Technical Report: Compressive Temporal Higher Order Cyclostationary Statistics

TL;DR

This paper develops a theoretical framework for estimating Temporal Higher Order Cyclostationary Statistics (THOCS) from compressively sensed signals, enabling efficient detection of hidden periodicities in cyclostationary signals.

Contribution

It introduces a novel approach combining THOCS estimation with compressive sensing, providing a theoretical basis for low-rate acquisition of cyclostationary signals.

Findings

Framework demonstrated with simulated data

Effective detection of hidden periodicities

Supports compressive sensing for cyclostationary analysis

Abstract

The application of nonlinear transformations to a cyclostationary signal for the purpose of revealing hidden periodicities has proven to be useful for applications requiring signal selectivity and noise tolerance. The fact that the hidden periodicities, referred to as cyclic moments, are often compressible in the Fourier domain motivates the use of compressive sensing (CS) as an efficient acquisition protocol for capturing such signals. In this work, we consider the class of Temporal Higher Order Cyclostationary Statistics (THOCS) estimators when CS is used to acquire the cyclostationary signal assuming compressible cyclic moments in the Fourier domain. We develop a theoretical framework for estimating THOCS using the low-rate nonuniform sampling protocol from CS and illustrate the performance of this framework using simulated data.