  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.
