Statistical signal processing plays a fundamental role in fields as diverse as personal communications, national security, and medical image processing. To support the continued advancement of these fields and many others, there is a need to develop efficient near-optimal solutions to increasingly challenging detection and estimation problems. The focus of this research is addressing detection and estimation challenges in environments that exhibit high degrees of complexity and high levels of model uncertainty. In such scenarios, optimal detection and estimation solutions are often computationally infeasible, if not impossible, to determine. This research explores the effectiveness of tree search techniques, originally developed for sequential decoding, to address these challenges. The intellectual merit of the work is in the development of approximate detection and estimation algorithms that achieve near-optimal performance with dramatically reduced computational complexity requirements.
There are two primary technical objectives of this research. The first is to characterize the detection/estimation problem space for which tree search techniques provide competitive solutions through analysis of computational complexity as a function of system properties, and to frame conclusions in the context of existing results for competing approaches. The second objective is to develop and evaluate tree search approaches to three benchmark problems: channel estimation and data detection for broadly dispersive, rapidly varying channels; multiple transmitter location estimation for cognitive radio applications; and dynamic state estimation under model uncertainty or absence. The aims of the education component of this research are to design and implement elementary-level engineering curriculum centered around hands-on telecommunications activities, and to develop college-level problem-based learning curriculum that deepens students' understanding of probability and random processes by connecting abstract concepts to real-world problems with probabilistic models.
