Nonlinear Acoustic Echo Cancellation Based on Sparse Functional Link Representations

Abstract

Recently, a new class of nonlinear adaptive filtering architectures has been introduced based on the functional link adaptive filter (FLAF) model. Here we focus specifically on the split FLAF (SFLAF) architecture, which separates the adaptation of linear and nonlinear coefficients using two different adaptive filters in parallel. This property makes the SFLAF a well-suited method for problems like nonlinear acoustic echo cancellation (NAEC), in which the separation of filtering tasks brings some performance improvement. Although flexibility is one of the main features of the SFLAF, some problem may occur when the nonlinearity degree of the input signal is not known a priori. This implies a non-optimal choice of the number of coefficients to be adapted in the nonlinear path of the SFLAF. In order to tackle this problem, we propose a proportionate FLAF (PFLAF), which is based on sparse representations of functional links, thus giving less importance to those coefficients that do not actively contribute to the nonlinear modeling. Experimental results show that the proposed PFLAF achieves performance improvement with respect to the SFLAF in several nonlinear scenarios

Full proportionate functional link adaptive filters for nonlinear acoustic echo cancellation

“…The optimization procedure involves a formulation similar to [23], but with a novel resulting derivation due to the full weighted mask. Let us define the following joint input and weight vectors, respectively:…”

“…Taking into account the least-perturbation property and the natural gradient adaptation, as suggested in [23], it is possible to express the constrained optimization problem as:…”

“…In particular, the estimation of the AIR has been proved to be robust to disturbing signals when regularization is taken into account in the least-square solution [18]- [22]. On the other hand, in the nonlinear modeling, the expansion of the input signal may also show some sparse behavior, and this has encouraged the use of proportionate algorithms even for LIP nonlinear filters [23]- [27]. Therefore, in this work, we propose an SFLAF model for NAEC that is capable of exploiting the capabilities of both the linear and nonlinear modeling, by providing a general formulation for the joint optimization problem involving both the estimation processes.…”

The Krylov-proportionate normalized least mean fourth approach: Formulation and performance analysis

“…A formulation of the proportionate update based algorithms using the natural gradient descent adaptation has been studied in [28,29].…”

“…Furthermore, in the following, we provide the steady-state MSD of the mixed-norm algorithms under the assumption that the estimation error gets so small that we can neglect the relatively high order error terms. Since (28) for mixed-norm error objective yields …”