Adaptive Precoding and Resource Allocation in Cognitive Radio Networks

In this thesis, we develop efficient resource allocation and adaptive precoding schemes for two scenarios: multiuser MIMO-OFDM and multiuser MIMO based CR networks. In the context of the multiuser MIMO-OFDM CR network, we have developed resource allocation and adaptive precoding schemes for both the downlink (DL) and uplink (UL). The proposed schemes are characterized by both computational and spectral efficiencies. The adaptive precoder operates based on generating degrees of freedom (DoF). The resource allocation has been formulated as a sum-rate maximization problem subject to the upper-limit of total power and interference at primary user constraints. The formulated optimization problem is a mixed integer programming having a combinatorial complexity which is hard to solve, and therefore we separated it into a two-phase procedure to elaborate computational efficiency: Adaptive precoding (DoF assignment) and subcarrier mapping. From the implementation perspective, the resource allocation of the DL is central based processing, but the UL is semi-distributed based. The DL and UL problems are sorted out using the Lagrange multiplier theory which is regarded as an efficient alternative methodology compared to the convex optimization theory. The solution is not only characterized by low-complexity, but also by optimality. Numerical simulations illustrate remarkable spectral and SNR gains provided by the proposed schemes.In dieser Dissertation werden effiziente Ressourcenallokation und adaptive Vorkodierungsverfahren für zwei Szenarios entwickelt: Mehrbenutzer-MIMO-OFDM und Mehrbenutzer-MIMO jeweils basierend auf CR-Netzwerken. Im Bereich der Mehrbenutzer-MIMO-OFDM CR-Netzwerke wurden Verfahren zur Ressourcenallokation und zur adaptiven Vorkodierung jeweils für den Downlink (DL) und den Uplink (UL) entwickelt. Die Ressourcenallokation wurde als Optimierungsproblem formuliert, bei dem die Summenrate maximiert wird, wobei die Gesamtsendeleistung und die Interferenz an den Primärnutzern begrenzt ist. Das formulierte Optimierungsproblem ist ein sogenanntes Mixed-Integer-Programm, dessen kombinatorische Komplexität nur extrem aufwendig lösbar ist. Auf Grund dessen wurde es zur Komplexitätsreduktion in zwei Phasen aufgeteilt: Adaptive Vorkodierung (DoF-Zuordnung) und Subkanalzuordnung. Während die Ressourcenallokation für den DL aus Implementierungssicht ein zentralistischer Prozess ist, kann sie für den UL als semiverteilt eingeordnet werden. Die Aufgabe der zentralen Ressourcenallokation wird gelöst, um die zentrale adaptive Vorkodierung und die Subkanalzuordnung für UL und DL zu verwalten. Die Subkanalzuordnung ist für den DL optimal und effizient gelöst, indem das Problem als konvexes Problem modelliert ist. Für den UL wiederum ist das Problem trotz der Konvexität quasi-optimal gelöst, da in der Problemformulierung eine Begrenzung der Ressourcen pro Benutzer existiert

Listening to Distances and Hearing Shapes:Inverse Problems in Room Acoustics and Beyond

A central theme of this thesis is using echoes to achieve useful, interesting, and sometimes surprising results. One should have no doubts about the echoes' constructive potential; it is, after all, demonstrated masterfully by Nature. Just think about the bat's intriguing ability to navigate in unknown spaces and hunt for insects by listening to echoes of its calls, or about similar (albeit less well-known) abilities of toothed whales, some birds, shrews, and ultimately people. We show that, perhaps contrary to conventional wisdom, multipath propagation resulting from echoes is our friend. When we think about it the right way, it reveals essential geometric information about the sources--channel--receivers system. The key idea is to think of echoes as being more than just delayed and attenuated peaks in 1D impulse responses; they are actually additional sources with their corresponding 3D locations. This transformation allows us to forget about the abstract \emph{room}, and to replace it by more familiar \emph{point sets}. We can then engage the powerful machinery of Euclidean distance geometry. A problem that always arises is that we do not know \emph{a priori} the matching between the peaks and the points in space, and solving the inverse problem is achieved by \emph{echo sorting}---a tool we developed for learning correct labelings of echoes. This has applications beyond acoustics, whenever one deals with waves and reflections, or more generally, time-of-flight measurements. Equipped with this perspective, we first address the ``Can one hear the shape of a room?'' question, and we answer it with a qualified ``yes''. Even a single impulse response uniquely describes a convex polyhedral room, whereas a more practical algorithm to reconstruct the room's geometry uses only first-order echoes and a few microphones. Next, we show how different problems of localization benefit from echoes. The first one is multiple indoor sound source localization. Assuming the room is known, we show that discretizing the Helmholtz equation yields a system of sparse reconstruction problems linked by the common sparsity pattern. By exploiting the full bandwidth of the sources, we show that it is possible to localize multiple unknown sound sources using only a single microphone. We then look at indoor localization with known pulses from the geometric echo perspective introduced previously. Echo sorting enables localization in non-convex rooms without a line-of-sight path, and localization with a single omni-directional sensor, which is impossible without echoes. A closely related problem is microphone position calibration; we show that echoes can help even without assuming that the room is known. Using echoes, we can localize arbitrary numbers of microphones at unknown locations in an unknown room using only one source at an unknown location---for example a finger snap---and get the room's geometry as a byproduct. Our study of source localization outgrew the initial form factor when we looked at source localization with spherical microphone arrays. Spherical signals appear well beyond spherical microphone arrays; for example, any signal defined on Earth's surface lives on a sphere. This resulted in the first slight departure from the main theme: We develop the theory and algorithms for sampling sparse signals on the sphere using finite rate-of-innovation principles and apply it to various signal processing problems on the sphere