A Statistical Framework and Analysis for Perfect Radar Pulse Compression

TL;DR

This paper develops a rigorous mathematical framework for perfect radar pulse compression, analyzing the statistical equivalence of pulse codes and exploring the fundamental limits of radar experiments.

Contribution

It introduces a statistical theory for radar pulse compression, generalizes properties of the Itô measure, and analyzes the posterior in high-dimensional inverse problems, including infinite-dimensional cases.

Findings

Establishes a statistical equivalence framework for radar pulse codes

Provides estimates for the structure function in Bayesian inverse problems

Suggests the posterior distribution is non-Gaussian in infinite-dimensional settings

Abstract

Perfect radar pulse compression coding is a potential emerging field which aims at providing rigorous analysis and fundamental limit radar experiments. It is based on finding non-trivial pulse codes, which we can make statistically equivalent, to the radar experiments carried out with elementary pulses of some shape. A common engineering-based radar experiment design, regarding pulse-compression, often omits the rigorous theory and mathematical limitations. In this work our aim is to develop a mathematical theory which coincides with understanding the radar experiment in terms of the theory of comparison of statistical experiments. We review and generalize some properties of the It\^{o} measure. We estimate the unknown i.e. the structure function in the context of Bayesian statistical inverse problems. We study the posterior for generalized $d$-dimensional inverse problems, where we consider both real-valued and complex-valued inputs for posteriori analysis. Finally this is then extended to the infinite dimensional setting, where our analysis suggests the underlying posterior is non-Gaussian.