Publikationen

Full Matrix Capture is a multi-channel data acquisition method which enables flexible, high resolution imaging using ultrasound arrays. However, the measurement time and data volume are increased considerably. Both of these costs can be circumvented via compressed sensing, which exploits prior knowledge of the underlying model and its sparsity to reduce the amount of data needed to produce a high resolution image. In order to design compression matrices that are physically realizable without sophisticated hardware constraints, structured subsampling patterns are designed and evaluated in this work. The design is based on the analysis of the Cramér–Rao Bound of a single scatterer in a homogeneous, isotropic medium. A numerical comparison of the point spread functions obtained with different compression matrices and the Fast Iterative Shrinkage/Thresholding Algorithm shows that the best performance is achieved when each transmit event can use a different subset of receiving elements and each receiving element uses a different section of the echo signal spectrum. Such a design has the advantage of outperforming other structured patterns to the extent that suboptimal selection matrices provide a good performance and can be efficiently computed with greedy approaches.

We propose a compact hardware architecture for measuring sparse channel impulse responses (IR) by extending the M-Sequence ultra-wideband (UWB) measurement principle with the concept of compressed sensing. A channel is excited with a periodic M-sequence and its response signal is observed using a Random Demodulator (RD), which observes pseudo-random linear combinations of the response signal at a rate significantly lower than the measurement bandwidth. The excitation signal and the RD mixing signal are generated from compactly implementable Linear Feedback Shift registers (LFSR) and operated from a common clock. A linear model is derived that allows retrieving an IR from a set of observations using Sparse-Signal-Recovery (SSR). A Matrix-free model implementation is possible due to the choice of synchronous LFSRs as signal generators, resulting in low computational complexity. For validation, real measurement data of a time-variant channel containing multipath components is processed by simulation models of our proposed architecture and the classic M-Sequence method. We show successful IR recovery using our architecture and SSR, outperforming the classic method significantly in terms of IR measurement rate. Compared to the classic method, the proposed architecture allows faster measurements of sparse time-varying channels, resulting in higher Doppler tolerance without increasing hardware or data stream complexity.

Purpose The purpose of this paper is to present the advantageous applicability of the bicomplex analysis in the context of the Finite Element Method (FEM). This method can be applied for wave propagation problems in various environments. Design/methodology/approach In this paper, the bicomplex number system is introduced and accordingly the differential equation for time-harmonic Maxwell’s equations in homogeneous media is derived in detail. Besides that, numerical simulations of wave propagation are performed and compared to the traditional approach based on classical FEM related to the Helmholtz equation. The appropriate error norm is investigated for different discretizations. Findings The results show that the use of bicomplex analysis in FEM leads to the higher accuracy of the electromagnetic field determination compared to the traditional Helmholtz approach. By using the bicomplex-valued formulation, the complex-valued electric and magnetic fields can be found directly and no additional FEM calculations are necessary to get the whole field. Originality/value The direct bicomplex formulation overcomes the use of the second order derivatives, which leads to the higher accuracy. In general, accurate calculations of the wave propagation in FEM is still an open problem and the approach described in this paper is a contribution to this class of problems.

Die Lokalisierung oder Positionierung von Benutzern ist aus verschiedenen Gründen ein unverzichtbarer Bestandteil von drahtlosen Kommunikationsnetzen. Zahlreiche standortbezogene Dienste (Location Based Services, LBS), die Teil unseres täglichen Lebens sind, hängen hauptsächlich von der Position der Benutzer innerhalb der Kanalumgebung ab. Standortinformationen sind auch wichtig für die Aufrechterhaltung und Verbesserung verschiedener netzwerkbezogener Funktionen wie Handover, Ressourcenzuweisung, Tarifanpassung und andere RRM-Funktionen des Funkressourcenmanagements. Channel Charting (CC) ist ein neuartiges, datengesteuertes Basisbandverfahren, das darauf abzielt, die niedrigdimensionale Darstellung, d.h. Kanaldiagramm unter Verwendung hochdimensionaler Channel State Information (CSI) zu erlernen, die an der Basisstation (BS) gesammelt wird, um den wahren Standort der UEs zu erhalten. Vereinfacht ausgedrückt werden virtual maps oder charts so erstellt, dass die räumlich nahe beieinanderliegenden Punkte auch im Kanaldiagramm nahe beieinander liegen. Diese Kanaldiagramme werden völlig unbeaufsichtigt erstellt, d.h. ohne Zugang zu irgendwelchen Standortinformationen an der BS. CC arbeitet, indem es Merkmale aus der CSI extrahiert, die die Nachbarschaftsinformationen zwischen den UEs bewahren, und dann unüberwachte vielfältige Lernmethoden anwendet, um die extrahierten Merkmale auf dem Kanaldiagramm abzubilden. Der jüngste Erfolg des Tiefenlernens hat gezeigt, dass neuronale Netze leistungsfähige Funktions-Approximatoren sind, die in der Lage sind, komplexe Merkmale aus Rohdaten zu extrahieren. Convolutional Neural Networks (CNNs) sind wahrscheinlich die am weitesten verbreiteten neuronalen Netze, die für die Extraktion relevanter raumzeitlicher Merkmale aus Rohdaten bekannt sind. In der vorliegenden Masterarbeit wird die Idee der Verwendung von Convolutional Neural Networks CNNs zur Lösung des CC-Problems untersucht. Convolutional AutoEncoders (CAE) bieten einen völlig unbeaufsichtigten Tiefenlernansatz, der es auch erlaubt, die Nebeninformationen wie z.B. Beschränkungen des maximalen Abstands zwischen Abtastpunkten in das Lernen einzubeziehen. Für die Merkmalsextraktion schlagen wir vor, CSI-basierte Channel Impulse Response zu verwenden. Darüber hinaus schlagen wir auch vor, einen hybriden Ansatz zu verwenden, indem wir zwei vielfältige Methoden kombinieren, nämlich (CAE) und Uniform Manifold Approximation (UMAP), um genaue Kanaldiagramme zu erstellen.