In this thesis, we focus on precisely analyzing the high dimensional error performance of such regularized convex optimization problems under the presence of different impairments (such as uncertainties and/or correlations) in the measurement matrix, which has independent Gaussian entries. The precise nature of our analysis allows performance comparison between different types of these estimators and enables us to optimally tune the involved hyperparameters. In particular, we study the performance of some of the most popular cases in linear inverse problems, such as the Least Squares (LS), Regularized Least Squares (RLS), LASSO, Elastic Net, and their box-constrained variants.

The Internet of Things (IoT) is a foundational building block for the upcoming information revolution and imminent smart-world era. Particularly, the IoT bridges the cyber domain to everything and anything within our physical world which enables unprecedented ubiquitous monitoring, connectivity, and smart control. In this Ph.D. defense, we present Unmanned Aerial Vehicles (UAVs) enabled IoT network designs for enhanced estimation, detection, and connectivity. The utilization of UAVs can offer an extra level of flexibility which results in more advanced and efficient connectivity and data aggregation for the IoT devices.

Tareq Al-Naffouri is a professor of Electrical Engineering (EE) and Principale investigator of the Information System Lab (ISL). He is also an active member of the Sensor Initiative (SI) at the King Abdullah University of Sciences and Technology, Saudi Arabia.

Random matrix theory is an outstanding mathematical tool that has demonstrated its usefulness in many areas ranging from wireless communication to finance and economics. The main motivation behind its use comes from the fundamental role that random matrices play in modeling unknown and unpredictable physical quantities. In many situations, meaningful metrics expressed as scalar functionals of these random matrices arise naturally. Along this line, the present work consists in leveraging tools from random matrix theory in an attempt to answer fundamental questions related to applications from statistical signal processing and machine learning.