used to model a simple stope excavation problem. It is found that there is a large difference in the wavefields and ground motions between the results from the uniform and non-uniform velocity models. A relatively stronger amplification is observed in the low confinement zones and on the excavation surface in the non-uniform velocity models. Because stress redistribution and rock mass failure around an excavation are considered, a realistic non-uniform velocity field can be obtained. The proposed coupled numerical procedure offers a method to improve the understanding of the site amplification effect and ground motion near excavation boundaries. This thesis presents some insights with regard to seismic wave propagation due to fault-slip seismic events in underground mines. If seismic wave propagation in underground mines can be modeled properly using techniques such as these presented in this thesis, then it is possible to conduct forensic analysis after a large seismic event so as to explain one of many factors that caused rockburst damage localization. Alternatively, the modeling approach may provide valuable inputs for decision-making with regard to strengthening high risk areas to prevent rockburst, thus improving mine safety.Doctor of Philosophy (PhD) in Natural Resources Engineerin