Date

2016

Document Type

Dissertation

Degree

Doctor of Philosophy

Department

Electrical Engineering

First Adviser

Blum, Rick S.

Other advisers/committee members

Kishore, Shalinee; Cheng, Liang; Wu, Ping-Shi

Abstract

The theory of signal detection and estimation concerns the recovery of useful information from signals corrupted by random perturbations. This dissertation discusses the application of signal detection and estimation principles to two problems of significant practical interest: MIMO (multiple-input multiple output) radar, and time synchronization over packet switched networks. Under the first topic, we study the extension of several conventional radar analysis techniques to recently developed MIMO radars. Under the second topic, we develop new estimation techniques to improve the performance of widely used packet-based time synchronization algorithms. The ambiguity function is a popular mathematical tool for designing and optimizing the performance of radar detectors. Motivated by Neyman-Pearson testing principles, an alternative definition of the ambiguity function is proposed under the first topic. This definition directly associates with each pair of true and assumed target parameters the probability that the radar will declare a target present. We demonstrate that the new definition is better suited for the analysis of MIMO radars that perform non-coherent processing, while being equivalent to the original ambiguity function when applied to conventional radars. Based on the nature of antenna placements, transmit waveforms and the observed clutter and noise, several types of MIMO radar detectors have been individually studied in literature. A second investigation into MIMO radar presents a general method to model and analyze the detection performance of such systems. We develop closed-form expressions for a Neyman-Pearson optimum detector that is valid for a wide class of radars. Further, general closed-form expressions for the detector SNR, another tool used to quantify radar performance, are derived. Theoretical and numerical results demonstrating the value of the proposed techniques to optimize and predict the performance of arbitrary radar configurations are presented.There has been renewed recent interest in the application of packet-based time synchronization algorithms such as the IEEE 1588 Precision Time Protocol (PTP), to meet challenges posed by next-generation mobile telecommunication networks. In packet based time synchronization protocols, clock phase offsets are determined via two-way message exchanges between a master and a slave. Since the end-to-end delays in packet networks are inherently stochastic in nature, the recovery of phase offsets from message exchanges must be treated as a statistical estimation problem. While many simple intuitively motivated estimators for this problem exist in the literature, in the second part of this dissertation we use estimation theoretic principles to develop new estimators that offer significant performance benefits. To this end, we first describe new lower bounds on the error variance of phase offset estimation schemes. These bounds are obtained by re-deriving two Bayesian estimation bounds, namely the Ziv-Zakai and Weiss-Weinstien bounds, for use under a non-Bayesian formulation. Next, we describe new minimax estimators for the problem of phase offset estimation, that are optimum in terms of minimizing the maximum mean squared error over all possible values of the unknown parameters.Minimax estimators that utilize information from past timestamps to improve accuracy are also introduced. These minimax estimators provide fundamental limits on the performance of phase offset estimation schemes.Finally, a restricted class of estimators referred to as L-estimators are considered, that are linear functions of order statistics. The problem of designing optimum L-estimators is studied under several hitherto unconsidered criteria of optimality. We address the case where the queuing delay distributions are fully known, as well as the case where network model uncertainty exists.Optimum L-estimators that utilize information from past observation windows to improve performance are also described.Simulation results indicate that significant performance gains over conventional estimators can be obtained via the proposed optimum processing techniques.

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