Functional Link Adaptive Filter Research Articles

A New Class of Efficient Adaptive Filters for Online Nonlinear Modeling

Nonlinear models are known to provide excellent performance in real-world applications that often operate in non-ideal conditions. However, such applications often require online processing to be performed with limited computational resources. To address this problem, we propose a new class of efficient nonlinear models for online applications. The proposed algorithms are based on linear-in-the-parameters (LIP) nonlinear filters using functional link expansions. In order to make this class of functional link adaptive filters (FLAFs) efficient, we propose low-complexity expansions and frequency-domain adaptation of the parameters. Among this family of algorithms, we also define the partitioned-block frequency-domain FLAF, whose implementation is particularly suitable for online nonlinear modeling problems. We assess and compare frequency-domain FLAFs with different expansions providing the best possible tradeoff between performance and computational complexity. Experimental results prove that the proposed algorithms can be considered as an efficient and effective solution for online applications, such as the acoustic echo cancellation, even in the presence of adverse nonlinear conditions and with limited availability of computational resources.

Re-weighted zero attracting adaptive exponential FLAF with maximum correntropy criterion for robust sparse nonlinear system identification

The profoundly employed linear-in-the-parameter nonlinear adaptive filtering techniques of functional link adaptive filter (FLAF) and adaptive exponential FLAF (AEFLAF) often exhibit deteriorated performances in the wake of varying sparsity conditions and impulsive noise interferences. In this regard, a robust nonlinear adaptive filtering technique is introduced leveraging the benefits of nonlinear similarity index maximum correntropy criterion (MCC). Additionally a log sum penalty function is included in the derived cost function in response for sparse system identification. The entire robust nonlinear adaptive filter in this paper is constructed upon the framework of AEFLAF based on affine projection algorithm (APA) as MCC based reweighted zero attracting AEFLAF (MR-AEFLAF). Besides, steady state analysis of the proposed MR-AEFLAF is carried out establishing the condition for stability. Simulations with white, colored noise and speech segment illustrate the efficacy of the proposed technique for robust nonlinear adaptive filtering in system identification and acoustic feedback cancellation in hearing aids scenario. The performance of the designed adaptive filter is assessed quantitatively and qualitatively both.

A generalized collaborative functional link adaptive filter for nonlinear active noise control

This paper derives a collaborative control algorithm called generalized collaborative functional link adaptive filter (GCFLAF) for nonlinear active noise control (NANC). The algorithm adopts the collaborative scheme by handling the noise cancellation problem divisionally and parallelly, and working coordinately. It takes the characteristics of different nonlinear components into consideration and handles them separately. And a hierarchical adaption law is adopted in which linear filter is always prior to nonlinear filters no matter whether nonlinear distortions arise from the primary path as required by the filtering scenario. Thus the proposed scheme can tailor to different nonlinear characters arising from the primary path and can hierarchically adapt to the influences of the distinct nonlinearities. Particularly, since the zero-memory nonlinearity and memory nonlinearity are often unavoidable in NANC, it employs two shrinkage parameters to regulate the contribution of the different degrees of memory and zero-memory nonlinearity as required by the filtering scenario, aiming to achieve a better convergence performance and robustness to nonlinear distortions. Some numerical simulation results in the context of random noises as well as the real noise signals verify the improved convergence behavior of the presented architecture in NANC scenarios.

Combined functional link adaptive filter for nonlinear acoustic echo cancellation

The usage of low-quality components in communicating devices may introduce nonlinearity in the audio signals. The degree of nonlinearity may vary over time due to the nonstationary nature of audio signals. In the presence of nonlinear audio signals, the performance of an acoustic echo cancellation (AEC) scheme is impacted by two major limitations. The first one is related to the modeling accuracy, and the second one is related to the adaptation performance. The issue of modeling accuracy exists because the available nonlinear AEC (NAEC) schemes consider the nonlinearity as time-invariant and employ a fixed architecture to model the echo path. The adaptation performance issue occurs due to the conflicting requirements of fast convergence and low steady-state error. There is a need for an architecture that not only models the nonlinearity efficiently but also provides better performance in terms of convergence. In this paper, three new architectures convex combination functional link adaptive filter (CC-FLAF), improved CC-FLAF (ICC-FLAF), and variable step size CC-FLAF (VSSCC-FLAF) are proposed to overcome the above limitations. The proposed architectures are based on the combination of adaptive filters and variable step size approach. Computer simulations demonstrate the effectiveness of proposed architectures, in improving the nonlinear modeling performance for NAEC applications.

The wavelet transform-domain adaptive filter for nonlinear acoustic echo cancellation

The usage of low-quality components in communicating devices introduces acoustic nonlinearity. The presence of nonlinearity creates challenges in noise cancellation applications, especially the acoustic echo cancellation (AEC) that requires an adaptive filter of a very high order. However, the functional link adaptive filter (FLAF) algorithm models the acoustic nonlinearity efficiently but shows slow convergence performance due to a very high filter order. To improve the convergence performance of the FLAF, the wavelet transform-domain FLAF (WTD-FLAF) is proposed for nonlinear AEC (NAEC) applications. The convergence rate is improved by decomposing a higher-order adaptive filter into smaller-order subfilters. The convergence speed improvement is gained at the expense of increased computational complexity. A low complexity version of the WTD-FLAF, named as selective update WTD-FLAF (SU-WTD-FLAF) algorithm, is also presented. The SU-WTD-FLAF algorithm is based on the selective coefficient update approach. Computer simulations demonstrate that the convergence performance of the proposed algorithms outperforms the standard FLAF.

Nonlinear Acoustic Echo Cancellation Based on Multichannel Adaptive Filters: A Novel Approach

This paper presented a new class of non-linear adaptive filters, whose structure is based on Hammerstein model. Such filters designed from the functional link adaptive filter (FLAF) model, described by a non-linear input expansion which develops the illustration of the input signal through a projection in a higher dimensional space and a subsequent adaptive filtering. In order to give toughness against different degrees of non-linearity, a collaborative FLAF is proposed based on the adaptive combination of filters. Such architecture provided the best performance regardless of the nonlinearity degree in the echo path. Particularly this architecture can accomplish the linear and non-linear filters. Such as Normalized least mean square algorithm using FDAF, Affine projection and Lattice filters are used. When comparing their Echo return loss enhancement performance, Affine projection algorithm gives 20 dB more than others in this work.

De-Correlated Improved Adaptive Exponential FLAF-Based Nonlinear Adaptive Feedback Cancellation for Hearing Aids

Modern-day digital hearing aids are prone to an unavoidable acoustic feedback phenomenon, degrading sound quality and speech intelligibility. The linear adaptive feedback cancellation (AFC) systems based on finite-impulse-response filters do not yield satisfactory performance under nonlinearity encountered in the feedback path. In an endeavor to overcome this, a de-correlated improved adaptive exponential functional link adaptive filter (DI-AEF)-based nonlinear AFC (NAFC) system is developed in this paper. It utilizes cross terms of the input samples and trigonometrical expansion with exponentially varying amplitude. To save computations, the delayed outputs of the feedback canceler are appended at the input layer, inspired by the IIR filtering technique. The adaptive de-correlation filter is updated by variable convergence and forgetting factor windowed recursive least square algorithm to address the biased estimation problem. The corresponding update rules, convergence, and bounded-input bounded-output stability conditions have been derived. Extensive simulation results demonstrate the efficacy of the proposed NAFC system for real input signals in terms of perceptual evaluation of speech and audio quality and added stable gain (ASG). The DI-AEF-based system achieves nearly 4-dB improvement in ASG while consuming 53% and 37% less multiplications and additions than the existing nonlinear methods.

Combined nonlinear filtering architectures involving sparse functional link adaptive filters

Sparsity phenomena in learning processes have been extensively studied, since their detection allows to derive suited regularized optimization algorithms capable of improving the overall learning performance. In this paper, we investigate the sparsity behavior that may occur in nonlinear adaptive filtering problems and how to leverage it and develop enhanced algorithms. In particular, we focus on a particular class of linear-in-the-parameters nonlinear adaptive filters, whose nonlinear transformation is based on a functional link expansion. The analysis of the sparsity in functional links leads us to derive a family of adaptive combined filtering architectures that is capable of exploiting any sparseness degree in the nonlinear filtering. We propose two different filtering schemes based on a new block-based combined approach, well suited for sparse adaptive algorithms. Moreover, a hierarchical architecture is also proposed that generalizes the different combined schemes and does not need any a priori information about the nature of the nonlinearity to be modeled. Experimental results prove the effectiveness of the proposed combined architectures in exploiting any sparseness degree and improving the modeling performance in nonlinear system identification problems.

Improving nonlinear modeling capabilities of functional link adaptive filters

The functional link adaptive filter (FLAF) represents an effective solution for online nonlinear modeling problems. In this paper, we take into account a FLAF-based architecture, which separates the adaptation of linear and nonlinear elements, and we focus on the nonlinear branch to improve the modeling performance. In particular, we propose a new model that involves an adaptive combination of filters downstream of the nonlinear expansion. Such combination leads to a cooperative behavior of the whole architecture, thus yielding a performance improvement, particularly in the presence of strong nonlinearities. An advanced architecture is also proposed involving the adaptive combination of multiple filters on the nonlinear branch. The proposed models are assessed in different nonlinear modeling problems, in which their effectiveness and capabilities are shown.

Nonlinear Acoustic Echo Cancellation Based on Sparse Functional Link Representations

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.

Convergence properties of nonlinear functional link adaptive filters

The analysis of some convergence properties of a recent class of nonlinear adaptive filters, known as `functional link adaptive filters' (FLAFs) is aimed at. In particular, a convergence stability range is derived for nonlinear FLAFs using trigonometric series expansion.

Functional Link Adaptive Filters for Nonlinear Acoustic Echo Cancellation

This paper introduces a new class of nonlinear adaptive filters, whose structure is based on Hammerstein model. Such filters derive from the functional link adaptive filter (FLAF) model, defined by a nonlinear input expansion, which enhances the representation of the input signal through a projection in a higher dimensional space, and a subsequent adaptive filtering. In particular, two robust FLAF-based architectures are proposed and designed ad hoc to tackle nonlinearities in acoustic echo cancellation (AEC). The simplest architecture is the split FLAF, which separates the adaptation of linear and nonlinear elements using two different adaptive filters in parallel. In this way, the architecture can accomplish distinctly at best the linear and the nonlinear modeling. Moreover, in order to give robustness against different degrees of nonlinearity, a collaborative FLAF is proposed based on the adaptive combination of filters. Such architecture allows to achieve the best performance regardless of the nonlinearity degree in the echo path. Experimental results show the effectiveness of the proposed FLAF-based architectures in nonlinear AEC scenarios, thus resulting an important solution to the modeling of nonlinear acoustic channels.