ITC/USA 2010 Conference Proceedings / The Forty-Sixth Annual International Telemetering Conference and Technical Exhibition / October 25-28, 2010 / Town and Country Resort & Convention Center, San Diego, California / High data rate communication between airborne vehicles and ground stations over the bandwidth constrained Aeronautical Telemetry channel is attributed to the development of bandwidth efficient Advanced Range Telemetry (ARTM) waveforms. This communication takes place over a multipath channel consisting of two components - a line of sight and one or more ground reflected paths which result in frequency selective fading. We concentrate on the ARTM SOQPSKTG transmit waveform suite and decode information bits using the reduced complexity Viterbi algorithm. Two different methodologies are proposed to implement reduced complexity Viterbi decoders in multipath channels. The first method jointly equalizes the channel and decodes the information bits using the reduced complexity Viterbi algorithm while the second method utilizes the minimum mean square error equalizer prior to applying the Viterbi decoder. An extensive numerical study is performed in comparing the performance of the above methodologies. We also demonstrate the performance gain offered by our reduced complexity Viterbi decoders over the existing linear receiver. In the numerical study, both perfect and estimated channel state information are considered.

This thesis concerns methods of reduced complexity for electronic structure calculations.  When quantum chemistry methods are applied to large systems, it is important to optimally use computer resources and only store data and perform operations that contribute to the overall accuracy. At the same time, precarious approximations could jeopardize the reliability of the whole calculation.  In this thesis, the self-consistent field method is seen as a sequence of rotations of the occupied subspace. Errors coming from computational approximations are characterized as erroneous rotations of this subspace. This viewpoint is optimal in the sense that the occupied subspace uniquely defines the electron density. Errors should be measured by their impact on the overall accuracy instead of by their constituent parts. With this point of view, a mathematical framework for control of errors in Hartree-Fock/Kohn-Sham calculations is proposed.  A unifying framework is of particular importance when computational approximations are introduced to efficiently handle large systems. An important operation in Hartree-Fock/Kohn-Sham calculations is the calculation of the density matrix for a given Fock/Kohn-Sham matrix. In this thesis, density matrix purification is used to compute the density matrix with time and memory usage increasing only linearly with system size. The forward error of purification is analyzed and schemes to control the forward error are proposed. The presented purification methods are coupled with effective methods to compute interior eigenvalues of the Fock/Kohn-Sham matrix also proposed in this thesis.New methods for inverse factorizations of Hermitian positive definite matrices that can be used for congruence transformations of the Fock/Kohn-Sham and density matrices are suggested as well. Most of the methods above have been implemented in the Ergo quantum chemistry program. This program uses a hierarchic sparse matrix library, also presented in this thesis, which is parallelized for shared memory computer architectures. It is demonstrated that the Ergo program is able to perform linear scaling Hartree-Fock calculations. / QC 20100908

Recently, a study on obtaining better Euclidean distance for CPM (Continuous Phase Modulation) signals that fit well-known GSM spectral envelope has been carried out, and significant performance improvements were obtained. Two new pulse shapes, which are represented using 8th degree polynomials, were optimized to give the best error performance under the constraint that the PSD stays below GSM spectral standards. However, the approach uses parameters that cause the number of states to increase considerably, and thus yielding high complexity for receiver implementation. In this thesis, a study on finding a feasible receiver design that can provide a performance with acceptable degradation but affordable complexity is carried out for those new pulse shapes. After a survey about complexity reduction techniques, a decision is made to go on with a receiver structure based on Laurent Decomposition (LD) of phase modulated signals. Unlike other complexity reduction techniques, usage of LD based receivers permits reduction in both the number of matched filters and trellis states. Throughout the study, different numbers of matched filters and trellis states were used in LD based receivers for the new pulse shapes, and good results are obtained. For the pulse shape with pulse length L = 3, about a gain of 0.93dB in power is achieved by only 2 matched filters and 14 trellis states. For the case where L = 7, approximately a gain of 2.25dB is achieved with only 8 matched filters and 56 states, whereas 896 matched filters and 448 states are needed in the optimum case without complexity reduction.

It is well known that multiple antennas at the transmitter and receiver are imperative for reliable and high data-rate communication over wireless channels. However, these systems essentially need multiple radio frequency (RF) chains owing to multiple antennas, and hence pose challenges for applications with limited form-factor. Antenna Selection (AS) techniques alleviate this problem by using only a subset of the total available antennas and hence require only a few RF chains compared to the number of antennas. These systems operate in a closed-loop scenario, where the information fed back from the receiver is used for the transmit antenna subset selection. In contrast to this, a novel open-loop technique known as spatial modulation (SM) was recently proposed that uses a single RF-chain at the transmitter and achieves a higher spectral efficiency compared to single-input and AS based systems. The work in the thesis mainly focuses on the following aspects of SM system: Study of Mutual Information in SM systems operating in open-loop and closed-loop scenarios: We study the achievable mutual information in the SM system operating with finite and Gaussian input alphabet, and compare the results with that of the SIMO and AS based systems. Reduced-complexity maximum-likelihood (ML) decoding algorithms for SM systems: We propose ML-optimal sphere decoders for SM systems with arbitrary number of transmit antennas. Furthermore, a reduced-complexity ML detector is also proposed whose computational complexity is lowest among the known existing detectors in the literature. Transmit diversity techniques for SM systems: The conventional SM system achieves a transmit diversity order of one. We propose a complex interleaved orthogonal design baaed SM scheme that achieves a transit diversity order of two, while offering symbol-by- symbol ML decodability. Transmit antenna subset selection algorithms for SM systems: The SM system is considered in the closed-loop scenario, where only a subset of the total number of transmit antennas is chosen based on the information fed back by the receiver. Specifically, the Euclidean distance and capacity optimized antenna selection algorithms are studied in comparison with the conventional AS based systems. SM system operating in dispersive channels: The SM system operating in a dispersive channel with the aid of zero-padding is studied. It is shown that the SM system achieves full receive-diversity and multipath-diversity with ML decoding, but offers a decoding complexity that is exponential in the number of multipaths. Furthermore, a reduced complexity linear receiver is proposed that achieves achieves full multipath as well as receive-diversity, while offering a decoding complexity order same as that of the SM system operating in a frequency-flat channel.

Les littoraux sableux dominés par l'action des vagues sont des zones très dynamiques où l'aléa érosion menace les activités humaines et la sécurité des personnes. Comprendre et prévoir les évolutions du trait de côte est crucial pour informer et guider les gestionnaires du littoral. Actuellement, aucun modèle numérique ne permet de reproduire les évolutions du trait de côte sur l'ensemble des échelles spatio-temporelles et des configurations de côte requises du fait de limitations numériques et physiques. Cette thèse se concentre sur le développement de nouveaux outils de modélisation à complexité réduite pour simuler les évolutions du trait de côte le long des littoraux sableux dominés par l'action des vagues sur des échelles de temps allant de l'heure à plusieurs décennies avec des temps de calcul réduits. D'abord, un modèle statistique de trait de côte s'appuyant uniquement sur les occurrences saisonnières de régimes de temps est développé. Ce modèle permet de simuler la variabilité du trait de côte à l'échelle pluriannuelle, sans avoir besoin de connaitre les conditions de vagues ou de modéliser le transport sédimentaire. Puis, un nouveau modèle numérique de trait de côte basé sur les vagues (LX-Shore) est développé en intégrant entre autres les forces de certains modèles existants. Il inclut les processus cross-shore et longshore, et couple la dynamique du trait de côte à la propagation des vagues via le modèle spectral de vagues SWAN. Ce modèle permet de simuler l'évolution de formes complexes comme par exemple les flèches sableuses. Ces outils ouvrent aussi la voie vers une meilleure évaluation des évolutions futures du trait de côte, ainsi que de la contribution respective des processus impliqués. / Wave-dominated sandy coasts are highly dynamic and populated systems increasingly threatened by erosion hazard. Understanding and predicting shoreline change is critical to inform and guide stakeholders. However, there is currently no numerical model able to reproduce and predict shoreline evolution over the full range of temporal scales and coastal geometries owing to numerical and physical limitations. This thesis focuses on the development of new reduced-complexity models to simulate shoreline change along wave-dominated sandy coasts on the timescales from hours to decades with low computation time. First, a statistical shoreline change model based on the seasonal occurrences of some oceanic basin weather regimes is developed. This model allows simulating shoreline variability at the seasonal and interannual scales, without resorting to wave data or sediment transport modeling. Second, a new so-called LX-Shore numerical wave-driven shoreline change model is developed, which takes the best from some existing models and includes additional numerical and physical developments. LX-Shore couples the primary longshore and cross-shore processes and includes the feedback of shoreline and bathymetric evolution on the wave field using a spectral wave model. LX-Shore successfully simulates the dynamics of coastal embayments or the formation of subsequent nonlinear evolution of complex shoreline features such as flying sandspits. It is anticipated that LX-Shore will provide new and quantitative insight into the respective contributions of the processes controlling shoreline change on real coasts for a wide range of wave climates and geological settings.

Wird der Äquator-Pol-Energietransfer als Wärmediffusion berücksichtigt, so gehen Energiebilanzmodelle in Reaktions-Diffusionsgleichungen über, deren Modellfall die (deterministische) Chafee-Infante-Gleichung darstellt. Ihre Lösung besitzt zwei stabile Zustände und mehrere instabile auf der separierenden Mannigfaltigkeit (Separatrix) der stabilen Anziehungsgebiete. Es wird bewiesen, dass die Lösung auf geeignet verkleinerten Anziehungsgebieten mit Minimalabstand zur Separatrix innerhalb von Zeitskalen relaxiert, die höchstens logarithmisch darin anwachsen. Motiviert durch statistische Belege aus grönländischen Zeitreihen wird diese partielle Differentialgleichung unter Störung mit unendlichdimensionalem, Hilbertraum-wertigen, regulär variierenden Lévy''schen reinen Sprungrauschen mit index alpha und Intensität epsilon untersucht. Ein kanonisches Beispiel dieses Rauschens ist alpha-stabiles Rauschen im Hilbertraum. Durch Erweiterung einer Methode von Imkeller und Pavlyukevich auf stochastische partielle Differentialgleichungen wird unter milden Bedingungen bewiesen, dass im Gegensatz zu Gauß''schem Rauschen die erwarteten Austritts- und übertrittszeiten zwischen Anziehungsgebieten polynomiell mit Ordnung in der inversen Intensität für kleine Rauschintensität anwachsen. In Kapitel 6 wird eine zusätzliche natürliche “Separatrixhypothese” über das Sprungmaß, eingeführt, die eine obere Schranke für die Austrittszeiten aus einer Umgebung der Separatrix impliziert. Dies ermöglicht den Nachweis einer oberen Schranke für die Austrittszeiten, welche gleichmäßig für Anfangsbedingungen in dem ganzen Anziehungsgebiet gilt. Es folgen zwei Lokalisierungsergebnisse. Schließlich wird gezeigt, dass die Lösung metastabiles Verhalten aufweist. Unter der “Separatrixhypothese” wird dies auf ein Ergebnis erweitert, welches gleichmäßig im Raum gilt. / If equator-to-pole energy transfer by heat diffusion is taken into account, Energy Balance Models turn into reaction-diffusion equations, whose prototype is the (deterministic) Chafee-Infante equation. Its solution has two stable states and several unstable ones on the separating manifold (separatrix) of the stable domains of attraction. We show, that on appropriately reduced domains of attraction of a minimal distance to the separatrix the solution relaxes in time scales increasing only logarithmically in it. Motivated by the statistical evidence from Greenland ice core time series, we consider this partial differential equation perturbed by an infinite-dimensional Hilbert space-valued regularly varying (pure jump) Lévy noise of index alpha and intensity epsilon. A proto-type of this noise is alpha-stable noise in the Hilbert space. Extending a method developed by Imkeller and Pavlyukevich to the SPDE setting we prove under mild conditions that in contrast to Gaussian perturbations the expected exit and transition times between the domains of attraction increase polynomially in the inverse intensity. In Chapter 6 we introduce an additional natural separatrix hypothesis on the jump measure that implies an upper bound on the exit time of a neighborhood of the separatrix. This allows to obtain an upper bound for the asymptotic exit time uniform for the initial positions inside the entire domain of attraction. It is followed by two localization results. Finally we prove that the solution exhibits metastable behavior. Under the separatrix hypothesis we can extend this to a result that holds uniformly in space.