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
It is a well-known result of estimation theory that biased estimators can outperform unbiased ones in terms of expected quadratic error. In steady-state, many adaptive filtering algorithms offer an unbiased estimation of both the reference signal and the unknown true parameter vector. In this correspondence, we propose a simple yet effective scheme for adaptively biasing the weights of adaptive filters using an output multiplicative factor. We give theoretical results that show that the proposed configuration is able to provide a convenient bias vs variance tradeoff, leading to reductions in the filter mean-square error, especially in situations with a low signal-to-noise ratio (SNR). After reinterpreting the biased estimator as the combination of the original filter and a filter with constant output equal to 0, we propose practical schemes to adaptively adjust the multiplicative factor. Experiments are carried out for the normalized leastmean-squares (NLMS) adaptive filter, improving its mean-square performance in stationary situations and during the convergence phase.
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