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 Itô 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.