A precise bare simulation approach to the minimization of some distances. Foundations

In information theory -- as well as in the adjacent fields of statistics, machine learning, artificial intelligence, signal processing and pattern recognition -- many flexibilizations of the omnipresent Kullback-Leibler information distance (relative entropy) and of the closely related Shannon entropy have become frequently used tools. To tackle corresponding constrained minimization (respectively maximization) problems by a newly developed dimension-free bare (pure) simulation method, is the main goal of this paper. Almost no assumptions (like convexity) on the set of constraints are needed, within our discrete setup of arbitrary dimension, and our method is precise (i.e., converges in the limit). As a side effect, we also derive an innovative way of constructing new useful distances/divergences. To illustrate the core of our approach, we present numerous examples. The potential for widespread applicability is indicated, too; in particular, we deliver many recent references for uses of the involved distances/divergences and entropies in various different research fields (which may also serve as an interdisciplinary interface)

Design and Performance Analysis of Next Generation Heterogeneous Cellular Networks for the Internet of Things

The Internet of Things (IoT) is a system of inter-connected computing devices, objects and mechanical and digital machines, and the communications between these devices/objects and other Internet-enabled systems. Scalable, reliable, and energy-efficient IoT connectivity will bring huge benefits to the society, especially in transportation, connected self-driving vehicles, healthcare, education, smart cities, and smart industries. The objective of this dissertation is to model and analyze the performance of large-scale heterogeneous two-tier IoT cellular networks, and offer design insights to maximize their performance. Using stochastic geometry, we develop realistic yet tractable models to study the performance of such networks. In particular, we propose solutions to the following research problems: -We propose a novel analytical model to estimate the mean uplink device data rate utility function under both spectrum allocation schemes, full spectrum reuse (FSR) and orthogonal spectrum partition (OSP), for uplink two-hop IoT networks. We develop constraint gradient ascent optimization algorithms to obtain the optimal aggregator association bias (for the FSR scheme) and the optimal joint spectrum partition ratio and optimal aggregator association bias (for the OSP scheme). -We study the performance of two-tier IoT cellular networks in which one tier operates in the traditional sub-6GHz spectrum and the other, in the millimeter wave (mm-wave) spectrum. In particular, we characterize the meta distributions of the downlink signal-to-interference ratio (sub-6GHz spectrum), the signal-to-noise ratio (mm-wave spectrum) and the data rate of a typical device in such a hybrid spectrum network. Finally, we characterize the meta distributions of the SIR/SNR and data rate of a typical device by substituting the cumulative moment of the CSP of a user device into the Gil-Pelaez inversion theorem. -We propose to split the control plane (C-plane) and user plane (U-plane) as a potential solution to harvest densification gain in heterogeneous two-tier networks while minimizing the handover rate and network control overhead. We develop a tractable mobility-aware model for a two-tier downlink cellular network with high density small cells and a C-plane/U-plane split architecture. The developed model is then used to quantify effect of mobility on the foreseen densification gain with and without C-plane/U-plane splitting

Autonomous Swarm Navigation

Robotic swarm systems attract increasing attention in a wide variety of applications, where a multitude of self-organized robotic entities collectively accomplish sensing or exploration tasks. Compared to a single robot, a swarm system offers advantages in terms of exploration speed, robustness against single point of failures, and collective observations of spatio-temporal processes. Autonomous swarm navigation, including swarm self-localization, the localization of external sources, and swarm control, is essential for the success of an autonomous swarm application. However, as a newly emerging technology, a thorough study of autonomous swarm navigation is still missing. In this thesis, we systematically study swarm navigation systems, particularly emphasizing on their collective performance. The general theory of swarm navigation as well as an in-depth study on a specific swarm navigation system proposed for future Mars exploration missions are covered. Concerning swarm localization, a decentralized algorithm is proposed, which achieves a near-optimal performance with low complexity for a dense swarm network. Regarding swarm control, a position-aware swarm control concept is proposed. The swarm is aware of not only the position estimates and the estimation uncertainties of itself and the sources, but also the potential motions to enrich position information. As a result, the swarm actively adapts its formation to improve localization performance, without losing track of other objectives, such as goal approaching and collision avoidance. The autonomous swarm navigation concept described in this thesis is verified for a specific Mars swarm exploration system. More importantly, this concept is generally adaptable to an extensive range of swarm applications

The Ensemble Kalman Filter: A Signal Processing Perspective

The ensemble Kalman filter (EnKF) is a Monte Carlo based implementation of the Kalman filter (KF) for extremely high-dimensional, possibly nonlinear and non-Gaussian state estimation problems. Its ability to handle state dimensions in the order of millions has made the EnKF a popular algorithm in different geoscientific disciplines. Despite a similarly vital need for scalable algorithms in signal processing, e.g., to make sense of the ever increasing amount of sensor data, the EnKF is hardly discussed in our field. This self-contained review paper is aimed at signal processing researchers and provides all the knowledge to get started with the EnKF. The algorithm is derived in a KF framework, without the often encountered geoscientific terminology. Algorithmic challenges and required extensions of the EnKF are provided, as well as relations to sigma-point KF and particle filters. The relevant EnKF literature is summarized in an extensive survey and unique simulation examples, including popular benchmark problems, complement the theory with practical insights. The signal processing perspective highlights new directions of research and facilitates the exchange of potentially beneficial ideas, both for the EnKF and high-dimensional nonlinear and non-Gaussian filtering in general