  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.
