Cascade of Linear Predictors for Deconvolution of Non-Stationary Channels in Sparse and Antisparse Scenarios

Renan Brotto,Romis Attux,João Romano,Kenji Nose-Filho

doi:10.14209/jcis.2021.10

Abstract

This work deals with adaptive predictive deconvolution of non-stationary channels. In particular, we investigate the use of a cascade of linear predictors in the recovering of sparse and antisparse original signals. To do so, we first discuss the behavior of the Lp Prediction Error Filter (PEF), with p different of 2, showing that it has a superior ability to deal with non-minimum phase channels in comparison with the classical L2 PEF, although it still presents intrinsic limitations due to its direct linear structure. The cascade structure emerges as a possible solution to circumvent this issue. We apply the proposed cascade structure in the deconvolution of non-stationary channels, with minimum-, maximum- , mixed- and variable-phase response, and also noise scenarios. From the simulation results we observed that, besides the duality relation between the Lp norms, they present different algorithmic behavior: the L1 norm attains a fast convergence, enhancing the cascade tracking capacity, but is more sensible to noise. The L4 norm, on the other hand, is more robust to noise, but presents slower convergence and tracking capability.

Highlights

We investigated in [7] the phase-response of the l Prediction Error Filter (PEF), with ≠ 2, verifying that it can present a nonminimum phase response
The present paper further studies the potentialities of the cascade of linear predictors by applying it distinctly in two well-defined scenarios: for the blind deconvolution of antisparse signals, we propose to implement an MFE (Mean Fourth Error) cascade and for the blind deconvolution of sparse sources the MAE (Mean Absolute Error) cascade
In this work we extended our previous results in blind deconvolution using a cascade of linear predictors

Summary

INTRODUCTION

The problem of deconvolution consists in recovering a signal of interest ( ) that has been distorted by. We observed that the l PEF was not able to compensate the distortions of a channel with a generic phase response This limitation of the l PEF, with ≠ 2, is supported by the work of Knockaert [8], which shows that all of the zeros of this type of filter lay inside a circle of radius 2. This result shows that the l PEF, with ≠ 2, is more general than the classical one, since it provides nonlinear decorrelation and presents a non-minimum-phase response, but still has a restriction due to its forward linear structure.

PROPOSED STRUCTURE AND ALGORITHMS

Antisparse Deconvolution

Sparse Deconvolution

CONCLUSION