Shannon Entropy is the preeminent tool for measuring the level of uncertainty (and conversely, information content) in a random variable. In the field of communications, entropy can be used to express the information content of given signals (represented as time series) by considering random variables which sample from specified subsequences. In this paper, we will discuss how an entropy variant, the \textit{permutation entropy} can be used to study and classify radio frequency signals in a noisy environment. The permutation entropy is the entropy of the random variable which samples occurrences of permutation patterns from time series given a fixed window length, making it a function of the distribution of permutation patterns. Since the permutation entropy is a function of the relative order of data, it is (global) amplitude agnostic and thus allows for comparison between signals at different scales. This article is intended to describe a permutation patterns approach to a data driven problem in radio frequency communications research, and includes a primer on all non-permutation pattern specific background. An empirical analysis of the methods herein on radio frequency data is included. No prior knowledge of signals analysis is assumed, and permutation pattern specific notation will be included. This article serves as a self-contained introduction to the relationship between permutation patterns, entropy, and signals analysis for studying radio frequency signals and includes results on a classification task.

翻译：香农熵是衡量随机变量不确定性（反之则为信息量）的首要工具。在通信领域，通过考虑从特定子序列中采样的随机变量，熵可用于表达给定信号（以时间序列形式表示）的信息量。本文将讨论一种熵变体——排列熵，如何用于研究噪声环境下的射频信号分类。排列熵是对固定窗口长度下从时间序列中采样排列模式出现次数的随机变量的熵，因此它是排列模式分布的函数。由于排列熵依赖于数据的相对顺序，它不受（全局）幅度影响，从而允许在不同尺度下进行信号比较。本文旨在介绍一种基于排列模式的方法以解决射频通信研究中的数据驱动问题，并包含所有非排列模式特定背景知识的入门介绍。文中还对所提方法进行了射频数据的实证分析。假设读者无需信号分析先验知识，并将包含排列模式特定符号。本文作为一篇自洽的导论，阐述了排列模式、熵与信号分析在射频信号研究中的关系，并呈现了分类任务的结果。