UC San Diego

Parametric and non-parametric measurement models provide means to more insights when the amount of available data is limited. We focus on measurements from multi-sensor systems in three applications of practical interest and provide inference techniques to estimate underlying unknowns with higher accuracy than previous approaches under limited resources. In this pursuit we adopt the maximum likelihood estimation (MLE) framework to estimate the parameters from the measurements. The framework is widely used with varying degrees of success. In certain applications, framing problems under MLE leads to difficult non-convex optimization problems, and thus model selection becomes crucial. Other applications may even require one to design measurements upon which the MLE framework may be applied.

In the first problem, we consider the initial beam alignment in millimeter wave systems using phased arrays. For a single RF chain system, we propose a novel sensing methodology inspired from synthetic aperture radar, that enables more informative measurements in a structured manner. We also provide an inference technique that utilizes the measurements under proposed sensing to efficiently compute a posterior density on the unknown angle. The inference is carried without the knowledge of complex path gain, and demonstrates significant improvement over competing techniques.

In the second problem, we study sparse signal recovery with the aim to bridge the computational gap between the widely used Orthogonal Matching Pursuit algorithm and methods derived from the MLE objective. We propose a novel Light-Weight Sequential Sparse Bayesian Learning (LWS-SBL) algorithm and provide efficient recursive procedures to update the internal variables of the algorithm. We demonstrate superior support recovery performance using LWS-SBL over OMP and further elucidate the subtle differences in the underlying mechanisms in the two algorithms.

Lastly, we delve into the Direction-of-Arrival (DoA) estimation problem for narrowband signals and propose a novel two-step algorithm. In the first step, we recover a structured covariance matrix estimate for the received signal in the MLE sense. The second step involves estimating DoAs using root-MUSIC from the recovered structured covariance matrix. The first step draws inspiration from the SBL formulation, as it provides the basic model which we fit to the measurements. The proposed approach improves resolution, bias, identifiability, and can identify two or more sources with a single snapshot, unlike the traditional subspace-based algorithms.