Time reversal operation for distributed systems in stationary and dynamic environment

Abstract

The multiple scattered field interactions give rise to the resonances of the system, and the dissertation shows that these resonances are related to the spectrum of the TRO. Moreover, this investigation connects the eigen-system of the TRO to the poles of the Singularity Expansion Method (SEM), where the poles represent the natural frequencies of the system.

The motion correction technique introduces a Doppler operator which provides the necessary phase information to predict the future eigen-system of the TRO. This dissertation considers a single moving scatterer, but the ideas can be extended to multiple scatterers.

This dissertation considers a distributed wave-based sensing system that probes a scene consisting of multiple interacting idealized targets. Each sensor is a co-located transmit-receive pair that is capable of transmitting arbitrary wideband waveforms. The dissertation addresses the problem of finding the space-time transmit waveform that provides the best target detection performance in the sense of maximizing the energy scattered back into the receivers. This is done first for a stationary target undergoing multiple scattering, and then for a linearly moving target.

The approach in this dissertation is based on earlier work that constructed the solution by an iterative time-reversal (TR) process.

In this process, after the sensors in an array transmit, the received signals at the sensors are played back in reverse and re-transmitted.

The time-reversed waves interfere to produce a field which converges onto the scatterer; these stronger fields illuminate the scatterer and produce a larger reflected field.

The larger field energy at the target improves the Signal to Noise Ratio (SNR) for detection.

Previous theoretical and experimental work has shown that this process can be used in either acoustics or electromagnetics, without any a priori information about the environment, to produce fields that converge onto the strongest scatterer.

However, the effects of multiple scattering on the process have not previously been studied. This dissertation shows that somewhat different effects occur when the targets undergo multiple scattering or are moving.

This dissertation is a theoretical treatment of the TR Operator (TRO) in two parts. The first part addresses the effects of multiple scattering in a stationary target.

The goal of the second part of this thesis is to develop a correction to the TR process to account for linear target motion.