Sparse Signal Processing Concepts for Efficient 5G System Design

As it becomes increasingly apparent that 4G will not be able to meet the emerging demands of future mobile communication systems, the question what could make up a 5G system, what are the crucial challenges and what are the key drivers is part of intensive, ongoing discussions. Partly due to the advent of compressive sensing, methods that can optimally exploit sparsity in signals have received tremendous attention in recent years. In this paper we will describe a variety of scenarios in which signal sparsity arises naturally in 5G wireless systems. Signal sparsity and the associated rich collection of tools and algorithms will thus be a viable source for innovation in 5G wireless system design. We will discribe applications of this sparse signal processing paradigm in MIMO random access, cloud radio access networks, compressive channel-source network coding, and embedded security. We will also emphasize important open problem that may arise in 5G system design, for which sparsity will potentially play a key role in their solution.Comment: 18 pages, 5 figures, accepted for publication in IEEE Acces

Control and Optimization for Aerospace Systems with Stochastic Disturbances, Uncertainties, and Constraints

The topic of this dissertation is the control and optimization of aerospace systems under the influence of stochastic disturbances, uncertainties, and subject to chance constraints. This problem is motivated by the uncertain operating environments of many aerospace systems, and the ever-present push to extract greater performance from these systems while maintaining safety. Explicitly accounting for the stochastic disturbances and uncertainties in the constrained control design confers the ability to assign the probability of constraint satisfaction depending on the level of risk that is deemed acceptable and allows for the possibility of theoretical constraint satisfaction guarantees. Along these lines, this dissertation presents novel contributions addressing four different problems: 1) chance-constrained path planning for small unmanned aerial vehicles in urban environments, 2) chance-constrained spacecraft relative motion planning in low-Earth orbit, 3) stochastic optimization of suborbital launch operations, and 4) nonlinear model predictive control for tracking near rectilinear halo orbits and a proposed stochastic extension. For the first problem, existing dynamic and informed rapidly-expanding random trees algorithms are combined with a novel quadratic programming-based collision detection algorithm to enable computationally efficient, chance-constrained path planning. For the second problem, a previously proposed constrained relative motion approach based on chained positively invariant sets is extended in this dissertation to the case where the spacecraft dynamics are controlled using output feedback on noisy measurements and are subject to stochastic disturbances. Connectivity between nodes is determined through the use of chance-constrained admissible sets, guaranteeing that constraints are met with a specified probability. For the third problem, a novel approach to suborbital launch operations is presented. It utilizes linear covariance propagation and stochastic clustering optimization to create an effective software-only method for decreasing the probability of a dangerous landing with no physical changes to the vehicle and only minimal changes to its flight controls software. For the fourth problem, the use of suboptimal nonlinear model predictive control (NMPC) coupled with low-thrust actuators is considered for station-keeping on near rectilinear halo orbits. The nonlinear optimization problems in NMPC are solved with time-distributed sequential quadratic programming techniques utilizing the FBstab algorithm. A stochastic extension for this problem is also proposed. The results are illustrated using detailed numerical simulations.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/162992/1/awbe_1.pd

Abstract Hidden Markov Models: a monadic account of quantitative information flow

Hidden Markov Models, HMM's, are mathematical models of Markov processes with state that is hidden, but from which information can leak. They are typically represented as 3-way joint-probability distributions. We use HMM's as denotations of probabilistic hidden-state sequential programs: for that, we recast them as `abstract' HMM's, computations in the Giry monad $\mathbb{D}$, and we equip them with a partial order of increasing security. However to encode the monadic type with hiding over some state $\mathcal{X}$ we use $\mathbb{D}\mathcal{X}\to \mathbb{D}^2\mathcal{X}$ rather than the conventional $\mathcal{X}{\to}\mathbb{D}\mathcal{X}$ that suffices for Markov models whose state is not hidden. We illustrate the $\mathbb{D}\mathcal{X}\to \mathbb{D}^2\mathcal{X}$ construction with a small Haskell prototype. We then present uncertainty measures as a generalisation of the extant diversity of probabilistic entropies, with characteristic analytic properties for them, and show how the new entropies interact with the order of increasing security. Furthermore, we give a `backwards' uncertainty-transformer semantics for HMM's that is dual to the `forwards' abstract HMM's - it is an analogue of the duality between forwards, relational semantics and backwards, predicate-transformer semantics for imperative programs with demonic choice. Finally, we argue that, from this new denotational-semantic viewpoint, one can see that the Dalenius desideratum for statistical databases is actually an issue in compositionality. We propose a means for taking it into account

T\mathbb{T}-Operator Limits on Optical Communication: Metaoptics, Computation, and Input-Output Transformations

We present an optimization framework based on Lagrange duality and the scattering $\mathbb{T}$ operator of electromagnetism to construct limits on the possible features that may be imparted to a collection of output fields from a collection of input fields, i.e., constraints on achievable optical transformations and the characteristics of structured materials as communication channels. Implications of these bounds on the performance of representative optical devices having multi-wavelength or multiport functionalities are examined in the context of electromagnetic shielding, focusing, near-field resolution, and linear computing

Sparse Proteomics Analysis - A compressed sensing-based approach for feature selection and classification of high-dimensional proteomics mass spectrometry data

Background: High-throughput proteomics techniques, such as mass spectrometry (MS)-based approaches, produce very high-dimensional data-sets. In a clinical setting one is often interested in how mass spectra differ between patients of different classes, for example spectra from healthy patients vs. spectra from patients having a particular disease. Machine learning algorithms are needed to (a) identify these discriminating features and (b) classify unknown spectra based on this feature set. Since the acquired data is usually noisy, the algorithms should be robust against noise and outliers, while the identified feature set should be as small as possible. Results: We present a new algorithm, Sparse Proteomics Analysis (SPA), based on the theory of compressed sensing that allows us to identify a minimal discriminating set of features from mass spectrometry data-sets. We show (1) how our method performs on artificial and real-world data-sets, (2) that its performance is competitive with standard (and widely used) algorithms for analyzing proteomics data, and (3) that it is robust against random and systematic noise. We further demonstrate the applicability of our algorithm to two previously published clinical data-sets