Estimation and Deconvolution of Second Order Cyclostationary Signals

TL;DR

This paper introduces a blind deconvolution method for second-order cyclostationary signals that effectively removes transfer function effects without prior knowledge, demonstrated through simulations across various conditions.

Contribution

It presents a novel blind deconvolution and estimation technique specifically for noisy CS2 signals, proving the existence of a deconvolution filter that eliminates the transfer function effect.

Findings

High precision in signal reconstruction demonstrated in simulations

Effective across various signal types and SNR levels

Potential applications in machine learning training data preparation

Abstract

This method solves the dual problem of blind deconvolution and estimation of the time waveform of noisy second-order cyclo-stationary (CS2) signals that traverse a Transfer Function (TF) en route to a sensor. We have proven that the deconvolution filter exists and eliminates the TF effect from signals whose statistics vary over time. This method is blind, meaning it does not require prior knowledge about the signals or TF. Simulations demonstrate the algorithm high precision across various signal types, TFs, and Signal-to-Noise Ratios (SNRs). In this study, the CS2 signals family is restricted to the product of a deterministic periodic function and white noise. Furthermore, this method has the potential to improve the training of Machine Learning models where the aggregation of signals from identical systems but with different TFs is required.