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.

翻译：完美雷达脉冲压缩编码是一个潜在的新兴领域，旨在为雷达实验提供严格的分析和基本极限。它基于寻找非平凡脉冲编码，这些编码在统计上可等效于使用某种基本脉冲进行的雷达实验。常见的基于工程的雷达实验设计（涉及脉冲压缩）往往忽略了严格的理论和数学限制。本工作的目标是发展一种数学理论，该理论与基于统计实验比较理论理解雷达实验相一致。我们回顾并推广了伊藤测度的一些性质。在贝叶斯统计逆问题的背景下，我们估算了未知的结构函数。我们研究了广义 $d$ 维逆问题中的后验分布，其中在后验分析中考虑了实值和复值输入。最后，我们将此扩展到无穷维设定，我们的分析表明，潜在的后验分布是非高斯的。