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

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.