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Perfect radar pulse compression coding is a potential emerging field whichaims at providing rigorous analysis and fundamental limit radar experiments. Itis based on finding non-trivial pulse codes, which we can make statisticallyequivalent, to the radar experiments carried out with elementary pulses of someshape. A common engineering-based radar experiment design, regardingpulse-compression, often omits the rigorous theory and mathematicallimitations. In this work our aim is to develop a mathematical theory whichcoincides with understanding the radar experiment in terms of the theory ofcomparison of statistical experiments. We review and generalize some propertiesof the It\^{o} measure. We estimate the unknown i.e. the structure function inthe context of Bayesian statistical inverse problems. We study the posteriorfor generalized $d$-dimensional inverse problems, where we consider bothreal-valued and complex-valued inputs for posteriori analysis. Finally this isthen extended to the infinite dimensional setting, where our analysis suggeststhe underlying posterior is non-Gaussian.

A Statistical Framework and Analysis for Perfect Radar Pulse Compression